Competing Function Model Validation
Choosing a model is a competition, and points-touched is the wrong scoreboard. Two points determine a line, an exponential, and infinitely many quadratics at once, so passing through the data proves nothing by itself. The honest tests are the rate signatures (constant differences for linear, constant second differences for quadratic, constant ratios for exponential) and the residual plot, where random scatter blesses a family and a systematic bow convicts it.
The mistakes here are all shortcuts: validating a model because one prediction landed, reading growing gaps as automatically exponential, trusting residuals because they nearly sum to zero, and extrapolating far outside the window because the fit looked perfect inside it. The lesson names each shortcut and replaces it with the test that actually decides.
The work
3 ways in · any order
Lesson
Competing Function Model Validation
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Fitting is cheap: any family can touch two points. The lesson arms you with the difference test, the ratio test, and residual-pattern reading, then closes with ten scenarios where the plausible-looking model is wrong and the evidence says which rival wins.
Diagnostic
10-item topic check
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Ten items on the single Topic 2.6 misconception in its many disguises: models validated by one matched point, one zero residual, a near-zero residual sum, or a perfect in-window fit stretched far beyond the data. The bank ships with the Unit 2 data drop.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.