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Daily demand analysisExample datasetAdd your data.
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✓ 731 records recognized · source retainedTry it: drag the example file here, or click to use it.| Date | Daily rides | Weather |
|---|---|---|
| 01 Jan 2011 | 985 | Mist / cloudy |
| 02 Jan 2011 | 801 | Mist / cloudy |
| 03 Jan 2011 | 1,349 | Clear |
Three rows from the original public dataset. Your source file stays unchanged.
Choose your analysis goal.
Choose what to explain and which variables to consider. OptiMod determines the statistical approach.
How is weather associated
with bike-sharing demand?
Analysis complete.
OptiMod evaluates the data and method requirements, compares eligible models and computes the results.
731 records checked. Leakage and redundant columns excluded.
Count models compared against the data and diagnostic evidence.
Confidence intervals, sensitivity checks and remaining limits recorded.
Lower demand on rainy days.
Weather is associated with daily demand, after accounting for other variables.
Estimated association in this dataset.
95% interval: 38%–60% lower.
Model-based comparison; other variables held fixed. Clear weather = 100.
This is an association, not proof of cause and effect. Model limits remain part of the analysis.
Your analysis. Fully documented.
From model assumptions to named statistical tests: the scientific record behind your result.
SCIENTIFIC REPORTDaily bike-sharing
demand.
Data. Methods. Evidence.
- 01What was analysed
The question, source data and preparation.
- 02Assumptions & exact statistical tests
Test names, statistics, p-values and interpretation.
- 03What the evidence supports
Findings, uncertainty and limitations.
Keep and share the record independently of access to OptiMod.
Drop in your data. OptiMod handles the scientific analysis once you set the goal.
Real public dataInterface preview, in final development. The example uses real public data and independently computed results. Playback illustrates the analysis and report export workflow.
731 days of recorded bike-sharing demand in Washington, DC, from January 2011 to December 2012.
- Original source
- UCI Bike Sharing · day.csv · 16 columns
- Missing values / duplicate days
- 0 / 0
- Source integrity
- Original file retained; SHA-256 recorded in the report
The preview uses readable column labels. The downloadable CSV preserves the original names and normalized units.
Download the original CSVAn explanatory analysis of conditional relationships, using observed daily weather and calendar data.
- Outcome
cnt· daily rental count- Source variables
- Weather category, temperature, humidity, wind, holiday, weekday and date.
- Calendar adjustment
- Month, weekday and a continuous time trend; a quadratic temperature term.
- Excluded from predictors
casualandregisteredalready sum to the outcome;instantis an identifier;atempduplicates temperature information.
The question and setup are fixed for this example. This is not a future-weather forecast or an estimate of causal effects.
The checks make scientific choices visible. They also retain findings that need judgement.
Data preparation
All 731 rows are retained. No missing values are imputed and no outliers are silently removed. Two target-leakage columns and a redundant temperature variable are excluded.
One humidity reading is zero (10 March 2011). It is flagged and the analysis is repeated without it as a sensitivity check. Temperature stays in normalized source units because archive metadata conflict.
Model comparison
Poisson and Negative Binomial (NB2) are fitted to 547 training days. Training AIC is 66,197.6 for Poisson and 8,815.7 for NB2. Poisson dispersion is 109.20, indicating marked extra variation relative to its variance assumption.
NB2 is selected for the association analysis. Poisson has the lower prediction error in the 184-day holdout: 689 versus 863 rides/day. Model selection follows the question, not a universal winner.
Remaining review points
Coefficient intervals use 7-lag HAC covariance. Residual lag-1 correlation remains 0.387; this adjustment does not remove model limitations. Weather category 3 contains only 21 days. Study design, measurement and transfer to other settings still require review.
Light rain or snow is associated with a 50.4% lower expected daily count than clear weather, conditional on the included variables.
- Estimated count ratio
- 0.496 · clear weather = 1
- 95% confidence interval
- 0.399 to 0.617 · 38.3% to 60.1% lower demand
- Analysis sample
- Full dataset · 731 days · Negative Binomial regression
- Uncertainty
- Approximate pointwise HAC interval · 7 daily lags
The chart shows adjusted count ratios, not raw average demand. The mist/cloudy estimate is 0.910. These exploratory associations have no multiplicity adjustment and do not establish causation.
Evaluation is a separate question
Held-out prediction error uses a model fitted to the first 547 days. Its NB2 MAE is 863 rides/day and RMSE is 1,123; Poisson has a lower MAE of 689. The 184 held-out days use realized weather, not weather forecasts.
An exact record of the calculation: the question checked, the procedure used, its numerical result and the interpretation.
| Question / assumption | Test or diagnostic | Result |
|---|---|---|
| Residual autocorrelation through 7 daily lags | Ljung–Box Q df = 7 | Q = 251.9104 p = 1.0863 × 10−50 Dependence detected |
| Residual autocorrelation through 14 daily lags | Ljung–Box Q df = 14 | Q = 258.9912 p = 3.9574 × 10−47 Dependence detected |
| Can the mean-model coefficients be estimated? | Design-matrix rank | 26 of 26 columns Full rank · no p-value |
| Is Poisson variance consistent with the observed variation? | Pearson dispersion Training model | 109.20 Marked overdispersion · diagnostic, not a formal p-value test |
The interpretation is part of the record.
The Ljung–Box null is no residual autocorrelation through the stated lag. Both reference checks indicate remaining dependence. Here they are descriptive residual checks using model_df = 0, not definitive NB2 specification tests.
Seven-lag HAC covariance is used for coefficient uncertainty. It does not remove the dependence or guarantee that the model is correctly specified. The report preserves this finding alongside the model choice and results.