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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, 14 Dec 2016 14:17:33 +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/14/t1481721468zd27chioioh0amx.htm/, Retrieved Fri, 03 May 2024 16:53:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299401, Retrieved Fri, 03 May 2024 16:53:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-14 13:17:33] [57f1f1af0ba442a9c0352eeef9ded060] [Current]
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Dataseries X:
4393.9
4248
4346.2
4351.7
4424.4
4468.4
4519.1
4518.2
4574.5
4509.6
4337.9
4441.8
4414.1
4465.9
4426
4518.8
4606.3
4647.4
4650.8
4650.2
4720.1
4655
4520.8
4617.3
4488.1
4527.4
4618.3
4642.8
4667.3
4640.6
4716.9
4719.4
4817.3
4764.5
4514.1
4625
4617.7
4361.3
4474.9
4623.8
4692
4672.1
4721.5
4784.6
4858.7
4813.3
4628.2
4710.4
4698.4
4631
4727.4
4719.9
4890.6
4839.9
4867.5
4898.3
4675.7
4981.9
4771.1
4827.8
4685
4646.1
4815
4911.8
4958.4
5019.4
5024.3
5035.8
5082.4
5179.2
4963.2
4951.3
4876.4
4812.1
5004.1
5093.8
5063.1
5078.6
5251.5
5263.2
5280.5
5386.1
5227.3
5149.5
5128.6
5087.7
5188.5
5084
5258.6
5348.9
5280
5374.2
5458.4
5315
5294.5
5341.4
5068
5156.9
5184.7
5280.7
5339
5377.7
5388.6
5443.6
5528.7
5539
5292
5351.5
5163.7
5105
5248.1
5370.9
5484.9
5510.7
5484.9
5567.8
5275.6




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299401&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299401&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299401&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.272927620005395
beta0.0127384334044244
gamma0.341725519303665

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.272927620005395 \tabularnewline
beta & 0.0127384334044244 \tabularnewline
gamma & 0.341725519303665 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299401&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]0.272927620005395[/C][/ROW]
[ROW][C]beta[/C][C]0.0127384334044244[/C][/ROW]
[ROW][C]gamma[/C][C]0.341725519303665[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299401&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299401&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
alpha0.272927620005395
beta0.0127384334044244
gamma0.341725519303665







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134414.14335.4126224675878.687377532422
144465.94410.0525508260655.8474491739407
1544264387.3588492165238.6411507834819
164518.84491.2992306867827.500769313222
174606.34585.6281533655220.6718466344846
184647.44630.7287552429916.6712447570126
194650.84661.93674396186-11.1367439618625
204650.24661.22142079223-11.0214207922327
214720.14716.870846759253.2291532407462
2246554653.636075999151.36392400084878
234520.84475.2526948201545.5473051798463
244617.34593.2002383415924.0997616584118
254488.14591.84284876035-103.742848760349
264527.44612.82722684118-85.4272268411778
274618.34545.2987777190573.0012222809546
284642.84658.61330002006-15.8133000200623
294667.34741.63283140322-74.3328314032169
304640.64759.99977401075-119.399774010753
314716.94746.31850668752-29.4185066875161
324719.44739.42496101212-20.0249610121209
334817.34795.9159607889421.3840392110615
344764.54734.8165854405229.6834145594785
354514.14570.82164613408-56.7216461340813
3646254655.38092319232-30.3809231923178
374617.74605.3548392133812.3451607866236
384361.34662.09536691341-300.795366913409
394474.94573.27644132959-98.3764413295921
404623.84614.902840040018.89715995998722
4146924687.306412909364.69358709064272
424672.14713.74560817729-41.6456081772867
434721.54741.86348318961-20.3634831896052
444784.64737.9993871073746.6006128926292
454858.74821.6824540495337.0175459504699
464813.34765.0318592077548.2681407922455
474628.24582.0403922683946.1596077316071
484710.44701.312329197089.08767080291636
494698.44671.2128757294727.1871242705274
5046314651.51179278856-20.5117927885558
514727.44690.5064152480536.8935847519533
524719.94799.66787083201-79.7678708320136
534890.64849.1441956894641.4558043105399
