Module 6 · Regression & Correlation · Topic 3
Computation Insight. The formula standardizes each variable by subtracting its mean and dividing by its standard deviation, then averages the products. Positive products (both above or both below mean) increase r; mixed products decrease it.
r = Σ[(xᵢ − x̄)(yᵢ − ȳ)] / [(n − 1) × sₓ × sᵧ]
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.For five data points with x = {1,2,3,4,5} and y = {2,4,5,4,5}: x̄ = 3, ȳ = 4, sₓ = 1.58, sᵧ = 1.22. Computing the sum of standardized products and dividing by (n−1) gives r ≈ 0.77, a moderately strong positive correlation.
Pearson’s r is sensitive to outliers. A single extreme point can drastically inflate or deflate the correlation. Always check the scatter plot.
Go interactive
Start with the free descriptive-statistics module and daily practice; this module's tracked lesson unlocks with Premium.
Keep reading