161.251 Regression Modelling — Compiled Lectures

Jonathan Godfrey and Nick Knowlton

updated on 12 July 2026

Preface

These notes are the compiled lecture material for the course 161.251 Regression Modelling taught at Massey University by Jonathan Godfrey (Weeks 1–8 and appendices) and Nick Knowlton (Weeks 9–12).

We use R in almost every lecture; you should be able to run the code on your own. The material makes use of tidyverse packages. Graphs are made using a mixture of base R graphics and ggplot functions, with the choice being made on the basis of convenience.

Please ask for help if you don’t understand the R code being demonstrated.

Table of Contents

Week 1

• 1. Paper Overview
• 2. The Basics of Regression Modelling
• 3. Simple Linear Regression
• 4. Linear Regression Modelling with R

Week 2

• 5. Checking the Assumptions
• 6. Outliers and Influential Points
• 7. What to do When Assumptions Fail

Week 3

• 8. Prediction in Simple Linear Regression
• 9. Introduction to Multiple Linear Regression
• 10. Testing in Multiple Regression Models (1)

Week 4

• 11. Testing in Multiple Regression Models (2)
• 12. Basic Matrix Algebra
• 13. Matrices and Linear Regression Models

Week 5

• 14. Comparison of Multiple Linear Regression Models
• 15. Models with binary predictors

Week 6

• 16. Polynomial Regression Models
• 17. Models using orthogonal polynomials
• 18. Piecewise Regression Models

Week 7

• 19. Linear Models with One Factor
• 20. Diagnostics and Multiple Comparisons for Oneway ANOVA
• 21. Factor or Numerical Covariate?

Week 8

• 22. Introduction to the Two Factor Model
• 23. Orthogonal Factorial Models
• 24. Factors with Interactions

Week 9

• 25. The General Linear Model (NK)
• 26. Comparison of General Linear Models (NK)
• 27. Variable Selection (NK)

Week 10

• 28. Stepwise and Penalised Regression (NK)
• 29. Multicollinearity and Ridge Regression (NK)
• 30. Weighted regression (NK)

Week 11

• 31. Splines and LOESS: Flexible Regression Curves (NK)
• 32. Time-Indexed Regression: From Flexible Models to Trend (NK)
• 33. Regression Models for Trend and Seasonality (NK)

Week 12

• 34. Diagnosing Autocorrelated Errors (NK)
• 35. Regression with Autoregressive Errors (NK)

Appendices

• 36. Appendix: Introduction to R and RStudio
• 37. Appendix: Regression through the origin
• 38. Appendix: Transformations in regression models
• 39. Appendix: Models with Many Factors
• 40. Appendix: Nonlinear least squares