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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 Dec 2016 13:37:40 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/07/t1481114494pngbv43vni3utqf.htm/, Retrieved Sat, 18 May 2024 03:58:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298058, Retrieved Sat, 18 May 2024 03:58:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-07 12:37:40] [27c26e37291399ddf43c115158039444] [Current]
- RMPD    [ARIMA Backward Selection] [Paper ( Arima Bac...] [2016-12-21 14:38:05] [91e1ca4663e910c18c2cdaf49e7332ba]
- RMPD    [ARIMA Forecasting] [Paper( Arima Fore...] [2016-12-21 14:59:49] [91e1ca4663e910c18c2cdaf49e7332ba]
- R P       [ARIMA Forecasting] [Paper ( Arima bac...] [2016-12-21 22:48:59] [91e1ca4663e910c18c2cdaf49e7332ba]
- RMPD    [Spectral Analysis] [Paper ( spectral ...] [2016-12-21 15:12:24] [91e1ca4663e910c18c2cdaf49e7332ba]
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Dataseries X:
6600
6800
7500
7500
7400
7600
7300
7900
7100
7700
6500
5000
6200
7000
7400
7200
6900
7400
6400
5500
6600
7000
6200
5100
5600
6400
7200
7100
7000
7300
7600
7600
6700
6800
5900
5000
5600
5600
7100
7000
6600
7200
7200
7200
6200
6500
5800
4900
5800
6800
7100
6900
6800
7200
7200
7400
6400
6700
6200
5000
5600
6700
7000
6800
6900
7100
7300
7300
6600
6800
5900
4900
5500
6300
7100
6700
6700
7100
7300
7300
6200
6500
5800
4700
5500
6500
6800
6600
6300
6700
7200
7200
5900
6100
5500
4700
5400
6400
7500
6900
6400
6700
7100
7100
4000
6300
5400
4600
5400
6000
7200
6800
6400
7100
7500
7400
6400
6600
5600
4800
5400
6600




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298058&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298058&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298058&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.28500519920001
beta0.0313284402102492
gamma0.36717658864712

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.28500519920001 \tabularnewline
beta & 0.0313284402102492 \tabularnewline
gamma & 0.36717658864712 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298058&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]0.28500519920001[/C][/ROW]
[ROW][C]beta[/C][C]0.0313284402102492[/C][/ROW]
[ROW][C]gamma[/C][C]0.36717658864712[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298058&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298058&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
alpha0.28500519920001
beta0.0313284402102492
gamma0.36717658864712







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1362006319.12393162393-119.123931623933
1470007168.63733380039-168.63733380039
1574007585.86676857237-185.866768572367
1672007325.69283020252-125.692830202522
1769006973.21316162787-73.2131616278684
1874007401.70343475613-1.70343475613481
1964006754.72580892856-354.725808928561
2055007199.80103978813-1699.80103978813
2166005833.84570682454766.154293175458
2270006598.37461228246401.625387717537
2362005479.26357114035720.736428859648
2451004153.36945778867946.630542211331
2556005585.7017241351114.2982758648923
2664006462.3835870288-62.3835870287958
2772006908.46253408791291.537465912085
2871006807.50121588711292.49878411289
2970006599.07222725982400.927772740185
3073007196.78847087749103.211529122511
3176006503.290118348221096.70988165178
3276007038.12657001713561.873429982872
3367007013.55607376513-313.556073765134
3468007414.43208864254-614.432088642536
3559006120.21297193539-220.212971935387
3650004607.74327619963392.256723800368
3756005654.65771485817-54.6577148581746
3856006508.28600850801-908.28600850801
3971006815.37065169821284.629348301785
4070006721.80879695516278.19120304484
4166006546.7560550147353.2439449852654
4272006973.10514878764226.894851212362
4372006582.66780561852617.332194381484
4472006843.17674565837356.823254341629
4562006531.21698614855-331.216986148547
4665006848.79011691652-348.790116916516
4758005736.8656410217963.13435897821
4849004471.56383125394428.436168746064
4958005417.40563101558382.594368984419
5068006181.39887093242618.601129067584
5171007260.31111557566-160.311115575656
