{"id":60243,"date":"2026-01-15T10:05:27","date_gmt":"2026-01-15T02:05:27","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/60243.html"},"modified":"2026-01-15T10:05:27","modified_gmt":"2026-01-15T02:05:27","slug":"%e7%94%a8%e6%9c%80%e5%b0%8f%e4%ba%8c%e4%b9%98%e6%b3%95%e6%b1%82%e8%a7%a3%e4%b8%80%e5%85%83%e4%b8%80%e6%ac%a1%e6%96%b9%e7%a8%8b%e6%a8%a1%e5%9e%8b%e7%9a%84%e5%8f%82%e6%95%b0","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/60243.html","title":{"rendered":"\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u6c42\u89e3\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u6a21\u578b\u7684\u53c2\u6570"},"content":{"rendered":"

\u63a5\u4e0b\u6765，\u5728\u91c7\u7528\u516c\u5f0f<\/p>\n

J<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

)<\/p>\n

=<\/p>\n

1<\/p>\n

2<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

y<\/p>\n

p<\/p>\n

i<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

2<\/p>\n

J\\\\left( \\\\mathbf{\\\\theta} \\\\right) = \\\\frac{1}{2m}\\\\sum_{i = 0}^{m – 1}{(y_{pi} – y_{i})}^{2}<\/p>\n

<\/span><\/span>J<\/span><\/span>(<\/span>\u03b8<\/span>)<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>m<\/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>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>p<\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u8fd9\u6837\u7684\u4f18\u5316\u51fd\u6570\u7684\u60c5\u51b5\u4e0b，\u4e00\u8d77\u6765\u6c42\u89e3\u6a21\u578b\u7684\u53c2\u6570\u3002<\/p>\n

\u5728\u6781\u503c\u70b9\u5fc5\u6709\u5bfc\u6570\u503c\u4e3a0\u3002\u5bfc\u6570\u503c\u4e3a0\u5219\u8868\u660e\u51fd\u6570\u968f\u672a\u77e5\u53d8\u91cf\u7684\u53d8\u5316\u7387\u4e3a0\u3002\u4e0b\u9762\u5148\u5bf9<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

\\\\theta_{0}<\/p>\n

<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6c42\u504f\u5bfc\u6570：<\/p>\n

<\/p>\n

\u2202<\/p>\n

J<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

)<\/p>\n

\u2202<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

=<\/p>\n

\u2202<\/p>\n

\u2202<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

(<\/p>\n

1<\/p>\n

2<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

2<\/p>\n

)<\/p>\n

=<\/p>\n

1<\/p>\n

2<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

\u2202<\/p>\n

\u2202<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

2<\/p>\n

=<\/p>\n

1<\/p>\n

2<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

2<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

\u2202<\/p>\n

\u2202<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

)<\/p>\n

=<\/p>\n

1<\/p>\n

2<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

2<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

\u2202<\/p>\n

\u2202<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

)<\/p>\n

=<\/p>\n

1<\/p>\n

2<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

2<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

)<\/p>\n

=<\/p>\n

1<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

\\\\frac{\\\\partial J\\\\left( \\\\mathbf{\\\\theta} \\\\right)}{\\\\partial\\\\theta_{0}} = \\\\frac{\\\\partial}{\\\\partial\\\\theta_{0}}\\\\left( \\\\frac{1}{2m}\\\\sum_{i = 0}^{m – 1}\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right)^{2} \\\\right) = \\\\frac{1}{2m}\\\\sum_{i = 0}^{m – 1}{\\\\frac{\\\\partial}{\\\\partial\\\\theta_{0}}\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right)^{2}} = \\\\frac{1}{2m}\\\\sum_{i = 0}^{m – 1}\\\\left( 2\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right)\\\\frac{\\\\partial}{\\\\partial\\\\theta_{0}}\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right) \\\\right) = \\\\frac{1}{2m}\\\\sum_{i = 0}^{m – 1}\\\\left( 2\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right)\\\\frac{\\\\partial}{\\\\partial\\\\theta_{0}}\\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) \\\\right) = \\\\frac{1}{2m}\\\\sum_{i = 0}^{m – 1}\\\\left( 2\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right) \\\\right) = \\\\frac{1}{m}\\\\sum_{i = 0}^{m – 1}\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right)<\/p>\n

