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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 06 Jun 2009 05:41:56 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/06/t1244288549w3rv1ixd8digtc0.htm/, Retrieved Mon, 29 Apr 2024 06:02:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41971, Retrieved Mon, 29 Apr 2024 06:02:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2009-06-06 11:41:56] [2f928979fcb5db36e984611041f4b2ce] [Current]
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Dataseries X:
2.98
2.98
2.98
3.03
3.07
3.08
3.08
3.08
3.08
3.08
3.08
3.08
3.08
3.08
3.12
3.15
3.15
3.15
3.15
3.16
3.19
3.2
3.2
3.2
3.21
3.21
3.21
3.21
3.21
3.28
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.45
3.49
3.5
3.54
3.64
3.67
3.67
3.68
3.68
3.68
3.68
3.7
3.83
3.87
3.87
3.87
3.87
3.87
3.87
3.87
3.87
3.87
3.88
3.88
3.88
3.88
3.88
3.88
3.89
3.89
3.91
3.95
3.99
3.99
3.99




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41971&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]2 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=41971&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41971&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.865625929532432
beta0.0279541213592297
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.865625929532432 \tabularnewline
beta & 0.0279541213592297 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41971&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]0.865625929532432[/C][/ROW]
[ROW][C]beta[/C][C]0.0279541213592297[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41971&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41971&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
alpha0.865625929532432
beta0.0279541213592297
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133.083.032180571624220.0478194283757842
143.083.076586510445360.00341348955464138
153.123.12098274303256-0.000982743032556854
163.153.149885960428650.000114039571347480
173.153.149322980032380.000677019967616932
183.153.149266003058200.000733996941795212
193.153.18347764010211-0.0334776401021055
203.163.154535492631410.00546450736859105
213.193.157707694080780.0322923059192242
223.23.183940270465060.0160597295349381
233.23.199056880570970.000943119429031913
243.23.20325491989269-0.00325491989269056
253.213.21086127093729-0.000861270937285497
263.213.207158382468230.00284161753176626
273.213.25229595455108-0.0422959545510846
283.213.2457125917697-0.0357125917696992
293.213.2126444686849-0.00264446868490165
303.283.208089225452190.0719107745478067
313.33.3003046227353-0.000304622735299631
323.33.30623521015310-0.00623521015310402
333.33.30334739022062-0.00334739022061781
343.33.296012397392190.00398760260781206
353.33.297962784411050.00203721558895253
363.33.30199796556584-0.00199796556583953
373.33.31074846677059-0.0107484667705950
383.453.298104154081850.151895845918155
393.493.471061788450880.0189382115491159
403.53.52483229925198-0.0248322992519761
413.543.509965790234650.0300342097653479
423.643.549147106780760.0908528932192354
433.673.655299014616140.0147009853838607
443.673.67942078021977-0.00942078021977322
453.683.679807092536190.000192907463814951
463.683.68149108074878-0.00149108074877935
473.683.68343826048178-0.00343826048177487
