In the linear regression portion of the Stan user guide, it states that the following are “statistically equivalent”. Could someone please clarify why this is the case?

```
model {
y ~ normal(x * beta + alpha, sigma); // likelihood
}
```

vs.

```
model {
for (n in 1:N) {
y[n] ~ normal(x[n] * beta, sigma);
}
}
```

How does the alpha get incorporated into beta and x[n] in the second model code block?

Thanks!