{"id":25323,"date":"2023-12-07T00:21:01","date_gmt":"2023-12-07T00:21:01","guid":{"rendered":"https:\/\/masterskills.org\/blog\/phuong-phap-binh-phuong-toi-thieu-least-squares-method-la-gi-dac-diem-va-vi-du.html"},"modified":"2023-12-22T10:25:07","modified_gmt":"2023-12-22T03:25:07","slug":"phuong-phap-binh-phuong-toi-thieu-least-squares-method-la-gi-dac-diem-va-vi-du","status":"publish","type":"post","link":"https:\/\/masterskills.org\/blog\/phuong-phap-binh-phuong-toi-thieu-least-squares-method-la-gi-dac-diem-va-vi-du.html","title":{"rendered":"Ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u (Least Squares Method) l\u00e0 g\u00ec? \u0110\u1eb7c \u0111i\u1ec3m v\u00e0 v\u00ed d\u1ee5"},"content":{"rendered":"<div class=\"vnbcbc-body vceditor-content wi-active\" data-role=\"content\">\n<figure class=\"VCSortableInPreviewMode\" type=\"Photo\" style=\"\">\n<div><\/div><figcaption class=\"PhotoCMS_Caption\">\n<p data-placeholder=\"[Nh\u1eadp ch\u00fa th\u00edch \u1ea3nh]\">Hi\u0300nh minh ho\u0323a. Ngu\u00f4\u0300n: Jmp.com<\/p>\n<\/figcaption><\/figure>\n<h2><font style=\"line-height: 22px; font-size: 22px;\" color=\"#3d85c6\">Ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u<\/font><\/h2>\n<p><b>Kha\u0301i ni\u00ea\u0323m<\/b><\/p>\n<p><b>Ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u<\/b> trong ti\u00ea\u0301ng Anh la\u0300 <b>Least Squares Method.<\/b><\/p>\n<p><b>Ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u<\/b> l\u00e0 m\u1ed9t d\u1ea1ng ph\u00e2n t\u00edch h\u1ed3i qui to\u00e1n h\u1ecdc \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1eddng bi\u1ec3u di\u1ec5n ph\u00f9 h\u1ee3p nh\u1ea5t cho m\u1ed9t t\u1eadp d\u1eef li\u1ec7u, cung c\u1ea5p m\u1ed9t ph\u00e9p minh h\u1ecda tr\u1ef1c quan v\u1ec1 m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u trong t\u1eadp d\u1eef li\u1ec7u.\u00a0<\/p>\n<p>M\u1ed7i \u0111i\u1ec3m d\u1eef li\u1ec7u bi\u1ec3u th\u1ecb m\u1ed1i quan h\u1ec7 gi\u1eefa m\u1ed9t bi\u1ebfn \u0111\u1ed9c l\u1eadp \u0111\u00e3 bi\u1ebft v\u00e0 m\u1ed9t bi\u1ebfn ph\u1ee5 thu\u1ed9c ch\u01b0a bi\u1ebft.     \u00a0\u00a0<\/p>\n<h3><font style=\"line-height: 22px; font-size: 22px;\" color=\"#3d85c6\">\u0110\u1eb7c \u0111i\u1ec3m Ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u\u00a0<\/font><\/h3>\n<p><b>Ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u<\/b> cung c\u1ea5p c\u01a1 s\u1edf l\u00ed lu\u1eadn chung cho vi\u1ec7c s\u1eafp x\u1ebfp t\u1ea1o ra \u0111\u01b0\u1eddng bi\u1ec3u di\u1ec5n ph\u00f9 h\u1ee3p nh\u1ea5t t\u1eeb c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u \u0111ang \u0111\u01b0\u1ee3c nghi\u00ean c\u1ee9u.\u00a0<\/p>\n<p>\u1ee8ng d\u1ee5ng ph\u1ed5 bi\u1ebfn nh\u1ea5t c\u1ee7a ph\u01b0\u01a1ng ph\u00e1p n\u00e0y l\u00e0 c\u00e1c ph\u01b0\u01a1ng ph\u00e1p x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1eddng tuy\u1ebfn t\u00ednh, v\u1ebd ra m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng t\u1ed1i thi\u1ec3u h\u00f3a t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a c\u00e1c l\u1ed7i c\u00f3 th\u1ec3 xu\u1ea5t hi\u1ec7n trong c\u00e1c k\u1ebft qu\u1ea3 c\u1ee7a c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh li\u00ean quan.