<\/span><\/span><\/span><\/span>\u2202<\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>J<\/span><\/span>(<\/span>\u03b8<\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span><\/span><\/span>2<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>2<\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>)<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>2<\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>)<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>2<\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>)<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8981\u60f3\u6253\u597d\u673a\u5668\u5b66\u4e60\u7684\u6570\u5b66\u57fa\u7840，\u8bf7\u53c2\u89c1\u6e05\u534e\u5927\u5b66\u51fa\u7248\u793e\u7684\u4eba\u4eba\u53ef\u61c2\u7cfb\u5217，\u5305\u62ec\u300a\u4eba\u4eba\u53ef\u61c2\u7684\u5fae\u79ef\u5206\u300b（\u5df2\u4e0a\u5e02）\u3001\u300a\u4eba\u4eba\u53ef\u61c2\u7684\u7ebf\u6027\u4ee3\u6570\u300b（\u5373\u5c06\u4e0a\u5e02）\u3001\u300a\u4eba\u4eba\u53ef\u61c2\u7684\u6982\u7387\u7edf\u8ba1\u300b（\u5373\u5c06\u4e0a\u5e02）\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

\u518d\u5bf9<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

\\\\theta_{1}<\/p>\n

<\/span><\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6c42\u504f\u5bfc\u6570：<\/p>\n

<\/p>\n

\u2202<\/p>\n

J<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

)<\/p>\n

\u2202<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

=<\/p>\n

\u2202<\/p>\n

\u2202<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

(<\/p>\n

1<\/p>\n

2<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

2<\/p>\n

)<\/p>\n

=<\/p>\n

1<\/p>\n

2<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

\u2202<\/p>\n

\u2202<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

2<\/p>\n

=<\/p>\n

1<\/p>\n

2<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

2<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

\u2202<\/p>\n

\u2202<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

)<\/p>\n

=<\/p>\n

1<\/p>\n

2<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

2<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

\u2202<\/p>\n

\u2202<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

)<\/p>\n

=<\/p>\n

1<\/p>\n

2<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

2<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

\u2202<\/p>\n

\u2202<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

)<\/p>\n

=<\/p>\n

1<\/p>\n

2<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

2<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

=<\/p>\n

1<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

=<\/p>\n

1<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

x<\/p>\n

i<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\\\\frac{\\\\partial J(\\\\mathbf{\\\\theta})}{\\\\partial\\\\theta_{1}} = \\\\frac{\\\\partial}{\\\\partial\\\\theta_{1}}\\\\left( \\\\frac{1}{2m}\\\\sum_{i = 0}^{m – 1}\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right)^{2} \\\\right) = \\\\frac{1}{2m}\\\\sum_{i = 0}^{m – 1}{\\\\frac{\\\\partial}{\\\\partial\\\\theta_{1}}\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right)^{2}} = \\\\frac{1}{2m}\\\\sum_{i = 0}^{m – 1}\\\\left( 2\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right)\\\\frac{\\\\partial}{\\\\partial\\\\theta_{1}}\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right) \\\\right) = \\\\frac{1}{2m}\\\\sum_{i = 0}^{m – 1}\\\\left( 2\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right)\\\\frac{\\\\partial}{\\\\partial\\\\theta_{1}}\\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) \\\\right) = \\\\frac{1}{2m}\\\\sum_{i = 0}^{m – 1}\\\\left( 2\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right)\\\\frac{\\\\partial}{\\\\partial\\\\theta_{1}}(\\\\theta_{1}x_{i}) \\\\right) = \\\\frac{1}{2m}\\\\sum_{i = 0}^{m – 1}\\\\left( 2\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right)x_{i} \\\\right) = \\\\frac{1}{m}\\\\sum_{i = 0}^{m – 1}\\\\left( \\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right)x_{i} \\\\right) = \\\\frac{1}{m}\\\\sum_{i = 0}^{m – 1}\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right)x_{i} – y_{i}x_{i} \\\\right)<\/p>\n

<\/span><\/span><\/span><\/span>\u2202<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>J<\/span>(<\/span>\u03b8<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span><\/span><\/span>2<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>2<\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>)<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>2<\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>)<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>2<\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>)<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>2<\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u7531\u6b64，\u53ef\u5f97\u5230\u65b9\u7a0b\u7ec4：<\/p>\n

