added HW4

HW04/multiple_regression.stan

@@ -0,0 +1,28 @@
+data {
+  int<lower=0> N;             // Number of training samples
+  int<lower=0> M;             // Number of predictors (3: bmi, age, children)
+  matrix[N, M] X;             // Training predictors
+  vector[N] y;                // Training target (charges)
+  int<lower=0> N_test;        // Number of test samples
+  matrix[N_test, M] X_test;   // Test predictors
+}
+parameters {
+  real alpha;                 // Intercept
+  vector[M] beta;             // Regression coefficients
+  real<lower=0> sigma;        // Noise term
+}
+model {
+  // Priors
+  sigma ~ inv_gamma(2, 2);
+  alpha ~ normal(0, 10);
+  beta ~ normal(0, 1);
+
+  // Likelihood
+  y ~ normal(alpha + X * beta, sigma);
+}
+generated quantities {
+  vector[N_test] y_pred;      
+  for (i in 1:N_test) {
+    y_pred[i] = normal_rng(alpha + X_test[i] * beta, sigma);
+  }
+}