544839.94874.63182554415-34.731825544146
554867.54911.65200430534-44.1520043053424
564898.34918.56936996015-20.2693699601505
574675.74983.59039739489-307.890397394891
584981.94833.6473343663148.252665633701
594771.14673.1187612792897.9812387207248
604827.84798.6147309425529.1852690574469
6146854777.25857889057-92.2585788905717
624646.14711.59011002739-65.4901100273901
6348154752.1323819474562.867618052549
644911.84839.1636968147972.6363031852088
654958.44961.87691193243-3.47691193242645
665019.44955.3374299428164.0625700571918
675024.35017.56252111796.73747888210437
685035.85044.66293375418-8.86293375418336
695082.45039.6974405747342.7025594252664
705179.25101.4678191224277.7321808775841
714963.24900.3695328048462.8304671951591
724951.35002.9150053128-51.6150053128022
734876.44927.2125334341-50.8125334341003
744812.14878.41778786656-66.3177878665547
755004.14954.4002852583749.699714741635
765093.85043.2134276503950.5865723496136
775063.15144.28583314066-81.1858331406565
785078.65133.59197145201-54.9919714520056
795251.55149.49086911585102.009130884152
805263.25199.2718403355263.928159664476
815280.55227.4191377336653.0808622663408
825386.15302.8593167971783.2406832028337
835227.35091.56260246794135.737397532055
845149.55188.12024961325-38.6202496132455
855128.65114.0044551064714.5955448935301
865087.75077.977555120739.72244487926764
875188.55210.30710363815-21.8071036381516
8850845283.77185971892-199.771859718921
895258.65285.26428074689-26.6642807468897
905348.95296.5636842364952.3363157635113
9152805383.78694838236-103.786948382364
925374.25367.990416189336.20958381067248
935458.45377.4313914988280.9686085011772
9453155469.40892505493-154.408925054932
955294.55201.7034877528192.7965122471942
965341.45242.2801703719599.1198296280518
9750685217.26833276804-149.268332768038
985156.95133.6927407383323.207259261666
995184.75262.07299794009-77.3729979400932
1005280.75274.602691014626.09730898537873
10153395376.39621361818-37.3962136181772
1025377.75404.279967273-26.5799672730036
1035388.65430.50716897401-41.9071689740076
1045443.65458.7775455242-15.1775455241959
1055528.75480.3989501976948.3010498023123
10655395503.8540452633935.1459547366067
10752925344.98559336706-52.9855933670578
1085351.55346.636495547834.86350445216704
1095163.75231.64335265574-67.9433526557423
11051055212.26428194911-107.264281949111
1115248.15279.42622637811-31.3262263781126
1125370.95324.6592089545346.2407910454695
1135484.95426.5813075933758.3186924066276
1145510.75483.1857226762627.5142773237403
1155484.95520.32409474188-35.4240947418803
1165567.85557.320747954610.4792520454002
1175275.65602.03892550145-326.438925501447

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4414.1 & 4335.41262246758 & 78.687377532422 \tabularnewline
14 & 4465.9 & 4410.05255082606 & 55.8474491739407 \tabularnewline
15 & 4426 & 4387.35884921652 & 38.6411507834819 \tabularnewline
16 & 4518.8 & 4491.29923068678 & 27.500769313222 \tabularnewline
17 & 4606.3 & 4585.62815336552 & 20.6718466344846 \tabularnewline
18 & 4647.4 & 4630.72875524299 & 16.6712447570126 \tabularnewline
19 & 4650.8 & 4661.93674396186 & -11.1367439618625 \tabularnewline
20 & 4650.2 & 4661.22142079223 & -11.0214207922327 \tabularnewline
21 & 4720.1 & 4716.87084675925 & 3.2291532407462 \tabularnewline
22 & 4655 & 4653.63607599915 & 1.36392400084878 \tabularnewline
23 & 4520.8 & 4475.25269482015 & 45.5473051798463 \tabularnewline
24 & 4617.3 & 4593.20023834159 & 24.0997616584118 \tabularnewline
25 & 4488.1 & 4591.84284876035 & -103.742848760349 \tabularnewline
26 & 4527.4 & 4612.82722684118 & -85.4272268411778 \tabularnewline
27 & 4618.3 & 4545.29877771905 & 73.0012222809546 \tabularnewline
28 & 4642.8 & 4658.61330002006 & -15.8133000200623 \tabularnewline
29 & 4667.3 & 4741.63283140322 & -74.3328314032169 \tabularnewline
30 & 4640.6 & 4759.99977401075 & -119.399774010753 \tabularnewline
31 & 4716.9 & 4746.31850668752 & -29.4185066875161 \tabularnewline
32 & 4719.4 & 4739.42496101212 & -20.0249610121209 \tabularnewline
