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Information
| Code | ISB471 |
| Name | Econometric Models |
| Term | 2024-2025 Academic Year |
| Semester | 7. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 4 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. MAHMUDE REVAN ÖZKALE |
| Course Instructor |
1 2 |
Course Goal / Objective
The aim of this course is to use of mathematical techniques that are required for matrix operations and use matrix operations to solve problems that may arise in various fields such as statistics
Course Content
In this course, matrix operations, find the determinant and rank of a matrix, partitioned matrices, find the generalized inverse, solution to linear systems, linear, bilinear and quadratic forms and their derivatives, positive definiteness, positice semidefiniteness and nonnegative definiteness of a matrix are covered.
Course Precondition
none
Resources
1. Schott, J. R. (2005), Matrix Analysis for Statistics. John Wiley and Sons 2. Harville, D. A. (1997), Matrix Algebra from a Statisticians Perspective. Springer Verlag
Notes
Graybill, F.A. (1983), Matrices with Applications in Statistics. Wadsworth Publishing, Belmont
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Do matrix operations |
| LO02 | Apply the properties of the determinant |
| LO03 | Find the inverse of a matrix |
| LO04 | Do operations with partitioned matrices |
| LO05 | Find the generalized inverse of matrices |
| LO06 | Solve linear systems |
| LO07 | Find the least squares solution of linear systems |
| LO08 | Define linear, bilinear and quadratic forms |
| LO09 | Define positive definite, positive semidefinite and nonnegative definite matrices |
| LO10 | Derive the linear and quadratic forms |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explain the essence fundamentals and concepts in the field of Statistics | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Emphasize the importance of Statistics in life | 2 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Define basic principles and concepts in the field of Law and Economics | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Produce numeric and statistical solutions in order to overcome the problems | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Use proper methods and techniques to gather and/or to arrange the data | 1 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Utilize computer programs and builds models, solves problems, does analyses and comments about problems concerning randomization | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Apply the statistical analyze methods | 2 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Make statistical inference (estimation, hypothesis tests etc.) | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Generate solutions for the problems in other disciplines by using statistical techniques and gain insight | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Discover the visual, database and web programming techniques and posses the ability of writing programs | |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Distinguish the difference between the statistical methods | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Make oral and visual presentation for the results of statistical methods | 1 |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Have capability on effective and productive work in a group and individually | 1 |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Professional development in accordance with their interests and abilities, as well as the scientific, cultural, artistic and social fields, constantly improve themselves by identifying training needs | |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Develop scientific and ethical values in the fields of statistics-and scientific data collection |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Speical matrices and matrix operations | Source reading | Öğretim Yöntemleri: Anlatım |
| 2 | Linear independence and rank of matrix | Source reading | Öğretim Yöntemleri: Anlatım |
| 3 | Determinants and determinant properties | Source reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 4 | Finding the inverse of a matrix | Source reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 5 | Partitioned matrices | Source reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 6 | Elementary transformations, echelon form, equivalent matrices | Source reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 7 | Moore Penrose inverse and properties | Source reading | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Generalized inverse | Source reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 10 | Systems of linear equations | Source reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 11 | General solution Systems of linear equations | Source reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 12 | Least squares solution to systems of linear equations | Source reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 13 | Linear, bilinear and quadratic forms | Source reading | Öğretim Yöntemleri: Anlatım |
| 14 | Derivatives of linear and quadratic forms | Source reading | Öğretim Yöntemleri: Anlatım |
| 15 | Kronecker multiplication | Source reading | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
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 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 7 | 7 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 109 | ||
| Total Workload / 25 (h) | 4,36 | ||
| ECTS | 4 ECTS | ||