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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.

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    $\begingroup$ Hello - "residual plot" can refer to many different things. What is your goal? Also you may want to look into partial plots, a.k.a. partial regression plots. $\endgroup$
    – rolando2
    Commented Apr 27, 2020 at 15:17
  • $\begingroup$ My goal is to check heteroscadisticity and linearity of the data. I have ten independent variables and I'm not sure whether to plot the residuals individually against dependent variable or all of them at the same time, like when doing a multiple linear regression $\endgroup$ Commented Apr 27, 2020 at 15:22
  • $\begingroup$ Each plot is valuable, and in addition you should inspect fitted values versus residuals. But no finite amount of plots will be guaranteed to "catch" heteroscedasticity or non-linearity if it exists. $\endgroup$
    – AdamO
    Commented Apr 27, 2020 at 15:45

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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.
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