12 Modeling with Nonlinear Data

In the last chapter, we learned a lot about different types of functions that can be used to model data when the data does not represent a proportional relationship. In this chapter, we’re going to put this knowledge to use making and interpreting regression models of such non-proportional data. To do this, we need to go through a few steps.

First we transform the data using some of these functions. There are only four transformations that we need; combining them in different ways can produce all of the models we have talked about. Next we perform the regression, using these transformed variables, and some of the original variables, if needed. Unfortunately, we’ll need to compute the summary measures (R² and S_E) by hand for some of the nonlinear models. Finally, we have to make sense of the models we get by putting them into a useful form and determining what the parameters in the model actually mean.

As a result of this chapter, students will learn

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

√: Which transformations of the data will linearize the data
√: That some summary measures are not accurate when using nonlinear regression
√: That transformations of data can help to minimize non-constant variance in data
√: What the parameters in each of the nonlinear models actually mean

√: Transform variables for use in nonlinear modeling
√: Accurately compute R² and S_E for nonlinear models containing log(response)
√: Transform the regression equations of nonlinear models into standard form
√: Calculate the effects of changes in the explanatory variable on the response variable using ”parameter analysis”

Chapter 12Modeling with Nonlinear Data1

Chapter 12
Modeling with Nonlinear Data¹