33 & 4817.3 & 4795.91596078894 & 21.3840392110615 \tabularnewline
34 & 4764.5 & 4734.81658544052 & 29.6834145594785 \tabularnewline
35 & 4514.1 & 4570.82164613408 & -56.7216461340813 \tabularnewline
36 & 4625 & 4655.38092319232 & -30.3809231923178 \tabularnewline
37 & 4617.7 & 4605.35483921338 & 12.3451607866236 \tabularnewline
38 & 4361.3 & 4662.09536691341 & -300.795366913409 \tabularnewline
39 & 4474.9 & 4573.27644132959 & -98.3764413295921 \tabularnewline
40 & 4623.8 & 4614.90284004001 & 8.89715995998722 \tabularnewline
41 & 4692 & 4687.30641290936 & 4.69358709064272 \tabularnewline
42 & 4672.1 & 4713.74560817729 & -41.6456081772867 \tabularnewline
43 & 4721.5 & 4741.86348318961 & -20.3634831896052 \tabularnewline
44 & 4784.6 & 4737.99938710737 & 46.6006128926292 \tabularnewline
45 & 4858.7 & 4821.68245404953 & 37.0175459504699 \tabularnewline
46 & 4813.3 & 4765.03185920775 & 48.2681407922455 \tabularnewline
47 & 4628.2 & 4582.04039226839 & 46.1596077316071 \tabularnewline
48 & 4710.4 & 4701.31232919708 & 9.08767080291636 \tabularnewline
49 & 4698.4 & 4671.21287572947 & 27.1871242705274 \tabularnewline
50 & 4631 & 4651.51179278856 & -20.5117927885558 \tabularnewline
51 & 4727.4 & 4690.50641524805 & 36.8935847519533 \tabularnewline
52 & 4719.9 & 4799.66787083201 & -79.7678708320136 \tabularnewline
53 & 4890.6 & 4849.14419568946 & 41.4558043105399 \tabularnewline
54 & 4839.9 & 4874.63182554415 & -34.731825544146 \tabularnewline
55 & 4867.5 & 4911.65200430534 & -44.1520043053424 \tabularnewline
56 & 4898.3 & 4918.56936996015 & -20.2693699601505 \tabularnewline
57 & 4675.7 & 4983.59039739489 & -307.890397394891 \tabularnewline
58 & 4981.9 & 4833.6473343663 & 148.252665633701 \tabularnewline
59 & 4771.1 & 4673.11876127928 & 97.9812387207248 \tabularnewline
60 & 4827.8 & 4798.61473094255 & 29.1852690574469 \tabularnewline
61 & 4685 & 4777.25857889057 & -92.2585788905717 \tabularnewline
62 & 4646.1 & 4711.59011002739 & -65.4901100273901 \tabularnewline
63 & 4815 & 4752.13238194745 & 62.867618052549 \tabularnewline
64 & 4911.8 & 4839.16369681479 & 72.6363031852088 \tabularnewline
65 & 4958.4 & 4961.87691193243 & -3.47691193242645 \tabularnewline
66 & 5019.4 & 4955.33742994281 & 64.0625700571918 \tabularnewline
67 & 5024.3 & 5017.5625211179 & 6.73747888210437 \tabularnewline
68 & 5035.8 & 5044.66293375418 & -8.86293375418336 \tabularnewline
69 & 5082.4 & 5039.69744057473 & 42.7025594252664 \tabularnewline
70 & 5179.2 & 5101.46781912242 & 77.7321808775841 \tabularnewline
71 & 4963.2 & 4900.36953280484 & 62.8304671951591 \tabularnewline
72 & 4951.3 & 5002.9150053128 & -51.6150053128022 \tabularnewline
73 & 4876.4 & 4927.2125334341 & -50.8125334341003 \tabularnewline
74 & 4812.1 & 4878.41778786656 & -66.3177878665547 \tabularnewline
75 & 5004.1 & 4954.40028525837 & 49.699714741635 \tabularnewline
76 & 5093.8 & 5043.21342765039 & 50.5865723496136 \tabularnewline
77 & 5063.1 & 5144.28583314066 & -81.1858331406565 \tabularnewline
78 & 5078.6 & 5133.59197145201 & -54.9919714520056 \tabularnewline
79 & 5251.5 & 5149.49086911585 & 102.009130884152 \tabularnewline
80 & 5263.2 & 5199.27184033552 & 63.928159664476 \tabularnewline
81 & 5280.5 & 5227.41913773366 & 53.0808622663408 \tabularnewline
82 & 5386.1 & 5302.85931679717 & 83.2406832028337 \tabularnewline
83 & 5227.3 & 5091.56260246794 & 135.737397532055 \tabularnewline
84 & 5149.5 & 5188.12024961325 & -38.6202496132455 \tabularnewline
85 & 5128.6 & 5114.00445510647 & 14.5955448935301 \tabularnewline
86 & 5087.7 & 5077.97755512073 & 9.72244487926764 \tabularnewline
87 & 5188.5 & 5210.30710363815 & -21.8071036381516 \tabularnewline
88 & 5084 & 5283.77185971892 & -199.771859718921 \tabularnewline
89 & 5258.6 & 5285.26428074689 & -26.6642807468897 \tabularnewline
90 & 5348.9 & 5296.56368423649 & 52.3363157635113 \tabularnewline
91 & 5280 & 5383.78694838236 & -103.786948382364 \tabularnewline
92 & 5374.2 & 5367.99041618933 & 6.20958381067248 \tabularnewline
93 & 5458.4 & 5377.43139149882 & 80.9686085011772 \tabularnewline
