{"id":82519,"date":"2026-07-25T10:09:48","date_gmt":"2026-07-25T02:09:48","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/82519.html"},"modified":"2026-07-25T10:09:48","modified_gmt":"2026-07-25T02:09:48","slug":"%e7%bb%9f%e8%ae%a1%e5%ad%a6%e5%ad%a6%e4%b9%a0%e6%95%99%e7%a8%8b%ef%bc%8c%e4%bb%8e%e5%85%a5%e9%97%a8%e5%88%b0%e7%b2%be%e9%80%9a%ef%bc%8c%e4%b8%80%e5%85%83%e7%ba%bf%e6%80%a7%e5%9b%9e%e5%bd%92","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/82519.html","title":{"rendered":"\u7edf\u8ba1\u5b66\u5b66\u4e60\u6559\u7a0b\uff0c\u4ece\u5165\u95e8\u5230\u7cbe\u901a\uff0c\u4e00\u5143\u7ebf\u6027\u56de\u5f52 \u2014\u2014 \u77e5\u8bc6\u70b9\u8be6\u89e3(20\uff09"},"content":{"rendered":"

\u56db\u3001\u6b8b\u5dee\u5206\u6790<\/h3>\n

4.1 \u6b8b\u5dee\u7684\u5b9a\u4e49<\/h4>\n

ei=yi\u2212y^i=yi\u2212(\u03b2^0+\u03b2^1xi),i=1,2,\u2026,ne_i = y_i – \\\\hat{y}_i = y_i – (\\\\hat{\\\\beta}_0 + \\\\hat{\\\\beta}_1 x_i), \\\\quad i = 1, 2, \\\\ldots, n<\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>(<\/span><\/span>\u03b2<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span>\u03b2<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>,<\/span><\/span><\/span>i<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

4.2 \u6807\u51c6\u5316\u6b8b\u5dee<\/h4>\n

ei\u2217=ei\u03c3^=eiQe\/(n\u22122)e_i^* = \\\\frac{e_i}{\\\\hat{\\\\sigma}} = \\\\frac{e_i}{\\\\sqrt{Q_e\/(n-2)}}<\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u2217<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c3<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/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><\/span><\/span><\/span><\/span>Q<\/span><\/span>e<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span>(<\/span>n<\/span><\/span>\u2212<\/span><\/span>2<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/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><\/span><\/p>\n

4.3 \u6b8b\u5dee\u7684\u6027\u8d28<\/h4>\n

\u7531\u6b63\u89c4\u65b9\u7a0b，\u6b8b\u5dee\u6ee1\u8db3：<\/p>\n

  • \u2211ei=0\\\\sum e_i = 0<\/span><\/span>\u2211<\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/li>\n
  • \u2211xiei=0\\\\sum x_i e_i = 0<\/span><\/span>\u2211<\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/li>\n
  • \u2211y^iei=0\\\\sum \\\\hat{y}_i e_i = 0<\/span><\/span>\u2211<\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/li>\n
  • e\u02c9=0\\\\bar{e} = 0<\/span><\/span><\/span>e<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/li>\n

    4.4 \u6b8b\u5dee\u5206\u6790\u7684\u76ee\u7684\u4e0e\u65b9\u6cd5<\/h4>\n

    \u76ee\u7684： \u68c0\u9a8c\u56de\u5f52\u6a21\u578b\u7684\u57fa\u672c\u5047\u8bbe\u662f\u5426\u6210\u7acb\u3002<\/p>\n

    \u4e09\u5927\u5047\u8bbe\u68c0\u9a8c：<\/p>\n\n\u5047\u8bbe\u6b63\u5e38\u6b8b\u5dee\u56fe\u8868\u73b0\u8fdd\u53cd\u65f6\u6b8b\u5dee\u56fe\u8868\u73b0<\/tr>\n\n\n\n\n
    \u7ebf\u6027\u6027 E(\u03b5)=0E(\\\\varepsilon)=0<\/span><\/span>E<\/span>(<\/span>\u03b5<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/td>\n\u6b8b\u5dee\u5728 e=0e=0<\/span><\/span>e<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u4e24\u4fa7\u968f\u673a\u5206\u5e03<\/td>\n\u5448\u73b0\u66f2\u7ebf\u8d8b\u52bf<\/td>\n<\/tr>\n
    \u7b49\u65b9\u5dee\u6027 D(\u03b5)=\u03c32D(\\\\varepsilon)=\\\\sigma^2<\/span><\/span>D<\/span>(<\/span>\u03b5<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n\u6b8b\u5dee\u5e26\u5bbd\u6052\u5b9a<\/td>\n\u5448\u5587\u53ed\u5f62\u6216\u6f0f\u6597\u5f62<\/td>\n<\/tr>\n
    \u6b63\u6001\u6027 \u03b5\u223cN(0,\u03c32)\\\\varepsilon \\\\sim N(0,\\\\sigma^2)<\/span><\/span>\u03b5<\/span><\/span>\u223c<\/span><\/span><\/span><\/span>N<\/span>(<\/span>0<\/span>,<\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/td>\n\u6b8b\u5dee\u8fd1\u4f3c\u6b63\u6001\u5206\u5e03<\/td>\n\u504f\u6001\u6216\u6709\u5f02\u5e38\u70b9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    \u5e38\u7528\u6b8b\u5dee\u56fe：<\/p>\n

  • \u6b8b\u5dee vs \u62df\u5408\u503c\u56fe（eie_i<\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> vs y^i\\\\hat{y}_i<\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>）：\u68c0\u9a8c\u7b49\u65b9\u5dee\u6027\u548c\u7ebf\u6027\u6027<\/li>\n
  • \u6b8b\u5dee vs \u81ea\u53d8\u91cf\u56fe（eie_i<\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> vs xix_i<\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>）：\u68c0\u9a8c\u7ebf\u6027\u6027<\/li>\n
  • \u6b8b\u5dee\u6b63\u6001Q-Q\u56fe：\u68c0\u9a8c\u6b63\u6001\u6027<\/li>\n
  • \u6b8b\u5dee\u76f4\u65b9\u56fe：\u7c97\u7565\u68c0\u9a8c\u6b63\u6001\u6027<\/li>\n

    4.5 \u5f02\u5e38\u70b9\u7684\u8bc6\u522b<\/h4>\n
      \n
    • \u79bb\u7fa4\u70b9（Outlier）： \u2223ei\u2217\u2223>2|e_i^*| > 2<\/span><\/span>\u2223<\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u2217<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span>><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u7684\u70b9<\/li>\n
    • \u9ad8\u6760\u6746\u70b9： xix_i<\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8fdc\u79bb x\u02c9\\\\bar{x}<\/span><\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u70b9<\/li>\n
    • \u5f3a\u5f71\u54cd\u70b9： \u5220\u9664\u8be5\u70b9\u540e\u56de\u5f52\u7cfb\u6570\u53d8\u5316\u5f88\u5927\u7684\u70b9<\/li>\n<\/ul>\n
      \n

