how to find correlation coefficient in a for loop that is to be repeated 5000 times? and save the statistic - r

Question

for 2 independent normally distributed variables x and y, they are found using x = rnorm(50) and y = rnorm(50). calculate the correlation 5000 times and save the result each time. What is the likelihood that a correlation with absolute value greater than 0.3 is computed? (default set.seed(42) and to plot a histogram of the coefficient spread)
This is what i have tried so far...
set.seed(42)
n <- 50 #length of random sequence
x_norm <- rnorm(n)
y_norm <- rnorm(n)
nrun <- 5000
corr <- numeric(nrun)
for (i in 1:nrun) {
corrxy <- cor(x_norm,y_norm)
corr[i] <- sum(abs(corrxy > 0.3)) / n #save statistic in the vector
}
hist(corr)
it is expected that i get 5000 different coefficient numbers saved in [i], and when plotted using hist(0), these coefficients should follow approx a normal distribution. but i do not understand how the for loop works and how to incorporate the value of coefficient being greater than 0.3.

Answer 1

I think you were nearly there. You just had to shift some code outside and inside the for loop.
You want new data for each run of the loop (otherwise you get the same correlation 5000 times) and you need to save the correlation each time the loop runs. This results in a vector of 5000 correlations which you can use to look at the proportion of correlations (divide by the number of runs, not the number of observations) that are higher than .3 outside of the for loop.
Edit: One final correction is needed in the bracketing of the absolute function. You want to find the absolute correlations > .3 not the absolute value of corrxy > .3.
set.seed(42)
n <- 50 #length of random sequence
nrun <- 5000
corrxy <- numeric(nrun) # The correlation is the statistic you want to save
for (i in 1:nrun) {
x_norm <- rnorm(n) # Compute a new dataset for each run (otherwise you get the same correlation)
y_norm <- rnorm(n)
corrxy[i] <- cor(x_norm,y_norm) # Calculate the correlation
}
hist(corrxy)
sum(abs(corrxy) > 0.3) / nrun # look at the proportion of runs that have cor > .3
Below is the resulting histogram of the 5000 correlations. The proportion of correlations that is higher than |.3| is 0.034 in this case.

Answer 2

Here's another way of doing this kind of simulations without explicitly calling a loop:
Define first your simulation:
my_sim <- function(n) { # n is the norm distribution size
x <- rnorm(n)
y <- rnorm(n)
corrxy <- cor(x, y)
corrxy # return the correlation (single value)
}
Now we can call this function many times with replicate():
set.seed(123)
nrun <- 10
my_results <- replicate(nrun, my_sim(n=50))
#my_results
# [1] -0.0358698314 -0.0077403045 -0.0512509071 -0.0998484901 0.1230261286 0.1001124010 -0.0002023124
# [8] 0.2017120443 0.0644662387 0.0567232640
Now in my_results you have all the correlations from each simulations (just 10 for example).
And you can compute your statistics:
sum(abs(my_results)> 0.3) / nrun # nrun is 10
or plot:
hist(my_results)