1 ************************************************************************;
2 *** EXST7034 Example 1 using PC-SAS - Airline vial breakage ***;
3 *** Problem from Neter, Kutner, Nachtsheim & Wasserman 1996, #1.21 ***;
4 ************************************************************************;
5 OPTIONS LS=88 PS=256 NOCENTER NODATE NONUMBER;
6 DATA ONE; INFILE CARDS MISSOVER;
7 TITLE1 `EXST7034 - Example 1 : Airline vial breakage - NKNW Example
7 ! 1.21`;
8 * LABEL X = `Breakage per 1000 vials`;
9 * LABEL Y = `Number of airline transfers`;
10 INPUT X1 Y;
11 X0 = 1;
12 CARDS;
NOTE: The data set WORK.ONE has 10 observations and 3 variables.
NOTE: DATA statement used:
real time 0.06 seconds
cpu time 0.06 seconds
23 ;
24
25 PROC IML; ***RESET PRINT;
NOTE: IML Ready
25 ! USE ONE;
26 READ ALL VAR{X0 X1} INTO X;
27 READ ALL VAR{Y} INTO Y;
28 CLOSE ONE;
29 ******************************************;
30 **** Calculation of the Full Model ****;
31 ******************************************;
32 **** Intermediate calculations ****;
33 ******************************************;
34 N = NROW(X); P = NCOL(X);
35 YPY = Y`*Y; XPX = X`*X; XPY = X`*Y;
36 PRINT ,,"Intermediate statistics",
37 N P XPX YPY XPY;
EXST7034 - Example 1 : Airline vial breakage - NKNW Example 1.21
Intermediate statistics
N P XPX YPY XPY
10 2 10 10 2194 142
10 20 182
38 ******************************************;
39 **** Solution & Analysis of Variance ****;
40 ******************************************;
41 XSumSq = VECDIAG(XPX);
42 XPXINV = INV(XPX);
43 B = XPXINV * XPY; CF = (J(1,N,1)*Y)##2/N;
44 USSTOTAL = YPY; USSREG = B`*XPY;
45 SSTOTAL = YPY - CF; SSREG = B`*XPY - CF;
46 SSERROR = YPY - B`*XPY; dfE = N-P;
47 MSE = SSERROR / (N-P); RSquare = SSReg / SSTotal;
48 PRINT ,,"Reg coefficients and ANOVA table info",
49 B XPXINV XSumSq CF USSTOTAL USSREG,,
50 SSTOTAL SSREG SSERROR MSE DFE RSquare;
Reg coefficients and ANOVA table info
B XPXINV XSUMSQ CF USSTOTAL USSREG
10.2 0.2 -0.1 10 2016.4 2194 2176.4
4 -0.1 0.1 20
SSTOTAL SSREG SSERROR MSE DFE RSQUARE
177.6 160 17.6 2.2 8 0.9009009
51 ***********************************************;
52 **** Test of B and observation diagnostics ****;
53 ***********************************************;
54 hatmatrix = X*XPXinv*X`;
55 VARCOV = MSE * XPXINV;
56 VarResid = (I(N) - HatMatrix) * MSE;
57 VarPred = HatMatrix * MSE;
58 PRINT ,,"Variance information",,
