Colorful Tile, Inc., is a rapidly growing chain of ceramic tile outlets that caters to the do-it-yourself home remodeling market. In 2020, 33 stores were operated in small to medium-size metropolitan markets. An in-house study of sales by these outlets revealed the following (standard errors or standard deviations are in parentheses)
Q = 4 – 5P + 2A + 0.2I + 0.25HF
(3) (1.8) (0.7) (0.1) (0.1)
R^2 = 0.93, standard error of the estimate (SEE) = 6
Here, Q is tile sales (in thousands of cases), P is tile price (per case), A is advertising expenditures (in thousands of dollars), I is disposable income per household (in thousands of dollars), and HF is household formation (in hundreds).
(A) Fully evaluate and interpret these empirical results on an overall basis using R^2, adjusted R^2, and F statistic.
(B) Which regression analysis problem might apply to this regression estimate? Why?
(C) Which independent variables are statistically significant at the 95% confidence level?
(D) Is quantity demanded sensitive to own price (P)?
(E) Austin, Texas, was a typical market covered by this analysis. During 2020 in the Austin market, price (P) was $5, advertising (A) was $30,000, income (I) was an average $55,000 per household, and the number of household formations (HF) was 4000. Calculate and interpret the relevant advertising point elasticity.
(F) Given the values of the independent variables in part E above, give a point estimate and an interval estimate of Q with 95% confidence level.
(G) Assume that the preceding model and data are relevant for the coming period. Estimate the probability that the Austin store will make a profit during 2021 if total costs are projected to be $300000.
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