Depending on the boxcox transformation you can interprete your predicted values in meaningful way. First log transformation of the regressors would result in interpreting coefficient as 1% change in a regressor results in \beta change in outcome variable. Now it depends on the transformation that was ultimately done to the outcome variable. as boxcox finds optimal power transformation you must look at at which power the outcome variable is transformed at. We just need to back transform it. for example if power transform was done at -1, and the confidence interval found for beta values are say .1 and .2 then the resulting interpretation would be that 1% change in the regressor results in change in y value by between 10 and 5 (which are inverse of .1 and .2). if power transformation was done at 1/2, then the CI for beta of 2 and 3 can be interpreted as 1% change in the regressor results in change in y value by between 4 and 9. and so on. OR I have totally misunderstood your question.
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