[Python] Gradient Descent blowing up in linear regression

I am coding a linear regression code in python,I used the formulas I learnt and checked them up, and also tried normalising the the dataset what happened then is the values of weight and bias changed the exponential increase of values but still there is some error because the bias is still like in in the range of 10^-18 i am using the real estate dataset from kaggle heres the link https://www.kaggle.com/datasets/nitinsharma05/real-estate-analysis-dataset

here is the code i wrote

m -> weight

c -> bias

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

def gradient_descent(x, y, m, c, n):
delta_m = (-2/n) * np.sum(x * (y - (m*x + c)))
delta_c = (-2/n) * np.sum(y - (m*x + c))
return delta_m, delta_c

def linear_regression(epochs, m, c, learning_rate, x, y):
n = len(x)
for i in range(epochs):
delta_m, delta_c = gradient_descent(x, y, m, c, n)
m -= learning_rate * delta_m
c -= learning_rate * delta_c
if (i+1) % 1000 == 0:
print(f"After {i+1} epochs: m = {m}, c = {c}")
return m, c

df = pd.read_csv("archive/real_estate.csv")

df = df[['apartment_total_area', 'price_in_USD']].dropna()

df['apartment_total_area'] = (
df['apartment_total_area']
.astype(str)
.str.replace(' m²', '', regex=False)
.str.replace(' ', '', regex=False)
.str.replace(',', '.', regex=False)
.astype(float)
)

# Clean price_in_USD
df['price_in_USD'] = (
df['price_in_USD']
.astype(str)
.str.replace('$', '', regex=False)
.str.replace(',', '', regex=False)
.str.strip()
.astype(float)
)

x = df['apartment_total_area'].to_numpy()
y = df['price_in_USD'].to_numpy()

x_mean, x_std = x.mean(), x.std()
y_mean, y_std = y.mean(), y.std()
x_s = (x - x_mean)/x_std
y_s = (y - y_mean)/y_std

m, c = 0, 0
epochs = 20000
learning_rate = 0.0001


m_s, c_s = linear_regression(epochs, m, c, learning_rate, x_s, y_s)

m_orig = m_s * (y_std / x_std)
c_orig = y_mean + c_s * y_std - m_orig * x_mean

print(f"Final slope (m): {m_orig}")
print(f"Final intercept (c): {c_orig}")

plt.scatter(x, y, color="blue")
plt.plot(x, m_orig*x + c_orig, color="red")
plt.xlabel("Apartment Total Area (m²)")
plt.ylabel("Price in USD")
plt.show()



can someone help me figure out whats the problem?

I also tried changing the learning rate from 1 to 10^-18 but nothing worked and specially the values fo wieghts and biases didnt change this image shows the current slope of linear regression of my code

Continue reading...