### Linearity
of Independent Variables - Partial Plots

A partial regression
plot is a scatterplot of the partial correlation of each independent with the
dependent variable after removing the linear effects of the other independent
variables in the model. The values plotted on this chart are two sets of
residuals. The residuals from regressing the dependent variable on the other
independent variables are plotted on the vertical axis. The residuals from
regressing the particular predictor variable on all other independent variables
are plotted on the horizontal axis.

The partial
regression, thus, shows the relationship between the dependent variable and a
specific independent variable. We examine each plot to see if it shows a linear
or nonlinear pattern. If the specific independent variable shows a linear
relationship to the dependent variable, it meets the linearity assumption of
multiple regression. If there is an obvious nonlinear pattern, we should
consider a transformation of either the dependent or independent variable.

I like to add a total
fit line to the scatterplot to make it easier to interpret. We added the fit line to scatterplots in previous
examples when we examined scatterplots for linearity.

The partial
regression plots for the three independent variables in the analysis are shown
below. None of the plots demonstrates an obvious nonlinear pattern.