Hi Geoff - just have a quick minute.. so, I'll hazard a response without thinking about it too much :)
On 8/16/06, Geoffrey Poole < [EMAIL PROTECTED]> wrote: > > > Doesn't sqrt(SSx) increase with n? If so, won't the "standard error of > the slope" decrease with increasing sample size?? Yes - the standard error of the slope will decrease with increasing sample size. > I realize SE of estimate and SE of slope do not represent the same > thing, statistically, but by comparing the SE of estimate across > regressions of the same X and Y variables from different environments, > couldn't one assess the expected accuracy of resulting predictions > across environments using data sets with different sample size? I think > this is what Sarah is looking for... Well - (again, not having thought about this much!) if I wanted to assess the "accuracy" of predictions, I would take a look at the prediction bands of the regression lines. But, all of these things (SE estimate, prediction intervals, R^2, etc.) are all related measures of the "accuracy" of a regression. > I suspect that what Zar is referring to here > > is that the standard error of the estimate is in the same units as the > > dependent variable. Hence, you can divide it by the mean to get a > > "unitless" measure. > > > If your suspicion is true, why would Zar have continued on to say "... > making the examination of [the SE of estimate] a poor method for > comparing regressions" (page 335, fourth edition). Why would a unit-ed > (i.e. non-unitless) measure automatically be poor for comparing > regressions? The continuation of the statement would make a lot more > sense to me if Zar really were talking about instances where SE of > estimate were proportional to the magnitude of the dependent variable. I read Zar's comment "(a unitless measure)" (p335) as a reminder that > you would want to correct for any effect of the magnitude of Y by > dividing the SE of estimate (not residual variance) by the mean to avoid > mixed units... > > Also, what would be the point of dividing by the mean Y if not to remove > an effect of increasing magnitude of Y? Is there another compelling > reason to do this? Well - the only reason I can think of is to avoid "mixed units" - as you pointed out. It's the same basic principle of using a coefficient of variation. Perhaps a better characterization of the relationship between the SE of the estimate and the magnitude of Y is that, "the SE of the estimate TENDS to be proportinal to the magnitude of the dependent variable." That is - although it is not necessarily so (as in adding a constant to all values), observations with a larger mean tend to have a larger variance than observations with a smaller mean, as in your example of weights. I'd appreciate your thoughts... > > Thanks, > > -Geoff >
