Multivariate Analysis |
KOBAYASHI, Yasuyuki |
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【Master's program･2nd semester】
14-3-1028 |
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Objectives |
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Multivariate analysis, which analyzes and estimates numerical data with multi-variables, is an important method applied to various fields such as technology. We aim to understand fundamental methods in statistics and multivariate analysis and aim to cultivate skill to apply actual problems.
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Outline |
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We will review the basics of statistical methods, and will mainly study regression analysis, which is a fundamental method of multivariate analysis, principal component analysis, discriminant analysis, and cluster analysis etc. The student will understand theories essential for interpreting analytical results and will cultivate an applied skill by learning examples and exercises with computers.
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Requirements (Assignments) |
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It is desirable for undergraduates to understand mathematical statistics and linear algebra, although these topics will be reviewed in class. You had better review the features, procedure, and methods to cope with problems of each method after the class, and learn to apply these skills to your own tasks.
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Schedule |
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(1) Introduction, basics of statistics (1): handling data.
(2) Basics of statistics (2): a correlation analysis.
(3) Basics of statistics (3): basics of probability and normal distributions.
(4) Basics of statistics (4): inferences and tests
(5) Basics of statistics (5): selecting methods of statistical models.
(6) Regression analysis (1): a single regression analysis and formulation.
(7) Regression analysis (2): cautions fora single regression analysis.
(8) Regression analysis (3): a multiple regression analysis and formulation.
(9) Regression analysis (4): cautions for a multiple regression analysis and selecting methods for variables.
(10) Regression analysis (5): treatment for qualitative variables and important knowledge of linear algebra for the multivariate analysis.
(11) Regression analysis (6): a logistic regression analysis.
(12) Cluster analysis: a hierarchical and non- hierarchical method.
(13) Other methods (a principal component analysis, a discriminant analysis, and etc.), Exercises with computers.
(14) Workshop of exercises with computers
(15) Conclusions.
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Grading Policy |
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The grade will be comprehensively evaluated by workshop of exercises with computers and submitted reports.
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Textbook and Reference |
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No texts are used. Some articles are posted on LMS. For a reference book, there is Nagata and Munetika, “Introduction for multivariate analysis,” Science-sha (2001), you can find that many excellent reference books are available. Therefore I want you to find the book which is suit to your purposes. The spreadsheet program Excel will be used for exercises in order to analyze your problems by yourself after taking this class.
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Note |
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You will have lectures and exercises with computers on almost every class in order to help your understanding. Therefore this class will be conducted in the CL room for postgraduates. The content of this class may be arbitrarily changed in case of the students’ understanding depth and the study problems.
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