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, [email protected] 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.