python线性回归

线性回归主要用于处理回归问题，少数情况用于处理分类问题。
一元线性回归：y=a*x+b ,描述自变量和因变量都只有一个的情况，且自变量和因变量之间呈线性关系的回归模型。
python例子：

import numpy as np
import  matplotlib.pyplot as plt

if __name__=='__main__':
    x=np.array([1,2,4,6,9])
    y=np.array([2,5,7,8,10])
    x_mean=np.mean(x)
    y_mean=np.mean(y)
    denominator=0.0
    numerator=0.0
    for x_i,y_i in zip(x,y):
        numerator+=(x_i-x_mean)*(y_i-y_mean)
        denominator+=(x_i-x_mean)**2
    a=numerator/denominator
    b=y_mean-a*x_mean
    y_predict=a*x+b
    plt.scatter(x,y,color='b')
    plt.plot(x,y_predict,color='r')
    plt.xlabel('X',fontproperties='simHei',fontsize=15)
    plt.ylabel('Y',fontproperties='simHei',fontsize=15)
    plt.show()

结果

一元线性回归算法封装
写一个linearRegression.py文件

import  numpy as np
class linearRegressionSelf:
    def __init__(self):
        self.a_=None
        self.b_=None
    def fit(self,x_train,y_train):
        assert x_train.ndim==1
        x_mean = np.mean(x_train)
        y_mean = np.mean(y_train)
        denominator = 0.0
        numerator = 0.0
        for x_i, y_i in zip(x_train, y_train):
            numerator += (x_i - x_mean) * (y_i - y_mean)
            denominator += (x_i - x_mean) ** 2
        self.a_ = numerator / denominator
        self.b_ = y_mean -self.a_* x_mean
        return  self
    def predict(self,x_test_group):
        return  np.array([self._predict(x_test) for x_test in x_test_group])
    def _predict(self,x_test):
        return self.a_*x_test+self.b_
    def mean_squared_error(self,y_true,y_predict):
        return np.sum((y_true-y_predict)**2)/len(y_true)
    def r_square(self,y_true,y_predict):
        return  1-(self.mean_squared_error(y_true,y_predict))/np.var(y_true)
if __name__ == '__main__':
    x = np.array([1, 2, 4, 6, 9])
    y = np.array([2, 5, 7, 8, 10])
    lr=linearRegressionSelf()
    lr.fit(x,y)
    print(lr.predict([7]))
    print(lr.r_square([8,9],lr.predict([6,8])))

测试：

import numpy as np
from linearRegression import linearRegressionSelf

# 按间距中的绿色按钮以运行脚本。
if __name__ == '__main__':
    x = np.array([1, 2, 4, 6, 9])
    y = np.array([2, 5, 7, 8, 10])
    lr=linearRegressionSelf()
    lr.fit(x,y)
    print(lr.predict([7]))
    print(lr.r_square([8,9],lr.predict([6,8])))