{"id":478803,"date":"2023-08-09T09:38:20","date_gmt":"2023-08-09T09:38:20","guid":{"rendered":""},"modified":"2023-09-05T11:17:36","modified_gmt":"2023-09-05T11:17:36","slug":"r-squared","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/vn\/wiki\/r-squared\/","title":{"rendered":"b\u00ecnh ph\u01b0\u01a1ng R"},"content":{"rendered":"

R b\u00ecnh ph\u01b0\u01a1ng, c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u1ec7 s\u1ed1 x\u00e1c \u0111\u1ecbnh, l\u00e0 th\u01b0\u1edbc \u0111o th\u1ed1ng k\u00ea bi\u1ec3u th\u1ecb t\u1ef7 l\u1ec7 ph\u01b0\u01a1ng sai c\u1ee7a m\u1ed9t bi\u1ebfn ph\u1ee5 thu\u1ed9c \u0111\u01b0\u1ee3c gi\u1ea3i th\u00edch b\u1eb1ng m\u1ed9t bi\u1ebfn \u0111\u1ed9c l\u1eadp ho\u1eb7c c\u00e1c bi\u1ebfn trong m\u00f4 h\u00ecnh h\u1ed3i quy. N\u00f3 cung c\u1ea5p c\u00e1i nh\u00ecn s\u00e2u s\u1eafc v\u1ec1 m\u1ee9c \u0111\u1ed9 d\u1ef1 \u0111o\u00e1n c\u1ee7a m\u00f4 h\u00ecnh ph\u00f9 h\u1ee3p v\u1edbi d\u1eef li\u1ec7u th\u1ef1c t\u1ebf.<\/p>\n

L\u1ecbch s\u1eed ngu\u1ed3n g\u1ed1c c\u1ee7a R b\u00ecnh ph\u01b0\u01a1ng v\u00e0 s\u1ef1 \u0111\u1ec1 c\u1eadp \u0111\u1ea7u ti\u00ean v\u1ec1 n\u00f3<\/h2>\n

Kh\u00e1i ni\u1ec7m R b\u00ecnh ph\u01b0\u01a1ng c\u00f3 th\u1ec3 b\u1eaft ngu\u1ed3n t\u1eeb \u0111\u1ea7u th\u1ebf k\u1ef7 20 khi n\u00f3 \u0111\u01b0\u1ee3c gi\u1edbi thi\u1ec7u l\u1ea7n \u0111\u1ea7u ti\u00ean trong b\u1ed1i c\u1ea3nh ph\u00e2n t\u00edch t\u01b0\u01a1ng quan v\u00e0 h\u1ed3i quy. Karl Pearson \u0111\u01b0\u1ee3c ghi nh\u1eadn l\u00e0 ng\u01b0\u1eddi \u0111i ti\u00ean phong trong kh\u00e1i ni\u1ec7m t\u01b0\u01a1ng quan, trong khi c\u00f4ng tr\u00ecnh c\u1ee7a Ng\u00e0i Francis Galton \u0111\u00e3 \u0111\u1eb7t n\u1ec1n m\u00f3ng cho ph\u00e2n t\u00edch h\u1ed3i quy. S\u1ed1 li\u1ec7u R b\u00ecnh ph\u01b0\u01a1ng, nh\u01b0 \u0111\u01b0\u1ee3c bi\u1ebft \u0111\u1ebfn ng\u00e0y nay, b\u1eaft \u0111\u1ea7u thu h\u00fat s\u1ef1 ch\u00fa \u00fd v\u00e0o nh\u1eefng n\u0103m 1920 v\u00e0 1930 nh\u01b0 m\u1ed9t c\u00f4ng c\u1ee5 h\u1eefu \u00edch \u0111\u1ec3 t\u00f3m t\u1eaft m\u1ee9c \u0111\u1ed9 ph\u00f9 h\u1ee3p c\u1ee7a m\u1ed9t m\u00f4 h\u00ecnh.<\/p>\n

Th\u00f4ng tin chi ti\u1ebft v\u1ec1 R-squared: M\u1edf r\u1ed9ng ch\u1ee7 \u0111\u1ec1<\/h2>\n

R b\u00ecnh ph\u01b0\u01a1ng n\u1eb1m trong kho\u1ea3ng t\u1eeb 0 \u0111\u1ebfn 1, trong \u0111\u00f3 gi\u00e1 tr\u1ecb 0 bi\u1ec3u th\u1ecb r\u1eb1ng m\u00f4 h\u00ecnh kh\u00f4ng gi\u1ea3i th\u00edch b\u1ea5t k\u1ef3 s\u1ef1 bi\u1ebfn thi\u00ean n\u00e0o trong bi\u1ebfn ph\u1ea3n h\u1ed3i, trong khi gi\u00e1 tr\u1ecb 1 cho th\u1ea5y m\u00f4 h\u00ecnh gi\u1ea3i th\u00edch ho\u00e0n h\u1ea3o s\u1ef1 bi\u1ebfn thi\u00ean. C\u00f4ng th\u1ee9c t\u00ednh R b\u00ecnh ph\u01b0\u01a1ng \u0111\u01b0\u1ee3c cho b\u1edfi:<\/p>\n

