Assignment 7 Question 1
58
Part a for smokers and non-smokers separately
13:55 Tuesday, November 29, 2005
--------------------------------------------- SMK=0 ---------------------------------------------The REG Procedure
Model: MODEL1
Dependent Variable: SBP
Number of Observations Read
Number of Observations Used
15
15
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
1
13
14
1702.83966
627.56034
2330.40000
1702.83966
48.27387
Root MSE
Dependent Mean
Coeff Var
6.94794
140.80000
4.93462
R-Square
Adj R-Sq
F Value
Pr > F
35.27
<.0001
0.7307
0.7100
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error
t Value
Pr > |t|
Intercept
QUET
1
1
49.31176
26.30283
15.50814
4.42865
3.18
5.94
0.0072
<.0001
Assignment 7 Question 1
59
Part a for smokers and non-smokers separately
13:55 Tuesday, November 29, 2005
--------------------------------------------- SMK=1 ---------------------------------------------The REG Procedure
Model: MODEL1
Dependent Variable: SBP
Number of Observations Read
Number of Observations Used
17
17
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
1
15
16
2088.16977
1614.30082
3702.47059
2088.16977
107.62005
Root MSE
Dependent Mean
Coeff Var
10.37401
147.82353
7.01783
R-Square
Adj R-Sq
Parameter Estimates
Parameter
Standard
F Value
Pr > F
19.40
0.0005
0.5640
0.5349
Variable
DF
Estimate
Error
t Value
Pr > |t|
Intercept
QUET
1
1
79.25533
20.11804
15.76837
4.56719
5.03
4.40
0.0002
0.0005
Assignment 7 Question 1
60
Part b) c) for smokers and non-smokers together
13:55 Tuesday, November 29, 2005
The REG Procedure
Model: MODEL1
Dependent Variable: SBP
Number of Observations Read
Number of Observations Used
32
32
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
3
28
31
4184.10759
2241.86116
6425.96875
1394.70253
80.06647
Root MSE
Dependent Mean
Coeff Var
8.94799
144.53125
6.19104
R-Square
Adj R-Sq
F Value
Pr > F
17.42
<.0001
0.6511
0.6137
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error
t Value
Pr > |t|
Intercept
QUET
SMK
QS
1
1
1
1
49.31176
26.30283
29.94357
-6.18478
19.97235
5.70349
24.16355
6.93171
2.47
4.61
1.24
-0.89
0.0199
<.0001
0.2256
0.3799
Assignment 7 Question 1
61
Part b) c) for smokers and non-smokers together
13:55 Tuesday, November 29, 2005
The REG Procedure
Model: MODEL2
Dependent Variable: SBP
Number of Observations Read
Number of Observations Used
32
32
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
2
29
31
4120.36649
2305.60226
6425.96875
2060.18325
79.50353
Root MSE
Dependent Mean
Coeff Var
8.91647
144.53125
6.16924
R-Square
Adj R-Sq
F Value
Pr > F
25.91
<.0001
0.6412
0.6165
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error
t Value
Pr > |t|
Intercept
QUET
SMK
1
1
1
63.87603
22.11560
8.57101
11.46811
3.22996
3.16670
5.57
6.85
2.71
<.0001
<.0001
0.0113
Assignment 7 Question 1
62
Part b) c) for smokers and non-smokers together
13:55 Tuesday, November 29, 2005
The REG Procedure
Model: MODEL3
Dependent Variable: SBP
Number of Observations Read
Number of Observations Used
32
32
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
1
30
31
3537.94574
2888.02301
6425.96875
3537.94574
96.26743
Root MSE
Dependent Mean
Coeff Var
9.81160
144.53125
6.78856
R-Square
Adj R-Sq
F Value
Pr > F
36.75
<.0001
0.5506
0.5356
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error
t Value
Pr > |t|
Intercept
QUET
1
1
70.57640
21.49167