      \u4e94\u3001\u516c\u5f0f\u901f\u67e5\u8868<\/h3>\n\n\u516c\u5f0f\u540d\u79f0\u516c\u5f0f<\/tr>\n\n\n\n\n\n\n\n\n\n\n\n
      LxyL_{xy}<\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n\u2211xiyi\u2212nx\u02c9y\u02c9\\\\sum x_iy_i – n\\\\bar{x}\\\\bar{y}<\/span><\/span>\u2211<\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>n<\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      LxxL_{xx}<\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n\u2211xi2\u2212nx\u02c92\\\\sum x_i^2 – n\\\\bar{x}^2<\/span><\/span>\u2211<\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>n<\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      LyyL_{yy}<\/span><\/span>L<\/span><\/span>y<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n\u2211yi2\u2212ny\u02c92\\\\sum y_i^2 – n\\\\bar{y}^2<\/span><\/span>\u2211<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>n<\/span><\/span>y<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      \u659c\u7387 \u03b2^1\\\\hat{\\\\beta}_1<\/span><\/span><\/span>\u03b2<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nLxy\/LxxL_{xy}\/L_{xx}<\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      \u622a\u8ddd \u03b2^0\\\\hat{\\\\beta}_0<\/span><\/span><\/span>\u03b2<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\ny\u02c9\u2212\u03b2^1x\u02c9\\\\bar{y} – \\\\hat{\\\\beta}_1\\\\bar{x}<\/span><\/span><\/span>y<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>\u03b2<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      \u76f8\u5173\u7cfb\u6570 rr<\/span><\/span>r<\/span><\/span><\/span><\/span><\/span><\/td>\nLxy\/LxxLyyL_{xy}\/\\\\sqrt{L_{xx}L_{yy}}<\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>y<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      \u51b3\u5b9a\u7cfb\u6570 R2R^2<\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nSSR\/SST=r2SSR\/SST = r^2<\/span><\/span>S<\/span>S<\/span>R<\/span>\/<\/span>S<\/span>S<\/span>T<\/span><\/span>=<\/span><\/span><\/span><\/span>r<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      \u6b8b\u5dee\u5e73\u65b9\u548c QeQ_e<\/span><\/span>Q<\/span><\/span>e<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\nLyy\u2212Lxy2\/LxxL_{yy} – L_{xy}^2\/L_{xx}<\/span><\/span>L<\/span><\/span>y<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      FF<\/span><\/span>F<\/span><\/span><\/span><\/span><\/span> \u7edf\u8ba1\u91cf<\/td>\n(SSR\/1)\/(SSE\/(n\u22122))(SSR\/1)\/(SSE\/(n-2))<\/span><\/span>(<\/span>S<\/span>S<\/span>R<\/span>\/1<\/span>)<\/span>\/<\/span>(<\/span>S<\/span>S<\/span>E<\/span>\/<\/span>(<\/span>n<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>2<\/span>))<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      tt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span> \u7edf\u8ba1\u91cf<\/td>\n\u03b2^1\/Se2\/Lxx\\\\hat{\\\\beta}_1\/\\\\sqrt{S_e^2\/L_{xx}}<\/span><\/span><\/span>\u03b2<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span><\/span>S<\/span><\/span>e<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
      \n

      \u516d\u3001\u601d\u8003\u4e0e\u7ec3\u4e60<\/h3>\n

      \u4e60\u98981（\u57fa\u7840\u8ba1\u7b97\u9898）<\/h4>\n

      \u67d0\u516c\u53f8\u7814\u7a76\u5e7f\u544a\u6295\u5165 xx<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>（\u4e07\u5143）\u4e0e\u9500\u552e\u989d yy<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>（\u4e07\u5143）\u7684\u5173\u7cfb，\u968f\u673a\u62bd\u53d6 8 \u4e2a\u6708\u7684\u6570\u636e\u5982\u4e0b：<\/p>\n\nxix_i<\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>235678910<\/tr>\n\n\n
      yiy_i<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n20<\/td>\n25<\/td>\n30<\/td>\n34<\/td>\n38<\/td>\n40<\/td>\n44<\/td>\n48<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \u8981\u6c42：
      \n（1）\u8ba1\u7b97\u76f8\u5173\u7cfb\u6570 rr<\/span><\/span>r<\/span><\/span><\/span><\/span><\/span>，\u5e76\u68c0\u9a8c\u5176\u663e\u8457\u6027（\u03b1=0.05\\\\alpha = 0.05<\/span><\/span>\u03b1<\/span><\/span>=<\/span><\/span><\/span><\/span>0.05<\/span><\/span><\/span><\/span><\/span>）
      \n（2）\u6c42\u56de\u5f52\u65b9\u7a0b y^=\u03b2^0+\u03b2^1x\\\\hat{y} = \\\\hat{\\\\beta}_0 + \\\\hat{\\\\beta}_1 x<\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>\u03b2<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span>\u03b2<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>
      \n（3）\u5bf9\u56de\u5f52\u65b9\u7a0b\u8fdb\u884c FF<\/span><\/span>F<\/span><\/span><\/span><\/span><\/span> \u68c0\u9a8c（\u03b1=0.05\\\\alpha = 0.05<\/span><\/span>\u03b1<\/span><\/span>=<\/span><\/span><\/span><\/span>0.05<\/span><\/span><\/span><\/span><\/span>）
      \n（4）\u5f53\u5e7f\u544a\u6295\u5165 x0=6.5x_0 = 6.5<\/span><\/span>x<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>6.5<\/span><\/span><\/span><\/span><\/span> \u4e07\u5143\u65f6，\u6c42\u9500\u552e\u989d\u5747\u503c\u7684 95% \u7f6e\u4fe1\u533a\u95f4\u548c\u4e2a\u522b\u503c\u7684 95% \u9884\u6d4b\u533a\u95f4<\/p>\n

