Les logiciels d'analyse statistique

fr Covariance

en Covariance

en <p>The covariance is a measurement data item about the strength of correlation between a set (2 or more) of random variables. The covariance is obtained by forming :</p>

<p><a href="https://www.codecogs.com/eqnedit.php?latex=cov(X,Y)=\sum_{i=1}^{N}\frac{(X_{i}-\overline{X})(Y_{i}-\overline{Y})}{N}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?cov(X,Y)=\sum_{i=1}^{N}\frac{(X_{i}-\overline{X})(Y_{i}-\overline{Y})}{N}" title="cov(X,Y)=\sum_{i=1}^{N}\frac{(X_{i}-\overline{X})(Y_{i}-\overline{Y})}{N}" /></a><br />
where <a href="https://www.codecogs.com/eqnedit.php?latex=\overline{X}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\overline{X}" title="\overline{X}" /></a>&nbsp;,&nbsp;&nbsp;<a href="https://www.codecogs.com/eqnedit.php?latex=\overline{Y}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\overline{Y}" title="\overline{Y}" /></a>&nbsp; is the expected value (mean) of variable X and Y respectively. Covariance is symmetric so cov(X,Y)=cov(Y,X). The covariance is usefull when looking at the variance of the sum of the 2 random variables since : var(X+Y) = var(X) +var(Y) +2cov(X,Y). The covariance cov(x,y) is used to obtain the coefficient of correlation cor(x,y) by normalizing (dividing) cov(x,y) but the product of the standard deviations of x and y.</p>

fr <p>La covariance est une donn&eacute;e de mesure de la force de corr&eacute;lation entre un ensemble (2 ou plus) de variables al&eacute;atoires. La covariance est obtenue par la formule :</p>

<p><a href="https://www.codecogs.com/eqnedit.php?latex=cov(X,Y)=\sum_{i=1}^{N}\frac{(X_{i}-\overline{X})(Y_{i}-\overline{Y})}{N}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?cov(X,Y)=\sum_{i=1}^{N}\frac{(X_{i}-\overline{X})(Y_{i}-\overline{Y})}{N}" title="cov(X,Y)=\sum_{i=1}^{N}\frac{(X_{i}-\overline{X})(Y_{i}-\overline{Y})}{N}" /></a><br />
o&ugrave;&nbsp;<a href="https://www.codecogs.com/eqnedit.php?latex=\overline{X}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\overline{X}" title="\overline{X}" /></a>&nbsp;,&nbsp;&nbsp;<a href="https://www.codecogs.com/eqnedit.php?latex=\overline{Y}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\overline{Y}" title="\overline{Y}" /></a>&nbsp;est la valeur attendue (moyenne) des variables X et Y respectivement.&nbsp;</p>

<p>covariance est sym&eacute;trique donc cov(X,Y)=cov(Y,X).</p>

<p>La covariance est utile lorsque l&#39;on regarde la variance de la somme des 2 variables al&eacute;atoires depuis :&nbsp;var(X+Y) = var(X) +var(Y) +2cov(X,Y).&nbsp;La covariance cov(x,y) est utilis&eacute;e pour obtenir le coefficient de corr&eacute;lation cor(x,y) en normalisant (divisant) cov(x,y) mais le produit des &eacute;carts types de x et y.</p>

en Alejandra Gonzalez-Beltran

en Philippe Rocca-Serra

en Orlaith Burke

fr Jean-Marc Meunier

<p>adapted from :&nbsp;<a href="http://mathworld.wolfram.com/Covariance.html" onclick="window.open(this.href, '', 'resizable=yes,status=no,location=no,toolbar=no,menubar=no,fullscreen=no,scrollbars=yes,dependent=no'); return false;">http://mathworld.wolfram.com/Covariance.html</a>&nbsp;and&nbsp;<a href="https://fr.wikipedia.org/wiki/Covariance" onclick="window.open(this.href, '', 'resizable=yes,status=no,location=no,toolbar=no,menubar=no,fullscreen=no,scrollbars=yes,dependent=no'); return false;">https://fr.wikipedia.org/wiki/Covariance</a></p>

en Covariance

<p>cov(x, y = NULL, use = &quot;everything&quot;, method = c(&quot;pearson&quot;, &quot;kendall&quot;, &quot;spearman&quot;))</p>

<p>from :&nbsp;<a href="http://stat.ethz.ch/R-manual/R-patched/library/stats/html/cor.html" onclick="window.open(this.href, '', 'resizable=yes,status=no,location=no,toolbar=no,menubar=no,fullscreen=no,scrollbars=yes,dependent=no'); return false;">http://stat.ethz.ch/R-manual/R-patched/library/stats/html/cor.html</a></p>

<p>Traductions :&nbsp;<a href="http://isi.cbs.nl/glossary/term787.htm" onclick="window.open(this.href, '', 'resizable=yes,status=no,location=no,toolbar=no,menubar=no,fullscreen=no,scrollbars=yes,dependent=no'); return false;">http://isi.cbs.nl/glossary/term787.htm</a></p>

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