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 entire data set appears in the file P10_23.xlsx.
a. Estimate a simple linear 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 the R2 value.
b. Add another explanatory variable—annual advertising expenditures—to the regression equation in part a. Estimate and interpret this expanded equation. How does the R2 value for this equation compare to the equation in part a? Explain any difference between the two R2 values. What, if anything, does the adjusted R2 value for the revised equation indicate?
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 R2 and adjusted R2 values, in comparison to the corresponding values for the equation of part b? Explain any changes in these values.