      \n

      \u89e3\u7b54：<\/p>\n

      \u7b2c\u4e00\u6b65：\u8ba1\u7b97\u57fa\u672c\u7edf\u8ba1\u91cf<\/p>\n

      n=8n = 8<\/span><\/span>n<\/span><\/span>=<\/span><\/span><\/span><\/span>8<\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u2211xi=2+3+5+6+7+8+9+10=50\\\\sum x_i = 2+3+5+6+7+8+9+10 = 50<\/span><\/span>\u2211<\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span>+<\/span><\/span><\/span><\/span>3<\/span><\/span>+<\/span><\/span><\/span><\/span>5<\/span><\/span>+<\/span><\/span><\/span><\/span>6<\/span><\/span>+<\/span><\/span><\/span><\/span>7<\/span><\/span>+<\/span><\/span><\/span><\/span>8<\/span><\/span>+<\/span><\/span><\/span><\/span>9<\/span><\/span>+<\/span><\/span><\/span><\/span>10<\/span><\/span>=<\/span><\/span><\/span><\/span>50<\/span><\/span><\/span><\/span><\/span>，x\u02c9=50\/8=6.25\\\\bar{x} = 50\/8 = 6.25<\/span><\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>50\/8<\/span><\/span>=<\/span><\/span><\/span><\/span>6.25<\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u2211yi=20+25+30+34+38+40+44+48=279\\\\sum y_i = 20+25+30+34+38+40+44+48 = 279<\/span><\/span>\u2211<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>20<\/span><\/span>+<\/span><\/span><\/span><\/span>25<\/span><\/span>+<\/span><\/span><\/span><\/span>30<\/span><\/span>+<\/span><\/span><\/span><\/span>34<\/span><\/span>+<\/span><\/span><\/span><\/span>38<\/span><\/span>+<\/span><\/span><\/span><\/span>40<\/span><\/span>+<\/span><\/span><\/span><\/span>44<\/span><\/span>+<\/span><\/span><\/span><\/span>48<\/span><\/span>=<\/span><\/span><\/span><\/span>279<\/span><\/span><\/span><\/span><\/span>，y\u02c9=279\/8=34.875\\\\bar{y} = 279\/8 = 34.875<\/span><\/span><\/span>y<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>279\/8<\/span><\/span>=<\/span><\/span><\/span><\/span>34.875<\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u2211xi2=4+9+25+36+49+64+81+100=368\\\\sum x_i^2 = 4+9+25+36+49+64+81+100 = 368<\/span><\/span>\u2211<\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>4<\/span><\/span>+<\/span><\/span><\/span><\/span>9<\/span><\/span>+<\/span><\/span><\/span><\/span>25<\/span><\/span>+<\/span><\/span><\/span><\/span>36<\/span><\/span>+<\/span><\/span><\/span><\/span>49<\/span><\/span>+<\/span><\/span><\/span><\/span>64<\/span><\/span>+<\/span><\/span><\/span><\/span>81<\/span><\/span>+<\/span><\/span><\/span><\/span>100<\/span><\/span>=<\/span><\/span><\/span><\/span>368<\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u2211yi2=400+625+900+1156+1444+1600+1936+2304=10365\\\\sum y_i^2 = 400+625+900+1156+1444+1600+1936+2304 = 10365<\/span><\/span>\u2211<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>400<\/span><\/span>+<\/span><\/span><\/span><\/span>625<\/span><\/span>+<\/span><\/span><\/span><\/span>900<\/span><\/span>+<\/span><\/span><\/span><\/span>1156<\/span><\/span>+<\/span><\/span><\/span><\/span>1444<\/span><\/span>+<\/span><\/span><\/span><\/span>1600<\/span><\/span>+<\/span><\/span><\/span><\/span>1936<\/span><\/span>+<\/span><\/span><\/span><\/span>2304<\/span><\/span>=<\/span><\/span><\/span><\/span>10365<\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u2211xiyi=40+75+150+204+266+320+396+480=1931\\\\sum x_iy_i = 40+75+150+204+266+320+396+480 = 1931<\/span><\/span>\u2211<\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>40<\/span><\/span>+<\/span><\/span><\/span><\/span>75<\/span><\/span>+<\/span><\/span><\/span><\/span>150<\/span><\/span>+<\/span><\/span><\/span><\/span>204<\/span><\/span>+<\/span><\/span><\/span><\/span>266<\/span><\/span>+<\/span><\/span><\/span><\/span>320<\/span><\/span>+<\/span><\/span><\/span><\/span>396<\/span><\/span>+<\/span><\/span><\/span><\/span>480<\/span><\/span>=<\/span><\/span><\/span><\/span>1931<\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u7b2c\u4e8c\u6b65：\u8ba1\u7b97 LxyL_{xy}<\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，LxxL_{xx}<\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，LyyL_{yy}<\/span><\/span>L<\/span><\/span>y<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      Lxy=\u2211xiyi\u2212nx\u02c9y\u02c9=1931\u22128\u00d76.25\u00d734.875=1931\u22121743.75=187.25L_{xy} = \\\\sum x_iy_i – n\\\\bar{x}\\\\bar{y} = 1931 – 8 \\\\times 6.25 \\\\times 34.875 = 1931 – 1743.75 = 187.25<\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2211<\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>n<\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1931<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>8<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>6.25<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>34.875<\/span><\/span>=<\/span><\/span><\/span><\/span>1931<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1743.75<\/span><\/span>=<\/span><\/span><\/span><\/span>187.25<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      Lxx=\u2211xi2\u2212nx\u02c92=368\u22128\u00d76.252=368\u2212312.5=55.5L_{xx} = \\\\sum x_i^2 – n\\\\bar{x}^2 = 368 – 8 \\\\times 6.25^2 = 368 – 312.5 = 55.5<\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2211<\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>n<\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>368<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>8<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>6.2<\/span>5<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>368<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>312.5<\/span><\/span>=<\/span><\/span><\/span><\/span>55.5<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      Lyy=\u2211yi2\u2212ny\u02c92=10365\u22128\u00d734.8752=10365\u22129730.125=634.875L_{yy} = \\\\sum y_i^2 – n\\\\bar{y}^2 = 10365 – 8 \\\\times 34.875^2 = 10365 – 9730.125 = 634.875<\/span><\/span>L<\/span><\/span>y<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2211<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>n<\/span><\/span>y<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>10365<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>8<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>34.87<\/span>5<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>10365<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>9730.125<\/span><\/span>=<\/span><\/span><\/span><\/span>634.875<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      （1）\u76f8\u5173\u7cfb\u6570：<\/p>\n

      r=LxyLxx\u22c5Lyy=187.2555.5\u00d7634.875=187.2535235.5625=187.25187.71\u22480.9975r = \\\\frac{L_{xy}}{\\\\sqrt{L_{xx} \\\\cdot L_{yy}}} = \\\\frac{187.25}{\\\\sqrt{55.5 \\\\times 634.875}} = \\\\frac{187.25}{\\\\sqrt{35235.5625}} = \\\\frac{187.25}{187.71} \\\\approx 0.9975<\/span><\/span>r<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span>L<\/span><\/span>y<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/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>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/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><\/span><\/span><\/span><\/span>55.5<\/span><\/span>\u00d7<\/span><\/span>634.875<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>187.25<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>35235.5625<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>187.25<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>187.71<\/span><\/span><\/span><\/span><\/span><\/span><\/span>187.25<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>0.9975<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u663e\u8457\u6027\u68c0\u9a8c：<\/p>\n

