search
HomeBackend DevelopmentPython TutorialResidual analysis techniques in Python

Residual analysis techniques in Python

Jun 10, 2023 am 08:52 AM
Skillpython programmingResidual analysis

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.

  1. 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.

  1. 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.

  1. 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.

The above is the detailed content of Residual analysis techniques in Python. For more information, please follow other related articles on the PHP Chinese website!

Statement
The content of this article is voluntarily contributed by netizens, and the copyright belongs to the original author. This site does not assume corresponding legal responsibility. If you find any content suspected of plagiarism or infringement, please contact admin@php.cn
Are Python lists dynamic arrays or linked lists under the hood?Are Python lists dynamic arrays or linked lists under the hood?May 07, 2025 am 12:16 AM

Pythonlistsareimplementedasdynamicarrays,notlinkedlists.1)Theyarestoredincontiguousmemoryblocks,whichmayrequirereallocationwhenappendingitems,impactingperformance.2)Linkedlistswouldofferefficientinsertions/deletionsbutslowerindexedaccess,leadingPytho

How do you remove elements from a Python list?How do you remove elements from a Python list?May 07, 2025 am 12:15 AM

Pythonoffersfourmainmethodstoremoveelementsfromalist:1)remove(value)removesthefirstoccurrenceofavalue,2)pop(index)removesandreturnsanelementataspecifiedindex,3)delstatementremoveselementsbyindexorslice,and4)clear()removesallitemsfromthelist.Eachmetho

What should you check if you get a 'Permission denied' error when trying to run a script?What should you check if you get a 'Permission denied' error when trying to run a script?May 07, 2025 am 12:12 AM

Toresolvea"Permissiondenied"errorwhenrunningascript,followthesesteps:1)Checkandadjustthescript'spermissionsusingchmod xmyscript.shtomakeitexecutable.2)Ensurethescriptislocatedinadirectorywhereyouhavewritepermissions,suchasyourhomedirectory.

How are arrays used in image processing with Python?How are arrays used in image processing with Python?May 07, 2025 am 12:04 AM

ArraysarecrucialinPythonimageprocessingastheyenableefficientmanipulationandanalysisofimagedata.1)ImagesareconvertedtoNumPyarrays,withgrayscaleimagesas2Darraysandcolorimagesas3Darrays.2)Arraysallowforvectorizedoperations,enablingfastadjustmentslikebri

For what types of operations are arrays significantly faster than lists?For what types of operations are arrays significantly faster than lists?May 07, 2025 am 12:01 AM

Arraysaresignificantlyfasterthanlistsforoperationsbenefitingfromdirectmemoryaccessandfixed-sizestructures.1)Accessingelements:Arraysprovideconstant-timeaccessduetocontiguousmemorystorage.2)Iteration:Arraysleveragecachelocalityforfasteriteration.3)Mem

Explain the performance differences in element-wise operations between lists and arrays.Explain the performance differences in element-wise operations between lists and arrays.May 06, 2025 am 12:15 AM

Arraysarebetterforelement-wiseoperationsduetofasteraccessandoptimizedimplementations.1)Arrayshavecontiguousmemoryfordirectaccess,enhancingperformance.2)Listsareflexiblebutslowerduetopotentialdynamicresizing.3)Forlargedatasets,arrays,especiallywithlib

How can you perform mathematical operations on entire NumPy arrays efficiently?How can you perform mathematical operations on entire NumPy arrays efficiently?May 06, 2025 am 12:15 AM

Mathematical operations of the entire array in NumPy can be efficiently implemented through vectorized operations. 1) Use simple operators such as addition (arr 2) to perform operations on arrays. 2) NumPy uses the underlying C language library, which improves the computing speed. 3) You can perform complex operations such as multiplication, division, and exponents. 4) Pay attention to broadcast operations to ensure that the array shape is compatible. 5) Using NumPy functions such as np.sum() can significantly improve performance.

How do you insert elements into a Python array?How do you insert elements into a Python array?May 06, 2025 am 12:14 AM

In Python, there are two main methods for inserting elements into a list: 1) Using the insert(index, value) method, you can insert elements at the specified index, but inserting at the beginning of a large list is inefficient; 2) Using the append(value) method, add elements at the end of the list, which is highly efficient. For large lists, it is recommended to use append() or consider using deque or NumPy arrays to optimize performance.

See all articles

Hot AI Tools

Undresser.AI Undress

Undresser.AI Undress

AI-powered app for creating realistic nude photos

AI Clothes Remover

AI Clothes Remover

Online AI tool for removing clothes from photos.

Undress AI Tool

Undress AI Tool

Undress images for free

Clothoff.io

Clothoff.io

AI clothes remover

Video Face Swap

Video Face Swap

Swap faces in any video effortlessly with our completely free AI face swap tool!

Hot Tools

WebStorm Mac version

WebStorm Mac version

Useful JavaScript development tools

SublimeText3 English version

SublimeText3 English version

Recommended: Win version, supports code prompts!

MantisBT

MantisBT

Mantis is an easy-to-deploy web-based defect tracking tool designed to aid in product defect tracking. It requires PHP, MySQL and a web server. Check out our demo and hosting services.

SAP NetWeaver Server Adapter for Eclipse

SAP NetWeaver Server Adapter for Eclipse

Integrate Eclipse with SAP NetWeaver application server.

Atom editor mac version download

Atom editor mac version download

The most popular open source editor