{"id":298,"date":"2014-10-09T12:16:39","date_gmt":"2014-10-09T10:16:39","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/la-regression-lineaire-multiple\/"},"modified":"2023-10-14T20:14:37","modified_gmt":"2023-10-14T18:14:37","slug":"la-regression-lineaire-multiple","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/le-logiciel-r\/les-regressions-avec-r\/la-regression-lineaire-multiple\/","title":{"rendered":"La r\u00e9gression lin\u00e9aire multiple"},"content":{"rendered":"

Un fichier de donn\u00e9es<\/h2>\n

Travaillons sur une enqu\u00eate de satisfactions dans un h\u00f4pital, r\u00e9cup\u00e9r\u00e9 lors d’un cours de FUN (France Unit\u00e9 Num\u00e9rique). Les fichiers sont disponibles ici<\/a>.<\/p>\n

Par la suite, ces donn\u00e9es seront stock\u00e9es dans la variable satis<\/em> .<\/p>\n

Dans ces donn\u00e9es comme souvent, les observations sont en lignes et les variables en colonnes.<\/p>\n

Pr\u00e9sentation<\/h2>\n

On cherche \u00e0 expliquer une variable quantitative Y par des variables quantitatives ou cat\u00e9gorielles. Ces derni\u00e8res seront par le logiciel cod\u00e9es en plusieurs variables binaires.<\/p>\n Y=a+b \\times X_1 + c \\times X_2 + \\cdots + bruit <\/span>\n

NB : le bruit devra avoir une distribution normale.<\/p>\n

Un exemple<\/h2>\n

Cherchons \u00e0 expliquer le score de relation avec les variables suivantes :
\n– \u00e2ge
\n– sexe
\n– score.information
\n– profession<\/p>\n

Les variables cat\u00e9gorielles<\/h2>\n

Il faudra faire tr\u00e8s attention \u00e0 bien convertir les variables cat\u00e9gorielles pour qu’elles ne soient pas interpr\u00e9t\u00e9es comme des variables quantitatives.<\/p>\n

satis$sexe.cat<-factor(satis$sexe,labels=c(\"H\",\"F\")) \nsatis$profession.cat<-factor(satis$profession) \nsatis$service.cat<-factor(satis$service)<\/pre>\n
Dans le logiciel, la premi\u00e8re cat\u00e9gorie servira de r\u00e9f\u00e9rence. Par exemple, pour le sexe cod\u00e9 (\u00ab\u00a0H\u00a0\u00bb,\u00a0\u00bbF\u00a0\u00bb), \u00ab\u00a0H\u00a0\u00bb sera la r\u00e9f\u00e9rence. On cherchera donc \u00e0 savoir si le fait d’\u00eatre une femme modifie le score de relation.<\/p>\n
Pour changer cette r\u00e9f\u00e9rence, on peut le faire de la sorte :<\/p>\n
satis$sexe.cat <- relevel(satis$sexe.cat,ref=\"F\")<\/pre>\n
La r\u00e9gression multiple<\/h2>\n
mod.sr.m<-lm(score.relation~age+sexe.cat+score.information+profession.cat,data=satis) \nsummary(mod.sr.m)<\/pre>\n

\nCall:
\nlm(formula = score.relation ~ age + sexe.cat + score.information +
\nprofession.cat, data = satis)<\/code><\/p>\n
<\/code><\/code><\/p>\n
Residuals:
\nMin 1Q Median 3Q Max
\n-19.9512 -2.0524 0.7879 2.5011 8.9167<\/p>\n
<\/code><\/code><\/p>\n
Coefficients:
\nEstimate Std. Error t value Pr(>|t|)
\n(Intercept) 22.02989 4.36455 5.047 7.67e-07 ***
\nage 0.04289 0.01534 2.795 0.00551 **
\nsexe.catF -0.67479 0.47778 -1.412 0.15886
\nscore.information 0.31210 0.03473 8.987 < 2e-16 *** profession.cat2 1.95365 4.21957 0.463 0.64369 profession.cat3 0.66762 4.16591 0.160 0.87278 profession.cat4 0.85505 4.16932 0.205 0.83764 profession.cat5 2.30864 4.17398 0.553 0.58059 profession.cat6 0.70852 4.20634 0.168 0.86635 profession.cat7 0.87308 4.27127 0.204 0.83817 profession.cat8 1.93984 4.21116 0.461 0.64538
\n\u2014\u00a0–
\nSignif. codes: 0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1<\/p>\n

