Is all in the title. I would like to know if there is any difference in terms of coefficients, residuals, p-values, but also conceptually.
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$\begingroup$ The difference is in how the errors are modeled. You should look up the formulas. I'd guess there should be some duplicates here already. $\endgroup$ – Roland Mar 28 '15 at 14:56
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6$\begingroup$ In the first case, you assume that log(y) is normal given x (and that the mean of log(y) is a linear function of x), and in the second case you assume that y itself is normal given x (and the log of its mean is a linear function of x). These are two different models, and may potentially give very different answers. $\endgroup$ – Karl Ove Hufthammer Mar 28 '15 at 15:52
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4$\begingroup$ Just to add to @Roland’s comment: If you model log(y) ~ x, you assume that log(y) equals a linear function of x plus an error term (which is normally distributed). This means that y equals a (non-linear) function of x times an error term (which is log-normally distributed). $\endgroup$ – Karl Ove Hufthammer Mar 28 '15 at 15:55
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$\begingroup$ @KarlOveHufthammer, your comments seem to have the makings of an answer (& I think a better answer than those at the other Q, including mine). Why not turn them into an official answer here before this gets closed? $\endgroup$ – gung - Reinstate Monica♦ Mar 29 '15 at 1:29
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1$\begingroup$ Although none of them are close duplicates, you may get some benefit from this question or this one and possibly even this answer or this question $\endgroup$ – Glen_b Mar 29 '15 at 9:31
