<div class="article_data_left">2018-03-15<span class="a_username"> <a href="http://www.360doc.com/userhome/48898194" id="savernickname" target="_blank" onclick="artStatistics('20-7-1');">Greatguy瑞</a></span><span id="articleinfo"><span id="docsource" class="a_from" style="display: none;"> <a href="http://blog.csdn.net/northeastsqure/article/details/50163031" target="_blank" onclick="artStatistics('20-12');">来源</a></span><span id="360doc_Readnum"> 阅 1652 </span><span id="360docResaveCount" style="display: none;"><span onclick="ShowSaverUser();artStatistics('20-13');" id="360doc_saverNum" style="cursor: pointer;"></span><span id="360doc_saverUser"><div style="position: absolute; height: 305px; width: 144px; left: 0px; z-index: 2;" id="sameArtOuter"><div onclick="event.cancelBubble=true;" style="overflow-y: auto; height: 300px; overflow-x: hidden; z-index: 100; right: 0px; margin-top: -10px;" id="sameArt"></div></div></span></span></span></div><div id="resavelayer1" class="bdsharebuttonbox article_data_right bdshare-button-style0-16" data-bd-bind="1582275510035"><div class="zcommond"><a class="p2" href="javascript:void(0);" onclick="SaveArt();artStatistics('20-3-1');">转藏到我的图书馆</a><div class="s2 f_right" onclick="setTimeout(function(){$('.article_data_right .sharelist_new').slideToggle(0);},10);"><span onclick="artStatistics('20-8-2');"></span></div><a class="p1" href="javascript:void(0);" onclick="shareWeixin();artStatistics('20-8-5');shareStatic.addStatic();pushUserInterestRedis(4);">微信</a> <span class="s1" onclick="setTimeout(function(){$('.article_data_right .sharelist_new').slideToggle(0);},10);artStatistics('20-8-1');" onmouseover="this.style.color='#0f659c'" onmouseout="this.style.color=''">分享：</span></div><div class="sharelist_new" id="fenxiangLayer"> <a class="slbg1" href="javascript:void(0);" data-cmd="qzone" onclick="artStatistics('20-8-7');shareStatic.addStatic();pushUserInterestRedis(4);">QQ空间</a> <a class="slbg2" href="javascript:void(0);" data-cmd="sqq" onclick="artStatistics('20-8-9');shareStatic.addStatic();pushUserInterestRedis(4);">QQ好友</a> <a class="slbg3" href="javascript:void(0);" data-cmd="tsina" onclick="artStatistics('20-8-11');shareStatic.addStatic();pushUserInterestRedis(4);">新浪微博</a><a class="slbg5" href="javascript:void(0);" onclick="showdivemail1();artStatistics('20-8-15');shareStatic.addStatic();pushUserInterestRedis(4);">推荐给朋友</a> </div><div style="position: absolute;display:none;z-index:1;left:143px;" id="fuzhitishidiv"></div></div></div><div id="articlecontent" class="article_container" onmousedown="newhighlight = true;" onmouseup="NewHighlight(event);"><div class="article_showall"><div><a href="javascript:void(0);" onclick="$('body').removeClass('articleMaxH')" datatype="360doczkqw">展开全文</a></div></div><table style="width: 656px;"><tbody><tr><td id="artContent" style="max-width: 656px"><div style="width: 656px; margin: 0; padding: 0; height: 0;"></div><p>协方差代表了两个变量之间的是否同时偏离均值。</p><p><img src="http://1053.edu.pinggu.com/forum/201410/09/101133h1w1dhc1d7v9db1f.png" alt="3a6f9c262fc67167d50742c3.png" title="3a6f9c262fc67167d50742c3.png"><span> </span><br></p><p>如果正相关，这个计算公式，每个样本对（Xi, Yi）, 每个求和项大部分都是正数，即两个同方向偏离各自均值，而不同时偏离的也有，但是少，这样当样本多时，总和结果为正。下面这个图就很直观。下面转载自：http://blog.csdn.net/wuhzossibility/article/details/8087863</p><p></p><p align="center"><span>在概率论中，两个随机变量 X 与 Y 之间相互关系，大致有下列3种情况：</span></p><p align="center"><img src="http://image109.360doc.com/DownloadImg/2018/03/1517/127287968_1_20180315054300878.jpg" alt=""><br></p><p align="center"></p><p><span><span></span>当 X, Y 的联合分布像上图那样时，我们可以看出，大致上有： X 越大 Y 也越大， X 越小 Y 也越小，这种情况，我们称为“<strong><span>正相关</span></strong>”。