简介

线性回归：根据数据，确定两种或两种以上变量间相互依赖的定量关系

评价曲线的拟合效果使用均方误差和R方值进行拟合质量评估

\[M S E=\frac{1}{m} \sum_{i=1}^{m}\left(y_{i}^{\prime}-y_{i}\right)^{2} \]

R方值 \(\left(R^{2}\right)\) :

\[R^{2}=1-\frac{\sum_{i=1}^{m}\left(y_{i}^{\prime}-y_{i}\right)^{2}}{\sum_{i=1}^{m}\left(y_{i}-\overline{y_{i}}\right)^{2}}=1-\frac{M S E}{\text { 方差 }} \]

MSE越接近0越好R方值越接近1越好。

对于离散数据点。

x	y
1	7
2	9
3	11
4	13
5	15

进行机器学习线性回归操作

code

import pandas as pd data = pd.read_csv('generated_data.csv') data.head() x = data.loc[:,'x'] y = data.loc[:,'y'] print(x,y) from matplotlib import pyplot as plt plt.figure(figsize=(10,10)) plt.scatter(x,y) plt.show() from sklearn.linear_model import LinearRegression lr_model = LinearRegression() import numpy as np x = np.array(x) x = x.reshape(-1,1) y = np.array(y) y = y.reshape(-1,1) print(x,y) lr_model.fit(x,y) y_predict = lr_model.predict(x) print(y_predict) y_3 = lr_model.predict([[3.5]]) print(y_3) from sklearn.metrics import mean_squared_error,r2_score MSE = mean_squared_error(y,y_predict) R2 = r2_score(y,y_predict) print(MSE,R2) plt.figure() plt.scatter(y,y_predict) plt.show() 

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