/* Lesson 11-1 */
/* File Name = les1101.sas 12/12/07 */
data gakusei;
infile 'all07be.prn'
firstobs=2;
input sex $ shintyou taijyuu kyoui
jitaku $ kodukai carryer $ tsuuwa;
if sex^='M' & sex^='F' then delete;
proc print data=gakusei(obs=10);
run;
proc reg data=gakusei; : 回帰分析
model taijyuu=shintyou kyoui; : 複数変量を指定
output out=outreg1 predicted=pred1 residual=resid1; : 結果項目の保存
run; :
proc print data=outreg1(obs=15);
run;
:
proc plot data=outreg1; : 散布図を描く
where shintyou^=. and taijyuu^=. and kyoui^=.; : 解析に使ったデータのみ
plot taijyuu*shintyou; :
plot taijyuu*kyoui; :
plot taijyuu*pred1; : 観測値と予測値
plot resid1*pred1 /vref=0; : 残差と予測値(残差解析)
plot resid1*shintyou/vref=0; : 残差と説明変量(残差解析)
plot resid1*kyoui /vref=0; : 残差と説明変量(残差解析)
plot resid1*taijyuu /vref=0; : 残差と目的変量(残差解析)
run; :
:
proc univariate data=outreg1 plot normal; : 残差を正規プロットして確かめる
var resid1; :
run; :
SAS システム 2
10:46 Wednesday, December 5, 2007
Model: MODEL1
Dependent Variable: TAIJYUU
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 2 8180.70433 4090.35216 86.580 0.0001
Error 112 5291.27515 47.24353
C Total 114 13471.97948
Root MSE 6.87339 R-square 0.6072
Dep Mean 58.69043 Adj R-sq 0.6002
C.V. 11.71127
SAS システム 3
10:46 Wednesday, December 5, 2007
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 -107.005473 12.69531157 -8.429 0.0001
SHINTYOU 1 0.808766 0.07834342 10.323 0.0001
KYOUI 1 0.352816 0.08165699 4.321 0.0001
SAS システム 4
10:46 Wednesday, December 5, 2007
S
H T K C
I A J O A T R
N I K I D R S P E
T J Y T U R U R S
O S Y Y O A K Y U E I
B E O U U K A E W D D
S X U U I U I R A 1 1
1 F 145.0 38.0 . J 10000 . . .
2 F 146.7 41.0 85 J 10000 Vodafone 6000 41.6299 -0.62987
3 F 148.0 42.0 . J 50000 . . .
4 F 148.0 43.0 80 J 50000 DoCoMo 4000 40.9172 2.08282
5 F 148.9 . . J 60000 . . .
6 F 149.0 45.0 . G 60000 . . .
7 F 150.0 46.0 86 40000 . 44.6516 1.34839
8 F 150.0 . . J 10000 softbank 80 . .
9 F 151.0 45.0 . J 20000 docomo 5000 . .
10 F 151.0 50.0 . G 60000 J-PHONE . . .
11 F 151.7 41.5 80 J 35000 . 43.9096 -2.40962
12 F 152.0 35.0 77 J 60000 DoCoMo 2000 43.0938 -8.09380
13 F 152.0 43.0 . J 20000 au 3500 . .
14 F 152.0 44.0 . 45000 DoCoMo 4000 . .
15 F 153.0 41.0 . J 125000 No . . .
SAS システム 6
10:46 Wednesday, December 5, 2007
プロット : TAIJYUU*SHINTYOU. 凡例: A = 1 OBS, B = 2 OBS, ...
100 + A
| A A
TAIJYUU | A A A A
| B BABAB BACAA B B A AA
| A A B A B BBA BAGBC ACAA AABBA
50 + A A ADB CDEAD BBACB A
| A A B A A
|
|
|
0 +
--+-----------+-----------+-----------+-----------+-----------+-
140 150 160 170 180 190
SHINTYOU
SAS システム 7
10:46 Wednesday, December 5, 2007
プロット : TAIJYUU*KYOUI. 凡例: A = 1 OBS, B = 2 OBS, ...
