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You are required to investigate the sampling distribution of the F-statistic for testing the overall significance of the regression (assuming the null hypothesis holds) in the following specific situation:

y-hat = b0 + b1*x1 + b2*x2 + b3*x3 + b4*x4
sigma = 2

Using this underlying model, you are required to write R code that will produce a histogram that illustrates the sampling distribution of the F-statistic. Your answer should include your R code and a histogram that illustrates the sampling distribution.

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关键词：distribution significance Illustrate underlying regression hypothesis following situation required specific

x1=1:1000   
set.seed(99900)
x2=runif(length(x1),1,50000)
set.seed(1)
x3=runif(length(x1),2000,80000)
set.seed(500)
x4=runif(length(x1),3566,60000)
n=length(x1)
y=rep(0,n)
numsamp=1000
f=rep(0,numsamp)
for(i in 1:numsamp){errors=rnorm(n,0,2)
y=1+2*x1+3*x2+4*x3+5*x4+errors
slrfit=lm(y~x1+x2+x3+x4)
b=anova(slrfit)
f[i]=mean(b[1,2],b[2,2],b[3,2],b[4,2])/b[5,3]}
hist(f)

我的这个有什么问题？可是我就是解不到，因为我拿到的图是normal的，可是F distribution不应该是normal。

代码过程写的比较简单，希望对你有用

1. F_value=c()
   
2. for(i in 1:1000){
   
3.    error<-rnorm(1000,mean=0,sd=2)
   
4.    x1<-runif(1000,1,5)
   
5.    x2<-runif(1000,5,10)
   
6.    x3<-runif(1000,10,20)
   
7.    y_value<-x1+x2+x3+error
   
8.    y<-x1+x2+x3
   
9.    mymodel<-lm(y_fit~x1+x2+x3)
   
10.    res<-residuals(mymodel)
    
11.    mean_model<-mean(y_value)
    
12.    SSR<-sum((fitted(mymodel)-mean_model)^2)
    
13.    SSE<-sum((y_value-fitted(mymodel))^2)
    
14.    F_value<-c(F_value,SSR/(SSE/(1000-2)))
    
15.                    }
    
16. hist(F_value,breaks=20)

复制代码

simF <- function(N) {
        X <- matrix(rnorm(N*4), nrow=N, ncol=4)
        y <- 1 + rnorm(N, 0, 2)
        fit <- lm(y~X)
        summary(fit)$fstatistic[1]       
}

Fs <- sapply(1:10000, function(x) simF(100))

hist(Fs, breaks=50, freq=F)
x <- seq(0, 6, length.out=1000)
y <- df(x, 4, 95)
lines(x, y, col=2)