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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Nov 2014 14:50:44 +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/2014/Nov/28/t1417186299zablyzz91tyf2fx.htm/, Retrieved Sun, 19 May 2024 14:10:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260917, Retrieved Sun, 19 May 2024 14:10:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-28 14:50:44] [81bcec4b91879990466572cf43afb80d] [Current]
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Dataseries X:
79.26
79.38
79.35
78.91
79.11
79.22
79.22
79.21
79.26
79.82
80.04
80.2
80.2
80.27
80.37
80.57
79.99
79.86
79.86
79.81
79.88
80.2
80.53
80.52
80.52
80.48
80.29
79.54
79.39
79.3
79.3
79.49
79.63
79.74
80.17
80.06
80.06
80.22
80.5
80.58
80.24
80.34
80.34
80.41
80.59
80.77
80.94
80.8
80.8
80.76
80.94
81.03
81.35
81.41
81.41
81.44
81.55
81.8
81.97
81.99
79.36
79.44
79.46
79.77
79.49
79.42
80.32
80.48
80.6
80.53
80.84
80.68




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260917&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260917&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260917&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.955968001319672
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.955968001319672 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260917&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]0.955968001319672[/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=260917&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260917&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
alpha0.955968001319672
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1380.279.71224358974360.487756410256395
1480.2780.2619788213430.00802117865704588
1580.3780.383935855761-0.0139358557610052
1680.5780.5940693345382-0.0240693345381828
1779.9980.019932198529-0.0299321985290248
1879.8679.8926903521485-0.0326903521484923
1979.8679.9907284658317-0.130728465831723
2079.8179.8446286132573-0.0346286132573397
2179.8879.84706381134230.0329361886577004
2280.280.3920054647402-0.192005464740177
2380.5380.38774342865910.142256571340894
2480.5280.6855252031275-0.165525203127515
2580.5280.5605543394274-0.0405543394274304
2680.4880.5841176984911-0.104117698491123
2780.2980.5979067425411-0.307906742541093
2879.5480.5265672629128-0.986567262912772
2979.3979.03205475242150.357945247578456
3079.379.27548988593680.024510114063176
3179.379.4238930008867-0.123893000886653
3279.4979.28855910265560.201440897344355
3379.6379.51964421223180.110355787768214
3479.7480.1286918944688-0.388691894468764
3580.1779.9511221508050.218877849195039
3680.0680.3085991684349-0.248599168434936
3780.0680.1097149690637-0.0497149690637428
3880.2280.12172223758080.0982777624192295
3980.580.32002162695470.179978373045287
4080.5880.6852019270097-0.105201927009716
4180.2480.09244804820180.147551951798192
4280.3480.12007210790.21992789209996
4380.3480.4487538797804-0.108753879780394
4480.4180.34221759867260.0677824013273636
4580.5980.44151880352730.148481196472659
4680.7781.0650390896373-0.295039089637314
4780.9481.0037509407774-0.0637509407774246
4880.881.0704599315187-0.270459931518658
4980.880.8594348109593-0.0594348109592602
5080.7680.8686666374036-0.10866663740363
