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 accompanying table.
Standard Error of Mean Value
Coefficient Coefficient of Variable
Intercept 4,516.3 4,988.2 —
Price (dollars) 3,590.6 702.8 7.50
Competitors’
price (dollars) 4,226.5 851.0 6.50
Income ($000) 777.1 66.4 40
Population (000) .40 .31 2,300
Time (1 to 8) 356.1 92.3 —
N48. R^2 .93. Standard error of regression1,442a. 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?172 Chapter 4 Estimating and Forecasting Demandc04EstimatingandForecastingDemand.qxd 9/5/11 5:49 PM Page 172