Thread: Pearson Correlation Coefficient Boundary Proof

Given two sequences of numbers x1, .... , xn and y1, ....... , yn,
the Pearson Correlation Coefficient (PCC) is computed as



Prove that the -1 <= PCC <= 1, regardless of the values of x and y.


I do not even know where to start, I know that this correlation is a ratio which tells me to prove the -1 <= PCC <= 1 of any ratio means to prove that denominator >= numerator no matter what values there are.


Thanks for any guidance/advice

Originally Posted by aaboyd

Given two sequences of numbers x1, .... , xn and y1, ....... , yn,
the Pearson Correlation Coefficient (PCC) is computed as



Prove that the -1 <= PCC <= 1, regardless of the values of x and y.


I do not even know where to start, I know that this correlation is a ratio which tells me to prove the -1 <= PCC <= 1 of any ratio means to prove that denominator >= numerator no matter what values there are.


Thanks for any guidance/advice

It is just the Cauchy-Schwarz inequality.

CB