5180.9480.87273124367390.067268756326115
5281.0381.1176076981087-0.0876076981086698
5381.3580.55280259759620.797197402403825
5481.4181.20465377758420.205346222415841
5581.4181.504923424495-0.0949234244949935
5681.4481.41938186138050.0206181386194686
5781.5581.4771488695220.0728511304779857
5881.882.0088401479507-0.208840147950681
5981.9782.0401395085562-0.0701395085562098
6081.9982.0916394229191-0.101639422919135
6179.3682.0512931643774-2.69129316437738
6279.4479.5423848452311-0.102384845231143
6379.4679.5602014308338-0.100201430833764
6479.7779.63816222533140.131837774668597
6579.4979.32209971184650.167900288153447
6679.4279.34630259691220.0736974030878059
6780.3279.50749871243740.812501287562611
6880.4880.29451366361130.18548633638872
6980.680.5121893162840.0878106837160004
7080.5381.0457780189222-0.515778018922205
7180.8480.78976186285660.0502381371434524
7280.6880.9549519503949-0.274951950394865

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 80.2 & 79.7122435897436 & 0.487756410256395 \tabularnewline
14 & 80.27 & 80.261978821343 & 0.00802117865704588 \tabularnewline
15 & 80.37 & 80.383935855761 & -0.0139358557610052 \tabularnewline
16 & 80.57 & 80.5940693345382 & -0.0240693345381828 \tabularnewline
17 & 79.99 & 80.019932198529 & -0.0299321985290248 \tabularnewline
18 & 79.86 & 79.8926903521485 & -0.0326903521484923 \tabularnewline
19 & 79.86 & 79.9907284658317 & -0.130728465831723 \tabularnewline
20 & 79.81 & 79.8446286132573 & -0.0346286132573397 \tabularnewline
21 & 79.88 & 79.8470638113423 & 0.0329361886577004 \tabularnewline
22 & 80.2 & 80.3920054647402 & -0.192005464740177 \tabularnewline
23 & 80.53 & 80.3877434286591 & 0.142256571340894 \tabularnewline
24 & 80.52 & 80.6855252031275 & -0.165525203127515 \tabularnewline
25 & 80.52 & 80.5605543394274 & -0.0405543394274304 \tabularnewline
26 & 80.48 & 80.5841176984911 & -0.104117698491123 \tabularnewline
27 & 80.29 & 80.5979067425411 & -0.307906742541093 \tabularnewline
28 & 79.54 & 80.5265672629128 & -0.986567262912772 \tabularnewline
29 & 79.39 & 79.0320547524215 & 0.357945247578456 \tabularnewline
30 & 79.3 & 79.2754898859368 & 0.024510114063176 \tabularnewline
31 & 79.3 & 79.4238930008867 & -0.123893000886653 \tabularnewline
32 & 79.49 & 79.2885591026556 & 0.201440897344355 \tabularnewline
33 & 79.63 & 79.5196442122318 & 0.110355787768214 \tabularnewline
34 & 79.74 & 80.1286918944688 & -0.388691894468764 \tabularnewline
35 & 80.17 & 79.951122150805 & 0.218877849195039 \tabularnewline
36 & 80.06 & 80.3085991684349 & -0.248599168434936 \tabularnewline
37 & 80.06 & 80.1097149690637 & -0.0497149690637428 \tabularnewline
38 & 80.22 & 80.1217222375808 & 0.0982777624192295 \tabularnewline
39 & 80.5 & 80.3200216269547 & 0.179978373045287 \tabularnewline
40 & 80.58 & 80.6852019270097 & -0.105201927009716 \tabularnewline
41 & 80.24 & 80.0924480482018 & 0.147551951798192 \tabularnewline
42 & 80.34 & 80.1200721079 & 0.21992789209996 \tabularnewline
43 & 80.34 & 80.4487538797804 & -0.108753879780394 \tabularnewline
44 & 80.41 & 80.3422175986726 & 0.0677824013273636 \tabularnewline
45 & 80.59 & 80.4415188035273 & 0.148481196472659 \tabularnewline
46 & 80.77 & 81.0650390896373 & -0.295039089637314 \tabularnewline
