From 440bda2762522ff7ebf918ae24b3af8a7ab084e3 Mon Sep 17 00:00:00 2001
From: Dorian Goepp <dorian.goepp@gmail.com>
Date: Wed, 26 Oct 2022 12:31:10 +0200
Subject: [PATCH] Exercises 2, 3 and 5

---
 module2/exo2/exercice_R_fr.org      |  21 +++-
 module2/exo3/exercice_R_fr.org      |  19 ++++
 module2/exo5/exo5_R_fr.org          | 151 +++++++++++++++++++++++-----
 module2/exo5/proba_estimate_all.png | Bin 0 -> 15563 bytes
 4 files changed, 163 insertions(+), 28 deletions(-)
 create mode 100644 module2/exo5/proba_estimate_all.png

diff --git a/module2/exo2/exercice_R_fr.org b/module2/exo2/exercice_R_fr.org
index 1bb8f61..506a078 100644
--- a/module2/exo2/exercice_R_fr.org
+++ b/module2/exo2/exercice_R_fr.org
@@ -1,6 +1,6 @@
-#+TITLE:  Votre titre
-#+AUTHOR: Votre nom
-#+DATE:   La date du jour
+#+TITLE:  Analyse de données simples
+#+AUTHOR: Dorian Goepp
+#+DATE:   2022-10-25
 #+LANGUAGE: fr
 # #+PROPERTY: header-args :eval never-export
 
@@ -82,3 +82,18 @@ faisant ~<r~ ou ~<R~ suivi de ~Tab~).
 
 Maintenant, à vous de jouer! Vous pouvez effacer toutes ces
 informations et les remplacer par votre document computationnel.
+
+* Mon travail
+
+#+begin_src R :results output :session *R* :exports both
+donnees = c(14.0, 7.6, 11.2, 12.8, 12.5, 9.9, 14.9, 9.4, 16.9, 10.2, 14.9, 18.1, 7.3, 9.8, 10.9,12.2, 9.9, 2.9, 2.8, 15.4, 15.7, 9.7, 13.1, 13.2, 12.3, 11.7, 16.0, 12.4, 17.9, 12.2, 16.2, 18.7, 8.9, 11.9, 12.1, 14.6, 12.1, 4.7, 3.9, 16.9, 16.8, 11.3, 14.4, 15.7, 14.0, 13.6, 18.0, 13.6, 19.9, 13.7, 17.0, 20.5, 9.9, 12.5, 13.2, 16.1, 13.5, 6.3, 6.4, 17.6, 19.1, 12.8, 15.5, 16.3, 15.2, 14.6, 19.1, 14.4, 21.4, 15.1, 19.6, 21.7, 11.3, 15.0, 14.3, 16.8, 14.0, 6.8, 8.2, 19.9, 20.4, 14.6, 16.4, 18.7, 16.8, 15.8, 20.4, 15.8, 22.4, 16.2, 20.3, 23.4, 12.1, 15.5, 15.4, 18.4, 15.7, 10.2, 8.9, 21.0)
+summary(donnees)
+sd(donnees)
+#+end_src
+
+#+RESULTS:
+: 
+:    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
+:    2.80   11.85   14.50   14.11   16.80   23.40
+: 
+: [1] 4.334094
diff --git a/module2/exo3/exercice_R_fr.org b/module2/exo3/exercice_R_fr.org
index 1bb8f61..5aec098 100644
--- a/module2/exo3/exercice_R_fr.org
+++ b/module2/exo3/exercice_R_fr.org
@@ -82,3 +82,22 @@ faisant ~<r~ ou ~<R~ suivi de ~Tab~).
 
