修正异方差的方法

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library(lmtest)
## Loadingrequired package: zoo
##
## Attaching package: 'zoo'
## The followingobjects are masked from 'package:base':
##
##     as.Date,as.Date.numeric
library(MASS)
library(car)
## Loadingrequired package: carData
library(caret)
## Warning:package 'caret' was built under R version 3.6.2
## Loadingrequired package: lattice
## Loadingrequired package: ggplot2
x      = rep(1:100)
a      = 10
b      = 2
sigma2_2 = x*10
eps    = rnorm(x,mean=0,sd=sqrt(sigma2_2))
y2      = a+b*x+ eps
model2    = lm(y2~ x)

sigma2_3 = x^2*10
eps    = rnorm(x,mean=0,sd=sqrt(sigma2_3))
y3      = a+b*x+ eps
model3    = lm(y3~ x)

bptest(model2)
##
##  studentizedBreusch-Pagan test
##
## data:  model2
## BP = 17.713, df = 1, p-value = 2.569e-05
bptest(model3)
##
##  studentizedBreusch-Pagan test
##
## data:  model3
## BP = 22.914, df = 1, p-value = 1.694e-06
model2_new <- lm(y2~x, weights = 1/sqrt(x*10))
summary(model2_new)
##
## Call:
## lm(formula = y2 ~ x, weights = 1/sqrt(x * 10))
##
## Weighted Residuals:
##     Min      1Q Median      3Q     Max
## -8.8801 -3.0583 0.1019  2.7379 12.0636
##
## Coefficients:
##            Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 13.1094     2.7914   4.696 8.63e-06 ***
## x            1.9094     0.0598  31.929 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.287 on 98 degrees offreedom
## Multiple R-squared: 0.9123, Adjusted R-squared: 0.9114
## F-statistic: 1019 on 1 and 98 DF,  p-value:< 2.2e-16

bptest(model2_new)
##
##  studentizedBreusch-Pagan test
##
## data: model2_new
## BP = 17.713, df = 1, p-value = 2.569e-05
model3_new <- lm(y3~x, weights = 1/x)
summary(model3_new)
##
## Call:
## lm(formula = y3 ~ x, weights = 1/x)
##
## Weighted Residuals:
##    Min     1Q Median     3Q   Max
## -57.00 -14.29  1.27  13.17  54.10
##
## Coefficients:
##            Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 11.8506    13.2823   0.892   0.374   
## x            2.2725     0.4257   5.338 6.07e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 23.79 on 98 degrees offreedom
## Multiple R-squared: 0.2253, Adjusted R-squared: 0.2174
## F-statistic: 28.5 on 1 and 98 DF,  p-value:6.068e-07

bptest(model3_new)
##
##  studentizedBreusch-Pagan test
##
## data: model3_new
## BP = 22.914, df = 1, p-value = 1.694e-06
y2BCMod<-BoxCoxTrans(y2)
print(y2BCMod)
## Box-CoxTransformation
##
## 100 data points used to estimate Lambda
##
## Input data summary:
##    Min. 1stQu.  Median    Mean 3rd Qu.    Max.
##   12.24   64.51 105.43  109.66  156.76 269.81
##
## Largest/Smallest: 22
## Sample Skewness: 0.25
##
## Estimated Lambda: 0.7
y2_new=predict(y2BCMod, y2)
Mod2_bc <- lm(y2_new ~ x)
bptest(Mod2_bc)
##
##  studentizedBreusch-Pagan test
##
## data: Mod2_bc
## BP = 8.393, df = 1, p-value = 0.003767
y3BCMod<-BoxCoxTrans(y3+450)
print(y3BCMod)
## Box-CoxTransformation
##
## 100 data points used to estimate Lambda
##
## Input data summary:
##    Min. 1stQu.  Median    Mean 3rd Qu.    Max.
##   120.3   452.1  538.1   576.6   710.6 1169.6
##
## Largest/Smallest: 9.72
## Sample Skewness: 0.626
##
## Estimated Lambda: 0.5
y3_new=predict(y3BCMod, y3)
Mod3_bc <- lm(y3_new ~ x)
bptest(Mod3_bc)
##
##  studentizedBreusch-Pagan test
##
## data: Mod3_bc
## BP = 5.5629, df = 1, p-value = 0.01834

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关键词：异方差 statistic Intercept following required

我想比较box-cox和加权最小二乘法在修正异方差过程中的异同，但不管我用哪种方法，好像效果都不是很好，bptest始终通不过，是我的代码有问题么？还是数据不应该这么生成？有人知道么？