# Regression Model Report: [Model name and study question] > A working document for one regression model, from the question it answers > to the sign-off: purpose and estimand, data and sample, variable > definitions, model specification with its justification, an assumption and > diagnostics checklist that records the evidence, the results table, model > comparison, validation, sensitivity analyses, limitations, reproducibility > details and review. It is for thesis writers who must defend a model to a > supervisor or examiner, students submitting a regression project, and > analysts handing a model to a reviewer or a client. It speeds up learning > because every section asks a question you must answer in writing, and > because the filled example shows what a complete answer looks like. The > worked examples use fictional data; replace them with your own. > Based on standard regression practice, the distinction between explanatory > and predictive modelling (Shmueli 2010), TRIPOD reporting items for > prediction models (named only) and APA JARS-Quant (named only). ## Document control | Field | Value | |---|---| | Course or project | [*Example:* STAT 210 regression project / thesis chapter 4] | | Learner or analyst | [Your name] | | Model ID | [*Example:* LKM-EXAM-M2] | | Data set | [*Example:* Lakemoor University exam study, n = 20, fictional, file `exam_v1.csv`] | | Software and versions | [*Example:* R 4.5.1 with car 3.1.5; Python 3.14 with numpy 2.5.4, pandas 3.1.0, statsmodels 0.15.0] | | Analysis plan reference | [*Example:* Analysis plan v1.0, dated YYYY-MM-DD] | | Status | [Draft / Under review / Approved] | | Date | YYYY-MM-DD | | Version | [0.1] | ## 1. Purpose and estimand The purpose decides what "a good model" means. An **explanatory** model is judged by whether its key coefficient is estimated without bias and with an honest interval, so confounders must be adjusted for and the specification is fixed in advance. A **predictive** model is judged by its accuracy on new data, so validation matters more than the meaning of any one coefficient. Mixing the two aims (choosing predictors by p-value, then interpreting the coefficients as effects) is the most common weakness in student reports. | Item | Entry | |---|---| | Purpose (describe / explain / predict) | [*Example:* Explain, with a secondary prediction check] | | Research question | [*Example:* How is weekly study time associated with exam score in introductory statistics at Lakemoor University?] | | Primary estimand | [*Example:* The difference in mean exam score (points) per additional weekly study hour, holding nightly sleep and course section constant] | | Target population | [*Example:* Students taking the introductory statistics course in the current academic year] | | Causal or associational claim | [*Example:* Associational only: study time was not randomised] | | Secondary questions | [*Example:* Section difference (online vs in-person); does the hours slope differ by section? (exploratory)] | ## 2. Data and sample | Item | Entry | |---|---| | Source | [*Example:* Course records joined to an end-of-term survey (fictional)] | | Sampling | [*Example:* Convenience sample of students who completed the survey] | | Unit of analysis | [*Example:* One student] | | Period | [*Example:* Autumn term, YYYY] | | Eligible / consented / analysed | [*Example:* 26 / 22 / 20] | | Exclusions and reasons | [*Example:* 2 with missing sleep data (complete-case analysis)] | | Missing data handling | [*Example:* Complete cases; 2 of 22 (9%) excluded; sensitivity with multiple imputation listed as future work] | | Ethics or data permission | [*Example:* Course data use approved by the department (fictional)] | The flowchart shows how the analysed sample was reached; adapt the counts. ```mermaid flowchart TD A["Enrolled students: 26"] --> B["Completed the survey: 22"] B --> C["Missing sleep data: 2 excluded"] C --> D["Analysed sample: 20"] D --> E["In-person: 10"] D --> F["Online: 10"] ``` ## 3. Variable definitions | Variable | Role | Definition and unit | Coding or transformation | Source | |---|---|---|---|---| | *Example:* `score` | Outcome | Final exam score, points 0 to 100 | None | Course records | | *Example:* `hours` | Exposure of interest | Mean weekly study hours over the term | None; mean 8.05 | Survey | | *Example:* `sleep` | Confounder | Mean nightly sleep, hours | None | Survey | | *Example:* `section` | Confounder | Course section taken | Reference: `in_person`; dummy `online` | Course records | | [Variable] | [Role] | [Definition] | [Coding] | [Source] | **Descriptives of the analysed sample** (fill from your data): score mean 75.7 (SD 11.46), hours mean 8.05, 10 in-person and 10 online students. ## 4. Model specification and justification **Primary model (M2, specified before analysis).** $$ \text{score}_i = \beta_0 + \beta_1\,\text{hours}_i + \beta_2\,\text{sleep}_i + \beta_3\,\text{online}_i + \varepsilon_i, \qquad \varepsilon_i \sim N(0, \sigma^2) $$ | Decision | Choice | Justification | |---|---|---| | Model family | *Example:* OLS linear regression | Continuous outcome with a bounded but not crowded range (55 to 94) | | Predictor of interest | *Example:* `hours` | The research question | | Adjustment set | *Example:* `sleep`, `section` | Both plausibly affect study time and score (confounders); chosen from prior knowledge, not from p-values | | Not adjusted for | *Example:* Coursework mark | Likely a mediator (study time raises coursework, which raises exam score); adjusting would remove part of the effect of interest | | Functional form | *Example:* Linear in hours | Scatterplot roughly linear; checked in diagnostics | | Interaction | *Example:* `hours x section` only as exploratory model M3 | Not pre-specified; too few students to test it with good power | | Standard errors | *Example:* Classical, with HC3 as a sensitivity analysis | n = 20; HC3 guards against unequal variance | | Comparison models | *Example:* M1 = hours only; M3 = M2 plus `hours x section` | To show how adjustment and the interaction change the estimate | **Sample size check.** With p = 4 coefficients and n = 20, there are 5 observations per coefficient, below the common guide of 10 to 20. The primary model is kept small for this reason, and this is listed as a limitation. ## 5. Assumption and diagnostics checklist | Check | Method | Evidence | Verdict | Action | |---|---|---|---|---| | Linearity | Residual vs fitted plot; component-plus-residual plots | *Example:* No curve; adding `hours^2` not needed | Met | None | | Independence | Design review | *Example:* One row per student; no clustering beyond section, which is in the model | Met | None | | Normality of errors | Q-Q plot; Shapiro-Wilk as a weak check | *Example:* Points close to the line; W = 0.961, *p* = .559 | Met | None | | Equal variance | Scale-location plot; score test | *Example:* Flat; χ²(1) = 0.45, *p* = .504 | Met | HC3 SEs as sensitivity anyway | | Influence | Cook's distance, leverage | *Example:* Student 10: Cook's *D* = 0.50 (> 4/n = 0.20, < 1); all others < 0.20 | Flag | Sensitivity analysis without student 10 | | Collinearity | VIF | *Example:* 1.11 to 1.29 | Met | None | | Outcome range | Fitted values within 0 to 100 | *Example:* Fitted 58.0 to 97.2 | Met | None | | [Check] | [Method] | [Evidence] | [Verdict] | [Action] | ## 6. Results **Primary model M2** (OLS, n = 20). *F*(3, 16) = 104.04, *p* < .001, *R*² = .951, adjusted *R*² = .942, residual SE = 2.76 points. | Term | *b* | SE | 95% CI | *t*(16) | *p* | Partial η² | |---|---|---|---|---|---|---| | *Example:* Intercept | 39.94 | 4.60 | [30.20, 49.69] | 8.69 | < .001 | | | *Example:* Study hours (per hour) | 2.89 | 0.20 | [2.48, 3.31] | 14.64 | < .001 | .931 | | *Example:* Sleep (per hour) | 2.39 | 0.74 | [0.82, 3.97] | 3.22 | .005 | .393 | | *Example:* Online (vs in-person) | -7.41 | 1.35 | [-10.26, -4.55] | -5.50 | < .001 | .654 | | [Term] | [ ] | [ ] | [ ] | [ ] | [ ] | [ ] | **Estimand in plain language.