首先导入库并避免显示错误FutureWorning
import numpy as npimport matplotlib.pyplot as pltimport pandas as pdimport seaborn as snsfrom sklearn.datasets import load_bostonfrom sklearn.model_selection import train_test_splitfrom sklearn.linear_model import LinearRegressionfrom sklearn import metricsfrom sklearn import preprocessingimport warningswarnings.filterwarnings("ignore") # 避免显示FutureWorning
预处理数据并筛选相关系数较大的特征值
注释的第一部分：为显示各个影响因素与价格的关系图
注释的第二部分：通过一元线性回归，将筛选的三个相关系数最大的特征值与价格的关系图绘制出来
boston = load_boston()x = boston['data'] # 所有特征信息y = boston['target'] # 房价feature_names = boston['feature_names'] # 十三个影响因素boston_data = pd.DataFrame(x, columns=feature_names) # 特征信息和影响因素boston_data['price'] = y # 添加价格列'''for i in range(13):plt.figure(figsize=(10, 7))plt.scatter(x[:,i],y,s=2)#某影响因素的特征信息与房价plt.title(feature_names[i])plt.show()'''cor = boston_data.corr()['price'] # 求取相关系数print(cor)# 取相关系数大于0.5的特征值 RM LSTAT PTRATIO priceboston_data = boston_data[['LSTAT', 'PTRATIO', 'RM', 'price']] # 保留该四组因素y = np.array(boston_data['price'])feature_names = ['LSTAT', 'PTRATIO', 'RM', 'price']'''for i in range(3):x = np.array(boston_data[feature_names[i]])var = np.var(x,ddof=1)cov = np.cov(x,y)[0][1]k = cov/varb = np.mean(y) - k*np.mean(x)y_price = k*x + bplt.plot(x,y,'b.')plt.plot(x,y_price,'k-')plt.show()'''
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使用模型求解
通过LinearRegression库直接实现
boston_data = boston_data.drop(['price'], axis=1)x = np.array(boston_data)print(x)train_x, test_x, train_y, test_y = train_test_split(x, y, test_size=0.3, random_state=0) # 分割训练集和测试集# 直接使用模型求解# 加载模型li = LinearRegression()# 拟合数据li.fit(train_x, train_y)# 进行预测y_predict = li.predict(test_x)plt.figure(figsize=(10, 7))plt.plot(y_predict, 'b-')plt.plot(test_y, 'r--')plt.legend(['predict', 'true'])plt.title('Module')plt.show()mes = metrics.mean_squared_error(y_predict, test_y)print(mes)
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最小二乘法求解
对系数B矩阵求偏导，偏导为0时，即为目标解
boston_data.insert(loc=0, column='one', value=1)print(boston_data)x = np.array(boston_data)train_x, test_x, train_y, test_y = train_test_split(x, y, test_size=0.3, random_state=0) # 分割训练集和测试集xT = x.Tx_mat = np.mat(train_x)y_mat = np.mat(train_y).TxT = x_mat.TB = (xT * x_mat).I * xT * y_matprint(B)y_predict = test_x * Bplt2 = plt.figure(figsize=(10, 7))plt2 = plt.plot(y_predict, 'b-')plt2 = plt.plot(test_y, 'r--')plt2 = plt.legend(['predict', 'true'])plt2 = plt.title('Least Sqaure Method')plt.show()# [[22.17686885]# [-0.55760828]# [-1.11165635]# [ 4.44512502]]
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多元线性回归
简单多元线性回归（梯度下降算法与矩阵法）
机器学习方法之线性回归(LR)
首先处理x中的数据，在x每一行前添加1
print(boston_data)x = np.array(boston_data)train_x, test_x, train_y, test_y = train_test_split(x, y, test_size=0.3, random_state=0) # 分割训练集和测试集xT = x.Tprint(xT)x_mat = np.mat(train_x)y_mat = np.mat(train_y).TxT = x_mat.TB = [[22.1768],[-0.5576],[-1.11165],[4.44512]]B = np.mat(B)Bp = -2*xT*(y_mat-x_mat*B) # 即B的偏导while 1:B = B - 0.000005*BpBp = -2 * xT * (y_mat - x_mat * B)for i in range(4):sum = 0sum += abs(Bp[i])print(sum)if sum <=0.00001: breakprint(B)print("最终B：",B)# 最终B： [[22.17682455]# [-0.55760809]# [-1.11165553]# [ 4.44512921]]y_predict = test_x*Bplt3 = plt.figure(figsize=(10, 7))plt3 = plt.plot(y_predict,'b-')plt3 = plt.plot(test_y,'r--')plt3 = plt.legend(['predict', 'true'])plt.title('Multiple Linear Regression')plt.show()
