Once I've estimated a regression model, how do I use that model to make out of sample predictions for y-hat. I have a large number of MSA dummy variables (202), so creating a new variable that manually calculates that value would be very tedious and vulnerable to human error.
You need to create a data set with the values of the independent variables that you want to make predictions for, concatenate this data with the original data set (leaving the value of the response variable as missing), then rerun the regression model specifying the P option in the model statement.
And after you follow polingjw's advice, keep your fingers crossed that the predicted values mean anything.
If you really have 202 dummy variables, I'm skeptical that any such prediction of out of sample values will have meaning. More than likely, you will be extrapolating, in other words, predicting in a region of X-space where you have no data.