Development of Insulin using Recombinant DNA Technologies

Development of Insulin using Recombinant DNA Technologies Alistair Jones The use of biotechnology within medicine; diabetes and development of insulin using recombinant DNA technologies Abstract Proteins act as a catalyst for metabolic reactions and responsible for inter and intracellular reactions and signalling events essential for life(Ferrer-Miralles, et al., 2009) Diabetes mellitus is a metabolic disorder with numerous aetiologies; it can be defined by chronic hyperglycaemia which will cause an effect on the metabolism of carbohydrates, fats and proteins. This detrimental effect is from the lack of insulin action, insulin secretion or a combination of them both. Diabetes causes long term damage, dysfunction and failure of a range of major organs. (Consulation, 1999) Through the use of clinical administration missing proteins can be sourced from external sources to reach normal concentrations within the tissular or systemic level. As a number of important studies have all confirmed the importance of the use of strengthened insulin treatment for the reduction and minimisation of long term diabetic complications; it is of great importance and pharmaceutical value that huma n proteins can be sourced (Lindholm, 2002) Through the use of biochemical and genetic knowledge the production of insulin has become available and this industrial scale of therapeutic protein production is the first true application of recombinant DNA technology. (Swartz, 2001, Walsh, 2003) E.coli can be considered as the first microorganism for the production of proteins and is primarily used for genetic modification, cloning and small-scale production for research purposes. Many historical developments within molecular genetics and microbial physiology have been based within this species which has results in a collection of both information and molecular tools. (Ferrer-Miralles, et al., 2009) Discussion Proteins act as a catalyst for metabolic reactions and responsible for inter and intracellular reactions and signalling events essential for life; consequently , a deficiency in the production of polypeptides or production of non-functional of relevant proteins will derive in pathologies which can range from mild to severe (Ferrer-Miralles, et al., 2009). Diabetes mellitus is a metabolic disorder with numerous aetiologies; it can be defined by chronic hyperglycaemia which will cause an effect on the metabolism of carbohydrates, fats and proteins. This detrimental effect is from the lack of insulin action, insulin secretion or a combination of them both. Diabetes causes long term damage, dysfunction and failure of a range of major organs. The characteristics presented with diabetes are weight loss, polyuria, blurring of vision and thirst; the more severe cases will cause ketoacidosis or a non-ketotic hypersmolar state which will lead onto comas, stupor and left untreated death. As the symptoms are often not severe and go undetected for long periods of time, hyperglycaemia can cause pathological and functional changes before a diagnosis can be made. Diabetes causes a multitude of long term affects which include, but not limited to; the failure of the renal system, a two to four times increased risk of cardiovascular disease and potentia l blindness. There are a number of pathogenetic processes which can be involved in the development of diabetes; these will include the processes which destroy the insulin creating beta cells within the pancreas and the creation of a resistance to insulin action ( Alberti, et al., 2006, Consulation, 1999) A combination of metabolic disorders known as metabolic syndrome (MetS) is the combination of hyperglycaemia, hypertension and gout and other cardiovascular risk factors which predict a high risk of developing diabetes. People who have MetS are of the highest risk of the development of type 2 diabetes as it is present up to five times higher within people with this syndrome; this is due to the fact that glucose dysregulation is already present (Alberti, et al., 2006). Type 2 diabetes and atherosclerotic cardiovascular disease can be seen to be of similar ascendants. Inflammation markers have been associated with the development of type 2 diabetes in adults; although this may be part of the autoimmune response they will also reflect the pathogenesis (Schmidt, et al., 1999) Abnormal metabolism of proteins, fats and carbohydrates is caused by the deficient insulin action on target tissues due to the insensitivity or lack of insulin. (Consulation, 1999) Through the use of clinical administration missing proteins can be sourced from external sources to reach normal concentrations within the tissular or systemic level. As a number of important studies have all confirmed the importance of the use of strengthened insulin treatment for the reduction and minimisation of