R语言与概率统计(三) 多元统计分析（上）

> #############6.2一元线性回归分析
> x<-c(0.10,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.20,0.21,0.23)
> y<-c(42.0,43.5,45.0,45.5,45.0,47.5,49.0,53.0,50.0,55.0,55.0,60.0)
> plot(x~y)
> lm.sol<-lm(y ~ x)
> summary(lm.sol)

Call:
lm(formula = y ~ x)

Residuals:
    Min      1Q  Median      3Q     Max
-2.0431 -0.7056  0.1694  0.6633  2.2653 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   28.493      1.580   18.04 5.88e-09 ***
x            130.835      9.683   13.51 9.50e-08 ***    #所以y=130.835x+28.493,***表示显著性水平，*越多越好
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1    #显著性水平

Residual standard error: 1.319 on 10 degrees of freedom
Multiple R-squared:  0.9481,	Adjusted R-squared:  0.9429
F-statistic: 182.6 on 1 and 10 DF,  p-value: 9.505e-08    ￥F检验，检验所有系数全是0的假设

> new=data.frame(x=0.16)#怎么预测多个数值的结果？
> lm.pred=predict(lm.sol,new,interval='prediction',level=0.95)
> lm.pred
       fit      lwr      upr
1 49.42639 46.36621 52.48657

先求对数，再*100

> X<-matrix(c(
+   194.5, 20.79, 1.3179, 131.79,
+   194.3, 20.79, 1.3179, 131.79,
+   197.9, 22.40, 1.3502, 135.02,
+   198.4, 22.67, 1.3555, 135.55,
+   199.4, 23.15, 1.3646, 136.46,
+   199.9, 23.35, 1.3683, 136.83,
+   200.9, 23.89, 1.3782, 137.82,
+   201.1, 23.99, 1.3800, 138.00,
+   201.4, 24.02, 1.3806, 138.06,
+   201.3, 24.01, 1.3805, 138.05,
+   203.6, 25.14, 1.4004, 140.04,
+   204.6, 26.57, 1.4244, 142.44,
+   209.5, 28.49, 1.4547, 145.47,
+   208.6, 27.76, 1.4434, 144.34,
+   210.7, 29.04, 1.4630, 146.30,
+   211.9, 29.88, 1.4754, 147.54,
+   212.2, 30.06, 1.4780, 147.80),
+   ncol=4, byrow=T,
+   dimnames = list(1:17, c("F", "h", "log", "log100")))#如何改变行和列的名称，如何按列排列数据？
>
> forbes<-data.frame(X)#把矩阵X转化为数据框
> plot(forbes$F, forbes$log100)#画出两个变量之间的散点图，观察是否存在线性趋势；学习
> #如何从数据框里面调取向量。怎么写坐标轴的名字和标题？
> #如何从数据框里面调取向量。怎么写坐标轴的名字和标题？
> lm.sol<-lm(log100~F, data=forbes)
> summary(lm.sol)

Call:
lm(formula = log100 ~ F, data = forbes)

Residuals:
     Min       1Q   Median       3Q      Max
-0.32261 -0.14530 -0.06750  0.02111  1.35924 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept) -42.13087    3.33895  -12.62 2.17e-09 ***
F             0.89546    0.01645   54.45  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3789 on 15 degrees of freedom
Multiple R-squared:  0.995,	Adjusted R-squared:  0.9946
F-statistic:  2965 on 1 and 15 DF,  p-value: < 2.2e-16

> abline(lm.sol)#在散点图上添加直线

#残差检验
y.res<-residuals(lm.sol);plot(y.res)#画出残差图
text(12,y.res[12], labels=12,adj=1.2)

#异常值的判断
library(car)
outlierTest(lm.sol)

> outlierTest(lm.sol)
   rstudent unadjusted p-value Bonferroni p
12 12.40369         6.1097e-09   1.0386e-07

> plot(lm.sol)
Hit <Return> to see next plot: return
Hit <Return> to see next plot: return
Hit <Return> to see next plot: return
Hit <Return> to see next plot: return

##################################6.6多元回归分析
blood<-data.frame(
  X1=c(76.0, 91.5, 85.5, 82.5, 79.0, 80.5, 74.5,
       79.0, 85.0, 76.5, 82.0, 95.0, 92.5),
  X2=c(50, 20, 20, 30, 30, 50, 60, 50, 40, 55,
       40, 40, 20),
  Y= c(120, 141, 124, 126, 117, 125, 123, 125,
       132, 123, 132, 155, 147)
)

#多元回归分析时，最好先检查变量之间的相关性
cor(blood)
library(car)
scatterplotMatrix(blood,spread=F,lty.smooth=2,main='blood plot matrix')

