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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 22 Dec 2010 12:32:43 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/22/t1293021211ynd2qrgc1y8unmq.htm/, Retrieved Mon, 06 May 2024 02:50:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114178, Retrieved Mon, 06 May 2024 02:50:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave10 oefening 2] [2010-12-22 12:32:43] [93d384e9a6425954483697e7ea0f3a20] [Current]
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Dataseries X:
105,23
105,22
105,13
105
105,01
105,01
105,01
105,01
105,57
106,05
106,09
106,2
106,19
106,2
106,09
106,23
106,23
106,22
106,22
106,61
106,95
107,74
107,8
107,8
107,2
107,56
107,72
108,14
108,16
108,16
108,16
108,1
108,95
110,49
110,72
110,82
110,82
110,75
110,71
110,86
110,84
110,84
110,84
110,92
111,46
112,46
113,04
113,15
113,15
113,21
113,37
113,47
113,71
113,71
113,71
113,8
115,46
117
117,94
118,08
118,08
118,47
118,49
118,45
118,54
118,55
118,55
118,55
119,04
121,37
122
122,14




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114178&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114178&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114178&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.938027433409238
beta0.0620541839691078
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.938027433409238 \tabularnewline
beta & 0.0620541839691078 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114178&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]0.938027433409238[/C][/ROW]
[ROW][C]beta[/C][C]0.0620541839691078[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114178&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114178&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
alpha0.938027433409238
beta0.0620541839691078
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13106.19105.6139823717950.576017628205136
14106.2106.1901380822280.00986191777190015
15106.09106.108714919066-0.0187149190664542
16106.23106.24564653112-0.0156465311200549
17106.23106.230795613716-0.00079561371580894
18106.22106.223578952746-0.00357895274564157
19106.22106.357293117842-0.137293117841750
20106.61106.2809214310300.329078568970289
21106.95107.221174359354-0.271174359353694
22107.74107.4921722472620.247827752737777
23107.8107.813600709393-0.0136007093935007
24107.8107.959843758246-0.159843758246112
25107.2107.875716503113-0.675716503112625
26107.56107.2013205855970.358679414403014
27107.72107.4243264252750.295673574724916
28108.14107.8536529179050.286347082095475
29108.16108.1378789400180.0221210599816288
30108.16108.168198498953-0.00819849895314917
31108.16108.305236137954-0.145236137954029
32108.1108.265796924267-0.165796924267383
33108.95108.6913188692480.258681130752166
34110.49109.5090167631380.980983236862315
35110.72110.5621568178560.157843182143907
36110.82110.930328407856-0.110328407855775
37110.82110.933732692014-0.113732692013883
38110.75110.956364166402-0.206364166401798
39110.71110.718315628215-0.00831562821501564
40110.86110.917095794235-0.0570957942349679
41110.84110.897978779773-0.0579787797726681
42110.84110.881811585024-0.0418115850237086
43110.84111.007398159038-0.167398159037560
44110.92110.973177644372-0.0531776443720844
45111.46111.564482447818-0.104482447818015
46112.46112.0989835304860.361016469514482
