task 1.4 without plots

A2.py

@@ -1,10 +1,11 @@
 import numpy as np
 import matplotlib.pyplot as plt
 import warnings
+from sklearn.model_selection import train_test_split
 warnings.filterwarnings('ignore')
 
 #reproducibility
-np.random.seed(1)
+np.random.seed(2)
 
 #__________________________________________________________________________________
 #Task 1
@@ -150,13 +151,46 @@ for i, D in enumerate(D_i):
         plt.ylabel('y')
     if i >= 9:  
         plt.xlabel('x')
-        
-
 
 plt.tight_layout()
 plt.show()
 
-
-
 #__________________________________________________________________________________
 #1.4 Model Selection
+
+# Split the data into training and validation sets 
+x_train, x_val, y_train, y_val = train_test_split(x, y_noisy, test_size=0.2, random_state=42)
+
+# range of basis functions to test
+D_values = list(range(0, 46))  # 0 to 45
+
+# Initialize arrays to store errors
+train_sse = []
+val_sse = []
+
+
+# For each number of basis functions
+for D in D_values:
+    # Create and fit the model
+    model = GaussianRegression(sigma=1.0)
+    model.fit(x_train, y_train, D)
+    
+    # predict on training then validation 
+    yh_train = model.predict(x_train)
+    yh_train = yh_train.flatten() if yh_train.ndim > 1 else yh_train
+    
+    yh_val = model.predict(x_val)
+    yh_val = yh_val.flatten() if yh_val.ndim > 1 else yh_val
+    
+    # compute SSE
+    sse_train = np.sum((y_train - yh_train)**2)
+    sse_val = np.sum((y_val - yh_val)**2)
+    
+    train_sse.append(sse_train)
+    val_sse.append(sse_val)
+    
+    print(f"D={D:2d}: Train SSE = {sse_train:8.2f}, Val SSE = {sse_val:8.2f}")
+
+
+
+