Build constrained cubic and quartic models, then distinguish interpolation, regression scores and new predictive evidence. This focused school-level sequence requires algebra and graph reading, not calculus.
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Model construction and validation require different evidence.
No. A different polynomial can agree at all the observed inputs and disagree elsewhere. State the permitted family, domain and constraints, then evaluate predictions on observations not used to fit.
Residual signs connect numerical errors to the scatterplot.
Residual is observed y minus predicted y at the same x. A positive residual means the observation is above the fitted curve. Compare errors on the same response scale.
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Polynomial model evidence: mixed practice
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Construct cubic and quartic models while keeping dimensions, domains and assumptions visible.
6 practice tasks.
Separate matching a calibration table from predicting new observations with a stated domain and error criterion.
6 practice tasks.
