|
The summary table below shows the NIST Coefficients and Standard
Errors, the coefficients and standard errors from Betahat using the
Singular Value Decomposition and also these values using the Cholesky
option. The Cholesky option allows for very large regressions
and is faster, but provides coefficients that are less
accurate. The accuracy is usually not a problem unless the
data has very strong collinearity.
The last 4 columns in the table show a measure of the number of
the correct significant of both the coefficients and standard errors
for both of the regression methods (SVD and Cholesky). This
number is from the Log(base 10) of the relative error as described
in McCullough, B. D. (1998), "Assessing the Reliability of Statistical Software:
Part I," The American Statistician, 52, 358-366.
As an example, a number of 15 would mean that a particular value
matched the certified value for all 15 digits.
| NIST
Coefficients |
NIST SE |
Betahat Coefficients SVD |
Betahat SE SVD |
Betahat Coefficients Cholesky |
Betahat SE Cholesky |
SVD |
|
Cholesky |
|
| Noris |
|
|
|
|
|
Coefficients |
SE |
Coefficients |
SE |
| -2.623230737740290E-01 |
2.328182343011520E-01 |
-2.623230737740410E-01 |
2.328182343011550E-01 |
-2.623230737741050E-01 |
2.328182343011550E-01 |
13.3400 |
13.8902 |
12.5381 |
13.8902 |
| 1.002116818020450E+00 |
4.297968481999370E-04 |
1.002116818020450E+00 |
4.297968481999410E-04 |
1.002116818020450E+00 |
4.297968481999410E-04 |
15.0000 |
14.0359 |
15.0000 |
14.0359 |
| |
|
|
|
|
|
|
|
|
|
| Pontius |
|
|
|
|
|
|
|
|
|
| 6.735657894736840E-04 |
1.079386120330770E-04 |
6.735657894732730E-04 |
1.079386119709060E-04 |
6.735657894718740E-04 |
1.079386120330730E-04 |
12.2145 |
9.2396 |
11.5707 |
13.4299 |
| 7.320591604010030E-07 |
1.578173999816590E-10 |
7.320591604010030E-07 |
1.578173999650930E-10 |
7.320591604010090E-07 |
1.578173999816530E-10 |
15.0000 |
9.9789 |
14.0839 |
13.4202 |
| -3.160818713450290E-15 |
4.866528499920360E-17 |
-3.160818713450480E-15 |
4.866528498914150E-17 |
-3.160818713450560E-15 |
4.866528499920190E-17 |
13.2208 |
9.6845 |
13.0688 |
13.4581 |
| |
|
|
|
|
|
|
|
|
|
| Noint1 |
|
|
|
|
|
|
|
|
|
| 2.074380165289260E+00 |
1.652892561983470E-02 |
2.074380165289260E+00 |
1.652892561983470E-02 |
2.074380165289260E+00 |
1.652892561983470E-02 |
15.0000 |
15.0000 |
15.0000 |
15.0000 |
| |
|
|
|
|
|
|
|
|
|
| Noint2 |
|
|
|
|
|
|
|
|
|
| 7.272727272727270E-01 |
4.208273180784320E-02 |
7.272727272727270E-01 |
4.208273180784320E-02 |
7.272727272727270E-01 |
4.208273180784320E-02 |
15.0000 |
15.0000 |
15.0000 |
15.0000 |
| |
|
|
|
|
|
|
|
|
|
| Filip |
|
|
|
|
|
|
|
|
|
| -1.467489614229800E+03 |
2.980845309955370E+02 |
-1.467485667700760E+03 |
2.981682574202440E+02 |
NA |
NA |
5.5704 |
3.5515 |
NA |
NA |
| -2.772179591933420E+03 |
5.597798654749500E+02 |
