Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 09 Aug 2011 12:25:58 -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/09/t1312907271phb5cveb0il2ow4.htm/, Retrieved Tue, 14 May 2024 15:43:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123507, Retrieved Tue, 14 May 2024 15:43:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Boxel Dieter
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [TIJDREEKS A - STA...] [2010-08-19 19:40:26] [166e4c1abdecfa2d7f2760a70ccac6ef]
- RMPD    [Exponential Smoothing] [Tijdreeks A - sta...] [2011-08-09 16:25:58] [f91e4cd4d3d1892f3fcf702e4827e40c] [Current]
Feedback Forum

Post a new message
Dataseries X:
1069.108
1059.362
1049.495
1029.082
1231.089
1220.388
1069.108
968.521
978.233
978.233
989.056
1008.514
1069.108
1049.495
1079.775
1129.547
1412.683
1412.683
1352.244
1291.65
1341.422
1401.983
1412.683
1442.964
1533.833
1473.244
1473.244
1564.114
1816.014
1836.427
1785.734
1664.578
1755.42
1755.42
1765.165
1816.014
1856.04
1876.453
1876.453
1937.014
2169.452
2229.89
2239.603
2088.322
2169.452
2139.171
2078.582
2209.478
2239.603
2188.909
2199.61
2269.916
2532.64
2663.352
2663.352
2602.913
2693.66
2602.913
2552.092
2744.509
2774.634
2703.378
2884.967
2956.228
3168.103
3308.711
3289.258
3278.43
3359.559
3349.692
3228.692
3410.253
3470.847
3410.253
3662.154
3783.309
4065.362
4176.65
4146.492
4085.897
4136.624
4197.185
3995.056
4156.204
4257.779
4216.798
4479.366
4570.08
4953.837
5024.138
4933.418
4984.117
5014.398
5044.678
4852.261
5033.856
5134.437
5033.856
5326.854
5417.607
5811.037
5871.631
5891.089
5992.631
5992.631
6032.657
5851.063
5941.938
6002.377
5891.089
6214.246
6274.812
6678.021
6749.283
6849.864
6940.739
6950.451
6961.152
6779.563
6961.152




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=123507&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=123507&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123507&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
alpha0.214234531505848
beta0.107870793550094
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.214234531505848 \tabularnewline
beta & 0.107870793550094 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123507&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]0.214234531505848[/C][/ROW]
[ROW][C]beta[/C][C]0.107870793550094[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123507&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123507&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
alpha0.214234531505848
beta0.107870793550094
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131069.1081008.1965820519760.9114179480326
141049.4951000.0879912491149.4070087508923
151079.7751035.3769481769844.3980518230198
161129.5471085.5980739208743.9489260791302
171412.6831358.8005982918453.8824017081643
181412.6831360.6570019857552.0259980142521
191352.2441273.172347161779.0716528382984
201291.651195.7373306632395.9126693367687
211341.4221256.5217089506984.9002910493057
221401.9831298.99311265217102.989887347826
231412.6831354.2403757129358.4426242870652
241442.9641408.4218497605234.5421502394836
251533.8331581.84949355035-48.0164935503494
261473.2441531.95586280843-58.7118628084272
271473.2441551.74932606419-78.5053260641873
281564.1141591.89263001172-27.7786300117173
291816.0141964.71854771211-148.704547712108
301836.4271911.15119167049-74.724191670495
311785.7341782.299212701433.43478729857043
321664.5781665.43129313268-0.853293132678346
331755.421693.5784649730461.8415350269572
341755.421742.2068811974713.2131188025264
351765.1651728.7925784107936.3724215892137
361816.0141750.8592350901465.1547649098579
371856.041874.72105588992-18.6810558899176
381876.4531799.8794633651376.5735366348724
391876.4531827.4023433419449.0506566580582
401937.0141952.37386299427-15.359862994269
412169.4522293.64062321584-124.188623215839
422229.892306.3141668626-76.4241668625987
432239.6032220.842361448518.7606385514973
442088.3222069.9227514472518.3992485527474
452169.4522166.19104940613.26095059390127
