Styjun

I am writing code for linear regression in which my model will predict price of houses on basis of the area. So, i have only one feature that is the area of the house and my output is the price. My input that is the area which is in range 1000 - 9000 and the price of the houses are in range 280000 - 800000 . So how should i perform feature scaling and how should i manage it with the output. I mean to ask that if i am bringing the house area in range 0 - 1 and house prices also in range 0 - 1 and than find out value of theta1 and theta2 (as i am applying linear regression equation like output = theta1 + theta2*input ) or i should scale down house prices to range of 1000 - 9000.

I am applying feature scaling in which i am bringing both the values input as well as output in between 0 - 1 my model is not giving right answers. I can figure out the mistake in it but i am not able to correct it. Please tell me how should i proceed.

from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import normalize
import numpy as np
X=np.random.randint(1000,9000,(10,))
Y=np.random.randint(100,200,(10,))+100*X
reg = LinearRegression().fit(X.reshape(-1,1), Y)
print(reg.score(X.reshape(-1,1),Y))
print(reg.coef_)
0.9999999822251018
[100.00518473]

X1=normalize(X.reshape(-1,1),axis=0)
Y1=normalize(Y.reshape(-1,1),axis=0)
reg = LinearRegression().fit(X1.reshape(-1,1), Y1)
print(reg.score(X1.reshape(-1,1),Y1))
print(reg.coef_)

0.9999999822251019
[[0.99982554]]

This is just ordinary Linear Regression using non normalized and normalized data. There will be no difference in these cases. Only the heading of your question includes "Gradient Descent" So If you use gradient descent method the weights will be automatically adjusted.

As the normal SGD is:
w=w-alpha*delta

Where alpha is the learning rate, The weight will be automatically adjusted as time goes on. So there is no difference between these two. Only that normalized one has to deal with numbers less than 1 so computation will be easier.