59 HatMatrix, VarCov, VarResid, VarPred;
Variance information
HATMATRIX
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
0.1 0.2 0 0.2 -0.1 0.1 0.2 0.1 0 0.2
0.1 0 0.2 0 0.3 0.1 0 0.1 0.2 0
0.1 0.2 0 0.2 -0.1 0.1 0.2 0.1 0 0.2
0.1 -0.1 0.3 -0.1 0.5 0.1 -0.1 0.1 0.3 -0.1
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
0.1 0.2 0 0.2 -0.1 0.1 0.2 0.1 0 0.2
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
0.1 0 0.2 0 0.3 0.1 0 0.1 0.2 0
0.1 0.2 0 0.2 -0.1 0.1 0.2 0.1 0 0.2
VARCOV
0.44 -0.22
-0.22 0.22
VARRESID
1.98 -0.22 -0.22 -0.22 -0.22 -0.22 -0.22 -0.22 -0.22 -0.22
-0.22 1.76 0 -0.44 0.22 -0.22 -0.44 -0.22 0 -0.44
-0.22 0 1.76 0 -0.66 -0.22 0 -0.22 -0.44 0
-0.22 -0.44 0 1.76 0.22 -0.22 -0.44 -0.22 0 -0.44
-0.22 0.22 -0.66 0.22 1.1 -0.22 0.22 -0.22 -0.66 0.22
-0.22 -0.22 -0.22 -0.22 -0.22 1.98 -0.22 -0.22 -0.22 -0.22
-0.22 -0.44 0 -0.44 0.22 -0.22 1.76 -0.22 0 -0.44
-0.22 -0.22 -0.22 -0.22 -0.22 -0.22 -0.22 1.98 -0.22 -0.22
-0.22 0 -0.44 0 -0.66 -0.22 0 -0.22 1.76 0
-0.22 -0.44 0 -0.44 0.22 -0.22 -0.44 -0.22 0 1.76
VARPRED
0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22
0.22 0.44 0 0.44 -0.22 0.22 0.44 0.22 0 0.44
0.22 0 0.44 0 0.66 0.22 0 0.22 0.44 0
0.22 0.44 0 0.44 -0.22 0.22 0.44 0.22 0 0.44
0.22 -0.22 0.66 -0.22 1.1 0.22 -0.22 0.22 0.66 -0.22
0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22
0.22 0.44 0 0.44 -0.22 0.22 0.44 0.22 0 0.44
0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22
0.22 0 0.44 0 0.66 0.22 0 0.22 0.44 0
0.22 0.44 0 0.44 -0.22 0.22 0.44 0.22 0 0.44
60 ***********************************************;
61 StdErrB = sqrt(vecdiag(VarCov));
62 t = B / StdErrB;
63 Probt = 1 - ProbF(t#t, 1, dfe);
64 PRINT ,,"Tests of regression coefficients",
65 StdErrB t Probt;
Tests of regression coefficients
STDERRB T PROBT
0.663325 15.377079 3.1783E-7
0.4690416 8.5280287 0.0000275
66 ***********************************************;
67 hatvalues = vecdiag(hatmatrix);
68 YHat = X * B;
69 Resid = Y - YHat;
70 /*Must specify t value */ TVal = 2.306005626;
71 LowerCLM = YHAT - TVAL # SQRT(hatvalues*MSE);
72 UpperCLM = YHAT + TVAL # SQRT(hatvalues*MSE);
73 LowerCLI = YHAT - TVAL # SQRT(hatvalues*MSE+MSE);
74 UpperCLI = YHAT + TVAL # SQRT(hatvalues*MSE+MSE);
75 PRINT ,,"Observation information" ,
76 Y YHAT RESID HatValues LowerCLM UpperCLM LowerCLI UpperCLI;
77 quit;
NOTE: Exiting IML.
NOTE: The PROCEDURE IML printed page 1.
