Problem 4 (no need to show details of your work)a. Suppose that you want to choose a subset among seven independent variables, X₁, X2, X3, X4,X5, X6, and X7, by applying a best-subsets regression. By considering the best-subsets solutionsgiven below, write down the resulting selected variables.ConstantX3x1X5SR-sqR-sq (adj)R-sq (pred)Mallows' CpCandidate terms: X1, X2, x3, x4, X5, X6----Step 1----Coef14.2010.09Vars R-Sq1 67.2283.9391.893.145 93.76 93.87 93.8 92.1b. In a linear regression study, six predictors were evaluated by using a stepwise regression. Theprocedure stopped after 3 steps. Answer the following True or False questions (circle the correctanswer). Use dentry - aremove = 0.15.PConstantR-Sq(adj)0.0005.2187467.18%66.09%62.26%45.64X1X2X3X4X5X6(pred)R-Sq MallowsCp100.0 5.218766.162.382.879.636.8 3.718090.988.8X X8.0 2.70204.9 2.501792.3 90.0X X X4.8 2.4951 X X X XX90.088.486.5х х6.2 2.4858 X X X X8.0 2.5266 XX X X X X X0.12-1.318.93-0.0065----Step 1-----Coef-15.41.0260.0079892.492.3Candidate terms: X1, X2, X3, X4, X5, X6P0.0000.197----Step 2----CoefP-21.86.301.0200.9640.2130.0630.8873.3310588.86%86.18%79.38%7.004.1563779.88%78.49%75.65%19.150.0000.000i. True or False? X2, X4, and X6 were not significant at a = 0.15 when the procedure stopped.ii. True or False? In Step 2, only X1 and X3 were significant.iii. True or False? In Step 1, X3 has the highest t-value when the initial 6-variable model, Y~X1+X2+X3+X4+X5+X6 was solved.c. In a linear regression study, six predictors were evaluated by using a backward eliminationstepwise regression by setting a = 0.10, and the procedure stopped after 3 steps. Answer thefollowing True or False questions (circle the correct answer).X X X X X X XS 1 2 3 4 5 6 7XX----Step 2-----CoefP-15.51.029 0.0000.0070.00822-1.3469.12-0.0062-----Step 3----CoefP-15.660.0110.0000.8893.291.0603.1813.2664988.86%86.71%82.1185.000.0150.0000.0003.2665488.00%86.71%84.74%2.93XXX-1.3509.12----Step 3-----CoefP-16.21.0340.008240.0000.0060.0090.000SR-sqR-sq (adj)R-sq (pred)Mallows' Cpi. True or False? In step 1, six 1-variable models (Y-X1, Y-X2, ..., Y-X6) were solved and theresulting p values were depicted.3.2066488.85%87.20%84.70%3.02ii. True or False? The resulting solution of this procedure is {X1, X2, X4, X5}.iii. True or False? The regular stepwise regression and the backward elimination can producedifferent results.

Problem 4 (no need to show details of your work) a. Suppose that you want to choose a subset among seven independent variables, X₁, X2, X3, X4, X5, X6, and X7, by applying a best-subsets regression. By considering the best-subsets solutions given below, write down the resulting selected variables. Constant X3 X1 X5 S R-sq R-sq (adj) R-sq (pred) Mallows' Cp R-Sq Vars R-Sq (adj) 67.2 66.1 83.9 82.8 90.9 92.3 92.4 6 93.8 92.3 7 93.8 92.1 1 2 3 91.8 4 93.1 5 93.7 Candidate terms: X1, X2, x3, x4, X5, X6 ----Step 1---- ----Step 2- Coef Coef 14.20 -21.8 10.09 0.000 6.30 1.020 Constant x1 x2 X3 X4 X5 X6 S R-sq R-sq (adj) R-sq (pred) Mallows' Cp P 5.21874 67.18% b. In a linear regression study, six predictors were evaluated by using a stepwise regression. The procedure stopped after 3 steps. Answer the following True or False questions (circle the correct answer). Use dentry=dremove= 0.15. (pred) R-Sq Mallows Cp 100.0 5.2187 S 36.8 3.7180 66.09% 62.26% 45.64 62.3 79.6 0.12 -1.31 8.93 -0.0065 88.8 90.0 90.0 88.4 86.5 Candidate terms: x1, x2, X3, x4, X5, X6 ----Step 1----- Coef P -15.4 1.026 3.33105 88.86% 86.18% 79.38% 7.00 X X X X X X X 4.8 2.4951 x x x x 6.2 2.4858 XXXX 8.0 2.5266 XXXXXXX 8.0 2.7020 4.9 2.5017 0.000 0.000 4.15637 79.88% 78.49% 75.65% 19.15 P 0.000 0.00798 0.197 0.00822 0.964 0.213 0.063 0.887 -1.346 9.12 -0.0062 -----Step 3--- Coef -15.66 3.29 1.060 3.181 i. True or False? X2, X4, and X6 were not significant at a= 0.15 when the procedure stopped. ii. True or False? In Step 2, only X1 and X3 were significant. iii. True or False? In Step 1, X3 has the highest t-value when the initial 6-variable model, Y~ X1+X2+X3+X4+X5+X6 was solved. х х х х 123 c. In a linear regression study, six predictors were evaluated by using a backward elimination stepwise regression by setting a =0.10, and the procedure stopped after 3 steps. Answer the following True or False questions (circle the correct answer). -----Step 2----- Coef P -15.5 1.029 0.000 0.007 0.011 0.000 0.889 P 0.015 0.000 0.000 3.26649 88.86% 86.719 82.118 5.00 3.26654 88.00% 86.718 84.74% 2.93 X X x XX -1.350 9.12 -----Step 3----- Coef -16.2 1.034 0.00824 P 0.000 0.006 0.009 0.000 3.20664 88.85% 87.20% 84.70% 3.02 i. True or False? In step 1, six 1-variable models (Y-X1,Y~X2, ..., Y-X6) were solved and the resulting p values were depicted. ii. True or False? The resulting solution of this procedure is {X1, X2, X4, X5}. iii. True or False? The regular stepwise regression and the backward elimination can produce different results.