press.liu: Predicted Residual Sum of Squares

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

The press.liu function computes predicted residual sum of squares (PRESS), computed from by following Ozkale and Kaciranlar (2007) <doi:10.1080/03610920601126522>.

Usage

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press(object, predr = FALSE, ...)
## S3 method for class 'liu'
press(object, predr = FALSE, ...)

Arguments

object

An object of class "liu".

predr

If TRUE then predicted residuals are returned.

...

Not presently used in this implementation.

Details

For all of the n leave-one-out predicted residual sum of squares is calculated by fitting full regression model. PRESS is computed by using, ∑ (\hat{e}_{d(i)})^2 or ∑ [(\hat{e}_{di})/(1-h_{1-ii})-(e_i)/((1-h_{1-ii})(1-h_{ii}))*(h_{1-ii}-\widetilde{H}_{d-ii})]^2 , where H_{ii}=X(X'X)^{-1}X''s ith diagonal element, h_{1-ii}=X(X'X+I)^{-1}X''s ith diagonal element and \hat{e}_{di} is the ith residual at specific value of d.

Value

The press.liu produces a vector of PRESS for scalar or vector values of biasing parameter d. If argument predr is TRUE then predicted residuals are returned instead of predicted residual sum of squares.

Author(s)

Muhammad Imdad Ullah, Muhammad Aslam

References

Akdeniz, F. and Kaciranlar, S. (1995). On the Almost Unbiased Generalized Liu Estimators and Unbiased Estimation of the Bias and MSE. Communications in Statistics-Theory and Methods, 24, 1789–1897. http://doi.org/10.1080/03610929508831585.

Allen, D. M. (1971). Mean Square Error of Prediction as a Criterion for Selecting Variables. Technometrics, 13, 469-475. http://www.jstor.org/stable/1267161.

Allen, D. M. (1974). The Relationship between Variable Selection and Data Augmentation and Method for Prediction. Technometrics, 16, 125-127. http://www.jstor.org/stable/1267500.

Imdad, M. U. (2017). Addressing Linear Regression Models with Correlated Regressors: Some Package Development in R (Doctoral Thesis, Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan).

Imdadullah, M., Aslam, M., and Altaf, S. (2017). liureg: A comprehensive R Package for the Liu Estimation of Linear Regression Model with Collinear Regressors. The R Journal, 9 (2), 232–247.

Liu, K. (1993). A new Class of Biased Estimate in Linear Regression. Journal of Statistical Planning and Inference, 141, 189–196. http://doi.org/10.1080/03610929308831027.

Ozkale, R. M. and Kaciranlar, S. (2007). A Prediction-Oriented Criterion for Choosing the Biasing Parameter in Liu Estimation. Commincations in Statistics-Theory and Methods, 36(10): 1889–1903. http://doi.org/10.1080/03610920601126522.

See Also

The ridge model fitting liu, Liu residual residuals, Liu predicted value predict

Examples

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mod<-liu(y~., data = as.data.frame(Hald), d = seq(-5, 5, 0.1))
## PRESS
press(mod)

