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quantitative analysis for management
Quantitative Analysis For Management 12th Edition Barry Render, Ralph M. Stair, Michael E. Hanna - Solutions
5-8 What is MAD, and why is it important in the selection and use of forecasting models?
5-9 Explain how the number of seasons is determined when forecasting with a seasonal component.
5-10 A seasonal index may be less than one, equal to one, or greater than one. Explain what each of these values would mean.
5-11 How is the impact of seasonality removed from a time series?
5-12 In using the decomposition method, the forecast based on trend is found using the trend line. How is the seasonal index used to adjust this forecast based on trend?
5-13 Explain what would happen if the smoothing constant in an exponential smoothing model was equal to zero. Explain what would happen if the smoothing constant was equal to one.
5-14 Explain when a CMA (rather than an overall average) should be used in computing a seasonal index.Explain why this is necessary.
5-15 Develop a four-month moving average forecast for Wallace Garden Supply and compute the MAD. A three-month moving average forecast was developed in the section on moving averages in Table 5.2.
5-16 Using MAD, determine whether the forecast in Problem 5-15 or the forecast in the section concerning Wallace Garden Supply is more accurate.
5-17 Data collected on the yearly demand for 50-pound bags of fertilizer at Wallace Garden Supply are shown in the following table. Develop a 3-year moving average to forecast sales. Then estimate demand again with a weighted moving average in which sales in the most recent year are given a weight
5-18 Develop a trend line for the demand for fertilizer in Problem 5-17, using any computer software.
5-19 In Problems 5-17 and 5-18, three different forecasts were developed for the demand for fertilizer.These three forecasts are a 3-year moving average, a weighted moving average, and a trend line. Which one would you use? Explain your answer.
5-20 Use exponential smoothing with a smoothing constant of 0.3 to forecast the demand for fertilizer given in Problem 5-17. Assume that last period’s forecast for year 1 is 5,000 bags to begin the procedure. Would you prefer to use, the exponential smoothing model or the weighted average model
5-21 Sales of Cool-Man air conditioners have grown steadily during the past 5 years:Year Sales 1 450 2 495 3 518 4 563 5 584 6 ?The sales manager had predicted, before the business started, that year 1’s sales would be 410 air conditioners. Using exponential smoothing with a weight of develop
5-22 Using smoothing constants of 0.6 and 0.9, develop forecasts for the sales of Cool-Man air conditioners(see Problem 5-21).
5-23 What effect did the smoothing constant have on the forecast for Cool-Man air conditioners? (See Problems 5-21 and 5-22.) Which smoothing constant gives the most accurate forecast?
5-24 Use a three-year moving average forecasting model to forecast the sales of Cool-Man air conditioners(see Problem 5-21).
5-25 Using the trend projection method, develop a forecasting model for the sales of Cool-Man air conditioners (see Problem 5-21).
5-26 Would you use exponential smoothing with a smoothing constant of 0.3, a 3-year moving average, or a trend to predict the sales of Cool-Man air conditioners? Refer to Problems 5-21, 5-24, and 5-25.
5-27 Sales of industrial vacuum cleaners at R. Lowenthal Supply Co. over the past 13 months are as follows:Sales ($1,000s) Month Sales ($1,000s) Month 11 January 14 August 14 February 17 September 16 March 12 October 10 April 14 November 15 May 16 December 17 June 11 January 11 July(a) Using a
5-28 Passenger miles flown on Northeast Airlines, a commuter firm serving the Boston hub, are as follows for the past 12 weeks:Actual Pass enger Actual Pass enger Week Miles (1,000s) Week Miles (1,000s)1 17 7 20 2 21 8 18 3 19 9 22 4 23 10 20 5 18 11 15 6 16 12 22(a) Assuming an initial forecast
5-29 Emergency calls to Winter Park, Florida’s 911 system, for the past 24 weeks are as follows:Week Calls Week Calls Week Calls 1 50 9 35 17 55 2 35 10 20 18 40 3 25 11 15 19 35 4 40 12 40 20 60 5 45 13 55 21 75 6 35 14 35 22 50 7 20 15 25 23 40 8 30 16 55 24 65(a) Compute the exponentially
5-32 Resolve Problem 5-31 with α = 0.3. Using MAD, which smoothing constant provides a better forecast?
