{"id":160,"date":"2008-04-29T22:56:09","date_gmt":"2008-04-29T20:56:09","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/regression-lineaire-avec-xcas\/"},"modified":"2023-10-14T20:14:04","modified_gmt":"2023-10-14T18:14:04","slug":"regression-lineaire-avec-xcas","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/","title":{"rendered":"R\u00e9gression lin\u00e9aire avec Xcas"},"content":{"rendered":"

\nVoici comment on peut r\u00e9soudre un exercice classique sur les statistiques \u00e0 deux variables.<\/p>\n

Enonc\u00e9<\/h2>\n
\n

Le tableau suivant donne la population d’une ville nouvelle entre less ann\u00e9es 1970 et 2000. <\/p>\n\n\n\n\n\n\n
Ann\u00e9e <\/td>\n 1970 <\/td>\n 1975 <\/td>\n 1980 <\/td>\n 1985 <\/td>\n 1990 <\/td>\n 1995 <\/td>\n 2000<\/td>\n<\/tr>\n
Rang de l’ann\u00e9e $x$ <\/td>\n 0 <\/td>\n 5 <\/td>\n 10 <\/td>\n15 <\/td>\n 20 <\/td>\n 25 <\/td>\n 30<\/td>\n<\/tr>\n
Population en milliers <\/td>\n <\/td>\n <\/td>\n <\/td>\n <\/td>\n <\/td>\n <\/td>\n <\/td>\n<\/tr>\n
d’habitants $y$ <\/td>\n 18<\/td>\n 21<\/td>\n 25<\/td>\n 30<\/td>\n 36<\/td>\n42<\/td>\n 50<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

1) D\u00e9terminer les coordonn\u00e9es du point moyen du nuage de points correspondants.<\/p>\n

2) D\u00e9terminer une \u00e9quation de la droite d’ajustement affine de $y$ en $x$ par la m\u00e9thode des moindres carr\u00e9s. <\/p>\n

3) D\u00e9duire de cet ajustement une estimation de la population en 2003, \u00e0 un millier pr\u00e8s. <\/p>\n

4) Tracer dans un rep\u00e8re le nuage de points et la droite de r\u00e9gression.<\/p>\n

R\u00e9solution \u00e0 l’aide de Xcas<\/h2>\n
\n

\n\nX:=[0,5,10,15,20,25,30]\n<\/code>\n<\/font color><\/p>\n

$$[0,5,10,15,20,25,30]$$<\/p>\n

\n\nY:=[18,21,25,30,36,42,50]\n<\/code>\n<\/font color><\/p>\n

$$[18,21,25,30,36,42,50]$$<\/p>\n

1) D\u00e9terminer les coordonn\u00e9es du point moyen du nuage de points correspondants.<\/p>\n

\n\nmoyenne(X)\n<\/code>\n<\/font color><\/p>\n

$$15$$<\/p>\n

\n\nmoyenne(Y)\n<\/code>\n<\/font color><\/p>\n

$$\\dfrac222<\/em>7<\/em>$$<\/p>\n

2) D\u00e9terminer une \u00e9quation de la droite d’ajustement affine de $y$ en $x$ par la m\u00e9thode des moindres carr\u00e9s. <\/p>\n

\n\nlinear_regression(X,Y)\n<\/code>\n<\/font color><\/p>\n

$$\\dfrac149<\/em>140<\/em> \\quad , \\quad \\dfrac63<\/em>4<\/em>$$<\/p>\n

d’o\u00f9 $y=\\dfrac149<\/em>140<\/em>x+\\dfrac63<\/em>4<\/em>$.<\/p>\n

3) D\u00e9duire de cet ajustement une estimation de la population en 2003, \u00e0 un millier pr\u00e8s. <\/p>\n

\n\nest(x):=149\/140*x+63\/4\n<\/code>\n<\/font color><\/p>\n

$$x-> \\dfrac149<\/em>140<\/em>x+\\dfrac63<\/em>4<\/em>$$<\/p>\n

\n\nevalf(est(33))\n<\/code>\n<\/font color><\/p>\n

$$50.8714285714$$<\/p>\n

4) Tracer dans un rep\u00e8re le nuage de points et la droite de r\u00e9gression.<\/p>\n

