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I have estimated a log linear regression model using SAS with the following functional form:
lnY = a + XB1 + Xb2 + Xb3 + Xb4
The dependent variable is in log form, the independent/explanatory variables in linear form.
With the equation I can estimate/forecast the linear value of Y by taking the antilog/exponent of the forecast from the equation so that I can see the value in the orginal Y values instead of the logs. This is fine.
But I also want to decompose the forecast/estimate by the respective explanatory X variable.
For example if the total forecast in log form = 5, then the anti log/exponent of that gives me a forecast of 148 in the original Y series. Now of that 148, what I need to calculate is how much is X1, X2 etc is worth, e.g
a = 2
X1 = 45
X2 = 15
X3 = 25
x4 = 61
Total = 148
Does anyone know how to do this?