12.32187
3.54515
5.73
6.06
<.0001
<.0001
------------------------------------------------------------------------------------------------Assignment 7 Question 2
63
13:55 Tuesday, November 29, 2005
part a)
The REG Procedure
Model: MODEL1
Dependent Variable: SBP
Number of Observations Read
Number of Observations Used
32
32
Forward Selection: Step 1
Variable AQ Entered: R-Square = 0.6553 and C(p) = 12.3877
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
1
30
31
4210.80067
2215.16808
6425.96875
4210.80067
73.83894
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
57.03
<.0001
F Value
Pr > F
Intercept
AQ
99.86787
0.24022
6.10637
0.03181
19750
4210.80067
267.48
57.03
<.0001
<.0001
Bounds on condition number: 1, 1
-------------------------------------------------------------------------------------------------Forward Selection: Step 2
Variable AS Entered: R-Square = 0.7692 and C(p) = 1.0396
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
2
29
31
4942.90997
1483.05878
6425.96875
2471.45498
51.13996
Assignment 7 Question 2
F Value
Pr > F
48.33
<.0001
64
13:55 Tuesday, November 29, 2005
part a)
The REG Procedure
Model: MODEL1
Dependent Variable: SBP
Forward Selection: Step 2
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
Intercept
AQ
AS
95.13960
0.23866
0.18042
5.23323
0.02648
0.04768
16902
4155.36683
732.10930
330.51
81.25
14.32
<.0001
<.0001
0.0007
Bounds on condition number: 1.0002, 4.001
--------------------------------------------------------------------------------------------------
No other variable met the 0.0500 significance level for entry into the model.
Summary of Forward Selection
Step
1
2
Variable
Entered
AQ
AS
Number
Vars In
1
2
Partial
R-Square
Model
R-Square
C(p)
0.6553
0.1139
0.6553
0.7692
12.3877
1.0396
Assignment 7 Question 2
F Value
Pr > F
57.03
14.32
<.0001
0.0007
65
13:55 Tuesday, November 29, 2005
part a)
The REG Procedure
Model: MODEL2
Dependent Variable: SBP
Number of Observations Read
Number of Observations Used
32
32
Backward Elimination: Step 0
All Variables Entered: R-Square = 0.7952 and C(p) = 8.0000
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
7
24
31
5109.62716
1316.34159
6425.96875
729.94674
54.84757
F Value
Pr > F
13.31
<.0001
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
Intercept
QUET
AGE
SMK
AQ
AS
QS
AQS
120.56337
-10.79511
-0.30114
89.47959
0.38753
-1.36571
-28.03527
0.48106
135.35266
40.64862
2.53075
163.18074
0.72355
3.10917
48.18851
0.86928
43.51656
3.86830
0.77658
16.49178
15.73340
10.58239
18.56436
16.79731
0.79
0.07
0.01
0.30
0.29
0.19
0.34
0.31
0.3819
0.7928
0.9063
0.5885
0.5972
0.6644
0.5661
0.5851
Bounds on condition number: 4166.7, 120684
-------------------------------------------------------------------------------------------------Backward Elimination: Step 1
Variable AGE Removed: R-Square = 0.7950 and C(p) = 6.0142
Assignment 7 Question 2
66
13:55 Tuesday, November 29, 2005
part a)
The REG Procedure
Model: MODEL2
Dependent Variable: SBP
Backward Elimination: Step 1
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
6
25
31
5108.85058
1317.11817
6425.96875
851.47510
52.68473
F Value
Pr > F
16.16
<.0001
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
Intercept
QUET
SMK
AQ
AS
QS
AQS
104.87005
-6.33550
105.17291
0.30304
-1.66684
-32.49488
0.56554
29.83008
15.42440
94.17985
0.13662
