Question

You are working for Verizon and are trying to predict sales of phones in your region based on the number of weeks since the phone’s release date and whether it is Apple or Android. You found that the best model includes both a dummy variable and an interaction variable. The resulting regression equation is shown below.

Weekly Salesˆ= 5.2 − 0.3(Weeks) + 0.5(Apple) − 0.04(Weeks×Apple)

Variable Descriptions

Weekly Sales: # of phone sales per week measured in 1,000s

Weeks: # of weeks since the phone’s release

Apple: A dummy variable that equals 1 if the phone is an iPhone and 0 if it is an Android

In the equation for Apple phones specifically, what is the slope associated with Weeks? Hint, it might be helpful to write out the equation for when the Apple dummy variable equals 0 and then for when it equals 1 like we did in class for other dummy variables.

Answer 1

The regression equation is,

Weekly Salesˆ= 5.2 − 0.3(Weeks) + 0.5(Apple) − 0.04(Weeks×Apple)

For Apple phones,  Apple = 1

Weekly Salesˆ= 5.2 − 0.3(Weeks) + 0.5 * 1 − 0.04(Weeks * 1)

=>  Weekly Salesˆ= 5.7 − 0.34(Weeks)

Thus, the slope associated with Weeks is -0.34.