. Jerry Sam owns and operates a chain of 12 department stores in New Ville. Sales figures and advertising expenses for the stores are provided in the table below. Sales are given in millions of dollars; advertising expenses are in tens of thousands of dollars. Store Advertising Sales 1 14 6 2 11 3 3 15 5 4 16 5 5 24 15 6 28 18 7 22 17 8 21 12 9 26 15 10 43 20 11 34 14 12 9 5 i. Calculate the slope for the regression line. (show all working) ii. Calculate the intercept for the regression line. (show all working) iii. Write the equation for the regression line. iv. Forecast sales for a store if advertising spending is:- 1. $240,000 2. $300,000

. Jerry Sam owns and operates a chain of 12 department stores in New Ville. Sales figures and advertising expenses for the stores are provided in the table below. Sales are given in millions of dollars; advertising expenses are in tens of thousands of dollars. Store Advertising Sales 1 14 6 2 11 3 3 15 5 4 16 5 5 24 15 6 28 18 7 22 17 8 21 12 9 26 15 10 43 20 11 34 14 12 9 5 i. Calculate the slope for the regression line. (show all working) ii. Calculate the intercept for the regression line. (show all working) iii. Write the equation for the regression line. iv. Forecast sales for a store if advertising spending is:- 1. $240,000 2. $300,000

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 15P: Stock market analysts are continually looking for reliable predictors of stock prices. Consider the...

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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?
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.
The file P13_42.xlsx contains monthly data on consumer revolving credit (in millions of dollars) through credit unions. a. Use these data to forecast consumer revolving credit through credit unions for the next 12 months. Do it in two ways. First, fit an exponential trend to the series. Second, use Holts method with optimized smoothing constants. b. Which of these two methods appears to provide the best forecasts? Answer by comparing their MAPE values.
The file P13_26.xlsx contains the monthly number of airline tickets sold by the CareFree Travel Agency. a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think will provide the best forecasting model? Why? b. Use simple exponential smoothing to forecast these data, using a smoothing constant of 0.1. c. Repeat part b, but search for the smoothing constant that makes RMSE as small as possible. Does it make much of an improvement over the model in part b?
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.
Under what conditions might a firm use multiple forecasting methods?
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?
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.
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.
The file P13_02.xlsx contains five years of monthly data on sales (number of units sold) for a particular company. The company suspects that except for random noise, its sales are growing by a constant percentage each month and will continue to do so for at least the near future. a. Explain briefly whether the plot of the series visually supports the companys suspicion. b. By what percentage are sales increasing each month? c. What is the MAPE for the forecast model in part b? In words, what does it measure? Considering its magnitude, does the model seem to be doing a good job? d. In words, how does the model make forecasts for future months? Specifically, given the forecast value for the last month in the data set, what simple arithmetic could you use to obtain forecasts for the next few months?
The following data describes weekly gross revenue ($1000s), television advertising expenditures ($1000s), and newspaper advertising expenditures ($1000s) for Showtime Movie Theaters. × Weekly Gross + Revenue ($1000s) 99 90 95 92 95 94 94 94 a. Find an estimated regression equation relating weekly gross revenue to television advertising expenditures and newspaper advertising expenditures (to 2 decimals). 2.84 Television Advertising ($1000s) 5.0 2.0 4.0 2.5 3.0 3.5 2.5 3.0 Revenue = 81.73 1.29 News Adv TV Adv + b. Choose the correct plot of the standardized residuals against ĝ. Newspaper Advertising ($1000s) 1.5 2.0 1.5 2.5 3.3 2.3 4.2 2.5