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📘 Linear Regression Algorithm – Explained for Beginners

Linear Regression is one of the most important and commonly used Machine Learning algorithms. It is usually the first algorithm students learn because it is simple, mathematically clear, and widely used in real-world applications.

1️⃣ What is Linear Regression?

Linear Regression is a supervised learning regression algorithm used to predict continuous numerical values such as price, salary, marks, or sales.

It works by fitting the best possible straight line through the data points.

2️⃣ Linear Regression Equation

Simple Linear Regression:

y = b0 + b1x

Multiple Linear Regression:

y = b0 + b1x1 + b2x2 + ... + bnxn

3️⃣ Cost Function – Mean Squared Error

Linear Regression minimizes error using the Mean Squared Error (MSE):

MSE = (1/n) Σ (y − ŷ)²

4️⃣ Gradient Descent (How Learning Happens)

• Moves parameters step-by-step to reduce error
• Uses learning rate to control speed
• Stops when minimum error is reached

5️⃣ Real-World Applications

• House price prediction
• Sales forecasting
• Business analytics
• Finance risk analysis

6️⃣ Python Example (scikit-learn)

from sklearn.linear_model import LinearRegression
import numpy as np

X = np.array([[1],[2],[3],[4],[5]])
y = np.array([3,4,2,5,6])

model = LinearRegression()
model.fit(X, y)

print(model.intercept_)
print(model.coef_)
print(model.predict([[6]]))

7️⃣ Advantages & Limitations

Advantages: Simple, fast, interpretable

Limitations: Assumes linearity, sensitive to outliers

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