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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 May 2008 13:48:37 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/27/t1211917793otsox47usmh8a0k.htm/, Retrieved Sun, 19 May 2024 21:47:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13391, Retrieved Sun, 19 May 2024 21:47:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2008-05-27 19:48:37] [0de5017ea2334b95113159299296029a] [Current]
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Dataseries X:
66.2
66.2
66.08
66.31
66.39
66.37
66.23
66.27
66.27
66.27
66.28
66.28
66.28
66.26
66.13
65.86
65.9
65.94
65.94
65.91
65.95
65.91
66.08
66.47
66.47
66.56
66.78
67.08
67.28
67.27
67.27
67.26
67.37
67.5
67.63
67.64
67.64
67.71
67.87
67.93
68.33
68.39
68.39
68.58
68.44
68.49
68.52
68.54
68.54
68.54
68.62
68.75
68.71
68.72
68.72
68.72
68.92
68.9
69.12
69.09
69.09
69.1
69.16
68.83
68.52
68.53
68.53
68.51
68.38
68.44
68.41
68.42
68.42
68.45
68.63
68.84
68.72
68.37
68.37
68.47
68.69
68.46
68.17
68.17




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13391&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13391&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13391&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.831008185222246
beta0.0653557661833785
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.831008185222246 \tabularnewline
beta & 0.0653557661833785 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13391&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]0.831008185222246[/C][/ROW]
[ROW][C]beta[/C][C]0.0653557661833785[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13391&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13391&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
alpha0.831008185222246
beta0.0653557661833785
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1366.2866.19850555555560.0814944444444166
1466.2666.3090027158319-0.0490027158318611
1566.1366.1996442726144-0.0696442726144255
1665.8665.9293500643624-0.0693500643623537
1765.965.9605338619797-0.0605338619796498
1865.9465.9728396640016-0.0328396640016138
1965.9465.9501260104337-0.0101260104337371
2065.9165.9111543000223-0.00115430002233552
2165.9565.93040879633920.0195912036608235
2265.9165.84963366401270.0603663359872826
2366.0865.98560490047390.0943950995260678
2466.4766.37039769356080.0996023064392375
2566.4766.579115797402-0.109115797401998
2666.5666.5022197285330.0577802714669673
2766.7866.4769684713040.303031528695982
2867.0866.53551898808080.544481011919189
2967.2867.13072755340830.149272446591723
3067.2767.3858952883628-0.115895288362850
3167.2767.3573203843956-0.0873203843956532
3267.2667.3108433774492-0.0508433774492119
3367.3767.34474070621870.0252592937812892
3467.567.3283033496250.171696650374969
3567.6367.62132493432050.00867506567951182
3667.6467.9898914602985-0.349891460298451
3767.6467.8195201855698-0.179520185569828
3867.7167.7382130901932-0.0282130901932334
3967.8767.70416722670760.165832773292436
4067.9367.703277141370.226722858630012
4168.3367.96415094880870.365849051191333
4268.3968.36275884947930.0272411505206662
4368.3968.4740087424403-0.084008742440318
4468.5868.4526762315720.127323768428028
