Linear Regression and Gradient Descent

                                
# Gradient Descent implementation in Python
import numpy as np

# Example data
X = np.array([1, 2, 3, 4, 5])
Y = np.array([2, 4, 6, 8, 10])

# Initialize parameters
m, b = 0, 0  # slope and intercept
learning_rate = 0.01
iterations = 1000

# Gradient Descent
for _ in range(iterations):
    Y_pred = m * X + b
    dm = -2 * np.sum(X * (Y - Y_pred)) / len(X)
    db = -2 * np.sum(Y - Y_pred) / len(Y)
    m -= learning_rate * dm
    b -= learning_rate * db

print(f'Optimized slope: {m}, Optimized intercept: {b}')

                              

                                
# Choosing the learning rate
learning_rate = 0.01  # This is an example of a learning rate
# A larger learning rate might cause overshooting, while a smaller one might be too slow.

                              

                                
# Implementing Gradient Descent in Python
import numpy as np

# Generate some data
np.random.seed(0)
X = 2 * np.random.rand(100, 1)
Y = 4 + 3 * X + np.random.randn(100, 1)

# Initialize parameters
m = 0
b = 0
learning_rate = 0.01
iterations = 1000

# Gradient Descent
for _ in range(iterations):
    Y_pred = m * X + b
    dm = -2 * np.sum(X * (Y - Y_pred)) / len(X)
    db = -2 * np.sum(Y - Y_pred) / len(Y)
    m -= learning_rate * dm
    b -= learning_rate * db

print(f'Optimized slope: {m}, Optimized intercept: {b}')

                              

                                
# Updating parameters
# Example code snippet inside a loop
m -= learning_rate * dm
b -= learning_rate * db
# Here, dm and db are gradients calculated in the current iteration.