47 & 80.94 & 81.0037509407774 & -0.0637509407774246 \tabularnewline
48 & 80.8 & 81.0704599315187 & -0.270459931518658 \tabularnewline
49 & 80.8 & 80.8594348109593 & -0.0594348109592602 \tabularnewline
50 & 80.76 & 80.8686666374036 & -0.10866663740363 \tabularnewline
51 & 80.94 & 80.8727312436739 & 0.067268756326115 \tabularnewline
52 & 81.03 & 81.1176076981087 & -0.0876076981086698 \tabularnewline
53 & 81.35 & 80.5528025975962 & 0.797197402403825 \tabularnewline
54 & 81.41 & 81.2046537775842 & 0.205346222415841 \tabularnewline
55 & 81.41 & 81.504923424495 & -0.0949234244949935 \tabularnewline
56 & 81.44 & 81.4193818613805 & 0.0206181386194686 \tabularnewline
57 & 81.55 & 81.477148869522 & 0.0728511304779857 \tabularnewline
58 & 81.8 & 82.0088401479507 & -0.208840147950681 \tabularnewline
59 & 81.97 & 82.0401395085562 & -0.0701395085562098 \tabularnewline
60 & 81.99 & 82.0916394229191 & -0.101639422919135 \tabularnewline
61 & 79.36 & 82.0512931643774 & -2.69129316437738 \tabularnewline
62 & 79.44 & 79.5423848452311 & -0.102384845231143 \tabularnewline
63 & 79.46 & 79.5602014308338 & -0.100201430833764 \tabularnewline
64 & 79.77 & 79.6381622253314 & 0.131837774668597 \tabularnewline
65 & 79.49 & 79.3220997118465 & 0.167900288153447 \tabularnewline
66 & 79.42 & 79.3463025969122 & 0.0736974030878059 \tabularnewline
67 & 80.32 & 79.5074987124374 & 0.812501287562611 \tabularnewline
68 & 80.48 & 80.2945136636113 & 0.18548633638872 \tabularnewline
69 & 80.6 & 80.512189316284 & 0.0878106837160004 \tabularnewline
70 & 80.53 & 81.0457780189222 & -0.515778018922205 \tabularnewline
71 & 80.84 & 80.7897618628566 & 0.0502381371434524 \tabularnewline
72 & 80.68 & 80.9549519503949 & -0.274951950394865 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260917&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]80.2[/C][C]79.7122435897436[/C][C]0.487756410256395[/C][/ROW]
[ROW][C]14[/C][C]80.27[/C][C]80.261978821343[/C][C]0.00802117865704588[/C][/ROW]
[ROW][C]15[/C][C]80.37[/C][C]80.383935855761[/C][C]-0.0139358557610052[/C][/ROW]
[ROW][C]16[/C][C]80.57[/C][C]80.5940693345382[/C][C]-0.0240693345381828[/C][/ROW]
[ROW][C]17[/C][C]79.99[/C][C]80.019932198529[/C][C]-0.0299321985290248[/C][/ROW]
[ROW][C]18[/C][C]79.86[/C][C]79.8926903521485[/C][C]-0.0326903521484923[/C][/ROW]
[ROW][C]19[/C][C]79.86[/C][C]79.9907284658317[/C][C]-0.130728465831723[/C][/ROW]
[ROW][C]20[/C][C]79.81[/C][C]79.8446286132573[/C][C]-0.0346286132573397[/C][/ROW]
[ROW][C]21[/C][C]79.88[/C][C]79.8470638113423[/C][C]0.0329361886577004[/C][/ROW]
[ROW][C]22[/C][C]80.2[/C][C]80.3920054647402[/C][C]-0.192005464740177[/C][/ROW]
[ROW][C]23[/C][C]80.53[/C][C]80.3877434286591[/C][C]0.142256571340894[/C][/ROW]
[ROW][C]24[/C][C]80.52[/C][C]80.6855252031275[/C][C]-0.165525203127515[/C][/ROW]
[ROW][C]25[/C][C]80.52[/C][C]80.5605543394274[/C][C]-0.0405543394274304[/C][/ROW]
[ROW][C]26[/C][C]80.48[/C][C]80.5841176984911[/C][C]-0.104117698491123[/C][/ROW]
[ROW][C]27[/C][C]80.29[/C][C]80.5979067425411[/C][C]-0.307906742541093[/C][/ROW]
[ROW][C]28[/C][C]79.54[/C][C]80.5265672629128[/C][C]-0.986567262912772[/C][/ROW]
[ROW][C]29[/C][C]79.39[/C][C]79.0320547524215[/C][C]0.357945247578456[/C][/ROW]
