EXST7034 - Homework Example
NWK 11.12 : Mathematician salaries
Sorted Raw Data Listing
Obs
Y X1 X2
X3 IDENT
1
30.1 3.1 5
5.8 i
2
33.2 3.5 9
6.1 a
3
33.6 3.7 21 4.4
p
4
35.1 3.9 15 5.0
y
5
38.0 4.0 35 6.0
s
6
41.4 4.2 31 7.5
e
7
35.9 4.5 23 3.5
t
8
38.2 4.5 25 5.0
k
9
45.2 4.8 34 8.0
x
10
31.8 4.9 11 6.4
l
11
38.7 5.1 18 7.4
c
12
40.3 5.3 20 6.4
b
13
40.7 5.5 30 4.0
h
14
36.8 5.6 27 4.3
w
15
46.8 5.8 33 6.7
d
16
40.4 5.9 33 4.9
v
17
37.5 6.0 13 5.9
f
18
34.2 6.2 7
5.5 q
19
44.1 6.5 35 7.0
n
20
42.8 6.6 39 5.0
o
21
39.0 6.8 25 6.0
g
22
48.0 7.0 40 7.0
r
23
52.9 7.2 47 8.3
j
24
43.3 8.0 23 7.6
m
45
OPTIONS LS=99 PS=256;
46
PROC REG DATA=ONE lineprinter; TITLE2 'PROC REG diagnostics';
47
MODEL Y = X1 X2 X3 / COLLIN VIF influence;
48
output out=next1 COOKD=COOKD DFFITS=DFFITS H=HatValue P=Yhat R=E
49
RSTUDENT=RSTUDENT STUDENT=STUDENT LCL=LowerCLI UCL=UpperCLI
50
LCLM=LowerCLM UCLM=UpperCLM STDI=StdI STDP=StdP STDR=StdR;
51
RUN;
NOTE: 24 observations read.
NOTE: 24 observations used
in computations.
51
! QUIT;
NOTE: The data set WORK.NEXT1
has 24 observations and 20 variables.
NOTE: The PROCEDURE REG printed
pages 2-3.
NOTE: PROCEDURE REG used:
real time 0.60
seconds
cpu time
0.19 seconds
EXST7034 - Homework Example
NWK 11.12 : Mathematician salaries
PROC REG diagnostics
The REG Procedure
Model: MODEL1
Dependent Variable: Y Thousands
of dollars
Analysis of Variance
Sum of Mean
Source
DF Squares
Square F Value Pr > F
Model
3 627.81700
209.27233 68.12 <.0001
Error
20 61.44300
3.07215
Corrected Total
23 689.26000
Root MSE
1.75276 R-Square 0.9109
Dependent Mean
39.50000 Adj R-Sq 0.8975
Coeff Var
4.43735
Parameter Estimates
Parameter Standard
Variance
Variable
Label
DF Estimate
Error t Value Pr > |t|
Inflation
Intercept Intercept
1 17.84693
2.00188 8.92 <.0001
0
X1
Index of publication quality 1
1.10313 0.32957
3.35 0.0032
1.35619
X2
Number of years experience 1
0.32152 0.03711
8.66 <.0001
1.29852
X3
Grant support success
1 1.28894
0.29848 4.32 0.0003
1.13347
Collinearity Diagnostics
Condition -----------------Proportion of Variation----------------
Number
Eigenvalue Index
Intercept
X1
X2
X3
1 3.84270
1.00000 0.00211
0.00257 0.00780
0.00252
2 0.10602
6.02033 0.04063
0.00514 0.86188
0.04344
3 0.03089
11.15391 0.00246
0.78277 0.09403
0.43758
4 0.02039
13.72794 0.95481
0.20951 0.03629
0.51646
EXST7034 - Homework Example
