Properties of Solutions Essay

A solution is a mixture of materials, one of which is usually a fluid. A fluid is a material that flows, such as a liquid or a gas. The fluid of a solution is usually the solvent. The material other than the solvent is the solute. We say that we dissolve the solute into the solvent. Some solutions are so common to us that we give them a unique name. A solution of water and sugar is called syrup. A solution of sodium chloride (common table salt) in water is called brine. A sterilized specific concentration (0.15 molar) of sodium chloride in water is called saline. A solution of carbon dioxide in water is called seltzer, and a solution of ammonia gas in water is called ammonia water. A solution is said to be dilute if there is less of the solute. The process of adding more solvent to a solution or removing some of the solute is called diluting. A solution is said to be concentrated if it has more solute. The process of adding more solute or removing some of the solvent is called concentrating. The concentration of a solution is some measurement of how much solute there is in the solution. It might initially offend your sensibilities to consider a solution in which the solvent is a gas or a solid. The molecules of a gas do not have much interaction among them, and so do not participate to a large extent in the dissolving process. Solids are difficult to consider as solvents because there is a lack of motion of the particles of a solid relative to each other. There are, however, some good reasons to view some mixtures of these types as solutions. The molecules of a gas do knock against each other, and the motion of a gas can assist in vaporizing material from a liquid or solid state. The fan in a ‘frost free’ home freezer moves air around inside the freezer to sublimate any exposed ice directly into water vapor, a process clearly akin to dissolving. Solid metals can absorb hydrogen gas in a mixing process in which the metal clearly provides the structure. True solutions with liquid solvents have the following properties: PROPERTIES OF SOLUTIONS 1.The particles of solute are the size of individual small molecules or individual small ions. One nanometer is about the maximum diameter for a solute particle. 2.The mixture does not separate on standing. In a gravity environment the solution will not come apart due to any difference in density of the materials in the solution. 3.The mixture does not separate  by common fiber filter. The entire solution will pass through the filter. 4.Once it is completely mixed, the mixture is homogeneous. If you take a sample of the solution from any point in the solution, the proportions of the materials will be the same. 5.The mixture appears clear rather than cloudy. It may have some color to it, but it seems to be transparent otherwise. The mixture shows no Tyndall effect. Light is not scattered by the solution. If you shine a light into the solution, the pathway of the light through the solution is not revealed to an observer out of the pathway. 6.The solute is completely dissolved into the solvent up to a point characteristic of the solvent, solute, and temperature. At a saturation point the solvent no longer can dissolve any more of the solute. If there is a saturation point, the point is distinct and characteristic of the type of materials and temperature of the solution. 7.The solution of an ionic material into water will result in an electrolyte solution. The ions of solute will separate in water to permit the solution to carry an electric current. 8.The solution shows an increase in osmotic pressure between it and a reference solution as the amount of solute is increased. 9.The solution shows an increase in boiling point as the amount of solute is increased. 10.The solution shows a decrease in melting point as the amount of solute is increased. 11.A solution of a solid non-volatile solute in a liquid solvent shows a decrease in vapor pressure above the solution as the amount of solute is increased. These last four of the properties of solutions collectively are called colligative properties. These characteristics are all dependent only on the number of particles of solute rather than the type of particle or the mass of material in solution. OTHER TYPES OF MIXTURE Take a spoonful of dirt and vigorously mix it with a glass of water. As soon as you stop mixing, a portion of the dirt drops to the bottom. Any material that is suspended by the fluid motion alone is only in temporary suspension. A portion of the dirt makes a true solution in the water with all of the properties of the above table, but there are some particles, having a diameter roughly between 1 nm and 500 nm, that are suspended in a more lasting fashion. A suspended mixture of particles of this type is called a colloid, or colloidal suspension, or colloidal dispersion. For colloids or  temporary suspensions the phrase dispersed material or the word dispersants describes the material in suspension, analogous to the solute of a solution. The phrase dispersing medium is used for the material of similar function to a solvent in solutions. As with true solutions, it is a bit of a stretch to consider solids as a dispersing medium or gases as forming a large enough particle to be a coll oid, but most texts list some such. A sol is a liquid or solid with a solid dispersed through it, such as milk or gelatin. Foams are liquids or solids with a gas dispersed into them. Emulsions are liquids or solids with liquids dispersed through them, such as butter or gold-tinted glass. Aerosols are colloids with a gas as the dispersing medium and either a solid or liquid dispersant. Fine dust or smoke in the air are good examples of colloidal solid in a gas. Fog and mist are exampes of colloidal liquid in a gas. Liquid dispersion media with solid or liquid dispersants are the most often considered. Homogenized whole milk is a good example of a liquid dispersed into a liquid. The cream does not break down into molecular sized materials to spread through the milk, but collects in small micelles of oily material and proteins with the more ionic or hydrophilic portions on the outside of the globule and the more fatty, or oily, or non-polar, or hydrophobic portions inside the ball-shaped little particle. Blood carries liquid lipids (fats) in small bundles called lipoproteins with specific proteins making a small package with the fat. Proteins are in a size range to be considered in colloidal suspension in water. Broth or the independent proteins of blood or the casein (an unattached protein) in milk are colloidal. There are many proteins in the cellular fluids of living things that are in colloidal suspension. Colloidal dispersants in water stay in suspension by having a layer of charge on the outside of the particle that is attractive to one end of water molecules. The common charge of the particles and the water solvation layer keep the particles dispersed. A Cottrel precipitator collects the smoke particles from air by a high voltage charge and collection device. Boiling an egg will denature and coagulate the protein in it. Proteins can be fractionally ‘salted out’ of blood by adding specific amounts of sodium chloride to make the proteins coagulate. The salt adds ions to the liquid that interfere with the dispersion of the colloidal particles. Colloids with liquid as a dispersing agent have the following properties: PROPERTIES OF COLLOIDS 1.The particles of dispersant are the between about 500 nm to 1 nm in diameter. 2.The mixture does not separate on standing in a standard gravity condition. (One ‘g.’) 3.The mixture does not separate by common fiber filter, but might be filterable by materials with a smaller mesh. 4.The mixture is not necessarily completely homogeneous, but usually close to being so. 5.The mixture may appear cloudy or almost totally transparent, but if you shine a light beam through it, the pathway of the light is visible from any angle. This scattering of light is called the Tyndall effect 6.There usually is not a definite, sharp saturation point at which no more dispersant can be taken by the dispersing agent. 7.The dispersant can be coagulated, or separated by clumping the dispersant particles with heat or an increase in the concentration of ionic particles in solution into the mixture. 8.There is usually only small effect of any of the colligative properties due to the dispersant. CONCENTRATION The concentration of a solution is an indication of how much solute there is dissolved into the solvent. There are a number of ways to express concentration of a solution. By far the most used and the most useful of the units of concentration is molarity. You might see ‘6 M HCl’ on a reagent bottle. The ‘M’ is the symbol for molar. One molar is one mol of solute per liter of solution. The reagent bottle has six mols of HCl per liter of acid solution. Since the unit ‘molar’ rarely appears in the math of chemistry other than as a concentration, to do the unit analysis correctly, you will have to insert concentrations into the math as ‘mols per liter’ and change answers of ‘mols per liter’ into molar. Molality is concentration in mols of solute per kilogram of solvent. Mol fraction is the number of mols of solute per number of mols of solution. Weight-weight percent (really mass percent) is the number of grams of solute pe r grams of solution expressed in the form of a percent. Mass-volume concentration is the number of grams of solute per milliliter of solution. There are other older units of concentration, such as BaumÃÆ'ƒÂ ©, that are still in use, mainly in industrial chemicals. Normality is the number of mols of effective material per liter. In acid-base titrations, the hydroxide ion of bases and the hydrogen (hydronium) ion of acids is the effective material. Sulfuric acid (H2SO4)  has two ionizable hydrogens per formla of acid, or one mol of acid has two mols of ionizable hydrogen. 0.6 M H2SO4 is the same concentration as 1.2 N H2SO4. We say that sulfuric acid is diprotic because it has two protons (hydrogen ions) per formula available. Hydrochloric acid (HCl) is monoprotic, phosphoric acid (H3PO4) is triprotic, and acids with two or more ionizable hydrogens are called polyprotic. Sodium hydroxide (NaOH) is monobasic, calcium hydroxide (Ca(OH)2) is dibasic, and aluminum hydroxide (Al(OH)3) is tribasic. Where ‘X’ is the number of available hydrogen ions or hydroxide ions in an acid or base, N, the normality, is equal to the molarity, M, times X. The normality system can be used for redox reactions, but the effective material is now available electrons or absorption sites for electrons. Consider the following reaction, #43 in the redox section. In a sulfuric acid solution potassium permanganate will titrate with oxalic acid to produce manganese II sulfate, carbon dioxide, water, and potassium sulfate in solution.

Modernist Styles, Including Cubism, Orphism, and Futurism

Modernist styles, including Cubism, Orphism, and Futurism challenged the practices of traditional representational art. I will argue that modernist styles including Cubism, Orphism and Futurism did challenge the practices of traditional representational art. While some may argue that that the fact that modern styles were concerned with subject gives doubt to how challenging they really were to representational art I oppose this idea entirely. All art is representational in some way.Rather than a dismissing the concept of representation in art the modernist styles challenged the validity of the external representation, which had previously en the foundation of art, by focusing on conceptual representation. Traditional representational art is based on the representation of an image as it is, at a fixed point in time, from a singular viewpoint. This type of art aimed to be entirely familiar to the viewer; the subjects involved easily recognizable and derived from sources of reality.Mel Gooding, in his book Abstract Art defines representational art as ‘any mode of representation in painting and sculpture that offers the eye the illusion of a perceived reality. ‘ I would expand on this definition to include art that aims to render n image realistically from a fixed viewpoint at a specific point in time. Based on these definitions, it is evident that Cubism, Orphism and Futurism rejected traditional concepts and conventions as these could not portray the conceptual representation modern art was concerned with.It is evident in the works produced by the artists associated with these movements that they made a conscious decision to expand what was acceptable in art by challenging the artistic techniques and practices of representational art that had been adhered to for hundreds of years. The introduction of new media, new concepts of space and form and new techniques tit light and color were all innovative and effective ways to display experiences of the wor ld in ways that weren't bound by traditional artistic conventions.These new conventions were only able to develop because modernist artists ‘consciously sought radically new ways to represent their experience of the world. ‘ Modern art at this time was all about stimulating the experience of a subject by portraying its essence through new artistic conventions. In this way these modern works challenged the more objective representational art by uncovering new concepts of reality that did not involve the burden of realism. The artist Delaney explained this as ‘historically there was a change of understanding, hence of techniques, of modes of seeing. In some ways these artists were set free from the burden of realism by the invention of the camera, which could render an image perfectly. They were given the freedom to portray their understanding of an image, not how it is observed. New modernist styles marked a change in the definition of what reality expressed through art really was, moving away from the traditional illusionist's visual mimicry to a more conceptual and internal representation. This idea was first formally established by Maurice Urinal an art critic and close friend of many of the artists involved in these modern movements.He stated that â€Å"if art is a meaner of augmenting knowledge, its function will only be served by painting forms as they are conceived in the mind. † I will argue that this conceptual form of art is more intellectually stimulating due to its complexity than the blatancy of figurative art. This is a sentiment that abstract artists wished to express and the reason they challenged the traditions of art at all. I will set out in my argument how the innovative use of artistic conventions by modernist artists proves that the practices of traditional representational art were rejected.It was only through this purposeful rejection of traditional representational art to a truer, more conceptual representation that the innovative concepts associated with these modernist styles were able to develop and this marks the development of modern art into abstraction. Space and form All three styles, Cubism, Orphism and Futurism show a pictorial space and form which would be unrecognizable to traditional representational art.. Although theses three modern styles varied, the works involved all occupied a new and more complex pace.Mel Gooding explains this as a trend in modern art away from the representation of recognizable objects in pictorial space and towards presentation of a painting or sculpture as a real object in real space. ‘ Up until this time the pictorial space created in the art work aimed to create the illusion of a real pictorial space for the spectator. The technique of one point perspective which was very much adhered to during the renaissance created a space in the picture which vanished into a single point in order to replicate the three dimensionality of our vision.This co upled with the use of shading and toning to accentuate the weight of form worked to create the illusion of looking into a realistic space. The use of formal conventions such as perspective and tone are illusionist's and therefore they were abandoned by these modern artists who were inspired to achieve a more conceptual representation of space and form. For example, Baroque said of Cubism What most attracted me and what was the governing principle of Cubism, was the materialistic of this new space which I sensed. The art movement of Cubism was in fact sparked by the idea f exploring a new anti naturalistic space which can be seen to be developed and refined throughout the phases of cubism. The driving force behind the experimentations with form that developed cubism was the rejection of the deceptive singular viewpoint perspective which governed the illusionist of representational art. Initially the search for a new, more truthful pictorial space was found in the introduction of time , the fourth dimension, into space.Around this time in history the concept that space and time where interlinked was suggested by Einstein theory of relativity which destroyed the concept that the dimensions of an object were absolute, by demonstrating that they depended on the relative position of the viewer. This abstract concept was portrayed in Cubism through the use of synthesized impressions of an image or space. As you view an image or object, your impression is not static but a moving collection of impressions over time. The use of multiple viewpoints aimed to compress a multiplicity of information gathered from various experiences of an object into one image.This innovation off truer space is most evidently portrayed by the analytic phase of Cubism. Through the incorporation of the new artistic conventions the fragmentation of form was developed. The intention was to encompass the entire visual experience of an object into one image and through this idea an effective techni que of breaking up form into planes and facets which each expressed a sample of visual information. The Cubist works now possessed a shallow pictorial space due to the abandonment of perspective on which these fragmented facets could be hung.This concept worked not to bring the viewer into an illusionist's space like traditional representational works, but to accentuate the flatness of the picture plane in order to bring the space forward to the viewer for hem to experience its analysis of the image and to stimulate those sensations provided by the experience of the objects. In Futurism the concept of time in an image was portrayed by movement. This inclusion of time as a meaner of transforming the static imagery once associated with art into a capturing of movement created a new optical and temporal space.Futurists were also interested in the use of fragmentation of form to challenge the idea of a fixed viewpoint that was used in representational art. However, they developed this i dea further and produced works which captured the idea of movement in a way that was not possible wrought traditional conventions. They achieved this through the use of rhythmic repetitions of space and form which is effective in evolving a static image into one which is in constant motion. Evidence of all of these ideas can be seen in artworks associated with all three of these modernist art styles.One of my favorite examples is Marcel Duchess's Nude Descending a Staircase No. 2. This work portrays the mechanical movement of a nude figure as it moves down a staircase. The form is made up of the synthesis of various static positions of the nude as it is in motion and Leary expresses the idea of form changing over time. The form consists of layers of superimposed facets and angular planes which is evidence of cubist ideals of space and form. At the same time the still phases of the form placed in succession create the effect of a fluid movement, this is an illustration of the futuris t need to recreate the visual experience of motion.These ideas coupled with the mechanized and almost robotic form of the image alludes to the Futurists focus on industrialization of the world. The painting was initially rejected by the hanging committee of the Salon des Independents exhibition in Paris. Their reasoning for this was ‘a nude never descends a staircase a nude always reclines. ‘ The fact that Decamp was not adhering to traditional conventions was not accepted at this time. Many found the painting unintelligible because they did not recognize the figure at face value.But this was Duchess's intention to redefine representation in art. Today the art work is treasured as a symbol of the innovative practices associated with these modern styles. Light and color Traditionally light and color were artistic conventions used to create those optical delusions necessary to form a ‘realistic' image. The light source in a representational work would be realistic an d consistently come from one light source. Color was used only as a tool for portraying the effects of light on form through shade and tone.This toning gave form the weight and the illusion of three dimensions. However, in modern art the illusion of the description of form and the natural effect of light on an image was no longer a concern. Orphism changed how color was viewed as a tool for portrayal. This was a movement that found significance in the symphony of sensations that colors are able to stimulate when crafted together. Because modernist artists no longer wanted to be confined to naturalism they were free to experiment with the effect of the relationships of color.This involved the color theory of contrasting and complementary colors and the optimum placement of these colors together to enhance hues. Delaney, a key Orphism artist was able to develop these color techniques from his studies of a chemist, Michael-Eugene Chevron's treatise, On the Law of the Simultaneous Contr ast of Colors. This treatise dealt with the concept that a color is observed differently according to its surrounding colors. An example of a modern work based upon the use of the application of color techniques is Homage to Bibelot by Robert Delaney.This work contains various circular forms all made up of highly organized bright block colors. The colors of these circular forms, which are mostly primary, are surrounded by a background of opposing colors such as a yellow, green and red image surrounded by blue, red and green respectively. It is this complete contrast which illuminates the effect of the colors to a point where they are so much more successful in their specific function when Juxtaposed in this purposeful way. It is not only this illumination that the use of these color techniques create but a pictorial space.A depth is created by the advancing and receding of colors according to their characteristics. These techniques had not been used in traditional representational a rt and are another example of how these abstract artists redefined accepted artist conventions. Media The use of different media is also an example of the development of new practices in the art world which stemmed from the rejection of traditional practices. During the Cubist movement the introduction of new media was achieved through collage, eliding the purposeful rejection of the observed for the conceptual.Cubist artists began to incorporate new materials into their works such as strips of newspaper or wallpaper. This innovation was a monumental step away from traditional art. Picasso ‘Still Life with Chair Caning consists of sections of a kitchen scene, a knife, a lemon a glass. Within the painting Picasso has also incorporated a section of chair caning patterned oil cloth. Instead of portraying the image of a chair Picasso chose to use something that would stimulate the viewer's experience of the object.The cloth as significance in the work because the viewer can relate it to the image of a chair without the image of a chair being displayed. Picasso is no longer concerned about displaying any illusionist's craftsmanship; he found a material; that would evoke the image he wished to portray and chose to incorporate it into the work. As a result, the whole purpose of art was challenged; it was no longer to replicate an external observation ‘realistically but to portray the essence of an image through pictorial clues.The images in a work may have meaning but when a foreign material is introduced it has the ability to change those meanings. For example a glass cut from newspaper confusingly evokes two images in the mind. Picasso explains this example â€Å"If a newspaper can become a bottle, that gives us something to think about in connection with both newspapers and bottles, too. This displaced object has entered a universe for which it was not made and where it retains, in a measure, its strangeness.And this strangeness was what we wanted to make people think about because we were quite aware that our world was becoming very strange and not exactly reassuring. â€Å"This peculiarity activates the mind on a higher level. The evolution of art to involve new media is a natural progression by an art movement which aims to confront the conventions of representational art and to create works which stimulate a higher level of perception than ever before. Picasso also says in the same statement about the introduction of new media â€Å"We didn't any longer want to fool the eye; we wanted to fool the mind. This idea pretty much sums up the whole purpose of these modern works. Subject Even the subject matter itself in these forms of art worked to separate itself from traditional subjects. Many works incorporated images that would activate memories f the more mundane, relatable experiences of life. It is evident that the artists involved in these styles were challenging the idea that art had to be a glorification of something, s uch as the biblical frescoes often associated with traditional art or a work that aimed to be ‘pretty.This introduction of everyday life into art effectively broadened the accessibility of art to everyday people. It was no longer a craft only obtainable by those with the ability to render the illusion of realism perfectly, it was open to anyone who wished to capture the conceptual essence of a subject through art. It is this idea which democratic art making. For cubists, subject was a platform onto which experiments with space and form could be conducted. This isn't to say that subject wasn't still taken into consideration.The easily relatable subject matter in these works was a purposeful decision in order to make the portrayal of the desired experiences easier. This was initially a playful experiment by the artists who developed these abstract artistic conventions due to the fact that they ‘enjoyed exploring the tension between apparent abstraction and suggested repres entation. ‘ Their new conceptual ideals had lead to the distortion and abstraction of the subject matter but they incorporated artistic clues to evoke the image of the object..By viewing modern works associated with these styles and considering what they seek to express, it is apparent that unlike representational art which relies on observation, the subject is not fixed but is instead based on individual and unique encounters. The work Just has to present itself and the spectator becomes the decider of the meanings of the subject. In this sense the fact that a subject of a modern work could e open to interpretation and is not obvious, modernist art styles transcended the level of intellectuality that figurative art could produce.Modern works were free to move away for the burden of only being able to portray observable images. In terms of Orphism and Futurism these movements aspired to move away from the external manifestations of human life. ‘ While Futurism chose to f ocus on the force of a dynamic subject, Orphism broke subject down into the lyricism of color. These modern artists felt that they were able to employ the dynamic forces of life such as speed and movement as the subject of a work. The inspiration for this sort of subject matter was inspired by the new technology fuelled age which was more exciting and dynamic than ever before.Because of this changing world the artists were living in they felt the need to express their excitement about life through art. This meaner that the fixed images of settings, people or landscapes associated with representational art was abandoned. Many futurist works portrayed mechanized and robotic figures or symbols of industrialization and technology immersed in some sort of movement. In conclusion, modernist styles including Cubism, Orphism and Futurism challenged he practices of traditional representational art by creating art which was more conceptual and internally driven.This focus on conceptual repres entation of a subject lead to the development of new ideas about space, form, color, light, and media and how these conventions come together to portray a subject. This redefinition of representation is evident in the works produced by these modernist artists. In the search for the ability to portray more truthfully modern artists created an art form which was more intellectually intriguing than art the world had seen before By Yachtsmen And

