Question

Suppose we want to simulate the following linear model: Bo + BiX; + Ei where ti~ N(0,22). Assume Xi~ N(0,12), Bo = 0.5 and 31 = 2. 1. Fix the sample size at 10, and the number of simulations at 100. For each simulation obtain a least squares estimation of B1 from the linear regression model (using the Im function). You may find the following lines of code useful for your simulation: set.seed (1002224444) e<-rnorm(n, 0,2) x<-rnorm(n, 0, 1) y<-0.5 + 2*x + e model<- Im(yºx) n.sim=100 n=10

I need to plot a histogram for estimates of Beta_0 and Beta_1 (over the 100 simulations). I know I can use the coefficients function with the model to display these estimates for each simulation, but how can I access them individually, or save them to a column vector such that I can plot the histogram as needed?

Answer 1

R code:

n.sim=100
b0=1:n.sim*0
b1=1:n.sim*0
for(i in 1:n.sim)
{
e=rnorm(10,0,2)
x=rnorm(10,0,1)
y=0.5+2*x+e
model=lm(y~x)
b0[i]=model$coefficients[1]
b1[i]=model$coefficients[2]
}
par(mfrow=c(1,2))
hist(b0,xlab=expression(beta[0]),main=expression(beta[0]),freq=FALSE)
hist(b1,xlab=expression(beta[1]),main=expression(beta[1]),freq=FALSE)

Density 0.0 0.1 0.2 0.3 0.4 0.5 0.6 - -1.5 -0.5 BO Во 0.5 - 1.5 Density 0.0 0.1 0.2 0.3 0.4 0.5 - 0 1 B1 N 1 B1 3 1 +