Lack-of-fit Testing for Polynomial Regression Models Without Replications
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Bibliographic record
Abstract
Parametric and non-parametric approaches are developed to test the adequacy of the polynomial model Y=β°+j=1pβjXj+ε  when there is no replication in the values of the independent variable. The proposed tests avoid partitioning of the sample space of the continuous covariate. This paper suggests three tests based on the following concept: if the model is appropriate for a selected application, then the error component ε1,ε2,…,εn is a random sample with zero mean and constant variance. Simulation results are provided to illustrate the power and size of the proposed tests. An example is used to illustrate the methodologies. These tests are also compared with the classical lack-of-fit test to demonstrate their advantage.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it