01 Key Concepts
Correlation Coefficient (r)
A number between -1 and 1 that quantifies both the strength and direction of a linear relationship.
Positive vs. Negative Correlation
Positive (r > 0): as one variable increases, so does the other. Negative (r < 0): as one increases, the other decreases.
Strength 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.
Correlation 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.
Correlation vs. Regression
Correlation measures how strongly two variables are related; regression goes further, providing an equation to predict one variable from the other.
02 Key Formulas
- -1 <= r <= 1
03 Solved Examples
Example 1 A study finds r = 0.9 between hours studied and exam score. Interpret this value.
- r is close to 1, and positive.
- This indicates a strong positive linear relationship.
Answer: Strong positive correlation — more study hours are strongly associated with higher scores
Example 2 A study finds r = -0.85 between temperature and hot chocolate sales. Interpret this value.
- r is close to -1, and negative.
- This indicates a strong negative linear relationship.
Answer: Strong negative correlation — as temperature rises, hot chocolate sales tend to fall
Example 3 A study finds r = 0.05 between shoe size and IQ. Interpret this value.
- r is very close to 0.
- This indicates essentially no linear relationship between the variables.
Answer: Very weak or no correlation — shoe size and IQ are not linearly related
04 Practice Questions
1Is r = 0.95 a strong or weak correlation?
Strong (positive)
2Is r = -0.1 a strong or weak correlation?
Weak
3What does r = 0 suggest?
No linear relationship between the variables
4Can r ever be greater than 1 or less than -1?
No, r is always between -1 and 1
5Does a strong correlation prove causation?
No, correlation does not imply causation
📄 Correlation — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.