Multivariate Regression Modeling

Abstract

An empirical or regression modeling approach is simple to develop and easy to use compared to detailed hourly simulations of energy use in commercial buildings. Therefore, regression models developed from measured energy data are becoming an increasingly popular method for determining retrofit savings or identifying operational and maintenance (O&M) problems. Because energy consumption in large commercial buildings is a complex function of climatic conditions, building characteristics, building usage, system characteristics and type of heating, ventilation, and air conditioning (HVAC) equipment used, a multiple linear regression (MLR) model provides better accuracy than a single-variable model for modeling energy consumption. Also, when hourly monitored data are available, an issue which arises is what time resolution to adopt for regression models to be most accurate. This paper addresses both these topics. This paper reviews the literature on MLR models of building energy use, describes the methodology to develop MLR models, and highlights the usefulness of MLR models as baseline models and in detecting deviations in energy consumption resulting from major operational changes. The paper first develops the functional basis of cooling energy use for two commonly used HVAC systems: dual-duct constant volume (DDCV) and dual-duct variable air volume (DDVAV). Using these functional forms, the cooling energy consumption in five large commercial buildings located in central Texas were modeled at monthly, daily, hourly, and hour-of-day (HOD) time scales. Compared to the single-variable model (two-parameter model with outdoor dry-bulb as the only variable), MLR models showed a decrease in coefficient of variation (CV) between 10 percent to 60 percent, with an average decrease of about 33 percent, thus clearly indicating the superiority of MLR models. Although the models at the monthly time scale had higher coefficient of determination (R2) and lower CV than daily, hourly, and HOD models, the daily and HOD models proved more accurate at predicting cooling energy use.