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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 computationSun, 18 Dec 2016 17:05:28 +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/18/t14820771558jntj7oo9iqobgu.htm/, Retrieved Fri, 01 Nov 2024 03:27:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301156, Retrieved Fri, 01 Nov 2024 03:27:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Structural Time Series Models] [Structural time s...] [2016-12-12 12:07:55] [e37f5c813d0dfcb3787d64bb91655c98]
- RMP     [Exponential Smoothing] [ES F1 2] [2016-12-18 16:05:28] [10299735033611e1e2dae6371997f8c9] [Current]
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Dataseries X:
3567.2
3968.25
4285.35
4130.95
4219.4
4626.2
3860.75
4174.15
4668.65
4630.05
4553.7
4603.85
4310.7
4831.3
5145.3
4886.65
4934.05
5304.7
4419.45
4804.85
5105
5132.6
4982.5
4906.7
4506.4
5010.85
5392.25
5049.7
5143.9
5449.9
4520.4
4936.95
5358.55
5289.5
5123.55
4985.65
4682.65
5175.55
5374.7
5289
5176.15
5604.25
4608.8
4898.15
5448.65
5373.05
5078.6
5233.4
4629.2
5387.8
5736.65
5357.9
5337.95
5795.5
4804.05
5120.5
5850.45
5734.75
5539
5582.85
4983.1
5672
6185.8
5835.6
5930.4
6444.65
5171.05
5739.1
6413.9
6230.2
6015.45
6174.25
5579.25
6133.45
6478.7
6184.4
6185.65
6556
5123.25
6028.9
6499.95
6190.05
6027.95
6034
5128.75
6087.7
6628.15
6075.3
6352.1
6824
5412.35
6171.25
6521.35
6457.6
5930.95
5842.7
5120.1
5719.95
5946.7
5921.1
6072
6489.4
5291.15
5986.45
6538.15
6442.8
6169.55
5793
5254.85
6050.75
6606.15
6221.15
6293.4
6908.4
5498.95
6145.35




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=301156&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=301156&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301156&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
alpha0.588088031469787
beta0.0293866113305454
gamma0.786809940727211

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.588088031469787 \tabularnewline
beta & 0.0293866113305454 \tabularnewline
gamma & 0.786809940727211 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301156&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]0.588088031469787[/C][/ROW]
[ROW][C]beta[/C][C]0.0293866113305454[/C][/ROW]
[ROW][C]gamma[/C][C]0.786809940727211[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301156&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301156&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
alpha0.588088031469787
beta0.0293866113305454
gamma0.786809940727211







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134310.73977.4013968436333.298603156398
144831.34688.71239117238142.587608827623
155145.35101.6270135721843.6729864278241
164886.654893.06828837865-6.41828837864705
174934.054960.30936542319-26.2593654231932
185304.75350.03511194802-45.3351119480203
194419.454450.31118956405-30.8611895640543
204804.854776.1213149750728.7286850249302
2151055338.09202139296-233.092021392962
225132.65139.49817726506-6.89817726506044
234982.55039.69185781864-57.1918578186396
244906.75053.26972776222-146.56972776222
254506.44768.98499941854-262.584999418545
265010.855086.87122721386-76.0212272138624
275392.255334.4212967651257.8287032348753
285049.75089.91352523028-40.2135252302796
295143.95116.0951158179527.8048841820473
305449.95529.7704667344-79.8704667344018
314520.44571.40740913795-51.0074091379474
324936.954898.9284417841338.0215582158689
335358.555374.37153077489-15.8215307748878
345289.55363.53861625019-74.0386162501854
355123.555189.79289314694-66.2428931469394
364985.655155.06071846936-169.410718469363
374682.654797.28369389617-114.633693896169
385175.555273.62098677291-98.0709867729129
395374.75551.5582879505-176.858287950497
4052895118.97708418137170.02291581863
415176.155280.9716905344-104.821690534402
425604.255572.5483250203131.7016749796894
434608.84656.09164911284-47.2916491128353
444898.155012.02150342888-113.871503428876
455448.655367.526429242681.123570757396
465373.055381.72303081685-8.67303081685259
475078.65235.42578940538-156.82578940538
485233.45100.57698756126132.823012438744