<\/p>\n

{<\/p>\n

\u2202<\/p>\n

J<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

)<\/p>\n

\u2202<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

=<\/p>\n

1<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

=<\/p>\n

0<\/p>\n

\u2202<\/p>\n

J<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

)<\/p>\n

\u2202<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

=<\/p>\n

1<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

x<\/p>\n

i<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

=<\/p>\n

0<\/p>\n

\u00a0<\/p>\n

\\\\left\\\\{ \\\\begin{matrix} \\\\frac{\\\\partial J(\\\\mathbf{\\\\theta})}{\\\\partial\\\\theta_{0}} = \\\\frac{1}{m}\\\\sum_{i = 0}^{m – 1}\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right) = 0 \\\\\\\\ \\\\frac{\\\\partial J(\\\\mathbf{\\\\theta})}{\\\\partial\\\\theta_{1}} = \\\\frac{1}{m}\\\\sum_{i = 0}^{m – 1}\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right)x_{i} – y_{i}x_{i} \\\\right) = 0 \\\\\\\\ \\\\end{matrix} \\\\right.\\\\ <\/p>\n

<\/span><\/span>{<\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>J<\/span>(<\/span>\u03b8<\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/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>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>J<\/span>(<\/span>\u03b8<\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/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>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/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>\u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

（\u65b9\u7a0b\u7ec41）<\/p>\n

\u600e\u4e48\u6c42\u89e3\u8fd9\u4e2a\u65b9\u7a0b\u7ec4\u5462？\u53ef\u6839\u636e\u65b9\u7a0b\u7ec4\u7684\u7b2c1\u4e2a\u65b9\u7a0b，\u5f97\u5230：<\/p>\n

<\/p>\n

1<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

=<\/p>\n

0<\/p>\n

\u27f9<\/p>\n

1<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

)<\/p>\n

=<\/p>\n

0<\/p>\n

\\\\frac{1}{m}\\\\sum_{i = 0}^{m – 1}\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right) – y_{i} \\\\right) = 0 \\\\Longrightarrow \\\\frac{1}{m}\\\\sum_{i = 0}^{m – 1}\\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} – y_{i} \\\\right) = 0<\/p>\n

<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span>\u27f9<\/span><\/span><\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

\u27f9<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

=<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

y<\/p>\n

i<\/p>\n

\u2212<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\u27f9<\/p>\n

m<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

=<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

y<\/p>\n

i<\/p>\n

\u2212<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\\\\Longrightarrow \\\\sum_{i = 0}^{m – 1}\\\\theta_{0} = \\\\sum_{i = 0}^{m – 1}\\\\left( y_{i} – \\\\theta_{1}x_{i} \\\\right) \\\\Longrightarrow m\\\\theta_{0} = \\\\sum_{i = 0}^{m – 1}\\\\left( y_{i} – \\\\theta_{1}x_{i} \\\\right)<\/p>\n

<\/span><\/span>\u27f9<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u27f9<\/span><\/span><\/span><\/span>m<\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

\u27f9<\/p>\n

m<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

=<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

y<\/p>\n

i<\/p>\n

\u2212<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\u27f9<\/p>\n

m\u03b8<\/p>\n

0<\/p>\n

=<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

y<\/p>\n

i<\/p>\n

\u2212<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\\\\Longrightarrow m\\\\theta_{0} = \\\\sum_{i = 0}^{m – 1}y_{i} – \\\\sum_{i = 0}^{m – 1}\\\\left( \\\\theta_{1}x_{i} \\\\right) \\\\Longrightarrow \\\\text{m\u03b8}_{0} = \\\\sum_{i = 0}^{m – 1}y_{i} – \\\\theta_{1}\\\\sum_{i = 0}^{m – 1}x_{i}<\/p>\n

<\/span><\/span>\u27f9<\/span><\/span><\/span><\/span>m<\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u27f9<\/span><\/span><\/span><\/span>m\u03b8<\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

\u27f9<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

=<\/p>\n

1<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

y<\/p>\n

i<\/p>\n

\u2212<\/p>\n

1<\/p>\n

m<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\\\\Longrightarrow \\\\theta_{0} = \\\\frac{1}{m}\\\\sum_{i = 0}^{m – 1}y_{i} – {\\\\frac{1}{m}\\\\theta}_{1}\\\\sum_{i = 0}^{m – 1}x_{i}<\/p>\n

<\/span><\/span>\u27f9<\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b8<\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6839\u636e\u65b9\u7a0b\u7ec44-5\u7684\u7b2c2\u4e2a\u65b9\u7a0b，\u53ef\u5f97：<\/p>\n