4568.4468.6733972916619-0.233397291661888
4668.4968.47861761277970.0113823872202801
4768.5268.6140172656088-0.0940172656088407
4868.5468.8342233209066-0.294223320906596
4968.5468.7394999838469-0.199499983846906
5068.5468.6666699541216-0.126669954121581
5168.6268.57776126623370.0422387337663253
5268.7568.47190438350780.278095616492209
5368.7168.7892216109981-0.0792216109980899
5468.7268.7268189234054-0.00681892340541879
5568.7268.7551831907983-0.0351831907983353
5668.7268.777009246645-0.057009246644995
5768.9268.74044848200470.179551517995307
5868.968.9094854681044-0.0094854681044012
5969.1268.98788578788930.132114212110736
6069.0969.3526109382738-0.262610938273767
6169.0969.292317295045-0.202317295044978
6269.169.2214528005383-0.121452800538307
6369.1669.15770621042040.00229378957959625
6468.8369.0486255925776-0.218625592577609
6568.5268.8559151873218-0.335915187321788
6668.5368.541627612602-0.0116276126019415
6768.5368.51013543964310.0198645603568934
6868.5168.5259408593804-0.0159408593803505
6968.3868.5176382229576-0.137638222957591
7068.4468.32806841598830.111931584011657
7168.4168.474816971077-0.0648169710770219
7268.4268.5420102967654-0.12201029676541
7368.4268.5492071759047-0.129207175904739
7468.4568.4971950293378-0.0471950293378285
7568.6368.46453424550370.165465754496338
7668.8468.41104418996920.428955810030772
7768.7268.7291560485346-0.0091560485346207
7868.3768.7514544109398-0.38145441093981
7968.3768.4081138047678-0.038113804767832
8068.4768.35669777629080.113302223709240
8168.6968.4292605560210.260739443978949
8268.4668.6285866800685-0.168586680068472
8368.1768.5127834999137-0.342783499913665
8468.1768.3246527691646-0.154652769164557

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 66.28 & 66.1985055555556 & 0.0814944444444166 \tabularnewline
14 & 66.26 & 66.3090027158319 & -0.0490027158318611 \tabularnewline
15 & 66.13 & 66.1996442726144 & -0.0696442726144255 \tabularnewline
16 & 65.86 & 65.9293500643624 & -0.0693500643623537 \tabularnewline
17 & 65.9 & 65.9605338619797 & -0.0605338619796498 \tabularnewline
18 & 65.94 & 65.9728396640016 & -0.0328396640016138 \tabularnewline
19 & 65.94 & 65.9501260104337 & -0.0101260104337371 \tabularnewline
20 & 65.91 & 65.9111543000223 & -0.00115430002233552 \tabularnewline
21 & 65.95 & 65.9304087963392 & 0.0195912036608235 \tabularnewline
22 & 65.91 & 65.8496336640127 & 0.0603663359872826 \tabularnewline
23 & 66.08 & 65.9856049004739 & 0.0943950995260678 \tabularnewline
24 & 66.47 & 66.3703976935608 & 0.0996023064392375 \tabularnewline
25 & 66.47 & 66.579115797402 & -0.109115797401998 \tabularnewline
26 & 66.56 & 66.502219728533 & 0.0577802714669673 \tabularnewline
27 & 66.78 & 66.476968471304 & 0.303031528695982 \tabularnewline
28 & 67.08 & 66.5355189880808 & 0.544481011919189 \tabularnewline
29 & 67.28 & 67.1307275534083 & 0.149272446591723 \tabularnewline
30 & 67.27 & 67.3858952883628 & -0.115895288362850 \tabularnewline
31 & 67.27 & 67.3573203843956 & -0.0873203843956532 \tabularnewline
32 & 67.26 & 67.3108433774492 & -0.0508433774492119 \tabularnewline
33 & 67.37 & 67.3447407062187 & 0.0252592937812892 \tabularnewline
34 & 67.5 & 67.328303349625 & 0.171696650374969 \tabularnewline
