{"id":907,"date":"2018-10-06T14:46:48","date_gmt":"2018-10-06T14:46:48","guid":{"rendered":"http:\/\/lash.utrng.edu.mx\/?p=907"},"modified":"2018-10-06T15:34:47","modified_gmt":"2018-10-06T15:34:47","slug":"coeficientes-de-correlacion-y-determinacion","status":"publish","type":"post","link":"https:\/\/lash.utrng.edu.mx\/?p=907","title":{"rendered":"Coeficientes de correlaci\u00f3n y determinaci\u00f3n"},"content":{"rendered":"\n<p>La media y desviaci\u00f3n t\u00edpica(est\u00e1ndar)<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/media-DesvStdr.png\"><img loading=\"lazy\" decoding=\"async\" width=\"433\" height=\"174\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/media-DesvStdr.png\" alt=\"\" class=\"wp-image-908\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/media-DesvStdr.png 433w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/media-DesvStdr-300x121.png 300w\" sizes=\"auto, (max-width: 433px) 100vw, 433px\" \/><\/a><\/figure><\/div>\n\n\n\n<!--more-->\n\n\n\n<p>Ejemplo. Se indica a continuaci\u00f3n el peso, X, (kg) y la estatura, Y , (cm) de 12 personas:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/t04.png\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"163\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/t04.png\" alt=\"\" class=\"wp-image-909\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/t04.png 936w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/t04-300x52.png 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/t04-768x134.png 768w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/a><\/figure>\n\n\n\n<p>En el Ejemplo anterior, se tiene:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"726\" height=\"39\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/media-DesvStdr-2.png\" alt=\"\" class=\"wp-image-910\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/media-DesvStdr-2.png 726w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/media-DesvStdr-2-300x16.png 300w\" sizes=\"auto, (max-width: 726px) 100vw, 726px\" \/><\/figure>\n\n\n\n<p>Para calcular un valor t\u00edpico que exprese el grado de relaci\u00f3n (o correlaci\u00f3n) lineal entre ambas variables en la muestra, diferente a los resultados obtenidos, \u00e9stos se deben conjugar.<\/p>\n\n\n\n<p><strong>Covarianza<\/strong>: la covarianza muestral es una primera medida del grado de correlaci\u00f3n y se define mediante:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/cova.png\"><img loading=\"lazy\" decoding=\"async\" width=\"328\" height=\"72\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/cova.png\" alt=\"\" class=\"wp-image-911\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/cova.png 328w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/cova-300x66.png 300w\" sizes=\"auto, (max-width: 328px) 100vw, 328px\" \/><\/a><\/figure><\/div>\n\n\n\n<p>La covarianza, en el caso del Ejemplo anterior se expresar\u00e1 en kg.cm, puede ser tanto positiva como negativa, pero puede probarse que debe estar comprendida entre los siguientes valores:<\/p>\n\n\n\n<p><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"340\" height=\"41\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/cov2.png\" alt=\"\" class=\"wp-image-912\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/cov2.png 340w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/cov2-300x36.png 300w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/figure><\/div>\n\n\n\n<p>s<sub>xy<\/sub> debe estar comprendida entre -630.71 y 630.71. A trav\u00e9s del programa estad\u00edstico obtenemos su valor concreto en este caso, que es s<sub>xy<\/sub> = 577:86 kg.cm.<\/p>\n\n\n\n<p><strong>Coeficiente de correlaci\u00f3n lineal de Pearson<\/strong>: supone una medida adimensional de grado de correlaci\u00f3n lineal observado en la muestra y se define como sigue:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/coe01.png\"><img loading=\"lazy\" decoding=\"async\" width=\"151\" height=\"67\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/coe01.png\" alt=\"\" class=\"wp-image-913\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/coe01.png 151w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/coe01-150x67.png 150w\" sizes=\"auto, (max-width: 151px) 100vw, 151px\" \/><\/a><\/figure><\/div>\n\n\n\n<p>Este par\u00e1metro, que se denota normalmente de forma simplificada por r, se interpreta en los mismos t\u00e9rminos que la covarianza con la salvedad de que se encuentra en todo caso entre -1 y 1 y alcanza esos valores cuando se da en la muestra una correlaci\u00f3n lineal perfecta, bien sea inversa o directa, respectivamente. La proximidad a 0 indica que en la muestra se observa escasa correlaci\u00f3n lineal. As\u00ed, los datos del Ejemplo corresponden a r = 0.916.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>La media y desviaci\u00f3n t\u00edpica(est\u00e1ndar)<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[29],"tags":[],"class_list":["post-907","post","type-post","status-publish","format-standard","hentry","category-primerparcialestadistica"],"_links":{"self":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/907","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=907"}],"version-history":[{"count":5,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/907\/revisions"}],"predecessor-version":[{"id":919,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/907\/revisions\/919"}],"wp:attachment":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=907"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=907"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=907"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}