Start with the right question
Linear model: x=b+mt. Quadratic model: x=b+mt+ct². Both are fit by least squares to the first five points t=0,1,2,3,4 s. The sixth at t=5 s is held out from fitting. Residual = observed position − predicted position, with unit meters. Training RMSE = √(mean squared training residual), also in meters.
Models differ in complexity: quadratic has three parameters and may fit training data better because it is more flexible. Also examine the holdout, residual pattern and plausible motion mechanism.
1. Choose a case and make a prediction
2. Compare model fits
Position (m) versus time (s); point at t=5 s is held out.
Residual = observed − predicted (m), plotted for the five training points only.
3. Study the numbers and test the prediction
| t (s) | Measured-style synthetic x (m) | Linear prediction (m) | Linear residual (m) | Quadratic prediction (m) | Quadratic residual (m) | Split |
|---|
4. Science notebook and result history
| # | Dataset | Linear RMSE (m) | Quadratic RMSE (m) | Linear holdout error (m) | Quadratic holdout error (m) |
|---|
5. Seven-round model detective game
Interpret randomly selected synthetic position tables, choosing the physically plausible simpler linear or accelerating quadratic model. Answer feedback explains the underlying trend. The game draws seven distinct cases from ten.
Start a seven-round investigation.
Score: 0 / 7