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.
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