      t=rn\u221221\u2212r2=0.9975\u00d761\u22120.9950=0.9975\u00d72.44950.0050=2.44340.0707=34.56t = \\\\frac{r\\\\sqrt{n-2}}{\\\\sqrt{1-r^2}} = \\\\frac{0.9975 \\\\times \\\\sqrt{6}}{\\\\sqrt{1-0.9950}} = \\\\frac{0.9975 \\\\times 2.4495}{\\\\sqrt{0.0050}} = \\\\frac{2.4434}{0.0707} = 34.56<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span>r<\/span><\/span>2<\/span><\/span><\/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>r<\/span><\/span>n<\/span><\/span>\u2212<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span>0.9950<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0.9975<\/span><\/span>\u00d7<\/span><\/span><\/span>6<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>0.0050<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0.9975<\/span><\/span>\u00d7<\/span><\/span>2.4495<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>0.0707<\/span><\/span><\/span><\/span><\/span><\/span><\/span>2.4434<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>34.56<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u67e5\u8868 t0.025(6)=2.447t_{0.025}(6) = 2.447<\/span><\/span>t<\/span><\/span>0.025<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>6<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>2.447<\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u7531\u4e8e \u2223t\u2223=34.56>2.447|t| = 34.56 > 2.447<\/span><\/span>\u2223<\/span>t<\/span>\u2223<\/span><\/span>=<\/span><\/span><\/span><\/span>34.56<\/span><\/span>><\/span><\/span><\/span><\/span>2.447<\/span><\/span><\/span><\/span><\/span>，\u62d2\u7edd H0H_0<\/span><\/span>H<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u7ebf\u6027\u5173\u7cfb\u9ad8\u5ea6\u663e\u8457\u3002<\/p>\n

      （2）\u56de\u5f52\u65b9\u7a0b：<\/p>\n

      \u03b2^1=LxyLxx=187.2555.5=3.374\\\\hat{\\\\beta}_1 = \\\\frac{L_{xy}}{L_{xx}} = \\\\frac{187.25}{55.5} = 3.374<\/span><\/span><\/span>\u03b2<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/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><\/span><\/span><\/span>55.5<\/span><\/span><\/span><\/span><\/span><\/span><\/span>187.25<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>3.374<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u03b2^0=y\u02c9\u2212\u03b2^1x\u02c9=34.875\u22123.374\u00d76.25=34.875\u221221.088=13.787\\\\hat{\\\\beta}_0 = \\\\bar{y} – \\\\hat{\\\\beta}_1\\\\bar{x} = 34.875 – 3.374 \\\\times 6.25 = 34.875 – 21.088 = 13.787<\/span><\/span><\/span>\u03b2<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>y<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>\u03b2<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>34.875<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>3.374<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>6.25<\/span><\/span>=<\/span><\/span><\/span><\/span>34.875<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>21.088<\/span><\/span>=<\/span><\/span><\/span><\/span>13.787<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      y^=13.787+3.374x\\\\boxed{\\\\hat{y} = 13.787 + 3.374x}<\/span><\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>13.787<\/span><\/span>+<\/span><\/span>3.374<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      （3）FF<\/span><\/span>F<\/span><\/span><\/span><\/span><\/span> \u68c0\u9a8c：<\/p>\n

      SSR=\u03b2^1Lxy=3.374\u00d7187.25=631.78SSR = \\\\hat{\\\\beta}_1 L_{xy} = 3.374 \\\\times 187.25 = 631.78<\/span><\/span>S<\/span>S<\/span>R<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>\u03b2<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>3.374<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>187.25<\/span><\/span>=<\/span><\/span><\/span><\/span>631.78<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      SSE=Lyy\u2212SSR=634.875\u2212631.78=3.095SSE = L_{yy} – SSR = 634.875 – 631.78 = 3.095<\/span><\/span>S<\/span>S<\/span>E<\/span><\/span>=<\/span><\/span><\/span><\/span>L<\/span><\/span>y<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>S<\/span>S<\/span>R<\/span><\/span>=<\/span><\/span><\/span><\/span>634.875<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>631.78<\/span><\/span>=<\/span><\/span><\/span><\/span>3.095<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n\n\u65b9\u5dee\u6765\u6e90\u5e73\u65b9\u548c\u81ea\u7531\u5ea6\u5747\u65b9FF<\/span><\/span>F<\/span><\/span><\/span><\/span><\/span><\/tr>\n\n\n\n\n
      \u56de\u5f52<\/td>\n631.78<\/td>\n1<\/td>\n631.78<\/td>\n1224.83<\/td>\n<\/tr>\n
      \u6b8b\u5dee<\/td>\n3.095<\/td>\n6<\/td>\n0.516<\/td>\n<\/td>\n<\/tr>\n
      \u603b\u8ba1<\/td>\n634.875<\/td>\n7<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      F0.05(1,6)=5.99F_{0.05}(1,6) = 5.99<\/span><\/span>F<\/span><\/span>0.05<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1<\/span>,<\/span><\/span>6<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>5.99<\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u7531\u4e8e F=1224.83\u226b5.99F = 1224.83 \\\\gg 5.99<\/span><\/span>F<\/span><\/span>=<\/span><\/span><\/span><\/span>1224.83<\/span><\/span>\u226b<\/span><\/span><\/span><\/span>5.99<\/span><\/span><\/span><\/span><\/span>，\u56de\u5f52\u65b9\u7a0b\u9ad8\u5ea6\u663e\u8457\u3002<\/p>\n

      R2=631.78\/634.875=0.9951R^2 = 631.78\/634.875 = 0.9951<\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>631.78\/634.875<\/span><\/span>=<\/span><\/span><\/span><\/span>0.9951<\/span><\/span><\/span><\/span><\/span>，\u5373\u5e7f\u544a\u6295\u5165\u89e3\u91ca\u4e86\u9500\u552e\u989d 99.51% \u7684\u53d8\u5f02\u3002<\/p>\n