1.77019
29.68706
0.49157
651.14657
8.88853
65.70168
259.21984
46.71257
63.12194
69.73594
12.36
0.17
1.25
4.92
0.89
1.20
1.32
0.0017
0.6848
0.2747
0.0359
0.3554
0.2841
0.2608
Bounds on condition number: 1634.8, 34572
-------------------------------------------------------------------------------------------------Backward Elimination: Step 2
Variable QUET Removed: R-Square = 0.7936 and C(p) = 4.1762
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
5
26
31
5099.96205
1326.00670
6425.96875
1019.99241
51.00026
Assignment 7 Question 2
F Value
Pr > F
20.00
<.0001
67
13:55 Tuesday, November 29, 2005
part a)
The REG Procedure
Model: MODEL2
Dependent Variable: SBP
Backward Elimination: Step 2
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
Intercept
SMK
AQ
AS
QS
AQS
93.07315
116.96980
0.24951
-1.66684
-38.83038
0.61908
7.92958
88.24821
0.04032
1.74166
24.95672
0.46633
7026.21152
89.60001
1953.17097
46.71257
123.46412
89.88052
137.77
1.76
38.30
0.92
2.42
1.76
<.0001
0.1965
<.0001
0.3474
0.1318
0.1959
Bounds on condition number: 1338.1, 25202
-------------------------------------------------------------------------------------------------Backward Elimination: Step 3
Variable AS Removed: R-Square = 0.7864 and C(p) = 3.0279
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
4
27
31
5053.24948
1372.71927
6425.96875
1263.31237
50.84145
F Value
Pr > F
24.85
<.0001
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
Intercept
SMK
AQ
QS
AQS
93.07315
34.56347
0.24951
-17.51051
0.19126
7.91722
19.29924
0.04026
11.23322
0.13260
7026.21152
163.06937
1953.17097
123.53987
105.77296
138.20
3.21
38.42
2.43
2.08
<.0001
0.0845
<.0001
0.1307
0.1607
Bounds on condition number: 242.55, 1631.4
-------------------------------------------------------------------------------------------------Backward Elimination: Step 4
Assignment 7 Question 2
68
13:55 Tuesday, November 29, 2005
part a)
The REG Procedure
Model: MODEL2
Dependent Variable: SBP
Backward Elimination: Step 4
Variable AQS Removed: R-Square = 0.7699 and C(p) = 2.9564
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
3
28
31
4947.47652
1478.49223
6425.96875
1649.15884
52.80329
F Value
Pr > F
31.23
<.0001
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
Intercept
SMK
AQ
QS
89.70127
18.87686
0.26714
-2.68777
7.70878
16.24781
0.03909
4.62280
7149.68328
71.27391
2466.20859
17.84981
135.40
1.35
46.71
0.34
<.0001
0.2551
<.0001
0.5656
Bounds on condition number: 39.84, 244.51
-------------------------------------------------------------------------------------------------Backward Elimination: Step 5
Variable QS Removed: R-Square = 0.7671 and C(p) = 1.2818
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
2
29
31
4929.62671
1496.34204
6425.96875
2464.81336
51.59800
Assignment 7 Question 2
F Value
Pr > F
47.77
<.0001
69
13:55 Tuesday, November 29, 2005
part a)
The REG Procedure
Model: MODEL2
Dependent Variable: SBP
Backward Elimination: Step 5
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
Intercept
SMK
AQ
92.83938
9.55079
0.25073
5.44080
2.55885
0.02674
15024
718.82604
4536.52855
291.16
13.93
87.92
<.0001
0.0008
<.0001
Bounds on condition number: 1.0112, 4.0449
-------------------------------------------------------------------------------------------------All variables left in the model are significant at the 0.0500 level.
