Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 04 Aug 2011 09:59:10 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Aug/04/t1312466433006ozmfjsx4m8i5.htm/, Retrieved Wed, 15 May 2024 15:08:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123395, Retrieved Wed, 15 May 2024 15:08:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSergeyssels Ivan
Estimated Impact223
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A - Sta...] [2011-08-04 13:59:10] [bc909d11ab9ae813672fa3903785080c] [Current]
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Dataseries X:
192528
190773
188996
185320
221698
219771
192528
174414
176163
176163
178112
181616
192528
188996
194449
203412
254400
254400
243516
232604
241567
252473
254400
259853
276217
265306
265306
281670
327033
330709
321580
299762
316121
316121
317876
327033
334241
337917
337917
348823
390681
401565
403314
376071
390681
385228
374317
397889
403314
394185
396112
408773
456085
479624
479624
468740
485082
468740
459588
494239
499664
486832
519533
532366
570521
595842
592339
590389
604999
603222
581432
614128
625040
614128
659491
681309
732102
752143
746712
735800
744935
755841
719441
748461
766753
759373
806657
822993
892101
904761
888424
897554
903007
908460
873809
906511
924624
906511
959275
975618
1046468
1057380
1060884
1079170
1079170
1086378
1053676
1070041
1080925
1060884
1119079
1129986
1202597
1215430
1233543
1249908
1251657
1253584
1220883
1253584




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123395&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123395&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123395&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.972370526401543
beta0.0390650774281997
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.972370526401543 \tabularnewline
beta & 0.0390650774281997 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123395&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.972370526401543[/C][/ROW]
[ROW][C]beta[/C][C]0.0390650774281997[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123395&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123395&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.972370526401543
beta0.0390650774281997
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3188996189018-22
4185320187240.772162361-1920.7721623613
5221698183544.27230512738153.7276948735
6219771220264.332164351-493.332164351217
7192528219386.390502042-26858.3905020423
8174414191851.607618071-17437.6076180714
9176163172814.9360929713348.0639070287
10176163174116.8175816122046.18241838805
11178112174230.5136145073881.48638549261
12181616176276.2462254645339.75377453625
13192528179942.78950976612585.2104902345
14188996191132.659761182-2136.659761182
15194449187926.2547060316522.74529396897
16203412193387.77114364310024.2288563573
17254400202634.80464582151765.1953541785
18254400254435.862443084-35.8624430840719
19243516255865.736140789-12349.736140789
20232604244852.8482476-12248.8482476
21241567233472.7793270658094.22067293472
22252473242181.17592166910291.8240783307
23254400253417.399746046982.600253953598
24259853255638.9334877734214.06651222677
25276217261162.72416843215054.2758315682
26265306277799.062546861-12493.0625468611
27265306267174.622905732-1868.62290573213
28281670266810.09422618214859.9057738181
29327033283276.35815179443756.6418482058
30330709329503.0845240441205.91547595628
31321580334400.546274496-12820.5462744962
32299762325172.092221121-25410.0922211211
33316121302736.71384855413384.2861514462
34316121318532.257474231-2411.25747423066
35317876318877.086654667-1001.08665466739
36327033320555.0973699666477.90263003448
37334241329751.5246926224489.47530737834
38337917337184.999889267732.000110733323
39337917340992.622509504-3075.62250950438
40348823340980.9953522347842.00464776577
41390681351883.23133138138797.7686686191
42401565394359.7014281237205.29857187672
43403314406390.283271991-3076.28327199141
44376071408306.503100623-32235.5031006226
45390681380644.66788096910036.3321190309
46385228394467.956726897-9239.95672689739
47374317389196.563940101-14879.5639401009
48397889377876.17222180420012.827778196
49403314401244.315676612069.68432339031
