Statistics · Quick Reference

Correlation Cheat Sheet

Statistics · Lesson 10/11

In one line: correlation measures the strength and direction of a linear relationship between two variables — how closely they move together.

Key Ideas

1Correlation Coefficient (r). A number between -1 and 1 that quantifies both the strength and direction of a linear relationship.

2Positive vs. Negative Correlation. Positive (r > 0): as one variable increases, so does the other. Negative (r < 0): as one increases, the other decreases.

3Strength of Correlation. Values of r close to 1 or -1 indicate a strong relationship; values close to 0 indicate a weak or no linear relationship.

4Correlation Does Not Imply Causation. Two variables can be strongly correlated without one causing the other — there may be a third factor, or the link may be coincidental.

5Correlation vs. Regression. Correlation measures how strongly two variables are related; regression goes further, providing an equation to predict one variable from the other.

Worked Examples

A study finds r = 0.9 between hours studied and exam score. Interpret this value.

Strong positive correlation — more study hours are strongly associated with higher scores

A study finds r = -0.85 between temperature and hot chocolate sales. Interpret this value.

Strong negative correlation — as temperature rises, hot chocolate sales tend to fall

A study finds r = 0.05 between shoe size and IQ. Interpret this value.

Very weak or no correlation — shoe size and IQ are not linearly related

Formulas

-1 <= r <= 1

Practice Yourself

Is r = 0.95 a strong or weak correlation?

Strong (positive)

Is r = -0.1 a strong or weak correlation?

Weak

What does r = 0 suggest?

No linear relationship between the variables