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How does component plus residual plot work? You create these plots by plotting:enter image description here

But how do they work?

The books says that you want to get rid of the influences from other predictors. A linear relationship between the dependent variable and the independent variable exists, if the plot follows a straight line.

When you plot β*Xj versus Xj, you always get a straight line. The residuals can bent the line, for example when they become larger for larger Xi. But then, why do you know that this independent variable causes non-linearity? The residuals are influenced by all independent variables and not only by xj.

Thanks!

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