Business Forecasting 1st Edition John E. Hanke - Solutions

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1. Analyze the significance of the variables in Dorothy’s regression model. Develop a regression model (be sure to include additive dummy variables for the seasonal component, if necessary), and use it to forecast the number of new clients for the first three months of 1993. Compare your
1. Write a memo to John with a careful analysis of the results of his two attempts to develop a seasonal forecasting model. Which model is better? Be sure your discussion includes an evaluation of model fit, potential forecast accuracy, and any remaining problems—for example , autocorrelation.
4. Would another type of forecasting model be more effective for forecasting weekly sales?
3. Do you agree with Jim’s conclusions?
2. Was it correct for Jim to use sales lagged one week as a predictor variable?
1. Was Jim’s use of a dummy variable correct?
6. What conclusions can be drawn from a comparison of the Spokane County business activity index and the GNP?
5. Is there any potential for the use of lagged data?
4. Should the regression done on the first differences have been through the origin?
3. How does the small sample size affect the analysis?
2. Would it have been better to eliminate multicollinearity first and then tackle autocorrelation?
1. Why did Young choose to solve the autocorrelation problem first?
7. Examine the residuals from your fitted model. In particular, check for autocorrelation. Once you are satisfied with your forecasting equation, generate forecasts for the next six time periods. If possible, compare your forecasts with the actual values.
6. Develop a forecasting equation for your dependent variable using one or more of the identified predictor variables.
5. Identify several potential predictor variables for your dependent variable. You may use company records and other data sources in this process.
4. Compute the first differences for your data, and construct the autocorrelation function for the differenced data. Describe the resulting patterns in the time series of first differences.
3. Based on the pattern of the autocorrelation function, describe the patterns in your time series.
2. Calculate several autocorrelation coefficients, and plot the autocorrelation function.
1. Identify a company or organization that interests you.The company can be a local or national company that has published records, including the measurement of time series variables. Identify a key variable for your chosen company, and record its values for several years, quarters, or months.
24. Consider the bivariate system where are each independently distributed with mean zero and variance . Develop an expression for , and show that X and Y are cointegrated. What is the cointegrating linear combination in this case?
23. Refer to Problem 20. Run a simple linear regression of chicken consumption on chicken consumption lagged one time period. Examine the residuals. Interpret the results of your regression analysis. Is this year’s chicken consumption likely to be a good predictor of next year’s chicken
22. Refer to Problem 20. Consider only the variables chicken consumption, income, and chicken price in the original units. Compute simple differences for each of the variables. Using the differenced data, regress the change in chicken consumption on the change in income and the change in chicken
21. Repeat parts b and c of Problem 20 with the log-transformed data. Give an interpretation of the coefficients of income and chicken price in terms of elasticities. Using your final fitted regression function, indicate how a forecast of the following year’s chicken consumption would be
20. The demand for a commodity typically depends on the income of the consumer, the real price of the commodity, and the real price of complementary or competing products. Table P-20 gives the per capita consumption of chicken in the United States (in pounds); the per capita disposable income (in
19. Circuit City Inc. is a retailer of video and audio equipment and other consumer electronics and office products. Recently, sales have been weak, declining by a total TABLE P-19 Year May 31 Aug 31 Nov 30 Feb 28 1996 1,742 1,806 1,999 2,897 1997 1,851 1,948 2,039 3,156 1998 2,078 2,369 2,222
18. Although the time series data in Table P-18 are old, they provide the basis for some interesting regression modeling. Using the data in Table P-18, attempt to relate personal savings to personal income (in billions of dollars) for the time period from 1935 to 1954.a. Fit a simple linear
17. Refer to Example 5. Using the Sears data in Table 5, convert the sales and disposable income values to simple differences. That is, create the numbers and . Fit a simple linear regression model to the differenced data. Compare your results to the results obtained by the method of generalized
16. The data in Table P-16 show seasonally adjusted quarterly sales for Dickson Corporation and for the entire industry for 20 quarters.a. Fit a linear regression model, and store the residuals. Plot the residuals against time, and obtain the residual autocorrelations. What do you find?b. Calculate
15. National Presto is a manufacturer of small electrical appliances and housewares, including pressure cookers, heaters, canners, fry pans, griddles, roaster ovens, deep fryers, corn poppers, can openers, coffee makers, slicers, hand mixers, and portable ranges. Its quarterly sales in millions of
14. Thomas Furniture Company concludes that production scheduling can be improved by developing an accurate method of predicting quarterly sales. The company analyst, Mr. Estes, decides to investigate the relationship between housing construction permits and furniture sales in the Springfield
13. Thompson Airlines has determined that 5% of the total number of U.S. domestic airline passengers fly on Thompson planes. You are given the task of forecasting the number of passengers who will fly on Thompson Airlines in 2007. The data are presented in Table P-13.a. Develop a time series
12. Paul Raymond, president of Washington Water Power, was worried about the possibility of a takeover attempt and the fact that the number of common shareholders has been decreasing since 1983. Suppose he instructed you to study the number of common shareholders since 1968 and be prepared to
11. Jim Jackson, a rate analyst for the Washington Water Power Company, while preparing for a rate case needed to forecast electric residential revenue for 1996. Jim decided to investigate three potential predictor variables: residential use in kilowatt-hours (kWh), residential charge per kWh
10. Decision Science Associates was asked to do a feasibility study for a proposed destination resort to be located within half a mile of the Grand Coulee Dam. Mark Craze was not happy with the regression model that used the price of a regular gallon of gasoline to predict the number of visitors
9. Tamson Russell, an economist working for the government, was trying to determine the demand function for passenger car motor fuel in the United States. Tamson developed a model that used the actual price of a gallon of regular gasoline to predict motor fuel consumed per year. After adding a
