I did a regression and found that my residuals pointed out that my data is heteroscedastic.
I applied the Box-Cox transformation and my new model looks as follows,
y^(1/5) = b0 + b1x1 + b2x2
with my lambda = 1/5 and I found my b0, b1 and b2 values. This transformed model does not seem to have heteroscedasticity but now I want to use these coefficients to forecast data on a hold out set I have and test the accuracy. But is it correct if i use the coefficients from the transformed model and the resulting value I must get the power of 5 in order to get the actual value forecasted that I want to compare with the actual?
Best Answer
Yes and no.
Yes - You can use the reverse transformation of your data to get predictions for future observations.
No - the meaning of that prediction is different than if you had not done any transformation. If you are fitting a linear model to the variables as is (and assuming you are using OLS), then you predict a feature value based on the expected value (given a set of predictors). However, if you are doing this and then running a reverse transformation on it (assuming the transformation is not linear, as is the case with the box cox transformation), then you are no longer using the expected value as your prediction. HOWEVER, you are using the (estimated) median value as your prediction (since the median is robust to this type of monotonic transformation).