####################
###  1. zadatak  ###
####################

data("mtcars")

# 1. (a)
apply(mtcars[c(1,4,6,7)], 2, function(x) c("Mean" = mean(x), "SD" = sd(x), "MIN" = min(x), "MAX" = max(x)))

# 1. (b)

Index = mtcars$mpg^2/mtcars$wt + 0.5*mtcars$qsec - log(mtcars$hp)
data = cbind(mtcars, round(Index,2))
data

# 1. (v)

classter1_condition = (data$mpg > mean(data$mpg)) & (data$qsec > mean(data$qsec)) & (data$Index < mean(data$Index))
classter2_condition = (data$mpg > mean(data$mpg)) & (data$qsec < mean(data$qsec)) & (data$Index < mean(data$Index))
classter3_condition = (data$mpg < mean(data$mpg)) & (data$qsec < mean(data$qsec)) & (data$Index < mean(data$Index))

Classter = ifelse(classter1_condition, 1, ifelse(classter2_condition, 2, ifelse(classter3_condition, 3, 4)))
fClasster = factor(Classter, levels = 1:4)
data = cbind(data, fClasster)
data

# 1. (g)

Lista = list(c(rownames(data[data$fClasster == 1,]), mean(data[data$fClasster == 1,]$Index)), 
             c(rownames(data[data$fClasster == 2,]), mean(data[data$fClasster == 2,]$Index)), 
             c(rownames(data[data$fClasster == 3,]), mean(data[data$fClasster == 3,]$Index)), 
             c(rownames(data[data$fClasster == 4,]), mean(data[data$fClasster == 4,]$Index)))
Lista

####################
###  2. zadatak  ###
####################

data("airquality")
airquality

# 2. (a)

round(apply(airquality[c(-5,-6)], 2, function(x) c(mean(x, na.rm = T), var(x, na.rm = T))), 5)

scaled_air <- apply(airquality[c(-5,-6)], 2, function(x){
  round((x - mean(x, na.rm = T)) / sd(x, na.rm = T), 5)
})

round(apply(scaled_air, 2, function(x) c(mean(x, na.rm = T), var(x, na.rm = T))), 5)

# 2. (b)

Iqr_Func <- function(x){
  as.numeric(diff(quantile(x, probs = c(0.25, 0.75), na.rm = T)))
}

# 2. (v)

HotDays <- function(){
  Mean <- mean(airquality$Wind, na.rm = T)
  Iqr <- Iqr_Func(airquality$Temp)
  
  condition <- airquality$Wind <= Mean & airquality$Temp >= 6.5*Iqr
  
  return (list(airquality[condition,], nrow(airquality[!condition,])))
}

HotDays()

####################
###  3. zadatak  ###
####################

xk = c(58.3, 62.1, 54.7, 59.5, 61.0, 57.8, 63.2, 60.5, 56.9, 59.1, 64.0, 60.2)
xt = c(65.1, 68.4, 70.2, 66.8, 67.5, 69.3, 71.0, 66.0, 68.1, 67.9, 69.7, 68.3)

## 3. (a)

var.test(xk, xt, ratio = 1, alternative = "two.sided")
t.test(xk, xt, var.equal = T)

## 3. (b)

confidence_interval_m <- function(x, alfa = 0.95) {
  n <- length(x) 
  C <- qt((1 + alfa)/2, df = n - 1)
  
  c(mean(x) - C * sd(x) / sqrt(n-1),mean(x) + C * sd(x) / sqrt(n-1))
}

confidence_interval_m(xk)

## 3. (v)

confidence_interval_s2 <- function(x, alfa = 0.90) {
  n <- length(x) 
  c1 <- qchisq((1 + alfa)/2, df = n - 1)
  c2 <- qchisq((1 - alfa)/2, df = n - 1)
  c(n * var(x) / c1, n * var(x) / c2)
}

confidence_interval_s2(xk)

sqrt(confidence_interval_s2(xt))

####################
###  4. zadatak  ###
####################

set.seed(123)
n <- 100   
dani <- 31

temp <- rnorm(dani, mean = -2, sd = 4)

sedmica <- rep(1:7, length.out = dani)
vikendi <- ifelse(sedmica == 6 | sedmica == 7, TRUE, FALSE)