47113.04112.4961759684300.543824031570168
48113.15113.208866599562-0.0588665995624922
49113.15113.262405712819-0.112405712818855
50113.21113.282691774758-0.0726917747575726
51113.37113.1922365111280.177763488871747
52113.47113.583303680854-0.113303680854344
53113.71113.5288983467890.181101653211215
54113.71113.769404540243-0.059404540242511
55113.71113.901088918017-0.191088918017215
56113.8113.880728756492-0.0807287564916521
57115.46114.4704110574790.989588942521038
58117116.1511142519010.848885748098681
59117.94117.1367536337810.803246366219327
60118.08118.190022961225-0.110022961224772
61118.08118.323864025975-0.243864025974972
62118.47118.3472537421220.122746257877736
63118.49118.590976213751-0.100976213751323
64118.45118.821644832206-0.371644832205973
65118.54118.647220923428-0.107220923428486
66118.55118.689652470034-0.139652470033809
67118.55118.820514781338-0.270514781337923
68118.55118.810480533070-0.260480533069696
69119.04119.365408234687-0.325408234687316
70121.37119.7948713787461.57512862125446
71122121.4921747519620.507825248037676
72122.14122.227793936455-0.0877939364546307

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 106.19 & 105.613982371795 & 0.576017628205136 \tabularnewline
14 & 106.2 & 106.190138082228 & 0.00986191777190015 \tabularnewline
15 & 106.09 & 106.108714919066 & -0.0187149190664542 \tabularnewline
16 & 106.23 & 106.24564653112 & -0.0156465311200549 \tabularnewline
17 & 106.23 & 106.230795613716 & -0.00079561371580894 \tabularnewline
18 & 106.22 & 106.223578952746 & -0.00357895274564157 \tabularnewline
19 & 106.22 & 106.357293117842 & -0.137293117841750 \tabularnewline
20 & 106.61 & 106.280921431030 & 0.329078568970289 \tabularnewline
21 & 106.95 & 107.221174359354 & -0.271174359353694 \tabularnewline
22 & 107.74 & 107.492172247262 & 0.247827752737777 \tabularnewline
23 & 107.8 & 107.813600709393 & -0.0136007093935007 \tabularnewline
24 & 107.8 & 107.959843758246 & -0.159843758246112 \tabularnewline
25 & 107.2 & 107.875716503113 & -0.675716503112625 \tabularnewline
26 & 107.56 & 107.201320585597 & 0.358679414403014 \tabularnewline
27 & 107.72 & 107.424326425275 & 0.295673574724916 \tabularnewline
28 & 108.14 & 107.853652917905 & 0.286347082095475 \tabularnewline
29 & 108.16 & 108.137878940018 & 0.0221210599816288 \tabularnewline
30 & 108.16 & 108.168198498953 & -0.00819849895314917 \tabularnewline
31 & 108.16 & 108.305236137954 & -0.145236137954029 \tabularnewline
32 & 108.1 & 108.265796924267 & -0.165796924267383 \tabularnewline
33 & 108.95 & 108.691318869248 & 0.258681130752166 \tabularnewline
34 & 110.49 & 109.509016763138 & 0.980983236862315 \tabularnewline
35 & 110.72 & 110.562156817856 & 0.157843182143907 \tabularnewline
36 & 110.82 & 110.930328407856 & -0.110328407855775 \tabularnewline
37 & 110.82 & 110.933732692014 & -0.113732692013883 \tabularnewline
38 & 110.75 & 110.956364166402 & -0.206364166401798 \tabularnewline
39 & 110.71 & 110.718315628215 & -0.00831562821501564 \tabularnewline
40 & 110.86 & 110.917095794235 & -0.0570957942349679 \tabularnewline
41 & 110.84 & 110.897978779773 & -0.0579787797726681 \tabularnewline
42 & 110.84 & 110.881811585024 & -0.0418115850237086 \tabularnewline
43 & 110.84 & 111.007398159038 & -0.167398159037560 \tabularnewline
44 & 110.92 & 110.973177644372 & -0.0531776443720844 \tabularnewline