50394185407243.69375466-13058.6937546598
51396112398036.638863507-1924.63886350719
52408773399582.9019758199190.09802418121
53456085412285.90022775343799.0997722468
54479624460305.41250161919318.5874983806
55479624485254.626815984-5630.6268159835
56468740485730.077004769-16990.0770047691
57485082474514.55215772310567.4478422774
58468740490496.564472021-21756.5644720208
59459588474221.220935208-14633.2209352084
60494239464316.55312497329922.4468750272
61499664498873.129462573790.87053742673
62486832505133.061376497-18301.0613764971
63519533492133.38223087527399.6177691253
64532366524612.4910030067753.50899699354
65570521538282.82534519732238.174654803
66595842576985.91751683318856.0824831666
67592339603392.919735412-11053.9197354118
68590389600296.426142604-9907.42614260351
69604999597938.4083146667060.59168533445
70603222612347.792642783-9125.79264278326
71581432610671.364026754-29239.3640267539
72614128588326.41283182925801.5871681712
73625040620481.7524451884558.24755481223
74614128632153.843096625-18025.8430966253
75659491621181.10482588638309.895174114
76681309666442.80736337314866.1926366274
77732102689473.2477018642628.7522981402
78752143741118.46706355611024.5329364442
79746712762451.449938438-15739.4499384377
80735800757162.050202489-21362.050202489
81744935745593.946618878-658.94661887805
82755841754131.9001967241709.09980327648
83719441765037.393724127-45596.3937241269
84748461728212.40731205920248.5926879412
85766753756182.30257115110570.6974288487
86759373775143.233380117-15770.2333801172
87806657767891.97560678238765.0243932185
88822993815141.7128882237851.28711177665
89892101832630.08004788859470.9199521123
90904761902570.9030675342190.09693246579
91888424916896.734485391-28472.7344853909
92897554900325.374774749-2771.37477474904
93903007908639.987041526-5632.98704152636
94908460913958.078757795-5498.07875779516
95873809919198.502778254-45389.5027782538
96906511883925.52843207622585.4715679241
97924624915607.3412957289016.65870427166
98906511934437.744814673-27926.744814673
99959275916284.65382124342990.3461787571
100975618968722.2716063346895.72839366633
1011046468986324.48617171860143.5138282821
10210573801057987.87316156-607.873161560856
10310608841070555.31149874-9671.31149873626
10410791701073942.357702595227.64229741204
10510791701092015.28326037-12845.2832603701
10610863781092026.69121946-5648.69121946278
10710536761098821.2835107-45145.2835107029
10810700411065495.677018824545.32298117899
10910809251080660.40912975264.590870253742
11010608841091672.73418192-30788.7341819194
11111190791071320.1886659147758.8113340901
11211299861129159.11463867826.885361333843
11312025971141394.2288922561202.7711077486
11412154301214661.90688364768.093116362346
11512335431229193.861801294349.13819870981
11612499081247373.124599662534.87540034135
11712516571263884.54081804-12227.5408180414
11812535841265576.94654431-11992.9465443073
11912208831267041.90399984-46158.9039998443
12012535841233531.5117593820052.4882406183

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 188996 & 189018 & -22 \tabularnewline
4 & 185320 & 187240.772162361 & -1920.7721623613 \tabularnewline
5 & 221698 & 183544.272305127 & 38153.7276948735 \tabularnewline
6 & 219771 & 220264.332164351 & -493.332164351217 \tabularnewline
7 & 192528 & 219386.390502042 & -26858.3905020423 \tabularnewline
8 & 174414 & 191851.607618071 & -17437.6076180714 \tabularnewline
9 & 176163 & 172814.936092971 & 3348.0639070287 \tabularnewline
10 & 176163 & 174116.817581612 & 2046.18241838805 \tabularnewline
11 & 178112 & 174230.513614507 & 3881.48638549261 \tabularnewline
12 & 181616 & 176276.246225464 & 5339.75377453625 \tabularnewline
13 & 192528 & 179942.789509766 & 12585.2104902345 \tabularnewline
14 & 188996 & 191132.659761182 & -2136.659761182 \tabularnewline
15 & 194449 & 187926.254706031 & 6522.74529396897 \tabularnewline
16 & 203412 & 193387.771143643 & 10024.2288563573 \tabularnewline
17 & 254400 & 202634.804645821 & 51765.1953541785 \tabularnewline
18 & 254400 & 254435.862443084 & -35.8624430840719 \tabularnewline
19 & 243516 & 255865.736140789 & -12349.736140789 \tabularnewline
