How Does Gase Have The Audacity To Be Irritated?

Ah.. the formula for Pearson correlation does that for you automatically.



As you can see, the standard deviation for each random variable is in the denominator.

You can also see in the equation itself why multiplying one random variable (say each x) by some non-negative scalar k has no effect. That k factors out of both the numerator and denominator and cancels out. However, if k is negative, it factors out unchanged in the numerator (so it's still negative) but becomes positive in the denominator. So multiplying by a negative scalar flips the correlation. And of course dividing by zero is undefined so zero is an exception.

 

I feel Dumb...