ABSTRACT
We now study some extensions of the simple regression model from Chapter 1, and then various aspects of multiple regression, including polynomial regression and weighted regression.
4.1.1 The model
A fundamental principle in statistical model building is that of parsimony, by which, when choosing between two models that explain a given set of data equally well, we choose the model with fewer parameters. For example, the simple linear regression model
Yi ~ Nfa + faxi,*2), i = 1 , . . . , n, (1.1)
may be said to be parsimonious, using only three parameters to describe the variation of n observations. Furthermore, if a test shows that we may accept the hypothesis (3 2 — 0 in model (1.1), then by the principle of parsimony, we adopt the simpler model
Yi~N(pu<T2), i = l , . . . , n .