      （4）\u9884\u6d4b（x0=6.5x_0 = 6.5<\/span><\/span>x<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>6.5<\/span><\/span><\/span><\/span><\/span>）：<\/p>\n

      y^0=13.787+3.374\u00d76.5=13.787+21.931=35.718\\\\hat{y}_0 = 13.787 + 3.374 \\\\times 6.5 = 13.787 + 21.931 = 35.718<\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>13.787<\/span><\/span>+<\/span><\/span><\/span><\/span>3.374<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>6.5<\/span><\/span>=<\/span><\/span><\/span><\/span>13.787<\/span><\/span>+<\/span><\/span><\/span><\/span>21.931<\/span><\/span>=<\/span><\/span><\/span><\/span>35.718<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u03c3^=Se2=0.516=0.718\\\\hat{\\\\sigma} = \\\\sqrt{S_e^2} = \\\\sqrt{0.516} = 0.718<\/span><\/span><\/span>\u03c3<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>S<\/span><\/span>e<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/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>0.516<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.718<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      1n+(x0\u2212x\u02c9)2Lxx=18+(6.5\u22126.25)255.5=0.125+0.062555.5=0.125+0.001126=0.1261=0.3552\\\\sqrt{\\\\frac{1}{n} + \\\\frac{(x_0 – \\\\bar{x})^2}{L_{xx}}} = \\\\sqrt{\\\\frac{1}{8} + \\\\frac{(6.5 – 6.25)^2}{55.5}} = \\\\sqrt{0.125 + \\\\frac{0.0625}{55.5}} = \\\\sqrt{0.125 + 0.001126} = \\\\sqrt{0.1261} = 0.3552<\/span><\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>2<\/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><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>8<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>55.5<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>6.5<\/span><\/span>\u2212<\/span><\/span>6.25<\/span>)<\/span><\/span>2<\/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><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>0.125<\/span><\/span>+<\/span><\/span><\/span><\/span>55.5<\/span><\/span><\/span><\/span><\/span><\/span><\/span>0.0625<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/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>0.125<\/span><\/span>+<\/span><\/span>0.001126<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>0.1261<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.3552<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u5747\u503c\u7684 95% \u7f6e\u4fe1\u533a\u95f4：<\/p>\n

      35.718\u00b12.447\u00d70.718\u00d70.3552=35.718\u00b10.62435.718 \\\\pm 2.447 \\\\times 0.718 \\\\times 0.3552 = 35.718 \\\\pm 0.624<\/span><\/span>35.718<\/span><\/span>\u00b1<\/span><\/span><\/span><\/span>2.447<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>0.718<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>0.3552<\/span><\/span>=<\/span><\/span><\/span><\/span>35.718<\/span><\/span>\u00b1<\/span><\/span><\/span><\/span>0.624<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      [35.094,\u00a036.342]\\\\boxed{[35.094, \\\\ 36.342]}<\/span><\/span><\/span>[<\/span>35.094<\/span>,<\/span>\u00a0<\/span><\/span>36.342<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u4e2a\u522b\u503c\u7684 95% \u9884\u6d4b\u533a\u95f4：<\/p>\n

      1+0.1261=1.1261=1.0612\\\\sqrt{1 + 0.1261} = \\\\sqrt{1.1261} = 1.0612<\/span><\/span><\/span>1<\/span><\/span>+<\/span><\/span>0.1261<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>1.1261<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1.0612<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      35.718\u00b12.447\u00d70.718\u00d71.0612=35.718\u00b11.86535.718 \\\\pm 2.447 \\\\times 0.718 \\\\times 1.0612 = 35.718 \\\\pm 1.865<\/span><\/span>35.718<\/span><\/span>\u00b1<\/span><\/span><\/span><\/span>2.447<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>0.718<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1.0612<\/span><\/span>=<\/span><\/span><\/span><\/span>35.718<\/span><\/span>\u00b1<\/span><\/span><\/span><\/span>1.865<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      [33.853,\u00a037.583]\\\\boxed{[33.853, \\\\ 37.583]}<\/span><\/span><\/span>[<\/span>33.853<\/span>,<\/span>\u00a0<\/span><\/span>37.583<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \n

      \u4e60\u98982（\u6b8b\u5dee\u5206\u6790\u9898）<\/h4>\n

      \u5bf9\u4e60\u98981\u7684\u56de\u5f52\u65b9\u7a0b，\u8ba1\u7b97\u6bcf\u4e2a\u89c2\u6d4b\u70b9\u7684\u6b8b\u5dee eie_i<\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c\u6807\u51c6\u5316\u6b8b\u5dee ei\u2217e_i^*<\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u2217<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u7ed8\u5236\u6b8b\u5dee\u8868，\u5e76\u5bf9\u56de\u5f52\u5047\u8bbe\u8fdb\u884c\u8bc4\u4ef7\u3002<\/p>\n

      \u89e3\u7b54：<\/p>\n\nii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>xix_i<\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>yiy_i<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y^i\\\\hat{y}_i<\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>ei=yi\u2212y^ie_i = y_i – \\\\hat{y}_i<\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>ei\u2217=ei\/0.718e_i^* = e_i\/0.718<\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u2217<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/0.718<\/span><\/span><\/span><\/span><\/span><\/tr>\n\n\n\n\n\n\n\n\n\n
      1<\/td>\n2<\/td>\n20<\/td>\n20.535<\/td>\n\u22120.535-0.535<\/span><\/span>\u2212<\/span>0.535<\/span><\/span><\/span><\/span><\/span><\/td>\n\u22120.745-0.745<\/span><\/span>\u2212<\/span>0.745<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      2<\/td>\n3<\/td>\n25<\/td>\n23.909<\/td>\n1.0911.091<\/span><\/span>1.091<\/span><\/span><\/span><\/span><\/span><\/td>\n1.5201.520<\/span><\/span>1.520<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      3<\/td>\n5<\/td>\n30<\/td>\n30.657<\/td>\n\u22120.657-0.657<\/span><\/span>\u2212<\/span>0.657<\/span><\/span><\/span><\/span><\/span><\/td>\n\u22120.915-0.915<\/span><\/span>\u2212<\/span>0.915<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      4<\/td>\n6<\/td>\n34<\/td>\n34.031<\/td>\n\u22120.031-0.031<\/span><\/span>\u2212<\/span>0.031<\/span><\/span><\/span><\/span><\/span><\/td>\n\u22120.043-0.043<\/span><\/span>\u2212<\/span>0.043<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      5<\/td>\n7<\/td>\n38<\/td>\n37.405<\/td>\n0.5950.595<\/span><\/span>0.595<\/span><\/span><\/span><\/span><\/span><\/td>\n0.8290.829<\/span><\/span>0.829<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      6<\/td>\n8<\/td>\n40<\/td>\n40.779<\/td>\n\u22120.779-0.779<\/span><\/span>\u2212<\/span>0.779<\/span><\/span><\/span><\/span><\/span><\/td>\n\u22121.085-1.085<\/span><\/span>\u2212<\/span>1.085<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      7<\/td>\n9<\/td>\n44<\/td>\n44.153<\/td>\n\u22120.153-0.153<\/span><\/span>\u2212<\/span>0.153<\/span><\/span><\/span><\/span><\/span><\/td>\n\u22120.213-0.213<\/span><\/span>\u2212<\/span>0.213<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
      8<\/td>\n10<\/td>\n48<\/td>\n47.527<\/td>\n0.4730.473<\/span><\/span>0.473<\/span><\/span><\/span><\/span><\/span><\/td>\n0.6590.659<\/span><\/span>0.659<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \u9a8c\u8bc1： \u2211ei=\u22120.535+1.091\u22120.657\u22120.031+0.595\u22120.779\u22120.153+0.473\u22480\\\\sum e_i = -0.535+1.091-0.657-0.031+0.595-0.779-0.153+0.473 \\\\approx 0<\/span><\/span>\u2211<\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>0.535<\/span><\/span>+<\/span><\/span><\/span><\/span>1.091<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.657<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.031<\/span><\/span>+<\/span><\/span><\/span><\/span>0.595<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.779<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.153<\/span><\/span>+<\/span><\/span><\/span><\/span>0.473<\/span><\/span>\u2248<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u2713<\/p>\n