** *Example:* Holding sleep and section constant, each additional weekly study hour is associated with an exam score 2.89 points higher (95% CI 2.48 to 3.31). Over a realistic change of 5 hours a week that is about 14.5 points, more than one standard deviation of the scores (11.46). The coefficient plot shows the three slopes with their 95% CIs; an interval that does not cross the zero line is significant at α = 0.05. ```vega-lite { "$schema": "https://vega.github.io/schema/vega-lite/v5.json", "description": "Coefficient plot for the primary model with 95% confidence intervals", "width": 360, "height": 150, "data": {"values": [ {"term": "Study hours (per hour)", "b": 2.89, "lo": 2.48, "hi": 3.31}, {"term": "Sleep (per hour)", "b": 2.39, "lo": 0.82, "hi": 3.97}, {"term": "Online vs in-person", "b": -7.41, "lo": -10.26, "hi": -4.55} ]}, "layer": [ { "mark": {"type": "rule", "strokeWidth": 2}, "encoding": { "y": {"field": "term", "type": "nominal", "title": null, "sort": null}, "x": {"field": "lo", "type": "quantitative", "title": "Coefficient (exam points), 95% CI"}, "x2": {"field": "hi"} } }, { "mark": {"type": "point", "filled": true, "size": 80}, "encoding": { "y": {"field": "term", "type": "nominal", "sort": null}, "x": {"field": "b", "type": "quantitative"} } }, { "data": {"values": [{"zero": 0}]}, "mark": {"type": "rule", "strokeDash": [4, 4], "color": "#888888"}, "encoding": {"x": {"field": "zero", "type": "quantitative"}} } ] } ``` ## 7. Model comparison | Model | Terms | Adj. *R*² | AIC (R) | BIC (R) | LOOCV RMSE | Nested test vs previous | |---|---|---|---|---|---|---| | *Example:* M1 | hours | .847 | 120.62 | 123.61 | 4.670 | | | *Example:* M2 (primary) | hours, sleep, section | .942 | 102.86 | 107.84 | 3.144 | *F*(2, 15) = 17.21, *p* < .001 | | *Example:* M3 (exploratory) | M2 + hours x section | .947 | 101.79 | 107.77 | 3.036 | *F*(1, 15) = 2.49, *p* = .136 | | [Model] | [Terms] | [ ] | [ ] | [ ] | [ ] | [ ] | **Reading the comparison.** *Example:* Adding sleep and section (M1 to M2) clearly improves the fit and reduces the hours slope from 3.14 to 2.89, showing why adjustment matters for the estimand. The interaction (M3) lowers AIC by about 1 and BIC by less than 0.1, and its F test is not significant; by a common rule of thumb, AIC differences below about 2 do not separate two models. M2 stays primary, because it was pre-specified and M3 does not change the answer to the research question. **Why *F*(2, 15) and not *F*(2, 16)?** When `anova()` (or `anova_lm`) compares three or more nested models in one call, every *F* uses the residual mean square of the largest model (M3, 15 df) as its denominator: (239.33 / 2) / (104.33 / 15) = 17.21. Comparing M1 and M2 on their own, `anova(m1, m2)`, uses M2's residual df instead and gives *F*(2, 16) = 15.74. Report the df that match the test you ran. **Software note.** For the same models statsmodels reports AIC values exactly 2 lower (118.62, 100.86, 99.79), because R counts the residual variance as an estimated parameter. Differences between models are the same in both programs; never mix AIC values from the two. ## 8. Validation | Item | Entry | |---|---| | Is prediction an aim? | [*Example:* Secondary: to check overfitting, not to deploy] | | Method | [*Example:* Leave-one-out CV (exact formula for OLS) and 5-fold CV with seed 2026] | | Baseline | [*Example:* M1 (hours only); predicting the sample mean for everyone gives an in-sample RMSE of 11.17] | | Result | [*Example:* LOOCV RMSE: M1 4.67, M2 3.14, M3 3.04. 5-fold RMSE: M1 4.67, M2 3.03, M3 2.81] | | Calibration (for prediction models) | [*Example:* Not applicable for this aim] | | External validation | [*Example:* None; next cohort planned] | **Interpretation.