Summary of Backward Elimination
Step
1
2
3
4
5
Variable
Removed
AGE
QUET
AS
AQS
QS
Number
Vars In
6
5
4
3
2
Partial
R-Square
Model
R-Square
0.0001
0.0014
0.0073
0.0165
0.0028
0.7950
0.7936
0.7864
0.7699
0.7671
C(p)
6.0142
4.1762
3.0279
2.9564
1.2818
F Value
Pr > F
0.01
0.17
0.92
2.08
0.34
0.9063
0.6848
0.3474
0.1607
0.5656
Assignment 7 Question 2
70
13:55 Tuesday, November 29, 2005
part a)
The REG Procedure
Model: MODEL3
Dependent Variable: SBP
R-Square Selection Method
Number of Observations Read
Number of Observations Used
Number in
Model
R-Square
C(p)
MSE
32
32
Variables in Model
1
0.6553
12.3877
73.83894
AQ
1
0.6009
18.7539
85.47795
AGE
1
0.5506
24.6554
96.26743
QUET
1
0.2143
64.0557
168.30101
AQS
1
0.1382
72.9740
184.60597
QS
1
0.1226
74.8017
187.94752
AS
1
0.0612
81.9934
201.09569
SMK
-----------------------------------------------------------------------------2
0.7692
1.0396
51.13996
AQ AS
2
0.7671
1.2818
51.59800
SMK AQ
2
0.7609
2.0078
52.97104
AQ AQS
2
0.7588
2.2559
53.44021
AQ QS
2
0.7525
2.9935
54.83534
AGE AQS
2
0.7466
3.6859
56.14476
AGE QS
2
0.7373
4.7833
58.22022
AGE AS
2
0.7298
5.6565
59.87188
AGE SMK
2
0.6635
13.4206
74.55597
QUET AQ
2
0.6566
14.2373
76.10058
AGE AQ
2
0.6520
14.7751
77.11769
QUET AS
2
0.6437
15.7485
78.95869
QUET AQS
2
0.6412
16.0324
79.49574
QUET AGE
2
0.6412
16.0365
79.50353
QUET SMK
2
0.6320
17.1161
81.54529
QUET QS
2
0.4781
35.1517
115.65588
QS AQS
2
0.4632
36.8912
118.94587
SMK AQS
2
0.4493
38.5158
122.01841
SMK AS
2
0.4228
41.6301
127.90843
AS AQS
2
0.3861
45.9212
136.02417
SMK QS
2
0.1559
72.8904
187.03105
AS QS
-----------------------------------------------------------------------------3
0.7842
1.2875
49.53416
QUET AQ AS
3
0.7841
1.2903
49.53959
QUET AQ AQS
3
0.7832
1.3949
49.74462
QUET AQ QS
3
0.7822
1.5141
49.97809
QUET SMK AQ
3
0.7795
1.8370
50.61056
AQ AS QS
3
0.7750
2.3615
51.63794
AGE AQ AS
3
0.7731
2.5879
52.08146
AGE SMK AQ
Assignment 7 Question 2
71
13:55 Tuesday, November 29, 2005
part a)
The REG Procedure
Model: MODEL3
Dependent Variable: SBP
R-Square Selection Method
Number in
Model
R-Square
C(p)
MSE
Variables in Model
3
0.7724
2.6691
52.24058
AGE AQ AQS
3
0.7722
2.6923
52.28606
AQ AS AQS
3
0.7704
2.8950
52.68297
AGE AQ QS
3
0.7699
2.9564
52.80329
SMK AQ QS
3
0.7692
3.0370
52.96122
SMK AQ AS
3
0.7672
3.2803
53.43783
SMK AQ AQS
3
0.7644
3.6023
54.06854
QUET AGE AQS
3
0.7638
3.6782
54.21714
QUET AGE AS
3
0.7612
3.9767
54.80200
QUET AGE QS
3
0.7610
4.0010
54.84959
AQ QS AQS
3
0.7609
4.0075
54.86225
QUET AGE SMK
3
0.7576
4.3992
55.62959
AGE AS AQS
3
0.7548
4.7232
56.26417
AGE SMK AQS
3
0.7539
4.8275
56.46844
AGE QS AQS
3
0.7531
4.9325
56.67420
AGE SMK QS
3
0.7510
5.1764
57.15198
AGE AS QS
3
0.7405
6.4033
59.55518
AGE SMK AS
3
0.7269
7.9935
62.67021
QUET AS QS
3
0.6776
13.7682
73.98197
QUET AGE AQ
3
0.6654
15.2018
76.79006
QUET SMK AS
3
0.6612
15.6914
77.74922
QUET QS AQS
3
0.6585
16.0156
78.38424
QUET AS AQS
3
0.6511
16.8744
80.06647
