AMS 578: Regression Theory

Classical least-squares theory for regression including the Gauss-Markov theorem and classical normal statistical theory. An introduction to stepwise regression, procedures, and exploratory data analysis techniques. Analysis of variance problems as a subject of regression. Brief discussions of robustness of estimation and robustness of design.

Required Textbook: Introduction to Linear Regression Analysis by Douglas C. Montgomery, Elizabeth A. Peck and G. Geoffrey Vining, 5th edition, 2012, Wiley

Supplementary Textbooks:

1. Applied Linear Regression Models by Michael H. Kutner, Christopher J. Nachtsheim and John Neter, 4th edition, 2003, McGraw Hill
2. Applied Linear Statistical Models by Michael H. Kutner, Christopher J. Nachtsheim, John Neter and William Li, 5th edition, 2013, McGraw Hill
3. Regression Analysis by Example by Samprit Chatterjee and Ali S. Hadi, 5th edition, 2012, Wiley
4. Flexible Imputation of Missing Data by Stef van Buuren, 2nd edition, 2021, Chapman and Hall/CRC

Learning Outcomes

1. Extend knowledge of probability theory.
   • Central chi-square and central F-distributions;
   • Bonferroni’s inequality applied to multiple tests of hypotheses;
   • Scheffe’s multiple comparison procedures;
   • Decomposing chi-square sums of squares;
   • Expected value and variance of multiple linear combinations of random variables.
2. Learn statistical procedures for the linear model.
   • One predictor linear regression;
   • Multiple predictor linear regression;
   • Introduction to structural equation modeling issues, specifically mediation;
   • Expected mean square computations and power calculations using the non-centrality parameter;
   • Tests and confidence intervals for the one way and two way analysis of variance;
   • Statistical procedures for multiple comparisons.
3. Review scientific studies that use the techniques of the course.
   • Read papers posted on class blackboard;
   • Reference to papers for examples as techniques are studied in lecture.
4. Learn the statistical computing package of the student’s choice and apply it to obtain the statistical model that generated a set of synthetic data;
   • One predictor linear regression group project using synthetic data that requires students to merge separate files;
   • Multiple predictor linear regression group project using synthetic data to recreate the statistical model that generated the data. Model includes non-linear predictors and interactions of up to three predictors.