[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7733#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7733","headline":"\u975e\u7dda\u5f62\u6700\u5c0f\u4e8c\u4e57\u6cd5 – Wikipedia","name":"\u975e\u7dda\u5f62\u6700\u5c0f\u4e8c\u4e57\u6cd5 – Wikipedia","description":"\u975e\u7dda\u5f62\u6700\u5c0f\u4e8c\u4e57\u6cd5[1][2]\uff08\u3072\u305b\u3093\u3051\u3044\u3055\u3044\u3057\u3087\u3046\u306b\u3058\u3087\u3046\u307b\u3046\u3001\u82f1: non-linear least squares\uff09\u3068\u306f\u3001\u89b3\u6e2c\u30c7\u30fc\u30bf\u306b\u5bfe\u3059\u308b\u30ab\u30fc\u30d6\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u624b\u6cd5\u306e\u4e00\u3064\u3067\u3042\u308a\u3001\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3092\u975e\u7dda\u5f62\u306a\u30e2\u30c7\u30eb\u95a2\u6570\u306b\u62e1\u5f35\u3057\u305f\u3082\u306e\u3067\u3042\u308b\u3002\u975e\u7dda\u5f62\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306f\u3001\u672a\u77e5\u30d1\u30e9\u30e1\u30fc\u30bf\uff08\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u30d1\u30e9\u30e1\u30fc\u30bf\uff09\u3092\u975e\u7dda\u5f62\u306e\u5f62\u3067\u6301\u3064\u95a2\u6570\u30e2\u30c7\u30eb\u3092\u7528\u3044\u3066\u3001\u89b3\u6e2c\u30c7\u30fc\u30bf\u3092\u8a18\u8ff0\u3059\u308b\u3053\u3068\u3001\u3059\u306a\u308f\u3061\u3001\u30c7\u30fc\u30bf\u306b\u6700\u3082\u5f53\u3066\u306f\u307e\u308a\u306e\u826f\u3044[\u6ce8 1]\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u63a8\u5b9a\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3059\u308b\u3002 Table of Contents \u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u4e3b\u5f35[\u7de8\u96c6]\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u5c24\u3082\u3089\u3057\u3055[\u7de8\u96c6]\u52fe\u914d\u65b9\u7a0b\u5f0f\u3078\u306e\u5e30\u7740[\u7de8\u96c6]\u6570\u5024\u89e3\u6cd5[\u7de8\u96c6]\u811a\u6ce8\u30fb\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u811a\u6ce8[\u7de8\u96c6] \u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u4e3b\u5f35[\u7de8\u96c6] m{displaystyle m} \u500b\u306e\u30c7\u30fc\u30bf\u30dd\u30a4\u30f3\u30c8 (xi,yi),(x2,y2),\u2026,(xm,ym){displaystyle (x_{i},y_{i}),(x_{2},y_{2}),dots ,(x_{m},y_{m})} \u304b\u3089\u306a\u308b\u30bb\u30c3\u30c8\u306b\u5bfe\u3057\u3001 n{displaystyle n} \u500b[\u6ce8","datePublished":"2019-10-31","dateModified":"2019-10-31","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/0a07d98bb302f3856cbabc47b2b9016692e3f7bc","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/0a07d98bb302f3856cbabc47b2b9016692e3f7bc","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7733","about":["Wiki"],"wordCount":8648,"articleBody":"\u975e\u7dda\u5f62\u6700\u5c0f\u4e8c\u4e57\u6cd5[1][2]\uff08\u3072\u305b\u3093\u3051\u3044\u3055\u3044\u3057\u3087\u3046\u306b\u3058\u3087\u3046\u307b\u3046\u3001\u82f1: non-linear least