Consider a classical linear regression model that explains sales revenue (S, in thousands of dollars) of...

 

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Consider a classical linear regression model that explains sales revenue (S, in thousands of dollars) of a fast-food chain by product price (P, in dollars) and advertising expenditure (A, in thousands of dollars): Si = Bo + B.P; + B24; + B34} + uj, where i represents different locations. The OLS estimates are based on a random sample of 75 locations: Si =109.72 - 7.640 P; +12.151 A; -2.768 A. (3.556) (6.80) (1.046) (0.941) Standard errors are reported in parentheses; SSR = 1532.084 and R2 = 0.448. (a) What is the estimated impact of an increase in advertising expenditure on sales revenue? Use proper units of measurement. (b) Construct a 90% confidence interval for the price coefficient B1. Use this interval to determine if the coefficient is statistically significant; specify the significance level. (c) Compare two statements: "B, is statistically significant at the 10% level" and "Bi is statistically significant at the 1% level". Which one is stronger and why? (d) Test at the 5% level the hypothesis that a one-dollar increase in the product price does not reduce sales revenue by more than $7000. Report the p-value. (e) You wish to test a hypothesis at the 5% level that advertising does not have any effect on sales revenue. The sum of squared residuals in the restricted model is 1896. 391. Write down the equation for the restricted model and perform the test; interpret the results. Consider a classical linear regression model that explains sales revenue (S, in thousands of dollars) of a fast-food chain by product price (P, in dollars) and advertising expenditure (A, in thousands of dollars): Si = Bo + B.P; + B24; + B34} + uj, where i represents different locations. The OLS estimates are based on a random sample of 75 locations: Si =109.72 - 7.640 P; +12.151 A; -2.768 A. (3.556) (6.80) (1.046) (0.941) Standard errors are reported in parentheses; SSR = 1532.084 and R2 = 0.448. (a) What is the estimated impact of an increase in advertising expenditure on sales revenue? Use proper units of measurement. (b) Construct a 90% confidence interval for the price coefficient B1. Use this interval to determine if the coefficient is statistically significant; specify the significance level. (c) Compare two statements: "B, is statistically significant at the 10% level" and "Bi is statistically significant at the 1% level". Which one is stronger and why? (d) Test at the 5% level the hypothesis that a one-dollar increase in the product price does not reduce sales revenue by more than $7000. Report the p-value. (e) You wish to test a hypothesis at the 5% level that advertising does not have any effect on sales revenue. The sum of squared residuals in the restricted model is 1896. 391. Write down the equation for the restricted model and perform the test; interpret the results.

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