I am currently attempting to determine the most predictive weighted multiple linear regression model to use and am trying to figure out the best combination of variables to use in the model.
My first idea was to use take the weighted mean of errors from LOOCV for all possible variable combinations. However, being that my data has 20 variables, this would forever for my computer to run all of these regressions. After doing a bit of research, my impression is that using LOOCV for model selection is similar to comparing the AIC of each run of the regression. Is this true? If so, would another method for determining the best model be by running a single regression using all observations for each variable combination and then choosing the model with the lowest AIC? Would the results be impacted by the fact that the observations in my model are weighted differently?
Any help would be greatly appreciated!