And down the rabbit hole I go...

Currently I am reading the book "Statistics for the Utterly Confused". So far it's been excellent - for instance, I now have a good understanding of standard deviation, variability, percentiles and even box-plots.

And so now I start learning about bivariate data, and of course I get to learning about the correlation coefficient. Or more specifically the Pearson product-moment correlation coefficient, of which they present the following spectacular and complex formula:



Of course, there is no attempt to explain why this formula works. So now I'm looking up Wikipedia on this topic. Sadly, Wikipedia does not have a good broad overview of this that I can see, and assumes prior knowledge, so I'm now in the process of following a trail of topics (from bottom to top):

• Pearson product-moment correlation coefficient
• Covariance
• Random Variable
• Second moment
• Expected value
• Random vector
• Vector space
  
• Plane
• Euclidean vector

And, as Wikipedia doesn't seem to want to explain Vectors well, I'm also reading the following introduction to vectors.

Update: When I did a Google search, as it turns out there is actually a much simpler version of this formula (who knew?) that is explained here.