QUET SMK QS
3
0.6440
17.7099
81.70301
QUET SMK AQS
3
0.4848
36.3640
118.24350
AS QS AQS
3
0.4824
36.6388
118.78179
SMK QS AQS
3
0.4705
38.0382
121.52292
SMK AS AQS
3
0.4620
39.0373
123.48004
SMK AS QS
-----------------------------------------------------------------------------4
0.7922
2.3455
49.45522
QUET AGE AQ AS
4
0.7906
2.5328
49.83565
QUET AGE AQ QS
4
0.7905
2.5499
49.87054
QUET AGE AQ AQS
4
0.7901
2.5924
49.95688
QUET AGE SMK AQ
4
0.7864
3.0279
50.84145
SMK AQ QS AQS
4
0.7850
3.1912
51.17321
QUET SMK AQ AQS
4
0.7846
3.2315
51.25498
QUET AQ AS AQS
4
0.7843
3.2770
51.34752
QUET AQ QS AQS
4
0.7842
3.2857
51.36505
QUET AQ AS QS
4
0.7842
3.2872
51.36811
QUET SMK AQ AS
4
0.7833
3.3834
51.56357
QUET SMK AQ QS
4
0.7797
3.8098
52.42988
AQ AS QS AQS
4
0.7797
3.8150
52.44027
SMK AQ AS QS
Assignment 7 Question 2
72
13:55 Tuesday, November 29, 2005
part a)
The REG Procedure
Model: MODEL3
Dependent Variable: SBP
R-Square Selection Method
Number in
Model
4
4
4
4
4
4
4
4
4
4
4
4
R-Square
C(p)
MSE
0.7795
0.7751
0.7750
0.7744
0.7743
0.7731
0.7724
0.7650
0.7648
0.7646
0.7646
0.7639
3.8346
4.3511
4.3610
4.4273
4.4374
4.5812
4.6686
5.5376
5.5544
5.5757
5.5769
5.6625
52.48024
53.52938
53.54957
53.68410
53.70461
53.99684
54.17435
55.93961
55.97387
56.01697
56.01942
56.19343
Variables in Model
AGE AQ AS QS
AGE AQ AS AQS
AGE SMK AQ AS
SMK AQ AS AQS
AGE SMK AQ AQS
AGE SMK AQ QS
AGE AQ QS AQS
QUET AGE AS QS
QUET AGE SMK AQS
QUET AGE QS AQS
QUET AGE AS AQS
QUET AGE SMK AS
4
0.7616
5.9256
56.72789
AGE SMK AS AQS
4
0.7616
5.9357
56.74834
QUET AGE SMK QS
4
0.7578
6.3707
57.63207
AGE AS QS AQS
4
0.7549
6.7157
58.33287
AGE SMK QS AQS
4
0.7531
6.9248
58.75749
AGE SMK AS QS
4
0.7474
7.5920
60.11298
QUET SMK QS AQS
4
0.7290
9.7511
64.49883
QUET AS QS AQS
4
0.7270
9.9905
64.98524
QUET SMK AS QS
4
0.7024
12.8699
70.83450
QUET SMK AS AQS
4
0.4897
37.7871
121.45102
SMK AS QS AQS
-----------------------------------------------------------------------------5
0.7936
4.1762
51.00026
SMK AQ AS QS AQS
5
0.7925
4.3063
51.27458
QUET AGE AQ AS QS
5
0.7922
4.3428
51.35172
QUET AGE SMK AQ AS
5
0.7922
4.3455
51.35733
QUET AGE AQ AS AQS
5
0.7918
4.3875
51.44602
QUET AGE SMK AQ AQS
5
0.7910
4.4922
51.66680
QUET AGE AQ QS AQS
5
0.7908
4.5061
51.69621
QUET AGE SMK AQ QS
5
0.7878
4.8658
52.45503
QUET SMK AQ QS AQS
5
0.7866
5.0041
52.74667
AGE SMK AQ QS AQS
5
0.7852
5.1650
53.08616
QUET SMK AQ AS AQS
5
0.7848
5.2121
53.18538
QUET AQ AS QS AQS
5
0.7842
5.2856
53.34054
QUET SMK AQ AS QS
5
0.7809
5.6746
54.16111
AGE SMK AS QS AQS
5
0.7797
5.8094
54.44553
AGE SMK AQ AS QS
5
0.7797
5.8097
54.44619
AGE AQ AS QS AQS
5
0.7753
6.3216
55.52592
AGE SMK AQ AS AQS
5
0.7750
6.3632
55.61377
QUET AGE SMK QS AQS
5
0.7668
7.3238
57.64010
QUET AGE AS QS AQS
5
0.7650
7.5314
58.07815
QUET AGE SMK AS AQS
Assignment 7 Question 2
73
13:55 Tuesday, November 29, 2005
part a)
The REG Procedure
Model: MODEL3
Dependent Variable: SBP
R-Square Selection Method
Number in
