I need to make a residual plot and I was wondering whether I make the plots in multiple linear regression on one independent variable at a time (like making a simple linear regression) or the all of the ten independent variables at the same time (like multiple linear regression)? They produce different results for me obviously.
To check for overall heteroscedasticity:
- On the Y-axis: your model's residuals
- On the X-axis: either your dependent variable or your predicted value for it. You might try a plot using each.
Note that John Fox in Regression Diagnostics finds that, typically, only when the variance of the residuals varies by a factor of three or more is it a serious problem for regression estimation.
To check for overall linearity:
- On the Y-axis: your dependent variable
- On the X-axis: your predicted value for the dependent variable
Then you might create a linear fitline and one using a lowess and/or a quadratic or even a cubic fit, to compare to the linear one.
To check for heteroscedasticity, linearity, and influential points with respect to each X-Y relationship:
- Create partial plots, a.k.a. partial regression plots. Each will show an individual X-Y relationship while controlling for the other predictors.