100 + A
| A A
TAIJYUU | A AA A
| A ACACFACCA A A
| A A CCAAFBFKAAAA A
50 + A A AA FEHICB
| AA B B
|
|
|
0 +
---+-----------+-----------+-----------+-----------+--
40 60 80 100 120
KYOUI
SAS システム 8
10:46 Wednesday, December 5, 2007
プロット : TAIJYUU*PRED1. 凡例: A = 1 OBS, B = 2 OBS, ...
100 + A
| A A
TAIJYUU | A A A A
| A BBCAABBB B ABC A
| A A BA AABBBABAAECDAC C BA
50 + AA CCCBCDCCDAD B
| AA AB A
|
|
|
0 +
---+-----------+-----------+-----------+-----------+--
40 50 60 70 80
Predicted Value of TAIJYUU
SAS システム 9
10:46 Wednesday, December 5, 2007
プロット : RESID1*PRED1. 凡例: A = 1 OBS, B = 2 OBS, ...
|
R 50 +
e |
s | A
i 25 + A A
d | A
u | A A A BA A A BAABB A A A
a 0 +---AA--BB---CBDACCC-BBACB-BAB-BDBDBCBAAA--ABA---A--------
l | A A ABB AB B A AB B CB A
| A
-25 +
---+------------+------------+------------+------------+--
40 50 60 70 80
Predicted Value of TAIJYUU
SAS システム 10
10:46 Wednesday, December 5, 2007
プロット : RESID1*SHINTYOU. 凡例: A = 1 OBS, B = 2 OBS, ...
|
R 50 +
e |
s | A
i 25 + A A
d | A
u | A A B A A CABAB AB A
a 0 +----------A-A-A-A-AAADB-CDEAB-BACBB-BAGAC-CBCAA-B-A-A--A---------
l | A A C AA CB A A A BACAA A
| A
-25 +
---+-----------+-----------+-----------+-----------+-----------+--
140 150 160 170 180 190
SHINTYOU
SAS システム 11
10:46 Wednesday, December 5, 2007
プロット : RESID1*KYOUI. 凡例: A = 1 OBS, B = 2 OBS, ...
|
R 50 +
e |
s | A
i 25 + A A
d | A
u | A BB C ABEA B
a 0 +----------------------B--C--GCENBGBIBBE--B--A---A--------
l | AAACBAG BACA A
| A
-25 +
---+------------+------------+------------+------------+--
40 60 80 100 120
KYOUI
SAS システム 12
10:46 Wednesday, December 5, 2007
プロット : RESID1*TAIJYUU. 凡例: A = 1 OBS, B = 2 OBS, ...
|
R 50 +
e |
s | A
i 25 + A A
d | A
u | AAAAAB C ABBAA AA
a 0 +----------------BABDDEGDAE-CFEECAC-E----A----------------
l | A A BE AB AAAD CAA
| A
-25 +
---+------------+------------+------------+------------+--
20 40 60 80 100
TAIJYUU
SAS システム 13
10:46 Wednesday, December 5, 2007
Univariate Procedure
Variable=RESID1 Residual
Moments
N 115 Sum Wgts 115
Mean 0 Sum 0
Std Dev 6.812833 Variance 46.41469
Skewness 2.039563 Kurtosis 7.30075
USS 5291.275 CSS 5291.275
CV . Std Mean 0.6353
T:Mean=0 0 Pr>|T| 1.0000
Num ^= 0 115 Num > 0 43
M(Sign) -14.5 Pr>=|M| 0.0087
Sgn Rank -535 Pr>=|S| 0.1361
W:Normal 0.864992 Pr<W 0.0001
SAS システム 17
10:46 Wednesday, December 5, 2007
Univariate Procedure
Variable=RESID1 Residual
Histogram # Boxplot
35+* 1 *
.* 2 *
.** 4 0
.****************** 36 +--+--+
.*********************************** 70 *-----*
-15+* 2 0
----+----+----+----+----+----+----+
* may represent up to 2 counts
SAS システム 18
10:46 Wednesday, December 5, 2007
Univariate Procedure
Variable=RESID1 Residual
Normal Probability Plot
35+ *
| * *
| +**+*++++++
| +++*************
| ** *********************
-15+*++*+++++++
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
/* Lesson 11-2 */
/* File Name = les1102.sas 12/12/07 */
data gakusei;
