Compare regression coefficients

#1
Hi all,
I have two independent measures of my dependent variable. I hypothesized that one of the two is better in prediction the dependent variable. Let’s imagine that I would have measured the height of a bottle with (a) a ruler and (b) just my hand span. I want to be able to say that a predicts the height of a bottle better than b. Does anyone know how I can compare the two predictions? Can you recommend any papers on that topic? I know that I could compare correlation coefficients but I would like to compare explained variance or regression models.

Thanks a lot!
 

hlsmith

Less is more. Stay pure. Stay poor.
#4
I would look at the partial R-squared values in a multiple regression. So regress true height on X1 and X2 and calculate the partial R-square values with confidence intervals. This isn't a direct comparison between them, but it will quantify the amount of variability in Y explained by each predictor.

For a formal test, which doesn't give you measures estimates of each, would be conducting a -2loglikelihood test.
 
#5
You could also compare the predicted and real values with each tool and calculate a MAPE (or MSE or many similar measures).