Energy baseline regression calculator

Paste a driver such as degree days or production next to energy use. Get the baseline equation, R², CV(RMSE), the slope t-statistic, a chart, and avoided energy for a reporting period.

Paste your data: driver (X) and energy (Y)One row per period (for example one month). Two columns separated by a tab, comma, semicolon or space, so you can paste straight from a spreadsheet. X can be degree days, production or occupancy.

Data points (n): —
R²: —
CV(RMSE): —
t-statistic of the slope: —
Standard error of the estimate: —
Baseline X range: —

Avoided energy in a reporting period (optional)

Adjusted baseline = the baseline equation applied to reporting-period conditions. Avoided energy = adjusted baseline − measured energy.

Number of reporting periods (k)

Total driver in the reporting period (ΣX)

Measured energy in the reporting period

Adjusted baseline: —
Avoided energy: —
Savings: —

Formula

\hat{Y} = a + b\,X

b = \frac{\sum (X_i - \bar{X})(Y_i - \bar{Y})}{\sum (X_i - \bar{X})^{2}}

a = \bar{Y} - b\,\bar{X}

R^{2} = 1 - \frac{\sum (Y_i - \hat{Y}_i)^{2}}{\sum (Y_i - \bar{Y})^{2}}

\mathrm{CV(RMSE)} = \frac{100}{\bar{Y}} \sqrt{\frac{\sum (Y_i - \hat{Y}_i)^{2}}{n - 2}}

t = \frac{b}{\mathrm{SE}_b}

\mathrm{SE}_b = \sqrt{\frac{\sum (Y_i - \hat{Y}_i)^{2} / (n - 2)}{\sum (X_i - \bar{X})^{2}}}

E_{\text{avoided}} = \left(k\,a + b \sum X_{\text{rep}}\right) - E_{\text{measured}}

How it works

The calculator fits a straight line by least squares: energy = a + b × driver. The intercept a is the base load per period and the slope b is the extra energy per unit of the driver, for example therms per heating degree day.

R² shows how much of the variation the driver explains, and CV(RMSE) shows the typical scatter around the line as a percentage of mean energy. A slope t-statistic above about 2 means the driver is significant at roughly 95% confidence. Your M&V plan, or the guideline it follows such as ASHRAE Guideline 14 or IPMVP, sets the limits that apply to your project.

Use the model only for reporting periods whose conditions fall inside the baseline X range. Outside that range the straight line is an extrapolation and the savings become uncertain.

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Results are estimates for study and screening. Check the inputs, units and assumptions before you use them for design, billing or contract decisions.