infile 'all07be.prn'
firstobs=2;
input sex $ shintyou taijyuu kyoui
jitaku $ kodukai carryer $ tsuuwa;
if sex^='M' & sex^='F' then delete; : 性別不明は除外
if shintyou=. | taijyuu=. | kyoui=. then delete; : 欠損のあるデータは除外
proc print data=gakusei(obs=10);
run;
proc corr data=gakusei; : 相関係数
where sex='M'; : 男性について
run; :
:
proc reg data=gakusei; : 回帰分析
model taijyuu=shintyou kyoui; :
where sex='M'; : 男性について
output out=outreg1 predicted=pred1 residual=resid1; :
run; :
proc print data=outreg1(obs=15);
run;
proc plot data=outreg1;
where sex='M'; : 対象データについて
plot taijyuu*shintyou;
plot taijyuu*kyoui;
plot taijyuu*pred1;
plot resid1*(pred1 shintyou kyoui taijyuu)/vref=0; : まとめて記述
/*
plot resid1*pred1 /vref=0;
plot resid1*shintyou/vref=0;
plot resid1*kyoui /vref=0;
plot resid1*taijyuu /vref=0;
*/
run;
proc univariate data=outreg1 plot normal;
var resid1;
run;
SAS システム 2
10:46 Wednesday, December 5, 2007
Correlation Analysis
5 'VAR' Variables: SHINTYOU TAIJYUU KYOUI KODUKAI TSUUWA
Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
SHINTYOU 71 172.5 5.9351 12250.1 156.0 185.0
TAIJYUU 71 64.7282 9.0651 4595.7 46.0000 100.0
KYOUI 71 88.0986 9.6853 6255.0 46.0000 112.0
KODUKAI 67 56358.2 66471.6 3776000 0 350000
TSUUWA 14 6632.1 4247.9 92850.0 350.0 15000.0
SAS システム 3
10:46 Wednesday, December 5, 2007
Correlation Analysis
Pearson Correlation Coefficients / Prob > |R| under Ho: Rho=0
/ Number of Observations
SHINTYOU TAIJYUU KYOUI KODUKAI TSUUWA
SHINTYOU 1.00000 0.39968 0.15872 0.09516 0.11552
0.0 0.0006 0.1862 0.4437 0.6941
71 71 71 67 14
TAIJYUU 0.39968 1.00000 0.40227 0.11042 0.14591
0.0006 0.0 0.0005 0.3737 0.6187
71 71 71 67 14
KYOUI 0.15872 0.40227 1.00000 -0.37945 -0.38661
0.1862 0.0005 0.0 0.0015 0.1721
71 71 71 67 14
KODUKAI 0.09516 0.11042 -0.37945 1.00000 0.53783
0.4437 0.3737 0.0015 0.0 0.0473
67 67 67 67 14
TSUUWA 0.11552 0.14591 -0.38661 0.53783 1.00000
0.6941 0.6187 0.1721 0.0473 0.0
14 14 14 14 14
SAS システム 6
10:46 Wednesday, December 5, 2007
Model: MODEL1
Dependent Variable: TAIJYUU
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 2 1596.38065 798.19033 13.060 0.0001
Error 68 4155.98301 61.11740
C Total 70 5752.36366
Root MSE 7.81776 R-square 0.2775
Dep Mean 64.72817 Adj R-sq 0.2563
C.V. 12.07784
SAS システム 7
10:46 Wednesday, December 5, 2007
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 -54.721337 27.50850038 -1.989 0.0507
SHINTYOU 1 0.526195 0.15945819 3.300 0.0015
KYOUI 1 0.325335 0.09771516 3.329 0.0014
SAS システム 10
10:46 Wednesday, December 5, 2007
プロット : TAIJYUU*SHINTYOU. 凡例: A = 1 OBS, B = 2 OBS, ...
TAIJYUU |
100 + A
| A A
| A
75 + A A A A A AA
| B B A D A A A B C A A A D A A A
| A A A A B A B A D B C A AAA A A A AA A
50 + A B A
|
|
25 +
--+---------+---------+---------+---------+---------+---------+-
155 160 165 170 175 180 185
SHINTYOU
SAS システム 11
10:46 Wednesday, December 5, 2007
プロット : TAIJYUU*KYOUI. 凡例: A = 1 OBS, B = 2 OBS, ...