<\/p>\n

1<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

x<\/p>\n

i<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

=<\/p>\n

0<\/p>\n

\u27f9<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

)<\/p>\n

x<\/p>\n

i<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

=<\/p>\n

0<\/p>\n

\\\\frac{1}{m}\\\\sum_{i = 0}^{m – 1}\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right)x_{i} – y_{i}x_{i} \\\\right) = 0 \\\\Longrightarrow \\\\sum_{i = 0}^{m – 1}\\\\left( \\\\left( \\\\theta_{1}x_{i} + \\\\theta_{0} \\\\right)x_{i} – y_{i}x_{i} \\\\right) = 0<\/p>\n

<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span>\u27f9<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

\u27f9<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

2<\/p>\n

+<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

x<\/p>\n

i<\/p>\n

\u2212<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

=<\/p>\n

0<\/p>\n

\u27f9<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

=<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

\u2212<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

2<\/p>\n

)<\/p>\n

\\\\Longrightarrow \\\\sum_{i = 0}^{m – 1}\\\\left( \\\\theta_{1}{x_{i}}^{2} + \\\\theta_{0}x_{i} – y_{i}x_{i} \\\\right) = 0 \\\\Longrightarrow \\\\sum_{i = 0}^{m – 1}\\\\left( \\\\theta_{0}x_{i} \\\\right) = \\\\sum_{i = 0}^{m – 1}\\\\left( y_{i}x_{i} – \\\\theta_{1}{x_{i}}^{2} \\\\right)<\/p>\n

<\/span><\/span>\u27f9<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span>\u27f9<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

\u27f9<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

=<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\u2212<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

2<\/p>\n

\\\\Longrightarrow \\\\theta_{0}\\\\sum_{i = 0}^{m – 1}x_{i} = \\\\sum_{i = 0}^{m – 1}\\\\left( y_{i}x_{i} \\\\right) – \\\\theta_{1}\\\\sum_{i = 0}^{m – 1}{x_{i}}^{2}<\/p>\n

<\/span><\/span>\u27f9<\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

\u27f9<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

=<\/p>\n

(<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\u2212<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

2<\/p>\n

)<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\\\\Longrightarrow \\\\theta_{0} = \\\\frac{\\\\left( \\\\sum_{i = 0}^{m – 1}\\\\left( y_{i}x_{i} \\\\right) – \\\\theta_{1}\\\\sum_{i = 0}^{m – 1}{x_{i}}^{2} \\\\right)}{\\\\sum_{i = 0}^{m – 1}x_{i}}<\/p>\n

<\/span><\/span>\u27f9<\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/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><\/p>\n

\u56e0\u6b64，\u53ef\u5f97：<\/p>\n

<\/p>\n

1<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

y<\/p>\n

i<\/p>\n

\u2212<\/p>\n

1<\/p>\n

m<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

=<\/p>\n

(<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\u2212<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

2<\/p>\n

)<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\\\\frac{1}{m}\\\\sum_{i = 0}^{m – 1}y_{i} – {\\\\frac{1}{m}\\\\theta}_{1}\\\\sum_{i = 0}^{m – 1}x_{i} = \\\\frac{\\\\left( \\\\sum_{i = 0}^{m – 1}\\\\left( y_{i}x_{i} \\\\right) – \\\\theta_{1}\\\\sum_{i = 0}^{m – 1}{x_{i}}^{2} \\\\right)}{\\\\sum_{i = 0}^{m – 1}x_{i}}<\/p>\n

<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b8<\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/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><\/p>\n

<\/p>\n

\u27f9<\/p>\n

1<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

y<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\u2212<\/p>\n

1<\/p>\n

m<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

=<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\u2212<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

2<\/p>\n

\\\\Longrightarrow \\\\frac{1}{m}\\\\sum_{i = 0}^{m – 1}y_{i}\\\\sum_{i = 0}^{m – 1}x_{i} – \\\\frac{1}{m}\\\\theta_{1}\\\\sum_{i = 0}^{m – 1}x_{i}\\\\sum_{i = 0}^{m – 1}x_{i} = \\\\sum_{i = 0}^{m – 1}\\\\left( y_{i}x_{i} \\\\right) – \\\\theta_{1}\\\\sum_{i = 0}^{m – 1}{x_{i}}^{2}<\/p>\n

<\/span><\/span>\u27f9<\/span><\/span><\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

\u27f9<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

y<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\u2212<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