An Examination of the Team Development Stages in the Movie 12 Angry Men

An Examination of the Team Development Stages in the Movie 12 Angry Men 12 Angry Men: Team Development Stages Team development is a crucial aspect of any group setting and consists of six stages: stage one – forming, stage two – storming, stage three – norming, stage four – performing, and stage five – adjourning (or deforming). In the movie 12 Angry Men, the 12 jury members go through these stages at various points of the deliberation; this paper will serve to explore how and when the jury went through the stages of team development. Forming The movie starts out with our group already been formed, as they were selected to be part of the jury; they really begin the team development process at the beginning of the deliberation, as the jury members all sit down and define what their goals and obligations are, saying that if the defendant is found guilty, they must send him to the electric chair. The forming stage continues as jury members start falling into their respective roles; the members find out that juror 3 and juror 10 are alpha type males, that juror 8 takes his civic duty seriously, but has some biased views (he is just a youth, how could he commit such a crime?), and general introductions from members of the group. Storming The storming stage follows the forming stage, and starts after the jury’s first round of guilty/not guilty voting; the storming stage is set off by juror 8’s not guilty vote, which is the first and only difference among the group at the time. The storming stage is furthered by the jury member’s perception of civic duty, and ignited to another level when juror 8 is attempting to make a case, while some of his fellow jury members are playing games and goofing off. In the storming stage the alpha males of the group try to insert and enforce their brand of â€Å"leadership† through verbal force and intimidation, such as Juror 3 cutting off other jurors during the initial deliberation, telling the group that they are going to skip the set speaking rotation. This struggle of power, juror 3’s intimidation technique versus juror 8’s logical argument technique, continues throughout the story. Norming The norming stage starts when juror 8 starts making his arguments for a not guilty verdict, while persuading others to his side; it is also the stage that lasts the longest throughout the deliberation and takes place in non-connected stages. Once there are a few jurors on the not guilty side of the verdict, open discussion becomes much freer flowing and direct; the jury members start having an actual debate about the facts of the case and whether they could be debated. The discussion, and norming stage, really takes off when juror 8 slams the similar knife into the table; before this the discussion was fairly closed off, with most of the other jury members saying that there was no way the kid was not guilty. Performing The performing stage gradually takes over from the norming stage as more solid arguments are made in favor of the defendant being not guilty. Juror by juror realizes that they may have indeed been so close to sending a potentially innocent person to jail, and feel further obligated to explore the facts in order to render a fair verdict. Jury members put together their individual experiences and knowledge in order to help each other come to a not guilty verdict, such as Juror 8 trying to recreate the witness who had to walk to his door with a limp, or questioning Juror 4 about his week in order to establish that memory can be fuzzy. The final sense of civic obligation come when Juror 9 notices Juror 4 rubbing his nose, making the final argument about one of the witnesses not using her glasses regularly. Adjourning The adjourning stage is the stage where the team evaluates its processes and performance, disbanding on either a temporary or permanent basis; the jury members do not disband on a temporary process, and any breaks are portrayed as short breathers, therefore the focus will be on the disbanding of the jury upon rendering a not guilty verdict. The movie does not go into too much detail about the aftermath of the team’s decision, but the audience could tell through the interactions of Juror 8 with Jurors 3 and 9 that the process took place in the manner it should have, and that the team was happy with their process and performance.

Performance enhancing drugs in sports (which ones athletes use and the Research Paper

Performance enhancing drugs in sports (which ones athletes use and the benefits and possible side effects of using them) - Research Paper Example Some of them accept athletes as roll models in their life. This is a competitive world and the competition is spread in almost all sectors. By all means, sport is an important part of the competence. For surviving and winning in the competence at the sports field athletes want to maintain and boost their performance more and more. For this reason they always seek the methods for enhancing their performance in competitions and consider drug as the suitable stimuli for achieving their aims. Athletes prefer different types of performance enhancing drugs like anabolic steroids. There are certain reasons behind the use of drugs by athletes. In the book, Drugs in sports, David R. Mottram reveals many important factors related to the use of drugs in sports. In this book he denominates four reasons for the use of drugs in sports. They are listed below. Performance maintenance: - As part of the treatments which occurs at the time of their practicing or some other situation they forced to take treatments. At this time the medicines they took for the sports injuries many include drugs. From the above mentioned four points it is clear that athletes use drugs for improving their performance. Some of the important factors regarding the performance enhancing drugs in sports are discussed below. Almost all kinds of drugs preferred by the athletes contain substances which help the improvement of their athletic performance. It is not a new phenomenon; in the historical period itself athletes prefer drugs for their performance enrichment. It is not limited to one or two types. The most commonly preferred drug types are steroids and amphetamines and health supplements. First two types come under controlled substances, that is its production and distribution are controlled by the legal authority. One of the major reasons for this strict controlling is its high possibility of abuse especially by the athletes and trainers. Health supplements are

Byzantine Constantinople Essay Example | Topics and Well Written Essays - 2500 words

Byzantine Constantinople - Essay Example However, the structures are also indicative of the insecurities felt by the royal family members despite their feelings of need to show status (Mango 39) C. The Basilica cistern considerably reveals political power resting on religiously affiliated personalities, but, that the authority does not render the ruling party immune to the vulnerabilities of the century, in as much as subjugation was the trend. The cistern itself apparently allows unobserved entrance and exit of ruling parties to and from their palace which were eventually turned into huge family mausoleums (Alpaslan 192). D. The architecture is a mixture of a typical Roman design for the famous colonnades and extensive spaces that indicates reputation, and those of the Greeks which are the rolling tendrils of vines with leaves another symbol of power and status. In addition, Christian cross carved on columns can not be mistaken for the influence of religion on the design. A. The Byzantinian church, Hagia Sophia in Istanbul Turkey is lavishly decorated with mosaic of murals of cherubs and holy people who have long gone but was considered as sacred. The edifice was believed to be constructed in AD 532. This was designed by architects Anthemius of Tralles and Isidrous of Miletus. During the Ottoman Empire, the church was converted into an Islamic Mosque. The decorations were all carefully plastered. This was to hide the images as they were a taboo to Islam. But, the plasters were torn off in 1935 to reveal the original images which were grandiose (Jack 75). B. Hagia Sophia was named as Christian Church of Divine Wisdom apparently because of the internal ornaments depicting colorful images of angels and saints constructed under the Roman Emperor who ruled Turkey. But, it was actually a tomb apparently designed for the Emperor and his family's mausoleum. C. The lavishness of Hagia Sophia is a reflection of Roman power in Constantinople. Additionally, authority is coupled to Christian religious affinity. D. The general architecture depicts the complexity of the ideas of the architects in both the interior and exterior part of Hagia Sophia. The posh internal decoration which is a mixture of colors and images represents an abode only meant for royalties. The focal part of the edifice are the vaults right under the biggest dome held by arching pillars and decorated by images of seraphs, saints and flowers in a rainbow of colors. Much similar to what most people usually call as paradise on land. E. Hagia Sophia is a total reflection of a creative mind or minds of people living in the past. It is also an edifice reflective of human desire to dwell in a sanctuary where only beauty exists even after death. 3. The Topkapi palace, Istanbul Turkey A. The Topkapi palace was the imperial palace of the Ottomans in 1465 while the sultans ruled Turkey. As the structure was intended for residence, its size and decorations emits an aura of power. Construction of the huge edifice took place in the 15th century. According to literatures, the palace is actually constructed with varied materials influenced by old structures in Turkey which is mostly of stones. Decorative designs

Personal emergency and disaster plan Essay Example | Topics and Well Written Essays - 1000 words

Personal emergency and disaster plan - Essay Example Thunderstorms are also not rare here (about 40-50 days annually) with March and April being the periods of most severe storms. Not being part of Tornado Alley, Indiana is vulnerable to tornadoes. Three most severe tornadoes in the history of the United States – the 1925 Tri-State Tornado, the 1965 Palm Sunday Tornado Outbreak and the 1974 Super Outbreak – affected Indiana. The 2005 Evansville Tornado took away the lives of 25 people (Indiana State Climate Office 2008). The accidental disasters include technological disasters such as hazardous material incidents, household chemical emergencies, nuclear power plants, fires. For instance, chemicals are used in all the industries providing everyday life of modern people. The sources of hazardous materials include chemical manufacturing, hospitals, service stations, waste sites. All of them are hazardous for people and it is impossible to guarantee safety from mistakes. Humans are inclined to make mistakes sometimes. No one can guarantee entire safety from fires. Finally, one is to be aware of the possibility of intentional disasters, that is, those related to terrorism and wars. Acts of terrorism may include: the usage of chemical, biological, nuclear or radiological weapons, assassinations, bombing. Universities and colleges are considered the secondary, â€Å"soft† targets (FEMA 2006; IUK 2006, SUU 200, Northwestern University 2005). We are not safeguarded from disasters. However, one can get prepared to them and know what to do if any of the disasters occurs. Tornadoes are the nature’s most violent storms, causing devastates and fatalities. Appearing as a rotating, funnel-shaped cloud extending from a thunderstorm to the ground with whirling winds, tornadoes reach 300 miles per hour, their damage paths being more than one mile wide and 50 miles long. Some of them are not visible at the beginning, a cloud of debris marking the location of a tornado. They

Dance - an Art or Sport Term Paper Example | Topics and Well Written Essays - 1250 words

Dance - an Art or Sport - Term Paper Example Dancing expressions differ on whether can be used as an instrument of gesture and symbolism. As a result, some argue that they tend to be used for religious, ritual and ceremonial purposes. The expressions have differed in the way they define the cultural sequences of the body movement. The emotional expressions are also different as some explain that a person can dance without expressing emotions and that many groups do not just dance to music but rhythms in their minds. The expression does not inclusively compare dance to everyday movement, but they agree that it is repetitive (Ambrosio 58). Modern dance is a kind of theatrical dancing that is not as limited as classical ballet. In modern dance, movements express the feelings. Around the 1900s some American dancers started to rebel against the strict and confining style of Classical Ballet. Modern dance is very vivid, ever-changing and full of expression. Dancer’s like Alvin Ailey helped upgrade modern dance as we now see it. Art is basically one’s way of seeing them and expressing emotions. Because modern dance is without restriction deeper feelings and a stronger understanding is obtained. It is done easily due to this non-conforming way of dance. Urban dance or â€Å"street dance† describes any dance that has not come from formal beginnings like break dancing. This style is much improvised and can evolve without warning due to the individual. The beginnings of this style can be traced as far as West African culture. Dancing also plays an important role in culture. The rituals, dances, arts, music, and beliefs of a population are passed down from generation to generation. As previously discussed street dance is a modern take on old dance styles from older cultures. Some of the movements mimicked in modern times have come from Western Africa. Dances of celebration, acts of war, religious ceremony and been spread all over the world, but more so in the Caribbean and South American countries due to the old world slave trade. In Brazil, the African slaves that were shipped there also brought with them their culture of song and dance (Ambrosio 61).

