Building an Energy Baseline with Regression: From Choosing Variables to Re-baselining

An Energy Baseline (EnB) is the reference point against which current or future energy performance is compared. When more than one variable affects consumption, the simplest and most defensible way to build an EnB is multivariate linear regression on historical data. The process usually starts by gathering at least 12 months of consumption data along with candidate variables (production, weather, operating hours); several regression models with different variable combinations are then built and statistically compared to select the model with the best fit and the strongest engineering logic.

Choosing driver variables

A driver variable needs both a meaningful statistical correlation with consumption and a physically justifiable link to it. Multicollinearity between drivers should also be avoided; for instance, using 'tonnes produced' and 'line operating hours' together, when the two move almost in lockstep, destabilises the model and makes its coefficients hard to interpret.

Model acceptance criteria: R² and CV(RMSE)

The coefficient of determination (R²) shows how much of the variation in consumption is explained by the driver variables — a value closer to one indicates a better fit. The coefficient of variation of the root-mean-square error (CV(RMSE)) expresses the model's error relative to average consumption, providing a scale that's comparable across different models.

• R² of at least 0.75 for monthly data, as a common rule of thumb
• CV(RMSE) of roughly 20-25% or less for monthly data, per common guidelines such as ASHRAE's
• Checking the statistical significance (p-value) of each coefficient, not just the overall fit
• Confirming that each coefficient's sign is consistent with the process's physical logic

A simple numerical example

For a production facility with monthly electricity consumption between 800 and 1,100 megawatt-hours, a single-variable model based on monthly production tonnage typically yields an R² near 0.70 and a CV(RMSE) of around 18%. Adding auxiliary equipment operating hours (such as a cooling system) as a second variable often pushes R² above 0.85 and brings CV(RMSE) down below 12% — an improvement that shows the second variable genuinely captures a portion of the consumption variation that was previously unexplained. For extra confidence, it's good practice to hold out the last 2-3 months of historical data, build the model using only the remaining months, and then check its predictive accuracy against those held-out months; this simple technique reveals the difference between a model that has genuinely learned the consumption behaviour and one that merely fits the historical data well.

• At least 12 months of historical data with no significant gaps are available
• The residual-versus-time plot has been reviewed and shows no systematic pattern
• No undocumented static factor occurred during the data period
• The calculation method and model variables are documented in the energy data collection plan

Checking the residuals

Once a model is chosen, the residuals (the difference between actual and predicted values) should be plotted against time. A systematic pattern in the residuals — such as an upward trend or an unexplained seasonal swing — signals that an important variable is missing or that the process's behaviour has changed over time.

Static factors

Unlike driver variables, which are measured continuously, static factors are discrete events that change operating conditions — such as adding a new work shift, replacing a major piece of equipment, or a permanent shift in product mix. These factors aren't part of the regression model, but they need to be documented so they can inform how future deviations are interpreted and whether the baseline needs to be redefined.

When should the baseline be re-established?

Re-baselining is needed when one or more significant static factors occur, when the existing model no longer meets the R² and CV(RMSE) criteria, or after an extended shutdown or a fundamental process change. For example, if a new production line is commissioned alongside the old one, the previous baseline no longer explains current consumption behaviour and needs to be rebuilt using post-change data.

A baseline is valid for as long as its statistical assumptions still hold, not for as long as it's recorded in an audit document.