[next] [prev] [prev-tail] [tail] [up]

Chapter 11
Graphical Approaches to Nonlinear Data1

The basic idea of this chapter is that not all relationships are linear. In fact, many of the most commonly occurring relationships come from other families of functions such as exponentials or polynomials. In this chapter, we’ll explore the shapes of these different functions and learn how to control their shapes through the parameters of the model. Then, we will put our knowledge of nonlinear models to work in chapter 12 to build and interpret nonlinear regression models.

As a result of this chapter, students will learn

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

√

Know what the parameters, constants and coefficients in a model are

√

Know the basic shapes for each of the basic non-proportional models of interest (logarithmic/log, exponential, square, square root and reciprocal)

√

Logs and exponentials are inverse functions to each other
√

Select and justify a choice of non-proportional model from among several possible candidates

√

Choose an appropriate non-proportional model based on a scatterplot

√

Determine something about the parameters of a model from looking at a scatterplot

√

Shift the graph of a model around in order to make it better fit the data

√

Stretch the graph of a model in order to make it better fit the data

 11.1 What if the Data is Not Proportional
  11.1.1 Definitions and Formulas
  11.1.2 Worked Examples
  11.1.3 Exploration 11A: Non-proportional data
 11.2 Transformations of Graphs
  11.2.1 Definitions and Formulas
  11.2.2 Worked Examples
  11.2.3 Exploration 11B: Shifting and Scaling the Basic Models
 11.3 Homework
  Mechanics and Techniques Problems
  Application and Reasoning Problems
 11.4 Memo Problem: DataCon Contract

[next] [prev] [prev-tail] [front] [up]