SYLLABUS
STA 6246--01 Linear Models
Text:
Linear Models in Statistics, by Alvin C. Rencher,
John Wiley & Sons, Inc.,2000
Office:
DM--402
Phone & e-mail:
(305)348—2602, mi@fiu.edu
Course Objectives and Learning Outcomes:
Based on the materials learnt from STA 6246, students will learn how to
establish a linear model for prediction. Students will learn the
estimation of the regression coefficients including both point
estimation and interval estimation, learn test of hypotheses on a
subset of the regression coefficients and the general linear function
of the regression coefficients, prediction of
the value of response
variable, and analysis of variance models.
Course Content
Ch. 1
Introduction
1.1--1.3
Ch. 2 Matrix Algebra
2.1--2.7, 2.9-2.14
Ch. 3 Random Vectors and Matrices
3.1--3.6
Ch. 4 Multivariate Normal Distribution
4.1-4.4
Ch. 5 Distribution of Quadratic Forms in y
5.1--5.6
Ch. 6 Simple Linear Regression
6.1—6.4
Ch. 7 Multiple Regression: Estimation
7.1--7.10
Ch. 8 Multiple Regression: Tests of Hypotheses and Confidence
Intervals
8.1—8.7
Ch. 12 One-Way Analysis of Variance: Balanced Case
12.1, 12.3, 12.4
Ch. 13 Two-Way Analysis of Variance: Balanced Case
13.1, 13.4
Major Topics:
Inverse matrix, positive definite matrix, generalized matrix, random
vector, mean vector, covariance matrix, correlation matrix, linear
functions of random vectors, multivariate normal density function,
properties of multivariate normal distribution, partial correlation,
mean and variance of quadratic forms, distribution of quadratic forms,
full rank model, least square estimator, multiple regression
(estimation and testing hypotheses), confidence interval, prediction
interval, non-full-rank model, one-way model, reparameterization, side
conditions, contrast, two-way model.