The marketing manager of a large supermarket chain faced the business problem of determining the effect on the sales of specialty pet food of shelf space and whether the product was placed at the front (= 1) or back (= 0) of the aisle. Data are collected from a random sample of 12 equal-sized stores and organized and stored in Pet food. These data arc:

For (a) through (m), do not include an interaction term.
a. State the multiple regression equation that predicts weekly sales based on shelf space and location.
b. Interpret the regression coefficients in (a).
c. Predict the weekly sales of specialty pet food for a store with 8 square feet of shelf space situated at the back of the aisle. Construct a 95% confidence interval estimate and a 95% prediction interval.
d. Perform a residual analysis on the results and determine whether the regression assumptions are valid.
e. Is there a significant relationship between sales and the two independent variables (shelf space and aisle position) at the 0.05 level of significance?
f. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model. Indicate the most appropriate regression model for this set of data.
g. Construct and interpret 95% confidence interval estimates of the population slope for the relationship between sales and shelf space and between sales and aisle location.
h. Compare the slope in (b) with the slope for the simple linear regression model of Problem 13.4 on page 481. Explain the difference in the results.
i. Compute and interpret the meaning of the coefficient of multiple determination, r2.
j. Compute and interpret the adjusted r2.
k. Compare r with the r2 value computed in Problem 13.16(a) on page 487.
1. Compute the coefficients of partial determination and interpret their meaning.
m. What assumption about the slope of shelf space with sales do you need to make in this problem?
n. Add an interaction term to the model and, at the 0.05 level of significance, determine whether it makes a significant contribution to the model.
o. On the basis of the results of (f) and (n), which model is most appropriate? Explain.

Transcribed Image Text:

Shelf Space Weekly Store (square feet) Location Sales ($) 10 t0 10 15 15 15 20 20 20 Back Front Back Back Back Front Back Back Front Back Back Front 160 220 140 190 240 260 230 270 280 260 290 310 4. 10 12