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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. A video for the Biostatistical Methods I (BIOS 6611) course in the Department of Biostatistics and Informatics at the University of Colorado-Anschutz Medical Campus taught by Dr. Alex Kaizer. Slides and additional material available at https://www.alexkaizer.com/bios_6611. 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