## Predicted residual
press(mod, predr = TRUE)

Example output

                 d=-5                d=-4.9                d=-4.8 
             73.87829              73.88127              73.89170 
               d=-4.7                d=-4.6                d=-4.5 
             73.90958              73.93491              73.96768 
               d=-4.4                d=-4.3                d=-4.2 
             74.00791              74.05559              74.11071 
               d=-4.1                  d=-4                d=-3.9 
             74.17329              74.24331              74.32078 
               d=-3.8                d=-3.7                d=-3.6 
             74.40571              74.49808              74.59790 
               d=-3.5                d=-3.4                d=-3.3 
             74.70517              74.81990              74.94207 
               d=-3.2                d=-3.1                  d=-3 
             75.07169              75.20876              75.35328 
               d=-2.9                d=-2.8                d=-2.7 
             75.50525              75.66466              75.83153 
               d=-2.6                d=-2.5                d=-2.4 
             76.00585              76.18762              76.37683 
               d=-2.3                d=-2.2                d=-2.1 
             76.57350              76.77761              76.98918 
                 d=-2                d=-1.9                d=-1.8 
             77.20819              77.43466              77.66857 
               d=-1.7                d=-1.6                d=-1.5 
             77.90993              78.15874              78.41501 
               d=-1.4                d=-1.3                d=-1.2 
             78.67872              78.94988              79.22849 
               d=-1.1                  d=-1  d=-0.899999999999999 
             79.51455              79.80806              80.10902 
               d=-0.8                d=-0.7                d=-0.6 
             80.41742              80.73328              81.05659 
               d=-0.5  d=-0.399999999999999                d=-0.3 
             81.38735              81.72555              82.07121 
 d=-0.199999999999999 d=-0.0999999999999996                   d=0 
             82.42431              82.78487              83.15287 
  d=0.100000000000001                 d=0.2   d=0.300000000000001 
             83.52832              83.91123              84.30158 
                d=0.4                 d=0.5   d=0.600000000000001 
             84.69938              85.10463              85.51734 
                d=0.7   d=0.800000000000001                 d=0.9 
             85.93749              86.36509              86.80014 
                  d=1                 d=1.1                 d=1.2 
             87.24263              87.69258              88.14998 
                d=1.3                 d=1.4                 d=1.5 
             88.61483              89.08713              89.56687 
                d=1.6                 d=1.7                 d=1.8 
             90.05407              90.54871              91.05081 
                d=1.9                   d=2                 d=2.1 
