Page 303 - Applied Statistics with R

Chapter 14

Transformations

“Give me a lever long enough and a fulcrum on which to place it,
and I shall move the world.”
— Archimedes

Please note: some data currently used in this chapter was used, changed, and
passed around over the years in STAT 420 at UIUC. Its original sources, if they
exist, are at this time unknown to the author. As a result, they should only be
considered for use with STAT 420. Going forward they will likely be replaced
with alternative sourceable data that illustrates the same concepts. At the end
of this chapter you can find code seen in videos for Week 8 for STAT 420 in
the MCS-DS program. It is currently in the process of being merged into the
narrative of this chapter.

After reading this chapter you will be able to:

• Understand the concept of a variance stabilizing transformation.
• Use transformations of the response to improve regression models.
• Use polynomial terms as predictors to fit more flexible regression models.

Last chapter we checked the assumptions of regression models and looked at
ways to diagnose possible issues. This chapter we will use transformations of
both response and predictor variables in order to correct issues with model
diagnostics, and to also potentially simply make a model fit data better.

14.1 Response Transformation

Let’s look at some (fictional) salary data from the (fictional) company Initech.
We will try to model salary as a function of years of experience. The data
can be found in initech.csv.

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