long term diabetic complications; with human insulin being the first line of treatment; it is of great importance and pharmaceutical value that human proteins can be sourced, as this is difficult to do from natural sources (Lindholm, 2002) . We are far past the times of animal sourced insulin’s and we are reaching the turning point in the use of recombinant DNA technologies; which were developed during the late 70’s and uses E.coli as a biological framework for the production of pr oteins of interest through relatively inexpensive procedures. Recombinant DNA technology not only offers the ability to create straightforward proteins but also provides the tools to produce protein molecules with alternative and modified features. (Mariusz, 2011) There are several obstacles in the production of proteins through the use of E.coli however, as it lacks the ability to make post-translational modifications (PTMs) present within the majority of eukaryotic proteins (Ferrer-Miralles, et al., 2009). Recombinant DNA insulin’s are, therefore, gradually being replaced by the more highly efficient insulin analogues (Bell, 2007, Ferrer-Miralles, et al., 2009). Clinically, insulin analogues have been used since the late 1990s, the reason behind insulin modification for subcutaneous injection is to produce absorption properties that better suit the rate of supply from the injection to the physiological need. (Jonassen, et al., 2012) Insulin analogues have the properties of being able to be either rapid acting such as glusine, aspart or lispro or be a long lasting molecule such as glargine and detemir, these can also be used in combination with protamine, these premixed insulin’s provide a more sustained action (Bell, 2007). The combination of biotechnology and the pharmaceutical industry is a product of an evolution within technology and product innovation; which has become a result in advances within science and business practices. The biotechnology based products are thought of as intelligent pharmaceuticals as they often provide new modes and mechanisms in the action and approach to disease control with improved success rate and better patient care. (Evens Kaitin, 2014) Through the use of biochemical and genetic knowledge the production of insulin has become available and this industrial scale of therapeutic protein production is the first true application of recombinant DNA technology. (Swartz, 2001, Walsh, 2003) Although, as insulin is required in such high volumes the product yields of the vast amount of the currently available secretory systems are not currently sufficient enough to make it fully competitive. The current ideas and strategies being used to help improve the efficiency and producti vity of secretion are numerous. (Schmidt, 2004) Cultivation of insulin can be done conveniently within microbial cells such as bacteria and yeast. During the 80’s the FDA approved the use of human insulin produced from recombinant E.coli for the treatment of diabetes, this was the first recombinant protein pharmaceutical to enter the market. Thanks to the versatility and possibilities created through the use of recombinant protein production a large sector of opportunities for pharmaceutical companies opened up. (Ferrer-Miralles, et al., 2009) Since the approval of insulin in 1982 there are now currently more than 200 biotech products available commercially and research has expanded this to over 900 products being tested within clinical trials. Pharmaceuticals are engaged within the development of these products substantially as well as their commercialisation (Evens Kaitin, 2014). This acknowledges the fact that although the microbial systems lack the post translational modifications they are able to efficiently and conve niently produce functional mammalian recombinant proteins. Specific strains of many microbial species have now been created and adapted towards protein production; and the incorporation of yeasts and eukaryotic systems is now in place for protein production. (Ferrer-Miralles, et al., 2009). The use of E.coli expression system is the preferable choice for production of therapeutic proteins, amongst the 151 pharmaceuticals licensed in January 2009 30% where obtained in E.coli, this is due its ability to allow for efficient and economical production of proteins on both a lab scale and within industry (Mariusz, 2011, Swartz, 2001). During insulin production within E.coli the gene is fused with a synthetic fragment encoding for two IgG binding domains which have been derived from staphylococcal protein A. This product is then secreted into the growth medium of E.coli and purified using the IgG affinity. (Moks, et al., 1987) E.coli can be considered as the first microorganism for the production of proteins and is primarily used for genetic modification, cloning and small-scale production for research purposes. Many historical