STA 302 Topics

This is a list of the topics to be covered in STA302 (Regression Analysis) at UTM in the Fall of 2013. The numbered items below are lecture units. Some are based on overheads that are posted on the Course Website, and some are based on handwritten lecture notes. These units are in the same order as the homework assignments, but they do not correspond to the homework assignments in a one-to-one manner.

  1. Introduction
    1. Objectives, some vocabulary, idea of simple regression, least squares line, and correlation, need for multiple regression. Overheads.
    2. Idea of multiple regression, tools we will need. Handwritten.
    3. Review of moment-generating functions for a scalar random variable. Handwritten. See your STA257 text if necessary.
  2. Brief introduction to R. Overheads.
  3. More linear algebra: Quick review of some things you already know, Spectral decomposition, Positive definite matrices, Square root matrices, Matrix algebra with R. Overheads. See Chapter 2 for more detail, except for the R part.
  4. Random vectors: Basic definitions and results, Moment-generating functions. Overheads. See Chapter 3 for more detail.
  5. General linear model and least squares: General linear model in scalar and matrix form, least squares estimation. Handwritten. See Chapter 7 for more detail.
  6. Least squares with R.
  7. Properties of the least-squares estimates: Unbiased, BLUE (Gauss-Markov Theorem). Handwritten. See Chapter 7 for more detail.
  8. The multivariate normal distribution. Handwritten. See Chapter 4 for more detail, but the approach in lecture is based on moment-generating functions, which is not how the book does it.
  9. Inference for the normal linear model, Part One. Multivariate normal distribution for beta-hat, Y-hat and epsilon-hat; independence of beta-hat and SSE, distribution of SSE, t-distribution for linear combinations of regression coefficients, tests and confidence intervals, Analysis of variance, decomposition of SS, R2, F-test for H0: β1 = ... = βk = 0. Handwritten. See Chapter 8 for more detail, especially Sections 8.5 and 8.6. Note that the authors of the textbook approach things differently than in lecture, obtaining the t distribution from the F distribution via F = t2. Also, they use material from Chapter 5, which we did not cover. I think the treatment in lecture is simpler and easier to follow.
  10. Basic inference with R. Overheads.
  11. Prediction intervals. The text covers this in Section 8.6. The final answers are the same, but the way of getting the t-distribution is different. Handwritten.
  12. Prediction intervals with R. Overheads.
  13. General linear test. This is Theorem 8.4g on p. 203 in the text. Also see the other parts of Theorem 8.4. Handwritten..
  14. General linear test with R. Overheads.