EXST7034 - Bodyfat Example,
NKNW Table 7.1
Obs
Run rep X1
X2 X3
Y SUBJECT
1
1 1 29.8
54.3 31.1 20.1
4
2
1 2 30.7
51.9 37.0 18.7
3
3
1 3 27.7
55.3 25.7 22.6
17
4
1 4 19.5
43.1 29.1 11.9
1
5
1 5 30.2
58.6 24.6 25.4
18
6
1 6 19.5
43.1 29.1 11.9
1
7
1 7 24.7
49.8 28.2 22.8
2
8
1 8 27.9
52.1 30.6 25.4
8
9
1 9 29.8
54.3 31.1 20.1
4
10
1 10 25.6 53.9
23.7 21.7 6
11
1 11 30.7 51.9
37.0 18.7 3
12
1 12 27.7 55.3
25.7 22.6 17
13
1 13 30.2 58.6
24.6 25.4 18
14
1 14 25.5 53.5
24.8 19.3 10
15
1 15 27.7 55.3
25.7 22.6 17
16
1 16 29.8 54.3
31.1 20.1 4
17
1 17 30.4 56.7
28.3 27.2 12
18
1 18 22.7 48.2
27.1 14.8 19
19
1 19 24.7 49.8
28.2 22.8 2
20
1 20 24.7 49.8
28.2 22.8 2
21
2 1 27.9
52.1 30.6 25.4
8
22
2 2 30.4
56.7 28.3 27.2
12
23
2 3 14.6
42.7 21.3 12.8
15
24
2 4 31.1
56.6 30.0 25.4
11
25
2 5 30.2
58.6 24.6 25.4
18
26
2 6 25.2
51.0 27.5 21.1
20
27
2 7 29.5
54.4 30.1 23.9
16
28
2 8 30.7
51.9 37.0 18.7
3
29
2 9 30.7
51.9 37.0 18.7
3
30
2 10 22.7 48.2
27.1 14.8 19
31
2 11 29.5 54.4
30.1 23.9 16
32
2 12 22.1 49.9
23.2 21.3 9
33
2 13 27.9 52.1
30.6 25.4 8
34
2 14 29.5 54.4
30.1 23.9 16
35
2 15 19.1 42.2
30.9 12.9 5
36
2 16 27.9 52.1
30.6 25.4 8
37
2 17 22.1 49.9
23.2 21.3 9
38
2 18 27.9 52.1
30.6 25.4 8
39
2 19 19.7 44.2
28.6 17.8 14
40
2 20 31.1 56.6
30.0 25.4 11
53
PROC SORT DATA=BOOTS; BY run rep; run;
NOTE: There were 1000 observations
read from the data set WORK.BOOTS.
NOTE: The data set WORK.BOOTS
has 1000 observations and 7 variables.
NOTE: PROCEDURE SORT used:
real time 0.00
seconds
54
55
PROC REG DATA=one; TITLE2 'Ordinary Regression';
56
MODEL Y = X1 X2 X3 / vif collin;
57
RUN;
NOTE: 20 observations read.
NOTE: 20 observations used
in computations.
58
NOTE: The PROCEDURE REG printed
page 5.
NOTE: PROCEDURE REG used:
real time 0.10
seconds
EXST7034 - Bodyfat Example,
NKNW Table 7.1
Ordinary Regression
The REG Procedure
Model: MODEL1
Dependent Variable: Y Body
Fat
Analysis of Variance
Sum of Mean
Source
DF Squares
Square F Value Pr > F
Model
3 396.98461
132.32820 21.52 <.0001
Error
16 98.40489
6.15031
Corrected Total
19 495.38950
Root MSE
2.47998 R-Square 0.8014
Dependent Mean
20.19500 Adj R-Sq 0.7641
Coeff Var
12.28017
Parameter Estimates
Parameter Standard
Variance
Variable Label
DF Estimate
Error t Value Pr > |t| Inflation
Intercept Intercept
1 117.08469 99.78240
1.17 0.2578
0
X1
Triceps skinfold thickness 1
4.33409 3.01551 1.44
0.1699 708.84291
X2
Thigh circumference
1 -2.85685 2.58202
-1.11 0.2849 564.34339
X3
Midarm circumference 1
-2.18606 1.59550 -1.37
0.1896 104.60601
Collinearity Diagnostics
Condition -----------------Proportion of Variation----------------
Number
Eigenvalue Index
Intercept
X1
X2
X3
1 3.96796
1.00000 0.00000195 0.00000320
0.00000110 0.00000980
2 0.02052
13.90482 0.00037152
0.00132 0.00003262
0.00139
3 0.01151
18.56570 0.00059915 0.00021875
0.00032550 0.00693
4 0.00000865 677.37207
0.99903 0.99846
0.99964 0.99167
59
PROC REG DATA=boots outest=BVALUES NOPRINT; by run;
60
TITLE2 'Bootstrap regression';
61
MODEL Y = X1 X2 X3;
62
RUN;
NOTE: 20 observations read.
NOTE: 20 observations used
in computations.
NOTE: The above message was
for the following by-group:
Run=1
NOTE: 20 observations read.
NOTE: 20 observations used
in computations.
NOTE: The above message was
for the following by-group:
Run=2
NOTE: 20 observations read.
NOTE: 20 observations used
in computations.
NOTE: The above message was
for the following by-group:
Run=3
. . .
NOTE: 20 observations read.
NOTE: 20 observations used
in computations.
NOTE: The above message was
for the following by-group:
Run=50
NOTE: Interactivity disabled
with BY processing.
NOTE: PROCEDURE REG used:
real time 0.04
seconds
NOTE: The data set WORK.BVALUES
has 50 observations and 10 variables.
63
proc sort data=BVALUES; by x1 x2 x3; run;
NOTE: There were 50 observations
read from the data set WORK.BVALUES.
NOTE: The data set WORK.BVALUES
has 50 observations and 10 variables.
NOTE: PROCEDURE SORT used:
real time 0.00
seconds
64
proc print data=BVALUES; run;
NOTE: There were 50 observations
read from the data set WORK.BVALUES.
NOTE: The PROCEDURE PRINT
printed page 6.
NOTE: PROCEDURE PRINT used:
real time 0.00
seconds
EXST7034 - Bodyfat Example,
NKNW Table 7.1
Bootstrap regression
Obs Run
_MODEL_ _TYPE_ _DEPVAR_ _RMSE_
Intercept X1
X2 X3
Y
1
45 MODEL1 PARMS
Y 2.02826 -86.069
-2.2746 2.69354 0.96798
-1
2
3 MODEL1 PARMS
Y 2.57250 -93.869
-1.8845 2.47138 1.27658
-1
3
11 MODEL1 PARMS
Y 2.55378 -83.508
-1.6238 2.18801 1.20208
-1
4
6 MODEL1 PARMS
Y 2.58466 -68.778
-1.3964 2.00652 0.75932
-1
5
50 MODEL1 PARMS
Y 2.47264 -69.455
-1.1752 1.73600 1.12700
-1
6
38 MODEL1 PARMS
Y 2.29334 -37.944
-0.5274 1.30906 0.17175
-1
7
49 MODEL1 PARMS
Y 2.17482 -54.870
-0.4746 1.36310 0.62290
-1
8
29 MODEL1 PARMS
Y 1.71841 -10.626
0.2922 0.60947 -0.29663 -1
9
44 MODEL1 PARMS
Y 2.40471
6.600 1.2401 -0.17689 -0.28207
-1
10
35 MODEL1 PARMS
Y 1.84837
26.990 1.4657 -0.37080
-0.89895 -1
11
32 MODEL1 PARMS
Y 2.70628
24.093 1.4936 -0.42727
-0.69926 -1
12
16 MODEL1 PARMS
Y 2.42875
28.031 1.6422 -0.64958
-0.58204 -1
13
40 MODEL1 PARMS
Y 2.10121
38.661 1.7080 -0.64762
-1.02238 -1
14
17 MODEL1 PARMS
Y 2.84546
40.393 2.0076 -0.88047
-0.95489 -1
15
15 MODEL1 PARMS
Y 2.31671
45.586 2.1730 -0.95736
-1.12663 -1
16
27 MODEL1 PARMS
Y 1.88707
58.810 2.4313 -1.25808
-1.28893 -1
17
47 MODEL1 PARMS
Y 2.10667
39.182 2.4336 -1.15205
-0.77021 -1
18
46 MODEL1 PARMS
Y 2.19939
53.957 2.5141 -1.38110
-0.95129 -1
19
28 MODEL1 PARMS
Y 1.93668
69.801 2.9387 -1.71871
-1.29085 -1
20
23 MODEL1 PARMS
Y 2.42737
81.924 3.2264 -1.90584
-1.67519 -1
21
48 MODEL1 PARMS
Y 2.41676
91.942 3.7038 -2.24583
-1.83223 -1
22
18 MODEL1 PARMS
Y 2.10993 102.046
3.7187 -2.41609 -1.88916 -1
23
25 MODEL1 PARMS
Y 2.15277
98.314 3.7342 -2.31042
-1.98330 -1
24
7 MODEL1 PARMS
Y 1.85771
92.992 3.7852 -2.28726
-1.87444 -1
25
13 MODEL1 PARMS
Y 2.32050 127.377
4.6226 -3.36044 -1.85601 -1
26
26 MODEL1 PARMS
Y 2.37111 133.914
4.7175 -3.18471 -2.52731 -1
27
22 MODEL1 PARMS
Y 1.94202 131.030
4.9349 -3.16099 -2.71435 -1
28
14 MODEL1 PARMS
Y 1.95453 130.200
4.9617 -3.21599 -2.60675 -1
29
36 MODEL1 PARMS
Y 2.29776 138.831
5.1255 -3.47801 -2.55601 -1
30
8 MODEL1 PARMS
Y 1.98470 147.198
5.1976 -3.59410 -2.71967 -1
31
39 MODEL1 PARMS
Y 2.58372 150.196
5.2636 -3.72834 -2.61851 -1
32
33 MODEL1 PARMS
Y 2.20953 146.101
5.3011 -3.71116 -2.51520 -1
33
19 MODEL1 PARMS
Y 1.77352 149.207
5.4396 -3.68593 -2.84126 -1
34
42 MODEL1 PARMS
Y 2.30561 157.401
5.9257 -4.02984 -2.93899 -1
35
9 MODEL1 PARMS
Y 1.85783 175.036
6.0075 -4.30338 -3.13580 -1
36
31 MODEL1 PARMS
Y 2.41120 172.321
6.1022 -4.24178 -3.21940 -1
37
21 MODEL1 PARMS
Y 2.11778 178.011
6.2960 -4.51068 -3.11575 -1
38
41 MODEL1 PARMS
Y 2.28227 179.042
6.3081 -4.46844 -3.26730 -1
39
37 MODEL1 PARMS
Y 2.10368 190.881
6.6623 -4.73044 -3.51688 -1
40
4 MODEL1 PARMS
Y 1.84715 188.573
6.8525 -4.76859 -3.59560 -1
41
34 MODEL1 PARMS
Y 1.24266 218.639
7.0207 -5.52998 -3.33280 -1
42
43 MODEL1 PARMS
Y 2.32869 203.406
7.0778 -5.18465 -3.52981 -1
43
2 MODEL1 PARMS
Y 2.14797 223.911
7.3580 -5.54262 -3.81904 -1
44
30 MODEL1 PARMS
Y 1.67673 245.073
7.9449 -6.14498 -3.99649 -1
45
12 MODEL1 PARMS
Y 2.29412 254.024
8.3006 -6.38929 -4.20551 -1
46
24 MODEL1 PARMS
Y 2.08328 249.820
8.8414 -6.41505 -4.57029 -1
47
1 MODEL1 PARMS
Y 2.25141 279.694
9.5525 -7.13374 -4.97738 -1
48
20 MODEL1 PARMS
Y 2.52198 315.426
9.9770 -7.97082 -5.07632 -1
49
5 MODEL1 PARMS
Y 1.97195 303.961
10.1455 -7.67782 -5.34358 -1
50
10 MODEL1 PARMS
Y 1.83336 365.081
12.0749 -9.32553 -6.28819 -1
65
proc univariate data=bvalues plot normal; var x1 x2 x3; run;
NOTE: The PROCEDURE UNIVARIATE
printed pages 7-9.