NOTE: PROCEDURE IML used:
real time 0.07 seconds
cpu time 0.07 seconds
NOTE: SAS Institute Inc., SAS Campus Drive, Cary, NC USA 27513-2414
NOTE: The SAS System used:
real time 0.70 seconds
cpu time 0.50 seconds
Observation information
Y YHAT RESID HATVALUES LOWERCLM UPPERCLM LOWERCLI UPPERCLI
16 14.2 1.8 0.1 13.118387 15.281613 10.612697 17.787303
9 10.2 -1.2 0.2 8.6703689 11.729631 6.4531843 13.946816
17 18.2 -1.2 0.2 16.670369 19.729631 14.453184 21.946816
12 10.2 1.8 0.2 8.6703689 11.729631 6.4531843 13.946816
22 22.2 -0.2 0.5 19.781441 24.618559 18.010933 26.389067
13 14.2 -1.2 0.1 13.118387 15.281613 10.612697 17.787303
8 10.2 -2.2 0.2 8.6703689 11.729631 6.4531843 13.946816
15 14.2 0.8 0.1 13.118387 15.281613 10.612697 17.787303
19 18.2 0.8 0.2 16.670369 19.729631 14.453184 21.946816
11 10.2 0.8 0.2 8.6703689 11.729631 6.4531843 13.946816
1 ************************************************************************;
2 *** EXST7034 Example 1 using PC-SAS - Airline vial breakage ***;
3 *** Problem from Neter, Kutner, Nachtsheim & Wasserman 1996, #1.21 ***;
4 ************************************************************************;
5 OPTIONS LS=88 PS=256 NOCENTER NODATE NONUMBER;
6 DATA ONE; INFILE CARDS MISSOVER;
7 TITLE1 'EXST7015 Multiple Regression from Snedecor & Cochran (1967)';
8 * LABEL Y ='Plant available phosphorus';
9 * LABEL X1='Inorganic phosphorus';
10 * LABEL X2='Hydrolized organic phosphorus';
11 * LABEL X3='Nonhydrolized phosphorus';
12 INPUT X1 X2 X3 Y;
13 X0 = 1;
14 CARDS; RUN;
NOTE: The data set WORK.ONE has 18 observations and 5 variables.
NOTE: DATA statement used:
real time 0.05 seconds
cpu time 0.05 seconds
35 PROC IML; ***RESET PRINT;
NOTE: IML Ready
35 ! USE ONE;
36 READ ALL VAR{X0 X1 X2 X3} INTO X;
37 READ ALL VAR{Y} INTO Y;
38 CLOSE ONE;
39 ******************************************;
40 **** Calculation of the Full Model ****;
41 ******************************************;
42 **** Intermediate calculations ****;
43 ******************************************;
44 N = NROW(X); P = NCOL(X);
45 YPY = Y`*Y; XPX = X`*X; XPY = X`*Y;
46 PRINT ,,"Intermediate statistics",
47 N P XPX YPY XPY;
EXST7015 Multiple Regression from Snedecor & Cochran (1967)
Intermediate statistics
N P XPX YPY XPY
18 4 18 215 758 2214 131299 1463
215 4321.02 10139.5 27645 20706.2
758 10139.5 35076 96598 63825
2214 27645 96598 307894 187542
48 ******************************************;
49 **** Solution & Analysis of Variance ****;
50 ******************************************;
51 XSumSq = VECDIAG(XPX);
52 XPXINV = INV(XPX);
53 B = XPXINV * XPY; CF = (J(1,N,1)*Y)##2/N;
54 USSTOTAL = YPY; USSREG = B`*XPY;
55 SSTOTAL = YPY - CF; SSREG = B`*XPY - CF;
56 SSERROR = YPY - B`*XPY; dfE = N-P;
57 MSE = SSERROR / (N-P); RSquare = SSReg / SSTotal;
