11  Covariance and Correlation

• Covariance

$$Covariance=\frac{1}{N-1}\sum _{i=1}^N(x_i-\overline{x})(y_i-\overline{y})$$

• Correlation

$$Correlation=\frac{\sum _{i=1}^N(x_i-\overline{x})(y_i-\overline{y})}{{\sigma }_x{\sigma }_y}$$

ct <- c(1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,4,5,5,6,6,14)
mean_ct <- mean(ct)

vr <- sum((ct-mean_ct)^2)/(length(ct)-1)
sd <- sqrt(vr)