94 & 5315 & 5469.40892505493 & -154.408925054932 \tabularnewline
95 & 5294.5 & 5201.70348775281 & 92.7965122471942 \tabularnewline
96 & 5341.4 & 5242.28017037195 & 99.1198296280518 \tabularnewline
97 & 5068 & 5217.26833276804 & -149.268332768038 \tabularnewline
98 & 5156.9 & 5133.69274073833 & 23.207259261666 \tabularnewline
99 & 5184.7 & 5262.07299794009 & -77.3729979400932 \tabularnewline
100 & 5280.7 & 5274.60269101462 & 6.09730898537873 \tabularnewline
101 & 5339 & 5376.39621361818 & -37.3962136181772 \tabularnewline
102 & 5377.7 & 5404.279967273 & -26.5799672730036 \tabularnewline
103 & 5388.6 & 5430.50716897401 & -41.9071689740076 \tabularnewline
104 & 5443.6 & 5458.7775455242 & -15.1775455241959 \tabularnewline
105 & 5528.7 & 5480.39895019769 & 48.3010498023123 \tabularnewline
106 & 5539 & 5503.85404526339 & 35.1459547366067 \tabularnewline
107 & 5292 & 5344.98559336706 & -52.9855933670578 \tabularnewline
108 & 5351.5 & 5346.63649554783 & 4.86350445216704 \tabularnewline
109 & 5163.7 & 5231.64335265574 & -67.9433526557423 \tabularnewline
110 & 5105 & 5212.26428194911 & -107.264281949111 \tabularnewline
111 & 5248.1 & 5279.42622637811 & -31.3262263781126 \tabularnewline
112 & 5370.9 & 5324.65920895453 & 46.2407910454695 \tabularnewline
113 & 5484.9 & 5426.58130759337 & 58.3186924066276 \tabularnewline
114 & 5510.7 & 5483.18572267626 & 27.5142773237403 \tabularnewline
115 & 5484.9 & 5520.32409474188 & -35.4240947418803 \tabularnewline
116 & 5567.8 & 5557.3207479546 & 10.4792520454002 \tabularnewline
117 & 5275.6 & 5602.03892550145 & -326.438925501447 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299401&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]4414.1[/C][C]4335.41262246758[/C][C]78.687377532422[/C][/ROW]
[ROW][C]14[/C][C]4465.9[/C][C]4410.05255082606[/C][C]55.8474491739407[/C][/ROW]
[ROW][C]15[/C][C]4426[/C][C]4387.35884921652[/C][C]38.6411507834819[/C][/ROW]
[ROW][C]16[/C][C]4518.8[/C][C]4491.29923068678[/C][C]27.500769313222[/C][/ROW]
[ROW][C]17[/C][C]4606.3[/C][C]4585.62815336552[/C][C]20.6718466344846[/C][/ROW]
[ROW][C]18[/C][C]4647.4[/C][C]4630.72875524299[/C][C]16.6712447570126[/C][/ROW]
[ROW][C]19[/C][C]4650.8[/C][C]4661.93674396186[/C][C]-11.1367439618625[/C][/ROW]
[ROW][C]20[/C][C]4650.2[/C][C]4661.22142079223[/C][C]-11.0214207922327[/C][/ROW]
[ROW][C]21[/C][C]4720.1[/C][C]4716.87084675925[/C][C]3.2291532407462[/C][/ROW]
[ROW][C]22[/C][C]4655[/C][C]4653.63607599915[/C][C]1.36392400084878[/C][/ROW]
[ROW][C]23[/C][C]4520.8[/C][C]4475.25269482015[/C][C]45.5473051798463[/C][/ROW]
[ROW][C]24[/C][C]4617.3[/C][C]4593.20023834159[/C][C]24.0997616584118[/C][/ROW]
[ROW][C]25[/C][C]4488.1[/C][C]4591.84284876035[/C][C]-103.742848760349[/C][/ROW]
[ROW][C]26[/C][C]4527.4[/C][C]4612.82722684118[/C][C]-85.4272268411778[/C][/ROW]
[ROW][C]27[/C][C]4618.3[/C][C]4545.29877771905[/C][C]73.0012222809546[/C][/ROW]
[ROW][C]28[/C][C]4642.8[/C][C]4658.61330002006[/C][C]-15.8133000200623[/C][/ROW]
[ROW][C]29[/C][C]4667.3[/C][C]4741.63283140322[/C][C]-74.3328314032169[/C][/ROW]
[ROW][C]30[/C][C]4640.6[/C][C]4759.99977401075[/C][C]-119.399774010753[/C][/ROW]
[ROW][C]31[/C][C]4716.9[/C][C]4746.31850668752[/C][C]-29.4185066875161[/C][/ROW]
[ROW][C]32[/C][C]4719.4[/C][C]4739.42496101212[/C][C]-20.0249610121209[/C][/ROW]
[ROW][C]33[/C][C]4817.3[/C][C]4795.91596078894[/C][C]21.3840392110615[/C][/ROW]
[ROW][C]34[/C][C]4764.5[/C][C]4734.81658544052[/C][C]29.6834145594785[/C][/ROW]
[ROW][C]35[/C][C]4514.1[/C][C]4570.82164613408[/C][C]-56.7216461340813[/C][/ROW]
[ROW][C]36[/C][C]4625[/C][C]4655.38092319232[/C][C]-30.3809231923178[/C][/ROW]
[ROW][C]37[/C][C]4617.7[/C][C]4605.35483921338[/C][C]12.3451607866236[/C][/ROW]
[ROW][C]38[/C][C]4361.3[/C][C]4662.09536691341[/C][C]-300.795366913409[/C][/ROW]
[ROW][C]39[/C][C]4474.9[/C][C]4573.27644132959[/C][C]-98.3764413295921[/C][/ROW]
[ROW][C]40[/C][C]4623.8[/C][C]4614.90284004001[/C][C]8.89715995998722[/C][/ROW]
[ROW][C]41[/C][C]4692[/C][C]4687.30641290936[/C][C]4.69358709064272[/C][/ROW]