462139.1712158.19192154751-19.020921547512
472078.5822150.66643918217-72.0844391821702
482209.4782171.4636827703938.0143172296107
492239.6032223.772667246215.8303327538024
502188.9092223.68678010647-34.7777801064676
512199.612193.793417165665.81658283434172
522269.9162258.9185602137610.997439786237
532532.642551.16258695868-18.5225869586811
542663.3522628.0728375631535.2791624368542
552663.3522636.1730614733527.1789385266466
562602.9132453.38185128391149.531148716089
572693.662578.22515631176115.434843688242
582602.9132570.8447053518532.0682946481529
592552.0922523.2728617303728.8191382696282
602744.5092681.5467464416362.9622535583712
612774.6342730.7573067258443.8766932741569
622703.3782690.6054643956312.7725356043657
632884.9672709.46576468545175.501235314553
642956.2282839.90210592166116.325894078341
653168.1033212.37422000732-44.2712200073179
663308.7113369.32724536671-60.6162453667134
673289.2583357.3194245662-68.0614245662009
683278.433230.6611259533447.768874046656
693359.5593324.8616658675734.6973341324274
703349.6923211.94828592224137.743714077758
713228.6923172.7631578582155.9288421417864
723410.2533410.57764309433-0.324643094329076
733470.8473437.322818715633.5241812844042
743410.2533353.3630189448956.8899810551143
753662.1543544.04942395405118.104576045951
763783.3093625.07241969264158.236580307361
774065.3623932.37268370257132.989316297429
784176.654156.0031860630920.6468139369063
794146.4924159.09970072728-12.6077007272797
804085.8974135.94546397268-50.048463972681
814136.6244221.91034482379-85.2863448237922
824197.1854154.4955681421242.6894318578798
833995.0563996.87072797344-1.81472797343713
844156.2044218.51848161471-62.3144816147123
854257.7794266.9911199423-9.21211994229634
864216.7984170.6398462078246.1581537921766
874479.3664452.0853371254927.2806628745147
884570.084554.9619169567715.118083043234
894953.8374850.97531306797102.861686932029
905024.1384988.1488922599535.9891077400489
914933.4184950.79046115675-17.3724611567541
924984.1174875.71694485651108.400055143495
935014.3984973.0724644244841.3255355755236
945044.6785038.471259951626.20674004838475
954852.2614791.8266096897760.4343903102272
965033.8565009.9266574962823.9293425037176
975134.4375137.47161691537-3.03461691537268
985033.8565073.07989708571-39.2238970857134
995326.8545368.64667094163-41.7926709416333
1005417.6075458.5394321344-40.9324321344029
1015811.0375873.32069787778-62.2836978777823
1025871.6315922.97398421921-51.3429842192099
1035891.0895797.2589130951293.8300869048762
1045992.6315839.5045201737153.126479826302
1055992.6315888.39971979922104.231280200782
1066032.6575937.06746662695.5895333740045
1075851.0635709.28584333526141.777156664739
1085941.9385944.18478542544-2.24678542544189
1096002.3776058.4497635788-56.0727635788035
1105891.0895932.23132316944-41.1423231694371
1116214.2466272.99086551959-58.7448655195876
1126274.8126371.47691273964-96.6649127396431
1136678.0216820.30642786214-142.285427862141
1146749.2836864.8775180046-115.594518004603
1156849.8646829.6220025939220.2419974060767
1166940.7396901.7407156404838.998284359518
1176950.4516870.2748521735580.176147826448
1186961.1526895.3677986944665.7842013055351
1196779.5636651.73043880878127.832561191222
1206961.1526768.51349707652192.63850292348

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1069.108 & 1008.19658205197 & 60.9114179480326 \tabularnewline
14 & 1049.495 & 1000.08799124911 & 49.4070087508923 \tabularnewline
15 & 1079.775 & 1035.37694817698 & 44.3980518230198 \tabularnewline
16 & 1129.547 & 1085.59807392087 & 43.9489260791302 \tabularnewline
17 & 1412.683 & 1358.80059829184 & 53.8824017081643 \tabularnewline
18 & 1412.683 & 1360.65700198575 & 52.0259980142521 \tabularnewline
19 & 1352.244 & 1273.1723471617 & 79.0716528382984 \tabularnewline
20 & 1291.65 & 1195.73733066323 & 95.9126693367687 \tabularnewline
21 & 1341.422 & 1256.52170895069 & 84.9002910493057 \tabularnewline
22 & 1401.983 & 1298.99311265217 & 102.989887347826 \tabularnewline
23 & 1412.683 & 1354.24037571293 & 58.4426242870652 \tabularnewline
