Diagnostic Plots

Diagnostic plots are essential tools for evaluating the assumptions and performance of regression models. In the context of linear regression, these plots help identify potential issues such as non-linearity, non-constant variance, outliers, high leverage points, and collinearity. The statsmodels library in Python provides several functions to generate these diagnostic plots, aiding in assessing model fit and validity.

Common diagnostic plots include:

• Residual plots: Check for homoscedasticity and non-linearity.
• Q-Q plots: Assess the normality of residuals.
• Leverage plots: Identify influential points.
• Scale-location plots: Detect patterns in residual variance.

Syntax

There are several different methods for generating diagnostic plots in statsmodels. Two common methods are plot_partregress_grid() and plot_regress_exog(). These methods work with a fitted regression results object.

plot_partregress_grid()

The plot_partregress_grid() method generates diagnostic plots for all explanatory variables in the model. It helps assess the relationship between the residuals and each independent variable.

The syntax for using plot_partregress_grid() is:

results.plot_partregress_grid()

• results refers to the fitted regression results object.

plot_regress_exog()

The plot_regress_exog() method generates residual plots for a specific independent variable. This can help check the assumption of linearity with respect to a particular predictor.

The syntax for using plot_regress_exog() is:

results.plot_regress_exog(exog_idx)

• results refers to the fitted regression results object.
• exog_idx is the index of the explanatory variable whose relationship with the dependent variable you want to plot.

Example

Below is an example demonstrating how to generate diagnostic plots for a linear regression model using statsmodels:

import statsmodels.api as sm
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# Create synthetic data
np.random.seed(0)
X = np.random.rand(100, 2)
X = sm.add_constant(X)  # Add constant (intercept)
y = X[:, 1] + X[:, 2] + np.random.randn(100)  # Dependent variable with some noise

# Fit linear regression model
model = sm.OLS(y, X)
results = model.fit()

# Generate diagnostic plots for all variables
fig = plt.figure(figsize=(10, 8))
fig = sm.graphics.plot_partregress_grid(results)
plt.show()

# Alternatively, generate a residual plot for the first independent variable
fig = plt.figure(figsize=(10, 8))
fig = sm.graphics.plot_regress_exog(results, 1)
plt.show()

The output will be as follows: