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 appear in the file P10_23.xlsx.
a. Estimate a multiple regression equation that includes annual sales as the dependent variable and the following explanatory variables: year, size of the population residing within 10 miles of the restaurant, annual advertising expenditures, and advertising expenditures in the previous year.
b. Which of the explanatory variables have significant effects on sales at the 10% significance level? Do any of these results surprise you? Explain why or why not.
c. Exclude all insignificant explanatory variables from the equation in part a and estimate the equation with the remaining variables. Comment on the significance of each remaining variable.
d. Based on your analysis of this problem, does multicollinearity appear to be present in the original or revised versions of the model? Explain.