TAIJYUU |
100 + A
| A A
| A
75 + AA BA A A
| A ACABIBCBB A
| A A BCAADBEF AA A
50 + A A AA
|
|
25 +
---+-----------+-----------+-----------+-----------+--
40 60 80 100 120
KYOUI
SAS システム 12
10:46 Wednesday, December 5, 2007
プロット : TAIJYUU*PRED1. 凡例: A = 1 OBS, B = 2 OBS, ...
TAIJYUU |
100 + A
| A A
| A
75 + AA AAAA A
| A AABCAB BCAA B BBB A
| B A A A A BAAACBEAAABB A
50 + A A AA
|
|
25 +
--+---------+---------+---------+---------+---------+---------+-
50 55 60 65 70 75 80
Predicted Value of TAIJYUU
SAS システム 13
10:46 Wednesday, December 5, 2007
プロット : RESID1*PRED1. 凡例: A = 1 OBS, B = 2 OBS, ...
|
R 50 +
e |
s | A
i 25 + A A
d | A
u | A BBAA A A
a 0 +------A--------A-A-A-A---BAABBCDB-BCAA-BA-CB-------A-------------
l | A AA A A A AAB AABB C A
|
-25 +
---+---------+---------+---------+---------+---------+---------+--
50 55 60 65 70 75 80
Predicted Value of TAIJYUU
SAS システム 14
10:46 Wednesday, December 5, 2007
プロット : RESID1*SHINTYOU. 凡例: A = 1 OBS, B = 2 OBS, ...
|
R 50 +
e |
s | A
i 25 + A A
d | A
u | A A A A B B A
a 0 +----------------A-A-----A-C-D-A-G-A-B-B-BAC-A-A-BA--B---A---A----
l | A B A A A A A A A A A A A BAA A A
|
-25 +
---+---------+---------+---------+---------+---------+---------+--
155 160 165 170 175 180 185
SHINTYOU
SAS システム 15
10:46 Wednesday, December 5, 2007
プロット : RESID1*KYOUI. 凡例: A = 1 OBS, B = 2 OBS, ...
|
R 50 +
e |
s | A
i 25 + A A
d | A
u | A BD B
a 0 +------------A---------A--A-AB-AE-CAHCBE--B--A---A--------
l | A ABB C DADA A
|
-25 +
---+------------+------------+------------+------------+--
40 60 80 100 120
KYOUI
SAS システム 16
10:46 Wednesday, December 5, 2007
プロット : RESID1*TAIJYUU. 凡例: A = 1 OBS, B = 2 OBS, ...
|
R 50 +
e |
s | A
i 25 + A A
d | A
u | A AAB A A AA
a 0 +----------------AAA---FAED-GBAB-DB------A------------------------
l | A A A CAABAE A B A
|
-25 +
---+---------+---------+---------+---------+---------+---------+--
40 50 60 70 80 90 100
TAIJYUU
SAS システム 17
10:46 Wednesday, December 5, 2007
Univariate Procedure
Variable=RESID1 Residual
Moments
N 71 Sum Wgts 71
Mean 0 Sum 0
Std Dev 7.70527 Variance 59.37119
Skewness 2.013612 Kurtosis 5.673909
USS 4155.983 CSS 4155.983
CV . Std Mean 0.914447
T:Mean=0 0 Pr>|T| 1.0000
Num ^= 0 71 Num > 0 27
M(Sign) -8.5 Pr>=|M| 0.0568
Sgn Rank -260 Pr>=|S| 0.1374
W:Normal 0.837353 Pr<W 0.0001
SAS システム 20
10:46 Wednesday, December 5, 2007
Univariate Procedure
Variable=RESID1 Residual
Stem Leaf # Boxplot
3 3 1 *
2 5 1 *
2 4 1 0
1 6 1 0
1 0 1 |
0 5566799 7 |
0 111222222334444 15 +--+--+
-0 4444444333333322221111110 25 *-----*
-0 99877766655555555 17 +-----+
-1 21 2 |
----+----+----+----+----+
Multiply Stem.Leaf by 10**+1
SAS システム 21
10:46 Wednesday, December 5, 2007
Univariate Procedure
Variable=RESID1 Residual
Normal Probability Plot
32.5+ *
|
| * *
17.5+ * ++++++
| +++++++
| ++++*****
2.5+ +++********
| ***********
| * *********+
-12.5+ * *+++++++
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
where sex='M' and taijyuu<85;
/* Lesson 11-4 */
/* File Name = les1104.sas 12/12/07 */