</span></p><p><span><img src="http://image109.360doc.com/DownloadImg/2018/03/1517/127287968_2_2018031505430135.jpg" alt=""><br></span></p><p><span></span></p><p><span></span>当X, Y 的联合分布像上图那样时，我们可以看出，大致上有：X 越大Y 反而越小，X 越小 Y 反而越大，这种情况，我们称为“<strong><span>负相关</span></strong>”。</p><div><img src="http://image109.360doc.com/DownloadImg/2018/03/1517/127287968_3_20180315054301331.jpg" alt=""></div><div><span></span>当X, Y 的联合分布像上图那样时，我们可以看出：既不是X 越大Y 也越大，也不是 X 越大 Y 反而越小，这种情况我们称为“<strong><span>不相关</span></strong>”。<br></div><div><p>怎样将这3种相关情况，用一个简单的数字表达出来呢？</p><p><span></span>在图中的区域（1）中，有 X>EX ，Y-EY>0 ，所以(X-EX)(Y-EY)>0；</p><p><span></span>在图中的区域（2）中，有 <span>X<ex ，y-ey="">0 ，</ex></span>所以<span>(X-EX)(Y-EY)<></span></p><p><span></span>在图中的区域（3）中，有 <span>X<ex></ex><0><!--0--></span>所以<span>(X-EX)(Y-EY)>0；</span></p><p><span></span>在图中的区域（4）中，有 <span>X>EX ，Y-EY<0><!--0--></span>所以<span>(X-EX)(Y-EY)<></span>。</p><p><strong><span><span></span>当</span>X </strong><span><strong>与</strong></span><strong>Y </strong><span><strong>正相关</strong></span><span><strong>时，它们的分布大部分在区域（</strong></span><span><strong>1</strong></span><span><strong>）和（</strong></span><span><strong>3</strong></span><span><strong>）中，小部分在区域（</strong></span><span><strong>2</strong></span><span><strong>）和（</strong></span><span><strong>4</strong></span><strong><span>）中，所以平均来说，有</span><span>E</span>(<span>X-EX)(Y-EY)>0</span> </strong><span><strong>。</strong></span></p><p><strong><span><span></span>当</span> X<span>与</span><span> </span>Y<span>负相关</span><span>时，它们的分布大部分在区域（</span><span>2</span><span>）和（</span><span>4</span><span>）中，小部分在区域（</span><span>1</span><span>）和（</span><span>3</span><span>）中，所以平均来说，有</span><span><strong>(X-EX)(Y-EY)<></strong></span><span> </span><span><strong>。</strong></span><span></span></strong></p><p><strong><span><span></span>当</span> X<span>与</span> Y<span>不相关</span><span>时，它们在区域（</span><span>1</span><span>）和（</span><span>3</span><span>）中的分布，与在区域（</span><span>2</span><span>）和（</span><span>4</span><span>）中的分布几乎一样多，所以平均来说，有</span><span><strong>(X-EX)(Y-EY)=0</strong></span><span> </span><span><strong>。</strong></span><span></span></strong></p><span></span><span>所以，我们可以定义一个表示X, Y 相互关系的数字特征，也就是</span><span><strong><span><a href="http://zh.wikipedia.org/wiki/%E5%8D%8F%E6%96%B9%E5%B7%AE">协方差</a></span></strong></span></div><div><div>cov(X, Y) = E(X-EX)(Y-EY)<span>。</span></div><span></span><p><strong><span>当</span> <span>cov(X, Y)>0</span></strong><span><strong>时，</strong></span><span><strong>表明</strong></span><span> X</span><span><strong>与</strong></span><span>Y</span><span> </span><span><strong>正相关</strong></span><span><strong>；</strong></span></p><span></span><p><strong><span>当</span> <span><strong>cov(X, Y)<></strong></span><span>时，表明</span><span><strong>X</strong></span><span><strong>与</strong></span><span><strong>Y</strong></span><span>负相关</span><span>；</span></strong></p><p><strong><span>当 </span><span><strong><strong>cov(X, Y)=0</strong></strong></span><span>时，表明</span><span><strong>X</strong></span><span><strong>与</strong></span><span><strong>Y</strong></span><span>不相关</span><span>。</span></strong></p><p>这就是协方差的意义。</p></div><br><p><br></p></td></tr></tbody></table><!--阅读全文（测试用，现在可能不用了）--><div id="viewerPlaceHolder" style="width: 717px; 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