squares\uff09\u3068\u306f\u3001\u89b3\u6e2c\u30c7\u30fc\u30bf\u306b\u5bfe\u3059\u308b\u30ab\u30fc\u30d6\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u624b\u6cd5\u306e\u4e00\u3064\u3067\u3042\u308a\u3001\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3092\u975e\u7dda\u5f62\u306a\u30e2\u30c7\u30eb\u95a2\u6570\u306b\u62e1\u5f35\u3057\u305f\u3082\u306e\u3067\u3042\u308b\u3002\u975e\u7dda\u5f62\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306f\u3001\u672a\u77e5\u30d1\u30e9\u30e1\u30fc\u30bf\uff08\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u30d1\u30e9\u30e1\u30fc\u30bf\uff09\u3092\u975e\u7dda\u5f62\u306e\u5f62\u3067\u6301\u3064\u95a2\u6570\u30e2\u30c7\u30eb\u3092\u7528\u3044\u3066\u3001\u89b3\u6e2c\u30c7\u30fc\u30bf\u3092\u8a18\u8ff0\u3059\u308b\u3053\u3068\u3001\u3059\u306a\u308f\u3061\u3001\u30c7\u30fc\u30bf\u306b\u6700\u3082\u5f53\u3066\u306f\u307e\u308a\u306e\u826f\u3044[\u6ce8 1]\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u63a8\u5b9a\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3059\u308b\u3002  Table of Contents\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u4e3b\u5f35[\u7de8\u96c6]\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u5c24\u3082\u3089\u3057\u3055[\u7de8\u96c6]\u52fe\u914d\u65b9\u7a0b\u5f0f\u3078\u306e\u5e30\u7740[\u7de8\u96c6]\u6570\u5024\u89e3\u6cd5[\u7de8\u96c6]\u811a\u6ce8\u30fb\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u811a\u6ce8[\u7de8\u96c6]\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u4e3b\u5f35[\u7de8\u96c6]m{displaystyle m} \u500b\u306e\u30c7\u30fc\u30bf\u30dd\u30a4\u30f3\u30c8   (xi,yi),(x2,y2),\u2026,(xm,ym){displaystyle (x_{i},y_{i}),(x_{2},y_{2}),dots ,(x_{m},y_{m})} \u304b\u3089\u306a\u308b\u30bb\u30c3\u30c8\u306b\u5bfe\u3057\u3001n{displaystyle n} \u500b[\u6ce8 2]\u306e\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u30d1\u30e9\u30e1\u30fc\u30bf \u03b21,\u03b22,\u2026,\u03b2n{displaystyle beta _{1},beta _{2},dots ,beta _{n}} \u3092\u6301\u3064\u30e2\u30c7\u30eb\u95a2\u6570  y=f(x,\u03b2){displaystyle y=f(x,{boldsymbol {beta }})}  (1-1)\u3092\u3042\u3066\u306f\u3081\u308b\u5834\u5408\u3092\u8003\u3048\u308b\u3002\u3053\u3053\u3067\u3001\u305d\u308c\u305e\u308c\u306e\u30c7\u30fc\u30bf (xm,ym){displaystyle (x_{m},y_{m})} \u306b\u304a\u3044\u3066\u3001xi{displaystyle x_{i}} \u306f\u8aac\u660e\u5909\u6570\u3068\u3057\u3001yi{displaystyle y_{i}} \u306f\u76ee\u7684\u5909\u6570\u3068\u3059\u308b\u3002\u03b2=(\u03b21,\u03b22,\u2026,\u03b2n){displaystyle {boldsymbol {beta }}=(beta _{1},beta _{2},dots ,beta _{n})} \u306f\u3001\u524d\u8a18\u306e n{displaystyle n} \u500b\u306e\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u30d1\u30e9\u30e1\u30fc\u30bf \u03b2i{displaystyle beta _{i}} \u304b\u3089\u306a\u308b\u5b9f\u6570\u30d9\u30af\u30c8\u30eb\u3068\u3059\u308b\u3002\u307e\u305f\u3001\u4ee5\u4e0b\u3067\u5b9a\u307e\u308b\u6b8b\u5deeri=yi\u2212f(xi,\u03b2)(i=1,2,\u2026,m){displaystyle r_{i}=y_{i}-f(x_{i},{boldsymbol {beta }})qquad (i=1,2,dots ,m)}  (1-2)\u306e\u305d\u308c\u305e\u308c\u306f\u3001\u305d\u308c\u305e\u308c\u3001\u671f\u5f85\u5024 0{displaystyle 