{"id":25421,"date":"2025-03-14T17:28:33","date_gmt":"2025-03-14T10:28:33","guid":{"rendered":"https:\/\/interdata.vn\/blog\/?p=25421"},"modified":"2025-03-14T17:31:25","modified_gmt":"2025-03-14T10:31:25","slug":"hoi-quy-tuyen-tinh","status":"publish","type":"post","link":"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/","title":{"rendered":"H\u1ed3i quy tuy\u1ebfn t\u00ednh l\u00e0 g\u00ec? Gi\u1ea3i th\u00edch to\u00e0n t\u1eadp t\u1eeb A-Z"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">N\u1ed8I DUNG<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Hoi-quy-tuyen-tinh-la-gi\" >H\u1ed3i quy tuy\u1ebfn t\u00ednh l\u00e0 g\u00ec?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Tai-sao-hoi-quy-tuyen-tinh-lai-quan-trong\" >T\u1ea1i sao h\u1ed3i quy tuy\u1ebfn t\u00ednh l\u1ea1i quan tr\u1ecdng?<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Kha-nang-du-doan\" >Kh\u1ea3 n\u0103ng d\u1ef1 \u0111o\u00e1n<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Hieu-ro-moi-quan-he-giua-cac-bien\" >Hi\u1ec3u r\u00f5 m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c bi\u1ebfn<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Tinh-don-gian-va-de-hieu\" >T\u00ednh \u0111\u01a1n gi\u1ea3n v\u00e0 d\u1ec5 hi\u1ec3u<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Ung-dung-rong-rai\" >\u1ee8ng d\u1ee5ng r\u1ed9ng r\u00e3i<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Nen-tang-cho-cac-phuong-phap-nang-cao\" >N\u1ec1n t\u1ea3ng cho c\u00e1c ph\u01b0\u01a1ng ph\u00e1p n\u00e2ng cao<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Hoi-quy-tuyen-tinh-hoat-dong-nhu-the-nao\" >H\u1ed3i quy tuy\u1ebfn t\u00ednh ho\u1ea1t \u0111\u1ed9ng nh\u01b0 th\u1ebf n\u00e0o?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Hoi-quy-tuyen-tinh-trong-may-hoc-la-gi\" >H\u1ed3i quy tuy\u1ebfn t\u00ednh trong m\u00e1y h\u1ecdc l\u00e0 g\u00ec?<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Cach-thuc-hoat-dong\" >C\u00e1ch th\u1ee9c ho\u1ea1t \u0111\u1ed9ng<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Vi-du-minh-hoa\" >V\u00ed d\u1ee5 minh h\u1ecda<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Uu-diem-va-nhuoc-diem\" >\u01afu \u0111i\u1ec3m v\u00e0 nh\u01b0\u1ee3c \u0111i\u1ec3m<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Moi-lien-he-voi-cac-khai-niem-khac\" >M\u1ed1i li\u00ean h\u1ec7 v\u1edbi c\u00e1c kh\u00e1i ni\u1ec7m kh\u00e1c<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Co-nhung-loai-hoi-quy-tuyen-tinh-nao\" >C\u00f3 nh\u1eefng lo\u1ea1i h\u1ed3i quy tuy\u1ebfn t\u00ednh n\u00e0o?<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Hoi-quy-tuyen-tinh-don-bien-simple-linear-regression\" >H\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111\u01a1n bi\u1ebfn (simple linear regression)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/#Hoi-quy-tuyen-tinh-da-bien-multiple-linear-regression\" >H\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111a bi\u1ebfn (multiple linear regression)<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><a href=\"https:\/\/interdata.vn\/blog\/hoi-quy-tuyen-tinh\/\"><strong>H\u1ed3i quy tuy\u1ebfn t\u00ednh<\/strong><\/a> l\u00e0 m\u1ed9t trong nh\u1eefng kh\u00e1i ni\u1ec7m quan tr\u1ecdng v\u00e0 \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i nh\u1ea5t trong th\u1ed1ng k\u00ea, ph\u00e2n t\u00edch d\u1eef li\u1ec7u v\u00e0 m\u00e1y h\u1ecdc. Nghe c\u00f3 v\u1ebb ph\u1ee9c t\u1ea1p, nh\u01b0ng th\u1ef1c t\u1ebf h\u1ed3i quy tuy\u1ebfn t\u00ednh l\u1ea1i kh\u00e1 d\u1ec5 hi\u1ec3u. B\u00e0i vi\u1ebft n\u00e0y c\u1ee7a <strong>InterData<\/strong> s\u1ebd gi\u1ea3i th\u00edch <i>t\u1ea5t t\u1ea7n t\u1eadt<\/i> v\u1ec1 h\u1ed3i quy tuy\u1ebfn t\u00ednh, t\u1eeb \u0111\u1ecbnh ngh\u0129a, c\u00e1ch ho\u1ea1t \u0111\u1ed9ng, t\u1ea7m quan tr\u1ecdng, \u0111\u1ebfn c\u00e1c lo\u1ea1i h\u1ed3i quy tuy\u1ebfn t\u00ednh v\u00e0 \u1ee9ng d\u1ee5ng trong th\u1ef1c t\u1ebf. D\u00f9 b\u1ea1n l\u00e0 ng\u01b0\u1eddi m\u1edbi b\u1eaft \u0111\u1ea7u hay \u0111\u00e3 c\u00f3 kinh nghi\u1ec7m, b\u00e0i vi\u1ebft n\u00e0y \u0111\u1ec1u cung c\u1ea5p th\u00f4ng tin h\u1eefu \u00edch.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Hoi-quy-tuyen-tinh-la-gi\"><\/span>H\u1ed3i quy tuy\u1ebfn t\u00ednh l\u00e0 g\u00ec?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>H\u1ed3i quy tuy\u1ebfn t\u00ednh (linear regression)<\/strong> l\u00e0 m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p th\u1ed1ng k\u00ea d\u00f9ng \u0111\u1ec3 <strong>m\u00f4 h\u00ecnh h\u00f3a m\u1ed1i quan h\u1ec7<\/strong> gi\u1eefa m\u1ed9t bi\u1ebfn s\u1ed1 ph\u1ee5 thu\u1ed9c (bi\u1ebfn m\u1ee5c ti\u00eau) v\u00e0 m\u1ed9t ho\u1eb7c nhi\u1ec1u bi\u1ebfn s\u1ed1 \u0111\u1ed9c l\u1eadp (bi\u1ebfn d\u1ef1 \u0111o\u00e1n) b\u1eb1ng m\u1ed9t <strong>ph\u01b0\u01a1ng tr\u00ecnh tuy\u1ebfn t\u00ednh<\/strong>. N\u00f3i m\u1ed9t c\u00e1ch \u0111\u01a1n gi\u1ea3n, n\u00f3 gi\u00fap ch\u00fang ta &#8220;v\u1ebd&#8221; m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng (ho\u1eb7c m\u1eb7t ph\u1eb3ng, si\u00eau ph\u1eb3ng trong kh\u00f4ng gian nhi\u1ec1u chi\u1ec1u) ph\u00f9 h\u1ee3p nh\u1ea5t v\u1edbi d\u1eef li\u1ec7u, \u0111\u1ec3 t\u1eeb \u0111\u00f3 c\u00f3 th\u1ec3 <strong>d\u1ef1 \u0111o\u00e1n<\/strong> gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn ph\u1ee5 thu\u1ed9c.