The Sensitivity of the Regression Parameters

Theory of statistics and its application to data analysis in all fields of endeavor, forms the base of statistical analysis. While data collection and validation is not dealt with in this thesis, the importance of data on the analysis results is obvious. In general data are discrete observations in a continuous process. Number of variables involved is also very important. Hence, multivariate statistical analysis has gained importance, especially after computers could be used to process huge amounts of data. In this thesis, simple and multivariate regression techniques, principal component analysis are explained in detail, and also used in the analysis of a real life data. Since the matrix algebra is implemented in all computations, a brief introduction to certain concepts of matrix algebra is also given under Chapter 3. Chapter 4 introduces some important concepts of multivariate linear regression theory, while Chapter 5 gives basic theoretical background to principal component analysis. In the application section a data set consisting of 8 variables affecting the heating load of buildings is studied. Following careful examination of the variables and pairwise correlations, it was considered useful to reduce the number of variables to 5, all having a high correlation with the dependent variable. An attempt is made to estimate the predictor variables after the principal components were obtained. The methodology used proved to be a successful one as estimation errors were minimal.