24 & 1442.964 & 1408.42184976052 & 34.5421502394836 \tabularnewline
25 & 1533.833 & 1581.84949355035 & -48.0164935503494 \tabularnewline
26 & 1473.244 & 1531.95586280843 & -58.7118628084272 \tabularnewline
27 & 1473.244 & 1551.74932606419 & -78.5053260641873 \tabularnewline
28 & 1564.114 & 1591.89263001172 & -27.7786300117173 \tabularnewline
29 & 1816.014 & 1964.71854771211 & -148.704547712108 \tabularnewline
30 & 1836.427 & 1911.15119167049 & -74.724191670495 \tabularnewline
31 & 1785.734 & 1782.29921270143 & 3.43478729857043 \tabularnewline
32 & 1664.578 & 1665.43129313268 & -0.853293132678346 \tabularnewline
33 & 1755.42 & 1693.57846497304 & 61.8415350269572 \tabularnewline
34 & 1755.42 & 1742.20688119747 & 13.2131188025264 \tabularnewline
35 & 1765.165 & 1728.79257841079 & 36.3724215892137 \tabularnewline
36 & 1816.014 & 1750.85923509014 & 65.1547649098579 \tabularnewline
37 & 1856.04 & 1874.72105588992 & -18.6810558899176 \tabularnewline
38 & 1876.453 & 1799.87946336513 & 76.5735366348724 \tabularnewline
39 & 1876.453 & 1827.40234334194 & 49.0506566580582 \tabularnewline
40 & 1937.014 & 1952.37386299427 & -15.359862994269 \tabularnewline
41 & 2169.452 & 2293.64062321584 & -124.188623215839 \tabularnewline
42 & 2229.89 & 2306.3141668626 & -76.4241668625987 \tabularnewline
43 & 2239.603 & 2220.8423614485 & 18.7606385514973 \tabularnewline
44 & 2088.322 & 2069.92275144725 & 18.3992485527474 \tabularnewline
45 & 2169.452 & 2166.1910494061 & 3.26095059390127 \tabularnewline
46 & 2139.171 & 2158.19192154751 & -19.020921547512 \tabularnewline
47 & 2078.582 & 2150.66643918217 & -72.0844391821702 \tabularnewline
48 & 2209.478 & 2171.46368277039 & 38.0143172296107 \tabularnewline
49 & 2239.603 & 2223.7726672462 & 15.8303327538024 \tabularnewline
50 & 2188.909 & 2223.68678010647 & -34.7777801064676 \tabularnewline
51 & 2199.61 & 2193.79341716566 & 5.81658283434172 \tabularnewline
52 & 2269.916 & 2258.91856021376 & 10.997439786237 \tabularnewline
53 & 2532.64 & 2551.16258695868 & -18.5225869586811 \tabularnewline
54 & 2663.352 & 2628.07283756315 & 35.2791624368542 \tabularnewline
55 & 2663.352 & 2636.17306147335 & 27.1789385266466 \tabularnewline
56 & 2602.913 & 2453.38185128391 & 149.531148716089 \tabularnewline
57 & 2693.66 & 2578.22515631176 & 115.434843688242 \tabularnewline
58 & 2602.913 & 2570.84470535185 & 32.0682946481529 \tabularnewline
59 & 2552.092 & 2523.27286173037 & 28.8191382696282 \tabularnewline
60 & 2744.509 & 2681.54674644163 & 62.9622535583712 \tabularnewline
61 & 2774.634 & 2730.75730672584 & 43.8766932741569 \tabularnewline
62 & 2703.378 & 2690.60546439563 & 12.7725356043657 \tabularnewline
63 & 2884.967 & 2709.46576468545 & 175.501235314553 \tabularnewline
64 & 2956.228 & 2839.90210592166 & 116.325894078341 \tabularnewline
65 & 3168.103 & 3212.37422000732 & -44.2712200073179 \tabularnewline
66 & 3308.711 & 3369.32724536671 & -60.6162453667134 \tabularnewline
67 & 3289.258 & 3357.3194245662 & -68.0614245662009 \tabularnewline
68 & 3278.43 & 3230.66112595334 & 47.768874046656 \tabularnewline
69 & 3359.559 & 3324.86166586757 & 34.6973341324274 \tabularnewline
70 & 3349.692 & 3211.94828592224 & 137.743714077758 \tabularnewline
71 & 3228.692 & 3172.76315785821 & 55.9288421417864 \tabularnewline
72 & 3410.253 & 3410.57764309433 & -0.324643094329076 \tabularnewline
73 & 3470.847 & 3437.3228187156 & 33.5241812844042 \tabularnewline
74 & 3410.253 & 3353.36301894489 & 56.8899810551143 \tabularnewline
75 & 3662.154 & 3544.04942395405 & 118.104576045951 \tabularnewline
76 & 3783.309 & 3625.07241969264 & 158.236580307361 \tabularnewline
77 & 4065.362 & 3932.37268370257 & 132.989316297429 \tabularnewline
78 & 4176.65 & 4156.00318606309 & 20.6468139369063 \tabularnewline
79 & 4146.492 & 4159.09970072728 & -12.6077007272797 \tabularnewline
80 & 4085.897 & 4135.94546397268 & -50.048463972681 \tabularnewline
81 & 4136.624 & 4221.91034482379 & -85.2863448237922 \tabularnewline
82 & 4197.185 & 4154.49556814212 & 42.6894318578798 \tabularnewline
