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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Dec 2013 03:28:19 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/16/t1387182597iw1wpnz81gk7uq9.htm/, Retrieved Fri, 19 Apr 2024 19:39:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232370, Retrieved Fri, 19 Apr 2024 19:39:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-16 08:28:19] [d5e0951e56f9204e3d256e2fd8efefc4] [Current]
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Dataseries X:
104.4
104.4
104.4
104.4
104.4
104.41
104.42
104.68
106.02
106.35
106.38
106.47
106.5
106.56
113.07
116.26
118
118.02
118.04
118.12
118.12
118.17
118.22
118.22
118.23
118.23
118.23
119.94
120.88
121.14
121.16
121.2
121.2
121.2
121.2
121.2
121.22
121.22
121.95
123.05
123.44
123.65
123.79
123.87
123.91
123.94
124.28
126.28
126.68
126.69
126.69
126.99
128.79
128.84
128.95
128.97
128.97
128.97
128.97
128.97
128.97
128.98
128.99
129.07
129.76
130.47
130.76
130.88
131.04
131.06
131.13
131.15
131.16
131.33
131.42
131.86
134.39
135.59
136.01
136.14
136.74
136.89
136.82
136.82




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232370&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232370&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232370&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0679531906831734
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0679531906831734 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232370&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0679531906831734[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232370&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232370&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
alpha1
beta0.0679531906831734
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3104.4104.40
4104.4104.40
5104.4104.40
6104.41104.40.00999999999999091
7104.42104.4106795319070.0093204680931791
8104.68104.4213128874520.258687112547577
9106.02104.6988915021391.32110849786135
10106.35106.1286650398070.221334960193019
11106.38106.473705456562-0.0937054565618354
12106.47106.497337871804-0.027337871804022
13106.5106.585480176188-0.0854801761884545
14106.56106.609671525476-0.0496715254762847
15113.07106.6662961868346.40370381316592
16116.26113.6114482931292.6485517068713
17118116.98142583231.01857416770002
18118.02118.790641196943-0.770641196942648
19118.04118.758273668738-0.71827366873849
20118.12118.729464681164-0.609464681164013
21118.12118.76804961147-0.648049611470213
22118.17118.72401257265-0.554012572649825
23118.22118.73636565066-0.516365650659679
24118.22118.751276957138-0.531276957138147
25118.23118.715174992764-0.485174992764158
26118.23118.692205803966-0.462205803966157
27118.23118.660797444834-0.430797444834369
28119.94118.631523383921.30847661608027
29120.88120.4304385449170.449561455083298
30121.14121.400987680198-0.260987680197772
31121.16121.643252734599-0.483252734599347
32121.2121.630414169377-0.430414169376945
33121.2121.641166153253-0.441166153252539
34121.2121.611187505518-0.411187505517603
35121.2121.583246002549-0.383246002548631
36121.2121.557203213859-0.357203213858881
37121.22121.532930115755-0.312930115754881
38121.22121.531665515928-0.311665515928482
39121.95121.5104868496950.439513150304776
40123.05122.2703531706060.779646829394352
41123.44123.4233326602690.0166673397309864
42123.65123.814465259184-0.164465259183928
43123.79124.013289320066-0.223289320065845
44123.87124.138116098322-0.268116098321897
45123.91124.199896753967-0.289896753967412
