{"id":125914,"date":"2023-01-15T10:21:17","date_gmt":"2023-01-15T02:21:17","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=125914"},"modified":"2024-04-17T09:56:36","modified_gmt":"2024-04-17T01:56:36","slug":"multivariate-analysis-104-academic-year","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/institute-of-statistic\/multivariate-analysis-104-academic-year","title":{"rendered":"Multivariate Analysis -104 Academic Year"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"125914\" class=\"elementor elementor-125914\">\n\t\t\t\t\t\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-10 elementor-section elementor-top-section elementor-element elementor-element-90a0113 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"90a0113\" data-element_type=\"section\">\n\t\t\t\t\t\t<div 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href=\"https:\/\/ocw.nycu.edu.tw\/\">Homepage<\/a><\/span><\/span><\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-20 elementor-section elementor-top-section elementor-element elementor-element-0025485 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0025485\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"penci-ercol-50 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-0446ed9\" data-id=\"0446ed9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2f5840a elementor-widget elementor-widget-penci-info-box\" data-id=\"2f5840a\" data-element_type=\"widget\" data-widget_type=\"penci-info-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"penci_info_box_73502\" class=\"penci-block-vc penci-info-box penci-ibox-float-left penci-view-default penci-shape-circle\">\r\n\t\t\t<div class=\"penci-ibox-inner\">\r\n\t\t\t\t\t\t\t\t<div class=\"penci-ibox-icon penci-ibox-icon--icon penci-icon penci-tibox-text\"><span class=\"penci-ibox-icon-fa\"><\/span><\/div>\t\t\t\t<div class=\"penci-ibox-content-wrap\">\r\n\t\t\t\t\t\t\t\t\t\t<h3 class=\"penci-ibox-title\">Multivariate Analysis -104 Academic Year<\/h3>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c6381f4 elementor-widget elementor-widget-eael-adv-tabs\" data-id=\"c6381f4\" data-element_type=\"widget\" data-widget_type=\"eael-adv-tabs.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t        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251.47a12 12 0 0 0-1.6 16.9l25.5 31A12 12 0 0 0 45.15 301l235.22-193.74a12.19 12.19 0 0 1 15.3 0L530.9 301a12 12 0 0 0 16.9-1.6l25.5-31a12 12 0 0 0-1.7-16.93z\"><\/path><\/svg>                                                            \n                                                            <span class=\"eael-tab-title  title-after-icon\">Course Homepage<\/span>                            \n                                                    <\/li>\n                                            <li id=\"video\" class=\"inactive eael-tab-item-trigger\" aria-selected=\"false\" data-tab=\"2\" role=\"tab\" tabindex=\"-1\" aria-controls=\"video-tab\" aria-expanded=\"false\">\n                            \n                                                                <svg class=\"e-font-icon-svg e-fas-video\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M336.2 64H47.8C21.4 64 0 85.4 0 111.8v288.4C0 426.6 21.4 448 47.8 448h288.4c26.4 0 47.8-21.4 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0-48-21.5-48-48V112c0-26.5 21.5-48 48-48h48V12c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v52h128V12c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v52h48c26.5 0 48 21.5 48 48zm-48 346V160H48v298c0 3.3 2.7 6 6 6h340c3.3 0 6-2.7 6-6z\"><\/path><\/svg>                                                            \n                                                            <span class=\"eael-tab-title  title-after-icon\">Course Calendar<\/span>                            \n                                                    <\/li>\n                                    <\/ul>\n            <\/div>\n            \n            <div class=\"eael-tabs-content\">\n\t\t        \n                    <div id=\"home-tab\" class=\"clearfix eael-tab-content-item active-default\" data-title-link=\"home-tab\">\n\t\t\t\t        \t\t\t\t\t        <p style=\"margin-bottom: 10px; line-height: 28px; color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">This course is provided by the <a href=\"https:\/\/stat.nycu.edu.tw\/\" target=\"_blank\" rel=\"noopener\">NYCU\u00a0Institute of Statistic<\/a> .<\/p><p>The aims of this course are:<\/p><p>(1) To illustrate extensions of univariate statistical methodology to multivariate data.<br \/>(2) To introduce students to some of the distinctive statistical methodologies which arise only in multivariate data.<br \/>(3) To introduce students to some of the computational techniques required for multivariate analysis available in standard statistical packages.<\/p><p>Topics include: multivariate techniques and analyses, multivariate analysis of variance, principal component analysis and factor analysis, cluster analysis, discrimination and classification.<\/p><p>\u00a0<\/p><p><span style=\"color: #3366ff; font-size: 16px;\">Textbooks\uff1a<\/span><\/p><p>Johnson, R.A. and Wichern, D.W., 2007. Applied Multivariate Statistical Analysis (6th Edition). Prentice Hall, Upper Saddle River, NJ.<\/p><p><span style=\"color: #ff00ff;\">For perfect learning results, please buy textbooks!