Module 6 · Regression & Correlation · Topic 2
Correlation. Correlation measures the strength and direction of the linear relationship between two quantitative variables. It is denoted by r and ranges from −1 to +1.
Interpreting r. r = +1: perfect positive linear relationship. r = −1: perfect negative. r = 0: no linear relationship. |r| > 0.7 is often considered strong, 0.3–0.7 moderate, < 0.3 weak.
Properties of Correlation. Correlation is unitless, so it doesn’t depend on the scales of measurement. It is symmetric: r(x, y) = r(y, x). It only measures linear association - a strong curved relationship can have r near 0.
yhat = a + bx — Line that minimizes the sum of squared residuals.r = sum((x_i-xbar)(y_i-ybar)) / sqrt(sum((x_i-xbar)^2)sum((y_i-ybar)^2)) — Measures direction and strength of a linear association.A high correlation does not prove that one variable causes the other. Lurking variables or coincidence can produce strong correlations between unrelated variables.
Go interactive
Start with the free descriptive-statistics module and daily practice; this module's tracked lesson unlocks with Premium.
Keep reading