31 May A soft-drink bottler collected the following monthly data on its sales of 12-ounce cans at different prices.
Question
Month 1 2 3 4 5 6 7 8 9 10 11 12
Price .45 .50 .45 .40 .35 .35 .50 .55 .45 .50 .40 .40
Quantity 98 80 95 123 163 168 82 68 96 77 130 125
a. Use the Ordinary Least-Squares (OLS) regression to estimate a linear demand equation. If the price is 0.4 dollars, how much is the expected quantity? Is the expected quantity greater or smaller than the actual quantities? If the price is 0.5 dollars, how much is the expected quantity? If the price increases from 0.4 dollars to 0.5 dollars, how much does the expected quantity change?
b. What is the t-value for the coefficient of price? How do you interpret the t-value? What is the R-square? How do you interpret it?
c. There is considerable debate within your firm concerning the effect of advertising on sales. The marketing department believes advertising has a large positive effect; others are not so sure. For instance, the production and technical staffs believe the price of the product itself largely determines sales. To clarify the debate, you have gathered the data for the expenditure on advertising. Perform the multiple regression analysis of sales on price and advertising. What is the effect of advertising on sales besides the effect of price? What is the t-value for the coefficient of advertising? Does advertising have an explanatory power on sales given the data? How about price? What is your conclusion in the debate?
Month 1 2 3 4 5 6 7 8 9 10 11 12
Price .45 .50 .45 .40 .35 .35 .50 .55 .45 .50 .40 .40
Advertising 8.4 8.3 8.5 9 9.5 8.7 8 7 8.6 7.5 8.9 8.3
Quantity 98 80 95 123 163 168 82 68 96 77 130 125
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