483.683.68744456719865-0.00744456719865161
493.73.696299992353670.00370000764632605
503.833.724649339525570.105350660474434
513.873.845817754961380.0241822450386211
523.873.90557337660747-0.0355733766074660
533.873.89401496738218-0.0240149673821812
543.873.89886491323324-0.0288649132332428
553.873.89217940142879-0.0221794014287879
563.873.88073831118437-0.0107383111843657
573.873.8809594803103-0.0109594803102966
583.873.87175396268486-0.00175396268486416
593.873.87229346628109-0.00229346628108607
603.883.876046163358710.00395383664128701
613.883.89638452904704-0.0163845290470395
623.883.92135090838234-0.041350908382344
633.883.90061684364766-0.0206168436476633
643.883.90846348793655-0.0284634879365453
653.883.89967136198188-0.0196713619818771
663.893.90279039115096-0.0127903911509573
673.893.90646336068969-0.0164633606896918
683.913.897156922779550.0128430772204462
693.953.913962907792530.0360370922074695
703.993.943817827516630.0461821724833702
713.993.983962292413380.00603770758662137
723.993.99427826004811-0.00427826004810994

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3.08 & 3.03218057162422 & 0.0478194283757842 \tabularnewline
14 & 3.08 & 3.07658651044536 & 0.00341348955464138 \tabularnewline
15 & 3.12 & 3.12098274303256 & -0.000982743032556854 \tabularnewline
16 & 3.15 & 3.14988596042865 & 0.000114039571347480 \tabularnewline
17 & 3.15 & 3.14932298003238 & 0.000677019967616932 \tabularnewline
18 & 3.15 & 3.14926600305820 & 0.000733996941795212 \tabularnewline
19 & 3.15 & 3.18347764010211 & -0.0334776401021055 \tabularnewline
20 & 3.16 & 3.15453549263141 & 0.00546450736859105 \tabularnewline
21 & 3.19 & 3.15770769408078 & 0.0322923059192242 \tabularnewline
22 & 3.2 & 3.18394027046506 & 0.0160597295349381 \tabularnewline
23 & 3.2 & 3.19905688057097 & 0.000943119429031913 \tabularnewline
24 & 3.2 & 3.20325491989269 & -0.00325491989269056 \tabularnewline
25 & 3.21 & 3.21086127093729 & -0.000861270937285497 \tabularnewline
26 & 3.21 & 3.20715838246823 & 0.00284161753176626 \tabularnewline
27 & 3.21 & 3.25229595455108 & -0.0422959545510846 \tabularnewline
28 & 3.21 & 3.2457125917697 & -0.0357125917696992 \tabularnewline
29 & 3.21 & 3.2126444686849 & -0.00264446868490165 \tabularnewline
30 & 3.28 & 3.20808922545219 & 0.0719107745478067 \tabularnewline
31 & 3.3 & 3.3003046227353 & -0.000304622735299631 \tabularnewline
32 & 3.3 & 3.30623521015310 & -0.00623521015310402 \tabularnewline
33 & 3.3 & 3.30334739022062 & -0.00334739022061781 \tabularnewline
34 & 3.3 & 3.29601239739219 & 0.00398760260781206 \tabularnewline
35 & 3.3 & 3.29796278441105 & 0.00203721558895253 \tabularnewline
36 & 3.3 & 3.30199796556584 & -0.00199796556583953 \tabularnewline
37 & 3.3 & 3.31074846677059 & -0.0107484667705950 \tabularnewline
38 & 3.45 & 3.29810415408185 & 0.151895845918155 \tabularnewline
39 & 3.49 & 3.47106178845088 & 0.0189382115491159 \tabularnewline
40 & 3.5 & 3.52483229925198 & -0.0248322992519761 \tabularnewline
41 & 3.54 & 3.50996579023465 & 0.0300342097653479 \tabularnewline
42 & 3.64 & 3.54914710678076 & 0.0908528932192354 \tabularnewline
43 & 3.67 & 3.65529901461614 & 0.0147009853838607 \tabularnewline
44 & 3.67 & 3.67942078021977 & -0.00942078021977322 \tabularnewline
45 & 3.68 & 3.67980709253619 & 0.000192907463814951 \tabularnewline