=<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\u2212<\/p>\n

m<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

2<\/p>\n

\\\\Longrightarrow \\\\sum_{i = 0}^{m – 1}y_{i}\\\\sum_{i = 0}^{m – 1}x_{i} – \\\\theta_{1}\\\\sum_{i = 0}^{m – 1}x_{i}\\\\sum_{i = 0}^{m – 1}x_{i} = m\\\\sum_{i = 0}^{m – 1}\\\\left( y_{i}x_{i} \\\\right) – m\\\\theta_{1}\\\\sum_{i = 0}^{m – 1}{x_{i}}^{2}<\/p>\n

<\/span><\/span>\u27f9<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>m<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

\u27f9<\/p>\n

\u00a0<\/p>\n

m<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

2<\/p>\n

\u2212<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

=<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\u2212<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

y<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\\\\Longrightarrow \\\\ m\\\\theta_{1}\\\\sum_{i = 0}^{m – 1}{x_{i}}^{2} – \\\\theta_{1}\\\\sum_{i = 0}^{m – 1}x_{i}\\\\sum_{i = 0}^{m – 1}x_{i} = m\\\\sum_{i = 0}^{m – 1}\\\\left( y_{i}x_{i} \\\\right) – \\\\sum_{i = 0}^{m – 1}y_{i}\\\\sum_{i = 0}^{m – 1}x_{i}<\/p>\n

<\/span><\/span>\u27f9<\/span>\u00a0<\/span><\/span><\/span><\/span>m<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

\u27f9<\/p>\n

\u00a0<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

(<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

2<\/p>\n

\u2212<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

=<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\u2212<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

y<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\\\\Longrightarrow \\\\ \\\\theta_{1}\\\\left( m\\\\sum_{i = 0}^{m – 1}{x_{i}}^{2} – \\\\sum_{i = 0}^{m – 1}x_{i}\\\\sum_{i = 0}^{m – 1}x_{i} \\\\right) = m\\\\sum_{i = 0}^{m – 1}\\\\left( y_{i}x_{i} \\\\right) – \\\\sum_{i = 0}^{m – 1}y_{i}\\\\sum_{i = 0}^{m – 1}x_{i}<\/p>\n

<\/span><\/span>\u27f9<\/span>\u00a0<\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>m<\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

\u27f9<\/p>\n

\u00a0<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

=<\/p>\n

(<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\u2212<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

y<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

(<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

2<\/p>\n

\u2212<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\\\\Longrightarrow \\\\ \\\\theta_{1} = \\\\frac{\\\\left( m\\\\sum_{i = 0}^{m – 1}\\\\left( y_{i}x_{i} \\\\right) – \\\\sum_{i = 0}^{m – 1}y_{i}\\\\sum_{i = 0}^{m – 1}x_{i} \\\\right)}{\\\\left( m\\\\sum_{i = 0}^{m – 1}{x_{i}}^{2} – \\\\sum_{i = 0}^{m – 1}x_{i}\\\\sum_{i = 0}^{m – 1}x_{i} \\\\right)}<\/p>\n

<\/span><\/span>\u27f9<\/span>\u00a0<\/span><\/span><\/span><\/span>\u03b8<\/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><\/span>m<\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>m<\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/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><\/span><\/p>\n

\u81f3\u6b64，\u5df2\u6c42\u89e3\u5f97\u76f4\u7ebf\u6a21\u578b\u76842\u4e2a\u53c2\u6570\u503c\u4e3a：<\/p>\n

<\/p>\n

{<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

=<\/p>\n

(<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\u2212<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

y<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

(<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

2<\/p>\n

\u2212<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\u03b8<\/p>\n

0<\/p>\n

=<\/p>\n

1<\/p>\n

m<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

y<\/p>\n

i<\/p>\n

\u2212<\/p>\n

1<\/p>\n

m<\/p>\n

\u03b8<\/p>\n

1<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\u00a0<\/p>\n

\\\\left\\\\{ \\\\begin{matrix} \\\\theta_{1} = \\\\frac{\\\\left( m\\\\sum_{i = 0}^{m – 1}\\\\left( y_{i}x_{i} \\\\right) – \\\\sum_{i = 0}^{m – 1}y_{i}\\\\sum_{i = 0}^{m – 1}x_{i} \\\\right)}{\\\\left( m\\\\sum_{i = 0}^{m – 1}{x_{i}}^{2} – \\\\sum_{i = 0}^{m – 1}x_{i}\\\\sum_{i = 0}^{m – 1}x_{i} \\\\right)} \\\\\\\\ \\\\theta_{0} = \\\\frac{1}{m}\\\\sum_{i = 0}^{m – 1}y_{i} – {\\\\frac{1}{m}\\\\theta}_{1}\\\\sum_{i = 0}^{m – 1}x_{i} \\\\\\\\ \\\\end{matrix} \\\\right.\\\\ <\/p>\n

