Question

PLEASE HELP WITH THE FOLLOWING R CODE!

I NEED HELP WITH PART C AND D,

provided is part a and b!!!!

a)

chiNum <- c()
for (i in 1:1000)
{
g1 <- rnorm(20,10,4)
g2 <- rnorm(20,10,4)
g3 <- rnorm(20,10,4)
g4 <- rnorm(20,10,4)
g5 <- rnorm(20,10,4)
g6 <- rnorm(20,10,4)
mse <- (var(g1)+var(g2)+var(g3)+var(g4)+var(g5)+var(g6))/6
M <- (mean(g1)+mean(g2)+mean(g3)+mean(g4)+mean(g5)+mean(g6))/6
msb <- ((((mean(g1)-M)^2)+((mean(g2)-M)^2)+((mean(g3)-M)^2)+((mean(g4)-M)^2)+((mean(g5)-M)^2)+((mean(g6)-M)^2))/5)*20
chiNum[i] <- msb/mse
}
# plot a histogram of F statistics
h <- hist(chiNum,plot=FALSE)
ylim <- (range(0, 0.8))
x <- seq(0,6,0.01)
hist(chiNum,freq=FALSE, ylim=ylim)
curve(df(x,5,114),add=T) # df = 6groups-1=5, 20*6 data - 6 groups = 114

b)

s <- rnorm(1000)
sum(s^2)
s <- rnorm(1000)
x <- rep(NA, 1000)
for (j in 1:1000)
{
x[j] <-sum(rnorm(10)^2)
    }
h <- hist(x, plot=F)
ylim <- range(0, h$density, 0.10)
hist(x, freq=F, ylim=ylim)
curve(dchisq(x,df=20), add = TRUE)

Answer 1

(c)

I have generated 1000 draws of $\chi^2$ distribution with DF = 5 and DF = 20 as below.

> chiNum <- rchisq(1000, 5)
> chiDen <- rchisq(1000, 20)

We know that F distribution with DF = d1, d2 is ratio of Chi-square distribution as given below

F = (U₁ / d₁) / (U₂ / d₂)

where U₁ and U₂ have chi-squared distributions with d₁ and d₂ degrees of freedom respectively,

F distribution with DF = 5, 20 is simulated as below,

F.sim <- (chiNum / 5) / (chiDen / 20)

(d)

Simulate 1000 draws of F distribution with DF = 5, 20

F.dst <- rf(1000, 5, 20)

Ran the below commands to compare both distributions.

> op <- par(mfrow=c(2,1),mar=c(2,3,1.5,0.5))
> plot(density(F.sim), main = "Simulated F distribution")
> plot(density(F.dst), main = "Sampled F distribution")

Simulated F distribution 4 Sampled F distribution 2 4

Both the distribution looks similar.