NOTE: PROCEDURE UNIVARIATE
used:
real time 0.00
seconds
EXST7034 - Bodyfat Example,
NKNW Table 7.1
Bootstrap regression
The UNIVARIATE Procedure
Variable: X1
(Triceps skinfold thickness)
Moments
N
50 Sum Weights
50
Mean
4.18327267 Sum Observations 209.163634
Std Deviation
3.40267416 Variance
11.5781914
Skewness
0.01136057 Kurtosis
-0.437222
Uncorrected SS
1442.31989 Corrected SS
567.331379
Coeff Variation
81.3400039 Std Error Mean
0.48121079
Basic Statistical Measures
Location
Variability
Mean
4.183273 Std Deviation
3.40267
Median 4.670047
Variance
11.57819
Mode
. Range
14.34952
Interquartile Range 4.60007
Tests for Location: Mu0=0
Test
-Statistic- -----p Value------
Student's t
t 8.693223 Pr > |t| <.0001
Sign
M 18 Pr >=
|M| <.0001
Signed Rank
S 586.5 Pr >= |S|
<.0001
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk
W 0.984593 Pr < W
0.7540
Kolmogorov-Smirnov
D 0.07136 Pr > D
>0.1500
Cramer-von Mises
W-Sq 0.029461 Pr > W-Sq >0.2500
Anderson-Darling
A-Sq 0.206462 Pr > A-Sq >0.2500
Quantiles (Definition 5)
Quantile
Estimate
100% Max
12.074908
99%
12.074908
95%
9.977006 <== 95th percentile used in calculating confidence intervals
90%
8.571038
75% Q3
6.308094
50% Median
4.670047
25% Q1
1.708026
10%
-0.851315
5%
-1.623760 <== 5th percentile used in calculating confidence intervals
1%
-2.274612
0% Min
-2.274612
Extreme Observations
------Lowest-----
------Highest-----
Value
Obs Value
Obs
-2.27461
1 8.84144
46
-1.88453
2 9.55255
47
-1.62376
3 9.97701
48
-1.39637
4 10.14549
49
-1.17521
5 12.07491
50
Stem Leaf
# Boxplot
12 1
1 |
11
|
10 01
2 |
9 6
1 |
8 38
2 |
7 0149
4 |
6 013379
6 +-----+
5 0123349
7 | |
4 679
3 *--+--*
3 27778
5 | |
2 024459
6 | |
1 25567
5 +-----+
0 3
1 |
-0 55
2 |
-1 9642
4 |
-2 3
1 |
----+----+----+----+
Normal Probability Plot
12.5+
*+++
|
++
|
*++
9.5+
**+
|
**+
|
***
6.5+
****
|
***+
|
**+
3.5+
***
|
****
|
***
0.5+
++*
| +++**
| *+** *
-2.5+
*+++
+----+----+----+----+----+----+----+----+----+----+
-2 -1
0 +1
+2
EXST7034 - Bodyfat Example,
NKNW Table 7.1
Bootstrap regression
The UNIVARIATE Procedure
Variable: X2
(Thigh circumference)
Moments
N
50 Sum Weights
50
Mean
-2.7179113 Sum Observations -135.89557
Std Deviation
2.8926404 Variance
8.36736846
Skewness
-0.019163 Kurtosis
-0.4632498
Uncorrected SS
779.353152 Corrected SS
410.001054
Coeff Variation
-106.4288 Std Error Mean
0.40908113
Basic Statistical Measures
Location
Variability
Mean
-2.71791 Std Deviation
2.89264
Median -3.17285
Variance
8.36737
Mode
. Range
12.01907
Interquartile Range 3.86110
Tests for Location: Mu0=0
Test
-Statistic- -----p Value------
Student's t
t -6.64394 Pr > |t| <.0001
Sign
M -17 Pr >= |M|
<.0001
Signed Rank
S -513.5 Pr >= |S| <.0001
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk
W 0.984508 Pr < W
0.7503
Kolmogorov-Smirnov
D 0.08087 Pr > D
>0.1500
Cramer-von Mises
W-Sq 0.026751 Pr > W-Sq >0.2500
Anderson-Darling
A-Sq 0.194131 Pr > A-Sq >0.2500
Quantiles (Definition 5)
Quantile
Estimate
100% Max
2.693542
99%
2.693542
95%
2.188008 <== 95th percentile used in calculating confidence intervals
90%
1.549550
75% Q3
-0.649579
50% Median
-3.172851
25% Q1
-4.510678
10%
-6.402169
5%
-7.677820 <== 5th percentile used in calculating confidence intervals
1%
-9.325527
0% Min
-9.325527
Extreme Observations
------Lowest-----
-----Highest-----
Value
Obs Value
Obs
-9.32553
50 1.73600
5
-7.97082
48 2.00652
4
-7.67782
49 2.18801
3
-7.13374
47 2.47138
2
-6.41505
46 2.69354
1
Stem Leaf
# Boxplot
2 0257
4 |
1 347
3 |
0 6
1 |
-0 966442
6 +-----+
-1 974320
6 | |
-2 4332
4 | + |
-3 777654222
9 *-----*
-4 8755320
7 +-----+
-5 552
3 |
-6 441
3 |
-7 71
2 |
-8 0
1 |
-9 3
1 |
----+----+----+----+
Normal Probability Plot
2.5+
**+*+ *
|
***+++
|
*++
|
****
|
***
|
+**
-3.5+
*****
|
*****
|
+**+
| +***
| *+**
| +++
-9.5++++*
+----+----+----+----+----+----+----+----+----+----+
-2 -1
0 +1
+2
EXST7034 - Bodyfat
Example, NKNW Table 7.1
Bootstrap regression
The UNIVARIATE Procedure
Variable: X3
(Midarm circumference)
Moments
N
50 Sum Weights
50
Mean
-2.0835004 Sum Observations -104.17502
Std Deviation
1.81430845 Variance
3.29171514
Skewness
0.00238801 Kurtosis
-0.4188596
Uncorrected SS
378.342743 Corrected SS
161.294042
Coeff Variation
-87.079821 Std Error Mean
0.25658196
Basic Statistical Measures
Location
Variability
Mean
-2.08350 Std Deviation
1.81431
Median -2.24925
Variance
3.29172
Mode
. Range
7.56477
Interquartile Range 2.36835
Tests for Location: Mu0=0
Test
-Statistic- -----p Value------
Student's t
t -8.12021 Pr > |t| <.0001
Sign
M -18 Pr >= |M|
<.0001
Signed Rank
S -564.5 Pr >= |S| <.0001
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk
W 0.982552 Pr < W
0.6634
Kolmogorov-Smirnov
D 0.094037 Pr > D
>0.1500
Cramer-von Mises
W-Sq 0.03496 Pr > W-Sq >0.2500
Anderson-Darling
A-Sq 0.235474 Pr > A-Sq >0.2500
Quantiles (Definition 5)
Quantile
Estimate
100% Max
1.276578
99%
1.276578
95%
1.127003 <== 95th percentile used in calculating confidence intervals
90%
0.691110
75% Q3
-0.898947
50% Median
-2.249251
25% Q1
-3.267301
10%
-4.387901
5%
-5.076321 <== 5th percentile used in calculating confidence intervals
1%
-6.288195
0% Min
-6.288195
Extreme Observations
------Lowest-----
------Highest-----
Value
Obs Value
Obs
-6.28819
50 0.759323
4
-5.34358
49 0.967975
1
-5.07632
48 1.127003
5
-4.97738
47 1.202083
3
-4.57029
46 1.276578
2
Stem Leaf
# Boxplot
1 0123
4 |
0 68
2 |
0 2
1 |
-0 33
2 |
-0 9876
4 +-----+
-1 331000
6 | |
-1 99987
5 | |
-2 0
1 *--+--*
-2 987766655
9 | |
-3 33211
5 +-----+
-3 8655
4 |
-4 20
2 |
-4 6
1 |
-5 310
3 |
-5
|
-6 3
1 |
----+----+----+----+
Normal Probability Plot
1.25+
*+*+ *
|
** *+
|
*+++
-0.25+
**+
|
****
|
***
-1.75+
****
|
+++
|
+*****
-3.25+
***
|
****
| +*+
-4.75+
+*+*
| *+*
| +++
-6.25+ ++*
+----+----+----+----+----+----+----+----+----+----+
-2 -1
0 +1
+2
68
*******************************************;
69
*** Ridge Regression section
***;
70
*******************************************;
71
72
PROC REG DATA=ONE outest=ridge1 outvif; TITLE2 'Ridge Regression';
73
MODEL Y = X1 X2 X3 / ridge= 0.00 to 0.10 by 0.005;
74
output out=next1 r=e p=yhat;
75
RUN;
NOTE: 20 observations read.