<\/p>\n<p>\u0110\u1ec3 d\u1ec5 h\u00ecnh dung, h\u00e3y t\u01b0\u1edfng t\u01b0\u1ee3ng b\u1ea1n \u0111ang c\u1ed1 g\u1eafng t\u00ecm hi\u1ec3u xem <strong>chi\u1ec1u cao<\/strong> c\u1ee7a m\u1ed9t ng\u01b0\u1eddi (bi\u1ebfn ph\u1ee5 thu\u1ed9c) c\u00f3 li\u00ean quan nh\u01b0 th\u1ebf n\u00e0o \u0111\u1ebfn <strong>chi\u1ec1u d\u00e0i b\u00e0n ch\u00e2n<\/strong> c\u1ee7a h\u1ecd (bi\u1ebfn \u0111\u1ed9c l\u1eadp). H\u1ed3i quy tuy\u1ebfn t\u00ednh s\u1ebd gi\u00fap b\u1ea1n t\u00ecm ra m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh, v\u00ed d\u1ee5: <i>Chi\u1ec1u cao = 80 + 3.5 * Chi\u1ec1u d\u00e0i b\u00e0n ch\u00e2n<\/i>. Ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y cho th\u1ea5y, trung b\u00ecnh, c\u1ee9 m\u1ed7i cm chi\u1ec1u d\u00e0i b\u00e0n ch\u00e2n t\u0103ng l\u00ean, chi\u1ec1u cao s\u1ebd t\u0103ng th\u00eam 3.5 cm. D\u0129 nhi\u00ean, s\u1ebd c\u00f3 nh\u1eefng sai s\u1ed1 nh\u1ea5t \u0111\u1ecbnh, nh\u01b0ng m\u00f4 h\u00ecnh n\u00e0y cung c\u1ea5p m\u1ed9t c\u00e1ch x\u1ea5p x\u1ec9 kh\u00e1 t\u1ed1t.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/03\/Hoi-quy-tuyen-tinh.png\" alt=\"H\u1ed3i quy tuy\u1ebfn t\u00ednh\" width=\"800\" height=\"420\" class=\"aligncenter size-full wp-image-25436\" title=\"\" srcset=\"https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/03\/Hoi-quy-tuyen-tinh.png 800w, https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/03\/Hoi-quy-tuyen-tinh-300x158.png 300w, https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/03\/Hoi-quy-tuyen-tinh-768x403.png 768w, https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/03\/Hoi-quy-tuyen-tinh-750x394.png 750w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>Ph\u01b0\u01a1ng tr\u00ecnh t\u1ed5ng qu\u00e1t c\u1ee7a h\u1ed3i quy tuy\u1ebfn t\u00ednh (\u0111\u01a1n bi\u1ebfn) c\u00f3 d\u1ea1ng: <strong>y = \u03b2\u2080 + \u03b2\u2081x + \u03b5<\/strong>. Trong \u0111\u00f3, <strong>y<\/strong> l\u00e0 bi\u1ebfn ph\u1ee5 thu\u1ed9c, <strong>x<\/strong> l\u00e0 bi\u1ebfn \u0111\u1ed9c l\u1eadp, <strong>\u03b2\u2080<\/strong> l\u00e0 h\u1ec7 s\u1ed1 ch\u1eb7n (gi\u00e1 tr\u1ecb c\u1ee7a y khi x = 0), <strong>\u03b2\u2081<\/strong> l\u00e0 h\u1ec7 s\u1ed1 g\u00f3c (cho bi\u1ebft m\u1ee9c \u0111\u1ed9 thay \u0111\u1ed5i c\u1ee7a y khi x thay \u0111\u1ed5i 1 \u0111\u01a1n v\u1ecb), v\u00e0 <strong>\u03b5<\/strong> (epsilon) \u0111\u1ea1i di\u1ec7n cho sai s\u1ed1 ng\u1eabu nhi\u00ean \u2013 ph\u1ea7n m\u00e0 m\u00f4 h\u00ecnh kh\u00f4ng gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c.<\/p>\n<p>C\u00e1c nh\u00e0 khoa h\u1ecdc d\u1eef li\u1ec7u th\u01b0\u1eddng s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p <strong>b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u (Ordinary Least Squares &#8211; OLS)<\/strong> \u0111\u1ec3 t\u00ecm ra c\u00e1c h\u1ec7 s\u1ed1 <strong>\u03b2\u2080<\/strong> v\u00e0 <strong>\u03b2\u2081<\/strong> &#8220;t\u1ed1t nh\u1ea5t&#8221;. &#8220;T\u1ed1t nh\u1ea5t&#8221; \u1edf \u0111\u00e2y c\u00f3 ngh\u0129a l\u00e0 c\u00e1c h\u1ec7 s\u1ed1 n\u00e0y l\u00e0m cho t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng c\u00e1c sai s\u1ed1 (s\u1ef1 kh\u00e1c bi\u1ec7t gi\u1eefa gi\u00e1 tr\u1ecb th\u1ef1c t\u1ebf v\u00e0 gi\u00e1 tr\u1ecb d\u1ef1 \u0111o\u00e1n) l\u00e0 nh\u1ecf nh\u1ea5t.<\/p>\n<p>H\u1ed3i quy tuy\u1ebfn t\u00ednh kh\u00f4ng ch\u1ec9 d\u1eebng l\u1ea1i \u1edf m\u1ed9t bi\u1ebfn \u0111\u1ed9c l\u1eadp. Khi c\u00f3 nhi\u1ec1u bi\u1ebfn \u0111\u1ed9c l\u1eadp (v\u00ed d\u1ee5: chi\u1ec1u cao kh\u00f4ng ch\u1ec9 ph\u1ee5 thu\u1ed9c v\u00e0o chi\u1ec1u d\u00e0i b\u00e0n ch\u00e2n m\u00e0 c\u00f2n ph\u1ee5 thu\u1ed9c v\u00e0o c\u00e2n n\u1eb7ng, \u0111\u1ed9 tu\u1ed5i,&#8230;), ch\u00fang ta c\u00f3 <strong>h\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111a bi\u1ebfn<\/strong>. Ph\u01b0\u01a1ng tr\u00ecnh l\u00fac n\u00e0y s\u1ebd c\u00f3 d\u1ea1ng: y = \u03b2\u2080 + \u03b2\u2081x\u2081 + \u03b2\u2082x\u2082 + &#8230; + \u03b2\u209ax\u209a + \u03b5.<\/p>\n<p>M\u1ed9t v\u00ed d\u1ee5 th\u1ef1c t\u1ebf kh\u00e1c: m\u1ed9t c\u00f4ng ty c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng h\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111\u1ec3 d\u1ef1 \u0111o\u00e1n doanh s\u1ed1 b\u00e1n h\u00e0ng (bi\u1ebfn ph\u1ee5 thu\u1ed9c) d\u1ef1a tr\u00ean c\u00e1c y\u1ebfu t\u1ed1 nh\u01b0 chi ph\u00ed qu\u1ea3ng c\u00e1o, gi\u00e1 s\u1ea3n ph\u1ea9m, v\u00e0 s\u1ed1 l\u01b0\u1ee3ng nh\u00e2n vi\u00ean b\u00e1n h\u00e0ng (c\u00e1c bi\u1ebfn \u0111\u1ed9c l\u1eadp). M\u00f4 h\u00ecnh n\u00e0y gi\u00fap c\u00f4ng ty \u0111\u01b0a ra c\u00e1c quy\u1ebft \u0111\u1ecbnh kinh doanh hi\u1ec7u qu\u1ea3 h\u01a1n. Theo m\u1ed9t nghi\u00ean c\u1ee9u c\u1ee7a <i>Harvard Business Review<\/i>, c\u00e1c c\u00f4ng ty s\u1eed d\u1ee5ng ph\u00e2n t\u00edch d\u1eef li\u1ec7u (trong \u0111\u00f3 c\u00f3 h\u1ed3i quy tuy\u1ebfn t\u00ednh) c\u00f3 n\u0103ng su\u1ea5t cao h\u01a1n 5-6% so v\u1edbi c\u00e1c \u0111\u1ed1i th\u1ee7 kh\u00f4ng s\u1eed d\u1ee5ng.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Tai-sao-hoi-quy-tuyen-tinh-lai-quan-trong\"><\/span>T\u1ea1i sao h\u1ed3i quy tuy\u1ebfn t\u00ednh l\u1ea1i quan tr\u1ecdng?