TODO: Polynomial Regression with Ordinary Least Squares (OLS) and Regularization *Please complete the TODOs. * !pip install wget import os import random import traceback from pdb import set_trace import sys import numpy as np from abc import ABC, abstractmethod import traceback from util.timer import Timer from util.data import split_data, feature_label_split, Standardization from util.metrics import mse from datasets.HousingDataset import HousingDataset class BaseModel(ABC):     """ Super class for ITCS Machine Learning Class"""     @abstractmethod     def fit(self, X, y):         pass     @abstractmethod     def predict(self, X):         pass class LinearModel(BaseModel):     """         Abstract class for a linear model         Attributes         ==========         w       ndarray                 weight vector/matrix     """     def __init__(self):         """             weight vector w is initialized as None         """         self.w = None     # check if the matrix is 2-dimensional. if not, raise an exception     def _check_matrix(self, mat, name):         if len(mat.shape) != 2:             raise ValueError(f"Your matrix {name} shape is not 2D! Matrix {name} has the shape {mat.shape}")     # add a biases     def add_ones(self, X):         """             add a column basis to X input matrix         """         self._check_matrix(X, 'X')         return np.hstack((np.ones((X.shape[0], 1)), X))     ####################################################     #### abstract funcitons ############################     @abstractmethod     def fit(self, X: np.ndarray, y: np.ndarray):         """             train linear model             Args:                 X:  Input data                 y:  targets/labels         """         pass     @abstractmethod     def predict(self, X: np.ndarray):         """             apply the learned model to input X             parameters             ----------             X     2d array                   input data         """         pass class PolynomialRegressionRegularized(PolynomialRegression):     """         Performs polynomial regression with l2 regularization using the ordinary least squares algorithm              attributes:             w (np.ndarray): weight matrix that is inherited from OrdinaryLeastSquares                          degree (int): the number of polynomial degrees to include when adding                 polynomial features.     """     def __init__(self, degree: int, lamb: float):         super().__init__(degree)         self.lamb = lamb              def fit(self, X: np.ndarray, y: np.ndarray) -> None:         """ Used to train our model to learn optimal weights.                      TODO:                 Finish this method by adding code to perform polynomial regression using                 the closed form solution OLS with L2 regularization to learn                  the weights `self.w`.                              Hint:                 Add the bias after computing polynomial features. Typically we don't want                 to include the bias when computing polynomial features.         """         pass # TODO replace this line with your code          def predict(self, X: np.ndarray) -> np.ndarray:         """ Used to make a prediction using the learned weights.             TODO:                 This predict() method is exactly the same as the predict() method in the above class `PolynomialRegression`,                  so you can just simply copy them here.          """         # TODO (REQUIRED) Add code below         # TODO (REQUIRED) Store predictions below by replacing np.ones()         y_hat = np.ones([len(X), 1])         return y_hat