Chapter 2: Regression and the Normal Distribution

The regression method may be considered as a way of approximating a random variable of interest, as a function of several other related random variables. This task can only be effective if there is some sort of dependence between the variable of interest (called the response) and the approximating (or explanatory) variables. We will assume here that there is such a stochastic dependence, and that the realized values of the explanatory variables are observed, while the corresponding value of the response is unknown and is to be assessed. In such a situation, we try to identify the best possible approximation, and study its properties under certain assumptions…