input: 
  import numpy as np
  
  class LinearRegressionModel:
      def __init__(self, input_dim, output_dim):
          """ Initialises the weights and bias of the linear regression model
          Arguments:
              input_dim {int} -- Number of input features
              output_dim {int} -- Number of outputs
          """
          self.weights = np.zeros((input_dim, output_dim))
          self.bias = np.zeros((1, output_dim))
  
      def forward(self, x):
          """ Calculates the forward pass of the linear regression model
          Arguments:
              x {numpy array} -- Input data of size (N, input_dim)
          Returns:
              out {numpy array} -- Output of the linear regression model of size (N, output_dim)
          """
          out = np.dot(x, self.weights) + self.bias
          return out
  
output:     
      def backward(self, x, grad_output, learning_rate):
          """ Calculates the backward pass of the linear regression model and updates the weights and bias
          Arguments:
              x {numpy array} -- Input data of size (N, input_dim)
              grad_output {numpy array} -- Gradient of the loss with respect to the output of size (N, output_dim)
              learning_rate {float} -- Learning rate for the gradient descent update
          """
          grad_weights = np.dot(x.T, grad_output)
          grad_bias = np.sum(grad_output, axis=0, keepdims=True)
          
          self.weights -= learning_rate * grad_weights
          self.bias -= learning_rate * grad_bias
  