应用回归分析，R语言，多元线性回归总结（下）

cor1<-cor(data3_1[,-1])
 round(cor1,digits = 3)

      x2     x3     x4     x5     x6     x7     x8     x9      y
x2 1.000  0.305  0.646  0.470  0.460  0.615  0.144  0.013  0.512
x3 0.305  1.000  0.584  0.736  0.539  0.777 -0.178 -0.325  0.781
x4 0.646  0.584  1.000  0.488  0.381  0.651  0.070 -0.110  0.494
x5 0.470  0.736  0.488  1.000  0.747  0.814 -0.104 -0.374  0.941
x6 0.460  0.539  0.381  0.747  1.000  0.780 -0.018 -0.499  0.785
x7 0.615  0.777  0.651  0.814  0.780  1.000 -0.020 -0.262  0.873
x8 0.144 -0.178  0.070 -0.104 -0.018 -0.020  1.000 -0.130 -0.130
x9 0.013 -0.325 -0.110 -0.374 -0.499 -0.262 -0.130  1.000 -0.361
y  0.512  0.781  0.494  0.941  0.785  0.873 -0.130 -0.361  1.000

lm3<-update(lm1,.~.-x9)
 lm3

Call:
lm(formula = y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8, data = data3_1)

Coefficients:
(Intercept)           x1           x2           x3           x4           x5           x6  
 947.138614     1.314540     1.669009     2.136855    -0.021107     1.679586     0.008060  
         x7           x8  
   0.004812   -22.326103  

 summary(lm3)

Call:
lm(formula = y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8, data = data3_1)

Residuals:
    Min      1Q  Median      3Q     Max 
-932.95 -188.17    7.63  242.43  448.20 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  9.471e+02  3.414e+03   0.277 0.784035    
x1           1.315e+00  1.038e-01  12.659 1.41e-11 ***
x2           1.669e+00  2.894e-01   5.768 8.40e-06 ***
x3           2.137e+00  4.946e-01   4.321 0.000276 ***
x4          -2.111e-02  4.647e-01  -0.045 0.964181    
x5           1.680e+00  2.094e-01   8.022 5.64e-08 ***
x6           8.060e-03  1.139e-02   0.708 0.486471    
x7           4.812e-03  9.922e-03   0.485 0.632473    
x8          -2.233e+01  2.990e+01  -0.747 0.463213    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 381.5 on 22 degrees of freedom
Multiple R-squared:  0.9922,	Adjusted R-squared:  0.9894 
F-statistic: 350.4 on 8 and 22 DF,  p-value: < 2.2e-16

多元线性回归模型的基本假设：解释变量是确定性变量，自变量列之间不相关，样本量的个数大于解释变量的个数。随机误差项具有0均值和等方差。正态分布的假定条件为e~N(0,d^2),相互独立。

拒绝H0，认为在显著性