I've got a paper to deliver in which I have to choose between different models of regression. Trying to be concise, in the first exercise I've got a lin-lin (or level-level) model vs a lin-log with the same variables. I thought about using the R^2, since the dependent variable is the same, but they are really similar (the lin-lin takes the upperhand). (I'm using STATA to compute all this)
Looking at the square sum of the residuals, they're really similar too, and the lin-lin has a lower value.
We have not seen different criteria (like Akaike's) to choose from, so we should not calculate any of that. What we can do is look at the scatterplots. In this case, the values are really weird. The y is a percental value which is 0 for 78% of the population and then goes up till 99%, maybe.
Therefore, the scatterplots are weird too. The ones of the lin-log are a little bit more centered, but I don't see a real difference, maybe because I'm not an expert.
I've tried to do a residuals vs fitted values plot too, but to no avail, I don't see a real difference (in the lin-log, there seems to be less horizontal spread).
Is there anything I've been missing? Should I choose the one with the lowest R square? In consecutive exercises, it seems they've chosen the lin-log (they expand using that model), but I can't seem to know why.
Thanks in advance, and sorry for anything not well written (this is not my first language or subject of expertise). Thanks!!
PS: I have not talked about the adjusted R square because the number of variables is the same, but they're also almost equal.