developments within molecular genetics and microbial physiology have been based within this species which has results in a collection of both information and molecular tools. (Ferrer-Miralles, et al., 2009) E.coli flourishes at a temperature of 37Â °C but the proteins are in insoluble form. Fusion protein technology has been able to increase the solubility of over expressed proteins, through the modification of selected amino acid residues allowing for the collection of soluble proteins (Zhang, et al., 1998). Due to the lack of the mechanisms to enable PTMs in bacterial cells protein maturation and disulfide bridges can be, to an extent overcome through the use of protein engineering (Mariusz, 2011). PTMs are crucial in protein folding, stability, processing and activity; therefore, proteins lacking the PMTs may be unstable, insoluble or inactive. However it is possible to synthetically bind PTMs to products, and through genetic engineering of DNA, the amino acid sequence of the polysaccharide can be changed to alter its properties this has been observed within insulin. (Ferrer-Miralles, et al., 2009) For more sophisticated modifications the genetic fusion of two proteins is required (Mariusz, 2011) An increase number of proteins being produced are engineered and tailored to display altered pharmacokinetic profiles and reduce immunogenicity. (Walsh, 2003) Even with the pharmaceutical market progressively producing more protein drugs from non-microbial systems; cell-free protein synthesis and oxidative cytoplasmic folding offers alternatives to the standard recombinant production techniques, it has not effect or impaired the development and progression of products developed within microbial systems proving the robustness of the microbial systems. (Ferrer-Miralles, et al., 2009, Swartz, 2001) In the future Radio Frequency Identification technology will play an important role; however there are some barriers in place for the pharmaceutical supply chain, as there have been concerns raised concerning the potential detrimental effect on the proteins due to the electromagnetic exposure. Alterations have been detected after the RFID however the effect and damages to the protein remain unknown (Acierno, et al., 2010) Works Cited Acierno, R. et al., 2010. Potential effects of RFID systems on biotechnology insulin preparation: A study using HPLC and NMR spectroscopy. Complex Medical Engineering (CME), pp. 198 203. Alberti, K. G. M. M., Zimmet, P. Shaw, J., 2006. Metabolic syndrome—a new world-wide definition. A Consensus Statement from the International Diabetes Federation. Diabetic Medicine, 23(5), pp. 469-480. Bell, D., 2007. Insulin therapy in diabetes mellitus: how can the currently available injectable insulins be most prudently and efficaciously utilised?. Drugs, 67(13), pp. 1813-1827. Consulation, 1999. Definition, diagnosis and classification of diabetes mellitus and its complications. W. H. O., Volume 1. Evens, R. Kaitin, K., 2014. The Biotechnology Innovation Machine—A Source of Intelligent Biopharmaceuticals for the Pharma Industry: Mapping Biotechnology’s Success. [Pre press] submitted to: Clinical Pharmacology Therapeutics, Volume Last excessed, 27/03/2014, p. Avalible from: http://www.nature.com/clpt/journal/vaop/naam/abs/clpt201414a.html. Ferrer-Miralles, N. et al., 2009. Microbial factories for recombinant pharmaceuticals. Microbial Cell Factories , 8(7). Jonassen, I. et al., 2012. Design of the Novel Protraction Mechanism of Insulin Degludec, an Ultra-long-Acting Basal Insulin. [Online] Available at: http://link.springer.com/article/10.1007/s11095-012-0739-z/fulltext.html [Accessed 2014 March 27]. Lindholm, A., 2002. New insulins in the treatment of diabetes mellitus.. Best Pract Res Clin Gastroenterol, 16(3), pp. 475-92. Mariusz, K., 2011. Engineering of Therapeutic Proteins Production in Escherichia coli. Current Pharmaceutical Biotechnology, 12(2), pp. 268-274. Moks, T. et al., 1987. Large–Scale Affinity Purification of Human Insulin–Like Growth Factor I from Culture Medium of Escherichia Coli. Nature Biotechnology, Volume 5, pp. 379-382. Schmidt, F., 2004. Recombinant expression systems in the pharmaceutical industry. Applied Microbiology and Biotechnology, 65(4), pp. 363-372. Schmidt, M. et al., 1999. Markers of inflammation and prediction of diabetes mellitus in adults (Atherosclerosis Risk in Communities study): a cohort study. The Lancet, 353(9165), p. 1649–1652. Swartz, J., 2001. Advances in Escherichia coli production of therapeutic proteins. Current Opinion in Biotechnology, 12(2), pp. 195-201. Walsh, G., 2003. Pharmaceutical biotechnology products approved within the European Union. European Journal of Pharmaceutics and Biopharmaceutics, 55(1), pp. 3-10. Zhang, Y. et al., 1998. Expression of Eukaryotic Proteins in Soluble Form in Escherichia coli. Protein Expression and Purification, 12(2), pp. 159-165.

