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%u2019s 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%u2019 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.
Coefficient Standard Error of Coefficent Mean of ValueVariable
Intercept -4,516.3 4,988.2 ------
Price (dollars) -3,690.6 702.8 7.50
Competitor's
price (dollars) 4226.5 851.0 6.50
Income ($000) 777.1 66.4 40
Population(000) .40 .31 2,300
Time (1 to 8) 356.1 92.3 -----
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%u2019s 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?
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%u2019s 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%u2019 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.
Coefficient Standard Error of Coefficent Mean of ValueVariable
Intercept -4,516.3 4,988.2 ------
Price (dollars) -3,690.6 702.8 7.50
Competitor's
price (dollars) 4226.5 851.0 6.50
Income ($000) 777.1 66.4 40
Population(000) .40 .31 2,300
Time (1 to 8) 356.1 92.3 -----
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%u2019s mean price: ($7.50) and mean weekly sales quantity (20,000 pies). Next, compute the cross-price elasticity of demand. Comment on these estimates.
c. Other things equal, how much do we expect sales to grow (or fall over the next year?
d. How accurate is the regression equation in predicting sales next quarter? Two years from now? Why might these answers differ?
e. How confident are you about applying these test-market results to decisions concerning national pricing strategies for pies?
Related textbook solutions
Related questions
A food company has recently introduced a new line of fruit pies in 6 US cities: Atlanta, Baltimore, Chicago, Denver, St. Louis, and Fort Lauderdale. Based on the pies apparent success, the company is considering a nationwide launch. Before doing so, it has decided to use data collected during a two-year market test to guide it in setting prices and forecasting future demand.
For each of the 6 markets, the firm has collected eight quarters of data for a total of 48 observations. Each observation consists of data on quantity demanded (number f pies purchased per week), the price per pie, a competitor's average price per pie, income, and population. The company has also included a time-trend variable. A value of 1 denotes the 1st quarter observation, 2 the 2nd quarter, and so on, up to 8 for the 8th and last quarter.
A company forecaster has run a regression on the data, obtaining the results displayed in the accompanying table.
| Coefficient | Stand. Error of Coefficient | Mean Value of Variable | |||||||||||||||||||||
| Intercept | -4,516.3 | 4,988.2 | ------ | ||||||||||||||||||||
| Price ($) | -3,590.6 | 702.8 | 7.5 | ||||||||||||||||||||
| Competitors'price($) | 4,226.5 | 851 | 6.5 | ||||||||||||||||||||
| Income ($000) | 777.1 | 66.4 | 40 | ||||||||||||||||||||
| Population (000) | 0.40 | 0.31 | 2,300 | ||||||||||||||||||||
| Time (1 to 8) | 356.1 | 92.3 | ------ | ||||||||||||||||||||
| N = 48 | R^2 = 0.93 | Standard error regression = 1,442 |
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 new 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?
