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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 16 Jan 2011 10:37:02 +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/2011/Jan/16/t1295174234z3h1pfdfozbw94o.htm/, Retrieved Thu, 16 May 2024 14:06:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117373, Retrieved Thu, 16 May 2024 14:06:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact151
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Oef 10 eigen reeks] [2011-01-16 10:37:02] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
95.05
96.84
96.92
97.44
97.78
97.69
96.67
98.29
98.2
98.71
98.54
98.2
96.92
99.06
99.65
99.82
99.99
100.33
99.31
101.1
101.1
100.93
100.85
100.93
99.6
101.88
101.81
102.38
102.74
102.82
101.72
103.47
102.98
102.68
102.9
103.03
101.29
103.69
103.68
104.2
104.08
104.16
103.05
104.66
104.46
104.95
105.85
106.23
104.86
107.44
108.23
108.45
109.39
110.15
109.13
110.28
110.17
109.99
109.26
109.11
107.06
109.53
108.92
109.24
109.12
109
107.23
109.49
109.04
109.02
109.23
109.46




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117373&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117373&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117373&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 time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.839609756658078
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.839609756658078 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117373&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]0.839609756658078[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117373&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117373&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
alpha0.839609756658078
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1396.9295.7278870472961.19211295270411
1499.0698.84871990906040.211280090939638
1599.6599.58875724252020.0612427574798033
1699.8299.80762398304160.0123760169583988
1799.99100.010119190138-0.0201191901382174
18100.33100.334018833715-0.00401883371455369
1999.3199.13754901367020.172450986329821
20101.1100.9820686919460.117931308054267
21101.1100.9872038414970.112796158503414
22100.93101.598450835749-0.668450835748814
23100.85100.878253803231-0.0282538032312516
24100.93100.5104843951410.419515604859185
2599.699.7298619234008-0.12986192340081
26101.88101.6321872019470.247812798052678
27101.81102.388005016662-0.578005016662289
28102.38102.0611421910470.318857808952927
29102.74102.5151329821090.224867017891199
30102.82103.05088109085-0.230881090849579
31101.72101.6576007121410.062399287859165
32103.47103.4367002528810.0332997471185479
33102.98103.362779918081-0.382779918080601
34102.68103.435473316207-0.755473316207357
35102.9102.7399345598050.160065440195226
36103.03102.5921764677460.437823532253759
37101.29101.710067548379-0.420067548379052
38103.69103.4620611362650.227938863735389
39103.68104.071839373849-0.391839373848569
40104.2104.0467163582120.153283641787837
41104.08104.345839755097-0.265839755096749
42104.16104.397254524234-0.237254524233691
43103.05103.0274129884850.0225870115147302
44104.66104.788107920917-0.128107920917117
45104.46104.50729605908-0.0472960590800113
46104.95104.8029053033820.147094696618282
47105.85105.0092339308050.84076606919524