8. What are the predictor variables in an autoregressive model?
7. Suggest ways to solve the problem of serial correlation.
6. You test for serial correlation, at the .05 level, with 61 residuals from a regression with one independent variable. If the calculated Durbin-Watson statistic is equal to 1.6, what is your conclusion?
5. You test for serial correlation, at the .01 level, with 32 residuals from a regression with two independent variables. If the calculated Durbin-Watson statistic is equal to 1.0, what is your conclusion?
4. Name a statistic that is commonly used to detect serial correlation.
2. What is a major cause of serial correlation? 3. Which underlying regression assumption is often violated when time series variables are analyzed?
1. What is serial correlation, and why can it be a problem when time series data are analyzed?
1. The expert consensus indicated the project was doomed to failure. Were the experts right?
3. Develop a model to forecast ERA using the predictor variable WHIP instead of OBA. Which model do you prefer, the one with OBA as a predictor variable or the one with WHIP as a predictor variable? Why?
2. Are there any nonlinear relationships between the predictor variables and earned run average? If so, develop a new model including the appropriate variable transformation.
1. Comment on the model that Dr. Hanke developed to forecast ERA. Examine the residual plots shown in Figure 4 and determine whether this model is valid.
4. Develop a multiple regression equation using the transformed average temperature variable created in step 2 and the lagged unemployment variable created in step 3. Is this a good model? Have any of the underlying assumptions been violated?
3. Create a new unemployment rate variable and relate it to emergency road service. Give unemployment a lagged effect on emergency road service by using the unemployment rate for the month (1) three months prior to the current month and (2) 11 months prior to the current month as the data for the
2. Create a new temperature variable and relate it to emergency road service. Remember that temperature is a relative scale and that the selection of the zero point is arbitrary. If vehicles are designed to operate best at 65 degrees Fahrenheit, then every degree above or below 65 degrees should
1. Develop a multiple regression equation using unemployment rate and average monthly temperature to predict emergency road service calls.
24. The 1991 accounting numbers for major league baseball are given in Table P-24. All figures are in millions of dollars. The numerical variables are GtReceit (Gate Receipts), MediaRev (Media Revenue), StadRev (Stadium Revenue), TotRev (Total Revenue), PlayerCt (Player Costs), OpExpens (Operating
23. Refer to Problem 22. Using your final fitted regression function, forecast Taste (quality) for . (All three independent variable values may not be required.) Although n in this case is small, construct the TABLE P-21 Assets ($ billions) X Number of accounts (1,000s) Y 219.0 2,500 21.1 909 38.8
22. The quality of cheese is determined by tasters whose scores are summarized in a dependent variable called Taste. The independent (predictor) variables are three chemicals that are present in the cheese: acetic acid, hydrogen sulfide (H2S), and lactic acid. The 15 cases in the data set are given
21. Table P-21 contains the number of accounts (in thousands) and the assets (in billions of dollars) for 10 online stock brokerages. Plot the assets versus the number of accounts. Investigate the possibility the relationship is curved by running a multiple regression to forecast assets using the
20. Recall Example 12. The full data set related to CEO compensation is contained in Appendix: Data Sets and Databases. Use stepwise regression to select the “best” model with predictor variables. Fit the stepwise model, and interpret the estimated coefficients. Examine the residuals. Identify
19. Refer to the data in Table P-18. Find the “best” regression model using the stepwise regression procedure and the all possible regressions procedure. Compare the results. Are you confident using a regression model to predict the final exam score with fewer than the original three
18. The scores for two within-term examinations, and ; the current grade point average (GPA), ; and the final exam score, Y, for 20 students in a business statistics class are listed in Table P-18.a. Fit a multiple regression model to predict the final exam score from the scores on the within-term
17. Ms. Haight, a real estate broker, wishes to forecast the importance of four factors in determining the prices of lots. She accumulates data on price, area, elevation, and slope and rates the view for 50 lots. She runs the data on a correlation program and obtains the correlation matrix given in
16. Cindy Lawson just bought a major league baseball team. She has been receiving a lot of advice about what she should do to create a winning ball club. Cindy asks you to study this problem and write a report.You decide to use multiple regression analysis to determine which statistics are
15. We might expect credit card purchases to differ from cash purchases at the same store. Table P-15 contains daily gross sales and items sold for cash purchases and daily gross sales and items sold for credit card purchases at the same consignment store for 25 consecutive days.a. Make a scatter
14. The Nelson Corporation decides to develop a multiple regression equation to forecast sales performance. A random sample of 14 salespeople is interviewed and given an aptitude test. Also, an index of effort expended is calculated for each salesperson on the basis of a ratio of the mileage on his
