correlation matrix

corr_arr <- function(a,b){

  corr = 0
  a_bar <-  sum(a)/length(a)

  b_bar <- sum(b)/length(b)

  var_a  =  sum((a - a_bar)^2)/(length(a) - 1)

  var_b  =  sum((b - b_bar)^2)/(length(b) - 1)

  covar_a_b =  sum((a -  a_bar) * (b -  b_bar))/ (length(b) - 1)

  corr = covar_a_b/sqrt(var_a * var_b)
  return(corr)
}
data <-  data_loader("death_rates.csv",",")

female_data = data[data$Sex == "F",]
male_data = data[data$Sex == "M",]

display_correlation  <-  function(female_data){
  #we are encoding the sex feature (F,M) -> (1,2)
  data$Sex = as.numeric(factor(data$Sex,levels = c("F","M"),labels = c(1, 2)))
  result <- matrix(, nrow = ncol(data), ncol =ncol(data))
  for (i in  1:ncol(data)){
    for (j in 1:ncol(data)){
      result[i,j] <- corr_arr(data[,i],data[,j])
    }
  }
  colnames(result) <- colnames(data)
  rownames(result) <- colnames(data)
  return(result)
}