20 & 232604 & 244852.8482476 & -12248.8482476 \tabularnewline
21 & 241567 & 233472.779327065 & 8094.22067293472 \tabularnewline
22 & 252473 & 242181.175921669 & 10291.8240783307 \tabularnewline
23 & 254400 & 253417.399746046 & 982.600253953598 \tabularnewline
24 & 259853 & 255638.933487773 & 4214.06651222677 \tabularnewline
25 & 276217 & 261162.724168432 & 15054.2758315682 \tabularnewline
26 & 265306 & 277799.062546861 & -12493.0625468611 \tabularnewline
27 & 265306 & 267174.622905732 & -1868.62290573213 \tabularnewline
28 & 281670 & 266810.094226182 & 14859.9057738181 \tabularnewline
29 & 327033 & 283276.358151794 & 43756.6418482058 \tabularnewline
30 & 330709 & 329503.084524044 & 1205.91547595628 \tabularnewline
31 & 321580 & 334400.546274496 & -12820.5462744962 \tabularnewline
32 & 299762 & 325172.092221121 & -25410.0922211211 \tabularnewline
33 & 316121 & 302736.713848554 & 13384.2861514462 \tabularnewline
34 & 316121 & 318532.257474231 & -2411.25747423066 \tabularnewline
35 & 317876 & 318877.086654667 & -1001.08665466739 \tabularnewline
36 & 327033 & 320555.097369966 & 6477.90263003448 \tabularnewline
37 & 334241 & 329751.524692622 & 4489.47530737834 \tabularnewline
38 & 337917 & 337184.999889267 & 732.000110733323 \tabularnewline
39 & 337917 & 340992.622509504 & -3075.62250950438 \tabularnewline
40 & 348823 & 340980.995352234 & 7842.00464776577 \tabularnewline
41 & 390681 & 351883.231331381 & 38797.7686686191 \tabularnewline
42 & 401565 & 394359.701428123 & 7205.29857187672 \tabularnewline
43 & 403314 & 406390.283271991 & -3076.28327199141 \tabularnewline
44 & 376071 & 408306.503100623 & -32235.5031006226 \tabularnewline
45 & 390681 & 380644.667880969 & 10036.3321190309 \tabularnewline
46 & 385228 & 394467.956726897 & -9239.95672689739 \tabularnewline
47 & 374317 & 389196.563940101 & -14879.5639401009 \tabularnewline
48 & 397889 & 377876.172221804 & 20012.827778196 \tabularnewline
49 & 403314 & 401244.31567661 & 2069.68432339031 \tabularnewline
50 & 394185 & 407243.69375466 & -13058.6937546598 \tabularnewline
51 & 396112 & 398036.638863507 & -1924.63886350719 \tabularnewline
52 & 408773 & 399582.901975819 & 9190.09802418121 \tabularnewline
53 & 456085 & 412285.900227753 & 43799.0997722468 \tabularnewline
54 & 479624 & 460305.412501619 & 19318.5874983806 \tabularnewline
55 & 479624 & 485254.626815984 & -5630.6268159835 \tabularnewline
56 & 468740 & 485730.077004769 & -16990.0770047691 \tabularnewline
57 & 485082 & 474514.552157723 & 10567.4478422774 \tabularnewline
58 & 468740 & 490496.564472021 & -21756.5644720208 \tabularnewline
59 & 459588 & 474221.220935208 & -14633.2209352084 \tabularnewline
60 & 494239 & 464316.553124973 & 29922.4468750272 \tabularnewline
61 & 499664 & 498873.129462573 & 790.87053742673 \tabularnewline
62 & 486832 & 505133.061376497 & -18301.0613764971 \tabularnewline
63 & 519533 & 492133.382230875 & 27399.6177691253 \tabularnewline
64 & 532366 & 524612.491003006 & 7753.50899699354 \tabularnewline
65 & 570521 & 538282.825345197 & 32238.174654803 \tabularnewline
66 & 595842 & 576985.917516833 & 18856.0824831666 \tabularnewline
67 & 592339 & 603392.919735412 & -11053.9197354118 \tabularnewline
68 & 590389 & 600296.426142604 & -9907.42614260351 \tabularnewline
69 & 604999 & 597938.408314666 & 7060.59168533445 \tabularnewline
70 & 603222 & 612347.792642783 & -9125.79264278326 \tabularnewline
71 & 581432 & 610671.364026754 & -29239.3640267539 \tabularnewline
72 & 614128 & 588326.412831829 & 25801.5871681712 \tabularnewline
73 & 625040 & 620481.752445188 & 4558.24755481223 \tabularnewline
74 & 614128 & 632153.843096625 & -18025.8430966253 \tabularnewline
75 & 659491 & 621181.104825886 & 38309.895174114 \tabularnewline
76 & 681309 & 666442.807363373 & 14866.1926366274 \tabularnewline
77 & 732102 & 689473.24770186 & 42628.7522981402 \tabularnewline
78 & 752143 & 741118.467063556 & 11024.5329364442 \tabularnewline
79 & 746712 & 762451.449938438 & -15739.4499384377 \tabularnewline
80 & 735800 & 757162.050202489 & -21362.050202489 \tabularnewline
81 & 744935 & 745593.946618878 & -658.94661887805 \tabularnewline
82 & 755841 & 754131.900196724 & 1709.09980327648 \tabularnewline