58 PRINT ,,"Reg coefficients and ANOVA table info",
59 B XPXINV XSumSq CF USSTOTAL USSREG,,
60 SSTOTAL SSREG SSERROR MSE DFE RSquare;
Reg coefficients and ANOVA table info
B XPXINV
Col1 Col2 Col3 Col4 Col5
ROW1 43.652198 0.8133157 0.0019185 -0.011398 -0.002445
ROW2 1.7847797 0.0019185 0.0007249 -0.000248 -9.691E-7
ROW3 -0.083397 -0.011398 -0.000248 0.0004375 -0.000033
ROW4 0.1611327 -0.002445 -9.691E-7 -0.000033 0.0000313
XSUMSQ CF USSTOTAL USSREG
Col6 Col7 Col8 Col9
ROW1 18 118909.39 131299 125715.5
ROW2 4321.02
ROW3 35076
ROW4 307894
SSTOTAL SSREG SSERROR MSE DFE RSQUARE
12389.611 6806.1115 5583.4997 398.8214 14 0.5493402
61 ***********************************************;
62 **** Test of B and observation diagnostics ****;
63 ***********************************************;
64 hatmatrix = X*XPXinv*X`;
65 VARCOV = MSE * XPXINV;
66 VarResid = (I(N) - HatMatrix) * MSE;
67 VarPred = HatMatrix * MSE;
68 PRINT ,,"Variance information",,
69 HatMatrix, VarCov, VarResid, VarPred;
Variance information
HATMATRIX
COL1 COL2 COL3 COL4 COL5 COL6 COL7 COL8 COL9
ROW1 0.2804123 0.0898651 -0.060047 0.1544019 -0.029023 0.3175679 0.0385927 -0.00039 0.0117839
ROW2 0.0898651 0.3037333 0.082666 0.2166979 0.0843716 -0.06289 -0.093709 0.1266609 0.2407672
ROW3 -0.060047 0.082666 0.3430106 0.0382104 0.2744963 -0.054615 0.1951249 0.1245554 0.026436
ROW4 0.1544019 0.2166979 0.0382104 0.1870174 0.0484735 0.0770947 -0.035366 0.0796078 0.1490809
ROW5 -0.029023 0.0843716 0.2744963 0.0484735 0.2226066 -0.0292 0.157257 0.1097935 0.0385842
ROW6 0.3175679 -0.06289 -0.054615 0.0770947 -0.0292 0.477301 0.170022 -0.055321 -0.141838
ROW7 0.0385927 -0.093709 0.1951249 -0.035366 0.157257 0.170022 0.2587848 0.0300573 -0.119465
ROW8 -0.00039 0.1266609 0.1245554 0.0796078 0.1097935 -0.055321 0.0300573 0.0985578 0.1192347
ROW9 0.0117839 0.2407672 0.026436 0.1490809 0.0385842 -0.141838 -0.119465 0.1192347 0.2500576
ROW10 0.1429617 -0.07592 -0.004399 0.0072644 0.0067074 0.2546866 0.1447647 -0.012308 -0.080453
ROW11 0.0251027 0.0714964 0.1051302 0.0554465 0.0935431 0.0140087 0.0670627 0.073386 0.0658236
ROW12 -0.049881 -0.028818 0.0465051 -0.033363 0.0448009 -0.03516 0.0683344 0.0535076 0.0421984
ROW13 -0.009053 -0.018226 -0.012155 -0.013942 0.0008233 0.0001648 0.0349846 0.0403041 0.0529216
ROW14 -0.076766 -0.087285 0.1361661 -0.0753 0.1111148 -0.010053 0.1648528 0.0523623 -0.029481
ROW15 0.0551725 0.005233 -0.107817 0.0205552 -0.070728 0.0501715 -0.024909 0.021222 0.0769911
ROW16 0.142468 0.1718181 0.0541392 0.1564136 0.0590982 0.0955999 0.0042628 0.0705234 0.1103796
ROW17 0.0523988 0.0423982 -0.185349 0.0393674 -0.12879 0.0014372 -0.109083 0.0242436 0.1412053
ROW18 -0.085567 -0.06886 -0.002058 -0.07166 0.0060701 -0.068979 0.0484307 0.0440025 0.0457739
HATMATRIX
COL10 COL11 COL12 COL13 COL14 COL15 COL16 COL17 COL18