** *Example:* The out-of-sample error of M2 (about 3.1 points) is close to its in-sample residual SE (2.76), so M2 is not badly overfitted. M3 predicts slightly better in both CV schemes, which is consistent with a small interaction that these 20 students cannot confirm. With n = 20, CV estimates are themselves noisy: rerunning the 5-fold CV with 40 other seeds gave an M2 RMSE between 2.85 and 3.63, and M3 beat M2 in only about two splits out of three. Treat the ranking of M2 and M3 as undecided. ## 9. Sensitivity analyses | Analysis | Why | Hours slope (95% CI) | Other change | Conclusion changes? | |---|---|---|---|---| | *Example:* Primary M2 | Reference | 2.89 [2.48, 3.31] | | | | *Example:* HC3 robust SEs | Unequal variance | 2.89, SE 0.22, *p* < .001 | Sleep *p* = .027 (was .005) | No | | *Example:* Without student 10 (Cook's *D* = 0.50) | Influence | 2.96 [2.62, 3.30] | Sleep slope 1.59 [0.21, 2.97] (was 2.39) | No for hours; sleep estimate less certain | | *Example:* With interaction (M3), hours slope by section | Specification | 2.64 (in-person); 3.22 (online) | Interaction *p* = .136 | No | | [Analysis] | [Why] | [ ] | [ ] | [ ] | ## 10. Limitations | Limitation | Consequence | Mitigation or next step | |---|---|---| | *Example:* Observational design | Hours slope may include effects of motivation or prior ability (likely upward bias) | Add a prior-achievement measure; describe as association | | *Example:* n = 20, 5 observations per coefficient | Wide CIs for sleep and section; interaction not testable | Larger cohort; pre-specify interaction tests | | *Example:* Self-reported study hours and sleep | Measurement error tends to bias slopes towards zero | Use learning-platform logs if available | | *Example:* One influential student | Sleep estimate depends on one row | Reported sensitivity analysis | | *Example:* Complete-case analysis (2 excluded) | Bias if missingness relates to the outcome | Multiple imputation as sensitivity | | [Limitation] | [Consequence] | [Mitigation] | ## 11. Reproducibility | Item | Entry | |---|---| | Data file and version | [*Example:* `exam_v1.csv`, checksum recorded in the repository] | | Code location | [*Example:* `analysis/model_report.R` and `analysis/model_report.py`, commit `[hash]`] | | Software | [*Example:* R 4.5.1, car 3.1.5; Python 3.14, numpy 2.5.4, pandas 3.1.0, statsmodels 0.15.0] | | Random seed | [*Example:* 2026 (5-fold CV split)] | | Run time and environment | [*Example:* Under 1 s on a laptop; no internet needed] | **R code** (model comparison, LOOCV, partial η², sensitivity). ```r # Model report: Lakemoor exam study. R 4.5.1, car 3.1.5 library(car) d <- data.frame( hours = c(2, 3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 12, 12, 13, 14), sleep = c(6, 7, 5, 8, 6, 7, 6, 8, 7, 5, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7), section = factor(c("in_person", "online", "in_person", "online", "in_person", "online", "online", "in_person", "online", "in_person", "online", "in_person", "online", "in_person", "online", "in_person", "online", "in_person", "online", "in_person"), levels = c("in_person", "online")), score = c(61, 55, 64, 66, 72, 65, 66, 81, 69, 69, 75, 82, 75, 86, 77, 89, 83, 92, 93, 94)) m1 <- lm(score ~ hours, data = d) # baseline m2 <- lm(score ~ hours + sleep + section, data = d) # primary (pre-specified) m3 <- lm(score ~ hours * section + sleep, data = d) # exploratory interaction anova(m1, m2, m3) # nested F tests data.frame(model = c("M1", "M2", "M3"), AIC = round(sapply(list(m1, m2, m3), AIC), 2), BIC = round(sapply(list(m1, m2, m3), BIC), 2), adjR2 = round(sapply(list(m1, m2, m3), function(m) summary(m)$adj.r.squared), 3)) # Leave-one-out CV RMSE (exact shortcut for OLS: e_i / (1 - h_ii)) loocv <- function(m) sqrt(mean((resid(m) / (1 - hatvalues(m)))^2)) round(sapply(list(M1 = m1, M2 = m2, M3 = m3), loocv), 3) # Effect sizes: partial eta-squared from type II sums of squares a <- Anova(m2); ss <- a$`Sum Sq` round(ss[1:3] / (ss[1:3] + ss[4]), 3) # Sensitivity: drop the most influential student (row 10, Cook's D = 0.50) m2b <- update(m2, data = d[-10, ]) round(cbind(full = coef(m2), drop10 = coef(m2b)), 3) round(confint(m2b), 3) ``` **R output** (output abridged: headings, significance codes and blank lines between results removed). ```text Model 1: score ~ hours Model 2: score ~ hours + sleep + section Model 3: score ~ hours * section + sleep Res.Df RSS Df Sum of Sq F Pr(>F) 1 18 360.95 2 16 121.62 2 239.33 17.2050 0.0001309 *** 3 15 104.33 1 17.29 2.4859 0.1357256 model AIC BIC adjR2 1 M1 120.62 123.61 0.847 2 M2 102.86 107.84 0.942 3 M3 101.79 107.77 0.947 M1 M2 M3 4.670 3.144 3.036 [1] 0.931 0.393 0.654 full drop10 (Intercept) 39.943 45.379 