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Components + resiudal plots or partial residual plots can be used to detect deviations from linearity in multiple linear regression.

They work by plotting the variable on the x-axis and the component+residual on the y-axis. But what do you do in polynomial regression. Then the independent variable x occurs twice or multiple times in the equation.

Do you plot a partial residual plot for each occurrence? Meaning a plot for xi, a plot for xi^2, a plot for xi^3 etc.?

Thanks!

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