-2.772175904782780E+03 |
5.599370404926860E+02 |
NA |
NA |
5.8761 |
3.5516 |
NA |
NA |
| -2.316371081608930E+03 |
4.664775721277960E+02 |
-2.316369471581460E+03 |
4.666084982400530E+02 |
NA |
NA |
6.1580 |
3.5518 |
NA |
NA |
| -1.127973940983720E+03 |
2.272042744777510E+02 |
-1.127973535579780E+03 |
2.272680286743220E+02 |
NA |
NA |
6.4444 |
3.5519 |
NA |
NA |
| -3.544782337033490E+02 |
7.164786608759270E+01 |
-3.544781698928130E+02 |
7.166796995750290E+01 |
NA |
NA |
6.7447 |
3.5519 |
NA |
NA |
| -7.512420173937570E+01 |
1.528971787474000E+01 |
-7.512419480361510E+01 |
1.529400834519610E+01 |
NA |
NA |
7.0347 |
3.5519 |
NA |
NA |
| -1.087531803553430E+01 |
2.236911598160330E+00 |
-1.087531743292170E+01 |
2.237539349215620E+00 |
NA |
NA |
7.2564 |
3.5519 |
NA |
NA |
| -1.062214985889470E+00 |
2.216243219342270E-01 |
-1.062214940516420E+00 |
2.216865195910320E-01 |
NA |
NA |
7.3694 |
3.5518 |
NA |
NA |
| -6.701911545934080E-02 |
1.423637631547240E-02 |
-6.701911280022730E-02 |
1.424037170361760E-02 |
NA |
NA |
7.4015 |
3.5518 |
NA |
NA |
| -2.467810782754790E-03 |
5.356174088898210E-04 |
-2.467810683414040E-03 |
5.357677268494260E-04 |
NA |
NA |
7.3952 |
3.5518 |
NA |
NA |
| -4.029625250804040E-05 |
8.966328373738680E-06 |
-4.029625079362060E-05 |
8.968844723992690E-06 |
NA |
NA |
7.3711 |
3.5518 |
NA |
NA |
| |
|
|
|
|
|
|
|
|
|
| Longley |
|
|
|
|
|
|
|
|
|
| -3.482258634595820E+06 |
8.904203836073730E+05 |
-3.482258634595820E+06 |
8.904203836077140E+05 |
-3.482258600573540E+06 |
8.904203794559520E+05 |
15.0000 |
12.4169 |
8.0101 |
8.3314 |
| 1.506187227137330E+01 |
8.491492577476690E+01 |
1.506187227137330E+01 |
8.491492577481880E+01 |
1.506187166117890E+01 |
8.491492576450800E+01 |
15.0000 |
12.2138 |
7.3924 |
9.9179 |
| -3.581917929259100E-02 |
3.349100777224320E-02 |
-3.581917929259130E-02 |
3.349100777226380E-02 |
-3.581917820551440E-02 |
3.349100767085970E-02 |
14.0794 |
12.2112 |
7.5179 |
8.5190 |
| -2.020229803816830E+00 |
4.883996816516990E-01 |
-2.020229803816830E+00 |
4.883996816518920E-01 |
-2.020229788699000E+00 |
4.883996800917570E-01 |
15.0000 |
12.4032 |
8.1259 |
8.4957 |
| -1.033226867173590E+00 |
2.142741631616750E-01 |
-1.033226867173590E+00 |
2.142741631617660E-01 |
-1.033226862691210E+00 |
2.142741628698430E-01 |
15.0000 |
12.3719 |
8.3627 |
8.8658 |
| -5.110410565358070E-02 |
2.260732000693700E-01 |
-5.110410565358050E-02 |
2.260732000694550E-01 |
-5.110410900653050E-02 |
2.260731999097800E-01 |
14.4048 |
12.4249 |
7.1830 |
9.1512 |
| 1.829151464613550E+03 |
4.554784991422120E+02 |
1.829151464613550E+03 |
4.554784991423900E+02 |
1.829151446048170E+03 |
4.554784970185970E+02 |
15.0000 |
12.4081 |
7.9935 |
8.3314 |
| |
|
|
|
|
|
|
|
|
|
| Wampler1 |
|
|
|
|
|
|
|
|
|
| 1.000000000000000E+00 |
0.000000000000000E+00 |
1.000000000757840E+00 |
5.435194457486820E-10 |