R<\/mi>2<\/mn><\/msup>=<\/mo>1<\/mn>\u2212<\/mo>S<\/mi>S<\/mi>\u0111\u1ed9 ph\u00e2n gi\u1ea3i<\/mtext><\/msub><\/mrow>S<\/mi>S<\/mi>con<\/mtext><\/msub><\/mrow><\/mfrac><\/mrow> R^2 = 1 \u2013 frac{SS_{text{res}}}{SS_{text{tot}}}<\/annotation><\/semantics><\/math><\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span>S<\/span>S<\/span><\/span>con<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>S<\/span>S<\/span><\/span>\u0111\u1ed9 ph\u00e2n gi\u1ea3i<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u1ede \u0111\u00e2u S<\/mi>S<\/mi>\u0111\u1ed9 ph\u00e2n gi\u1ea3i<\/mtext><\/msub><\/mrow>SS_{v\u0103n b\u1ea3n{res}}<\/annotation><\/semantics><\/math><\/span><\/span>S<\/span>S<\/span><\/span>\u0111\u1ed9 ph\u00e2n gi\u1ea3i<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> l\u00e0 t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng c\u00f2n l\u1ea1i, v\u00e0 S<\/mi>S<\/mi>con<\/mtext><\/msub><\/mrow>SS_{v\u0103n b\u1ea3n{tot}}<\/annotation><\/semantics><\/math><\/span><\/span>S<\/span>S<\/span><\/span>con<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> l\u00e0 t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng<\/p>\n

C\u1ea5u tr\u00fac b\u00ean trong c\u1ee7a b\u00ecnh ph\u01b0\u01a1ng R: C\u00e1ch th\u1ee9c ho\u1ea1t \u0111\u1ed9ng c\u1ee7a b\u00ecnh ph\u01b0\u01a1ng R<\/h2>\n

B\u00ecnh ph\u01b0\u01a1ng R \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng bi\u1ebfn th\u1ec3 \u0111\u01b0\u1ee3c gi\u1ea3i th\u00edch tr\u00ean t\u1ed5ng bi\u1ebfn th\u1ec3. \u0110\u00e2y l\u00e0 c\u00e1ch n\u00f3 ho\u1ea1t \u0111\u1ed9ng:<\/p>\n

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  1. T\u00ednh t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng (SST):<\/strong> N\u00f3 \u0111o l\u01b0\u1eddng t\u1ed5ng ph\u01b0\u01a1ng sai trong d\u1eef li\u1ec7u \u0111\u01b0\u1ee3c quan s\u00e1t.<\/li>\n
  2. T\u00ednh t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng h\u1ed3i quy (SSR):<\/strong> N\u00f3 \u0111o m\u1ee9c \u0111\u1ed9 ph\u00f9 h\u1ee3p c\u1ee7a d\u00f2ng v\u1edbi d\u1eef li\u1ec7u.<\/li>\n
  3. T\u00ednh t\u1ed5ng sai s\u1ed1 c\u1ee7a b\u00ecnh ph\u01b0\u01a1ng (SSE):<\/strong> N\u00f3 \u0111o l\u01b0\u1eddng s\u1ef1 kh\u00e1c bi\u1ec7t gi\u1eefa gi\u00e1 tr\u1ecb quan s\u00e1t \u0111\u01b0\u1ee3c v\u00e0 gi\u00e1 tr\u1ecb d\u1ef1 \u0111o\u00e1n.<\/li>\n
  4. T\u00ednh R b\u00ecnh ph\u01b0\u01a1ng:<\/strong> C\u00f4ng th\u1ee9c \u0111\u01b0\u1ee3c \u0111\u01b0a ra b\u1edfi: R<\/mi>2<\/mn><\/msup>=<\/mo>S<\/mi>S<\/mi>R<\/mi><\/mrow>S<\/mi>S<\/mi>T<\/mi><\/mrow><\/mfrac><\/mrow>R^2 = frac{SSR}{SST}<\/annotation><\/semantics><\/math><\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>SST<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>SSR<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ol>\n

    Ph\u00e2n t\u00edch c\u00e1c t\u00ednh n\u0103ng ch\u00ednh c\u1ee7a b\u00ecnh ph\u01b0\u01a1ng R<\/h2>\n