NOTE: 20 observations used
in computations.
NOTE: The data set WORK.RIDGE1
has 43 observations and 11 variables.
NOTE: The data set WORK.NEXT1
has 20 observations and 7 variables.
NOTE: The PROCEDURE REG printed
page 10.
NOTE: PROCEDURE REG used:
real time 0.05
seconds
76
proc print data=ridge1; run;
NOTE: There were 43 observations
read from the data set WORK.RIDGE1.
NOTE: The PROCEDURE PRINT
printed page 11.
NOTE: PROCEDURE PRINT used:
real time 0.00
seconds
EXST7034 - Bodyfat Example,
NKNW Table 7.1
Ridge Regression
The REG Procedure
Model: MODEL1
Dependent Variable: Y Body
Fat
Analysis of Variance
Sum of Mean
Source
DF Squares
Square F Value Pr > F
Model
3 396.98461
132.32820 21.52 <.0001
Error
16 98.40489
6.15031
Corrected Total
19 495.38950
Root MSE
2.47998 R-Square 0.8014
Dependent Mean
20.19500 Adj R-Sq 0.7641
Coeff Var
12.28017
Parameter Estimates
Parameter Standard
Variable
Label
DF Estimate
Error t Value Pr > |t|
Intercept
Intercept
1 117.08469
99.78240 1.17
0.2578
X1
Triceps skinfold thickness 1
4.33409 3.01551
1.44 0.1699
X2
Thigh circumference
1 -2.85685
2.58202 -1.11
0.2849
X3
Midarm circumference
1 -2.18606
1.59550 -1.37
0.1896
78
data ridgeK ridgeV; set ridge1;
79
if _type_ eq 'PARMS' then delete;
80
if _type_ eq 'RIDGE' then output ridgeK;
81
if _type_ eq 'RIDGEVIF' then output ridgeV;
82
run;
NOTE: There were 43 observations
read from the data set WORK.RIDGE1.
NOTE: The data set WORK.RIDGEK
has 21 observations and 11 variables.
NOTE: The data set WORK.RIDGEV
has 21 observations and 11 variables.
NOTE: DATA statement used:
real time 0.04
seconds
EXST7034 - Bodyfat Example,
NKNW Table 7.1
Ridge Regression
Obs _MODEL_ _TYPE_
_DEPVAR_ _RIDGE_ _PCOMIT_ _RMSE_ Intercept
X1 X2
X3 Y
1 MODEL1 PARMS
Y .
. 2.47998 117.085 4.334
-2.857 -2.186 -1
2 MODEL1 RIDGEVIF
Y 0.000 .
. .
708.843 564.343 104.606 -1
3 MODEL1 RIDGE
Y 0.000 .
2.47998 117.085 4.334 -2.857
-2.186 -1
4 MODEL1 RIDGEVIF
Y 0.005 .
. .
11.643 9.476 2.580 -1
5 MODEL1 RIDGE
Y 0.005 .
2.57755 4.268 0.918
0.065 -0.385 -1
6 MODEL1 RIDGEVIF
Y 0.010 .
. .
3.486 2.981 1.377 -1
7 MODEL1 RIDGE
Y 0.010 .
2.59104 -3.312 0.685 0.262
-0.262 -1
8 MODEL1 RIDGEVIF
Y 0.015 .
. .
1.745 1.594 1.113 -1
9 MODEL1 RIDGE
Y 0.015 .
2.59630 -6.029 0.600 0.332
-0.216 -1
10 MODEL1 RIDGEVIF
Y 0.020 .
. .
1.103 1.081 1.011 -1
11 MODEL1 RIDGE
Y 0.020 .
2.59924 -7.403 0.555 0.368
-0.192 -1
12 MODEL1 RIDGEVIF
Y 0.025 .
. .
0.796 0.834 0.957 -1
13 MODEL1 RIDGE
Y 0.025 .
2.60122 -8.218 0.528 0.389
-0.176 -1
14 MODEL1 RIDGEVIF
Y 0.030 .
. .
0.626 0.697 0.923 -1
15 MODEL1 RIDGE
Y 0.030 .
2.60276 -8.746 0.509 0.403
-0.165 -1
16 MODEL1 RIDGEVIF
Y 0.035 .
. .
0.521 0.612 0.900 -1
17 MODEL1 RIDGE
Y 0.035 .
2.60405 -9.107 0.495 0.413
-0.157 -1
18 MODEL1 RIDGEVIF
Y 0.040 .
. .
0.453 0.555 0.881 -1
19 MODEL1 RIDGE
Y 0.040 .
2.60522 -9.364 0.484 0.420
-0.151 -1
20 MODEL1 RIDGEVIF
Y 0.045 .
. .
0.405 0.515 0.866 -1
21 MODEL1 RIDGE
Y 0.045 .
2.60632 -9.550 0.475 0.425
-0.145 -1
22 MODEL1 RIDGEVIF
Y 0.050 .
. .
0.370 0.486 0.853 -1
23 MODEL1 RIDGE
Y 0.050 .
2.60740 -9.687 0.468 0.428
-0.141 -1
24 MODEL1 RIDGEVIF
Y 0.055 .
. .
0.344 0.463 0.841 -1
25 MODEL1 RIDGE
Y 0.055 .
2.60847 -9.788 0.462 0.431
-0.137 -1
26 MODEL1 RIDGEVIF
Y 0.060 .
. .
0.324 0.445 0.831 -1
27 MODEL1 RIDGE
Y 0.060 .
2.60956 -9.862 0.457 0.433
-0.133 -1
28 MODEL1 RIDGEVIF
Y 0.065 .
. .
0.308 0.431 0.821 -1
29 MODEL1 RIDGE
Y 0.065 .
2.61066 -9.915 0.452 0.435
-0.130 -1
30 MODEL1 RIDGEVIF
Y 0.070 .
. .
0.296 0.419 0.811 -1
31 MODEL1 RIDGE
Y 0.070 .
2.61180 -9.951 0.448 0.436
-0.127 -1
32 MODEL1 RIDGEVIF
Y 0.075 .
. .
0.285 0.409 0.802 -1
33 MODEL1 RIDGE
Y 0.075 .
2.61297 -9.974 0.445 0.437
-0.125 -1
34 MODEL1 RIDGEVIF
Y 0.080 .
. .
0.276 0.400 0.793 -1
35 MODEL1 RIDGE
Y 0.080 .
2.61418 -9.987 0.441 0.438
-0.122 -1
36 MODEL1 RIDGEVIF
Y 0.085 .
. .
0.269 0.392 0.785 -1
37 MODEL1 RIDGE
Y 0.085 .
2.61542 -9.991 0.438 0.438
-0.120 -1
38 MODEL1 RIDGEVIF
Y 0.090 .
. .
0.262 0.385 0.777 -1
39 MODEL1 RIDGE
Y 0.090 .
2.61671 -9.987 0.435 0.438
-0.118 -1
40 MODEL1 RIDGEVIF
Y 0.095 .
. .
0.257 0.379 0.769 -1
41 MODEL1 RIDGE
Y 0.095 .
2.61804 -9.978 0.433 0.438
-0.116 -1
42 MODEL1 RIDGEVIF
Y 0.100 .
. .
0.252 0.373 0.761 -1
43 MODEL1 RIDGE
Y 0.100 .
2.61942 -9.963 0.430 0.438
-0.114 -1
83
data ridgev; set ridgev; vx1=x1; vx2=x2; vx3=x3;
84
drop x1 x2 x3;
85
run;
NOTE: There were 21 observations
read from the data set WORK.RIDGEV.
