Suppose you want to predict sneaker sales on the basis of advertising expenditures and sneaker color, red or blue. You create one dummy variable for the sneaker color (Red = 1 for red sneakers and Red = 0 for blue sneakers) and run the regression on data collected over ten years using the dummy variable and advertising expenditures as your independent variables. The equation you obtain is:

Sales = 631,085 + 533,024(Red) + 50.5(Advertising)

a. How would you interpret the regression model?

b. How would you interpret the coefficient for red sneakers?

a. This implies the sales of sneaker increase when the color of the sneaker is red and Advertising expenses increase.

This implies that the sneaker sales increases by $533,024 when the sneaker color is red.

Explanation:

a. How would you interpret the regression model?

The estimated regression model given in the question is as follows:

Sales = 631,085 + 533,024(Red) + 50.5(Advertising) (1)

From equation (1), Sales is the estimated dependent variables; 631,085 is the estimated constant; 533,024 is the estimated coefficient of the red color; and 50.5 is the estimated coefficient of the advertising expenditures

The interpretation of the above is that sneaker color and the advertising expenditures have positive effect on the sales of sneaker. This implies the sales of sneaker increase when the color of the sneaker is red and Advertising expenses increase.

b. How would you interpret the coefficient for red sneakers?

From equation (1) in part a above, the estimated coefficient of the sneaker color is 533,024.

Since the sign in front of it is positive, this implies that the sneaker sales increases by $533,024 when the sneaker color is red.

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