35 & 67.63 & 67.6213249343205 & 0.00867506567951182 \tabularnewline
36 & 67.64 & 67.9898914602985 & -0.349891460298451 \tabularnewline
37 & 67.64 & 67.8195201855698 & -0.179520185569828 \tabularnewline
38 & 67.71 & 67.7382130901932 & -0.0282130901932334 \tabularnewline
39 & 67.87 & 67.7041672267076 & 0.165832773292436 \tabularnewline
40 & 67.93 & 67.70327714137 & 0.226722858630012 \tabularnewline
41 & 68.33 & 67.9641509488087 & 0.365849051191333 \tabularnewline
42 & 68.39 & 68.3627588494793 & 0.0272411505206662 \tabularnewline
43 & 68.39 & 68.4740087424403 & -0.084008742440318 \tabularnewline
44 & 68.58 & 68.452676231572 & 0.127323768428028 \tabularnewline
45 & 68.44 & 68.6733972916619 & -0.233397291661888 \tabularnewline
46 & 68.49 & 68.4786176127797 & 0.0113823872202801 \tabularnewline
47 & 68.52 & 68.6140172656088 & -0.0940172656088407 \tabularnewline
48 & 68.54 & 68.8342233209066 & -0.294223320906596 \tabularnewline
49 & 68.54 & 68.7394999838469 & -0.199499983846906 \tabularnewline
50 & 68.54 & 68.6666699541216 & -0.126669954121581 \tabularnewline
51 & 68.62 & 68.5777612662337 & 0.0422387337663253 \tabularnewline
52 & 68.75 & 68.4719043835078 & 0.278095616492209 \tabularnewline
53 & 68.71 & 68.7892216109981 & -0.0792216109980899 \tabularnewline
54 & 68.72 & 68.7268189234054 & -0.00681892340541879 \tabularnewline
55 & 68.72 & 68.7551831907983 & -0.0351831907983353 \tabularnewline
56 & 68.72 & 68.777009246645 & -0.057009246644995 \tabularnewline
57 & 68.92 & 68.7404484820047 & 0.179551517995307 \tabularnewline
58 & 68.9 & 68.9094854681044 & -0.0094854681044012 \tabularnewline
59 & 69.12 & 68.9878857878893 & 0.132114212110736 \tabularnewline
60 & 69.09 & 69.3526109382738 & -0.262610938273767 \tabularnewline
61 & 69.09 & 69.292317295045 & -0.202317295044978 \tabularnewline
62 & 69.1 & 69.2214528005383 & -0.121452800538307 \tabularnewline
63 & 69.16 & 69.1577062104204 & 0.00229378957959625 \tabularnewline
64 & 68.83 & 69.0486255925776 & -0.218625592577609 \tabularnewline
65 & 68.52 & 68.8559151873218 & -0.335915187321788 \tabularnewline
66 & 68.53 & 68.541627612602 & -0.0116276126019415 \tabularnewline
67 & 68.53 & 68.5101354396431 & 0.0198645603568934 \tabularnewline
68 & 68.51 & 68.5259408593804 & -0.0159408593803505 \tabularnewline
69 & 68.38 & 68.5176382229576 & -0.137638222957591 \tabularnewline
70 & 68.44 & 68.3280684159883 & 0.111931584011657 \tabularnewline
71 & 68.41 & 68.474816971077 & -0.0648169710770219 \tabularnewline
72 & 68.42 & 68.5420102967654 & -0.12201029676541 \tabularnewline
73 & 68.42 & 68.5492071759047 & -0.129207175904739 \tabularnewline
74 & 68.45 & 68.4971950293378 & -0.0471950293378285 \tabularnewline
75 & 68.63 & 68.4645342455037 & 0.165465754496338 \tabularnewline
76 & 68.84 & 68.4110441899692 & 0.428955810030772 \tabularnewline
77 & 68.72 & 68.7291560485346 & -0.0091560485346207 \tabularnewline
78 & 68.37 & 68.7514544109398 & -0.38145441093981 \tabularnewline
79 & 68.37 & 68.4081138047678 & -0.038113804767832 \tabularnewline
80 & 68.47 & 68.3566977762908 & 0.113302223709240 \tabularnewline
81 & 68.69 & 68.429260556021 & 0.260739443978949 \tabularnewline
82 & 68.46 & 68.6285866800685 & -0.168586680068472 \tabularnewline
