Sample Covariance for 2 vectors

Question

I'm trying to calculate sample covariance between these two vectors. I defined a function with two input variables. I don't know if it is correct? Also my formula for sample covariance won't run. Can anyone help me write it out in R?

  xv = c(1., 5.5, 7.8, 4.2, -2.7, -5.4, 8.9)
  yv = c(0.1, 1.5, 0.8, -4.2, 2.7, -9.4, -1.9)
  sampleCov= function(x,y){ 
    cov(xv,yv) = frac{sum_{i=1}^{n}(x_i-\mu_x)(y_i-\mu_y)}{n-1}].
    return (Cov(xv,yv)
  }

Answer 1

There is a base function in R called cov that does exactly what you want, but if you want to write a function (no need to do that) you can try the following:

COV<- function(x,y) {
  if(length(x)!=length(y)) {stop('x must have the same length as y ')}
  x.bar <- mean(x)
  y.bar <- mean(y)
  N <- length(x)

  Cov <- (sum((x-x.bar)*(y-y.bar))) / (N-1)
  return(Cov)
}

COV(xv, yv)
[1] 8.697381

cov(xv, yv)
[1] 8.697381

As you can see COV gives the same result as cov so you don't have to write a function for that.

Besides, the body of your function doesn't have R syntax, instead you wrote LaTex syntax which are not the same.