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.