Conway Inn - Conway, TX Research Paper Example | Topics and Well Written Essays - 2500 words

Conway Inn - Conway, TX - Research Paper Example In this paper, the focus will be on some deficient areas that need to be taken care of by the hotel’s management in order to improve the levels of customer satisfaction and organizational productivity. Customer service quality raises many issues for almost every company related to hospitality industry in some way or other. Although the management of Conway Inn hotel takes good care of every business process to meet the required standards of quality, but there is an area which still needs some focus in order to bring it in line with the quality of all other business process. The area which needs improvement is the customer service area the quality of which has gone down a little in the past couple of years. Customers have made complaints about the behavior, food serving, and room service of the employees of the hotel. The management of the hotel needs to resolve these customer service quality issues in order win the trust of the precious customers and protect the customer base from shortening because of the customer service issues. It is essential for a company from the hospitality industry to implement a well-developed quality management system because it helps in attracting and retaining customers, as well as in gaining competitive advantage in the market. Quality management system is implemented in a company to ensure that the quality of the products and services meet the standards. It acts as the foundation for an organization’s success because without the implementation of an effective quality management system, an organization cannot become able to ensure the optimum level of quality in its business processes. Quality management in hotel industry improves overall business performance. In our case, decreasing customer satisfaction due to low quality customer service is causing problems for the company. A quality management system will be needed to improve this area and get the trust of the

Water Chemistry Essay Example | Topics and Well Written Essays - 250 words

Water Chemistry - Essay Example Solutions Polysaccharide- these are polymers that are made of several chains of either monosaccharide units or disaccharide units Glucose- this is an example of a monosaccharide. It is a simple sugar consisting of a hydroxyl group (OH) in the structure. Glucose structure Amino acids- organic compounds with an amino group (NH2) and a carboxyl group (COOH). Fats- organic compounds with carbon, hydrogen and oxygen present in their structure. Fats contain glycerol which houses hydroxyl (OH) group and fatty acids which houses carboxyl (COOH) group. Proteins- Contain carbon, hydrogen and oxygen in their structure. Proteins consist of both amine (NH2) and carboxyl (COOH) groups. #2 Solutions (a) Entropy- this is a measure of how much a system is disordered. Denoted by S. (b) Enthalpy- this is the product of pressure of a system and volume of a system added to the internal energy of a system. (c) Gibbs Free Energy- this is the product of entropy and absolute temperature subtracted from the e nthalpy of a system. (d) Exothermic reaction- this is a chemical reaction in which energy is released in the form of either light or heat. Endothermic reaction- this is a chemical reaction where energy is absorbed from the surrounding. The energy can be in form of heat but not in all cases.

Wilkerson Company Case Essay Example for Free

Wilkerson Company Case Essay 1. The Wilkerson Company is in the business of manufacturing valves, pumps and flow controllers. The company has been experiencing profit losses due to price reductions as a result of heavy competition in the pump category, which is considered a commodity product. In the valves category, Wilkerson seems to be a market leader with a loyal customer base. The valve business is less competitive, with no price reductions, and therefore the company has maintained its gross margin target while not compromising market share. Similarly to the valve business, the flow controller category is not as competitive as the pump industry, hence Wilkersons ability to increase price by 10% without sacrificing volume. In addition, the company needs to take into consideration its increase in indirect expenses relatively to the direct labor expenses. All in all, the company has seen its pre-tax margin decrease from 10% to 3%. 2. Adopting a periodic expense approach will severe the already current problems with Wilkersons cost system by distorting even more the actual cost picture. The reason is that the periodic method would ignore the companys product mix as each of the 3 categories has a differentiated direct cost structure. This would therefore create an even more incorrect analysis of the companys profit structure. Although the current cost allocating system is not optimal (as will be discussed later), it is still preferable over the periodic system, which does not take into account any overhead costs when analyzing product margins and the margins effect on the overall profit. 3. Today, Wilkerson uses a simple cost accounting system which charges each unit of product for direct material and labor cost. Material cost is based on the component price, while labor rates are charged to products based on the production run times of each product. Then, the overhead costs are allocated to each of the 3 products as a percentage of production run direct labor costs (currently 300%). 4. Table 1: Activity Based Costs Drivers and Rates Table 2: Calculations of product margins based on current method: Table 3: Calculations of product margins using proposed Activity Based Costing: The shifts in costs and profitability seen above are driven by all the factors that are not taken into account in the current cost allocation system: production runs, number of shipments and hours of engineering work. We believe that these factors are optimal for estimating the cost per product. For example, if we look at the flow controllers, we can see that they have the least machine hours but the highest values of all cost drivers mentioned above. This dramatic difference distorts the cost analysis and favors the flow controllers on the account of the valves and especially the pumps. 5. There are number of options to improve the companys profitability: * Flow Controller Price Increase: As described in the case, Wilkerson has recently raised flow controller prices by 10% without effect on volume. This leads us to believe that it would be possible to further increase prices in order to improve the products losing gross margin (-10%). * Flow Controller Cost Reduction: In addition to a possible price increase, Wilkerson must find a way to lower costs. This may be done by lowering the number of shipments (cost driver) to customers. According to the current agreements with customers, products are packaged and shipped for just-in-time delivery. This method substantially increases the number of shipments and packaging related expenses. This change can be successfully carried out by offering customers volume related discounts in order to decrease the total number of shipments by increasing the size of each shipment. The rationale behind this recommendation is that the cost driver is the number of shipments, rather than the size of each shipment. * Company Product Mix: Based on our profitability calculations for each category, Wilkerson can improve its total profit and profitability by changing its mix to favor valves rather than pumps. Moreover, there is room to consider reducing or even stopping the manufacturing of flow controllers. 6. Our concern regarding our cost estimates used in the previous sections is that the data in exhibits 1, 2, 4, used for all calculations, is based on a single month and does not necessarily reflect a typical month. A more accurate way to estimate cost would be to rely on a longer period of time (perhaps annual). In order to improve our cost and profitability estimates it would be helpful to have information regarding GA, Selling and Marketing cost drivers so we could allocate them directly to each product cost as well. Lastly, we assumed it possible to further increase flow controller prices without affecting the sales volume. It would be helpful to have more data regarding changes in prices and effect on their sales volume. 7. A number of changes may be made to the current compensation method in order to improve profit: * Higher compensation for sales of high profit margin products in order to improve sales mix as mentioned above. * Relative compensation to quantity of sale. This will also promote the goal of cost reduction as it will decrease the number of shipments.

The Evolution And Implementation Of Internet Banking Information Technology Essay

The Evolution And Implementation Of Internet Banking Information Technology Essay In a world moving at an overwhelming pace, technology has become the essential key driver in all aspects of our life. Internet is the catalysis without which, this would have never been possible. Now that Information Technology has been heartily accepted at home as well as at work, handling activities electronically can be envisaged (Tero et al; 2004). Bill Gates (2008) once said, Banking is essential, banks are not. By this, he meant that traditional banking will gradually disappear and electronic banking, which attracts more and more new users, will replace it. According to Alter (2002), the evolution of electronic banking started with Automatic teller machines (ATMs) and has passed through telephone banking, direct bill payment, electronic fund transfer and the revolutionary online banking, which has been selected to be the future of financial electronic transactions. Internet Banking services were introduced in the early 80s by the Nottingham Building Society and the Bank of Scotland (Tait and Davis, 1989). Unfortunately these services were discontinued as the bank customers were wary and not fully ready to accept internet banking. With the rapid growth of IT in the 90s, banks launched internet banking again (Daniel, 1998) and this time, it met such an astonishing success that these electronic services ended up becoming industry standards. Internet banking is the newest delivery channel that enables bank customers, through safe and appropriate systems, to gain access to general bank information on products and services offered and their accounts. Pikkarainen, Pikkarainen, Karjaluoto and Pahnila (2004, p.224) defines internet banking to be the internet portal through which customers can use different kinds of banking services ranging from bill payment to making investment. This happens through the banks website without any intervention or inconvenience of sending faxes, letters, original signatures and telephone confirmations (Thulani et al, 2009; Henry, 2000). Through the banks website, the bank customers can carry out activities such as balance reporting, inter-account transfers, bill payment via a telecommunication network without having to leave their work or home (Aladwani, 2001; Daniel, 1999; Mols, 1998; Sathye, 1999). With just a simple click of the mouse, Internet banking gives customers access to almost all typ es of bank transactions, apart from ultimate transaction, that is, the withdrawal of cash (De Young, 2001). Using Internet as an alternative channel for the distribution of financial services has become a necessity in order to achieve competitive advantage with the arrival of globalization and more hostile competition (Flavian et al, 2004; Gan et al, 2006). THE MAURITIAN INTERNET BANKING SECTOR Internet Banking is a relatively recent phenomenon in the country and one can assure that it has started to operate locally since 1997. Due to its diversification skills ranging from agriculture, information technology and financial services, Mauritius has experienced a rapid economic growth, thus joining the league of banks that use the internet as a distribution channel for banking services. The banking sector plays an important role in the economy, both in the reduction of unemployment and in the flow of foreign currency to the economy. The two largest local banks are the Mauritius Commercial Bank Ltd and the State Bank of Mauritius Ltd. Some of the banks offering the internet banking services are the Mauritius Commercial Bank Ltd (MCB), the State Bank of Mauritius Ltd (SBM) and the Hong Kong Shanghai Bank (HSBC). The service offered encloses mainly inter account fund transfer, transfer of fund to credit card account, payment to other account, SWIFT payment orders, recharging mobile phones, foreign transfers, cheque and credit card transactions, current statement of account issue, standing order transactions, application for various accounts, loan and credit cards, bill payments. Given the cross border implications of Internet Banking which almost eradicates all geographically boundaries, it is very important to have clear supervisory rules specifying which country supervisors have control over the internet banking activities as well as the elaboration of the applicable legal regime. To keep pace with the development in this line of business, a guideline on Internet Banking was issued to all banks in February 2001. The guideline sets out a regulatory framework for providing Internet banking services in Mauritius and establishes the minimum standards that should be followed by banks providing Internet Banking services. It further describes the requirements and processes to adopt in order to obtain the approval of the Bank by financial institutions who want to offer Internet Banking services. According to this guideline which came into effect the 2 April 2001, Internet Banking refers to banking products and services offered by institutions on the internet throu gh access devices, including personal computers and other intelligent devices. Types of Internet Banking There are different forms of online banking which are web-based banking where customers can access their accounts when they use the internet (Aladwani, 2001). A second form of online banking is where the bank customer, through a modem, dials-up to the banks server to access his bank account. This is known to be dial-up banking. A type of dial-up banking, called Extranet, is a private network between a bank and its corporate customers. Currently there are three kinds of internet banking which are employed in the market place (Thulani et al, 2009; Yibin, 2003; Diniz, 1998) and these are Informational, Communicative and Transactional. An Informational website is the first level of Internet Banking. Marketing information about the banks products and services are found on a standalone server. There are typically no path between the banks internal network and the server. A Communicative/simple transactional website allows a limited amount of interaction between the customer and the banks system. The interaction is restricted to e-mail, account inquiry, loan application or static file updates (name and address). Fund transfers are not allowed. An Advanced website allows bank customers to make queries about their accounts, electronic transfer funds to and from their accounts, pay bills, update their account information and conduct other banking transactions online. Therefore a bank who is planning to offer internet banking services, is expected to create an informational website first, then introduce a communicative website and finally an advanced transactional website where customers can perform the basic transactions. Advantages of Internet Banking Both the provider and the consumer benefit from internet banking. Online banking is considered to be the most important way to decrease cost and enhance or maintain services for consumers (Hua, 2009). From the banks perspective, it is the cheapest banking products delivery channel (Pikkarainen et al, 2004). Together with saving time and money, this service minimizes the possibility of bank tellers committing mistakes ( Jayawardhena Foley, 2000). Less staff is required since the customers serve themselves in cyberspace. Karjaluoto et al (2002, p.261) argued that time and location were no longer limiting factors in banking as all over the world, customers can now easily access their accounts 24/7. Internet makes the transactions efficiently and expertly at an unmatched speed. Internet banking offers the possibility to manage several bank accounts on one site and these sites are compatible with software such as Microsoft money. With increasing competitive pressures from existing firms and new blood on the market, competition is an important logic to be considered. Using internet banking as an alternate channel has allowed banks to target various demographic segments more efficiently, thus retaining existing customers and attracting new ones. While supplying internet banking services, banks establish and extend their customer relationship (Robinson, 2000). The concept of online banking is an uprising in the field of banking and finance as the account holder does not have to visit the bank and queue to perform the basic transactions like balance inquiry, recent transactions record, transfer fund to employees accounts in the form of salary, bill payments and phone account top up. On top of this, the interest rates are higher for online banking than with traditional banking (3.4% to 4%). Many persons like internet banking as there is no credit check. If someone has a bad banking history of financial problems, at a traditional bank, their application to open a bank account would be turned down. This is not the case with internet banking. Some banks offer the facility of online loaning where an instant loan is provided by only filling a form. Internet banking web-sites are highly performing systems, easy to understand and navigate, with simple instructions designed to answer all queries about banking. Customers also have a wide range of opportunities to invest such as stock quotations and news updates (Lee, 2009). Qureshi et al (2008) stated that it is essential to extend internet banking to customers in order to maximize the advantages for both the service providers and the customers. The navigability if the site is a very vital part of internet banking as it can become one of the biggest competitive advantage of a financial body (Ortega et al, 2007). The banking sector performance increases everyday due to the rise in technology usage. Online banking is time saving (Qureshi et al, 2008). E-banking is now less vulnerable to safety and security related issues. Secure Socket Layer (SSL), Password Based Encryption (PBE) and electronic signatures has increased the level of security. If any inconsistency occurs in an account, it can be traced easily, making internet banking more trustworthy. Avinandan Prithwiraj, 2003; Urban, Sultan and Qualls, 2000 have identified trust to be an important factor for the financial online services. Furthermore an empirical study has shown that consumers make online decisions based only on trust. In developing countries, trust plays a crucial role for customers to accept and use online banking (Benamati and Serva, 2007). Belanger, Hiller and Smith (2002) defined privacy as being the ability to control and manage information about oneself. Some banks offer real time customer assistance to customers who have trouble finding their way through the web site or the proceedings of the internet banking registration through instant messaging, email or even the telephone. Disadvantages of Internet Banking Indisputably since the emergence of internet banking, it has been playing an important role for both the service providers and the consumers. Nevertheless, this phenomenon is observed differently among customers who either accept it heartily or reject it. Those who accept it, as proposed by Clark and Mills (1993), prefer impersonal relationship, that is, exchange oriented customers. They like the 24 hour availability of services, the simplicity of the transactions, the no-queuing factor and no fixed branch-operating hours (Al-Somali et al,2009) while those who reject it look for the human touch and social benefits of traditional banking. These are known as the communally oriented customers (Clark and Mills, 1993). Those who reject internet banking are wary of the risks involved in it. Featherman and Pavlou (2003) defined perceived risk as the potential for loss in the pursuit of a desired outcome of using an e-service. The risks perceived are; Financial risk it is the constant anxiety of transactions faults causing a monetary loss suffered by customers who perform online transactions. Clearly internet banking lacks the assurance provided in traditional banking (Lee et al., 2009, p.2) and this is due to the fact that online banking is considered as an innovation which is incompatible with consumers habits (Kuisma et al., 2007, p.77). Performance risk This risk is innate from the consumers fright of losses incurred by failures of online banking websites. Customers are often troubled that a disconnection from the Internet might occur while performing electronic transactions which might lead to huge unexpected losses (Kuisma et al., 2007). This was confirmed by Sathye (1999) who claimed that Internet access is a decisive variable on which the adoption of online banking depends and by Almogbil (2005) who succeeded in showing that a significant relationship exists between the speed of Internet access and the acceptance of electronic banking. Social risk It stems from the fear of being seen in a negative way by others (Kuisma et al., 2007, p.77) or causing the disapproval of ones friends/family/work group by adopting online banking (Agarwal et al., 2009, p.4). Venkatesh and Morris (2000) approve that social influence plays a central role in determining the approval of new information technologies. Nonetheless, it is commendable to note that others opinions are particularly informative in the early stages of experience (Hartwick and Barki, 1994) when potential information technologies adopters are not sufficiently informed. Privacy risk It refers to the possible loss due to fraud or a hacker, putting at risk the security of an online customer (Lee et al., 2009, p.2). This risk is emphasized since the appearance of phishers whose hobby consists on attempting to deceptively collect personal information, such as usernames, passwords and credit card details. They not only lead to users monetary loss, but also violate users privacy (Entrust, 2008). Suh and Han (2002) point out that, unlike in offline banking, that is traditional banking, trust is a pressing need in internet banking. Time risk It is the times loss and the lateness in receiving the payment or the difficulty of navigation (Lee et al., 2009, p.2). This can be due to a disorganized Web site, to slow-downloadable pages, to the long time needed to be a PC-literate. Apart from this, the credulity of an institution must be verified before opening an account in an internet bank and entrusting the life-savings of an individual. The institution must be legitimate and must be checked against the listing of the FDIC. A major disadvantage would be that when several failed attempts have been done to login the account, after having given the wrong password, the account becomes inactive. The customer will have to go through a lengthy procedure to get it reactivated again. Weeldreyer (2002) claims that internet banking is not living up to the hype. Another problem would be the down time of internet, where no customer will be able to access hi/her bank account because there is no internet connection for hours probably. The connection could also be unstable during bad climatic conditions such as heavy rain.