46123.94124.220197344567-0.280197344566616
47124.28124.2311570409820.0488429590176338
48126.28124.574476075891.70552392410998
49126.68126.69037186832-0.0103718683197798
50126.69127.089667066774-0.399667066774114
51126.69127.072508414376-0.38250841437582
52126.99127.046515747156-0.056515747155828
53128.79127.3426753218131.44732467818726
54128.84129.24102565165-0.401025651650059
55128.95129.263774679075-0.313774679074669
56128.97129.352452688476-0.382452688475922
57128.97129.346463808009-0.376463808008623
58128.97129.320881891078-0.350881891077705
59128.97129.297038347026-0.327038347026047
60128.97129.27481504787-0.304815047869852
61128.97129.254101892799-0.284101892798873
62128.98129.234796262704-0.254796262704048
63128.99129.227482043679-0.237482043679137
64129.07129.221344381081-0.15134438108123
65129.76129.2910600474950.468939952505224
66130.47130.0129260135060.457073986493697
67130.76130.7539856492670.00601435073315315
68130.88131.044394343589-0.164394343589038
69131.04131.153223223412-0.113223223411893
70131.06131.305529344122-0.245529344121621
71131.13131.308844841782-0.178844841782222
72131.15131.366691764146-0.216691764145878
73131.16131.371966867377-0.211966867377413
74131.33131.36756304242-0.0375630424199755
75131.42131.535010513836-0.115010513835813
76131.86131.6171951824590.242804817541497
77134.39132.0736945445242.31630545547625
78135.59134.761094890820.828905109179829
79136.01136.017421637763-0.00742163776254756
80136.14136.436917313796-0.296917313796484
81136.74136.5467408349550.193259165045106
82136.89137.159873411849-0.269873411848522
83136.82137.291534652433-0.471534652432837
84136.82137.189492368282-0.369492368282351

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 104.4 & 104.4 & 0 \tabularnewline
4 & 104.4 & 104.4 & 0 \tabularnewline
5 & 104.4 & 104.4 & 0 \tabularnewline
6 & 104.41 & 104.4 & 0.00999999999999091 \tabularnewline
7 & 104.42 & 104.410679531907 & 0.0093204680931791 \tabularnewline
8 & 104.68 & 104.421312887452 & 0.258687112547577 \tabularnewline
9 & 106.02 & 104.698891502139 & 1.32110849786135 \tabularnewline
10 & 106.35 & 106.128665039807 & 0.221334960193019 \tabularnewline
11 & 106.38 & 106.473705456562 & -0.0937054565618354 \tabularnewline
12 & 106.47 & 106.497337871804 & -0.027337871804022 \tabularnewline
13 & 106.5 & 106.585480176188 & -0.0854801761884545 \tabularnewline
14 & 106.56 & 106.609671525476 & -0.0496715254762847 \tabularnewline
15 & 113.07 & 106.666296186834 & 6.40370381316592 \tabularnewline
16 & 116.26 & 113.611448293129 & 2.6485517068713 \tabularnewline
17 & 118 & 116.9814258323 & 1.01857416770002 \tabularnewline
18 & 118.02 & 118.790641196943 & -0.770641196942648 \tabularnewline
19 & 118.04 & 118.758273668738 & -0.71827366873849 \tabularnewline
20 & 118.12 & 118.729464681164 & -0.609464681164013 \tabularnewline
21 & 118.12 & 118.76804961147 & -0.648049611470213 \tabularnewline
22 & 118.17 & 118.72401257265 & -0.554012572649825 \tabularnewline
23 & 118.22 & 118.73636565066 & -0.516365650659679 \tabularnewline
24 & 118.22 & 118.751276957138 & -0.531276957138147 \tabularnewline
25 & 118.23 & 118.715174992764 & -0.485174992764158 \tabularnewline
26 & 118.23 & 118.692205803966 & -0.462205803966157 \tabularnewline
27 & 118.23 & 118.660797444834 & -0.430797444834369 \tabularnewline
28 & 119.94 & 118.63152338392 & 1.30847661608027 \tabularnewline
29 & 120.88 & 120.430438544917 & 0.449561455083298 \tabularnewline
30 & 121.14 & 121.400987680198 & -0.260987680197772 \tabularnewline