46 & 3.68 & 3.68149108074878 & -0.00149108074877935 \tabularnewline
47 & 3.68 & 3.68343826048178 & -0.00343826048177487 \tabularnewline
48 & 3.68 & 3.68744456719865 & -0.00744456719865161 \tabularnewline
49 & 3.7 & 3.69629999235367 & 0.00370000764632605 \tabularnewline
50 & 3.83 & 3.72464933952557 & 0.105350660474434 \tabularnewline
51 & 3.87 & 3.84581775496138 & 0.0241822450386211 \tabularnewline
52 & 3.87 & 3.90557337660747 & -0.0355733766074660 \tabularnewline
53 & 3.87 & 3.89401496738218 & -0.0240149673821812 \tabularnewline
54 & 3.87 & 3.89886491323324 & -0.0288649132332428 \tabularnewline
55 & 3.87 & 3.89217940142879 & -0.0221794014287879 \tabularnewline
56 & 3.87 & 3.88073831118437 & -0.0107383111843657 \tabularnewline
57 & 3.87 & 3.8809594803103 & -0.0109594803102966 \tabularnewline
58 & 3.87 & 3.87175396268486 & -0.00175396268486416 \tabularnewline
59 & 3.87 & 3.87229346628109 & -0.00229346628108607 \tabularnewline
60 & 3.88 & 3.87604616335871 & 0.00395383664128701 \tabularnewline
61 & 3.88 & 3.89638452904704 & -0.0163845290470395 \tabularnewline
62 & 3.88 & 3.92135090838234 & -0.041350908382344 \tabularnewline
63 & 3.88 & 3.90061684364766 & -0.0206168436476633 \tabularnewline
64 & 3.88 & 3.90846348793655 & -0.0284634879365453 \tabularnewline
65 & 3.88 & 3.89967136198188 & -0.0196713619818771 \tabularnewline
66 & 3.89 & 3.90279039115096 & -0.0127903911509573 \tabularnewline
67 & 3.89 & 3.90646336068969 & -0.0164633606896918 \tabularnewline
68 & 3.91 & 3.89715692277955 & 0.0128430772204462 \tabularnewline
69 & 3.95 & 3.91396290779253 & 0.0360370922074695 \tabularnewline
70 & 3.99 & 3.94381782751663 & 0.0461821724833702 \tabularnewline
71 & 3.99 & 3.98396229241338 & 0.00603770758662137 \tabularnewline
72 & 3.99 & 3.99427826004811 & -0.00427826004810994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41971&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]3.08[/C][C]3.03218057162422[/C][C]0.0478194283757842[/C][/ROW]
[ROW][C]14[/C][C]3.08[/C][C]3.07658651044536[/C][C]0.00341348955464138[/C][/ROW]
[ROW][C]15[/C][C]3.12[/C][C]3.12098274303256[/C][C]-0.000982743032556854[/C][/ROW]
[ROW][C]16[/C][C]3.15[/C][C]3.14988596042865[/C][C]0.000114039571347480[/C][/ROW]
[ROW][C]17[/C][C]3.15[/C][C]3.14932298003238[/C][C]0.000677019967616932[/C][/ROW]
[ROW][C]18[/C][C]3.15[/C][C]3.14926600305820[/C][C]0.000733996941795212[/C][/ROW]
[ROW][C]19[/C][C]3.15[/C][C]3.18347764010211[/C][C]-0.0334776401021055[/C][/ROW]
[ROW][C]20[/C][C]3.16[/C][C]3.15453549263141[/C][C]0.00546450736859105[/C][/ROW]
[ROW][C]21[/C][C]3.19[/C][C]3.15770769408078[/C][C]0.0322923059192242[/C][/ROW]
[ROW][C]22[/C][C]3.2[/C][C]3.18394027046506[/C][C]0.0160597295349381[/C][/ROW]
[ROW][C]23[/C][C]3.2[/C][C]3.19905688057097[/C][C]0.000943119429031913[/C][/ROW]
[ROW][C]24[/C][C]3.2[/C][C]3.20325491989269[/C][C]-0.00325491989269056[/C][/ROW]
[ROW][C]25[/C][C]3.21[/C][C]3.21086127093729[/C][C]-0.000861270937285497[/C][/ROW]
[ROW][C]26[/C][C]3.21[/C][C]3.20715838246823[/C][C]0.00284161753176626[/C][/ROW]
[ROW][C]27[/C][C]3.21[/C][C]3.25229595455108[/C][C]-0.0422959545510846[/C][/ROW]
[ROW][C]28[/C][C]3.21[/C][C]3.2457125917697[/C][C]-0.0357125917696992[/C][/ROW]
[ROW][C]29[/C][C]3.21[/C][C]3.2126444686849[/C][C]-0.00264446868490165[/C][/ROW]