83 & 3995.056 & 3996.87072797344 & -1.81472797343713 \tabularnewline
84 & 4156.204 & 4218.51848161471 & -62.3144816147123 \tabularnewline
85 & 4257.779 & 4266.9911199423 & -9.21211994229634 \tabularnewline
86 & 4216.798 & 4170.63984620782 & 46.1581537921766 \tabularnewline
87 & 4479.366 & 4452.08533712549 & 27.2806628745147 \tabularnewline
88 & 4570.08 & 4554.96191695677 & 15.118083043234 \tabularnewline
89 & 4953.837 & 4850.97531306797 & 102.861686932029 \tabularnewline
90 & 5024.138 & 4988.14889225995 & 35.9891077400489 \tabularnewline
91 & 4933.418 & 4950.79046115675 & -17.3724611567541 \tabularnewline
92 & 4984.117 & 4875.71694485651 & 108.400055143495 \tabularnewline
93 & 5014.398 & 4973.07246442448 & 41.3255355755236 \tabularnewline
94 & 5044.678 & 5038.47125995162 & 6.20674004838475 \tabularnewline
95 & 4852.261 & 4791.82660968977 & 60.4343903102272 \tabularnewline
96 & 5033.856 & 5009.92665749628 & 23.9293425037176 \tabularnewline
97 & 5134.437 & 5137.47161691537 & -3.03461691537268 \tabularnewline
98 & 5033.856 & 5073.07989708571 & -39.2238970857134 \tabularnewline
99 & 5326.854 & 5368.64667094163 & -41.7926709416333 \tabularnewline
100 & 5417.607 & 5458.5394321344 & -40.9324321344029 \tabularnewline
101 & 5811.037 & 5873.32069787778 & -62.2836978777823 \tabularnewline
102 & 5871.631 & 5922.97398421921 & -51.3429842192099 \tabularnewline
103 & 5891.089 & 5797.25891309512 & 93.8300869048762 \tabularnewline
104 & 5992.631 & 5839.5045201737 & 153.126479826302 \tabularnewline
105 & 5992.631 & 5888.39971979922 & 104.231280200782 \tabularnewline
106 & 6032.657 & 5937.067466626 & 95.5895333740045 \tabularnewline
107 & 5851.063 & 5709.28584333526 & 141.777156664739 \tabularnewline
108 & 5941.938 & 5944.18478542544 & -2.24678542544189 \tabularnewline
109 & 6002.377 & 6058.4497635788 & -56.0727635788035 \tabularnewline
110 & 5891.089 & 5932.23132316944 & -41.1423231694371 \tabularnewline
111 & 6214.246 & 6272.99086551959 & -58.7448655195876 \tabularnewline
112 & 6274.812 & 6371.47691273964 & -96.6649127396431 \tabularnewline
113 & 6678.021 & 6820.30642786214 & -142.285427862141 \tabularnewline
114 & 6749.283 & 6864.8775180046 & -115.594518004603 \tabularnewline
115 & 6849.864 & 6829.62200259392 & 20.2419974060767 \tabularnewline
116 & 6940.739 & 6901.74071564048 & 38.998284359518 \tabularnewline
117 & 6950.451 & 6870.27485217355 & 80.176147826448 \tabularnewline
118 & 6961.152 & 6895.36779869446 & 65.7842013055351 \tabularnewline
119 & 6779.563 & 6651.73043880878 & 127.832561191222 \tabularnewline
120 & 6961.152 & 6768.51349707652 & 192.63850292348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123507&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]13[/C][C]1069.108[/C][C]1008.19658205197[/C][C]60.9114179480326[/C][/ROW]
[ROW][C]14[/C][C]1049.495[/C][C]1000.08799124911[/C][C]49.4070087508923[/C][/ROW]
[ROW][C]15[/C][C]1079.775[/C][C]1035.37694817698[/C][C]44.3980518230198[/C][/ROW]
[ROW][C]16[/C][C]1129.547[/C][C]1085.59807392087[/C][C]43.9489260791302[/C][/ROW]
[ROW][C]17[/C][C]1412.683[/C][C]1358.80059829184[/C][C]53.8824017081643[/C][/ROW]
[ROW][C]18[/C][C]1412.683[/C][C]1360.65700198575[/C][C]52.0259980142521[/C][/ROW]
[ROW][C]19[/C][C]1352.244[/C][C]1273.1723471617[/C][C]79.0716528382984[/C][/ROW]
[ROW][C]20[/C][C]1291.65[/C][C]1195.73733066323[/C][C]95.9126693367687[/C][/ROW]
[ROW][C]21[/C][C]1341.422[/C][C]1256.52170895069[/C][C]84.9002910493057[/C][/ROW]
[ROW][C]22[/C][C]1401.983[/C][C]1298.99311265217[/C][C]102.989887347826[/C][/ROW]
[ROW][C]23[/C][C]1412.683[/C][C]1354.24037571293[/C][C]58.4426242870652[/C][/ROW]
[ROW][C]24[/C][C]1442.964[/C][C]1408.42184976052[/C][C]34.5421502394836[/C][/ROW]
[ROW][C]25[/C][C]1533.833[/C][C]1581.84949355035[/C][C]-48.0164935503494[/C][/ROW]
[ROW][C]26[/C][C]1473.244[/C][C]1531.95586280843[/C][C]-58.7118628084272[/C][/ROW]
[ROW][C]27[/C][C]1473.244[/C][C]1551.74932606419[/C][C]-78.5053260641873[/C][/ROW]
[ROW][C]28[/C][C]1564.114[/C][C]1591.89263001172[/C][C]-27.7786300117173[/C][/ROW]