1.000000206724510E+00 |
4.715917377911300E-05 |
9.1204 |
9.2648 |
6.6846 |
4.3264 |
| 1.000000000000000E+00 |
0.000000000000000E+00 |
9.999999999020280E-01 |
5.968594820249070E-10 |
9.999996742117220E-01 |
5.178729161418710E-05 |
10.0089 |
9.2241 |
6.4871 |
4.2858 |
| 1.000000000000000E+00 |
0.000000000000000E+00 |
9.999999999948860E-01 |
1.968049040047880E-10 |
1.000000133324650E+00 |
1.707603424520960E-05 |
11.2912 |
9.7060 |
6.8751 |
4.7676 |
| 1.000000000000000E+00 |
0.000000000000000E+00 |
1.000000000004350E+00 |
2.562525625586240E-11 |
9.999999790779840E-01 |
2.223408789421740E-06 |
11.3615 |
10.5913 |
7.6794 |
5.6530 |
| 1.000000000000000E+00 |
0.000000000000000E+00 |
9.999999999995600E-01 |
1.425680136726610E-12 |
1.000000001996110E+00 |
1.237009969869760E-07 |
12.3566 |
11.8460 |
8.6998 |
6.9076 |
| 1.000000000000000E+00 |
0.000000000000000E+00 |
1.000000000000010E+00 |
2.836500407388710E-14 |
9.999999999757630E-01 |
2.461126583089750E-09 |
14.0003 |
13.5472 |
10.6155 |
8.6089 |
| |
|
|
|
|
|
|
|
|
|
| Wampler2 |
|
|
|
|
|
|
|
|
|
| 1.000000000000000E+00 |
0.000000000000000E+00 |
1.000000000001060E+00 |
6.472599927709450E-13 |
1.000000000004860E+00 |
1.414345471854660E-09 |
11.9747 |
12.1889 |
11.3134 |
8.8494 |
| 1.000000000000000E-01 |
0.000000000000000E+00 |
1.000000000000010E-01 |
7.107809426920550E-13 |
9.999999999027940E-02 |
1.553146832834950E-09 |
14.0003 |
12.1483 |
10.0123 |
8.8088 |
| 1.000000000000000E-02 |
0.000000000000000E+00 |
9.999999999966160E-03 |
2.343686904669210E-13 |
1.000000000354670E-02 |
5.121254207096430E-10 |
11.4706 |
12.6301 |
9.4502 |
9.2906 |
| 1.000000000000000E-03 |
0.000000000000000E+00 |
1.000000000002580E-03 |
3.051630131848560E-14 |
9.999999997476470E-04 |
6.668200270279720E-11 |
11.5884 |
13.5155 |
9.5980 |
10.1760 |
| 1.000000000000000E-04 |
0.000000000000000E+00 |
9.999999999992830E-05 |
1.697797056221660E-15 |
1.000000000360300E-04 |
3.709902674968510E-12 |
12.1444 |
14.7701 |
9.4433 |
11.4306 |
| 1.000000000000000E-05 |
0.000000000000000E+00 |
1.000000000000100E-05 |
3.377897971345300E-17 |
9.999999999520920E-06 |
7.381137029155980E-14 |
13.0002 |
16.4714 |
10.3196 |
13.1319 |
| |
|
|
|
|
|
|
|
|
|
| Wampler3 |
|
|
|
|
|
|
|
|
|
| 1.000000000000000E+00 |
2.152326246781700E+03 |
1.000000000571500E+00 |
2.152326246809130E+03 |
1.000000206724510E+00 |
2.152326246769490E+03 |
9.2430 |
10.8947 |
6.6846 |
11.2462 |
| 1.000000000000000E+00 |
2.363551734696810E+03 |
9.999999999292380E-01 |
2.363551734657000E+03 |
9.999996742117220E-01 |
2.363551734650780E+03 |
10.1502 |
10.7736 |
6.4871 |
10.7105 |
| 1.000000000000000E+00 |
7.793435243315830E+02 |
9.999999999862550E-01 |
7.793435243274050E+02 |
1.000000133324650E+00 |
7.793435243129190E+02 |
10.8619 |
11.2708 |
6.8751 |
10.6207 |
| 1.000000000000000E+00 |
1.014755075503500E+02 |