[ROW][C]42[/C][C]4672.1[/C][C]4713.74560817729[/C][C]-41.6456081772867[/C][/ROW]
[ROW][C]43[/C][C]4721.5[/C][C]4741.86348318961[/C][C]-20.3634831896052[/C][/ROW]
[ROW][C]44[/C][C]4784.6[/C][C]4737.99938710737[/C][C]46.6006128926292[/C][/ROW]
[ROW][C]45[/C][C]4858.7[/C][C]4821.68245404953[/C][C]37.0175459504699[/C][/ROW]
[ROW][C]46[/C][C]4813.3[/C][C]4765.03185920775[/C][C]48.2681407922455[/C][/ROW]
[ROW][C]47[/C][C]4628.2[/C][C]4582.04039226839[/C][C]46.1596077316071[/C][/ROW]
[ROW][C]48[/C][C]4710.4[/C][C]4701.31232919708[/C][C]9.08767080291636[/C][/ROW]
[ROW][C]49[/C][C]4698.4[/C][C]4671.21287572947[/C][C]27.1871242705274[/C][/ROW]
[ROW][C]50[/C][C]4631[/C][C]4651.51179278856[/C][C]-20.5117927885558[/C][/ROW]
[ROW][C]51[/C][C]4727.4[/C][C]4690.50641524805[/C][C]36.8935847519533[/C][/ROW]
[ROW][C]52[/C][C]4719.9[/C][C]4799.66787083201[/C][C]-79.7678708320136[/C][/ROW]
[ROW][C]53[/C][C]4890.6[/C][C]4849.14419568946[/C][C]41.4558043105399[/C][/ROW]
[ROW][C]54[/C][C]4839.9[/C][C]4874.63182554415[/C][C]-34.731825544146[/C][/ROW]
[ROW][C]55[/C][C]4867.5[/C][C]4911.65200430534[/C][C]-44.1520043053424[/C][/ROW]
[ROW][C]56[/C][C]4898.3[/C][C]4918.56936996015[/C][C]-20.2693699601505[/C][/ROW]
[ROW][C]57[/C][C]4675.7[/C][C]4983.59039739489[/C][C]-307.890397394891[/C][/ROW]
[ROW][C]58[/C][C]4981.9[/C][C]4833.6473343663[/C][C]148.252665633701[/C][/ROW]
[ROW][C]59[/C][C]4771.1[/C][C]4673.11876127928[/C][C]97.9812387207248[/C][/ROW]
[ROW][C]60[/C][C]4827.8[/C][C]4798.61473094255[/C][C]29.1852690574469[/C][/ROW]
[ROW][C]61[/C][C]4685[/C][C]4777.25857889057[/C][C]-92.2585788905717[/C][/ROW]
[ROW][C]62[/C][C]4646.1[/C][C]4711.59011002739[/C][C]-65.4901100273901[/C][/ROW]
[ROW][C]63[/C][C]4815[/C][C]4752.13238194745[/C][C]62.867618052549[/C][/ROW]
[ROW][C]64[/C][C]4911.8[/C][C]4839.16369681479[/C][C]72.6363031852088[/C][/ROW]
[ROW][C]65[/C][C]4958.4[/C][C]4961.87691193243[/C][C]-3.47691193242645[/C][/ROW]
[ROW][C]66[/C][C]5019.4[/C][C]4955.33742994281[/C][C]64.0625700571918[/C][/ROW]
[ROW][C]67[/C][C]5024.3[/C][C]5017.5625211179[/C][C]6.73747888210437[/C][/ROW]
[ROW][C]68[/C][C]5035.8[/C][C]5044.66293375418[/C][C]-8.86293375418336[/C][/ROW]
[ROW][C]69[/C][C]5082.4[/C][C]5039.69744057473[/C][C]42.7025594252664[/C][/ROW]
[ROW][C]70[/C][C]5179.2[/C][C]5101.46781912242[/C][C]77.7321808775841[/C][/ROW]
[ROW][C]71[/C][C]4963.2[/C][C]4900.36953280484[/C][C]62.8304671951591[/C][/ROW]
[ROW][C]72[/C][C]4951.3[/C][C]5002.9150053128[/C][C]-51.6150053128022[/C][/ROW]
[ROW][C]73[/C][C]4876.4[/C][C]4927.2125334341[/C][C]-50.8125334341003[/C][/ROW]
[ROW][C]74[/C][C]4812.1[/C][C]4878.41778786656[/C][C]-66.3177878665547[/C][/ROW]
[ROW][C]75[/C][C]5004.1[/C][C]4954.40028525837[/C][C]49.699714741635[/C][/ROW]
[ROW][C]76[/C][C]5093.8[/C][C]5043.21342765039[/C][C]50.5865723496136[/C][/ROW]
[ROW][C]77[/C][C]5063.1[/C][C]5144.28583314066[/C][C]-81.1858331406565[/C][/ROW]
[ROW][C]78[/C][C]5078.6[/C][C]5133.59197145201[/C][C]-54.9919714520056[/C][/ROW]
[ROW][C]79[/C][C]5251.5[/C][C]5149.49086911585[/C][C]102.009130884152[/C][/ROW]
[ROW][C]80[/C][C]5263.2[/C][C]5199.27184033552[/C][C]63.928159664476[/C][/ROW]
[ROW][C]81[/C][C]5280.5[/C][C]5227.41913773366[/C][C]53.0808622663408[/C][/ROW]
[ROW][C]82[/C][C]5386.1[/C][C]5302.85931679717[/C][C]83.2406832028337[/C][/ROW]
[ROW][C]83[/C][C]5227.3[/C][C]5091.56260246794[/C][C]135.737397532055[/C][/ROW]
[ROW][C]84[/C][C]5149.5[/C][C]5188.12024961325[/C][C]-38.6202496132455[/C][/ROW]
[ROW][C]85[/C][C]5128.6[/C][C]5114.00445510647[/C][C]14.5955448935301[/C][/ROW]
[ROW][C]86[/C][C]5087.7[/C][C]5077.97755512073[/C][C]9.72244487926764[/C][/ROW]
[ROW][C]87[/C][C]5188.5[/C][C]5210.30710363815[/C][C]-21.8071036381516[/C][/ROW]
[ROW][C]88[/C][C]5084[/C][C]5283.77185971892[/C][C]-199.771859718921[/C][/ROW]
[ROW][C]89[/C][C]5258.6[/C][C]5285.26428074689[/C][C]-26.6642807468897[/C][/ROW]
[ROW][C]90[/C][C]5348.9[/C][C]5296.56368423649[/C][C]52.3363157635113[/C][/ROW]
[ROW][C]91[/C][C]5280[/C][C]5383.78694838236[/C][C]-103.786948382364[/C][/ROW]
