{"id":1024,"date":"2024-01-03T02:23:18","date_gmt":"2024-01-03T02:23:18","guid":{"rendered":"https:\/\/lasstatistique.com\/?p=1024"},"modified":"2024-08-14T02:53:37","modified_gmt":"2024-08-14T02:53:37","slug":"cours-4-stata","status":"publish","type":"post","link":"https:\/\/lasstatistique.com\/?p=1024","title":{"rendered":"Cours 4 : STATA"},"content":{"rendered":"<p><span style=\"color: #000080;\"><b>CHAPITRE V : LA REGRESSION LINEAIRE<\/b><\/span><\/p>\n<p><span style=\"color: #000080;\"><b><i>D\u00e9finition et hypoth\u00e8ses<\/i><\/b><\/span><\/p>\n<ul>\n<li>La r\u00e9gression lin\u00e9aire est une des techniques les plus simple pour expliquer une variable quantitative continue en fonction d\u2019autres variables.<\/li>\n<\/ul>\n<p>Math\u00e9matiquement on cherche \u00e0 estimer le vecteur de param\u00e8tre \u03b2\u00a0 dans l\u2019\u00e9quation : <span style=\"color: #000080;\">\u00a0y=X\u03b2+ \u03b5<\/span><\/p>\n<p>O\u00f9 y est le vecteur des observations de la variable \u00e0 expliquer, X la matrice des variables explicatives et \u03b5 le vecteur des erreurs.<\/p>\n<ul>\n<li>La commande<span style=\"color: #000080;\"> Stata<\/span> qui permet de r\u00e9aliser une r\u00e9gression lin\u00e9aire est <span style=\"color: #000080;\">regress<\/span>.<\/li>\n<li>Syntaxe :<span style=\"color: #000080;\"> regress y var1 var2 \u2026 varn<\/span> o\u00f9 y est la variable \u00e0 expliquer et<span style=\"color: #000080;\"> Var1, var2, \u2026 ,varn <\/span>sont les variables explicatives.<\/li>\n<\/ul>\n<p>Pour valider notre mod\u00e8le lin\u00e9aire apr\u00e8s estimation, on doit v\u00e9rifier les hypoth\u00e8ses suivantes sur les r\u00e9sidus :<\/p>\n<p><span style=\"color: #000080;\">H1 : Les erreurs sont de moyenne nulle<\/span><\/p>\n<p><span style=\"color: #000080;\">H2 : La variance des erreurs est constante (Homosc\u00e9dasticit\u00e9)<\/span><\/p>\n<p><span style=\"color: #000080;\">H3 : Les erreurs sont ind\u00e9pendants<\/span><\/p>\n<p><span style=\"color: #000080;\">H4 : Les erreurs suivent une loi normale<\/span><\/p>\n<p><span style=\"color: #000080;\"><b><i>Cas pratique<\/i><\/b><\/span><\/p>\n<ul>\n<li>En guise d\u2019illustration pour cette partie, supposons qu\u2019on veut expliquer la consommation (<span style=\"color: #000080;\">CONS<\/span>) des m\u00e9nages par le pib par habitant not\u00e9 PIBR et l\u2019indice des prix \u00e0 la consommation not\u00e9 IPC.<\/li>\n<\/ul>\n<p>On a le mod\u00e8le :\u00a0<span style=\"color: #000080;\"> CONS = \u03b1PIBR+ \u03b2IPC+ \u03b5<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1025\" src=\"https:\/\/lasstatistique.com\/wp-content\/uploads\/2024\/01\/Capture-9-300x104.png\" alt=\"\" width=\"730\" height=\"253\" srcset=\"https:\/\/lasstatistique.com\/wp-content\/uploads\/2024\/01\/Capture-9-300x104.png 300w, https:\/\/lasstatistique.com\/wp-content\/uploads\/2024\/01\/Capture-9-768x267.png 768w, https:\/\/lasstatistique.com\/wp-content\/uploads\/2024\/01\/Capture-9.png 889w\" sizes=\"auto, (max-width: 730px) 100vw, 730px\" \/><\/p>\n<p>Les r\u00e9sultats de commande<span style=\"color: #000080;\"> regress <\/span>sont pr\u00e9sent\u00e9s dans le tableau pr\u00e9c\u00e9dent.<\/p>\n<p>Dans la partie haute du tableau, on retrouve le<span style=\"color: #000080;\"> R2<\/span> et le <span style=\"color: #000080;\">R2 ajust\u00e9<\/span> au nombre d\u2019explicatives. Ils donnent la le pourcentage de variance expliqu\u00e9e par notre mod\u00e8le (<span style=\"color: #000080;\">0,97 ou 97%<\/span>). On y retrouve \u00e9galement la statistique de<span style=\"color: #000080;\"> Fisher<\/span> et la<span style=\"color: #000080;\"> p-value<\/span> associ\u00e9e (<span style=\"color: #000080;\">0,0000<\/span>) qui montre que notre mod\u00e8le est globalement significatif.