I am reviewing a regression model that is structured like this:
Y = β0*(X1^β1*X2^β2*X3^β3*X4^β4)
The analyst performed a transformation to obtain:
Ln(Y) = lnβ0 + β1lnX1 + β2lnX2 + β3lnX3 + β4lnX4
The analyst then regressed the ln equation to find the coefficients and provided the equation in both the ln form and the power law form.
When I regress the power law form against the experimental result, there is a severe violation of the constant variance assumption. A severe triangle increasing to the right on the residuals vs fit plot.
When I regress the ln form of the regression against the ln of experimental data the constant variance assumption is met, slightly increasing variation, (naturally since it is an ln function).
The analyst says that the equation for Y is valid because the equation for ln(Y) satisfies the constant variance assumption.
Since I am not interested in the value of ln(Y), I am only interested in Y, I am telling the analyst that the violation of the constant variance assumption makes the regression model of interest (Y) invalid, regardless of the result of residuals vs fits for the ln form of the equation.
Is there something I am missing here? Doesn’t the model for Y have to meet the constant variance assumption? Am I supposed to care whether or not the ln(Y) model meets the constant variance assumption when ln(Y) is not the number I care about?
By the way, if I take the antilog of the result of the ln form of the equation, the severe violation of the constant variance assumption returns (as would be expected).
Thanks in advance for the help.
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