<\/span><\/span><\/span>\u23a9<\/span><\/span><\/span><\/span><\/p>\n

<\/span><\/span><\/span>\u23a8<\/span><\/span><\/span><\/span><\/p>\n

<\/span><\/span><\/span>\u23a7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span><\/span>m<\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>m<\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u2212<\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/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>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/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>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b8<\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/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>\u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

（\u65b9\u7a0b\u7ec42\u7684\u89e3）<\/p>\n

\u8981\u60f3\u6253\u597d\u673a\u5668\u5b66\u4e60\u7684\u6570\u5b66\u57fa\u7840，\u8bf7\u53c2\u89c1\u6e05\u534e\u5927\u5b66\u51fa\u7248\u793e\u7684\u4eba\u4eba\u53ef\u61c2\u7cfb\u5217，\u5305\u62ec\u300a\u4eba\u4eba\u53ef\u61c2\u7684\u5fae\u79ef\u5206\u300b（\u5df2\u4e0a\u5e02）\u3001\u300a\u4eba\u4eba\u53ef\u61c2\u7684\u7ebf\u6027\u4ee3\u6570\u300b（\u5373\u5c06\u4e0a\u5e02）\u3001\u300a\u4eba\u4eba\u53ef\u61c2\u7684\u6982\u7387\u7edf\u8ba1\u300b（\u5373\u5c06\u4e0a\u5e02）\u3002<\/p>\n

\u63d0\u793a：<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

\\\\sum_{i = 0}^{m – 1}\\\\left( y_{i}x_{i} \\\\right)<\/p>\n

<\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>\u4e0e<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

y<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\\\\sum_{i = 0}^{m – 1}y_{i}\\\\sum_{i = 0}^{m – 1}x_{i}<\/p>\n

<\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e0d\u540c，\u53ea\u8981\u5c06\u8fd92\u4e2a\u5f0f\u5b50\u5c55\u5f00\u6765\u5c31\u53ef\u4ee5\u770b\u5f97\u5f88\u6e05\u695a\u4e86：<\/p>\n

<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

(<\/p>\n

y<\/p>\n

i<\/p>\n

x<\/p>\n

i<\/p>\n

)<\/p>\n

=<\/p>\n

y<\/p>\n

0<\/p>\n

x<\/p>\n

0<\/p>\n

+<\/p>\n

\u2026<\/p>\n

+<\/p>\n

y<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

\\\\sum_{i = 0}^{m – 1}\\\\left( y_{i}x_{i} \\\\right) = y_{0}x_{0} + \\\\ldots + y_{m – 1}x_{m – 1}<\/p>\n

<\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>y<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u2026<\/span><\/span>+<\/span><\/span><\/span><\/span>y<\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

y<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

=<\/p>\n

(<\/p>\n

y<\/p>\n

0<\/p>\n

+<\/p>\n

\u2026<\/p>\n

+<\/p>\n

y<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

)<\/p>\n

(<\/p>\n

x<\/p>\n

0<\/p>\n

+<\/p>\n

\u2026<\/p>\n

+<\/p>\n

x<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

)<\/p>\n

\\\\sum_{i = 0}^{m – 1}y_{i}\\\\sum_{i = 0}^{m – 1}x_{i} = (y_{0} + \\\\ldots + y_{m – 1})(x_{0} + \\\\ldots + x_{m – 1})<\/p>\n

<\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u2026<\/span><\/span>+<\/span><\/span><\/span><\/span>y<\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>(<\/span>x<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u2026<\/span><\/span>+<\/span><\/span><\/span><\/span>x<\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8fd92\u4e2a\u5f0f\u5b50\u660e\u663e\u4e0d\u540c\u3002\u518d\u6765\u770b<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

2<\/p>\n

\\\\sum_{i = 0}^{m – 1}{x_{i}}^{2}<\/p>\n

<\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\\\\sum_{i = 0}^{m – 1}x_{i}\\\\sum_{i = 0}^{m – 1}x_{i}<\/p>\n

<\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5c06\u8fd92\u4e2a\u5f0f\u5b50\u5c55\u5f00\u6765\u5c31\u53ef\u4ee5\u770b\u5f97\u5f88\u6e05\u6670：<\/p>\n