5269007057.75747607076-157.757476070756
5368006715.0181142513784.981885748628
5472007211.90080484989-11.9008048498854
5572006869.67422854059330.32577145941
5674006991.19849653932408.801503460684
5764006525.09104550814-125.091045508138
5867006910.30712481402-210.307124814016
5962005960.73921629236239.260783707637
6050004857.85532163725142.144678362752
6156005723.83003077473-123.830030774735
6267006414.68892996992285.311070030077
6370007200.38912292981-200.389122929806
6468006992.99027576078-192.990275760783
6569006709.52783215107190.472167848935
6671007217.57539191021-117.57539191021
6773006940.66612649102359.333873508978
6873007096.90964043345203.090359566553
6966006436.02383484878163.976165151224
7068006887.84772003462-87.8477200346179
7159006098.89343185499-198.893431854987
7249004849.4125836813250.5874163186827
7355005622.42443968768-122.424439687685
7463006424.06564843714-124.065648437145
7571006964.89572223687135.104277763133
7667006857.36712685929-157.367126859294
7767006687.3561572702512.6438427297453
7871007064.8909502696435.1090497303558
7973006959.10426557887340.895734421127
8073007071.31371637601228.686283623992
8162006409.92220899982-209.922208999817
8265006688.20145113551-188.201451135507
8358005839.72653278041-39.7265327804107
8447004700.75975182351-0.759751823505212
8555005412.9128686225387.087131377466
8665006274.90194033054225.098059669459
8768006987.46964230414-187.469642304143
8866006712.52772972786-112.527729727857
8963006601.63370713424-301.633707134237
9067006894.3940452547-194.394045254697
9172006800.32509002127399.67490997873
9272006897.20278733066302.79721266934
9359006139.82154634281-239.821546342814
9461006413.05056369126-313.050563691256
9555005564.62617974557-64.6261797455709
9647004425.22462703475274.775372965253
9754005237.86109491062162.138905089384
9864006157.03437443104242.965625568962
9975006766.10497208456733.895027915436
10069006781.37956221357118.620437786431
10164006696.7302975045-296.730297504504
10267007029.09767123707-329.097671237072
10371007061.4512619998438.5487380001578
10471007035.6017136876764.3982863123256
10540006071.32240935191-2071.32240935191
10663005790.48656627349509.513433726514
10754005236.20754848139163.792451518612
10846004247.54051768331352.459482316686
10954005049.97175988431350.028240115692
11060006042.8162618201-42.8162618201004
11172006695.67163178595504.328368214046
11268006478.29186170129321.708138298713
11364006338.5961819587661.403818041239
11471006763.84824529545336.15175470455
11575007087.57120307087412.428796929133
11674007183.65581735346216.344182646539
11764005711.93933995482688.060660045176
11866006929.67189803788-329.67189803788
11956006072.5506194569-472.550619456903
12048004973.46320564024-173.463205640244
12154005642.07970048199-242.079700481985
12266006374.46457927503225.535420724966

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6200 & 6319.12393162393 & -119.123931623933 \tabularnewline
14 & 7000 & 7168.63733380039 & -168.63733380039 \tabularnewline
15 & 7400 & 7585.86676857237 & -185.866768572367 \tabularnewline
16 & 7200 & 7325.69283020252 & -125.692830202522 \tabularnewline
17 & 6900 & 6973.21316162787 & -73.2131616278684 \tabularnewline
18 & 7400 & 7401.70343475613 & -1.70343475613481 \tabularnewline
19 & 6400 & 6754.72580892856 & -354.725808928561 \tabularnewline
20 & 5500 & 7199.80103978813 & -1699.80103978813 \tabularnewline
21 & 6600 & 5833.84570682454 & 766.154293175458 \tabularnewline
22 & 7000 & 6598.37461228246 & 401.625387717537 \tabularnewline
23 & 6200 & 5479.26357114035 & 720.736428859648 \tabularnewline
24 & 5100 & 4153.36945778867 & 946.630542211331 \tabularnewline
25 & 5600 & 5585.70172413511 & 14.2982758648923 \tabularnewline
26 & 6400 & 6462.3835870288 & -62.3835870287958 \tabularnewline
27 & 7200 & 6908.46253408791 & 291.537465912085 \tabularnewline
28 & 7100 & 6807.50121588711 & 292.49878411289 \tabularnewline
29 & 7000 & 6599.07222725982 & 400.927772740185 \tabularnewline
30 & 7300 & 7196.78847087749 & 103.211529122511 \tabularnewline
31 & 7600 & 6503.29011834822 & 1096.70988165178 \tabularnewline