　　

> lm.sol<-lm(Y ~ X1+X2, data=blood)
> summary(lm.sol)

Call:
lm(formula = Y ~ X1 + X2, data = blood)

Residuals:
    Min      1Q  Median      3Q     Max
-4.0404 -1.0183  0.4640  0.6908  4.3274 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept) -62.96336   16.99976  -3.704 0.004083 **
X1            2.13656    0.17534  12.185 2.53e-07 ***
X2            0.40022    0.08321   4.810 0.000713 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.854 on 10 degrees of freedom
Multiple R-squared:  0.9461,	Adjusted R-squared:  0.9354
F-statistic: 87.84 on 2 and 10 DF,  p-value: 4.531e-07

> #回归系数的区间估计
> confint(lm.sol)
                   2.5 %      97.5 %
(Intercept) -100.8411862 -25.0855320
X1             1.7458709   2.5272454
X2             0.2148077   0.5856246
> #6.8预测
> new=data.frame(X1=80,X2=40)#怎么做多组预测？
> lm.pred=predict(lm.sol,new,interval='prediction',level=0.95)
> lm.pred
       fit      lwr      upr
1 123.9699 117.2889 130.6509

 

所有代码：

#############6.2一元线性回归分析
x<-c(0.10,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.20,0.21,0.23)
y<-c(42.0,43.5,45.0,45.5,45.0,47.5,49.0,53.0,50.0,55.0,55.0,60.0)
plot(x~y)
lm.sol<-lm(y ~ x)
summary(lm.sol)
#6.4做预测
new=data.frame(x=0.16)#怎么预测多个数值的结果？
lm.pred=predict(lm.sol,new,interval='prediction',level=0.95)
lm.pred
######
X<-matrix(c(
  194.5, 20.79, 1.3179, 131.79,
  194.3, 20.79, 1.3179, 131.79,
  197.9, 22.40, 1.3502, 135.02,
  198.4, 22.67, 1.3555, 135.55,
  199.4, 23.15, 1.3646, 136.46,
  199.9, 23.35, 1.3683, 136.83,
  200.9, 23.89, 1.3782, 137.82,
  201.1, 23.99, 1.3800, 138.00,
  201.4, 24.02, 1.3806, 138.06,
  201.3, 24.01, 1.3805, 138.05,
  203.6, 25.14, 1.4004, 140.04,
  204.6, 26.57, 1.4244, 142.44,
  209.5, 28.49, 1.4547, 145.47,
  208.6, 27.76, 1.4434, 144.34,
  210.7, 29.04, 1.4630, 146.30,
  211.9, 29.88, 1.4754, 147.54,
  212.2, 30.06, 1.4780, 147.80),
  ncol=4, byrow=T,
  dimnames = list(1:17, c("F", "h", "log", "log100")))#如何改变行和列的名称，如何按列排列数据？

forbes<-data.frame(X)#把矩阵X转化为数据框
plot(forbes$F, forbes$log100)#画出两个变量之间的散点图，观察是否存在线性趋势；学习
#如何从数据框里面调取向量。怎么写坐标轴的名字和标题？
lm.sol<-lm(log100~F, data=forbes)
summary(lm.sol)
abline(lm.sol)#在散点图上添加直线

#残差检验
y.res<-residuals(lm.sol);plot(y.res)#画出残差图
text(12,y.res[12], labels=12,adj=1.2)

#异常值的判断
library(car)
outlierTest(lm.sol)

#去除异常值
i<-1:17; forbes12<-data.frame(X[i!=12, ])
lm12<-lm(log100~F, data=forbes12)
summary(lm12)

##################################6.6多元回归分析
blood<-data.frame(
  X1=c(76.0, 91.5, 85.5, 82.5, 79.0, 80.5, 74.5,
       79.0, 85.0, 76.5, 82.0, 95.0, 92.5),
  X2=c(50, 20, 20, 30, 30, 50, 60, 50, 40, 55,
       40, 40, 20),
  Y= c(120, 141, 124, 126, 117, 125, 123, 125,
       132, 123, 132, 155, 147)
)

#多元回归分析时，最好先检查变量之间的相关性
cor(blood)
library(car)
scatterplotMatrix(blood,spread=F,lty.smooth=2,main='blood plot matrix')

lm.sol<-lm(Y ~ X1+X2, data=blood)
summary(lm.sol)

#回归系数的区间估计
confint(lm.sol)

#6.8预测
new=data.frame(X1=80,X2=40)#怎么做多组预测？
lm.pred=predict(lm.sol,new,interval='prediction',level=0.95)
lm.pred