 Maintenant, à vous de jouer! Vous pouvez effacer toutes ces
 informations et les remplacer par votre document computationnel.
+* Mon analyse
+
+#+begin_src R :results output :session *R* :exports both
+donnees = c(14.0, 7.6, 11.2, 12.8, 12.5, 9.9, 14.9, 9.4, 16.9, 10.2, 14.9, 18.1, 7.3, 9.8, 10.9,12.2, 9.9, 2.9, 2.8, 15.4, 15.7, 9.7, 13.1, 13.2, 12.3, 11.7, 16.0, 12.4, 17.9, 12.2, 16.2, 18.7, 8.9, 11.9, 12.1, 14.6, 12.1, 4.7, 3.9, 16.9, 16.8, 11.3, 14.4, 15.7, 14.0, 13.6, 18.0, 13.6, 19.9, 13.7, 17.0, 20.5, 9.9, 12.5, 13.2, 16.1, 13.5, 6.3, 6.4, 17.6, 19.1, 12.8, 15.5, 16.3, 15.2, 14.6, 19.1, 14.4, 21.4, 15.1, 19.6, 21.7, 11.3, 15.0, 14.3, 16.8, 14.0, 6.8, 8.2, 19.9, 20.4, 14.6, 16.4, 18.7, 16.8, 15.8, 20.4, 15.8, 22.4, 16.2, 20.3, 23.4, 12.1, 15.5, 15.4, 18.4, 15.7, 10.2, 8.9, 21.0)
+#+end_src
+
+#+RESULTS:
+
+#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
+plot(donnees, type="l")
+#+end_src
+
+#+RESULTS:
+
+#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
+hist(donnees)
+#+end_src
+
+#+RESULTS:
diff --git a/module2/exo5/exo5_R_fr.org b/module2/exo5/exo5_R_fr.org
index 336a9f7..7c2e011 100644
--- a/module2/exo5/exo5_R_fr.org
+++ b/module2/exo5/exo5_R_fr.org
@@ -38,34 +38,36 @@ Nous commençons donc par charger ces données:
 #+begin_src R :results output :session *R* :exports both
 data = read.csv("shuttle.csv",header=T)
 data
+original_data = data
 #+end_src
 
 #+RESULTS:
 #+begin_example
-        Date Count Temperature Pressure Malfunction
-1    4/12/81     6          66       50           0
-2   11/12/81     6          70       50           1
-3    3/22/82     6          69       50           0
-4   11/11/82     6          68       50           0
-5    4/04/83     6          67       50           0
-6    6/18/82     6          72       50           0
-7    8/30/83     6          73      100           0
-8   11/28/83     6          70      100           0
-9    2/03/84     6          57      200           1
-10   4/06/84     6          63      200           1
-11   8/30/84     6          70      200           1
-12  10/05/84     6          78      200           0
-13  11/08/84     6          67      200           0
-14   1/24/85     6          53      200           2
-15   4/12/85     6          67      200           0
-16   4/29/85     6          75      200           0
-17   6/17/85     6          70      200           0
-18 7/29/85     6          81      200           0
-19   8/27/85     6          76      200           0
-20  10/03/85     6          79      200           0
-21  10/30/85     6          75      200           2
-22  11/26/85     6          76      200           0
-23   1/12/86     6          58      200           1
+
+       Date Count Temperature Pressure Malfunction
+1   4/12/81     6          66       50           0
+2  11/12/81     6          70       50           1
+3   3/22/82     6          69       50           0
+4  11/11/82     6          68       50           0
+5   4/04/83     6          67       50           0
+6   6/18/82     6          72       50           0
+7   8/30/83     6          73      100           0
+8  11/28/83     6          70      100           0
+9   2/03/84     6          57      200           1
+10  4/06/84     6          63      200           1
+11  8/30/84     6          70      200           1
+12 10/05/84     6          78      200           0
+13 11/08/84     6          67      200           0
+14  1/24/85     6          53      200           2
+15  4/12/85     6          67      200           0
+16  4/29/85     6          75      200           0
+17  6/17/85     6          70      200           0
+18  7/29/85     6          81      200           0
+19  8/27/85     6          76      200           0
+20 10/03/85     6          79      200           0
+21 10/30/85     6          75      200           2
+22 11/26/85     6          76      200           0
+23  1/12/86     6          58      200           1
 #+end_example
 
 Le jeu de données nous indique la date de l'essai, le nombre de joints
@@ -85,6 +87,7 @@ data
 #+end_src
 
 #+RESULTS:
+: 
 :        Date Count Temperature Pressure Malfunction
 : 2  11/12/81     6          70       50           1
 : 9   2/03/84     6          57      200           1
@@ -104,12 +107,37 @@ plot(data=data, Malfunction/Count ~ Temperature, ylim=c(0,1))
 #+end_src
 
 #+RESULTS:
-[[file:freq_temp.png]]
+
 
 À première vue, ce n'est pas flagrant mais bon, essayons quand même
 d'estimer l'impact de la température $t$ sur la probabilité de
 dysfonctionnements d'un joint. 
 
+** Admettons qu'en fait les tests sans défaut de joint soient importants
+
+Comment les représenterait-on alors ?
+
+#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
+plot(data=original_data, Malfunction/Count ~ Temperature, ylim=c(0, 1))
+#+end_src
+
+#+RESULTS:
+
+Toutes les observations en dessous de 66°F ont rencontré au moins une
+défaillance de joint torique. Ce n'est probablement pas une
+information à négliger !
+
+** Et si la pression avait un rôle ?
+
+#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
+plot(data=original_data, Malfunction/Count ~ Pressure, ylim=c(0, 1))
+#+end_src
+
+#+RESULTS:
+
+Une fois encore, nous avons très peu de données, mais il ne semble
+rien y avoir à en tirer.
+
 * Estimation de l'influence de la température
 
 Supposons que chacun des 6 joints toriques est endommagé avec la même
@@ -120,6 +148,10 @@ température $t$ suit une loi binomiale de paramètre $n=6$ et
 $p=p(t)$. Pour relier $p(t)$ à $t$, on va donc effectuer une
 régression logistique.
 