[ROW][C]30[/C][C]3.28[/C][C]3.20808922545219[/C][C]0.0719107745478067[/C][/ROW]
[ROW][C]31[/C][C]3.3[/C][C]3.3003046227353[/C][C]-0.000304622735299631[/C][/ROW]
[ROW][C]32[/C][C]3.3[/C][C]3.30623521015310[/C][C]-0.00623521015310402[/C][/ROW]
[ROW][C]33[/C][C]3.3[/C][C]3.30334739022062[/C][C]-0.00334739022061781[/C][/ROW]
[ROW][C]34[/C][C]3.3[/C][C]3.29601239739219[/C][C]0.00398760260781206[/C][/ROW]
[ROW][C]35[/C][C]3.3[/C][C]3.29796278441105[/C][C]0.00203721558895253[/C][/ROW]
[ROW][C]36[/C][C]3.3[/C][C]3.30199796556584[/C][C]-0.00199796556583953[/C][/ROW]
[ROW][C]37[/C][C]3.3[/C][C]3.31074846677059[/C][C]-0.0107484667705950[/C][/ROW]
[ROW][C]38[/C][C]3.45[/C][C]3.29810415408185[/C][C]0.151895845918155[/C][/ROW]
[ROW][C]39[/C][C]3.49[/C][C]3.47106178845088[/C][C]0.0189382115491159[/C][/ROW]
[ROW][C]40[/C][C]3.5[/C][C]3.52483229925198[/C][C]-0.0248322992519761[/C][/ROW]
[ROW][C]41[/C][C]3.54[/C][C]3.50996579023465[/C][C]0.0300342097653479[/C][/ROW]
[ROW][C]42[/C][C]3.64[/C][C]3.54914710678076[/C][C]0.0908528932192354[/C][/ROW]
[ROW][C]43[/C][C]3.67[/C][C]3.65529901461614[/C][C]0.0147009853838607[/C][/ROW]
[ROW][C]44[/C][C]3.67[/C][C]3.67942078021977[/C][C]-0.00942078021977322[/C][/ROW]
[ROW][C]45[/C][C]3.68[/C][C]3.67980709253619[/C][C]0.000192907463814951[/C][/ROW]
[ROW][C]46[/C][C]3.68[/C][C]3.68149108074878[/C][C]-0.00149108074877935[/C][/ROW]
[ROW][C]47[/C][C]3.68[/C][C]3.68343826048178[/C][C]-0.00343826048177487[/C][/ROW]
[ROW][C]48[/C][C]3.68[/C][C]3.68744456719865[/C][C]-0.00744456719865161[/C][/ROW]
[ROW][C]49[/C][C]3.7[/C][C]3.69629999235367[/C][C]0.00370000764632605[/C][/ROW]
[ROW][C]50[/C][C]3.83[/C][C]3.72464933952557[/C][C]0.105350660474434[/C][/ROW]
[ROW][C]51[/C][C]3.87[/C][C]3.84581775496138[/C][C]0.0241822450386211[/C][/ROW]
[ROW][C]52[/C][C]3.87[/C][C]3.90557337660747[/C][C]-0.0355733766074660[/C][/ROW]
[ROW][C]53[/C][C]3.87[/C][C]3.89401496738218[/C][C]-0.0240149673821812[/C][/ROW]
[ROW][C]54[/C][C]3.87[/C][C]3.89886491323324[/C][C]-0.0288649132332428[/C][/ROW]
[ROW][C]55[/C][C]3.87[/C][C]3.89217940142879[/C][C]-0.0221794014287879[/C][/ROW]
[ROW][C]56[/C][C]3.87[/C][C]3.88073831118437[/C][C]-0.0107383111843657[/C][/ROW]
[ROW][C]57[/C][C]3.87[/C][C]3.8809594803103[/C][C]-0.0109594803102966[/C][/ROW]
[ROW][C]58[/C][C]3.87[/C][C]3.87175396268486[/C][C]-0.00175396268486416[/C][/ROW]
[ROW][C]59[/C][C]3.87[/C][C]3.87229346628109[/C][C]-0.00229346628108607[/C][/ROW]
[ROW][C]60[/C][C]3.88[/C][C]3.87604616335871[/C][C]0.00395383664128701[/C][/ROW]
[ROW][C]61[/C][C]3.88[/C][C]3.89638452904704[/C][C]-0.0163845290470395[/C][/ROW]
[ROW][C]62[/C][C]3.88[/C][C]3.92135090838234[/C][C]-0.041350908382344[/C][/ROW]
[ROW][C]63[/C][C]3.88[/C][C]3.90061684364766[/C][C]-0.0206168436476633[/C][/ROW]
[ROW][C]64[/C][C]3.88[/C][C]3.90846348793655[/C][C]-0.0284634879365453[/C][/ROW]
[ROW][C]65[/C][C]3.88[/C][C]3.89967136198188[/C][C]-0.0196713619818771[/C][/ROW]
[ROW][C]66[/C][C]3.89[/C][C]3.90279039115096[/C][C]-0.0127903911509573[/C][/ROW]
[ROW][C]67[/C][C]3.89[/C][C]3.90646336068969[/C][C]-0.0164633606896918[/C][/ROW]
[ROW][C]68[/C][C]3.91[/C][C]3.89715692277955[/C][C]0.0128430772204462[/C][/ROW]
[ROW][C]69[/C][C]3.95[/C][C]3.91396290779253[/C][C]0.0360370922074695[/C][/ROW]