NOTE: The data set WORK.RIDGEV
has 21 observations and 11 variables.
NOTE: DATA statement used:
real time 0.05
seconds
86
data combo; merge ridgek ridgev; by _ridge_; run;
NOTE: There were 21 observations
read from the data set WORK.RIDGEK.
NOTE: There were 21 observations
read from the data set WORK.RIDGEV.
NOTE: The data set WORK.COMBO
has 21 observations and 14 variables.
NOTE: DATA statement used:
real time 0.00
seconds
87
proc print data=combo; run;
NOTE: There were 21 observations
read from the data set WORK.COMBO.
NOTE: The PROCEDURE PRINT
printed page 12.
NOTE: PROCEDURE PRINT used:
real time 0.00
seconds
EXST7034 - Bodyfat Example,
NKNW Table 7.1
Ridge Regression
I
_ _
n
_
D _ P t
M _
E R C _ e
O T
P I O R r
D Y
V D M M c
O
E P
A G I S e
v v
v
b
L E
R E T E p
X X
X
x x
x
s
_ _
_ _ _ _ t
1 2
3 Y
1 2
3
1 MODEL1
RIDGEVIF Y 0.000 . . . 4.33409
-2.85685 -2.18606 -1 708.843 564.343 104.606
2 MODEL1
RIDGEVIF Y 0.005 . . . 0.91772
0.06535 -0.38521 -1 11.643 9.476
2.580
3 MODEL1
RIDGEVIF Y 0.010 . . . 0.68530
0.26183 -0.26185 -1 3.486
2.981 1.377
4 MODEL1
RIDGEVIF Y 0.015 . . . 0.60000
0.33238 -0.21602 -1 1.745
1.594 1.113
5 MODEL1
RIDGEVIF Y 0.020 . . . 0.55535
0.36814 -0.19163 -1 1.103
1.081 1.011
6 MODEL1
RIDGEVIF Y 0.025 . . . 0.52766
0.38942 -0.17618 -1 0.796
0.834 0.957
7 MODEL1
RIDGEVIF Y 0.030 . . . 0.50864
0.40327 -0.16531 -1 0.626
0.697 0.923
8 MODEL1
RIDGEVIF Y 0.035 . . . 0.49466
0.41283 -0.15712 -1 0.521
0.612 0.900
9 MODEL1
RIDGEVIF Y 0.040 . . . 0.48386
0.41968 -0.15062 -1 0.453
0.555 0.881
10 MODEL1 RIDGEVIF
Y 0.045 . . . 0.47521 0.42471
-0.14526 -1 0.405 0.515
0.866
11 MODEL1 RIDGEVIF
Y 0.050 . . . 0.46806 0.42847
-0.14072 -1 0.370 0.486
0.853
12 MODEL1 RIDGEVIF
Y 0.055 . . . 0.46202 0.43129
-0.13676 -1 0.344 0.463
0.841
13 MODEL1 RIDGEVIF
Y 0.060 . . . 0.45681 0.43342
-0.13327 -1 0.324 0.445
0.831
14 MODEL1 RIDGEVIF
Y 0.065 . . . 0.45225 0.43501
-0.13012 -1 0.308 0.431
0.821
15 MODEL1 RIDGEVIF
Y 0.070 . . . 0.44819 0.43618
-0.12726 -1 0.296 0.419
0.811
16 MODEL1 RIDGEVIF
Y 0.075 . . . 0.44455 0.43701
-0.12462 -1 0.285 0.409
0.802
17 MODEL1 RIDGEVIF
Y 0.080 . . . 0.44124 0.43757
-0.12217 -1 0.276 0.400
0.793
18 MODEL1 RIDGEVIF
Y 0.085 . . . 0.43820 0.43791
-0.11988 -1 0.269 0.392
0.785
19 MODEL1 RIDGEVIF
Y 0.090 . . . 0.43539 0.43807
-0.11773 -1 0.262 0.385
0.777
20 MODEL1 RIDGEVIF
Y 0.095 . . . 0.43278 0.43807
-0.11569 -1 0.257 0.379
0.769
21 MODEL1 RIDGEVIF
Y 0.100 . . . 0.43034 0.43795
-0.11375 -1 0.252 0.373
0.761
89
OPTIONS LS=99 PS=56;
90
proc plot data=combo; title1 'Plot of Ridge trace';
91
plot x1*_ridge_='1' x2*_ridge_='2' x3*_ridge_='3' / vref=0 overlay;
92
run;
NOTE: There were 21 observations
read from the data set WORK.COMBO.
NOTE: The PROCEDURE PLOT
printed page 13.
NOTE: PROCEDURE PLOT used:
real time 0.04
seconds
95
proc plot data=combo; title1 'Plot of Ridge VIF values';
96
plot Vx1*_ridge_='1' Vx2*_ridge_='2' Vx3*_ridge_='3' / overlay;
97
run;
NOTE: There were 21 observations
read from the data set WORK.COMBO.
NOTE: The PROCEDURE PLOT
printed page 14.
NOTE: PROCEDURE PLOT used:
real time 0.00
seconds
99
proc plot data=next1; plot e*yhat / vref=0; run;
100
OPTIONS LS=99 PS=256;
NOTE: There were 20 observations
read from the data set WORK.NEXT1.
NOTE: The PROCEDURE PLOT
printed page 15.
NOTE: PROCEDURE PLOT used:
real time 0.00
seconds
Residual plot
Plot of e*yhat. Legend: A = 1 obs, B = 2 obs, etc.
5 +
|
|
|
|
A
4 +
|
|
|
|
A
3 +
|
|
A
|
|
A
2 +
|
A
|
|
A
R |
A
e 1 +
A
s |
A
i |
A
d |
u |
A
a 0 +---------------------------------------------------------------------------------------------
l |
|
A
|
A
|
-1 +
|
A
|
A
|
|
-2 +
|
A
|
|
|
-3 +
A
A
|
|
A
|
|
A
-4 +
--+---------+---------+---------+---------+---------+---------+---------+---------+---------+-
10 12
14 16
18 20
22 24
26 28
Predicted Value of Y
101
proc univariate data=next1 normal plot; var e; run;
NOTE: The PROCEDURE UNIVARIATE
printed page 16.
NOTE: PROCEDURE UNIVARIATE
used:
real time 0.00
seconds
Proc univariate of residuals
The UNIVARIATE Procedure
Variable: e (Residual)
Moments
N
20 Sum Weights
20
Mean
0 Sum Observations
0
Std Deviation
2.2757866 Variance
5.17920464
Skewness
-0.0920396 Kurtosis
-0.9101278
Uncorrected SS
98.4048882 Corrected SS
98.4048882
Coeff Variation
. Std Error Mean 0.50888135
Basic Statistical Measures
Location
Variability
Mean
0.000000 Std Deviation
2.27579
Median 0.392310
Variance
5.17920
Mode
. Range
7.85397
Interquartile Range 3.38172
Tests for Location: Mu0=0
Test
-Statistic- -----p Value------
Student's t
t 0 Pr
> |t| 1.0000
Sign
M 1 Pr
>= |M| 0.8238
Signed Rank
S 1 Pr
>= |S| 0.9854
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk
W 0.966027 Pr < W
0.6698
Kolmogorov-Smirnov
D 0.106019 Pr > D
>0.1500
Cramer-von Mises
W-Sq 0.034763 Pr > W-Sq >0.2500
Anderson-Darling
A-Sq 0.241832 Pr > A-Sq >0.2500
Quantiles (Definition 5)
Quantile
Estimate
100% Max
4.12769
99%
4.12769
95%
3.62853
90%
2.85526
75% Q3
1.54543
50% Median
0.39231
25% Q1
-1.83629
10%
-3.16836
5%
-3.51784
1%
-3.72628
0% Min
-3.72628
Extreme Observations
------Lowest-----
-----Highest-----
Value
Obs Value
Obs
-3.72628
19 1.70518
9
-3.30940
13 2.20769
12
-3.02732
4 2.58116
2
-2.95499
1 3.12936
8
-2.28668
3 4.12769
14
Stem Leaf
# Boxplot
4 1
1 |
3 1
1 |
2 26
2 |
1 0147
4 +-----+
0 268
3 *--+--*
-0 54
2 | |
-1 42
2 +-----+
-2 3
1 |
-3 7300
4 |
----+----+----+----+
Normal Probability Plot
4.5+
+*++
|
*+++
|
*+*++
|
*+**+
0.5+
*+***+
|
+**+
|
++*+*
| ++++*
*
-3.5+
* +++* *
+----+----+----+----+----+----+----+----+----+----+
-2 -1
0 +1
+2
Original fit of the bodyfat
example
Parameter Estimates
Parameter Standard
Variance
Variable Label
DF Estimate
Error t Value Pr > |t| Inflation
Intercept Intercept
1 117.08469 99.78240
1.17 0.2578
0
X1
Triceps skinfold thickness 1
4.33409 3.01551 1.44
0.1699 708.84291
X2
Thigh circumference
1 -2.85685 2.58202
-1.11 0.2849 564.34339
X3
Midarm circumference 1
-2.18606 1.59550 -1.37
0.1896 104.60601
Results from Bootstrap for the bodyfat example. The bootstrap technique is not usually considered a way of addressing multicollinearity because it does not address fluctuations in the regression coefficients. It is used here only to demonstrate the stabilizing effect on the variance.
