Exercícios - tranformações

Lista 7.3 - q1

bac <- c(10, 15, 22, 35, 40, 50, 120, 300)
# descritivas: variabilidade muito alta
m.bac <- mean(bac)
print(m.bac)

[1] 74

sd.bac <- sd(bac)
print(sd.bac)

[1] 97.63343

var(bac)

[1] 9532.286

hist(bac, probability = T)
curve(dnorm(x,mean(bac),sd(bac)),add = T,col = "red")

log.bac <- log10(bac)
mean(log.bac)

[1] 1.614989

sd(log.bac)

[1] 0.4804955

var(log.bac)

[1] 0.2308759

hist(log.bac, probability = T, ylim = c(0,0.8),
     main = "Histograma do log dos dados")
curve(dnorm(x, mean(log.bac),sd(log.bac)), add = T,
      col = "blue")

# assimetria dos dados "normais"
AS.bac = 3*(m.bac - median(bac))/sd.bac
print(AS.bac)

[1] 1.121542

# assimetria dos dados transformados
AS.log.bac = 3*(mean(log.bac) - median(log.bac))/sd(log.bac)
print(AS.log.bac)

[1] 0.2617629

### dados flor de Íris
# carregar dos dados

IRIS <- iris
# lendo as 6 primeiras linhas
head(IRIS)

  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa
4          4.6         3.1          1.5         0.2  setosa
5          5.0         3.6          1.4         0.2  setosa
6          5.4         3.9          1.7         0.4  setosa

tail(IRIS) # 6 últimas linhas

    Sepal.Length Sepal.Width Petal.Length Petal.Width   Species
145          6.7         3.3          5.7         2.5 virginica
146          6.7         3.0          5.2         2.3 virginica
147          6.3         2.5          5.0         1.9 virginica
148          6.5         3.0          5.2         2.0 virginica
149          6.2         3.4          5.4         2.3 virginica
150          5.9         3.0          5.1         1.8 virginica

attach(IRIS)
m.sepal <- mean(Sepal.Length)
print(m.sepal)

[1] 5.843333

sd.sepal <- sd(Sepal.Length)
print(sd.sepal)

[1] 0.8280661

hist(Sepal.Length, probability = T,ylim = c(0,0.6))
curve(dnorm(x, mean(Sepal.Length),sd(Sepal.Length)),add=T,
      col = "red")

Padronização (score z)

\[ z = \dfrac{X-\bar{X}}{s} \]

z.sepal <- (Sepal.Length - m.sepal)/sd.sepal

hist(z.sepal, probability = T, ylim = c(0,0.5),
     main = "Score z de Sepal.lenght")
curve(dnorm(x, mean(z.sepal), sd(z.sepal)),add = T,
      col = "blue")