# Should R squared value be changing when both predictions and actual values are transformed together?

I have a regression prediction task where my outcome variable is right skewed. I performed a log transformation of the outcome variable and put it in a linear regression model. I assessed the R squared of the model and found it to be greatly improved (over non-transformed model).

Next I converted my dev set prediction values and dev set actual outcome values out of log scale (log -> exp). When I calculate R squared with the converted values it is quite a bit lower (.80 -> .70).

Am I wrong to think the R squared shouldn't be changing?

• Could you explain what "dev set prediction" and "dev set actual outcome" values are? And if you expected $R^2$ not to change, why did you transform the variables in the first place? – whuber Jul 6 '18 at 18:32
• By dev set prediction and actual outcomes I just mean that after forming my model with my data, I had a held out set of data that I wanted to predict values for (of which I already new the true value). Because my model's outcome variable is log transformed, so are my predictions. I used these two sets (true values and predicted values) to calculate an R squared. But ultimately I don't want my predictions in log values, so I converted back. However when I then calculate R squared using the converted predictions (and non-log true values), my R squared drops significantly. – David Skarbrevik Jul 6 '18 at 19:10