494629.24921.29165847812-292.091658478123
505387.85293.7686460661594.0313539338522
515736.655658.8629940950277.7870059049837
525357.95469.47181482535-111.57181482535
535337.955366.76457276424-28.8145727642423
545795.55751.4608648475244.0391351524759
554804.054779.6570547531824.3929452468192
565120.55163.73292848505-43.2329284850512
575850.455640.95820822669209.491791773314
585734.755694.0526405373440.6973594626634
5955395512.7345611788626.2654388211367
605582.855582.813915557250.0360844427505072
614983.15154.65675608946-171.556756089458
6256725779.98042251001-107.980422510006
636185.86036.56743341209149.23256658791
645835.65804.7091128097630.890887190244
655930.45811.58317085671118.816829143289
666444.656351.8654015242492.7845984757632
675171.055298.01628091355-126.966280913545
685739.15601.71107447391137.388925526095
696413.96332.1262603362181.7737396637931
706230.26244.44416905552-14.2441690555252
716015.456007.630793664727.81920633528443
726174.256062.04820465778112.201795342225
735579.255596.93647047076-17.6864704707614
746133.456424.86577148791-291.415771487906
756478.76698.46131795768-219.761317957682
766184.46184.68707621256-0.287076212555803
776185.656198.30516516952-12.6551651695163
7865566667.39621401388-111.396214013881
795123.255383.90325596576-260.653255965762
806028.95688.34450252545340.555497474548
816499.956529.91737812011-29.9673781201054
826190.056333.50762686196-143.45762686196
836027.956016.8087578603511.1412421396499
8460346096.34583687933-62.345836879329
855128.755484.74121277776-355.991212777757
866087.75963.43949966195124.260500338049
876628.156480.74809982924147.40190017076
886075.36243.09008412304-167.790084123039
896352.16144.18590680394207.914093196061
9068246709.20435404478114.795645955223
915412.355464.07152560602-51.7215256060181
926171.256118.9206040485552.3293959514467
936521.356679.2325381738-157.882538173799
946457.66361.0717406887596.5282593112461
955930.956226.64108531428-295.691085314275
965842.76094.79156445562-252.09156445562
975120.15273.37457058543-153.274570585432
985719.956023.4108182901-303.460818290096
995946.76264.50302040303-317.80302040303
1005921.15665.15484105866255.945158941337
10160725916.79691677175155.203083228247
1026489.46383.87398574984105.52601425016
1035291.155140.94112234572150.208877654276
1045986.455913.0623080430373.3876919569702
1056538.156390.65502489377147.494975106227
1066442.86329.72432823518113.075671764825
1076169.556072.5582563720896.9917436279156
10857936186.0767174399-393.076717439897
1095254.855301.79569305714-46.9456930571423
1106050.756084.84106307582-34.0910630758181
1116606.156504.78987452754101.360125472464
1126221.156325.5570248641-104.407024864096
1136293.46341.96426969121-48.5642696912109
1146908.46690.39441449633218.005585503674
1155498.955463.2093490578835.7406509421244
1166145.356170.25065469498-24.9006546949749

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4310.7 & 3977.4013968436 & 333.298603156398 \tabularnewline
14 & 4831.3 & 4688.71239117238 & 142.587608827623 \tabularnewline
15 & 5145.3 & 5101.62701357218 & 43.6729864278241 \tabularnewline
16 & 4886.65 & 4893.06828837865 & -6.41828837864705 \tabularnewline
17 & 4934.05 & 4960.30936542319 & -26.2593654231932 \tabularnewline
18 & 5304.7 & 5350.03511194802 & -45.3351119480203 \tabularnewline
19 & 4419.45 & 4450.31118956405 & -30.8611895640543 \tabularnewline
20 & 4804.85 & 4776.12131497507 & 28.7286850249302 \tabularnewline
21 & 5105 & 5338.09202139296 & -233.092021392962 \tabularnewline
22 & 5132.6 & 5139.49817726506 & -6.89817726506044 \tabularnewline
23 & 4982.5 & 5039.69185781864 & -57.1918578186396 \tabularnewline
24 & 4906.7 & 5053.26972776222 & -146.56972776222 \tabularnewline
25 & 4506.4 & 4768.98499941854 & -262.584999418545 \tabularnewline
26 & 5010.85 & 5086.87122721386 & -76.0212272138624 \tabularnewline
27 & 5392.25 & 5334.42129676512 & 57.8287032348753 \tabularnewline
28 & 5049.7 & 5089.91352523028 & -40.2135252302796 \tabularnewline
29 & 5143.9 & 5116.09511581795 & 27.8048841820473 \tabularnewline
