How to simulate 10000 datasets in R with 30 observations each and create histogram with F-statistics and superimpose F-distribution? - r

Question

What am I doing wrong in my following code?
My simulation study module asks me to use simple linear regression i.e., p=2. I'm supposed to generate B=10,000 independent simulations from a simple linear regression with N= 30 (number of observations) and B_0=B_1=0. For each simulation, one creates a dataset and extracts the F-statistic for the global F test. Then one should verify that the histogram resembles that of an F(1, N-2) distribution. I am confused whether my loop is the problem or my ggplot code or if it's a mix of the two.
My current output looks like:
n=30
F1 = array(NA,dim=Nsim)
for(i in 1:Nsim){
X=rnorm(n,0,sd=sigmax) # generate x
res=rnorm(n,0,sd=sigma) # generate sigma
Y=b0+b1*X+res # generate Y
mod = lm(Y~X)
res = summary(mod)
F1[i]=res$fstatistic[1] # F statistic
}
df<-tibble(F1=F1)
x=seq(1,10,1)
y=df(x,df1 = 1, df2 = n-2)
df2 = tibble(x=x,y=y)
ggplot() + geom_histogram(data=df, aes(x=F1,y=..density..), binwidth=0.1,color="black", fill="white")+
xlab("F") +
xlim(c(NA,10))+
ggtitle("n=30") +
geom_line(data = df2, aes(x = x, y = y), color = "red")

Answer 1

There are a number of problems with your code - you've left out a number of variable declarations so the code doesn't run as-is. Below I've added a number of variables to make the code run, but you should check what I've done to see if it is consistent with your intentions.
For your plot, the histogram is fine, but the line is only defined for x in the range [1, 10] in integer steps, but your histogram goes from 0 to 10 in steps of 0.1. If you change the range of x for your line to match the histogram, the plot covers the range and has a point at each histogram bar.
library(tibble)
library(ggplot2)
n=30
Nsim = 10000 ### added
sigmax = 1.0 ### added
sigma = 1.0 ### added
b0 = 0 ### added
b1 = 0 ### added
F1 = array(NA,dim=Nsim)
for(i in 1:Nsim){
X=rnorm(n,0,sd=sigmax) # generate x
res=rnorm(n,0,sd=sigma) # generate sigma
Y=b0+b1*X+res # generate Y
mod = lm(Y~X)
res = summary(mod)
F1[i]=res$fstatistic[1] # F statistic
}
df<-tibble(F1=F1)
x=seq(0,10,.10) ### changed to range from 0 to 10 in steps of 0.1
y=df(x,df1 = 1, df2 = n-2)
df2 = tibble(x=x,y=y)
ggplot() + geom_histogram(data=df, aes(x=F1,y=..density..), binwidth=0.1,color="black", fill="white")+
xlab("F") +
xlim(c(NA,10))+
ggtitle("n=30") +
geom_line(data = df2, aes(x = x, y = y), color = "red")