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. 
Prerequisite: AMS 572
3 credits, ABCF grading 

Text (recommended):
"Introduction to Linear Regression Analysis" by D.C. Montgomery, E.A. Peck, and G.G. Vining, 6th edition, Wiley & Sons Publishing; ISBN: 978-1-119-57872-7 (earlier editions of the textbook are also acceptable.)

Actuarial Exam: A student receiving a B- or better in this course and in AMS 586 satisfies the Actuarial Exam test in Applied Statistics, through the Society of Actuaries Validation by Educational Experience program. For more details about actuarial preparation at Stony Brook see Actuarial Program 

Spring Semester

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.