Chapter 15.5, Problem 22E

Testing Significance in Shoe Sales Prediction. In exercise 4, the following estimated regression equation relating sales to inventory investment and advertising expenditures was given.

$\hat{y}=25+10x_1+8x_2$

The data used to develop the model came from a survey of 10 stores; for these data SST = 16,000 and SSR = 12,000.

1. a. Compute SSE, MSE, and MSR.
2. b. Use an F test and a .05 level of significance to determine whether there is a relationship among the variables.

4. Shoe Sales. A shoe store developed the following estimated regression equation relating sales to inventory investment and advertising expenditures.

$\hat{y}=25+10x_1+8x_2$

where

$\begin{array}{c}{x}_{\text{1}}\text{=}\text{inventory investment }\left(\$\text{1}000\text{s}\right)\\ x_{\text{2}}\text{=}\text{advertising expenditures }\left(\$\text{1}000\text{s}\right)\\ y\text{= sales }\left(\$\text{1}000\text{s}\right)\end{array}$

1. a. Predict the sales resulting from a $15,000 investment in inventory and an advertising budget of $10,000.
2. b. Interpret b₁ and b₂ in this estimated regression equation.