ROW1 0.1429617 0.0251027 -0.049881 -0.009053 -0.076766 0.0551725 0.142468 0.0523988 -0.085567
ROW2 -0.07592 0.0714964 -0.028818 -0.018226 -0.087285 0.005233 0.1718181 0.0423982 -0.06886
ROW3 -0.004399 0.1051302 0.0465051 -0.012155 0.1361661 -0.107817 0.0541392 -0.185349 -0.002058
ROW4 0.0072644 0.0554465 -0.033363 -0.013942 -0.0753 0.0205552 0.1564136 0.0393674 -0.07166
ROW5 0.0067074 0.0935431 0.0448009 0.0008233 0.1111148 -0.070728 0.0590982 -0.12879 0.0060701
ROW6 0.2546866 0.0140087 -0.03516 0.0001648 -0.010053 0.0501715 0.0955999 0.0014372 -0.068979
ROW7 0.1447647 0.0670627 0.0683344 0.0349846 0.1648528 -0.024909 0.0042628 -0.109083 0.0484307
ROW8 -0.012308 0.073386 0.0535076 0.0403041 0.0523623 0.021222 0.0705234 0.0242436 0.0440025
ROW9 -0.080453 0.0658236 0.0421984 0.0529216 -0.029481 0.0769911 0.1103796 0.1412053 0.0457739
ROW10 0.1764697 0.033044 0.0525862 0.0638153 0.0790943 0.0771839 0.029232 0.0491451 0.056126
ROW11 0.033044 0.065554 0.0571015 0.0466681 0.0679039 0.0301959 0.0558435 0.0219846 0.0507046
ROW12 0.0525862 0.0571015 0.1358751 0.1243763 0.1439654 0.105446 -0.019752 0.115985 0.1762924
ROW13 0.0638153 0.0466681 0.1243763 0.127104 0.1115795 0.1314869 -0.006374 0.1572317 0.1682902
ROW14 0.0790943 0.0679039 0.1439654 0.1115795 0.2009727 0.0564609 -0.043702 0.0253717 0.1727436
ROW15 0.0771839 0.0301959 0.105446 0.1314869 0.0564609 0.1742998 0.0170395 0.2268269 0.1551691
ROW16 0.029232 0.0558435 -0.019752 -0.006374 -0.043702 0.0170395 0.1355044 0.0224105 -0.054905
ROW17 0.0491451 0.0219846 0.115985 0.1572317 0.0253717 0.2268269 0.0224105 0.3187639 0.1844514
ROW18 0.056126 0.0507046 0.1762924 0.1682902 0.1727436 0.1551691 -0.054905 0.1844514 0.2439751
VARCOV
324.36769 0.7651496 -4.545863 -0.97495
0.7651496 0.2891165 -0.099046 -0.000386
-4.545863 -0.099046 0.1744779 -0.013159
-0.97495 -0.000386 -0.013159 0.0124691
VARRESID
COL1 COL2 COL3 COL4 COL5 COL6 COL7 COL8 COL9
ROW1 286.98696 -35.84012 23.948119 -61.57878 11.574855 -126.6529 -15.39159 0.1556033 -4.699675
ROW2 -35.84012 277.68605 -32.96898 -86.42376 -33.64919 25.081681 37.373055 -50.51509 -96.02312
ROW3 23.948119 -32.96898 262.02145 -15.23913 -109.475 21.781438 -77.82 -49.67534 -10.54326
ROW4 -61.57878 -86.42376 -15.23913 324.23485 -19.33228 -30.74702 14.104634 -31.7493 -59.45664
ROW5 11.574855 -33.64919 -109.475 -19.33228 310.04115 11.645401 -62.71748 -43.78801 -15.38821
ROW6 -126.6529 25.081681 21.781438 -30.74702 11.645401 208.46357 -67.80842 22.063003 56.567965
ROW7 -15.39159 37.373055 -77.82 14.104634 -62.71748 -67.80842 295.6125 -11.9875 47.645317
ROW8 0.1556033 -50.51509 -49.67534 -31.7493 -43.78801 22.063003 -11.9875 359.51446 -47.55336
ROW9 -4.699675 -96.02312 -10.54326 -59.45664 -15.38821 56.567965 47.645317 -47.55336 299.09308