32 & 7600 & 7038.12657001713 & 561.873429982872 \tabularnewline
33 & 6700 & 7013.55607376513 & -313.556073765134 \tabularnewline
34 & 6800 & 7414.43208864254 & -614.432088642536 \tabularnewline
35 & 5900 & 6120.21297193539 & -220.212971935387 \tabularnewline
36 & 5000 & 4607.74327619963 & 392.256723800368 \tabularnewline
37 & 5600 & 5654.65771485817 & -54.6577148581746 \tabularnewline
38 & 5600 & 6508.28600850801 & -908.28600850801 \tabularnewline
39 & 7100 & 6815.37065169821 & 284.629348301785 \tabularnewline
40 & 7000 & 6721.80879695516 & 278.19120304484 \tabularnewline
41 & 6600 & 6546.75605501473 & 53.2439449852654 \tabularnewline
42 & 7200 & 6973.10514878764 & 226.894851212362 \tabularnewline
43 & 7200 & 6582.66780561852 & 617.332194381484 \tabularnewline
44 & 7200 & 6843.17674565837 & 356.823254341629 \tabularnewline
45 & 6200 & 6531.21698614855 & -331.216986148547 \tabularnewline
46 & 6500 & 6848.79011691652 & -348.790116916516 \tabularnewline
47 & 5800 & 5736.86564102179 & 63.13435897821 \tabularnewline
48 & 4900 & 4471.56383125394 & 428.436168746064 \tabularnewline
49 & 5800 & 5417.40563101558 & 382.594368984419 \tabularnewline
50 & 6800 & 6181.39887093242 & 618.601129067584 \tabularnewline
51 & 7100 & 7260.31111557566 & -160.311115575656 \tabularnewline
52 & 6900 & 7057.75747607076 & -157.757476070756 \tabularnewline
53 & 6800 & 6715.01811425137 & 84.981885748628 \tabularnewline
54 & 7200 & 7211.90080484989 & -11.9008048498854 \tabularnewline
55 & 7200 & 6869.67422854059 & 330.32577145941 \tabularnewline
56 & 7400 & 6991.19849653932 & 408.801503460684 \tabularnewline
57 & 6400 & 6525.09104550814 & -125.091045508138 \tabularnewline
58 & 6700 & 6910.30712481402 & -210.307124814016 \tabularnewline
59 & 6200 & 5960.73921629236 & 239.260783707637 \tabularnewline
60 & 5000 & 4857.85532163725 & 142.144678362752 \tabularnewline
61 & 5600 & 5723.83003077473 & -123.830030774735 \tabularnewline
62 & 6700 & 6414.68892996992 & 285.311070030077 \tabularnewline
63 & 7000 & 7200.38912292981 & -200.389122929806 \tabularnewline
64 & 6800 & 6992.99027576078 & -192.990275760783 \tabularnewline
65 & 6900 & 6709.52783215107 & 190.472167848935 \tabularnewline
66 & 7100 & 7217.57539191021 & -117.57539191021 \tabularnewline
67 & 7300 & 6940.66612649102 & 359.333873508978 \tabularnewline
68 & 7300 & 7096.90964043345 & 203.090359566553 \tabularnewline
69 & 6600 & 6436.02383484878 & 163.976165151224 \tabularnewline
70 & 6800 & 6887.84772003462 & -87.8477200346179 \tabularnewline
71 & 5900 & 6098.89343185499 & -198.893431854987 \tabularnewline
72 & 4900 & 4849.41258368132 & 50.5874163186827 \tabularnewline
73 & 5500 & 5622.42443968768 & -122.424439687685 \tabularnewline
74 & 6300 & 6424.06564843714 & -124.065648437145 \tabularnewline
75 & 7100 & 6964.89572223687 & 135.104277763133 \tabularnewline
76 & 6700 & 6857.36712685929 & -157.367126859294 \tabularnewline
77 & 6700 & 6687.35615727025 & 12.6438427297453 \tabularnewline
78 & 7100 & 7064.89095026964 & 35.1090497303558 \tabularnewline
79 & 7300 & 6959.10426557887 & 340.895734421127 \tabularnewline
80 & 7300 & 7071.31371637601 & 228.686283623992 \tabularnewline
81 & 6200 & 6409.92220899982 & -209.922208999817 \tabularnewline
82 & 6500 & 6688.20145113551 & -188.201451135507 \tabularnewline
83 & 5800 & 5839.72653278041 & -39.7265327804107 \tabularnewline
84 & 4700 & 4700.75975182351 & -0.759751823505212 \tabularnewline
85 & 5500 & 5412.91286862253 & 87.087131377466 \tabularnewline
86 & 6500 & 6274.90194033054 & 225.098059669459 \tabularnewline
87 & 6800 & 6987.46964230414 & -187.469642304143 \tabularnewline
88 & 6600 & 6712.52772972786 & -112.527729727857 \tabularnewline
89 & 6300 & 6601.63370713424 & -301.633707134237 \tabularnewline
90 & 6700 & 6894.3940452547 & -194.394045254697 \tabularnewline
91 & 7200 & 6800.32509002127 & 399.67490997873 \tabularnewline
92 & 7200 & 6897.20278733066 & 302.79721266934 \tabularnewline
93 & 5900 & 6139.82154634281 & -239.821546342814 \tabularnewline
94 & 6100 & 6413.05056369126 & -313.050563691256 \tabularnewline
95 & 5500 & 5564.62617974557 & -64.6261797455709 \tabularnewline