      \u6b8b\u5dee\u5206\u6790\u8bc4\u4ef7：<\/p>\n

    • \u7ebf\u6027\u6027： \u6b8b\u5dee\u5728 e=0e = 0<\/span><\/span>e<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u4e24\u4fa7\u968f\u673a\u6ce2\u52a8，\u65e0\u660e\u663e\u7684\u66f2\u7ebf\u8d8b\u52bf，\u7ebf\u6027\u5047\u8bbe\u6210\u7acb\u3002<\/li>\n
    • \u7b49\u65b9\u5dee\u6027： \u6b8b\u5dee\u7684\u6ce2\u52a8\u5e45\u5ea6\u5728\u4e0d\u540c xx<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u503c\u5904\u57fa\u672c\u4e00\u81f4，\u7b49\u65b9\u5dee\u5047\u8bbe\u5408\u7406\u3002<\/li>\n
    • \u6b63\u6001\u6027： \u6240\u6709\u6807\u51c6\u5316\u6b8b\u5dee\u7edd\u5bf9\u503c\u5747\u5c0f\u4e8e 2，\u65e0\u79bb\u7fa4\u70b9\u3002<\/li>\n
    • \u72ec\u7acb\u6027： \u6b8b\u5dee\u65e0\u660e\u663e\u81ea\u76f8\u5173\u6a21\u5f0f\u3002<\/li>\n

      \u7ed3\u8bba：\u56de\u5f52\u6a21\u578b\u7684\u57fa\u672c\u5047\u8bbe\u5747\u5f97\u5230\u6ee1\u8db3，\u6a21\u578b\u62df\u5408\u6548\u679c\u826f\u597d\u3002<\/p>\n

      \n

      \u4e60\u98983（\u6982\u5ff5\u8fa8\u6790\u9898）<\/h4>\n

      \u5224\u65ad\u4e0b\u5217\u8bf4\u6cd5\u662f\u5426\u6b63\u786e，\u5e76\u8bf4\u660e\u7406\u7531：<\/p>\n

      （1） \u76f8\u5173\u7cfb\u6570 r=0.95r = 0.95<\/span><\/span>r<\/span><\/span>=<\/span><\/span><\/span><\/span>0.95<\/span><\/span><\/span><\/span><\/span>，\u8bf4\u660e xx<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u548c yy<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span> \u4e4b\u95f4\u5b58\u5728\u56e0\u679c\u5173\u7cfb\u3002<\/p>\n

      \u4e0d\u6b63\u786e\u3002 \u76f8\u5173\u7cfb\u6570\u53ea\u80fd\u5ea6\u91cf\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7ebf\u6027\u76f8\u5173\u7684\u5f3a\u5f31，\u4e0d\u80fd\u8bc1\u660e\u56e0\u679c\u5173\u7cfb\u3002\u9ad8\u76f8\u5173\u53ef\u80fd\u7531\u7b2c\u4e09\u4e2a\u6df7\u6742\u53d8\u91cf\u5bfc\u81f4，\u4e5f\u53ef\u80fd\u7eaf\u5c5e\u5de7\u5408\u3002\u56e0\u679c\u5173\u7cfb\u9700\u8981\u901a\u8fc7\u5b9e\u9a8c\u8bbe\u8ba1\u6216\u9886\u57df\u77e5\u8bc6\u6765\u786e\u7acb\u3002<\/p>\n

      （2） R2=0.90R^2 = 0.90<\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.90<\/span><\/span><\/span><\/span><\/span>，\u8bf4\u660e\u6a21\u578b\u62df\u5408\u5f88\u597d，\u65e0\u9700\u505a\u6b8b\u5dee\u5206\u6790\u3002<\/p>\n

      \u4e0d\u6b63\u786e\u3002 R2R^2<\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u53ea\u53cd\u6620\u4e86\u6a21\u578b\u89e3\u91ca\u53d8\u5f02\u7684\u6bd4\u4f8b，\u4e0d\u80fd\u4ee3\u66ff\u6b8b\u5dee\u5206\u6790\u3002\u9ad8 R2R^2<\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u6a21\u578b\u4ecd\u53ef\u80fd\u5b58\u5728\u975e\u7ebf\u6027\u6a21\u5f0f\u3001\u5f02\u65b9\u5dee\u6027\u6216\u5f02\u5e38\u70b9\u3002\u6b8b\u5dee\u5206\u6790\u662f\u68c0\u9a8c\u6a21\u578b\u5047\u8bbe\u662f\u5426\u6210\u7acb\u7684\u5fc5\u8981\u6b65\u9aa4\u3002<\/p>\n

      （3） \u9884\u6d4b\u533a\u95f4\u6bd4\u7f6e\u4fe1\u533a\u95f4\u5bbd，\u662f\u56e0\u4e3a\u9884\u6d4b\u503c y^0\\\\hat{y}_0<\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u65b9\u5dee\u66f4\u5927\u3002<\/p>\n

      \u4e0d\u5b8c\u5168\u6b63\u786e\u3002 \u9884\u6d4b\u533a\u95f4\u6bd4\u7f6e\u4fe1\u533a\u95f4\u5bbd\u7684\u539f\u56e0\u4e0d\u662f y^0\\\\hat{y}_0<\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u65b9\u5dee\u66f4\u5927，\u800c\u662f\u9884\u6d4b\u4e2a\u522b\u503c Y0Y_0<\/span><\/span>Y<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u65f6，\u9664\u4e86 Y^0\\\\hat{Y}_0<\/span><\/span><\/span>Y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u4e0d\u786e\u5b9a\u6027（\u65b9\u5dee \u03c32[1n+(x0\u2212x\u02c9)2Lxx]\\\\sigma^2[\\\\frac{1}{n}+\\\\frac{(x_0-\\\\bar{x})^2}{L_{xx}}]<\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>2<\/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><\/span>）\u5916，\u8fd8\u8981\u52a0\u4e0a Y0Y_0<\/span><\/span>Y<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u81ea\u8eab\u7684\u968f\u673a\u8bef\u5dee\u65b9\u5dee \u03c32\\\\sigma^2<\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