\u00a0<\/p>\n<p><i>Ch\u1eb3ng h\u1ea1n nh\u01b0 nh\u01b0 ph\u1ea7n d\u01b0 hay m\u1ee9c ch\u00eanh l\u1ec7ch gi\u1eefa gi\u00e1 tr\u1ecb quan s\u00e1t v\u00e0 gi\u00e1 tr\u1ecb d\u1ef1 \u0111o\u00e1n b\u00ecnh ph\u01b0\u01a1ng.  \u00a0  \u00a0\u00a0<\/i><\/p>\n<p>Ph\u01b0\u01a1ng ph\u00e1p ph\u00e2n t\u00edch h\u1ed3i qui n\u00e0y \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n b\u1eb1ng c\u00e1ch bi\u1ec3u di\u1ec5n t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u tr\u00ean bi\u1ec3u \u0111\u1ed3 g\u1ed3m c\u00f3 tr\u1ee5c x v\u00e0 tr\u1ee5c y.\u00a0<\/p>\n<p>Sau \u0111\u00f3, nh\u00e0 ph\u00e2n t\u00edch s\u1ebd x\u00e1c \u0111\u1ecbnh m\u1ed9t \u0111\u01b0\u1eddng bi\u1ec3u di\u1ec5n ph\u00f9 h\u1ee3p nh\u1ea5t gi\u1ea3i th\u00edch m\u1ed1i quan h\u1ec7 ti\u1ec1m n\u0103ng gi\u1eefa c\u00e1c bi\u1ebfn \u0111\u1ed9c l\u1eadp v\u00e0 ph\u1ee5 thu\u1ed9c.  \u00a0\u00a0<\/p>\n<p><i>Trong ph\u00e2n t\u00edch h\u1ed3i qui, c\u00e1c bi\u1ebfn ph\u1ee5 thu\u1ed9c \u0111\u01b0\u1ee3c minh h\u1ecda tr\u00ean tr\u1ee5c y hay tr\u1ee5c ho\u00e0nh, trong khi c\u00e1c bi\u1ebfn \u0111\u1ed9c l\u1eadp \u0111\u01b0\u1ee3c minh h\u1ecda tr\u00ean tr\u1ee5c x hay tr\u1ee5c tung.\u00a0<\/i><\/p>\n<p>Ng\u01b0\u1ee3c l\u1ea1i v\u1edbi b\u00e0i to\u00e1n tuy\u1ebfn t\u00ednh l\u00e0 b\u00e0i to\u00e1n b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u phi tuy\u1ebfn t\u00ednh kh\u00f4ng c\u00f3 k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng m\u00e0 \u0111\u01b0\u1ee3c gi\u1ea3i quy\u1ebft b\u1eb1ng c\u00e1ch l\u1eb7p l\u1ea1i.\u00a0<\/p>\n<p><i>Nh\u00e0 to\u00e1n h\u1ecdc v\u00e0 nh\u00e0 khoa h\u1ecdc ng\u01b0\u1eddi \u0110\u1ee9c, Carl Friedrich Gauss l\u00e0 ng\u01b0\u1eddi \u0111\u00e3 ph\u00e1t hi\u1ec7n ra ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u v\u00e0o n\u0103m 1795.\u00a0<\/i><\/p>\n<h3><font style=\"line-height: 22px; font-size: 22px;\" color=\"#3d85c6\">V\u00ed d\u1ee5 v\u1ec1 Ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u\u00a0<\/font><\/h3>\n<p>Gi\u1ea3 s\u1eed m\u1ed9t nh\u00e0 ph\u00e2n t\u00edch mu\u1ed1n ki\u1ec3m tra m\u1ed1i quan h\u1ec7 gi\u1eefa l\u1ee3i nhu\u1eadn c\u1ed5 phi\u1ebfu c\u1ee7a c\u00f4ng ty A v\u00e0 l\u1ee3i nhu\u1eadn c\u1ee7a ch\u1ec9 s\u1ed1 B m\u00e0 c\u1ed5 phi\u1ebfu c\u00f4ng ty A l\u00e0 th\u00e0nh ph\u1ea7n.\u00a0<\/p>\n<p>Trong v\u00ed d\u1ee5 n\u00e0y, nh\u00e0 ph\u00e2n t\u00edch t\u00ecm c\u00e1ch ki\u1ec3m tra s\u1ef1 ph\u1ee5 thu\u1ed9c c\u1ee7a l\u1ee3i nhu\u1eadn c\u1ed5 phi\u1ebfu A v\u00e0o l\u1ee3i nhu\u1eadn c\u1ee7a ch\u1ec9 s\u1ed1 B.   \u0110\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c \u0111i\u1ec1u n\u00e0y, t\u1ea5t c\u1ea3 c\u00e1c t\u1ec9 l\u1ec7 l\u1ee3i nhu\u1eadn c\u1ee7a c\u1ea3 c\u1ed5 phi\u1ebfu A v\u00e0 ch\u1ec9 s\u1ed1 B \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n tr\u00ean bi\u1ec3u \u0111\u1ed3.\u00a0<\/p>\n<p>V\u1edbi l\u1ee3i nhu\u1eadn c\u1ee7a ch\u1ec9 s\u1ed1 B l\u00e0 bi\u1ebfn \u0111\u1ed9c l\u1eadp v\u00e0 l\u1ee3i nhu\u1eadn c\u1ee7a c\u1ed5 phi\u1ebfu A l\u00e0 bi\u1ebfn ph\u1ee5 thu\u1ed9c.   \u0110\u01b0\u1eddng th\u1eb3ng \u0111\u00fang nh\u1ea5t s\u1ebd l\u00e0 \u0111\u01b0\u1eddng gi\u1ea3i th\u00edch m\u1ed1i quan h\u1ec7 gi\u1eefa hai bi\u1ebfn tr\u00ean, c\u0169ng nh\u01b0 cung c\u1ea5p c\u00e1c h\u1ec7 s\u1ed1 gi\u1ea3i th\u00edch m\u1ee9c \u0111\u1ed9 ph\u1ee5 thu\u1ed9c cho nh\u00e0 ph\u00e2n t\u00edch.  \u00a0<\/p>\n<h3><font style=\"line-height: 22px; font-size: 22px;\" color=\"#3d85c6\"><font style=\"line-height: 22px;\">\u0110\u01b0\u1eddng h\u1ed3i qui\u00a0<\/font>b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u\u00a0<\/font><\/h3>\n<p>\u0110\u01b0\u1eddng bi\u1ec3u di\u1ec5n ph\u00f9 h\u1ee3p nh\u1ea5t \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi <b>ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u<\/b> c\u00f3 d\u1ea1ng ph\u01b0\u01a1ng tr\u00ecnh t\u1ed5ng qu\u00e1t \u0111\u1ec3 cho bi\u1ebft m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u.   \u00a0\u00a0<\/p>\n<p>N\u1ebfu d\u1eef li\u1ec7u cho th\u1ea5y m\u1ed1i quan h\u1ec7 r\u00f5 r\u00e0ng gi\u1eefa hai bi\u1ebfn nh\u1ea5t \u0111\u1ecbnh, \u0111\u01b0\u1eddng bi\u1ec3u di\u1ec5n ph\u00f9 h\u1ee3p nh\u1ea5t v\u1edbi m\u1ed1i quan h\u1ec7 tuy\u1ebfn t\u00ednh n\u00e0y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng h\u1ed3i qui b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u.\u00a0  <\/p>\n<p>\u0110\u01b0\u1eddng h\u1ed3i qui b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u c\u00f3 kho\u1ea3ng c\u00e1ch sao cho gi\u1eefa c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u \u0111\u1ebfn \u0111\u01b0\u1eddng n\u00e0y b\u00ecnh ph\u01b0\u01a1ng nh\u1ecf nh\u1ea5t.\u00a0<\/p>\n<p>Nguy\u00ean nh\u00e2n c\u1ea7n ph\u1ea3i b\u00ecnh ph\u01b0\u01a1ng kho\u1ea3ng c\u00e1ch gi\u1eefa c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u v\u00e0 \u0111\u01b0\u1eddng h\u1ed3i qui l\u00e0 \u0111\u1ec3 ng\u0103n c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u tr\u00e1i d\u1ea5u tri\u1ec7t ti\u00eau cho nhau.\u00a0 \u00a0<\/p>\n<p>(Theo <i>Investopedia<\/i>)<\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"<div class=\"vnbcbc-sapo\" data-role=\"sapo\">\n                            Ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u (ti\u1ebfng Anh: Least Squares Method) l\u00e0 m\u1ed9t d\u1ea1ng ph\u00e2n t\u00edch h\u1ed3i qui to\u00e1n h\u1ecdc x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1eddng h\u1ed3i qui ph\u00f9 h\u1ee3p nh\u1ea5t cho m\u1ed9t t\u1eadp d\u1eef li\u1ec7u, l\u00e0 m\u1ed9t ph\u00e9p minh h\u1ecda tr\u1ef1c quan v\u1ec1 m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c \u0111i\u1ec3m trong t\u1eadp d\u1eef li\u1ec7u.\n                        <\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[414],"tags":[],"_links":{"self":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/25323"}],"collection":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/comments?post=25323"}],"version-history":[{"count":0,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/25323\/revisions"}],"wp:attachment":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/media?parent=25323"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/categories?post=25323"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/tags?post=25323"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}