Partitioning Sum of Squares & Goodness-of-Fit (R-squared)

Quantify simple-regression fit through sums of squares, explained variation and residual error scales. Derive the intercept-model decomposition, connect goodness of fit to correlation, and examine constant responses, origin-constrained fits and test-sample scores. Prerequisites: OLS coefficients and residual orthogonality. Worked examples distinguish relative fit from error in meaningful units and from model validation.

Further reading: R-squared definitions.