diff --git a/M1/General Linear Models/TP1/TP1.Rmd b/M1/General Linear Models/TP1/TP1.Rmd new file mode 100644 index 0000000..27ee182 --- /dev/null +++ b/M1/General Linear Models/TP1/TP1.Rmd @@ -0,0 +1,93 @@ +```{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 diff --git a/M1/General Linear Models/TP1/TP1.Rproj b/M1/General Linear Models/TP1/TP1.Rproj new file mode 100644 index 0000000..8e3c2eb --- /dev/null +++ b/M1/General Linear Models/TP1/TP1.Rproj @@ -0,0 +1,13 @@ +Version: 1.0 + +RestoreWorkspace: Default +SaveWorkspace: Default +AlwaysSaveHistory: Default + +EnableCodeIndexing: Yes +UseSpacesForTab: Yes +NumSpacesForTab: 2 +Encoding: UTF-8 + +RnwWeave: Sweave +LaTeX: pdfLaTeX diff --git a/M1/General Linear Models/TP1/health.txt b/M1/General Linear Models/TP1/health.txt new file mode 100755 index 0000000..1a1ee11 --- /dev/null +++ b/M1/General Linear Models/TP1/health.txt @@ -0,0 +1,26 @@ +"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