```Date: Nov 26, 2012 8:06 AM
Author: Halitsky
Subject: Them there is some neat algebraic mechanics !

Thanks for that algebraic legerdemain ? it certainly clarifies why theu^2 in c on u,u^2 models the change in slope with change in u.Some questions.1.You say ?This is because a1 is only the slope of the function at x =0?This makes partial sense to me inasmuch as a1 = a01+a10 and a01 is theslope in the ?intercept? function A0 = a00+a01*x.  But why are youfree to disregard a10 here?  Is it necessarily 0 when x is 0?  If so,the reason why is eluding me.2.Putting aside for a moment the matter of whether we need a?meaningful? definition for a1, may I operate with a2 the same wayI?ve operated with usual slope coefficients to develop the 2-ways?That is, is it permissible to develop the 2-way a2 interactionsinvolving coreXcomp and nonrandXrand (for each of the dicodon sets1,2,3) using the same mechanics I?ve previously used for linearregression slopes of the usual type (first roll-up across lengthintervals within fold and then roll-up across folds)?If so, I?d like to go ahead and do that, in order to see whether a2behaves as one might expect it to, given our current understanding ofthe probable relationship between c and u( namely that c variesdirectly with u.)3.Regarding a ?meaningful? defintion for a1, it would be useful to haveone for two reasons:a) to see what happens with its coreXcomp and nonrandXrand 2-waysb) to see if this behavior of a1 helps to validate the use ofresiduals from c on (u,u^2) in the construction of predictors forlogistic regressions involving structural alignability.4.Does anything you've said change if we use your suggested u/(1+u)instead of u itself?
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