<\/span><\/p><p>\u00a0<\/p><table style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\" border=\"1\"><tbody><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\" width=\"100\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">Instructor(s)<\/span><\/span><\/th><td bgcolor=\"#EEEEEE\" width=\"518\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Institute of Statistic Prof. Guan-Hua Huang<\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">Course Credits<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a03 Credits<\/span><\/span><\/span><\/span><\/td><\/tr><tr><th class=\"text\" style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">Academic Year<\/span><\/span><\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0104 Academic Year<\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">Level<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Graduate Student<\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">Prior Knowledge<\/span><\/span><\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Linear Algebra, Probability, Mathematical Statistics and Linear Regression<\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">Related Resources<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0<a href=\"#video\">Course Video<\/a>\u00a0 \u00a0<a href=\"#syllabus\">Course Syllabus<\/a>\u00a0 \u00a0<a href=\"#calendar\">Course Calendar<\/a><\/span><\/span><\/span><\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"video-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"video-tab\">\n\t\t\t\t        \t\t\t\t\t        <p>\n<table id=\"tablepress-578\" class=\"tablepress tablepress-id-578\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">Week<\/th><th class=\"column-2\">Course Content<\/th><th class=\"column-3\">Course Video<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n\t<td class=\"column-1\">Week 1<\/td><td class=\"column-2\">Introduction<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=125937\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\">Week 1<\/td><td class=\"column-2\">Aspects of multivariate analysis<br \/>\n-introduction<br \/>\n-review of linear algebra and matrices<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=126013\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\">Week 1<\/td><td class=\"column-2\">Matrix algebra and random vectors<br \/>\n-random vectors<br \/>\n-distance<br \/>\n-sample geometry<br \/>\n-random sampling of sample mean vector and covariance matrix<br \/>\n-generalized variance<br \/>\n-matrix operations of sample values<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=126019\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\">Week 2<\/td><td class=\"column-2\">Multivariate normal distribution<br \/>\n-density and properties<br \/>\n-sampling from multivariate normal and MLE<br \/>\n-sampling distribution and large sample behavior of X and S<br \/>\n-assessing the assumption of normality<br \/>\n-transformation to near normality<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=126024\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\">Week 3<\/td><td class=\"column-2\">Inferences about a mean vector<br \/>\n-inference for a normal population mean<br \/>\n-Hotelling's T2 and likelihood ratio test<br \/>\n-confidence regions and simultaneous comparisons of component means<br \/>\n-large sample inferences about a population mean vector<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=126029\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\">Week 4<\/td><td class=\"column-2\">Comparisons of several multivariate means<br \/>\n-paired comparisons and repeated measures design<br \/>\n-comparing mean vectors from two populations<br \/>\n-comparing several multivariate population means (one-way MANOVA)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=126034\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\">Week 5<\/td><td class=\"column-2\">Principal components<br \/>\n-introduction<br \/>\n-population principal components<br \/>\n-summarizing sample variation by principal components<br \/>\n-large sample inferences<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=126039\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\">Week 6<\/td><td class=\"column-2\">Factor analysis (1\/2)<br \/>\n-introduction<br \/>\n-orthogonal factor model<br \/>\n-methods of estimation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=126044\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\">Week 8<\/td><td class=\"column-2\">Factor analysis (2\/2)<br \/>\n-factor rotation<br \/>\n-factor scores<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=126049\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\">Week 10<\/td><td class=\"column-2\">Clustering (1\/2)<br \/>\n-introduction<br \/>\n-similarity measures<br \/>\n-hierarchical clustering methods<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=126054\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\">Week 11<\/td><td class=\"column-2\">Clustering (2\/2)<br \/>\n-k-means clustering methods<br \/>\n-model-based clustering<br \/>\n-multidimensional scaling\u3000<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=126059\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\">Week 12<\/td><td class=\"column-2\">Discrimination and classification (1\/2)<br \/>\n-introduction<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=126064\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\">Week 13<\/td><td class=\"column-2\">Discrimination and classification (2\/2)<br \/>\n-evaluation of classification functions<br \/>\n-classification with several populations<br \/>\n-fisher's method for discriminating among several populations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=126070\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\">Week 14<\/td><td class=\"column-2\">Canonical correlation analysis (1\/2)<br \/>\n-introduction<br \/>\n-canonical variates and canonical correlations<br \/>\n-interpreting the population canonical variables<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=126076\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\">Week 15<\/td><td class=\"column-2\">Canonical correlation analysis (2\/2)<br \/>\n-sample canonical variates and sample canonical correlations<br \/>\n-sample descriptive measures of goodness-of-fit<br \/>\n-proportions of explained sample variance<br \/>\n-large sample inferences<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=126081\">Watch Online<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-578 from cache --><\/p>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"syllabus-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"syllabus-tab\">\n\t\t\t\t        \t\t\t\t\t        <p class=\"title\"><strong>Course Objectives<\/strong><\/p><p>The aims of this course are:<\/p><p>(1) To illustrate extensions of univariate statistical methodology to multivariate data.