      （4） \u4e00\u5143\u7ebf\u6027\u56de\u5f52\u4e2d，FF<\/span><\/span>F<\/span><\/span><\/span><\/span><\/span> \u68c0\u9a8c\u548c tt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span> \u68c0\u9a8c\u662f\u7b49\u4ef7\u7684\u3002<\/p>\n

      \u6b63\u786e\u3002 \u5728\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u4e2d，FF<\/span><\/span>F<\/span><\/span><\/span><\/span><\/span> \u7edf\u8ba1\u91cf\u548c tt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span> \u7edf\u8ba1\u91cf\u6ee1\u8db3 F=t2F = t^2<\/span><\/span>F<\/span><\/span>=<\/span><\/span><\/span><\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u4e24\u79cd\u68c0\u9a8c\u7684 PP<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span> \u503c\u76f8\u540c，\u56e0\u6b64\u7ed3\u8bba\u4e00\u81f4\u3002<\/p>\n

      \n

      \u4e60\u98984（\u7efc\u5408\u5e94\u7528\u9898）<\/h4>\n

      \u67d0\u7ecf\u6d4e\u5b66\u5bb6\u6536\u96c6\u4e86\u67d0\u5730\u533a 10 \u4e2a\u5e74\u4efd\u7684\u4eba\u5747GDP xx<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>（\u4e07\u5143）\u548c\u4eba\u5747\u6d88\u8d39\u652f\u51fa yy<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>（\u4e07\u5143）\u7684\u6570\u636e，\u7ecf\u521d\u6b65\u8ba1\u7b97\u5f97\u5230：<\/p>\n

      n=10,x\u02c9=8,y\u02c9=6,Lxx=20,Lxy=15,Lyy=12n = 10, \\\\quad \\\\bar{x} = 8, \\\\quad \\\\bar{y} = 6, \\\\quad L_{xx} = 20, \\\\quad L_{xy} = 15, \\\\quad L_{yy} = 12<\/span><\/span>n<\/span><\/span>=<\/span><\/span><\/span><\/span>10<\/span>,<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>8<\/span>,<\/span><\/span><\/span><\/span>y<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>6<\/span>,<\/span><\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>20<\/span>,<\/span><\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>15<\/span>,<\/span><\/span><\/span>L<\/span><\/span>y<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>12<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u8981\u6c42：
      \n（1）\u5efa\u7acb\u4e00\u5143\u7ebf\u6027\u56de\u5f52\u65b9\u7a0b
      \n（2）\u8ba1\u7b97 R2R^2<\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c Se2S_e^2<\/span><\/span>S<\/span><\/span>e<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
      \n（3）\u5f53\u4eba\u5747GDP\u4e3a12\u4e07\u5143\u65f6，\u9884\u6d4b\u4eba\u5747\u6d88\u8d39\u652f\u51fa\u5747\u503c\u768495%\u7f6e\u4fe1\u533a\u95f4（\u5df2\u77e5 t0.025(8)=2.306t_{0.025}(8) = 2.306<\/span><\/span>t<\/span><\/span>0.025<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>2.306<\/span><\/span><\/span><\/span><\/span>）<\/p>\n

      \u89e3\u7b54：<\/p>\n

      （1）\u56de\u5f52\u65b9\u7a0b：<\/p>\n

      \u03b2^1=LxyLxx=1520=0.75\\\\hat{\\\\beta}_1 = \\\\frac{L_{xy}}{L_{xx}} = \\\\frac{15}{20} = 0.75<\/span><\/span><\/span>\u03b2<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/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><\/span><\/span><\/span>20<\/span><\/span><\/span><\/span><\/span><\/span><\/span>15<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.75<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u03b2^0=y\u02c9\u2212\u03b2^1x\u02c9=6\u22120.75\u00d78=6\u22126=0\\\\hat{\\\\beta}_0 = \\\\bar{y} – \\\\hat{\\\\beta}_1 \\\\bar{x} = 6 – 0.75 \\\\times 8 = 6 – 6 = 0<\/span><\/span><\/span>\u03b2<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>y<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>\u03b2<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>6<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.75<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>8<\/span><\/span>=<\/span><\/span><\/span><\/span>6<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>6<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      y^=0.75x\\\\boxed{\\\\hat{y} = 0.75x}<\/span><\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>0.75<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u542b\u4e49：\u4eba\u5747GDP\u6bcf\u589e\u52a01\u4e07\u5143，\u4eba\u5747\u6d88\u8d39\u652f\u51fa\u5e73\u5747\u589e\u52a00.75\u4e07\u5143（\u8fb9\u9645\u6d88\u8d39\u503e\u5411\u4e3a0.75）\u3002<\/p>\n

      （2）R2R^2<\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c Se2S_e^2<\/span><\/span>S<\/span><\/span>e<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>：<\/p>\n

      R2=Lxy2Lxx\u22c5Lyy=15220\u00d712=225240=0.9375R^2 = \\\\frac{L_{xy}^2}{L_{xx} \\\\cdot L_{yy}} = \\\\frac{15^2}{20 \\\\times 12} = \\\\frac{225}{240} = 0.9375<\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span>L<\/span><\/span>y<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/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><\/span><\/span><\/span>20<\/span><\/span>\u00d7<\/span><\/span>12<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span>5<\/span><\/span>2<\/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><\/span><\/span><\/span>240<\/span><\/span><\/span><\/span><\/span><\/span><\/span>225<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.9375<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      Qe=Lyy\u2212Lxy2Lxx=12\u221222520=12\u221211.25=0.75Q_e = L_{yy} – \\\\frac{L_{xy}^2}{L_{xx}} = 12 – \\\\frac{225}{20} = 12 – 11.25 = 0.75<\/span><\/span>Q<\/span><\/span>e<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>L<\/span><\/span>y<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/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><\/span>12<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span>20<\/span><\/span><\/span><\/span><\/span><\/span><\/span>225<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>12<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>11.25<\/span><\/span>=<\/span><\/span><\/span><\/span>0.75<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      Se2=Qen\u22122=0.758=0.09375S_e^2 = \\\\frac{Q_e}{n-2} = \\\\frac{0.75}{8} = 0.09375<\/span><\/span>S<\/span><\/span>e<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>n<\/span><\/span>\u2212<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>Q<\/span><\/span>e<\/span><\/span><\/span><\/span>\u200b<\/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><\/span><\/span><\/span>8<\/span><\/span><\/span><\/span><\/span><\/span><\/span>0.75<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.09375<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      （3）x0=12x_0 = 12<\/span><\/span>x<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>12<\/span><\/span><\/span><\/span><\/span> \u65f6\u7684\u9884\u6d4b：<\/p>\n