13. The sales manager of Hartman Auto Supplies decides to investigate a new independent variable, personal income by region (see Problem 12). The data for this new variable are presented in Table P-13.a. Does personal income by region make a contribution to the forecasting of sales?TABLE P-12
12. The sales manager of a large automotive parts distributor, Hartman Auto Supplies, wants to develop a model to forecast as early as May the total annual sales of a region. If regional sales can be forecast, then the total sales for the company can be forecast. The number of retail outlets in the
11. A taxi company is interested in the relationship between mileage, measured in miles per gallon, and the age of cars in its fleet.The 12 fleet cars are the same make and size and are in good operating condition as a result of regular maintenance. The company employs both male and female drivers,
10. Beer sales at the Shapiro One-Stop Store are analyzed using temperature and number of people (age 21 or over) on the street as independent variables.TABLE P-10 Minitab Output Correlations Y X1 X1 0.827 X2 0.822 0.680 Regression Analysis The regression equation is Y = -26.7 + .782 X1 + .068 X2
9. Table P-9 contains data on food expenditures, annual income, and family size for a sample of 10 families.TABLE P-8 Customer Checkout Time (minutes) Y Amount ($) X1 Number of items X2 1 3.0 36 9 2 1.3 13 5 3 .5 3 2 4 7.4 81 14 5 5.9 78 13 6 8.4 103 16 7 5.0 64 12 8 8.1 67 11 9 1.9 25 7 10 6.2 55
7. Most computer solutions for multiple regression begin with a correlation matrix. Examining this matrix is often the first step when analyzing a regression problem that involves more than one independent variable.Answer the following questions concerning the correlation matrix given in Table
6. Explain each of the following concepts:a. Correlation matrixb. c. Multicollinearityd. Residuale. Dummy variablef. Stepwise regression
5. Your estimated multiple regression equation is . Predict the value of Y if and .
4. What does the standard error of the estimate measure in multiple regression?
3. What does the partial, or net, regression coefficient measure in multiple regression?
2. What are the assumptions associated with the multiple regression model?
1. What are the characteristics of a good predictor variable?
4. If a nonlinear relationship exists between calls and the new temperature variable, develop the best model.
3. Develop a scatter diagram. Is there a linear relationship between calls and the new temperature variable?
2. Create a new temperature variable and relate it to emergency road service. Remember that temperature is a relative scale and that the selection of the zero point is arbitrary. If vehicles are designed to operate best at 65 degrees Fahrenheit, then every degree above or below 65 degrees should
1. Run four simple linear regression models using total number of emergency road service calls as the dependent variable and unemployment rate, temperature, rainfall, and number of members as the four independent variables. Would any of these independent variables be useful for predicting the
6. Assume that you developed a good regression equation. Would you be able to use this equation to forecast for the rest of 1993? Explain your answer.
5. The data consist of a time series. Does this mean the independence assumption has been violated?
4. Would the business activity index be a good predictor of the number of new clients?
3. Compare the results of your forecast with the actual observations for the first three months of 1993.
2. Develop a regression equation and use it to forecast the number of new clients for the first three months of 1993.
1. Determine whether there is a significant relationship between the number of new clients seen and the number of people on food stamps and/or the business activity index. Don’t forget the possibility of data transformations.
3. How do John’s data violate one of the assumptions of regression analysis
2. What is your opinion regarding the adequacy of John’s forecasting method?
1. Comment on John’s belief that his monthly sales are highly seasonal and therefore lead to a “low” value.
7. Has an effective forecasting method been developed?
6. Should Bill McGone proceed to take a large sample of company employees based on the preliminary results of his sample?
5. Suppose a newly hired person is 24 years old. How many absent days would you forecast for this person during the fiscal year?
4. Is there a significant relation between absent days and age? In answering this question, use proper statistical procedures to support your answer.
3. What percentage of the variability in absent days can be explained through knowledge of age?
2. What is the forecasting equation for absent days using age as a predictor variable?
1. How well are absent days and age correlated? Can this correlation be generalized to the entire workforce?
4. Do you think Gene has developed an effective forecasting tool?
3. Based on the results of the regression analysis as shown earlier, what action would you advise Gene to take in order to increase daily output?
2. How many units would you forecast for a day in which the high temperature is 41 degrees?
1. How many units would you forecast for a day in which the high temperature is 89 degrees?
1. Prepare a memo for Tiger’s top management that summarizes the analysis. Include comments on the extent to which your work will improve forecasts for fuel needs and truck revenue.
20. Refer to Problem 19. Observation 12 corresponds to Dun and Bradstreet. Redo the straight-line regression analysis omitting this observation. Do your conclusions in parts b and d of Problem 19 change? What, if anything, does this imply about the influence of a single observation on a regression

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Business Forecasting 1st Edition John E. Hanke - Solutions

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