<br \/>(2) To introduce students to some of the distinctive statistical methodologies which arise only in multivariate data.<br \/>(3) To introduce students to some of the computational techniques required for multivariate analysis available in standard statistical packages.<\/p><p>Topics include: multivariate techniques and analyses, multivariate analysis of variance, principal component analysis and factor analysis, cluster analysis, discrimination and classification.<\/p><p>\u00a0<\/p><p><strong>Course Outline<\/strong><\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#e4d8b0\"><strong>Unit<\/strong><\/td><td bgcolor=\"#e4d8b0\"><b>Content<\/b><\/td><td bgcolor=\"#e4d8b0\"><strong>Textbook Scope<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Aspects of multivariate analysis<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">(1) introduction<br \/>(2) review of linear algebra and matrices<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">1-30,<br \/>49-110<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Matrix algebra and random vectors<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">(1) random vectors<br \/>(2) distance<br \/>(3) sample geometry<br \/>(4) random sampling of sample mean vector and covariance matrix<br \/>(5) generalized variance<br \/>(6) matrix operations of sample values<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">30-37, 60-78,<br \/>111-148<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Multivariate normal distribution<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">(1) density and properties<br \/>(2) sampling from multivariate normal and MLE<br \/>(3) sampling distribution and large sample behavior of X and S<br \/>(4) assessing the assumption of normality<br \/>(5) transformation to near normality<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">149-209<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Inferences about a mean vector<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">(1) inference for a normal population mean<br \/>(2) Hotelling's T2 and likelihood ratio test<br \/>(3) confidence regions and simultaneous comparisons of component means<br \/>(4) large sample inferences about a population mean vector<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">210-238<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Comparisons of several multivariate<br \/>means<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">(1) paired comparisons and repeated measures design<br \/>(2) comparing mean vectors from two populations<br \/>(3) comparing several multivariate population means (one-way MANOVA)<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">273-312<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Principal components<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">(1) introduction<br \/>(2) population principal components<br \/>(3) summarizing sample variation by principal components<br \/>(4) large sample inferences<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">430-459<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Factor analysis<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">(1) introduction<br \/>(2) orthogonal factor model<br \/>(3) methods of estimation<br \/>(4) factor rotation<br \/>(5) factor scores<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">481-526<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Clustering<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">(1) introduction<br \/>(2) similarity measures<br \/>(3) hierarchical clustering methods<br \/>(4) k-means clustering methods<br \/>(5) multidimensional scaling<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">671-715<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Discrimination and classification<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">(1) introduction<br \/>(2) separation and classification for two populations<br \/>(3) classification with two multivariate normal populations<br \/>(4) evaluating classification functions<br \/>(5) fisher discriminant function<br \/>(6) classification with several population<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">575-644<\/span><\/td><\/tr><\/tbody><\/table><p>\u00a0<\/p><p class=\"title\"><strong>Reference Books<\/strong><\/p><p class=\"text\">Johnson, R.A. and Wichern, D.W., 2007. Applied Multivariate Statistical Analysis (6th Edition). Prentice Hall, Upper Saddle River, NJ.<\/p>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"calendar-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"calendar-tab\">\n\t\t\t\t        \t\t\t\t\t        <p>This course calendar provides information on course progress and exams.