48106.23105.4650388313610.764961168639005
49104.86104.6721406611740.187859338825831
50107.44107.1082299173620.331770082637519
51108.23107.7094131020090.52058689799091
52108.45108.545512138583-0.095512138582734
53109.39108.5639954964480.826004503551815
54110.15109.5400062555990.609993744400697
55109.13108.8475199699750.28248003002453
56110.28110.890403901729-0.610403901729413
57110.17110.197317126773-0.0273171267728145
58109.99110.549331001305-0.559331001305367
59109.26110.272003742513-1.01200374251302
60109.11109.143324199726-0.0333241997262803
61107.06107.540451122751-0.480451122750992
62109.53109.4837520073060.0462479926938073
63108.92109.877890495608-0.957890495608495
64109.24109.374508207608-0.134508207607581
65109.12109.507465484342-0.387465484342073
66109109.429465967802-0.429465967801519
67107.23107.826001432288-0.596001432287935
68109.49108.9636588188140.526341181185899
69109.04109.320879329347-0.280879329347314
70109.02109.3735197325-0.353519732499947
71109.23109.1958985217690.0341014782313351
72109.46109.1026163466680.357383653332107

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 96.92 & 95.727887047296 & 1.19211295270411 \tabularnewline
14 & 99.06 & 98.8487199090604 & 0.211280090939638 \tabularnewline
15 & 99.65 & 99.5887572425202 & 0.0612427574798033 \tabularnewline
16 & 99.82 & 99.8076239830416 & 0.0123760169583988 \tabularnewline
17 & 99.99 & 100.010119190138 & -0.0201191901382174 \tabularnewline
18 & 100.33 & 100.334018833715 & -0.00401883371455369 \tabularnewline
19 & 99.31 & 99.1375490136702 & 0.172450986329821 \tabularnewline
20 & 101.1 & 100.982068691946 & 0.117931308054267 \tabularnewline
21 & 101.1 & 100.987203841497 & 0.112796158503414 \tabularnewline
22 & 100.93 & 101.598450835749 & -0.668450835748814 \tabularnewline
23 & 100.85 & 100.878253803231 & -0.0282538032312516 \tabularnewline
24 & 100.93 & 100.510484395141 & 0.419515604859185 \tabularnewline
25 & 99.6 & 99.7298619234008 & -0.12986192340081 \tabularnewline
26 & 101.88 & 101.632187201947 & 0.247812798052678 \tabularnewline
27 & 101.81 & 102.388005016662 & -0.578005016662289 \tabularnewline
28 & 102.38 & 102.061142191047 & 0.318857808952927 \tabularnewline
29 & 102.74 & 102.515132982109 & 0.224867017891199 \tabularnewline
30 & 102.82 & 103.05088109085 & -0.230881090849579 \tabularnewline
31 & 101.72 & 101.657600712141 & 0.062399287859165 \tabularnewline
32 & 103.47 & 103.436700252881 & 0.0332997471185479 \tabularnewline
33 & 102.98 & 103.362779918081 & -0.382779918080601 \tabularnewline
34 & 102.68 & 103.435473316207 & -0.755473316207357 \tabularnewline
35 & 102.9 & 102.739934559805 & 0.160065440195226 \tabularnewline
36 & 103.03 & 102.592176467746 & 0.437823532253759 \tabularnewline
37 & 101.29 & 101.710067548379 & -0.420067548379052 \tabularnewline
38 & 103.69 & 103.462061136265 & 0.227938863735389 \tabularnewline
39 & 103.68 & 104.071839373849 & -0.391839373848569 \tabularnewline
40 & 104.2 & 104.046716358212 & 0.153283641787837 \tabularnewline
41 & 104.08 & 104.345839755097 & -0.265839755096749 \tabularnewline
42 & 104.16 & 104.397254524234 & -0.237254524233691 \tabularnewline
43 & 103.05 & 103.027412988485 & 0.0225870115147302 \tabularnewline
44 & 104.66 & 104.788107920917 & -0.128107920917117 \tabularnewline
