Review of Simple Regression

Abstract

This chapter reviews the elementary regression results for a linear model in one variable. The primary purpose is to establish a common notation and to point out the need for matrix notation. A light reading should suffice for most students. Modeling refers to the development of mathematical expressions that describe in some sense the behavior of a random variable of interest. This variable may be the price of wheat in the world market, the number of deaths from lung cancer, the rate of growth of a particular type of tumor, or the tensile strength of metal wire. In all cases, this variable is called the dependent variable and denoted with Y. A subscript on Y identifies the particular unit from which the observation was taken, the time at which the price was recorded, the county in which the deaths were recorded, the experimental unit on which the tumor growth was recorded, and so forth. Most commonly the modeling is aimed at describing how the mean of the dependent variable E(Y) changes with changing conditions; the variance of the dependent variable is assumed to be unaffected by the changing conditions. Other variables which are thought to provide information on the behavior of the dependent variable are incorporated into the model as predictor or explanatory variables. These variables are called the independent variables and are denoted by X with subscripts as needed to identify different independent variables. Additional subscripts denote the observational unit from which the data were taken. The Xs are assumed to be known con