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>H\u1ed3i quy tuy\u1ebfn t\u00ednh<\/strong> l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 quan tr\u1ecdng b\u1eadc nh\u1ea5t trong ph\u00e2n t\u00edch d\u1eef li\u1ec7u v\u00e0 th\u1ed1ng k\u00ea v\u00ec n\u00f3 cung c\u1ea5p m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p <strong>\u0111\u01a1n gi\u1ea3n, d\u1ec5 hi\u1ec3u v\u00e0 hi\u1ec7u qu\u1ea3<\/strong> \u0111\u1ec3 <strong>m\u00f4 h\u00ecnh h\u00f3a m\u1ed1i quan h\u1ec7<\/strong> gi\u1eefa c\u00e1c bi\u1ebfn s\u1ed1, t\u1eeb \u0111\u00f3 \u0111\u01b0a ra <strong>d\u1ef1 \u0111o\u00e1n<\/strong> v\u00e0 <strong>r\u00fat ra k\u1ebft lu\u1eadn<\/strong> c\u00f3 gi\u00e1 tr\u1ecb.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Kha-nang-du-doan\"><\/span>Kh\u1ea3 n\u0103ng d\u1ef1 \u0111o\u00e1n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>M\u1ed9t trong nh\u1eefng l\u00fd do ch\u00ednh khi\u1ebfn h\u1ed3i quy tuy\u1ebfn t\u00ednh tr\u1edf n\u00ean quan tr\u1ecdng l\u00e0 kh\u1ea3 n\u0103ng <strong>d\u1ef1 \u0111o\u00e1n<\/strong> gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn ph\u1ee5 thu\u1ed9c. V\u00ed d\u1ee5, m\u1ed9t c\u00f4ng ty b\u1ea5t \u0111\u1ed9ng s\u1ea3n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng h\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111\u1ec3 d\u1ef1 \u0111o\u00e1n gi\u00e1 nh\u00e0 d\u1ef1a tr\u00ean di\u1ec7n t\u00edch, s\u1ed1 ph\u00f2ng ng\u1ee7, v\u1ecb tr\u00ed v\u00e0 c\u00e1c y\u1ebfu t\u1ed1 kh\u00e1c. B\u1eb1ng c\u00e1ch x\u00e2y d\u1ef1ng m\u1ed9t m\u00f4 h\u00ecnh h\u1ed3i quy, c\u00f4ng ty c\u00f3 th\u1ec3 \u0111\u01b0a ra \u01b0\u1edbc t\u00ednh gi\u00e1 nh\u00e0 ch\u00ednh x\u00e1c h\u01a1n, gi\u00fap c\u1ea3 ng\u01b0\u1eddi mua v\u00e0 ng\u01b0\u1eddi b\u00e1n \u0111\u01b0a ra quy\u1ebft \u0111\u1ecbnh t\u1ed1t h\u01a1n.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Hieu-ro-moi-quan-he-giua-cac-bien\"><\/span>Hi\u1ec3u r\u00f5 m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c bi\u1ebfn<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>H\u1ed3i quy tuy\u1ebfn t\u00ednh kh\u00f4ng ch\u1ec9 gi\u00fap d\u1ef1 \u0111o\u00e1n, m\u00e0 c\u00f2n gi\u00fap ch\u00fang ta <strong>hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 m\u1ed1i quan h\u1ec7<\/strong> gi\u1eefa c\u00e1c bi\u1ebfn s\u1ed1. B\u1eb1ng c\u00e1ch xem x\u00e9t c\u00e1c h\u1ec7 s\u1ed1 h\u1ed3i quy, ch\u00fang ta c\u00f3 th\u1ec3 bi\u1ebft \u0111\u01b0\u1ee3c bi\u1ebfn \u0111\u1ed9c l\u1eadp n\u00e0o c\u00f3 \u1ea3nh h\u01b0\u1edfng l\u1edbn nh\u1ea5t \u0111\u1ebfn bi\u1ebfn ph\u1ee5 thu\u1ed9c, v\u00e0 \u1ea3nh h\u01b0\u1edfng \u0111\u00f3 l\u00e0 t\u00edch c\u1ef1c hay ti\u00eau c\u1ef1c. V\u00ed d\u1ee5, trong nghi\u00ean c\u1ee9u y t\u1ebf, h\u1ed3i quy tuy\u1ebfn t\u00ednh c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh c\u00e1c y\u1ebfu t\u1ed1 nguy c\u01a1 g\u00e2y b\u1ec7nh tim m\u1ea1ch, ch\u1eb3ng h\u1ea1n nh\u01b0 huy\u1ebft \u00e1p, m\u1ee9c cholesterol, v\u00e0 th\u00f3i quen h\u00fat thu\u1ed1c.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Tinh-don-gian-va-de-hieu\"><\/span>T\u00ednh \u0111\u01a1n gi\u1ea3n v\u00e0 d\u1ec5 hi\u1ec3u<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>So v\u1edbi c\u00e1c ph\u01b0\u01a1ng ph\u00e1p h\u1ecdc m\u00e1y ph\u1ee9c t\u1ea1p h\u01a1n, h\u1ed3i quy tuy\u1ebfn t\u00ednh c\u00f3 \u01b0u \u0111i\u1ec3m l\u00e0 <strong>t\u01b0\u01a1ng \u0111\u1ed1i \u0111\u01a1n gi\u1ea3n v\u00e0 d\u1ec5 hi\u1ec3u<\/strong>. \u0110i\u1ec1u n\u00e0y l\u00e0m cho n\u00f3 tr\u1edf th\u00e0nh m\u1ed9t c\u00f4ng c\u1ee5 l\u00fd t\u01b0\u1edfng cho nh\u1eefng ng\u01b0\u1eddi m\u1edbi b\u1eaft \u0111\u1ea7u l\u00e0m quen v\u1edbi ph\u00e2n t\u00edch d\u1eef li\u1ec7u, c\u0169ng nh\u01b0 cho c\u00e1c chuy\u00ean gia mu\u1ed1n gi\u1ea3i th\u00edch k\u1ebft qu\u1ea3 c\u1ee7a h\u1ecd cho nh\u1eefng ng\u01b0\u1eddi kh\u00f4ng c\u00f3 chuy\u00ean m\u00f4n. K\u1ebft qu\u1ea3 \u0111\u01b0\u1ee3c th\u1ec3 hi\u1ec7n qua m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh d\u1ec5 h\u00ecnh dung, c\u00f3 th\u1ec3 hi\u1ec3u r\u00f5 \u00fd ngh\u0129a c\u1ee7a t\u1eebng h\u1ec7 s\u1ed1.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Ung-dung-rong-rai\"><\/span>\u1ee8ng d\u1ee5ng r\u1ed9ng r\u00e3i<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>H\u1ed3i quy tuy\u1ebfn t\u00ednh c\u00f3 <strong>\u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i<\/strong> trong nhi\u1ec1u l\u0129nh v\u1ef1c, t\u1eeb kinh doanh, t\u00e0i ch\u00ednh, kinh t\u1ebf, \u0111\u1ebfn y h\u1ecdc, k\u1ef9 thu\u1eadt, khoa h\u1ecdc x\u00e3 h\u1ed9i, v\u00e0 nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c. B\u1ea5t c\u1ee9 n\u01a1i n\u00e0o c\u00f3 d\u1eef li\u1ec7u v\u00e0 nhu c\u1ea7u ph\u00e2n t\u00edch m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c bi\u1ebfn, h\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111\u1ec1u c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng. Theo m\u1ed9t kh\u1ea3o s\u00e1t c\u1ee7a <i>KDnuggets<\/i>, h\u1ed3i quy tuy\u1ebfn t\u00ednh l\u00e0 m\u1ed9t trong ba ph\u01b0\u01a1ng ph\u00e1p ph\u00e2n t\u00edch d\u1eef li\u1ec7u \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng ph\u1ed5 bi\u1ebfn nh\u1ea5t.