{"id":478465,"date":"2023-08-09T09:33:12","date_gmt":"2023-08-09T09:33:12","guid":{"rendered":""},"modified":"2023-09-05T11:16:48","modified_gmt":"2023-09-05T11:16:48","slug":"polynomial-regression","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/vn\/wiki\/polynomial-regression\/","title":{"rendered":"H\u1ed3i quy \u0111a th\u1ee9c"},"content":{"rendered":"<p>H\u1ed3i quy \u0111a th\u1ee9c l\u00e0 m\u1ed9t lo\u1ea1i ph\u00e2n t\u00edch h\u1ed3i quy trong th\u1ed1ng k\u00ea li\u00ean quan \u0111\u1ebfn vi\u1ec7c m\u00f4 h\u00ecnh h\u00f3a m\u1ed1i quan h\u1ec7 gi\u1eefa m\u1ed9t bi\u1ebfn \u0111\u1ed9c l\u1eadp <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\"><math ><semantics><mrow><mi>X<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">X<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span> v\u00e0 m\u1ed9t bi\u1ebfn ph\u1ee5 thu\u1ed9c <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\"><math ><semantics><mrow><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.1944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><\/span><\/span> d\u01b0\u1edbi d\u1ea1ng \u0111a th\u1ee9c b\u1eadc n. Kh\u00f4ng gi\u1ed1ng nh\u01b0 h\u1ed3i quy tuy\u1ebfn t\u00ednh, m\u00f4 h\u00ecnh h\u00f3a m\u1ed1i quan h\u1ec7 d\u01b0\u1edbi d\u1ea1ng \u0111\u01b0\u1eddng th\u1eb3ng, h\u1ed3i quy \u0111a th\u1ee9c kh\u1edbp m\u1ed9t \u0111\u01b0\u1eddng cong v\u1edbi c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u, mang l\u1ea1i s\u1ef1 ph\u00f9 h\u1ee3p linh ho\u1ea1t h\u01a1n.<\/p>\n<h2>L\u1ecbch s\u1eed ngu\u1ed3n g\u1ed1c c\u1ee7a h\u1ed3i quy \u0111a th\u1ee9c v\u00e0 s\u1ef1 \u0111\u1ec1 c\u1eadp \u0111\u1ea7u ti\u00ean v\u1ec1 n\u00f3<\/h2>\n<p>H\u1ed3i quy \u0111a th\u1ee9c c\u00f3 ngu\u1ed3n g\u1ed1c t\u1eeb l\u0129nh v\u1ef1c n\u1ed9i suy \u0111a th\u1ee9c r\u1ed9ng h\u01a1n, b\u1eaft ngu\u1ed3n t\u1eeb c\u00e1c c\u00f4ng tr\u00ecnh to\u00e1n h\u1ecdc c\u1ee7a Isaac Newton v\u00e0 Carl Friedrich Gauss. Ph\u01b0\u01a1ng ph\u00e1p n\u1ed9i suy \u0111a th\u1ee9c c\u1ee7a Newton \u0111\u01b0\u1ee3c ph\u00e1t tri\u1ec3n v\u00e0o cu\u1ed1i th\u1ebf k\u1ef7 17 v\u00e0 cung c\u1ea5p m\u1ed9t trong nh\u1eefng k\u1ef9 thu\u1eadt s\u1edbm nh\u1ea5t \u0111\u1ec3 kh\u1edbp c\u00e1c \u0111\u01b0\u1eddng cong \u0111a th\u1ee9c v\u1edbi c\u00e1c \u0111i\u1ec3m d\u1eef li\u1ec7u.<\/p>\n<p>Trong b\u1ed1i c\u1ea3nh ph\u00e2n t\u00edch h\u1ed3i quy, h\u1ed3i quy \u0111a th\u1ee9c b\u1eaft \u0111\u1ea7u c\u00f3 s\u1ee9c h\u00fat v\u00e0o th\u1ebf k\u1ef7 20 khi c\u00e1c c\u00f4ng c\u1ee5 t\u00ednh to\u00e1n \u0111\u01b0\u1ee3c c\u1ea3i ti\u1ebfn, cho ph\u00e9p m\u00f4 h\u00ecnh h\u00f3a m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c bi\u1ebfn ph\u1ee9c t\u1ea1p h\u01a1n.<\/p>\n<h2>Th\u00f4ng tin chi ti\u1ebft v\u1ec1 h\u1ed3i quy \u0111a th\u1ee9c. M\u1edf r\u1ed9ng h\u1ed3i quy \u0111a th\u1ee9c ch\u1ee7 \u0111\u1ec1<\/h2>\n<p>H\u1ed3i quy \u0111a th\u1ee9c m\u1edf r\u1ed9ng tr\u00ean h\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111\u01a1n gi\u1ea3n b\u1eb1ng c\u00e1ch cho ph\u00e9p m\u1ed1i quan h\u1ec7 gi\u1eefa bi\u1ebfn \u0111\u1ed9c l\u1eadp v\u00e0 bi\u1ebfn ph\u1ee5 thu\u1ed9c \u0111\u01b0\u1ee3c m\u00f4 h\u00ecnh h\u00f3a d\u01b0\u1edbi