Question

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 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 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), 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 1^st quarter observation, 2 the 2^nd quarter, and so on, up to 8 for the 8^th 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 much 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?

Answer 1

c.) The coefficient of the time trend is 356.1 and the trend is quarterly. So the sales are expected to increase as the coefficient has a positive sign and the increase would be by 1424.4

d.) The accuracy is low in determining sales new quarter using this regression because the standard error of the coefficient is high. In other words, one can say that the precision of estimating sales per quarter is 92.3 which is a high number. Hence, the accuracy is questionable. The answers might differ because of changing market conditions in the two years and other variables might need to be controlled for to get accurate results.

(e.) The coefficients are not seemingly significant and hence using these results would not be a wise step to build national strategies. The regression equation needs to be more refines by controlling for other effects that would affect the sale of pie. Although the R^2 of the regression is quite high, the insignificance of coefficients pose questions on plausible issues like multicollinearity in the regression. Hence, correcting for these issues is a must before using the results for national pricing strategies.