[ROW][C]70[/C][C]3.99[/C][C]3.94381782751663[/C][C]0.0461821724833702[/C][/ROW]
[ROW][C]71[/C][C]3.99[/C][C]3.98396229241338[/C][C]0.00603770758662137[/C][/ROW]
[ROW][C]72[/C][C]3.99[/C][C]3.99427826004811[/C][C]-0.00427826004810994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41971&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41971&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
133.083.032180571624220.0478194283757842
143.083.076586510445360.00341348955464138
153.123.12098274303256-0.000982743032556854
163.153.149885960428650.000114039571347480
173.153.149322980032380.000677019967616932
183.153.149266003058200.000733996941795212
193.153.18347764010211-0.0334776401021055
203.163.154535492631410.00546450736859105
213.193.157707694080780.0322923059192242
223.23.183940270465060.0160597295349381
233.23.199056880570970.000943119429031913
243.23.20325491989269-0.00325491989269056
253.213.21086127093729-0.000861270937285497
263.213.207158382468230.00284161753176626
273.213.25229595455108-0.0422959545510846
283.213.2457125917697-0.0357125917696992
293.213.2126444686849-0.00264446868490165
303.283.208089225452190.0719107745478067
313.33.3003046227353-0.000304622735299631
323.33.30623521015310-0.00623521015310402
333.33.30334739022062-0.00334739022061781
343.33.296012397392190.00398760260781206
353.33.297962784411050.00203721558895253
363.33.30199796556584-0.00199796556583953
373.33.31074846677059-0.0107484667705950
383.453.298104154081850.151895845918155
393.493.471061788450880.0189382115491159
403.53.52483229925198-0.0248322992519761
413.543.509965790234650.0300342097653479
423.643.549147106780760.0908528932192354
433.673.655299014616140.0147009853838607
443.673.67942078021977-0.00942078021977322
453.683.679807092536190.000192907463814951
463.683.68149108074878-0.00149108074877935
473.683.68343826048178-0.00343826048177487
483.683.68744456719865-0.00744456719865161
493.73.696299992353670.00370000764632605
503.833.724649339525570.105350660474434
513.873.845817754961380.0241822450386211
523.873.90557337660747-0.0355733766074660
533.873.89401496738218-0.0240149673821812
543.873.89886491323324-0.0288649132332428
553.873.89217940142879-0.0221794014287879
563.873.88073831118437-0.0107383111843657
573.873.8809594803103-0.0109594803102966
583.873.87175396268486-0.00175396268486416
593.873.87229346628109-0.00229346628108607
603.883.876046163358710.00395383664128701
613.883.89638452904704-0.0163845290470395
623.883.92135090838234-0.041350908382344
633.883.90061684364766-0.0206168436476633
643.883.90846348793655-0.0284634879365453
653.883.89967136198188-0.0196713619818771
663.893.90279039115096-0.0127903911509573
673.893.90646336068969-0.0164633606896918
683.913.897156922779550.0128430772204462
693.953.913962907792530.0360370922074695
703.993.943817827516630.0461821724833702
713.993.983962292413380.00603770758662137
723.993.99427826004811-0.00427826004810994







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
734.003297886488773.936482918524194.07011285445336
744.038671183996323.949024718929854.1283176490628
754.056629323584993.94808547945484.16517316771517
764.082214415072283.956606465505144.20782236463943
774.100601524185893.959356957846494.24184609052528
784.123792658779423.967619545821874.27996577173698