Model
R-Square
C(p)
MSE
Variables in Model
5
0.7650
7.5370
58.08994
QUET AGE SMK AS QS
5
0.7547
8.7403
60.62838
QUET SMK AS QS AQS
-----------------------------------------------------------------------------6
0.7950
6.0142
52.68473
QUET SMK AQ AS QS AQS
6
0.7946
6.0705
52.80840
AGE SMK AQ AS QS AQS
6
0.7935
6.1929
53.07696
QUET AGE SMK AQ QS AQS
6
0.7927
6.2869
53.28300
QUET AGE SMK AS QS AQS
6
0.7926
6.3007
53.31333
QUET AGE AQ AS QS AQS
6
0.7925
6.3063
53.32556
QUET AGE SMK AQ AS QS
6
0.7923
6.3385
53.39624
QUET AGE SMK AQ AS AQS
-----------------------------------------------------------------------------7
0.7952
8.0000
54.84757
QUET AGE SMK AQ AS QS AQS
Assignment 7 Question 2
74
13:55 Tuesday, November 29, 2005
part b)
--------------------------------------------- SMK=0 ---------------------------------------------The REG Procedure
Model: MODEL1
Dependent Variable: SBP
Number of Observations Read
Number of Observations Used
15
15
Stepwise Selection: Step 1
Variable AQ Entered: R-Square = 0.8381 and C(p) = 0.2892
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
1
13
14
1953.17097
377.22903
2330.40000
1953.17097
29.01762
F Value
Pr > F
67.31
<.0001
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
Intercept
AQ
93.07315
0.24951
5.98129
0.03041
7026.21152
1953.17097
242.14
67.31
<.0001
<.0001
Bounds on condition number: 1, 1
-------------------------------------------------------------------------------------------------All variables left in the model are significant at the 0.0500 level.
No other variable met the 0.0500 significance level for entry into the model.
Assignment 7 Question 2
75
13:55 Tuesday, November 29, 2005
part b)
--------------------------------------------- SMK=0 ---------------------------------------------The REG Procedure
Model: MODEL1
Dependent Variable: SBP
Summary of Stepwise Selection
Step
1
Variable
Entered
AQ
Variable
Removed
Number
Vars In
1
Partial
R-Square
Model
R-Square
0.8381
0.8381
C(p)
0.2892
F Value
Pr > F
67.31
<.0001
Assignment 7 Question 2
76
13:55 Tuesday, November 29, 2005
part b)
--------------------------------------------- SMK=1 ---------------------------------------------The REG Procedure
Model: MODEL1
Dependent Variable: SBP
Number of Observations Read
Number of Observations Used
17
17
Stepwise Selection: Step 1
Variable AQ Entered: R-Square = 0.6978 and C(p) = 2.3328
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
1
15
16
2583.44049
1119.03010
3702.47059
2583.44049
74.60201
F Value
Pr > F
34.63
<.0001
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
Intercept
AQ
102.21983
0.25167
8.02769
0.04277
12096
2583.44049
162.14
34.63
<.0001
<.0001
Bounds on condition number: 1, 1
__________________________________________________________________________________________________
All variables left in the model are significant at the 0.0500 level.
No other variable met the 0.0500 significance level for entry into the model.
