Using and Interpreting R^2.

You have been introduced to the notion that R^2 can capture “the % of variation in Y explained by the regression model.”  This interpretation holds for simple and multivariate regression (as you have seen: as long as the model contains an intercept.)  It is important to note, however, that R^2 cannot be used formally to hypothesis test whether a model is “good” or “not.”  Therefore, the magnitude is often open to interpretation.  I have noticed that there is often a desire to identify a “global value for R^2” that suggests the model is “good.”  (Global in the sense that the value could be used across all models, 0.70?  0.80?  0.90?)  Often I am asked, “what is a good value for R^2?”

My response is always this: “Before I answer your question, tell me what you are using for your dependent variable, Y.”  The fact of the matter is that some Ys are simply easier to explain than others.  It also tends to be true that time series models are “easier to fit” than cross-section models. Therefore, in my experience, it is not difficult to find a time series model of US GDP with an R^2 of 0.90 or greater.  On the other hand, researchers trying to estimate cross-section models of RGDP growth in Sub-Saharan Africa are often ecstatic if they can get R^2 of 0.25 or higher.

Can you think of dependent variables Y that you would consider might be easier to fit?  Can you think of dependent variables Y that even with many X regressors still might be different to explain?  You do not have to substantiate your example with concrete evidence but rather feel free to assert examples for which you have a strong “hunch.”