Chapter 13
Nonlinear Multivariable Models1

Most problems in the real world involve many variables. So far, you have encountered two types of models that have multiple independent variables: linear models and multiplicative models. These are definitely the most commonly used multivariable models since they are easier to interpret and can cover a variety of situations. But they do not cover all the possibilities. Probably the next most commonly used model is a quadratic multivariable model. This is the generalization of a parabola. This chapter will introduce you to this model in several ways. First, you will learn how to create such models using regression and interaction terms. Then you will learn how to graph and visualize some of these models. This approach to graphing quadratics can then be used to graph other types of nonlinear models.

As a result of this chapter, students will learn

As a result of this chapter, students will be able to

How to interpret certain quadratic models of two variables

The different shapes that the graph of a function of two variables can assume

How to simplify models with more than two variables when there are surrogate relationships

The difference between substitute and complementary commodities

Create a contour plot of a function of two variables

Create a 3D surface plot of a function of two variables

Use the discrimminant to determine the shape of a quadratic model

 13.1 Models with Numerical Interaction Terms
  13.1.1 Definitions and Formulas
  13.1.2 Worked Examples
  13.1.3 Exploration 13A: Revenue and Demand Functions
 13.2 Interpreting Quadratic Models in Several Variables
  13.2.1 Definitions and Formulas
  13.2.2 Worked Examples
  13.2.3 Exploration 13B: Exploring Quadratic Models
 13.3 Homework
  Mechanics and Techniques Problems
  Application and Reasoning Problems
 13.4 Memo Problem: Revenue Projections