## 4. (a)

potrosnja <- matrix(0, nrow = n, ncol = dani)

for (d in 1:dani) {
  if (vikendi[d]) {
    osnovna_potrosnja <- rnorm(n, mean = 34, sd = 6)
  } else {
    osnovna_potrosnja <- rnorm(n, mean = 28, sd = 5)
  }
  
  if (temp[d] < 0) {
    osnovna_potrosnja <- osnovna_potrosnja * 1.2
  }
  
  potrosnja[, d] <- osnovna_potrosnja
}

## 4. (b)

prosecna_po_danu <- colMeans(potrosnja)

plot(1:dani, prosecna_po_danu, type = "l", col = "blue", lwd = 2,
     xlab = "Дан", ylab = "Просечна потрошња (kWh)",
     main = "Просечна дневна потрошња за 100 домаћинстава")

####################
###  5. zadatak  ###
####################

set.seed(123)

n <- 25
N <- 100000

X <- sample(1:n, N, replace = TRUE)
Y <- sample(1:n, N, replace = TRUE)
Z <- X + Y

# moguce vrednosti Z
z_values <- 2:(2 * n)

means <- numeric(length(z_values))  

# E[X|Z=z]
for (i in seq(length(z_values))) {
  idx <- Z == z_values[i]               
  means[i] <- mean(X[idx])      
}

result <- data.frame(Z = z_values, E_X_given_Z = means)
print(result)

####################
###  6. zadatak  ###
####################

library(dplyr)
library(tidyr)

data(satfruit , package = "PASWR")

## 6. (a)

satfruit %>%
  summarise(
    AF_mean = mean(AF, na.rm = TRUE),
    AF_md   = median(AF, na.rm = TRUE),
    AL_mean = mean(AL, na.rm = TRUE),
    AL_md   = median(AL, na.rm = TRUE),
    OL_mean = mean(OL, na.rm = TRUE),
    OL_md   = median(OL, na.rm = TRUE)
  )

## 6. (b)

satfruit <- satfruit %>%
  mutate(
    Total.Arable = WH + BA + COR + SF + VI + PS + ES + AF + CO + AR + AL + OL + FR,
    Fruit.Share = FR / Total.Arable
  )

satfruit %>%
  group_by(SArea) %>%
  summarise(AvgFruitShare = mean(Fruit.Share, na.rm = TRUE)) %>%
  arrange(AvgFruitShare)

## 6. (v)

satfruit %>%
  group_by(SArea) %>%
  summarise(
    AvgCOR = mean(COR, na.rm = TRUE),
    MedianSF = median(SF, na.rm = TRUE),
    MaxFR = max(FR, na.rm = TRUE)
  )

####################
###  7. zadatak  ###
####################

library(ggplot2)
library(nycflights13)

# 7. (a)
flights_jan <- flights %>%
  filter(month == 1, !is.na(dep_delay), !is.na(arr_delay), !is.na(air_time)) %>%
  mutate(air_time_diff = air_time - dep_delay) 

# 7. (b)

joined_data <- flights_jan %>%
  left_join(airports, by = c("dest" = "faa"))

# 7. (v)

summary_airports <- joined_data %>%
  group_by(name) %>%
  summarise(
    avg_arr_delay = mean(arr_delay, na.rm = TRUE),
    avg_air_time_diff = mean(air_time_diff, na.rm = TRUE)
  )

# 7. (g)

summary_airports <- summary_airports %>%
  mutate(
    punctuality_level = ifelse(
      avg_arr_delay < 0, "high",
      ifelse(avg_arr_delay <= 10, "medium", "low")
    )
  )

# 7. (d)

summary_airports %>%
  count(punctuality_level)

# 7. (dj)

ggplot(summary_airports, aes(x = avg_air_time_diff, y = avg_arr_delay)) +
  geom_point(aes(color = punctuality_level), size = 3, alpha = 0.75) +
  labs(
    title = "Одступање дужине лета vs. просечно кашњење по аеродромима",
    x = "Одступање просечне дужине лета (мин)  [avg_air_time_diff]",
    y = "Просечно кашњење при доласку (мин)   [avg_arr_delay]",
    color = "Ниво тачности"
  ) +
  theme_minimal()