Archimedes :: essays papers

Archimedes Few certain details remain about the life of antiquit^s greatest mathematician, Archimedes. We know he was born in 287 B.C. around Syracuse from a report about 1400 years after the fact. Archimedes tells about his father, Pheidias, in his book The Sandreckoner. Pheidias was an astronomer, who was famous for being the author of a treatise on the diameters of the sun and the moon. Historians speculate that Pheidias^ profession explains why Archimedes chose his career. Some scholars have characterized Archimedes as an aristocrat who actively participated in the Syracusan court and may have been related to the ruler of Syracuse, King Hieron II. We also know Archimedes died in 212 B.C. at the age of 75 in Syracuse. It is said that he was killed by a Roman soldier, who was offended by Achimedes, while the Romans seized Syracuse. Archimedes had a wide variety of interests, which included encompassing statics, hydrostatics, optics, astronomy, engineering, geometry, and arithmetic. Archimedes had more stories passed down through history about his clever inventions than his mathematical theorems. This is believed to be so because the average mind of that period would have no interest in the Archimedean spiral, but would pay attention to an invention that could move the earth. Archimedes^? most famous story is attributed to a Roman architect under Emperor Augustus, named Vitruvius. Vitruvius asked Archimedes to devise some way to test the weight of a gold wreath. Archimedes was unsuccessful until one day as he entered a full bath, he noticed that the deeper he submerged into the tub, the more water flowed out of the tub. This made him realize that the amount of water that flowed out of the tub was equal to the volume of the object being submerged. Therefore by putting the wreath into the water, he could tell by the rise in water level the volume of the wreath, despite its irregular shape. This discovery marked the Law of Hydrostatics, which states that a body immersed in fluid loses weight equal to the weight of the amount of fluid it displaces. There are three main mechanical inventions credited to Archimedes. The first one is the Archimedean screw which supposedly could serve as a water pump. The second invention was the compound pulley. The third invention was the way of finding the volume of something by displacement as demonstrated in the story above. Most historians would agree that more important than his great mechanical inventions were his mathematical discoveries. The mathematical works that have been presented to us by Archimedes could be classified into three groups. The first group consists of works that have as their major objective the proof of Archimedes :: essays papers Archimedes Few certain details remain about the life of antiquit^s greatest mathematician, Archimedes. We know he was born in 287 B.C. around Syracuse from a report about 1400 years after the fact. Archimedes tells about his father, Pheidias, in his book The Sandreckoner. Pheidias was an astronomer, who was famous for being the author of a treatise on the diameters of the sun and the moon. Historians speculate that Pheidias^ profession explains why Archimedes chose his career. Some scholars have characterized Archimedes as an aristocrat who actively participated in the Syracusan court and may have been related to the ruler of Syracuse, King Hieron II. We also know Archimedes died in 212 B.C. at the age of 75 in Syracuse. It is said that he was killed by a Roman soldier, who was offended by Achimedes, while the Romans seized Syracuse. Archimedes had a wide variety of interests, which included encompassing statics, hydrostatics, optics, astronomy, engineering, geometry, and arithmetic. Archimedes had more stories passed down through history about his clever inventions than his mathematical theorems. This is believed to be so because the average mind of that period would have no interest in the Archimedean spiral, but would pay attention to an invention that could move the earth. Archimedes^? most famous story is attributed to a Roman architect under Emperor Augustus, named Vitruvius. Vitruvius asked Archimedes to devise some way to test the weight of a gold wreath. Archimedes was unsuccessful until one day as he entered a full bath, he noticed that the deeper he submerged into the tub, the more water flowed out of the tub. This made him realize that the amount of water that flowed out of the tub was equal to the volume of the object being submerged. Therefore by putting the wreath into the water, he could tell by the rise in water level the volume of the wreath, despite its irregular shape. This discovery marked the Law of Hydrostatics, which states that a body immersed in fluid loses weight equal to the weight of the amount of fluid it displaces. There are three main mechanical inventions credited to Archimedes. The first one is the Archimedean screw which supposedly could serve as a water pump. The second invention was the compound pulley. The third invention was the way of finding the volume of something by displacement as demonstrated in the story above. Most historians would agree that more important than his great mechanical inventions were his mathematical discoveries. The mathematical works that have been presented to us by Archimedes could be classified into three groups. The first group consists of works that have as their major objective the proof of

Alfred Tennyson And His Work :: essays research papers fc

Alfred Tennyson and His Work Alfred Tennyson was born on August 6th, 1809, at Somersby, Lincolnshire, fourth of twelve children of George and Elizabeth Tennyson. Tennyson, said to be the best poet of the Victorian era and his poetry will be discussed in this essay. Tennyson had a lifelong fear of mental illness, because several men in his family had a mild form of epilepsy, which then was thought of as a shameful disease. His father and brother Arthur made their epilepsy worse by excessive drinking. His brother Edward had to be put in a mental institution after 1833, and he spent a few weeks himself under doctor's care in 1843. In the late twenties his father's physical and mental condition got worse, and he became paranoid, abusive, and violent. In 1827 Tennyson escaped his troubled home when he followed his two older brothers to Trinity College, Cambridge, where his teacher was William Whewell. Because each of them had won university prizes for poetry the Tennyson brothers became well known at Cambridge. In 1829 The Apostles, an undergraduate club, invited him to join. The members of this group would remain Tennyson's friends all his life. Arthur Hallam was the most important of these friendships. Hallam, a brilliant Victorian young man was recognized by his peers as having unusual promise. He and Tennyson knew each other only four years, but their intense friendship had a major influence on the poet. On a visit to Somersby, Hallam met and later became engaged to Emily Tennyson, and the two friends looked forward to a life-long companionship. Hallam died from illness in 1833 at the age of 22 and shocked Tennyson profoundly. His grief lead to most of his best poetry, including "In Memoriam", "The Passing of Arthur", "Ulysses", and "Tithonus". Since Tennyson was always sensitive to criticism, The bad reviews of his 1832 poems hurt him greatly. Critics in those days took great joy in the harshness of their reviews. John Wilson Croker's harsh criticisms of some of the poems he wrote kept Tennyson from publishing again for another nine years. The success of his 1842 poems made Tennyson a popular poet, and in 1845 he got a government pension of 200 pounds a year, which helped him with his financial difficulties. The success of "The Princess" and "In Memoriam" and his appointment as Poet Laureate in 1850 finally established him as the most popular poet of the Victorian era. By now Tennyson, only 41, had written some of his greatest poetry, but he continued to write and to gain popularity. Prince Albert admired his poetry so much that he would drop by unexpectedly to here some of Tennyson's poetry.

Indian Cuisne :: India Food

India which is also called 'The Republic Of India', is a very large country in South Asia. By size is it the 7th largest country in the world. It also the 2nd most populated democratic country in the world. It is nearly surrounded by water but connected at the north end of the country the the rest of Asia. On it's south is the Indian Ocean. On the west, the Arabian Sea and on the east the Bay Of Bengal. It is connected to countries such as China, Nepal and Pakistan which also have had an affect on India's cuisine. India is also subdivided into 28 States and 7 Union Territories which each have different variations of Indian cuisine . Bhapa This technique is simply steaming, usually in banana leaves or in foil. This is used in Eastern India and other parts of India for Fish and Vegetables. Bhunao/Kasha This is the process of cooking mainly rich meat dishes in a onion spice base on low heat stirring frequently for a very long time. Bagar/Chowk Or Sambara This is the process of tempering foods with the final addition of spices and ghee. It is used for most lentil dishes. Dum-Pukth This is cooking in a sealed steam pot, this method is typical of the cooking of Lucknow and is used for rice dishes such as Biryanis and Pillaus. Talna This is the term for frying both deep and shallow. Tikkis and Kababs are cooked this way. Sekhna Is the process of pan roasting for nuts and griddle breads. Garam Masal Garam Masala is a term for a mixture of spices used in Indian cooking. There are many commercial brands are available, but keen cooks can grind and blend their own. This ensures freshness and means you have control over the quality and quantities of the individual spices. There is no official recipe for Garam Masala, but many Indian families have their own variety. Common ingerdients are Nutmeg, Cumin seeds, toasted Black peppercorns, Whole cloves, Cinnamon sticks, Black or green cardamom. Cumin Cumin from Western Asia, where it has been harvested since Biblical times. People cook with the fruits of the plant, which are usually called the seeds. Cumin is a very weak spice often used in highly spiced cuisines, especially Mexican and Indian. Ginger Ginger is used a lot as a cooking ingredient or spice in Asian cuisine. It is also used in many western dishes such as Gingerbread Men, Ginger Beer and Ginger Snaps.

My Graduation Plan at IUBAT

Every student should have a graduation plan on their mind. A student couldn’t progress without his graduation plan. Such as, a boat without boatman or a computer without processor. Graduation plan refers to what we will do in our future, our educational plan at the organization and what we want to be just like the aim in our life. It’s very important to every student. I’ve also my graduation plan. I’m Shantanu Sarkar.I’m a student of BCSE at IUBAT. IUBAT- International University Of Business Agriculture & Technology. It’s the first non-government university established in Bangladesh. The initial planning began in 1989 and the university established in 1991. Degree programs started in 1992 with agreement with assumption university of Bangkok, Thailand. IUBAT strongly lobbied forth creation of non –government universities and supported the initiative of the government of Bangladesh in passing legislation for formal establishment of non-g overnment universities in the country. IUBAT now operates as a Non-government university Act of 1992. I’ve a graduation plan at IUBAT.I’m a student of BCSE (Bachelor Of Computer Science & Engineering). And I want to be a software engineer. So, the BCSE degree will be conferred only to the student who has fully complied with the graduation plans and has applied for it. The plans are:†¢I’ve to complete all the prescribed courses with a minimum of 141 credit hours plus such courses recommended by the department after reviewing individual background. †¢I’ve to earn ‘A’ grades in each of the core, specialization courses, and English courses. †¢I’ve to achieve the fulfillment of English language requirement, when relevant. †¢I’ve to earn a cumulative grade point average (CGPA) of 3.8. †¢I’ve to earn at least ‘A’ or ‘A-’ grade in the practicum. †¢I’ve to earn at leas t ‘A’ or ‘A-’ grade in the comprehensive examination. †¢I’ve to satisfactory behavior and discipline.So, this is my graduation plan at IUBAT. And I’ve to follow this plan. If I follow this plan carefully and sincerely, I’ll be succeed.

My Belief

Jounal What is My Belief? Belief is something inspirational that encourages others to progress and work towards self-improvement. That is especially important for today’s youth and can play an important role in shaping our society. Beliefs can influence a young one’s values, conviction, and attitudes, which will shape the person that one will grow to be. That has the ability to focus that efforts on others rather than on themselves and inspire others not only by their words, but more so by it actions that move us to do the same.Beliefs help others by offering good examples, by inspiring others realize the endless possibilities to reach our goals, and by moving others to be the best that I can be. In my opinion, parents are the most effective and influential role models in the lives of their children. The youth of society can learn from, and aspire to be like their parents as they are being reared in their childhood years. Fathers and mothers strive to teach their childr en important values and beliefs as well as demonstrate attitudes and behaviors considered appropriate and beneficial for society’s well-being.Something that has been the strong belief in my life is love of my parents as family. Because my role models are my parents and they possess the quality of good parents. I know they are not perfect, but they carry the virtue and quality of a parent that everyone could wish for. My parents are very responsible, good providers, committed to their duties and responsibilities, loving and determined in pursuing their plans to nurture us with good values and norms so that we will became responsible, well-disciplined, and God-loving. And they also taught us to love others, as we grow old.Now I want to explain several lessons about why the loves of my parents are strong belief to me. First of all, I remember when I was young, my parents made sure that they provided us with what we needed and they do their best, even in the midst of hardships. E specially, my dad has always taught me that I have to work my hardest for whatever I want in life. My dad had me with his wife, my mother, when he was twenty-five. My parents had very little money to raise me on their own, so my dad went to work right away to help support his family.He gave up all his freedom and the fun on a young’s life to help support his family. My dad has been working at least two jobs at a time since the age of twenty-five. They didn’t stop or even pause in fulfilling their duties and responsibilities as parents they always seek a solution or find ways to keep our life better and meaningful. Second, my parents always show and teach us the good values so that we can past it on to the next generation. They are always there to support us in our endeavor and in pursuing our dreams.They are very supportive especially when I need to decide on my own, they are always there on my side, not to be hindered in my plans but instead to give advice and support that I needed most. At a point when I was failing in a subject of 12th standard, third, as I was not very good in academics. My parent then had a long conversation with me about life; they told me that it would be smarter if I will study hard because it would be easier for me to get a job and earn more money, and that this was the best way I could help the family.They always tell us about what they went through because of not having the chance to concentrate on studies at all and â€Å"Only you can change your life. No one can do it for you†. By telling us this, they want us to take advantage of what we have to have a better future. But what got my parents to where they is today was not from being lazy by no means but working hard and driving himself to become something better than what they was and to achieve them dreams. My parents don’t only give advice about having a good future but also about morals.They always tell us that if I order for people to respect us, we have to respect them at all times. To him having good morals is really important because not only does it make us do the right thing but also they will help us succeed in life. Therefore, I should thank God for met my parents. Fourth, my parents are a real understanding person. they gives me the best advice I can get and that is why I think my parents have given me the best emotional support I can receive. My parents have also been the best role model for me.They have thought me not to worry about what others might think or say about me, as long as I’m doing the right thing. They have shown me that being humble and warm hearted could win more love then being filled with superficial materials. They also teach me to stand up for what I believe in no matter what the case is. They have though me that no mountain is high enough. Those are a few reasons why they are an excellent role model in my life. In conclusion, here are some of the reasons on how my parents have impacted my l ife and how the love made an impact in society too.My parents are my role model because I want to be like them, the way they nurtured me. And my parents have also taught me that to be a person in the future, it will give other the hope and desire by saying it ‘I can do it so you can’, my parents make sure that they are on my side in every step of the way of our life. To me the love of my parents are my strongest beliefs because I want to be like them, the way they nurtured us. Furthermore, they always tell me that if I order for people to respect us we have to respect them at all times. This saying always makes me strong.