30 & 5449.9 & 5529.7704667344 & -79.8704667344018 \tabularnewline
31 & 4520.4 & 4571.40740913795 & -51.0074091379474 \tabularnewline
32 & 4936.95 & 4898.92844178413 & 38.0215582158689 \tabularnewline
33 & 5358.55 & 5374.37153077489 & -15.8215307748878 \tabularnewline
34 & 5289.5 & 5363.53861625019 & -74.0386162501854 \tabularnewline
35 & 5123.55 & 5189.79289314694 & -66.2428931469394 \tabularnewline
36 & 4985.65 & 5155.06071846936 & -169.410718469363 \tabularnewline
37 & 4682.65 & 4797.28369389617 & -114.633693896169 \tabularnewline
38 & 5175.55 & 5273.62098677291 & -98.0709867729129 \tabularnewline
39 & 5374.7 & 5551.5582879505 & -176.858287950497 \tabularnewline
40 & 5289 & 5118.97708418137 & 170.02291581863 \tabularnewline
41 & 5176.15 & 5280.9716905344 & -104.821690534402 \tabularnewline
42 & 5604.25 & 5572.54832502031 & 31.7016749796894 \tabularnewline
43 & 4608.8 & 4656.09164911284 & -47.2916491128353 \tabularnewline
44 & 4898.15 & 5012.02150342888 & -113.871503428876 \tabularnewline
45 & 5448.65 & 5367.5264292426 & 81.123570757396 \tabularnewline
46 & 5373.05 & 5381.72303081685 & -8.67303081685259 \tabularnewline
47 & 5078.6 & 5235.42578940538 & -156.82578940538 \tabularnewline
48 & 5233.4 & 5100.57698756126 & 132.823012438744 \tabularnewline
49 & 4629.2 & 4921.29165847812 & -292.091658478123 \tabularnewline
50 & 5387.8 & 5293.76864606615 & 94.0313539338522 \tabularnewline
51 & 5736.65 & 5658.86299409502 & 77.7870059049837 \tabularnewline
52 & 5357.9 & 5469.47181482535 & -111.57181482535 \tabularnewline
53 & 5337.95 & 5366.76457276424 & -28.8145727642423 \tabularnewline
54 & 5795.5 & 5751.46086484752 & 44.0391351524759 \tabularnewline
55 & 4804.05 & 4779.65705475318 & 24.3929452468192 \tabularnewline
56 & 5120.5 & 5163.73292848505 & -43.2329284850512 \tabularnewline
57 & 5850.45 & 5640.95820822669 & 209.491791773314 \tabularnewline
58 & 5734.75 & 5694.05264053734 & 40.6973594626634 \tabularnewline
59 & 5539 & 5512.73456117886 & 26.2654388211367 \tabularnewline
60 & 5582.85 & 5582.81391555725 & 0.0360844427505072 \tabularnewline
61 & 4983.1 & 5154.65675608946 & -171.556756089458 \tabularnewline
62 & 5672 & 5779.98042251001 & -107.980422510006 \tabularnewline
63 & 6185.8 & 6036.56743341209 & 149.23256658791 \tabularnewline
64 & 5835.6 & 5804.70911280976 & 30.890887190244 \tabularnewline
65 & 5930.4 & 5811.58317085671 & 118.816829143289 \tabularnewline
66 & 6444.65 & 6351.86540152424 & 92.7845984757632 \tabularnewline
67 & 5171.05 & 5298.01628091355 & -126.966280913545 \tabularnewline
68 & 5739.1 & 5601.71107447391 & 137.388925526095 \tabularnewline
69 & 6413.9 & 6332.12626033621 & 81.7737396637931 \tabularnewline
70 & 6230.2 & 6244.44416905552 & -14.2441690555252 \tabularnewline
71 & 6015.45 & 6007.63079366472 & 7.81920633528443 \tabularnewline
72 & 6174.25 & 6062.04820465778 & 112.201795342225 \tabularnewline
73 & 5579.25 & 5596.93647047076 & -17.6864704707614 \tabularnewline
74 & 6133.45 & 6424.86577148791 & -291.415771487906 \tabularnewline
75 & 6478.7 & 6698.46131795768 & -219.761317957682 \tabularnewline
76 & 6184.4 & 6184.68707621256 & -0.287076212555803 \tabularnewline
77 & 6185.65 & 6198.30516516952 & -12.6551651695163 \tabularnewline
78 & 6556 & 6667.39621401388 & -111.396214013881 \tabularnewline
79 & 5123.25 & 5383.90325596576 & -260.653255965762 \tabularnewline
80 & 6028.9 & 5688.34450252545 & 340.555497474548 \tabularnewline
81 & 6499.95 & 6529.91737812011 & -29.9673781201054 \tabularnewline
82 & 6190.05 & 6333.50762686196 & -143.45762686196 \tabularnewline
83 & 6027.95 & 6016.80875786035 & 11.1412421396499 \tabularnewline
84 & 6034 & 6096.34583687933 & -62.345836879329 \tabularnewline
85 & 5128.75 & 5484.74121277776 & -355.991212777757 \tabularnewline
86 & 6087.7 & 5963.43949966195 & 124.260500338049 \tabularnewline
87 & 6628.15 & 6480.74809982924 & 147.40190017076 \tabularnewline
88 & 6075.3 & 6243.09008412304 & -167.790084123039 \tabularnewline
89 & 6352.1 & 6144.18590680394 & 207.914093196061 \tabularnewline
