text: """
  MVPD - Linear Regression Model + L2 Regularization 
  """
  import sklearn
  from sklearn import linear_model
  
  def L2_LR(ROI_1_train, ROI_2_train, ROI_1_test, ROI_2_test, alpha):
      """
      Build a linear regression model with L2 regularization.
      """
      # initialize and fit model on training data
      ridgereg = linear_model.Ridge(alpha)
      ridgereg.fit(ROI_1_train, ROI_2_train)
      # predict on test set
      predict_ROI_2_test = ridgereg.predict(ROI_1_test)
      err_LR = predict_ROI_2_test - ROI_2_test
      # coefficients and intercept
      coef = ridgereg.coef_
      intercept = ridgereg.intercept_
  
      return predict_ROI_2_test, err_LR
  
  
  
  