相关系数的数值范围极其判断标准

\u76f8\u5173\u7cfb\u6570\u7684\u6570\u503c\u8303\u56f4\u53ca\u5176\u5224\u65ad\u6807\u51c6\u662f\u4ec0\u4e48

\u76f8\u5173\u7cfb\u6570\u7684\u6570\u503c\u8303\u56f4\u4e3a[-1\uff0c1]\uff1b\u5224\u65ad\u6807\u51c6\u4e3a\uff1a1\u4e3a\u6b63\u76f8\u5173\uff0c-1\u4e3a\u8d1f\u76f8\u5173\uff0c0\u4e3a\u4e0d\u76f8\u5173\u3002
\u5206\u6790\u8fc7\u7a0b\u5982\u4e0b\uff1a
(1\uff09\u7528\u76f8\u5173\u7cfb\u6570r\u53ef\u4ee5\u8861\u91cf\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u5173\u7cfb\u7684\u5f3a\u5f31\uff1b
(2\uff09r\u7684\u7edd\u5bf9\u503c\u8d8a\u63a5\u8fd1\u4e8e1\uff0c\u8868\u793a\u4e24\u4e2a\u53d8\u91cf\u7684\u7ebf\u6027\u76f8\u5173\u6027\u8d8a\u5f3a;
(3\uff09r\u7684\u7edd\u5bf9\u503c\u63a5\u8fd1\u4e8e0\u65f6\uff0c\u8868\u793a\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u51e0\u4e4e\u4e0d\u5b58\u5728\u76f8\u5173\u5173\u7cfb;
(4\uff09\u6839\u636e\u76f8\u5173\u7cfb\u6570\u7684\u6027\u8d28\uff0c\u53ef\u77e5\u76f8\u5173\u7cfb\u6570\u7684\u53d6\u503c\u8303\u56f4\u662f[-1\uff0c1]\u3002
\u5bf9\u4e8e\u4e24\u4e2a\u53d8\u91cfX\u548cY\uff0c\u76f8\u5173\u7cfb\u6570\u5b9a\u91cf\u5730\u523b\u753b\u4e86 X \u548c Y\u7684\u76f8\u5173\u7a0b\u5ea6\uff0c\u5373|\u03c1XY|\u8d8a\u5927\uff0c\u76f8\u5173\u7a0b\u5ea6\u8d8a\u5927\uff1b|\u03c1XY|=0\uff0cX\u548cY\u5bf9\u5e94\u76f8\u5173\u7a0b\u5ea6\u6700\u4f4e\uff0c\u4e3a\u4e0d\u76f8\u5173\uff1b
X \u548cY\u5b8c\u5168\u76f8\u5173\u7684\u542b\u4e49\u662f\u5728\u6982\u7387\u4e3a1\u7684\u610f\u4e49\u4e0b\u5b58\u5728\u7ebf\u6027\u5173\u7cfb\uff0c\u5373|\u03c1XY|=1\u3002\u8fd9\u65f6\u5019\u5b58\u5728\u4e24\u79cd\u60c5\u51b5\uff0c|\u03c1XY=1\u65f6\uff0cX\u548cY\u5b8c\u5168\u6b63\u76f8\u5173\uff1b\u03c1XY=-1\u65f6\uff0cX\u548cY\u5b8c\u5168\u8d1f\u76f8\u5173\u3002

\u6269\u5c55\u8d44\u6599\uff1a
\u76f8\u5173\u7cfb\u6570\u7684\u6027\u8d28\uff1a
\u8fd9\u91cc\uff0c\u03c1xy=r(x,y)\uff0c\u03c1xy\u662f\u4e00\u4e2a\u53ef\u4ee5\u8868\u5f81x\u548cy\u4e4b\u95f4\u7ebf\u6027\u5173\u7cfb\u7d27\u5bc6\u7a0b\u5ea6\u7684\u91cf\u3002\u5b83\u5177\u6709\u4e24\u4e2a\u6027\u8d28\uff1a
\uff081\uff09|\u03c1XY|\u22641\uff1b
\uff082\uff09|\u03c1XY|=1\u7684\u5145\u8981\u6761\u4ef6\u662f\uff0c\u5b58\u5728\u5e38\u6570a\uff0cb\uff0c\u4f7f\u5f97