96 & 4700 & 4425.22462703475 & 274.775372965253 \tabularnewline
97 & 5400 & 5237.86109491062 & 162.138905089384 \tabularnewline
98 & 6400 & 6157.03437443104 & 242.965625568962 \tabularnewline
99 & 7500 & 6766.10497208456 & 733.895027915436 \tabularnewline
100 & 6900 & 6781.37956221357 & 118.620437786431 \tabularnewline
101 & 6400 & 6696.7302975045 & -296.730297504504 \tabularnewline
102 & 6700 & 7029.09767123707 & -329.097671237072 \tabularnewline
103 & 7100 & 7061.45126199984 & 38.5487380001578 \tabularnewline
104 & 7100 & 7035.60171368767 & 64.3982863123256 \tabularnewline
105 & 4000 & 6071.32240935191 & -2071.32240935191 \tabularnewline
106 & 6300 & 5790.48656627349 & 509.513433726514 \tabularnewline
107 & 5400 & 5236.20754848139 & 163.792451518612 \tabularnewline
108 & 4600 & 4247.54051768331 & 352.459482316686 \tabularnewline
109 & 5400 & 5049.97175988431 & 350.028240115692 \tabularnewline
110 & 6000 & 6042.8162618201 & -42.8162618201004 \tabularnewline
111 & 7200 & 6695.67163178595 & 504.328368214046 \tabularnewline
112 & 6800 & 6478.29186170129 & 321.708138298713 \tabularnewline
113 & 6400 & 6338.59618195876 & 61.403818041239 \tabularnewline
114 & 7100 & 6763.84824529545 & 336.15175470455 \tabularnewline
115 & 7500 & 7087.57120307087 & 412.428796929133 \tabularnewline
116 & 7400 & 7183.65581735346 & 216.344182646539 \tabularnewline
117 & 6400 & 5711.93933995482 & 688.060660045176 \tabularnewline
118 & 6600 & 6929.67189803788 & -329.67189803788 \tabularnewline
119 & 5600 & 6072.5506194569 & -472.550619456903 \tabularnewline
120 & 4800 & 4973.46320564024 & -173.463205640244 \tabularnewline
121 & 5400 & 5642.07970048199 & -242.079700481985 \tabularnewline
122 & 6600 & 6374.46457927503 & 225.535420724966 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298058&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]6200[/C][C]6319.12393162393[/C][C]-119.123931623933[/C][/ROW]
[ROW][C]14[/C][C]7000[/C][C]7168.63733380039[/C][C]-168.63733380039[/C][/ROW]
[ROW][C]15[/C][C]7400[/C][C]7585.86676857237[/C][C]-185.866768572367[/C][/ROW]
[ROW][C]16[/C][C]7200[/C][C]7325.69283020252[/C][C]-125.692830202522[/C][/ROW]
[ROW][C]17[/C][C]6900[/C][C]6973.21316162787[/C][C]-73.2131616278684[/C][/ROW]
[ROW][C]18[/C][C]7400[/C][C]7401.70343475613[/C][C]-1.70343475613481[/C][/ROW]
[ROW][C]19[/C][C]6400[/C][C]6754.72580892856[/C][C]-354.725808928561[/C][/ROW]
[ROW][C]20[/C][C]5500[/C][C]7199.80103978813[/C][C]-1699.80103978813[/C][/ROW]
[ROW][C]21[/C][C]6600[/C][C]5833.84570682454[/C][C]766.154293175458[/C][/ROW]
[ROW][C]22[/C][C]7000[/C][C]6598.37461228246[/C][C]401.625387717537[/C][/ROW]
[ROW][C]23[/C][C]6200[/C][C]5479.26357114035[/C][C]720.736428859648[/C][/ROW]
[ROW][C]24[/C][C]5100[/C][C]4153.36945778867[/C][C]946.630542211331[/C][/ROW]
[ROW][C]25[/C][C]5600[/C][C]5585.70172413511[/C][C]14.2982758648923[/C][/ROW]
[ROW][C]26[/C][C]6400[/C][C]6462.3835870288[/C][C]-62.3835870287958[/C][/ROW]
[ROW][C]27[/C][C]7200[/C][C]6908.46253408791[/C][C]291.537465912085[/C][/ROW]
[ROW][C]28[/C][C]7100[/C][C]6807.50121588711[/C][C]292.49878411289[/C][/ROW]
[ROW][C]29[/C][C]7000[/C][C]6599.07222725982[/C][C]400.927772740185[/C][/ROW]
[ROW][C]30[/C][C]7300[/C][C]7196.78847087749[/C][C]103.211529122511[/C][/ROW]
[ROW][C]31[/C][C]7600[/C][C]6503.29011834822[/C][C]1096.70988165178[/C][/ROW]
[ROW][C]32[/C][C]7600[/C][C]7038.12657001713[/C][C]561.873429982872[/C][/ROW]
[ROW][C]33[/C][C]6700[/C][C]7013.55607376513[/C][C]-313.556073765134[/C][/ROW]
[ROW][C]34[/C][C]6800[/C][C]7414.43208864254[/C][C]-614.432088642536[/C][/ROW]
[ROW][C]35[/C][C]5900[/C][C]6120.21297193539[/C][C]-220.212971935387[/C][/ROW]
[ROW][C]36[/C][C]5000[/C][C]4607.74327619963[/C][C]392.256723800368[/C][/ROW]
[ROW][C]37[/C][C]5600[/C][C]5654.65771485817[/C][C]-54.6577148581746[/C][/ROW]
[ROW][C]38[/C][C]5600[/C][C]6508.28600850801[/C][C]-908.28600850801[/C][/ROW]
[ROW][C]39[/C][C]7100[/C][C]6815.37065169821[/C][C]284.629348301785[/C][/ROW]
[ROW][C]40[/C][C]7000[/C][C]6721.80879695516[/C][C]278.19120304484[/C][/ROW]
[ROW][C]41[/C][C]6600[/C][C]6546.75605501473[/C][C]53.2439449852654[/C][/ROW]