1.000000000005390E+00 |
1.014755075501110E+02 |
9.999999790779840E-01 |
1.014755075478000E+02 |
11.2684 |
11.6280 |
7.6794 |
10.5998 |
| 1.000000000000000E+00 |
5.645665121707520E+00 |
9.999999999995070E-01 |
5.645665121703780E+00 |
1.000000001996110E+00 |
5.645665121566270E+00 |
12.3071 |
12.1788 |
8.6998 |
10.6017 |
| 1.000000000000000E+00 |
1.123248546793120E-01 |
1.000000000000010E+00 |
1.123248546792640E-01 |
9.999999999757630E-01 |
1.123248546765740E-01 |
14.0003 |
12.3692 |
10.6155 |
10.6130 |
| |
|
|
|
|
|
|
|
|
|
| Wampler4 |
|
|
|
|
|
|
|
|
|
| 1.000000000000000E+00 |
2.152326246781700E+05 |
9.999999990673700E-01 |
2.152326246809160E+05 |
1.000000206724510E+00 |
2.152326246769490E+05 |
9.0303 |
10.8942 |
6.6846 |
11.2462 |
| 1.000000000000000E+00 |
2.363551734696810E+05 |
1.000000002624100E+00 |
2.363551734657030E+05 |
9.999996742117220E-01 |
2.363551734650780E+05 |
8.5810 |
10.7739 |
6.4871 |
10.7105 |
| 1.000000000000000E+00 |
7.793435243315830E+04 |
9.999999991324560E-01 |
7.793435243274150E+04 |
1.000000133324650E+00 |
7.793435243129180E+04 |
9.0617 |
11.2718 |
6.8751 |
10.6207 |
| 1.000000000000000E+00 |
1.014755075503500E+04 |
1.000000000107790E+00 |
1.014755075501120E+04 |
9.999999790779840E-01 |
1.014755075478000E+04 |
9.9674 |
11.6298 |
7.6794 |
10.5998 |
| 1.000000000000000E+00 |
5.645665121707520E+02 |
9.999999999942750E-01 |
5.645665121703860E+02 |
1.000000001996110E+00 |
5.645665121566260E+02 |
11.2422 |
12.1881 |
8.6998 |
10.6017 |
| 1.000000000000000E+00 |
1.123248546793120E+01 |
1.000000000000110E+00 |
1.123248546792660E+01 |
9.999999999757630E-01 |
1.123248546765740E+01 |
12.9590 |
12.3876 |
10.6155 |
10.6130 |
| |
|
|
|
|
|
|
|
|
|
| Wampler5 |
|
|
|
|
|
|
|
|
|
| 1.000000000000000E+00 |
2.152326246781700E+07 |
9.999998288368490E-01 |
2.152326246809160E+07 |
1.000000206724510E+00 |
2.152326246769490E+07 |
6.7666 |
10.8942 |
6.6846 |
11.2462 |
| 1.000000000000000E+00 |
2.363551734696810E+07 |
1.000000272446680E+00 |
2.363551734657030E+07 |
9.999996742117220E-01 |
2.363551734650780E+07 |
6.5647 |
10.7739 |
6.4871 |
10.7105 |
| 1.000000000000000E+00 |
7.793435243315830E+06 |
9.999999137263700E-01 |
7.793435243274150E+06 |
1.000000133324650E+00 |
7.793435243129190E+06 |
7.0641 |
11.2718 |
6.8751 |
10.6207 |
| 1.000000000000000E+00 |
1.014755075503500E+06 |
1.000000010343790E+00 |
1.014755075501120E+06 |
9.999999790779840E-01 |
1.014755075478000E+06 |
7.9853 |
11.6298 |
7.6794 |
10.5998 |
| 1.000000000000000E+00 |
5.645665121707520E+04 |
9.999999994716380E-01 |
5.645665121703860E+04 |
1.000000001996110E+00 |
5.645665121566260E+04 |
9.2771 |
12.1882 |
8.6998 |
10.6017 |
| 1.000000000000000E+00 |
1.123248546793120E+03 |
1.000000000009700E+00 |
1.123248546792650E+03 |
9.999999999757630E-01 |
1.123248546765740E+03 |
11.0132 |
12.3875 |
10.6155 |
10.6130 |
|