45 & 104.46 & 104.50729605908 & -0.0472960590800113 \tabularnewline
46 & 104.95 & 104.802905303382 & 0.147094696618282 \tabularnewline
47 & 105.85 & 105.009233930805 & 0.84076606919524 \tabularnewline
48 & 106.23 & 105.465038831361 & 0.764961168639005 \tabularnewline
49 & 104.86 & 104.672140661174 & 0.187859338825831 \tabularnewline
50 & 107.44 & 107.108229917362 & 0.331770082637519 \tabularnewline
51 & 108.23 & 107.709413102009 & 0.52058689799091 \tabularnewline
52 & 108.45 & 108.545512138583 & -0.095512138582734 \tabularnewline
53 & 109.39 & 108.563995496448 & 0.826004503551815 \tabularnewline
54 & 110.15 & 109.540006255599 & 0.609993744400697 \tabularnewline
55 & 109.13 & 108.847519969975 & 0.28248003002453 \tabularnewline
56 & 110.28 & 110.890403901729 & -0.610403901729413 \tabularnewline
57 & 110.17 & 110.197317126773 & -0.0273171267728145 \tabularnewline
58 & 109.99 & 110.549331001305 & -0.559331001305367 \tabularnewline
59 & 109.26 & 110.272003742513 & -1.01200374251302 \tabularnewline
60 & 109.11 & 109.143324199726 & -0.0333241997262803 \tabularnewline
61 & 107.06 & 107.540451122751 & -0.480451122750992 \tabularnewline
62 & 109.53 & 109.483752007306 & 0.0462479926938073 \tabularnewline
63 & 108.92 & 109.877890495608 & -0.957890495608495 \tabularnewline
64 & 109.24 & 109.374508207608 & -0.134508207607581 \tabularnewline
65 & 109.12 & 109.507465484342 & -0.387465484342073 \tabularnewline
66 & 109 & 109.429465967802 & -0.429465967801519 \tabularnewline
67 & 107.23 & 107.826001432288 & -0.596001432287935 \tabularnewline
68 & 109.49 & 108.963658818814 & 0.526341181185899 \tabularnewline
69 & 109.04 & 109.320879329347 & -0.280879329347314 \tabularnewline
70 & 109.02 & 109.3735197325 & -0.353519732499947 \tabularnewline
71 & 109.23 & 109.195898521769 & 0.0341014782313351 \tabularnewline
72 & 109.46 & 109.102616346668 & 0.357383653332107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117373&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]96.92[/C][C]95.727887047296[/C][C]1.19211295270411[/C][/ROW]
[ROW][C]14[/C][C]99.06[/C][C]98.8487199090604[/C][C]0.211280090939638[/C][/ROW]
[ROW][C]15[/C][C]99.65[/C][C]99.5887572425202[/C][C]0.0612427574798033[/C][/ROW]
[ROW][C]16[/C][C]99.82[/C][C]99.8076239830416[/C][C]0.0123760169583988[/C][/ROW]
[ROW][C]17[/C][C]99.99[/C][C]100.010119190138[/C][C]-0.0201191901382174[/C][/ROW]
[ROW][C]18[/C][C]100.33[/C][C]100.334018833715[/C][C]-0.00401883371455369[/C][/ROW]
[ROW][C]19[/C][C]99.31[/C][C]99.1375490136702[/C][C]0.172450986329821[/C][/ROW]
[ROW][C]20[/C][C]101.1[/C][C]100.982068691946[/C][C]0.117931308054267[/C][/ROW]
[ROW][C]21[/C][C]101.1[/C][C]100.987203841497[/C][C]0.112796158503414[/C][/ROW]
[ROW][C]22[/C][C]100.93[/C][C]101.598450835749[/C][C]-0.668450835748814[/C][/ROW]
[ROW][C]23[/C][C]100.85[/C][C]100.878253803231[/C][C]-0.0282538032312516[/C][/ROW]
[ROW][C]24[/C][C]100.93[/C][C]100.510484395141[/C][C]0.419515604859185[/C][/ROW]
[ROW][C]25[/C][C]99.6[/C][C]99.7298619234008[/C][C]-0.12986192340081[/C][/ROW]
[ROW][C]26[/C][C]101.88[/C][C]101.632187201947[/C][C]0.247812798052678[/C][/ROW]
[ROW][C]27[/C][C]101.81[/C][C]102.388005016662[/C][C]-0.578005016662289[/C][/ROW]
[ROW][C]28[/C][C]102.38[/C][C]102.061142191047[/C][C]0.318857808952927[/C][/ROW]
[ROW][C]29[/C][C]102.74[/C][C]102.515132982109[/C][C]0.224867017891199[/C][/ROW]
