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.?