Problem:
Colorful Tile, Inc, is a rapidly growing chain of ceramic tile outlets that cater to the do-it-yourself home remodeling market. In 2002, 33 stores were operated in small to medium-size metropolitian markets. An in-house study of sales by these outlets revealed the following (standard error in parenthesis):
Q = 5 - 5P + 1.5A + 0.5I + 0.2HF
(3) (1.8) (0.7) (0.2) (0.1)
R-square = 93%, Standard Error of Estimate = 6
Here, Q is tile sales (in thousands of cases), P is tile price (per case), A is advertising expenses (in thousands of dollars), I is disposable income per capita (in thousands of dollars), and HF is Household formation (in hundreds).
1. Fully evaluate and interpret these empirical results on an overall basis using R-square, R-square(bar), F statistic, and SEE information.
2. Is quantity demanded sensitive to "own" price?
3. Austin, Texas, was a typical market covered by this analysis. During 2002 in the Austin market, price was $5, advertising was $30,000, income was an average $40,000 per household, and the number of household formations was 5,000. Calculate and interpret the relevant advertising point elasticity.
4. 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 2003 if total costs are projected to be $300,000.