5-33 A major source of revenue in Texas is a state sales tax on certain types of goods and services. Data are compiled and the state comptroller uses them to project future revenues for the state budget. One particular category of goods is classified as Retail Trade. Four years of quarterly data
5-34 Using the data in Problem 5-33, develop a multiple regression model to predict sales (both trend and seasonal components), using dummy variables to incorporate the seasonal factor into the model. Use this model to predict sales for each quarter of the next year. Comment on the accuracy of this
5-35 Trevor Harty, an avid mountain biker, always wanted to start a business selling top-of-the-line mountain bikes and other outdoor supplies. A little over 6 years ago, he and a silent partner opened a store called Hale and Harty Trail Bikes and Supplies.Growth was rapid in the first 2 years,
5. What does the slope of this line indicate?
(b) Use the multiplicative decomposition model to incorporate both trend and seasonal components into the forecast. What does the slope of this line indicate?
(c) Compare the slope of the trend line in part (a)to the slope in the trend line for the decomposition model that was based on the deseasonalized sales figures. Discuss why these are so different and explain which one is best to use.
5-36 The unemployment rates in the United States during a 10-year period are given in the following table.Use exponential smoothing to find the best forecast for next year. Use smoothing constants of 0.2, 0.4, 0.6, and 0.8. Which one had the lowest MAD?Year 1 2 3 4 5 6 7 8 9 10 Unemployment rate
5-39 The following table provides the Dow Jones Industrial Average (DJIA) opening index value on the first working day of 1994–2013:Develop a trend line and use it to predict the opening DJIA index value for years 2014, 2015, and 2016.Find the MSE for this model.Year DJIA Year DJIA 2013 13,104
5-40 Using the DJIA data in Problem 5-39, use exponential smooth with trend adjustment to forecast the opening DJIA value for 2014. Use α = 0.8. andβ = 0.2. Compare the MSE for this technique with the MSE for the trend line.
5-41 Refer to the DJIA data in Problem 5-39.(a) Use an exponential smoothing model with a smoothing constant of 0.4 to predict the opening DJIA index value for 2014. Find the MSE for this.(b) Use QM for Windows or Excel and find the smoothing constant that would provide the lowest MSE.
5-43 For the data in Problem 5-42, develop an exponential smoothing model with a smoothing constant of 0.3. Using the MSE, compare this with the model in Problem 5-42.
1. Develop a forecasting model, justify its selection over other techniques, and project attendance through 2015.
2. What revenues are to be expected in 2014 and 2015?
3. Discuss the school’s options.
1. Prepare a graph of the data. On this same graph, plot a 12-month moving average forecast. Discuss any apparent trend and seasonal patterns.
2. Use regression to develop a trend line that could be used to forecast monthly sales for the next year. Is the slope of this line consistent with what you observed in question 1?If not, discuss a possible explanation.
3. Use the multiplicative decomposition model on these data. Use this model to forecast sales for each month of the next year. Discuss why the slope of the trend equation with this model is so different from that of the trend equation in question 2.
1. Apply the forecasting techniques you have learnt to predict the commercial vehicle production for the next four periods.
=2. What should be the best price for the new motorcycle if the displacement is 150cc, the Power is 14 Ps and the mileage is 60 kmpl?.
=1. Fit a linear regression model to each segment independently and comment about the R2 and the fit of the models. Compare the results you have obtained with a regression model that is fit to all the data taken together..
=1. Prepare Peg Jones’s response to Stephen Ruth.
=(c) Which of the two stocks is most highly correlated to the Dow Jones Industrial Average over this time period?
=(b) Develop a regression model to predict the price of stock 2 based on the Dow Jones Industrial Average.
=(a) Develop a regression model to predict the price of stock 1 based on the Dow Jones Industrial Average.
=4-32 The closing stock price for each of two stocks was recorded over a 12-month period. The closing price for the Dow Jones Industrial Average(DJIA) was also recorded over this same time period. These values are shown in the following table:Month DJIA Stock 1 Stock 2 1 11,168 48.5 32.4 2 11,150
=(f) Find the best multiple regression model to predict the number of wins. Use any combination of the variables to find the best model.
=(e) Which of the four models is better for predicting the number of victories?
