25.1: Computing Covariance and Correlation (Section 24.3)

Let’s first look at our toy example of covariance and correlation. For this example, we first start by generating a set of X values.

df <-
tibble(x = c(3, 5, 8, 10, 12))

Then we create a related Y variable by adding some random noise to the X variable:

We compute the deviations and multiply them together to get the crossproduct:

And then we compute the covariance and correlation:

results_df <- tibble(
covXY=sum(df$crossproduct) / (nrow(df) - 1), corXY= sum(df$crossproduct) /
((nrow(df) - 1) * sd(df$x) * sd(df$y)))

kable(results_df)
covXY corXY
17 0.89