<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

2<\/p>\n

=<\/p>\n

x<\/p>\n

0<\/p>\n

2<\/p>\n

+<\/p>\n

\u2026<\/p>\n

+<\/p>\n

x<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

2<\/p>\n

\\\\sum_{i = 0}^{m – 1}{x_{i}}^{2} = {x_{0}}^{2} + \\\\ldots + {x_{m – 1}}^{2}<\/p>\n

<\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>x<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u2026<\/span><\/span>+<\/span><\/span><\/span><\/span>x<\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

\u2211<\/p>\n

i<\/p>\n

=<\/p>\n

0<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

x<\/p>\n

i<\/p>\n

=<\/p>\n

(<\/p>\n

x<\/p>\n

0<\/p>\n

+<\/p>\n

\u2026<\/p>\n

+<\/p>\n

x<\/p>\n

m<\/p>\n

\u2212<\/p>\n

1<\/p>\n

)<\/p>\n

2<\/p>\n

\\\\sum_{i = 0}^{m – 1}x_{i}\\\\sum_{i = 0}^{m – 1}x_{i} = {(x_{0} + \\\\ldots + x_{m – 1})}^{2}<\/p>\n

<\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>x<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u2026<\/span><\/span>+<\/span><\/span>x<\/span><\/span>m<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8fd92\u4e2a\u5f0f\u5b50\u770b\u8d77\u6765\u4e5f\u660e\u663e\u4e0d\u540c\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u63a5\u4e0b\u6765，\u5728\u91c7\u7528\u516c\u5f0fJ(\u03b8)12m\u2211i0m\u22121(ypi\u2212yi)2J\\\\left( \\\\mathbf{\\\\theta} \\\\right) \\\\frac{1}{2m}\\\\sum_{i 0}^{m – 1}{(y_{pi} – y_{i})}^{2}J(\u03b8)2m1\u200b\u2211i0m\u22121\u200b(ypi\u200b\u2212yi\u200b)2\u8fd9\u6837\u7684\u4f18\u5316\u51fd\u6570\u7684\u60c5\u51b5\u4e0b，\u4e00\u8d77\u6765\u6c42\u89e3\u6a21\u578b\u7684\u53c2\u6570\u3002
\n\u5728\u6781\u503c\u70b9\u5fc5\u6709\u5bfc\u6570\u503c\u4e3a0\u3002\u5bfc\u6570\u503c\u4e3a0\u5219\u8868\u660e\u51fd\u6570\u968f\u672a\u77e5\u53d8\u91cf\u7684\u53d8\u5316\u7387\u4e3a0\u3002\u4e0b\u9762\u5148\u5bf9\u03b80\\\\theta_{0}\u03b80\u200b\u6c42\u504f\u5bfc\u6570&<\/p>\n","protected":false},"author":2,"featured_media":60242,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[6353,207,427],"topic":[],"class_list":["post-60243","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-6353","tag-207","tag-427"],"yoast_head":"\n\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u6c42\u89e3\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u6a21\u578b\u7684\u53c2\u6570 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/60243.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u6c42\u89e3\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u6a21\u578b\u7684\u53c2\u6570 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u63a5\u4e0b\u6765，\u5728\u91c7\u7528\u516c\u5f0fJ(\u03b8)12m\u2211i0m\u22121(ypi\u2212yi)2J\\left( \\mathbf{\\theta} \\right) \\frac{1}{2m}\\sum_{i 0}^{m - 1}{(y_{pi} - y_{i})}^{2}J(\u03b8)2m1\u200b\u2211i0m\u22121\u200b(ypi\u200b\u2212yi\u200b)2\u8fd9\u6837\u7684\u4f18\u5316\u51fd\u6570\u7684\u60c5\u51b5\u4e0b，\u4e00\u8d77\u6765\u6c42\u89e3\u6a21\u578b\u7684\u53c2\u6570\u3002 \u5728\u6781\u503c\u70b9\u5fc5\u6709\u5bfc\u6570\u503c\u4e3a0\u3002\u5bfc\u6570\u503c\u4e3a0\u5219\u8868\u660e\u51fd\u6570\u968f\u672a\u77e5\u53d8\u91cf\u7684\u53d8\u5316\u7387\u4e3a0\u3002\u4e0b\u9762\u5148\u5bf9\u03b80\\theta_{0}\u03b80\u200b\u6c42\u504f\u5bfc\u6570&\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/60243.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-01-15T02:05:27+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260115020526-69684b6696310.jpg\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"11 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/60243.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/60243.html\",\"name\":\"\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u6c42\u89e3\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u6a21\u578b\u7684\u53c2\u6570 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"isPartOf\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\"},\"datePublished\":\"2026-01-15T02:05:27+00:00\",\"dateModified\":\"2026-01-15T02:05:27+00:00\",\"author\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\"},\"breadcrumb\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/60243.html#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.wsisp.com\/helps\/60243.html\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/60243.html#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9875\",\"item\":\"https:\/\/www.wsisp.com\/helps\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u6c42\u89e3\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u6a21\u578b\u7684\u53c2\u6570\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\",\"url\":\"https:\/\/www.wsisp.com\/helps\/\",\"name\":\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"description\":\"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"contentUrl\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"caption\":\"admin\"},\"sameAs\":[\"http:\/\/wp.wsisp.com\"],\"url\":\"https:\/\/www.wsisp.com\/helps\/author\/admin\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u6c42\u89e3\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u6a21\u578b\u7684\u53c2\u6570 