April 2012
Beginner
672 pages
17h 39m
English
book
Introduction to Linear Regression Analysis, 5th Edition
by Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining
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CHAPTER 7
POLYNOMIAL REGRESSION MODELS
7.1 INTRODUCTION
The linear regression model y = Xβ + ε is a general model for fitting any relationship that is linear in the unknown parameters β. This includes the important class of polynomial regression models. For example, the second-order polynomial in one variable
and the second-order polynomial in two variables
are linear regression models.
Polynomials are widely used in situations where the response is curvilinear, as even complex nonlinear relationships can be adequately modeled by polynomials over reasonably small ranges of the x's. This chapter will survey several problems and issues associated with fitting polynomials.
7.2 POLYNOMIAL MODELS IN ONE VARIABLE
7.2.1 Basic Principles
As an example of a polynomial regression model in one variable, consider
Figure 7.1 An example of a quadratic polynomial.
This model is called a second-order model in one variable. It is also sometimes called a quadratic model, since the expected value of y is
which describes a quadratic function. A typical example is shown in Figure 7.1. We often call
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