Analysis of 2012/2013 Botswana Budget Speech

UNIVERSITY OF BOTSWANA NAME: MATILDAH TILLY KAUNDA COURSE: MGT 306 LECTURER: DR MAROBELA TOPIC: ANALYSIS OF THE BUDGET SPEECH ? INTRODUCTION Neo-liberalism is a set of economic policies that have become widespread during the last 25 years or so. Neo-liberalism is the case where the rich grow richer and the poor grow poorer. These are a set of policies that are under the influence exerted by the International Monetary Fund (IMF), the World Bank and the Inter- American Development Bank.They include frameworks of free market trade and no government intervention as well as elements of privatization. This report explores the theories of Managerialism, New public Management and finally neoliberalism implementation in Botswana, to assess whether such a change is constructive to the development of Botswana and Batswana by referring to the budget speech to evaluate whether Botswana is prepared for such a change Managerialism is the pursuit of goals by managers other that for profit maximizati on.According to Locke & Spender (2011) Managerialism is what occurs when a special group called managers ensconces itself systematically in a n organization and deprives owners and employees in their decision making power including the distribution of emoluments and justifies that takeover on the grounds of the managing group’ education and exclusive possession of codified knowledge and know- how necessary to the efficient running of the organization. Application of managerialism to the public sector involves privatization profit motive, incentives for managers and delegation of power.According to Pollitt & Bonkaert (2011) New Public Management refers to deliberate changes to the structures and processes of public sector organization with the objective of getting them to run better. It basically means changes in the way things are done to make them more efficient, more responsive to those who use them; their main focus is on achieving objectives like reduction of poverty. The main emphasis of New Public management is the need to change inefficient, money losing state enterprises into competitive, profit making, taxpaying businesses that provide quality goods services to consumers.This is greatly in line with the words that Honorable Math ambo said in the recent budget speech. He talked of the need for transfer of state owned enterprises to private ones. In the budget Speech Mr Mathambo stated that â€Å" a Privatization Master Plan adopted in 2005 and aimed at identifying all public enterprises suitable for privatization is being revised to among others, identify services and Public Enterprises that are suitable for outsourcing and divestiture during the period 2012 to 2017.In Botswana as said by the minister a new master plan or NDP 10 set out a prudent strategy for ensuring fiscal sustainability while supporting private sector development. A central feature of the strategy is for Government to reduce its dominance by cutting Government expenditure as a share of GDP from 40 to 30 percent Neoliberalism explains the state of no government intervention, free market trade and privatization.According to a journal of sociology (2007) this term broadly means the project of economic and social transformation under the sign of the free market and needs which are formerly met by public agencies in communities and families met by companies selling services in the market. Basically the policy recommendations of neoliberalism are concerned mainly with dismantling what remains of the regulations welfare state. These recommendations include deregulation of business; privatization of public activities and assets; elimination of, or cutbacks in, social welfare programs; and reduction of taxes on businesses and the investing class.The theory of neoliberals advocates for no or rather reduced government spending in the economy. Locke, R (2011) stated that International monetary fund which was created to administer the international monetary system is a strong supporter of neoliberalism or rather privatization. According to an article by Victor Baatweeng dated 12 January 2011,The international Monetary fund (IMF) has advised Botswana and other Southern African Customs Union (SACU) member states to slash their expenditure in order to ensure fiscal and debt sustainability.As a result, the IMF has recommended an appropriate mix of revenue and recurrent expenditure measures, with particular emphasis on reducing the wage bill. The Minister of Finance and Development Planning, Kenneth Matambo announced during his budget speech on Wednesday that the government is concerned that due to its dominance in Economic activities, the public sector wage bill has escalated over time and is high compared to that of other comparable middle income countries and that it needs to be reduced.According to Matambo, this can be achieved by reducing the size of the public sector, with functions and activities which are better carried out in a commercial environment being provided by the private sector. It looks like finally the government is responding to the pressures of IMF. However this is a drastic move that will only cause social upheavals and throw some people into the labor market. This move that can be taken by developed countries rather than developmental states like Botswana.Considering the fact that unemployment as mentioned in the recent budget speech continues to be high, and the government planning to cut wage bill and freeze posts, this initiative will solve nothing but rather lead the county into a downhill. Also the introduction of privatization will cause people who were employed by the government to lose their jobs when the private companies take over. The reason for this is that cost cutting has become the main strategy companies adopt in response to the liberalization of markets.These companies will come with short term contracts, part time positions, minimum wages and no job security. Instead of finding ways to curb the issue the government plans to add fuel to the fire. H0 This move to privatization and outsourcing of services most importantly essential services like water and electricity will only have a negative impact on the poor . According to Steger and Roy (2010), there should be state ownership of crucial national enterprises like energy and railroads.They further stated that Keynes in particular advocates for massive government spending in time of economic crises to create new jobs and lift consumer spending. The paramount objective of the capitalist’s economy is to make profit rather than enhancing wellbeing in economically efficient ways. Prices in the private sector tend to be high unlike in the public sector where they are subsidized to cater for those below the poverty line. In the budget speech the Minister stated that individuals below Botswana Poverty Datum Line declined from 30. 6% of population in 2002/03 to 20. % in 2009/10 but taking this initiative of privat ization will negatively affect those living below poverty datum line and may even end up increasing their number. State intervention is important as well as crucial to the economy as well as to the welfare of its citizens. It ensures social efficiency and fair and just allocation of resources and prevents market failure. According to monopolistic competition economy is a further reason for intervention by the government because it has the potential for the misallocation of resources through fixing wrong prices and making the customers worse off.Hughes(2003)’ s view on privatization was that market systems does not necessarily bring high employment , price stability and the socially desired rate of economic growth and thus the essentiality of public policy to secure such objectives. There are a number of reasons for the need of neoliberalism and why less state intervention in a state may be appropriate and viable. According to a journal by Wendy Larner† Liberalization is essentially about the introduction of competition. The main argument for avocation of liberalization is that competition forces alternative providers to improve productivity and service quality. She further stated that though there is reduction of employment as a consequence of liberalization and privatization, in many cases, lower staff levels result in work intensification. According to Locke (2001) Private sector practices and technologies are superior to those used in the public sector, thus there is high efficiency and effectiveness. He further stated that this idea has a long tradition that can be traced back to 1868. Privatization comes with competition and thus considered a viable strategy for improving performance of public bureaucracies because it lowers costs and increases efficiency.A further argument for privatization is to reduce cross subsidies and charges for services in accordance with their true cost. The argument is that subsidies are economically undesirable as true costs and inefficiencies are can be hidden. There are other mechanisms preferable like direct funding from the budget or giving cash to those to be given assistance. Neoliberasation also reduces government borrowing. The government should only borrow for long term assets such as power stations. A lower government borrowing has lower interest rates and thus helping the economy. Hughes 2003 pg 104). CONCLUSION Government intervention in the market is mainly aimed at reducing injustices and inequalities. While state intervention should be reduced to a minimum to promote efficiency, government should always keep an eye out for situations that only government intervention will regulate in everyone’s best interest against the interest of just a firm. It is difficult to choose a stance between state interventions in the economy because it comes with both advantages and disadvantages for the country.However for a developmental state like Botswana I believe that it is advisable n ot to undergo this change as it not well developed and the welfare of Batswana depends on it. REFERENCES Baatweng, V. (2011, January 12). IMF SLASHES WAGE BILL. Larner W, Neo- liberalism:policy, ideology Governmentality. studies in political economy . Journal of Sociology  © 2009 the Australian Sociological Association, Volume 45(4): 331–338 Locke, R. R. (2011). confronting managerialism. New York: Zed Book Ltd. Kotz M (2002). Globalisarion and Neoliberalism. Rethinking Marxism, Volume 12, Number 2, Summer 2002, pp. 64-79. , 64-79.Matambo, O. (2012). BUDGET SPEECH 2012. Gaborone: Government Printing and Publishing Services,. Steger& Roy (2010) NEO LIBERISALISM- A VERY SHORT INTRODUCTION. New York, USA: Oxford University Press. Locke & Spender (2011). Confronting Managerialism: How the Business Elite and Their Schools Threw Our Lives Out of Balance (Economic Controversies) by. new york, USA: zed Books Ltd. Hughes E (2003). public management and administration. An introductio n. NEW YORK, USA: Palgrave macmillan. Pollit et al (2011) Comparative Analysis- New Public Management, Governance and †¦. , New York, USA, XFORD University Press