45 & 111.46 & 111.564482447818 & -0.104482447818015 \tabularnewline
46 & 112.46 & 112.098983530486 & 0.361016469514482 \tabularnewline
47 & 113.04 & 112.496175968430 & 0.543824031570168 \tabularnewline
48 & 113.15 & 113.208866599562 & -0.0588665995624922 \tabularnewline
49 & 113.15 & 113.262405712819 & -0.112405712818855 \tabularnewline
50 & 113.21 & 113.282691774758 & -0.0726917747575726 \tabularnewline
51 & 113.37 & 113.192236511128 & 0.177763488871747 \tabularnewline
52 & 113.47 & 113.583303680854 & -0.113303680854344 \tabularnewline
53 & 113.71 & 113.528898346789 & 0.181101653211215 \tabularnewline
54 & 113.71 & 113.769404540243 & -0.059404540242511 \tabularnewline
55 & 113.71 & 113.901088918017 & -0.191088918017215 \tabularnewline
56 & 113.8 & 113.880728756492 & -0.0807287564916521 \tabularnewline
57 & 115.46 & 114.470411057479 & 0.989588942521038 \tabularnewline
58 & 117 & 116.151114251901 & 0.848885748098681 \tabularnewline
59 & 117.94 & 117.136753633781 & 0.803246366219327 \tabularnewline
60 & 118.08 & 118.190022961225 & -0.110022961224772 \tabularnewline
61 & 118.08 & 118.323864025975 & -0.243864025974972 \tabularnewline
62 & 118.47 & 118.347253742122 & 0.122746257877736 \tabularnewline
63 & 118.49 & 118.590976213751 & -0.100976213751323 \tabularnewline
64 & 118.45 & 118.821644832206 & -0.371644832205973 \tabularnewline
65 & 118.54 & 118.647220923428 & -0.107220923428486 \tabularnewline
66 & 118.55 & 118.689652470034 & -0.139652470033809 \tabularnewline
67 & 118.55 & 118.820514781338 & -0.270514781337923 \tabularnewline
68 & 118.55 & 118.810480533070 & -0.260480533069696 \tabularnewline
69 & 119.04 & 119.365408234687 & -0.325408234687316 \tabularnewline
70 & 121.37 & 119.794871378746 & 1.57512862125446 \tabularnewline
71 & 122 & 121.492174751962 & 0.507825248037676 \tabularnewline
72 & 122.14 & 122.227793936455 & -0.0877939364546307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114178&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]106.19[/C][C]105.613982371795[/C][C]0.576017628205136[/C][/ROW]
[ROW][C]14[/C][C]106.2[/C][C]106.190138082228[/C][C]0.00986191777190015[/C][/ROW]
[ROW][C]15[/C][C]106.09[/C][C]106.108714919066[/C][C]-0.0187149190664542[/C][/ROW]
[ROW][C]16[/C][C]106.23[/C][C]106.24564653112[/C][C]-0.0156465311200549[/C][/ROW]
[ROW][C]17[/C][C]106.23[/C][C]106.230795613716[/C][C]-0.00079561371580894[/C][/ROW]
[ROW][C]18[/C][C]106.22[/C][C]106.223578952746[/C][C]-0.00357895274564157[/C][/ROW]
[ROW][C]19[/C][C]106.22[/C][C]106.357293117842[/C][C]-0.137293117841750[/C][/ROW]
[ROW][C]20[/C][C]106.61[/C][C]106.280921431030[/C][C]0.329078568970289[/C][/ROW]
[ROW][C]21[/C][C]106.95[/C][C]107.221174359354[/C][C]-0.271174359353694[/C][/ROW]
[ROW][C]22[/C][C]107.74[/C][C]107.492172247262[/C][C]0.247827752737777[/C][/ROW]
[ROW][C]23[/C][C]107.8[/C][C]107.813600709393[/C][C]-0.0136007093935007[/C][/ROW]
[ROW][C]24[/C][C]107.8[/C][C]107.959843758246[/C][C]-0.159843758246112[/C][/ROW]
[ROW][C]25[/C][C]107.2[/C][C]107.875716503113[/C][C]-0.675716503112625[/C][/ROW]
[ROW][C]26[/C][C]107.56[/C][C]107.201320585597[/C][C]0.358679414403014[/C][/ROW]
[ROW][C]27[/C][C]107.72[/C][C]107.424326425275[/C][C]0.295673574724916[/C][/ROW]
[ROW][C]28[/C][C]108.14[/C][C]107.853652917905[/C][C]0.286347082095475[/C][/ROW]
