Investigating factors affecting heating/cooling efficiency of buildings using nonlinear and nonparametric regression models

Abstract

Nonlinear regression models are fitted when the relationships between the response (dependent) and the explanatory variables (predictors) is a nonlinear combination of the model parameters and depends on one or more independent variables. Hence numerical optimization algorithms have to be applied to determine the best-fitting parameters. In contrast to linear regression, there may be many local maxima of the function to be optimized. The best-fit curve is often assumed to be that which minimizes the sum of squared residuals. However, when the dependent variable does not have constant variance, the sum of weighted squared residuals is minimized, where each weight is equal to the reciprocal of the variance of the observation. Unlike linear regression models, nonparametric regression is agnostic about the functional form between the dependent variable and the predictors and is therefore not subject to mis-specification errors. Kernel density estimation is a fundamental data smoothing problem where inferences about the population are made, based on a finite data sample. This dissertation focusses on three kernel density functions, including the Epanechnikov, Gaussian and Quartic (Biweight) kernel functions. Moreover, the bandwidth of the kernel is a free parameter which exhibits a strong influence on the resulting estimate. Nonlinear and nonparametric regression models will be used to analyze a dataset comprising of 768 observations. The purpose of this analysis is to relate the heating/cooling efficiency of buildings to three predictors, including the building relative compactness, the building glazing area and the aperture orientation of the building.