83 & 68.17 & 68.5127834999137 & -0.342783499913665 \tabularnewline
84 & 68.17 & 68.3246527691646 & -0.154652769164557 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13391&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]66.28[/C][C]66.1985055555556[/C][C]0.0814944444444166[/C][/ROW]
[ROW][C]14[/C][C]66.26[/C][C]66.3090027158319[/C][C]-0.0490027158318611[/C][/ROW]
[ROW][C]15[/C][C]66.13[/C][C]66.1996442726144[/C][C]-0.0696442726144255[/C][/ROW]
[ROW][C]16[/C][C]65.86[/C][C]65.9293500643624[/C][C]-0.0693500643623537[/C][/ROW]
[ROW][C]17[/C][C]65.9[/C][C]65.9605338619797[/C][C]-0.0605338619796498[/C][/ROW]
[ROW][C]18[/C][C]65.94[/C][C]65.9728396640016[/C][C]-0.0328396640016138[/C][/ROW]
[ROW][C]19[/C][C]65.94[/C][C]65.9501260104337[/C][C]-0.0101260104337371[/C][/ROW]
[ROW][C]20[/C][C]65.91[/C][C]65.9111543000223[/C][C]-0.00115430002233552[/C][/ROW]
[ROW][C]21[/C][C]65.95[/C][C]65.9304087963392[/C][C]0.0195912036608235[/C][/ROW]
[ROW][C]22[/C][C]65.91[/C][C]65.8496336640127[/C][C]0.0603663359872826[/C][/ROW]
[ROW][C]23[/C][C]66.08[/C][C]65.9856049004739[/C][C]0.0943950995260678[/C][/ROW]
[ROW][C]24[/C][C]66.47[/C][C]66.3703976935608[/C][C]0.0996023064392375[/C][/ROW]
[ROW][C]25[/C][C]66.47[/C][C]66.579115797402[/C][C]-0.109115797401998[/C][/ROW]
[ROW][C]26[/C][C]66.56[/C][C]66.502219728533[/C][C]0.0577802714669673[/C][/ROW]
[ROW][C]27[/C][C]66.78[/C][C]66.476968471304[/C][C]0.303031528695982[/C][/ROW]
[ROW][C]28[/C][C]67.08[/C][C]66.5355189880808[/C][C]0.544481011919189[/C][/ROW]
[ROW][C]29[/C][C]67.28[/C][C]67.1307275534083[/C][C]0.149272446591723[/C][/ROW]
[ROW][C]30[/C][C]67.27[/C][C]67.3858952883628[/C][C]-0.115895288362850[/C][/ROW]
[ROW][C]31[/C][C]67.27[/C][C]67.3573203843956[/C][C]-0.0873203843956532[/C][/ROW]
[ROW][C]32[/C][C]67.26[/C][C]67.3108433774492[/C][C]-0.0508433774492119[/C][/ROW]
[ROW][C]33[/C][C]67.37[/C][C]67.3447407062187[/C][C]0.0252592937812892[/C][/ROW]
[ROW][C]34[/C][C]67.5[/C][C]67.328303349625[/C][C]0.171696650374969[/C][/ROW]
[ROW][C]35[/C][C]67.63[/C][C]67.6213249343205[/C][C]0.00867506567951182[/C][/ROW]
[ROW][C]36[/C][C]67.64[/C][C]67.9898914602985[/C][C]-0.349891460298451[/C][/ROW]
[ROW][C]37[/C][C]67.64[/C][C]67.8195201855698[/C][C]-0.179520185569828[/C][/ROW]
[ROW][C]38[/C][C]67.71[/C][C]67.7382130901932[/C][C]-0.0282130901932334[/C][/ROW]
[ROW][C]39[/C][C]67.87[/C][C]67.7041672267076[/C][C]0.165832773292436[/C][/ROW]
[ROW][C]40[/C][C]67.93[/C][C]67.70327714137[/C][C]0.226722858630012[/C][/ROW]
[ROW][C]41[/C][C]68.33[/C][C]67.9641509488087[/C][C]0.365849051191333[/C][/ROW]
[ROW][C]42[/C][C]68.39[/C][C]68.3627588494793[/C][C]0.0272411505206662[/C][/ROW]
[ROW][C]43[/C][C]68.39[/C][C]68.4740087424403[/C][C]-0.084008742440318[/C][/ROW]
[ROW][C]44[/C][C]68.58[/C][C]68.452676231572[/C][C]0.127323768428028[/C][/ROW]
[ROW][C]45[/C][C]68.44[/C][C]68.6733972916619[/C][C]-0.233397291661888[/C][/ROW]
[ROW][C]46[/C][C]68.49[/C][C]68.4786176127797[/C][C]0.0113823872202801[/C][/ROW]
[ROW][C]47[/C][C]68.52[/C][C]68.6140172656088[/C][C]-0.0940172656088407[/C][/ROW]
[ROW][C]48[/C][C]68.54[/C][C]68.8342233209066[/C][C]-0.294223320906596[/C][/ROW]
[ROW][C]49[/C][C]68.54[/C][C]68.7394999838469[/C][C]-0.199499983846906[/C][/ROW]