794.14010580244063.969846293027674.31036531185352
804.151139300659523.967457138297604.33482146302144
814.161732009797543.965010094809724.35845392478536
824.162153330364733.953136808950444.37116985177901
834.156134185513833.93538651466384.37688185636385
844.15929595911847-0.5216799969935678.8402719152305

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 4.00329788648877 & 3.93648291852419 & 4.07011285445336 \tabularnewline
74 & 4.03867118399632 & 3.94902471892985 & 4.1283176490628 \tabularnewline
75 & 4.05662932358499 & 3.9480854794548 & 4.16517316771517 \tabularnewline
76 & 4.08221441507228 & 3.95660646550514 & 4.20782236463943 \tabularnewline
77 & 4.10060152418589 & 3.95935695784649 & 4.24184609052528 \tabularnewline
78 & 4.12379265877942 & 3.96761954582187 & 4.27996577173698 \tabularnewline
79 & 4.1401058024406 & 3.96984629302767 & 4.31036531185352 \tabularnewline
80 & 4.15113930065952 & 3.96745713829760 & 4.33482146302144 \tabularnewline
81 & 4.16173200979754 & 3.96501009480972 & 4.35845392478536 \tabularnewline
82 & 4.16215333036473 & 3.95313680895044 & 4.37116985177901 \tabularnewline
83 & 4.15613418551383 & 3.9353865146638 & 4.37688185636385 \tabularnewline
84 & 4.15929595911847 & -0.521679996993567 & 8.8402719152305 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41971&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]4.00329788648877[/C][C]3.93648291852419[/C][C]4.07011285445336[/C][/ROW]
[ROW][C]74[/C][C]4.03867118399632[/C][C]3.94902471892985[/C][C]4.1283176490628[/C][/ROW]
[ROW][C]75[/C][C]4.05662932358499[/C][C]3.9480854794548[/C][C]4.16517316771517[/C][/ROW]
[ROW][C]76[/C][C]4.08221441507228[/C][C]3.95660646550514[/C][C]4.20782236463943[/C][/ROW]
[ROW][C]77[/C][C]4.10060152418589[/C][C]3.95935695784649[/C][C]4.24184609052528[/C][/ROW]
[ROW][C]78[/C][C]4.12379265877942[/C][C]3.96761954582187[/C][C]4.27996577173698[/C][/ROW]
[ROW][C]79[/C][C]4.1401058024406[/C][C]3.96984629302767[/C][C]4.31036531185352[/C][/ROW]
[ROW][C]80[/C][C]4.15113930065952[/C][C]3.96745713829760[/C][C]4.33482146302144[/C][/ROW]
[ROW][C]81[/C][C]4.16173200979754[/C][C]3.96501009480972[/C][C]4.35845392478536[/C][/ROW]
[ROW][C]82[/C][C]4.16215333036473[/C][C]3.95313680895044[/C][C]4.37116985177901[/C][/ROW]
[ROW][C]83[/C][C]4.15613418551383[/C][C]3.9353865146638[/C][C]4.37688185636385[/C][/ROW]
[ROW][C]84[/C][C]4.15929595911847[/C][C]-0.521679996993567[/C][C]8.8402719152305[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41971&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41971&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
734.003297886488773.936482918524194.07011285445336
744.038671183996323.949024718929854.1283176490628
754.056629323584993.94808547945484.16517316771517
764.082214415072283.956606465505144.20782236463943
774.100601524185893.959356957846494.24184609052528
784.123792658779423.967619545821874.27996577173698
794.14010580244063.969846293027674.31036531185352
804.151139300659523.967457138297604.33482146302144
814.161732009797543.965010094809724.35845392478536
824.162153330364733.953136808950444.37116985177901
834.156134185513833.93538651466384.37688185636385
844.15929595911847-0.5216799969935678.8402719152305



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