Suppose we define activity level as the number of calories burned in a single workout. We define a multiple linear regression model as (|)=0+1+21(=)+31(=)E(Y|X)=0+1age+21(sex=male)+31(sex=male)age where the third term is an interaction term between these two predictors. Considering this model,

• What does this interaction term do to the relationship between age, sex and activity level? How do we interpret all the parameters in this model?
• How would the interpretation of the coefficients change if instead we only fit the model (|)=0+1+21(=)E(Y|X)=0+1age+21(sex=male)age?
• If the true relationship in the population was actually (|)=0+1+21(=)+31(=)+4(length of workout)E(Y|X)=0+1age+21(sex=male)+31(sex=male)age+4(length of workout), what does this mean for the statistical properties of the estimated coefficients? What about whether assumptions are satisfied?
• Suppose we had instead measured activity level as either being high (Y=1) or low (Y=0). Will each of our assumptions in linear regression be satisfied? Why or why not?