Question 1.

This question is really about reconciling Maddala's three objectives with the statistical terminology.

In the broader context it provides answers to the questions of "why bother with regression" and "what can it do for me"?

Would you like to be able to measure how changes in policy might relate to changes in outcomes? If so, then you need to look at the regression coefficents which tell you how changes in X are associated with changes in Y.

If you want to forcast the most likely outcome of any particular set of policies, then you are in the business of prediction. Regression allows you do do this by "fitting a line/plane" to the data. It is the values of y on the plane, the so called y-hats, that are the fitted or forecasted values.

Finally, after all this analysis, it would be useful to be able to measure just how effective the entire regression analysis had been -- how much of the varability in outcomes was explained by the model. That is, did any of the variables explain a "significant" amount of variability. Partitioning total variability into components related to the part explained by the regression model and the variability left over (sometimes called Error) is the domain of the analysis of variance.