             91.56035              92.07735              92.60179 
                d=2.2                 d=2.3                 d=2.4 
             93.13368              93.67303              94.21982 
                d=2.5                 d=2.6                 d=2.7 
             94.77406              95.33575              95.90489 
                d=2.8                 d=2.9                   d=3 
             96.48148              97.06552              97.65701 
                d=3.1                 d=3.2                 d=3.3 
             98.25595              98.86234              99.47617 
                d=3.4                 d=3.5                 d=3.6 
            100.09746             100.72620             101.36238 
                d=3.7                 d=3.8                 d=3.9 
            102.00602             102.65710             103.31564 
                  d=4                 d=4.1                 d=4.2 
            103.98162             104.65505             105.33594 
                d=4.3                 d=4.4                 d=4.5 
            106.02427             106.72005             107.42328 
                d=4.6                 d=4.7                 d=4.8 
            108.13396             108.85209             109.57767 
                d=4.9                   d=5 
            110.31070             111.05118 
       d=-5   d=-4.9   d=-4.8   d=-4.7   d=-4.6   d=-4.5   d=-4.4   d=-4.3
1   0.98025  0.96406  0.94787  0.93169  0.91550  0.89931  0.88313  0.86694
2   0.82036  0.84055  0.86075  0.88094  0.90114  0.92133  0.94153  0.96172
3  -2.37639 -2.39249 -2.40858 -2.42467 -2.44077 -2.45686 -2.47295 -2.48905
4  -2.63734 -2.63021 -2.62308 -2.61595 -2.60881 -2.60168 -2.59455 -2.58742
5   0.45433  0.45257  0.45080  0.44904  0.44728  0.44552  0.44376  0.44199
6   3.90973  3.91323  3.91674  3.92024  3.92375  3.92725  3.93076  3.93426
7  -1.96852 -1.96973 -1.97093 -1.97214 -1.97334 -1.97455 -1.97575 -1.97696
8  -3.54838 -3.56841 -3.58844 -3.60847 -3.62850 -3.64853 -3.66856 -3.68860
9   0.26897  0.29384  0.31871  0.34358  0.36845  0.39332  0.41820  0.44307
10  2.75321  2.71979  2.68637  2.65294  2.61952  2.58609  2.55267  2.51924
11  3.60800  3.59881  3.58962  3.58042  3.57123  3.56204  3.55284  3.54365
12  1.91784  1.90580  1.89376  1.88172  1.86968  1.85763  1.84559  1.83355
13 -1.82616 -1.84517 -1.86419 -1.88321 -1.90223 -1.92125 -1.94027 -1.95929
     d=-4.2   d=-4.1     d=-4   d=-3.9   d=-3.8   d=-3.7   d=-3.6   d=-3.5
1   0.85075  0.83457  0.81838  0.80219  0.78601  0.76982  0.75363  0.73745
2   0.98192  1.00211  1.02231  1.04250  1.06270  1.08289  1.10309  1.12328
3  -2.50514 -2.52124 -2.53733 -2.55342 -2.56952 -2.58561 -2.60170 -2.61780
4  -2.58029 -2.57316 -2.56603 -2.55889 -2.55176 -2.54463 -2.53750 -2.53037
5   0.44023  0.43847  0.43671  0.43494  0.43318  0.43142  0.42966  0.42790
6   3.93777  3.94128  3.94478  3.94829  3.95179  3.95530  3.95880  3.96231
7  -1.97816 -1.97937 -1.98057 -1.98178 -1.98298 -1.98419 -1.98539 -1.98660
8  -3.70863 -3.72866 -3.74869 -3.76872 -3.78875 -3.80878 -3.82881 -3.84884
9   0.46794  0.49281  0.51768  0.54255  0.56742  0.59229  0.61716  0.64203
10  2.48582  2.45240  2.41897  2.38555  2.35212  2.31870  2.28527  2.25185
