Module 6 · Regression & Correlation · Topic 7
Residual Plots. Plot residuals on the y-axis against x (or ŷ) on the x-axis. A good linear model shows randomly scattered residuals with no pattern. Patterns indicate the model is inadequate.
What Patterns Reveal. A curved pattern suggests a nonlinear relationship. A funnel shape (increasing spread) indicates heteroscedasticity. Clusters may indicate subgroups in the data.
Residual = yᵢ − ŷᵢ (observed minus predicted)
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.Before trusting regression results, always examine the residual plot. A model with a high R² can still be inappropriate if the residual plot shows a clear pattern.
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