[ROW][C]42[/C][C]7200[/C][C]6973.10514878764[/C][C]226.894851212362[/C][/ROW]
[ROW][C]43[/C][C]7200[/C][C]6582.66780561852[/C][C]617.332194381484[/C][/ROW]
[ROW][C]44[/C][C]7200[/C][C]6843.17674565837[/C][C]356.823254341629[/C][/ROW]
[ROW][C]45[/C][C]6200[/C][C]6531.21698614855[/C][C]-331.216986148547[/C][/ROW]
[ROW][C]46[/C][C]6500[/C][C]6848.79011691652[/C][C]-348.790116916516[/C][/ROW]
[ROW][C]47[/C][C]5800[/C][C]5736.86564102179[/C][C]63.13435897821[/C][/ROW]
[ROW][C]48[/C][C]4900[/C][C]4471.56383125394[/C][C]428.436168746064[/C][/ROW]
[ROW][C]49[/C][C]5800[/C][C]5417.40563101558[/C][C]382.594368984419[/C][/ROW]
[ROW][C]50[/C][C]6800[/C][C]6181.39887093242[/C][C]618.601129067584[/C][/ROW]
[ROW][C]51[/C][C]7100[/C][C]7260.31111557566[/C][C]-160.311115575656[/C][/ROW]
[ROW][C]52[/C][C]6900[/C][C]7057.75747607076[/C][C]-157.757476070756[/C][/ROW]
[ROW][C]53[/C][C]6800[/C][C]6715.01811425137[/C][C]84.981885748628[/C][/ROW]
[ROW][C]54[/C][C]7200[/C][C]7211.90080484989[/C][C]-11.9008048498854[/C][/ROW]
[ROW][C]55[/C][C]7200[/C][C]6869.67422854059[/C][C]330.32577145941[/C][/ROW]
[ROW][C]56[/C][C]7400[/C][C]6991.19849653932[/C][C]408.801503460684[/C][/ROW]
[ROW][C]57[/C][C]6400[/C][C]6525.09104550814[/C][C]-125.091045508138[/C][/ROW]
[ROW][C]58[/C][C]6700[/C][C]6910.30712481402[/C][C]-210.307124814016[/C][/ROW]
[ROW][C]59[/C][C]6200[/C][C]5960.73921629236[/C][C]239.260783707637[/C][/ROW]
[ROW][C]60[/C][C]5000[/C][C]4857.85532163725[/C][C]142.144678362752[/C][/ROW]
[ROW][C]61[/C][C]5600[/C][C]5723.83003077473[/C][C]-123.830030774735[/C][/ROW]
[ROW][C]62[/C][C]6700[/C][C]6414.68892996992[/C][C]285.311070030077[/C][/ROW]
[ROW][C]63[/C][C]7000[/C][C]7200.38912292981[/C][C]-200.389122929806[/C][/ROW]
[ROW][C]64[/C][C]6800[/C][C]6992.99027576078[/C][C]-192.990275760783[/C][/ROW]
[ROW][C]65[/C][C]6900[/C][C]6709.52783215107[/C][C]190.472167848935[/C][/ROW]
[ROW][C]66[/C][C]7100[/C][C]7217.57539191021[/C][C]-117.57539191021[/C][/ROW]
[ROW][C]67[/C][C]7300[/C][C]6940.66612649102[/C][C]359.333873508978[/C][/ROW]
[ROW][C]68[/C][C]7300[/C][C]7096.90964043345[/C][C]203.090359566553[/C][/ROW]
[ROW][C]69[/C][C]6600[/C][C]6436.02383484878[/C][C]163.976165151224[/C][/ROW]
[ROW][C]70[/C][C]6800[/C][C]6887.84772003462[/C][C]-87.8477200346179[/C][/ROW]
[ROW][C]71[/C][C]5900[/C][C]6098.89343185499[/C][C]-198.893431854987[/C][/ROW]
[ROW][C]72[/C][C]4900[/C][C]4849.41258368132[/C][C]50.5874163186827[/C][/ROW]
[ROW][C]73[/C][C]5500[/C][C]5622.42443968768[/C][C]-122.424439687685[/C][/ROW]
[ROW][C]74[/C][C]6300[/C][C]6424.06564843714[/C][C]-124.065648437145[/C][/ROW]
[ROW][C]75[/C][C]7100[/C][C]6964.89572223687[/C][C]135.104277763133[/C][/ROW]
[ROW][C]76[/C][C]6700[/C][C]6857.36712685929[/C][C]-157.367126859294[/C][/ROW]
[ROW][C]77[/C][C]6700[/C][C]6687.35615727025[/C][C]12.6438427297453[/C][/ROW]
[ROW][C]78[/C][C]7100[/C][C]7064.89095026964[/C][C]35.1090497303558[/C][/ROW]
[ROW][C]79[/C][C]7300[/C][C]6959.10426557887[/C][C]340.895734421127[/C][/ROW]
[ROW][C]80[/C][C]7300[/C][C]7071.31371637601[/C][C]228.686283623992[/C][/ROW]
[ROW][C]81[/C][C]6200[/C][C]6409.92220899982[/C][C]-209.922208999817[/C][/ROW]
[ROW][C]82[/C][C]6500[/C][C]6688.20145113551[/C][C]-188.201451135507[/C][/ROW]
[ROW][C]83[/C][C]5800[/C][C]5839.72653278041[/C][C]-39.7265327804107[/C][/ROW]
[ROW][C]84[/C][C]4700[/C][C]4700.75975182351[/C][C]-0.759751823505212[/C][/ROW]
[ROW][C]85[/C][C]5500[/C][C]5412.91286862253[/C][C]87.087131377466[/C][/ROW]
[ROW][C]86[/C][C]6500[/C][C]6274.90194033054[/C][C]225.098059669459[/C][/ROW]
[ROW][C]87[/C][C]6800[/C][C]6987.46964230414[/C][C]-187.469642304143[/C][/ROW]
[ROW][C]88[/C][C]6600[/C][C]6712.52772972786[/C][C]-112.527729727857[/C][/ROW]
[ROW][C]89[/C][C]6300[/C][C]6601.63370713424[/C][C]-301.633707134237[/C][/ROW]
[ROW][C]90[/C][C]6700[/C][C]6894.3940452547[/C][C]-194.394045254697[/C][/ROW]
[ROW][C]91[/C][C]7200[/C][C]6800.32509002127[/C][C]399.67490997873[/C][/ROW]
[ROW][C]92[/C][C]7200[/C][C]6897.20278733066[/C][C]302.79721266934[/C][/ROW]
[ROW][C]93[/C][C]5900[/C][C]6139.82154634281[/C][C]-239.821546342814[/C][/ROW]