11  3.53446  3.52526  3.51607  3.50688  3.49768  3.48849  3.47930  3.47010
12  1.82151  1.80947  1.79743  1.78539  1.77335  1.76131  1.74927  1.73723
13 -1.97831 -1.99733 -2.01635 -2.03537 -2.05439 -2.07341 -2.09243 -2.11144
     d=-3.4   d=-3.3   d=-3.2   d=-3.1     d=-3   d=-2.9   d=-2.8   d=-2.7
1   0.72126  0.70507  0.68889  0.67270  0.65651  0.64033  0.62414  0.60795
2   1.14348  1.16367  1.18387  1.20406  1.22426  1.24445  1.26465  1.28484
3  -2.63389 -2.64998 -2.66608 -2.68217 -2.69826 -2.71436 -2.73045 -2.74654
4  -2.52324 -2.51611 -2.50897 -2.50184 -2.49471 -2.48758 -2.48045 -2.47332
5   0.42613  0.42437  0.42261  0.42085  0.41909  0.41732  0.41556  0.41380
6   3.96581  3.96932  3.97282  3.97633  3.97983  3.98334  3.98684  3.99035
7  -1.98780 -1.98901 -1.99021 -1.99142 -1.99262 -1.99383 -1.99503 -1.99624
8  -3.86888 -3.88891 -3.90894 -3.92897 -3.94900 -3.96903 -3.98906 -4.00909
9   0.66690  0.69177  0.71664  0.74151  0.76638  0.79125  0.81612  0.84099
10  2.21843  2.18500  2.15158  2.11815  2.08473  2.05131  2.01788  1.98446
11  3.46091  3.45172  3.44252  3.43333  3.42414  3.41494  3.40575  3.39655
12  1.72519  1.71315  1.70111  1.68907  1.67703  1.66499  1.65295  1.64091
13 -2.13046 -2.14948 -2.16850 -2.18752 -2.20654 -2.22556 -2.24458 -2.26360
     d=-2.6   d=-2.5   d=-2.4   d=-2.3   d=-2.2   d=-2.1     d=-2   d=-1.9
1   0.59176  0.57558  0.55939  0.54320  0.52702  0.51083  0.49464  0.47846
2   1.30504  1.32523  1.34543  1.36562  1.38582  1.40601  1.42621  1.44640
3  -2.76264 -2.77873 -2.79483 -2.81092 -2.82701 -2.84311 -2.85920 -2.87529
4  -2.46619 -2.45905 -2.45192 -2.44479 -2.43766 -2.43053 -2.42340 -2.41627
5   0.41204  0.41027  0.40851  0.40675  0.40499  0.40323  0.40146  0.39970
6   3.99385  3.99736  4.00087  4.00437  4.00788  4.01138  4.01489  4.01839
7  -1.99744 -1.99865 -1.99985 -2.00106 -2.00226 -2.00347 -2.00467 -2.00588
8  -4.02913 -4.04916 -4.06919 -4.08922 -4.10925 -4.12928 -4.14931 -4.16934
9   0.86586  0.89074  0.91561  0.94048  0.96535  0.99022  1.01509  1.03996
10  1.95103  1.91761  1.88418  1.85076  1.81734  1.78391  1.75049  1.71706
11  3.38736  3.37817  3.36897  3.35978  3.35059  3.34139  3.33220  3.32301
12  1.62886  1.61682  1.60478  1.59274  1.58070  1.56866  1.55662  1.54458
13 -2.28262 -2.30164 -2.32066 -2.33968 -2.35870 -2.37771 -2.39673 -2.41575
     d=-1.8   d=-1.7   d=-1.6   d=-1.5   d=-1.4   d=-1.3   d=-1.2   d=-1.1
1   0.46227  0.44608  0.42990  0.41371  0.39752  0.38134  0.36515  0.34896
2   1.46660  1.48679  1.50699  1.52718  1.54738  1.56757  1.58777  1.60796
3  -2.89139 -2.90748 -2.92357 -2.93967 -2.95576 -2.97185 -2.98795 -3.00404
4  -2.40913 -2.40200 -2.39487 -2.38774 -2.38061 -2.37348 -2.36635 -2.35921
5   0.39794  0.39618  0.39442  0.39265  0.39089  0.38913  0.38737  0.38560
6   4.02190  4.02540  4.02891  4.03241  4.03592  4.03942  4.04293  4.04643
7  -2.00708 -2.00829 -2.00949 -2.01070 -2.01190 -2.01311 -2.01431 -2.01552
8  -4.18938 -4.20941 -4.22944 -4.24947 -4.26950 -4.28953 -4.30956 -4.32959
9   1.06483  1.08970  1.11457  1.13944  1.16431  1.18918  1.21405  1.23892
10  1.68364  1.65022  1.61679  1.58337  1.54994  1.51652  1.48309  1.44967
