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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS EMT 4005 MULTIVARIATE STATISTICAL ANALYSIS COMPULSORY 3 0 0 5

Offered By

Econometrics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

Offered to

Econometrics (Evening) Econometrics

Course Objective

The purpose of the courses is to examine and analyze the correlation structure between variables.

Learning Outcomes of the Course Unit

1   To be able to define the random vectors and the distributions of the random vectors 2   To be able to define the variance, covariance and correlation structure of the random vectors 3   To be able to adapt the mathematical properties and theorems of multivariate normal distribution to economics, marketing and business issues. 4   To be able to formulate the mathematical properties and theorems of multivariate normal distribution 5   To be able to formulate the mathematical properties of dimension reduction theory

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Random variable, random vector and random matrix concepts 2 Multivariate random sample, random variable space and observation space. 3 The variance and covariance structure of random vectors, population mean vector, population covariance and correlation matrices and the expected values 4 The transpoze and inverse of real matrices, the eigenvalue-eigenvector structure of variance-covariance matrix and proof of related theorems 5 Eigen value and eigenvector analysis of 2x2 and 3x3 real matrices and examples. 6 Quadratic forms, the positive definite, positive semi definite, negative definite, negative semi definite quadratic forms 7 The linear combination, the linear combination of random vectors, the variance and covariance structure of linear combination. 8 Mid term 9 Mid term 10 Multivariate normal distribution, probability density function ,transformation of variables, Jacobian Matrix and Jacobian Determinant 11 The Quadratic form of p-variate normal distribution, the mathematical properties of quadratic form and geometrically interpretation, the distribution of the quadratic form of p-variate normal distribution 12 The partition of random vectors, conditional expected value, conditional variance-covariance matrix, the conditional distributions of sub vectors 13 The plausibility of _0 as a value for a normal population mean, Hotelling T-squared statistic 14 The distribution of random matrices, the Wishart distribution

Recomended or Required Reading

Morrison, Donald F. Multivariate Statistical Methods, McGraw Hill, New York. Recommended (for those without background in matrix algebra): Matrix Operations, Richard Bronson, Schaum Outline Series, McGraw-Hill, 1989. Johnson R.A. and Wichern D.W. (2002). Applied Multivariate Statistical Analysis. 5th edition, Prentice Hall.

Planned Learning Activities and Teaching Methods

This course will be presented using class lectures, class discussions, overhead projections, and demonstrations.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 MTEG MIDTERM GRADE MTEG * 1 3 FIN FINAL EXAM 4 FCGR FINAL COURSE GRADE MTEG * 0.40 + FIN * 0.60 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) MTEG * 0.40 + RST * 0.60

Further Notes About Assessment Methods

None

Assessment Criteria

Mid-term exam 40% Final-exam 60%

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

Doç. Dr. Kadir ERTAŞ: kadir.ertaş@deu.edu.tr Yrd. Doç. Dr. Istem KÖYMEN KESER: istem.koymen@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 12 3 36 Preparations before/after weekly lectures 12 2 24 Preparation for midterm exam 1 25 25 Preparation for final exam 1 28 28 Final 1 1 1 Midterm 1 1 1 TOTAL WORKLOAD (hours) 115

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 LO.1 1 LO.2 1 LO.3 1 LO.4 1 LO.5 1