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Nen-tang-cho-cac-phuong-phap-nang-cao\"><\/span>N\u1ec1n t\u1ea3ng cho c\u00e1c ph\u01b0\u01a1ng ph\u00e1p n\u00e2ng cao<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>H\u1ed3i quy tuy\u1ebfn t\u00ednh l\u00e0 <strong>n\u1ec1n t\u1ea3ng<\/strong> cho nhi\u1ec1u ph\u01b0\u01a1ng ph\u00e1p ph\u00e2n t\u00edch d\u1eef li\u1ec7u v\u00e0 h\u1ecdc m\u00e1y n\u00e2ng cao h\u01a1n. Vi\u1ec7c hi\u1ec3u r\u00f5 h\u1ed3i quy tuy\u1ebfn t\u00ednh s\u1ebd gi\u00fap b\u1ea1n d\u1ec5 d\u00e0ng ti\u1ebfp c\u1eadn v\u00e0 l\u00e0m ch\u1ee7 c\u00e1c k\u1ef9 thu\u1eadt ph\u1ee9c t\u1ea1p h\u01a1n, ch\u1eb3ng h\u1ea1n nh\u01b0 h\u1ed3i quy logistic, h\u1ed3i quy \u0111a th\u1ee9c (Polynomial Regression), m\u00f4 h\u00ecnh tuy\u1ebfn t\u00ednh t\u1ed5ng qu\u00e1t (Generalized Linear Models &#8211; GLMs), v\u00e0 th\u1eadm ch\u00ed c\u1ea3 c\u00e1c m\u1ea1ng n\u01a1-ron (Neural Networks). Hi\u1ec3u \u0111\u01b0\u1ee3c n\u00f3 gi\u00fap b\u1ea1n c\u00f3 b\u01b0\u1edbc \u0111\u1ec7m t\u1ed1t trong l\u0129nh v\u1ef1c n\u00e0y.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Hoi-quy-tuyen-tinh-hoat-dong-nhu-the-nao\"><\/span>H\u1ed3i quy tuy\u1ebfn t\u00ednh ho\u1ea1t \u0111\u1ed9ng nh\u01b0 th\u1ebf n\u00e0o?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>H\u1ed3i quy tuy\u1ebfn t\u00ednh<\/strong> ho\u1ea1t \u0111\u1ed9ng b\u1eb1ng c\u00e1ch t\u00ecm ra m\u1ed9t <strong>\u0111\u01b0\u1eddng th\u1eb3ng<\/strong> (ho\u1eb7c m\u1eb7t ph\u1eb3ng, si\u00eau ph\u1eb3ng trong kh\u00f4ng gian nhi\u1ec1u chi\u1ec1u) <strong>ph\u00f9 h\u1ee3p nh\u1ea5t<\/strong> v\u1edbi d\u1eef li\u1ec7u, sao cho <strong>t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng sai s\u1ed1<\/strong> gi\u1eefa gi\u00e1 tr\u1ecb th\u1ef1c t\u1ebf v\u00e0 gi\u00e1 tr\u1ecb d\u1ef1 \u0111o\u00e1n l\u00e0 <strong>nh\u1ecf nh\u1ea5t<\/strong>. \u0110\u01b0\u1eddng th\u1eb3ng n\u00e0y \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh tuy\u1ebfn t\u00ednh.<\/p>\n<p>H\u00e3y t\u01b0\u1edfng t\u01b0\u1ee3ng b\u1ea1n c\u00f3 m\u1ed9t t\u1eadp d\u1eef li\u1ec7u v\u1ec1 chi\u1ec1u cao v\u00e0 c\u00e2n n\u1eb7ng c\u1ee7a m\u1ed9t nh\u00f3m ng\u01b0\u1eddi. B\u1ea1n mu\u1ed1n t\u00ecm ra m\u1ed1i quan h\u1ec7 gi\u1eefa hai bi\u1ebfn n\u00e0y. H\u1ed3i quy tuy\u1ebfn t\u00ednh s\u1ebd gi\u00fap b\u1ea1n &#8220;v\u1ebd&#8221; m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng tr\u00ean bi\u1ec3u \u0111\u1ed3 ph\u00e2n t\u00e1n (scatter plot) c\u1ee7a d\u1eef li\u1ec7u, sao cho \u0111\u01b0\u1eddng th\u1eb3ng n\u00e0y &#8220;g\u1ea7n&#8221; v\u1edbi t\u1ea5t c\u1ea3 c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u nh\u1ea5t c\u00f3 th\u1ec3.<\/p>\n<p>Ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng n\u00e0y c\u00f3 d\u1ea1ng: <strong>y = \u03b2\u2080 + \u03b2\u2081x + \u03b5<\/strong>.<\/p>\n<ul>\n<li><strong>y<\/strong> l\u00e0 bi\u1ebfn ph\u1ee5 thu\u1ed9c (c\u00e2n n\u1eb7ng).<\/li>\n<li><strong>x<\/strong> l\u00e0 bi\u1ebfn \u0111\u1ed9c l\u1eadp (chi\u1ec1u cao).<\/li>\n<li><strong>\u03b2\u2080<\/strong> l\u00e0 h\u1ec7 s\u1ed1 ch\u1eb7n (gi\u00e1 tr\u1ecb c\u1ee7a c\u00e2n n\u1eb7ng khi chi\u1ec1u cao b\u1eb1ng 0 \u2013 m\u1ed9t gi\u00e1 tr\u1ecb l\u00fd thuy\u1ebft, kh\u00f4ng c\u00f3 \u00fd ngh\u0129a th\u1ef1c t\u1ebf trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y).<\/li>\n<li><strong>\u03b2\u2081<\/strong> l\u00e0 h\u1ec7 s\u1ed1 g\u00f3c (cho bi\u1ebft c\u00e2n n\u1eb7ng thay \u0111\u1ed5i bao nhi\u00eau khi chi\u1ec1u cao thay \u0111\u1ed5i 1 \u0111\u01a1n v\u1ecb).<\/li>\n<li><strong>\u03b5<\/strong> l\u00e0 sai s\u1ed1 (ph\u1ea7n ch\u00eanh l\u1ec7ch gi\u1eefa gi\u00e1 tr\u1ecb th\u1ef1c t\u1ebf v\u00e0 gi\u00e1 tr\u1ecb d\u1ef1 \u0111o\u00e1n).<\/li>\n<\/ul>\n<p>\u0110\u1ec3 t\u00ecm ra c\u00e1c h\u1ec7 s\u1ed1 <strong>\u03b2\u2080<\/strong> v\u00e0 <strong>\u03b2\u2081<\/strong> &#8220;t\u1ed1t nh\u1ea5t&#8221;, h\u1ed3i quy tuy\u1ebfn t\u00ednh s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p <strong>b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u (Ordinary Least Squares &#8211; OLS)<\/strong>. Ph\u01b0\u01a1ng ph\u00e1p n\u00e0y s\u1ebd t\u00ecm ra c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a <strong>\u03b2\u2080<\/strong> v\u00e0 <strong>\u03b2\u2081<\/strong> sao cho t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a c\u00e1c sai s\u1ed1 (\u03b5) l\u00e0 nh\u1ecf nh\u1ea5t. N\u00f3i c\u00e1ch kh\u00e1c, n\u00f3 t\u00ecm ra \u0111\u01b0\u1eddng th\u1eb3ng &#8220;g\u1ea7n&#8221; v\u1edbi t\u1ea5t c\u1ea3 c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u nh\u1ea5t.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/03\/Hoi-quy-tuyen-tinh-01.webp\" alt=\"H\u1ed3i quy tuy\u1ebfn t\u00ednh\" width=\"800\" height=\"516\" class=\"aligncenter wp-image-25434\" title=\"\" srcset=\"https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/03\/Hoi-quy-tuyen-tinh-01.webp 1024w, https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/03\/Hoi-quy-tuyen-tinh-01-300x193.webp 300w, https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/03\/Hoi-quy-tuyen-tinh-01-768x495.webp 768w, https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/03\/Hoi-quy-tuyen-tinh-01-750x483.webp 750w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>V\u00ed d\u1ee5, gi\u1ea3 s\u1eed sau khi th\u1ef1c hi\u1ec7n h\u1ed3i quy tuy\u1ebfn t\u00ednh, b\u1ea1n t\u00ecm \u0111\u01b0\u1ee3c ph\u01b0\u01a1ng tr\u00ecnh: <i>C\u00e2n n\u1eb7ng = -100 + 0.8 * Chi\u1ec1u cao<\/i>. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0:<\/p>\n<ul>\n<li>Khi chi\u1ec1u cao b\u1eb1ng 0 (m\u1ed9t gi\u00e1 tr\u1ecb kh\u00f4ng th\u1ef1c t\u1ebf), c\u00e2n n\u1eb7ng \u01b0\u1edbc t\u00ednh l\u00e0 -100 kg (h\u1ec7 s\u1ed1 ch\u1eb7n \u03b2\u2080).<\/li>\n<li>M\u1ed7i khi chi\u1ec1u cao t\u0103ng th\u00eam 1 cm, c\u00e2n n\u1eb7ng \u01b0\u1edbc t\u00ednh s\u1ebd t\u0103ng th\u00eam 0.8 kg (h\u1ec7 s\u1ed1 g\u00f3c \u03b2\u2081).<\/li>\n<li>Ph\u01b0\u01a1ng tr\u00ecnh tr\u00ean s\u1ebd c\u00f3 sai s\u1ed1 v\u00ec tr\u00ean th\u1ef1c t\u1ebf s\u1ebd kh\u00f4ng c\u00f3 m\u1ed1i li\u00ean h\u1ec7 ho\u00e0n h\u1ea3o.<\/li>\n<\/ul>\n<p>M\u1ed9t khi \u0111\u00e3 c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh h\u1ed3i quy, b\u1ea1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng n\u00f3 \u0111\u1ec3 <strong>d\u1ef1 \u0111o\u00e1n<\/strong> c\u00e2n n\u1eb7ng c\u1ee7a m\u1ed9t ng\u01b0\u1eddi d\u1ef1a tr\u00ean chi\u1ec1u cao c\u1ee7a h\u1ecd. V\u00ed d\u1ee5, n\u1ebfu m\u1ed9t ng\u01b0\u1eddi cao 170 cm, b\u1ea1n c\u00f3 th\u1ec3 d\u1ef1 \u0111o\u00e1n c\u00e2n n\u1eb7ng c\u1ee7a h\u1ecd l\u00e0: -100 + 0.8 * 170 = 36 kg. T\u1ea5t nhi\u00ean, \u0111\u00e2y ch\u1ec9 l\u00e0 m\u1ed9t gi\u00e1 tr\u1ecb d\u1ef1 \u0111o\u00e1n, v\u00e0 gi\u00e1 tr\u1ecb th\u1ef1c t\u1ebf c\u00f3 th\u1ec3 kh\u00e1c m\u1ed9t ch\u00fat.<\/p>\n<p>Quan tr\u1ecdng c\u1ea7n l\u01b0u \u00fd l\u00e0 h\u1ed3i quy tuy\u1ebfn t\u00ednh d\u1ef1a tr\u00ean m\u1ed9t s\u1ed1 <strong>gi\u1ea3 \u0111\u1ecbnh<\/strong> v\u1ec1 d\u1eef li\u1ec7u. V\u00ed d\u1ee5, m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c bi\u1ebfn ph\u1ea3i l\u00e0 tuy\u1ebfn t\u00ednh, sai s\u1ed1 ph\u1ea3i c\u00f3 ph\u00e2n ph\u1ed1i chu\u1ea9n, v\u00e0 kh\u00f4ng c\u00f3 hi\u1ec7n t\u01b0\u1ee3ng \u0111a c\u1ed9ng tuy\u1ebfn (trong tr\u01b0\u1eddng h\u1ee3p h\u1ed3i quy \u0111a bi\u1ebfn). N\u1ebfu c\u00e1c gi\u1ea3 \u0111\u1ecbnh n\u00e0y b\u1ecb vi ph\u1ea1m, k\u1ebft qu\u1ea3 c\u1ee7a m\u00f4 h\u00ecnh c\u00f3 th\u1ec3 kh\u00f4ng ch\u00ednh x\u00e1c.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Hoi-quy-tuyen-tinh-trong-may-hoc-la-gi\"><\/span>H\u1ed3i quy tuy\u1ebfn t\u00ednh trong m\u00e1y h\u1ecdc l\u00e0 g\u00ec?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Trong <strong>m\u00e1y h\u1ecdc (Machine Learning)<\/strong>, <strong>h\u1ed3i quy tuy\u1ebfn t\u00ednh<\/strong> l\u00e0 m\u1ed9t thu\u1eadt to\u00e1n <strong>h\u1ecdc c\u00f3 gi\u00e1m s\u00e1t (Supervised Learning)<\/strong> c\u01a1 b\u1ea3n, \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 <strong>d\u1ef1 \u0111o\u00e1n<\/strong> m\u1ed9t bi\u1ebfn m\u1ee5c ti\u00eau (bi\u1ebfn ph\u1ee5 thu\u1ed9c) c\u00f3 gi\u00e1 tr\u1ecb li\u00ean t\u1ee5c d\u1ef1a tr\u00ean m\u1ed9t ho\u1eb7c nhi\u1ec1u bi\u1ebfn \u0111\u1ea7u v\u00e0o (bi\u1ebfn \u0111\u1ed9c l\u1eadp). N\u00f3 thu\u1ed9c nh\u00f3m c\u00e1c b\u00e0i to\u00e1n <strong>h\u1ed3i quy (Regression)<\/strong>.<\/p>\n<p>N\u00f3i m\u1ed9t c\u00e1ch \u0111\u01a1n gi\u1ea3n, m\u00e1y t\u00ednh s\u1ebd &#8220;h\u1ecdc&#8221; t\u1eeb d\u1eef li\u1ec7u hu\u1ea5n luy\u1ec7n (training data) \u0111\u1ec3 t\u00ecm ra m\u1ed1i quan h\u1ec7 tuy\u1ebfn t\u00ednh gi\u1eefa c\u00e1c bi\u1ebfn \u0111\u1ea7u v\u00e0o v\u00e0 bi\u1ebfn m\u1ee5c ti\u00eau. Sau \u0111\u00f3, m\u00f4 h\u00ecnh \u0111\u00e3 h\u1ecdc c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 d\u1ef1 \u0111o\u00e1n gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn m\u1ee5c ti\u00eau cho c\u00e1c d\u1eef li\u1ec7u m\u1edbi.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/03\/Hoi-quy-tuyen-tinh-trong-hoc-may.webp\" alt=\"H\u1ed3i quy tuy\u1ebfn t\u00ednh trong h\u1ecdc m\u00e1y\" width=\"800\" height=\"461\" class=\"aligncenter wp-image-25435\" title=\"\" srcset=\"https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/03\/Hoi-quy-tuyen-tinh-trong-hoc-may.webp 724w, https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/03\/Hoi-quy-tuyen-tinh-trong-hoc-may-300x173.webp 300w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Cach-thuc-hoat-dong\"><\/span>C\u00e1ch th\u1ee9c ho\u1ea1t \u0111\u1ed9ng<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Qu\u00e1 tr\u00ecnh &#8220;h\u1ecdc&#8221; c\u1ee7a thu\u1eadt to\u00e1n h\u1ed3i quy tuy\u1ebfn t\u00ednh trong m\u00e1y h\u1ecdc bao g\u1ed3m c\u00e1c b\u01b0\u1edbc ch\u00ednh sau:<\/p>\n<ol>\n<li><strong>Chu\u1ea9n b\u1ecb d\u1eef li\u1ec7u:<\/strong> Thu th\u1eadp v\u00e0 ti\u1ec1n x\u1eed l\u00fd d\u1eef li\u1ec7u, bao g\u1ed3m l\u00e0m s\u1ea1ch d\u1eef li\u1ec7u, x\u1eed l\u00fd c\u00e1c gi\u00e1 tr\u1ecb thi\u1ebfu, v\u00e0 chu\u1ea9n h\u00f3a d\u1eef li\u1ec7u (n\u1ebfu c\u1ea7n).