Model Assessment Concepts

A residual is the difference between an observed data value and the value predicted by a statistical model, calculated as $\text{residual} = y_{\text{observed}} - y_{\text{predicted}}$. Positive residuals mean the model underestimated; negative residuals mean it overestimated.

"If your model predicts 80 but the actual value is 85, the residual is +5. Residuals are 'leftovers' - what the model couldn't explain. Patterns in residuals reveal model problems."

Why it matters: Residuals gives students a careful language for comparing variables without jumping to a causal story. It is useful for reading scatter plots, two-way tables, regression models, and real-world claims where patterns are tempting but hidden variables may matter.

R-squared (the coefficient of determination) is the proportion of variance in the dependent variable that is explained by the independent variable(s) in a regression model. It ranges from 0 to 1, where 0 means the model explains none of the variability and 1 means it explains all of it.

"$R^2 = 0.80$ means the model explains 80% of why $Y$ values differ. The other 20% is unexplained variation. Higher $R^2$ = better predictions."

Why it matters: R-Squared (Coefficient of Determination) gives students a careful language for comparing variables without jumping to a causal story. It is useful for reading scatter plots, two-way tables, regression models, and real-world claims where patterns are tempting but hidden variables may matter.