Agency revenues. An economic consultant was retained by a large employment agency in a metropolitan area to develop a regression model for predicting monthly agency revenues ( y ). She decided that three economic indicators for the area were potentially useful as independent variables, namely, average weekly overtime hours of production workers in manufacturing ( 1 x ), number of job vacancies in manufacturing ( 2 x ), and index of help wanted advertising in newspapers ( 3 x ). Monthly observations on agency revenues and the three independent variables were obtained for the past 25 months. The ANOVA table for the model  is as follows:

The consultant decided to screen the independent variables to determine the best set for predicting agency revenues. The regression sums of squares for all possible regression models were found to be as follows:

(a) Determine the subset of variables that is selected as best by the forward selection procedure using F0* = 4.2  (to-add-variable). Show your steps.
 
(b) Determine the subset of variables that is selected as best by the backward elimination procedure  using  F0** = 4.1 (to-delete-variable). Show your steps.

NOTE:   ( t0** ) 2  = F0**
 
(c) Determine the subset of variables that is selected as best by the stepwise regression procedure using  F0* = 4.2  (to-add) and F0**
= 4.1 (to-delete). Show your steps.