Linear Regression in For Loop - r

Question

I get an error for running the code below. I haven not figured out what I am doing wrong - sorry if it is obvious, I am new to R. The idea is to "generate" 100 regressions and output the estimated slope 100 times.
set.seed(21)
x <- seq(1,40,1)
for (i in 1:100 ) {
y[i] = 2*x+1+5*rnorm(length(x))
reg[i] <- lm(y[i]~x)
slp[i] <- coef(reg[i])[2]
}

Answer 1

There are several problems with the way you use indexing. You'll probably need to spend some time again on a short tutorial about R for beginners, and not "rush" to loops and regressions...
In the end, you want to have a vector containing 100 slope values. You need to define this (empty) vector 'slp' prior to running the loop and then fill each ith element with its value in the loop.
On the other hand,
1) at each iteration you don't fill the ith element of y but create a whole new vector y with as many values as there are in x...
2) you don't need to keep every regression so you don't need to "index" your object reg.
So here it is:
set.seed(21)
x <- seq(1,40,1)
slp=rep(NA,100)
for (i in 1:100) {
y = 2*x+1+5*rnorm(length(x))
reg <- lm(y~x)
slp[i]<-coef(reg)[2]
}
print(slp)

Answer 2

In addition to the other answers, there is a better (more efficient and easier) possibility. lm accepts a matrix as input for y:
set.seed(21)
y <- matrix(rep(2*x + 1, 100) + 5 *rnorm(length(x) * 100), ncol = 100)
reg1 <- lm(y ~ x)
slp1 <- coef(reg1)[2,]
all.equal(slp, slp1)
#[1] TRUE
If you had a function other than lm and needed a loop, you should use replicate instead of a for loop:
set.seed(21)
slp2 <- replicate(100, {
y = 2*x+1+5*rnorm(length(x))
reg <- lm(y~x)
unname(coef(reg)[2])
})
all.equal(slp, slp2)
#[1] TRUE

Answer 3

You need to create the matrix/vector y, reg, slp first, to be able to write to position i like: y[i] <-. You can do something along:
set.seed(21)
x <- seq(1,40,1)
slp <- numeric(100)
for (i in 1:100 ) {
y <- 2*x+1+5*rnorm(length(x))
reg <- lm(y~x)
slp[i] <- coef(reg)[2]
}
> slp
[1] 2.036344 1.953487 1.949170 1.961897 2.098186 2.027659 2.002638 2.107278
[9] 2.036880 1.980800 1.893701 1.925230 1.927503 2.073176 2.101303 1.943719
...
[97] 1.966039 2.041239 2.063801 2.066801