Variable: X1 (Triceps
skinfold thickness)
Moments
N
50 Sum Weights
50
Mean
4.18327267 Sum Observations 209.163634
Std Deviation
3.40267416 Variance
11.5781914
Uncorrected SS
1442.31989 Corrected SS
567.331379
Coeff Variation
81.3400039 Std Error Mean
0.48121079
Variable: X2 (Thigh
circumference)
Moments
N
50 Sum Weights
50
Mean
-2.7179113 Sum Observations -135.89557
Std Deviation
2.8926404 Variance
8.36736846
Uncorrected SS
779.353152 Corrected SS
410.001054
Coeff Variation
-106.4288 Std Error Mean
0.40908113
Variable: X3 (Midarm
circumference)
Moments
N
50 Sum Weights
50
Mean
-2.0835004 Sum Observations -104.17502
Std Deviation
1.81430845 Variance
3.29171514
Uncorrected SS
378.342743 Corrected SS
161.294042
Coeff Variation
-87.079821 Std Error Mean
0.25658196
Results from Ridge regression
for the bodyfat example Compare changes in the regression coefficients
and the VIF values to the original regression above.
I
_ _
n
_
D _ P t
M _
E R C _ e
O T
P I O R r
D Y
V D M M c
O
E P
A G I S e
v v
v
b
L E
R E T E p
X X
X
x x
x
s
_ _
_ _ _ _ t
1 2
3 Y
1 2
3
1 MODEL1
RIDGEVIF Y 0.000 . . . 4.33409
-2.85685 -2.18606 -1 708.843 564.343 104.606
2 MODEL1
RIDGEVIF Y 0.005 . . . 0.91772
0.06535 -0.38521 -1 11.643 9.476
2.580
3 MODEL1
RIDGEVIF Y 0.010 . . . 0.68530
0.26183 -0.26185 -1 3.486
2.981 1.377
4 MODEL1
RIDGEVIF Y 0.015 . . . 0.60000
0.33238 -0.21602 -1 1.745
1.594 1.113
5 MODEL1
RIDGEVIF Y 0.020 . . . 0.55535
0.36814 -0.19163 -1 1.103
1.081 1.011
6 MODEL1
RIDGEVIF Y 0.025 . . . 0.52766
0.38942 -0.17618 -1 0.796
0.834 0.957
7 MODEL1
RIDGEVIF Y 0.030 . . . 0.50864
0.40327 -0.16531 -1 0.626
0.697 0.923
8 MODEL1
RIDGEVIF Y 0.035 . . . 0.49466
0.41283 -0.15712 -1 0.521
0.612 0.900
9 MODEL1
RIDGEVIF Y 0.040 . . . 0.48386
0.41968 -0.15062 -1 0.453
0.555 0.881
10 MODEL1 RIDGEVIF
Y 0.045 . . . 0.47521 0.42471
-0.14526 -1 0.405 0.515
0.866
11 MODEL1 RIDGEVIF
Y 0.050 . . . 0.46806 0.42847
-0.14072 -1 0.370 0.486
0.853
12 MODEL1 RIDGEVIF
Y 0.055 . . . 0.46202 0.43129
-0.13676 -1 0.344 0.463
0.841
13 MODEL1 RIDGEVIF
Y 0.060 . . . 0.45681 0.43342
-0.13327 -1 0.324 0.445
0.831
14 MODEL1 RIDGEVIF
Y 0.065 . . . 0.45225 0.43501
-0.13012 -1 0.308 0.431
0.821
15 MODEL1 RIDGEVIF
Y 0.070 . . . 0.44819 0.43618
-0.12726 -1 0.296 0.419
0.811
16 MODEL1 RIDGEVIF
Y 0.075 . . . 0.44455 0.43701
-0.12462 -1 0.285 0.409
0.802
17 MODEL1 RIDGEVIF
Y 0.080 . . . 0.44124 0.43757
-0.12217 -1 0.276 0.400
0.793
18 MODEL1 RIDGEVIF
Y 0.085 . . . 0.43820 0.43791
-0.11988 -1 0.269 0.392
0.785
19 MODEL1 RIDGEVIF
Y 0.090 . . . 0.43539 0.43807
-0.11773 -1 0.262 0.385
0.777
20 MODEL1 RIDGEVIF
Y 0.095 . . . 0.43278 0.43807
-0.11569 -1 0.257 0.379
0.769
21 MODEL1 RIDGEVIF
Y 0.100 . . . 0.43034 0.43795
-0.11375 -1 0.252 0.373
0.761
1 *************************************************************************;
2 *** EXST7034
Example of Piecewise Regression
***;
3 *** Problem
from Neter, Kutner, Nachtsheim, & Wasserman 1996, #11.17 ***;
4 *************************************************************************;
5 OPTIONS
LS=99 PS=256 NOCENTER NODATE NONUMBER;
6
7 DATA
ONE; INFILE CARDS MISSOVER;
8
TITLE1 'EXST7034 - NKNW Table 11.11';
9
INPUT state $ 1-25 mathprof parents homelib reading tvwatch absences;
10
weight = 1;
11 *---+----1----+----2----+----3----+----4----+----5----+----6;
12 CARDS;
NOTE: The data set WORK.ONE
has 40 observations and 8 variables.
NOTE: DATA statement used:
real time 0.26
seconds
12 !
RUN;
53 ;
54 OPTIONS LS=99
PS=56;
55 PROC REG DATA=ONE
lineprinter; weight weight; id state;
56
MODEL mathprof = homelib / influence;
57
output out=next1a r=e p=yhat;
58
plot residual.*homelib;
59 run;
NOTE: 40 observations read.
NOTE: 40 observations used
in computations.
NOTE: Some ID variables have
been truncated to 16 characters.
NOTE: The data set WORK.NEXT1A
has 40 observations and 10 variables.
NOTE: PROCEDURE REG used:
real time 0.75
seconds
Original fit of the model.
EXST7034 - NKNW Table 11.11
The REG Procedure
Model: MODEL1
Dependent Variable: mathprof
Weight: weight
Analysis of Variance
Sum of Mean
Source
DF Squares
Square F Value Pr > F
Model
1 3769.30965 3769.30965
47.42 <.0001
Error
38 3020.59035
79.48922
Corrected Total
39 6789.90000
Root MSE
8.91567 R-Square 0.5551
Dependent Mean
260.95000 Adj R-Sq 0.5434
Coeff Var
3.41662
Parameter Estimates
Parameter Standard
Variable
DF Estimate
Error t Value Pr > |t|
Intercept
1 135.55589
18.26408 7.42
<.0001
homelib
1 1.55963
0.22649 6.89
<.0001
Output Statistics
Weight
Hat Diag Cov
-------DFBETAS-------
Obs state
Variable Residual RStudent
H Ratio
DFFITS Intercept homelib
1
Alabama
1.0000 -5.2069
-0.5875 0.0287
1.0660 -0.1010 -0.0435
0.0363
2
Arizona
1.0000 9.5912
1.1133 0.0603
1.0509 0.2821
0.2293 -0.2159
3
Arkansas
1.0000 0.3527
0.0397 0.0325
1.0901 0.0073
0.0040 -0.0035
4
California
1.0000 14.3894
1.7726 0.1242
1.0232 0.6676
0.6180 -0.5966
5
Colorado
1.0000 -1.1243
-0.1269 0.0387
1.0962 -0.0255
0.0135 -0.0151
6
Connecticut
1.0000 0.3161
0.0358 0.0452
1.1047 0.0078
-0.0047 0.0052
7
Delaware
1.0000 -4.0050
-0.4512 0.0294
1.0748 -0.0785
0.0246 -0.0302
8
Distric of Colum 1.0000
-23.0876 -2.8821
0.0375 0.7309 -0.5688
-0.3632 0.3284
9
Florida
1.0000 5.5912
0.6419 0.0603
1.0979 0.1627
0.1322 -0.1245
10
Georgia
1.0000 -2.3261
-0.2610 0.0251
1.0780 -0.0419 -0.0059
0.0027
11
Guam
1.0000 -4.3721
-0.5427 0.1986
1.2954 -0.2701 -0.2592
0.2525
12
Hawaii
1.0000 7.8298
0.9286 0.1089
1.1303 0.3246
0.2960 -0.2849
13
Idaho
1.0000 5.4353
0.6150 0.0334
1.0692 0.1143
-0.0494 0.0572
14
Illinois
1.0000 -3.4454
-0.3873 0.0267
1.0749 -0.0641
0.0111 -0.0160
15
Indiana
1.0000 0.4353
0.0490 0.0334
1.0910 0.0091
-0.0039 0.0046
16
Iowa
1.0000 5.1968
0.5968 0.0623
1.1035 0.1538
-0.1111 0.1190
17
Kentucky
1.0000 -1.2069
-0.1356 0.0287
1.0849 -0.0233 -0.0100
0.0084
18
Louisiana
1.0000 -8.0876
-0.9228 0.0375
1.0471 -0.1821 -0.1163
0.1051
19
Maryland
1.0000 -5.0050
-0.5647 0.0294
1.0682 -0.0982
0.0307 -0.0379
20
Michigan
1.0000 -2.5647
-0.2890 0.0334
1.0863 -0.0537
0.0232 -0.0269
21
Minnesota
1.0000 3.1968
0.3660 0.0623
1.1167 0.0943
-0.0681 0.0730
22
Montana
1.0000 7.1968
0.8302 0.0623
1.0841 0.2139
-0.1546 0.1655
23
Nebraska
1.0000 3.1968