[ROW][C]29[/C][C]108.16[/C][C]108.137878940018[/C][C]0.0221210599816288[/C][/ROW]
[ROW][C]30[/C][C]108.16[/C][C]108.168198498953[/C][C]-0.00819849895314917[/C][/ROW]
[ROW][C]31[/C][C]108.16[/C][C]108.305236137954[/C][C]-0.145236137954029[/C][/ROW]
[ROW][C]32[/C][C]108.1[/C][C]108.265796924267[/C][C]-0.165796924267383[/C][/ROW]
[ROW][C]33[/C][C]108.95[/C][C]108.691318869248[/C][C]0.258681130752166[/C][/ROW]
[ROW][C]34[/C][C]110.49[/C][C]109.509016763138[/C][C]0.980983236862315[/C][/ROW]
[ROW][C]35[/C][C]110.72[/C][C]110.562156817856[/C][C]0.157843182143907[/C][/ROW]
[ROW][C]36[/C][C]110.82[/C][C]110.930328407856[/C][C]-0.110328407855775[/C][/ROW]
[ROW][C]37[/C][C]110.82[/C][C]110.933732692014[/C][C]-0.113732692013883[/C][/ROW]
[ROW][C]38[/C][C]110.75[/C][C]110.956364166402[/C][C]-0.206364166401798[/C][/ROW]
[ROW][C]39[/C][C]110.71[/C][C]110.718315628215[/C][C]-0.00831562821501564[/C][/ROW]
[ROW][C]40[/C][C]110.86[/C][C]110.917095794235[/C][C]-0.0570957942349679[/C][/ROW]
[ROW][C]41[/C][C]110.84[/C][C]110.897978779773[/C][C]-0.0579787797726681[/C][/ROW]
[ROW][C]42[/C][C]110.84[/C][C]110.881811585024[/C][C]-0.0418115850237086[/C][/ROW]
[ROW][C]43[/C][C]110.84[/C][C]111.007398159038[/C][C]-0.167398159037560[/C][/ROW]
[ROW][C]44[/C][C]110.92[/C][C]110.973177644372[/C][C]-0.0531776443720844[/C][/ROW]
[ROW][C]45[/C][C]111.46[/C][C]111.564482447818[/C][C]-0.104482447818015[/C][/ROW]
[ROW][C]46[/C][C]112.46[/C][C]112.098983530486[/C][C]0.361016469514482[/C][/ROW]
[ROW][C]47[/C][C]113.04[/C][C]112.496175968430[/C][C]0.543824031570168[/C][/ROW]
[ROW][C]48[/C][C]113.15[/C][C]113.208866599562[/C][C]-0.0588665995624922[/C][/ROW]
[ROW][C]49[/C][C]113.15[/C][C]113.262405712819[/C][C]-0.112405712818855[/C][/ROW]
[ROW][C]50[/C][C]113.21[/C][C]113.282691774758[/C][C]-0.0726917747575726[/C][/ROW]
[ROW][C]51[/C][C]113.37[/C][C]113.192236511128[/C][C]0.177763488871747[/C][/ROW]
[ROW][C]52[/C][C]113.47[/C][C]113.583303680854[/C][C]-0.113303680854344[/C][/ROW]
[ROW][C]53[/C][C]113.71[/C][C]113.528898346789[/C][C]0.181101653211215[/C][/ROW]
[ROW][C]54[/C][C]113.71[/C][C]113.769404540243[/C][C]-0.059404540242511[/C][/ROW]
[ROW][C]55[/C][C]113.71[/C][C]113.901088918017[/C][C]-0.191088918017215[/C][/ROW]
[ROW][C]56[/C][C]113.8[/C][C]113.880728756492[/C][C]-0.0807287564916521[/C][/ROW]
[ROW][C]57[/C][C]115.46[/C][C]114.470411057479[/C][C]0.989588942521038[/C][/ROW]
[ROW][C]58[/C][C]117[/C][C]116.151114251901[/C][C]0.848885748098681[/C][/ROW]
[ROW][C]59[/C][C]117.94[/C][C]117.136753633781[/C][C]0.803246366219327[/C][/ROW]
[ROW][C]60[/C][C]118.08[/C][C]118.190022961225[/C][C]-0.110022961224772[/C][/ROW]
[ROW][C]61[/C][C]118.08[/C][C]118.323864025975[/C][C]-0.243864025974972[/C][/ROW]
[ROW][C]62[/C][C]118.47[/C][C]118.347253742122[/C][C]0.122746257877736[/C][/ROW]
[ROW][C]63[/C][C]118.49[/C][C]118.590976213751[/C][C]-0.100976213751323[/C][/ROW]
[ROW][C]64[/C][C]118.45[/C][C]118.821644832206[/C][C]-0.371644832205973[/C][/ROW]
[ROW][C]65[/C][C]118.54[/C][C]118.647220923428[/C][C]-0.107220923428486[/C][/ROW]
[ROW][C]66[/C][C]118.55[/C][C]118.689652470034[/C][C]-0.139652470033809[/C][/ROW]
[ROW][C]67[/C][C]118.55[/C][C]118.820514781338[/C][C]-0.270514781337923[/C][/ROW]
[ROW][C]68[/C][C]118.55[/C][C]118.810480533070[/C][C]-0.260480533069696[/C][/ROW]
[ROW][C]69[/C][C]119.04[/C][C]119.365408234687[/C][C]-0.325408234687316[/C][/ROW]
