Function Coefficient of Correlation

Compute Coefficient of Correlation

coff_cor <- function(x,y){
  
# r = nΣxy - (Σx)(Σy) / √ [nΣx²- (Σx)²][ nΣy²- (Σy)²]

x<- c(20,18,19,19,19,19,21,21,20,19,20)
y <- c(2,1,2,1,2,3,3.5,1,2,1,0.5)

# Σxy
sum_xy <- sum(x*y)
sum_xy

# length
n <- length(x)
n

# (Σx)(Σy)
sum_x_sum_y <-  sum(x) * sum(y)
sum_x_sum_y

numerator <- (n * sum_xy) - (sum_x_sum_y)
numerator


# Σx²
sum_x_sqr <-  sum(x^2)
sum_x_sqr

 #(Σx)²
sum_x_whole_sqr <- sum(x)^2
sum_x_whole_sqr

# Σy²
sum_y_sqr <-  sum(y^2)
sum_y_sqr

 #(Σy)²
sum_y_whole_sqr <-  sum(y)^2
sum_y_whole_sqr

# √ [nΣx²- (Σx)²][ nΣy²- (Σy)²]

denominator <-(n * sum_x_sqr - sum_x_whole_sqr) * (n * sum_y_sqr - sum_y_whole_sqr) 
denominator <- sqrt(denominator)
denominator

r <- numerator / denominator
r

return(r)
}

coff_cor(x,y)

## [1] 0.2454316