0.3660 0.0623
1.1167 0.0943
-0.0681 0.0730
24
New Hampshire 1.0000
0.1968 0.0225
0.0623 1.1248
0.0058 -0.0042
0.0045
25
New Jersey
1.0000 2.4353
0.2744 0.0334
1.0868 0.0510
-0.0220 0.0255
26
New Mexico
1.0000 8.1509
0.9470 0.0705
1.0818 0.2609
0.2210 -0.2096
27
New York
1.0000 2.2335
0.2507 0.0263
1.0796 0.0412
0.0121 -0.0090
28
North Carolina 1.0000
-7.2069 -0.8166
0.0287 1.0479 -0.1404
-0.0605 0.0505
29
North Dakota
1.0000 5.0776
0.5901 0.0845
1.1307 0.1792
-0.1424 0.1504
30
Ohio
1.0000 -2.5647
-0.2890 0.0334
1.0863 -0.0537
0.0232 -0.0269
31
Oklahoma
1.0000 5.7931
0.6543 0.0287
1.0613 0.1125
0.0485 -0.0405
32
Oregon
1.0000 7.5546
0.8558 0.0267
1.0420 0.1416
-0.0246 0.0353
33
Pennsylvania
1.0000 -3.6839
-0.4183 0.0452
1.0944 -0.0910
0.0555 -0.0609
34
Rhode Island
1.0000 -0.3261
-0.0366 0.0251
1.0819 -0.0059 -0.0008
0.0004
35
Texas
1.0000 13.2701
1.5959 0.0948
1.0200 0.5165
0.4623 -0.4432
36
Virgin Islands 1.0000
-36.0876 -5.4792
0.0375 0.3340 -1.0814
-0.6905 0.6243
37
Virginia
1.0000 0.5546
0.0622 0.0267
1.0834 0.0103
-0.0018 0.0026
38
West Virginia 1.0000
-4.3261 -0.4865
0.0251 1.0682 -0.0781
-0.0110 0.0050
39
Wisconsin
1.0000 4.3161
0.4905 0.0452
1.0905 0.1068
-0.0651 0.0714
40
Wyoming
1.0000 2.3161
0.2626 0.0452
1.1007 0.0572
-0.0348 0.0382
Sum of Residuals
0
Sum of Squared Residuals
3020.59035
Predicted Residual SS (PRESS)
3367.16839
----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----
20 +
+
|
|
|
|
|
|
|
1
|
|
1
|
|
|
10 +
1
+
|
1
|
|
1
1
1 |
|
1
1
1 1
1 |
|
1
|
|
1
1 1 2
|
|
|
0 +
1 1 1
1 1 1
+
|
1
1
|
|
1 1 2
|
R RESIDUAL |
1
1 1
1
|
e
|
1
1
|
s
|
1
|
i
|
1
|
d
-10 +
+
u
|
|
a
|
|
l
|
|
|
|
|
|
|
|
-20 +
+
|
|
|
1
|
|
|
|
|
|
|
|
|
-30 +
+
|
|
|
|
|
|
|
1
|
|
|
|
|
-40 +
+
----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----
64 66 68 70
72 74 76 78
80 82 84 86
88 90
homelib
First reweighting of the data.
EXST7034 - NKNW Table 11.11
m
a
a p h r t b
m
t a o e v s w
e s
h r m a w e e
d t
p e e d a n i
y
a
O
i a
r n l i t c g
h
b m
b
a t
o t i n c e h
a
s a
m
s
n e
f s b g h s t
t e
e d
u
1 4.32112
. . . . . . 1.00000 .
. . 6.40640
.
2 .
Alabama
252 75 78 34 18 18 1.00000 257.207 -5.2069 5.2069 6.40640 -0.81276
3 .
Arizona
259 75 73 41 12 26 0.89838 249.409 9.5912 9.5912 6.40640
1.49714
4 .
Arkansas
256 77 77 28 20 23 1.00000 255.647 0.3527 0.3527 6.40640
0.05506
5 .
California 256 78
68 42 11 28 0.59882 241.611 14.3894 14.3894 6.40640 2.24610
6 .
Colorado
267 78 85 38 9 25 1.00000 268.124 -1.1243 1.1243 6.40640
-0.17549
7 .
Connecticut 270 79 86 43
12 22 1.00000 269.684 0.3161 0.3161 6.40640 0.04934
8 .
Delaware
261 75 83 32 18 28 1.00000 265.005 -4.0050 4.0050 6.40640 -0.62516
9 .
Distric of Columbia 231 47 76 24 33 37 0.37321 254.088 -23.0876 23.0876
6.40640 -3.60384
10 .
Florida
255 75 73 31 19 27 1.00000 249.409 5.5912 5.5912 6.40640
0.87276
11 .
Georgia
258 73 80 36 17 22 1.00000 260.326 -2.3261 2.3261 6.40640 -0.36310
12 .
Guam
231 81 64 32 20 28 1.00000 235.372 -4.3721 4.3721 6.40640 -0.68246
13 .
Hawaii
251 78 69 36 23 26 1.00000 243.170 7.8298 7.8298 6.40640
1.22218
14 .
Idaho
272 84 84 48 7 21 1.00000 266.565 5.4353 5.4353
6.40640 0.84842
15 .
Illinois
260 78 82 43 14 21 1.00000 263.445 -3.4454 3.4454 6.40640 -0.53781
16 .
Indiana
267 81 84 37 11 23 1.00000 266.565 0.4353 0.4353 6.40640
0.06795
17 .
Iowa
278 83 88 43 8 20 1.00000 272.803 5.1968 5.1968
6.40640 0.81119
18 .
Kentucky
256 79 78 36 14 23 1.00000 257.207 -1.2069 1.2069 6.40640 -0.18839
19 .
Louisiana 246
73 76 36 19 27 1.00000 254.088 -8.0876 8.0876 6.40640 -1.26243
20 .
Maryland
260 75 83 34 19 27 1.00000 265.005 -5.0050 5.0050 6.40640 -0.78126
21 .
Michigan
264 77 84 31 14 25 1.00000 266.565 -2.5647 2.5647 6.40640 -0.40033
22 .
Minnesota 276
83 88 36 7 20 1.00000 272.803 3.1968 3.1968 6.40640
0.49901
23 .
Montana
280 83 88 44 6 21 1.00000 272.803 7.1968 7.1968
6.40640 1.12338
24 .
Nebraska
276 85 88 42 9 19 1.00000 272.803 3.1968 3.1968
6.40640 0.49901
25 .
New Hampshire 273 83 88 40 7
22 1.00000 272.803 0.1968 0.1968 6.40640 0.03072
26 .
New Jersey 269 79
84 41 13 23 1.00000 266.565 2.4353 2.4353 6.40640
0.38014
27 .
New Mexico 256 77
72 40 11 27 1.00000 247.849 8.1509 8.1509 6.40640
1.27230
28 .
New York
261 76 79 35 17 29 1.00000 258.767 2.2335 2.2335 6.40640
0.34863
29 .
North Carolina 250 74 78 37 21 25 1.00000
257.207 -7.2069 7.2069 6.40640 -1.12495
30 .
North Dakota 281 85 90 41
6 14 1.00000 275.922 5.0776 5.0776 6.40640 0.79258
31 .
Ohio
264 79 84 36 11 22 1.00000 266.565 -2.5647 2.5647 6.40640 -0.40033
32 .
Oklahoma
263 78 78 37 14 22 1.00000 257.207 5.7931 5.7931 6.40640
0.90427
33 .
Oregon
271 81 82 41 9 31 1.00000 263.445 7.5546 7.5546
6.40640 1.17923
34 .
Pennsylvania 266 80 86 34 10
24 1.00000 269.684 -3.6839 3.6839 6.40640 -0.57504
35 .
Rhode Island 260 78 80 38 12
28 1.00000 260.326 -0.3261 0.3261 6.40640 -0.05091
36 .
Texas
258 77 70 34 15 18 0.64932 244.730 13.2701 13.2701 6.40640
2.07139
37 .
Virgin Islands 218 63 76 23 27 22 0.23877
254.088 -36.0876 36.0876 6.40640 -5.63306
38 .
Virginia
264 78 82 33 16 24 1.00000 263.445 0.5546 0.5546 6.40640
0.08657
39 .
West Virginia 256 82 80 36 16 25 1.00000
260.326 -4.3261 4.3261 6.40640 -0.67529
40 .
Wisconsin 274
81 86 38 8 21 1.00000 269.684 4.3161 4.3161 6.40640
0.67371
41 .
Wyoming
272 85 86 43 7 23 1.00000 269.684 2.3161 2.3161
6.40640 0.36153
First refit of the model.
EXST7034 - NKNW Table 11.11
The REG Procedure
Model: MODEL1
Dependent Variable: mathprof
Weight: weight
Analysis of Variance
Sum of Mean
Source
DF Squares
Square F Value Pr > F
Model
1 3218.16321 3218.16321
80.84 <.0001
Error
38 1512.79288
39.81034
Corrected Total
39 4730.95609
Root MSE
6.30954 R-Square 0.6802
Dependent Mean
262.39830 Adj R-Sq 0.6718
Coeff Var
2.40457
Parameter Estimates
Parameter Standard
Variable
DF Estimate
Error t Value Pr > |t|
Intercept
1 140.36603
13.61156 10.31
<.0001
homelib
1 1.51011
0.16796 8.99
<.0001
Second reweighting of the data.
EXST7034 - NKNW Table 11.11
m
a
a p h r t b
m
t a o e v s w
e s
h r m a w e e
d t
p e e d a n i
y
a
O
i a
r n l i t c g
h
b m
b
a t
o t i n c e h
a
s a
m
s
n e
f s b g h s t
t e
e d
u
1 4.55057
. . . . . . 1.00000 .