d\u1ea1ng ph\u01b0\u01a1ng tr\u00ecnh \u0111a th\u1ee9c c\u00f3 d\u1ea1ng:<br \/>\n<span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\"><math ><semantics><mrow><mi>y<\/mi><mo>=<\/mo><msub><mi>\u03b2<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><msub><mi>\u03b2<\/mi><mn>1<\/mn><\/msub><mi>x<\/mi><mo>+<\/mo><msub><mi>\u03b2<\/mi><mn>2<\/mn><\/msub><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mo>\u2026<\/mo><mo>+<\/mo><msub><mi>\u03b2<\/mi><mi>N<\/mi><\/msub><msup><mi>x<\/mi><mi>N<\/mi><\/msup><mo>+<\/mo><mi>\u03f5<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y = beta_0 + beta_1 x + beta_2 x^2 + ldots + beta_n x^n + epsilon<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.1944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em; vertical-align: -0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.05278em;\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em;\"><span style=\"top: -2.55em; margin-left: -0.0528em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em; vertical-align: -0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.05278em;\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em;\"><span style=\"top: -2.55em; margin-left: -0.0528em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0085em; vertical-align: -0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.05278em;\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em;\"><span style=\"top: -2.55em; margin-left: -0.0528em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em;\"><span style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em; vertical-align: -0.0833em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em; vertical-align: -0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.05278em;\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em;\"><span style=\"top: -2.55em; margin-left: -0.0528em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">N<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6644em;\"><span style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">N<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em;\"><\/span><span class=\"mord mathnormal\">\u03f5<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>Gi\u1ea3i th\u00edch ph\u01b0\u01a1ng tr\u00ecnh:<\/h3>\n<ul>\n<li><span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\"><math ><semantics><mrow><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.1944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><\/span><\/span>: Bi\u1ebfn ph\u1ee5 thu\u1ed9c<\/li>\n<li><span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\"><math ><semantics><mrow><msub><mi>\u03b2<\/mi><mi>T\u00f4i<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">beta_i<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em; vertical-align: -0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.05278em;\">\u03b2<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em;\"><span style=\"top: -2.55em; margin-left: -0.0528em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">T\u00f4i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>: h\u1ec7 s\u1ed1<\/li>\n<li><span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\"><math ><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em;\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span>: Bi\u1ebfn \u0111\u1ed9c l\u1eadp<\/li>\n<li><span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\"><math ><semantics><mrow><mi>\u03f5<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">epsilon<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em;\"><\/span><span class=\"mord mathnormal\">\u03f5<\/span><\/span><\/span><\/span><\/span>: L\u1ed7i \u0111i\u1ec1u kho\u1ea3n<\/li>\n<li><span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\"><math ><semantics><mrow><mi>N<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">N<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em;\"><\/span><span class=\"mord mathnormal\">N<\/span><\/span><\/span><\/span><\/span>: B\u1eadc c\u1ee7a \u0111a th\u1ee9c<\/li>\n<\/ul>\n<p>B\u1eb1ng c\u00e1ch kh\u1edbp ph\u01b0\u01a1ng tr\u00ecnh \u0111a th\u1ee9c v\u1edbi d\u1eef li\u1ec7u, m\u00f4 h\u00ecnh c\u00f3 th\u1ec3 n\u1eafm b\u1eaft c\u00e1c m\u1ed1i quan h\u1ec7 phi tuy\u1ebfn t\u00ednh v\u00e0 cung c\u1ea5p s\u1ef1 hi\u1ec3u bi\u1ebft s\u00e2u s\u1eafc h\u01a1n v\u1ec1 c\u00e1c m\u1eabu c\u01a1 b\u1ea3n trong d\u1eef li\u1ec7u.<\/p>\n<h2>C\u1ea5u tr\u00fac b\u00ean trong c\u1ee7a h\u1ed3i quy \u0111a th\u1ee9c. C\u00e1ch th\u1ee9c ho\u1ea1t \u0111\u1ed9ng c\u1ee7a h\u1ed3i quy \u0111a th\u1ee9c<\/h2>\n<p>H\u1ed3i quy \u0111a th\u1ee9c ho\u1ea1t \u0111\u1ed9ng b\u1eb1ng c\u00e1ch t\u00ecm c\u00e1c h\u1ec7 s\u1ed1 gi\u1ea3m thi\u1ec3u t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng ch\u00eanh l\u1ec7ch gi\u1eefa c\u00e1c gi\u00e1 tr\u1ecb quan s\u00e1t \u0111\u01b0\u1ee3c v\u00e0 c\u00e1c gi\u00e1 tr\u1ecb \u0111\u01b0\u1ee3c d\u1ef1 \u0111o\u00e1n b\u1edfi m\u00f4 h\u00ecnh \u0111a th\u1ee9c. Qu\u00e1 tr\u00ecnh n\u00e0y th\u01b0\u1eddng \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n th\u00f4ng qua ph\u01b0\u01a1ng ph\u00e1p b\u00ecnh ph\u01b0\u01a1ng t\u1ed1i thi\u1ec3u.<\/p>\n<h3>C\u00e1c b\u01b0\u1edbc trong h\u1ed3i quy \u0111a th\u1ee9c:<\/h3>\n<ol>\n<li><strong>Ch\u1ecdn b\u1eadc c\u1ee7a \u0111a th\u1ee9c<\/strong>: B\u1eadc c\u1ee7a \u0111a th\u1ee9c ph\u1ea3i \u0111\u01b0\u1ee3c ch\u1ecdn d\u1ef1a tr\u00ean m\u1ed1i quan h\u1ec7 c\u01a1 b\u1ea3n trong d\u1eef li\u1ec7u.<\/li>\n<li><strong>Chuy\u1ec3n \u0111\u1ed5i d\u1eef li\u1ec7u<\/strong>: T\u1ea1o \u0111\u1eb7c tr\u01b0ng \u0111a th\u1ee9c cho b\u1eadc \u0111\u00e3 ch\u1ecdn.<\/li>\n<li><strong>Ph\u00f9 h\u1ee3p v\u1edbi m\u00f4 h\u00ecnh<\/strong>: S\u1eed d\u1ee5ng k\u1ef9 thu\u1eadt h\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111\u1ec3 t\u00ecm c\u00e1c h\u1ec7 s\u1ed1 gi\u1ea3m thi\u1ec3u sai s\u1ed1.<\/li>\n<li><strong>\u0110\u00e1nh gi\u00e1 m\u00f4 h\u00ecnh<\/strong>: \u0110\u00e1nh gi\u00e1 m\u1ee9c \u0111\u1ed9 ph\u00f9 h\u1ee3p c\u1ee7a m\u00f4 h\u00ecnh b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng c\u00e1c s\u1ed1 li\u1ec7u nh\u01b0 b\u00ecnh ph\u01b0\u01a1ng R, sai s\u1ed1 b\u00ecnh ph\u01b0\u01a1ng trung b\u00ecnh, v.v.<\/li>\n<\/ol>\n<h2>Ph\u00e2n t\u00edch c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m ch\u00ednh c\u1ee7a h\u1ed3i quy \u0111a th\u1ee9c<\/h2>\n<ul>\n<li><strong>Uy\u1ec3n chuy\u1ec3n<\/strong>: C\u00f3 th\u1ec3 m\u00f4 h\u00ecnh h\u00f3a c\u00e1c m\u1ed1i quan h\u1ec7 phi tuy\u1ebfn.