hours 2.894 2.955 sleep 2.395 1.592 sectiononline -7.408 -7.626 2.5 % 97.5 % (Intercept) 36.711 54.048 hours 2.615 3.295 sleep 0.211 2.973 sectiononline -9.931 -5.321 ``` **Python code** (nested tests, AIC and BIC, seeded 5-fold CV). ```python # Model report: Lakemoor exam study. Python 3.14, numpy 2.5.4, pandas 3.1.0, statsmodels 0.15.0 import numpy as np import pandas as pd import statsmodels.formula.api as smf from statsmodels.stats.anova import anova_lm d = pd.DataFrame({ "hours": [2, 3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 12, 12, 13, 14], "sleep": [6, 7, 5, 8, 6, 7, 6, 8, 7, 5, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7], "section": ["in_person", "online", "in_person", "online", "in_person", "online", "online", "in_person", "online", "in_person", "online", "in_person", "online", "in_person", "online", "in_person", "online", "in_person", "online", "in_person"], "score": [61, 55, 64, 66, 72, 65, 66, 81, 69, 69, 75, 82, 75, 86, 77, 89, 83, 92, 93, 94]}) formulas = {"M1": "score ~ hours", "M2": "score ~ hours + sleep + section", "M3": "score ~ hours * section + sleep"} fits = {k: smf.ols(f, data=d).fit() for k, f in formulas.items()} print(anova_lm(fits["M1"], fits["M2"], fits["M3"]).round(4)) for k, m in fits.items(): print(k, "AIC", round(m.aic, 2), "BIC", round(m.bic, 2)) # 5-fold cross-validation with a fixed seed rng = np.random.default_rng(2026) folds = rng.permutation(np.arange(len(d)) % 5) for k, f in formulas.items(): err = [] for j in range(5): train, test = d[folds != j], d[folds == j] err.extend(test["score"] - smf.ols(f, data=train).fit().predict(test)) print(k, "5-fold CV RMSE:", round(float(np.sqrt(np.mean(np.square(err)))), 3)) ``` **Python output.** ```text df_resid ssr df_diff ss_diff F Pr(>F) 0 18.0 360.9523 0.0 NaN NaN NaN 1 16.0 121.6199 2.0 239.3324 17.2050 0.0001 2 15.0 104.3299 1.0 17.2900 2.4859 0.1357 M1 AIC 118.62 BIC 120.61 M2 AIC 100.86 BIC 104.84 M3 AIC 99.79 BIC 104.77 M1 5-fold CV RMSE: 4.671 M2 5-fold CV RMSE: 3.033 M3 5-fold CV RMSE: 2.814 ``` The nested F tests agree exactly between R and Python. AIC and BIC differ by a constant (2 for AIC, ln 20 = 3.00 for BIC) for the reason given in section 7. ## 12. Review and sign-off | Role | Name | Decision | Date | Comments | |---|---|---|---|---| | Analyst | [Name] | [Submitted] | YYYY-MM-DD | [ ] | | Reviewer or supervisor | [Name] | [Approved / Changes requested] | YYYY-MM-DD | [*Example:* Add prior-achievement covariate in next cohort] | | Open issues | [List] | | | | **Reviewer checklist.** - [ ] Purpose and estimand stated before results - [ ] Every excluded row is accounted for - [ ] Adjustment set justified by reasoning, not by p-values - [ ] Every diagnostic row has evidence - [ ] Primary model is the pre-specified one, or the change is explained - [ ] Effect of interest reported with CI and in plain language - [ ] Validation matches the purpose - [ ] Sensitivity analyses reported, including any that weaken the result - [ ] Limitations give consequences, not only labels - [ ] Code reruns and reproduces the numbers ## Common mistakes in model reports - **Selecting predictors by stepwise p-values and then interpreting the coefficients as effects.** The CIs and p-values after selection are too narrow and too small. For explanation, choose the adjustment set from subject knowledge; for prediction, validate the whole selection process. - **Adjusting for a mediator or a collider.** Controlling for coursework marks would remove part of the study-hours effect you want to estimate. - **Reporting only p-values.** The estimand needs a size, a unit and an interval. - **Using AIC to choose a model and then reporting its p-values as confirmatory.** Say which model was pre-specified and which was chosen after looking at the data. - **Calling in-sample R² "accuracy".** Prediction claims need out-of-sample error, and a baseline to compare with. - **Hiding a sensitivity analysis that weakened the result.** The sleep estimate dropping by a third without one student is information a reader needs. - **Listing limitations without consequences.