31 & 121.16 & 121.643252734599 & -0.483252734599347 \tabularnewline
32 & 121.2 & 121.630414169377 & -0.430414169376945 \tabularnewline
33 & 121.2 & 121.641166153253 & -0.441166153252539 \tabularnewline
34 & 121.2 & 121.611187505518 & -0.411187505517603 \tabularnewline
35 & 121.2 & 121.583246002549 & -0.383246002548631 \tabularnewline
36 & 121.2 & 121.557203213859 & -0.357203213858881 \tabularnewline
37 & 121.22 & 121.532930115755 & -0.312930115754881 \tabularnewline
38 & 121.22 & 121.531665515928 & -0.311665515928482 \tabularnewline
39 & 121.95 & 121.510486849695 & 0.439513150304776 \tabularnewline
40 & 123.05 & 122.270353170606 & 0.779646829394352 \tabularnewline
41 & 123.44 & 123.423332660269 & 0.0166673397309864 \tabularnewline
42 & 123.65 & 123.814465259184 & -0.164465259183928 \tabularnewline
43 & 123.79 & 124.013289320066 & -0.223289320065845 \tabularnewline
44 & 123.87 & 124.138116098322 & -0.268116098321897 \tabularnewline
45 & 123.91 & 124.199896753967 & -0.289896753967412 \tabularnewline
46 & 123.94 & 124.220197344567 & -0.280197344566616 \tabularnewline
47 & 124.28 & 124.231157040982 & 0.0488429590176338 \tabularnewline
48 & 126.28 & 124.57447607589 & 1.70552392410998 \tabularnewline
49 & 126.68 & 126.69037186832 & -0.0103718683197798 \tabularnewline
50 & 126.69 & 127.089667066774 & -0.399667066774114 \tabularnewline
51 & 126.69 & 127.072508414376 & -0.38250841437582 \tabularnewline
52 & 126.99 & 127.046515747156 & -0.056515747155828 \tabularnewline
53 & 128.79 & 127.342675321813 & 1.44732467818726 \tabularnewline
54 & 128.84 & 129.24102565165 & -0.401025651650059 \tabularnewline
55 & 128.95 & 129.263774679075 & -0.313774679074669 \tabularnewline
56 & 128.97 & 129.352452688476 & -0.382452688475922 \tabularnewline
57 & 128.97 & 129.346463808009 & -0.376463808008623 \tabularnewline
58 & 128.97 & 129.320881891078 & -0.350881891077705 \tabularnewline
59 & 128.97 & 129.297038347026 & -0.327038347026047 \tabularnewline
60 & 128.97 & 129.27481504787 & -0.304815047869852 \tabularnewline
61 & 128.97 & 129.254101892799 & -0.284101892798873 \tabularnewline
62 & 128.98 & 129.234796262704 & -0.254796262704048 \tabularnewline
63 & 128.99 & 129.227482043679 & -0.237482043679137 \tabularnewline
64 & 129.07 & 129.221344381081 & -0.15134438108123 \tabularnewline
65 & 129.76 & 129.291060047495 & 0.468939952505224 \tabularnewline
66 & 130.47 & 130.012926013506 & 0.457073986493697 \tabularnewline
67 & 130.76 & 130.753985649267 & 0.00601435073315315 \tabularnewline
68 & 130.88 & 131.044394343589 & -0.164394343589038 \tabularnewline
69 & 131.04 & 131.153223223412 & -0.113223223411893 \tabularnewline
70 & 131.06 & 131.305529344122 & -0.245529344121621 \tabularnewline
71 & 131.13 & 131.308844841782 & -0.178844841782222 \tabularnewline
72 & 131.15 & 131.366691764146 & -0.216691764145878 \tabularnewline
73 & 131.16 & 131.371966867377 & -0.211966867377413 \tabularnewline
74 & 131.33 & 131.36756304242 & -0.0375630424199755 \tabularnewline
75 & 131.42 & 131.535010513836 & -0.115010513835813 \tabularnewline
76 & 131.86 & 131.617195182459 & 0.242804817541497 \tabularnewline
77 & 134.39 & 132.073694544524 & 2.31630545547625 \tabularnewline
78 & 135.59 & 134.76109489082 & 0.828905109179829 \tabularnewline
79 & 136.01 & 136.017421637763 & -0.00742163776254756 \tabularnewline
80 & 136.14 & 136.436917313796 & -0.296917313796484 \tabularnewline
81 & 136.74 & 136.546740834955 & 0.193259165045106 \tabularnewline
82 & 136.89 & 137.159873411849 & -0.269873411848522 \tabularnewline