<\/li>\n<li><strong>S\u1ef1 \u0111\u01a1n gi\u1ea3n<\/strong>: M\u1edf r\u1ed9ng h\u1ed3i quy tuy\u1ebfn t\u00ednh v\u00e0 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c gi\u1ea3i b\u1eb1ng c\u00e1c k\u1ef9 thu\u1eadt tuy\u1ebfn t\u00ednh.<\/li>\n<li><strong>Nguy c\u01a1 trang b\u1ecb qu\u00e1 m\u1ee9c<\/strong>: \u0110a th\u1ee9c b\u1eadc cao h\u01a1n c\u00f3 th\u1ec3 kh\u1edbp d\u1eef li\u1ec7u qu\u00e1 m\u1ee9c, thu \u0111\u01b0\u1ee3c nhi\u1ec5u h\u01a1n l\u00e0 t\u00edn hi\u1ec7u.<\/li>\n<li><strong>Di\u1ec5n d\u1ecbch<\/strong>: Vi\u1ec7c gi\u1ea3i th\u00edch c\u00f3 th\u1ec3 kh\u00f3 kh\u0103n h\u01a1n so v\u1edbi h\u1ed3i quy tuy\u1ebfn t\u00ednh \u0111\u01a1n gi\u1ea3n.<\/li>\n<\/ul>\n<h2>C\u00e1c lo\u1ea1i h\u1ed3i quy \u0111a th\u1ee9c<\/h2>\n<p>H\u1ed3i quy \u0111a th\u1ee9c c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ph\u00e2n lo\u1ea1i d\u1ef1a tr\u00ean m\u1ee9c \u0111\u1ed9 c\u1ee7a \u0111a th\u1ee9c:<\/p>\n<table>\n<thead>\n<tr>\n<th>B\u1eb1ng c\u1ea5p<\/th>\n<th>S\u1ef1 mi\u00eau t\u1ea3<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1<\/td>\n<td>Tuy\u1ebfn t\u00ednh (\u0110\u01b0\u1eddng th\u1eb3ng)<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>B\u1eadc hai (\u0110\u01b0\u1eddng cong Parabol)<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>Kh\u1ed1i (\u0110\u01b0\u1eddng cong h\u00ecnh ch\u1eef S)<\/td>\n<\/tr>\n<tr>\n<td>N<\/td>\n<td>\u0110\u01b0\u1eddng cong \u0111a th\u1ee9c b\u1eadc n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>C\u00e1ch s\u1eed d\u1ee5ng h\u1ed3i quy \u0111a th\u1ee9c, c\u00e1c v\u1ea5n \u0111\u1ec1 v\u00e0 gi\u1ea3i ph\u00e1p li\u00ean quan \u0111\u1ebfn vi\u1ec7c s\u1eed d\u1ee5ng<\/h2>\n<h3>C\u00f4ng d\u1ee5ng:<\/h3>\n<ul>\n<li>Kinh t\u1ebf v\u00e0 t\u00e0i ch\u00ednh \u0111\u1ec3 m\u00f4 h\u00ecnh h\u00f3a c\u00e1c xu h\u01b0\u1edbng phi tuy\u1ebfn.<\/li>\n<li>Khoa h\u1ecdc m\u00f4i tr\u01b0\u1eddng \u0111\u1ec3 m\u00f4 h\u00ecnh h\u00f3a c\u00e1c m\u00f4 h\u00ecnh t\u0103ng tr\u01b0\u1edfng.<\/li>\n<li>K\u1ef9 thu\u1eadt ph\u00e2n t\u00edch h\u1ec7 th\u1ed1ng.<\/li>\n<\/ul>\n<h3>V\u1ea5n \u0111\u1ec1 v\u00e0 gi\u1ea3i ph\u00e1p:<\/h3>\n<ul>\n<li><strong>Trang b\u1ecb qu\u00e1 m\u1ee9c<\/strong>: Gi\u1ea3i ph\u00e1p l\u00e0 s\u1eed d\u1ee5ng x\u00e1c th\u1ef1c ch\u00e9o v\u00e0 ch\u00ednh quy h\u00f3a.<\/li>\n<li><strong>\u0110a c\u1ed9ng tuy\u1ebfn<\/strong>: Gi\u1ea3i ph\u00e1p l\u00e0 s\u1eed d\u1ee5ng t\u1ef7 l\u1ec7 ho\u1eb7c chuy\u1ec3n \u0111\u1ed5i.<\/li>\n<\/ul>\n<h2>C\u00e1c \u0111\u1eb7c \u0111i\u1ec3m ch\u00ednh v\u00e0 nh\u1eefng so s\u00e1nh kh\u00e1c v\u1edbi c\u00e1c thu\u1eadt ng\u1eef t\u01b0\u01a1ng t\u1ef1<\/h2>\n<table>\n<thead>\n<tr>\n<th>\u0110\u1eb7c tr\u01b0ng<\/th>\n<th>H\u1ed3i quy \u0111a th\u1ee9c<\/th>\n<th>H\u1ed3i quy tuy\u1ebfn t\u00ednh<\/th>\n<th>H\u1ed3i quy phi tuy\u1ebfn<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>M\u1ed1i quan h\u1ec7<\/td>\n<td>Phi tuy\u1ebfn<\/td>\n<td>tuy\u1ebfn t\u00ednh<\/td>\n<td>Phi tuy\u1ebfn<\/td>\n<\/tr>\n<tr>\n<td>Uy\u1ec3n chuy\u1ec3n<\/td>\n<td>Cao<\/td>\n<td>Th\u1ea5p<\/td>\n<td>Bi\u1ebfn \u0111\u1ed5i<\/td>\n<\/tr>\n<tr>\n<td>\u0110\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n<\/td>\n<td>V\u1eeba ph\u1ea3i<\/td>\n<td>Th\u1ea5p<\/td>\n<td>Cao<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Quan \u0111i\u1ec3m v\u00e0 c\u00f4ng ngh\u1ec7 c\u1ee7a t\u01b0\u01a1ng lai li\u00ean quan \u0111\u1ebfn h\u1ed3i quy \u0111a th\u1ee9c<\/h2>\n<p>Nh\u1eefng ti\u1ebfn b\u1ed9 trong h\u1ecdc m\u00e1y v\u00e0 tr\u00ed tu\u1ec7 nh\u00e2n t\u1ea1o c\u00f3 kh\u1ea3 n\u0103ng t\u0103ng c\u01b0\u1eddng \u1ee9ng d\u1ee5ng h\u1ed3i quy \u0111a th\u1ee9c, k\u1ebft h\u1ee3p c\u00e1c k\u1ef9 thu\u1eadt nh\u01b0 ch\u00ednh quy h\u00f3a, ph\u01b0\u01a1ng ph\u00e1p t\u1eadp h\u1ee3p v\u00e0 \u0111i\u1ec1u ch\u1ec9nh si\u00eau tham s\u1ed1 t\u1ef1 \u0111\u1ed9ng.<\/p>\n<h2>C\u00e1ch s\u1eed d\u1ee5ng ho\u1eb7c li\u00ean k\u1ebft m\u00e1y ch\u1ee7 proxy v\u1edbi h\u1ed3i quy \u0111a th\u1ee9c<\/h2>\n<p>C\u00e1c m\u00e1y ch\u1ee7 proxy, gi\u1ed1ng nh\u01b0 c\u00e1c m\u00e1y ch\u1ee7 do OneProxy cung c\u1ea5p, c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng c\u00f9ng v\u1edbi h\u1ed3i quy \u0111a th\u1ee9c trong vi\u1ec7c thu th\u1eadp v\u00e0 ph\u00e2n t\u00edch d\u1eef li\u1ec7u. B\u1eb1ng c\u00e1ch cho ph\u00e9p truy c\u1eadp d\u1eef li\u1ec7u m\u1ed9t c\u00e1ch an to\u00e0n v\u00e0 \u1ea9n danh, m\u00e1y ch\u1ee7 proxy c\u00f3 th\u1ec3 t\u1ea1o \u0111i\u1ec1u ki\u1ec7n thu\u1eadn l\u1ee3i cho vi\u1ec7c thu th\u1eadp th\u00f4ng tin \u0111\u1ec3 l\u1eadp m\u00f4 h\u00ecnh, \u0111\u1ea3m b\u1ea3o k\u1ebft qu\u1ea3 kh\u00f4ng thi\u00ean v\u1ecb v\u00e0 tu\u00e2n th\u1ee7 c\u00e1c quy \u0111\u1ecbnh v\u1ec1 quy\u1ec1n ri\u00eang t\u01b0.<\/p>\n<h2>Li\u00ean k\u1ebft li\u00ean quan<\/h2>\n<ul>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Polynomial_regression\" target=\"_new\" rel=\"noopener nofollow\">Wikipedia: H\u1ed3i quy \u0111a th\u1ee9c<\/a><\/li>\n<li><a href=\"https:\/\/www.jstor.org\/stable\/xyz\" target=\"_new\" rel=\"noopener nofollow\">Ph\u01b0\u01a1ng ph\u00e1p h\u1ecdc th\u1ed1ng k\u00ea cho h\u1ed3i quy \u0111a th\u1ee9c<\/a><\/li>\n<li><a href=\"https:\/\/oneproxy.pro\/vn\/\" target=\"_new\" rel=\"noopener\">OneProxy: Thu th\u1eadp d\u1eef li\u1ec7u an to\u00e0n \u0111\u1ec3 ph\u00e2n t\u00edch<\/a><\/li>\n<\/ul>","protected":false},"featured_media":469187,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-478465","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Polynomial Regression<\/mark>","faq_items":[{"question":"What is Polynomial Regression?","answer":"<p>Polynomial Regression is a statistical technique that models the relationship between an independent variable <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\"><math ><semantics><mrow><mi>X<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">X<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span> and a dependent variable <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\"><math ><semantics><mrow><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.1944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><\/span><\/span> as an nth degree polynomial. Unlike linear regression, it fits a curve to the data points, allowing for the modeling of nonlinear relationships.