A Broadway investor is interested in predicting the gross sales in millions. He started with Attendance, New Productions, and Mean Ticket.Run the Backwards Elimination method using AIC criterion and determine what variable should be removed first.| Season | Gross ($M) | Attendance | New Productions | Mean Ticket ||--------|------------|------------|-----------------|-------------|| 2001 | 643 | 10.95 | 36 | 58.72 || 2002 | 721 | 11.42 | 36 | 63.13 || 2003 | 771 | 11.61 | 38 | 66.41 || 2004 | 769 | 11.53 | 39 | 66.69 || 2005 | 862 | 12 | 39 | 71.83 || 2006 | 939 | 12.31 | 35 | 76.27 || 2007 | 938 | 12.27 | 36 | 76.45 || 2008 | 943 | 12.15 | 43 | 77.61 || 2009 | 1020 | 11.89 | 39 | 85.78 || 2010 | 1081 | 12.53 | 42 | 86.27 |Selection Options:- Attendance- New Productions- Mean Ticket

We will use R software for calculations.1> Gross=c(643,721,771,769,862,939,938,943,1020,1081) 2> attendance=c(10.95,11.42,11.61,11.53,12,12.31,12.27,12.15,11.89,12.53) 3> NewProd=c(36,36,38,39,39,35,36,43,39,42) 4> MeanTicket=c(58.72,63.13,66.41,66.69,71.83,76.27,76.45,77.61,85.78,86.27) 5> DF1=data.frame(Gross,attendance,NewProd,MeanTicket) 6> DF1 7 Gross attendance NewProd MeanTicket 81 643 10.95 36 58.72 92 721 11.42 36 63.13 103 771 11.61 38 66.41 114 769 11.53 39 66.69 125 862 12.00 39 71.83 136 939 12.31 35 76.27 147 938 12.27 36 76.45 158 943 12.15 43 77.61 169 1020 11.89 39 85.78 1710 1081 12.53 42 86.271> M0=lm(Gross~1, data = DF1) #null model 2> M1=lm(Gross~., data=DF1) #full model 3> M1.back <- step(M1, scope = list(lower = M0, 4+ upper = M1),direction = "backward", k = 2) 5Start: AIC=33.92 6Gross ~ attendance + NewProd + MeanTicket 7 8 Df Sum of Sq RSS AIC 9- NewProd 1 0.7 134.4 31.979 10<none> 133.6 33.923 11- attendance 1 2696.3 2829.9 62.454 12- MeanTicket 1 25444.5 25578.1 84.469 13 14Step: AIC=31.98 15Gross ~ attendance + MeanTicket 16 17 Df Sum of Sq RSS AIC 18<none> 134.4 31.979 19- attendance 1 2720.3 2854.6 60.541 20- MeanTicket 1 29795.7 29930.0 84.040From the above output, it is evident that the first variable that was removed from the model with backward selection using AIC was "New Productions".The first variable that was removed from the model with backward selection using AIC was "New Productions".