      y^0=0.75\u00d712=9（\u4e07\u5143）\\\\hat{y}_0 = 0.75 \\\\times 12 = 9 \\\\text{（\u4e07\u5143）}<\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.75<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>12<\/span><\/span>=<\/span><\/span><\/span><\/span>9<\/span>（\u4e07\u5143）<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u03c3^=0.09375=0.3062\\\\hat{\\\\sigma} = \\\\sqrt{0.09375} = 0.3062<\/span><\/span><\/span>\u03c3<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>0.09375<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.3062<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      1n+(x0\u2212x\u02c9)2Lxx=110+(12\u22128)220=0.1+0.8=0.9=0.9487\\\\sqrt{\\\\frac{1}{n} + \\\\frac{(x_0 – \\\\bar{x})^2}{L_{xx}}} = \\\\sqrt{\\\\frac{1}{10} + \\\\frac{(12-8)^2}{20}} = \\\\sqrt{0.1 + 0.8} = \\\\sqrt{0.9} = 0.9487<\/span><\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>2<\/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><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>10<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>20<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>12<\/span><\/span>\u2212<\/span><\/span>8<\/span>)<\/span><\/span>2<\/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><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>0.1<\/span><\/span>+<\/span><\/span>0.8<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>0.9<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.9487<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      95%\u7f6e\u4fe1\u533a\u95f4：<\/p>\n

      9\u00b12.306\u00d70.3062\u00d70.9487=9\u00b10.6709 \\\\pm 2.306 \\\\times 0.3062 \\\\times 0.9487 = 9 \\\\pm 0.670<\/span><\/span>9<\/span><\/span>\u00b1<\/span><\/span><\/span><\/span>2.306<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>0.3062<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>0.9487<\/span><\/span>=<\/span><\/span><\/span><\/span>9<\/span><\/span>\u00b1<\/span><\/span><\/span><\/span>0.670<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      [8.330,\u00a09.670]\\\\boxed{[8.330, \\\\ 9.670]}<\/span><\/span><\/span>[<\/span>8.330<\/span>,<\/span>\u00a0<\/span><\/span>9.670<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \n

      \u4e60\u98985（\u601d\u8003\u9898）<\/h4>\n

      \u95ee： \u5982\u679c\u5c06\u81ea\u53d8\u91cf xx<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u548c\u56e0\u53d8\u91cf yy<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span> \u4e92\u6362，\u91cd\u65b0\u5efa\u7acb\u56de\u5f52\u65b9\u7a0b x^=\u03b1^0+\u03b1^1y\\\\hat{x} = \\\\hat{\\\\alpha}_0 + \\\\hat{\\\\alpha}_1 y<\/span><\/span><\/span>x<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>\u03b1<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span>\u03b1<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>，\u4e24\u6761\u56de\u5f52\u7ebf\u662f\u5426\u91cd\u5408？\u4e3a\u4ec0\u4e48？<\/p>\n

      \u7b54： \u4e00\u822c\u60c5\u51b5\u4e0b，\u4e24\u6761\u56de\u5f52\u7ebf\u4e0d\u91cd\u5408\u3002<\/p>\n

      \u539f\u56e0：\u4ee5 yy<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span> \u5bf9 xx<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u56de\u5f52\u4e3a\u4f8b：<\/p>\n

      y^=y\u02c9+LxyLxx(x\u2212x\u02c9)\u659c\u7387\u4e3ab1=LxyLxx\\\\hat{y} = \\\\bar{y} + \\\\frac{L_{xy}}{L_{xx}}(x – \\\\bar{x}) \\\\quad \\\\text{\u659c\u7387\u4e3a} \\\\quad b_1 = \\\\frac{L_{xy}}{L_{xx}}<\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>y<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u659c\u7387\u4e3a<\/span><\/span><\/span>b<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/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><\/span><\/p>\n

      \u4ee5 xx<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u5bf9 yy<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span> \u56de\u5f52\u4e3a\u4f8b：<\/p>\n

      x^=x\u02c9+LxyLyy(y\u2212y\u02c9)\u659c\u7387\u4e3aa1=LxyLyy\\\\hat{x} = \\\\bar{x} + \\\\frac{L_{xy}}{L_{yy}}(y – \\\\bar{y}) \\\\quad \\\\text{\u659c\u7387\u4e3a} \\\\quad a_1 = \\\\frac{L_{xy}}{L_{yy}}<\/span><\/span><\/span>x<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>y<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>y<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u659c\u7387\u4e3a<\/span><\/span><\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>y<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/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><\/span><\/p>\n

      \u5c06\u7b2c\u4e8c\u6761\u7ebf\u8868\u793a\u4e3a yy<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span> \u5173\u4e8e xx<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u51fd\u6570：y=y\u02c9+LyyLxy(x\u2212x\u02c9)y = \\\\bar{y} + \\\\dfrac{L_{yy}}{L_{xy}}(x – \\\\bar{x})<\/span><\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>y<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>y<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u5176\u659c\u7387\u4e3a LyyLxy\\\\dfrac{L_{yy}}{L_{xy}}<\/span><\/span><\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>y<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/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>，\u4e0e\u7b2c\u4e00\u6761\u7ebf\u7684\u659c\u7387 LxyLxx\\\\dfrac{L_{xy}}{L_{xx}}<\/span><\/span><\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/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> \u4e00\u822c\u4e0d\u76f8\u7b49\u3002<\/p>\n

      \u53ea\u6709\u5f53 \u2223r\u2223=1|r| = 1<\/span><\/span>\u2223<\/span>r<\/span>\u2223<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>（\u5b8c\u5168\u7ebf\u6027\u76f8\u5173）\u65f6，Lxy2=LxxLyyL_{xy}^2 = L_{xx}L_{yy}<\/span><\/span>L<\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>L<\/span><\/span>xx<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span>y<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u4e24\u6761\u7ebf\u624d\u91cd\u5408\u3002<\/p>\n

      \u51e0\u4f55\u7406\u89e3： \u4e24\u6761\u56de\u5f52\u7ebf\u90fd\u7ecf\u8fc7\u70b9 (x\u02c9,y\u02c9)(\\\\bar{x}, \\\\bar{y})<\/span><\/span>(<\/span><\/span>x<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span>y<\/span><\/span><\/span>\u02c9<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>，\u4f46\u659c\u7387\u4e0d\u540c（\u5206\u522b\u6700\u5c0f\u5316 yy<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span> \u65b9\u5411\u548c xx<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u65b9\u5411\u7684\u504f\u5dee），\u56e0\u6b64\u4e00\u822c\u5f62\u6210\u4e00\u4e2a\u5939\u89d2\u3002\u76f8\u5173\u7cfb\u6570 rr<\/span><\/span>r<\/span><\/span><\/span><\/span><\/span> \u7684\u7edd\u5bf9\u503c\u8d8a\u5927，\u5939\u89d2\u8d8a\u5c0f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

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      \n4.2 \u6807\u51c6\u5316\u6b8b\u5dee
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