[ROW][C]94[/C][C]6100[/C][C]6413.05056369126[/C][C]-313.050563691256[/C][/ROW]
[ROW][C]95[/C][C]5500[/C][C]5564.62617974557[/C][C]-64.6261797455709[/C][/ROW]
[ROW][C]96[/C][C]4700[/C][C]4425.22462703475[/C][C]274.775372965253[/C][/ROW]
[ROW][C]97[/C][C]5400[/C][C]5237.86109491062[/C][C]162.138905089384[/C][/ROW]
[ROW][C]98[/C][C]6400[/C][C]6157.03437443104[/C][C]242.965625568962[/C][/ROW]
[ROW][C]99[/C][C]7500[/C][C]6766.10497208456[/C][C]733.895027915436[/C][/ROW]
[ROW][C]100[/C][C]6900[/C][C]6781.37956221357[/C][C]118.620437786431[/C][/ROW]
[ROW][C]101[/C][C]6400[/C][C]6696.7302975045[/C][C]-296.730297504504[/C][/ROW]
[ROW][C]102[/C][C]6700[/C][C]7029.09767123707[/C][C]-329.097671237072[/C][/ROW]
[ROW][C]103[/C][C]7100[/C][C]7061.45126199984[/C][C]38.5487380001578[/C][/ROW]
[ROW][C]104[/C][C]7100[/C][C]7035.60171368767[/C][C]64.3982863123256[/C][/ROW]
[ROW][C]105[/C][C]4000[/C][C]6071.32240935191[/C][C]-2071.32240935191[/C][/ROW]
[ROW][C]106[/C][C]6300[/C][C]5790.48656627349[/C][C]509.513433726514[/C][/ROW]
[ROW][C]107[/C][C]5400[/C][C]5236.20754848139[/C][C]163.792451518612[/C][/ROW]
[ROW][C]108[/C][C]4600[/C][C]4247.54051768331[/C][C]352.459482316686[/C][/ROW]
[ROW][C]109[/C][C]5400[/C][C]5049.97175988431[/C][C]350.028240115692[/C][/ROW]
[ROW][C]110[/C][C]6000[/C][C]6042.8162618201[/C][C]-42.8162618201004[/C][/ROW]
[ROW][C]111[/C][C]7200[/C][C]6695.67163178595[/C][C]504.328368214046[/C][/ROW]
[ROW][C]112[/C][C]6800[/C][C]6478.29186170129[/C][C]321.708138298713[/C][/ROW]
[ROW][C]113[/C][C]6400[/C][C]6338.59618195876[/C][C]61.403818041239[/C][/ROW]
[ROW][C]114[/C][C]7100[/C][C]6763.84824529545[/C][C]336.15175470455[/C][/ROW]
[ROW][C]115[/C][C]7500[/C][C]7087.57120307087[/C][C]412.428796929133[/C][/ROW]
[ROW][C]116[/C][C]7400[/C][C]7183.65581735346[/C][C]216.344182646539[/C][/ROW]
[ROW][C]117[/C][C]6400[/C][C]5711.93933995482[/C][C]688.060660045176[/C][/ROW]
[ROW][C]118[/C][C]6600[/C][C]6929.67189803788[/C][C]-329.67189803788[/C][/ROW]
[ROW][C]119[/C][C]5600[/C][C]6072.5506194569[/C][C]-472.550619456903[/C][/ROW]
[ROW][C]120[/C][C]4800[/C][C]4973.46320564024[/C][C]-173.463205640244[/C][/ROW]
[ROW][C]121[/C][C]5400[/C][C]5642.07970048199[/C][C]-242.079700481985[/C][/ROW]
[ROW][C]122[/C][C]6600[/C][C]6374.46457927503[/C][C]225.535420724966[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298058&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298058&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
1362006319.12393162393-119.123931623933
1470007168.63733380039-168.63733380039
1574007585.86676857237-185.866768572367
1672007325.69283020252-125.692830202522
1769006973.21316162787-73.2131616278684
1874007401.70343475613-1.70343475613481
1964006754.72580892856-354.725808928561
2055007199.80103978813-1699.80103978813
2166005833.84570682454766.154293175458
2270006598.37461228246401.625387717537
2362005479.26357114035720.736428859648
2451004153.36945778867946.630542211331
2556005585.7017241351114.2982758648923
2664006462.3835870288-62.3835870287958
2772006908.46253408791291.537465912085
2871006807.50121588711292.49878411289
2970006599.07222725982400.927772740185
3073007196.78847087749103.211529122511
3176006503.290118348221096.70988165178
3276007038.12657001713561.873429982872
3367007013.55607376513-313.556073765134
3468007414.43208864254-614.432088642536
3559006120.21297193539-220.212971935387
3650004607.74327619963392.256723800368
3756005654.65771485817-54.6577148581746
3856006508.28600850801-908.28600850801
3971006815.37065169821284.629348301785
4070006721.80879695516278.19120304484
4166006546.7560550147353.2439449852654
4272006973.10514878764226.894851212362
4372006582.66780561852617.332194381484
4472006843.17674565837356.823254341629
4562006531.21698614855-331.216986148547
4665006848.79011691652-348.790116916516
4758005736.8656410217963.13435897821
4849004471.56383125394428.436168746064
4958005417.40563101558382.594368984419
5068006181.39887093242618.601129067584
5171007260.31111557566-160.311115575656
5269007057.75747607076-157.757476070756
5368006715.0181142513784.981885748628
