Let's say there are two correlated random variables $X$ and $Y$ with coefficient of correlation as $r$. Assume during some hypothesis testing we found that due to some change in the environment mean $\mu_x$ of $X$ has jumped by 25%. What will be the change in the $\mu_y$ of $Y$ which is also affected by a new change in a similar way? What will be the confidence interval in this case.

  • $\begingroup$ If the mean of $X$ has changed, then the distribution of $(X,Y)$ has changed, so you can no longer say anything about $E[Y].$ $\endgroup$ – whuber Feb 23 at 13:20
  • $\begingroup$ We have the sample for $X$ after the process change but not for $Y$. What I am saying is we knew earlier the correlation exists, now when we see due to some underlying process change which affects both equally mean of $X$ is changed(observed). Can we estimate how much the mean of $Y$ will change? $\endgroup$ – Bhupendra dubey Feb 23 at 13:28
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    $\begingroup$ Not with that little information. You would have to make strong assumptions to justify any estimate, assumptions that are tantamount to supposing there is a linear relationship between $X$ and the conditional expectation of $Y$ that is preserved by the process change. $\endgroup$ – whuber Feb 23 at 14:16
  • $\begingroup$ Let us take an example. $X$ was the mean revenue for an app released on the android platform, $Y$ is for the same app on IOS. A new change has caused $\mu_x$ to go up by 25% anything can be said about $Y$? May be a most likely estimate if not correct? $\endgroup$ – Bhupendra dubey Feb 23 at 14:52
  • $\begingroup$ Little can be said at all about $Y.$ For instance, if the platforms compete, possibly $Y$ decreases. $\endgroup$ – whuber Feb 23 at 14:59

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