data air;
infile 'usair2.prn';
input id $ y x1 x2 x3 x4 x5 x6;
/*
label y='SO2 of air in micrograms per cubic metre'
x1='Average annual temperature in F'
x2='Number of manufacturing enterprises employing 20 or more workers'
x3='Population size (1970 census); in thousands'
x4='Average annual wind speed in miles per hour'
x5='Average annual precipitation in inches'
x6='Average number of days with precipitation per year'
;
*/
proc print data=air(obs=10);
run;
proc corr data=air;
run;
proc reg data=air; :
model y=x1 x2 x3 x4 x5 x6; : フルモデル
output out=outreg1 predicted=pred1 residual=resid1; :
run; :
proc plot data=outreg1;
plot resid1*pred1 /vref=0; :
plot resid1*x1 /vref=0; : ズラズラと列記
plot resid1*x2 /vref=0; :
plot resid1*x3 /vref=0; :
plot resid1*x4 /vref=0; :
plot resid1*x5 /vref=0; :
plot resid1*x6 /vref=0; :
plot resid1*y /vref=0; :
run;
proc reg data=air; :
model y=x1-x6 / selection=stepwise; : 逐次増減法
output out=outreg1 predicted=pred1 residual=resid1; : 連続変数の指定方法
run; :
proc print data=outreg1(obs=15);
run;
proc plot data=outreg1;
plot resid1*pred1 /vref=0; :
plot resid1*(x1 x2 x3 x4 x5 x6) /vref=0; : 簡略形(上と比較せよ)
plot resid1*(x1-x6) /vref=0; : 簡略形(これも同じ意味)
plot resid1*y /vref=0; :
run;
proc reg data=air; :
model y=x1-x6 / selection=rsquare; : 総当り法
run; :
SAS システム 1
10:49 Wednesday, December 5, 2007
OBS ID Y X1 X2 X3 X4 X5 X6
1 Phoenix 10 70.3 213 582 6.0 7.05 36
2 Little_R 13 61.0 91 132 8.2 48.52 100
3 San_Fran 12 56.7 453 716 8.7 20.66 67
4 Denver 17 51.9 454 515 9.0 12.95 86
5 Hartford 56 49.1 412 158 9.0 43.37 127
6 Wilmingt 36 54.0 80 80 9.0 40.25 114
7 Washingt 29 57.3 434 757 9.3 38.89 111
8 Jacksonv 14 68.4 136 529 8.8 54.47 116
9 Miami 10 75.5 207 335 9.0 59.80 128
10 Atlanta 24 61.5 368 497 9.1 48.34 115
SAS システム 2
10:49 Wednesday, December 5, 2007
Correlation Analysis
7 'VAR' Variables: Y X1 X2 X3 X4
X5 X6
Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
Y 41 30.0488 23.4723 1232.0 8.0000 110.0
X1 41 55.7634 7.2277 2286.3 43.5000 75.5000
X2 41 463.1 563.5 18987.0 35.0000 3344.0
X3 41 608.6 579.1 24953.0 71.0000 3369.0
X4 41 9.4439 1.4286 387.2 6.0000 12.7000
X5 41 36.7690 11.7715 1507.5 7.0500 59.8000
X6 41 113.9 26.5064 4670.0 36.0000 166.0
SAS システム 3
10:49 Wednesday, December 5, 2007
Correlation Analysis
Pearson Correlation Coefficients / Prob > |R| under Ho: Rho=0 / N = 41
Y X1 X2 X3 X4 X5 X6
Y 1.00000 -0.43360 0.64477 0.49378 0.09469 0.05429 0.36956
0.0 0.0046 0.0001 0.0010 0.5559 0.7360 0.0174
X1 -0.43360 1.00000 -0.19004 -0.06268 -0.34974 0.38625 -0.43024
0.0046 0.0 0.2340 0.6970 0.0250 0.0126 0.0050
X2 0.64477 -0.19004 1.00000 0.95527 0.23795 -0.03242 0.13183
0.0001 0.2340 0.0 0.0001 0.1341 0.8405 0.4113
X3 0.49378 -0.06268 0.95527 1.00000 0.21264 -0.02612 0.04208
0.0010 0.6970 0.0001 0.0 0.1819 0.8712 0.7939
X4 0.09469 -0.34974 0.23795 0.21264 1.00000 -0.01299 0.16411
0.5559 0.0250 0.1341 0.1819 0.0 0.9357 0.3052
X5 0.05429 0.38625 -0.03242 -0.02612 -0.01299 1.00000 0.49610
0.7360 0.0126 0.8405 0.8712 0.9357 0.0 0.0010