. . 6.74658
.
2 .
Alabama
252 75 78 34 18 18 1.00000 258.155 -6.1549 6.1549 6.74658 -0.91230
3 .
Arizona
259 75 73 41 12 26 1.00000 250.604 8.3957 8.3957 6.74658
1.24444
4 .
Arkansas
256 77 77 28 20 23 1.00000 256.645 -0.6448 0.6448 6.74658 -0.09557
5 .
California 256 78
68 42 11 28 0.70091 243.054 12.9463 12.9463 6.74658 1.91894
6 .
Colorado
267 78 85 38 9 25 1.00000 268.726 -1.7257 1.7257 6.74658
-0.25579
7 .
Connecticut 270 79 86 43
12 22 1.00000 270.236 -0.2358 0.2358 6.74658 -0.03495
8 .
Delaware
261 75 83 32 18 28 1.00000 265.705 -4.7054 4.7054 6.74658 -0.69746
9 .
Distric of Columbia 231 47 76 24 33 37 0.37598 255.135 -24.1347 24.1347
6.74658 -3.57732
10 .
Florida
255 75 73 31 19 27 1.00000 250.604 4.3957 4.3957 6.74658
0.65154
11 .
Georgia
258 73 80 36 17 22 1.00000 261.175 -3.1751 3.1751 6.74658 -0.47063
12 .
Guam
231 81 64 32 20 28 1.00000 237.013 -6.0133 6.0133 6.74658 -0.89131
13 .
Hawaii
251 78 69 36 23 26 1.00000 244.564 6.4361 6.4361 6.74658
0.95399
14 .
Idaho
272 84 84 48 7 21 1.00000 267.216 4.7844 4.7844
6.74658 0.70916
15 .
Illinois
260 78 82 43 14 21 1.00000 264.195 -4.1953 4.1953 6.74658 -0.62185
16 .
Indiana
267 81 84 37 11 23 1.00000 267.216 -0.2156 0.2156 6.74658 -0.03195
17 .
Iowa
278 83 88 43 8 20 1.00000 273.256 4.7440 4.7440
6.74658 0.70317
18 .
Kentucky
256 79 78 36 14 23 1.00000 258.155 -2.1549 2.1549 6.74658 -0.31940
19 .
Louisiana 246
73 76 36 19 27 0.99338 255.135 -9.1347 9.1347 6.74658 -1.35397
20 .
Maryland
260 75 83 34 19 27 1.00000 265.705 -5.7054 5.7054 6.74658 -0.84568
21 .
Michigan
264 77 84 31 14 25 1.00000 267.216 -3.2156 3.2156 6.74658 -0.47662
22 .
Minnesota 276
83 88 36 7 20 1.00000 273.256 2.7440 2.7440 6.74658
0.40672
23 .
Montana
280 83 88 44 6 21 1.00000 273.256 6.7440 6.7440
6.74658 0.99962
24 .
Nebraska
276 85 88 42 9 19 1.00000 273.256 2.7440 2.7440
6.74658 0.40672
25 .
New Hampshire 273 83 88 40 7
22 1.00000 273.256 -0.2560 0.2560 6.74658 -0.03795
26 .
New Jersey 269 79
84 41 13 23 1.00000 267.216 1.7844 1.7844 6.74658
0.26450
27 .
New Mexico 256 77
72 40 11 27 1.00000 249.094 6.9058 6.9058 6.74658
1.02360
28 .
New York
261 76 79 35 17 29 1.00000 259.665 1.3350 1.3350 6.74658
0.19788
29 .
North Carolina 250 74 78 37 21 25 1.00000
258.155 -8.1549 8.1549 6.74658 -1.20874
30 .
North Dakota 281 85 90 41
6 14 1.00000 276.276 4.7238 4.7238 6.74658 0.70017
31 .
Ohio
264 79 84 36 11 22 1.00000 267.216 -3.2156 3.2156 6.74658 -0.47662
32 .
Oklahoma
263 78 78 37 14 22 1.00000 258.155 4.8451 4.8451 6.74658
0.71816
33 .
Oregon
271 81 82 41 9 31 1.00000 264.195 6.8047 6.8047
6.74658 1.00861
34 .
Pennsylvania 266 80 86 34 10
24 1.00000 270.236 -4.2358 4.2358 6.74658 -0.62784
35 .
Rhode Island 260 78 80 38 12
28 1.00000 261.175 -1.1751 1.1751 6.74658 -0.17418
36 .
Texas
258 77 70 34 15 18 0.76087 246.074 11.9260 11.9260 6.74658
1.76771
37 .
Virgin Islands 218 63 76 23 27 22 0.24436
255.135 -37.1347 37.1347 6.74658 -5.50422
38 .
Virginia
264 78 82 33 16 24 1.00000 264.195 -0.1953 0.1953 6.74658 -0.02895
39 .
West Virginia 256 82 80 36 16 25 1.00000
261.175 -5.1751 5.1751 6.74658 -0.76707
40 .
Wisconsin 274
81 86 38 8 21 1.00000 270.236 3.7642 3.7642 6.74658
0.55794
41 .
Wyoming
272 85 86 43 7 23 1.00000 270.236 1.7642 1.7642
6.74658 0.26150
Second refit of the model.
EXST7034 - NKNW Table 11.11
The REG Procedure
Model: MODEL1
Dependent Variable: mathprof
Weight: weight
Analysis of Variance
Sum of Mean
Source
DF Squares
Square F Value Pr > F
Model
1 3189.86848 3189.86848
77.68 <.0001
Error
38 1560.48524
41.06540
Corrected Total
39 4750.35372
Root MSE
6.40823 R-Square 0.6715
Dependent Mean
262.35324 Adj R-Sq 0.6629
Coeff Var
2.44260
Parameter Estimates
Parameter Standard
Variable
DF Estimate
Error t Value Pr > |t|
Intercept
1 142.49768
13.63869 10.45
<.0001
homelib
1 1.48478
0.16847 8.81
<.0001
Third reweighting of the data.
EXST7034 - NKNW Table 11.11
m
a
a p h r t b
m
t a o e v s w
e s
h r m a w e e
d t
p e e d a n i
y
a
O
i a
r n l i t c g
h
b m
b
a t
o t i n c e h
a
s a
m
s
n e
f s b g h s t
t e
e d
u
1 4.46955
. . . . . . 1.00000 .
. . 6.62647
.
2 .
Alabama
252 75 78 34 18 18 1.00000 258.310 -6.3103 6.3103 6.62647 -0.95229
3 .
Arizona
259 75 73 41 12 26 1.00000 250.886 8.1136 8.1136 6.62647
1.22442
4 .
Arkansas
256 77 77 28 20 23 1.00000 256.826 -0.8255 0.8255 6.62647 -0.12458
5 .
California 256 78
68 42 11 28 0.71088 243.463 12.5375 12.5375 6.62647 1.89203
6 .
Colorado
267 78 85 38 9 25 1.00000 268.704 -1.7038 1.7038 6.62647
-0.25711
7 .
Connecticut 270 79 86 43
12 22 1.00000 270.189 -0.1885 0.1885 6.62647 -0.02845
8 .
Delaware
261 75 83 32 18 28 1.00000 265.734 -4.7342 4.7342 6.62647 -0.71444
9 .
Distric of Columbia 231 47 76 24 33 37 0.36616 255.341 -24.3408 24.3408
6.62647 -3.67326
10 .
Florida
255 75 73 31 19 27 1.00000 250.886 4.1136 4.1136 6.62647
0.62078
11 .
Georgia
258 73 80 36 17 22 1.00000 261.280 -3.2799 3.2799 6.62647 -0.49496
12 .
Guam
231 81 64 32 20 28 1.00000 237.523 -6.5234 6.5234 6.62647 -0.98445
13 .
Hawaii
251 78 69 36 23 26 1.00000 244.947 6.0527 6.0527 6.62647
0.91341
14 .
Idaho
272 84 84 48 7 21 1.00000 267.219 4.7810 4.7810
6.62647 0.72150
15 .
Illinois
260 78 82 43 14 21 1.00000 264.249 -4.2494 4.2494 6.62647 -0.64128
16 .
Indiana
267 81 84 37 11 23 1.00000 267.219 -0.2190 0.2190 6.62647 -0.03305
17 .
Iowa
278 83 88 43 8 20 1.00000 273.158 4.8419 4.8419
6.62647 0.73069
18 .
Kentucky
256 79 78 36 14 23 1.00000 258.310 -2.3103 2.3103 6.62647 -0.34865
19 .
Louisiana 246
73 76 36 19 27 0.95416 255.341 -9.3408 9.3408 6.62647 -1.40961
20 .
Maryland
260 75 83 34 19 27 1.00000 265.734 -5.7342 5.7342 6.62647 -0.86535
21 .
Michigan
264 77 84 31 14 25 1.00000 267.219 -3.2190 3.2190 6.62647 -0.48578
22 .
Minnesota 276
83 88 36 7 20 1.00000 273.158 2.8419 2.8419 6.62647
0.42887
23 .
Montana
280 83 88 44 6 21 1.00000 273.158 6.8419 6.8419
6.62647 1.03251
24 .
Nebraska
276 85 88 42 9 19 1.00000 273.158 2.8419 2.8419
6.62647 0.42887
25 .
New Hampshire 273 83 88 40 7
22 1.00000 273.158 -0.1581 0.1581 6.62647 -0.02386
26 .
New Jersey 269 79
84 41 13 23 1.00000 267.219 1.7810 1.7810 6.62647
0.26877
27 .