The Ethical Imperative †Contrarieties

The Ethical Imperative – Contrarieties â€Å"A global ethic is only practicable as a personal commitment,† says the author, Dalla Costa. He explains that for businesspeople, this does not mean valuing profit less, but instead valuing people more. Throughout the article, the author shows that business reflects who we are as a society and the beliefs that we live by as individuals. He uses several examples of organizations that have been hurt by unethical behavior to support his statement.Business leaders must assess their values and make appropriate changes since they operate in a global economy where market forces have left the human aspect weaker and the profit element skyrocketed. Dalla Costa attempts to convince businesses to pursue moral and ethical policies. He addresses the principle of right and wrong but emphasizes the importance of ethical behavior to long-term survival and profit. The article dissects the different characteristics attributed to those optimisti c and pessimistic.It describes the institutional pessimism of business, and explains how it is a product of fear – the fear of making mistake and of trying something new. The author argues that today's universal interdependence requires a global ethic – concern for the consumers, workers, and the environment of the overall community. He also discusses the pressures that lead to unethical behavior by individuals and organizations. He develops on five core fallacies that ground the pessimists' antipathy and prevent correction.In the article, Dalla Costa outlines the process for incorporating ethical principles to the direct benefit of customers, shareholders, employees and profits. The author makes clear why corporate ethics must be a fundamental component of any firm. As managers and consumers, many people are concerned about issues like discrimination in the workplace, and are struggling to integrate their beliefs into their jobs. The Ethical Imperative links these per sonal values to business performance. ’Costly though they may be, ethics are not an expenditure but an investment’’ (Dalla Costa, 1998). This article can be related to any business. [From Tesco’s point of view] as trust is essential among network actors, we believe to be optimistic is the best way to achieve ethical practices and reach trust between the firm and the market. Since industry, employer, and peer pressure are important factors influencing employees’ decisions, and since they do what they think is expected from them, we will work on modifying our business culture to build ethic and trust.Teams will be built to assess unethical issues, gather feedbacks and comments. This will in turn create a positive feedback loop. Also, Tesco will co-create supply chain transparency by 1. Demanding full transparency from its suppliers, 2. Working together with Tesco-Motorola-Food suppliers-Customers, and 3. Allowing customers to be true to their respect ive code of ethics.

