Correlation (AI SL)
Pearson's product-moment correlation coefficient \(r\) tells you how strong a linear relationship is between two variables, and in which direction it points. This page covers reading and interpreting \(r\) - the sign, the magnitude, and the trap of assuming a strong correlation proves cause and effect. It's part of the broader Correlation & Regression topic.
33 questions on this sub-topic.
Reading the coefficient
Covered under IB syllabus reference SL4.4: linear correlation of bivariate data, Pearson's product-moment correlation coefficient \(r\) calculated using technology, and the awareness that correlation does not imply causation.
Positive correlation
As \(x\) increases, \(y\) tends to increase too - points trend upward left to right, giving a positive gradient and \(r>0\).
Negative correlation
As \(x\) increases, \(y\) tends to decrease - points trend downward left to right, giving a negative gradient and \(r<0\).
No correlation
The points show no clear upward or downward trend - \(r\) is close to zero, and fitting a line wouldn't be meaningful.
Range of Pearson's correlation coefficient: \(-1\le r\le 1\) (not in the booklet - it's GDC output). Need the full syllabus wording and formula-booklet reference table? See Correlation & Regression. For calculator steps, see the parent topic's GDC guidance.
Worked examples
For each value of \(r,\) state the strength and direction of the correlation.
(a) \(r=0.05\)
(b) \(r=-0.97\)
(c) \(r=0.62\)
Worked solution
Judge strength by \(|r|\) (near 1 = strong, near 0 = none) and direction by the sign. R1
\(\bullet\ r=0.05:\) \(|r|\) near 0 - very weak / essentially no linear correlation. A1
\(\bullet\ r=-0.97:\) \(|r|\) near 1 and negative - strong negative linear correlation. A1
\(\bullet\ r=0.62:\) mid-range and positive - moderate positive linear correlation. A1
A strong positive data set has \(r=0.95.\) A single faulty reading far from the trend is added.
(a) State the likely effect on \(r.\)
(b) State what should be done before refitting.
Worked solution
(a) Effect on \(r.\) A point lying far from the existing trend disrupts the tight linear pattern, R1
so \(r\) is likely to decrease (move toward 0) - the correlation weakens. A1
(b) Before refitting. Investigate the suspect reading. R1
If it is a genuine error (mis-recorded or faulty measurement) it should be corrected or removed; only then refit the regression line. A1
Common mistakes
- Claiming causation from correlation. A strong \(r\) shows association, not cause and effect - always consider whether a confounding factor could explain the relationship instead.
- Confusing \(r\) with \(r^2\). Some GDC output screens display both - always quote the value the question actually asks for, since \(r^2\) is always positive and reads differently.
- Ignoring outlier effects. A single extreme point can pull \(r\) noticeably toward zero even when the rest of the data is tightly linear - don't describe the correlation from \(r\) alone without a glance at the scatter diagram.
Ready to practise properly?
33 correlation questions, marked instantly like the real exam.
Quick answers
What does Pearson's correlation coefficient r measure?
\(r\) measures the strength and direction of a linear relationship between two variables. It ranges from \(-1\) (perfect negative) to \(+1\) (perfect positive), with values near \(0\) showing little or no linear relationship. It is calculated using technology, not by hand.
Does a strong correlation mean one variable causes the other?
No. A strong \(r\) shows association, not cause and effect. A confounding factor could explain the relationship instead, so correlation alone never proves causation.