[ROW][C]50[/C][C]68.54[/C][C]68.6666699541216[/C][C]-0.126669954121581[/C][/ROW]
[ROW][C]51[/C][C]68.62[/C][C]68.5777612662337[/C][C]0.0422387337663253[/C][/ROW]
[ROW][C]52[/C][C]68.75[/C][C]68.4719043835078[/C][C]0.278095616492209[/C][/ROW]
[ROW][C]53[/C][C]68.71[/C][C]68.7892216109981[/C][C]-0.0792216109980899[/C][/ROW]
[ROW][C]54[/C][C]68.72[/C][C]68.7268189234054[/C][C]-0.00681892340541879[/C][/ROW]
[ROW][C]55[/C][C]68.72[/C][C]68.7551831907983[/C][C]-0.0351831907983353[/C][/ROW]
[ROW][C]56[/C][C]68.72[/C][C]68.777009246645[/C][C]-0.057009246644995[/C][/ROW]
[ROW][C]57[/C][C]68.92[/C][C]68.7404484820047[/C][C]0.179551517995307[/C][/ROW]
[ROW][C]58[/C][C]68.9[/C][C]68.9094854681044[/C][C]-0.0094854681044012[/C][/ROW]
[ROW][C]59[/C][C]69.12[/C][C]68.9878857878893[/C][C]0.132114212110736[/C][/ROW]
[ROW][C]60[/C][C]69.09[/C][C]69.3526109382738[/C][C]-0.262610938273767[/C][/ROW]
[ROW][C]61[/C][C]69.09[/C][C]69.292317295045[/C][C]-0.202317295044978[/C][/ROW]
[ROW][C]62[/C][C]69.1[/C][C]69.2214528005383[/C][C]-0.121452800538307[/C][/ROW]
[ROW][C]63[/C][C]69.16[/C][C]69.1577062104204[/C][C]0.00229378957959625[/C][/ROW]
[ROW][C]64[/C][C]68.83[/C][C]69.0486255925776[/C][C]-0.218625592577609[/C][/ROW]
[ROW][C]65[/C][C]68.52[/C][C]68.8559151873218[/C][C]-0.335915187321788[/C][/ROW]
[ROW][C]66[/C][C]68.53[/C][C]68.541627612602[/C][C]-0.0116276126019415[/C][/ROW]
[ROW][C]67[/C][C]68.53[/C][C]68.5101354396431[/C][C]0.0198645603568934[/C][/ROW]
[ROW][C]68[/C][C]68.51[/C][C]68.5259408593804[/C][C]-0.0159408593803505[/C][/ROW]
[ROW][C]69[/C][C]68.38[/C][C]68.5176382229576[/C][C]-0.137638222957591[/C][/ROW]
[ROW][C]70[/C][C]68.44[/C][C]68.3280684159883[/C][C]0.111931584011657[/C][/ROW]
[ROW][C]71[/C][C]68.41[/C][C]68.474816971077[/C][C]-0.0648169710770219[/C][/ROW]
[ROW][C]72[/C][C]68.42[/C][C]68.5420102967654[/C][C]-0.12201029676541[/C][/ROW]
[ROW][C]73[/C][C]68.42[/C][C]68.5492071759047[/C][C]-0.129207175904739[/C][/ROW]
[ROW][C]74[/C][C]68.45[/C][C]68.4971950293378[/C][C]-0.0471950293378285[/C][/ROW]
[ROW][C]75[/C][C]68.63[/C][C]68.4645342455037[/C][C]0.165465754496338[/C][/ROW]
[ROW][C]76[/C][C]68.84[/C][C]68.4110441899692[/C][C]0.428955810030772[/C][/ROW]
[ROW][C]77[/C][C]68.72[/C][C]68.7291560485346[/C][C]-0.0091560485346207[/C][/ROW]
[ROW][C]78[/C][C]68.37[/C][C]68.7514544109398[/C][C]-0.38145441093981[/C][/ROW]
[ROW][C]79[/C][C]68.37[/C][C]68.4081138047678[/C][C]-0.038113804767832[/C][/ROW]
[ROW][C]80[/C][C]68.47[/C][C]68.3566977762908[/C][C]0.113302223709240[/C][/ROW]
[ROW][C]81[/C][C]68.69[/C][C]68.429260556021[/C][C]0.260739443978949[/C][/ROW]
[ROW][C]82[/C][C]68.46[/C][C]68.6285866800685[/C][C]-0.168586680068472[/C][/ROW]
[ROW][C]83[/C][C]68.17[/C][C]68.5127834999137[/C][C]-0.342783499913665[/C][/ROW]
[ROW][C]84[/C][C]68.17[/C][C]68.3246527691646[/C][C]-0.154652769164557[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13391&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13391&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
1366.2866.19850555555560.0814944444444166
1466.2666.3090027158319-0.0490027158318611
1566.1366.1996442726144-0.0696442726144255
1665.8665.9293500643624-0.0693500643623537
1765.965.9605338619797-0.0605338619796498