Assignment 7 Question 2
77
13:55 Tuesday, November 29, 2005
part b)
--------------------------------------------- SMK=1 ---------------------------------------------The REG Procedure
Model: MODEL1
Dependent Variable: SBP
Summary of Stepwise Selection
Step
1
Variable
Entered
AQ
Variable
Removed
Number
Vars In
1
Partial
R-Square
Model
R-Square
0.6978
0.6978
Assignment 7 Question 3
part A) B) C) D)
C(p)
2.3328
F Value
Pr > F
34.63
<.0001
78
13:55 Tuesday, November 29, 2005
The REG Procedure
Model: MODEL1
Dependent Variable: Y
Number of Observations Read
Number of Observations Used
29
29
Forward Selection: Step 1
Variable X4 Entered: R-Square = 0.7205 and C(p) = 38.4923
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
1
27
28
10579
4103.24370
14682
10579
151.97199
F Value
Pr > F
69.61
<.0001
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
Intercept
X4
607.10327
-21.40246
42.90608
2.56525
30426
10579
200.21
69.61
<.0001
<.0001
Bounds on condition number: 1, 1
-------------------------------------------------------------------------------------------------Forward Selection: Step 2
Variable X3 Entered: R-Square = 0.8587 and C(p) = 9.0975
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
2
26
28
12608
2074.33007
14682
6303.79910
79.78193
Assignment 7 Question 3
F Value
Pr > F
79.01
<.0001
79
13:55 Tuesday, November 29, 2005
part A) B) C) D)
The REG Procedure
Model: MODEL1
Dependent Variable: Y
Forward Selection: Step 2
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
Intercept
X3
X4
483.67033
4.79629
-24.21503
39.56708
0.95110
1.94054
11922
2028.91363
12423
149.43
25.43
155.71
<.0001
<.0001
<.0001
Bounds on condition number: 1.09, 4.3602
--------------------------------------------------------------------------------------------------
No other variable met the 0.0500 significance level for entry into the model.
Summary of Forward Selection
Step
1
2
Variable
Entered
X4
X3
Number
Vars In
1
2
Partial
R-Square
Model
R-Square
C(p)
0.7205
0.1382
0.7205
0.8587
38.4923
9.0975
F Value
Pr > F
69.61
25.43
<.0001
<.0001
Assignment 7 Question 3
80
13:55 Tuesday, November 29, 2005
part A) B) C) D)
The REG Procedure
Model: MODEL2
Dependent Variable: Y
Number of Observations Read
Number of Observations Used
29
29
Backward Elimination: Step 0
All Variables Entered: R-Square = 0.8988 and C(p) = 6.0000
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
5
23
28
13196
1486.39502
14682
2639.10665
64.62587
F Value
Pr > F
40.84
<.0001
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
Intercept
X1
X2
X3
X4
X5
325.43612
0.06753
2.55198
3.80019
-22.94947
2.41748
96.12721
0.02899
1.24824
1.46114
2.70360
1.80829
740.70491
350.55826
270.12607
437.15160
4656.56198
115.50363
11.46
5.42
4.18
6.76
72.05
1.79
0.0025
0.0290
0.0525
0.0160
<.0001
0.1943
Bounds on condition number: 5.3701, 74.163
-------------------------------------------------------------------------------------------------Backward Elimination: Step 1
Variable X5 Removed: R-Square = 0.8909 and C(p) = 5.7873
Assignment 7 Question 3
81
13:55 Tuesday, November 29, 2005
part A) B) C) D)
The REG Procedure
Model: MODEL2
Dependent Variable: Y
Backward Elimination: Step 1
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
F Value
Pr > F
Model
4
13080
3270.00740
48.99
<.0001
Error
Corrected Total
24
28
1601.89866
14682
66.74578
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
Intercept
X1
X2
X3
X4
270.21013
0.05156
2.95141
5.33861
-21.11940
88.21060
0.02685
1.23167
0.91506
2.36936
626.30449
246.16289
383.25933
2271.87822
5303.02903
9.38
3.69
5.74
34.04
79.45
0.0053
0.0668
0.0247
<.0001
<.0001
Bounds on condition number: 1.9424, 25.408
-------------------------------------------------------------------------------------------------Backward Elimination: Step 2
Variable X1 Removed: R-Square = 0.8741 and C(p) = 7.5963
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
Model
Error
Corrected Total
3
25
28
12834
1848.06155
14682
4277.95558
73.92246
Assignment 7 Question 3
F Value
Pr > F
57.87
<.0001
82
13:55 Tuesday, November 29, 2005
part A) B) C) D)
The REG Procedure
Model: MODEL2
Dependent Variable: Y
Backward Elimination: Step 2
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
Intercept
X2
X3
X4
389.16592
2.12475
5.31847
-24.13239
66.09372
1.21446
0.96293
1.86852
2562.86405
226.26853
2255.06669
12331
34.67
3.06
30.51
166.80
<.0001
0.0925
<.0001
<.0001
Bounds on condition number: 1.2059, 10.255
-------------------------------------------------------------------------------------------------Backward Elimination: Step 3
Variable X2 Removed: R-Square = 0.8587 and C(p) = 9.0975
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
F Value
Pr > F
Model
Error
Corrected Total
2
26
28
12608
2074.33007
14682
6303.79910
79.78193
79.01
Variable
Parameter
Estimate
Standard
Error
Type II SS
F Value
Pr > F
Intercept
X3
X4
483.67033
4.79629
-24.21503
39.56708
0.95110
1.94054
11922
2028.91363
12423
149.43
25.43
155.71
<.0001
<.0001
<.0001
<.0001
Bounds on condition number: 1.09, 4.3602
-------------------------------------------------------------------------------------------------All variables left in the model are significant at the 0.0500 level.