<\/p>"},{"question":"What is the history of Polynomial Regression?","answer":"<p>Polynomial Regression has its roots in polynomial interpolation, which dates back to the mathematical works of Isaac Newton and Carl Friedrich Gauss. It started to gain traction in the 20th century with advancements in computational tools.<\/p>"},{"question":"How does Polynomial Regression work?","answer":"<p>Polynomial Regression works by finding the coefficients that minimize the sum of the squared differences between the observed values and the values predicted by the polynomial model. This is done through the method of least squares, and the process includes choosing the degree of the polynomial, transforming the data, fitting the model, and evaluating its fit.<\/p>"},{"question":"What are the key features of Polynomial Regression?","answer":"<p>Key features of Polynomial Regression include its flexibility in modeling nonlinear relationships, its extension of linear regression techniques, a potential risk of overfitting with higher-degree polynomials, and the challenge of interpretation compared to simpler models.<\/p>"},{"question":"What types of Polynomial Regression exist?","answer":"<p>Polynomial Regression can be categorized based on the degree of the polynomial, with common examples being linear (1st degree), quadratic (2nd degree), cubic (3rd degree), and nth degree polynomial curves.<\/p>"},{"question":"How can Polynomial Regression be used, and what problems may arise?","answer":"<p>Polynomial Regression is used in various fields like economics, environmental sciences, and engineering. Common problems include overfitting, which can be addressed by using cross-validation and regularization, and multicollinearity, which can be resolved through scaling or transformation.<\/p>"},{"question":"How does Polynomial Regression compare to Linear and Nonlinear Regression?","answer":"<p>Polynomial Regression is nonlinear and offers high flexibility, unlike linear regression. It has moderate computational complexity compared to the low complexity of linear regression and the potentially high complexity of other nonlinear regression methods.<\/p>"},{"question":"What are the future perspectives and technologies related to Polynomial Regression?","answer":"<p>Future advancements in machine learning and artificial intelligence are likely to enhance Polynomial Regression, with techniques like regularization, ensemble methods, and automated hyperparameter tuning becoming more prevalent.<\/p>"},{"question":"How can proxy servers like OneProxy be associated with Polynomial Regression?","answer":"<p>Proxy servers, such as those provided by OneProxy, can be used with Polynomial Regression in data gathering and analysis. They allow secure and anonymous access to data, facilitating the collection of information for modeling and ensuring unbiased results while adhering to privacy regulations.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/478465","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/478465\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media\/469187"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media?parent=478465"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}