NWK 11.12 : Mathematician salaries
PROC REG diagnostics
The REG Procedure
Model: MODEL1
Dependent Variable: Y Thousands
of dollars
Output Statistics
Hat Diag Cov
---------------DFBETAS--------------
Obs Residual RStudent
H Ratio DFFITS Intercept
X1 X2
X3
1 -0.2501 -0.1597 0.2408
1.6085 -0.0900 -0.0459 0.0439
0.0440 -0.0223
2 0.7359 0.4554 0.1838
1.4402 0.2161 0.0928 -0.1068
-0.0974 0.0727
3 -0.7518 -0.4562 0.1512
1.3847 -0.1925 -0.1742 0.1050 -0.0399
0.0919
4 1.6834 1.0191 0.1102
1.1152 0.3587 0.2894 -0.1571
-0.0808 -0.0829
5 -3.2463 -2.2733 0.1979
0.5847 -1.1293 -0.4066 0.8766 -0.8117
-0.0938
6 -0.7142 -0.4504 0.2139
1.4969 -0.2349 0.0096 0.1692
-0.0954 -0.1493
7 1.1827 0.7490 0.2063
1.3768 0.3818 0.3170 -0.0360
0.0661 -0.3194
8 0.9063 0.5302 0.0832
1.2627 0.1597 0.1208 -0.0673
0.0495 -0.0718
9 0.8148 0.5182 0.2247
1.4971 0.2790 -0.0732 -0.1574
0.1138 0.2026
10 -3.2382 -2.1501 0.1279
0.5892 -0.8236 -0.0646 -0.0491 0.6169
-0.2929
11 -0.0984 -0.0587 0.1319
1.4132 -0.0229 0.0059 0.0028
0.0099 -0.0170
12 1.9269 1.1418 0.0590
1.0005 0.2858 -0.0049 0.0193
-0.1283 0.1010
13 1.9845 1.2686 0.1791
1.0804 0.5926 0.3323 0.0876
0.1921 -0.5012
14 -1.4479 -0.8838 0.1358
1.2093 -0.3504 -0.1857 -0.0912 -0.0566
0.2886
15 3.3089 2.1228 0.0705
0.5638 0.5845 -0.1666 -0.0386
0.2651 0.1773
16 -0.8814 -0.5255 0.1175
1.3132 -0.1918 -0.0599 -0.0417 -0.0840
0.1289
17 1.2498 0.7636 0.1462
1.2742 0.3159 -0.0133 0.1906
-0.2496 -0.0104
18 0.1738 0.1130 0.2673
1.6711 0.0682 0.0008 0.0446
-0.0576 -0.0098
19 -1.1931 -0.7075 0.0976
1.2261 -0.2327 0.1261 -0.0626 -0.0753
-0.0707
20 -1.3116 -0.8224 0.1855
1.3106 -0.3925 -0.0331 -0.1354 -0.2003
0.2374
21 -2.1199 -1.3080 0.1147
0.9822 -0.4708 0.1299 -0.3756
0.1576 0.0872
22 0.5478 0.3307 0.1465
1.4058 0.1370 -0.0758 0.0478
0.0599 0.0213
23 1.3009 0.8745 0.2881
1.4728 0.5563 -0.3787 0.0580
0.2825 0.2629
24 -0.5629 -0.3812 0.3205
1.7526 -0.2618 0.1718 -0.2074
0.1314 -0.0745
Sum of Residuals
0
Sum of Squared Residuals
61.44300
Predicted Residual SS (PRESS)
83.81944
52
proc print data=next1; var Y X1 X2 X3 IDENT COOKD DFFITS HatValue Yhat
E
53
RSTUDENT STUDENT LowerCLI UpperCLI LowerCLM UpperCLM StdI StdP StdR;
54
TITLE2 'PROC REG diagnostics - output listing';
55
run;
NOTE: There were 24 observations
read from the data set WORK.NEXT1.
NOTE: The PROCEDURE PRINT
printed page 4.
