Residual analysis techniques in Python

Python is a widely used programming language, and its powerful data analysis and visualization capabilities make it one of the preferred tools for data scientists and machine learning engineers. In these applications, residual analysis is a common technique used to evaluate model accuracy and identify any model bias. In this article, we will introduce several ways to use residual analysis techniques in Python.

1. Understanding Residuals

Before introducing residual analysis techniques in Python, let us first understand what residuals are. In statistics, the residual is the difference, or error, between the actual observed value and the predicted value. After building any model, we can calculate the residual for each observation, which helps us evaluate whether the model can accurately predict future outcomes.

In Python, we can use libraries such as Pandas and NumPy to calculate the residuals. Refer to the following code:

import pandas as pd
import numpy as np

# 创建数据集
y_true = pd.Series([1, 2, 3, 4, 5])
y_pred = pd.Series([1.2, 2.1, 2.8, 3.7, 4.5])

# 计算残差
residuals = y_true - y_pred
print(residuals)

The above code creates two Pandas Series objects, representing the true value and the predicted value respectively. Then calculate their residuals by subtraction and print them out.

2. Residual scatter plot

The residual scatter plot is a commonly used residual analysis tool used to visualize the error distribution of the model. It shows the relationship between the residual value for each observation and the predicted value for that observation.

In Python, we can create scatter plots using the scatter() function in the Matplotlib library. Refer to the following code:

import matplotlib.pyplot as plt

# 绘制残差散点图
plt.scatter(y_pred, residuals)
plt.title('Residual plot')
plt.ylabel('Residuals')
plt.xlabel('Fitted values')
plt.axhline(y=0, color='r', linestyle='-')
plt.show()

The above code uses the scatter() function to create a scatter plot. The horizontal axis represents predicted values, and the vertical axis represents residuals. Among them, the axhline() function is used to draw a horizontal line in the graph to help us judge whether the distribution between the predicted values ​​and the residuals is random. If the residual values ​​are randomly distributed around 0, the model can be considered accurate.

3. Residual histogram

In addition to scatter plots, the residual histogram is also an effective residual analysis tool for evaluating whether the model error distribution is positive. state distribution. In the case of a normal distribution, the residual values ​​should be randomly distributed around 0, so we can use a histogram to display the distribution of our residuals.

In Python, we can create histograms using the hist() function in the Matplotlib library. Refer to the following code:

# 绘制残差直方图
plt.hist(residuals, bins=10)
plt.title('Residuals distribution')
plt.xlabel('Residuals')
plt.ylabel('Frequency')
plt.show()

The above code uses the hist() function to draw the histogram and sets the relevant labels and titles. Here, we adjust the granularity of the horizontal axis by setting the bins parameter to better display the distribution of the residuals.

4. Q-Q plot

The Q-Q plot is a tool used to test whether our residuals conform to the normal distribution. It is constructed by comparing quantiles between sample data and a standard normal distribution. If the residuals are normally distributed, the data points should be on a straight line in the Q-Q plot. If the data points deviate from this straight line, we can assume that the residuals are not normally distributed.

In Python, we can use the probplot() function in the Scipy library to draw Q-Q plots. Refer to the following code:

from scipy.stats import probplot

# 绘制Q-Q图
probplot(residuals, dist='norm', plot=plt)
plt.title('Q-Q plot')
plt.show()

The above code uses the probplot() function to create a Q-Q plot, and sets the dist parameter to 'norm', which means using the standard normal distribution as the comparison benchmark. If the data points deviate from the straight line, then we can confirm that the residuals are normally distributed by examining the plotted graph.

Summary

In this article, we introduced the residual analysis techniques in Python and introduced several main tools, such as residual scatter plots and residual histograms. and Q-Q plot. These techniques are commonly used to evaluate model accuracy and identify model biases. Being proficient in these techniques can help us better understand and analyze data, and provide better suggestions for improvements and adjustments to our machine learning models.

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