Polynomial Regression

In certain regression models we might be better able to meet the linear regression model assumptions by including polynomial terms (e.g., x^2, x^3, etc.). In this lecture we introduce how higher order polynomial terms can be used.

Further, if we have replicates within each given level included, we are able to partition our variance to estimate the pure error inherent in our outcome versus the lack of fit error due to our model choice. The lack of fit F-test is defined with examples calculated by hand and using R.


Table of Contents:

00:00 - Intro Song
00:18 - Welcome
01:02 - Polynomial Models
03:41 - Motivating Example
04:46 - Model without Polynomials
06:53 - Quadratic Model
11:32 - SLR vs. Quadratic Model Comparison
12:38 - Should I add higher order terms?
14:02 - Testing Lack of Fit with Replicates
18:43 - Lack of Fit F-test
20:09 - Test Lack of Fit for Straight-Line Model
21:40 - Test Lack of Fit for Quadratic Model
23:05 - Hierarchical Modeling and Collinearity