90 & 6824 & 6709.20435404478 & 114.795645955223 \tabularnewline
91 & 5412.35 & 5464.07152560602 & -51.7215256060181 \tabularnewline
92 & 6171.25 & 6118.92060404855 & 52.3293959514467 \tabularnewline
93 & 6521.35 & 6679.2325381738 & -157.882538173799 \tabularnewline
94 & 6457.6 & 6361.07174068875 & 96.5282593112461 \tabularnewline
95 & 5930.95 & 6226.64108531428 & -295.691085314275 \tabularnewline
96 & 5842.7 & 6094.79156445562 & -252.09156445562 \tabularnewline
97 & 5120.1 & 5273.37457058543 & -153.274570585432 \tabularnewline
98 & 5719.95 & 6023.4108182901 & -303.460818290096 \tabularnewline
99 & 5946.7 & 6264.50302040303 & -317.80302040303 \tabularnewline
100 & 5921.1 & 5665.15484105866 & 255.945158941337 \tabularnewline
101 & 6072 & 5916.79691677175 & 155.203083228247 \tabularnewline
102 & 6489.4 & 6383.87398574984 & 105.52601425016 \tabularnewline
103 & 5291.15 & 5140.94112234572 & 150.208877654276 \tabularnewline
104 & 5986.45 & 5913.06230804303 & 73.3876919569702 \tabularnewline
105 & 6538.15 & 6390.65502489377 & 147.494975106227 \tabularnewline
106 & 6442.8 & 6329.72432823518 & 113.075671764825 \tabularnewline
107 & 6169.55 & 6072.55825637208 & 96.9917436279156 \tabularnewline
108 & 5793 & 6186.0767174399 & -393.076717439897 \tabularnewline
109 & 5254.85 & 5301.79569305714 & -46.9456930571423 \tabularnewline
110 & 6050.75 & 6084.84106307582 & -34.0910630758181 \tabularnewline
111 & 6606.15 & 6504.78987452754 & 101.360125472464 \tabularnewline
112 & 6221.15 & 6325.5570248641 & -104.407024864096 \tabularnewline
113 & 6293.4 & 6341.96426969121 & -48.5642696912109 \tabularnewline
114 & 6908.4 & 6690.39441449633 & 218.005585503674 \tabularnewline
115 & 5498.95 & 5463.20934905788 & 35.7406509421244 \tabularnewline
116 & 6145.35 & 6170.25065469498 & -24.9006546949749 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301156&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]4310.7[/C][C]3977.4013968436[/C][C]333.298603156398[/C][/ROW]
[ROW][C]14[/C][C]4831.3[/C][C]4688.71239117238[/C][C]142.587608827623[/C][/ROW]
[ROW][C]15[/C][C]5145.3[/C][C]5101.62701357218[/C][C]43.6729864278241[/C][/ROW]
[ROW][C]16[/C][C]4886.65[/C][C]4893.06828837865[/C][C]-6.41828837864705[/C][/ROW]
[ROW][C]17[/C][C]4934.05[/C][C]4960.30936542319[/C][C]-26.2593654231932[/C][/ROW]
[ROW][C]18[/C][C]5304.7[/C][C]5350.03511194802[/C][C]-45.3351119480203[/C][/ROW]
[ROW][C]19[/C][C]4419.45[/C][C]4450.31118956405[/C][C]-30.8611895640543[/C][/ROW]
[ROW][C]20[/C][C]4804.85[/C][C]4776.12131497507[/C][C]28.7286850249302[/C][/ROW]
[ROW][C]21[/C][C]5105[/C][C]5338.09202139296[/C][C]-233.092021392962[/C][/ROW]
[ROW][C]22[/C][C]5132.6[/C][C]5139.49817726506[/C][C]-6.89817726506044[/C][/ROW]
[ROW][C]23[/C][C]4982.5[/C][C]5039.69185781864[/C][C]-57.1918578186396[/C][/ROW]
[ROW][C]24[/C][C]4906.7[/C][C]5053.26972776222[/C][C]-146.56972776222[/C][/ROW]
[ROW][C]25[/C][C]4506.4[/C][C]4768.98499941854[/C][C]-262.584999418545[/C][/ROW]
[ROW][C]26[/C][C]5010.85[/C][C]5086.87122721386[/C][C]-76.0212272138624[/C][/ROW]
[ROW][C]27[/C][C]5392.25[/C][C]5334.42129676512[/C][C]57.8287032348753[/C][/ROW]
[ROW][C]28[/C][C]5049.7[/C][C]5089.91352523028[/C][C]-40.2135252302796[/C][/ROW]
[ROW][C]29[/C][C]5143.9[/C][C]5116.09511581795[/C][C]27.8048841820473[/C][/ROW]
[ROW][C]30[/C][C]5449.9[/C][C]5529.7704667344[/C][C]-79.8704667344018[/C][/ROW]
[ROW][C]31[/C][C]4520.4[/C][C]4571.40740913795[/C][C]-51.0074091379474[/C][/ROW]
[ROW][C]32[/C][C]4936.95[/C][C]4898.92844178413[/C][C]38.0215582158689[/C][/ROW]
[ROW][C]33[/C][C]5358.55[/C][C]5374.37153077489[/C][C]-15.8215307748878[/C][/ROW]
[ROW][C]34[/C][C]5289.5[/C][C]5363.53861625019[/C][C]-74.0386162501854[/C][/ROW]
[ROW][C]35[/C][C]5123.55[/C][C]5189.79289314694[/C][C]-66.2428931469394[/C][/ROW]
[ROW][C]36[/C][C]4985.65[/C][C]5155.06071846936[/C][C]-169.410718469363[/C][/ROW]
[ROW][C]37[/C][C]4682.65[/C][C]4797.28369389617[/C][C]-114.633693896169[/C][/ROW]
[ROW][C]38[/C][C]5175.55[/C][C]5273.62098677291[/C][C]-98.0709867729129[/C][/ROW]
[ROW][C]39[/C][C]5374.7[/C][C]5551.5582879505[/C][C]-176.858287950497[/C][/ROW]