[ROW][C]30[/C][C]102.82[/C][C]103.05088109085[/C][C]-0.230881090849579[/C][/ROW]
[ROW][C]31[/C][C]101.72[/C][C]101.657600712141[/C][C]0.062399287859165[/C][/ROW]
[ROW][C]32[/C][C]103.47[/C][C]103.436700252881[/C][C]0.0332997471185479[/C][/ROW]
[ROW][C]33[/C][C]102.98[/C][C]103.362779918081[/C][C]-0.382779918080601[/C][/ROW]
[ROW][C]34[/C][C]102.68[/C][C]103.435473316207[/C][C]-0.755473316207357[/C][/ROW]
[ROW][C]35[/C][C]102.9[/C][C]102.739934559805[/C][C]0.160065440195226[/C][/ROW]
[ROW][C]36[/C][C]103.03[/C][C]102.592176467746[/C][C]0.437823532253759[/C][/ROW]
[ROW][C]37[/C][C]101.29[/C][C]101.710067548379[/C][C]-0.420067548379052[/C][/ROW]
[ROW][C]38[/C][C]103.69[/C][C]103.462061136265[/C][C]0.227938863735389[/C][/ROW]
[ROW][C]39[/C][C]103.68[/C][C]104.071839373849[/C][C]-0.391839373848569[/C][/ROW]
[ROW][C]40[/C][C]104.2[/C][C]104.046716358212[/C][C]0.153283641787837[/C][/ROW]
[ROW][C]41[/C][C]104.08[/C][C]104.345839755097[/C][C]-0.265839755096749[/C][/ROW]
[ROW][C]42[/C][C]104.16[/C][C]104.397254524234[/C][C]-0.237254524233691[/C][/ROW]
[ROW][C]43[/C][C]103.05[/C][C]103.027412988485[/C][C]0.0225870115147302[/C][/ROW]
[ROW][C]44[/C][C]104.66[/C][C]104.788107920917[/C][C]-0.128107920917117[/C][/ROW]
[ROW][C]45[/C][C]104.46[/C][C]104.50729605908[/C][C]-0.0472960590800113[/C][/ROW]
[ROW][C]46[/C][C]104.95[/C][C]104.802905303382[/C][C]0.147094696618282[/C][/ROW]
[ROW][C]47[/C][C]105.85[/C][C]105.009233930805[/C][C]0.84076606919524[/C][/ROW]
[ROW][C]48[/C][C]106.23[/C][C]105.465038831361[/C][C]0.764961168639005[/C][/ROW]
[ROW][C]49[/C][C]104.86[/C][C]104.672140661174[/C][C]0.187859338825831[/C][/ROW]
[ROW][C]50[/C][C]107.44[/C][C]107.108229917362[/C][C]0.331770082637519[/C][/ROW]
[ROW][C]51[/C][C]108.23[/C][C]107.709413102009[/C][C]0.52058689799091[/C][/ROW]
[ROW][C]52[/C][C]108.45[/C][C]108.545512138583[/C][C]-0.095512138582734[/C][/ROW]
[ROW][C]53[/C][C]109.39[/C][C]108.563995496448[/C][C]0.826004503551815[/C][/ROW]
[ROW][C]54[/C][C]110.15[/C][C]109.540006255599[/C][C]0.609993744400697[/C][/ROW]
[ROW][C]55[/C][C]109.13[/C][C]108.847519969975[/C][C]0.28248003002453[/C][/ROW]
[ROW][C]56[/C][C]110.28[/C][C]110.890403901729[/C][C]-0.610403901729413[/C][/ROW]
[ROW][C]57[/C][C]110.17[/C][C]110.197317126773[/C][C]-0.0273171267728145[/C][/ROW]
[ROW][C]58[/C][C]109.99[/C][C]110.549331001305[/C][C]-0.559331001305367[/C][/ROW]
[ROW][C]59[/C][C]109.26[/C][C]110.272003742513[/C][C]-1.01200374251302[/C][/ROW]
[ROW][C]60[/C][C]109.11[/C][C]109.143324199726[/C][C]-0.0333241997262803[/C][/ROW]
[ROW][C]61[/C][C]107.06[/C][C]107.540451122751[/C][C]-0.480451122750992[/C][/ROW]
[ROW][C]62[/C][C]109.53[/C][C]109.483752007306[/C][C]0.0462479926938073[/C][/ROW]
[ROW][C]63[/C][C]108.92[/C][C]109.877890495608[/C][C]-0.957890495608495[/C][/ROW]
[ROW][C]64[/C][C]109.24[/C][C]109.374508207608[/C][C]-0.134508207607581[/C][/ROW]
[ROW][C]65[/C][C]109.12[/C][C]109.507465484342[/C][C]-0.387465484342073[/C][/ROW]
[ROW][C]66[/C][C]109[/C][C]109.429465967802[/C][C]-0.429465967801519[/C][/ROW]
[ROW][C]67[/C][C]107.23[/C][C]107.826001432288[/C][C]-0.596001432287935[/C][/ROW]
[ROW][C]68[/C][C]109.49[/C][C]108.963658818814[/C][C]0.526341181185899[/C][/ROW]
[ROW][C]69[/C][C]109.04[/C][C]109.320879329347[/C][C]-0.280879329347314[/C][/ROW]