11  3.31381  3.30462  3.29543  3.28623  3.27704  3.26785  3.25865  3.24946
12  1.53254  1.52050  1.50846  1.49642  1.48438  1.47234  1.46030  1.44826
13 -2.43477 -2.45379 -2.47281 -2.49183 -2.51085 -2.52987 -2.54889 -2.56791
       d=-1 d=-0.899999999999999   d=-0.8   d=-0.7   d=-0.6   d=-0.5
1   0.33278              0.31659  0.30040  0.28422  0.26803  0.25184
2   1.62816              1.64835  1.66855  1.68874  1.70894  1.72913
3  -3.02013             -3.03623 -3.05232 -3.06841 -3.08451 -3.10060
4  -2.35208             -2.34495 -2.33782 -2.33069 -2.32356 -2.31643
5   0.38384              0.38208  0.38032  0.37856  0.37679  0.37503
6   4.04994              4.05344  4.05695  4.06046  4.06396  4.06747
7  -2.01672             -2.01793 -2.01913 -2.02034 -2.02154 -2.02275
8  -4.34963             -4.36966 -4.38969 -4.40972 -4.42975 -4.44978
9   1.26379              1.28866  1.31353  1.33840  1.36328  1.38815
10  1.41625              1.38282  1.34940  1.31597  1.28255  1.24913
11  3.24027              3.23107  3.22188  3.21269  3.20349  3.19430
12  1.43622              1.42418  1.41214  1.40010  1.38805  1.37601
13 -2.58693             -2.60595 -2.62497 -2.64398 -2.66300 -2.68202
   d=-0.399999999999999   d=-0.3 d=-0.199999999999999 d=-0.0999999999999996
1               0.23565  0.21947              0.20328               0.18709
2               1.74933  1.76952              1.78972               1.80991
3              -3.11670 -3.13279             -3.14888              -3.16498
4              -2.30929 -2.30216             -2.29503              -2.28790
5               0.37327  0.37151              0.36975               0.36798
6               4.07097  4.07448              4.07798               4.08149
7              -2.02395 -2.02516             -2.02636              -2.02757
8              -4.46981 -4.48984             -4.50988              -4.52991
9               1.41302  1.43789              1.46276               1.48763
10              1.21570  1.18228              1.14885               1.11543
11              3.18511  3.17591              3.16672               3.15753
12              1.36397  1.35193              1.33989               1.32785
13             -2.70104 -2.72006             -2.73908              -2.75810
        d=0 d=0.100000000000001    d=0.2 d=0.300000000000001    d=0.4    d=0.5
1   0.17091             0.15472  0.13853             0.12235  0.10616  0.08997
2   1.83011             1.85030  1.87050             1.89069  1.91089  1.93108
3  -3.18107            -3.19716 -3.21326            -3.22935 -3.24544 -3.26154
4  -2.28077            -2.27364 -2.26651            -2.25937 -2.25224 -2.24511
5   0.36622             0.36446  0.36270             0.36093  0.35917  0.35741
6   4.08499             4.08850  4.09200             4.09551  4.09901  4.10252
7  -2.02877            -2.02998 -2.03118            -2.03239 -2.03359 -2.03480
8  -4.54994            -4.56997 -4.59000            -4.61003 -4.63006 -4.65009
9   1.51250             1.53737  1.56224             1.58711  1.61198  1.63685
10  1.08200             1.04858  1.01516             0.98173  0.94831  0.91488
11  3.14833             3.13914  3.12995             3.12075  3.11156  3.10237