83 & 136.82 & 137.291534652433 & -0.471534652432837 \tabularnewline
84 & 136.82 & 137.189492368282 & -0.369492368282351 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232370&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]3[/C][C]104.4[/C][C]104.4[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]104.4[/C][C]104.4[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]104.4[/C][C]104.4[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]104.41[/C][C]104.4[/C][C]0.00999999999999091[/C][/ROW]
[ROW][C]7[/C][C]104.42[/C][C]104.410679531907[/C][C]0.0093204680931791[/C][/ROW]
[ROW][C]8[/C][C]104.68[/C][C]104.421312887452[/C][C]0.258687112547577[/C][/ROW]
[ROW][C]9[/C][C]106.02[/C][C]104.698891502139[/C][C]1.32110849786135[/C][/ROW]
[ROW][C]10[/C][C]106.35[/C][C]106.128665039807[/C][C]0.221334960193019[/C][/ROW]
[ROW][C]11[/C][C]106.38[/C][C]106.473705456562[/C][C]-0.0937054565618354[/C][/ROW]
[ROW][C]12[/C][C]106.47[/C][C]106.497337871804[/C][C]-0.027337871804022[/C][/ROW]
[ROW][C]13[/C][C]106.5[/C][C]106.585480176188[/C][C]-0.0854801761884545[/C][/ROW]
[ROW][C]14[/C][C]106.56[/C][C]106.609671525476[/C][C]-0.0496715254762847[/C][/ROW]
[ROW][C]15[/C][C]113.07[/C][C]106.666296186834[/C][C]6.40370381316592[/C][/ROW]
[ROW][C]16[/C][C]116.26[/C][C]113.611448293129[/C][C]2.6485517068713[/C][/ROW]
[ROW][C]17[/C][C]118[/C][C]116.9814258323[/C][C]1.01857416770002[/C][/ROW]
[ROW][C]18[/C][C]118.02[/C][C]118.790641196943[/C][C]-0.770641196942648[/C][/ROW]
[ROW][C]19[/C][C]118.04[/C][C]118.758273668738[/C][C]-0.71827366873849[/C][/ROW]
[ROW][C]20[/C][C]118.12[/C][C]118.729464681164[/C][C]-0.609464681164013[/C][/ROW]
[ROW][C]21[/C][C]118.12[/C][C]118.76804961147[/C][C]-0.648049611470213[/C][/ROW]
[ROW][C]22[/C][C]118.17[/C][C]118.72401257265[/C][C]-0.554012572649825[/C][/ROW]
[ROW][C]23[/C][C]118.22[/C][C]118.73636565066[/C][C]-0.516365650659679[/C][/ROW]
[ROW][C]24[/C][C]118.22[/C][C]118.751276957138[/C][C]-0.531276957138147[/C][/ROW]
[ROW][C]25[/C][C]118.23[/C][C]118.715174992764[/C][C]-0.485174992764158[/C][/ROW]
[ROW][C]26[/C][C]118.23[/C][C]118.692205803966[/C][C]-0.462205803966157[/C][/ROW]
[ROW][C]27[/C][C]118.23[/C][C]118.660797444834[/C][C]-0.430797444834369[/C][/ROW]
[ROW][C]28[/C][C]119.94[/C][C]118.63152338392[/C][C]1.30847661608027[/C][/ROW]
[ROW][C]29[/C][C]120.88[/C][C]120.430438544917[/C][C]0.449561455083298[/C][/ROW]
[ROW][C]30[/C][C]121.14[/C][C]121.400987680198[/C][C]-0.260987680197772[/C][/ROW]
[ROW][C]31[/C][C]121.16[/C][C]121.643252734599[/C][C]-0.483252734599347[/C][/ROW]
[ROW][C]32[/C][C]121.2[/C][C]121.630414169377[/C][C]-0.430414169376945[/C][/ROW]
[ROW][C]33[/C][C]121.2[/C][C]121.641166153253[/C][C]-0.441166153252539[/C][/ROW]
[ROW][C]34[/C][C]121.2[/C][C]121.611187505518[/C][C]-0.411187505517603[/C][/ROW]
[ROW][C]35[/C][C]121.2[/C][C]121.583246002549[/C][C]-0.383246002548631[/C][/ROW]
[ROW][C]36[/C][C]121.2[/C][C]121.557203213859[/C][C]-0.357203213858881[/C][/ROW]
[ROW][C]37[/C][C]121.22[/C][C]121.532930115755[/C][C]-0.312930115754881[/C][/ROW]
[ROW][C]38[/C][C]121.22[/C][C]121.531665515928[/C][C]-0.311665515928482[/C][/ROW]
[ROW][C]39[/C][C]121.95[/C][C]121.510486849695[/C][C]0.439513150304776[/C][/ROW]
[ROW][C]40[/C][C]123.05[/C][C]122.270353170606[/C][C]0.779646829394352[/C][/ROW]
[ROW][C]41[/C][C]123.44[/C][C]123.423332660269[/C][C]0.0166673397309864[/C][/ROW]
[ROW][C]42[/C][C]123.65[/C][C]123.814465259184[/C][C]-0.164465259183928[/C][/ROW]
[ROW][C]43[/C][C]123.79[/C][C]124.013289320066[/C][C]-0.223289320065845[/C][/ROW]