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

Physiological Characteristics of Soccer Athletes - Free Essay Example

Sample details Pages: 10 Words: 2877 Downloads: 6 Date added: 2019/04/15 Category Sports Essay Level High school Tags: Soccer Essay Did you like this example? Physiological Characteristics of Soccer Athletes The development of sport and exercise research has provided scientific and practical support for the total evolution in this field. The constant overcoming of limits and records gives the competitive sports scene a need for in-depth knowledge in order to increase the understanding and possibilities of planning of all aspects involved in the sport. The exercise physiology, through the techniques of anthropometric, physiological, cardiovascular, and neuromuscular evaluation, constitutes a singular and important basis in corroboration of this reasoning. Don’t waste time! Our writers will create an original "Physiological Characteristics of Soccer Athletes" essay for you Create order McArdle (2003), emphasizes the importance of measuring the human energetic capacities for sports, saying that the principles of performance and the principles of training must respect the specificity of the sport. For him, speed, power and endurance must be applied accurately within the context of specific patterns of movement and metabolic demands and activity. The planning of the routines of evaluations referring to specificity of each sport is an optimized model for sports success, and with soccer it is no different. Silva et. al (2002) emphasizes the importance of establishing a plan of evaluation routines in controlled environments, such as in a laboratory of exercise physiology, to rule out possibilities of interference of external factors harmful to soccer performance. For the author, it is important to perform functional tests in controlled environments, constituting a safe, precision and secure means of control for the scientific development of training. Within this context, the characterization of the parameters relevant to the physical requirements of the sport becomes essential for the success of the sports field. Garret Jr. (2003) briefly describes the physiological aspects and general principles relevant to soccer and points out as important the following characteristics: aerobic power, anaerobic power, body composition, strength, flexibility, agility and speed. According to Silva et. al (2002), it becomes essential for professional soccer team to periodically systematize on the athletes schedule. This author further stresses the importance of conducting tests in controlled environments in order to avoid that intervening factors impact the reliability of the evaluations. Stolen et. al (2005) states that soccer is not a science, but that science, through assessments and training control, can help an optimized performance in this sport. Therefore, the purpose of this literature review is to demonstrate the anthropometric, physiological, cardiovascular and neuromuscular factors that impact professional soccer players. General Physiological Characteristics of High Athletes Yield The application of assessments of the performance capacities of an athlete is one of the main characteristics in the development of sports training science, both in research and in its practice. For Silva et. al (2002), evaluations should occur before the athletic season begins, as well as during the competitive phase, and must obey a consistent planning and in accordance with modern techniques, used and proven internationally through experience and technical scientific support. McArdle (2003) argues that appropriate physiological measurements and performance tests assess the ability of each energy system, according to the specificity of each sport. In this sense, the specificity of the sport is not only a fundamental principle of training, but equally important in the evaluative aspects of the sport. The author further states that the concept of specificity has been recognized in attempts to adapt the assessment task to the specific characteristics of the different sports modalities. According to Garret Jr. (2003), one of the major challenges facing researchers in the field of sports medicine and physiology of exercise is to understand the factors that contribute to a successful performance in the sport. In this perspective, the author emphasizes that it is extremely important to be able to measure these capabilities and incorporating the data into training, planning, and performance analysis for athletes and coaches. According to the author, the use of tests implies evaluating the athletes current capacity and comparing with established standards, as well as monitoring physiological changes as a result of training, providing guidance on the sporting event to be selected, and serving as an instrument of motivation. Based on these considerations, Stolen et. al (2005) identifies the relevant physiological characteristics employed in high-performance soccer. In his study, the author reviewed 843 scientific articles on the physiology of soccer, and described, among the physiological characteristics of soccer, the main evaluations that permeate modern professional soccer. Among the most important aspects are, the laboratorial evaluations of maximum oxygen intake, anaerobic threshold, body composition, muscle strength and power, speed and agility field assessments. Adopting an evaluative approach, Alves et al. (2015) states that analyzing the level of urea and creatine kinase concentration in the blood, a few hours after training, helps to determine if the volume of the load was adequate. In the same evaluation perspective, Schneider et al. (2018), with reference to studies on soccer training and game monitoring, suggests the use of the heart rate monitor as a general training load detector. In this regard, it is expressed the importance of knowing ones heart rate