Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y = total sales (thousands of dollars), X1 = display floor space (square meters), X2 = competitors’ advertising expenditures (thousands of dollars), X3 = advertised price (dollars per unit). (a) Write the fitted regression equation. (b) Interpret each coefficient. (c) Would the intercept seem to have meaning in this regression? (d) Make a prediction for Sales when FloorSpace = 80, CompetingAds = 100, and Price = 1,200.

Question

Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y = total sales (thousands of dollars), X1 = display floor space (square meters), X2 = competitors’ advertising expenditures (thousands of dollars), X3 = advertised price (dollars per unit). (a) Write the fitted regression equation. (b) Interpret each coefficient. (c) Would the intercept seem to have meaning in this regression? (d) Make a prediction for Sales when FloorSpace = 80, CompetingAds = 100, and Price = 1,200.

Predictor Coefficient
Intercept 1225.44
FloorSpace 11.52
CompetingAds -6.935
Price -0.1496

Answer 1

(a) The fitted regression equation is:

Y = 1225.44 + 11.52*X1 - 6.935*X2 - 0.1496*X3

(b) Interpretation of each coefficient:
- Intercept (1225.44): This represents the estimated sales when all predictor variables (FloorSpace, CompetingAds, and Price) are zero. It indicates the baseline level of sales when there is no display floor space, no competitors' advertising expenditures, and no advertised price.
- FloorSpace (11.52): For every additional square meter of display floor space, the estimated sales increase by 11.52 thousand dollars, holding other variables constant. It suggests that more display space generally leads to higher sales.
- CompetingAds (-6.935): For every additional thousand dollars spent on competitors' advertising expenditures, the estimated sales decrease by 6.935 thousand dollars, holding other variables constant. It indicates that higher advertising expenditures by competitors may have a negative impact on sales for the mountain bike.
- Price (-0.1496): For every additional dollar increase in the advertised price per unit, the estimated sales decrease by 0.1496 thousand dollars, holding other variables constant. It suggests that higher prices tend to reduce the demand for the mountain bike.

(c) The intercept may or may not have meaningful interpretation in this regression. In some cases, the intercept value may represent a plausible scenario, such as when all predictor variables are zero. However, in other cases, the intercept may not have any relevant meaning, especially if the predictor variables should never be zero in practice. Therefore, it is important to consider the context and interpretability of the intercept value in each specific regression analysis.

(d) To make a prediction for Sales when FloorSpace = 80, CompetingAds = 100, and Price = 1,200, substitute these values into the regression equation:

Y = 1225.44 + 11.52*80 - 6.935*100 - 0.1496*1200

Y = 1225.44 + 920.8 - 693.5 - 179.52

Y = 1273.22

Therefore, the predicted sales for the mountain bike would be 1273.22 thousand dollars when the FloorSpace is 80 square meters, CompetingAds is 100 thousand dollars, and Price is 1,200 dollars per unit.