5472007211.90080484989-11.9008048498854
5572006869.67422854059330.32577145941
5674006991.19849653932408.801503460684
5764006525.09104550814-125.091045508138
5867006910.30712481402-210.307124814016
5962005960.73921629236239.260783707637
6050004857.85532163725142.144678362752
6156005723.83003077473-123.830030774735
6267006414.68892996992285.311070030077
6370007200.38912292981-200.389122929806
6468006992.99027576078-192.990275760783
6569006709.52783215107190.472167848935
6671007217.57539191021-117.57539191021
6773006940.66612649102359.333873508978
6873007096.90964043345203.090359566553
6966006436.02383484878163.976165151224
7068006887.84772003462-87.8477200346179
7159006098.89343185499-198.893431854987
7249004849.4125836813250.5874163186827
7355005622.42443968768-122.424439687685
7463006424.06564843714-124.065648437145
7571006964.89572223687135.104277763133
7667006857.36712685929-157.367126859294
7767006687.3561572702512.6438427297453
7871007064.8909502696435.1090497303558
7973006959.10426557887340.895734421127
8073007071.31371637601228.686283623992
8162006409.92220899982-209.922208999817
8265006688.20145113551-188.201451135507
8358005839.72653278041-39.7265327804107
8447004700.75975182351-0.759751823505212
8555005412.9128686225387.087131377466
8665006274.90194033054225.098059669459
8768006987.46964230414-187.469642304143
8866006712.52772972786-112.527729727857
8963006601.63370713424-301.633707134237
9067006894.3940452547-194.394045254697
9172006800.32509002127399.67490997873
9272006897.20278733066302.79721266934
9359006139.82154634281-239.821546342814
9461006413.05056369126-313.050563691256
9555005564.62617974557-64.6261797455709
9647004425.22462703475274.775372965253
9754005237.86109491062162.138905089384
9864006157.03437443104242.965625568962
9975006766.10497208456733.895027915436
10069006781.37956221357118.620437786431
10164006696.7302975045-296.730297504504
10267007029.09767123707-329.097671237072
10371007061.4512619998438.5487380001578
10471007035.6017136876764.3982863123256
10540006071.32240935191-2071.32240935191
10663005790.48656627349509.513433726514
10754005236.20754848139163.792451518612
10846004247.54051768331352.459482316686
10954005049.97175988431350.028240115692
11060006042.8162618201-42.8162618201004
11172006695.67163178595504.328368214046
11268006478.29186170129321.708138298713
11364006338.5961819587661.403818041239
11471006763.84824529545336.15175470455
11575007087.57120307087412.428796929133
11674007183.65581735346216.344182646539
11764005711.93933995482688.060660045176
11866006929.67189803788-329.67189803788
11956006072.5506194569-472.550619456903
12048004973.46320564024-173.463205640244
12154005642.07970048199-242.079700481985
12266006374.46457927503225.535420724966







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1237261.266579973136436.762519343628085.77064060264
1246861.527881976376002.144180001117720.91158395163
1256568.254177998665673.326131619297463.18222437802
1267054.034963500786122.915786762637985.15414023893
1277304.876196597636336.935661818718272.81673137656
1287231.154322248566225.777540489578236.53110400754
1295818.902191452024775.488516559216862.31586634483
1306564.489823380165482.451865545117646.52778121522
1315757.90106380984636.663800160586879.13832745903
1324870.315725501273709.315696681066031.31575432148
1335570.208571861454368.893154854516771.52398886839
1346496.363872126925254.19062075757738.53712349634
1357259.677437490655905.290693506448614.06418147487
1366859.938739493895465.765053475818254.11242551198
1376566.665035516185132.091841337778001.23822969459
1387052.44582101835576.874137683988528.01750435263
1397303.287054115165786.130737593438820.44337063689
1407229.565179766085670.250224366058788.88013516612

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
123 & 7261.26657997313 & 6436.76251934362 & 8085.77064060264 \tabularnewline
124 & 6861.52788197637 & 6002.14418000111 & 7720.91158395163 \tabularnewline
125 & 6568.25417799866 & 5673.32613161929 & 7463.18222437802 \tabularnewline
126 & 7054.03496350078 & 6122.91578676263 & 7985.15414023893 \tabularnewline
