{"id":3091,"date":"2022-01-18T15:39:50","date_gmt":"2022-01-18T15:39:50","guid":{"rendered":"https:\/\/ricovictor.com\/?p=3091"},"modified":"2022-01-18T15:39:53","modified_gmt":"2022-01-18T15:39:53","slug":"regresion-lineal-multiple-mco-matricial","status":"publish","type":"post","link":"https:\/\/ricovictor.com\/index.php\/2022\/01\/18\/regresion-lineal-multiple-mco-matricial\/","title":{"rendered":"REGRESI\u00d3N LINEAL M\u00daLTIPLE| MCO MATRICIAL"},"content":{"rendered":"\n<p>El Modelo de Regresi\u00f3n Lineal M\u00faltiple permite generar un modelo lineal en el que el valor de la variable dependiente o respuesta(Y) se determina a partir de un conjunto de variables independientes llamadas predictores(X1, X2,X3 &#8230;&#8230; ). <strong>Este modelo puede emplearse para predecir el valor de la variable dependiente o para evaluar la influencia que tienen los predictores sobre ella<\/strong>. De manera evidente es una extensi\u00f3n de la Regresi\u00f3n lineal simple, por lo que es muy importante comprender esta \u00faltima. <\/p>\n\n\n\n<p>En la regresi\u00f3n simple nos bas\u00e1bamos en el <strong>m\u00e9todo de m\u00ednimos cuadrados ordinarios(MCO)<\/strong> para el c\u00e1lculo de las betas del modelo. En la regresi\u00f3n m\u00faltiple utilizaremos ese mismo m\u00e9todo pero en forma o notaci\u00f3n matricial. Por ello en el siguiente tutorial te explico como debes hacer ese proceso y hago el ejemplo paso a paso en R. Abajo dejo tambi\u00e9n el c\u00f3digo para que lo copies<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><\/code><\/pre>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"ast-oembed-container \" style=\"height: 100%;\"><iframe loading=\"lazy\" title=\"Modelo de Regresi\u00f3n Lineal M\u00daLTIPLE | M\u00ednimos Cuadrados en Notaci\u00f3n Matricial. Ejemplo en R\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/GlgEdz8k_3k?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/div>\n<\/div><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>#C\u00d3DIGO EN R DEL V\u00cdDEO\n\n#MODELO DE REGRESI\u00d3N LINEAL MULTIPLE \r\n\r\n\r\n\r\n#install.packages(\"quantmod\")\r\nlibrary(quantmod)\r\n#install.packages(\"tseries\")\r\nlibrary(tseries)\r\n#install.packages(\"fImport\")\r\nlibrary(fImport)\r\n#install.packages(\"forecast\")\r\nlibrary(forecast)\r\n#install.packages(\"TSA\")\r\nlibrary(TSA)\r\n#install.packages(\"Quandl\")\r\nlibrary(Quandl)\r\n#install.packages(\"lmtest\")\r\nlibrary(lmtest)\r\n#install.packages(\"stats\")\r\nlibrary(stats)\r\n\r\n\r\n#NOTACI\u00d3N MATRICIAL PARA MCO\r\n\r\n# Y= B0 + B1*X + B2*Z + .....+ U\r\n\r\n\r\n# EJEMPLO 1\r\n\r\nVENTAS &lt;- c(10,6,5,12,10,15,5,12,17,20) # Y\r\n\r\nPRECIO &lt;- c(1.30,2,1.7,1.5,1.6,1.2,1.6,1.4,1,1.10) #X\r\n\r\nPUBLICIDAD &lt;- c(9,7,5,14,15,12,6,10,15,21) #x2 O Z\r\n\r\n\r\nplot(VENTAS,type=\"l\")\r\nplot(PRECIO,type=\"l\")\r\nplot(PUBLICIDAD,type=\"l\")\r\n\r\n\r\n#B = ((TRAS_X*X)-1) * (TRAS_X*Y)\r\n\r\n\r\n#PASOS\r\n\r\n#1 CONSTRUIR LA MATRIX X \r\n\r\nintercepto&lt;- c(1,1,1,1,1,1,1,1,1,1)\r\n\r\nx&lt;- data.frame(intercepto,PRECIO,PUBLICIDAD)\r\n\r\nmatriz_X &lt;- cbind(intercepto,PRECIO,PUBLICIDAD) #10*3\r\n\r\n\r\n\r\n# 2. HACER LA TRANSPUESTA (cambiar filas por columnas)\r\n\r\ntras_X &lt;- t(matriz_X)   #3*10\r\ntras_X\r\n\r\n# MULTIPLICACION E INVERSA\r\n\r\nmulti_X &lt;- tras_X %*% matriz_X  #3*3\r\nmulti_X \r\n\r\ninversa &lt;- solve(multi_X)   \r\n\r\nY &lt;- cbind(VENTAS) #10*1\r\n\r\n# inversa * XT*Y\r\n\r\nmulti_X_Y &lt;- tras_X %*% Y\r\nmulti_X_Y\r\n\r\n#B = ((TRAS_X*X)-1) * (TRAS_X*Y)\r\n\r\nbetas &lt;- inversa %*% multi_X_Y\r\n\r\n\r\nbetas&#91;1] #intercepto\r\nbetas&#91;2] # beta1\r\nbetas&#91;3] #beta 2 \r\n\r\n                    #int     \r\ny_pronosticada &lt;- betas&#91;1]+ betas&#91;2]*PRECIO + betas&#91;3]*PUBLICIDAD\r\ny_pronosticada\r\n\r\n\r\n\r\n#***** comprobamos con la funci\u00f3n de R\r\n\r\nmodelo &lt;-lm(VENTAS ~ PRECIO + PUBLICIDAD)\r\nsummary(modelo)\r\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>El Modelo de Regresi\u00f3n Lineal M\u00faltiple permite generar un modelo lineal en el que el valor de la variable dependiente o respuesta(Y) se determina a partir de un conjunto de variables independientes llamadas predictores(X1, X2,X3 &#8230;&#8230; ). Este modelo puede emplearse para predecir el valor de la variable dependiente o para evaluar la influencia que &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/ricovictor.com\/index.php\/2022\/01\/18\/regresion-lineal-multiple-mco-matricial\/\"> <span class=\"screen-reader-text\">REGRESI\u00d3N LINEAL M\u00daLTIPLE| MCO MATRICIAL<\/span> Leer m\u00e1s &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":3093,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[2],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>REGRESI\u00d3N LINEAL M\u00daLTIPLE| MCO MATRICIAL - V\u00edctor A. 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