1865.9465.9728396640016-0.0328396640016138
1965.9465.9501260104337-0.0101260104337371
2065.9165.9111543000223-0.00115430002233552
2165.9565.93040879633920.0195912036608235
2265.9165.84963366401270.0603663359872826
2366.0865.98560490047390.0943950995260678
2466.4766.37039769356080.0996023064392375
2566.4766.579115797402-0.109115797401998
2666.5666.5022197285330.0577802714669673
2766.7866.4769684713040.303031528695982
2867.0866.53551898808080.544481011919189
2967.2867.13072755340830.149272446591723
3067.2767.3858952883628-0.115895288362850
3167.2767.3573203843956-0.0873203843956532
3267.2667.3108433774492-0.0508433774492119
3367.3767.34474070621870.0252592937812892
3467.567.3283033496250.171696650374969
3567.6367.62132493432050.00867506567951182
3667.6467.9898914602985-0.349891460298451
3767.6467.8195201855698-0.179520185569828
3867.7167.7382130901932-0.0282130901932334
3967.8767.70416722670760.165832773292436
4067.9367.703277141370.226722858630012
4168.3367.96415094880870.365849051191333
4268.3968.36275884947930.0272411505206662
4368.3968.4740087424403-0.084008742440318
4468.5868.4526762315720.127323768428028
4568.4468.6733972916619-0.233397291661888
4668.4968.47861761277970.0113823872202801
4768.5268.6140172656088-0.0940172656088407
4868.5468.8342233209066-0.294223320906596
4968.5468.7394999838469-0.199499983846906
5068.5468.6666699541216-0.126669954121581
5168.6268.57776126623370.0422387337663253
5268.7568.47190438350780.278095616492209
5368.7168.7892216109981-0.0792216109980899
5468.7268.7268189234054-0.00681892340541879
5568.7268.7551831907983-0.0351831907983353
5668.7268.777009246645-0.057009246644995
5768.9268.74044848200470.179551517995307
5868.968.9094854681044-0.0094854681044012
5969.1268.98788578788930.132114212110736
6069.0969.3526109382738-0.262610938273767
6169.0969.292317295045-0.202317295044978
6269.169.2214528005383-0.121452800538307
6369.1669.15770621042040.00229378957959625
6468.8369.0486255925776-0.218625592577609
6568.5268.8559151873218-0.335915187321788
6668.5368.541627612602-0.0116276126019415
6768.5368.51013543964310.0198645603568934
6868.5168.5259408593804-0.0159408593803505
6968.3868.5176382229576-0.137638222957591
7068.4468.32806841598830.111931584011657
7168.4168.474816971077-0.0648169710770219
7268.4268.5420102967654-0.12201029676541
7368.4268.5492071759047-0.129207175904739
7468.4568.4971950293378-0.0471950293378285
7568.6368.46453424550370.165465754496338
7668.8468.41104418996920.428955810030772
7768.7268.7291560485346-0.0091560485346207
7868.3768.7514544109398-0.38145441093981
7968.3768.4081138047678-0.038113804767832
8068.4768.35669777629080.113302223709240
8168.6968.4292605560210.260739443978949
8268.4668.6285866800685-0.168586680068472
8368.1768.5127834999137-0.342783499913665
8468.1768.3246527691646-0.154652769164557







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8568.287068029947967.940755411110468.6333806487854
8668.346865636444567.884335298061468.8093959748276
8768.382503608474567.816974367994768.9480328489543
8868.220192547808867.558144978505968.8822401171116
8968.068658932880267.31361401316668.8237038525945
9067.997005580224767.150903699567368.843107460882
9168.010750611417467.074587591782568.9469136310522