\n<\/code><\/p>\n
Residual standard error: 4.127 on 308 degrees of freedom
\n(215 observations deleted due to missingness)
\nMultiple R-squared:  0.2311,\tAdjusted R-squared:  0.2061
\nF-statistic: 9.257 on 10 and 308 DF,  p-value: 2.068e-13
\n<\/code><\/p>\n
On voit les diff\u00e9rentes variables qui ont \u00e9t\u00e9 cr\u00e9\u00e9es :
\n– sexe.catF
\n– profession.cat2
\n– profession.cat3
\n– profession.cat4
\n– profession.cat5
\n– profession.cat6
\n– profession.cat7
\n– profession.cat8<\/p>\n
Pour voir appara\u00eetre les valeurs de p par variable :<\/p>\n
drop1(mod.sr.m,.~.,test=\"F\")<\/pre>\n

\nSingle term deletions<\/code><\/p>\n

\n<\/code><\/p>\n
Model:
\nscore.relation ~ age + sexe.cat + score.information + profession.cat
\nDf Sum of Sq    RSS    AIC F value    Pr(>F)
\n5246.0 915.21
\nage                1    133.08 5379.1 921.20  7.8134  0.005512 **
\nsexe.cat           1     33.98 5280.0 915.27  1.9947  0.158856
\nscore.information  1   1375.56 6621.6 987.50 80.7605 < 2.2e-16 ***
\nprofession.cat     7    136.28 5382.3 909.39  1.1430  0.335906<\/code><\/p>\n

\n<\/code><\/p>\n
\u2014\u00a0-
\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1
\n<\/code><\/p>\n
Cette fois-ci, pour l’\u00e2ge, on a une valeur de p faible (0.00551) et b=0.04289.<\/p>\n
Les autres crit\u00e8res \u00e9tant inchang\u00e9s, chaque augmentation de l’\u00e2ge de 10 ans augmentera le score de relation de 0.4289.<\/p>\n
On peut le voir en faisant deux pr\u00e9dictions.<\/p>\n
predict(mod.sr.m,data=satis,data.frame(age=30,sexe.cat=\"F\",score.information=4,profession.cat=\"5\"))<\/pre>\n

\n1
\n26.19871
\n<\/code><\/p>\n
predict(mod.sr.m,data=satis,data.frame(age=40,sexe.cat=\"F\",score.information=4,profession.cat=\"5\"))<\/pre>\n

\n1
\n26.62757
\n<\/code><\/p>\n
Calculons la diff\u00e9rence :<\/p>\n
26.62757-26.19871<\/p>\n

\n[1] 0.42886
\n<\/code><\/p>\n
Validit\u00e9 du mod\u00e8le<\/h2>\n
hist(resid(mod.sr.m),col=\"brown\")<\/pre>\n
\"histo_resid_03.png\"<\/p>\n","protected":false},"excerpt":{"rendered":"
Un fichier de donn\u00e9es Travaillons sur une enqu\u00eate de satisfactions dans un h\u00f4pital, r\u00e9cup\u00e9r\u00e9 lors d’un cours de FUN (France Unit\u00e9 Num\u00e9rique). Les fichiers sont disponibles ici. Par la suite,…<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2076,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-298","page","type-page","status-publish","hentry"],"yoast_head":"\nLa r\u00e9gression lin\u00e9aire multiple - 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\/le-logiciel-r\/les-regressions-avec-r\/la-regression-lineaire-multiple\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"La r\u00e9gression lin\u00e9aire multiple - Maths & Num\u00e9rique\" \/>\n<meta property=\"og:description\" content=\"Un fichier de donn\u00e9es Travaillons sur une enqu\u00eate de satisfactions dans un h\u00f4pital, r\u00e9cup\u00e9r\u00e9 lors d’un cours de FUN (France Unit\u00e9 Num\u00e9rique). 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