127 & 7304.87619659763 & 6336.93566181871 & 8272.81673137656 \tabularnewline
128 & 7231.15432224856 & 6225.77754048957 & 8236.53110400754 \tabularnewline
129 & 5818.90219145202 & 4775.48851655921 & 6862.31586634483 \tabularnewline
130 & 6564.48982338016 & 5482.45186554511 & 7646.52778121522 \tabularnewline
131 & 5757.9010638098 & 4636.66380016058 & 6879.13832745903 \tabularnewline
132 & 4870.31572550127 & 3709.31569668106 & 6031.31575432148 \tabularnewline
133 & 5570.20857186145 & 4368.89315485451 & 6771.52398886839 \tabularnewline
134 & 6496.36387212692 & 5254.1906207575 & 7738.53712349634 \tabularnewline
135 & 7259.67743749065 & 5905.29069350644 & 8614.06418147487 \tabularnewline
136 & 6859.93873949389 & 5465.76505347581 & 8254.11242551198 \tabularnewline
137 & 6566.66503551618 & 5132.09184133777 & 8001.23822969459 \tabularnewline
138 & 7052.4458210183 & 5576.87413768398 & 8528.01750435263 \tabularnewline
139 & 7303.28705411516 & 5786.13073759343 & 8820.44337063689 \tabularnewline
140 & 7229.56517976608 & 5670.25022436605 & 8788.88013516612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298058&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]123[/C][C]7261.26657997313[/C][C]6436.76251934362[/C][C]8085.77064060264[/C][/ROW]
[ROW][C]124[/C][C]6861.52788197637[/C][C]6002.14418000111[/C][C]7720.91158395163[/C][/ROW]
[ROW][C]125[/C][C]6568.25417799866[/C][C]5673.32613161929[/C][C]7463.18222437802[/C][/ROW]
[ROW][C]126[/C][C]7054.03496350078[/C][C]6122.91578676263[/C][C]7985.15414023893[/C][/ROW]
[ROW][C]127[/C][C]7304.87619659763[/C][C]6336.93566181871[/C][C]8272.81673137656[/C][/ROW]
[ROW][C]128[/C][C]7231.15432224856[/C][C]6225.77754048957[/C][C]8236.53110400754[/C][/ROW]
[ROW][C]129[/C][C]5818.90219145202[/C][C]4775.48851655921[/C][C]6862.31586634483[/C][/ROW]
[ROW][C]130[/C][C]6564.48982338016[/C][C]5482.45186554511[/C][C]7646.52778121522[/C][/ROW]
[ROW][C]131[/C][C]5757.9010638098[/C][C]4636.66380016058[/C][C]6879.13832745903[/C][/ROW]
[ROW][C]132[/C][C]4870.31572550127[/C][C]3709.31569668106[/C][C]6031.31575432148[/C][/ROW]
[ROW][C]133[/C][C]5570.20857186145[/C][C]4368.89315485451[/C][C]6771.52398886839[/C][/ROW]
[ROW][C]134[/C][C]6496.36387212692[/C][C]5254.1906207575[/C][C]7738.53712349634[/C][/ROW]
[ROW][C]135[/C][C]7259.67743749065[/C][C]5905.29069350644[/C][C]8614.06418147487[/C][/ROW]
[ROW][C]136[/C][C]6859.93873949389[/C][C]5465.76505347581[/C][C]8254.11242551198[/C][/ROW]
[ROW][C]137[/C][C]6566.66503551618[/C][C]5132.09184133777[/C][C]8001.23822969459[/C][/ROW]
[ROW][C]138[/C][C]7052.4458210183[/C][C]5576.87413768398[/C][C]8528.01750435263[/C][/ROW]
[ROW][C]139[/C][C]7303.28705411516[/C][C]5786.13073759343[/C][C]8820.44337063689[/C][/ROW]
[ROW][C]140[/C][C]7229.56517976608[/C][C]5670.25022436605[/C][C]8788.88013516612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298058&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298058&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
1237261.266579973136436.762519343628085.77064060264
1246861.527881976376002.144180001117720.91158395163
1256568.254177998665673.326131619297463.18222437802
1267054.034963500786122.915786762637985.15414023893
1277304.876196597636336.935661818718272.81673137656
1287231.154322248566225.777540489578236.53110400754
1295818.902191452024775.488516559216862.31586634483
1306564.489823380165482.451865545117646.52778121522
1315757.90106380984636.663800160586879.13832745903
1324870.315725501273709.315696681066031.31575432148
1335570.208571861454368.893154854516771.52398886839
1346496.363872126925254.19062075757738.53712349634
1357259.677437490655905.290693506448614.06418147487
1366859.938739493895465.765053475818254.11242551198
1376566.665035516185132.091841337778001.23822969459
1387052.44582101835576.874137683988528.01750435263
1397303.287054115165786.130737593438820.44337063689
1407229.565179766085670.250224366058788.88013516612



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
R code (references can be found in the software module):
par4 <- '18'
par3 <- 'additive'
par2 <- 'Single'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')