# Multiple regression

Multiple regression uses several predictors: y-hat = b0 + b1 x1 + b2 x2 + ... Each coefficient is the predicted change in y for a one-unit rise in that predictor while the others are held fixed.

Statistics (university) · Part 08: Correlation and regression · Card 8 of 9 · Last updated 2026-10-19

## Analogy

Pricing a house by adding up charges for size, bedrooms and location, each with its own rate.

## Example

**House price model**

Price (thousands) = 40 + 2.5 x area + 10 x bedrooms
House: 80 m2, 2 bedrooms
40 + 200 + 20 = 260
Extra 10 m2 adds 25, bedrooms held fixed

## In practice

Used to separate the effects of related factors, such as age and income on spending.

## Questions people ask

### What does holding the other variables fixed mean?

Each coefficient shows the change linked to one predictor when the others stay constant. In the house model, an extra bedroom adds 10 thousand at the same area. It is a statistical adjustment from the data, not an experiment, so it can only account for variables you actually measured.

### What is multicollinearity?

It happens when predictors are strongly correlated with each other, such as house area and number of rooms. The model cannot tell their effects apart, so coefficients become unstable and have large standard errors. Predictions can still be good, but individual coefficients are hard to trust.

## Related concepts

- [Least squares regression line](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-8/statistics-university-part-8-concept-2)
- [Slope and intercept](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-8/statistics-university-part-8-concept-3)
- [Residuals](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-8/statistics-university-part-8-concept-4)
- [R-squared](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-8/statistics-university-part-8-concept-5)

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