Tools › Building Systems › Energy › Energy Savings and Payback › Example
BPA Regression for M&V guide Section 6: degree-day regression of classroom heat-pump bills
| Tool | Energy Savings and Payback |
| Source | Bonneville Power Administration (2024). Regression for M&V: Reference Guide. Section 6, Tables 6-1 to 6-8. |
| Level | Professional |
Problem
Twelve monthly electricity bills of a classroom building heated by heat pumps are given with the heating degree days (base 65 °F) and the days in each period, from 24 September 2007 to 22 August 2008. Normalize the bills per day, regress kWh/day on HDD/day, report the model statistics against the Guideline 14 monthly criterion and the modeled use of each period with its 90 % confidence half-interval.
Inputs to Enter
- Bills (loaded by default): 09/24/2007 6,080 kWh, 113 HDD, 30 days; 10/24/2007 7,330, 311, 30; 11/21/2007 7,470, 463, 28; 12/19/2007 10,000, 669, 28; 01/23/2008 11,480, 877, 35; 02/25/2008 11,420, 782, 33
- 03/26/2008 9,970, 560, 30; 04/24/2008 7,840, 561, 29; 05/20/2008 6,800, 265, 26; 06/21/2008 5,980, 268, 32; 07/23/2008 4,310, 73, 32; 08/22/2008 3,330, 57, 30; CDD zero throughout
- Degree-day model (HDD only), base 65 °F, per-day normalization
Answers
- kWh/day = 132.24 + 8.8678 HDD/day (guide's spreadsheet rounding; full precision 132.17 + 8.872 HDD/day)
- R² = 0.879, CV(RMSE) = 11.7 % (meets the 15 % criterion), standard error 29.69 kWh/day, slope t = 8.56
- Modeled kWh/day by period: 165.5, 224.2, 278.8, 344.1, 354.4, 342.5, 297.7, 303.9, 222.4, 206.6, 152.6, 149.0 (total 3,041.8 = actual)
- 90 % confidence half-interval of the line by period: 24.3, 16.7, 16.4, 24.7, 26.5, 24.5, 18.2, 18.9, 16.9, 18.4, 26.5, 27.1 kWh/day
- In the temperature form (T = 65 − HDD/day) the 2P model gives the same fit with slope −8.872
Notes
The tool's default bills are this example; press Submit to reproduce it. Table 6-2 of the guide gives the per-day values (202.7 kWh/day and 3.7 HDD/day for the first period).