\n\nscatterplot(X,Y,affichage=bleu+point_width_3),linear_regression_plot(X,Y,affichage=rouge+line_width_3)\n<\/code>\n<\/font color><\/p>\n

\"regression.jpg\"<\/p>\n

<\/math><\/p>\n","protected":false},"excerpt":{"rendered":"

Voici comment on peut r\u00e9soudre un exercice classique sur les statistiques \u00e0 deux variables. Enonc\u00e9 Le tableau suivant donne la population d’une ville nouvelle entre less ann\u00e9es 1970 et 2000.…<\/p>\n","protected":false},"author":1,"featured_media":663,"parent":2228,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-160","page","type-page","status-publish","has-post-thumbnail","hentry"],"yoast_head":"\nR\u00e9gression lin\u00e9aire avec Xcas - Maths & Num\u00e9rique<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"R\u00e9gression lin\u00e9aire avec Xcas - Maths & Num\u00e9rique\" \/>\n<meta property=\"og:description\" content=\"Voici comment on peut r\u00e9soudre un exercice classique sur les statistiques \u00e0 deux variables. Enonc\u00e9 Le tableau suivant donne la population d’une ville nouvelle entre less ann\u00e9es 1970 et 2000.…\" \/>\n<meta property=\"og:url\" content=\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/\" \/>\n<meta property=\"og:site_name\" content=\"Maths & Num\u00e9rique\" \/>\n<meta property=\"article:modified_time\" content=\"2023-10-14T18:14:04+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2008\/04\/jpg_regression.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"599\" \/>\n\t<meta property=\"og:image:height\" content=\"239\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/\",\"url\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/\",\"name\":\"R\u00e9gression lin\u00e9aire avec Xcas - Maths & Num\u00e9rique\",\"isPartOf\":{\"@id\":\"https:\/\/wordpress.callac.online\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2008\/04\/jpg_regression.jpg\",\"datePublished\":\"2008-04-29T20:56:09+00:00\",\"dateModified\":\"2023-10-14T18:14:04+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/#primaryimage\",\"url\":\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2008\/04\/jpg_regression.jpg\",\"contentUrl\":\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2008\/04\/jpg_regression.jpg\",\"width\":599,\"height\":239,\"caption\":\"regression.jpg\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\/\/wordpress.callac.online\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Logiciels math\u00e9matiques\",\"item\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Xcas\",\"item\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Statistiques avec Xcas\",\"item\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/\"},{\"@type\":\"ListItem\",\"position\":5,\"name\":\"R\u00e9gression lin\u00e9aire avec Xcas\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/wordpress.callac.online\/#website\",\"url\":\"https:\/\/wordpress.callac.online\/\",\"name\":\"Maths & Num\u00e9rique\",\"description\":\"Des outils pour les enseignants de math\u00e9matiques et de num\u00e9rique\",\"publisher\":{\"@id\":\"https:\/\/wordpress.callac.online\/#\/schema\/person\/04061f1ca2c2c42039142a704be95940\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/wordpress.callac.online\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"fr-FR\"},{\"@type\":[\"Person\",\"Organization\"],\"@id\":\"https:\/\/wordpress.callac.online\/#\/schema\/person\/04061f1ca2c2c42039142a704be95940\",\"name\":\"dlefur\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/wordpress.callac.online\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/4a9e17be136808c6597f28aa2b6c13126dab066fdc2198ff60090972c9b7fafc?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/4a9e17be136808c6597f28aa2b6c13126dab066fdc2198ff60090972c9b7fafc?s=96&d=mm&r=g\",\"caption\":\"dlefur\"},\"logo\":{\"@id\":\"https:\/\/wordpress.callac.online\/#\/schema\/person\/image\/\"},\"description\":\"Enseignant de math\u00e9matiques Lyc\u00e9e Pasteur S\u00e3o Paulo\",\"sameAs\":[\"http:\/\/wordpress.callac.online\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"R\u00e9gression lin\u00e9aire avec Xcas - Maths & Num\u00e9rique","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/","og_locale":"fr_FR","og_type":"article","og_title":"R\u00e9gression lin\u00e9aire avec Xcas - Maths & Num\u00e9rique","og_description":"Voici comment on peut r\u00e9soudre un exercice classique sur les statistiques \u00e0 deux variables. Enonc\u00e9 Le tableau suivant donne la population d’une ville nouvelle entre less ann\u00e9es 1970 et 2000.