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Information
| Code | ISB423 |
| Name | Multivariate Statistical Analysis |
| Term | 2024-2025 Academic Year |
| Semester | 7. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 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. GÜLESEN ÜSTÜNDAĞ ŞİRAY |
| Course Instructor |
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Course Goal / Objective
The goal is to construct the necessary theoretical background for multivariate statistical analysis.
Course Content
The content of this course is basic concepts of multivariate statistics, multivariate normal distribution, testing hypothesis about the multivariate data.
Course Precondition
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Resources
1. Alvin C. Rencher. Methods of Multivariate Analysis (2nd Edition) Wiley series in probability and mathematical statistics 2. Using Multivariate Statistics (6th Edition). Barbara G. Tabachnick , Linda S. Fidell. Pearson Education, Boston. 3. Uygulamalı Çok değişkenli İstatistiksel Analiz. Hüseyin Tatlıdil
Notes
UC Irvine Machine Learning Repository-https://archive.ics.uci.edu/
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Define the basic concepts of multivariate statistics. |
| LO02 | Explain the purpose of using of multivariate statistics. |
| LO03 | Determine the mean vector, variance-covariance and correlation matrices for multivariate data. |
| LO04 | Explain the probability density function, marginal probability density function, conditional distribution and statistical independency for multivariate distributions with examples . |
| LO05 | Find the moment generating function for multivariate normal distribution. |
| LO06 | Find marginal probability density function, conditional probability density function for multivariate normal distribution. |
| LO07 | Make the parameter estimates for multivariate normal distribution. |
| LO08 | Test the hypothesis about the multivariate data. |
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 | 4 |
| 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 | 4 |
| 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 | 4 |
| 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 | |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Have capability on effective and productive work in a group and individually | |
| 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 | Basic concepts of multivariate statistics | Source reading | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | Matrix theory for multivariate statistical analysis | Source reading | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 3 | Matrix theory for multivariate statistical analysis 2 | Source reading | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 4 | Mean vector, variance-covariance matrix, correlation matrix | Source reading | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme, Alıştırma ve Uygulama |
| 5 | Probability density function, marginal probability density function, conditional distribution and statistical independency for multivariate distributions | Source reading | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme, Alıştırma ve Uygulama |
| 6 | Probability density function, characteristic functions, moments, moment generating function and parameter estimates | Source reading | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 7 | Maximum likelihood estimators for population parameters | Source reading | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 8 | Mid-Term Exam | Review the topics discussed in the lecture notes and sources. | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Marginal normal distribution, conditional normal distribution | Source reading | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme, Alıştırma ve Uygulama |
| 10 | Distribution of linear relations, independency of subvector variables | Source reading | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme, Alıştırma ve Uygulama |
| 11 | Obtaining the parameters given the density function | Source reading | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 12 | Multivariate test methods (likelihood ratio test) | Source reading | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 13 | Multivariate test methods (composition-intersection test) | Source reading | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 14 | Test on mean vectors | Source reading | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme, Alıştırma ve Uygulama |
| 15 | Test on covariance matrices, Testing hypothesis with statistical package programs. | Source reading | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme, Alıştırma ve Uygulama |
| 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 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||