Om Heizer Om10 Ism 04

Chapter FORECASTING Discussion Questions 1.? Qualitative models incorporate subjective factors into the forecasting model. Qualitative models are useful when subjective factors are important. When quantitative data are difficult to obtain, qualitative models may be appropriate. 2.? Approaches are qualitative and quantitative. Qualitative is relatively subjective; quantitative uses numeric models. 3.? Short-range (under 3 months), medium-range (3 months to 3 years), and long-range (over 3 years). 4.? The steps that should be used to develop a forecasting system are: (a)?Determine the purpose and use of the forecast (b)? Select the item or quantities that are to be forecasted (c)? Determine the time horizon of the forecast (d)? Select the type of forecasting model to be used (e)? Gather the necessary data (f)? Validate the forecasting model (g)? Make the forecast (h)? Implement and evaluate the results 5.? Any three of: sales planning, production planning and budgeting, cash budgeting, analyzing various operating plans. 6.? There is no mechanism for growth in these models; they are built exclusively from historical demand values. Such methods will always lag trends. .? Exponential smoothing is a weighted moving average where all previous values are weighted with a set of weights that decline exponentially. 8.? MAD, MSE, and MAPE are common measures of forecast accuracy. To find the more accurate forecasting model, forecast with each tool for several periods where the demand outcome is known, and calculate MSE, MAPE, or MAD for each. The smaller error indicates the better forecast. 9.? The Delphi technique involves: (a)? Assembling a group of experts in such a manner as to preclude direct communication between identifiable members of the group (b)?Assembling the responses of each expert to the questions or problems of interest (c)? Summarizing these responses (d)? Providing each expert with the summary of all responses (e)? Asking each expert to study the summary of the responses and respond again to the questions or problems of interest. (f)? Repeating steps (b) through (e) several times as necessary to obtain convergence in responses. If convergence has not been obtained by the end of the fourth cycle, the responses at that time should probably be accepted and the process terminated—little additional convergence is likely if the process is continued. 0.? A time series model predicts on the basis of the assumption that the future is a function of the past, whereas an associative model incorporates into the model the variables of factors that might influence the quantity being forecast. 11.? A time series is a sequence of evenly spaced data points with the four components of trend, seasonality, cyclical, and random variation. 12.? When the smoothing constant, (, is large (close to 1. 0), more weight is given to recent data; when ( is low (close to 0. 0), more weight is given to past data. 13.? Seasonal patterns are of fixed duration a nd repeat regularly.Cycles vary in length and regularity. Seasonal indices allow â€Å"generic† forecasts to be made specific to the month, week, etc. , of the application. 14.? Exponential smoothing weighs all previous values with a set of weights that decline exponentially. It can place a full weight on the most recent period (with an alpha of 1. 0). This, in effect, is the naive approach, which places all its emphasis on last period’s actual demand. 15.? Adaptive forecasting refers to computer monitoring of tracking signals and self-adjustment if a signal passes its present limit. 16.?Tracking signals alert the user of a forecasting tool to periods in which the forecast was in significant error. 17.? The correlation coefficient measures the degree to which the independent and dependent variables move together. A negative value would mean that as X increases, Y tends to fall. The variables move together, but move in opposite directions. 18.? Independent variable (x) is said to explain variations in the dependent variable (y). 19.? Nearly every industry has seasonality. The seasonality must be filtered out for good medium-range planning (of production and inventory) and performance evaluation. 20.? There are many examples.Demand for raw materials and component parts such as steel or tires is a function of demand for goods such as automobiles. 21.? Obviously, as we go farther into the future, it becomes more difficult to make forecasts, and we must diminish our reliance on the forecasts. Ethical Dilemma This exercise, derived from an actual situation, deals as much with ethics as with forecasting. Here are a few points to consider:  ¦ No one likes a system they don’t understand, and most college presidents would feel uncomfortable with this one. It does offer the advantage of depoliticizing the funds al- location if used wisely and fairly.But to do so means all parties must have input to the process (such as smoothing constants) and all data need to be open to everyone.  ¦ The smoothing constants could be selected by an agreed-upon criteria (such as lowest MAD) or could be based on input from experts on the board as well as the college.  ¦ Abuse of the system is tied to assigning alphas based on what results they yield, rather than what alphas make the most sense.  ¦ Regression is open to abuse as well. Models can use many years of data yielding one result or few years yielding a totally different forecast.Selection of associative variables can have a major impact on results as well. Active Model Exercises* ACTIVE MODEL 4. 1: Moving Averages 1.? What does the graph look like when n = 1? The forecast graph mirrors the data graph but one period later. 2.? What happens to the graph as the number of periods in the moving average increases? The forecast graph becomes shorter and smoother. 3.? What value for n minimizes the MAD for this data? n = 1 (a naive forecast) ACTIVE MODEL 4. 2: Exponential Smoothing 1.? Wha t happens to the graph when alpha equals zero? The graph is a straight line.The forecast is the same in each period. 2.? What happens to the graph when alpha equals one? The forecast follows the same pattern as the demand (except for the first forecast) but is offset by one period. This is a naive forecast. 3.? Generalize what happens to a forecast as alpha increases. As alpha increases the forecast is more sensitive to changes in demand. *Active Models 4. 1, 4. 2, 4. 3, and 4. 4 appear on our Web site, www. pearsonhighered. com/heizer. 4.? At what level of alpha is the mean absolute deviation (MAD) minimized? alpha = . 16 ACTIVE MODEL 4. 3: Exponential Smoothing with Trend Adjustment .? Scroll through different values for alpha and beta. Which smoothing constant appears to have the greater effect on the graph? alpha 2.? With beta set to zero, find the best alpha and observe the MAD. Now find the best beta. Observe the MAD. Does the addition of a trend improve the forecast? alpha = . 11, MAD = 2. 59; beta above . 6 changes the MAD (by a little) to 2. 54. ACTIVE MODEL 4. 4: Trend Projections 1.? What is the annual trend in the data? 10. 54 2.? Use the scrollbars for the slope and intercept to determine the values that minimize the MAD. Are these the same values that regression yields?No, they are not the same values. For example, an intercept of 57. 81 with a slope of 9. 44 yields a MAD of 7. 17. End-of-Chapter Problems [pic] (b) | | |Weighted | |Week of |Pints Used |Moving Average | |August 31 |360 | | |September 7 |389 |381 ( . 1 = ? 38. 1 | |September 14 |410 |368 ( . 3 = 110. 4 | |September 21 |381 |374 ( . 6 = 224. 4 | |September 28 |368 |372. | |October 5 |374 | | | |Forecast 372. 9 | | (c) | | | |Forecasting | Error | | |Week of |Pints |Forecast |Error |( . 20 |Forecast| |August 31 |360 |360 |0 |0 |360 | |September 7 |389 |360 |29 |5. 8 |365. 8 | |September 14 |410 |365. 8 |44. 2 |8. 84 |374. 64 | |September 21 |381 |374. 64 |6. 36 |1. 272 |375. 12 | |Se ptember 28 |368 |375. 912 |–7. 912 |–1. 5824 |374. 3296| |October 5 |374 |374. 3296 |–. 3296 |–. 06592 |374. 2636| The forecast is 374. 26. (d)? The three-year moving average appears to give better results. [pic] [pic] Naive tracks the ups and downs best but lags the data by one period. Exponential smoothing is probably better because it smoothes the data and does not have as much variation. TEACHING NOTE: Notice how well exponential smoothing forecasts the naive. [pic] (c)? The banking industry has a great deal of seasonality in its processing requirements [pic] b) | | |Two-Year | | | |Year |Mileage |Moving Average |Error ||Error| | |1 |3,000 | | | | | |2 |4,000 | | | | | |3 |3,400 |3,500 |–100 | |100 | |4 |3,800 |3,700 |100 | |100 | |5 |3,700 |3,600 |100 | |100 | | | |Totals| |100 | | |300 | | [pic] 4. 5? (c)? Weighted 2 year M. A. ith . 6 weight for most recent year. |Year |Mileage |Forecast |Error ||Error| | |1 |3,000 | | | | |2 |4,000 | | | | |3 |3,400 |3,600 |–200 |200 | |4 |3,800 |3,640 |160 |160 | |5 |3,700 |3,640 |60 |60 | | | | | | | 420 | | Forecast for year 6 is 3,740 miles. [pic] 4. 5? (d) | | |Forecast |Error ( |New | |Year |Mileage |Forecast |Error |( = . 50 |Forecast | |1 |3,000 |3,000 | ?0 | 0 |3,000 | |2 |4,000 |3,000 |1,000 |500 |3,500 | |3 |3,400 |3,500 | –100 |–50 |3,450 | |4 |3,800 |3,450 | 350 |175 |3,625 | |5 |3,700 |3,625 | 75 |? 38 |3,663 | | | |Total |1,325| | | | The forecast is 3,663 miles. 4. 6 |Y Sales |X Period |X2 |XY | |January |20 |1 |1 |20 | |February |21 |2 |4 |42 | |March |15 |3 |9 |45 | |April |14 |4 |16 |56 | |May |13 |5 |25 |65 | |June |16 |6 |36 |96 | |July |17 |7 |49 |119 | |August |18 |8 |64 |144 | |September |20 |9 |81 |180 | |October |20 |10 |100 |200 | |November |21 |11 |121 |231 | |December |23 |12 |144 |276 | |Sum | 18 |78 |650 |1,474 | |Average |? 18. 2 | 6. 5 | | | (a) [pic] (b)? [i]? NaiveThe coming January = December = 23 [ii]? 3-month moving (20 + 21 + 23)/3 = 21. 33 [iii]? 6-month weighted [(0. 1 ( 17) + (. 1 ( 18) + (0. 1 ( 20) + (0. 2 ( 20) + (0. 2 ( 21) + (0. 3 ( 23)]/1. 0 = 20. 6 [iv]? Exponential smoothing with alpha = 0. 3 [pic] [v]? Trend? [pic] [pic] Forecast = 15. 73? +?. 38(13) = 20. 67, where next January is the 13th month. (c)? Only trend provides an equation that can extend beyond one month 4. 7? Present = Period (week) 6. a) So: where [pic] )If the weights are 20, 15, 15, and 10, there will be no change in the forecast because these are the same relative weights as in part (a), i. e. , 20/60, 15/60, 15/60, and 10/60. c)If the weights are 0. 4, 0. 3, 0. 2, and 0. 1, then the forecast becomes 56. 3, or 56 patients. [pic] [pic] |Temperature |2 day M. A. | |Error||(Error)2| Absolute |% Error | |93 |— | — |— |— | |94 |— | — |— |— | |93 |93. 5 | 0. 5 |? 0. 25| 100(. 5/93) | = 0. 54% | |95 |93. 5 | 1. 5 | ? 2. 25| 100(1. 5/95) | = 1. 58% | |96 |94. 0 | 2. 0 |? 4. 0 0| 100(2/96) | = 2. 08% | |88 |95. 5 | 7. | 56. 25| 100(7. 5/88) | = 8. 52% | |90 |92. 0 | 2. 0 |? 4. 00| 100(2/90) | = 2. 22% | | | | |13. 5| | | 66. 75 | | |14. 94% | MAD = 13. 5/5 = 2. 7 (d)? MSE = 66. 75/5 = 13. 35 (e)? MAPE = 14. 94%/5 = 2. 99% 4. 9? (a, b) The computations for both the two- and three-month averages appear in the table; the results appear in the figure below. [pic] (c)? MAD (two-month moving average) = . 750/10 = . 075 MAD (three-month moving average) = . 793/9 = . 088 Therefore, the two-month moving average seems to have performed better. [pic] (c)? The forecasts are about the same. [pic] 4. 12? t |Day |Actual |Forecast | | | | |Demand |Demand | | |1 |Monday |88 |88 | | |2 |Tuesday |72 |88 | | |3 |Wednesday |68 |84 | | |4 |Thursday |48 |80 | | |5 |Friday | |72 |( Answer | Ft = Ft–1 + ((At–1 – Ft–1) Let ( = . 25. Let Monday forecast demand = 88 F2 = 88 + . 25(88 – 88) = 88 + 0 = 88 F3 = 88 + . 25(72 – 88) = 88 – 4 = 84 F4 = 84 + . 25(68 – 84) = 84 – 4 = 80 F5 = 80 + . 25(48 – 80) = 80 – 8 = 72 4. 13? (a)? Exponential smoothing, ( = 0. 6: | | |Exponential |Absolute | |Year |Demand |Smoothing ( = 0. |Deviation | |1 |45 |41 |4. 0 | |2 |50 |41. 0 + 0. 6(45–41) = 43. 4 |6. 6 | |3 |52 |43. 4 + 0. 6(50–43. 4) = 47. 4 |4. 6 | |4 |56 |47. 4 + 0. 6(52–47. 4) = 50. 2 |5. 8 | |5 |58 |50. 2 + 0. 6(56–50. 2) = 53. 7 |4. 3 | |6 |? |53. 7 + 0. 6(58–53. 7) = 56. 3 | | ( = 25. 3 MAD = 5. 06 Exponential smoothing, ( = 0. 9: | | |Exponential |Absolute | |Year |Demand |Smoothing ( = 0. |Deviation | |1 |45 |41 |4. 0 | |2 |50 |41. 0 + 0. 9(45–41) = 44. 6 |5. 4 | |3 |52 |44. 6 + 0. 9(50–44. 6 ) = 49. 5 |2. 5 | |4 |56 |49. 5 + 0. 9(52–49. 5) = 51. 8 |4. 2 | |5 |58 |51. 8 + 0. 9(56–51. 8) = 55. 6 |2. 4 | |6 |? |55. 6 + 0. 9(58–55. 6) = 57. 8 | | ( = 18. 5 MAD = 3. 7 (b)? 3-year moving average: | | |Three-Year |Absolute | |Year |Demand |Moving Average |Deviation | |1 45 | | | |2 |50 | | | |3 |52 | | | |4 |56 |(45 + 50 + 52)/3 = 49 |7 | |5 |58 | (50 + 52 + 56)/3 = 52. 7 |5. 3 | |6 |? | (52 + 56 + 58)/3 = 55. 3 | | ( = 12. 3 MAD = 6. 2 (c)? Trend projection: | | | |Absolute | |Year |Demand |Trend Projection |Deviation | |1 |45 |42. 6 + 3. 2 ( 1 = 45. 8 |0. 8 | |2 |50 |42. 6 + 3. 2 ( 2 = 49. 0 |1. 0 | |3 |52 |42. 6 + 3. 2 ( 3 = 52. 2 |0. 2 | |4 |56 |42. 6 + 3. 2 ( 4 = 55. 4 |0. | |5 |58 |42. 6 + 3. 2 ( 5 = 58. 6 |0. 6 | |6 |? |42. 6 + 3. 2 ( 6 = 61. 8 | | ( = 3. 2 MAD = 0. 64 [pic] | X |Y |XY |X2 | | 1 |45 | 45 | 1 | | 2 |50 |100 | 4 | | 3 |52 |156 | 9 | | 4 |56 |224 |16 | | 5 |58 |290 |25 | Then: (X = 15, (Y = 261, (XY = 815, (X2 = 55, [pic]= 3, [pic]= 52. 2 Therefore: [pic] (d)? Comparing the results of the forecasting methodologies for parts (a), (b), and (c). |Forecast Methodology |MAD | |Exponential smoothing, ( = 0. |5. 06 | |Exponential smoothing, ( = 0. 9 |3. 7 | |3-year moving average |6. 2 | |Trend projection |0. 64 | Based on a mean absolute deviation criterion, the trend projection is to be preferred over the exponential smoothing with ( = 0. 6, exponential smoothing with ( = 0. 9, or the 3-year moving average forecast methodologies. 4. 14 Method 1:MAD: (0. 20 + 0. 05 + 0. 05 + 0. 20)/4 = . 125 ( better MSE : (0. 04 + 0. 0025 + 0. 0025 + 0. 04)/4 = . 021 Method 2:MAD: (0. 1 + 0. 20 + 0. 10 + 0. 11) / 4 = . 1275 MSE : (0. 01 + 0. 