Ordinary squares problem from end of the module project in Data science course [Solved]

Question

First of all, in the problem description they said the formula is given in the image, but I can't see any image there. Is there actually an image? Or is it bug or they forget to put image.
Nevertheless the formula is on google. I used the formula and try to solve the problem. 4 test cases are correct but 1 is incorrect. I have no clue what to modify. Can anyone please revise my code or give a solution code?
https://code.sololearn.com/cu5GsMXgguJB/?ref=app

Answer 1

n, p = [int(x) for x in input().split()]
X = []
for i in range(n):
X.append([float(x) for x in input().split()])

y = [float(x) for x in input().split()]

import numpy as np
X_array=np.array(X).reshape(n,p)
y_array=np.array(y)
Beta=np.linalg.inv(X_array.T @ X_array) @ X_array.T @ y_array
print(Beta.round(2))

Answer 2

Mir Abir Hossain
@ == .dot()

A = np.array( [[1,1], [0,1]] )
B = np.array( [[2,0], [3,4]] )
A * B # elementwise product
# array([[2, 0], [0, 4]])
A @ B # matrix product
# array([[5, 4], [3, 4]])
A.dot(B) # another matrix product
#array([[5, 4], [3, 4]])

#https://numpy.org/doc/stable/user/quickstart.html

Answer 3

Mir Abir Hossain
I slightly modified your solution: 👍

# Xβ = y
β = np.matmul(np.matmul(X.T, y), np.linalg.inv(X.T @ X))
β = X.T @ y @ np.linalg.inv(X.T @ X)
β = np.linalg.pinv(X) @ y.T

print(β.round(2))

I have reported the lack of an image to SoloLearn❗❗❗

Answer 4

If you would like to dive into the mathematics... I found the equation (12) at: https://web.stanford.edu/~mrosenfe/soc_meth_proj3/matrix_OLS_NYU_notes.pdf

Answer 5

Turned out the if clause was unnecessary. The portion inside the 'else' code is the solution.
The reason I added 'if' clause was we can directly compute inverse matrix of a square matrix using numpy.linalg.inv(). So I thought it would be good. For non square matrix we need to compute the transpose matrix and then apply the formula in the code.

Answer 6

Yes! A good proper image would help much!

Answer 7

Janusz Bujak 🇵🇱 oh! Learnt new thing. Thank you ^_^

Answer 8

Is it me or does this solution include functions not covered in this DS course??

Answer 9

Nassim Abed yes I think some functions that required to solve this problem is not discussed in SL. Probably to check how much self study we are doing by ourselves :D

Answer 10

Janusz Bujak 🇵🇱 in your comment, what is '@'?

Answer 11

That wouldn't be fair then. Not when it comes to awarding certificates.

Answer 12

import numpy as np
n, p = [int(x) for x in input().split()]
X = []
for i in range(n):
X.append([float(x) for x in input().split()])

y = [float(x) for x in input().split()]

x1 = np.array(X)
y1 = np.array(y)

X_T = x1.T
XTX = np.dot(X_T, X)

XTX_INV = np.linalg.inv(XTX)

XTXINVXT = np.dot(XTX_INV, X_T)
beta = np.dot(XTXINVXT, y)
print(beta.round(2))

Answer 13

This is other solution

https://www.sololearn.com/compiler-playground/cbdoJJciE2Dt/#py

Answer 14

import numpy as np
n, p = [int(x) for x in input().split()]
X = []
for i in range(n):
X.append([float(x) for x in input().split()])

y = [float(x) for x in input().split()]
x_arr=np.array(X)
y=np.array(y)
x_arr_t=x_arr.transpose()
a=np.matmul(x_arr_t,x_arr)
a_inv=np.linalg.inv(a)
c=np.matmul(a_inv,x_arr_t)
beta=np.matmul(c,y).round(2)
print(beta)

Answer 15

import numpy as np
n, p = [int(x) for x in input().split()]
X = []
for i in range(n):
X.append([float(x) for x in input().split()])

y = [float(x) for x in input().split()]
x_arr=np.array(X)
y=np.array(y)
x_arr_t=x_arr.transpose()
# to multipy two arrays we can use matmul or dot functions and @ as an operator also
a=x_arr_t @ x_arr
a_inv=np.linalg.inv(a)
c=np.dot(a_inv,x_arr_t)
beta=np.matmul(c,y).round(2)
print(beta)