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Apr 2, 2013 at 2:22 vote accept Joe
Apr 1, 2013 at 22:43 comment added whuber For intuition, suppose $Y = X$ up to a relatively small (independent, homoscedastic) random error and that the values of $X$ are skewed. Then the values of $Y$, looking like those of $X$, will also be skewed: but you would have no reason to, and gain no benefit from, taking logarithms. For intuition about your method, consider that most of the averages $\bar{x}_i$ will be close to the mean of all the $x$'s and most of the $\bar{y}_i$ will be close to the mean of all the $y$'s. Thus any regression based on them will grossly extrapolate to the full range of $x$'s and probably be wildly wrong.
Apr 1, 2013 at 22:13 answer added Glen_b timeline score: 3
Apr 1, 2013 at 18:45 review First posts
Apr 1, 2013 at 18:46
Apr 1, 2013 at 18:43 comment added D L Dahly It seems like you could simulate date under one "model" and then estimate the relationship with the other.
Apr 1, 2013 at 18:37 comment added whuber Please explain how we are to construe "more or less": if that doesn't mean exactly the same, then how are we to determine how close is close enough? (We would have a built-in way to do that if your procedure provided accurate error estimates, but it does not.)
Apr 1, 2013 at 18:33 comment added Joe "equivalent" means the linear regression results of the two methods (coefficient estimates, etc.) will be more or less the same. In other words, they both arrive at the same relationship between X and Y.
Apr 1, 2013 at 18:29 comment added whuber It is clear the two approaches are different, because your proposal fails to obtain (correct) information about the uncertainty in the estimates. So in what sense do you mean "equivalent"?
Apr 1, 2013 at 18:26 history asked Joe CC BY-SA 3.0