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.

**Updated Question**

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?

**Contents**hide

#### Best Answer

When you regress *Age of marriage* on *Rate of marriage*, each of your residuals is computed as:

*residual* = *Age of marriage* – *(Estimated) Expected Age of marriage*

where *(Estimated) Expected Age of marriage* = *b0 + b1xRate of marriage"* and *b0* and *b1* are the estimated intercept and slope of the simple linear regression of *Age of marriage" on *Rate of marriage*.

When is a *residual* positive? When:

*Age of marriage* – *(Estimated) Expected Age of marriage* > 0

or, equivalently, when

*Age of marriage* > *(Estimated) Expected Age of marriage*. In other words, when the *Age of marriage" is older than the (estimated) expected *Age of marriage".

When is a *residual* negative? When:

*Age of marriage* – *(Estimated) Expected Age of marriage* < 0

or, equivalently, when

*Age of marriage* < *(Estimated) Expected Age of marriage*. In other words, when the *Age of marriage" is younger than the (estimated) expected *Age of marriage".

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