# Making a residual plot in multiple linear regression

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.

• 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. Apr 27, 2020 at 15:17
• 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 Apr 27, 2020 at 15:22
• 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. Apr 27, 2020 at 15:45

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.