OLS-Regression Forecasting Confidence Intervals Capture Rates: Precision Profiling in the Forecasting Model Selection Process
Bibliographic record
Abstract
Forecasting creates projections into an uncertain future. To understand the decision-making implications of the forecast, confidence intervals [CIs] are required. This seems simple enough. However, considering the details of the computations that underlie generating forecasting CIs, one encounters a practical disconnect that can create a decision-making paradox. In the OLS 2-parameter linear regression [OLSR] case, there are two forecasting Models that are often employed: {The Uni-variate Time Series & The Standard two-variable Regression Y:X}. Further, for each of these two Models individually, there are three (1-FPE[α]) %CIs Versions: {Excel, Fixed Effects & Random Effects} each of which is oriented around the same OLSR-forecast value. Given this component configuration, a paradox emerges because each of the forecasting models, {TS or Y:X}, individually produces a forecast with a markedly difference precision profile over the three CI-Versions. In our experience, this is paradoxical as forecasters assume that as the forecasts are the same in each model-class, their Capture Rate—the percentage of time that the actual future values are IN the CIs—should also be the same. To address this seeming paradox, we develop, detail, and illustrate a two-stage OLSR Decomposition and Screening protocol, termed: the [D&S-Triage] protocol that has the following components: (i) Stage A: decomposition of the Model & Version factor-sets to better understand the implications of their Precision differences, and (ii) Stage B: focusing on inferentially significant forecasting model components, create a multilevel quality-algorithm to identify a forecasting model-set that addresses the Quality of the Capture Rate that are the best in their class.
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How this classification was reachedexpand
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 | 0.007 | 0.023 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.003 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".