Correlation and Regression

Analyzing relationships between variables and predicting outcomes

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What is Pearson's correlation coefficient (r)?

A measure of the strength and direction of the linear relationship between two continuous variables.

r = Σ[(X − X̄)(Y − Ȳ)] / [(n − 1) × sₓ × sᵧ]

Example: r = 0.85 indicates a strong positive linear relationship; r = −0.3 indicates a weak negative relationship

Note: Range: −1 to +1; r² = proportion of variance explained; assumes linearity, normality, and no outliers