during games and or training, with how the game load influences the physical state of the soccer players. The author also considers the individualized evaluations of the maximal oxygen consumption and maximal heart rate as an important factor for the organization of a team. In the same line of reasoning, Silva et. al (2002) emphasizes the importance of establishing a periodic planning of soccer specific evaluation routines, as well as in any sport. In order to achieve success in the sports field, these three aspects need to be present: assessments necessary for the specific modality, exploring the specificity of this sport and establishing an organized evaluation routine that accompanies the periodization and schedule of the athletes. In soccer, according to the above authors mentioned, some anthropometric and body composition characteristics: functional and metabolic, cardiovascular, biochemical and neuromuscular, constitute an optimized and satisfactory test battery that can and should be applied in professional soccer teams, seeking the evolution in all directions. Anthropometric and Body Composition Characteristics of Soccer Players The techniques of body composition evaluation are of great importance for the individualized control of athletes training. Heyward (2000) argues that the anthropometric method is a cheap and effective field method (in terms of validity and reliability), which has been used in all population, sex and age groups. The author points out that athletes body composition has been of considerable interest on the part of exercise scientists, since the athletic population generally has considerably lower fat indexes than sedentary populations. In addition to formulating a guideline for weight determination ideal for an athlete to determine a minimum plateau or floor for maximum fat loss in an individualized athletic program, provides absolute and percentage data on athletes lean mass, as well as provides data on athletes dietary performance, among other relevant characteristics . The wide variety of body composition and size characteristics among elite athletes demonstrates the importance of the physicists potential for high-level performance in various sports (Garret, 2003). In this regard, McArdle (2003) points out that the evaluation of body composition quantifies in absolute terms and percentages the main components of the body. The current assessment of body composition separates body mass into two main components body fat and fat free mass. The author also states that it is of great importance to evaluate body composition, since athletes in general have unique somatotype characteristics for their specific sport, and since the specific requirement of each sport largely determines the anthropometric profile of the athlete. Garret (2003) reiterates this assertion by postulating that high-level performance seems to be improved by specific physical characteristics in terms of size, composition and body structures, as seen in the profiles of athletes of various sports. Based on the above arguments, it is clear the importance of establishing a routine program for assessments of body composition in athletes in general. In soccer, available literature indicates that the soccer athlete tends to be tall, strong and thin, with an average height of 180cm, average weight of 75 kg, and fat percentage usually ranging between 8 and 12% (Garret, 2003). Functional and Metabolic Characteristics of Soccer Athletes In exercise physiology, the maximum oxygen consumption (VO2 maximum) is a variable considered extremely important for most sports. For McArdle (2003) conception, maximal VO2 is a fundamental measure of physiological functional capacity for exercise, since it represents a high integration of pulmonary, cardiovascular and neuromuscular functions. According to Garret (2003), the maximum VO2 is physiologically defined as the highest rate of transport and oxygen utilization that can be reached at the peak of physical exercise. According to the author, the high capacity to consume oxygen is a prerequisite for success in endurance sports. Likewise, Weineck (2000) explains that a well-developed aerobic resistance causes the soccer player to have an increase in the physical performance, a good capacity of recovery, decrease of injuries and contusions, increase of psychic tolerance, prevention of tactical failures in fatigue function, reduction of technical errors, maintenance of high-speed action and reaction, and maintenance of health. The author concludes that the maximum VO2 represents a fundamental prerequisite for the performance of soccer players. Corroborating this idea, Godik (1996) affirms that the fundamental role of aerobic capacities in soccer is undeniable. According to McArdle (2003), a considerable research effort was able to develop and standardize tests capable of determining maximum aerobic power and to provide normative standards related to age, gender, training status and body size. Therefore, it is necessary to carry out periodic evaluations of the maximum VO2 in professional players. Silva et. al (2002), justifies the importance of these assessments by reiterating the above statements and adding that knowledge of these data is necessary for the evolution of athletes. For Weineck (2000), corroborating the above statements, the soccer player is required a satisfactorily developed aerobic resistance. However, in no way should this resistance be comparable to that of a long-distance runner. For the purposes of practical applicability, the development of aerobic power (VO2 maximum) does not represent the valence of greater interest in professional trainings, since according to Weineck (2000), for soccer players, the goal will never be the maximum development of resistance aerobic training; the training of this capacity should be directed, as a priority, to meet the specific requirements of the modality. Thus, aerobic