Understanding Linear Regression with Python: (A Practical Guide Using NumPy) by Boyle Jonathan

Author:Boyle, Jonathan [Boyle, Jonathan]
Language: eng
Format: epub
Published: 2024-09-29T00:00:00+00:00

6.1 Residual Analysis: Understanding the Residuals and Identifying Patterns

Residuals are the differences between the actual values of the dependent variable and the values predicted by the model. By analyzing the residuals, we can gain insights into the model's performance and identify potential issues.

Residual Plots

Visualizing residuals can help us identify patterns and anomalies that might indicate problems with the model. Common residual plots include: Residuals vs. fitted values: This plot helps to identify heteroscedasticity (non-constant variance) in the residuals. If there is a pattern in this plot, it suggests that the model's variance is not constant.

Residuals vs. time: This plot is useful for time series data and helps to identify autocorrelation in the residuals. Autocorrelation means that the residuals are correlated with each other over time.

Normal Q-Q plot: This plot helps to assess the normality of the residuals. If the residuals are normally distributed, the points should follow a straight line.

Interpreting Residual Plots

Random scatter: If the residuals are randomly scattered around zero, it suggests that the model is a good fit for the data.

Patterns: If there are patterns in the residuals, it may indicate that the model is not appropriate or that there are other issues with the data. For example, a U-shaped pattern in the residuals vs. fitted values plot suggests heteroscedasticity.

Example:

Python

import matplotlib.pyplot as plt # Calculate residuals

residuals = y_true - y_pred

# Plot residuals vs. fitted values

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