Least Square Implementation error "ValueError: shapes (3,3) and (1,3) not aligned: 3 (dim 1) != 1 (dim 0)"

Question

Hi am trying to implement the Linear regression module for a project but am getting stuck here is the git repo :least Square Method

the code :

import numpy as np
from numpy.linalg import inv

class linearregression :
  
  def __init__(self,training_data_X, training_data_Y) :
    # Linear regression module init
    pading = np.ones(training_data_X.shape[0])
    self.training_data_X = np.insert(training_data_X, 0, pading, axis=1) # The training data x => features numpy_matrix
    self.training_data_Y = training_data_Y # The training data y => response numpy_matrix
  
  def leastsquare(self):
    # Find beta parameter
    X_transpose = self.training_data_X.transpose()
    self.ajk = np.matmul(X_transpose, self.training_data_X)
    self.Hessian = 2 * self.ajk
    self.Beta = inv(self.ajk).dot(X_transpose).dot(self.training_data_Y)
    f_of_X = self.training_data_X.dot(self.Beta)
    self.rs = np.subtract(self.training_data_Y,f_of_X)
    self.rss = self.rs.dot(self.rs)
    return self.Beta , self.rss
    
if __name__ == "__main__" :
  x = np.matrix([[0,1],[1,4],[7,8]])
  y = np.matrix([2,9,23])
  Lr = linearregression(x,y)
  Beta, rss = Lr.leastsquare()
  print(Beta,rr)

The code return me this error statement :

Traceback (most recent call last):
  File "<string>", line 27, in <module>
File "<string>", line 17, in leastsquare
ValueError: shapes (3,3) and (1,3) not aligned: 3 (dim 1) != 1 (dim 0)

Answer 1

Y is 1x3, but it should be 3x1. Two ways to fix it:

• require training_data_Y to be nx1: y = np.matrix([[2],[9],[23]])
• take an array instead of a matrix: y = np.array([2,9,23])
• or, simply transpose it when computing beta: Beta = inv(self.ajk).dot(X_transpose).dot(self.training_data_Y.T)