Linear Regression

data.json

{
  "N": 10,
  "x": [
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9,
    10
  ],
  "y": [
    1.175246231294085,
    2.407986514262124,
    3.722795906507695,
    4.913215145535075,
    6.086548493077272,
    7.278023025499204,
    8.587414785721538,
    9.990151691417916,
    11.251678394115302,
    12.406899413685272
  ]
}

main.stan

data {
    int<lower=0> N;
    vector[N] x;
    vector[N] y;
}
parameters {
    real alpha;
    real beta;
    real<lower=0> sigma;
}
model {
    y ~ normal(alpha + beta * x, sigma);
}