[ROW][C]70[/C][C]121.37[/C][C]119.794871378746[/C][C]1.57512862125446[/C][/ROW]
[ROW][C]71[/C][C]122[/C][C]121.492174751962[/C][C]0.507825248037676[/C][/ROW]
[ROW][C]72[/C][C]122.14[/C][C]122.227793936455[/C][C]-0.0877939364546307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114178&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114178&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
13106.19105.6139823717950.576017628205136
14106.2106.1901380822280.00986191777190015
15106.09106.108714919066-0.0187149190664542
16106.23106.24564653112-0.0156465311200549
17106.23106.230795613716-0.00079561371580894
18106.22106.223578952746-0.00357895274564157
19106.22106.357293117842-0.137293117841750
20106.61106.2809214310300.329078568970289
21106.95107.221174359354-0.271174359353694
22107.74107.4921722472620.247827752737777
23107.8107.813600709393-0.0136007093935007
24107.8107.959843758246-0.159843758246112
25107.2107.875716503113-0.675716503112625
26107.56107.2013205855970.358679414403014
27107.72107.4243264252750.295673574724916
28108.14107.8536529179050.286347082095475
29108.16108.1378789400180.0221210599816288
30108.16108.168198498953-0.00819849895314917
31108.16108.305236137954-0.145236137954029
32108.1108.265796924267-0.165796924267383
33108.95108.6913188692480.258681130752166
34110.49109.5090167631380.980983236862315
35110.72110.5621568178560.157843182143907
36110.82110.930328407856-0.110328407855775
37110.82110.933732692014-0.113732692013883
38110.75110.956364166402-0.206364166401798
39110.71110.718315628215-0.00831562821501564
40110.86110.917095794235-0.0570957942349679
41110.84110.897978779773-0.0579787797726681
42110.84110.881811585024-0.0418115850237086
43110.84111.007398159038-0.167398159037560
44110.92110.973177644372-0.0531776443720844
45111.46111.564482447818-0.104482447818015
46112.46112.0989835304860.361016469514482
47113.04112.4961759684300.543824031570168
48113.15113.208866599562-0.0588665995624922
49113.15113.262405712819-0.112405712818855
50113.21113.282691774758-0.0726917747575726
51113.37113.1922365111280.177763488871747
52113.47113.583303680854-0.113303680854344
53113.71113.5288983467890.181101653211215
54113.71113.769404540243-0.059404540242511
55113.71113.901088918017-0.191088918017215
56113.8113.880728756492-0.0807287564916521
57115.46114.4704110574790.989588942521038
58117116.1511142519010.848885748098681
59117.94117.1367536337810.803246366219327
60118.08118.190022961225-0.110022961224772
61118.08118.323864025975-0.243864025974972
62118.47118.3472537421220.122746257877736
63118.49118.590976213751-0.100976213751323
64118.45118.821644832206-0.371644832205973
65118.54118.647220923428-0.107220923428486
66118.55118.689652470034-0.139652470033809
67118.55118.820514781338-0.270514781337923
68118.55118.810480533070-0.260480533069696
69119.04119.365408234687-0.325408234687316
70121.37119.7948713787461.57512862125446
71122121.4921747519620.507825248037676
72122.14122.227793936455-0.0877939364546307







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73122.391546495267121.649783695245123.13330929529
74122.697956637059121.650918023435123.744995250682
75122.837079715853121.530157807041124.144001624664
76123.175975060776121.630269527286124.721680594266
77123.418466423437121.645474457061125.191458389814
78123.617620638530121.623966175420125.611275101641
