8. A food-products company has recently introduced a new line of fruit pies in six U.S. cities: Atlanta, Baltimore, Chicago, Denver, St. Louis, and Fort Lauderdale. Based on the pie’s apparent success, the company is considering a nationwide launch. Before doing so, it has decided to use data collected during a two-year market test to guide it in setting prices and forecasting future demand.
For each of the six markets, the firm has collected eight quarters of data for a total of 48 observations. Each observation consists of data on quantity demanded (number of pies purchased per week), price per pie, competitors’ average price per pie, income, and population. The company has also included a time-trend variable for each observation. A value of 1 denotes the first quarter observation, 2 the second quarter, and so on, up to 8 for the eighth and last quarter.
A company forecaster has run a regression on the data, obtaining the results displayed in the accompanying table.
| | Coefficient | Standard Error of Coefficient | Mean Value of Variable |
| Intercept | -4,516.3 | 4,988.2 | — |
| Price (dollars) Competitors’ price (dollars) | -3,590.6 4,226.5 | 702.8 851.0 | 7.50 6.50 |
| Income ($000) | 777.1 | 66.4 | 40 |
| Population (000) | .40 | .31 | 2,300 |
| Time (1 to 8) | 356.1 | 92.3 | — |
N = 48. R2 = .93. Standard error of regression = 1,442
a. Which of the explanatory variables in the regression are statistically significant? Explain. How much of the total variation in pie sales does the regression model explain?
b. Compute the price elasticity of demand for pies at the firm’s mean price ($7.50) and mean weekly sales quantity (20,000 pies). Next, compute the cross-price elasticity of demand. Comment on these estimates.
c. Other things equal, how much do we expect sales to grow (or fall) over the next year?
d. How accurate is the regression equation in predicting sales next quarter? Two years from now? Why might these answers differ?
e. How confident are you about applying these test-market results to decisions concerning national pricing strategies for pies?