CODEWITHSUNDEEP
rcovariancepearson-correlation
moiaussi06
moiaussi06

Reputation: 221

Pearson Correlation Covariance Showing Positive when Negative Correlated

I'm trying to compute Pearson correlation for these two below. And it fits a linear line y=1/3*(x). When I calculate covariance, I got 4.5 and standard deviation for x and y are 4.74 and 1.58 respectively, which ends up a positive coefficient. However, the slides I have tells me the covariance is -7.5 and the coefficient -1, which confuses me. Who is actually correct on this?

x<-c(-3,-6,0,3,6)

y<-c(1,-2,0,-1,2)

Upvotes: 0

Views: 77

Answers (1)

Codutie
Codutie

Reputation: 1075

x<-c(-3,-6,0,3,6)
y<-c(1,-2,0,-1,2)

cor(x,y, method = "pearson") # pearson correlation
[1] 0.6

cov(x,y) # covariance
[1] 4.5

you can also compute the covariance and pearson correlation manually to double check:

N <- length(x)
x_ <- mean(x)
y_ <- mean(y)

cova <- 0
for(i in 1:length(x))
{
  cova <- cova + ((x[i]-x_)*(y[i]-y_))/(N-1)
}

cova
[1] 4.5

or:

cova <- as.numeric((x-x_)%*%(y-y_)/(N-1))

cova
[1] 4.5

for the pearson correlation:

cova / (sqrt(var(x)*var(y)))
[1] 0.6

Upvotes: 2

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