R语言多元线性回归

多元线性回归关键在于自变量筛选。一般采用后退法。

# 工业用电量的全变量回归
lm.fullind <- lm(data[,10] ~ data[,3]+data[,5]+data[,6]+data[,7]+
                   data[,14]+data[,15])
summary(lm.fullind)

R语言中summary可以打印每个自变量的p值（“Pr(>|t|)”）

Call:
lm(formula = data[, 10] ~ data[, 3] + data[, 5] + data[, 6] + 
    data[, 7] + data[, 14] + data[, 15])

Residuals:
   Min     1Q Median     3Q    Max 
-63.18 -19.56   5.48  17.19  53.79 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) 1832.67765  532.30742   3.443 0.001255 ** 
data[, 3]      0.11092    0.01781   6.227 1.43e-07 ***
data[, 5]     -0.12608    0.03110  -4.054 0.000197 ***
data[, 6]     -0.17146    0.07263  -2.361 0.022637 *  
data[, 7]      0.27577    0.11750   2.347 0.023389 *  
data[, 14]     4.11264    0.96517   4.261 0.000103 ***
data[, 15]   -15.69347    4.80593  -3.265 0.002094 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 28.97 on 45 degrees of freedom
  (22 observations deleted due to missingness)
Multiple R-squared:  0.6968,	Adjusted R-squared:  0.6564 
F-statistic: 17.24 on 6 and 45 DF,  p-value: 3.155e-10

每次剔除p值最大的自变量，直至所有自变量后面都有*号即可。