[ROW][C]30[/C][C]79.3[/C][C]79.2754898859368[/C][C]0.024510114063176[/C][/ROW]
[ROW][C]31[/C][C]79.3[/C][C]79.4238930008867[/C][C]-0.123893000886653[/C][/ROW]
[ROW][C]32[/C][C]79.49[/C][C]79.2885591026556[/C][C]0.201440897344355[/C][/ROW]
[ROW][C]33[/C][C]79.63[/C][C]79.5196442122318[/C][C]0.110355787768214[/C][/ROW]
[ROW][C]34[/C][C]79.74[/C][C]80.1286918944688[/C][C]-0.388691894468764[/C][/ROW]
[ROW][C]35[/C][C]80.17[/C][C]79.951122150805[/C][C]0.218877849195039[/C][/ROW]
[ROW][C]36[/C][C]80.06[/C][C]80.3085991684349[/C][C]-0.248599168434936[/C][/ROW]
[ROW][C]37[/C][C]80.06[/C][C]80.1097149690637[/C][C]-0.0497149690637428[/C][/ROW]
[ROW][C]38[/C][C]80.22[/C][C]80.1217222375808[/C][C]0.0982777624192295[/C][/ROW]
[ROW][C]39[/C][C]80.5[/C][C]80.3200216269547[/C][C]0.179978373045287[/C][/ROW]
[ROW][C]40[/C][C]80.58[/C][C]80.6852019270097[/C][C]-0.105201927009716[/C][/ROW]
[ROW][C]41[/C][C]80.24[/C][C]80.0924480482018[/C][C]0.147551951798192[/C][/ROW]
[ROW][C]42[/C][C]80.34[/C][C]80.1200721079[/C][C]0.21992789209996[/C][/ROW]
[ROW][C]43[/C][C]80.34[/C][C]80.4487538797804[/C][C]-0.108753879780394[/C][/ROW]
[ROW][C]44[/C][C]80.41[/C][C]80.3422175986726[/C][C]0.0677824013273636[/C][/ROW]
[ROW][C]45[/C][C]80.59[/C][C]80.4415188035273[/C][C]0.148481196472659[/C][/ROW]
[ROW][C]46[/C][C]80.77[/C][C]81.0650390896373[/C][C]-0.295039089637314[/C][/ROW]
[ROW][C]47[/C][C]80.94[/C][C]81.0037509407774[/C][C]-0.0637509407774246[/C][/ROW]
[ROW][C]48[/C][C]80.8[/C][C]81.0704599315187[/C][C]-0.270459931518658[/C][/ROW]
[ROW][C]49[/C][C]80.8[/C][C]80.8594348109593[/C][C]-0.0594348109592602[/C][/ROW]
[ROW][C]50[/C][C]80.76[/C][C]80.8686666374036[/C][C]-0.10866663740363[/C][/ROW]
[ROW][C]51[/C][C]80.94[/C][C]80.8727312436739[/C][C]0.067268756326115[/C][/ROW]
[ROW][C]52[/C][C]81.03[/C][C]81.1176076981087[/C][C]-0.0876076981086698[/C][/ROW]
[ROW][C]53[/C][C]81.35[/C][C]80.5528025975962[/C][C]0.797197402403825[/C][/ROW]
[ROW][C]54[/C][C]81.41[/C][C]81.2046537775842[/C][C]0.205346222415841[/C][/ROW]
[ROW][C]55[/C][C]81.41[/C][C]81.504923424495[/C][C]-0.0949234244949935[/C][/ROW]
[ROW][C]56[/C][C]81.44[/C][C]81.4193818613805[/C][C]0.0206181386194686[/C][/ROW]
[ROW][C]57[/C][C]81.55[/C][C]81.477148869522[/C][C]0.0728511304779857[/C][/ROW]
[ROW][C]58[/C][C]81.8[/C][C]82.0088401479507[/C][C]-0.208840147950681[/C][/ROW]
[ROW][C]59[/C][C]81.97[/C][C]82.0401395085562[/C][C]-0.0701395085562098[/C][/ROW]
[ROW][C]60[/C][C]81.99[/C][C]82.0916394229191[/C][C]-0.101639422919135[/C][/ROW]
[ROW][C]61[/C][C]79.36[/C][C]82.0512931643774[/C][C]-2.69129316437738[/C][/ROW]
[ROW][C]62[/C][C]79.44[/C][C]79.5423848452311[/C][C]-0.102384845231143[/C][/ROW]
[ROW][C]63[/C][C]79.46[/C][C]79.5602014308338[/C][C]-0.100201430833764[/C][/ROW]
[ROW][C]64[/C][C]79.77[/C][C]79.6381622253314[/C][C]0.131837774668597[/C][/ROW]
[ROW][C]65[/C][C]79.49[/C][C]79.3220997118465[/C][C]0.167900288153447[/C][/ROW]
[ROW][C]66[/C][C]79.42[/C][C]79.3463025969122[/C][C]0.0736974030878059[/C][/ROW]
[ROW][C]67[/C][C]80.32[/C][C]79.5074987124374[/C][C]0.812501287562611[/C][/ROW]
[ROW][C]68[/C][C]80.48[/C][C]80.2945136636113[/C][C]0.18548633638872[/C][/ROW]
[ROW][C]69[/C][C]80.6[/C][C]80.512189316284[/C][C]0.0878106837160004[/C][/ROW]
[ROW][C]70[/C][C]80.53[/C][C]81.0457780189222[/C][C]-0.515778018922205[/C][/ROW]