=(d) Develop a regression model that could be used to predict the number of victories based on the onbase percentage.
=(c) Develop a regression model that could be used to predict the number of victories based on the batting average.
=(b) Develop a regression model that could be used to predict the number of victories based on the runs scored.
=(a) Develop a regression model that could be used to predict the number of victories based on the ERA.
=4-31 The number of victories (W), earned run average(ERA), runs scored (R), batting average (AVG), and on-base percentage (OBP) for each team in the American League in the 2012 season are provided in the following table. The ERA is one measure of the effectiveness of the pitching staff, and a
=4-30 In 2012, the total payroll for the New York Yankees was almost $200 million, while the total payroll for the Oakland Athletics (a team known for using baseball analytics or sabermetrics) was about $55 million, less than one-third of the Yankees payroll. In the following table, you will see
=4-29 A sample of nine public universities and nine private universities was taken. The total cost for the year (including room and board) and the median SAT score(maximum total is 2400) at each school were recorded.It was felt that schools with higher median SAT scores would have a better
=4-28 Use the data in Problem 4-26 to find the best quadratic regression model. (There is more than one to consider.) How does this compare to the models in Problems 4-26 and 4-27?
=4-27 Use the data in Problem 4-26 to develop a multiple linear regression model. How does this compare with each of the models in Problem 4-26?
=4-26 A sample of 20 automobiles was taken, and the miles per gallon (MPG), horsepower, and total weight were recorded. Develop a linear regression model to predict MPG, using horsepower as the only independent variable. Develop another model with weight as the independent variable. Which of these
=4-25 The total expenses of a hospital are related to many factors. Two of these factors are the number of beds in the hospital and the number of admissions. Data were collected on 14 hospitals, as shown in the following table:Hospital Number of BEDs Admissions(100s)Total Expenses(Millions)1 215
=4-24 Use the data in Problem 4-22 and develop a regression model to predict selling price based on the square footage, number of bedrooms, and age. Use this to predict the selling price of a 10-year-old, 2,000-square-foot house with three bedrooms.
=4-23 Use the data in Problem 4-22 and develop a regression model to predict selling price based on the square footage and number of bedrooms. Use this to predict the selling price of a 2,000-square-foot house with three bedrooms. Compare this model with the models in Problem 4-22. Should the
=4-22 The following data give the selling price, square footage, number of bedrooms, and age of houses that have sold in a neighborhood in the past 6 months. Develop three regression models to predict the selling price based upon each of the other factors individually. Which of these is
=4-21 The following data give the starting salary for students who recently graduated from a local university and accepted jobs soon after graduation. The starting salary, grade-point average (GPA), and major (business or other) are provided.Salary $29,500 $46,000 $39,800 $36,500 GPA 3.1 3.5 3.8
=4-20 Use computer software to develop a regression model for the data in Problem 4-19. Explain what this output indicates about the usefulness of this model.
=4-19 Bus and subway ridership in Washington, D.C., during the summer months is believed to be heavily tied to the number of tourists visiting the city. During the past 12 years, the following data have been obtained:Year Number of Tourists(1,000,000s)Ridership(100,000s)1 7 15 2 2 10 3 6 13 4 4 15
=4-18 Thirteen students entered the undergraduate business program at Rollins College 2 years ago.The following table indicates what their grade-point averages (GPAs) were after being in the program for 2 years and what each student scored on the SAT exam (maximum 2400) when he or she was in high
=4-17 Accountants at the firm Walker and Walker believed that several traveling executives submit unusually high travel vouchers when they return from business trips. The accountants took a sample of 200 vouchers submitted from the past year; they then developed the following multiple regression
=4-16 Steve Caples, a real estate appraiser in Lake Charles, Louisiana, has developed a regression model to help appraise residential housing in the Lake Charles area. The model was developed using recently sold homes in a particular neighborhood. The price (Y) of the house is based on the square
=4-15 Using computer software, find the least-squares regression line for the data in Problem 4-13. Based on the F test, is there a statistically significant relationship between the first test grade and the final average in the course?
=4-14 Using the data in Problem 4-13, test to see if there is a statistically significant relationship between the grade on the first test and the final average at the 0.05 level of significance. Use the formulas in this chapter and Appendix D.
