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 regression equation for sales as a function of population, advertising in the current year, and advertising in the previous year. Can you expect predictions of sales in future years to be very accurate if they are based on this regression equation? Explain.
b. The company would like to predict sales in the next year (year 20). It doesn’t know what the population will be in year 20, so it assumes no change from year 19. Its planned advertising level for year 20 is $30,000. Find a prediction and a 95% prediction interval for sales in year 20.