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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 19 Dec 2011 13:48:11 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/19/t1324320623pamyn1fqndmn06g.htm/, Retrieved Fri, 31 May 2024 17:24:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157617, Retrieved Fri, 31 May 2024 17:24:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact126

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [voorspellen van t...] [2011-12-19 18:48:11] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2,12
2,13
2,16
2,25
2,26
2,39
2,36
2,26
2,26
2,27
2,29
2,21
2,17
2,17
2,08
2,12
2,18
2,13
2,21
2,06
1,91
1,99
2,04
2,02
2,01
2,1
2,01
2,07
2,05
2,1
2,15
2,15
1,96
2,06
2,07
2,05
2,08
2,14
2,16
2,35
2,31
2,2
2,3
2,22
2,14
2,17
2,12
2,1
2,17
2,29
2,17
2,25
2,13
2,23
2,17
2,24
2,13
2,16
2,1
2,05
2,03
2,24
2,17
2,13
2,21
2,18
2,21
2,23
2,09
2,16
2,13
2,12

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157617&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157617&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157617&T=0

As an alternative you can also use a QR Code:  
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'Herman Ole Andreas Wold' @ wold.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.655548240819451
beta0.0217664010476567
gamma0.673154673002191

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.655548240819451 \tabularnewline
beta & 0.0217664010476567 \tabularnewline
gamma & 0.673154673002191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157617&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]0.655548240819451[/C][/ROW]
[ROW][C]beta[/C][C]0.0217664010476567[/C][/ROW]
[ROW][C]gamma[/C][C]0.673154673002191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157617&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157617&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.655548240819451
beta0.0217664010476567
gamma0.673154673002191






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132.172.23286324786325-0.0628632478632474
142.172.19060193638328-0.0206019363832843
152.082.09408431912809-0.0140843191280933
162.122.134971679626-0.0149716796259973
172.182.19089703605644-0.010897036056444
182.132.13558802891069-0.00558802891068622
192.212.194512930222620.0154870697773797
202.062.08455789258925-0.0245578925892507
211.912.05341770223942-0.14341770223942
221.991.959396089534350.0306039104656453
232.041.989890723833830.0501092761661737
242.021.939303738520790.0806962614792064
252.011.938260055275930.0717399447240687
262.11.994243885471810.105756114528186
272.011.984081449675080.0259185503249166
282.072.053567815229430.01643218477057
292.052.13405374995918-0.0840537499591831
302.12.034003161250970.0659968387490339
312.152.147748682128530.00225131787147381
322.152.022649529691580.127350470308421
331.962.06851798329439-0.108517983294385
342.062.043208399041070.0167916009589342
352.072.07445731463281-0.00445731463280952
362.051.999699094071270.0503009059287285
372.081.980726999029250.0992730009707539
382.142.067114153878920.0728858461210802
392.162.020889539199740.139110460800264
402.352.167991941254110.18200805874589
412.312.34169671004787-0.0316967100478656
422.22.31948335777815-0.119483357778149
432.32.30293297327076-0.00293297327076303
442.222.209443889131860.0105561108681429
452.142.128392786820050.0116072131799463
462.172.21693600517702-0.0469360051770216
472.122.2066215991408-0.0866215991407979
482.12.094665251104370.00533474889563434
492.172.060896951912570.10910304808743
502.292.15107622468680.1389237753132
512.172.167906823686620.00209317631337758
522.252.237588042516920.0124119574830823
532.132.25059647379867-0.120596473798669
542.232.148515169983840.081484830016155
552.172.29236634676109-0.122366346761093
562.242.123639205352880.116360794647122
572.132.113630190894220.0163698091057789
582.162.19322739720009-0.0332273972000876
592.12.18439963306795-0.0843996330679526
602.052.09695531054366-0.0469553105436584
612.032.05395648043144-0.0239564804314387
622.242.062912149778120.177087850221883
632.172.072667709479740.0973322905202592
642.132.20816771592389-0.0781677159238892
652.212.130656098794720.0793439012052808
662.182.20905461373201-0.0290546137320109
672.212.23415054641911-0.0241505464191061
682.232.187539057765860.0424609422341389
692.092.10722277233578-0.0172227723357832
702.162.154141509077820.0058584909221806
712.132.160472030872-0.0304720308719979
722.122.119232403151920.00076759684808092