\uff083\uff09\u76f8\u5173\u7cfb\u6570\u5b9a\u91cf\u5730\u523b\u753b\u4e86 X \u548c Y\u7684\u76f8\u5173\u7a0b\u5ea6\uff0c\u5373|\u03c1XY|\u8d8a\u5927\uff0c\u76f8\u5173\u7a0b\u5ea6\u8d8a\u5927\uff1b|\u03c1XY|=0\u5bf9\u5e94\u76f8\u5173\u7a0b\u5ea6\u6700\u4f4e\uff1b
\uff084\uff09\u82e5X\u548cY\u4e0d\u76f8\u5173\uff0c|\u03c1XY|=0\uff0c\u901a\u5e38\u8ba4\u4e3aX\u548cY\u4e4b\u95f4\u4e0d\u5b58\u5728\u7ebf\u6027\u5173\u7cfb\uff0c\u4f46\u5e76\u4e0d\u80fd\u6392\u9664X\u548cY\u4e4b\u95f4\u53ef\u80fd\u5b58\u5728\u5176\u4ed6\u5173\u7cfb\uff1b\u82e5|\u03c1XY|=0\uff0c\u5219X\u548cY\u4e0d\u76f8\u5173\uff1b
\uff085\uff09\u82e5X\u548cY\u72ec\u7acb\uff0c\u5219\u5fc5\u6709|\u03c1XY|=0\uff0c\u56e0\u800cX\u548cY\u4e0d\u76f8\u5173\uff1b\u82e5X\u548cY\u4e0d\u76f8\u5173\uff0c\u5219\u4ec5\u4ec5\u662f\u4e0d\u5b58\u5728\u7ebf\u6027\u5173\u7cfb\uff0c\u53ef\u80fd\u5b58\u5728\u5176\u4ed6\u5173\u7cfb\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u76f8\u5173\u7cfb\u6570

\u76f8\u5173\u7cfb\u6570\u7684\u53d6\u503c\u8303\u56f4\u662f\uff08-1\uff0c0\uff09\u6216\uff080\uff0c1\uff09\u3002
\u53d6\u503c\u8303\u56f4\u662f\uff08-1\uff0c0\uff09\u65f6\uff0c\u610f\u4e49\u4e3a\u8d1f\u76f8\u5173\uff1b\u53d6\u503c\u8303\u56f4\u662f\uff080\uff0c1\uff09\u65f6\uff0c\u610f\u4e49\u4e3a\u6b63\u76f8\u5173\u3002
\u62d3\u5c55\u8d44\u6599\u76f8\u5173\u7cfb\u6570

\u76f8\u5173\u5173\u7cfb\u662f\u4e00\u79cd\u975e\u786e\u5b9a\u6027\u7684\u5173\u7cfb\uff0c\u76f8\u5173\u7cfb\u6570\u662f\u7814\u7a76\u53d8\u91cf\u4e4b\u95f4\u7ebf\u6027\u76f8\u5173\u7a0b\u5ea6\u7684\u91cf\u3002\u7531\u4e8e\u7814\u7a76\u5bf9\u8c61\u7684\u4e0d\u540c\uff0c\u76f8\u5173\u7cfb\u6570\u6709\u5982\u4e0b\u51e0\u79cd\u5b9a\u4e49\u65b9\u5f0f\u3002
\u7b80\u5355\u76f8\u5173\u7cfb\u6570\uff1a\u53c8\u53eb\u76f8\u5173\u7cfb\u6570\u6216\u7ebf\u6027\u76f8\u5173\u7cfb\u6570\uff0c\u4e00\u822c\u7528\u5b57\u6bcdr \u8868\u793a\uff0c\u7528\u6765\u5ea6\u91cf\u4e24\u4e2a\u53d8\u91cf\u95f4\u7684\u7ebf\u6027\u5173\u7cfb\u3002
\u5b9a\u4e49\u5f0f

\u5176\u4e2d\uff0cCov(X,Y)\u4e3aX\u4e0eY\u7684\u534f\u65b9\u5dee\uff0cVar[X]\u4e3aX\u7684\u65b9\u5dee\uff0cVar[Y]\u4e3aY\u7684\u65b9\u5dee
\u590d\u76f8\u5173\u7cfb\u6570\uff1a\u53c8\u53eb\u591a\u91cd\u76f8\u5173\u7cfb\u6570\u3002\u590d\u76f8\u5173\u662f\u6307\u56e0\u53d8\u91cf\u4e0e\u591a\u4e2a\u81ea\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u5173\u7cfb\u3002\u4f8b\u5982\uff0c\u67d0\u79cd\u5546\u54c1\u7684\u5b63\u8282\u6027\u9700\u6c42\u91cf\u4e0e\u5176\u4ef7\u683c\u6c34\u5e73\u3001\u804c\u5de5\u6536\u5165\u6c34\u5e73\u7b49\u73b0\u8c61\u4e4b\u95f4\u5448\u73b0\u590d\u76f8\u5173\u5173\u7cfb\u3002
\u5178\u578b\u76f8\u5173\u7cfb\u6570\uff1a\u662f\u5148\u5bf9\u539f\u6765\u5404\u7ec4\u53d8\u91cf\u8fdb\u884c\u4e3b\u6210\u5206\u5206\u6790\uff0c\u5f97\u5230\u65b0\u7684\u7ebf\u6027\u5173\u7cfb\u7684\u7efc\u5408\u6307\u6807\uff0c\u518d\u901a\u8fc7\u7efc\u5408\u6307\u6807\u4e4b\u95f4\u7684\u7ebf\u6027\u76f8\u5173\u7cfb\u6570\u6765\u7814\u7a76\u539f\u5404\u7ec4\u53d8\u91cf\u95f4\u76f8\u5173\u5173\u7cfb\u3002

1为正相关 -1为负相关 0为不相关。因此越接近1越相关。如果用来排序的话,具体数值就无所谓了,只要看哪个大哪个就更相关。

[-1,1]相关系数的数值范围

  • 浠涔堝彨鐩稿叧绯绘暟
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