83 & 719441 & 765037.393724127 & -45596.3937241269 \tabularnewline
84 & 748461 & 728212.407312059 & 20248.5926879412 \tabularnewline
85 & 766753 & 756182.302571151 & 10570.6974288487 \tabularnewline
86 & 759373 & 775143.233380117 & -15770.2333801172 \tabularnewline
87 & 806657 & 767891.975606782 & 38765.0243932185 \tabularnewline
88 & 822993 & 815141.712888223 & 7851.28711177665 \tabularnewline
89 & 892101 & 832630.080047888 & 59470.9199521123 \tabularnewline
90 & 904761 & 902570.903067534 & 2190.09693246579 \tabularnewline
91 & 888424 & 916896.734485391 & -28472.7344853909 \tabularnewline
92 & 897554 & 900325.374774749 & -2771.37477474904 \tabularnewline
93 & 903007 & 908639.987041526 & -5632.98704152636 \tabularnewline
94 & 908460 & 913958.078757795 & -5498.07875779516 \tabularnewline
95 & 873809 & 919198.502778254 & -45389.5027782538 \tabularnewline
96 & 906511 & 883925.528432076 & 22585.4715679241 \tabularnewline
97 & 924624 & 915607.341295728 & 9016.65870427166 \tabularnewline
98 & 906511 & 934437.744814673 & -27926.744814673 \tabularnewline
99 & 959275 & 916284.653821243 & 42990.3461787571 \tabularnewline
100 & 975618 & 968722.271606334 & 6895.72839366633 \tabularnewline
101 & 1046468 & 986324.486171718 & 60143.5138282821 \tabularnewline
102 & 1057380 & 1057987.87316156 & -607.873161560856 \tabularnewline
103 & 1060884 & 1070555.31149874 & -9671.31149873626 \tabularnewline
104 & 1079170 & 1073942.35770259 & 5227.64229741204 \tabularnewline
105 & 1079170 & 1092015.28326037 & -12845.2832603701 \tabularnewline
106 & 1086378 & 1092026.69121946 & -5648.69121946278 \tabularnewline
107 & 1053676 & 1098821.2835107 & -45145.2835107029 \tabularnewline
108 & 1070041 & 1065495.67701882 & 4545.32298117899 \tabularnewline
109 & 1080925 & 1080660.40912975 & 264.590870253742 \tabularnewline
110 & 1060884 & 1091672.73418192 & -30788.7341819194 \tabularnewline
111 & 1119079 & 1071320.18866591 & 47758.8113340901 \tabularnewline
112 & 1129986 & 1129159.11463867 & 826.885361333843 \tabularnewline
113 & 1202597 & 1141394.22889225 & 61202.7711077486 \tabularnewline
114 & 1215430 & 1214661.90688364 & 768.093116362346 \tabularnewline
115 & 1233543 & 1229193.86180129 & 4349.13819870981 \tabularnewline
116 & 1249908 & 1247373.12459966 & 2534.87540034135 \tabularnewline
117 & 1251657 & 1263884.54081804 & -12227.5408180414 \tabularnewline
118 & 1253584 & 1265576.94654431 & -11992.9465443073 \tabularnewline
119 & 1220883 & 1267041.90399984 & -46158.9039998443 \tabularnewline
120 & 1253584 & 1233531.51175938 & 20052.4882406183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123395&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]188996[/C][C]189018[/C][C]-22[/C][/ROW]
[ROW][C]4[/C][C]185320[/C][C]187240.772162361[/C][C]-1920.7721623613[/C][/ROW]
[ROW][C]5[/C][C]221698[/C][C]183544.272305127[/C][C]38153.7276948735[/C][/ROW]
[ROW][C]6[/C][C]219771[/C][C]220264.332164351[/C][C]-493.332164351217[/C][/ROW]
[ROW][C]7[/C][C]192528[/C][C]219386.390502042[/C][C]-26858.3905020423[/C][/ROW]
[ROW][C]8[/C][C]174414[/C][C]191851.607618071[/C][C]-17437.6076180714[/C][/ROW]
[ROW][C]9[/C][C]176163[/C][C]172814.936092971[/C][C]3348.0639070287[/C][/ROW]
[ROW][C]10[/C][C]176163[/C][C]174116.817581612[/C][C]2046.18241838805[/C][/ROW]
[ROW][C]11[/C][C]178112[/C][C]174230.513614507[/C][C]3881.48638549261[/C][/ROW]
[ROW][C]12[/C][C]181616[/C][C]176276.246225464[/C][C]5339.75377453625[/C][/ROW]
[ROW][C]13[/C][C]192528[/C][C]179942.789509766[/C][C]12585.2104902345[/C][/ROW]
[ROW][C]14[/C][C]188996[/C][C]191132.659761182[/C][C]-2136.659761182[/C][/ROW]
[ROW][C]15[/C][C]194449[/C][C]187926.254706031[/C][C]6522.74529396897[/C][/ROW]
[ROW][C]16[/C][C]203412[/C][C]193387.771143643[/C][C]10024.2288563573[/C][/ROW]
[ROW][C]17[/C][C]254400[/C][C]202634.804645821[/C][C]51765.1953541785[/C][/ROW]
[ROW][C]18[/C][C]254400[/C][C]254435.862443084[/C][C]-35.8624430840719[/C][/ROW]
[ROW][C]19[/C][C]243516[/C][C]255865.736140789[/C][C]-12349.736140789[/C][/ROW]
[ROW][C]20[/C][C]232604[/C][C]244852.8482476[/C][C]-12248.8482476[/C][/ROW]
[ROW][C]21[/C][C]241567[/C][C]233472.779327065[/C][C]8094.22067293472[/C][/ROW]
[ROW][C]22[/C][C]252473[/C][C]242181.175921669[/C][C]10291.8240783307[/C][/ROW]
