Multiple Regression

Introduction And Definitions Page 5

(Speaker)

Partial regression plots (sometimes called added variable plots) show the relationship between the response variable and an additional explanatory variable in a multiple regression, while controlling for the other variables.

Partial regression plots look similar to simple linear regression plots, but they are interpreted slightly differently. Let's return to the example relating body fat and height. Recall the following simple regression equation, which we want to turn into a multiple regression:

Body fat percentage equals 13.012 minus 0.031 times height.

Also recall that we have an additional variable available: waist size. With this second variable, we can create an added variable plot to determine whether it makes sense to add waist size to the model.

In this case, we can see from the partial regression that waist size is a strong indicator of body fat, so we may want to add it to our model. At this point, we can also run a partial regression plot on height, to see if that variable is still useful to the model.

Interestingly, while height was unimportant to body fat in the simple regression, it now is negatively related to body fat in the multiple regression.

Body fat percentage equals negative 3.10, plus 1.77 times waist size, minus 0.60 times height.

How would you interpret this?

For people of a certain waist size (in other words, controlling for the variable waist size), being taller is associated with lower body fat.

On the next screen, we will further explore how to interpret partial residual and partial regression plots.