=4-13 Students in a management science class have just received their grades on the first test. The instructor has provided information about the first test grades in some previous classes as well as the final average for the same students. Some of these grades have been sampled and are as
=4-12 Using computer software, find the least-squares regression line for the data in Problem 4-10. Based on the F test, is there a statistically significant relationship between the demand for guitars and the number of YouTube views?
=4-11 Using the data in Problem 4-10, test to see if there is a statistically significant relationship between sales and YouTube views at the 0.05 level of significance.Use the formulas in this chapter and Appendix D.
=4-10 The operations manager of a musical instrument distributor feels that demand for a particular type of guitar may be related to the number of YouTube views for a music video by the popular rock group Marble Pumpkins during the preceding month. The manager has collected the data shown in the
=4-9 John Smith has developed the following forecasting model:ˆY X = + 36 4 3. 1 whereˆY = Demand for K10 air conditioners X1 = the outside temperature (°F)(a) Forecast the demand for K10 when the temperature is 70°F.(b) What is the demand for a temperature of 80°F?(c) What is the demand for
=4-8 Explain how a plot of the residuals can be used in developing a regression model.
=4-7 What is the SSE? How is this related to the SST and the SSR?
=4-6 Explain what information is provided by the F test.
=4-5 Explain how the adjusted r2 value is used in developing a regression model.
=4-4 Explain how a scatter diagram can be used to identify the type of regression to use.
=4-3 Discuss how the coefficient of determination and the coefficient of correlation are related and how they are used in regression analysis.
=4-2 Discuss the use of dummy variables in regression analysis.
=4-1 What is the meaning of least squares in a regression model?
=12. A good regression model should havea. a low r 2 and a low significance level for the F test.b. a high r 2 and a high significance level for the F test.c. a high r 2 and a low significance level for the F test.d. a low r 2 and a high significance level for the F test.
=11. A new variable should not be added to a multiple regression model if that variable causesa. r 2 to decrease.b. the adjusted r 2 to decrease.c. the SST to decrease.d. the intercept to decrease.
=10. The overall significance of a regression model is tested using an F test. The model is significant ifa. the F value is low.b. the significance level of the F value is low.c. the r 2value is low.d. the slope is lower than the intercept.
=9. A multiple regression model differs from a simple linear regression model because the multiple regression model has more than onea. independent variable.b. dependent variable.c. intercept.d. error.
=8. When using dummy variables in a regression equation to model a qualitative or categorical variable, the number of dummy variables should equala. the number of categories.b. 1 more than the number of categories.c. 1 less than the number of categories.d. the number of other independent variables
=7. In a regression model, if every sample point is on the regression line (all errors are 0), thena. the correlation coefficient would be 0.b. the correlation coefficient would be −1 or 1.c. the coefficient of determination would be −1d. the coefficient of determination would be 0.
=6. The percentage of the variation in the dependent variable that is explained by a regression equation is measured bya. the coefficient of correlation.b. the MSE.c. the coefficient of determination.d. the slope.
=5. A quantity that provides a measure of how far each sample point is from the regression line isa. the SSR.b. the SSE.c. the SST.d. the MSR.
=4. In a regression model, Y is calleda. the independent variable.b. the dependent variable.c. the regression variable.d. the predictor variable.
=3. When using regression, an error is also calleda. an intercept.b. a prediction.c. a coefficient.d. a residual.
=2. A graph of the sample points that will be used to develop a regression line is calleda. a sample graph.b. a regression diagram.c. a scatter diagram.d. a regression plot.
=1. One of the assumptions in regression analysis is thata. the errors have a mean of 1.b. the errors have a mean of 0.c. the observations (Y) have a mean of 1.d. the observations (Y) have a mean of 0.
=3. Frederick Winslow Taylora. was a military researcher during World War II.b. pioneered the principles of scientific management.c. developed the use of the algorithm for QA.d. all of the above.
=8. A deterministic model is one in whicha. there is some uncertainty about the parameters used in the model.b. there is a measurable outcome.c. all parameters used in the model are known with complete certainty.d. there is no available computer software.
=9. The term algorithma. is named after Algorismus.b. is named after a ninth-century Arabic mathematician.c. describes a series of steps or procedures to be repeated.d. all of the above.
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