[ROW][C]70[/C][C]109.02[/C][C]109.3735197325[/C][C]-0.353519732499947[/C][/ROW]
[ROW][C]71[/C][C]109.23[/C][C]109.195898521769[/C][C]0.0341014782313351[/C][/ROW]
[ROW][C]72[/C][C]109.46[/C][C]109.102616346668[/C][C]0.357383653332107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117373&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117373&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
1396.9295.7278870472961.19211295270411
1499.0698.84871990906040.211280090939638
1599.6599.58875724252020.0612427574798033
1699.8299.80762398304160.0123760169583988
1799.99100.010119190138-0.0201191901382174
18100.33100.334018833715-0.00401883371455369
1999.3199.13754901367020.172450986329821
20101.1100.9820686919460.117931308054267
21101.1100.9872038414970.112796158503414
22100.93101.598450835749-0.668450835748814
23100.85100.878253803231-0.0282538032312516
24100.93100.5104843951410.419515604859185
2599.699.7298619234008-0.12986192340081
26101.88101.6321872019470.247812798052678
27101.81102.388005016662-0.578005016662289
28102.38102.0611421910470.318857808952927
29102.74102.5151329821090.224867017891199
30102.82103.05088109085-0.230881090849579
31101.72101.6576007121410.062399287859165
32103.47103.4367002528810.0332997471185479
33102.98103.362779918081-0.382779918080601
34102.68103.435473316207-0.755473316207357
35102.9102.7399345598050.160065440195226
36103.03102.5921764677460.437823532253759
37101.29101.710067548379-0.420067548379052
38103.69103.4620611362650.227938863735389
39103.68104.071839373849-0.391839373848569
40104.2104.0467163582120.153283641787837
41104.08104.345839755097-0.265839755096749
42104.16104.397254524234-0.237254524233691
43103.05103.0274129884850.0225870115147302
44104.66104.788107920917-0.128107920917117
45104.46104.50729605908-0.0472960590800113
46104.95104.8029053033820.147094696618282
47105.85105.0092339308050.84076606919524
48106.23105.4650388313610.764961168639005
49104.86104.6721406611740.187859338825831
50107.44107.1082299173620.331770082637519
51108.23107.7094131020090.52058689799091
52108.45108.545512138583-0.095512138582734
53109.39108.5639954964480.826004503551815
54110.15109.5400062555990.609993744400697
55109.13108.8475199699750.28248003002453
56110.28110.890403901729-0.610403901729413
57110.17110.197317126773-0.0273171267728145
58109.99110.549331001305-0.559331001305367
59109.26110.272003742513-1.01200374251302
60109.11109.143324199726-0.0333241997262803
61107.06107.540451122751-0.480451122750992
62109.53109.4837520073060.0462479926938073
63108.92109.877890495608-0.957890495608495
64109.24109.374508207608-0.134508207607581
65109.12109.507465484342-0.387465484342073
66109109.429465967802-0.429465967801519
67107.23107.826001432288-0.596001432287935
68109.49108.9636588188140.526341181185899
69109.04109.320879329347-0.280879329347314
70109.02109.3735197325-0.353519732499947
71109.23109.1958985217690.0341014782313351
72109.46109.1026163466680.357383653332107







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73107.750807798455106.892810333566108.608805263344
74110.19629940668109.066318720502111.326280092858
75110.389311105429109.049363613969111.72925859689
76110.825208958003109.301781319208112.348636596798
77111.03025025919109.345158035655112.715342482725
