python 線性回歸分析模型檢驗(yàn)標(biāo)準(zhǔn)--擬合優(yōu)度詳解

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from pandas import DataFrame,Series
from sklearn.cross_validation import train_test_split
from sklearn.linear_model import LinearRegression
 
#創(chuàng)建數(shù)據(jù)集
examDict = {'學(xué)習(xí)時間':[0.50,0.75,1.00,1.25,1.50,1.75,1.75,
           2.00,2.25,2.50,2.75,3.00,3.25,3.50,4.00,4.25,4.50,4.75,5.00,5.50],
       '分?jǐn)?shù)':[10,22,13,43,20,22,33,50,62,
          48,55,75,62,73,81,76,64,82,90,93]}
 
#轉(zhuǎn)換為DataFrame的數(shù)據(jù)格式
examDf = DataFrame(examDict)
#examDf
#繪制散點(diǎn)圖
plt.scatter(examDf.分?jǐn)?shù),examDf.學(xué)習(xí)時間,color = 'b',label = "Exam Data")
 
#添加圖的標(biāo)簽（x軸，y軸）
plt.xlabel("Hours")
plt.ylabel("Score")
#顯示圖像
plt.show()
 
#將原數(shù)據(jù)集拆分訓(xùn)練集和測試集
exam_X = examDf.學(xué)習(xí)時間
exam_Y = examDf.分?jǐn)?shù)
X_train,X_test,Y_train,Y_test = train_test_split(exam_X,exam_Y,train_size=0.8)
#X_train為訓(xùn)練數(shù)據(jù)標(biāo)簽,X_test為測試數(shù)據(jù)標(biāo)簽,exam_X為樣本特征,exam_y為樣本標(biāo)簽，train_size 訓(xùn)練數(shù)據(jù)占比
 
print("原始數(shù)據(jù)特征:",exam_X.shape,
   ",訓(xùn)練數(shù)據(jù)特征:",X_train.shape,
   ",測試數(shù)據(jù)特征:",X_test.shape)
 
print("原始數(shù)據(jù)標(biāo)簽:",exam_Y.shape,
   ",訓(xùn)練數(shù)據(jù)標(biāo)簽:",Y_train.shape,
   ",測試數(shù)據(jù)標(biāo)簽:",Y_test.shape)
 
model = LinearRegression()
 
#對于模型錯誤我們需要把我們的訓(xùn)練集進(jìn)行reshape操作來達(dá)到函數(shù)所需要的要求
# model.fit(X_train,Y_train)
 
#reshape如果行數(shù)=-1的話可以使我們的數(shù)組所改的列數(shù)自動按照數(shù)組的大小形成新的數(shù)組
#因?yàn)閙odel需要二維的數(shù)組來進(jìn)行擬合但是這里只有一個特征所以需要reshape來轉(zhuǎn)換為二維數(shù)組
X_train = X_train.values.reshape(-1,1)
X_test = X_test.values.reshape(-1,1)
 
model.fit(X_train,Y_train)
a = model.intercept_#截距
b = model.coef_#回歸系數(shù)
print("最佳擬合線:截距",a,",回歸系數(shù)：",b)
 

# 用訓(xùn)練集進(jìn)行擬合優(yōu)度，驗(yàn)證回歸方程是否合理
def get_lr_stats(x, y, model):
  message0 = '一元線性回歸方程為: '+'\ty' + '=' + str(model.intercept_)+' + ' +str(model.coef_[0]) + '*x'
  from scipy import stats
  n = len(x)
  y_prd = model.predict(x)
  Regression = sum((y_prd - np.mean(y))**2) # 回歸平方和
  Residual  = sum((y - y_prd)**2)     # 殘差平方和
  total = sum((y-np.mean(y))**2) #總體平方和
  R_square  = 1-Residual / total # 相關(guān)性系數(shù)R^2
  message1 = ('相關(guān)系數(shù)(R^2)： ' + str(R_square) + '；' + '\n'+ '總體平方和(TSS)： ' + str(total) + '；' + '\n')
  message2 = ('回歸平方和(RSS)： ' + str(Regression) + '；' + '\n殘差平方和(ESS)： ' + str(Residual) + '；' + '\n')
  return print(message0 +'\n' +message1 + message2 )
 
get_lr_stats(X_train,Y_train,model)

#訓(xùn)練數(shù)據(jù)的預(yù)測值
y_train_pred = model.predict(X_train)
#繪制最佳擬合線：標(biāo)簽用的是訓(xùn)練數(shù)據(jù)集中的極值預(yù)測值
X_train_pred = [min(X_train),max(X_train)]
y_train_pred = [a+b*min(X_train),a+b*max(X_train)]
plt.plot(X_train_pred, y_train_pred, color='green', linewidth=3, label="best line")
 
#測試數(shù)據(jù)散點(diǎn)圖
plt.scatter(X_test, Y_test, color='red', label="test data")
plt.scatter(X_train, Y_train, color="blue", label="train data")
 
#添加圖標(biāo)標(biāo)簽
plt.legend(loc=2)
plt.xlabel("Hours")
plt.ylabel("Score")
#顯示圖像
plt.savefig("lines.jpg")
plt.show()
#計(jì)算擬合優(yōu)度
score = model.score(X_test,Y_test)
print(score)