/* Lesson 17-1 */
/* File Name = les1701.sas 10/18/01 */
data air;
infile 'usair2.prn';
input id $ y x1 x2 x3 x4 x5 x6;
/*
label id='Cities (都市名)'
y='SO2 of air in micrograms per cubic metre (SO2 濃度)'
x1='Average annual temperature in F (気温)'
x2='Number of manufacturing enterprises employing 20 or more workers (製造業数)'
x3='Population size (1970 census); in thousands (人口)'
x4='Average annual wind speed in miles per hour (風速)'
x5='Average annual precipitation in inches (降雨量)'
x6='Average number of days with precipitation per year (降雨日数)'
;
*/
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; : 残差解析用
plot resid1*pred1; :
plot resid1*x1; : ズラズラと列記
plot resid1*x2; :
plot resid1*x3; :
plot resid1*x4; :
plot resid1*x5; :
plot resid1*x6; :
plot resid1*y; :
run;
proc reg data=air; :
model y=x1-x6 / selection=stepwise; : 逐次増減法
output out=outreg2 predicted=pred2 residual=resid2; : 連続した変数の指定方法
run; : (簡略形)
proc print data=outreg2(obs=15);
run;
proc plot data=outreg2; : 残差解析用
plot resid2*pred2; :
plot resid2*(x1 x2 x3 x4 x5 x6); : 簡略形(上と比較せよ)
plot resid2*(x1-x6); : 簡略形(これも同じ意味)
plot resid2*y; :
run;
proc reg data=air; :
model y=x1-x6 / selection=rsquare; : 総当り法
run; :
SAS システム 1
15:22 Wednesday, October 17, 2001
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
15:22 Wednesday, October 17, 2001
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 8.0000 110.0000
X1 41 55.7634 7.2277 2286 43.5000 75.5000
X2 41 463.0976 563.4739 18987 35.0000 3344
X3 41 608.6098 579.1130 24953 71.0000 3369
X4 41 9.4439 1.4286 387.2000 6.0000 12.7000
X5 41 36.7690 11.7715 1508 7.0500 59.8000
X6 41 113.9024 26.5064 4670 36.0000 166.0000
SAS システム 3
15:22 Wednesday, October 17, 2001
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
15:22 Wednesday, October 17, 2001
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
15:22 Wednesday, October 17, 2001
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
15:22 Wednesday, October 17, 2001
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
15:22 Wednesday, October 17, 2001
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.
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 19
15:22 Wednesday, October 17, 2001
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
13 Des_Moin 17 49.0 104 201 11.2 30.85 103 21.697 -4.6973
14 Wichita 8 56.6 125 277 12.7 30.58 82 16.053 -8.0528
15 Louisvil 30 55.6 291 593 8.3 43.11 123 19.522 10.4776
SAS システム 33
15:22 Wednesday, October 17, 2001
プロット : RESID2*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 34
15:22 Wednesday, October 17, 2001
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
2 0.41938296 X2 X4
2 0.40658556 X1 X3
2 0.36568424 X3 X6
2 0.24833602 X3 X5
2 0.24581729 X1 X5
2 0.24392958 X3 X4
2 0.22911013 X1 X6
2 0.19170531 X1 X4
2 0.15866623 X5 X6
2 0.13776827 X4 X6
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
3 0.56222293 X1 X2 X5
3 0.54523587 X1 X2 X6
3 0.54521259 X1 X2 X4
3 0.50833841 X2 X4 X6
3 0.50466594 X2 X5 X6
3 0.46486113 X1 X3 X5
3 0.44457816 X1 X3 X6
3 0.43203067 X1 X3 X4
3 0.42499409 X2 X4 X5
3 0.38078212 X3 X5 X6
3 0.37015732 X3 X4 X6
3 0.25498097 X1 X4 X5
3 0.24843679 X3 X4 X5
3 0.24617714 X1 X5 X6
3 0.23321543 X1 X4 X6
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
4 0.61759495 X2 X3 X5 X6
4 0.60282531 X1 X2 X4 X5
(中略)
4 0.38714016 X3 X4 X5 X6
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
-----------------------------------------
input id $ 1-20
y x1 x2 x3 x4 x5 x6;