Add TP1

M1/General Linear Models/TP1/TP1.Rmd

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+```{r}
+library(rmarkdown)
+health <- read.table("health.txt", header = TRUE, sep = " ", dec = ".")
+paged_table(health)
+```
+
+```{r}
+Health <- health[2:5]
+
+library(dplyr)
+library(corrplot)
+correlation_matrix<-cor(Health)
+corrplot(correlation_matrix, order = 'hclust',addrect = 3)
+```
+
+```{r}
+model <- lm(y ~ ., data = Health)
+
+coefficients(model)
+summary(model)
+```
+
+```{r}
+library(ggfortify)
+library(car)
+autoplot(model,1)
+```
+
+The points are not well distributed around 0 -> [P1] is not verified
+
+```{r}
+autoplot(model,3)
+```
+
+The points are not well distributed around 1 -> [P2] is not verified
+
+```{r}
+set.seed(0)
+durbinWatsonTest(model)
+```
+
+The p-value is 0.58 > 0.05 -> We do not reject H0 so the residuals are not autocorrelated -> [P3] is verified
+
+```{r}
+autoplot(model,2)
+```
+
+The QQPlot is align with the line y = x, so it is globally gaussian -> [P4] is verified
+
+```{r}
+library(GGally)
+ggpairs(Health, progress = F)
+```
+
+We observe that the variable age is correlated with the variable y. There is a quadratic relation between both variables.
+
+```{r}
+Health2 <- Health
+Health2$age_sq <- Health2$age^2
+Health2 <- Health2[1:24,]
+
+model2 <- lm(y ~ ., data = Health2)
+
+summary(model2)
+coefficients(model2)
+```
+
+```{r}
+library(ggfortify)
+library(car)
+autoplot(model2,1)
+```
+
+The points are well distributed around 0 -> [P1] is verified
+
+```{r}
+autoplot(model2,3)
+```
+
+The points are not well distributed around 1 -> [P2] is verified
+
+```{r}
+set.seed(0)
+durbinWatsonTest(model2)
+```
+
+The p-value is 0.294 > 0.05 -> We do not reject H0 so the residuals are not autocorrelated -> [P3] is verified
+
+```{r}
+autoplot(model2,2)
+```
+
+The QQPlot is align with the line y = x, so it is gaussian -> [P4] is verified

M1/General Linear Models/TP1/TP1.Rproj

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+Version: 1.0
+
+RestoreWorkspace: Default
+SaveWorkspace: Default
+AlwaysSaveHistory: Default
+
+EnableCodeIndexing: Yes
+UseSpacesForTab: Yes
+NumSpacesForTab: 2
+Encoding: UTF-8
+
+RnwWeave: Sweave
+LaTeX: pdfLaTeX

M1/General Linear Models/TP1/health.txt

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+"Id" "y" "age" "tri" "chol"
+"1" 0.344165525138049 61.3710178481415 255.998603752814 174.725536967162
+"2" 0.468648478326459 70.0093143060803 303.203193042427 191.830689532217
+"3" 0.0114155523307995 20.0903518591076 469.998112767935 126.269967628177
+"4" 0.472875443347101 71.2420938722789 146.105958395638 211.434927976225
+"5" 0 20.0899018836208 221.786231906153 240.876589370891
+"6" 0.143997241336945 43.2352053862996 266.090678572655 137.168468555901
+"7" 0.0414102111478797 25.8429238037206 372.907817093655 227.054411582649
+"8" 0.113811893132696 41.4695196016692 131.169532104395 131.447072112933
+"9" 0.109292366261165 35.7887735008262 430.398655338213 213.031274722889
+"10" 0.137468875629733 41.5359775861725 213.798411563039 248.683155018371
+"11" 0.0532629899999104 32.2978379554115 121.814481257461 216.917818398215
+"12" 0.353328774446386 61.3454213505611 407.593103558756 125.090295937844
+"13" 0.32693962726726 58.9427325245924 310.99092704244 234.297853410244
+"14" 0.160669457776164 45.8133233059198 146.624271371402 179.472973288503
+"15" 0.513130027249664 72.5317458156496 388.182279183529 179.566718712449
+"16" 0.617920854597292 80.2682227501646 227.86060355138 171.406586996745
+"17" 0.205049999385919 48.5804966441356 270.10274540633 216.100836060941
+"18" 0.0125951861990601 23.7895587598905 173.06959128473 246.627336950041
+"19" 0.321090735035653 58.1796469353139 451.47649507504 144.35365190031
+"20" 0.375862066828795 65.0117327272892 158.536369032227 127.305114357732
+"21" 0.0722375355431054 35.3545167273842 126.951391426846 193.100387256127
+"22" 0.0772129996198421 31.5452552819625 379.832963193767 235.720843761228
+"23" 0.0605716685358678 30.9160601114854 311.444346229546 191.08392035123
+"24" 0.157789955300155 44.7116475505754 164.532195450738 224.480235648807
+"25" 1 99 457.110102558509 239.30889045354