A **residual plot** is a type of plot that displays the fitted values against the residual values for a regression model. This type of plot is often used to assess whether or not a linear regression model is appropriate for a given dataset and to check for heteroscedasticity of residuals.

This tutorial explains how to create a residual plot for a linear regression model in Python.

**Example: Residual Plot in Python**

For this example we’ll use a dataset that describes the attributes of 10 basketball players:

import numpy as np import pandas as pd #create dataset df = pd.DataFrame({'rating': [90, 85, 82, 88, 94, 90, 76, 75, 87, 86], 'points': [25, 20, 14, 16, 27, 20, 12, 15, 14, 19], 'assists': [5, 7, 7, 8, 5, 7, 6, 9, 9, 5], 'rebounds': [11, 8, 10, 6, 6, 9, 6, 10, 10, 7]}) #view dataset df rating points assists rebounds 0 90 25 5 11 1 85 20 7 8 2 82 14 7 10 3 88 16 8 6 4 94 27 5 6 5 90 20 7 9 6 76 12 6 6 7 75 15 9 10 8 87 14 9 10 9 86 19 5 7

**Residual Plot for Simple Linear Regression**

Suppose we fit a simple linear regression model using *points *as the predictor variable and *rating *as the response variable:

#import necessary libraries import matplotlib.pyplot as plt import statsmodels.api as sm from statsmodels.formula.api import ols #fit simple linear regression model model = ols('rating ~ points', data=df).fit() #view model summary print(model.summary())

We can create a residual vs. fitted plot by using the plot_regress_exog() function from the statsmodels library:

#define figure size fig = plt.figure(figsize=(12,8)) #produce regression plots fig = sm.graphics.plot_regress_exog(model, 'points', fig=fig)

Four plots are produced. The one in the top right corner is the residual vs. fitted plot. The x-axis on this plot shows the actual values for the predictor variable *points* and the y-axis shows the residual for that value.

Since the residuals appear to be randomly scattered around zero, this is an indication that heteroscedasticity is not a problem with the predictor variable.

**Residual Plots for Multiple Linear Regression**

Suppose we instead fit a multiple linear regression model using *assists *and *rebounds *as the predictor variable and *rating *as the response variable:

#fit multiple linear regression model model = ols('rating ~ assists + rebounds', data=df).fit() #view model summary print(model.summary())

Once again we can create a residual vs. predictor plot for each of the individual predictors using the plot_regress_exog() function from the statsmodels library.

For example, here’s what the residual vs. predictor plot looks like for the predictor variable *assists*:

#create residual vs. predictor plot for 'assists' fig = plt.figure(figsize=(12,8)) fig = sm.graphics.plot_regress_exog(model, 'assists', fig=fig)

And here’s what the residual vs. predictor plot looks like for the predictor variable *rebounds*:

#create residual vs. predictor plot for 'assists' fig = plt.figure(figsize=(12,8)) fig = sm.graphics.plot_regress_exog(model, 'rebounds', fig=fig)

In both plots the residuals appear to be randomly scattered around zero, which is an indication that heteroscedasticity is not a problem with either predictor variable in the model.