Model Assessment Concepts
2 concepts · Grades 9-12
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Model Assessment concepts have 2 connections to other families.
All Model Assessment Concepts
Residuals
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: Residual analysis is used in economics, engineering, and medical research to evaluate whether a regression model is appropriate. Random residuals indicate a good fit, while patterns in residuals signal that the model is missing important structure in the data.
R-Squared (Coefficient of Determination)
The proportion of variance in the dependent variable that is explained by the independent variable(s) in a regression model, ranging from 0 to 1.
"$R^2 = 0.80$ means the model explains 80% of why $Y$ values differ. The other 20% is unexplained variation. Higher $R^2$ = better predictions."
Why it matters: $R^2$ is the standard measure of how well a regression model fits data. It helps compare models and assess prediction quality.