<\/li>\n<li><strong>Ch\u1ecdn m\u00f4 h\u00ecnh:<\/strong> Ch\u1ecdn m\u00f4 h\u00ecnh h\u1ed3i quy tuy\u1ebfn t\u00ednh (\u0111\u01a1n bi\u1ebfn ho\u1eb7c \u0111a bi\u1ebfn, t\u00f9y thu\u1ed9c v\u00e0o s\u1ed1 l\u01b0\u1ee3ng bi\u1ebfn \u0111\u1ea7u v\u00e0o).<\/li>\n<li><strong>Hu\u1ea5n luy\u1ec7n m\u00f4 h\u00ecnh:<\/strong> S\u1eed d\u1ee5ng d\u1eef li\u1ec7u hu\u1ea5n luy\u1ec7n \u0111\u1ec3 &#8220;hu\u1ea5n luy\u1ec7n&#8221; m\u00f4 h\u00ecnh, t\u1ee9c l\u00e0 t\u00ecm ra c\u00e1c h\u1ec7 s\u1ed1 h\u1ed3i quy (\u03b2\u2080, \u03b2\u2081, &#8230;, \u03b2\u209a) sao cho h\u00e0m m\u1ea5t m\u00e1t (loss function) \u2013 th\u01b0\u1eddng l\u00e0 t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng sai s\u1ed1 (SSE) \u2013 l\u00e0 nh\u1ecf nh\u1ea5t. Vi\u1ec7c n\u00e0y th\u01b0\u1eddng \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u (OLS) ho\u1eb7c c\u00e1c ph\u01b0\u01a1ng ph\u00e1p t\u1ed1i \u01b0u h\u00f3a kh\u00e1c nh\u01b0 Gradient Descent.<\/li>\n<li><strong>\u0110\u00e1nh gi\u00e1 m\u00f4 h\u00ecnh:<\/strong> S\u1eed d\u1ee5ng d\u1eef li\u1ec7u ki\u1ec3m tra (test data) \u2013 d\u1eef li\u1ec7u m\u00e0 m\u00f4 h\u00ecnh ch\u01b0a t\u1eebng &#8220;nh\u00ecn th\u1ea5y&#8221; \u2013 \u0111\u1ec3 \u0111\u00e1nh gi\u00e1 hi\u1ec7u su\u1ea5t c\u1ee7a m\u00f4 h\u00ecnh. C\u00e1c th\u01b0\u1edbc \u0111o \u0111\u00e1nh gi\u00e1 th\u01b0\u1eddng d\u00f9ng bao g\u1ed3m R-squared, RMSE (Root Mean Squared Error), MAE (Mean Absolute Error),&#8230;<\/li>\n<li><strong>D\u1ef1 \u0111o\u00e1n:<\/strong> S\u1eed d\u1ee5ng m\u00f4 h\u00ecnh \u0111\u00e3 hu\u1ea5n luy\u1ec7n \u0111\u1ec3 d\u1ef1 \u0111o\u00e1n gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn m\u1ee5c ti\u00eau cho c\u00e1c d\u1eef li\u1ec7u m\u1edbi.<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"Vi-du-minh-hoa\"><\/span>V\u00ed d\u1ee5 minh h\u1ecda<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Gi\u1ea3 s\u1eed b\u1ea1n mu\u1ed1n x\u00e2y d\u1ef1ng m\u1ed9t m\u00f4 h\u00ecnh m\u00e1y h\u1ecdc \u0111\u1ec3 d\u1ef1 \u0111o\u00e1n gi\u00e1 nh\u00e0 d\u1ef1a tr\u00ean di\u1ec7n t\u00edch. B\u1ea1n c\u00f3 d\u1eef li\u1ec7u v\u1ec1 di\u1ec7n t\u00edch v\u00e0 gi\u00e1 c\u1ee7a 100 c\u0103n nh\u00e0. B\u1ea1n s\u1ebd chia d\u1eef li\u1ec7u n\u00e0y th\u00e0nh hai ph\u1ea7n: 80 c\u0103n nh\u00e0 d\u00f9ng \u0111\u1ec3 hu\u1ea5n luy\u1ec7n m\u00f4 h\u00ecnh, v\u00e0 20 c\u0103n nh\u00e0 c\u00f2n l\u1ea1i d\u00f9ng \u0111\u1ec3 ki\u1ec3m tra m\u00f4 h\u00ecnh.<\/p>\n<p>M\u00f4 h\u00ecnh h\u1ed3i quy tuy\u1ebfn t\u00ednh s\u1ebd &#8220;h\u1ecdc&#8221; t\u1eeb 80 c\u0103n nh\u00e0 n\u00e0y \u0111\u1ec3 t\u00ecm ra ph\u01b0\u01a1ng tr\u00ecnh: <i>Gi\u00e1 nh\u00e0 = \u03b2\u2080 + \u03b2\u2081 * Di\u1ec7n t\u00edch<\/i>. Sau \u0111\u00f3, b\u1ea1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y \u0111\u1ec3 d\u1ef1 \u0111o\u00e1n gi\u00e1 c\u1ee7a 20 c\u0103n nh\u00e0 c\u00f2n l\u1ea1i, v\u00e0 so s\u00e1nh k\u1ebft qu\u1ea3 d\u1ef1 \u0111o\u00e1n v\u1edbi gi\u00e1 th\u1ef1c t\u1ebf \u0111\u1ec3 \u0111\u00e1nh gi\u00e1 hi\u1ec7u su\u1ea5t c\u1ee7a m\u00f4 h\u00ecnh.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Uu-diem-va-nhuoc-diem\"><\/span>\u01afu \u0111i\u1ec3m v\u00e0 nh\u01b0\u1ee3c \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u01afu \u0111i\u1ec3m:<\/strong><\/p>\n<ul>\n<li><strong>\u0110\u01a1n gi\u1ea3n, d\u1ec5 hi\u1ec3u v\u00e0 d\u1ec5 tri\u1ec3n khai:<\/strong> H\u1ed3i quy tuy\u1ebfn t\u00ednh l\u00e0 m\u1ed9t trong nh\u1eefng thu\u1eadt to\u00e1n m\u00e1y h\u1ecdc \u0111\u01a1n gi\u1ea3n nh\u1ea5t.<\/li>\n<li><strong>T\u1ed1c \u0111\u1ed9 hu\u1ea5n luy\u1ec7n nhanh:<\/strong> Th\u01b0\u1eddng kh\u00f4ng t\u1ed1n nhi\u1ec1u th\u1eddi gian \u0111\u1ec3 hu\u1ea5n luy\u1ec7n m\u00f4 h\u00ecnh.<\/li>\n<li><strong>Kh\u1ea3 n\u0103ng di\u1ec5n gi\u1ea3i cao:<\/strong> C\u00e1c h\u1ec7 s\u1ed1 h\u1ed3i quy cho bi\u1ebft m\u1ee9c \u0111\u1ed9 \u1ea3nh h\u01b0\u1edfng c\u1ee7a t\u1eebng bi\u1ebfn \u0111\u1ea7u v\u00e0o \u0111\u1ebfn bi\u1ebfn m\u1ee5c ti\u00eau.<\/li>\n<\/ul>\n<p><strong>Nh\u01b0\u1ee3c \u0111i\u1ec3m:<\/strong><\/p>\n<ul>\n<li><strong>Gi\u1ea3 \u0111\u1ecbnh v\u1ec1 m\u1ed1i quan h\u1ec7 tuy\u1ebfn t\u00ednh:<\/strong> Ch\u1ec9 ho\u1ea1t \u0111\u1ed9ng t\u1ed1t khi m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c bi\u1ebfn l\u00e0 tuy\u1ebfn t\u00ednh.<\/li>\n<li><strong>Nh\u1ea1y c\u1ea3m v\u1edbi d\u1eef li\u1ec7u ngo\u1ea1i lai (outliers):<\/strong> C\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u ngo\u1ea1i lai c\u00f3 th\u1ec3 \u1ea3nh h\u01b0\u1edfng l\u1edbn \u0111\u1ebfn k\u1ebft qu\u1ea3 c\u1ee7a m\u00f4 h\u00ecnh.<\/li>\n<li><strong>Kh\u00f4ng th\u1ec3 m\u00f4 h\u00ecnh h\u00f3a c\u00e1c m\u1ed1i quan h\u1ec7 ph\u1ee9c t\u1ea1p:<\/strong> Kh\u00f4ng ph\u00f9 h\u1ee3p cho c\u00e1c b\u00e0i to\u00e1n c\u00f3 m\u1ed1i quan h\u1ec7 phi tuy\u1ebfn ho\u1eb7c t\u01b0\u01a1ng t\u00e1c ph\u1ee9c t\u1ea1p gi\u1eefa c\u00e1c bi\u1ebfn.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Moi-lien-he-voi-cac-khai-niem-khac\"><\/span>M\u1ed1i li\u00ean h\u1ec7 v\u1edbi c\u00e1c kh\u00e1i ni\u1ec7m kh\u00e1c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>H\u1ed3i quy tuy\u1ebfn t\u00ednh c\u00f3 m\u1ed1i li\u00ean h\u1ec7 ch\u1eb7t ch\u1ebd v\u1edbi nhi\u1ec1u kh\u00e1i ni\u1ec7m kh\u00e1c trong m\u00e1y h\u1ecdc v\u00e0 th\u1ed1ng k\u00ea, ch\u1eb3ng h\u1ea1n nh\u01b0:<\/p>\n<ul>\n<li><strong>H\u1ecdc c\u00f3 gi\u00e1m s\u00e1t (Supervised Learning):<\/strong> H\u1ed3i quy tuy\u1ebfn t\u00ednh l\u00e0 m\u1ed9t v\u00ed d\u1ee5 \u0111i\u1ec3n h\u00ecnh c\u1ee7a h\u1ecdc c\u00f3 gi\u00e1m s\u00e1t.