Statistical investigation: vehicle efficiency, model revision and changed targets
Build one reproducible investigation using the local UCI Auto MPG data pack. Compare a declared mean baseline and two regression candidates on the same complete-case cohort, inspect assumptions, freeze a public chronological validation record and defend a revised manuscript. Then change the response target to fuel consumption rather than merely rerunning the same fit. This supported portfolio does not establish independent mastery, causal effects, or secure unseen evaluation.
Planning estimate: 18 hours, including analysis, writing and revision. Use the investigation and working agreement below. Keep a single coherent report across milestones rather than unrelated short answers.
Preparation and working agreement
The response is source-recorded city-cycle miles per gallon (MPG), a positive continuous measurement. Define w=source weight/1000 and h=source horsepower/100 for the fitted predictors; the original metadata does not fully specify measurement units/procedures or independence, so retain source labels rather than inventing a documented protocol. Use model years 70–72 for development, 73 for public validation and 74 for the changed transfer. These are chronological historical cohorts, not randomized groups or a representative sample of present vehicles. Predictive association does not identify the effect of changing a vehicle’s weight or power.
Use the supplied local UCI Auto MPG pack with its attribution, CC BY 4.0 license notice, original data version and source-row IDs. Preserve missing horsepower as missing, not zero. For the primary comparison, define eligibility before comparing models: observed MPG, weight and horsepower, valid positive quantities and the declared year. Use exactly that common eligible cohort for the mean baseline, weight-only model and weight-plus-horsepower model. Retain every excluded source-row ID and reason; complete-case results need not generalize to the excluded records. The local folder is /data/math-statistics-auto-mpg/: study-rows.csv and study-rows.json contain the 152 selected records; metadata.json and LICENSE.txt retain provenance. Source IDs are one-based positions in the processed 398-row auto-mpg.data file, not the 406-row original: UCI had already removed eight records with missing MPG. Do not misclassify those upstream exclusions as a new local eligibility decision.
Use an intercept in every candidate. Fit the baseline mean, weight-only least squares and weight-plus-horsepower least squares on development rows only. The fixed published divisors 1000 and 100 are unit-scale conventions, not fitted statistics. Any additional estimated centering or scaling constants must come from development only. Preserve raw source values and state coefficients relative to w and h; document any additional inverse transformation of predictions. Do not tune to year 73 or 74 while calling those observations untouched. Once an outcome or public solution is viewed, retain that exposure in the report and local history.
Keep a full manuscript, cohort manifest, row-level predictions and losses, figures, computation log, revisions and a reproduction guide separately. The page accepts a concise text response of at most 8,000 characters per milestone, not an upload of these artifacts and not automatic execution or verification of a referenced file. Name external artifacts and versions in each response. A noncoding route uses retained computation tables, transparent tool settings and independent hand checks; implementation proficiency additionally requires retained executable source and tests.
Reuse the fitted-regression bridge for QR, conditional intervals and residual plots. PCA is optional for predictor structure: a loading or explained-predictor-variance percentage is not evidence of predictive accuracy for MPG. Binomial and Poisson GLMs are inappropriate merely because MPG values are positive: MPG is neither a success count with trial totals nor an event count with exposure.
The approximately 18-hour budget is an unvalidated author estimate. Public data, frozen timestamps and reviewer labels are not secure examination controls. Retain source assistance and prior exposure. Actual independent review requires a person to inspect the evidence and pose a changed question; if unavailable, record a self-audit and leave independent review pending.
Use each argument's planning fields, immutable revisions and revision-specific feedback. Save derivations, data provenance, numerical checks and a reproducible method in the report. External code or files should be identified by filename and instructions in your response; this page stores text and does not run code or upload artifacts.
Data investigation: fit, freeze and challenge
This optional calculator supports the analysis. Your report must explain the question, design, evidence and revision. Fits and comparisons here are temporary. Written milestone revisions are saved separately by the project page.
A real dataset with a reproducible study
Source: Quinlan, R. (1993), Auto MPG, UCI Machine Learning Repository, CC BY 4.0. This adaptation selects model-year codes 70–74 from the 398-row processed source, retains five source fields and adds one-based source-row IDs. That source already excluded eight records with missing MPG. Missing horsepower remains missing. Retrieved 26 October 2026; attribution, changes and source hash are included below.