NOTE: PROCEDURE PRINT used:
real time 0.01
seconds
cpu time
0.01 seconds
EXST7034 - Homework
Example NWK 11.12 : Mathematician salaries
PROC REG diagnostics - output
listing
Hat
Obs
Y X1 X2 X3
IDENT COOKD DFFITS
Value Yhat
E RSTUDENT
1 30.1
3.1 5 5.8 i
0.00213 -0.08996 0.24082 30.3501
-0.25009 -0.15972
2 33.2
3.5 9 6.1 a
0.01216 0.21609 0.18377 32.4641
0.73590 0.45542
3 33.6
3.7 21 4.4 p
0.00965 -0.19254 0.15118 34.3518
-0.75177 -0.45623
4 35.1
3.9 15 5.0 y
0.03210 0.35866 0.11020 33.4166
1.68336 1.01913
5 38.0
4.0 35 6.0 s
0.26385 -1.12930 0.19793 41.2463
-3.24629 -2.27334
6 41.4
4.2 31 7.5 e
0.01437 -0.23494 0.21392 42.1142
-0.71425 -0.45036
7 35.9
4.5 23 3.5 t
0.03727 0.38184 0.20626 34.7173
1.18274 0.74905
8 38.2
4.5 25 5.0 k
0.00661 0.15971 0.08319 37.2937
0.90629 0.53022
9 45.2
4.8 34 8.0 x
0.02020 0.27902 0.22472 44.3852
0.81485 0.51825
10 31.8
4.9 11 6.4 l
0.14356 -0.82356 0.12794 35.0382
-3.23821 -2.15012
11 38.7
5.1 18 7.4 c
0.00014 -0.02289 0.13187 38.7984
-0.09841 -0.05874
12 40.3
5.3 20 6.4 b
0.02011 0.28580 0.05896 38.3731
1.92686 1.14182
13 40.7
5.5 30 4.0 h
0.08520 0.59259 0.17913 38.7155
1.98450 1.26855
14 36.8
5.6 27 4.3 w
0.03103 -0.35037 0.13582 38.2479
-1.44794 -0.88377
15 46.8
5.8 33 6.7 d
0.07268 0.58453 0.07048 43.4911
3.30886 2.12277
16 40.4
5.9 33 4.9 v
0.00954 -0.19176 0.11751 41.2814
-0.88136 -0.52550
17 37.5
6.0 13 5.9 f
0.02548 0.31593 0.14617 36.2502
1.24978 0.76357
18 34.2
6.2 7 5.5 q
0.00122 0.06823 0.26728 34.0262
0.17385 0.11298
19 44.1
6.5 35 7.0 n
0.01388 -0.23266 0.09758 45.2931
-1.19305 -0.70753
20 42.8
6.6 39 5.0 o
0.03914 -0.39249 0.18551 44.1116
-1.31156 -0.82240
21 39.0
6.8 25 6.0 g
0.05350 -0.47077 0.11468 41.1199
-2.11985 -1.30804
22 48.0
7.0 40 7.0 r
0.00491 0.13697 0.14647 47.4522
0.54778 0.33066
23 52.9
7.2 47 8.3 j
0.07829 0.55632 0.28811 51.5991
1.30090 0.87447
24 43.3
8.0 23 7.6 m
0.01790 -0.26177 0.32049 43.8629
-0.56288 -0.38116
Lower Upper
Lower Upper
Obs STUDENT
CLI CLI
CLM CLM
StdI StdP
StdR
1 -0.16376
26.2774 34.4228 28.5559
32.1443 1.95243 0.86014
1.52719
2
0.46472 28.4861 36.4421
30.8968 34.0314 1.90702
0.75137 1.58354
3 -0.46554
30.4289 38.2746 32.9302
35.7734 1.88058 0.68151
1.61484
4
1.01815 29.5643 37.2690
32.2029 34.6304 1.84681
0.58186 1.65336
5 -2.06804
37.2446 45.2480 39.6197
42.8729 1.91839 0.77978
1.56974
6 -0.45961
38.0859 46.1426 40.4232
43.8053 1.93115 0.81068
1.55401
7
0.75741 30.7017 38.7328
33.0568 36.3778 1.92505
0.79603 1.56156
8
0.54001 33.4885 41.0989
36.2392 38.3482 1.82420
0.50553 1.67827
9
0.52799 40.3390 48.4313
42.6520 46.1184 1.93972
0.83089 1.54330
10 -1.97838
31.1552 38.9212 33.7304
36.3460 1.86151 0.62694
1.63680
11 -0.06026
34.9086 42.6882 37.4707
40.1261 1.86475 0.63650
1.63310
12
