The Klein Corporation's marketing department, using regression analysis, estimates the firm's demand function, the result being
Q = - 104 - 2.1P + 3.2I + 1.5A + 1.6Z
R2 = 0.89
Standard error of estimate = 108
where Q is the quantity demanded of the firm's product (in tons), P is the price of the firm's product (in dollars per ton), I is per capita income (in dollars), A is the firm's advertising expenditure (in thousands of dollars), and Z is the price (in dollars) of a competing product.
The regression is based on 200 observations.
a. According to the statistical software, the probability is 0.005 that the t statistic for the regression coefficient of A would be as large (in absolute terms) as it is in this case if in fact A has no effect on Q. Interpret this result.
b. If I = 5,000, A = 20, and Z = 1,000, what is the Klein Corporation's demand curve?
c. If P = 500 (and the conditions in part b hold), estimate the quantity demanded of the Klein Corporation's product.
d. How well does this regression equation fit the data?