本文实例讲述了Python实现的简单线性回归算法。分享给大家供大家参考，具体如下：
用python实现R的线性模型(lm)中一元线性回归的简单方法，使用R的women示例数据，R的运行结果：> summary(fit)
Call:
lm(formula = weight ~ height, data = women)
Residuals:
Min 1Q Median 3Q Max
-1.7333 -1.1333 -0.3833 0.7417 3.1167
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -87.51667 5.93694 -14.74 1.71e-09 ***
height 3.45000 0.09114 37.85 1.09e-14 ***
—
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1
Residual standard error: 1.525 on 13 degrees of freedom
Multiple R-squared: 0.991, Adjusted R-squared: 0.9903
F-statistic: 1433 on 1 and 13 DF, p-value: 1.091e-14
python实现的功能包括：
计算pearson相关系数
使用最小二乘法计算回归系数
计算拟合优度判定系数R2R2
计算估计标准误差Se
计算显著性检验的F和P值
import numpy as np
import scipy.stats as ss
class Lm:
"""简单一元线性模型，计算回归系数、拟合优度的判定系数和
估计标准误差，显著性水平"""
def __init__(self, data_source, separator):
self.beta = np.matrix(np.zeros(2))
self.yhat = np.matrix(np.zeros(2))
self.r2 = 0.0
self.se = 0.0
self.f = 0.0
self.msr = 0.0
self.mse = 0.0
self.p = 0.0
data_mat = np.genfromtxt(data_source, delimiter=separator)
self.xarr = data_mat[:, :-1] self.yarr = data_mat[:, -1] self.ybar = np.mean(self.yarr)
self.dfd = len(self.yarr) - 2 # 自由度n-2
return
# 计算协方差
@staticmethod
def cov_custom(x, y):
result = sum((x - np.mean(x)) * (y - np.mean(y))) / (len(x) - 1)
return result
# 计算相关系数
@staticmethod
def corr_custom(x, y):
return Lm.cov_custom(x, y) / (np.std(x, ddof=1) * np.std(y, ddof=1))
# 计算回归系数
def simple_regression(self):
xmat = np.mat(self.xarr)
ymat = np.mat(self.yarr).T
xtx = xmat.T * xmat
if np.linalg.det(xtx) == 0.0:
print('Can not resolve the problem')
return
self.beta = np.linalg.solve(xtx, xmat.T * ymat) # xtx.I * (xmat.T * ymat)
self.yhat = (xmat * self.beta).flatten().A[0] return
# 计算拟合优度的判定系数R方，即相关系数corr的平方
def r_square(self):
y = np.mat(self.yarr)