X6 0.36956 -0.43024 0.13183 0.04208 0.16411 0.49610 1.00000
0.0174 0.0050 0.4113 0.7939 0.3052 0.0010 0.0
SAS システム 5
10:49 Wednesday, December 5, 2007
Model: MODEL1
Dependent Variable: Y
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 6 14754.63603 2459.10601 11.480 0.0001
Error 34 7283.26641 214.21372
C Total 40 22037.90244
Root MSE 14.63604 R-square 0.6695
Dep Mean 30.04878 Adj R-sq 0.6112
C.V. 48.70761
SAS システム 6
10:49 Wednesday, December 5, 2007
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 111.728481 47.31810073 2.361 0.0241
X1 1 -1.267941 0.62117952 -2.041 0.0491
X2 1 0.064918 0.01574825 4.122 0.0002
X3 1 -0.039277 0.01513274 -2.595 0.0138
X4 1 -3.181366 1.81501910 -1.753 0.0887
X5 1 0.512359 0.36275507 1.412 0.1669
X6 1 -0.052050 0.16201386 -0.321 0.7500
SAS システム 14
13:09 Thursday, July 5, 2007
プロット : RESID1*Y. 凡例: A = 1 OBS, B = 2 OBS, ...
|
R 50 + A
e |
s | A
i 25 +
d | A A AA
u | AA AA A A A A
a 0 +------AB------AAABA-A---------A--------------------------A-------
l | CAA C A
| ABA A
-25 + A
---+---------+---------+---------+---------+---------+---------+--
0 20 40 60 80 100 120
Y
SAS システム 15
10:49 Wednesday, December 5, 2007
Stepwise Procedure for Dependent Variable Y
Step 1 Variable X2 Entered R-square = 0.41572671 C(p) = 23.10893175
DF Sum of Squares Mean Square F Prob>F
Regression 1 9161.74469120 9161.74469120 27.75 0.0001
Error 39 12876.15774782 330.15789097
Total 40 22037.90243902
Parameter Standard Type II
Variable Estimate Error Sum of Squares F Prob>F
INTERCEP 17.61057438 3.69158676 7513.50474182 22.76 0.0001
X2 0.02685872 0.00509867 9161.74469120 27.75 0.0001
Bounds on condition number: 1, 1
------------------------------------------------------------------------
Step 2 Variable X3 Entered R-square = 0.58632019 C(p) = 7.55859687
DF Sum of Squares Mean Square F Prob>F
Regression 2 12921.26717485 6460.63358743 26.93 0.0001
Error 38 9116.63526417 239.91145432
Total 40 22037.90243902
Parameter Standard Type II
Variable Estimate Error Sum of Squares F Prob>F
INTERCEP 26.32508332 3.84043919 11272.71964000 46.99 0.0001
X2 0.08243410 0.01469656 7548.02378137 31.46 0.0001
X3 -0.05660660 0.01429968 3759.52248365 15.67 0.0003
Bounds on condition number: 11.43374, 45.73494
------------------------------------------------------------------------
Step 3 Variable X6 Entered R-square = 0.61740155 C(p) = 6.36100514
DF Sum of Squares Mean Square F Prob>F
Regression 3 13606.23518823 4535.41172941 19.90 0.0001
Error 37 8431.66725079 227.88289867
Total 40 22037.90243902
Parameter Standard Type II
Variable Estimate Error Sum of Squares F Prob>F
INTERCEP 6.96584888 11.77690656 79.72552238 0.35 0.5578
X2 0.07433399 0.01506613 5547.32153619 24.34 0.0001
X3 -0.04939437 0.01454421 2628.36952166 11.53 0.0016
X6 0.16435940 0.09480151 684.96801338 3.01 0.0913
Bounds on condition number: 12.65025, 78.63322
------------------------------------------------------------------------
All variables left in the model are significant at the 0.1500 level.