[ROW][C]44[/C][C]123.87[/C][C]124.138116098322[/C][C]-0.268116098321897[/C][/ROW]
[ROW][C]45[/C][C]123.91[/C][C]124.199896753967[/C][C]-0.289896753967412[/C][/ROW]
[ROW][C]46[/C][C]123.94[/C][C]124.220197344567[/C][C]-0.280197344566616[/C][/ROW]
[ROW][C]47[/C][C]124.28[/C][C]124.231157040982[/C][C]0.0488429590176338[/C][/ROW]
[ROW][C]48[/C][C]126.28[/C][C]124.57447607589[/C][C]1.70552392410998[/C][/ROW]
[ROW][C]49[/C][C]126.68[/C][C]126.69037186832[/C][C]-0.0103718683197798[/C][/ROW]
[ROW][C]50[/C][C]126.69[/C][C]127.089667066774[/C][C]-0.399667066774114[/C][/ROW]
[ROW][C]51[/C][C]126.69[/C][C]127.072508414376[/C][C]-0.38250841437582[/C][/ROW]
[ROW][C]52[/C][C]126.99[/C][C]127.046515747156[/C][C]-0.056515747155828[/C][/ROW]
[ROW][C]53[/C][C]128.79[/C][C]127.342675321813[/C][C]1.44732467818726[/C][/ROW]
[ROW][C]54[/C][C]128.84[/C][C]129.24102565165[/C][C]-0.401025651650059[/C][/ROW]
[ROW][C]55[/C][C]128.95[/C][C]129.263774679075[/C][C]-0.313774679074669[/C][/ROW]
[ROW][C]56[/C][C]128.97[/C][C]129.352452688476[/C][C]-0.382452688475922[/C][/ROW]
[ROW][C]57[/C][C]128.97[/C][C]129.346463808009[/C][C]-0.376463808008623[/C][/ROW]
[ROW][C]58[/C][C]128.97[/C][C]129.320881891078[/C][C]-0.350881891077705[/C][/ROW]
[ROW][C]59[/C][C]128.97[/C][C]129.297038347026[/C][C]-0.327038347026047[/C][/ROW]
[ROW][C]60[/C][C]128.97[/C][C]129.27481504787[/C][C]-0.304815047869852[/C][/ROW]
[ROW][C]61[/C][C]128.97[/C][C]129.254101892799[/C][C]-0.284101892798873[/C][/ROW]
[ROW][C]62[/C][C]128.98[/C][C]129.234796262704[/C][C]-0.254796262704048[/C][/ROW]
[ROW][C]63[/C][C]128.99[/C][C]129.227482043679[/C][C]-0.237482043679137[/C][/ROW]
[ROW][C]64[/C][C]129.07[/C][C]129.221344381081[/C][C]-0.15134438108123[/C][/ROW]
[ROW][C]65[/C][C]129.76[/C][C]129.291060047495[/C][C]0.468939952505224[/C][/ROW]
[ROW][C]66[/C][C]130.47[/C][C]130.012926013506[/C][C]0.457073986493697[/C][/ROW]
[ROW][C]67[/C][C]130.76[/C][C]130.753985649267[/C][C]0.00601435073315315[/C][/ROW]
[ROW][C]68[/C][C]130.88[/C][C]131.044394343589[/C][C]-0.164394343589038[/C][/ROW]
[ROW][C]69[/C][C]131.04[/C][C]131.153223223412[/C][C]-0.113223223411893[/C][/ROW]
[ROW][C]70[/C][C]131.06[/C][C]131.305529344122[/C][C]-0.245529344121621[/C][/ROW]
[ROW][C]71[/C][C]131.13[/C][C]131.308844841782[/C][C]-0.178844841782222[/C][/ROW]
[ROW][C]72[/C][C]131.15[/C][C]131.366691764146[/C][C]-0.216691764145878[/C][/ROW]
[ROW][C]73[/C][C]131.16[/C][C]131.371966867377[/C][C]-0.211966867377413[/C][/ROW]
[ROW][C]74[/C][C]131.33[/C][C]131.36756304242[/C][C]-0.0375630424199755[/C][/ROW]
[ROW][C]75[/C][C]131.42[/C][C]131.535010513836[/C][C]-0.115010513835813[/C][/ROW]
[ROW][C]76[/C][C]131.86[/C][C]131.617195182459[/C][C]0.242804817541497[/C][/ROW]
[ROW][C]77[/C][C]134.39[/C][C]132.073694544524[/C][C]2.31630545547625[/C][/ROW]
[ROW][C]78[/C][C]135.59[/C][C]134.76109489082[/C][C]0.828905109179829[/C][/ROW]
[ROW][C]79[/C][C]136.01[/C][C]136.017421637763[/C][C]-0.00742163776254756[/C][/ROW]
[ROW][C]80[/C][C]136.14[/C][C]136.436917313796[/C][C]-0.296917313796484[/C][/ROW]
[ROW][C]81[/C][C]136.74[/C][C]136.546740834955[/C][C]0.193259165045106[/C][/ROW]
[ROW][C]82[/C][C]136.89[/C][C]137.159873411849[/C][C]-0.269873411848522[/C][/ROW]
[ROW][C]83[/C][C]136.82[/C][C]137.291534652433[/C][C]-0.471534652432837[/C][/ROW]
[ROW][C]84[/C][C]136.82[/C][C]137.189492368282[/C][C]-0.369492368282351[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232370&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232370&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
