# 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. Commented 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 Commented 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. Commented 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.