<\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#e4d8b0\"><strong>Unit<\/strong><\/td><td bgcolor=\"#e4d8b0\"><strong>Date<\/strong><\/td><td bgcolor=\"#e4d8b0\"><strong>Course Progress, Contents, Topics<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">1<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">2\/23<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Aspects of multivariate analysis<br \/>-introduction<br \/>-review of linear algebra and matrices<br \/>Matrix algebra and random vectors<br \/>-random vectors<br \/>-distance<br \/>-sample geometry<br \/>-random sampling of sample mean vector and covariance matrix<br \/>-generalized variance<br \/>-matrix operations of sample values<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">3\/01<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Multivariate normal distribution<br \/>-density and properties<br \/>-sampling from multivariate normal and MLE<br \/>-sampling distribution and large sample behavior of X and S<br \/>-assessing the assumption of normality<br \/>-transformation to near normality<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">3<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">3\/08<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Inferences about a mean vector<br \/>-inference for a normal population mean<br \/>-Hotelling's T2 and likelihood ratio test<br \/>-confidence regions and simultaneous comparisons of component means<br \/>-large sample inferences about a population mean vector<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">4<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">3\/15<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Comparisons of several multivariate means<br \/>-paired comparisons and repeated measures design<br \/>-comparing mean vectors from two populations<br \/>-comparing several multivariate population means (one-way MANOVA)<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">5<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">3\/22<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Principal components<br \/>-introduction<br \/>-population principal components<br \/>-summarizing sample variation by principal components<br \/>-large sample inferences<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">6<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">3\/29<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Factor analysis (1\/2)<br \/>-introduction<br \/>-orthogonal factor model<br \/>-methods of estimation<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">7<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">4\/05<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Day-off<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">8<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">4\/12<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Factor analysis (2\/2)<br \/>-factor rotation<br \/>-factor scores<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">9<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">4\/19\u3000<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Midterm exam<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">10<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">4\/26<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Clustering (1\/2)<br \/>-introduction<br \/>-similarity measures<br \/>-hierarchical clustering methods<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">11<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">05\/03<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Clustering (2\/2)<br \/>-k-means clustering methods<br \/>-model-based clustering<br \/>-multidimensional scaling<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\">12<\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\">05\/10<\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Discrimination and classification (1\/2)<br \/>-introduction<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">13<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">05\/17<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Discrimination and classification (2\/2)<br \/>-evaluation of classification functions<br \/>-classification with several populations<br \/>-fisher's method for discriminating among several populations<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span style=\"font-family: Liberation Serif, serif;\"><span style=\"font-size: medium;\"><span lang=\"en-US\">14<\/span><\/span><\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">05\/24<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Canonical correlation analysis (1\/2)<br \/>-introduction<br \/>-canonical variates and canonical correlations<br \/>-interpreting the population canonical variables<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">15<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">05\/31<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\"><br \/>Canonical correlation analysis (2\/2)<br \/>-sample canonical variates and sample canonical correlations<br \/>-sample descriptive measures of goodness-of-fit<br \/>-proportions of explained sample variance<br \/>-large sample inferences<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">16<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">6\/07<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Day-off<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">17<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">6\/14<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Final exam<\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t                    <\/div>\n        <\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d7723a8 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"d7723a8\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.13.3 - 28-05-2023 *\/\n.elementor-widget-divider{--divider-border-style:none;--divider-border-width:1px;--divider-color:#0c0d0e;--divider-icon-size:20px;--divider-element-spacing:10px;--divider-pattern-height:24px;--divider-pattern-size:20px;--divider-pattern-url:none;--divider-pattern-repeat:repeat-x}.elementor-widget-divider .elementor-divider{display:flex}.elementor-widget-divider .elementor-divider__text{font-size:15px;line-height:1;max-width:95%}.elementor-widget-divider 