[ROW][C]71[/C][C]80.84[/C][C]80.7897618628566[/C][C]0.0502381371434524[/C][/ROW]
[ROW][C]72[/C][C]80.68[/C][C]80.9549519503949[/C][C]-0.274951950394865[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260917&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260917&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
1380.279.71224358974360.487756410256395
1480.2780.2619788213430.00802117865704588
1580.3780.383935855761-0.0139358557610052
1680.5780.5940693345382-0.0240693345381828
1779.9980.019932198529-0.0299321985290248
1879.8679.8926903521485-0.0326903521484923
1979.8679.9907284658317-0.130728465831723
2079.8179.8446286132573-0.0346286132573397
2179.8879.84706381134230.0329361886577004
2280.280.3920054647402-0.192005464740177
2380.5380.38774342865910.142256571340894
2480.5280.6855252031275-0.165525203127515
2580.5280.5605543394274-0.0405543394274304
2680.4880.5841176984911-0.104117698491123
2780.2980.5979067425411-0.307906742541093
2879.5480.5265672629128-0.986567262912772
2979.3979.03205475242150.357945247578456
3079.379.27548988593680.024510114063176
3179.379.4238930008867-0.123893000886653
3279.4979.28855910265560.201440897344355
3379.6379.51964421223180.110355787768214
3479.7480.1286918944688-0.388691894468764
3580.1779.9511221508050.218877849195039
3680.0680.3085991684349-0.248599168434936
3780.0680.1097149690637-0.0497149690637428
3880.2280.12172223758080.0982777624192295
3980.580.32002162695470.179978373045287
4080.5880.6852019270097-0.105201927009716
4180.2480.09244804820180.147551951798192
4280.3480.12007210790.21992789209996
4380.3480.4487538797804-0.108753879780394
4480.4180.34221759867260.0677824013273636
4580.5980.44151880352730.148481196472659
4680.7781.0650390896373-0.295039089637314
4780.9481.0037509407774-0.0637509407774246
4880.881.0704599315187-0.270459931518658
4980.880.8594348109593-0.0594348109592602
5080.7680.8686666374036-0.10866663740363
5180.9480.87273124367390.067268756326115
5281.0381.1176076981087-0.0876076981086698
5381.3580.55280259759620.797197402403825
5481.4181.20465377758420.205346222415841
5581.4181.504923424495-0.0949234244949935
5681.4481.41938186138050.0206181386194686
5781.5581.4771488695220.0728511304779857
5881.882.0088401479507-0.208840147950681
5981.9782.0401395085562-0.0701395085562098
6081.9982.0916394229191-0.101639422919135
6179.3682.0512931643774-2.69129316437738
6279.4479.5423848452311-0.102384845231143
6379.4679.5602014308338-0.100201430833764
6479.7779.63816222533140.131837774668597
6579.4979.32209971184650.167900288153447
6679.4279.34630259691220.0736974030878059
6780.3279.50749871243740.812501287562611
6880.4880.29451366361130.18548633638872
6980.680.5121893162840.0878106837160004
7080.5381.0457780189222-0.515778018922205
7180.8480.78976186285660.0502381371434524
7280.6880.9549519503949-0.274951950394865







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7380.634896831232179.780959417856481.4888342446078
7480.812773467093179.631411987237581.9941349469487
7580.928562828656779.492589017540982.3645366397725
7681.112530134708379.46073516367482.7643251057426
7780.672022831821278.829515717463782.5145299461788
7880.53157047268978.516319047535882.5468218978421