9268.000737689155466.97490203870269.0265733396087
9367.982049652956166.866518985518269.097580320394
9467.855974073968566.650437515249969.0615106326871
9567.82381361907466.527752090714369.1198751474336
9667.943931962251566.556672983916969.3311909405861

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 68.2870680299479 & 67.9407554111104 & 68.6333806487854 \tabularnewline
86 & 68.3468656364445 & 67.8843352980614 & 68.8093959748276 \tabularnewline
87 & 68.3825036084745 & 67.8169743679947 & 68.9480328489543 \tabularnewline
88 & 68.2201925478088 & 67.5581449785059 & 68.8822401171116 \tabularnewline
89 & 68.0686589328802 & 67.313614013166 & 68.8237038525945 \tabularnewline
90 & 67.9970055802247 & 67.1509036995673 & 68.843107460882 \tabularnewline
91 & 68.0107506114174 & 67.0745875917825 & 68.9469136310522 \tabularnewline
92 & 68.0007376891554 & 66.974902038702 & 69.0265733396087 \tabularnewline
93 & 67.9820496529561 & 66.8665189855182 & 69.097580320394 \tabularnewline
94 & 67.8559740739685 & 66.6504375152499 & 69.0615106326871 \tabularnewline
95 & 67.823813619074 & 66.5277520907143 & 69.1198751474336 \tabularnewline
96 & 67.9439319622515 & 66.5566729839169 & 69.3311909405861 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13391&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]85[/C][C]68.2870680299479[/C][C]67.9407554111104[/C][C]68.6333806487854[/C][/ROW]
[ROW][C]86[/C][C]68.3468656364445[/C][C]67.8843352980614[/C][C]68.8093959748276[/C][/ROW]
[ROW][C]87[/C][C]68.3825036084745[/C][C]67.8169743679947[/C][C]68.9480328489543[/C][/ROW]
[ROW][C]88[/C][C]68.2201925478088[/C][C]67.5581449785059[/C][C]68.8822401171116[/C][/ROW]
[ROW][C]89[/C][C]68.0686589328802[/C][C]67.313614013166[/C][C]68.8237038525945[/C][/ROW]
[ROW][C]90[/C][C]67.9970055802247[/C][C]67.1509036995673[/C][C]68.843107460882[/C][/ROW]
[ROW][C]91[/C][C]68.0107506114174[/C][C]67.0745875917825[/C][C]68.9469136310522[/C][/ROW]
[ROW][C]92[/C][C]68.0007376891554[/C][C]66.974902038702[/C][C]69.0265733396087[/C][/ROW]
[ROW][C]93[/C][C]67.9820496529561[/C][C]66.8665189855182[/C][C]69.097580320394[/C][/ROW]
[ROW][C]94[/C][C]67.8559740739685[/C][C]66.6504375152499[/C][C]69.0615106326871[/C][/ROW]
[ROW][C]95[/C][C]67.823813619074[/C][C]66.5277520907143[/C][C]69.1198751474336[/C][/ROW]
[ROW][C]96[/C][C]67.9439319622515[/C][C]66.5566729839169[/C][C]69.3311909405861[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13391&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13391&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
8568.287068029947967.940755411110468.6333806487854
8668.346865636444567.884335298061468.8093959748276
8768.382503608474567.816974367994768.9480328489543
8868.220192547808867.558144978505968.8822401171116
8968.068658932880267.31361401316668.8237038525945
9067.997005580224767.150903699567368.843107460882
9168.010750611417467.074587591782568.9469136310522
9268.000737689155466.97490203870269.0265733396087
9367.982049652956166.866518985518269.097580320394
9467.855974073968566.650437515249969.0615106326871
9567.82381361907466.527752090714369.1198751474336
9667.943931962251566.556672983916969.3311909405861



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')