[ROW][C]23[/C][C]254400[/C][C]253417.399746046[/C][C]982.600253953598[/C][/ROW]
[ROW][C]24[/C][C]259853[/C][C]255638.933487773[/C][C]4214.06651222677[/C][/ROW]
[ROW][C]25[/C][C]276217[/C][C]261162.724168432[/C][C]15054.2758315682[/C][/ROW]
[ROW][C]26[/C][C]265306[/C][C]277799.062546861[/C][C]-12493.0625468611[/C][/ROW]
[ROW][C]27[/C][C]265306[/C][C]267174.622905732[/C][C]-1868.62290573213[/C][/ROW]
[ROW][C]28[/C][C]281670[/C][C]266810.094226182[/C][C]14859.9057738181[/C][/ROW]
[ROW][C]29[/C][C]327033[/C][C]283276.358151794[/C][C]43756.6418482058[/C][/ROW]
[ROW][C]30[/C][C]330709[/C][C]329503.084524044[/C][C]1205.91547595628[/C][/ROW]
[ROW][C]31[/C][C]321580[/C][C]334400.546274496[/C][C]-12820.5462744962[/C][/ROW]
[ROW][C]32[/C][C]299762[/C][C]325172.092221121[/C][C]-25410.0922211211[/C][/ROW]
[ROW][C]33[/C][C]316121[/C][C]302736.713848554[/C][C]13384.2861514462[/C][/ROW]
[ROW][C]34[/C][C]316121[/C][C]318532.257474231[/C][C]-2411.25747423066[/C][/ROW]
[ROW][C]35[/C][C]317876[/C][C]318877.086654667[/C][C]-1001.08665466739[/C][/ROW]
[ROW][C]36[/C][C]327033[/C][C]320555.097369966[/C][C]6477.90263003448[/C][/ROW]
[ROW][C]37[/C][C]334241[/C][C]329751.524692622[/C][C]4489.47530737834[/C][/ROW]
[ROW][C]38[/C][C]337917[/C][C]337184.999889267[/C][C]732.000110733323[/C][/ROW]
[ROW][C]39[/C][C]337917[/C][C]340992.622509504[/C][C]-3075.62250950438[/C][/ROW]
[ROW][C]40[/C][C]348823[/C][C]340980.995352234[/C][C]7842.00464776577[/C][/ROW]
[ROW][C]41[/C][C]390681[/C][C]351883.231331381[/C][C]38797.7686686191[/C][/ROW]
[ROW][C]42[/C][C]401565[/C][C]394359.701428123[/C][C]7205.29857187672[/C][/ROW]
[ROW][C]43[/C][C]403314[/C][C]406390.283271991[/C][C]-3076.28327199141[/C][/ROW]
[ROW][C]44[/C][C]376071[/C][C]408306.503100623[/C][C]-32235.5031006226[/C][/ROW]
[ROW][C]45[/C][C]390681[/C][C]380644.667880969[/C][C]10036.3321190309[/C][/ROW]
[ROW][C]46[/C][C]385228[/C][C]394467.956726897[/C][C]-9239.95672689739[/C][/ROW]
[ROW][C]47[/C][C]374317[/C][C]389196.563940101[/C][C]-14879.5639401009[/C][/ROW]
[ROW][C]48[/C][C]397889[/C][C]377876.172221804[/C][C]20012.827778196[/C][/ROW]
[ROW][C]49[/C][C]403314[/C][C]401244.31567661[/C][C]2069.68432339031[/C][/ROW]
[ROW][C]50[/C][C]394185[/C][C]407243.69375466[/C][C]-13058.6937546598[/C][/ROW]
[ROW][C]51[/C][C]396112[/C][C]398036.638863507[/C][C]-1924.63886350719[/C][/ROW]
[ROW][C]52[/C][C]408773[/C][C]399582.901975819[/C][C]9190.09802418121[/C][/ROW]
[ROW][C]53[/C][C]456085[/C][C]412285.900227753[/C][C]43799.0997722468[/C][/ROW]
[ROW][C]54[/C][C]479624[/C][C]460305.412501619[/C][C]19318.5874983806[/C][/ROW]
[ROW][C]55[/C][C]479624[/C][C]485254.626815984[/C][C]-5630.6268159835[/C][/ROW]
[ROW][C]56[/C][C]468740[/C][C]485730.077004769[/C][C]-16990.0770047691[/C][/ROW]
[ROW][C]57[/C][C]485082[/C][C]474514.552157723[/C][C]10567.4478422774[/C][/ROW]
[ROW][C]58[/C][C]468740[/C][C]490496.564472021[/C][C]-21756.5644720208[/C][/ROW]
[ROW][C]59[/C][C]459588[/C][C]474221.220935208[/C][C]-14633.2209352084[/C][/ROW]
[ROW][C]60[/C][C]494239[/C][C]464316.553124973[/C][C]29922.4468750272[/C][/ROW]
[ROW][C]61[/C][C]499664[/C][C]498873.129462573[/C][C]790.87053742673[/C][/ROW]
[ROW][C]62[/C][C]486832[/C][C]505133.061376497[/C][C]-18301.0613764971[/C][/ROW]
[ROW][C]63[/C][C]519533[/C][C]492133.382230875[/C][C]27399.6177691253[/C][/ROW]
[ROW][C]64[/C][C]532366[/C][C]524612.491003006[/C][C]7753.50899699354[/C][/ROW]
[ROW][C]65[/C][C]570521[/C][C]538282.825345197[/C][C]32238.174654803[/C][/ROW]
[ROW][C]66[/C][C]595842[/C][C]576985.917516833[/C][C]18856.0824831666[/C][/ROW]
[ROW][C]67[/C][C]592339[/C][C]603392.919735412[/C][C]-11053.9197354118[/C][/ROW]
[ROW][C]68[/C][C]590389[/C][C]600296.426142604[/C][C]-9907.42614260351[/C][/ROW]
[ROW][C]69[/C][C]604999[/C][C]597938.408314666[/C][C]7060.59168533445[/C][/ROW]
[ROW][C]70[/C][C]603222[/C][C]612347.792642783[/C][C]-9125.79264278326[/C][/ROW]
[ROW][C]71[/C][C]581432[/C][C]610671.364026754[/C][C]-29239.3640267539[/C][/ROW]
[ROW][C]72[/C][C]614128[/C][C]588326.412831829[/C][C]25801.5871681712[/C][/ROW]
[ROW][C]73[/C][C]625040[/C][C]620481.752445188[/C][C]4558.24755481223[/C][/ROW]