<\/li>\n<li><strong>B\u00e0i to\u00e1n h\u1ed3i quy (Regression Problem):<\/strong> \u0110\u00e2y l\u00e0 lo\u1ea1i b\u00e0i to\u00e1n m\u00e0 h\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 gi\u1ea3i quy\u1ebft.<\/li>\n<li><strong>H\u00e0m m\u1ea5t m\u00e1t (Loss Function):<\/strong> \u0110\u1ea1i l\u01b0\u1ee3ng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 \u0111o l\u01b0\u1eddng m\u1ee9c \u0111\u1ed9 &#8220;t\u1ed1t&#8221; c\u1ee7a m\u00f4 h\u00ecnh.<\/li>\n<li><strong>Gradient Descent:<\/strong> M\u1ed9t thu\u1eadt to\u00e1n t\u1ed1i \u01b0u h\u00f3a th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ecm c\u00e1c h\u1ec7 s\u1ed1 h\u1ed3i quy.<\/li>\n<li><strong>H\u1ed3i quy Ridge v\u00e0 Lasso<\/strong>: C\u00e1c k\u1ef9 thu\u1eadt m\u1edf r\u1ed9ng \u0111\u1ec3 tr\u00e1nh hi\u1ec7n t\u01b0\u1ee3ng qu\u00e1 kh\u1edbp (Overfitting).<\/li>\n<\/ul>\n<p><strong>|| Xem th\u00eam: <a href=\"https:\/\/interdata.vn\/blog\/tri-tue-nhan-tao-ai\/\">Tr\u00ed tu\u1ec7 nh\u00e2n t\u1ea1o (AI) l\u00e0 g\u00ec? \u1ee8ng d\u1ee5ng, Th\u00e1ch th\u1ee9c v\u00e0 T\u01b0\u01a1ng lai<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Co-nhung-loai-hoi-quy-tuyen-tinh-nao\"><\/span>C\u00f3 nh\u1eefng lo\u1ea1i h\u1ed3i quy tuy\u1ebfn t\u00ednh n\u00e0o?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>C\u00f3 hai lo\u1ea1i h\u1ed3i quy tuy\u1ebfn t\u00ednh ch\u00ednh: <strong>h\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111\u01a1n bi\u1ebfn (Simple Linear Regression)<\/strong> v\u00e0 <strong>h\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111a bi\u1ebfn (Multiple Linear Regression)<\/strong>. Ngo\u00e0i ra, c\u00f2n c\u00f3 m\u1ed9t d\u1ea1ng m\u1edf r\u1ed9ng l\u00e0 <strong>h\u1ed3i quy tuy\u1ebfn t\u00ednh t\u1ed5ng qu\u00e1t (Generalized Linear Models &#8211; GLMs)<\/strong>, nh\u01b0ng d\u1ea1ng n\u00e0y ph\u1ee9c t\u1ea1p h\u01a1n v\u00e0 th\u01b0\u1eddng kh\u00f4ng \u0111\u01b0\u1ee3c coi l\u00e0 &#8220;h\u1ed3i quy tuy\u1ebfn t\u00ednh&#8221; theo ngh\u0129a c\u01a1 b\u1ea3n.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Hoi-quy-tuyen-tinh-don-bien-simple-linear-regression\"><\/span>H\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111\u01a1n bi\u1ebfn (simple linear regression)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0110\u00e2y l\u00e0 d\u1ea1ng \u0111\u01a1n gi\u1ea3n nh\u1ea5t c\u1ee7a h\u1ed3i quy tuy\u1ebfn t\u00ednh, trong \u0111\u00f3 ch\u1ec9 c\u00f3 <strong>m\u1ed9t bi\u1ebfn \u0111\u1ed9c l\u1eadp (x)<\/strong> v\u00e0 <strong>m\u1ed9t bi\u1ebfn ph\u1ee5 thu\u1ed9c (y)<\/strong>. M\u1ed1i quan h\u1ec7 gi\u1eefa ch\u00fang \u0111\u01b0\u1ee3c m\u00f4 h\u00ecnh h\u00f3a b\u1eb1ng m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng.<\/p>\n<p><strong>V\u00ed d\u1ee5:<\/strong> D\u1ef1 \u0111o\u00e1n \u0111i\u1ec3m thi cu\u1ed1i k\u1ef3 (y) d\u1ef1a tr\u00ean s\u1ed1 gi\u1edd h\u1ecdc (x). Ph\u01b0\u01a1ng tr\u00ecnh h\u1ed3i quy c\u00f3 d\u1ea1ng: <i>\u0110i\u1ec3m thi = \u03b2\u2080 + \u03b2\u2081 * S\u1ed1 gi\u1edd h\u1ecdc + \u03b5<\/i>.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Hoi-quy-tuyen-tinh-da-bien-multiple-linear-regression\"><\/span>H\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111a bi\u1ebfn (multiple linear regression)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Trong h\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111a bi\u1ebfn, c\u00f3 <strong>nhi\u1ec1u bi\u1ebfn \u0111\u1ed9c l\u1eadp (x\u2081, x\u2082, &#8230;, x\u209a)<\/strong> c\u00f9ng \u1ea3nh h\u01b0\u1edfng \u0111\u1ebfn <strong>m\u1ed9t bi\u1ebfn ph\u1ee5 thu\u1ed9c (y)<\/strong>. M\u1ed1i quan h\u1ec7 n\u00e0y \u0111\u01b0\u1ee3c m\u00f4 h\u00ecnh h\u00f3a b\u1eb1ng m\u1ed9t m\u1eb7t ph\u1eb3ng (trong kh\u00f4ng gian ba chi\u1ec1u) ho\u1eb7c si\u00eau ph\u1eb3ng (trong kh\u00f4ng gian nhi\u1ec1u chi\u1ec1u h\u01a1n).<\/p>\n<p><strong>V\u00ed d\u1ee5:<\/strong> D\u1ef1 \u0111o\u00e1n gi\u00e1 nh\u00e0 (y) d\u1ef1a tr\u00ean di\u1ec7n t\u00edch (x\u2081), s\u1ed1 ph\u00f2ng ng\u1ee7 (x\u2082), kho\u1ea3ng c\u00e1ch \u0111\u1ebfn trung t\u00e2m th\u00e0nh ph\u1ed1 (x\u2083). Ph\u01b0\u01a1ng tr\u00ecnh h\u1ed3i quy c\u00f3 d\u1ea1ng: <i>Gi\u00e1 nh\u00e0 = \u03b2\u2080 + \u03b2\u2081 * Di\u1ec7n t\u00edch + \u03b2\u2082 * S\u1ed1 ph\u00f2ng ng\u1ee7 + \u03b2\u2083 * Kho\u1ea3ng c\u00e1ch + \u03b5<\/i>.<\/p>\n<p><strong>\u0110i\u1ec3m kh\u00e1c bi\u1ec7t ch\u00ednh:<\/strong><\/p>\n<ul>\n<li><strong>S\u1ed1 l\u01b0\u1ee3ng bi\u1ebfn \u0111\u1ed9c l\u1eadp:<\/strong> \u0110\u01a1n bi\u1ebfn ch\u1ec9 c\u00f3 m\u1ed9t, \u0111a bi\u1ebfn c\u00f3 nhi\u1ec1u.<\/li>\n<li><strong>Ph\u01b0\u01a1ng tr\u00ecnh:<\/strong> \u0110\u01a1n bi\u1ebfn l\u00e0 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng, \u0111a bi\u1ebfn l\u00e0 ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng ho\u1eb7c si\u00eau ph\u1eb3ng.