I have two independent variables to predict my independent variable. For both theoretical and practical reasons, it made sense to log all of the three variables. In R formula:
log(y) ~ log(x1) + log(x2)
The model works great and meets all assumptions of linear regression with flying colors.
Now, I'd like to transform the fitted model including the fitted parameters to its 'unlogged' state, i.e., without the logs. I think this should be:
$$y = exp(\hat{\alpha}) \cdot exp(\hat{\beta_1})^{x_1} \cdot exp(\hat{\beta_2})^{x_2}$$
where each of the three parameters are the estimates from the regression, transformed exponential. Is this correct?
