prova

Segunda VA

VADeaths

library(ggplot2)
library(tidyr)
library(dplyr)

## 
## Anexando pacote: 'dplyr'

## Os seguintes objetos são mascarados por 'package:stats':
## 
##     filter, lag

## Os seguintes objetos são mascarados por 'package:base':
## 
##     intersect, setdiff, setequal, union

VADeaths

##       Rural Male Rural Female Urban Male Urban Female
## 50-54       11.7          8.7       15.4          8.4
## 55-59       18.1         11.7       24.3         13.6
## 60-64       26.9         20.3       37.0         19.3
## 65-69       41.0         30.9       54.6         35.1
## 70-74       66.0         54.3       71.1         50.0

df <- as.data.frame(VADeaths) %>%
  tibble::rownames_to_column("FaixaEtaria") %>%
  pivot_longer(
    cols = -FaixaEtaria,
    names_to = "Grupo",
    values_to = "Taxa"
  )

ggplot(df, aes(x = FaixaEtaria, y = Taxa, fill = Grupo)) +
  geom_bar(
    stat = "identity",
    position = position_dodge(width = 0.8),
    width = 0.7
  ) +
  scale_fill_manual(
    values = c("#E41A1C", "#377EB8", "#4DAF4A", "#984EA3"),
    name = "Grupo"
  ) +
  labs(
    title = "Taxas de Mortalidade por Grupos - Virginia (1940)",
    x = "Faixa Etária",
    y = "Mortes por 1000 Habitantes"
  ) +
  theme_minimal() +
  theme(
    plot.title = element_text(hjust = 0.5, face = "bold"),
    axis.text = element_text(size = 10),
    axis.title = element_text(size = 12)
  )

ClassificaçãoDoença

dados <- c("moderado", "leve", "leve", "severo", "leve", "moderado", "moderado", 
           "moderado", "leve", "leve", "severo", "leve", "moderado", "moderado", 
           "leve", "severo", "moderado", "moderado", "moderado", "leve")

frequencias <- table(dados)
x <- as.vector(frequencias)
labels <- names(frequencias)


pct <- round(x / sum(x) * 100)
lbls <- paste(pct, "%", sep = "")


pie(x,
    labels = lbls,
    main = "Distribuicao de Estagios da Doenca",
    col = rainbow(length(x)),
    cex = 1.2)


legend("topright",
       legend = labels,
       cex = 0.8,
       fill = rainbow(length(x)))

Teorema

flu <- read.csv2("C:/Users/ViniciusLima/Documents/CPAD/flu.csv")


hist(flu$age,
     probability = TRUE,
     main = "Distribuicao das Idades das Vitimas Fatais",
     xlab = "Idade (anos)",
     col = "lightgreen",
     border = "white",
     breaks = 30)
lines(density(flu$age, na.rm = TRUE), col = "red", lwd = 2)


abline(v = mean(flu$age), col = "blue", lwd = 2, lty = 2)
legend("topright", 
       legend = c(paste("Media:", round(mean(flu$age)), "anos"),
                  paste("Desvio Padrao:", round(sd(flu$age)), "anos")))

par(mar = c(5, 4, 4, 15)) 

set.seed(123)
medias_amostrais <- replicate(200, mean(sample(flu$age, size = 35, replace = TRUE)))

par(mar = c(5, 4, 4, 15)) 
set.seed(123)
medias_amostrais <- replicate(200, mean(sample(flu$age, size = 35, replace = TRUE)))

hist(medias_amostrais,
     probability = TRUE,
     main = "Distribuicao das Medias Amostrais (n = 35)",
     xlab = "Media das Idades (anos)",
     ylab = "Densidade",
     col = "lightgreen",
     border = "white",
     breaks = 20,
     ylim = c(0, 0.10),
     xlim = c(30, 55)) 

lines(density(medias_amostrais), col = "blue", lwd = 2)
curve(dnorm(x, mean = mean(flu$age), sd = sd(flu$age)/sqrt(35)), 
      add = TRUE, col = "purple", lwd = 2, lty = 2)
abline(v = mean(medias_amostrais), col = "darkblue", lwd = 2, lty = 2)

x_pos <- max(medias_amostrais) + 2 
y_pos <- 0.10  

legend(x = x_pos, y = y_pos,
       legend = c(
         paste("Densidade Observada (media =", round(mean(medias_amostrais), 1), ")"),
         "Distribuicao Normal Teorica (TLC)",
         paste("Erro padrao teorico:", round(sd(flu$age)/sqrt(35), 1))
       ),
       col = c("blue", "purple", "darkblue"), 
       lwd = 2, 
       lty = c(1, 2, 2),
       cex = 0.8,
       bty = "n",
       xpd = TRUE)

text(x = x_pos, 
     y = y_pos - 0.1,  
     labels = paste("Media populacional:", round(mean(flu$age), 1)),
     pos = 4,
     cex = 0.8,
     xpd = TRUE)

text(x = x_pos, 
     y = y_pos - 0.2,  
     labels = paste("Desvio padrao populacional:", round(sd(flu$age), 1)),
     pos = 4,
     cex = 0.8,
     xpd = TRUE)

par(mar = c(5, 4, 4, 2) + 0.1)