[ROW][C]29[/C][C]1816.014[/C][C]1964.71854771211[/C][C]-148.704547712108[/C][/ROW]
[ROW][C]30[/C][C]1836.427[/C][C]1911.15119167049[/C][C]-74.724191670495[/C][/ROW]
[ROW][C]31[/C][C]1785.734[/C][C]1782.29921270143[/C][C]3.43478729857043[/C][/ROW]
[ROW][C]32[/C][C]1664.578[/C][C]1665.43129313268[/C][C]-0.853293132678346[/C][/ROW]
[ROW][C]33[/C][C]1755.42[/C][C]1693.57846497304[/C][C]61.8415350269572[/C][/ROW]
[ROW][C]34[/C][C]1755.42[/C][C]1742.20688119747[/C][C]13.2131188025264[/C][/ROW]
[ROW][C]35[/C][C]1765.165[/C][C]1728.79257841079[/C][C]36.3724215892137[/C][/ROW]
[ROW][C]36[/C][C]1816.014[/C][C]1750.85923509014[/C][C]65.1547649098579[/C][/ROW]
[ROW][C]37[/C][C]1856.04[/C][C]1874.72105588992[/C][C]-18.6810558899176[/C][/ROW]
[ROW][C]38[/C][C]1876.453[/C][C]1799.87946336513[/C][C]76.5735366348724[/C][/ROW]
[ROW][C]39[/C][C]1876.453[/C][C]1827.40234334194[/C][C]49.0506566580582[/C][/ROW]
[ROW][C]40[/C][C]1937.014[/C][C]1952.37386299427[/C][C]-15.359862994269[/C][/ROW]
[ROW][C]41[/C][C]2169.452[/C][C]2293.64062321584[/C][C]-124.188623215839[/C][/ROW]
[ROW][C]42[/C][C]2229.89[/C][C]2306.3141668626[/C][C]-76.4241668625987[/C][/ROW]
[ROW][C]43[/C][C]2239.603[/C][C]2220.8423614485[/C][C]18.7606385514973[/C][/ROW]
[ROW][C]44[/C][C]2088.322[/C][C]2069.92275144725[/C][C]18.3992485527474[/C][/ROW]
[ROW][C]45[/C][C]2169.452[/C][C]2166.1910494061[/C][C]3.26095059390127[/C][/ROW]
[ROW][C]46[/C][C]2139.171[/C][C]2158.19192154751[/C][C]-19.020921547512[/C][/ROW]
[ROW][C]47[/C][C]2078.582[/C][C]2150.66643918217[/C][C]-72.0844391821702[/C][/ROW]
[ROW][C]48[/C][C]2209.478[/C][C]2171.46368277039[/C][C]38.0143172296107[/C][/ROW]
[ROW][C]49[/C][C]2239.603[/C][C]2223.7726672462[/C][C]15.8303327538024[/C][/ROW]
[ROW][C]50[/C][C]2188.909[/C][C]2223.68678010647[/C][C]-34.7777801064676[/C][/ROW]
[ROW][C]51[/C][C]2199.61[/C][C]2193.79341716566[/C][C]5.81658283434172[/C][/ROW]
[ROW][C]52[/C][C]2269.916[/C][C]2258.91856021376[/C][C]10.997439786237[/C][/ROW]
[ROW][C]53[/C][C]2532.64[/C][C]2551.16258695868[/C][C]-18.5225869586811[/C][/ROW]
[ROW][C]54[/C][C]2663.352[/C][C]2628.07283756315[/C][C]35.2791624368542[/C][/ROW]
[ROW][C]55[/C][C]2663.352[/C][C]2636.17306147335[/C][C]27.1789385266466[/C][/ROW]
[ROW][C]56[/C][C]2602.913[/C][C]2453.38185128391[/C][C]149.531148716089[/C][/ROW]
[ROW][C]57[/C][C]2693.66[/C][C]2578.22515631176[/C][C]115.434843688242[/C][/ROW]
[ROW][C]58[/C][C]2602.913[/C][C]2570.84470535185[/C][C]32.0682946481529[/C][/ROW]
[ROW][C]59[/C][C]2552.092[/C][C]2523.27286173037[/C][C]28.8191382696282[/C][/ROW]
[ROW][C]60[/C][C]2744.509[/C][C]2681.54674644163[/C][C]62.9622535583712[/C][/ROW]
[ROW][C]61[/C][C]2774.634[/C][C]2730.75730672584[/C][C]43.8766932741569[/C][/ROW]
[ROW][C]62[/C][C]2703.378[/C][C]2690.60546439563[/C][C]12.7725356043657[/C][/ROW]
[ROW][C]63[/C][C]2884.967[/C][C]2709.46576468545[/C][C]175.501235314553[/C][/ROW]
[ROW][C]64[/C][C]2956.228[/C][C]2839.90210592166[/C][C]116.325894078341[/C][/ROW]
[ROW][C]65[/C][C]3168.103[/C][C]3212.37422000732[/C][C]-44.2712200073179[/C][/ROW]
[ROW][C]66[/C][C]3308.711[/C][C]3369.32724536671[/C][C]-60.6162453667134[/C][/ROW]
[ROW][C]67[/C][C]3289.258[/C][C]3357.3194245662[/C][C]-68.0614245662009[/C][/ROW]
[ROW][C]68[/C][C]3278.43[/C][C]3230.66112595334[/C][C]47.768874046656[/C][/ROW]
[ROW][C]69[/C][C]3359.559[/C][C]3324.86166586757[/C][C]34.6973341324274[/C][/ROW]
[ROW][C]70[/C][C]3349.692[/C][C]3211.94828592224[/C][C]137.743714077758[/C][/ROW]
[ROW][C]71[/C][C]3228.692[/C][C]3172.76315785821[/C][C]55.9288421417864[/C][/ROW]
[ROW][C]72[/C][C]3410.253[/C][C]3410.57764309433[/C][C]-0.324643094329076[/C][/ROW]
[ROW][C]73[/C][C]3470.847[/C][C]3437.3228187156[/C][C]33.5241812844042[/C][/ROW]
[ROW][C]74[/C][C]3410.253[/C][C]3353.36301894489[/C][C]56.8899810551143[/C][/ROW]
[ROW][C]75[/C][C]3662.154[/C][C]3544.04942395405[/C][C]118.104576045951[/C][/ROW]
[ROW][C]76[/C][C]3783.309[/C][C]3625.07241969264[/C][C]158.236580307361[/C][/ROW]
[ROW][C]77[/C][C]4065.362[/C][C]3932.37268370257[/C][C]132.989316297429[/C][/ROW]