ROW10 -57.01619 30.278631 1.7545655 -2.897204 -2.675035 -101.5745 -57.73525 4.9088065 32.086555
ROW11 -10.01151 -28.51429 -41.92816 -22.11326 -37.30698 -5.586959 -26.74603 -29.26792 -26.25185
ROW12 19.893595 11.493322 -18.54721 13.305931 -17.86754 14.022749 -27.25323 -21.33999 -16.82964
ROW13 3.6107134 7.2687205 4.8478018 5.5605225 -0.328363 -0.065707 -13.95262 -16.07413 -21.10627
ROW14 30.615914 34.811173 -54.30597 30.031299 -44.31496 4.0094046 -65.74683 -20.88321 11.757849
ROW15 -22.00399 -2.087014 42.999563 -8.197863 28.20801 -20.00946 9.9342765 -8.463777 -30.70568
ROW16 -56.81929 -68.52473 -21.59186 -62.38111 -23.56965 -38.12728 -1.700081 -28.12622 -44.02175
ROW17 -20.89776 -16.90933 73.921145 -15.70057 51.36413 -0.573176 43.504443 -9.668863 -56.31569
ROW18 34.126017 27.462993 0.8208314 28.579685 -2.420871 27.510172 -19.31521 -17.54915 -18.25561
COL10 COL11 COL12 COL13 COL14 COL15 COL16 COL17 COL18
ROW1 -57.01619 -10.01151 19.893595 3.6107134 30.615914 -22.00399 -56.81929 -20.89776 34.126017
ROW2 30.278631 -28.51429 11.493322 7.2687205 34.811173 -2.087014 -68.52473 -16.90933 27.462993
ROW3 1.7545655 -41.92816 -18.54721 4.8478018 -54.30597 42.999563 -21.59186 73.921145 0.8208314
ROW4 -2.897204 -22.11326 13.305931 5.5605225 30.031299 -8.197863 -62.38111 -15.70057 28.579685
ROW5 -2.675035 -37.30698 -17.86754 -0.328363 -44.31496 28.20801 -23.56965 51.36413 -2.420871
ROW6 -101.5745 -5.586959 14.022749 -0.065707 4.0094046 -20.00946 -38.12728 -0.573176 27.510172
ROW7 -57.73525 -26.74603 -27.25323 -13.95262 -65.74683 9.9342765 -1.700081 43.504443 -19.31521
ROW8 4.9088065 -29.26792 -21.33999 -16.07413 -20.88321 -8.463777 -28.12622 -9.668863 -17.54915
ROW9 32.086555 -26.25185 -16.82964 -21.10627 11.757849 -30.70568 -44.02175 -56.31569 -18.25561
ROW10 328.44151 -13.17867 -20.97248 -25.45092 -31.54451 -30.78259 -11.65834 -19.60013 -22.38427
ROW11 -13.17867 372.67707 -22.77332 -18.61225 -27.08154 -12.04277 -22.27157 -8.767929 -20.22209
ROW12 -20.97248 -22.77332 344.6315 -49.60392 -57.41649 -42.05412 7.8773327 -46.2573 -70.30919
ROW13 -25.45092 -18.61225 -49.60392 348.12959 -44.50028 -52.4398 2.542002 -62.70737 -67.11773
ROW14 -31.54451 -27.08154 -57.41649 -44.50028 318.66919 -22.5178 17.429388 -10.11878 -68.89385
ROW15 -30.78259 -12.04277 -42.05412 -52.4398 -22.5178 329.30692 -6.795714 -90.46342 -61.88478
ROW16 -11.65834 -22.27157 7.8773327 2.542002 17.429388 -6.795714 344.77935 -8.937794 21.897309
ROW17 -19.60013 -8.767929 -46.2573 -62.70737 -10.11878 -90.46342 -8.937794 271.69155 -73.56318
ROW18 -22.38427 -20.22209 -70.30919 -67.11773 -68.89385 -61.88478 21.897309 -73.56318 301.51891
VARPRED
COL1 COL2 COL3 COL4 COL5 COL6 COL7 COL8 COL9
ROW1 111.83444 35.84012 -23.94812 61.578779 -11.57485 126.65288 15.391587 -0.155603 4.6996747