<\/li>\n<li><strong>\u0110\u1ed9 ph\u1ee9c t\u1ea1p:<\/strong> \u0110a bi\u1ebfn ph\u1ee9c t\u1ea1p h\u01a1n v\u1ec1 m\u1eb7t t\u00ednh to\u00e1n v\u00e0 di\u1ec5n gi\u1ea3i.<\/li>\n<li><strong>V\u1ea5n \u0111\u1ec1 \u0111a c\u1ed9ng tuy\u1ebfn:<\/strong> Trong h\u1ed3i quy \u0111a bi\u1ebfn, c\u1ea7n ch\u00fa \u00fd \u0111\u1ebfn hi\u1ec7n t\u01b0\u1ee3ng \u0111a c\u1ed9ng tuy\u1ebfn (multicollinearity), khi c\u00e1c bi\u1ebfn \u0111\u1ed9c l\u1eadp c\u00f3 t\u01b0\u01a1ng quan cao v\u1edbi nhau, l\u00e0m cho k\u1ebft qu\u1ea3 h\u1ed3i quy kh\u00f4ng \u1ed5n \u0111\u1ecbnh.<\/li>\n<\/ul>\n<p><strong>M\u1ed1i li\u00ean h\u1ec7:<\/strong> H\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111\u01a1n bi\u1ebfn c\u00f3 th\u1ec3 coi l\u00e0 m\u1ed9t tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t c\u1ee7a h\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111a bi\u1ebfn, khi s\u1ed1 l\u01b0\u1ee3ng bi\u1ebfn \u0111\u1ed9c l\u1eadp b\u1eb1ng 1.<\/p>\n<p><strong>H\u1ed3i quy tuy\u1ebfn t\u00ednh t\u1ed5ng qu\u00e1t (GLMs)<\/strong><\/p>\n<p>\u0110\u00e2y kh\u00f4ng h\u1eb3n l\u00e0 m\u1ed9t &#8220;lo\u1ea1i&#8221; h\u1ed3i quy tuy\u1ebfn t\u00ednh, m\u00e0 l\u00e0 m\u1ed9t h\u1ecd c\u00e1c m\u00f4 h\u00ecnh m\u1edf r\u1ed9ng, bao g\u1ed3m c\u1ea3 h\u1ed3i quy tuy\u1ebfn t\u00ednh th\u00f4ng th\u01b0\u1eddng. H\u1ed3i quy Logistic (Logistic Regression), d\u00f9 c\u00f3 ch\u1eef &#8220;h\u1ed3i quy&#8221;, l\u1ea1i thu\u1ed9c v\u00e0o h\u1ecd GLMs n\u00e0y, v\u00e0 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng cho b\u00e0i to\u00e1n ph\u00e2n lo\u1ea1i (classification), ch\u1ee9 kh\u00f4ng ph\u1ea3i h\u1ed3i quy (d\u1ef1 \u0111o\u00e1n gi\u00e1 tr\u1ecb li\u00ean t\u1ee5c). V\u00ec v\u1eady, GLMs v\u01b0\u1ee3t ra ngo\u00e0i ph\u1ea1m vi c\u1ee7a &#8220;h\u1ed3i quy tuy\u1ebfn t\u00ednh&#8221; c\u01a1 b\u1ea3n.<\/p>\n<hr \/>\n<p>Trong qu\u00e1 tr\u00ecnh ph\u00e2n t\u00edch h\u1ed3i quy tuy\u1ebfn t\u00ednh, vi\u1ec7c x\u1eed l\u00fd d\u1eef li\u1ec7u l\u1edbn v\u00e0 ph\u1ee9c t\u1ea1p \u0111\u00f2i h\u1ecfi s\u1ee9c m\u1ea1nh t\u00ednh to\u00e1n \u0111\u00e1ng k\u1ec3. N\u1ebfu b\u1ea1n \u0111ang t\u00ecm ki\u1ebfm gi\u1ea3i ph\u00e1p \u0111\u1ec3 t\u0103ng t\u1ed1c qu\u00e1 tr\u00ecnh n\u00e0y, h\u00e3y c\u00e2n nh\u1eafc <a href=\"http:\/\/interdata.vn\/thue-vps\/\"><strong>thu\u00ea VPS ch\u1ea5t l\u01b0\u1ee3ng gi\u00e1 r\u1ebb<\/strong><\/a> ho\u1eb7c <a href=\"http:\/\/interdata.vn\/cloud-server\/\"><strong>thu\u00ea Cloud Server gi\u00e1 r\u1ebb<\/strong><\/a> t\u1ea1i InterData. V\u1edbi ph\u1ea7n c\u1ee9ng th\u1ebf h\u1ec7 m\u1edbi, b\u1ed9 x\u1eed l\u00fd AMD EPYC\/Intel Platinum, SSD NVMe U.2 v\u00e0 b\u0103ng th\u00f4ng cao, <a href=\"http:\/\/interdata.vn\"><strong>InterData<\/strong><\/a> mang \u0111\u1ebfn cho b\u1ea1n t\u1ed1c \u0111\u1ed9 x\u1eed l\u00fd v\u01b0\u1ee3t tr\u1ed9i. C\u00e1c g\u00f3i d\u1ecbch v\u1ee5 c\u00f3 c\u1ea5u h\u00ecnh m\u1ea1nh m\u1ebd, \u0111\u00e1p \u1ee9ng m\u1ecdi nhu c\u1ea7u t\u00ednh to\u00e1n c\u1ee7a b\u1ea1n v\u1edbi chi ph\u00ed h\u1ee3p l\u00fd.<\/p>\n<p>N\u1ebfu b\u1ea1n mu\u1ed1n t\u00ecm hi\u1ec3u th\u00eam v\u1ec1 d\u1ecbch v\u1ee5 n\u00e0y, h\u00e3y li\u00ean h\u1ec7 v\u1edbi InterData \u0111\u1ec3 \u0111\u01b0\u1ee3c t\u01b0 v\u1ea5n chi ti\u1ebft nh\u00e9!<\/p>\n<p><strong>INTERDATA<\/strong><\/p>\n<ul>\n<li><strong>Website:<\/strong><span>\u00a0<\/span>Interdata.vn<\/li>\n<li><strong>Hotline:<\/strong><span>\u00a0<\/span>1900-636822<\/li>\n<li><strong>Email:<\/strong><span>\u00a0<\/span>Info@interdata.vn<\/li>\n<li><strong>VP\u0110D:<\/strong><span>\u00a0<\/span>240 Nguy\u1ec5n \u0110\u00ecnh Ch\u00ednh, P.11. Q. Ph\u00fa Nhu\u1eadn, TP. Ho\u0302\u0300 Ch\u00ed Minh<\/li>\n<li><strong>VPGD:<\/strong><span>\u00a0<\/span>S\u1ed1 211 \u0110\u01b0\u1eddng s\u1ed1 5, K\u0110T Lakeview City, P. An Ph\u00fa, TP. Th\u1ee7 \u0110\u1ee9c, TP. H\u1ed3 Ch\u00ed Minh<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>H\u1ed3i quy tuy\u1ebfn t\u00ednh l\u00e0 m\u1ed9t trong nh\u1eefng kh\u00e1i ni\u1ec7m quan tr\u1ecdng v\u00e0 \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i nh\u1ea5t trong th\u1ed1ng k\u00ea, ph\u00e2n t\u00edch d\u1eef li\u1ec7u v\u00e0 m\u00e1y h\u1ecdc. Nghe c\u00f3 v\u1ebb ph\u1ee9c t\u1ea1p, nh\u01b0ng th\u1ef1c t\u1ebf h\u1ed3i quy tuy\u1ebfn t\u00ednh l\u1ea1i kh\u00e1 d\u1ec5 hi\u1ec3u. B\u00e0i vi\u1ebft n\u00e0y c\u1ee7a InterData s\u1ebd gi\u1ea3i th\u00edch t\u1ea5t t\u1ea7n<\/p>\n","protected":false},"author":2,"featured_media":25436,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[108],"tags":[],"class_list":["post-25421","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ai"],"_links":{"self":[{"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/posts\/25421","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/comments?post=25421"}],"version-history":[{"count":0,"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/posts\/25421\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/media\/25436"}],"wp:attachment":[{"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/media?parent=25421"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/categories?post=25421"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/tags?post=25421"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}