<\/p>\n<p>La seconde partie donnes la liste des coefficients estim\u00e9s et leurs valeurs et p-value. Une variable est significative au seuil de<span style=\"color: #000080;\"> 5%<\/span> si la <span style=\"color: #000080;\">p-value<\/span> associ\u00e9 \u00e0 l\u2019estimation de son coefficient est inf\u00e9rieure \u00e0 <span style=\"color: #000080;\">0,05<\/span>. Dans notre cas, les 2 variables sont significatives.<\/p>\n<p><span style=\"color: #000080;\"><strong><i>Tests Post estimation<\/i><\/strong><\/span><\/p>\n<p>Test apr\u00e8s estimation : Apres estimation de notre mod\u00e8le, il est important d\u2019effectuer des tests afin de valider le mod\u00e8le. Il s\u2019agit du test d\u2019endog\u00e9n\u00e9it\u00e9, du test de normalit\u00e9 des r\u00e9sidus, du test d\u2019homosc\u00e9dasticit\u00e9 et du test de multi colin\u00e9arit\u00e9.<\/p>\n<ul>\n<li><span style=\"color: #000080;\">Test d\u2019endog\u00e9n\u00e9it\u00e9<\/span> : La pr\u00e9sence de variable endog\u00e8ne conduira \u00e0 des estimations biais\u00e9es. Pour corriger cet effet, on utilise g\u00e9n\u00e9ralement des variables instrumentales. Dans le cas de notre exemple, on fait le test de<span style=\"color: #000080;\"> Durbon<\/span> et<span style=\"color: #000080;\"> Wu Hausman<\/span>:<span style=\"color: #000080;\"> estat endogenous<\/span><\/li>\n<\/ul>\n<ul>\n<li><span style=\"color: #000080;\">Test de multi colin\u00e9arit\u00e9<\/span> : Pour v\u00e9rifier la multi colin\u00e9arit\u00e9 on peut utiliser le <span style=\"color: #000080;\">vif<\/span>. La syntaxe est : <span style=\"color: #000080;\">estat vif<\/span><\/li>\n<\/ul>\n<p>Aussi, on peut avoir une id\u00e9e gr\u00e2ce \u00e0 la matrice de corr\u00e9lation en utilisant <span style=\"color: #000080;\">pwcorr<\/span>. Lorsqu\u2019on a deux variables explicatives significativement corr\u00e9l\u00e9es, on garde un seul des deux ou bien on fait la moyenne des deux.<\/p>\n<ul>\n<li><span style=\"color: #000080;\">Test de normalit\u00e9 des r\u00e9sidus<\/span> : On peut utiliser le test de Shapiro<span style=\"color: #000080;\"> Wilk<\/span> vu pr\u00e9c\u00e9demment sur les r\u00e9sidus de la r\u00e9gression.<\/li>\n<\/ul>\n<p><span style=\"color: #000080;\">Predict residual, resid #<\/span> Pour cr\u00e9er la variable \u00ab<span style=\"color: #000080;\">\u00a0residual<\/span>\u00a0\u00bb vecteur des r\u00e9sidus<\/p>\n<p><span style=\"color: #000080;\">\u00a0swilk residual\u00a0 #<\/span>Fait le test de normalit\u00e9 sur le vecteur de r\u00e9sidu<\/p>\n<ul>\n<li><span style=\"color: #000080;\">Test d\u2019homosc\u00e9dasticit\u00e9<\/span> : On peut utiliser le test de<span style=\"color: #000080;\"> Breush pagan<\/span> donn\u00e9 par la commande<span style=\"color: #000080;\"> hettest<span style=\"color: #000000;\">.<\/span><\/span> L\u2019hypoth\u00e8se nulle est l\u2019homog\u00e9n\u00e9it\u00e9 des r\u00e9sidus.<\/li>\n<\/ul>\n<p>Syntaxe : <span style=\"color: #000080;\">estat hettest<\/span><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>CHAPITRE V : LA REGRESSION LINEAIRE D\u00e9finition et hypoth\u00e8ses La r\u00e9gression lin\u00e9aire est une des techniques les plus simple pour<\/p>\n","protected":false},"author":1,"featured_media":1000,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"colormag_page_container_layout":"default_layout","colormag_page_sidebar_layout":"default_layout","footnotes":""},"categories":[40,44],"tags":[],"class_list":["post-1024","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cours","category-stata"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - 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