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 Laurderdale. 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 8 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 in a time-trend variable for observation. A value of 1 denotes the first quarter observation, 2 the second quarter, and so on, up to 8 for the eight and last quarter.
A company forecaster has run a regression on the data, obtaining the results displayed in the table below
Intercept coefficient: -4,516.3
Price(dollars) coefficient -3590.6
Competitors
Price(dollars) 4226.5
Income($000) coefficient: 777.1
Population(000) coefficient: 0.40
Time(1-8) coefficient: 356.1
Intercept standard error of coefficient: 4988.2
Price standard error of coefficient: 702.8
Price: 851.0
Income: 66.4
Population: 0.31
Time: 92.3
Mean Value of Variable for Intercept = 0
Mean value of variable for price = 7.50
Mean value of variable for price = 6.50
Mean value of variable for income = 40
Mean value of variable for population = 2300
Mean value of variable for time = 0
N = 48, R squared = 0.93 Standard error of regression 1,442.
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?
Compute the price elasticity of demand for pies at the firm's mean price of $7.50 and mean weekly sales quantity of 20,000 pies. Next, 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?
How confident are you about applying these test market results to decisions concerning national pricing strategies for pies?