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I am looking for mathematical derivation of intercept and slope of simple linear regression model when the independent variable is random (not fixed). I.e., follows normal distribution or else. I want to check the impact of random x on the slope and intercept estimates and their variances.

Tahir Malik
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    This is part of the standard formulation of ordinary least squares, provided $X$ is independent of the errors in $Y$: all the estimates and variances are conditional on $X$. That enables you to assume any marginal distribution you want for $X$. – whuber Jul 17 '16 at 13:53
  • Thanks a lot whuber.... Yes i got it..... If i assumed normal distribution for X.... Can you share with me mathematical derivation or some reference for this.... – Tahir Malik Jul 17 '16 at 16:16
  • I need some mathematical explanation for my problems.... Can some one help me for this.... – Tahir Malik Jul 18 '16 at 12:23

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