7980.654845240748178.480530602360782.8291598791355
8080.637526238478478.315016822603182.9600356543538
8180.673582034671978.211782727873583.1353813414704
8281.096649316545678.50302990208383.6902687310082
8381.358623264990678.639566901617384.0776796283639
8481.461468531468578.622512147984584.3004249149526

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 80.6348968312321 & 79.7809594178564 & 81.4888342446078 \tabularnewline
74 & 80.8127734670931 & 79.6314119872375 & 81.9941349469487 \tabularnewline
75 & 80.9285628286567 & 79.4925890175409 & 82.3645366397725 \tabularnewline
76 & 81.1125301347083 & 79.460735163674 & 82.7643251057426 \tabularnewline
77 & 80.6720228318212 & 78.8295157174637 & 82.5145299461788 \tabularnewline
78 & 80.531570472689 & 78.5163190475358 & 82.5468218978421 \tabularnewline
79 & 80.6548452407481 & 78.4805306023607 & 82.8291598791355 \tabularnewline
80 & 80.6375262384784 & 78.3150168226031 & 82.9600356543538 \tabularnewline
81 & 80.6735820346719 & 78.2117827278735 & 83.1353813414704 \tabularnewline
82 & 81.0966493165456 & 78.503029902083 & 83.6902687310082 \tabularnewline
83 & 81.3586232649906 & 78.6395669016173 & 84.0776796283639 \tabularnewline
84 & 81.4614685314685 & 78.6225121479845 & 84.3004249149526 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260917&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]80.6348968312321[/C][C]79.7809594178564[/C][C]81.4888342446078[/C][/ROW]
[ROW][C]74[/C][C]80.8127734670931[/C][C]79.6314119872375[/C][C]81.9941349469487[/C][/ROW]
[ROW][C]75[/C][C]80.9285628286567[/C][C]79.4925890175409[/C][C]82.3645366397725[/C][/ROW]
[ROW][C]76[/C][C]81.1125301347083[/C][C]79.460735163674[/C][C]82.7643251057426[/C][/ROW]
[ROW][C]77[/C][C]80.6720228318212[/C][C]78.8295157174637[/C][C]82.5145299461788[/C][/ROW]
[ROW][C]78[/C][C]80.531570472689[/C][C]78.5163190475358[/C][C]82.5468218978421[/C][/ROW]
[ROW][C]79[/C][C]80.6548452407481[/C][C]78.4805306023607[/C][C]82.8291598791355[/C][/ROW]
[ROW][C]80[/C][C]80.6375262384784[/C][C]78.3150168226031[/C][C]82.9600356543538[/C][/ROW]
[ROW][C]81[/C][C]80.6735820346719[/C][C]78.2117827278735[/C][C]83.1353813414704[/C][/ROW]
[ROW][C]82[/C][C]81.0966493165456[/C][C]78.503029902083[/C][C]83.6902687310082[/C][/ROW]
[ROW][C]83[/C][C]81.3586232649906[/C][C]78.6395669016173[/C][C]84.0776796283639[/C][/ROW]
[ROW][C]84[/C][C]81.4614685314685[/C][C]78.6225121479845[/C][C]84.3004249149526[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260917&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260917&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
7380.634896831232179.780959417856481.4888342446078
7480.812773467093179.631411987237581.9941349469487
7580.928562828656779.492589017540982.3645366397725
7681.112530134708379.46073516367482.7643251057426
7780.672022831821278.829515717463782.5145299461788
7880.53157047268978.516319047535882.5468218978421
7980.654845240748178.480530602360782.8291598791355
8080.637526238478478.315016822603182.9600356543538
8180.673582034671978.211782727873583.1353813414704
8281.096649316545678.50302990208383.6902687310082
8381.358623264990678.639566901617384.0776796283639
8481.461468531468578.622512147984584.3004249149526



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')