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.
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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question

Transcribed Image Text: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
Candidate terms: X1, X2, x3, x4, X5, X6
----Step 1----
Coef
14.20
10.09
Vars R-Sq
1 67.2
2
83.9
3
91.8
93.1
4
5 93.7
6 93.8
7 93.8 92.1
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 - aremove = 0.15.
P
Constant
R-Sq
(adj)
0.000
5.21874
67.18%
66.09%
62.26%
45.64
X1
X2
X3
X4
X5
X6
(pred)
R-Sq Mallows
Cp
100.0 5.2187
66.1
62.3
82.8
79.6
36.8 3.7180
90.9
88.8
X X
8.0 2.7020
4.9 2.5017
92.3 90.0
X X X
4.8 2.4951 X X X X
X
90.0
88.4
86.5
х х
6.2 2.4858 X X X X
8.0 2.5266 XX X X X X X
0.12
-1.31
8.93
-0.0065
----Step 1-----
Coef
-15.4
1.026
0.00798
92.4
92.3
Candidate terms: X1, X2, X3, X4, X5, X6
P
0.000
0.197
----Step 2----
Coef
P
-21.8
6.30
1.020
0.964
0.213
0.063
0.887
3.33105
88.86%
86.18%
79.38%
7.00
4.15637
79.88%
78.49%
75.65%
19.15
0.000
0.000
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.
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).
X X X X X X X
S 1 2 3 4 5 6 7
X
X
----Step 2-----
Coef
P
-15.5
1.029 0.000
0.007
0.00822
-1.346
9.12
-0.0062
-----Step 3----
Coef
P
-15.66
0.011
0.000
0.889
3.29
1.060
3.181
3.26649
88.86%
86.71%
82.118
5.00
0.015
0.000
0.000
3.26654
88.00%
86.71%
84.74%
2.93
X
X
X
-1.350
9.12
----Step 3-----
Coef
P
-16.2
1.034
0.00824
0.000
0.006
0.009
0.000
S
R-sq
R-sq (adj)
R-sq (pred)
Mallows' Cp
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.
3.20664
88.85%
87.20%
84.70%
3.02
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.
Expert Solution
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