79123.937656256187121.727134393499126.148178118876
80124.264025740627121.838644251646126.689407229608
81125.156461378494122.517031137683127.795891619305
82126.125082841271123.27157880495128.978586877592
83126.303178231142123.234972936919129.371383525365
84126.520420996310123.236442339935129.804399652685

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 122.391546495267 & 121.649783695245 & 123.13330929529 \tabularnewline
74 & 122.697956637059 & 121.650918023435 & 123.744995250682 \tabularnewline
75 & 122.837079715853 & 121.530157807041 & 124.144001624664 \tabularnewline
76 & 123.175975060776 & 121.630269527286 & 124.721680594266 \tabularnewline
77 & 123.418466423437 & 121.645474457061 & 125.191458389814 \tabularnewline
78 & 123.617620638530 & 121.623966175420 & 125.611275101641 \tabularnewline
79 & 123.937656256187 & 121.727134393499 & 126.148178118876 \tabularnewline
80 & 124.264025740627 & 121.838644251646 & 126.689407229608 \tabularnewline
81 & 125.156461378494 & 122.517031137683 & 127.795891619305 \tabularnewline
82 & 126.125082841271 & 123.27157880495 & 128.978586877592 \tabularnewline
83 & 126.303178231142 & 123.234972936919 & 129.371383525365 \tabularnewline
84 & 126.520420996310 & 123.236442339935 & 129.804399652685 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114178&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]73[/C][C]122.391546495267[/C][C]121.649783695245[/C][C]123.13330929529[/C][/ROW]
[ROW][C]74[/C][C]122.697956637059[/C][C]121.650918023435[/C][C]123.744995250682[/C][/ROW]
[ROW][C]75[/C][C]122.837079715853[/C][C]121.530157807041[/C][C]124.144001624664[/C][/ROW]
[ROW][C]76[/C][C]123.175975060776[/C][C]121.630269527286[/C][C]124.721680594266[/C][/ROW]
[ROW][C]77[/C][C]123.418466423437[/C][C]121.645474457061[/C][C]125.191458389814[/C][/ROW]
[ROW][C]78[/C][C]123.617620638530[/C][C]121.623966175420[/C][C]125.611275101641[/C][/ROW]
[ROW][C]79[/C][C]123.937656256187[/C][C]121.727134393499[/C][C]126.148178118876[/C][/ROW]
[ROW][C]80[/C][C]124.264025740627[/C][C]121.838644251646[/C][C]126.689407229608[/C][/ROW]
[ROW][C]81[/C][C]125.156461378494[/C][C]122.517031137683[/C][C]127.795891619305[/C][/ROW]
[ROW][C]82[/C][C]126.125082841271[/C][C]123.27157880495[/C][C]128.978586877592[/C][/ROW]
[ROW][C]83[/C][C]126.303178231142[/C][C]123.234972936919[/C][C]129.371383525365[/C][/ROW]
[ROW][C]84[/C][C]126.520420996310[/C][C]123.236442339935[/C][C]129.804399652685[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114178&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114178&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
73122.391546495267121.649783695245123.13330929529
74122.697956637059121.650918023435123.744995250682
75122.837079715853121.530157807041124.144001624664
76123.175975060776121.630269527286124.721680594266
77123.418466423437121.645474457061125.191458389814
78123.617620638530121.623966175420125.611275101641
79123.937656256187121.727134393499126.148178118876
80124.264025740627121.838644251646126.689407229608
81125.156461378494122.517031137683127.795891619305
82126.125082841271123.27157880495128.978586877592
83126.303178231142123.234972936919129.371383525365
84126.520420996310123.236442339935129.804399652685



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=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')