04 + 0. 01 + 0. 0121) / 4 = . 018 ( better 4. 15 | |Forecast Three-Year |Absolute | |Year |Sales |Moving Average |Deviation | |2005 |450 | | | |2006 |495 | | | |2007 |518 | | | |2008 |563 |(450 + 495 + 518)/3 = 487. 7 |75. 3 | |2009 |584 |(495 + 518 + 563)/3 = 525. 3 |58. 7 | |2010 | |(518 + 563 + 584)/3 = 555. 0 | | | | | ( = 134 | | | | MAD = 67 | 4. 16 Year |Time Period X |Sales Y |X2 |XY | |2005 |1 |450 | 1 |450 | |2006 |2 |495 | 4 |990 | |2007 |3 |518 | 9 |1554 | |2008 |4 |563 |16 |2252 | |2009 |5 |584 |25 |2920 | | | | ( = 2610| |( = 55 | |( = 8166 | [pic] [pic] |Year |Sales |Forecast Trend |Absolute Deviation | |2005 |450 |454. 8 |4. 8 | |2006 |495 |488. 4 |6. | |2007 |518 |522. 0 |4. 0 | |2008 |563 |555. 6 |7. 4 | |2009 |584 |589. 2 |5. 2 | |2010 | |622. 8 | | | | | | ( = 28 | | | | | MAD = 5. 6 | 4. 17 | | |Forecast Exponential |Absolute | |Year |Sales |Smoothing ( = 0. 6 |Deviation | |2005 |450 |410. 0 |40. | |2006 |495 |410 + 0. 6(450 – 410) = 434. 0 |61. 0 | |2007 |518 |434 + 0. 6(495 – 434) = 470. 6 |47. 4 | |2008 |563 |470. 6 + 0. 6(518 – 470. 6) = 499. 0 |64. 0 | |2009 |584 |499 + 0. 6(563 – 499) = 537. 4 |46. 6 | |2010 | |537. 4 + 0. 6(584 – 537. 4) = 565. 6 | | | | | ( = 259 | | | | MAD = 51. 8 | | | |Forecast Exponential |Absolute | |Year |Sales |Smoothing ( = 0. |Deviation | |2005 |450 |410. 0 |40. 0 | |2006 |495 |410 + 0. 9(450 – 410) = 446. 0 |49. 0 | |2007 |518 |446 + 0. 9(495 – 446) = 490. 1 |27. 9 | |2008 |563 |490. 1 + 0. 9(518 – 490. 1) = 515. 2 |47. 8 | |2009 |584 |515. 2 + 0. 9(563 – 515. 2) = 558. 2 |25. 8 | |2010 | |558. 2 + 0. 9(584 – 558. 2) = 581. 4 | | | | |( = 190. 5 | | | |MAD = 38. 1 | (Refer to Solved Problem 4. 1)For ( = 0. 3, absolute deviations for 2005–2009 are 40. 0, 73. 0, 74. 1, 96. 9, 88. 8, respectively. So the MAD = 372. 8/5 = 74. 6. [pic] Because it gives the lowest MAD, the smoothing constant of ( = 0. 9 gives the most accurate forecast. 4. 18? We need to find the smoothing constant (. We know in general that Ft = Ft–1 + ((At–1 – Ft–1); t = 2, 3, 4. Choose either t = 3 or t = 4 (t = 2 won’t let us find ( because F2 = 50 = 50 + ((50 – 50) holds for any (). Let’s pick t = 3. Then F3 = 48 = 50 + ((42 – 50) or 48 = 50 + 42( – 50( or –2 = –8( So, . 25 = ( Now we can find F5 : F5 = 50 + ((46 – 50)F5 = 50 + 46( – 50( = 50 – 4( For ( = . 25, F5 = 50 – 4(. 25) = 49 The forecast for time period 5 = 49 units. 4. 19? Trend adjusted exponential smoothing: ( = 0. 1, ( = 0. 2 | | |Unadjusted | |Adjusted | | | |Month |Income |Forecast |Trend |Forecast ||Error||Error2 | |February |70. 0 | 65. 0 | 0. 0 | 65 |? 5. 0 |? 25. 0 | |March |68. 5 | 65. 5 | 0. 1 | 65. 6 |? 2. 9 |? 8. 4 | |April |64. 8 | 65. 9 | 0. 16 |66. 05 |? 1. 2 |? 1. 6 | |May |71. 7 | 65. 92 | 0. 13 |66. 06 |? 5. 6 |? 31. 9 | |June |71. | 66. 62 | 0. 25 |66. 87 |? 4. 4 |? 19. 7 | |July |72. 8 | 67. 31 | 0. 33 |67. 64 |? 5. 2 |? 26. 6 | |August | | 68. 16 | |68. 60 | |24. 3| | |113. 2| | MAD = 24. 3/6 = 4. 05, MSE = 113. 2/6 = 18. 87. Note that all numbers are rounded. Note: To use POM for Windows to solve this problem, a period 0, which contains the initial forecast and initial trend, must be added. 4. 20? Trend adjusted exponential smoothing: ( = 0. 1, ( = 0. 8 [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] 4. 23? Students must determine the naive forecast for the four months .The naive forecast for March is the February actual of 83, etc. |(a) | |Actual |Forecast ||Error| ||% Error| | | |March |101 |120 |19 |100 (19/101) = 18. 81% | | |April |? 96 |114 |18 |100 (18/96) ? = 18. 75% | | |May |? 89 |110 |21 |100 (21/89) ? = 23. 60% | | |June |108 |108 |? 0 |100 (0/108) ? = 0% | | | | | | |58 | | | 61. 16% | [pic] |(b)| |Actual |Naive ||Error| ||% Error| | | |March |101 |? 83 |18 |100 (18/101) = 17. 82% | | |April |? 96 |101 |? |100 (5/96) ? = 5. 21% | | |May |? 89 |? 96 |? 7 |100 (7/89) ? =? 7. 87% | | |June |108 |? 89 |19 |100 (19/108) = 17. 59% | | | | | | |49| | |48. 49% | | [pic] Naive outperforms management. (c)? MAD for the manager’s technique is 14. 5, while MAD for the naive forecast is only 12. 25. MAPEs are 15. 29% and 12. 12%, respectively. So the naive method is better. 4. 24? (a)? Graph of demand The observations obviously do not form a straight line but do tend to cluster about a straight line over the range shown. (b)? Least-squares regression: [pic] Assume Appearances X |Demand Y |X2 |Y2 |XY | |3 | 3 | 9 | 9 | 9 | |4 | 6 |16 | 36 |24 | |7 | 7 |49 | 49 |49 | |6 | 5 |36 | 25 |30 | |8 |10 |64 |100 |80 | |5 | 7 |25 | 49 |35 | |9 | ? | | | | (X = 33, (Y = 38, (XY = 227, (X2 = 199, [pic]= 5. 5, [pic]= 6. 33. Therefore: [pic] The following figure shows both the data and the resulting equation: [pic] (c) If there are nine performances by Stone Temple Pilots, the estimated sales are: (d) R = . 82 is the correlation coefficient, and R2 = . 68 means 68% of the variation in sales can be explained by TV appearances. 4. 25? |Number of | | | | | |Accidents | | | | |Month |(y) |x |xy |x2 | |January | 30 | 1 | 30 | 1 | |February | 40 | 2 | 80 | 4 | |March | 60 | 3 |180 | 9 | |April | 90 | 4 |360 |16 | |? Totals | |220 | | | [pic] The regression line is y = 5 + 20x. The forecast for May (x = 5) is y = 5 + 20(5) = 105. 4. 26 |Season |Year1 |Year2 |Average |Average |Seasonal |Year3 | | |Demand |Demand |Year1(Year2 |Season |Index |Demand | | | | |Demand |Demand | | | |Fall |200 |250 |225. 0 |250 |0. 90 |270 | |Winter |350 |300 |325. |250 |1. 30 |390 | |Spring |150 |165 |157. 5 |250 |0. 63 |189 | |Summer |300 |285 |292. 5 |250 |1. 17 |351 | 4. 27 | | Winter |Spring |Summer |Fall | |2006 |1,400 |1,500 |1,000 |600 | |2007 |1,200 |1,400 |2,100 |750 | |2008 |1,000 |1,600 |2,000 |650 | |2009 | 900 |1,500 |1,900 | 500 | | |4,500 |6,000 |7,000 |2,500 | 4. 28 | | | | |Average | | | | | | |Average |Quarterly |Seasonal | |Quarter |2007 |2008 |2009 |Demand |Demand |Index | |Winter | 73 | 65 | 89 | 75. 67 |106. 67 |0. 709 | |Spring |104 | 82 |146 |110. 67 |106. 67 |1. 037 | |Summer |168 |124 |205 |165. 67 |106. 67 |1. 553 | |Fall | 74 | 52 | 98 | 74. 67 |106. 67 |0. 700 | 4. 29? 2011 is 25 years beyond 1986. Therefore, the 2011 quarter numbers are 101 through 104. | | | | |(5) | | |(2) |(3) |(4) |Adjusted | |(1) |Quarter |Forecast |Seasonal |Forecast | |Quarter |Number |(77 + . 3Q) |Factor |[(3) ( (4)] | |Winter |101 |12 0. 43 | . 8 | 96. 344 | |Spring |102 |120. 86 |1. 1 |132. 946 | |Summer |103 |121. 29 |1. 4 |169. 806 | |Fall |104 |121. 72 | . 7 | 85. 204 | 4. 30? Given Y = 36 + 4. 3X (a) Y = 36 + 4. 3(70) = 337 (b) Y = 36 + 4. 3(80) = 380 (c) Y = 36 + 4. 3(90) = 423 4. 31 4. 33? (a)? See the table below. For next year (x = 6), the number of transistors (in millions) is forecasted as y = 126 + 18(6) = 126 + 108 = 234. Then y = a + bx, where y = number sold, x = price, and |4. 32? a) | x |y |xy |x2 | | | 16 | 330 | 5,280 |256 | | | 12 | 270 | 3,240 |144 | | | 18 | 380 | 6,840 |324 | | | 14 | 300 | 4,200 |196 | | | 60 |1,280 |19,560 |920 | So at x = 2. 80, y = 1,454. 6 – 277. 6($2. 80) = 677. 32. Now round to the nearest integer: Answer: 677 lattes. [pic] (b)? If the forecast is for 20 guests, the bar sales forecast is 50 + 18(20) = $410. Each guest accounts for an additional $18 in bar sales. |Table for Problem 4. 33 | | | | | |Year |Transistors | | | | | | | |(x) |(y) |xy |x2 |126 + 18x |E rror |Error2 ||% Error| | | |? 1 |140 |? 140 |? 1 |144 |–4 |? 16 |100 (4/140)? = 2. 86% | | |? 2 |160 |? 320 |? 4 |162 |–2 | 4 |100 (2/160)? = 1. 25% | | |? 3 |190 |? 570 |? 9 |180 |10 |100 |100 (10/190) = 5. 26% | | |? 4 |200 |? 800 |16 |198 |? 2 | 4 |100 (2/200) = 1. 00% | | |? |210 |1,050 |25 |216 |–6 |? 36 |100 (6/210)? = 2. 86% | |Totals |15 | | |900 | | |2,800 | | (b)? MSE = 160/5 = 32 (c)? MAPE = 13. 23%/5 = 2. 65% 4. 34? Y = 7. 5 + 3. 5X1 + 4. 5X2 + 2. 5X3 (a)? 28 (b)? 43 (c)? 58 4. 35? (a)? [pic] = 13,473 + 37. 65(1860) = 83,502 (b)? The predicted selling price is $83,502, but this is the average price for a house of this size. There are other factors besides square footage that will impact the selling price of a house. If such a house sold for $95,000, then these other factors could be contributing to the additional value. (c)?Some other quantitative variables would be age of the house, number of bedrooms, size of the lot, and size of the garage, etc. (d)? Coefficient of determination = (0. 63)2 = 0. 397. This means that only about 39. 7% of the variability in the sales price of a house is explained by this regression model that only includes square footage as the explanatory variable. 4. 36? (a)? Given: Y = 90 + 48. 5X1 + 0. 4X2 where: [pic] If: Number of days on the road ( X1 = 5 and distance traveled ( X2 = 300 then: Y = 90 + 48. 5 ( 5 + 0. 4 ( 300 = 90 + 242. 5 + 120 = 452. 5 Therefore, the expected cost of the trip is $452. 50. (b)? The reimbursement request is much higher than predicted by the model. This request should probably be questioned by the accountant. (c)?A number of other variables should be included, such as: 1.? the type of travel (air or car) 2.? conference fees, if any 3.? costs of entertaining customers 4.? other transportation costs—cab, limousine, special tolls, or parking In addition, the correlation coefficient of 0. 68 is not exceptionally high. It indicates that the model explains approximately 46% of the overall variation in trip cost. This correlation coefficient would suggest that the model is not a particularly good one. 4. 37? (a, b) |Period |Demand |Forecast |Error |Running sum ||error| | | 1 |20 |20 |0. 00 |0. 00 |0. 00 | | 2 |21 |20 |1. 00 |1. 0 |1. 00 | | 3 |28 |20. 5 |7. 50 |8. 50 |7. 50 | | 4 |37 |24. 25 |12. 75 |21. 25 |12. 75 | | 5 |25 |30. 63 |–5. 63 |15. 63 |5. 63 | | 6 |29 |27. 81 |1. 19 |16. 82 |1. 19 | | 7 |36 |28. 41 |7. 59 |24. 41 |7. 59 | | 8 |22 |32. 20 |–10. 20 |14. 21 |10. 20 | | 9 |25 |27. 11 |–2. 10 |12. 10 |2. 10 | |10 |28 |26. 05 | 1. 95 |14. 05 | | | | | | |1. 95 | | | | | | | | | | | | | | | |MAD[pic]5. 00 | Cumulative error = 14. 05; MAD = 5? Tracking = 14. 05/5 ( 2. 82 4. 38? (a)? least squares equation: Y = –0. 158 + 0. 1308X (b)? Y = –0. 158 + 0. 1308(22) = 2. 719 million (c)? coefficient of correlation = r = 0. 966 coefficient of determination = r2 = 0. 934 4. 39 |Year X |Patients Y |X2 |Y2 |XY | |? 1 |? 36 | 1 |? 1,296 | 36 | |? 2 |? 33 | |? 1,089 | 66 | |? 3 |? 40 | 9 |? 1,600 |? 120 | |? 4 |? 41 |? 16 |? 1,681 |? 164 | |? 5 |? 40 |? 25 |? 1,600 |? 200 | |? 6 |? 55 |? 36 |? 3,025 |? 330 | |? 7 |? 60 |? 49 |? 3,600 |? 420 | |? 8 |? 54 |? 64 |? 2,916 |? 432 | |? 9 |? 58 |? 81 |? 3,364 |? 522 | |10 |? 61 |100 |? 3,721 |? 10 | |55 | | |478 | | |X |Y |Forecast |Deviation |Deviation | |? 1 |36 |29. 8 + 3. 28 ( ? 1 = 33. 1 |? 2. 9 |2. 9 | |? 2 |33 |29. 8 + 3. 28 ( ? 2 = 36. 3 |–3. 3 |3. 3 | |? 3 |40 |29. 8 + 3. 28 ( ? 3 = 39. 6 |? 0. 4 |0. 4 | |? 4 |41 |29. 8 + 3. 28 ( ? 4 = 42. 9 |–1. 9 |1. 9 | |? 5 |40 |29. 8 + 3. 28 ( ? 5 = 46. 2 |–6. 2 |6. 2 | |? 6 |55 |29. 8 + 3. 28 ( ? 6 = 49. 4 |? 5. 6 |5. 6 | |? 7 |60 |29. 8 + 3. 28 ( ? 7 = 52. 7 |? 7. 3 |7. 3 | |? |54 |29. 8 + 3. 28 ( ? 8 = 56. 1 |–2. 1 |2. 1 | |? 9 |58 |29. 8 + 3. 28 ( ? 9 = 59. 3 |–1. 3 |1. 3 | |10 |61 |29. 8 + 3. 28 ( 10 = 62. 6 |–1. 6 |1. 6 | | | | | | ( = | | | | | |32. 6 | | | | | |MAD = 3. 26 | The MAD is 3. 26—this is approximately 7% of the average number of patients and 10% of the minimum number of patients. We also see absolute deviations, for years 5, 6, and 7 in the range 5. 6–7. 3.The comparison of the MAD with the average and minimum number of patients and the comparatively large deviations during the middle years indicate that the forecast model is not exceptionally accurate. It is more useful for predicting general trends than the actual number of patients to be seen in a specific year. 4. 40 | |Crime |Patients | | | | |Year |Rate X |Y |X2 |Y2 |XY | |? 1 |? 58. 3 |? 36 |? 3,398. 9 |? 1,296 |? 2,098. 8 | |? 2 |? 61. 1 |? 33 |? 3,733. 2 |? 1,089 |? 2,016. 3 | |? 3 |? 73. |? 40 |? 5,387. 6 |? 1,600 |? 2,936. 0 | |? 4 |? 75. 7 |? 41 |? 5,730. 5 |? 1,681 |? 3,103. 7 | |? 5 |? 81. 1 |? 40 |? 6,577. 2 |? 1,600 |? 3,244. 0 | |? 6 |? 89. 0 |? 55 |? 7,921. 0 |? 3,025 |? 4,895. 0 | |? 7 |101. 1 |? 60 |10,221. 2 |? 3,600 |? 6,066. 0 | |? 8 |? 94 . 8 |? 54 |? 8,987. 0 |? 2,916 |? 5,119. 2 | |? 9 |103. 3 |? 58 |10,670. 9 |? 3,364 |? 5,991. 4 | |10 |116. 2 |? 61 |13,502. 4 |? 3,721 |? 7,088. 2 | |Column | |854. | | |478 | |Totals | | | | | | |months) |(Millions) |(1,000,000s) | | | | |Year |(X) |(Y) |X2 |Y2 |XY | |? 1 |? 7 |1. 5 |? 49 |? 2. 25 |10. 5 | |? 2 |? 2 |1. 0 | 4 |? 1. 00 |? 2. 0 | |? 3 |? 6 |1. 3 |? 36 |? 1. 69 |? 7. 8 | |? 4 |? 4 |1. 5 |? 16 |? 2. 25 |? 6. 0 | |? 5 |14 |2. 5 |196 |? 6. 25 |35. 0 | |? 6 |15 |2. 7 |225 |? 7. 9 |40. 5 | |? 7 |16 |2. 4 |256 |? 5. 76 |38. 4 | |? 8 |12 |2. 0 |144 |? 4. 00 |24. 0 | |? 9 |14 |2. 7 |196 |? 7. 29 |37. 8 | |10 |20 |4. 4 |400 |19. 36 |88. 0 | |11 |15 |3. 4 |225 |11. 56 |51. 0 | |12 |? 7 |1. 7 |? 49 |? 2. 89 |11. 9 | Given: Y = a + bX where: [pic] and (X = 132, (Y = 27. 1, (XY = 352. 9, (X2 = 1796, (Y2 = 71. 59, [pic] = 11, [pic]= 2. 26. Then: [pic] andY = 0. 511 + 0. 159X (c)?Given a tourist population of 10,000,000, the model predicts a ridership of: Y = 0. 511 + 0. 159 ( 10 = 2. 101, or 2,101,000 persons. (d)? If there are no tourists at all, the model predicts a ridership of 0. 511, or 511,000 persons. One would not place much confidence in this forecast, however, because the number of tourists (zero) is outside the range of data used to develop the model. (e)? The standard error of the estimate is given by: (f)? The correlation coefficient and the coefficient of determination are given by: [pic] 4. 