Note : I have just started learning statistics and the question might be very basic. I know what is variance, standard deviation.
I have following 2 questions regarding covariance and correlation
What is the intuitive meaning of the product in the formula of Cov(X,Y). Why not add the two terms instead of multiplying ?
In addition to direction, why can't I use the magnitude of Cov(X,Y) to determine the strength of relation ? I know this is because of random variables being in different scales but I still lack the intuition to why this is problematic ?
Note : I understand what correlation and covariance means but I don't understand the intuition behind the formula, meaning, why this particular formula gives the meaning that these terms have.