# Regression assumptions

Linear regression assumes a straight-line relationship, independent errors, errors with constant spread, and roughly normal errors. Remember it as LINE: Linear, Independent, Normal, Equal spread.

Statistics (university) · Part 08: Correlation and regression · Card 6 of 9 · Last updated 2026-10-19

## Analogy

A recipe that only works if the ingredients are what it expects. Check the data before trusting the answer.

## Example

**Spotting a problem**

Curved residual pattern: not linear
Funnel shape: spread not equal
Runs above and below: errors linked
Skewed residual histogram: not normal

## In practice

Residual plots and histograms of residuals are the main way to check these assumptions.

## Practice

### Flashcards

- **What does LINE stand for?** Linear, Independent, Normal, Equal spread.

## Questions people ask

### What is an influential point in regression?

It is a point that changes the fitted line a lot if removed, usually one far from the others in x. An outlier in y alone changes the line less. Check unusual points, ask why they occurred, and report results with and without them.

### What can I do if the assumptions are violated?

Try transforming the variables, for example with a logarithm, to straighten curves and stabilise spread. Add missing predictors, or fit a curve. For correlated errors, such as in time series, use methods designed for that structure, because ordinary least squares then understates uncertainty.

## 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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