The Classical Linear Regression Model

Abstract

The regression model of Chapter 6 is revisited using the inferential framework developed in subsequent chapters. The theory underlying the least squares approach is developed in more detail, so providing the ‘algebra’ of regression. The concepts of population and sample regression functions are introduced, along with the ‘classical assumptions’ of regression. These assumptions allow the ordinary least squares (OLS) estimators to satisfy the Gauss-Markov theorem, thus becoming best linear unbiased estimators, this being illustrated by simulation. Statistical inference in regression is then developed along with a geometrical interpretation of hypothesis testing. Finally, the use of regressions for prediction and considerations of functional form and non-linearity are discussed. Several examples are used to illustrate these concepts throughout the chapter.