[ROW][C]78[/C][C]4176.65[/C][C]4156.00318606309[/C][C]20.6468139369063[/C][/ROW]
[ROW][C]79[/C][C]4146.492[/C][C]4159.09970072728[/C][C]-12.6077007272797[/C][/ROW]
[ROW][C]80[/C][C]4085.897[/C][C]4135.94546397268[/C][C]-50.048463972681[/C][/ROW]
[ROW][C]81[/C][C]4136.624[/C][C]4221.91034482379[/C][C]-85.2863448237922[/C][/ROW]
[ROW][C]82[/C][C]4197.185[/C][C]4154.49556814212[/C][C]42.6894318578798[/C][/ROW]
[ROW][C]83[/C][C]3995.056[/C][C]3996.87072797344[/C][C]-1.81472797343713[/C][/ROW]
[ROW][C]84[/C][C]4156.204[/C][C]4218.51848161471[/C][C]-62.3144816147123[/C][/ROW]
[ROW][C]85[/C][C]4257.779[/C][C]4266.9911199423[/C][C]-9.21211994229634[/C][/ROW]
[ROW][C]86[/C][C]4216.798[/C][C]4170.63984620782[/C][C]46.1581537921766[/C][/ROW]
[ROW][C]87[/C][C]4479.366[/C][C]4452.08533712549[/C][C]27.2806628745147[/C][/ROW]
[ROW][C]88[/C][C]4570.08[/C][C]4554.96191695677[/C][C]15.118083043234[/C][/ROW]
[ROW][C]89[/C][C]4953.837[/C][C]4850.97531306797[/C][C]102.861686932029[/C][/ROW]
[ROW][C]90[/C][C]5024.138[/C][C]4988.14889225995[/C][C]35.9891077400489[/C][/ROW]
[ROW][C]91[/C][C]4933.418[/C][C]4950.79046115675[/C][C]-17.3724611567541[/C][/ROW]
[ROW][C]92[/C][C]4984.117[/C][C]4875.71694485651[/C][C]108.400055143495[/C][/ROW]
[ROW][C]93[/C][C]5014.398[/C][C]4973.07246442448[/C][C]41.3255355755236[/C][/ROW]
[ROW][C]94[/C][C]5044.678[/C][C]5038.47125995162[/C][C]6.20674004838475[/C][/ROW]
[ROW][C]95[/C][C]4852.261[/C][C]4791.82660968977[/C][C]60.4343903102272[/C][/ROW]
[ROW][C]96[/C][C]5033.856[/C][C]5009.92665749628[/C][C]23.9293425037176[/C][/ROW]
[ROW][C]97[/C][C]5134.437[/C][C]5137.47161691537[/C][C]-3.03461691537268[/C][/ROW]
[ROW][C]98[/C][C]5033.856[/C][C]5073.07989708571[/C][C]-39.2238970857134[/C][/ROW]
[ROW][C]99[/C][C]5326.854[/C][C]5368.64667094163[/C][C]-41.7926709416333[/C][/ROW]
[ROW][C]100[/C][C]5417.607[/C][C]5458.5394321344[/C][C]-40.9324321344029[/C][/ROW]
[ROW][C]101[/C][C]5811.037[/C][C]5873.32069787778[/C][C]-62.2836978777823[/C][/ROW]
[ROW][C]102[/C][C]5871.631[/C][C]5922.97398421921[/C][C]-51.3429842192099[/C][/ROW]
[ROW][C]103[/C][C]5891.089[/C][C]5797.25891309512[/C][C]93.8300869048762[/C][/ROW]
[ROW][C]104[/C][C]5992.631[/C][C]5839.5045201737[/C][C]153.126479826302[/C][/ROW]
[ROW][C]105[/C][C]5992.631[/C][C]5888.39971979922[/C][C]104.231280200782[/C][/ROW]
[ROW][C]106[/C][C]6032.657[/C][C]5937.067466626[/C][C]95.5895333740045[/C][/ROW]
[ROW][C]107[/C][C]5851.063[/C][C]5709.28584333526[/C][C]141.777156664739[/C][/ROW]
[ROW][C]108[/C][C]5941.938[/C][C]5944.18478542544[/C][C]-2.24678542544189[/C][/ROW]
[ROW][C]109[/C][C]6002.377[/C][C]6058.4497635788[/C][C]-56.0727635788035[/C][/ROW]
[ROW][C]110[/C][C]5891.089[/C][C]5932.23132316944[/C][C]-41.1423231694371[/C][/ROW]
[ROW][C]111[/C][C]6214.246[/C][C]6272.99086551959[/C][C]-58.7448655195876[/C][/ROW]
[ROW][C]112[/C][C]6274.812[/C][C]6371.47691273964[/C][C]-96.6649127396431[/C][/ROW]
[ROW][C]113[/C][C]6678.021[/C][C]6820.30642786214[/C][C]-142.285427862141[/C][/ROW]
[ROW][C]114[/C][C]6749.283[/C][C]6864.8775180046[/C][C]-115.594518004603[/C][/ROW]
[ROW][C]115[/C][C]6849.864[/C][C]6829.62200259392[/C][C]20.2419974060767[/C][/ROW]
[ROW][C]116[/C][C]6940.739[/C][C]6901.74071564048[/C][C]38.998284359518[/C][/ROW]
[ROW][C]117[/C][C]6950.451[/C][C]6870.27485217355[/C][C]80.176147826448[/C][/ROW]
[ROW][C]118[/C][C]6961.152[/C][C]6895.36779869446[/C][C]65.7842013055351[/C][/ROW]
[ROW][C]119[/C][C]6779.563[/C][C]6651.73043880878[/C][C]127.832561191222[/C][/ROW]
[ROW][C]120[/C][C]6961.152[/C][C]6768.51349707652[/C][C]192.63850292348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123507&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123507&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
131069.1081008.1965820519760.9114179480326
141049.4951000.0879912491149.4070087508923
151079.7751035.3769481769844.3980518230198
161129.5471085.5980739208743.9489260791302
171412.6831358.8005982918453.8824017081643
181412.6831360.6570019857552.0259980142521
191352.2441273.172347161779.0716528382984