ROW2 35.84012 121.13535 32.968984 86.423762 33.649188 -25.08168 -37.37306 50.515093 96.023123
ROW3 -23.94812 32.968984 136.79996 15.239133 109.47499 -21.78144 77.820004 49.675342 10.543256
ROW4 61.578779 86.423762 15.239133 74.586558 19.33228 30.747018 -14.10463 31.749302 59.456643
ROW5 -11.57485 33.649188 109.47499 19.33228 88.780258 -11.6454 62.717477 43.788012 15.388205
ROW6 126.65288 -25.08168 -21.78144 30.747018 -11.6454 190.35784 67.808419 -22.063 -56.56797
ROW7 15.391587 -37.37306 77.820004 -14.10463 62.717477 67.808419 103.20891 11.987497 -47.64532
ROW8 -0.155603 50.515093 49.675342 31.749302 43.788012 -22.063 11.987497 39.306941 47.553364
ROW9 4.6996747 96.023123 10.543256 59.456643 15.388205 -56.56797 -47.64532 47.553364 99.728329
ROW10 57.016188 -30.27863 -1.754566 2.8972043 2.6750354 101.57448 57.735252 -4.908806 -32.08656
ROW11 10.011508 28.514295 41.928156 22.11326 37.30698 5.5869588 26.746026 29.26792 26.251846
ROW12 -19.89359 -11.49332 18.547213 -13.30593 17.86754 -14.02275 27.253228 21.339992 16.829643
ROW13 -3.610713 -7.26872 -4.847802 -5.560523 0.3283627 0.0657071 13.952618 16.074133 21.106272
ROW14 -30.61591 -34.81117 54.305973 -30.0313 44.314959 -4.009405 65.746829 20.883211 -11.75785
ROW15 22.00399 2.0870137 -42.99956 8.1978632 -28.20801 20.009458 -9.934277 8.4637772 30.705683
ROW16 56.819294 68.524726 21.591861 62.381108 23.569646 38.127278 1.7000805 28.126224 44.021751
ROW17 20.897759 16.909326 -73.92114 15.700565 -51.36413 0.5731759 -43.50444 9.6688633 56.315688
ROW18 -34.12602 -27.46299 -0.820831 -28.57968 2.4208707 -27.51017 19.315205 17.549146 18.255611
COL10 COL11 COL12 COL13 COL14 COL15 COL16 COL17 COL18
ROW1 57.016188 10.011508 -19.89359 -3.610713 -30.61591 22.00399 56.819294 20.897759 -34.12602
ROW2 -30.27863 28.514295 -11.49332 -7.26872 -34.81117 2.0870137 68.524726 16.909326 -27.46299
ROW3 -1.754566 41.928156 18.547213 -4.847802 54.305973 -42.99956 21.591861 -73.92114 -0.820831
ROW4 2.8972043 22.11326 -13.30593 -5.560523 -30.0313 8.1978632 62.381108 15.700565 -28.57968
ROW5 2.6750354 37.30698 17.86754 0.3283627 44.314959 -28.20801 23.569646 -51.36413 2.4208707
ROW6 101.57448 5.5869588 -14.02275 0.0657071 -4.009405 20.009458 38.127278 0.5731759 -27.51017
ROW7 57.735252 26.746026 27.253228 13.952618 65.746829 -9.934277 1.7000805 -43.50444 19.315205
ROW8 -4.908806 29.26792 21.339992 16.074133 20.883211 8.4637772 28.126224 9.6688633 17.549146
ROW9 -32.08656 26.251846 16.829643 21.106272 -11.75785 30.705683 44.021751 56.315688 18.255611
ROW10 70.379899 13.178666 20.972484 25.450916 31.544509 30.782589 11.658341 19.60013 22.384266
ROW11 13.178666 26.144335 22.773316 18.612247 27.081535 12.042766 22.271568 8.7679292 20.222093
ROW12 20.972484 22.773316 54.189903 49.60392 57.416487 42.054115 -7.877333 46.257299 70.309194