[ROW][C]92[/C][C]5374.2[/C][C]5367.99041618933[/C][C]6.20958381067248[/C][/ROW]
[ROW][C]93[/C][C]5458.4[/C][C]5377.43139149882[/C][C]80.9686085011772[/C][/ROW]
[ROW][C]94[/C][C]5315[/C][C]5469.40892505493[/C][C]-154.408925054932[/C][/ROW]
[ROW][C]95[/C][C]5294.5[/C][C]5201.70348775281[/C][C]92.7965122471942[/C][/ROW]
[ROW][C]96[/C][C]5341.4[/C][C]5242.28017037195[/C][C]99.1198296280518[/C][/ROW]
[ROW][C]97[/C][C]5068[/C][C]5217.26833276804[/C][C]-149.268332768038[/C][/ROW]
[ROW][C]98[/C][C]5156.9[/C][C]5133.69274073833[/C][C]23.207259261666[/C][/ROW]
[ROW][C]99[/C][C]5184.7[/C][C]5262.07299794009[/C][C]-77.3729979400932[/C][/ROW]
[ROW][C]100[/C][C]5280.7[/C][C]5274.60269101462[/C][C]6.09730898537873[/C][/ROW]
[ROW][C]101[/C][C]5339[/C][C]5376.39621361818[/C][C]-37.3962136181772[/C][/ROW]
[ROW][C]102[/C][C]5377.7[/C][C]5404.279967273[/C][C]-26.5799672730036[/C][/ROW]
[ROW][C]103[/C][C]5388.6[/C][C]5430.50716897401[/C][C]-41.9071689740076[/C][/ROW]
[ROW][C]104[/C][C]5443.6[/C][C]5458.7775455242[/C][C]-15.1775455241959[/C][/ROW]
[ROW][C]105[/C][C]5528.7[/C][C]5480.39895019769[/C][C]48.3010498023123[/C][/ROW]
[ROW][C]106[/C][C]5539[/C][C]5503.85404526339[/C][C]35.1459547366067[/C][/ROW]
[ROW][C]107[/C][C]5292[/C][C]5344.98559336706[/C][C]-52.9855933670578[/C][/ROW]
[ROW][C]108[/C][C]5351.5[/C][C]5346.63649554783[/C][C]4.86350445216704[/C][/ROW]
[ROW][C]109[/C][C]5163.7[/C][C]5231.64335265574[/C][C]-67.9433526557423[/C][/ROW]
[ROW][C]110[/C][C]5105[/C][C]5212.26428194911[/C][C]-107.264281949111[/C][/ROW]
[ROW][C]111[/C][C]5248.1[/C][C]5279.42622637811[/C][C]-31.3262263781126[/C][/ROW]
[ROW][C]112[/C][C]5370.9[/C][C]5324.65920895453[/C][C]46.2407910454695[/C][/ROW]
[ROW][C]113[/C][C]5484.9[/C][C]5426.58130759337[/C][C]58.3186924066276[/C][/ROW]
[ROW][C]114[/C][C]5510.7[/C][C]5483.18572267626[/C][C]27.5142773237403[/C][/ROW]
[ROW][C]115[/C][C]5484.9[/C][C]5520.32409474188[/C][C]-35.4240947418803[/C][/ROW]
[ROW][C]116[/C][C]5567.8[/C][C]5557.3207479546[/C][C]10.4792520454002[/C][/ROW]
[ROW][C]117[/C][C]5275.6[/C][C]5602.03892550145[/C][C]-326.438925501447[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299401&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299401&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
134414.14335.4126224675878.687377532422
144465.94410.0525508260655.8474491739407
1544264387.3588492165238.6411507834819
164518.84491.2992306867827.500769313222
174606.34585.6281533655220.6718466344846
184647.44630.7287552429916.6712447570126
194650.84661.93674396186-11.1367439618625
204650.24661.22142079223-11.0214207922327
214720.14716.870846759253.2291532407462
2246554653.636075999151.36392400084878
234520.84475.2526948201545.5473051798463
244617.34593.2002383415924.0997616584118
254488.14591.84284876035-103.742848760349
264527.44612.82722684118-85.4272268411778
274618.34545.2987777190573.0012222809546
284642.84658.61330002006-15.8133000200623
294667.34741.63283140322-74.3328314032169
304640.64759.99977401075-119.399774010753
314716.94746.31850668752-29.4185066875161
324719.44739.42496101212-20.0249610121209
334817.34795.9159607889421.3840392110615
344764.54734.8165854405229.6834145594785
354514.14570.82164613408-56.7216461340813
3646254655.38092319232-30.3809231923178
374617.74605.3548392133812.3451607866236
384361.34662.09536691341-300.795366913409
394474.94573.27644132959-98.3764413295921
404623.84614.902840040018.89715995998722
4146924687.306412909364.69358709064272
424672.14713.74560817729-41.6456081772867
434721.54741.86348318961-20.3634831896052
444784.64737.9993871073746.6006128926292
454858.74821.6824540495337.0175459504699
464813.34765.0318592077548.2681407922455
474628.24582.0403922683946.1596077316071
484710.44701.312329197089.08767080291636
494698.44671.2128757294727.1871242705274
5046314651.51179278856-20.5117927885558
514727.44690.5064152480536.8935847519533
524719.94799.66787083201-79.7678708320136
534890.64849.1441956894641.4558043105399
544839.94874.63182554415-34.731825544146
