Direction and strength of a relationship: A scatter diagram plots paired data.
Describe the correlation by its direction (positive: both rise together; negative: one rises as the other falls) and its strength (strong: points hug a line; weak: loosely scattered).
A scatter diagram shows the trend — positive or negative correlation, and how tightly the points hug the line.
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IB-style question — describe the correlation
On a scatter graph, as the daily temperature rises the number of cold drinks sold rises, and the points lie close to a straight line.
Describe the correlation.
Step by step
- Both increase together → direction.
- Points close to a line → strength.
Final answer
Strong positive (linear) correlation.
Always say both: A full description names the direction AND the strength — e.g. 'weak negative', 'strong positive'.
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A number from −1 to 1: Pearson's r measures linear correlation: it runs from −1 to 1.
Reading r
- The sign gives the direction.
- The size gives the strength — near ±1 is strong, near 0 is weak.
- r = ±1 means the points lie exactly on a line.
IB-style question — interpret r
Two data sets give r = 0.93 and r = −0.21.
Describe the correlation in each case.
Step by step
- r = 0.93: positive sign, close to 1.
- r = −0.21: negative sign, close to 0.
Final answer
r = 0.93 → strong positive; r = −0.21 → weak negative.
Sign = direction, size = strength: Read r in two parts: the +/− tells direction, and how close |r| is to 1 tells strength.
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LinReg gives r — but correlation is not cause: On Paper 2 you read r from the calculator's linear-regression output.
Two cautions: a strong r does not prove one variable causes the other, and r only measures a linear pattern (a strong curve can give a small r).
IB-style question — find and interpret r
Hours studied x and test score y for five students are (1,40), (2,50), (3,55), (4,70), (5,80).
Find r and describe the correlation.
Step by step
- Enter the pairs and run linear regression.
- Interpret the value.
Final answer
r ≈ 0.990 — a very strong positive correlation between hours studied and score.
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