A regression equation of $Y=100+20X$ at which observation is made on $x=5$ for which $Y=200$. No distribution of $Y$ is specified although Regression equation is assumed to follow normal but here in this case we have to assume $Y$ without any distribution. What will be the exact probability of $Y$ to fall between $195$ to $205$?

  • $\begingroup$ You could do this if you knew the mean and standard deviation of X $\endgroup$ – WW1 Sep 7 '17 at 3:59
  • $\begingroup$ X is generally assumed to be a constant for linear regression - you need a distribution for Y or $\epsilon$. $\endgroup$ – user137769 Sep 7 '17 at 4:15
  • $\begingroup$ Actually the error term is not introduced here(it was introduced in the later phase of the problem). So without error term can I assume that Y is also a constant and it's exact value within a range should be 1 in this case? $\endgroup$ – Mithun Ghosh Sep 7 '17 at 4:51

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