1.2StatisticsCore

Measuring Correlation

The product moment correlation coefficient (PMCC), r, measures the strength and direction of a linear relationship between two variables. It always lies between −1 and 1.

24 min Video by Zeeshan Zamurred Regression, Correlation and Hypothesis Testing

Edexcel A Level Maths: 1.2 Measuring CorrelationWatch the full walkthrough before the notes below.

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What you'll be able to do

Interpret the value of r
Know the range −1 ≤ r ≤ 1
Distinguish strength and direction
Read r from a calculator

What r tells you

The PMCC $r$ satisfies $- 1 \leq r \leq 1$ . Values near $\pm 1$ indicate strong linear correlation; near $0$ indicates weak or no linear correlation. The sign gives the direction.

- 1 \leq r \leq 1

r measures linear correlation.

1Close to

- 1

2Strong negative linear correlation.

AnswerStrong negative correlation.

Tip — r measures LINEAR correlation only — a strong curved pattern can still give small r.

Strength and direction

Sign: $r > 0$ positive (both rise together), $r < 0$ negative (one rises as the other falls). Magnitude: closer to 1 means stronger.

Formula recap

- 1 \leq r \leq 1

Range of the PMCC.

r \approx \pm 1 \Rightarrow strong

Strength.

Common mistakes to avoid

Claiming r near 0 means no relationship at all.

It means no LINEAR relationship; a curved one may exist.

Saying correlation proves causation.

Correlation does not imply causation.

Key takeaways

PMCC r lies in [−1, 1].
Sign = direction; magnitude = strength.
r measures linear correlation only.

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