本文實例講述了Python實現(xiàn)的簡單線性回歸算法。分享給大家供大家參考，具體如下：

用python實現(xiàn)R的線性模型(lm)中一元線性回歸的簡單方法，使用R的women示例數(shù)據(jù)，R的運行結果：

> 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實現(xiàn)的功能包括：

計算pearson相關系數(shù) 使用最小二乘法計算回歸系數(shù) 計算擬合優(yōu)度判定系數(shù)R2R2 計算估計標準誤差Se 計算顯著性檢驗的F和P值

import numpy as npimport scipy.stats as ssclass Lm:  """簡單一元線性模型，計算回歸系數(shù)、擬合優(yōu)度的判定系數(shù)和  估計標準誤差，顯著性水平"""  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  # 計算協(xié)方差  @staticmethod  def cov_custom(x, y):    result = sum((x - np.mean(x)) * (y - np.mean(y))) / (len(x) - 1)    return result  # 計算相關系數(shù)  @staticmethod  def corr_custom(x, y):    return Lm.cov_custom(x, y) / (np.std(x, ddof=1) * np.std(y, ddof=1))  # 計算回歸系數(shù)  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  # 計算擬合優(yōu)度的判定系數(shù)R方，即相關系數(shù)corr的平方  def r_square(self):    y = np.mat(self.yarr)    ybar = np.mean(y)    self.r2 = np.sum((self.yhat - ybar) ** 2) / np.sum((y.A - ybar) ** 2)    return  # 計算估計標準誤差  def estimate_deviation(self):    y = np.array(self.yarr)    self.se = np.sqrt(np.sum((y - self.yhat) ** 2) / self.dfd)    return  # 顯著性檢驗F  def sig_test(self):    ybar = np.mean(self.yarr)    self.msr = np.sum((self.yhat - ybar) ** 2)    self.mse = np.sum((self.yarr - self.yhat) ** 2) / self.dfd    self.f = self.msr / self.mse    self.p = ss.f.sf(self.f, 1, self.dfd)    return  def summary(self):    self.simple_regression()    corr_coe = Lm.corr_custom(self.xarr[:, -1], self.yarr)    self.r_square()    self.estimate_deviation()    self.sig_test()    print('The Pearson/'s correlation coefficient: %.3f' % corr_coe)    print('The Regression Coefficient: %s' % self.beta.flatten().A[0])    print('R square: %.3f' % self.r2)    print('The standard error of estimate: %.3f' % self.se)    print('F-statistic: %d on %s and %s DF, p-value: %.3e' % (self.f, 1, self.dfd, self.p))