0}\u3001\u6a19\u6e96\u504f\u5dee \u03c3i{displaystyle sigma _{i}} \u306e\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u3068\u3059\u308b\u3002\u307e\u305f\u3001\u8a71\u3092\u7c21\u5358\u306b\u3059\u308b\u305f\u3081\u3001xi{displaystyle x_{i}} \u305d\u308c\u305e\u308c\u306f\u3001\u3044\u305a\u308c\u3082\u8aa4\u5dee\u3092\u6301\u305f\u306a\u3044\u3068\u3059\u308b\u3002\u3053\u306e\u3068\u304d\u3001\u8003\u3048\u308b\u3079\u304d\u554f\u984c\u306f\u3001\u3082\u3063\u3068\u3082\u5f53\u3066\u306f\u307e\u308a\u306e\u3088\u3044 \u03b2{displaystyle {boldsymbol {beta }}} \u3092\u898b\u3064\u3051\u51fa\u3059\u3053\u3068\u3067\u3042\u308b\u3002\u975e\u7dda\u5f62\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u6b8b\u5dee\u5e73\u65b9\u548c\uff08\u3088\u308a\u6b63\u78ba\u306b\u8a00\u3048\u3070\u3001\u6a19\u6e96\u5316\u3055\u308c\u305f\u6b8b\u5dee\u5e73\u65b9\u548c\uff09S(\u03b2)=\u2211i=1mri22\u03c3i2=\u2211i=1m(yi\u2212f(xi,\u03b2))22\u03c3i2{displaystyle S({boldsymbol {beta }})=sum _{i=1}^{m}{frac {r_{i}^{2}}{2{sigma }_{i}^{2}}}=sum _{i=1}^{m}{frac {({y}_{i}-f({x}_{i},{boldsymbol {beta }}))^{2}}{2{sigma }_{i}^{2}}}}  (1-3)\u3092\u6700\u5c0f\u3068\u3059\u308b\u3088\u3046\u306a \u03b2{displaystyle {boldsymbol {beta }}} \u304c\u3001\u3082\u3063\u3068\u3082\u5f53\u3066\u306f\u307e\u308a\u306e\u826f\u3044 f{displaystyle f} \u3092\u4e0e\u3048\u308b\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u8003\u3048\u308b[1][2]\u3002\u3053\u306e\u8003\u3048\u65b9\u306f\u3001\u6570\u591a\u3042\u308b\u8003\u3048\u65b9\u306e\u4e00\u3064\u306b\u904e\u304e\u306a\u3044\u3002\u4ed6\u306e\u8003\u3048\u65b9\u3068\u3057\u3066\u306f\u3001\u4f8b\u3048\u3070\u2211i=1n|ri|{displaystyle {sum }_{i=1}^{n}|{r}_{i}|}\u3092\u6700\u5c0f\u306b\u3059\u308b\u8003\u3048\u65b9\u2211i=1m(yi\u2212f(xi,\u03b2))2{displaystyle sum _{i=1}^{m}(y_{i}-f(x_{i},{boldsymbol {beta }}))^{2}}\u3092\u6700\u5c0f\u3068\u3059\u308b\u8003\u3048\u65b9\uff08\u5358\u306b\u5404\u30c7\u30fc\u30bf\u306e\u30d0\u30e9\u3064\u304d\u304c\u540c\u3058\u3068\u52dd\u624b\u306b\u4eee\u5b9a\u3057\u305f\u3060\u3051\uff09\u3002\u30c7\u30fc\u30bf\u3001\u30e2\u30c7\u30eb\u95a2\u6570\u5171\u306b\u4f55\u3089\u304b\u306e\u5909\u63db\uff08\u4f8b\u3048\u3070\u5bfe\u6570\u5909\u63db\uff09\u3092\u52a0\u3048\u305f\u3046\u3048\u3067\u3001\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3092\u3059\u308b\u8003\u3048\u65b9\u3002\u30ab\u30a4\u4e8c\u4e57\u5024\u3092\u6700\u5c0f\u306b\u3059\u308b\u8003\u3048\u65b9[3]\u3002\u7b49\u304c\u3042\u308a\u5f97\u308b\u3002\u3053\u308c\u3089\u306e\u8003\u3048\u65b9\u3067\u201d\u6700\u9069\u201d\u3068\u306a\u3063\u305f\u30d5\u30c3\u30c6\u30a3\u30f3\u30b0\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u3001\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3067\u306f\u201d\u6700\u9069\u201d\u3068\u306f\u9650\u3089\u306a\u3044[\u6ce8 