[ROW][C]40[/C][C]5289[/C][C]5118.97708418137[/C][C]170.02291581863[/C][/ROW]
[ROW][C]41[/C][C]5176.15[/C][C]5280.9716905344[/C][C]-104.821690534402[/C][/ROW]
[ROW][C]42[/C][C]5604.25[/C][C]5572.54832502031[/C][C]31.7016749796894[/C][/ROW]
[ROW][C]43[/C][C]4608.8[/C][C]4656.09164911284[/C][C]-47.2916491128353[/C][/ROW]
[ROW][C]44[/C][C]4898.15[/C][C]5012.02150342888[/C][C]-113.871503428876[/C][/ROW]
[ROW][C]45[/C][C]5448.65[/C][C]5367.5264292426[/C][C]81.123570757396[/C][/ROW]
[ROW][C]46[/C][C]5373.05[/C][C]5381.72303081685[/C][C]-8.67303081685259[/C][/ROW]
[ROW][C]47[/C][C]5078.6[/C][C]5235.42578940538[/C][C]-156.82578940538[/C][/ROW]
[ROW][C]48[/C][C]5233.4[/C][C]5100.57698756126[/C][C]132.823012438744[/C][/ROW]
[ROW][C]49[/C][C]4629.2[/C][C]4921.29165847812[/C][C]-292.091658478123[/C][/ROW]
[ROW][C]50[/C][C]5387.8[/C][C]5293.76864606615[/C][C]94.0313539338522[/C][/ROW]
[ROW][C]51[/C][C]5736.65[/C][C]5658.86299409502[/C][C]77.7870059049837[/C][/ROW]
[ROW][C]52[/C][C]5357.9[/C][C]5469.47181482535[/C][C]-111.57181482535[/C][/ROW]
[ROW][C]53[/C][C]5337.95[/C][C]5366.76457276424[/C][C]-28.8145727642423[/C][/ROW]
[ROW][C]54[/C][C]5795.5[/C][C]5751.46086484752[/C][C]44.0391351524759[/C][/ROW]
[ROW][C]55[/C][C]4804.05[/C][C]4779.65705475318[/C][C]24.3929452468192[/C][/ROW]
[ROW][C]56[/C][C]5120.5[/C][C]5163.73292848505[/C][C]-43.2329284850512[/C][/ROW]
[ROW][C]57[/C][C]5850.45[/C][C]5640.95820822669[/C][C]209.491791773314[/C][/ROW]
[ROW][C]58[/C][C]5734.75[/C][C]5694.05264053734[/C][C]40.6973594626634[/C][/ROW]
[ROW][C]59[/C][C]5539[/C][C]5512.73456117886[/C][C]26.2654388211367[/C][/ROW]
[ROW][C]60[/C][C]5582.85[/C][C]5582.81391555725[/C][C]0.0360844427505072[/C][/ROW]
[ROW][C]61[/C][C]4983.1[/C][C]5154.65675608946[/C][C]-171.556756089458[/C][/ROW]
[ROW][C]62[/C][C]5672[/C][C]5779.98042251001[/C][C]-107.980422510006[/C][/ROW]
[ROW][C]63[/C][C]6185.8[/C][C]6036.56743341209[/C][C]149.23256658791[/C][/ROW]
[ROW][C]64[/C][C]5835.6[/C][C]5804.70911280976[/C][C]30.890887190244[/C][/ROW]
[ROW][C]65[/C][C]5930.4[/C][C]5811.58317085671[/C][C]118.816829143289[/C][/ROW]
[ROW][C]66[/C][C]6444.65[/C][C]6351.86540152424[/C][C]92.7845984757632[/C][/ROW]
[ROW][C]67[/C][C]5171.05[/C][C]5298.01628091355[/C][C]-126.966280913545[/C][/ROW]
[ROW][C]68[/C][C]5739.1[/C][C]5601.71107447391[/C][C]137.388925526095[/C][/ROW]
[ROW][C]69[/C][C]6413.9[/C][C]6332.12626033621[/C][C]81.7737396637931[/C][/ROW]
[ROW][C]70[/C][C]6230.2[/C][C]6244.44416905552[/C][C]-14.2441690555252[/C][/ROW]
[ROW][C]71[/C][C]6015.45[/C][C]6007.63079366472[/C][C]7.81920633528443[/C][/ROW]
[ROW][C]72[/C][C]6174.25[/C][C]6062.04820465778[/C][C]112.201795342225[/C][/ROW]
[ROW][C]73[/C][C]5579.25[/C][C]5596.93647047076[/C][C]-17.6864704707614[/C][/ROW]
[ROW][C]74[/C][C]6133.45[/C][C]6424.86577148791[/C][C]-291.415771487906[/C][/ROW]
[ROW][C]75[/C][C]6478.7[/C][C]6698.46131795768[/C][C]-219.761317957682[/C][/ROW]
[ROW][C]76[/C][C]6184.4[/C][C]6184.68707621256[/C][C]-0.287076212555803[/C][/ROW]
[ROW][C]77[/C][C]6185.65[/C][C]6198.30516516952[/C][C]-12.6551651695163[/C][/ROW]
[ROW][C]78[/C][C]6556[/C][C]6667.39621401388[/C][C]-111.396214013881[/C][/ROW]
[ROW][C]79[/C][C]5123.25[/C][C]5383.90325596576[/C][C]-260.653255965762[/C][/ROW]
[ROW][C]80[/C][C]6028.9[/C][C]5688.34450252545[/C][C]340.555497474548[/C][/ROW]
[ROW][C]81[/C][C]6499.95[/C][C]6529.91737812011[/C][C]-29.9673781201054[/C][/ROW]
[ROW][C]82[/C][C]6190.05[/C][C]6333.50762686196[/C][C]-143.45762686196[/C][/ROW]
[ROW][C]83[/C][C]6027.95[/C][C]6016.80875786035[/C][C]11.1412421396499[/C][/ROW]
[ROW][C]84[/C][C]6034[/C][C]6096.34583687933[/C][C]-62.345836879329[/C][/ROW]
[ROW][C]85[/C][C]5128.75[/C][C]5484.74121277776[/C][C]-355.991212777757[/C][/ROW]
[ROW][C]86[/C][C]6087.7[/C][C]5963.43949966195[/C][C]124.260500338049[/C][/ROW]
[ROW][C]87[/C][C]6628.15[/C][C]6480.74809982924[/C][C]147.40190017076[/C][/ROW]
[ROW][C]88[/C][C]6075.3[/C][C]6243.09008412304[/C][C]-167.790084123039[/C][/ROW]
[ROW][C]89[/C][C]6352.1[/C][C]6144.18590680394[/C][C]207.914093196061[/C][/ROW]
