(b) Use a regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. (Round your numerical values to the nearest integer.) Qrt1 = 1 if quarter 1, 0 otherwise; Qrt2 = 1 if quarter 2, 0 otherwise; Qrt3 = 1 if quarter 3, 0 otherwise ŷ, c+aQrtl + bQrt2 + c*Qrt3 + d*(t-2) X (c) Using the equation developed in part (b), compute the quarterly forecasts for year 4. (Round your answers to the nearest ten.) quarter 1 forecast quarter 2 forecast quarter 3 forecast quarter 4 forecast (d) Let t = 1 refer to the observation in Quarter 1 of Year 1; let t = 2 refer to the observation in Quarter 2 of Year 1; ... and t = 12 to refer to the observation in Quarter 4 of Year 3. Using the dummy variables defined in part (b) and also using t, develop an equation to account for seasonal effects and any linear trend in the time series. (Round your numerical values to the nearest integer.) = Based upon the seasonal effects in the data and linear trend, compute the quarterly forecasts for year 4. (Round your answers to the nearest ten.) quarter 1 forecast quarter 2 forecast quarter 3 forecast quarter 4 forecast

(b) Use a regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. (Round your numerical values to the nearest integer.) Qrt1 = 1 if quarter 1, 0 otherwise; Qrt2 = 1 if quarter 2, 0 otherwise; Qrt3 = 1 if quarter 3, 0 otherwise ŷ, c+aQrtl + bQrt2 + cQrt3 + d(t-2) X (c) Using the equation developed in part (b), compute the quarterly forecasts for year 4. (Round your answers to the nearest ten.) quarter 1 forecast quarter 2 forecast quarter 3 forecast quarter 4 forecast (d) Let t = 1 refer to the observation in Quarter 1 of Year 1; let t = 2 refer to the observation in Quarter 2 of Year 1; ... and t = 12 to refer to the observation in Quarter 4 of Year 3. Using the dummy variables defined in part (b) and also using t, develop an equation to account for seasonal effects and any linear trend in the time series. (Round your numerical values to the nearest integer.) = Based upon the seasonal effects in the data and linear trend, compute the quarterly forecasts for year 4. (Round your answers to the nearest ten.) quarter 1 forecast quarter 2 forecast quarter 3 forecast quarter 4 forecast

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter13: Regression And Forecasting Models

Section13.4: Multiple Regression Models

Problem 17P: The owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He...

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Quarter	Year 1	Year 2	Year 3
1	1,690	1,800	1,850
2	940	900	1,100
3	2,625	2,900	2,930
4	2,500	2,360	2,615

Similar questions

The owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He has also recorded data on potentially relevant variables. The data are listed in the file P13_17.xlsx. a. Estimate a simple regression equation involving annual sales (the dependent variable) and the size of the population residing within 10 miles of the restaurant (the explanatory variable). Interpret R-square for this regression. b. Add another explanatory variableannual advertising expendituresto the regression equation in part a. Estimate and interpret this expanded equation. How does the R-square value for this multiple regression equation compare to that of the simple regression equation estimated in part a? Explain any difference between the two R-square values. How can you use the adjusted R-squares for a comparison of the two equations? c. Add one more explanatory variable to the multiple regression equation estimated in part b. In particular, estimate and interpret the coefficients of a multiple regression equation that includes the previous years advertising expenditure. How does the inclusion of this third explanatory variable affect the R-square, compared to the corresponding values for the equation of part b? Explain any changes in this value. What does the adjusted R-square for the new equation tell you?
A small computer chip manufacturer wants to forecast monthly ozperating costs as a function of the number of units produced during a month. The company has collected the 16 months of data in the file P13_34.xlsx. a. Determine an equation that can be used to predict monthly production costs from units produced. Are there any outliers? b. How could the regression line obtained in part a be used to determine whether the company was efficient or inefficient during any particular month?
Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semifragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight and same distance shipped, but of different cargo types, are provided in the file P13_16.xlsx. a. Estimate a regression equation using the given sample data, and interpret the estimated regression coefficients. b. According to the estimated regression equation, which cargo type is the most costly to ship? Which cargo type is the least costly to ship? c. How well does the estimated equation fit the given sample data? How might the fit be improved? d. Given the estimated regression equation, predict the cost of shipping a package with semifragile cargo.
Stock market analysts are continually looking for reliable predictors of stock prices. Consider the problem of modeling the price per share of electric utility stocks (Y). Two variables thought to influence this stock price are return on average equity (X1) and annual dividend rate (X2). The stock price, returns on equity, and dividend rates on a randomly selected day for 16 electric utility stocks are provided in the file P13_15.xlsx. Estimate a multiple regression equation using the given data. Interpret each of the estimated regression coefficients. Also, interpret the standard error of estimate and the R-square value for these data.
Do the sales prices of houses in a given community vary systematically with their sizes (as measured in square feet)? Answer this question by estimating a simple regression equation where the sales price of the house is the dependent variable, and the size of the house is the explanatory variable. Use the sample data given in P13_06.xlsx. Interpret your estimated equation, the associated R-square value, and the associated standard error of estimate.
A trucking company wants to predict the yearly maintenance expense (Y) for a truck using the number of miles driven during the year (X1) and the age of the truck (X2, in years) at the beginning of the year. The company has gathered the data given in the file P13_13.xlsx. Note that each observation corresponds to a particular truck. Estimate a multiple regression equation using the given data. Interpret each of the estimated regression coefficients. Also, interpret the standard error of estimate and the R-square value for these data.
Management of a home appliance store would like to understand the growth pattern of the monthly sales of Blu-ray disc players over the past two years. Managers have recorded the relevant data in the file P13_33.xlsx. a. Create a scatterplot for these data. Comment on the observed behavior of monthly sales at this store over time. b. Estimate an appropriate regression equation to explain the variation of monthly sales over the given time period. Interpret the estimated regression coefficients. c. Analyze the estimated equations residuals. Do they suggest that the regression equation is adequate? If not, return to part b and revise your equation. Continue to revise the equation until the results are satisfactory.
An antique collector believes that the price received for a particular item increases with its age and with the number of bidders. The file P13_14.xlsx contains data on these three variables for 32 recently auctioned comparable items. Estimate a multiple regression equation using the given data. Interpret each of the estimated regression coefficients. Is the antique collector correct in believing that the price received for the item increases with its age and with the number of bidders? Interpret the standard error of estimate and the R-square value for these data.
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The file P13_29.xlsx contains monthly time series data for total U.S. retail sales of building materials (which includes retail sales of building materials, hardware and garden supply stores, and mobile home dealers). a. Is seasonality present in these data? If so, characterize the seasonality pattern. b. Use Winters method to forecast this series with smoothing constants = = 0.1 and = 0.3. Does the forecast series seem to track the seasonal pattern well? What are your forecasts for the next 12 months?
The file P13_22.xlsx contains total monthly U.S. retail sales data. While holding out the final six months of observations for validation purposes, use the method of moving averages with a carefully chosen span to forecast U.S. retail sales in the next year. Comment on the performance of your model. What makes this time series more challenging to forecast?