resistance must be optimally developed, but not maximally, so as not to overwhelm the volume of aerobic training, as this culminates in decreased hormone testosterone, responsible recovery and anabolic metabolism of proteins. In this perspective, the knowledge of the anaerobic threshold, as well as of the speed played in this level of intensity, receives great attention on the part of the coaches, physical trainers and scientists of the sport. According to McArdle (2003), the anaerobic threshold corresponds to the maximum intensity of exercise that can be sustained by aerobic metabolism, without excessive production of the metabolite lactic acid, due to the degradation of the glucose molecule. Garret (2003) expresses the anaerobic threshold as a probable indicator of the highest intensity of exercise performed at the expense of oxidative phosphorylation without extensive use of the anaerobic mechanism for obtaining energy. The author also explains that the importance of knowing the level of load reached at the anaerobic threshold, as well as its absolute value, lies in knowing the level of intensity that will determine fatigue. Cardiovascular Characteristics of Soccer Athletes The knowledge of cardiovascular aspects in the soccer athlete is also an important parameter within the optimized control of specific evaluations and exercise prescription to look for the evolution in the sport. According to McArdle (2003), the cardiovascular system acts as an integrating agent of the body, as a unit providing the active muscles with a continuous stream of nutrients and oxygen in order to maintain a high level of energy transference. Weineck (2000) argues that for a successful aerobic performance in soccer, there is a need for an effective transport system by the cardiovascular system, so that the performance of the musculature is not limited. The author further states that the heart representativeness works as the engine of this system, pumping blood through the vessels into the muscle cell. The physiological adaptations induced by the training depend mainly on the intensity of the overload, and the heart rate (HR) is an effective way to express the intensity of exercise (McArdle, 2003). For Godik (1996), it is necessary to know how the game load influences the physical state of the athletes in soccer, and the heart rate composes an evaluation index of the physiological stress represented by this load. In this regard, it is accepted that evaluations of the cardiovascular components related to physical fitness are of great relevance in order to achieve evolution and success in the sports environment in general. In soccer, the evaluation of maximum heart rate and subsequent monitoring of maximum heart rate percentages during training and games have been shown to be an effective characterizer of exercise intensity (Hoff et al., 2002). McArdle (2003) postulated that endurance training places the sinus node of the heart under a greater influence of acetylcholine, the parasympathetic hormone that slows the heart rate, with the concomitant decreased sympathetic activity. The author uses this explanation to justify the lower values of resting heart rate found in endurance athletes, or of mixed modalities that share the continuous aerobic requirement, as in the case of soccer. To emphasize the relevance of evaluation routines, it is recommended to perform periodic ergospirometric tests in the athletes, in order to verify the individual cardiovascular and physiological alterations by the progressive increase of workloads, as well as the determination of resting heart rate and maximal heart rate values. For McArdle (2003), the knowledge of the resting heart rate and maximum heart rate values allow the establishment of the exercise intensities in percentage terms percentage of the maximum heart rate and percentage of the frequency (Karvonen method) with wide use for training control. According to Weineck (2000), the monitoring of the heart rate during the games and trainings reflects the magnitude of the work performance physiological (in estimation) and cardiovascular stress in athletes. Based on these considerations, it is concluded that the evaluation of the cardiovascular profile of athletes is of paramount importance to professional soccer, as well as in most sports, and according to Silva et. al (2002), one should incorporate a routine of evaluations in the preparation of the periodization of the athletes soccer players. Neuromuscular Characteristics of Soccer Athletes As with all categories of assessments described so far, neuromuscular assessments are also of great importance for any sport. A widely used test for high-level soccer players, according to Krustrup et al. (2006), is the Yo-Yo Recovery. The author reports that this test has shown to have great reproducibility and to be sensitive to the adaptations of training, within the soccer scope. According to the author, the Yo-Yo Recovery test is an option for the 20-meter alternating-run test and was designed to reflect as closely as possible, the intermittent state of activity in sports such as soccer, as it interweaves moments of exercise with recovery periods. Bangsbo (1996) classifies the test as an important tool in determining the individuals level of conditioning. Each sport modality has a specificity of corporal requirement, in order to trace a characteristic profile in all possible biological aspects that can be modified through training stimuli, such as body composition and maximal oxygen consumption. Just as for all sports, for soccer there is the making of a physical profile considered standard among athletes, which can be slightly altered according to the specific position and function of each athlete. Besides, the specificity of the sport is not only a fundamental principle of training, but equally important in the evaluative aspects of the sport. 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