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...

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 P14_19.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 variable—annual advertising expenditures—to 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 year’s 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?