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menu-item-object-course_page ajax-mega-menu menu-item-132738\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-life-sciences-en\" class=\"elementor-item\">College of Life Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-141797\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/colege-of-medicine-en\" class=\"elementor-item\">College of Medicine<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118072\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-chinese-center\" class=\"elementor-item\">Course of Chinese Center<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-120431\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/liberal-arts-college\" class=\"elementor-item\">Forum Of Liberal Arts<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123746\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/speech-of-general-education-center\" class=\"elementor-item\">Contemporary Civilization<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-128240\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/reading-of-classic-masterpiece\" class=\"elementor-item\">Reading of Classic Masterpiece<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123745\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-general-education-center-2\" class=\"elementor-item\">Course of General Education Center<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t\t<div class=\"elementor-menu-toggle\" role=\"button\" tabindex=\"0\" aria-label=\"\u9078\u55ae\u5207\u63db\" 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href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-management\" class=\"elementor-item\" tabindex=\"-1\">College of Management<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5375\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-computer-science\" class=\"elementor-item\" tabindex=\"-1\">College of Computer Science<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5374\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-biological-science-and-technology\" class=\"elementor-item\" tabindex=\"-1\">College of Engineering Bioscience<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5379\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-humanities-and-social-sciences\" class=\"elementor-item\" tabindex=\"-1\">College of Humanities Arts and Social Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5378\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-hakka-affair-culture\" class=\"elementor-item\" tabindex=\"-1\">College of Hakka Affair Culture<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118070\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-law\" class=\"elementor-item\" tabindex=\"-1\">School of Law<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118069\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-nursing-2\" class=\"elementor-item\" tabindex=\"-1\">School of Nursing<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118071\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-photonics\" class=\"elementor-item\" tabindex=\"-1\">College of Photonics<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-125874\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-biomedical-science-and-engineering\" class=\"elementor-item\" tabindex=\"-1\">College of Biomedical Science and Engineering<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-132738\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-life-sciences-en\" class=\"elementor-item\" tabindex=\"-1\">College of Life Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-141797\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/colege-of-medicine-en\" class=\"elementor-item\" tabindex=\"-1\">College of Medicine<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118072\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-chinese-center\" class=\"elementor-item\" tabindex=\"-1\">Course of Chinese Center<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-120431\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/liberal-arts-college\" class=\"elementor-item\" tabindex=\"-1\">Forum Of Liberal Arts<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123746\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/speech-of-general-education-center\" class=\"elementor-item\" tabindex=\"-1\">Contemporary Civilization<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-128240\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/reading-of-classic-masterpiece\" class=\"elementor-item\" tabindex=\"-1\">Reading of Classic Masterpiece<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123745\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-general-education-center-2\" class=\"elementor-item\" tabindex=\"-1\">Course of General Education Center<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Multivariate A&hellip;<\/p>\n","protected":false},"featured_media":125698,"parent":125013,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","format":"standard","meta":{"footnotes":""},"categories":[250],"tags":[341,345,10163],"class_list":["post-125914","course_page","type-course_page","status-publish","format-standard","has-post-thumbnail","hentry","category-institute-of-statistics-en","tag-label-all-course-en","tag-label-college-of-science-en","tag-label-institute-of-statistics-en"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Multivariate Analysis -104 Academic Year - NYCU OCW<\/title>\n<meta name=\"description\" content=\"Multivariate Analysis -104 Academic Year Course Homepage Course Video Course Syllabus Course Calendar This course is provided by the NYCU\u00a0Institute of\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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