Course Name Code Semester T+U Hours Credit ECTS
Linear Models I MAT 619 0 3 + 0 3 6
Precondition Courses <p>Analysis I-II, Lineer Algebra I-II, Probablity, Statistic</p>
Recommended Optional Courses
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Doç.Dr. NESRİN GÜLER
Course Lecturers
Course Assistants

Research assistants from Applied Mathematics

Course Category
Course Objective

The pupose of this course is to introduce the Linear models and to present Parameter estimation under linear models, to introduce the subject of linear inference in the linear models such as tests of hypotheses.

Course Content

Description of the linear model and notations, scope of the linear model. Matrix algebra: Matrices, vectors, inverses and generalized inverses, vector space and projection, column space, matrix decomposition, Löwner order, solutions of linear equations, optimization of quadratic forms and functions, Some statistical results: Basic distributions, distribution of quadratic forms, regression, point estimation and Bayes estimation, tests of hypothesis, confidence region. Estimation in the linear models: Least square estimator (LSE), best linear unbiased estimator (BLUE), maximum likelihood estimator (MLE), linear restrictions, collinearity in the linear model.

# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/She recognizes the linear model and notations Lecture, Question-Answer, Discussion, Self Study, Testing, Homework, Performance Task,
2 He/She recalls linear algebra Lecture, Question-Answer, Discussion, Self Study, Testing, Homework, Performance Task,
3 He/She learns basic distributions and distribution of quadratic forms Lecture, Question-Answer, Discussion, Self Study, Testing, Homework, Performance Task,
4 He/She learns tests of hypotheses and confidence regions Lecture, Question-Answer, Discussion, Self Study, Testing, Homework, Performance Task,
5 He/She explains estimation in the linear models Lecture, Question-Answer, Discussion, Self Study, Testing, Homework, Performance Task,
Week Course Topics Preliminary Preparation
1 Description of the linear model and notations, scope of the linear model [1] 1-16
2 Matrices and vectors, inverses and generalized inverse [1] 23-28
3 Vector space, projection, column space [1] 31-36
4 Matrix decompositions, Löwner order [1] 40-45
5 Solution of linear equations [1] 47-48
6 Optimization of quadratic forms and functions [1] 48-52
7 Basic distribution, distribution of quadratic forms [1] 55-60
8 Regression [1] 61-66
9 Point and Bayesian estimations [1] 70-82
10 Tests of hypotheses and confidence regions [1] 82-87
11 Estimation in the linear model [1] 93-97
12 Least square estimation (LSE), Best linear unbiased estimation (BLUE), Maximum Likelihood estimation (MLE) [1] 100-107
13 Linear restrictions [1] 120-126
14 Collinearity in the linear model [1] 134-137
Resources
Course Notes <p>[1] D. Sengupta, S. R. Jammalamadaka, Linear models: An integrated approach. World scientific, Singapore, 2003</p>
Course Resources

[2]F. A. Graybill, An introduction to Linear statistical models, Mc Graw Hill co., New York, 1961.
[3]S. R. Searle, Linear models, John Wiley and Sons, Inc., New York, 1971.
[3]G. A. F. Seber, Linear regression Analysis. John Wiley, New York, 1977.
[4]S. Puntanen, G. P. H. Styan, J. Isotalo, Matrix tricks for linear models. Springer Heidelberg, 2011.

Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X
Evaluation System
Semester Studies Contribution Rate
1. Ödev 20
1. Performans Görevi (Seminer) 80
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 5 80
Assignment 1 3 3
Performance Task (Seminar) 1 5 5
Final examination 1 10 10
Total Workload 146
Total Workload / 25 (Hours) 5.84
dersAKTSKredisi 6