Calculate the standard error, Business Economics

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The Wallpaper Shop, Inc., is a rapidly growing chain of wallpaper shops that caters to the do-it-yourself home remodeling market. During the past year, 15 stores were operated in small to medium-size metropolitan markets. An in-house study of sales by these outlets revealed the following (standard errors in parentheses):

Q = -11,000 - 50P + 25PX + 0.5A + 0.1I + 500GR

(9,000) (20) (2.5) (0.3) (0.06) (200)

R2 = 0.9; Standard Error of the Estimate = 800.

Here, Q is the number of customers served, P is the average price per customer, PX is the average cost of professionally wallpapering a small room, A is advertising expenditures (in dollars), I is disposable income per capita (in dollars), and GR is the rate of population growth per year (in percent).

i) Using a 99% confidence level criterion, which independent factors have a statistically significant influence on the number of customers served?

ii) Fully evaluate F statistic and interpret it. What is the interpretation of R2 = 0.9? Is it appropriate to use R2 or should you use an adjusted R2? Why?

iii) Is quantity demanded sensitive to "own" price in these metropolitan markets? Explain your answer.

iv) Davis, California, is a typical metropolitan area market covered by this analysis. During the past year in the Davis market, P = $50, PX = $100, A = $50,000, I = $100,000 and GR = 2%. Calculate and interpret the relevant demand curve and the advertising elasticity.

v) Should Davis market increase its price to raise total revenue? Explain your answer.

vi) By what percentages the number of customers served change for

• an increase in advertising expenditure by 10%

• a decrease in per capita disposable income by15%?

vii) Assume that the preceding model and data are relevant for the coming period. Estimate the probability that the Davis store will make a profit during the coming year if total costs are projected to be $1.25 million.


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