Squaring Things Up with R2: What It Is and What It Can (and Cannot) Tell You
Bibliographic record
Abstract
The coefficient of correlation (r) and the coefficient of determination (R2 or r2) have long been used in analytical chemistry, bioanalysis and forensic toxicology as figures demonstrating linearity of the calibration data in method validation. We clarify here what these two figures are and why they should not be used for this purpose in the context of model fitting for prediction. R2 evaluates whether the data are better explained by the regression model used than by no model at all (i.e., a flat line of slope = 0 and intercept $\bar y$), and to what degree. Hopefully, in the context of calibration curves, the fact that a linear regression better explains the data than no model at all should not be a point of contention. Upon closer examination, a series of restrictions appear in the interpretation of these coefficients. They cannot indicate whether the dataset at hand is linear or not, because they assume that the regression model used is an adequate model for the data. For the same reason, they cannot disprove the existence of another functional relationship in the data. By definition, they are influenced by the variability of the data. The slope of the calibration curve will also change their value. Finally, when heteroscedastic data are analyzed, the coefficients will be influenced by calibration levels spacing within the dynamic range, unless a weighted version of the equations is used. With these considerations in mind, we suggest to stop using r and R2 as figures of merit to demonstrate linearity of calibration curves in method validations. Of course, this does not preclude their use in other contexts. Alternative paths for evaluation of linearity and calibration model validity are summarily presented.
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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 | 0.140 | 0.411 |
| Meta-epidemiology (narrow) | 0.004 | 0.002 |
| Meta-epidemiology (broad) | 0.006 | 0.004 |
| Bibliometrics | 0.009 | 0.011 |
| Science and technology studies | 0.003 | 0.021 |
| Scholarly communication | 0.015 | 0.029 |
| Open science | 0.007 | 0.006 |
| Research integrity | 0.013 | 0.023 |
| Insufficient payload (model declined to judge) | 0.006 | 0.010 |
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".