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)
R2 = 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 R2, adjusted R2, 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 aninterval estimate of Q with 95% confidence level.
(G)Assume that the preceding model and data are relevant for the coming period. Estimate theprobability that the Austin store will make a profit during 2021 if total costs are projected to be $300000.
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