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 2 columns in the table show a measure of the number of the correct significant digits of both the coefficients and standard errors for the regression method SVD. 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 Coef | NIST SE | Betahat Coef SVD | Betahat SE SVD | # digits accurate | # digits accurate |
| Noris | |||||
| -2.623230737740290E-01 | 2.328182343011520E-01 | -2.623230737740410E-01 | 2.328182343011550E-01 | 13.340 | 13.890 |
| 1.002116818020450E+00 | 4.297968481999370E-04 | 1.002116818020450E+00 | 4.297968481999410E-04 | 15.000 | 14.036 |
| Pontius | |||||
| 6.735657894736840E-04 | 1.079386120330770E-04 | 6.735657894726200E-04 | 1.079386119580410E-04 | 11.801 | 9.158 |
| 7.320591604010030E-07 | 1.578173999816590E-10 | 7.320591604010040E-07 | 1.578173999443180E-10 | 14.885 | 9.626 |
| -3.160818713450290E-15 | 4.866528499920360E-17 | -3.160818713450550E-15 | 4.866528499075220E-17 | 13.085 | 9.760 |
| Noint1 | |||||
| 2.074380165289260E+00 | 1.652892561983470E-02 | 2.074380165289260E+00 | 1.652892561983470E-02 | 15.000 | 15.000 |
| Noint2 | |||||
| 7.272727272727270E-01 | 4.208273180784320E-02 | 7.272727272727270E-01 | 4.208273180784320E-02 | 15.000 | 15.000 |
| Filip | |||||
| -1.467489614229800E+03 | 2.980845309955370E+02 | -1.467483103104890E+03 | 2.981205609976220E+02 | 5.353 | 3.918 |
| -2.772179591933420E+03 | 5.597798654749500E+02 | -2.772173586259430E+03 | 5.598464358025090E+02 | 5.664 | 3.925 |
| -2.316371081608930E+03 | 4.664775721277960E+02 | -2.316368767107610E+03 | 4.665327548516910E+02 | 6.000 | 3.927 |
| -1.127973940983720E+03 | 2.272042744777510E+02 | -1.127973446622410E+03 | 2.272311089978630E+02 | 6.358 | 3.928 |
| -3.544782337033490E+02 | 7.164786608759270E+01 | -3.544781652833520E+02 | 7.165632483401110E+01 | 6.714 | 3.928 |
| -7.512420173937570E+01 | 1.528971787474000E+01 | -7.512419467937400E+01 | 1.529152299270840E+01 | 7.027 | 3.928 |
| -1.087531803553430E+01 | 2.236911598160330E+00 | -1.087531745874620E+01 | 2.237175727483030E+00 | 7.275 | 3.928 |
| -1.062214985889470E+00 | 2.216243219342270E-01 | -1.062214951537100E+00 | 2.216504949476250E-01 | 7.490 | 3.928 |
| -6.701911545934080E-02 | 1.423637631547240E-02 | -6.701911411164930E-02 | 1.423805776502940E-02 | 7.697 | 3.928 |
| -2.467810782754790E-03 | 5.356174088898210E-04 | -2.467810745466700E-03 | 5.356806731116910E-04 | 7.821 | 3.928 |
| -4.029625250804040E-05 | 8.966328373738680E-06 | -4.029625177863510E-05 | 8.967387364384680E-06 | 7.742 | 3.928 |
| 6.831 | 3.927 | ||||
| Longley | |||||
| -3.482258634595820E+06 | 8.904203836073730E+05 | -3.482258634595820E+06 | 8.904203836078880E+05 | 15.000 | 12.238 |
| 1.506187227137330E+01 | 8.491492577476690E+01 | 1.506187227137380E+01 | 8.491492577467500E+01 | 13.480 | 11.966 |
| -3.581917929259100E-02 | 3.349100777224320E-02 | -3.581917929259140E-02 | 3.349100777226350E-02 | 13.949 | 12.218 |
| -2.020229803816830E+00 | 4.883996816516990E-01 | -2.020229803816830E+00 | 4.883996816519350E-01 | 15.000 | 12.316 |
| -1.033226867173590E+00 | 2.142741631616750E-01 | -1.033226867173590E+00 | 2.142741631617920E-01 | 15.000 | 12.263 |
| -5.110410565358070E-02 | 2.260732000693700E-01 | -5.110410565358000E-02 | 2.260732000694780E-01 | 13.863 | 12.321 |
| 1.829151464613550E+03 | 4.554784991422120E+02 | 1.829151464613550E+03 | 4.554784991424800E+02 | 15.000 | 12.230 |
| Wampler1 | |||||
| 1.000000000000000E+00 | 0.000000000000000E+00 | 1.000000000698490E+00 | 6.913029124369120E-10 | 9.156 | 9.160 |