[ROW][C]74[/C][C]614128[/C][C]632153.843096625[/C][C]-18025.8430966253[/C][/ROW]
[ROW][C]75[/C][C]659491[/C][C]621181.104825886[/C][C]38309.895174114[/C][/ROW]
[ROW][C]76[/C][C]681309[/C][C]666442.807363373[/C][C]14866.1926366274[/C][/ROW]
[ROW][C]77[/C][C]732102[/C][C]689473.24770186[/C][C]42628.7522981402[/C][/ROW]
[ROW][C]78[/C][C]752143[/C][C]741118.467063556[/C][C]11024.5329364442[/C][/ROW]
[ROW][C]79[/C][C]746712[/C][C]762451.449938438[/C][C]-15739.4499384377[/C][/ROW]
[ROW][C]80[/C][C]735800[/C][C]757162.050202489[/C][C]-21362.050202489[/C][/ROW]
[ROW][C]81[/C][C]744935[/C][C]745593.946618878[/C][C]-658.94661887805[/C][/ROW]
[ROW][C]82[/C][C]755841[/C][C]754131.900196724[/C][C]1709.09980327648[/C][/ROW]
[ROW][C]83[/C][C]719441[/C][C]765037.393724127[/C][C]-45596.3937241269[/C][/ROW]
[ROW][C]84[/C][C]748461[/C][C]728212.407312059[/C][C]20248.5926879412[/C][/ROW]
[ROW][C]85[/C][C]766753[/C][C]756182.302571151[/C][C]10570.6974288487[/C][/ROW]
[ROW][C]86[/C][C]759373[/C][C]775143.233380117[/C][C]-15770.2333801172[/C][/ROW]
[ROW][C]87[/C][C]806657[/C][C]767891.975606782[/C][C]38765.0243932185[/C][/ROW]
[ROW][C]88[/C][C]822993[/C][C]815141.712888223[/C][C]7851.28711177665[/C][/ROW]
[ROW][C]89[/C][C]892101[/C][C]832630.080047888[/C][C]59470.9199521123[/C][/ROW]
[ROW][C]90[/C][C]904761[/C][C]902570.903067534[/C][C]2190.09693246579[/C][/ROW]
[ROW][C]91[/C][C]888424[/C][C]916896.734485391[/C][C]-28472.7344853909[/C][/ROW]
[ROW][C]92[/C][C]897554[/C][C]900325.374774749[/C][C]-2771.37477474904[/C][/ROW]
[ROW][C]93[/C][C]903007[/C][C]908639.987041526[/C][C]-5632.98704152636[/C][/ROW]
[ROW][C]94[/C][C]908460[/C][C]913958.078757795[/C][C]-5498.07875779516[/C][/ROW]
[ROW][C]95[/C][C]873809[/C][C]919198.502778254[/C][C]-45389.5027782538[/C][/ROW]
[ROW][C]96[/C][C]906511[/C][C]883925.528432076[/C][C]22585.4715679241[/C][/ROW]
[ROW][C]97[/C][C]924624[/C][C]915607.341295728[/C][C]9016.65870427166[/C][/ROW]
[ROW][C]98[/C][C]906511[/C][C]934437.744814673[/C][C]-27926.744814673[/C][/ROW]
[ROW][C]99[/C][C]959275[/C][C]916284.653821243[/C][C]42990.3461787571[/C][/ROW]
[ROW][C]100[/C][C]975618[/C][C]968722.271606334[/C][C]6895.72839366633[/C][/ROW]
[ROW][C]101[/C][C]1046468[/C][C]986324.486171718[/C][C]60143.5138282821[/C][/ROW]
[ROW][C]102[/C][C]1057380[/C][C]1057987.87316156[/C][C]-607.873161560856[/C][/ROW]
[ROW][C]103[/C][C]1060884[/C][C]1070555.31149874[/C][C]-9671.31149873626[/C][/ROW]
[ROW][C]104[/C][C]1079170[/C][C]1073942.35770259[/C][C]5227.64229741204[/C][/ROW]
[ROW][C]105[/C][C]1079170[/C][C]1092015.28326037[/C][C]-12845.2832603701[/C][/ROW]
[ROW][C]106[/C][C]1086378[/C][C]1092026.69121946[/C][C]-5648.69121946278[/C][/ROW]
[ROW][C]107[/C][C]1053676[/C][C]1098821.2835107[/C][C]-45145.2835107029[/C][/ROW]
[ROW][C]108[/C][C]1070041[/C][C]1065495.67701882[/C][C]4545.32298117899[/C][/ROW]
[ROW][C]109[/C][C]1080925[/C][C]1080660.40912975[/C][C]264.590870253742[/C][/ROW]
[ROW][C]110[/C][C]1060884[/C][C]1091672.73418192[/C][C]-30788.7341819194[/C][/ROW]
[ROW][C]111[/C][C]1119079[/C][C]1071320.18866591[/C][C]47758.8113340901[/C][/ROW]
[ROW][C]112[/C][C]1129986[/C][C]1129159.11463867[/C][C]826.885361333843[/C][/ROW]
[ROW][C]113[/C][C]1202597[/C][C]1141394.22889225[/C][C]61202.7711077486[/C][/ROW]
[ROW][C]114[/C][C]1215430[/C][C]1214661.90688364[/C][C]768.093116362346[/C][/ROW]
[ROW][C]115[/C][C]1233543[/C][C]1229193.86180129[/C][C]4349.13819870981[/C][/ROW]
[ROW][C]116[/C][C]1249908[/C][C]1247373.12459966[/C][C]2534.87540034135[/C][/ROW]
[ROW][C]117[/C][C]1251657[/C][C]1263884.54081804[/C][C]-12227.5408180414[/C][/ROW]
[ROW][C]118[/C][C]1253584[/C][C]1265576.94654431[/C][C]-11992.9465443073[/C][/ROW]
[ROW][C]119[/C][C]1220883[/C][C]1267041.90399984[/C][C]-46158.9039998443[/C][/ROW]
[ROW][C]120[/C][C]1253584[/C][C]1233531.51175938[/C][C]20052.4882406183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123395&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123395&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3188996189018-22
4185320187240.772162361-1920.7721623613
5221698183544.27230512738153.7276948735
6219771220264.332164351-493.332164351217
7192528219386.390502042-26858.3905020423
8174414191851.607618071-17437.6076180714
