LINEAR MODELS
SPRING
2005
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Instructor: |
Guan-Hua Huang, Ph.D. |
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Office: 423 |
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Phone: 03-513-1334 |
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Email: ghuang@stat.nctu.edu.tw |
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Class meetings: |
Wednesday 9:00 am -12:00 pm at 406 Joint Education Hall |
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Office hours: |
By appointment |
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Class website: |
http://www.stat.nctu.edu.tw/subhtml/source/teachers/ghuang/course/linearmodels05/ |
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Credit: |
Three (3) credits |
COURSE SUMMARY
The objects of his course are
Ÿ
To present a rigorous introduction
to general linear model.
Ÿ
To emphasize general linear
models associated with design of experiments.
Topics include review of linear algebra and matrices,
random
vectors, multivariate normal distribution, generalized least squares,
hypothesis
testing, one-way ANOVA, nested models, higher order designs.
HANDOUTS AND
TEXTBOOKS
Handouts corresponding to each lecture will be
available on the class website before each class. There is no required textbook for this course. The Following book is recommended for
further reading:
Franklin
A. Graybill (2000). Theory and Application of the Linear Model.
Duxbury
Press.
PREREQUISITES
Students are expected to have
background on undergraduate probability, mathematical statistics, and linear
regression.
METHOD OF STUDENT
EVALUATION
The course grade will be based on four homework assignments (40%), one midterm exam (25%), and one final exam (35%).
COURSE OUTLINE
|
Module |
Topic |
|
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1 |
Introduction |
Chapter
1, 2 |
|
2 |
Review
of linear algebra and matrices |
Chapter 1, 2 |
|
3 |
Random
vectors |
Chapter 2 |
|
4 |
The
multivariate normal distribution and distributions of quadratic forms |
Chapter 3, 4 |
|
5 |
Least
squares estimation |
Chapter 5 |
|
6 |
Properties
of least squares estimates |
Chapter 5 |
|
7 |
Design
matrices of less than full rank |
Chapter 5 |
|
8 |
Orthogonal
structure in the design matrix |
Chapter
6.1-6.2 |
|
9 |
Generalized
least squares |
Chapter
13.1-13.3 |
|
10 |
Estimable
functions |
Chapter
13.1-13.3 |
|
11 |
Hypothesis
testing |
Chapter
6.3-6.11 |
|
12 |
Simultaneous
confidence intervals |
Chapter
8.1-8.5, 9.1-9.5 |
|
13 |
Effects
of departures from assumptions |
No reading |
|
14 |
Residuals
and influence |
No reading |
|
15 |
Introduction
to design and analysis of experiments |
Chapter
13.1-13.2 |
|
16 |
One-way
analysis of variance |
Chapter
13, 15.1-15.2 |
|
17 |
Nested
and higher order designs |
Chapter
13, 15.1-15.2 |
|
18 |
Some
more miscellaneous ANOVA topics |
Chapter
14, 15 |