** "The sample is small" should say what it does: wide intervals, an untestable interaction. ## Self-check questions 1. In the example, why is M2 kept as the primary model even though M3 has a lower AIC and a lower cross-validated RMSE? 2. Why is the coursework mark not in the adjustment set, even though it would increase R²? 3. The 5-fold CV RMSE of M2 is 3.03 and the LOOCV RMSE is 3.14. Is one of them wrong? 4. Removing student 10 changes the sleep coefficient from 2.39 to 1.59. Should student 10 be deleted from the primary analysis? 5. Which sections of this report would change most if the purpose were prediction for next year's students instead of explanation? ## Sources and further reading Structure aligned with common reporting guidance for regression analyses: APA JARS-Quant (named only), the TRIPOD statement for prediction models and its 2024 update TRIPOD+AI (named only), and the explain-versus-predict distinction. - Shmueli, G. (2010). To explain or to predict? *Statistical Science*, 25(3), 289-310. - Collins, G. S., Moons, K. G. M., Dhiman, P., and colleagues (2024). TRIPOD+AI statement: updated guidance for reporting clinical prediction models that use regression or machine learning methods. *BMJ*, 385, e078378 (supersedes the 2015 TRIPOD checklist). - Harrell, F. E. (2015). *Regression Modeling Strategies* (2nd ed.). Springer. - Collins, G. S., Reitsma, J. B., Altman, D. G., and Moons, K. G. M. (2015). Transparent reporting of a multivariable prediction model for individual prognosis or diagnosis (TRIPOD): the TRIPOD statement. *BMJ*, 350, g7594. - Akaike, H. (1974). A new look at the statistical model identification. *IEEE Transactions on Automatic Control*, 19(6), 716-723. - Schwarz, G. (1978). Estimating the dimension of a model. *Annals of Statistics*, 6(2), 461-464. - Cook, R. D. (1977). Detection of influential observation in linear regression. *Technometrics*, 19(1), 15-18. - Long, J. S., and Ervin, L. H. (2000). Using heteroscedasticity consistent standard errors in the linear regression model. *The American Statistician*, 54(3), 217-224. - Wasserstein, R. L., and Lazar, N. A. (2016). The ASA statement on p-values: context, process, and purpose. *The American Statistician*, 70(2), 129-133. - Further reading by name: de Smith, M. J., *Statistical Analysis Handbook* (StatsRef, 2024 edition); NIST/SEMATECH *e-Handbook of Statistical Methods*; APA *Publication Manual* (7th ed.). ## Answer key 1. M2 was pre-specified to answer the research question; M3 adds a term that was not planned and whose test is not significant (*p* = .136). The AIC difference (about 1) is below the usual threshold of 2, and the CV difference is within the noise of a 20-row data set. Choosing the primary model after seeing results would make its inference over-optimistic. M3 is reported as exploratory. 2. Coursework is likely on the causal path from study time to exam score (a mediator). Adjusting for it would estimate only the part of the study-hours association that does not pass through coursework, which is not the estimand. A higher R² does not make the estimand more correct. 3. No. They are two estimates of the same out-of-sample error from different resampling schemes; both are noisy at n = 20. LOOCV has low bias but high variance; 5-fold CV depends on the random split (seed 2026). 4. No, unless the row is a data error. It is a real student with an unusual combination (little sleep, average study, lower score). Keep the student, report the sensitivity analysis, and soften the claim about sleep. 5. Sections 1 (purpose and estimand: predicted score, not a slope), 4 (predictors chosen for predictive value, possibly including the interaction), 8 (validation becomes central, with calibration and ideally an external cohort) and 6 (accuracy metrics instead of coefficient interpretation). Section 10 would focus on transportability to new cohorts. ## Revision history | Version | Date | Author | Change | |---|---|---|---| | 0.1 | YYYY-MM-DD | [Name] | First draft from the template | | [0.2] | YYYY-MM-DD | [Name] | [Added sensitivity analysis without student 10 after review] |