New Mexico 256 77
72 40 11 27 1.00000 249.402 6.5984 6.5984 6.62647
0.99576
28 .
New York
261 76 79 35 17 29 1.00000 259.795 1.2049 1.2049 6.62647
0.18183
29 .
North Carolina 250 74 78 37 21 25 1.00000
258.310 -8.3103 8.3103 6.62647 -1.25411
30 .
North Dakota 281 85 90 41
6 14 1.00000 276.128 4.8724 4.8724 6.62647 0.73529
31 .
Ohio
264 79 84 36 11 22 1.00000 267.219 -3.2190 3.2190 6.62647 -0.48578
32 .
Oklahoma
263 78 78 37 14 22 1.00000 258.310 4.6897 4.6897 6.62647
0.70772
33 .
Oregon
271 81 82 41 9 31 1.00000 264.249 6.7506 6.7506
6.62647 1.01873
34 .
Pennsylvania 266 80 86 34 10
24 1.00000 270.189 -4.1885 4.1885 6.62647 -0.63209
35 .
Rhode Island 260 78 80 38 12
28 1.00000 261.280 -1.2799 1.2799 6.62647 -0.19314
36 .
Texas
258 77 70 34 15 18 0.77046 246.432 11.5679 11.5679 6.62647
1.74571
37 .
Virgin Islands 218 63 76 23 27 22 0.23868
255.341 -37.3408 37.3408 6.62647 -5.63509
38 .
Virginia
264 78 82 33 16 24 1.00000 264.249 -0.2494 0.2494 6.62647 -0.03764
39 .
West Virginia 256 82 80 36 16 25 1.00000
261.280 -5.2799 5.2799 6.62647 -0.79678
40 .
Wisconsin 274
81 86 38 8 21 1.00000 270.189 3.8115 3.8115 6.62647
0.57519
41 .
Wyoming
272 85 86 43 7 23 1.00000 270.189 1.8115 1.8115
6.62647 0.27337
Third refit of the model.
Weight: weight
Analysis of Variance
Sum of Mean
Source
DF Squares
Square F Value Pr > F
Model
1 3173.47847 3173.47847
78.00 <.0001
Error
38 1546.12340
40.68746
Corrected Total
39 4719.60187
Root MSE
6.37867 R-Square 0.6724
Dependent Mean
262.38205 Adj R-Sq 0.6638
Coeff Var
2.43106
Parameter Estimates
Parameter Standard
Variable
DF Estimate
Error t Value Pr > |t|
Intercept
1 142.89543
13.56897 10.53
<.0001
homelib
1 1.48019
0.16760 8.83
<.0001
Fourth reweighting of the data.
EXST7034 - NKNW Table 11.11
m
a
a p h r t b
m
t a o e v s w
e s
h r m a w e e
d t
p e e d a n i
y
a
O
i a
r n l i t c g
h
b m
b
a t
o t i n c e h
a
s a
m
s
n e
f s b g h s t
t e
e d
u
1 4.46039
. . . . . . 1.00000 .
. . 6.61288
.
2 .
Alabama
252 75 78 34 18 18 1.00000 258.350 -6.3505 6.3505 6.61288 -0.96032
3 .
Arizona
259 75 73 41 12 26 1.00000 250.950 8.0505 8.0505 6.61288
1.21739
4 .
Arkansas
256 77 77 28 20 23 1.00000 256.870 -0.8703 0.8703 6.61288 -0.13161
5 .
California 256 78
68 42 11 28 0.71432 243.549 12.4514 12.4514 6.61288 1.88291
6 .
Colorado
267 78 85 38 9 25 1.00000 268.712 -1.7118 1.7118 6.61288
-0.25886
7 .
Connecticut 270 79 86 43
12 22 1.00000 270.192 -0.1920 0.1920 6.61288 -0.02904
8 .
Delaware
261 75 83 32 18 28 1.00000 265.751 -4.7514 4.7514 6.61288 -0.71851
9 .
Distric of Columbia 231 47 76 24 33 37 0.36467 255.390 -24.3901 24.3901
6.61288 -3.68827
10 .
Florida
255 75 73 31 19 27 1.00000 250.950 4.0505 4.0505 6.61288
0.61251
11 .
Georgia
258 73 80 36 17 22 1.00000 261.311 -3.3109 3.3109 6.61288 -0.50067
12 .
Guam
231 81 64 32 20 28 1.00000 237.628 -6.6278 6.6278 6.61288 -1.00225
13 .
Hawaii
251 78 69 36 23 26 1.00000 245.029 5.9713 5.9713 6.61288
0.90297
14 .
Idaho
272 84 84 48 7 21 1.00000 267.232 4.7684 4.7684
6.61288 0.72107
15 .
Illinois
260 78 82 43 14 21 1.00000 264.271 -4.2713 4.2713 6.61288 -0.64590
16 .
Indiana
267 81 84 37 11 23 1.00000 267.232 -0.2316 0.2316 6.61288 -0.03503
17 .
Iowa
278 83 88 43 8 20 1.00000 273.152 4.8476 4.8476
6.61288 0.73305
18 .
Kentucky
256 79 78 36 14 23 1.00000 258.350 -2.3505 2.3505 6.61288 -0.35544
19 .
Louisiana 246
73 76 36 19 27 0.94720 255.390 -9.3901 9.3901 6.61288 -1.41997
20 .
Maryland
260 75 83 34 19 27 1.00000 265.751 -5.7514 5.7514 6.61288 -0.86973
21 .
Michigan
264 77 84 31 14 25 1.00000 267.232 -3.2316 3.2316 6.61288 -0.48869
22 .
Minnesota 276
83 88 36 7 20 1.00000 273.152 2.8476 2.8476 6.61288
0.43061
23 .
Montana
280 83 88 44 6 21 1.00000 273.152 6.8476 6.8476
6.61288 1.03549
24 .
Nebraska
276 85 88 42 9 19 1.00000 273.152 2.8476 2.8476
6.61288 0.43061
25 .
New Hampshire 273 83 88 40 7
22 1.00000 273.152 -0.1524 0.1524 6.61288 -0.02305
26 .
New Jersey 269 79
84 41 13 23 1.00000 267.232 1.7684 1.7684 6.61288
0.26741
27 .
New Mexico 256 77
72 40 11 27 1.00000 249.469 6.5307 6.5307 6.61288
0.98757
28 .
New York
261 76 79 35 17 29 1.00000 259.831 1.1693 1.1693 6.61288
0.17683
29 .
North Carolina 250 74 78 37 21 25 1.00000
258.350 -8.3505 8.3505 6.61288 -1.26276
30 .
North Dakota 281 85 90 41
6 14 1.00000 276.113 4.8872 4.8872 6.61288 0.73904
31 .
Ohio
264 79 84 36 11 22 1.00000 267.232 -3.2316 3.2316 6.61288 -0.48869
32 .
Oklahoma
263 78 78 37 14 22 1.00000 258.350 4.6495 4.6495 6.61288
0.70310
33 .
Oregon
271 81 82 41 9 31 1.00000 264.271 6.7287 6.7287
6.61288 1.01752
34 .
Pennsylvania 266 80 86 34 10
24 1.00000 270.192 -4.1920 4.1920 6.61288 -0.63392
35 .
Rhode Island 260 78 80 38 12
28 1.00000 261.311 -1.3109 1.3109 6.61288 -0.19823
36 .
Texas
258 77 70 34 15 18 0.77402 246.509 11.4911 11.4911 6.61288
1.73768
37 .
Virgin Islands 218 63 76 23 27 22 0.23788
255.390 -37.3901 37.3901 6.61288 -5.65413
38 .
Virginia
264 78 82 33 16 24 1.00000 264.271 -0.2713 0.2713 6.61288 -0.04102
39 .
West Virginia 256 82 80 36 16 25 1.00000
261.311 -5.3109 5.3109 6.61288 -0.80311
40 .
Wisconsin 274
81 86 38 8 21 1.00000 270.192 3.8080 3.8080 6.61288
0.57584
41 .
Wyoming
272 85 86 43 7 23 1.00000 270.192 1.8080 1.8080
6.61288 0.27340
Fourth and final refit of the model.
EXST7034 - NKNW Table 11.11
The REG Procedure
Model: MODEL1
Dependent Variable: mathprof
Weight: weight
Analysis of Variance
Sum of Mean
Source
DF Squares
Square F Value Pr > F
Model
1 3170.39031 3170.39031
78.00 <.0001
Error
38 1544.50010
40.64474
Corrected Total
39 4714.89041
Root MSE
6.37532 R-Square 0.6724
Dependent Mean
262.38623 Adj R-Sq 0.6638
Coeff Var
2.42975
Parameter Estimates
Parameter Standard
Variable
DF Estimate
Error t Value Pr > |t|
Intercept
1 142.99058
13.55814 10.55
<.0001
homelib
1 1.47908
0.16747 8.83
<.0001
----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----
20 +
+
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1
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1
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10 +
+
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1
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1
1 |
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1 1 1
1 |
|
2 |
|
1
1 1
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0 +
1 1 1
1 +
|
1 1
1
|
|
1 1
2
|
R RESIDUAL |
1 1 1
|
e
|
1 1 1
|
s
| 1
|
i
|
1
|
d
-10 +
1
+
u
|
|
a
|
|
l
|
|
|
|
|
|
|
|
-20 +
+
|
|
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1
|
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|
|
|
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-30 +
+
|
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1
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-40 +
+
----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----
64 66 68 70
72 74 76 78
80 82 84 86
88 90
homelib