[ROW][C]90[/C][C]6824[/C][C]6709.20435404478[/C][C]114.795645955223[/C][/ROW]
[ROW][C]91[/C][C]5412.35[/C][C]5464.07152560602[/C][C]-51.7215256060181[/C][/ROW]
[ROW][C]92[/C][C]6171.25[/C][C]6118.92060404855[/C][C]52.3293959514467[/C][/ROW]
[ROW][C]93[/C][C]6521.35[/C][C]6679.2325381738[/C][C]-157.882538173799[/C][/ROW]
[ROW][C]94[/C][C]6457.6[/C][C]6361.07174068875[/C][C]96.5282593112461[/C][/ROW]
[ROW][C]95[/C][C]5930.95[/C][C]6226.64108531428[/C][C]-295.691085314275[/C][/ROW]
[ROW][C]96[/C][C]5842.7[/C][C]6094.79156445562[/C][C]-252.09156445562[/C][/ROW]
[ROW][C]97[/C][C]5120.1[/C][C]5273.37457058543[/C][C]-153.274570585432[/C][/ROW]
[ROW][C]98[/C][C]5719.95[/C][C]6023.4108182901[/C][C]-303.460818290096[/C][/ROW]
[ROW][C]99[/C][C]5946.7[/C][C]6264.50302040303[/C][C]-317.80302040303[/C][/ROW]
[ROW][C]100[/C][C]5921.1[/C][C]5665.15484105866[/C][C]255.945158941337[/C][/ROW]
[ROW][C]101[/C][C]6072[/C][C]5916.79691677175[/C][C]155.203083228247[/C][/ROW]
[ROW][C]102[/C][C]6489.4[/C][C]6383.87398574984[/C][C]105.52601425016[/C][/ROW]
[ROW][C]103[/C][C]5291.15[/C][C]5140.94112234572[/C][C]150.208877654276[/C][/ROW]
[ROW][C]104[/C][C]5986.45[/C][C]5913.06230804303[/C][C]73.3876919569702[/C][/ROW]
[ROW][C]105[/C][C]6538.15[/C][C]6390.65502489377[/C][C]147.494975106227[/C][/ROW]
[ROW][C]106[/C][C]6442.8[/C][C]6329.72432823518[/C][C]113.075671764825[/C][/ROW]
[ROW][C]107[/C][C]6169.55[/C][C]6072.55825637208[/C][C]96.9917436279156[/C][/ROW]
[ROW][C]108[/C][C]5793[/C][C]6186.0767174399[/C][C]-393.076717439897[/C][/ROW]
[ROW][C]109[/C][C]5254.85[/C][C]5301.79569305714[/C][C]-46.9456930571423[/C][/ROW]
[ROW][C]110[/C][C]6050.75[/C][C]6084.84106307582[/C][C]-34.0910630758181[/C][/ROW]
[ROW][C]111[/C][C]6606.15[/C][C]6504.78987452754[/C][C]101.360125472464[/C][/ROW]
[ROW][C]112[/C][C]6221.15[/C][C]6325.5570248641[/C][C]-104.407024864096[/C][/ROW]
[ROW][C]113[/C][C]6293.4[/C][C]6341.96426969121[/C][C]-48.5642696912109[/C][/ROW]
[ROW][C]114[/C][C]6908.4[/C][C]6690.39441449633[/C][C]218.005585503674[/C][/ROW]
[ROW][C]115[/C][C]5498.95[/C][C]5463.20934905788[/C][C]35.7406509421244[/C][/ROW]
[ROW][C]116[/C][C]6145.35[/C][C]6170.25065469498[/C][C]-24.9006546949749[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301156&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301156&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
134310.73977.4013968436333.298603156398
144831.34688.71239117238142.587608827623
155145.35101.6270135721843.6729864278241
164886.654893.06828837865-6.41828837864705
174934.054960.30936542319-26.2593654231932
185304.75350.03511194802-45.3351119480203
194419.454450.31118956405-30.8611895640543
204804.854776.1213149750728.7286850249302
2151055338.09202139296-233.092021392962
225132.65139.49817726506-6.89817726506044
234982.55039.69185781864-57.1918578186396
244906.75053.26972776222-146.56972776222
254506.44768.98499941854-262.584999418545
265010.855086.87122721386-76.0212272138624
275392.255334.4212967651257.8287032348753
285049.75089.91352523028-40.2135252302796
295143.95116.0951158179527.8048841820473
305449.95529.7704667344-79.8704667344018
314520.44571.40740913795-51.0074091379474
324936.954898.9284417841338.0215582158689
335358.555374.37153077489-15.8215307748878
345289.55363.53861625019-74.0386162501854
355123.555189.79289314694-66.2428931469394
364985.655155.06071846936-169.410718469363
374682.654797.28369389617-114.633693896169
385175.555273.62098677291-98.0709867729129
395374.75551.5582879505-176.858287950497
4052895118.97708418137170.02291581863
415176.155280.9716905344-104.821690534402
425604.255572.5483250203131.7016749796894
434608.84656.09164911284-47.2916491128353
444898.155012.02150342888-113.871503428876
455448.655367.526429242681.123570757396
465373.055381.72303081685-8.67303081685259
475078.65235.42578940538-156.82578940538
485233.45100.57698756126132.823012438744
494629.24921.29165847812-292.091658478123
505387.85293.7686460661594.0313539338522
515736.655658.8629940950277.7870059049837
525357.95469.47181482535-111.57181482535
