数据挖掘 R 回归分析

• List item
  回归分析是统计的核心，通常指使用一个或多个预测变量来预测响应变量。
  回归分析也通常选择与响应变量有关的变量来作为解释变量，以此来描述两者之间的关系。也可以生成一个等式，用解释变量来解释响应变量。
  在R 中封装了lm()函数来实现单变量，多变量回归。
  R中符号的说明如下：
  

data(women)
fit<-lm(women$height~women$weight,data=women)
 summary(fit)

Call:
lm(formula = women$height ~ women$weight, data = women)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.83233 -0.26249  0.08314  0.34353  0.49790 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  25.723456   1.043746   24.64 2.68e-12 ***
women$weight  0.287249   0.007588   37.85 1.09e-14 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.44 on 13 degrees of freedom
Multiple R-squared:  0.991,	Adjusted R-squared:  0.9903 
F-statistic:  1433 on 1 and 13 DF,  p-value: 1.091e-14
fitted(fit)
       1        2        3        4        5        6 
58.75712 59.33162 60.19336 61.05511 61.91686 62.77861 
       7        8        9       10       11       12 
63.64035 64.50210 65.65110 66.51285 67.66184 68.81084 
      13       14       15 
69.95984 71.39608 72.83233 
residuals(fit)
          1           2           3           4           5 
-0.75711680 -0.33161526 -0.19336294 -0.05511062  0.08314170 
          6           7           8           9          10 
 0.22139402  0.35964634  0.49789866  0.34890175  0.48715407 
         11          12          13          14          15 
 0.33815716  0.18916026  0.04016335 -0.39608278 -0.83232892 

多项式回归
可以添加一项二次项sq（X）来提高回归的预测精度

fit<-lm(women$weight~women$height+I(women$height^2),data=women)
summary(fit)

Call:
lm(formula = women$weight ~ women$height + I(women$height^2), 
    data = women)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.50941 -0.29611 -0.00941  0.28615  0.59706 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)       261.87818   25.19677  10.393 2.36e-07 ***
women$height       -7.34832    0.77769  -9.449 6.58e-07 ***
I(women$height^2)   0.08306    0.00598  13.891 9.32e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3841 on 12 degrees of freedom
Multiple R-squared:  0.9995,	Adjusted R-squared:  0.9994 
F-statistic: 1.139e+04 on 2 and 12 DF,  p-value: < 2.2e-16

分析结果可以看书，回归系数都非常显著，模型方差解释率已经增加到了99.9%。
我们也可以可视化一下：
plot(women $height,women$weight)
lines(women$height,fitted(fit))