Travail sur les données iris

data(iris)

Travail sur les données iris

• Appliquer le modèle de régression linéaire pour étudier la dépendance entre la longueur et la largeur des sépales ("Sepal.Length" et "Sepal.Width").

Travail sur les données iris

par(mfrow = c(1, 2))
hist(iris$Sepal.Length)
hist(iris$Sepal.Width)

Travail sur les données iris

plot(x = iris$Sepal.Length, y = iris$Sepal.Width)

Travail sur les données iris

plot(x = iris$Sepal.Length, y = iris$Sepal.Width, 
  col = iris$Species, pch = 16)

Travail sur les données iris

summary(lm(iris$Sepal.Width ~ iris$Sepal.Length))

## 
## Call:
## lm(formula = iris$Sepal.Width ~ iris$Sepal.Length)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1095 -0.2454 -0.0167  0.2763  1.3338 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        3.41895    0.25356   13.48   <2e-16 ***
## iris$Sepal.Length -0.06188    0.04297   -1.44    0.152    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4343 on 148 degrees of freedom
## Multiple R-squared:  0.01382,    Adjusted R-squared:  0.007159 
## F-statistic: 2.074 on 1 and 148 DF,  p-value: 0.1519

Travail sur les données iris

spp <- unique(iris$Species)
lapply(spp, function(mySpp){
  lmX <- lm(iris$Sepal.Width[iris$Species == mySpp] ~ 
    iris$Sepal.Length[iris$Species == mySpp])
  summary(lmX)
})

## [[1]]
## 
## Call:
## lm(formula = iris$Sepal.Width[iris$Species == mySpp] ~ iris$Sepal.Length[iris$Species == 
##     mySpp])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.72394 -0.18273 -0.00306  0.15738  0.51709 
## 
## Coefficients:
##                                          Estimate Std. Error t value
## (Intercept)                               -0.5694     0.5217  -1.091
## iris$Sepal.Length[iris$Species == mySpp]   0.7985     0.1040   7.681
##                                          Pr(>|t|)    
## (Intercept)                                 0.281    
## iris$Sepal.Length[iris$Species == mySpp] 6.71e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2565 on 48 degrees of freedom
## Multiple R-squared:  0.5514, Adjusted R-squared:  0.542 
## F-statistic: 58.99 on 1 and 48 DF,  p-value: 6.71e-10
## 
## 
## [[2]]
## 
## Call:
## lm(formula = iris$Sepal.Width[iris$Species == mySpp] ~ iris$Sepal.Length[iris$Species == 
##     mySpp])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.65441 -0.12958 -0.00849  0.15137  0.60954 
## 
## Coefficients:
##                                          Estimate Std. Error t value
## (Intercept)                               0.87215    0.44466   1.961
## iris$Sepal.Length[iris$Species == mySpp]  0.31972    0.07463   4.284
##                                          Pr(>|t|)    
## (Intercept)                                0.0556 .  
## iris$Sepal.Length[iris$Species == mySpp] 8.77e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2697 on 48 degrees of freedom
## Multiple R-squared:  0.2766, Adjusted R-squared:  0.2615 
## F-statistic: 18.35 on 1 and 48 DF,  p-value: 8.772e-05
## 
## 
## [[3]]
## 
## Call:
## lm(formula = iris$Sepal.Width[iris$Species == mySpp] ~ iris$Sepal.Length[iris$Species == 
##     mySpp])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.63765 -0.18801  0.00438  0.16778  0.56814 
## 
## Coefficients:
##                                          Estimate Std. Error t value
## (Intercept)                                1.4463     0.4309   3.357
## iris$Sepal.Length[iris$Species == mySpp]   0.2319     0.0651   3.562
##                                          Pr(>|t|)    
## (Intercept)                              0.001549 ** 
## iris$Sepal.Length[iris$Species == mySpp] 0.000843 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2898 on 48 degrees of freedom
## Multiple R-squared:  0.2091, Adjusted R-squared:  0.1926 
## F-statistic: 12.69 on 1 and 48 DF,  p-value: 0.0008435

Travail sur les données iris

plot(x = iris$Sepal.Length, y = iris$Sepal.Width, 
  col = iris$Species, pch = 16)
spp <- unique(iris$Species)
lapply(spp, function(mySpp){
  lmX <- lm(iris$Sepal.Width[iris$Species == mySpp] ~ 
    iris$Sepal.Length[iris$Species == mySpp])
  points(x = iris$Sepal.Length[iris$Species == mySpp], 
    y = predict(lmX), type = 'l', lwd = 2, col = mySpp)
})