535337.955366.76457276424-28.8145727642423
545795.55751.4608648475244.0391351524759
554804.054779.6570547531824.3929452468192
565120.55163.73292848505-43.2329284850512
575850.455640.95820822669209.491791773314
585734.755694.0526405373440.6973594626634
5955395512.7345611788626.2654388211367
605582.855582.813915557250.0360844427505072
614983.15154.65675608946-171.556756089458
6256725779.98042251001-107.980422510006
636185.86036.56743341209149.23256658791
645835.65804.7091128097630.890887190244
655930.45811.58317085671118.816829143289
666444.656351.8654015242492.7845984757632
675171.055298.01628091355-126.966280913545
685739.15601.71107447391137.388925526095
696413.96332.1262603362181.7737396637931
706230.26244.44416905552-14.2441690555252
716015.456007.630793664727.81920633528443
726174.256062.04820465778112.201795342225
735579.255596.93647047076-17.6864704707614
746133.456424.86577148791-291.415771487906
756478.76698.46131795768-219.761317957682
766184.46184.68707621256-0.287076212555803
776185.656198.30516516952-12.6551651695163
7865566667.39621401388-111.396214013881
795123.255383.90325596576-260.653255965762
806028.95688.34450252545340.555497474548
816499.956529.91737812011-29.9673781201054
826190.056333.50762686196-143.45762686196
836027.956016.8087578603511.1412421396499
8460346096.34583687933-62.345836879329
855128.755484.74121277776-355.991212777757
866087.75963.43949966195124.260500338049
876628.156480.74809982924147.40190017076
886075.36243.09008412304-167.790084123039
896352.16144.18590680394207.914093196061
9068246709.20435404478114.795645955223
915412.355464.07152560602-51.7215256060181
926171.256118.9206040485552.3293959514467
936521.356679.2325381738-157.882538173799
946457.66361.0717406887596.5282593112461
955930.956226.64108531428-295.691085314275
965842.76094.79156445562-252.09156445562
975120.15273.37457058543-153.274570585432
985719.956023.4108182901-303.460818290096
995946.76264.50302040303-317.80302040303
1005921.15665.15484105866255.945158941337
10160725916.79691677175155.203083228247
1026489.46383.87398574984105.52601425016
1035291.155140.94112234572150.208877654276
1045986.455913.0623080430373.3876919569702
1056538.156390.65502489377147.494975106227
1066442.86329.72432823518113.075671764825
1076169.556072.5582563720896.9917436279156
10857936186.0767174399-393.076717439897
1095254.855301.79569305714-46.9456930571423
1106050.756084.84106307582-34.0910630758181
1116606.156504.78987452754101.360125472464
1126221.156325.5570248641-104.407024864096
1136293.46341.96426969121-48.5642696912109
1146908.46690.39441449633218.005585503674
1155498.955463.2093490578835.7406509421244
1166145.356170.25065469498-24.9006546949749







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1176626.800112854846366.429421645246887.17080406444
1186462.710973750386152.770070068526772.65187743223
1196128.044503583045779.779045283696476.30996188239
1206015.965336285595627.766860459846404.16381211133
1215458.171242100645053.165394600215863.17708960106
1226305.541535561475813.159720042816797.92335108013
1236811.726532265396249.104490655437374.34857387535
1246496.648823300455920.201250170547073.09639643035
1256599.077397826255978.896086462977219.25870918952
1267086.800050081956390.426207020017783.1738931439
1275631.619427668445029.641315387476233.5975399494
1286313.653084140295661.685324324176965.6208439564
1296805.464691738366008.859367812687602.07001566403
1306636.560963491635824.527234076057448.59469290721
1316292.523093908785484.545224893877100.50096292368
1326177.075333981345349.827667474657004.32300048802
1335604.017801318234811.185670260596396.84993237587
1346473.656138706495542.173216353067405.13906105993

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 6626.80011285484 & 6366.42942164524 & 6887.17080406444 \tabularnewline
118 & 6462.71097375038 & 6152.77007006852 & 6772.65187743223 \tabularnewline
119 & 6128.04450358304 & 5779.77904528369 & 6476.30996188239 \tabularnewline
120 & 6015.96533628559 & 5627.76686045984 & 6404.16381211133 \tabularnewline