554867.54911.65200430534-44.1520043053424
564898.34918.56936996015-20.2693699601505
574675.74983.59039739489-307.890397394891
584981.94833.6473343663148.252665633701
594771.14673.1187612792897.9812387207248
604827.84798.6147309425529.1852690574469
6146854777.25857889057-92.2585788905717
624646.14711.59011002739-65.4901100273901
6348154752.1323819474562.867618052549
644911.84839.1636968147972.6363031852088
654958.44961.87691193243-3.47691193242645
665019.44955.3374299428164.0625700571918
675024.35017.56252111796.73747888210437
685035.85044.66293375418-8.86293375418336
695082.45039.6974405747342.7025594252664
705179.25101.4678191224277.7321808775841
714963.24900.3695328048462.8304671951591
724951.35002.9150053128-51.6150053128022
734876.44927.2125334341-50.8125334341003
744812.14878.41778786656-66.3177878665547
755004.14954.4002852583749.699714741635
765093.85043.2134276503950.5865723496136
775063.15144.28583314066-81.1858331406565
785078.65133.59197145201-54.9919714520056
795251.55149.49086911585102.009130884152
805263.25199.2718403355263.928159664476
815280.55227.4191377336653.0808622663408
825386.15302.8593167971783.2406832028337
835227.35091.56260246794135.737397532055
845149.55188.12024961325-38.6202496132455
855128.65114.0044551064714.5955448935301
865087.75077.977555120739.72244487926764
875188.55210.30710363815-21.8071036381516
8850845283.77185971892-199.771859718921
895258.65285.26428074689-26.6642807468897
905348.95296.5636842364952.3363157635113
9152805383.78694838236-103.786948382364
925374.25367.990416189336.20958381067248
935458.45377.4313914988280.9686085011772
9453155469.40892505493-154.408925054932
955294.55201.7034877528192.7965122471942
965341.45242.2801703719599.1198296280518
9750685217.26833276804-149.268332768038
985156.95133.6927407383323.207259261666
995184.75262.07299794009-77.3729979400932
1005280.75274.602691014626.09730898537873
10153395376.39621361818-37.3962136181772
1025377.75404.279967273-26.5799672730036
1035388.65430.50716897401-41.9071689740076
1045443.65458.7775455242-15.1775455241959
1055528.75480.3989501976948.3010498023123
10655395503.8540452633935.1459547366067
10752925344.98559336706-52.9855933670578
1085351.55346.636495547834.86350445216704
1095163.75231.64335265574-67.9433526557423
11051055212.26428194911-107.264281949111
1115248.15279.42622637811-31.3262263781126
1125370.95324.6592089545346.2407910454695
1135484.95426.5813075933758.3186924066276
1145510.75483.1857226762627.5142773237403
1155484.95520.32409474188-35.4240947418803
1165567.85557.320747954610.4792520454002
1175275.65602.03892550145-326.438925501447







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1185518.365610376985435.13315886295601.59806189105
1195326.487828084635233.02528294185419.95037322746
1205355.561901746765251.849663819445459.27413967408
1215219.496564779285107.757511192185331.23561836637
1225207.465230424485087.00766235245327.92279849657
1235322.973835857255192.412517771355453.53515394316
1245395.991164286115256.206567969015535.77576060321
1255488.072561053815338.89103949935637.25408260832
1265520.115155457135362.885260166525677.34505074774
1275532.898219921695368.206507445375697.58993239801
1285590.141641051645417.086574786215763.19670731707
1295545.595951402495387.143179179425704.04872362557
1305633.734371837025436.602374565145830.86636910891
1315437.651461078275239.26793662755636.03498552903
1325467.138260150745261.834633818535672.44188648295
1335328.049710028865120.542988482885535.55643157484
1345315.580773564565102.402118954665528.75942817447
1355433.296654031885210.539093947845656.05421411593

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
118 & 5518.36561037698 & 5435.1331588629 & 5601.59806189105 \tabularnewline
119 & 5326.48782808463 & 5233.0252829418 & 5419.95037322746 \tabularnewline
120 & 5355.56190174676 & 5251.84966381944 & 5459.27413967408 \tabularnewline
121 & 5219.49656477928 & 5107.75751119218 & 5331.23561836637 \tabularnewline
122 & 5207.46523042448 & 5087.0076623524 & 5327.92279849657 \tabularnewline
