Simple linear regression with a binary predictor
One of the coolest things about linear regression is that we are not limited to using predictor variables that are continuous. For example, in the last section, we used the continuous variable wt (weight) to predict miles per gallon. But linear models are adaptable to using categorical variables, like am (automatic or manual transmission) as well.
Normally, in the simple linear regression equation 
, 
will hold the actual value of the predictor variable. In the case of a simple linear regression with a binary predictor (like am), will hold a dummy variable instead. Specifically, when the predictor is automatic, will be 0, and when the predictor is manual, will be 1.
More formally:
Put in this manner, the interpretation of the coefficients changes slightly, since the 
will be zero when the car is automatic, 
is the mean miles per gallon for automatic cars.
Similarly, since will equal 
when the car is manual, is equal to the mean difference...