9176163172814.9360929713348.0639070287
10176163174116.8175816122046.18241838805
11178112174230.5136145073881.48638549261
12181616176276.2462254645339.75377453625
13192528179942.78950976612585.2104902345
14188996191132.659761182-2136.659761182
15194449187926.2547060316522.74529396897
16203412193387.77114364310024.2288563573
17254400202634.80464582151765.1953541785
18254400254435.862443084-35.8624430840719
19243516255865.736140789-12349.736140789
20232604244852.8482476-12248.8482476
21241567233472.7793270658094.22067293472
22252473242181.17592166910291.8240783307
23254400253417.399746046982.600253953598
24259853255638.9334877734214.06651222677
25276217261162.72416843215054.2758315682
26265306277799.062546861-12493.0625468611
27265306267174.622905732-1868.62290573213
28281670266810.09422618214859.9057738181
29327033283276.35815179443756.6418482058
30330709329503.0845240441205.91547595628
31321580334400.546274496-12820.5462744962
32299762325172.092221121-25410.0922211211
33316121302736.71384855413384.2861514462
34316121318532.257474231-2411.25747423066
35317876318877.086654667-1001.08665466739
36327033320555.0973699666477.90263003448
37334241329751.5246926224489.47530737834
38337917337184.999889267732.000110733323
39337917340992.622509504-3075.62250950438
40348823340980.9953522347842.00464776577
41390681351883.23133138138797.7686686191
42401565394359.7014281237205.29857187672
43403314406390.283271991-3076.28327199141
44376071408306.503100623-32235.5031006226
45390681380644.66788096910036.3321190309
46385228394467.956726897-9239.95672689739
47374317389196.563940101-14879.5639401009
48397889377876.17222180420012.827778196
49403314401244.315676612069.68432339031
50394185407243.69375466-13058.6937546598
51396112398036.638863507-1924.63886350719
52408773399582.9019758199190.09802418121
53456085412285.90022775343799.0997722468
54479624460305.41250161919318.5874983806
55479624485254.626815984-5630.6268159835
56468740485730.077004769-16990.0770047691
57485082474514.55215772310567.4478422774
58468740490496.564472021-21756.5644720208
59459588474221.220935208-14633.2209352084
60494239464316.55312497329922.4468750272
61499664498873.129462573790.87053742673
62486832505133.061376497-18301.0613764971
63519533492133.38223087527399.6177691253
64532366524612.4910030067753.50899699354
65570521538282.82534519732238.174654803
66595842576985.91751683318856.0824831666
67592339603392.919735412-11053.9197354118
68590389600296.426142604-9907.42614260351
69604999597938.4083146667060.59168533445
70603222612347.792642783-9125.79264278326
71581432610671.364026754-29239.3640267539
72614128588326.41283182925801.5871681712
73625040620481.7524451884558.24755481223
74614128632153.843096625-18025.8430966253
75659491621181.10482588638309.895174114
76681309666442.80736337314866.1926366274
77732102689473.2477018642628.7522981402
78752143741118.46706355611024.5329364442
79746712762451.449938438-15739.4499384377
80735800757162.050202489-21362.050202489
81744935745593.946618878-658.94661887805
82755841754131.9001967241709.09980327648
83719441765037.393724127-45596.3937241269
84748461728212.40731205920248.5926879412
85766753756182.30257115110570.6974288487
86759373775143.233380117-15770.2333801172
87806657767891.97560678238765.0243932185
88822993815141.7128882237851.28711177665
89892101832630.08004788859470.9199521123
90904761902570.9030675342190.09693246579
91888424916896.734485391-28472.7344853909
92897554900325.374774749-2771.37477474904
93903007908639.987041526-5632.98704152636
94908460913958.078757795-5498.07875779516
95873809919198.502778254-45389.5027782538
96906511883925.52843207622585.4715679241
97924624915607.3412957289016.65870427166
98906511934437.744814673-27926.744814673
99959275916284.65382124342990.3461787571
100975618968722.2716063346895.72839366633
1011046468986324.48617171860143.5138282821
10210573801057987.87316156-607.873161560856
10310608841070555.31149874-9671.31149873626
10410791701073942.357702595227.64229741204
10510791701092015.28326037-12845.2832603701
10610863781092026.69121946-5648.69121946278
10710536761098821.2835107-45145.2835107029
10810700411065495.677018824545.32298117899
10910809251080660.40912975264.590870253742
