Suppose I have two standardized (i.e., z-scored) predictors Age at Marriage and Rate of Marriage, and a dependent variable Divorce and I fit a linear regression model to predict Divorce from the two predictors.
Predictor residual plot
First, we predict Age at Marriage (now as dep. variable) from Rate of Marriage, obtain the residuals from this prediction. Second, we plot these residuals against Divorce .
Picture below is the resultant Predictor residual plot.
This technique can be extended to several-predictor situations. Imagine, for example, we had $3$ predictors predicting $Divorce$. Then, we had to pick one of the predictors, and regress that predictor on the other $2$ predictors, and obtain the residuals and then plot the residual against Divorce.
My question is what would be the interpretation of such plots in 3-or more predictor situations?