…","og_url":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/","og_site_name":"Maths & Num\u00e9rique","article_modified_time":"2023-10-14T18:14:04+00:00","og_image":[{"width":599,"height":239,"url":"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2008\/04\/jpg_regression.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_misc":{"Dur\u00e9e de lecture estim\u00e9e":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/","url":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/","name":"R\u00e9gression lin\u00e9aire avec Xcas - Maths & Num\u00e9rique","isPartOf":{"@id":"https:\/\/wordpress.callac.online\/#website"},"primaryImageOfPage":{"@id":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/#primaryimage"},"image":{"@id":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/#primaryimage"},"thumbnailUrl":"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2008\/04\/jpg_regression.jpg","datePublished":"2008-04-29T20:56:09+00:00","dateModified":"2023-10-14T18:14:04+00:00","breadcrumb":{"@id":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/#breadcrumb"},"inLanguage":"fr-FR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/"]}]},{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/#primaryimage","url":"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2008\/04\/jpg_regression.jpg","contentUrl":"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2008\/04\/jpg_regression.jpg","width":599,"height":239,"caption":"regression.jpg"},{"@type":"BreadcrumbList","@id":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/regression-lineaire-avec-xcas\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Accueil","item":"https:\/\/wordpress.callac.online\/"},{"@type":"ListItem","position":2,"name":"Logiciels math\u00e9matiques","item":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/"},{"@type":"ListItem","position":3,"name":"Xcas","item":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/"},{"@type":"ListItem","position":4,"name":"Statistiques avec Xcas","item":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/"},{"@type":"ListItem","position":5,"name":"R\u00e9gression lin\u00e9aire avec Xcas"}]},{"@type":"WebSite","@id":"https:\/\/wordpress.callac.online\/#website","url":"https:\/\/wordpress.callac.online\/","name":"Maths & Num\u00e9rique","description":"Des outils pour les enseignants de math\u00e9matiques et de num\u00e9rique","publisher":{"@id":"https:\/\/wordpress.callac.online\/#\/schema\/person\/04061f1ca2c2c42039142a704be95940"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/wordpress.callac.online\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"fr-FR"},{"@type":["Person","Organization"],"@id":"https:\/\/wordpress.callac.online\/#\/schema\/person\/04061f1ca2c2c42039142a704be95940","name":"dlefur","image":{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/wordpress.callac.online\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/4a9e17be136808c6597f28aa2b6c13126dab066fdc2198ff60090972c9b7fafc?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/4a9e17be136808c6597f28aa2b6c13126dab066fdc2198ff60090972c9b7fafc?s=96&d=mm&r=g","caption":"dlefur"},"logo":{"@id":"https:\/\/wordpress.callac.online\/#\/schema\/person\/image\/"},"description":"Enseignant de math\u00e9matiques Lyc\u00e9e Pasteur S\u00e3o Paulo","sameAs":["http:\/\/wordpress.callac.online"]}]}},"_links":{"self":[{"href":"https:\/\/wordpress.callac.online\/index.php\/wp-json\/wp\/v2\/pages\/160","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wordpress.callac.online\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/wordpress.callac.online\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/wordpress.callac.online\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wordpress.callac.online\/index.php\/wp-json\/wp\/v2\/comments?post=160"}],"version-history":[{"count":1,"href":"https:\/\/wordpress.callac.online\/index.php\/wp-json\/wp\/v2\/pages\/160\/revisions"}],"predecessor-version":[{"id":1568,"href":"https:\/\/wordpress.callac.online\/index.php\/wp-json\/wp\/v2\/pages\/160\/revisions\/1568"}],"up":[{"embeddable":true,"href":"https:\/\/wordpress.callac.online\/index.php\/wp-json\/wp\/v2\/pages\/2228"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wordpress.callac.online\/index.php\/wp-json\/wp\/v2\/media\/663"}],"wp:attachment":[{"href":"https:\/\/wordpress.callac.online\/index.php\/wp-json\/wp\/v2\/media?parent=160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}