2

This is probably a really obvious question, but I don't see the explanation.

We have a population of $(X, Y)$ pairs for which $\rho_{XY}=\rho$ and $Y$ is given by the linear representation $Y = \alpha + \beta X + e$ where $\operatorname{Cov}(X,e) = 0$.

What is the best linear representation of the relation between $Y$ and $X$ with the variables reversed: $X = \gamma + \delta Y + u$. Specifically what would $\delta$ be in terms of $\alpha$ and $\beta$?

Davide Giraudo
  • 2,100
  • 2
  • 14
  • 23
Sophia
  • 21
  • 1
  • 5
    The hardest part of the answer is worked out at http://stats.stackexchange.com/questions/15878/. Additional useful information can be found at http://stats.stackexchange.com/questions/183778, http://stats.stackexchange.com/questions/20553/, http://stats.stackexchange.com/questions/4125 (which shows how to find $\hat\gamma$), and http://stats.stackexchange.com/questions/175551 (which completely solves the problem). – whuber Feb 21 '16 at 21:50

0 Answers0