Travail sur les données iris

Travail sur les données iris

plot(x = iris$Sepal.Length, y = iris$Sepal.Width, 
  type = 'n', axes = FALSE, panel.first = {
    grid()
    axis(1)
    axis(2)
  })
my3col <- c("#3b86ff", "#e653c8", "#ffd82b")
spp <- unique(iris$Species)
trash <- lapply(spp, function(mySpp){
  lmX <- lm(iris$Sepal.Width[iris$Species == mySpp] ~ 
    iris$Sepal.Length[iris$Species == mySpp])
  points(x = iris$Sepal.Length[iris$Species == mySpp], 
    y = predict(lmX), type = 'l', lwd = 2, col = my3col[mySpp])
  myCol <- colorRampPalette(c(my3col[mySpp], "darkred"))(101)
  colRank <- (iris$Sepal.Width[iris$Species == mySpp] - 
    predict(lmX))^2
  colRank <- round((colRank - min(colRank)) / 
    (max(colRank) - min(colRank)) * 100) + 1
  points(
    x = iris$Sepal.Length[iris$Species == mySpp],
    y = iris$Sepal.Width[iris$Species == mySpp], 
    bg = my3col[mySpp], col = myCol[colRank], pch = 21, 
    cex = 1 + colRank/100)
})

Travail sur les données iris

Travail sur les données iris

plot(x = iris$Sepal.Length, y = iris$Sepal.Width, 
  type = 'n', axes = FALSE, 
  ylim = c(2, 4.5), xlim = c(4, 8), 
  panel.first = {
    grid()
    axis(1)
    axis(2)
  })
my3col <- c("#3b86ff", "#e653c8", "#ffd82b")
spp <- unique(iris$Species)
trash <- lapply(spp, function(mySpp){
  lmX <- lm(iris$Sepal.Width[iris$Species == mySpp] ~ 
    iris$Sepal.Length[iris$Species == mySpp])
  points(x = iris$Sepal.Length[iris$Species == mySpp], 
    y = predict(lmX), type = 'l', lwd = 2, col = my3col[mySpp])
  myCol <- colorRampPalette(c(my3col[mySpp], "darkred"))(101)
  colRank <- (iris$Sepal.Width[iris$Species == mySpp] - 
    predict(lmX))^2
  colRank <- round((colRank - min(colRank)) / 
    (max(colRank) - min(colRank)) * 100) + 1
  segments(
    x0 = iris$Sepal.Length[iris$Species == mySpp],
    y0 = predict(lmX),
    x1 = iris$Sepal.Length[iris$Species == mySpp],
    y1 = iris$Sepal.Width[iris$Species == mySpp], 
    col = my3col[mySpp], lwd = 1 + colRank/50
  )
  points(
    x = iris$Sepal.Length[iris$Species == mySpp],
    y = iris$Sepal.Width[iris$Species == mySpp], 
    bg = my3col[mySpp], col = myCol[colRank], pch = 21, 
    cex = 1 + colRank/100)
})

Travail sur les données iris

Travail sur les données iris

plot(x = iris$Sepal.Length, y = iris$Sepal.Width, 
  type = 'n', axes = FALSE, 
  ylim = c(2, 4.5), xlim = c(4, 8), 
  panel.first = {
    grid()
    axis(1)
    axis(2)
  })
my3col <- c("#3b86ff", "#e653c8", "#ffd82b")
spp <- unique(iris$Species)
trash <- lapply(spp, function(mySpp){
  lmX <- lm(iris$Sepal.Width[iris$Species == mySpp] ~ 
    iris$Sepal.Length[iris$Species == mySpp])
  points(x = iris$Sepal.Length[iris$Species == mySpp], 
    y = predict(lmX), type = 'l', lwd = 2, col = my3col[mySpp])
  myCol <- colorRampPalette(c(my3col[mySpp], "darkred"))(101)
  colRank <- (iris$Sepal.Width[iris$Species == mySpp] - 
    predict(lmX))^2
  colRank <- round((colRank - min(colRank)) / 
    (max(colRank) - min(colRank)) * 100) + 1
  segments(
    x0 = iris$Sepal.Length[iris$Species == mySpp],
    y0 = predict(lmX),
    x1 = iris$Sepal.Length[iris$Species == mySpp],
    y1 = iris$Sepal.Width[iris$Species == mySpp], 
    col = my3col[mySpp], lwd = 1 + colRank/50
  )
  points(
    x = iris$Sepal.Length[iris$Species == mySpp],
    y = iris$Sepal.Width[iris$Species == mySpp], 
    bg = my3col[mySpp], col = myCol[colRank], pch = 21, 
    cex = 1 + colRank/100)
})
legend("topright", fill = my3col, 
  legend = levels(iris$Species), bty = "n")

Travail sur les données iris