42? (a)? This problem gives students a chance to tackle a realistic problem in business, i. e. , not enough data to make a good forecast.As can be seen in the accompanying figure, the data contains both seasonal and trend factors. [pic] Averaging methods are not appropriate with trend, seasonal, or other patterns in the data. Moving averages smooth out seasonality. Exponential smoothing can forecast January next year, but not farther. Because seasonality is strong, a naive model that students create on their own might be best. (b) One model might be: Ft+1 = At–11 That is forecastnext period = actualone year earlier to account for seasonality. But this ignores the trend. One very good approach would be to calculate the increase from each month last year to each month this year, sum all 12 increases, and divide by 12.The forecast for next year would equal the value for the same month this year plus the average increase over the 12 months of last year. (c) Using this model, the January forecast for next year becomes: [pic] where 148 = total monthly increases from last year to this year. The forecasts for each of the months of next year then become: |Jan. |29 | |July. |56 | |Feb. |26 | |Aug. |53 | |Mar. |32 | |Sep. |45 | |Apr. |35 | |Oct. |35 | |May. |42 | |Nov. |38 | |Jun. |50 | |Dec. |29 | Both history and forecast for the next year are shown in the accompanying figure: [pic] 4. 3? (a) and (b) See the following table: | |Actual |Smoothed | |Smoothed | | |Week |Value |Value |Forecast |Value |Forecast | |t |A(t) |Ft (( = 0. 2) |Err or |Ft (( = 0. 6)|Error | | 1 |50 |+50. 0 |? +0. 0 |+50. 0 |? +0. 0 | | 2 |35 |+50. 0 |–15. 0 |+50. 0 |–15. 0 | | 3 |25 |+47. 0 |–22. 0 |+41. 0 |–16. 0 | | 4 |40 |+42. 6 |? –2. 6 |+31. 4 |? +8. 6 | | 5 |45 |+42. 1 |? –2. 9 |+36. 6 |? +8. | | 6 |35 |+42. 7 |? –7. 7 |+41. 6 |? –6. 6 | | 7 |20 |+41. 1 |–21. 1 |+37. 6 |–17. 6 | | 8 |30 |+36. 9 |? –6. 9 |+27. 1 |? +2. 9 | | 9 |35 |+35. 5 |? –0. 5 |+28. 8 |? +6. 2 | |10 |20 |+35. 4 |–15. 4 |+32. 5 |–12. 5 | |11 |15 |+32. 3 |–17. 3 |+25. 0 |–10. 0 | |12 |40 |+28. 9 |+11. 1 |+19. 0 |+21. 0 | |13 |55 |+31. 1 |+23. 9 |+31. 6 |+23. 4 | |14 |35 |+35. 9 |? 0. 9 |+45. 6 |–10. 6 | |15 |25 |+36. 7 |–10. 7 |+39. 3 |–14. 3 | |16 |55 |+33. 6 |+21. 4 |+30. 7 |+24. 3 | |17 |55 |+37. 8 |+17. 2 |+45. 3 |? +9. 7 | |18 |40 |+41. 3 |? –1. 3 |+51. 1 |–11. 1 | |19 |35 |+41. 0 |? –6. 0 |+44. 4 |? –9. 4 | |20 |60 |+39. 8 |+20. 2 |+38. 8 |+21. 2 | |21 |75 |+43. 9 |+31. 1 |+51. 5 |+23. 5 | |22 |50 |+50. 1 |? –0. 1 |+65. 6 |–15. | |23 |40 |+50. 1 |–10. 1 |+56. 2 |–16. 2 | |24 |65 |+48. 1 |+16. 9 |+46. 5 |+18. 5 | |25 | |+51. 4 | |+57. 6 | | | | |MAD = 11. 8 |MAD = 13. 45 | (c)? Students should note how stable the smoothed values are for ( = 0. 2. When compared to actual week 25 calls of 85, the smoothing constant, ( = 0. 6, appears to do a slightly better job. On the basis of the standard error of the estimate and the MAD, the 0. 2 constant is better. However, other smoothing constants need to be examined. |4. 4 | | | | | | |Week |Actual Value |Smoothed Value |Trend Estimate |Forecast |Forecast | |t |At |Ft (( = 0. 3) |Tt (( = 0. 2) |FITt |Error | |? 1 |50. 000 |50. 000 |? 0. 000 |50. 000 | 0. 000 | |? 2 |35. 000 |50. 000 |? 0. 000 |50. 000 |–15. 000 | |? 3 |25. 000 |45. 500 |–0. 900 |44. 600 |–19. 600 | |? 4 |40. 000 |38. 720 |– 2. 076 |36. 644 | 3. 56 | |? 5 |45. 000 |37. 651 |–1. 875 |35. 776 | 9. 224 | |? 6 |35. 000 |38. 543 |–1. 321 |37. 222 |? –2. 222 | |? 7 |20. 000 |36. 555 |–1. 455 |35. 101 |–15. 101 | |? 8 |30. 000 |30. 571 |–2. 361 |28. 210 | 1. 790 | |? 9 |35. 000 |28. 747 |–2. 253 |26. 494 | 8. 506 | |10 |20. 000 |29. 046 |–1. 743 |27. 03 |? –7. 303 | |11 |15. 000 |25. 112 |–2. 181 |22. 931 |? –7. 931 | |12 |40. 000 |20. 552 |–2. 657 |17. 895 |? 22. 105 | |13 |55. 000 |24. 526 |–1. 331 |23. 196 |? 31. 804 | |14 |35. 000 |32. 737 |? 0. 578 |33. 315 | 1. 685 | |15 |25. 000 |33. 820 |? 0. 679 |34. 499 |? –9. 499 | |16 |55. 000 |31. 649 |? 0. 109 |31. 58 |? 23. 242 | |17 |55. 000 |38. 731 |? 1. 503 |40. 234 |? 14. 766 | |18 |40. 000 |44. 664 |? 2. 389 |47. 053 |? –7. 053 | |19 |35. 000 |44. 937 |? 1. 966 |46. 903 |–11. 903 | |20 |60. 000 |43. 332 |? 1. 252 |44. 584 |? 15. 416 | |21 |75. 00 0 |49. 209 |? 2. 177 |51. 386 |? 23. 614 | |22 |50. 000 |58. 470 |? 3. 94 |62. 064 |–12. 064 | |23 |40. 000 |58. 445 |? 2. 870 |61. 315 |–21. 315 | |24 |65. 000 |54. 920 |? 1. 591 |56. 511 | 8. 489 | |25 | |59. 058 |? 2. 100 |61. 158 | | To evaluate the trend adjusted exponential smoothing model, actual week 25 calls are compared to the forecasted value. The model appears to be producing a forecast approximately mid-range between that given by simple exponential smoothing using ( = 0. 2 and ( = 0. 6.Trend adjustment does not appear to give any significant improvement. 4. 45 |Month |At |Ft ||At – Ft | |(At – Ft) | |May |100 |100 | 0 | 0 | |June | 80 |104 |24 |–24 | |July |110 | 99 |11 |11 | |August |115 |101 |14 |14 | |September |105 |104 | 1 | 1 | |October |110 |104 |6 |6 | |November |125 |105 |20 |20 | December |120 |109 |11 |11 | | | | |Sum: 87 |Sum: 39 | |4. 46 (a) | |X |Y |X2 |Y2 |XY | | |? 421 |? 2. 90 |? 177241 | 8. 41 |? 1220. 9 | | |? 377 | ? 2. 93 |? 142129 | 8. 58 |? 1104. 6 | | |? 585 |? 3. 00 |? 342225 | 9. 00 |? 1755. 0 | | |? 690 |? 3. 45 |? 476100 |? 11. 90 |? 2380. 5 | | |? 608 |? 3. 66 |? 369664 |? 13. 40 |? 2225. 3 | | |? 390 |? 2. 88 |? 52100 | 8. 29 |? 1123. 2 | | |? 415 |? 2. 15 |? 172225 | 4. 62 | 892. 3 | | |? 481 |? 2. 53 |? 231361 | 6. 40 |? 1216. 9 | | |? 729 |? 3. 22 |? 531441 |? 10. 37 |? 2347. 4 | | |? 501 |? 1. 99 |? 251001 | 3. 96 | 997. 0 | | |? 613 |? 2. 75 |? 375769 | 7. 56 |? 1685. 8 | | |? 709 |? 3. 90 |? 502681 |? 15. 21 |? 2765. 1 | | |? 366 |? 1. 60 |? 133956 | 2. 56 | 585. 6 | | |Column |6885 | |36. 6 | | | |totals | | | | | |January |400 |— |— | — |— | |February |380 |400 |— |20. 0 |— | |March |410 |398 |— |12. 0 |— | |April |375 | 399. 2 |396. 67 |24. 2 |21. 67 | |May |405 | 396. 8 |388. 33 |8. 22 |16. 67 | | | | |MAD = | |16. 11| | |19. 17| | (d)Note that Amit has more forecast observations, while Barbara’s moving average does not start until month 4. Also note that the MAD for Amit is an average of 4 numbers, while Barbara’s is only 2. Amit’s MAD for exponential smoothing (16. 1) is lower than that of Barbara’s moving average (19. 17). So his forecast seems to be better. 4. 48? (a) |Quarter |Contracts X |Sales Y |X2 |Y2 |XY | |1 |? 153 |? 8 |? 23,409 |? 64 |? 1,224 | |2 |? 172 |10 |? 29,584 |100 |? 1,720 | |3 |? 197 |15 |? 38,809 |225 |? 2,955 | |4 |? 178 |? 9 |? 31,684 |? 81 |? 1,602 | |5 |? 185 |12 |? 34,225 |144 |? 2,220 | |6 |? 199 |13 |? 39,601 |169 |? 2,587 | |7 |? 205 |12 |? 42,025 |144 |? ,460 | |8 |? 226 |16 |? 51,076 |256 |? 3,616 | |Totals | | 1,515 | | |95 | b = (18384 – 8 ( 189. 375 ( 11. 875)/(290,413 – 8 ( 189. 375 ( 189. 375) = 0. 1121 a = 11. 875 – 0. 1121 ( 189. 375 = –9. 3495 Sales ( y) = –9. 349 + 0. 1121 (Contracts) (b) [pic] 4. 49? (a) |Method ( Exponential Smoothing | | | |0. 6 = ( | | | |Year |Deposits (Y) |Forecast ||E rror| |Error2 | | 1 |? 0. 25 |0. 25 |0. 00 |? 0. 00 | | 2 |? . 24 |0. 25 |0. 01 |? 0. 0001 | | 3 |? 0. 24 |0. 244 |0. 004 |? 0. 0000 | | 4 |? 0. 26 |0. 241 |0. 018 |? 0. 0003 | | 5 |? 0. 25 |0. 252 |0. 002 |? 0. 00 | | 6 |? 0. 30 |0. 251 |0. 048 |? 0. 0023 | | 7 |? 0. 31 |0. 280 |0. 029 |? 0. 0008 | | 8 |? 0. 32 |0. 298 |0. 021 |? 0. 0004 | | 9 |? 0. 24 |0. 311 |0. 071 |? 0. 0051 | |10 |? 0. 26 |0. 68 |0. 008 |? 0. 0000 | |11 |? 0. 25 |0. 263 |0. 013 |? 0. 0002 | |12 |? 0. 33 |0. 255 |0. 074 |? 0. 0055 | |13 |? 0. 50 |0. 300 |0. 199 |? 0. 0399 | |14 |? 0. 95 |0. 420 |0. 529 |? 0. 2808 | |15 |? 1. 70 |0. 738 |0. 961 |? 0. 925 | |16 |? 2. 30 |1. 315 |0. 984 |? 0. 9698 | |17 |? 2. 80 |1. 906 |0. 893 |? 0. 7990 | |18 |? 2. 80 |2. 442 |0. 357 |? 0. 278 | |19 |? 2. 70 |2. 656 |0. 043 |? 0. 0018 | |20 |? 3. 90 |2. 682 |1. 217 |? 1. 4816 | |21 |? 4. 90 |3. 413 |1. 486 |? 2. 2108 | |22 |? 5. 30 |4. 305 |0. 994 |? 0. 9895 | |23 |? 6. 20 |4. 90 |1. 297 |? 1. 6845 | |24 |? 4. 10 |5. 680 |1. 580 |? 2. 499 | |25 |? 4. 50 |4. 732 |0. 232 |? 0. 0540 | |26 |? 6. 10 |4. 592 |1. 507 |? 2. 2712 | |27 |? 7. 0 |5. 497 |2. 202 |? 4. 8524 | |28 |10. 10 |6. 818 |3. 281 |10. 7658 | |29 |15. 20 |8. 787 |6. 412 |41. 1195 | (Continued) 4. 49? (a)? (Continued) |Method ( Exponential Smoothing | | | |0. 6 = ( | | | |Year |Deposits (Y) |Forecast ||Error| |Error2 | |30 |? 18. 10 |12. 6350 | 5. 46498 |29. 8660 | |31 |? 24. 10 |15. 9140 |8. 19 |67. 01 | |32 |? 25. 0 |20. 8256 |4. 774 |22. 7949 | |33 |? 30. 30 |23. 69 | 6. 60976 |43. 69 | |34 |? 36. 00 |27. 6561 | 8. 34390 |69. 62 | |35 |? 31. 10 |32. 6624 | 1. 56244 | 2. 44121 | |36 |? 31. 70 |31. 72 | 0. 024975 | 0. 000624 | |37 |? 38. 50 |31. 71 |6. 79 |? 46. 1042 | |38 |? 47. 90 |35. 784 |12. 116 |146. 798 | |39 |? 49. 10 |43. 0536 |6. 046 |36. 56 | |40 |? 55. 80 |46. 814 | 9. 11856 | 83. 1481 | |41 |? 70. 10 |52. 1526 |17. 9474 |322. 11 | |42 |? 70. 90 |62. 9210 | 7. 97897 |63. 66 | |43 |? 79. 10 |67. 7084 |11. 3916 |129. 768 | |44 |? 94. 0 0 |74. 5434 | 19. 4566 | 378. 561 | |TOTALS | |787. 30 | | | |150. 3 | | |1,513. 22 | |AVERAGE | 17. 8932 | | 3. 416 | 34. 39 | | | | |(MAD) |(MSE) | |Next period forecast = 86. 2173 |Standard error = 6. 07519 | Method ( Linear Regression (Trend Analysis) | |Year |Period (X) |Deposits (Y) |Forecast |Error2 | |? 1 |? 1 |0. 25 |–17. 330 |309. 061 | |? 2 |? 2 |0. 24 |–15. 692 |253. 823 | |? 3 |? 3 |0. 24 |–14. 054 |204. 31 | |? 4 |? 4 |0. 26 |–12. 415 |160. 662 | |? 5 |? 5 |0. 25 |–10. 777 |121. 594 | |? 6 |? 6 |0. 30 |? –9. 1387 |89. 0883 | |? 7 |? 7 |0. 31 |? –7. 50 |61. 0019 | |? 8 |? 8 |0. 32 |? –5. 8621 |38. 2181 | |? |? 9 |0. 24 |? –4. 2238 |19. 9254 | |10 |10 |0. 26 |? –2. 5855 |8. 09681 | |11 |11 |0. 25 |? –0. 947 |1. 43328 | |12 |12 |0. 33 |? 0. 691098 |0. 130392 | |13 |13 |0. 50 |? 2. 329 |3. 34667 | |14 |14 |0. 95 |? 3. 96769 |9. 10642 | |15 |15 |1. 70 |? 5. 60598 |15. 2567 | |16 |16 |2. 30 |? 7. 24 427 |24. 4458 | |17 |17 |2. 0 |? 8. 88257 |36. 9976 | |18 |18 |2. 80 |? 10. 52 |59. 6117 | |19 |19 |2. 70 |? 12. 1592 |89. 4756 | |20 |20 |3. 90 |? 13. 7974 |97. 9594 | |21 |21 |4. 90 |? 15. 4357 |111. 0 | |22 |22 |5. 30 |? 17. 0740 |138. 628 | |23 |23 |6. 20 |? 18. 7123 |156. 558 | |24 |24 |4. 10 |? 20. 35 |264. 083 | |25 |25 |4. 50 |? 21. 99 |305. 62 | |26 |26 |6. 10 |? 23. 6272 |307. 203 | |27 |27 |7. 70 |? 25. 2655 |308. 547 | |28 |28 |10. 10 |? 26. 9038 |282. 367 | |29 |29 |15. 20 |? 28. 5421 |178. 011 | |30 |30 |18. 10 |? 30. 18 |145. 936 | |31 |31 |24. 10 |? 31. 8187 |59. 58 | |32 |32 |25. 60 |? 33. 46 |61. 73 | |33 |33 |30. 30 |? 35. 0953 |22. 9945 | |34 |34 |36. 0 |? 36. 7336 |0. 5381 | |35 |35 |31. 10 |? 38. 3718 |52. 8798 | |36 |36 |31. 70 |? 40. 01 |69. 0585 | |37 |37 |38. 50 |? 41. 6484 |9. 91266 | |38 |38 | 47. 90 |? 43. 2867 |21. 2823 | |39 | 39 |49. 10 |? 44. 9250 |17. 43 | |40 | 40 |55. 80 |? 46. 5633 |? ? 85. 3163 | |41 | 41 |70. 10 |? 48. 2016 |? 479. 54 | |42 | 4 2 |70. 90 |? 49. 84 |? 443. 28 | |43 | 43 |79. 10 |? 51. 4782 |? 762. 964 | |44 | 44 |94. 00 |? 53. 1165 | 1,671. 46 | |TOTALS | |990. 00 | | |787. 30 | | | | | | | | | | | | | |7,559. 95 | | |AVERAGE |22. 50 | 17. 893 | |171. 817 | | | | | |(MSE) | |Method ( Least squares–Simple Regression on GSP | | |a |b | | | | |–17. 636 |13. 936 | | | | |Coefficients: |GSP |Deposits | | | | |Year |(X) |(Y) |Forecast ||Error| |Error2 | |? 1 |0. 40 |? 0. 25 |–12. 198 |? 12. 4482 |? 154. 957 | |? 2 |0. 40 |? 0. 24 |–12. 198 |? 12. 4382 |? 154. 71 | |? 3 |0. 50 |? 0. 24 |–10. 839 |? 11. 0788 |? 122. 740 | |? 4 |0. 70 |? 0. 26 |–8. 12 | 8. 38 | 70. 226 | |? 5 |0. 90 |? 0. 25 |–5. 4014 | 5. 65137 | 31. 94 | |? 6 |1. 00 |? 0. 30 |–4. 0420 | 4. 342 | 18. 8530 | |? 7 |1. 40 |? 0. 31 |? 1. 39545 | 1. 08545 | 1. 17820 | |? 8 |1. 70 |? 0. 32 |? 5. 47354 | 5. 5354 | 26. 56 | |? 9 |1. 30 |? 0. 24 |? 0. 036086 | 0. 203914 | 0. 041581 | |10 |1. 20 |? 0. 2 6 |–1. 3233 | 1. 58328 | 2. 50676 | |11 |1. 10 |? 0. 25 |–2. 6826 | 2. 93264 | 8. 60038 | |12 |0. 90 |? 0. 33 |–5. 4014 | 5. 73137 | 32. 8486 | |13 |1. 20 |? 0. 50 |–1. 3233 | 1. 82328 | 3. 32434 | |14 |1. 20 |? 0. 95 |–1. 3233 | 2. 27328 | 5. 16779 | |15 |1. 20 |? 1. 70 |–1. 3233 | 3. 02328 | 9. 14020 | |16 |1. 60 |? 2. 30 |? 4. 11418 | 1. 81418 | 3. 9124 | |17 |1. 50 |? 2. 80 |? 2. 75481 | 0. 045186 | 0. 002042 | |18 |1. 60 |? 2. 80 |? 4. 11418 | 1. 31418 | 1. 727 | |19 |1. 70 |? 2. 70 |? 5. 47354 | 2. 77354 | 7. 69253 | |20 |1. 90 |? 3. 90 |? 8. 19227 | 4. 29227 | 18. 4236 | |21 |1. 90 |? 4. 90 |? 8. 19227 | 3. 29227 | 10. 8390 | |22 |2. 30 |? 5. 30 |13. 6297 | 8. 32972 | 69. 3843 | |23 |2. 50 |? 6. 20 |16. 3484 |? 10. 1484 |? 102. 991 | |24 |2. 80 |? 4. 10 |20. 4265 |? 16. 3265 |? 266. 56 | |25 |2. 90 |? 4. 50 |21. 79 |? 17. 29 |? 298. 80 | |26 |3. 40 |? 6. 10 |28. 5827 |? 22. 4827 |? 505. 473 | |27 |3. 80 |? 7. 70 |34. 02 |? 26. 32 |? 6 92. 752 | |28 |4. 10 |10. 10 |38. 0983 |? 27. 9983 |? 783. 90 | |29 |4. 00 |15. 20 |36. 74 |? 21. 54 |? 463. 924 | |30 |4. 00 |18. 10 |36. 74 |? 18. 64 |? 347. 41 | |31 |3. 90 |24. 10 |35. 3795 |? 11. 2795 |? 127. 228 | |32 |3. 80 |25. 60 |34. 02 | 8. 42018 | 70. 8994 | |33 |3. 0 |30. 30 |34. 02 | 3. 72018 | 13. 8397 | |34 |3. 70 |36. 00 |32. 66 | 3. 33918 | 11. 15 | |35 |4. 10 |31. 10 |38. 0983 | 6. 99827 | 48. 9757 | |36 |4. 10 |31. 70 |38. 0983 | 6. 39827 |? 40. 9378 | |37 |4. 00 |38. 50 |36. 74 | 1. 76 | 3. 10146 | |38 |4. 50 |47. 90 |43. 5357 | 4. 36428 | 19. 05 | |39 |4. 60 |49. 10 |44. 8951 | 4. 20491 | 17. 6813 | |40 |4. 50 |55. 80 |43. 5357 |? 12. 2643 |? 150. 412 | |41 |4. 60 |70. 10 |44. 951 |? 25. 20 |? 635. 288 | |42 |4. 60 |70. 90 |44. 8951 |? 26. 00 |? 676. 256 | |43 |4. 70 |79. 10 |46. 2544 |? 32. 8456 |1,078. 83 | |44 |5. 00 |94. 00 |50. 3325 |? 43. 6675 |1,906. 85 | |TOTALS | | | |451. 223 |9,016. 45 | |AVERAGE | | | |? 10. 2551 |? 204. 92 | | | | | |? (MAD) |? (MS E) | Given that one wishes to develop a five-year forecast, trend analysis is the appropriate choice. Measures of error and goodness-of-fit are really irrelevant.Exponential smoothing provides a forecast only of deposits for the next year—and thus does not address the five-year forecast problem. In order to use the regression model based upon GSP, one must first develop a model to forecast GSP, and then use the forecast of GSP in the model to forecast deposits. This requires the development of two models—one of which (the model for GSP) must be based solely on time as the independent variable (time is the only other variable we are given). (b)? One could make a case for exclusion of the older data. Were we to exclude data from roughly the first 25 years, the forecasts for the later year