What is multiple linear regression?

Multiple linear regression predicts a continuous numerical target using two or more input features.

It extends simple linear regression, which uses only one input feature.

Basic equation

A multiple linear regression model is written as:

ŷ = b0 + b1x1 + b2x2 + ... + bnxn

where:

• ŷ is the predicted target
• b0 is the intercept
• b1, b2, ... bn are coefficients
• x1, x2, ... xn are input features

Simple example

Suppose we want to predict house price using:

• house size
• number of rooms
• distance from the city center

The model might look like:

Predicted Price
= Intercept
+ b1 × Size
+ b2 × Rooms
+ b3 × Distance

Each feature contributes to the final prediction.

How are the coefficients interpreted?

Each coefficient represents the expected change in the predicted target for a one-unit change in that feature, while the other included features are held constant.

For example, if the coefficient for house size is positive, larger houses are associated with higher predicted prices after accounting for the other features in the model.

Why use multiple features?

Many real-world outcomes depend on several factors at the same time.

For example, house price may depend on size, location, age, and number of rooms rather than only one variable.

Multiple linear regression allows those factors to be modeled together.

It is still a linear model

Even with many features, the prediction is still a weighted sum of the inputs plus an intercept.

prediction = intercept + weighted features

The model is therefore linear in its coefficients.

More features are not automatically better

Adding irrelevant or highly redundant features can make the model harder to interpret and may introduce problems such as multicollinearity.

Feature choice should therefore be based on domain knowledge and validation.

In short, multiple linear regression predicts a numerical target using several input features, assigning a coefficient to each feature so their combined linear effect can be modeled.