No other variable met the 0.1500 significance level for entry into the
model.
SAS システム 20
10:49 Wednesday, December 5, 2007
Summary of Stepwise Procedure for Dependent Variable Y
Variable Number Partial Model
Step Entered Removed In R**2 R**2 C(p) F Prob>F
1 X2 1 0.4157 0.4157 23.1089 27.7496 0.0001
2 X3 2 0.1706 0.5863 7.5586 15.6705 0.0003
3 X6 3 0.0311 0.6174 6.3610 3.0058 0.0913
SAS システム 21
10:49 Wednesday, December 5, 2007
OBS ID Y X1 X2 X3 X4 X5 X6 PRED1 RESID1
1 Phoenix 10 70.3 213 582 6.0 7.05 36 -0.032 10.0316
2 Little_R 13 61.0 91 132 8.2 48.52 100 23.646 -10.6461
3 San_Fran 12 56.7 453 716 8.7 20.66 67 16.285 -4.2849
4 Denver 17 51.9 454 515 9.0 12.95 86 29.410 -12.4103
5 Hartford 56 49.1 412 158 9.0 43.37 127 50.661 5.3392
6 Wilmingt 36 54.0 80 80 9.0 40.25 114 27.698 8.3020
7 Washingt 29 57.3 434 757 9.3 38.89 111 20.079 8.9208
8 Jacksonv 14 68.4 136 529 8.8 54.47 116 10.011 3.9887
9 Miami 10 75.5 207 335 9.0 59.80 128 26.844 -16.8439
10 Atlanta 24 61.5 368 497 9.1 48.34 115 28.673 -4.6731
11 Chicago 110 50.6 3344 3369 10.4 34.44 122 109.181 0.8191
12 Indianap 28 52.3 361 746 9.7 38.74 121 16.840 11.1603
SAS システム 35
13:09 Thursday, July 5, 2007
プロット : RESID1*Y. 凡例: A = 1 OBS, B = 2 OBS, ...
50 + A
R |
e | A
s | AA
i | A ABA A A A
d 0 +--------BA-A--ABA-A-A---------A--------------------------A-------
u | AC C B A A
a | B A A A
l | A
|
-50 +
---+---------+---------+---------+---------+---------+---------+--
0 20 40 60 80 100 120
Y
SAS システム 36
10:49 Wednesday, December 5, 2007
N = 41 Regression Models for Dependent Variable: Y
Number in R-square Variables in Model
Model
1 0.41572671 X2
1 0.24381828 X3
1 0.18800913 X1
1 0.13657727 X6
1 0.00896628 X4
1 0.00294788 X5
--------------------------
2 0.58632019 X2 X3
2 0.51611499 X1 X2
2 0.49813569 X2 X6
2 0.42138706 X2 X5
≪略≫
2 0.01204980 X4 X5
-----------------------------
3 0.61740155 X2 X3 X6
3 0.61254683 X1 X2 X3
3 0.59304760 X2 X3 X5
3 0.59298732 X2 X3 X4
≪略≫
3 0.15899893 X4 X5 X6
--------------------------------
4 0.63964257 X1 X2 X3 X5
4 0.63287070 X1 X2 X3 X4
4 0.62909408 X1 X2 X3 X6
4 0.62847667 X2 X3 X4 X6
≪略≫
4 0.25499437 X1 X4 X5 X6
-----------------------------------
5 0.66850854 X1 X2 X3 X4 X5
5 0.65012088 X1 X2 X3 X4 X6
5 0.63964824 X1 X2 X3 X5 X6
5 0.62901313 X2 X3 X4 X5 X6
5 0.60403117 X1 X2 X4 X5 X6
5 0.50433666 X1 X3 X4 X5 X6
--------------------------------------
6 0.66951181 X1 X2 X3 X4 X5 X6
-----------------------------------------