Edexcel Further Stats 2 · Chapter 2
Correlation
Big idea: Correlation coefficients give you a single number between −1 and 1 that tells you
how strongly two things are related — and hypothesis testing tells you whether that relationship is
real, or just a fluke in your sample.
1. Product Moment Correlation Coefficient (PMCC)
Think of PMCC as answering one question: "If I drew a straight line through this scatter of points,
how well would that line actually fit?" It only cares about straight-line (linear) relationships,
and it only works properly when both variables are continuous and roughly normally distributed — things like
height, temperature, or exam marks, rather than categories or rankings.
The result, r, always lands somewhere between −1 and 1:
| r value | Meaning |
|---|
| −1 | Perfect negative linear correlation (as one goes up, the other goes down exactly) |
| −0.8 | Strong negative linear correlation |
| 0 | No linear correlation at all |
| 0.4 | Weak positive linear correlation |
| 1 | Perfect positive linear correlation |
Intuition check
The sign tells you the direction (both go up together, or one goes up as the other goes down).
The size (how close to ±1) tells you how tightly the points cluster around a straight line.
r = 0 doesn't mean "unrelated" — it just means "not linearly related." There could still be a strong curved relationship!
The Formula
Worked Example — Physics vs. Chemistry Marks
| Physics (p) | 73 | 89 | 56 | 55 | 85 | 98 | 88 | 63 | 47 | 93 |
|---|
| Chemistry (c) | 68 | 91 | 40 | 62 | 79 | 94 | 76 | 71 | 52 | 78 |
|---|
Given: Σp = 747, Σc = 711, Σc² = 53031, Σpc = 55499, and Spp = 3010.1
STEP 1 — Find Scc
Scc = 53031 − (711)²/10 = 2478.9
STEP 2 — Find Spc
Spc = 55499 − (747 × 711)/10 = 2387.3
STEP 3 — Find r
r = 2387.3 / √(3010.1 × 2478.9) = 0.874 (3 s.f.)
STEP 4 — Interpret, in context
Since r is close to +1, there is a strong, positive linear correlation between Physics and Chemistry marks — students who scored highly in Physics tended to score highly in Chemistry too.
Common mistake
Never say "there is a correlation" without a reason attached. Examiners want the r value quoted AND a
description (strong/weak, positive/negative) tied back to the context of the question — not just the number on its own.
Practice Question 1
For a sample of 8 houses, the correlation between floor area (x, in m²) and sale price (y, in £1000s)
is found to have Sxy = 412.5, Sxx = 640.2, Syy = 380.9. Calculate r and interpret it in context.
Practice Question 2
A dataset has Σx = 120, Σy = 340, Σx² = 1780, Σy² = 12200, Σxy = 4150, n = 12. Find Sxx, Syy, Sxy, then r.