3104.4104.40
4104.4104.40
5104.4104.40
6104.41104.40.00999999999999091
7104.42104.4106795319070.0093204680931791
8104.68104.4213128874520.258687112547577
9106.02104.6988915021391.32110849786135
10106.35106.1286650398070.221334960193019
11106.38106.473705456562-0.0937054565618354
12106.47106.497337871804-0.027337871804022
13106.5106.585480176188-0.0854801761884545
14106.56106.609671525476-0.0496715254762847
15113.07106.6662961868346.40370381316592
16116.26113.6114482931292.6485517068713
17118116.98142583231.01857416770002
18118.02118.790641196943-0.770641196942648
19118.04118.758273668738-0.71827366873849
20118.12118.729464681164-0.609464681164013
21118.12118.76804961147-0.648049611470213
22118.17118.72401257265-0.554012572649825
23118.22118.73636565066-0.516365650659679
24118.22118.751276957138-0.531276957138147
25118.23118.715174992764-0.485174992764158
26118.23118.692205803966-0.462205803966157
27118.23118.660797444834-0.430797444834369
28119.94118.631523383921.30847661608027
29120.88120.4304385449170.449561455083298
30121.14121.400987680198-0.260987680197772
31121.16121.643252734599-0.483252734599347
32121.2121.630414169377-0.430414169376945
33121.2121.641166153253-0.441166153252539
34121.2121.611187505518-0.411187505517603
35121.2121.583246002549-0.383246002548631
36121.2121.557203213859-0.357203213858881
37121.22121.532930115755-0.312930115754881
38121.22121.531665515928-0.311665515928482
39121.95121.5104868496950.439513150304776
40123.05122.2703531706060.779646829394352
41123.44123.4233326602690.0166673397309864
42123.65123.814465259184-0.164465259183928
43123.79124.013289320066-0.223289320065845
44123.87124.138116098322-0.268116098321897
45123.91124.199896753967-0.289896753967412
46123.94124.220197344567-0.280197344566616
47124.28124.2311570409820.0488429590176338
48126.28124.574476075891.70552392410998
49126.68126.69037186832-0.0103718683197798
50126.69127.089667066774-0.399667066774114
51126.69127.072508414376-0.38250841437582
52126.99127.046515747156-0.056515747155828
53128.79127.3426753218131.44732467818726
54128.84129.24102565165-0.401025651650059
55128.95129.263774679075-0.313774679074669
56128.97129.352452688476-0.382452688475922
57128.97129.346463808009-0.376463808008623
58128.97129.320881891078-0.350881891077705
59128.97129.297038347026-0.327038347026047
60128.97129.27481504787-0.304815047869852
61128.97129.254101892799-0.284101892798873
62128.98129.234796262704-0.254796262704048
63128.99129.227482043679-0.237482043679137
64129.07129.221344381081-0.15134438108123
65129.76129.2910600474950.468939952505224
66130.47130.0129260135060.457073986493697
67130.76130.7539856492670.00601435073315315
68130.88131.044394343589-0.164394343589038
69131.04131.153223223412-0.113223223411893
70131.06131.305529344122-0.245529344121621
71131.13131.308844841782-0.178844841782222
72131.15131.366691764146-0.216691764145878
73131.16131.371966867377-0.211966867377413
74131.33131.36756304242-0.0375630424199755
75131.42131.535010513836-0.115010513835813
76131.86131.6171951824590.242804817541497
77134.39132.0736945445242.31630545547625
78135.59134.761094890820.828905109179829
79136.01136.017421637763-0.00742163776254756
80136.14136.436917313796-0.296917313796484
81136.74136.5467408349550.193259165045106
82136.89137.159873411849-0.269873411848522
83136.82137.291534652433-0.471534652432837
84136.82137.189492368282-0.369492368282351







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85137.164384182924135.315069902433139.013698463415
