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Information
| Unit | INSTITUTE OF NATURAL AND APPLIED SCIENCES |
| STATISTICS (PhD) | |
| Code | ISB507 |
| Name | Theory of Linear Models-I |
| Term | 2024-2025 Academic Year |
| Term | Fall |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. SADULLAH SAKALLIOĞLU |
| Course Instructor |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
The objective of this course is to discuss different methods used in the simple/multiple lineer regression models.
Course Content
Multivariate normal distribution; distribution of quadratic forms; Paremeter estimation and hypothesis testing in simple linear regression; Properties of least squares estimator and geometry of least squares, Maximum likelihood estimators and its properties; Estimation, testing and coefficient of determination in multivariate normal distribution; Related topics in linear models.
Course Precondition
no
Resources
Linear Models Alvin C. Rencher John Wiley 2000
Notes
Linear Models S.R.Searle John Wiley 1971
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knowledge and understanding multivariate normal distribution and distribution of quadratic forms, |
| LO02 | To understand the basic logic of simple lineer regression(SLR) |
| LO03 | Perform parameter estimation and confidence interval |
| LO04 | Perform hypothesis testing for SLR model |
| LO05 | To learn parameter estimation and confidence interval for multiple linear regression(MLR), |
| LO06 | To know properties of least squares estimator and geometry of least squares |
| LO07 | To learn maximum likelihood estimators and its properties, |
| LO08 | To learn testing in multivariate normal regression |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Develops new methods and strategies in modeling statistical problems and generating problem-specific solutions. | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Can do detailed research on a specific subject in the field of statistics. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Have a good command of statistical theory to contribute to the statistical literature. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Can use the knowledge gained in the field of statistics in interdisciplinary studies. | 2 |
| PLO05 | Yetkinlikler - Öğrenme Yetkinliği | Can organize projects and events in the field of statistics. | 3 |
| PLO06 | Yetkinlikler - Öğrenme Yetkinliği | Can perform the stages of creating a project, executing it and reporting the results. | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Have the ability of scientific analysis. | 2 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Can produce scientific publications in the field of statistics. | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Have analytical thinking skills. | |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | Can follow professional innovations and developments both at national and international level. | |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Can follow statistical literature. | |
| PLO12 | Beceriler - Bilişsel, Uygulamalı | Can improve his/her foreign language knowledge at the level of making publications and presentations in a foreign language. | |
| PLO13 | Bilgi - Kuramsal, Olgusal | Can use information technologies at an advanced level. | |
| PLO14 | Bilgi - Kuramsal, Olgusal | Have the ability to work individually and make independent decisions. | |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Have the qualities necessary for teamwork. | |
| PLO16 | Bilgi - Kuramsal, Olgusal | Have a sense of professional and ethical responsibility. | |
| PLO17 | Bilgi - Kuramsal, Olgusal | Acts in accordance with scientific ethical rules. | 3 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Multivariate normal distribution | reading, examination of literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Distribution of quadratic forms | reading, examination of literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | Estimation, hypothesis test and confidence interval | reading, examination of literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | Multiple regression | reading, examination of literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 5 | Least squares estimator and its properties | reading, examination of literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | The model in centered form | reading, examination of literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Maximum likelihood estimators and its properties | reading, examination of literature | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 8 | Mid-Term Exam | Review the topics discussed in the lecture notes and references | Ölçme Yöntemleri: Yazılı Sınav, Ödev |
| 9 | Generalized least squares | reading, examination of literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | General linear hypothesis tests | reading, examination of literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Grup Çalışması |
| 11 | Confidence region and confidence interval | reading, examination of literature | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama |
| 12 | Simultaneous intervals | reading, examination of literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 13 | Estimation in multivariate normal regression | reading, examination of literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Grup Çalışması |
| 14 | Testing in multivariate normal regression | reading, examination of literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Tests and confidence interval for coefficient of determination | reading, examination of literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 16 | Term Exams | Review the topics discussed in the lecture notes and references | Ölçme Yöntemleri: Yazılı Sınav, Ödev |
| 17 | Term Exams | Review the topics discussed in the lecture notes and references | Ölçme Yöntemleri: Yazılı Sınav, Ödev |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||