201291.651195.7373306632395.9126693367687
211341.4221256.5217089506984.9002910493057
221401.9831298.99311265217102.989887347826
231412.6831354.2403757129358.4426242870652
241442.9641408.4218497605234.5421502394836
251533.8331581.84949355035-48.0164935503494
261473.2441531.95586280843-58.7118628084272
271473.2441551.74932606419-78.5053260641873
281564.1141591.89263001172-27.7786300117173
291816.0141964.71854771211-148.704547712108
301836.4271911.15119167049-74.724191670495
311785.7341782.299212701433.43478729857043
321664.5781665.43129313268-0.853293132678346
331755.421693.5784649730461.8415350269572
341755.421742.2068811974713.2131188025264
351765.1651728.7925784107936.3724215892137
361816.0141750.8592350901465.1547649098579
371856.041874.72105588992-18.6810558899176
381876.4531799.8794633651376.5735366348724
391876.4531827.4023433419449.0506566580582
401937.0141952.37386299427-15.359862994269
412169.4522293.64062321584-124.188623215839
422229.892306.3141668626-76.4241668625987
432239.6032220.842361448518.7606385514973
442088.3222069.9227514472518.3992485527474
452169.4522166.19104940613.26095059390127
462139.1712158.19192154751-19.020921547512
472078.5822150.66643918217-72.0844391821702
482209.4782171.4636827703938.0143172296107
492239.6032223.772667246215.8303327538024
502188.9092223.68678010647-34.7777801064676
512199.612193.793417165665.81658283434172
522269.9162258.9185602137610.997439786237
532532.642551.16258695868-18.5225869586811
542663.3522628.0728375631535.2791624368542
552663.3522636.1730614733527.1789385266466
562602.9132453.38185128391149.531148716089
572693.662578.22515631176115.434843688242
582602.9132570.8447053518532.0682946481529
592552.0922523.2728617303728.8191382696282
602744.5092681.5467464416362.9622535583712
612774.6342730.7573067258443.8766932741569
622703.3782690.6054643956312.7725356043657
632884.9672709.46576468545175.501235314553
642956.2282839.90210592166116.325894078341
653168.1033212.37422000732-44.2712200073179
663308.7113369.32724536671-60.6162453667134
673289.2583357.3194245662-68.0614245662009
683278.433230.6611259533447.768874046656
693359.5593324.8616658675734.6973341324274
703349.6923211.94828592224137.743714077758
713228.6923172.7631578582155.9288421417864
723410.2533410.57764309433-0.324643094329076
733470.8473437.322818715633.5241812844042
743410.2533353.3630189448956.8899810551143
753662.1543544.04942395405118.104576045951
763783.3093625.07241969264158.236580307361
774065.3623932.37268370257132.989316297429
784176.654156.0031860630920.6468139369063
794146.4924159.09970072728-12.6077007272797
804085.8974135.94546397268-50.048463972681
814136.6244221.91034482379-85.2863448237922
824197.1854154.4955681421242.6894318578798
833995.0563996.87072797344-1.81472797343713
844156.2044218.51848161471-62.3144816147123
854257.7794266.9911199423-9.21211994229634
864216.7984170.6398462078246.1581537921766
874479.3664452.0853371254927.2806628745147
884570.084554.9619169567715.118083043234
894953.8374850.97531306797102.861686932029
905024.1384988.1488922599535.9891077400489
914933.4184950.79046115675-17.3724611567541
924984.1174875.71694485651108.400055143495
935014.3984973.0724644244841.3255355755236
945044.6785038.471259951626.20674004838475
954852.2614791.8266096897760.4343903102272
965033.8565009.9266574962823.9293425037176
975134.4375137.47161691537-3.03461691537268
985033.8565073.07989708571-39.2238970857134
995326.8545368.64667094163-41.7926709416333
1005417.6075458.5394321344-40.9324321344029
1015811.0375873.32069787778-62.2836978777823
1025871.6315922.97398421921-51.3429842192099
1035891.0895797.2589130951293.8300869048762
1045992.6315839.5045201737153.126479826302
1055992.6315888.39971979922104.231280200782
1066032.6575937.06746662695.5895333740045
1075851.0635709.28584333526141.777156664739
1085941.9385944.18478542544-2.24678542544189
1096002.3776058.4497635788-56.0727635788035
1105891.0895932.23132316944-41.1423231694371
1116214.2466272.99086551959-58.7448655195876
1126274.8126371.47691273964-96.6649127396431