| 1.000000000000000E+00 | 0.000000000000000E+00 | 1.000000000249390E+00 | 7.591461567777370E-10 | 9.603 | 9.120 |
| 1.000000000000000E+00 | 0.000000000000000E+00 | 9.999999998805830E-01 | 2.503163491647690E-10 | 9.923 | 9.602 |
| 1.000000000000000E+00 | 0.000000000000000E+00 | 1.000000000017290E+00 | 3.259278840022200E-11 | 10.762 | 10.487 |
| 1.000000000000000E+00 | 0.000000000000000E+00 | 9.999999999989600E-01 | 1.813323955039780E-12 | 11.983 | 11.742 |
| 1.000000000000000E+00 | 0.000000000000000E+00 | 1.000000000000020E+00 | 3.607747631955870E-14 | 13.699 | 13.443 |
| Wampler2 | |||||
| 1.000000000000000E+00 | 0.000000000000000E+00 | 1.000000000005990E+00 | 2.700812095784400E-12 | 11.223 | 11.569 |
| 1.000000000000000E-01 | 0.000000000000000E+00 | 9.999999999875390E-02 | 2.965865014897740E-12 | 10.904 | 11.528 |
| 1.000000000000000E-02 | 0.000000000000000E+00 | 1.000000000007370E-02 | 9.779467313592410E-13 | 11.133 | 12.010 |
| 1.000000000000000E-03 | 0.000000000000000E+00 | 9.999999999979270E-04 | 1.273349143523170E-13 | 11.683 | 12.895 |
| 1.000000000000000E-04 | 0.000000000000000E+00 | 1.000000000000250E-04 | 7.084372397742490E-15 | 12.602 | 14.150 |
| 1.000000000000000E-05 | 0.000000000000000E+00 | 9.999999999999800E-06 | 1.409490437205870E-16 | 13.696 | 15.851 |
| Wampler3 | |||||
| 1.000000000000000E+00 | 2.152326246781700E+03 | 1.000000000814910E+00 | 2.152326246184200E+03 | 9.089 | 9.557 |
| 1.000000000000000E+00 | 2.363551734696810E+03 | 1.000000000071320E+00 | 2.363551734742190E+03 | 10.147 | 10.717 |
| 1.000000000000000E+00 | 7.793435243315830E+02 | 9.999999999262980E-01 | 7.793435243273480E+02 | 10.133 | 11.265 |
| 1.000000000000000E+00 | 1.014755075503500E+02 | 1.000000000012910E+00 | 1.014755075497060E+02 | 10.889 | 11.197 |
| 1.000000000000000E+00 | 5.645665121707520E+00 | 9.999999999991350E-01 | 5.645665121688370E+00 | 12.063 | 11.470 |
| 1.000000000000000E+00 | 1.123248546793120E-01 | 1.000000000000020E+00 | 1.123248546790430E-01 | 13.699 | 11.621 |
| Wampler4 | |||||
| 1.000000000000000E+00 | 2.152326246781700E+05 | 1.000000005122270E+00 | 2.152326246184180E+05 | 8.291 | 9.557 |
| 1.000000000000000E+00 | 2.363551734696810E+05 | 9.999999917237560E-01 | 2.363551734742170E+05 | 8.082 | 10.717 |
| 1.000000000000000E+00 | 7.793435243315830E+04 | 1.000000002926980E+00 | 7.793435243273400E+04 | 8.534 | 11.264 |
| 1.000000000000000E+00 | 1.014755075503500E+04 | 9.999999996161230E-01 | 1.014755075497060E+04 | 9.416 | 11.197 |
| 1.000000000000000E+00 | 5.645665121707520E+02 | 1.000000000021070E+00 | 5.645665121688320E+02 | 10.676 | 11.468 |
| 1.000000000000000E+00 | 1.123248546793120E+01 | 9.999999999995900E-01 | 1.123248546790420E+01 | 12.387 | 11.619 |
| Wampler5 | |||||
| 1.000000000000000E+00 | 2.152326246781700E+07 | 1.000000445754270E+00 | 2.152326246184180E+07 | 6.351 | 9.557 |
| 1.000000000000000E+00 | 2.363551734696810E+07 | 9.999991393152240E-01 | 2.363551734742170E+07 | 6.065 | 10.717 |
| 1.000000000000000E+00 | 7.793435243315830E+06 | 1.000000308436330E+00 | 7.793435243273400E+06 | 6.511 | 11.264 |
| 1.000000000000000E+00 | 1.014755075503500E+06 | 9.999999593253530E-01 | 1.014755075497060E+06 | 7.391 | 11.197 |
| 1.000000000000000E+00 | 5.645665121707520E+04 | 1.000000002242450E+00 | 5.645665121688320E+04 | 8.649 | 11.468 |
| 1.000000000000000E+00 | 1.123248546793120E+03 | 9.999999999561660E-01 | 1.123248546790420E+03 | 10.358 | 11.619 |