+> Les joints peuvent défaillir en même temps s'ils sont le produit d'une
+même série de production, ce qui limite le réalisme de l'hypothèse
+d'indépendance des probabilités de défaut d'un joint.
+
 #+begin_src R :results output :session *R* :exports both
 logistic_reg = glm(data=data, Malfunction/Count ~ Temperature, weights=Count, 
                    family=binomial(link='logit'))
@@ -156,6 +188,50 @@ et l'erreur standard de cet estimateur est de 0.049, autrement dit on
 ne peut pas distinguer d'impact particulier et il faut prendre nos
 estimations avec des pincettes.
 
+** Refaisons l'analyse avec toutes les données
+
+De même que dans la section précédente, prenons en compte les
+événements sans défaut de joint.
+
+#+begin_src R :results output :session *R* :exports both
+logistic_reg_full = glm(data=original_data, Malfunction/Count ~ Temperature, weights=Count, 
+                   family=binomial(link='logit'))
+summary(logistic_reg)
+#+end_src
+
+#+RESULTS:
+#+begin_example
+
+Call:
+glm(formula = Malfunction/Count ~ Temperature, family = binomial(link = "logit"), 
+    data = data, weights = Count)
+
+Deviance Residuals: 
+      2        9       10       11       14       21       23  
+-0.3015  -0.2836  -0.2919  -0.3015   0.6891   0.6560  -0.2850  
+
+Coefficients:
+             Estimate Std. Error z value Pr(>|z|)
+(Intercept) -1.389528   3.195752  -0.435    0.664
+Temperature  0.001416   0.049773   0.028    0.977
+
+(Dispersion parameter for binomial family taken to be 1)
+
+    Null deviance: 1.3347  on 6  degrees of freedom
+Residual deviance: 1.3339  on 5  degrees of freedom
+AIC: 18.894
+
+Number of Fisher Scoring iterations: 4
+#+end_example
+
+Cette fois-ci, avec la même erreur standard, on obtient un coefficient
+bien supérieur, donc une corrélation bien plus forte entre la
+température et les défaillances.
+
+Je ne suis pas cappable d'évaluer la signification de ces résultats,
+n'ayant pas eu le temps d'étudier la régression logistique. J'admets
+donc, pour pouvoir continuer, que l'incertitude n'est pas trop élevée.
+
 * Estimation de la probabilité de dysfonctionnant des joints toriques
 La température prévue le jour du décollage est de 31°F. Essayons
 d'estimer la probabilité de dysfonctionnement des joints toriques à
@@ -185,6 +261,7 @@ sum(data_full$Malfunction)/sum(data_full$Count)
 #+end_src
 
 #+RESULTS:
+: 
 : [1] 0.06521739
 
 Cette probabilité est donc d'environ $p=0.065$, sachant qu'il existe
@@ -205,3 +282,27 @@ problème... Saurez-vous le trouver ? Vous êtes libre de modifier cette
 analyse et de regarder ce jeu de données sous tous les angles afin
 d'expliquer ce qui ne va pas.
 
+** En prenant en compte les situations sans défaillance
+
+#+begin_src R :results output graphics :file "proba_estimate_all.png" :exports both :width 600 :height 400 :session *R* 
+# shuttle=shuttle[shuttle$r!=0,] 
+tempv = seq(from=30, to=90, by = .5)
+rmv <- predict(logistic_reg_full, list(Temperature=tempv), type="response")
+plot(tempv, rmv, type="l", ylim=c(0, 1))
+points(data=data, Malfunction/Count ~ Temperature)
+#+end_src
+
+#+RESULTS:
+
+Et maintenant la probabilité de défaillance d'un joint:
+
+#+begin_src R :results output :session *R* :exports both
+rmv[1]
+#+end_src
+
+#+RESULTS:
+:        1 
+: 0.834373
+
+The probability is here far too high to consider taking off, admitting
+that the pressure for the takeoff day was 200 PSI.
diff --git a/module2/exo5/proba_estimate_all.png b/module2/exo5/proba_estimate_all.png
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literal 0
HcmV?d00001

-- 
2.18.1