1136678.0216820.30642786214-142.285427862141
1146749.2836864.8775180046-115.594518004603
1156849.8646829.6220025939220.2419974060767
1166940.7396901.7407156404838.998284359518
1176950.4516870.2748521735580.176147826448
1186961.1526895.3677986944665.7842013055351
1196779.5636651.73043880878127.832561191222
1206961.1526768.51349707652192.63850292348







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1216881.996355038226744.536275491097019.45643458535
1226755.440123509266614.380161804046896.50008521448
1237132.048493198656985.859158212217278.23782818508
1247218.22077320457066.814039720247369.62750668876
1257711.802367914187552.392267987927871.21246784044
1267820.963251246947654.607565346437987.31893714745
1277933.891344168067759.873628335258107.90906000087
1288030.33738235477848.144126794738212.53063791468
1298021.473840160777831.681429812678211.26625050888
1308015.465461792397817.704535459868213.22638812491
1317770.967064346067568.306587013227973.62754167889
1327924.234155422897760.849750486268087.61856035952

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 6881.99635503822 & 6744.53627549109 & 7019.45643458535 \tabularnewline
122 & 6755.44012350926 & 6614.38016180404 & 6896.50008521448 \tabularnewline
123 & 7132.04849319865 & 6985.85915821221 & 7278.23782818508 \tabularnewline
124 & 7218.2207732045 & 7066.81403972024 & 7369.62750668876 \tabularnewline
125 & 7711.80236791418 & 7552.39226798792 & 7871.21246784044 \tabularnewline
126 & 7820.96325124694 & 7654.60756534643 & 7987.31893714745 \tabularnewline
127 & 7933.89134416806 & 7759.87362833525 & 8107.90906000087 \tabularnewline
128 & 8030.3373823547 & 7848.14412679473 & 8212.53063791468 \tabularnewline
129 & 8021.47384016077 & 7831.68142981267 & 8211.26625050888 \tabularnewline
130 & 8015.46546179239 & 7817.70453545986 & 8213.22638812491 \tabularnewline
131 & 7770.96706434606 & 7568.30658701322 & 7973.62754167889 \tabularnewline
132 & 7924.23415542289 & 7760.84975048626 & 8087.61856035952 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123507&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]6881.99635503822[/C][C]6744.53627549109[/C][C]7019.45643458535[/C][/ROW]
[ROW][C]122[/C][C]6755.44012350926[/C][C]6614.38016180404[/C][C]6896.50008521448[/C][/ROW]
[ROW][C]123[/C][C]7132.04849319865[/C][C]6985.85915821221[/C][C]7278.23782818508[/C][/ROW]
[ROW][C]124[/C][C]7218.2207732045[/C][C]7066.81403972024[/C][C]7369.62750668876[/C][/ROW]
[ROW][C]125[/C][C]7711.80236791418[/C][C]7552.39226798792[/C][C]7871.21246784044[/C][/ROW]
[ROW][C]126[/C][C]7820.96325124694[/C][C]7654.60756534643[/C][C]7987.31893714745[/C][/ROW]
[ROW][C]127[/C][C]7933.89134416806[/C][C]7759.87362833525[/C][C]8107.90906000087[/C][/ROW]
[ROW][C]128[/C][C]8030.3373823547[/C][C]7848.14412679473[/C][C]8212.53063791468[/C][/ROW]
[ROW][C]129[/C][C]8021.47384016077[/C][C]7831.68142981267[/C][C]8211.26625050888[/C][/ROW]
[ROW][C]130[/C][C]8015.46546179239[/C][C]7817.70453545986[/C][C]8213.22638812491[/C][/ROW]
[ROW][C]131[/C][C]7770.96706434606[/C][C]7568.30658701322[/C][C]7973.62754167889[/C][/ROW]
[ROW][C]132[/C][C]7924.23415542289[/C][C]7760.84975048626[/C][C]8087.61856035952[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123507&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123507&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
1216881.996355038226744.536275491097019.45643458535
1226755.440123509266614.380161804046896.50008521448
1237132.048493198656985.859158212217278.23782818508
1247218.22077320457066.814039720247369.62750668876
1257711.802367914187552.392267987927871.21246784044
1267820.963251246947654.607565346437987.31893714745
1277933.891344168067759.873628335258107.90906000087
1288030.33738235477848.144126794738212.53063791468
1298021.473840160777831.681429812678211.26625050888
1308015.465461792397817.704535459868213.22638812491
1317770.967064346067568.306587013227973.62754167889
1327924.234155422897760.849750486268087.61856035952



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')