3]\u3002\u305f\u3060\u3057\u3001\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u8003\u3048\u65b9\u306f\u3001\u78ba\u7387\u8ad6\u7684\u306b\u5c24\u3082\u3089\u3057\u3055\u304c\u88cf\u4ed8\u3051\u3089\u308c\u3066\u3044\u308b[2]\u3002\u3053\u306e\u3053\u3068\u306b\u3064\u3044\u3066\u306f\u3001\u6b21\u7bc0\u306b\u3066\u8ad6\u3058\u308b\u3002\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u5c24\u3082\u3089\u3057\u3055[\u7de8\u96c6]\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306f\u3001\u6b63\u898f\u5206\u5e03\u306b\u5bfe\u5fdc\u3057\u305f\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u6700\u5c24\u63a8\u5b9a\u6cd5\u3067\u3042\u308b[4]\u3002\u3053\u3053\u3067\u306f\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u5c24\u3082\u3089\u3057\u3055\u306b\u3064\u3044\u3066\u3001\u78ba\u7387\u8ad6\u3092\u63f4\u7528\u3057\u3066\u691c\u8a0e\u3059\u308b[2]\u3002\u3059\u306a\u308f\u3061\u3001\u6b8b\u5dee ri{displaystyle {boldsymbol {r_{i}}}} \u305d\u308c\u305e\u308c\u304c\u3001\u671f\u5f85\u5024 0{displaystyle {boldsymbol {0}}}\u3001\u6a19\u6e96\u504f\u5dee \u03c3i{displaystyle {boldsymbol {sigma _{i}}}} \u306e\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\u3067\u3042\u308a\u3001\u304b\u3064\u3001ri{displaystyle r_{i}} \u304b\u3089\u306a\u308b\u78ba\u7387\u5909\u6570\u306e\u65cf\u306f\u3001\u72ec\u7acb\u8a66\u884c\u3068\u8003\u3048\u3001\u78ba\u7387\u8ad6\u3092\u63f4\u7528\u3059\u308b\u3002\u4eee\u5b9a\u3088\u308a\u3001\u6b8b\u5dee ri{displaystyle r_{i}} \u305d\u308c\u305e\u308c\u306f\u3001\u3044\u305a\u308c\u3082\u3001\u671f\u5f85\u5024 0{displaystyle 0}\u3001\u6a19\u6e96\u504f\u5dee \u03c3i{displaystyle sigma _{i}} \u306e\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u305f\u3081\u3001\u3042\u308b\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8 (xi,yi){displaystyle (x_{i},y_{i})} \u306b\u304a\u3044\u3066\u3001\u305d\u306e\u6e2c\u5b9a\u5024\u304c yi{displaystyle y_{i}} \u3068\u306a\u308b\u78ba\u7387 P(yi){displaystyle P(y_{i})} \u306f\u3001P(yi)=1\u03c32\u03c0exp\u2061(\u2212ri22\u03c32){displaystyle {P}({y}_{i})={frac {1}{sigma {sqrt {2pi }}}}exp left(-{frac {{r}_{i}^{2}}{2sigma ^{2}}}right)}\u3000(2-1)\u3068\u306a\u308b\u3002\u4eca\u3001\u30c7\u30fc\u30bf\u306e\u6e2c\u5b9a\u306f\uff08\u6570\u5b66\u7684\u306b\u8a00\u3048\u3070\u6b8b\u5dee ri{displaystyle {boldsymbol {r_{i}}}} \u305d\u308c\u305e\u308c\u304c\uff09\u72ec\u7acb\u8a66\u884c\u3068\u8003\u3048\u3089\u308c\u308b\u305f\u3081\u3001m{displaystyle {boldsymbol {m}}} \u500b\u306e\u30c7\u30fc\u30bf\u30dd\u30a4\u30f3\u30c8\u306e\u30bb\u30c3\u30c8 (x1,y1),(x2,y2),\u2026,(xm,ym){displaystyle {boldsymbol {(x_{1},y_{1}),(x_{2},y_{2}),ldots ,(x_{m},y_{m})}}} \u304c\u5f97\u3089\u308c\u308b\u78ba\u7387 P(y1,\u2026,ym){displaystyle {boldsymbol {P(y_{1},ldots ,y_{m})}}} \u306f\u3001P(y1,\u2026,ym)=\u220fi=1mP(yi)=\u220fi=1m1\u03c32\u03c0exp\u2061(\u2212ri22\u03c32)=1(\u03c32\u03c0)mexp\u2061(\u2211i=1m(\u2212(yi\u2212f(xi,\u03b2))22\u03c32)){displaystyle {begin{aligned}P(y_{1},dots ,y_{m})&=prod _{i=1}^{m}P(y_{i})&=prod _{i=1}^{m}{frac {1}{sigma {sqrt {2pi }}}}exp left(-{frac {r_{i}^{2}}{2sigma ^{2}}}right)&={frac {1}{(sigma {sqrt {2pi }})^{m}}}exp left(sum _{i=1}^{m}left(-{frac {(y_{i}-f(x_{i},{boldsymbol {beta }}))^{2}}{2sigma ^{2}}}right)right)end{aligned}}}\u3000(2-2)\u3068\u306a\u308b\u3002\u3053\u3053\u3067\u3001\u03a0i=1n{displaystyle {Pi }_{i=1}^{n}}\u306f\u3001\u9023\u4e57\u7a4d\u3092\u8868\u3059\u3002\u4e0a\u5f0f\u306b\u304a\u3044\u3066\u3001\u6b63\u898f\u5206\u5e03\u306e\u5358\u5cf0\u6027\u3088\u308a\u3001\u78ba\u7387 P(yi,\u2026,ym){displaystyle P(y_{i},ldots ,y_{m})} \u306f\u3001S(\u03b2)=\u2211i=1m(yi\u2212f(xi,\u03b2))22\u03c32{displaystyle S(beta )=sum _{i=1}^{m}{frac {(y_{i}-f(x_{i},{boldsymbol {beta }}))^{2}}{2sigma ^{2}}}}\u3000(2-3)\u304c\u6700\u5c0f\uff08\u6700\u3082 0{displaystyle 0} \u306b\u8fd1\u3044\u3068\u304d\uff09\u306b\u304a\u3044\u3066\u3001\u6700\u5927\uff08\u6700\u5c24\uff09\u3068\u306a\u308b\u3002\u3059\u306a\u308f\u3061\u3001\u6700\u5c24\u6cd5\u306e\u6559\u3048\u308b\u3068\u3053\u308d\u306b\u3088\u308c\u3070\u3001\u3053\u306e\u3068\u304d\u3001\u3082\u3063\u3068\u3082\u5f53\u3066\u306f\u307e\u308a\u304c\u3088\u3044\u3068\u8003\u3048\u308b\u306e\u304c\u59a5\u5f53\u3060\u308d\u3046\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308b\u3002\u52fe\u914d\u65b9\u7a0b\u5f0f\u3078\u306e\u5e30\u7740[\u7de8\u96c6]\u6211\u3005\u304c\u8003\u3048\u308b\u3079\u304d\u554f\u984c\u306f\u3001\u6a19\u6e96\u5316\u3055\u308c\u305f\u6b8b\u5dee\u5e73\u65b9\u548cS(\u03b2)=\u2211i=1mri22\u03c3i2=\u2211i=1m(yi\u2212f(xi,\u03b2))22\u03c3i2{displaystyle S({boldsymbol {beta }})=sum _{i=1}^{m}{frac {r_{i}^{2}}{2sigma _{i}^{2}}}=sum _{i=1}^{m}{frac {(y_{i}-f(x_{i},{boldsymbol {beta }}))^{2}}{2sigma _{i}^{2}}}}\u3000(3-1)\u3092\u6700\u5c0f\u3068\u3059\u308b\u3088\u3046\u306a\u30d1\u30e9\u30e1\u30fc\u30bf \u03b2{displaystyle {boldsymbol {beta }}} \u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3042\u308b\u3002\u3053\u306e\u3088\u3046\u306a \u03b2{displaystyle {boldsymbol {beta }}} \u306b\u304a\u3044\u3066\u3001S{displaystyle S} \u306e\u52fe\u914d grad S{displaystyle S} \u306f 0{displaystyle 0} \u306b\u306a\u308b\uff08\u5fc5\u8981\u6761\u4ef6\uff09\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u3088\u3046\u306a \u03b2{displaystyle {boldsymbol {beta }}} \u306f\u3001\u4ee5\u4e0b\u306e\u9023\u7acb\u65b9\u7a0b\u5f0f\u306e\u89e3\u3068\u306a\u308b\u3002\u2202S\u2202\u03b2j=2\u2211i=1mri\u2202ri\u2202\u03b2j=0(j=1,\u2026,n)(1){displaystyle {frac {partial S}{partial beta _{j}}}=2sum _{i=1}^{m}r_{i}{frac {partial r_{i}}{partial beta _{j}}}=0quad (j=1,dots ,n)qquad (1)}\u3000(3-2)\u6570\u5024\u89e3\u6cd5[\u7de8\u96c6]\u7dda\u5f62\u306e\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3067\u306f\u3001\u5f0f(3-2)\u306f\u672a\u77e5\u30d1\u30e9\u30e1\u30fc\u30bf \u03b2{displaystyle {boldsymbol {beta }}} \u306b\u3064\u3044\u3066\u306e\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306b\u306a\u308b\u305f\u3081\u3001\u884c\u5217\u3092\u7528\u3044\u3066\u5bb9\u6613\u306b\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u304c\u3001\u975e\u7dda\u5f62\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3067\u306f\u53cd\u5fa9\u89e3\u6cd5\u3092\u7528\u3044\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\u89e3\u6cd5\u306b\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u65b9\u6cd5\u304c\u77e5\u3089\u308c\u3066\u3044\u308b[4]\u3002\u811a\u6ce8\u30fb\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]^ a b \u672c\u9593 \u4ec1; \u6625\u65e5\u5c4b \u4f38\u660c \u300e\u6b21\u5143\u89e3\u6790\u30fb\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3068\u5b9f\u9a13\u5f0f\u300f \u30b3\u30ed\u30ca\u793e\u30011989\u5e74\u3002\u00a0^ a b c d T. Strutz: Data Fitting and Uncertainty (A practical introduction to weighted least squares and beyond). Vieweg+Teubner, ISBN 978-3-8348-1022-9.Ch6\u306b\u3001\u975e\u7dda\u5f62\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u5c24\u3082\u3089\u3057\u3055\u306b\u95a2\u3059\u308b\u8a18\u8ff0\u304c\u8a18\u8f09\u3055\u308c\u3066\u3044\u308b\u3002^ http:\/\/www.hulinks.co.jp\/support\/kaleida\/curvefit.html^ a b \u4e2d\u5ddd\u5fb9; \u5c0f\u67f3\u7fa9\u592b \u300e\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306b\u3088\u308b\u5b9f\u9a13\u30c7\u30fc\u30bf\u89e3\u6790\u300f \u6771\u4eac\u5927\u5b66\u51fa\u7248\u4f1a\u30011982\u5e74\u300119, 95-124\u9801\u3002ISBN\u00a04-13-064067-4\u3002\u00a0\u811a\u6ce8[\u7de8\u96c6]^ \u5b9f\u969b\u306b\u306f\u3001\u91cd\u89e3\u304c\u51fa\u308b\u5834\u5408\u3082\u591a\u3044\u3002^ \u5c11\u306a\u304f\u3068\u3082 n}”\/> \u3067\u306a\u3051\u308c\u3070\u30ca\u30f3\u30bb\u30f3\u30b9\u3068\u306a\u308b\u3002^ \u7121\u8ad6\u3001\u4f8b\u3048\u3070\u4e00\u3064\u306e\u7279\u5225\u306a\u72b6\u6cc1\u3068\u3057\u3066\u3001\u3044\u305a\u308c\u306e\u6b8b\u5dee\u306e\u6a19\u6e96\u504f\u5dee\u3082\u3001\u5168\u3066\u540c\u3058\u5024\u03c3\u3067\u3042\u308b\u6642\u3001\u3059\u306a\u308f\u3061\u3001ri{displaystyle r_{i}} \u305d\u308c\u305e\u308c\u304c\u3001\u671f\u5f85\u5024 0{displaystyle 0}\u3001\u6a19\u6e96\u504f\u5dee \u03c3{displaystyle sigma } \u306e\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u5834\u5408\u306b\u306f\u3001\u6b8b\u5dee\u5e73\u65b9\u548c S{displaystyle S} \u304b\u3089\u3001\u5171\u901a\u9805 1\/(2\u03c3i2){displaystyle 1\/(2{sigma _{i}}^{2})} \u304c\u304f\u304f\u308a\u3060\u305b\u308b\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u5834\u5408\u306b\u306f\u3001\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306f\u3001\u2211i=1m(yi\u2212f(xi,\u03b2))2{displaystyle sum _{i=1}^{m}(y_{i}-f(x_{i},{boldsymbol {beta }}))^{2}}\u3092\u6700\u5c0f\u3068\u3059\u308b\u3088\u3046\u306a \u03b2{displaystyle {boldsymbol {beta }}} \u304c\u3001\u6700\u3082\u5f53\u3066\u306f\u307e\u308a\u304c\u826f\u3044\u3068\u8003\u3048\u308b\u306e\u3068\u540c\u7b49\u3067\u3042\u308b\u3002"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7733#breadcrumbitem","name":"\u975e\u7dda\u5f62\u6700\u5c0f\u4e8c\u4e57\u6cd5 – Wikipedia"}}]}]