使用sklearn实现多元线性回归

多元线性回归

import pandas as pdimport numpy as npimport matplotlib.pyplot as pltfrom sklearn.linear_model import LinearRegressionfrom sklearn.model_selection import train_test_split%config InlineBackend.figure_format = 'svg'import seaborn as snsdata = pd.read_csv('/Users/jingjingdehnaa/Documents/sales.csv')data.corr()            TV        radio   newspaper  salesTV        1.000000  0.054809  0.056648  0.782224radio     0.054809  1.000000  0.354104  0.576223newspaper 0.056648  0.354104  1.000000  0.228299sales     0.782224  0.576223  0.228299  1.000000sns.pairplot(data,x_vars=['TV','radio','newspaper'], y_vars='sales', size=4, aspect=0.8,kind = 'reg')plt.show()

#建立模型的第一步我们将建立训练集和检测集

X_train,X_test,Y_train,Y_test = train_test_split(data.iloc[:,:3],data.sales,train_size = 0.8)

#将训练集中的特征值与标签值放入LinearRegression()模型中且使用fit函数进行训练

#得到所对应的方程式(线性回归方程式)需要利用函数中的intercept_与coef_。

model = LinearRegression()model.fit(X_train,Y_train)a = model.intercept_b = model.coef_print("最佳拟合线:截距",a,",回归系数：",b)print('拟合函数: y = %f * x+%f * x+%f * x+ %f'%(b[0],b[1],b[2],a))最佳拟合线:截距 2.8359172600679603 ,回归系数：[ 0.04636284  0.18702274 -0.00105945]拟合函数: y = 0.046363 * x+0.187023 * x+-0.001059 * x+ 2.835917

#对数据集进行预测与模型测评

#使用predict与score函数来获取所需要的预测值与得分

plt.rcParams['font.sans-serif'] = 'SimHei'score = model.score(X_test,Y_test)print(score)Y_test_pred = model.predict(X_test)plt.plot(range(len(Y_test_pred)),Y_test,label = 'test',color = 'b')plt.plot(range(len(Y_test_pred)),Y_test_pred,color = 'r',label = 'predict')plt.xlabel('投入')plt.ylabel('销量')plt.legend()plt.show()0.9261973226814358

使用statsmodels实现多元线性回归

import statsmodels.api as smimport numpy as npdata = pd.read_csv('/Users/jingjingdehnaa/Documents/sales.csv')x =data.iloc[:,:3]X = sm.add_constant(x)y = data.salesmodels = sm.OLS(y,X).fit()print(models.summary())print('拟合函数: y = %f*x+%f*x+%f*x+ %f'%(models.params[1],models.params[2],models.params[3],models.params[0]))                             OLS Regression Results                            ==============================================================================Dep. Variable:                  sales   R-squared:                       0.897Model:                            OLS   Adj. R-squared:                  0.896Method:                 Least Squares   F-statistic:                     570.3Date:                Sun, 25 Oct 2020   Prob (F-statistic):           1.58e-96Time:                        14:57:23   Log-Likelihood:                -386.18No. Observations:                 200   AIC:                             780.4Df Residuals:                     196   BIC:                             793.6Df Model:                           3                                         Covariance Type:            nonrobust                                         ==============================================================================                 coef    std err          t      P>|t|      [0.025      0.975]------------------------------------------------------------------------------const          2.9389      0.312      9.422      0.000       2.324       3.554TV             0.0458      0.001     32.809      0.000       0.043       0.049radio          0.1885      0.009     21.893      0.000       0.172       0.206newspaper     -0.0010      0.006     -0.177      0.860      -0.013       0.011==============================================================================Omnibus:                       60.414   Durbin-Watson:                   2.084Prob(Omnibus):                  0.000   Jarque-Bera (JB):              151.241Skew:                          -1.327   Prob(JB):                     1.44e-33Kurtosis:                       6.332   Cond. No.                         454.==============================================================================拟合函数: y = 0.045765*x+0.188530*x+-0.001037*x+ 2.938889