1.13325 34.6107 42.1356
37.4854 39.2609 1.80368
0.42559 1.70030
13
1.24966 34.7453 42.6857
37.1681 40.2629 1.90328
0.74183 1.58803
14 -0.88864
34.3514 42.1445 36.9005
39.5954 1.86800 0.64596
1.62938
15
1.95807 39.7083 47.2740
42.5205 44.4618 1.81347
0.46532 1.68986
16 -0.53527
37.4163 45.1464 40.0280
42.5347 1.85288 0.60084
1.64656
17
0.77166 32.3359 40.1645
34.8524 37.6481 1.87649
0.67012 1.61960
18
0.11587 29.9103 38.1420
32.1359 35.9164 1.97314
0.90616 1.50034
19 -0.71653
41.4626 49.1235 44.1509
46.4352 1.83628 0.54753
1.66504
20 -0.82914
40.1307 48.0925 42.5368
45.6863 1.90842 0.75493
1.58184
21 -1.28539
37.2597 44.9800 39.8817
42.3580 1.85053 0.59356
1.64919
22
0.33828 43.5374 51.3670
46.0530 48.8515 1.87673
0.67079 1.61932
23
0.87966 47.4495 55.7487
49.6366 53.5616 1.98929
0.94081 1.47886
24 -0.38958
39.6615 48.0643 41.7930
45.9327 2.01414 0.99227
1.44483
56
OPTIONS LS=99 PS=45;
57
PROC REG DATA=ONE; ID IDENT; TITLE2 'PROC REG diagnostics -
partial residual plots';
58
MODEL Y = X1 X2 X3 / PARTIAL;
59
RUN;
NOTE: 24 observations read.
NOTE: 24 observations used
in computations.
59
! QUIT;
NOTE: The PROCEDURE REG printed
pages 5-9.
NOTE: PROCEDURE REG used:
real time 0.27
seconds
cpu time
0.08 seconds
EXST7034 - Homework Example
NWK 11.12 : Mathematician salaries
PROC REG diagnostics - partial
residual plots
The REG Procedure
Model: MODEL1
Dependent Variable: Y Thousands
of dollars
Analysis of Variance
Sum of Mean
Source
DF Squares
Square F Value Pr > F
Model
3 627.81700
209.27233 68.12 <.0001
Error
20 61.44300
3.07215
Corrected Total
23 689.26000
Root MSE
1.75276 R-Square 0.9109
Dependent Mean
39.50000 Adj R-Sq 0.8975
Coeff Var
4.43735
Parameter Estimates
Parameter Standard
Variable
Label
DF Estimate
Error t Value Pr > |t|
Intercept Intercept
1 17.84693
2.00188 8.92 <.0001
X1
Index of publication quality 1
1.10313 0.32957
3.35 0.0032
X2
Number of years experience 1
0.32152 0.03711
8.66 <.0001
X3
Grant support success
1 1.28894
0.29848 4.32 0.0003
EXST7034 - Homework Example
NWK 11.12 : Mathematician salaries
PROC REG diagnostics - partial
residual plots
The REG Procedure
Model: MODEL1
Partial Regression Residual
Plot
---+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+----
7.5 +
+
|
t |
|
|
|
y
|
|
h
|
T 5.0 +
+
h
|
k
p |
o
|
|
u
|
a i
|
s
|
|
a 2.5 +
+
n
|
d b
|
d Y |
w
|
s
|
f v
|
|
q
|
o 0.0 +
+
f
|
o s
|
|
x e
|
d
|
c
|
o
|
|
l -2.5 +
+
l
|
r
l
|
a
|
g
|
r
|
n
|
s
| j
|
-5.0 +
+
|
|
|
|
| m
|
|
|
-7.5 +
+
---+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+----
-0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10
0.15 0.20 0.25 0.30 0.35
Intercept
EXST7034 - Homework Example
NWK 11.12 : Mathematician salaries
PROC REG diagnostics - partial
residual plots