123 & 5322.97383585725 & 5192.41251777135 & 5453.53515394316 \tabularnewline
124 & 5395.99116428611 & 5256.20656796901 & 5535.77576060321 \tabularnewline
125 & 5488.07256105381 & 5338.8910394993 & 5637.25408260832 \tabularnewline
126 & 5520.11515545713 & 5362.88526016652 & 5677.34505074774 \tabularnewline
127 & 5532.89821992169 & 5368.20650744537 & 5697.58993239801 \tabularnewline
128 & 5590.14164105164 & 5417.08657478621 & 5763.19670731707 \tabularnewline
129 & 5545.59595140249 & 5387.14317917942 & 5704.04872362557 \tabularnewline
130 & 5633.73437183702 & 5436.60237456514 & 5830.86636910891 \tabularnewline
131 & 5437.65146107827 & 5239.2679366275 & 5636.03498552903 \tabularnewline
132 & 5467.13826015074 & 5261.83463381853 & 5672.44188648295 \tabularnewline
133 & 5328.04971002886 & 5120.54298848288 & 5535.55643157484 \tabularnewline
134 & 5315.58077356456 & 5102.40211895466 & 5528.75942817447 \tabularnewline
135 & 5433.29665403188 & 5210.53909394784 & 5656.05421411593 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299401&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]118[/C][C]5518.36561037698[/C][C]5435.1331588629[/C][C]5601.59806189105[/C][/ROW]
[ROW][C]119[/C][C]5326.48782808463[/C][C]5233.0252829418[/C][C]5419.95037322746[/C][/ROW]
[ROW][C]120[/C][C]5355.56190174676[/C][C]5251.84966381944[/C][C]5459.27413967408[/C][/ROW]
[ROW][C]121[/C][C]5219.49656477928[/C][C]5107.75751119218[/C][C]5331.23561836637[/C][/ROW]
[ROW][C]122[/C][C]5207.46523042448[/C][C]5087.0076623524[/C][C]5327.92279849657[/C][/ROW]
[ROW][C]123[/C][C]5322.97383585725[/C][C]5192.41251777135[/C][C]5453.53515394316[/C][/ROW]
[ROW][C]124[/C][C]5395.99116428611[/C][C]5256.20656796901[/C][C]5535.77576060321[/C][/ROW]
[ROW][C]125[/C][C]5488.07256105381[/C][C]5338.8910394993[/C][C]5637.25408260832[/C][/ROW]
[ROW][C]126[/C][C]5520.11515545713[/C][C]5362.88526016652[/C][C]5677.34505074774[/C][/ROW]
[ROW][C]127[/C][C]5532.89821992169[/C][C]5368.20650744537[/C][C]5697.58993239801[/C][/ROW]
[ROW][C]128[/C][C]5590.14164105164[/C][C]5417.08657478621[/C][C]5763.19670731707[/C][/ROW]
[ROW][C]129[/C][C]5545.59595140249[/C][C]5387.14317917942[/C][C]5704.04872362557[/C][/ROW]
[ROW][C]130[/C][C]5633.73437183702[/C][C]5436.60237456514[/C][C]5830.86636910891[/C][/ROW]
[ROW][C]131[/C][C]5437.65146107827[/C][C]5239.2679366275[/C][C]5636.03498552903[/C][/ROW]
[ROW][C]132[/C][C]5467.13826015074[/C][C]5261.83463381853[/C][C]5672.44188648295[/C][/ROW]
[ROW][C]133[/C][C]5328.04971002886[/C][C]5120.54298848288[/C][C]5535.55643157484[/C][/ROW]
[ROW][C]134[/C][C]5315.58077356456[/C][C]5102.40211895466[/C][C]5528.75942817447[/C][/ROW]
[ROW][C]135[/C][C]5433.29665403188[/C][C]5210.53909394784[/C][C]5656.05421411593[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299401&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299401&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
1185518.365610376985435.13315886295601.59806189105
1195326.487828084635233.02528294185419.95037322746
1205355.561901746765251.849663819445459.27413967408
1215219.496564779285107.757511192185331.23561836637
1225207.465230424485087.00766235245327.92279849657
1235322.973835857255192.412517771355453.53515394316
1245395.991164286115256.206567969015535.77576060321
1255488.072561053815338.89103949935637.25408260832
1265520.115155457135362.885260166525677.34505074774
1275532.898219921695368.206507445375697.58993239801
1285590.141641051645417.086574786215763.19670731707
1295545.595951402495387.143179179425704.04872362557
1305633.734371837025436.602374565145830.86636910891
1315437.651461078275239.26793662755636.03498552903
1325467.138260150745261.834633818535672.44188648295
1335328.049710028865120.542988482885535.55643157484
1345315.580773564565102.402118954665528.75942817447
1355433.296654031885210.539093947845656.05421411593



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 18 ;
R code (references can be found in the software module):
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')