Model Choice and Extrapolation at a Distribution Center
A 400,000 ft² distribution center has 14 months of hourly whole-building electricity data, hourly outdoor temperature, and a new LED lighting retrofit plus dock-door seal replacement. The M&V plan uses Option C. The analyst fits a change-point model to the 14 pre-install months: a 3-parameter heating-only model (constant base plus a temperature-dependent term below 58°F) gives adjusted R² = 0.91 and CV(RMSE) = 6.8%. The analyst then applies this model to the post-install year, which turns out to be the warmest on record, with 40% fewer heating degree days than the baseline period. Summer cooling load is substantial. The analyst reports savings equal to baseline minus reporting-period energy using the heating-only model.
1. What is wrong with the model selection and its application here, and what should have been done?
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Two problems. First, a heating-only model cannot represent a facility with substantial summer cooling load; the 0.91 R² is inflated because the baseline period may not have exercised the cooling regime, and the model will systematically mispredict warm months. A 4- or 5-parameter model (heating and cooling change points) is the appropriate form for a building with both heating and cooling, and the analyst should have tested it and compared fit statistics and residual behavior across seasons.
Second, applying a heating-only model to a year with 40% fewer HDDs extrapolates outside the range of the baseline data and attributes all warm-weather cooling to savings. The adjusted baseline will be far too low in summer, overstating savings. The fix: refit with a heating-and-cooling model, verify the cooling coefficients are supported by baseline data (if the baseline period lacks hot weather, the cooling term is not identifiable and Option C savings cannot be reliably claimed for summer), and check that the reporting-period temperatures fall within the baseline range. If they do not, disclose the extrapolation and its uncertainty.
2. The owner wants a single savings number anyway. How do you respond, and what would you report instead?
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Decline to present a single point estimate that implies precision the data do not support. Report instead: (1) savings with an explicit uncertainty band derived from the model's prediction error and the extrapolation, (2) a statement that the warm year limits the reliability of the cooling-season portion, and (3) a recommendation - either refit with a proper 4/5-parameter model if baseline data support it, or restrict the claim to the heating-season months where the model is valid, or revert to Option B (lighting and dock doors are separately measurable) for a defensible number. The professional answer is a clearly bounded claim, not a comfortable one.