The REG Procedure
Model: MODEL1
Partial Regression Residual
Plot
-+---------+---------+---------+---------+---------+---------+---------+---------+---------+--
4 +
+
|
|
|
d
|
|
|
|
f
|
T |
h
|
h 2 +
b
q m
+
o |
j
|
u |
r
|
s Y |
t
|
a |
y
|
n |
k
|
d 0 +
+
s |
c v
o
|
| x
a
n
g
|
o |
w
|
f |
|
|
i
|
d -2 +
p
+
o |
|
l |
e
|
l |
l
|
a |
|
r |
|
s -4 +
+
|
|
|
|
|
|
| s
|
|
|
-6 +
+
-+---------+---------+---------+---------+---------+---------+---------+---------+---------+--
-2.0
-1.5 -1.0 -0.5
0.0 0.5
1.0 1.5
2.0 2.5
Index of publication quality X1
---------+--------+--------+--------+--------+--------+--------+--------+--------+----------
7.5 +
+
|
|
|
|
|
|
|
j
|
T 5.0 +
d
+
h
|
|
o
|
h x
|
u
|
|
s
|
r
|
a 2.5 +
tk
+
n
|
e o
|
d Y |
v
s |
s
|
|
|
b y
p n
|
o 0.0 +
+
f
|
w
|
|
|
d
|
|
o
|
a
|
l -2.5 +
c
+
l
|
|
a
|
f
|
r
|
i g
|
s
|
|
-5.0 +
m
+
|
|
|
|
|
q
|
|
|
-7.5 +
l
+
---------+--------+--------+--------+--------+--------+--------+--------+--------+----------
-25 -20 -15
-10 -5
0 5
10 15
Number of years experience X2
EXST7034 - Homework Example
NWK 11.12 : Mathematician salaries
PROC REG diagnostics - partial
residual plots
The REG Procedure
Model: MODEL1
Partial Regression Residual
Plot
-+---------+---------+---------+---------+---------+---------+---------+---------+---------+--
Y |
|
4 +
d
+
|
|
|
x |
|
j |
T |
|
h |
b
|
o |
|
u 2 +
c +
s |
a
|
a |
e |
n |
y f
|
d |
r
|
s |
i m
|
|
|
o 0 +
k
+
f |
q
|
|
n
|
d |
h
|
o |
|
l |
|
l |
t
|
a -2 +
+
r |
p
l
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s |
v
g
|
|
s
|
|
o
|
|
|
|
w
|
-4 +
+
|
|
-+---------+---------+---------+---------+---------+---------+---------+---------+---------+--
-2.5
-2.0 -1.5 -1.0
-0.5 0.0
0.5 1.0
1.5 2.0
Grant support success X3
60
PROC REG DATA=ONE; TITLE2 'Do-it-yourself partial regression plot';
61
TITLE3 'Residuals of Y adjusted for x2 and x3';
62
MODEL Y = X2 X3; OUTPUT OUT=RESIDY R=EY;
NOTE: 24 observations read.
NOTE: 24 observations used
in computations.
NOTE: The data set WORK.RESIDY
has 24 observations and 7 variables.
NOTE: The PROCEDURE REG printed
page 10.
NOTE: PROCEDURE REG used:
real time 0.19
seconds
cpu time
0.09 seconds
63
PROC REG DATA=RESIDY;
64
TITLE3 'Residuals of X1 adjusted for x2 and x3';
65
MODEL X1 = X2 X3; OUTPUT OUT=RESIDXY RESIDUAL=EX1;
NOTE: 24 observations read.
NOTE: 24 observations used
in computations.
NOTE: The data set WORK.RESIDXY
has 24 observations and 8 variables.
NOTE: The PROCEDURE REG printed
page 11.
NOTE: PROCEDURE REG used:
real time 0.11
seconds
cpu time
0.10 seconds
66
PROC PLOT DATA=RESIDXY; PLOT EY*EX1='*' / VREF=0;
67
TITLE2 'Partial regression plot for Y on X1'; RUN;
NOTE: There were 24 observations
read from the data set WORK.RESIDXY.
