Correlation — SAT Math Explained
A statistical measure describing the strength and direction of the linear relationship between two variables, quantified by the correlation coefficient r, which ranges from -1 to +1.
The Core Idea
Correlation tells you how closely two variables move together in a linear pattern. r = 1 means a perfect positive line; r = -1 means a perfect negative line; r = 0 means no linear relationship.
Correlation Coefficient
Perfect positive linear relationship
Strong positive correlation
Moderate positive correlation
Weak positive correlation
No linear correlation
Moderate negative correlation
Perfect negative linear relationship
Correlation Vs Causation
This is one of the most important distinctions in statistics. Just because two variables are correlated doesn't mean one causes the other. Both could be caused by a third hidden variable (lurking variable). Example: ice cream sales and drowning rates are positively correlated, but ice cream doesn't cause drowning — both increase in summer.
Lurking Variables
Hidden variables that cause two unrelated variables to appear correlated
Common Errors to Avoid
Assuming correlation = causation (the most common critical thinking error in statistics)
Using r to describe non-linear relationships (r measures LINEAR correlation only)
Thinking r close to 0 means no relationship — it only means no LINEAR relationship
Practice: Correlation
5 SAT-style questions. Select your answer and get an instant explanation.
The correlation r always satisfies:
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