I am running a linear regression model where the dependent variable (Y) is log-transformed. I am struggling on how to interpret the adjusted R-squared of this log-transformed model that is meaningful. Any insight is very much appreciated! Thank you.
Is the model of log-transformed Y the only model you are considering? Then you can just interpret the (unadjusted) R-squared in the usual way. For example, if the R-squared is 70%, then 70% of the variability in the log-transformed values of Y is accounted for by the predictor variables included in the model.
If you are considering several competing models for the log-transformed Y, then it makes sense to compare their explanatory power via the adjusted R-squared. In that case, the model with the highest value for the adjusted R-squared would be preferred - as explained, for example, here: http://blog.minitab.com/blog/adventures-in-statistics-2/multiple-regession-analysis-use-adjusted-r-squared-and-predicted-r-squared-to-include-the-correct-number-of-variables.