Linear Regression¶
Concept overview¶
- Linear regression is designed to find a relationship between variables
- In Machine Learning, this relationship is between:
- Features (X)
- Label / target (Y)
- The goal is to model how changes in input features affect the output
Mathematical background¶
- Linear regression comes from school-level linear algebra
- In algebra, it is represented as a straight-line equation:
y = mx + b
Where:
- x — independent variable
- y — dependent variable
- m — slope of the line
- b — intercept
Linear regression in Machine Learning¶
In ML notation, the same idea is written as:
Y = B + WX
Where:
- Y — label (target variable)
- X — feature (input variable)
- W — weight
- B — bias
Features, weights, and bias¶
-
Feature (X)
Input data used to make predictions -
Label (Y)
The value the model is trying to predict -
Weight (W)
Determines how strongly a feature influences the prediction -
Bias (B)
Allows the model to shift predictions up or down independently of features
Both weights and bias are learned during training.
Multiple features¶
- Linear regression can use multiple features
- In that case:
- Each feature has its own weight
- The model combines them linearly
- The idea remains the same: a linear relationship between inputs and output
Summary¶
- Linear regression models linear relationships between variables
- The ML formulation directly mirrors the algebraic equation
- Training is the process of finding optimal weights and bias
- The model can scale from one feature to many without changing the core concept