11010608841091672.73418192-30788.7341819194
11111190791071320.1886659147758.8113340901
11211299861129159.11463867826.885361333843
11312025971141394.2288922561202.7711077486
11412154301214661.90688364768.093116362346
11512335431229193.861801294349.13819870981
11612499081247373.124599662534.87540034135
11712516571263884.54081804-12227.5408180414
11812535841265576.94654431-11992.9465443073
11912208831267041.90399984-46158.9039998443
12012535841233531.5117593820052.4882406183







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1211265164.834247741222436.616543261307893.05195223
1221277299.708189911216559.179438691338040.23694114
1231289434.582132091213963.428880331364905.73538384
1241301569.456074261212966.867665591390172.04448292
1251313704.330016431212916.177956411414492.48207644
1261325839.20395861213479.680970921438198.72694628
1271337974.077900771214463.26959741461484.88620414
1281350108.951842941215742.689913581484475.21377231
1291362243.825785111217233.313058031507254.33851219
1301374378.699727281218874.816170471529882.5832841
1311386513.573669461220622.681790161552404.46554875
1321398648.447611631222443.146649531574853.74857372

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 1265164.83424774 & 1222436.61654326 & 1307893.05195223 \tabularnewline
122 & 1277299.70818991 & 1216559.17943869 & 1338040.23694114 \tabularnewline
123 & 1289434.58213209 & 1213963.42888033 & 1364905.73538384 \tabularnewline
124 & 1301569.45607426 & 1212966.86766559 & 1390172.04448292 \tabularnewline
125 & 1313704.33001643 & 1212916.17795641 & 1414492.48207644 \tabularnewline
126 & 1325839.2039586 & 1213479.68097092 & 1438198.72694628 \tabularnewline
127 & 1337974.07790077 & 1214463.2695974 & 1461484.88620414 \tabularnewline
128 & 1350108.95184294 & 1215742.68991358 & 1484475.21377231 \tabularnewline
129 & 1362243.82578511 & 1217233.31305803 & 1507254.33851219 \tabularnewline
130 & 1374378.69972728 & 1218874.81617047 & 1529882.5832841 \tabularnewline
131 & 1386513.57366946 & 1220622.68179016 & 1552404.46554875 \tabularnewline
132 & 1398648.44761163 & 1222443.14664953 & 1574853.74857372 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123395&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]121[/C][C]1265164.83424774[/C][C]1222436.61654326[/C][C]1307893.05195223[/C][/ROW]
[ROW][C]122[/C][C]1277299.70818991[/C][C]1216559.17943869[/C][C]1338040.23694114[/C][/ROW]
[ROW][C]123[/C][C]1289434.58213209[/C][C]1213963.42888033[/C][C]1364905.73538384[/C][/ROW]
[ROW][C]124[/C][C]1301569.45607426[/C][C]1212966.86766559[/C][C]1390172.04448292[/C][/ROW]
[ROW][C]125[/C][C]1313704.33001643[/C][C]1212916.17795641[/C][C]1414492.48207644[/C][/ROW]
[ROW][C]126[/C][C]1325839.2039586[/C][C]1213479.68097092[/C][C]1438198.72694628[/C][/ROW]
[ROW][C]127[/C][C]1337974.07790077[/C][C]1214463.2695974[/C][C]1461484.88620414[/C][/ROW]
[ROW][C]128[/C][C]1350108.95184294[/C][C]1215742.68991358[/C][C]1484475.21377231[/C][/ROW]
[ROW][C]129[/C][C]1362243.82578511[/C][C]1217233.31305803[/C][C]1507254.33851219[/C][/ROW]
[ROW][C]130[/C][C]1374378.69972728[/C][C]1218874.81617047[/C][C]1529882.5832841[/C][/ROW]
[ROW][C]131[/C][C]1386513.57366946[/C][C]1220622.68179016[/C][C]1552404.46554875[/C][/ROW]
[ROW][C]132[/C][C]1398648.44761163[/C][C]1222443.14664953[/C][C]1574853.74857372[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123395&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123395&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1211265164.834247741222436.616543261307893.05195223
1221277299.708189911216559.179438691338040.23694114
1231289434.582132091213963.428880331364905.73538384
1241301569.456074261212966.867665591390172.04448292
1251313704.330016431212916.177956411414492.48207644
1261325839.20395861213479.680970921438198.72694628
1271337974.077900771214463.26959741461484.88620414
1281350108.951842941215742.689913581484475.21377231
1291362243.825785111217233.313058031507254.33851219
1301374378.699727281218874.816170471529882.5832841
1311386513.573669461220622.681790161552404.46554875
1321398648.447611631222443.146649531574853.74857372



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')