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.wsisp.com\/helps\/60243.html","og_locale":"zh_CN","og_type":"article","og_title":"\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u6c42\u89e3\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u6a21\u578b\u7684\u53c2\u6570 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","og_description":"\u63a5\u4e0b\u6765，\u5728\u91c7\u7528\u516c\u5f0fJ(\u03b8)12m\u2211i0m\u22121(ypi\u2212yi)2J\\left( \\mathbf{\\theta} \\right) \\frac{1}{2m}\\sum_{i 0}^{m - 1}{(y_{pi} - y_{i})}^{2}J(\u03b8)2m1\u200b\u2211i0m\u22121\u200b(ypi\u200b\u2212yi\u200b)2\u8fd9\u6837\u7684\u4f18\u5316\u51fd\u6570\u7684\u60c5\u51b5\u4e0b，\u4e00\u8d77\u6765\u6c42\u89e3\u6a21\u578b\u7684\u53c2\u6570\u3002 \u5728\u6781\u503c\u70b9\u5fc5\u6709\u5bfc\u6570\u503c\u4e3a0\u3002\u5bfc\u6570\u503c\u4e3a0\u5219\u8868\u660e\u51fd\u6570\u968f\u672a\u77e5\u53d8\u91cf\u7684\u53d8\u5316\u7387\u4e3a0\u3002\u4e0b\u9762\u5148\u5bf9\u03b80\\theta_{0}\u03b80\u200b\u6c42\u504f\u5bfc\u6570&","og_url":"https:\/\/www.wsisp.com\/helps\/60243.html","og_site_name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","article_published_time":"2026-01-15T02:05:27+00:00","og_image":[{"url":"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260115020526-69684b6696310.jpg"}],"author":"admin","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"admin","\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4":"11 \u5206"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.wsisp.com\/helps\/60243.html","url":"https:\/\/www.wsisp.com\/helps\/60243.html","name":"\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u6c42\u89e3\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u6a21\u578b\u7684\u53c2\u6570 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","isPartOf":{"@id":"https:\/\/www.wsisp.com\/helps\/#website"},"datePublished":"2026-01-15T02:05:27+00:00","dateModified":"2026-01-15T02:05:27+00:00","author":{"@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41"},"breadcrumb":{"@id":"https:\/\/www.wsisp.com\/helps\/60243.html#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.wsisp.com\/helps\/60243.html"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.wsisp.com\/helps\/60243.html#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u9996\u9875","item":"https:\/\/www.wsisp.com\/helps"},{"@type":"ListItem","position":2,"name":"\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u6c42\u89e3\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u6a21\u578b\u7684\u53c2\u6570"}]},{"@type":"WebSite","@id":"https:\/\/www.wsisp.com\/helps\/#website","url":"https:\/\/www.wsisp.com\/helps\/","name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","description":"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-Hans"},{"@type":"Person","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41","name":"admin","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/","url":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","contentUrl":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","caption":"admin"},"sameAs":["http:\/\/wp.wsisp.com"],"url":"https:\/\/www.wsisp.com\/helps\/author\/admin"}]}},"_links":{"self":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/60243","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/comments?post=60243"}],"version-history":[{"count":0,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/60243\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media\/60242"}],"wp:attachment":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media?parent=60243"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/categories?post=60243"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/tags?post=60243"},{"taxonomy":"topic","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/topic?post=60243"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}