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
  
  # Example usage:
  # >>> model = LinearRegressionModel(2, 1)
  # >>> input_data = np.array([[1, 2], [3, 4]])
  # >>> model.forward(input_data)
  # array([[0.], [0.]])
  
output:     
      def backward(self, x, y, learning_rate):
          """ Updates the weights and bias of the linear regression model using gradient descent
          Arguments:
              x {numpy array} -- Input data of size (N, input_dim)
              y {numpy array} -- True labels of size (N, output_dim)
              learning_rate {float} -- Learning rate for gradient descent
          """
          N = x.shape[0]
          predictions = self.forward(x)
          d_weights = np.dot(x.T, (predictions - y)) / N
          d_bias = np.sum(predictions - y, axis=0, keepdims=True) / N
          self.weights -= learning_rate * d_weights
          self.bias -= learning_rate * d_bias
  