A water expert was asked whether increased water consumption in a California community was lowering its water table. To answer this question, he estimated a linear regression equation of the form W = a + bt, where W height of the water table and t time measured from the start of the study period. (He used 10 years of water-table measurements.) The estimate for b was b=-4 with a t-value of -1.4.

a. From this evidence, would you conclude that the water table was falling?

b. A second expert suggests yearly rainfall also may affect the water table. The first expert agrees but argues that total rainfall fluctuates randomly from year to year. Rainy years would cancel out dry years and would not affect the results of the regression. Do you agree? 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 table.

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). In turn, compute the cross-price elasticity of demand. Comment on these estimates. Other things equal, how much do we expect sales to grow (or fall) over the next year? 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?