New User of Stan Model 'many' regressions

I am new at using Stan in R and want to know if what I am doing is possible or I am probably
replicating unnecessary code. My goal is to understand if there is a way to create a model that is a substitute
than running 1,000 times a stan_glm regression.
My data is as follows:
I have 1,000 different funds. Each fund has its own vector of returns (dependent variable), 240 values.
Each regression is ran against the same matrix of independent variables. I have a total of 3 independent

Using stan_glm it looks like this:
returns ← replicate(1000, rnorm(240,0,1)) #That way a have the 1,000 vectors with their returns
independenteVar ← replicate(3, rnorm(240,0,1))
stan_glm(returns[,i] ~ ., data = independentVar, refresh = 0) #I would use a loop and go through all the funds (i 1:1000)

So far here, I am running this 1,000 times (I do this as a Local Job, since it takes quite some time).
The idea of this is that I would have results for each fund based on their returns.
Now, is there a way to do this faster/more efficient with a proper Stan model.

In Stan I have this, but this is only for oen fund:
data {
int<lower=0> N; //Number of observations 240
int<lower=0> K; //Number of predictors, 3, all except the intercept
matrix[N, K] X; // predictor matrix
vector[N] y; // outcome vector
parameters {
real alpha; // intercept
vector[K] beta; // coefficients for predictors
real<lower=0> sigma; // error scale
model {
y ~ normal(alpha + X * beta, sigma); // target density
When I run this, it is only for one fund. I have to run it 1,000 times to have the 1,000 models. Somethins tells me this is not the correct way.

If more RC is necessary, I will try my best. As of now I do not care much about the priors, I am more interested in knowing how to do this.
Also, any reference to read, I will apreciate it. I felt that the Stan exampled do not solve my question, although,
I am probably wrong.
Thank you.

What you describe as many independent regressions can be described as an “unpooled” hierarchical model. See here for a tutorial (esp. why it makes sense to employ partial pooling instead)


Thanks for your reply. I will go thoruoghly to what you pointed me.