121 & 5458.17124210064 & 5053.16539460021 & 5863.17708960106 \tabularnewline
122 & 6305.54153556147 & 5813.15972004281 & 6797.92335108013 \tabularnewline
123 & 6811.72653226539 & 6249.10449065543 & 7374.34857387535 \tabularnewline
124 & 6496.64882330045 & 5920.20125017054 & 7073.09639643035 \tabularnewline
125 & 6599.07739782625 & 5978.89608646297 & 7219.25870918952 \tabularnewline
126 & 7086.80005008195 & 6390.42620702001 & 7783.1738931439 \tabularnewline
127 & 5631.61942766844 & 5029.64131538747 & 6233.5975399494 \tabularnewline
128 & 6313.65308414029 & 5661.68532432417 & 6965.6208439564 \tabularnewline
129 & 6805.46469173836 & 6008.85936781268 & 7602.07001566403 \tabularnewline
130 & 6636.56096349163 & 5824.52723407605 & 7448.59469290721 \tabularnewline
131 & 6292.52309390878 & 5484.54522489387 & 7100.50096292368 \tabularnewline
132 & 6177.07533398134 & 5349.82766747465 & 7004.32300048802 \tabularnewline
133 & 5604.01780131823 & 4811.18567026059 & 6396.84993237587 \tabularnewline
134 & 6473.65613870649 & 5542.17321635306 & 7405.13906105993 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301156&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]117[/C][C]6626.80011285484[/C][C]6366.42942164524[/C][C]6887.17080406444[/C][/ROW]
[ROW][C]118[/C][C]6462.71097375038[/C][C]6152.77007006852[/C][C]6772.65187743223[/C][/ROW]
[ROW][C]119[/C][C]6128.04450358304[/C][C]5779.77904528369[/C][C]6476.30996188239[/C][/ROW]
[ROW][C]120[/C][C]6015.96533628559[/C][C]5627.76686045984[/C][C]6404.16381211133[/C][/ROW]
[ROW][C]121[/C][C]5458.17124210064[/C][C]5053.16539460021[/C][C]5863.17708960106[/C][/ROW]
[ROW][C]122[/C][C]6305.54153556147[/C][C]5813.15972004281[/C][C]6797.92335108013[/C][/ROW]
[ROW][C]123[/C][C]6811.72653226539[/C][C]6249.10449065543[/C][C]7374.34857387535[/C][/ROW]
[ROW][C]124[/C][C]6496.64882330045[/C][C]5920.20125017054[/C][C]7073.09639643035[/C][/ROW]
[ROW][C]125[/C][C]6599.07739782625[/C][C]5978.89608646297[/C][C]7219.25870918952[/C][/ROW]
[ROW][C]126[/C][C]7086.80005008195[/C][C]6390.42620702001[/C][C]7783.1738931439[/C][/ROW]
[ROW][C]127[/C][C]5631.61942766844[/C][C]5029.64131538747[/C][C]6233.5975399494[/C][/ROW]
[ROW][C]128[/C][C]6313.65308414029[/C][C]5661.68532432417[/C][C]6965.6208439564[/C][/ROW]
[ROW][C]129[/C][C]6805.46469173836[/C][C]6008.85936781268[/C][C]7602.07001566403[/C][/ROW]
[ROW][C]130[/C][C]6636.56096349163[/C][C]5824.52723407605[/C][C]7448.59469290721[/C][/ROW]
[ROW][C]131[/C][C]6292.52309390878[/C][C]5484.54522489387[/C][C]7100.50096292368[/C][/ROW]
[ROW][C]132[/C][C]6177.07533398134[/C][C]5349.82766747465[/C][C]7004.32300048802[/C][/ROW]
[ROW][C]133[/C][C]5604.01780131823[/C][C]4811.18567026059[/C][C]6396.84993237587[/C][/ROW]
[ROW][C]134[/C][C]6473.65613870649[/C][C]5542.17321635306[/C][C]7405.13906105993[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301156&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301156&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
1176626.800112854846366.429421645246887.17080406444
1186462.710973750386152.770070068526772.65187743223
1196128.044503583045779.779045283696476.30996188239
1206015.965336285595627.766860459846404.16381211133
1215458.171242100645053.165394600215863.17708960106
1226305.541535561475813.159720042816797.92335108013
1236811.726532265396249.104490655437374.34857387535
1246496.648823300455920.201250170547073.09639643035
1256599.077397826255978.896086462977219.25870918952
1267086.800050081956390.426207020017783.1738931439
1275631.619427668445029.641315387476233.5975399494
1286313.653084140295661.685324324176965.6208439564
1296805.464691738366008.859367812687602.07001566403
1306636.560963491635824.527234076057448.59469290721
1316292.523093908785484.545224893877100.50096292368
1326177.075333981345349.827667474657004.32300048802
1335604.017801318234811.185670260596396.84993237587
1346473.656138706495542.173216353067405.13906105993



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):
par4 <- '18'
par3 <- 'additive'
par2 <- 'Triple'
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')