Python data analysis -- realizing linear regression in Python

Linear regression It's one of the basic statistical and machine learning technologies . economic , Computer science , In Social Sciences and so on , Whether it's statistical analysis , Or machine learning , Or scientific computing , There's a huge opportunity to use linear models . I suggest learning it first , And then try something more complicated .

This paper mainly introduces How to step in Python Linear regression is realized in . As for the mathematical derivation of linear regression 、 How does linear regression work , How parameter selection improves the regression model will be explained later .

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Regression analysis is one of the most important fields in statistics and machine learning . There are many regression methods available . Linear regression is one of them . And linear regression is probably one of the most important and widely used regression techniques . This is one of the simplest regression methods . One of its main advantages is that the results obtained by linear regression are very easy to explain . Well, the return mainly includes ：

Simple linear regression
Multiple linear regression
Polynomial regression

How to be in python Linear regression is realized in

Use of packages

NumPy

NumPy yes Python Basic science software package for , It allows many high-performance operations to be performed on single - and multi-dimensional arrays .

scikit-learn

scikit-learn Is in NumPy And some other packages based on the widely used Python Machine learning library . It provides preprocessing data , Reduce the dimension , Return to reality , classification , Clustering and so on .

statsmodels

If you want to achieve linear regression and need to function beyond scikit-learn The scope of the , The use of statsmodels Can be used to estimate statistical models , Perform tests, etc .

scikit-learn Simple linear regression of

1. Import used packages And the class

import numpy as np
from sklearn.linear_model import LinearRegression

2. Create data

x = np.array([5, 15, 25, 35, 45, 55]).reshape((-1, 1))
y = np.array([5, 20, 14, 32, 22, 38])

Now we have two arrays : Input x( Regression variables ) and Output y( Predictive variables ), Let's see

>>> print(x)
[[ 5]
 [15]
 [25]
 [35]
 [45]
 [55]]
>>> print(y)
[ 5 20 14 32 22 38]

You can see x It's two-dimensional and y It's one-dimensional , Because in a more complicated model , There's more than one coefficient . It's here .reshape() To switch .

3. Build a model

Create an instance of a class LinearRegression, It will represent the regression model ：

model = LinearRegression()

Now start fitting the model , First you can call .fit() Function to get the optimal