1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Property of correlation coefficient

  1. Mar 18, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove the following:
    Let [tex]\rho[/tex] be the correlation coefficient.
    Prove:
    [tex] \rho(X, Y) = 1 \iff P(Y=aX+b) = 1[/tex]


    2. Relevant equations
    [tex] \rho(X, Y) = cov(X,Y)/\sigma_x\sigma_y [/tex]


    3. The attempt at a solution
    I have no idea how to prove this, I know that rho must lie between 1 and -1 (inclusive) and that values close to 1 indicate that high values of X must go with high values of Y. But I don't know how to formally prove the above problem.
     
  2. jcsd
  3. Mar 19, 2012 #2
    bump. I can't believe nobody hasn't proven or seen the proof of this.
     
  4. Mar 19, 2012 #3

    lanedance

    User Avatar
    Homework Helper

    As this is an if and only if, you must prove both ways, I suggest starting with
    [tex] P(Y=aX+b)=1 \ \ \implies \ \ \rho(X,Y) = 1[/tex]

    Now as the probability is one, you can start with
    [tex] Y=aX+b[/tex]

    Now assume you know [itex] \mu_X, \sigma_x [/itex] and calculate [itex] \rho(X,Y)[/itex]

    The other direction may be slightly trickier, but you should get some good insights from the first exercise
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Property of correlation coefficient
Loading...