12  1.31581             1.30377  1.29173             1.27969  1.26765  1.25561
13 -2.77712            -2.79614 -2.81516            -2.83418 -2.85320 -2.87222
   d=0.600000000000001    d=0.7 d=0.800000000000001    d=0.9      d=1    d=1.1
1              0.07379  0.05760             0.04141  0.02523  0.00904 -0.00715
2              1.95128  1.97147             1.99167  2.01186  2.03206  2.05225
3             -3.27763 -3.29372            -3.30982 -3.32591 -3.34200 -3.35810
4             -2.23798 -2.23085            -2.22372 -2.21659 -2.20945 -2.20232
5              0.35565  0.35389             0.35212  0.35036  0.34860  0.34684
6              4.10602  4.10953             4.11303  4.11654  4.12005  4.12355
7             -2.03600 -2.03721            -2.03841 -2.03961 -2.04082 -2.04202
8             -4.67012 -4.69016            -4.71019 -4.73022 -4.75025 -4.77028
9              1.66172  1.68659             1.71146  1.73633  1.76120  1.78607
10             0.88146  0.84804             0.81461  0.78119  0.74776  0.71434
11             3.09317  3.08398             3.07479  3.06559  3.05640  3.04721
12             1.24357  1.23153             1.21949  1.20745  1.19541  1.18337
13            -2.89124 -2.91025            -2.92927 -2.94829 -2.96731 -2.98633
      d=1.2    d=1.3    d=1.4    d=1.5    d=1.6    d=1.7    d=1.8    d=1.9
1  -0.02333 -0.03952 -0.05571 -0.07189 -0.08808 -0.10427 -0.12046 -0.13664
2   2.07245  2.09264  2.11284  2.13303  2.15323  2.17342  2.19362  2.21381
3  -3.37419 -3.39029 -3.40638 -3.42247 -3.43857 -3.45466 -3.47075 -3.48685
4  -2.19519 -2.18806 -2.18093 -2.17380 -2.16667 -2.15953 -2.15240 -2.14527
5   0.34508  0.34331  0.34155  0.33979  0.33803  0.33627  0.33450  0.33274
6   4.12706  4.13056  4.13407  4.13757  4.14108  4.14458  4.14809  4.15159
7  -2.04323 -2.04443 -2.04564 -2.04684 -2.04805 -2.04925 -2.05046 -2.05166
8  -4.79031 -4.81034 -4.83037 -4.85041 -4.87044 -4.89047 -4.91050 -4.93053
9   1.81094  1.83582  1.86069  1.88556  1.91043  1.93530  1.96017  1.98504
10  0.68091  0.64749  0.61407  0.58064  0.54722  0.51379  0.48037  0.44695
11  3.03801  3.02882  3.01963  3.01043  3.00124  2.99205  2.98285  2.97366
12  1.17133  1.15928  1.14724  1.13520  1.12316  1.11112  1.09908  1.08704
13 -3.00535 -3.02437 -3.04339 -3.06241 -3.08143 -3.10045 -3.11947 -3.13849
        d=2    d=2.1    d=2.2    d=2.3    d=2.4    d=2.5    d=2.6    d=2.7
1  -0.15283 -0.16902 -0.18520 -0.20139 -0.21758 -0.23376 -0.24995 -0.26614
2   2.23401  2.25420  2.27440  2.29459  2.31479  2.33498  2.35518  2.37537
3  -3.50294 -3.51903 -3.53513 -3.55122 -3.56731 -3.58341 -3.59950 -3.61559
4  -2.13814 -2.13101 -2.12388 -2.11675 -2.10961 -2.10248 -2.09535 -2.08822
5   0.33098  0.32922  0.32745  0.32569  0.32393  0.32217  0.32041  0.31864
6   4.15510  4.15860  4.16211  4.16561  4.16912  4.17262  4.17613  4.17963
7  -2.05287 -2.05407 -2.05528 -2.05648 -2.05769 -2.05889 -2.06010 -2.06130
8  -4.95056 -4.97059 -4.99062 -5.01066 -5.03069 -5.05072 -5.07075 -5.09078
9   2.00991  2.03478  2.05965  2.08452  2.10939  2.13426  2.15913  2.18400
10  0.41352  0.38010  0.34667  0.31325  0.27982  0.24640  0.21298  0.17955
11  2.96446  2.95527  2.94608  2.93688  2.92769  2.91850  2.90930  2.90011
