Description Usage Arguments Details Value Author(s) References See Also Examples
The press.liu
function computes predicted residual sum of squares (PRESS), computed from by following Ozkale and Kaciranlar (2007) <doi:10.1080/03610920601126522>.
1 2 3 |
object |
An object of class "liu". |
predr |
If |
... |
Not presently used in this implementation. |
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.
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.
Muhammad Imdad Ullah, Muhammad Aslam
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.
The ridge model fitting liu
, Liu residual residuals
, Liu predicted value predict
1 2 3 4 5 6 |
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
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