ROW13 25.450916 18.612247 49.60392 50.691809 44.500284 52.439803 -2.542002 62.707365 67.117728
ROW14 31.544509 27.081535 57.416487 44.500284 80.152218 22.517804 -17.42939 10.118777 68.893847
ROW15 30.782589 12.042766 42.054115 52.439803 22.517804 69.514481 6.7957143 90.46342 61.884775
ROW16 11.658341 22.271568 -7.877333 -2.542002 -17.42939 6.7957143 54.042052 8.9377938 -21.89731
ROW17 19.60013 8.7679292 46.257299 62.707365 10.118777 90.46342 8.9377938 127.12985 73.56318
ROW18 22.384266 20.222093 70.309194 67.117728 68.893847 61.884775 -21.89731 73.56318 97.302494
70 ***********************************************;
71 StdErrB = sqrt(vecdiag(VarCov));
72 t = B / StdErrB;
73 Probt = 1 - ProbF(t#t, 1, dfe);
74 PRINT ,,"Tests of regression coefficients",
75 StdErrB t Probt;
Tests of regression coefficients
STDERRB T PROBT
18.010211 2.4237472 0.0294949
0.5376955 3.319313 0.0050639
0.4177056 -0.199655 0.8446212
0.1116652 1.4429978 0.1710214
76 ***********************************************;
77 hatvalues = vecdiag(hatmatrix);
78 YHat = X * B;
79 Resid = Y - YHat;
80 /*Must specify t value */
80 ! TVal = 2.144788596;
81 LowerCLM = YHAT - TVAL # SQRT(hatvalues*MSE);
82 UpperCLM = YHAT + TVAL # SQRT(hatvalues*MSE);
83 LowerCLI = YHAT - TVAL # SQRT(hatvalues*MSE+MSE);
84 UpperCLI = YHAT + TVAL # SQRT(hatvalues*MSE+MSE);
85 PRINT ,,"Observation information" ,
86 Y YHAT RESID HatValues LowerCLM UpperCLM LowerCLI UpperCLI;
87 quit;
Observation information
Y YHAT RESID HATVALUES LOWERCLM UPPERCLM LOWERCLI UPPERCLI
64 65.405031 -1.405031 0.2804123 42.723505 88.086557 16.937751 113.87231
60 68.712606 -8.712606 0.3037333 45.10674 92.318472 19.805935 117.61928
71 53.56238 17.43762 0.3430106 28.476608 78.648152 3.9244762 103.20028
61 67.185398 -6.185398 0.1870174 48.662251 85.708545 20.519216 113.85158
54 59.545962 -5.545962 0.2226066 39.337061 79.754862 12.185374 106.90655
77 61.084836 15.915164 0.477301 31.493138 90.676533 9.0243504 113.14532
81 64.17176 16.82824 0.2587848 42.38247 85.96105 16.115556 112.22796
93 77.945689 15.054311 0.0985578 64.498883 91.392494 33.052013 122.83936
93 89.813083 3.186917 0.2500576 68.394351 111.23182 41.923756 137.70241
51 79.350254 -28.35025 0.1764697 61.357037 97.343471 32.89187 125.80864
76 77.906334 -1.906334 0.065554 66.939701 88.872966 33.692167 122.1205
96 99.413471 -3.413471 0.1358751 83.624868 115.20207 53.763656 145.06328
77 102.30254 -25.30254 0.127104 87.032032 117.57304 56.829315 147.77576
93 90.296655 2.7033452 0.2009727 71.094841 109.49847 43.356957 137.23635
95 107.28067 -12.28067 0.1742998 89.398416 125.16291 60.865146 153.69618
54 67.08296 -13.08296 0.1355044 51.315911 82.850009 21.440596 112.72532
168 119.19607 48.803933 0.3187639 95.013174 143.37896 70.008286 168.38385
99 112.74431 -13.74431 0.2439751 91.587685 133.90094 64.971638 160.51699