Explain linear regression.

August 13, 2025

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Linear Regression is a statistical and machine learning method used to model the relationship between a dependent variable (target) and one or more independent variables (features) by fitting a straight line.

Simple Linear Regression (one feature) uses the equation:

$y = m x + b$

Where:

$y$ → predicted value
$x$ → input feature
$m$ → slope (effect of $x$ on $y$ )
$b$ → intercept (value of $y$ when $x = 0$ )

The model finds $m$ and $b$ by minimizing the Mean Squared Error (MSE) between predicted and actual values.

Multiple Linear Regression uses multiple features:

$y = b_0 + b_1x_1 + b_2x_2 + ... + b_nx_n$

Uses: Predicting prices, trends, or outcomes based on historical data.

Limitations: Works best when the relationship is linear and data meets assumptions like no multicollinearity and constant variance.

In short, linear regression draws the best-fit line to predict future outcomes from past data.

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