Course No.：S070103ZJ004
Course Category：Professional Basic Course
Period/Credits：40/2
Prerequisites：Linear Algebra, Mathematics Statistics.
Aims & Requirements：
This course is the basic course for the masters and doctors of the major of mathematics statistics, and also can be used as a select course for the masters of the major of applied science. Linear model is an important branch of modern statistics. It has rich contents and has been widely used in the fields of biology, medical science, economy, management, agriculture, industry, technology and so on. This course includes relevant knowledge of matrix theory, multiply normal distribution and other relevant distributions, parameter estimation of linear model, hypothesis test, confidence regions and prediction, criteria for choice and diagnose of best model, Analysis of variance, Analysis of covariance. Having followed this course, students should master some basic methods and techniques and have general knowledge about the development of this subject for further study and work.
Primary Coverage：
Chapter 1 General Introduction about Linear model and matrix theory
General Introduction about Linear Model, Projection Matrix, Generalized Inverse, Orthogonal Projection.
Chapter 2 Multivariate Normal Distribution and Other Relevant Distributions
Multivariate Normal Distribution, Quadratic Form of Normal Random Variable.
Chapter 3 Parameter Estimation of Linear Model and Distribution Theory
Least Squares Estimators and Distribution Theory, Estimable Function, Estimation with Linear Constraints, Generalized Least Squares Method.
Chapter 4 Hypothesis test
Test, Hypothesis Test with Initial Constraints.
Chapter 5 Confidence Regions and Confidence Band
Confidence Ellipsoid, Bonferroni Interval, Scheffe Interval, Confidence Band.
Chapter 6 Prediction
Point Prediction, Interval Prediction.
Chapter 7 Linear Regression Analysis
Parameter Estimation, Significance Test, Choice Regression Variables, Regression Diagnose, Box-Cox transformation, Collinearity, Ridge Estimate, Principal Component Analysis.
Chapter 8 Analysis of Variance and Analysis of Covariance
Single Factor Classification Model, Two Factors Classification Model, Test of Normality, Homogeneity Test for Variance, Analysis of Covariance.
References：
[1] Wan Jinglong Applied Linear Regression，China Statistics Press，1998.
[2] Wang Songgui et.al《Introduction to Linear Regression，Science Press，Beijing，2004.
[3] S.F.Arnold, The Theory of Linear Models and Multivariate Analysis, John Wiley & Son, New York, 1981.
[4] C.R.Rao, Linear Statistical Inference and Its Applications, John Wiley & Son, New York, 1973.
Author：Sanguo Zhang (School of Mathematical Sciences, GUCAS)
Date：June, 2009
