# Slope and intercept

The slope is the predicted change in y for each one-unit increase in x. The intercept is the predicted y when x is 0, which may be meaningless if x = 0 is far from your data.

Statistics (university) · Part 08: Correlation and regression · Card 3 of 9 · Last updated 2026-10-19

## Analogy

The slope is the price per extra kilometre on a taxi fare. The intercept is the starting charge.

## Example

**Reading the line**

Score = 50 + 5 x hours studied
Slope 5: each extra hour adds 5 points
Intercept 50: predicted score at 0 hours
At 4 hours: 50 + 20 = 70

## In practice

Always state the slope with units so readers know what a change means.

## Practice

### Flashcards

- **How do you interpret the slope?** Predicted change in y for each one-unit increase in x.

## Questions people ask

### How do I interpret the slope in words?

Say: for each one-unit increase in x, y is predicted to change by the slope, on average. For a slope of 5, each extra hour of study goes with 5 more points. Say predicted or on average, not guaranteed, because individual points scatter around the line and some will miss it badly.

### What if the intercept makes no sense?

Sometimes x = 0 is impossible or far outside the data, like a person with zero height. The intercept then just anchors the line and has no real-world meaning. Do not interpret it. Using centred x values can give an intercept that means something.

## Related concepts

- [Least squares regression line](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-8/statistics-university-part-8-concept-2)
- [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)
- [Regression assumptions](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-8/statistics-university-part-8-concept-6)

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