NOTE: The PROCEDURE PLOT
printed page 12.
NOTE: PROCEDURE PLOT used:
real time 0.02
seconds
cpu time
0.02 seconds
68
PROC PLOT DATA=NEXT1; PLOT E*YHAT=IDENT / VREF=0;
69
TITLE2 'Residual plot for Y on X1, X2 and X3'; RUN;
NOTE: There were 24 observations
read from the data set WORK.NEXT1.
NOTE: The PROCEDURE PLOT
printed page 13.
NOTE: PROCEDURE PLOT used:
real time 0.00
seconds
cpu time
0.00 seconds
EXST7034 - Homework Example
NWK 11.12 : Mathematician salaries
Do-it-yourself partial regression
plot
Residuals of Y adjusted for
x2 and x3
The REG Procedure
Model: MODEL1
Dependent Variable: Y Thousands
of dollars
Analysis of Variance
Sum of Mean
Source
DF Squares
Square F Value Pr > F
Model
2 593.39849
296.69924 65.00 <.0001
Error
21 95.86151
4.56483
Corrected Total
23 689.26000
Root MSE
2.13655 R-Square 0.8609
Dependent Mean
39.50000 Adj R-Sq 0.8477
Coeff Var
5.40898
Parameter Estimates
Parameter Standard
Variable
Label
DF Estimate
Error t Value Pr > |t|
Intercept
Intercept
1 21.02546
2.14819 9.79
<.0001
X2
Number of years experience 1
0.37376 0.04104
9.11 <.0001
X3
Grant support success
1 1.52753
0.35331 4.32
0.0003
EXST7034 - Homework Example
NWK 11.12 : Mathematician salaries
Do-it-yourself partial regression
plot
Residuals of X1 adjusted
for x2 and x3
The REG Procedure
Model: MODEL1
Dependent Variable: X1 Index
of publication quality
Analysis of Variance
Sum of Mean
Source
DF Squares
Square F Value Pr > F
Model
2 10.07450
5.03725 3.74 0.0408
Error
21 28.28384
1.34685
Corrected Total
23 38.35833
Root MSE
1.16054 R-Square 0.2626
Dependent Mean
5.35833 Adj R-Sq 0.1924
Coeff Var
21.65857
Parameter Estimates
Parameter Standard
Variable
Label
DF Estimate
Error t Value Pr > |t|
Intercept Intercept
1 2.88137
1.16686 2.47 0.0222
X2
Number of years experience 1
0.04736 0.02229
2.12 0.0457
X3
Grant support success
1 0.21629
0.19191 1.13 0.2724
EXST7034 - Homework Example
NWK 11.12 : Mathematician salaries
Partial regression plot for
Y on X1
Plot of EY*EX1. Symbol used is '*'.
|
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4 +
|
|
*
|
|
*
|
*
2 +
*
* *
|
*
|
*
|
*
|
*
R |
*
e 0 +---------------------------------------------------------------------------------------------
s |
* *
*
i |
* *
*
*
d |
*
u |
a |
*
l -2 +
*
|
| *
|
*
|
|
-4 +
|
|
|
| *
|
-6 +
|
--+---------+---------+---------+---------+---------+---------+---------+---------+---------+-
-2.0 -1.5 -1.0
-0.5 0.0
0.5 1.0
1.5 2.0
2.5
Residual
EXST7034 - Homework Example
NWK 11.12 : Mathematician salaries
Residual plot for Y on X1,
X2 and X3
Plot of E*Yhat. Symbol is value of IDENT.
|
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4 +
|
|
d
|
|
|
2 +
b h
|
y
R |
t f
j
e |
k
s |
a
x r
i |
q
d 0 +------------------------------------c--------------------------------------------------------
u |
i
a |
p
e m
l |
v
|
w
o n
|
-2 +
g
|
|
|
|
l
s
|
-4 +
|
--+---------+---------+---------+---------+---------+---------+---------+---------+---------+-
30.0 32.5 35.0
37.5 40.0 42.5
45.0 47.5 50.0
52.5
Predicted Value of Y