Development: 1970–72. Public validation: 1973. Separate transfer practice: 1974. These historical cohorts are not a random sample, a secure examination or evidence about current vehicles. Downloading the pack exposes every cohort; the buttons cannot make it unseen. Record earlier access, solutions and assistance in your report.
This session has displayed 1973 evaluation: not through this calculator; 1974 evaluation: not through this calculator. This does not track downloads or earlier sessions. Repeated evaluation of public rows is development practice, not independent new evidence. Do not use 1974 results retrospectively to choose a model supposedly selected on 1973.
0 of 7 milestones have recorded responses. This counts submissions, not quality, independent review or project mastery.
Freeze the question, target and comparison protocol
Before fitting or inspecting validation outcomes, write a concrete prediction question for the historical vehicle records and its limits. Define the response and predictor units, chronological splits, common complete-case eligibility, three candidate equations, loss functions and planned diagnostic plots. Predict which candidate will improve on the baseline and why that prediction may fail under year shift. State what would count as a revision and where it would be evaluated. Record any prior viewing of these public data or solutions.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Audit provenance, missingness and the row manifest
Create a data dictionary and a source manifest from the local pack: attribution/license, version, original row ID, model year, response, predictors and missing-value representation. Count all source rows and eligible/excluded rows by the three split roles; list excluded IDs and reasons. Show that all three primary candidates use identical development and validation IDs. Compare an available-case weight-only cohort with the common complete-case cohort as a labeled sensitivity analysis, not a competing main-score advantage. Explain why missing horsepower cannot be coded as zero.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Fit three candidates and independently check the arithmetic
Using development rows only, fit M0, M1 and M2. Report n, design rank, coefficients using the declared source scales w and h, development SSE/MSE/MAE and residual summaries. Retain row-level predictions keyed by source ID. Independently check the baseline mean, the weight-only slope by centered scalar sums, the M2 residual normal equations and at least three named row predictions by hand. Prove the nested training-SSE inequality. For implementation, test these checks and invalid/missing/rank cases in an executable artifact; for noncoding, preserve equivalent explicit tables and a second calculation method.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Audit residual patterns and conditional uncertainty
Inspect residual-versus-fitted and residual-versus-predictor plots, influence/leverage summaries and residual patterns by model year for each candidate. Select and explain one plausible concern and a concrete check or revision. At a development-supported target row of your choice, distinguish a conditional mean interval from an individual-response interval and show the formula and assumptions; do not claim the historical records verify them. Explain what grouping or dependence could invalidate ordinary inference and why PCA would not settle response-model adequacy.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Retain a frozen validation result and an exposed revision
Freeze all three development coefficient vectors, preprocessing constants, eligibility IDs and the comparison rule before evaluating year 73. Retain predictions, residuals, squared/absolute losses and a common-cohort summary. Compare your original prediction with the observed ranking. Investigate at least one failed prediction or influential validation record. If you revise a model or analysis after reading these outcomes, retain both versions and mark year 73 exposed; state what a later check can and cannot establish.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Assemble a reproducible analysis and retained artifact
Assemble one manuscript connecting the question, source/cohort manifest, candidate derivations, independent checks, diagnostics, frozen result and revision history. Supply a reproduction guide and a concise result table linked to row-level artifacts. For implementation, retain executable source and tests; for noncoding, retain sufficient computation tables, tool versions/settings and hand checks for another person to reproduce the analysis. Record all assistance and solution exposure. Explain how the text page points to these artifacts without pretending to upload or verify them.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Defend the decisions and revise after a challenge
Ask a reviewer to inspect the dossier and challenge one mathematical argument, one data/cohort decision and one interpretation. Record the actual questions, your answers and any revisions. Defend why a shared cohort is needed, why an additional predictor cannot worsen optimized training SSE yet can worsen validation loss, and why an observational slope does not establish a causal effect. If independent review is unavailable, conduct a recorded self-defense and leave review pending. Do not replace your observed results with the model solution.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Review, defend and revise
Ask a reviewer to examine the complete reasoning, reproduce selected results and pose an unfamiliar case. Record their feedback against the specific revision discussed. Reviewer labels are entered locally and do not verify identity or judgment. A complete set of text submissions does not certify an independently defended investigation.
Targeted lesson returns
Freeze the question, target and comparison protocol
