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**Residual plots** are often used to assess whether or not the residuals in a regression analysis are normally distributed and whether or not they exhibit heteroscedasticity.

This tutorial explains how to create residual plots for a regression model in R.

**Example: Residual Plots in R**

In this example we will fit a regression model using the built-in R datasetÂ **mtcarsÂ **and then produce three different residual plots to analyze the residuals.

**Step 1: Fit regression model.**

First, we will fit a regression model usingÂ **mpgÂ **as the response variable andÂ **disp** andÂ **hp** as explanatory variables:

#load the dataset data(mtcars) #fit a regression model model #get list of residuals res

**Step 2: Produce residual vs. fitted plot.**

Next, we will produce a residual vs. fitted plot, which is helpful for visually detecting heteroscedasticity â€“ e.g. a systematic change in the spread of residuals over a range of values.Â

#produce residual vs. fitted plot plot(fitted(model), res) #add a horizontal line at 0 abline(0,0)

The x-axis displays the fitted values and the y-axis displays the residuals. From the plot we can see that the spread of the residuals tends to be higher for higher fitted values, but it doesnâ€™t look serious enough that we would need to make any changes to the model.

**Step 3: Produce a Q-Q plot.**

We can also produce a Q-Q plot, which is useful for determining if the residuals follow a normal distribution. If the data values in the plot fall along a roughly straight line at a 45-degree angle, then the data is normally distributed.

#create Q-Q plot for residuals qqnorm(res) #add a straight diagonal line to the plot qqline(res)

We can see that the residuals tend to stray from the line quite a bit near the tails, which could indicate that theyâ€™re not normally distributed.

**Step 4: Produce a density plot.**

We can also produce a density plot, which is also useful for visually checking whether or not the residuals are normally distributed. If the plot is roughly bell-shaped, then the residuals likely follow a normal distribution.

#Create density plot of residuals plot(density(res))

We can see that the density plot roughly follows a bell shape, although it is slightly skewed to the right. Depending on the type of study, a researcher may or may not decide to perform a transformation on the data to ensure that the residuals are more normally distributed.

**Additional Resources**

How to Calculate Standardized Residuals in R

How to Calculate Studentized Residuals in R

How to Create a Histogram of Residuals in R