```Date: Dec 1, 2012 4:46 PM
Author: Ray Koopman
Subject: Re: Interpretation of coefficients in multiple regressions which<br> model linear dependence on an IV

On Dec 1, 11:00 am, Ray Koopman <koop...@sfu.ca> wrote:> [...]>> There are two average slopes. Call them Av1 and Av2:>> dy/dx1 = a1 + a3*x2  ==>  Av1 = a1 + a3*mean_x2>> dy/dx2 = a2 + a3*x1  ==>  Av2 = a2 + a3*mean_x1>> To estimate the coefficients, give your regression program> three predictors: x1, x2, and x3 = x1*x2. Then>> var[Av1] = var(a1) + 4*var(a3)*(mean_x2)^2 + 4*cov(a1,a3)*mean_x2,>> var[Av2] = var(a2) + 4*var(a3)*(mean_x1)^2 + 4*cov(a2,a3)*mean_x1,Those are a good example of the sort of mistake it is easy tomake when cutting and pasting instead of typing from scratch.The correct variances arevar[Av1] = var(a1) + var(a3)*(mean_x2)^2 + 2*cov(a1,a3)*mean_x2,var[Av2] = var(a2) + var(a3)*(mean_x1)^2 + 2*cov(a2,a3)*mean_x1.Also, there is a covariance that might be needed sometime:cov[Av1,Av2] = cov[a1,a2] + var[a3]*mean_x1*mean_x2 +               cov[a1,a3]*mean_x1 + cov[a2,a3]*mean_x2.
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