78111.271109369494109.43811488829113.104103850698
79109.970260455435108.022408602312111.918112308558
80111.829036005119109.726414876233113.931657134006
81111.605681470026109.390422853021113.820940087032
82111.883886601712109.55323058314114.214542620284
83112.064471549247109.625606462945114.503336635549
84111.986964880676107.269251912329116.704677849023

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 107.750807798455 & 106.892810333566 & 108.608805263344 \tabularnewline
74 & 110.19629940668 & 109.066318720502 & 111.326280092858 \tabularnewline
75 & 110.389311105429 & 109.049363613969 & 111.72925859689 \tabularnewline
76 & 110.825208958003 & 109.301781319208 & 112.348636596798 \tabularnewline
77 & 111.03025025919 & 109.345158035655 & 112.715342482725 \tabularnewline
78 & 111.271109369494 & 109.43811488829 & 113.104103850698 \tabularnewline
79 & 109.970260455435 & 108.022408602312 & 111.918112308558 \tabularnewline
80 & 111.829036005119 & 109.726414876233 & 113.931657134006 \tabularnewline
81 & 111.605681470026 & 109.390422853021 & 113.820940087032 \tabularnewline
82 & 111.883886601712 & 109.55323058314 & 114.214542620284 \tabularnewline
83 & 112.064471549247 & 109.625606462945 & 114.503336635549 \tabularnewline
84 & 111.986964880676 & 107.269251912329 & 116.704677849023 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117373&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]107.750807798455[/C][C]106.892810333566[/C][C]108.608805263344[/C][/ROW]
[ROW][C]74[/C][C]110.19629940668[/C][C]109.066318720502[/C][C]111.326280092858[/C][/ROW]
[ROW][C]75[/C][C]110.389311105429[/C][C]109.049363613969[/C][C]111.72925859689[/C][/ROW]
[ROW][C]76[/C][C]110.825208958003[/C][C]109.301781319208[/C][C]112.348636596798[/C][/ROW]
[ROW][C]77[/C][C]111.03025025919[/C][C]109.345158035655[/C][C]112.715342482725[/C][/ROW]
[ROW][C]78[/C][C]111.271109369494[/C][C]109.43811488829[/C][C]113.104103850698[/C][/ROW]
[ROW][C]79[/C][C]109.970260455435[/C][C]108.022408602312[/C][C]111.918112308558[/C][/ROW]
[ROW][C]80[/C][C]111.829036005119[/C][C]109.726414876233[/C][C]113.931657134006[/C][/ROW]
[ROW][C]81[/C][C]111.605681470026[/C][C]109.390422853021[/C][C]113.820940087032[/C][/ROW]
[ROW][C]82[/C][C]111.883886601712[/C][C]109.55323058314[/C][C]114.214542620284[/C][/ROW]
[ROW][C]83[/C][C]112.064471549247[/C][C]109.625606462945[/C][C]114.503336635549[/C][/ROW]
[ROW][C]84[/C][C]111.986964880676[/C][C]107.269251912329[/C][C]116.704677849023[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117373&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117373&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
73107.750807798455106.892810333566108.608805263344
74110.19629940668109.066318720502111.326280092858
75110.389311105429109.049363613969111.72925859689
76110.825208958003109.301781319208112.348636596798
77111.03025025919109.345158035655112.715342482725
78111.271109369494109.43811488829113.104103850698
79109.970260455435108.022408602312111.918112308558
80111.829036005119109.726414876233113.931657134006
81111.605681470026109.390422853021113.820940087032
82111.883886601712109.55323058314114.214542620284
83112.064471549247109.625606462945114.503336635549
84111.986964880676107.269251912329116.704677849023



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')