86137.508768365849134.803123599851140.214413131847
87137.853152548773134.427771523624141.278533573923
88138.197536731698134.112232299553142.282841163843
89138.541920914622133.827949202832143.255892626413
90138.886305097547133.560868923069144.211741272025
91139.230689280471133.302998326806145.158380234137
92139.575073463396133.049365657113146.100781269678
93139.91945764632132.796685592331147.04222970031
94140.263841829245132.542691499485147.984992159005
95140.608226012169132.285769120711148.930682903628
96140.952610195094132.024741193389149.880479196798

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 137.164384182924 & 135.315069902433 & 139.013698463415 \tabularnewline
86 & 137.508768365849 & 134.803123599851 & 140.214413131847 \tabularnewline
87 & 137.853152548773 & 134.427771523624 & 141.278533573923 \tabularnewline
88 & 138.197536731698 & 134.112232299553 & 142.282841163843 \tabularnewline
89 & 138.541920914622 & 133.827949202832 & 143.255892626413 \tabularnewline
90 & 138.886305097547 & 133.560868923069 & 144.211741272025 \tabularnewline
91 & 139.230689280471 & 133.302998326806 & 145.158380234137 \tabularnewline
92 & 139.575073463396 & 133.049365657113 & 146.100781269678 \tabularnewline
93 & 139.91945764632 & 132.796685592331 & 147.04222970031 \tabularnewline
94 & 140.263841829245 & 132.542691499485 & 147.984992159005 \tabularnewline
95 & 140.608226012169 & 132.285769120711 & 148.930682903628 \tabularnewline
96 & 140.952610195094 & 132.024741193389 & 149.880479196798 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232370&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]137.164384182924[/C][C]135.315069902433[/C][C]139.013698463415[/C][/ROW]
[ROW][C]86[/C][C]137.508768365849[/C][C]134.803123599851[/C][C]140.214413131847[/C][/ROW]
[ROW][C]87[/C][C]137.853152548773[/C][C]134.427771523624[/C][C]141.278533573923[/C][/ROW]
[ROW][C]88[/C][C]138.197536731698[/C][C]134.112232299553[/C][C]142.282841163843[/C][/ROW]
[ROW][C]89[/C][C]138.541920914622[/C][C]133.827949202832[/C][C]143.255892626413[/C][/ROW]
[ROW][C]90[/C][C]138.886305097547[/C][C]133.560868923069[/C][C]144.211741272025[/C][/ROW]
[ROW][C]91[/C][C]139.230689280471[/C][C]133.302998326806[/C][C]145.158380234137[/C][/ROW]
[ROW][C]92[/C][C]139.575073463396[/C][C]133.049365657113[/C][C]146.100781269678[/C][/ROW]
[ROW][C]93[/C][C]139.91945764632[/C][C]132.796685592331[/C][C]147.04222970031[/C][/ROW]
[ROW][C]94[/C][C]140.263841829245[/C][C]132.542691499485[/C][C]147.984992159005[/C][/ROW]
[ROW][C]95[/C][C]140.608226012169[/C][C]132.285769120711[/C][C]148.930682903628[/C][/ROW]
[ROW][C]96[/C][C]140.952610195094[/C][C]132.024741193389[/C][C]149.880479196798[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232370&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232370&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
85137.164384182924135.315069902433139.013698463415
86137.508768365849134.803123599851140.214413131847
87137.853152548773134.427771523624141.278533573923
88138.197536731698134.112232299553142.282841163843
89138.541920914622133.827949202832143.255892626413
90138.886305097547133.560868923069144.211741272025
91139.230689280471133.302998326806145.158380234137
92139.575073463396133.049365657113146.100781269678
93139.91945764632132.796685592331147.04222970031
94140.263841829245132.542691499485147.984992159005
95140.608226012169132.285769120711148.930682903628
96140.952610195094132.024741193389149.880479196798



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