Chapter 09: Nonlinearity
[09a] Polynomial Regression
Topics
- Polynomial Regression
- Quadratic Regression
- Adding Predictors
- Closing Thoughts
Files
Readings
- Applied Multiple Regression/Correlation Analysis, §6.1–6.2
Slides
*Note that you can click the three-line (hamburger) icon on the bottom-left of the slides to access a navigation menu. You can click inside the slides region and press the left and right arrow keys on your keyboard to advance and reverse the slides and animations.
Assignment
[09b] Piecewise & Splines
This lecture is planned but not yet written. The outline below shows what it is intended to cover.
Topics
- Why a global polynomial is the wrong tool for a local bend
- Piecewise regression: breakpoints as a dummy code and its interaction
- Choosing and justifying a breakpoint
- Splines as the smooth generalization
- Interpreting and plotting a fit you cannot read off a coefficient
Piecewise regression is built from machinery this course already teaches: a breakpoint is a dummy code, and letting the slope change at that point is the interaction from Chapter 08. Splines then generalize it, still as a single term inside lm(). The conceptual contrast with Chapter 09a is the point of the lecture — a polynomial’s shape near one end of x is constrained by data at the other end, and a spline’s is not.
Unit C Translation Activity
A closing activity for the unit: studies described the way a researcher would describe them, for you to translate into data frames, models, and assumptions.