Colorful Tile Inc is a chain of ceramic tile outlets with 33

Colorful Tile, Inc., is a chain of ceramic tile outlets with 33 stores. An in-house study of sales by these outlets revealed the following: Q = 5.00 - 5.00 P + 1.50A + 0.50 I + 0.20HF (-2.78) (2.14) (2.50) (2.00) N = 33 R^2 = 0.93 F = 93.0 The numbers in parentheses are t-statistics. Here Q is tile sales (in thousands of cases), P is the tile price (per case), A is advertising expenditure (in thousands of dollars), I is disposable income per capita (in thousands of dollars), and HF is household formation (in hundreds). Evaluate the results (A) in terms of the signs and values of the coefficients, (B) for the statistical significance of the coefficients, and (C) the explanatory power of the regression.

Solution

A.) Price coefficient has negative sign implies increase in price of tile by 1 unit leads to decrease in Q by 5 units(in thousands).Advertising expenditure has positive sign implies increase in advertising expenditure of tile by 1 unit(in thousands) leads to increase in Q by 1.50(in thousands of dollars).Disposable income per capita has positive sign implies increase in income by 1 unit leads to 0.50 increse in Q(in thousands of dollars).Household formation has positive sign implies increse in HF by 1 unit leads to 0.20 increase in Q(in thousands of dollars).

B.)Let level of significance =5%

N=33

Degrees of freedom=33-5=28; where 5 is number of coefficients including intercept.

T value from table =2.048

Since absolute t value for P,A and I are greater than t value from table.So these are all significant.

But t value for HF is less than t value from table, so it is not significant.

C.) R2 is a measure of the explanatory power of the model.

R2=0.93

It measures that 93% of the variation in quantity is explained by P,A,I,HF.