Teaching/Learning Multiple Regression Using Historical and Modern Family Data
Bibliographic record
Abstract
To deal with the new concepts involved when moving up from simple to multiple regression, I have found that it helps to use readily-understood real-world datasets that involve an engaging question, measurements that students can personally relate to, such as those involving themselves and their families, and just two regressors.I describe, provide copies of, and suggest possible didactic uses of "two-regressor" datasets involving family data.The late-19th century datasets, which gave rise to the very term "regression, " involve easily measured variables relating to students and their families, two weakly-correlated parental regressors, and a written protocol that would allow a modern version to be quickly assembled by today's students.The recent datasets involve a less easily measured but easily understood Y variable that can be modeled within the ordinary or the Poisson (generalized) linear model regression framework, two readily obtained but very strongly-correlated parental regressors, and an engaging example of the striking difference between the regression coefficients in the two "1-regressor-at-a-time"and the one "2-regressorsat-once" regression models.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.014 | 0.066 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.019 | 0.008 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".