\u4e8c\u7ef4\u76f4\u7ebf\u5e38\u7528\u659c\u622a\u5f0f\u65b9\u7a0b \\(y=kx+b\\)\u8868\u8fbe\u3002
\n\u5df2\u77e5\u79bb\u6563\u70b9\u00a0$$ \\{(x_1,y_1),(x_2,y_2),…,(x_n,y_n)\\}\u00a0$$\u00a0\u6b32\u6c42\u4e00\u6761\u76f4\u7ebf\\(y=kx+b\\)\uff0c\u4f7f\u5f97$$ {f=\\sum_{i=1}^n\u00a0(kx_i+b-y_i)^2}$$\u53d6\u5f97\u6700\u5c0f\u503c\u3002
\n\\(k\\),\\( b\\)\u4e3a\u672a\u77e5\u6570\u00a0\uff0c\u6839\u636e\u6700\u5c0f\u4e8c\u4e58\u89e3\u6cd5\uff0c\u4ee4 \\( f\\) \u5bf9\\( k\\),\\( b\\) \u504f\u5bfc\u6570\u5206\u522b\u4e3a0\uff0c\u6c42\u89e3\u51fa\u6765\u7684\\( k\\),\\(b\\)\u5373\u6240\u6c42\u76f4\u7ebf\u53c2\u6570$$ \\frac\u00a0{\\partial\u00a0f}{\\partial\u00a0k}\u00a0=\u00a0\\sum_{i=1}^n\u00a02x_i(kx_i+b-y_i)=0\u00a0$$
\n$$ \\frac\u00a0{\\partial\u00a0f}{\\partial\u00a0b}\u00a0=\u00a0\\sum_{i=1}^n\u00a02(kx_i+b-y_i)=0$$<\/p>\n
\u5316\u7b80\u540e\u5f97\u5230<\/p>\n
$$ \\sum\u00a0x^2k\u00a0+\u00a0\\sum\u00a0xb=\\sum\u00a0xy\u00a0$$
\n$$ \\sum\u00a0xk\u00a0+\u00a0nb\u00a0=\u00a0\\sum\u00a0y$$<\/p>\n
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\n$$ {\\left[\\begin{array}{cc}
\n\\sum\u00a0x^2\u00a0&\u00a0\\sum\u00a0x\\\\
\n\\sum\u00a0x\u00a0&n
\n\\end{array}
\n\\right\u00a0]}{\\left[\\begin{array}{cc}k\\\\b\\end{array}\\right\u00a0]}\u00a0=\u00a0{\\left[\\begin{array}{cc}\u00a0\\sum\u00a0xy\\\\\u00a0\\sum\u00a0y\\end{array}\\right\u00a0]}$$
\n\u6b64\u65f6\u53ef\u7528\u91c7\u7528\u514b\u62c9\u9ed8\u6cd5\u5219\u6c42\u89e3\u3002
\n$$\u00a0 k=\\frac\u00a0{n\\sum\u00a0xy\u00a0–\u00a0\\sum\u00a0x\\sum\u00a0y}{n\\sum\u00a0x^2\u00a0–\u00a0(\\sum\u00a0x)^2}$$
\n$$\u00a0 b=\\frac\u00a0{n\\sum\u00a0x^2\u00a0\\sum\u00a0y\u00a0–\u00a0\\sum\u00a0x\\sum\u00a0xy}{n\\sum\u00a0x^2\u00a0–\u00a0(\\sum\u00a0x)^2}$$
\n\u6211\u63a8\u8350\u53c2\u8003Eigen\u00a0<\/a>\u5bf9\u7ebf\u6027\u65b9\u7a0b\u7684\u6c42\u89e3\u3002
\n\u5728\u5b9e\u8df5\u4e2d\uff0c\u6709\u540c\u5b66\u91c7\u7528\u4e0a\u8ff0\u601d\u8def\u5b8c\u6210\u4e86\u7f16\u7801\uff0c\u6d4b\u8bd5\u65f6\u5374\u53d1\u73b0\u201c\u67d0\u4e9b\u201d\u60c5\u51b5\u4e0b\uff0c\u7b97\u6cd5\u4f3c\u4e4e\u53d6\u7684\u7ed3\u679c\u5b58\u5728\u95ee\u9898\u3002\u95ee\u9898\u5b58\u5728\u4e0e\u90a3\u4e00\u5757\u5462\uff1f
\n\u5176\u5b9e\u5c31\u5728\u4e0e \\( y=kx+b\\)\u65b9\u7a0b\u5f0f\u4e0a\u3002\u5982\u679c\u5f85\u6c42\u7684\u76f4\u7ebf\u4e3a\u4e00\u6761\u5782\u76f4\u4e0ex\u8f74\u7684\u76f4\u7ebf\uff0c\\( y=kx+b\\)\u662f\u65e0\u6cd5\u8868\u793a\u7684\uff0c\u56e0\u800c\u5728\u6570\u503c\u4e0a\u5b58\u5728\u95ee\u9898\uff0c\u8868\u73b0\u5c31\u662fk\u7684\u503c\u6c42\u4e0d\u51c6\u3002\u7ed3\u5408\u4e0a\u9762\u7684\u6c42\u89e3\u65b9\u7a0b\uff0c\u5c31\u662f\u7b49\u53f7\u5de6\u8fb9\u7684\\(2\\times2 \\)\u77e9\u9635\u5947\u5f02\u6216\u8005\u63a5\u8fd1\u5947\u5f02\u3002
\n\u5f88\u663e\u7136\uff0c\u5728\u7279\u5b9a\u7684\u5e94\u7528\u573a\u666f\u4e0b\uff0c\u6bd4\u5982\u51e0\u4f55\u7b97\u6cd5\u4e2d\uff0c\u659c\u622a\u5f0f\u65b9\u7a0b\u5b58\u5728\u7f3a\u9677\uff0c\u4e0d\u80fd\u8868\u8fbe\u6240\u6709\u60c5\u51b5\u3002\u6709\u6ca1\u6709\u66f4\u597d\u7684\u89e3\u51b3\u65b9\u6848\uff1f
\n\u90a3\u5c31\u662f\u00a0$$ Ax+By+C=0$$\u6db5\u76d6\u4e86\u6240\u6709\u60c5\u51b5\u3002\u5177\u4f53\u89e3\u6cd5\u6211\u4f1a\u5728\u4e0b\u4e00\u7bc7\u535a\u6587\u7ed9\u51fa\u3002\u656c\u8bf7\u5173\u6ce8\u3002<\/p>\n