2. The marketing manager of a large supermarket chain wants to determine how sales of the soft drinks are affected by shelf space and product placement. The soft drinks were placed either at the front or back of the aisle. Data collected from a random sample of 20 equal-sized stores is summarized below.

a. Write out the multiple regression equation.

b. Estimate the regression coefficients using ordinary least squares and interpret them.

c. Predict the weekly sales for a store with 10 feet of shelf space situated at the back of the aisle.

d. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model.

Sales Space Place

1.6 5 0

2.2 5 1

1.4 5 0

1.9 10 0

2.4 10 0

2.6 10 1

2.3 15 0

2.7 15 0

2.8 15 1

2.6 20 0

2.9 20 0

3.1 20 1

1.9 10 0

2.4 10 0

2.6 10 1

2.3 15 0

2.7 15 0

1.4 5 0

1.9 10 0

2.4 10 0

Place = 1 indicates front of aisle

Place = 0 indicates back of aisle

Space = feet of shelf space

Sales given in 1000/week

a. Write out the multiple regression equation.

b. Estimate the regression coefficients using ordinary least squares and interpret them.

c. Predict the weekly sales for a store with 10 feet of shelf space situated at the back of the aisle.

d. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model.

Sales Space Place

1.6 5 0

2.2 5 1

1.4 5 0

1.9 10 0

2.4 10 0

2.6 10 1

2.3 15 0

2.7 15 0

2.8 15 1

2.6 20 0

2.9 20 0

3.1 20 1

1.9 10 0

2.4 10 0

2.6 10 1

2.3 15 0

2.7 15 0

1.4 5 0

1.9 10 0

2.4 10 0

Place = 1 indicates front of aisle

Place = 0 indicates back of aisle

Space = feet of shelf space

Sales given in 1000/week

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