12  1.07500  1.06296  1.05092  1.03888  1.02684  1.01480  1.00276  0.99072
13 -3.15751 -3.17652 -3.19554 -3.21456 -3.23358 -3.25260 -3.27162 -3.29064
      d=2.8    d=2.9      d=3    d=3.1    d=3.2    d=3.3    d=3.4    d=3.5
1  -0.28232 -0.29851 -0.31470 -0.33088 -0.34707 -0.36326 -0.37944 -0.39563
2   2.39557  2.41576  2.43596  2.45615  2.47635  2.49654  2.51674  2.53693
3  -3.63169 -3.64778 -3.66388 -3.67997 -3.69606 -3.71216 -3.72825 -3.74434
4  -2.08109 -2.07396 -2.06683 -2.05969 -2.05256 -2.04543 -2.03830 -2.03117
5   0.31688  0.31512  0.31336  0.31160  0.30983  0.30807  0.30631  0.30455
6   4.18314  4.18665  4.19015  4.19366  4.19716  4.20067  4.20417  4.20768
7  -2.06251 -2.06371 -2.06492 -2.06612 -2.06733 -2.06853 -2.06974 -2.07094
8  -5.11081 -5.13084 -5.15087 -5.17091 -5.19094 -5.21097 -5.23100 -5.25103
9   2.20887  2.23374  2.25861  2.28348  2.30836  2.33323  2.35810  2.38297
10  0.14613  0.11270  0.07928  0.04586  0.01243 -0.02099 -0.05442 -0.08784
11  2.89092  2.88172  2.87253  2.86334  2.85414  2.84495  2.83576  2.82656
12  0.97868  0.96664  0.95460  0.94256  0.93051  0.91847  0.90643  0.89439
13 -3.30966 -3.32868 -3.34770 -3.36672 -3.38574 -3.40476 -3.42378 -3.44279
      d=3.6    d=3.7    d=3.8    d=3.9      d=4    d=4.1    d=4.2    d=4.3
1  -0.41182 -0.42800 -0.44419 -0.46038 -0.47657 -0.49275 -0.50894 -0.52513
2   2.55713  2.57732  2.59752  2.61771  2.63791  2.65810  2.67830  2.69849
3  -3.76044 -3.77653 -3.79262 -3.80872 -3.82481 -3.84090 -3.85700 -3.87309
4  -2.02404 -2.01691 -2.00977 -2.00264 -1.99551 -1.98838 -1.98125 -1.97412
5   0.30278  0.30102  0.29926  0.29750  0.29574  0.29397  0.29221  0.29045
6   4.21118  4.21469  4.21819  4.22170  4.22520  4.22871  4.23221  4.23572
7  -2.07215 -2.07335 -2.07456 -2.07576 -2.07697 -2.07817 -2.07938 -2.08058
8  -5.27106 -5.29109 -5.31112 -5.33115 -5.35119 -5.37122 -5.39125 -5.41128
9   2.40784  2.43271  2.45758  2.48245  2.50732  2.53219  2.55706  2.58193
10 -0.12127 -0.15469 -0.18811 -0.22154 -0.25496 -0.28839 -0.32181 -0.35523
11  2.81737  2.80818  2.79898  2.78979  2.78060  2.77140  2.76221  2.75302
12  0.88235  0.87031  0.85827  0.84623  0.83419  0.82215  0.81011  0.79807
13 -3.46181 -3.48083 -3.49985 -3.51887 -3.53789 -3.55691 -3.57593 -3.59495
      d=4.4    d=4.5    d=4.6    d=4.7    d=4.8    d=4.9      d=5
1  -0.54131 -0.55750 -0.57369 -0.58987 -0.60606 -0.62225 -0.63843
2   2.71869  2.73888  2.75908  2.77927  2.79947  2.81966  2.83986
3  -3.88918 -3.90528 -3.92137 -3.93746 -3.95356 -3.96965 -3.98575
4  -1.96699 -1.95985 -1.95272 -1.94559 -1.93846 -1.93133 -1.92420
5   0.28869  0.28693  0.28516  0.28340  0.28164  0.27988  0.27811
6   4.23922  4.24273  4.24624  4.24974  4.25325  4.25675  4.26026
7  -2.08179 -2.08299 -2.08420 -2.08540 -2.08661 -2.08781 -2.08902
8  -5.43131 -5.45134 -5.47137 -5.49140 -5.51144 -5.53147 -5.55150
9   2.60680  2.63167  2.65654  2.68141  2.70628  2.73115  2.75602
10 -0.38866 -0.42208 -0.45551 -0.48893 -0.52236 -0.55578 -0.58920
11  2.74382  2.73463  2.72544  2.71624  2.70705  2.69786  2.68866
12  0.78603  0.77399  0.76195  0.74991  0.73787  0.72583  0.71379
13 -3.61397 -3.63299 -3.65201 -3.67103 -3.69005 -3.70906 -3.72808

liureg documentation built on May 2, 2019, 8:34 a.m.