bias variance decomposition

from sklearn.feature_selection import SelectKBest, f_regression

# Select the top 10 features using SelectKBest
selector = SelectKBest(score_func=f_regression, k=10)
X_train_selected = selector.fit_transform(X_train, y_train)
X_test_selected = selector.transform(X_test)

# Train a linear regression model on the selected features
lr_selected = LinearRegression()
lr_selected.fit(X_train_selected, y_train)

# Evaluate the model using cross-validation
cv_scores_selected = cross_val_score(lr_selected, X_train_selected, y_train, cv=5, scoring='neg_mean_squared_error')
cv_scores_selected = -cv_scores_selected

# Calculate the average MSE and its standard deviation
avg_mse_selected = cv_scores_selected.mean()
std_mse_selected = cv_scores_selected.std()

print(f"Selected Features Cross-Validation MSE: {avg_mse_selected:.2f} +/- {std_mse_selected:.2f}")