Course Name Code Semester T+U Hours Credit ECTS
Linear Models II MAT 620 0 3 + 0 3 6
Precondition Courses Analysis I-II, Lineer Algebra I-II, Probablity, Statistic, Linear Models I
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 general linear models and multivariate linear models, to present the subject of inference from linear models. Also, analysis of variance and covariance, some estimators and relationship between the estimators are given.
Course Content Inference in the linear model: Distribution of estimators, confidence region, linear hypothesis tests. Analysis of variance: One-way and two-way classified data, covariance analysis. General linear models: estimation in general linear models. Misspecified and unknown dispersion. Multivariate linear model: description of multivariate linear model, best linear unbiased estimator (BLUE) and maximum likelihood estimator (MLE), hypothesis tests and confidence region. Linear inference: Admissible, Bayes and minimax estimators, biased estimators with smaller dispersion, other linear estimators, a geometric view of BLUE in the linear model.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/She learns the subject of inference from the linear model Lecture, Question-Answer, Discussion, Self Study, Testing, Homework, Performance Task,
2 He/She learns the subject of analysis variance Lecture, Question-Answer, Discussion, Self Study, Testing, Homework, Performance Task,
3 He/She learns the subject of general linear models Lecture, Question-Answer, Discussion, Self Study, Testing, Homework, Performance Task,
4 He/She learns the subject of misspecified and unknown dispersion Lecture, Question-Answer, Discussion, Self Study, Testing, Homework, Performance Task,
5 He/She learns the subject of multivariate linear model Lecture, Question-Answer, Discussion, Self Study, Testing, Homework, Performance Task,
6 He/She represents the subject of a geometric view of the BLUE in the linear model Lecture, Question-Answer, Discussion, Self Study, Testing, Homework, Performance Task,
Week Course Topics Preliminary Preparation
1 Inference from linear model: Distributions of the estimators
2 Confidence regions
3 Tests of linear hypotheses
4 Analsis of variance
5 One-way and two-way classified data
6 Analysis of covariance
7 General linear models
8 Estimation in the general linear models
9 Misspecified and unknown dispersion
10 Multivariate linear model:Description of the multivariate linear model, BLUE, UE of error dispersion, MLE
11 Multivariate linear model: Tests of linear hypotheses and Confidence regions
12 Linear inference, Admissible, Bayes and minimax linear estimator, biased estimators with smaller dispersion
13 Other linear estimators
14 A geometric view of the BLUE in the linear model
Resources
Course Notes
Course Resources
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