Assignment 7 Question 3
83
13:55 Tuesday, November 29, 2005
part A) B) C) D)
The REG Procedure
Model: MODEL2
Dependent Variable: Y
Summary of Backward Elimination
Step
1
2
3
Variable
Removed
X5
X1
X2
Number
Vars In
4
3
2
Partial
R-Square
Model
R-Square
0.0079
0.0168
0.0154
0.8909
0.8741
0.8587
C(p)
5.7873
7.5963
9.0975
Assignment 7 Question 3
F Value
Pr > F
1.79
3.69
3.06
0.1943
0.0668
0.0925
84
13:55 Tuesday, November 29, 2005
part A) B) C) D)
The REG Procedure
Model: MODEL3
Dependent Variable: Y
R-Square Selection Method
Number of Observations Read
Number of Observations Used
Number in
Model
R-Square
C(p)
29
29
MSE
Variables in Model
1
0.7205
38.4923
151.97199
X4
1
0.3939
112.6871
329.56104
X1
1
0.1233
174.1748
476.73509
X5
1
0.0126
199.3290
536.94287
X3
1
0.0105
199.8035
538.07856
X2
---------------------------------------------------------------------2
0.8587
9.0975
79.78193
X3 X4
2
0.8202
17.8461
101.52756
X4 X5
2
0.7339
37.4625
150.28610
X1 X4
2
0.7205
40.4905
157.81262
X2 X4
2
0.4492
102.1269
311.01665
X1 X2
2
0.4264
107.3205
323.92609
X1 X3
2
0.3943
114.6073
342.03804
X1 X5
2
0.3703
120.0469
355.55893
X3 X5
2
0.1296
174.7323
491.48536
X2 X5
2
0.0343
196.3958
545.33247
X2 X3
---------------------------------------------------------------------3
0.8741
7.5963
73.92246
X2 X3 X4
3
0.8648
9.7177
79.40632
X1 X3 X4
3
0.8638
9.9509
80.00926
X3 X4 X5
3
0.8629
10.1499
80.52370
X1 X4 X5
3
0.8202
19.8427
105.57990
X2 X4 X5
3
0.7362
38.9416
154.95108
X1 X2 X4
3
0.5297
85.8446
276.19711
X1 X2 X3
3
0.4657
100.3836
313.78094
X1 X3 X5
3
0.4609
101.4841
316.62567
X2 X3 X5
3
0.4549
102.8426
320.13742
X1 X2 X5
---------------------------------------------------------------------4
0.8909
5.7873
66.74578
X1 X2 X3 X4
4
0.8804
8.1798
73.18838
X1 X3 X4 X5
4
0.8749
9.4244
76.53972
X2 X3 X4 X5
4
0.8690
10.7643
80.14778
X1 X2 X4 X5
4
0.5816
76.0541
255.95654
X1 X2 X3 X5
---------------------------------------------------------------------5
0.8988
6.0000
64.62587
X1 X2 X3 X4 X5