From 789c182b821bd815399ce74093cfdbd537c4fdb7 Mon Sep 17 00:00:00 2001
From: "gael.cartierm" <gael.cartier-michaud@etu.hesge.ch>
Date: Sun, 12 Dec 2021 12:58:53 +0100
Subject: [PATCH] rapport -> conclusion

---
 images/CV_terminal.png      | Bin 27772 -> 0 bytes
 images/Cross_validation.png | Bin 95214 -> 0 bytes
 images/First_result.png     | Bin 29493 -> 0 bytes
 images/First_step.png       | Bin 163522 -> 0 bytes
 images/Full_sample.png      | Bin 76699 -> 0 bytes
 images/erreur_moyenne.png   | Bin 44872 -> 0 bytes
 images/erreur_relative.png  | Bin 61447 -> 0 bytes
 rapport.pdf                 | Bin 343680 -> 345954 bytes
 rapport.tex                 |  19 +++++++++++++++++--
 rapport.toc                 |  12 ------------
 10 files changed, 17 insertions(+), 14 deletions(-)
 delete mode 100644 images/CV_terminal.png
 delete mode 100644 images/Cross_validation.png
 delete mode 100644 images/First_result.png
 delete mode 100644 images/First_step.png
 delete mode 100644 images/Full_sample.png
 delete mode 100644 images/erreur_moyenne.png
 delete mode 100644 images/erreur_relative.png
 delete mode 100644 rapport.toc

diff --git a/images/CV_terminal.png b/images/CV_terminal.png
deleted file mode 100644
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diff --git a/rapport.pdf b/rapport.pdf
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Dq--l%

diff --git a/rapport.tex b/rapport.tex
index fde945f..697b614 100644
--- a/rapport.tex
+++ b/rapport.tex
@@ -145,7 +145,7 @@
 
             \begin{align*}
                 \frac{\partial E}{\partial a} &= \sum_{j=1}^{N}(a \cdot x_j + b - y_j)\cdot x_j\\
-                \frac{\partial E}{\delta b} &= \sum_{j=1}^{N}(a \cdot x_j + b - y_j)
+                \frac{\partial E}{\partial b} &= \sum_{j=1}^{N}(a \cdot x_j + b - y_j)
             \end{align*}  
             
             L'ensemble de ces dérivées forment le gradient de $E(a,b)$.\\
@@ -273,7 +273,22 @@
         \clearpage
         \newpage
 \section{Conclusion}
-blabla
+Lors de la collecte de données pour une étude statistique et/ou expérimentale, un biais humain ou matériel est souvent compris dans les données. Ce biais est du
+'bruit', une erreur souvent comprise dans un interval de valeurs plus ou moins grand et plus ou moins fixe.\\
+Cette collecte de données est réalisé en général pour connaître la tendance que suis le phénomène que l'on observe. Pour définir cette tendance on traduit donc 
+notre nuage de point en une fonction représentant la meilleure droite (cas de la régression linéaire) ou courbe passant par le maximum de point de notre échantillon.
+Notre étude a pu montrer qu'il est possible d'obtenir les paramètres $a$ et $b$ d'une droite d'équation $y = a \cdot x + b$ de façon analytique, ou à l'aide de la
+méthode de la descente de gradient pour optimiser la fonction d'erreur quadratique d'un nuage de point. La droite obtenue est la régression linéaire d'un nuage de point.
+A partir de cette régression linéaire, l'erreur moyenne de l'échantillon peut être calculée. Plus le bruit contenu dans un échantillon est important, plus la dispersion
+des points est importante, et par conséquent l'erreur moyenne se voit aussi augmenté. Cependant, l'erreur moyenne ne peut être interprétée seule. Une erreur peut 
+faible dans l'absolue, mais si les valeurs de l'échantillons de données sont aussi très faible, l'erreur peut fausser complètement la fiabilité de l'échantillon.
+L'erreur doit toujours être analysée en rapport avec l'ordre de grandeur des valeurs de l'échantillon. C'est pourquoi nous avons utilisé l'erreur relative. Cette 
+dernière correspond au rapport de la différence entre la valeur mesurée et la valeur théorique, sur la valeur théorique. L'erreur relative traduit le niveau de variation 
+que les valeurs d'un échantillons sont suceptible de subir par rapport aux valeurs théoriques calculées. Le niveau d'erreur acceptable doit être définit en fonction 
+du sujet/domaine de l'étude en cours.\\
+Certains phénomènes ne suivent pas des modèles linéaires. En effet, dans certains cas le modèle suivra plutôt une fonction quadratique (parabole), cubique, 
+logarithmique, ou encore exponentielle. Pour ce type de cas la régression linéaire est inadapté pour représenter le comportement de ces modèles. D'autres type de 
+régression existe permettant de mieux représenter ces phénomènes: regression logarithmique, regression polynomiale, regression non paramétrique, etc.
 
 \clearpage
 \newpage
diff --git a/rapport.toc b/rapport.toc
deleted file mode 100644
index 7864af1..0000000
--- a/rapport.toc
+++ /dev/null
@@ -1,12 +0,0 @@
-\babel@toc {french}{}
-\contentsline {section}{\numberline {1}Introduction}{1}{}%
-\contentsline {section}{\numberline {2}Théorie}{2}{}%
-\contentsline {subsection}{\numberline {2.1}Solution analytique}{2}{}%
-\contentsline {subsection}{\numberline {2.2}Solution numérique}{3}{}%
-\contentsline {subsection}{\numberline {2.3}Validation croisée}{4}{}%
-\contentsline {section}{\numberline {3}Résultats}{4}{}%
-\contentsline {subsection}{\numberline {3.1}Solution analytique}{4}{}%
-\contentsline {subsection}{\numberline {3.2}Solution numérique}{5}{}%
-\contentsline {subsection}{\numberline {3.3}Validation croisée}{7}{}%
-\contentsline {subsection}{\numberline {3.4}Evolution de l'erreur}{10}{}%
-\contentsline {section}{\numberline {4}Conclusion}{12}{}%
-- 
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