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2.17 & 2.23286324786325 & -0.0628632478632474 \tabularnewline
14 & 2.17 & 2.19060193638328 & -0.0206019363832843 \tabularnewline
15 & 2.08 & 2.09408431912809 & -0.0140843191280933 \tabularnewline
16 & 2.12 & 2.134971679626 & -0.0149716796259973 \tabularnewline
17 & 2.18 & 2.19089703605644 & -0.010897036056444 \tabularnewline
18 & 2.13 & 2.13558802891069 & -0.00558802891068622 \tabularnewline
19 & 2.21 & 2.19451293022262 & 0.0154870697773797 \tabularnewline
20 & 2.06 & 2.08455789258925 & -0.0245578925892507 \tabularnewline
21 & 1.91 & 2.05341770223942 & -0.14341770223942 \tabularnewline
22 & 1.99 & 1.95939608953435 & 0.0306039104656453 \tabularnewline
23 & 2.04 & 1.98989072383383 & 0.0501092761661737 \tabularnewline
24 & 2.02 & 1.93930373852079 & 0.0806962614792064 \tabularnewline
25 & 2.01 & 1.93826005527593 & 0.0717399447240687 \tabularnewline
26 & 2.1 & 1.99424388547181 & 0.105756114528186 \tabularnewline
27 & 2.01 & 1.98408144967508 & 0.0259185503249166 \tabularnewline
28 & 2.07 & 2.05356781522943 & 0.01643218477057 \tabularnewline
29 & 2.05 & 2.13405374995918 & -0.0840537499591831 \tabularnewline
30 & 2.1 & 2.03400316125097 & 0.0659968387490339 \tabularnewline
31 & 2.15 & 2.14774868212853 & 0.00225131787147381 \tabularnewline
32 & 2.15 & 2.02264952969158 & 0.127350470308421 \tabularnewline
33 & 1.96 & 2.06851798329439 & -0.108517983294385 \tabularnewline
34 & 2.06 & 2.04320839904107 & 0.0167916009589342 \tabularnewline
35 & 2.07 & 2.07445731463281 & -0.00445731463280952 \tabularnewline
36 & 2.05 & 1.99969909407127 & 0.0503009059287285 \tabularnewline
37 & 2.08 & 1.98072699902925 & 0.0992730009707539 \tabularnewline
38 & 2.14 & 2.06711415387892 & 0.0728858461210802 \tabularnewline
39 & 2.16 & 2.02088953919974 & 0.139110460800264 \tabularnewline
40 & 2.35 & 2.16799194125411 & 0.18200805874589 \tabularnewline
41 & 2.31 & 2.34169671004787 & -0.0316967100478656 \tabularnewline
42 & 2.2 & 2.31948335777815 & -0.119483357778149 \tabularnewline
43 & 2.3 & 2.30293297327076 & -0.00293297327076303 \tabularnewline
44 & 2.22 & 2.20944388913186 & 0.0105561108681429 \tabularnewline
45 & 2.14 & 2.12839278682005 & 0.0116072131799463 \tabularnewline
46 & 2.17 & 2.21693600517702 & -0.0469360051770216 \tabularnewline
47 & 2.12 & 2.2066215991408 & -0.0866215991407979 \tabularnewline
48 & 2.1 & 2.09466525110437 & 0.00533474889563434 \tabularnewline
49 & 2.17 & 2.06089695191257 & 0.10910304808743 \tabularnewline
50 & 2.29 & 2.1510762246868 & 0.1389237753132 \tabularnewline
51 & 2.17 & 2.16790682368662 & 0.00209317631337758 \tabularnewline
52 & 2.25 & 2.23758804251692 & 0.0124119574830823 \tabularnewline
53 & 2.13 & 2.25059647379867 & -0.120596473798669 \tabularnewline
54 & 2.23 & 2.14851516998384 & 0.081484830016155 \tabularnewline
55 & 2.17 & 2.29236634676109 & -0.122366346761093 \tabularnewline
56 & 2.24 & 2.12363920535288 & 0.116360794647122 \tabularnewline
57 & 2.13 & 2.11363019089422 & 0.0163698091057789 \tabularnewline
58 & 2.16 & 2.19322739720009 & -0.0332273972000876 \tabularnewline
59 & 2.1 & 2.18439963306795 & -0.0843996330679526 \tabularnewline
60 & 2.05 & 2.09695531054366 & -0.0469553105436584 \tabularnewline
61 & 2.03 & 2.05395648043144 & -0.0239564804314387 \tabularnewline
62 & 2.24 & 2.06291214977812 & 0.177087850221883 \tabularnewline
63 & 2.17 & 2.07266770947974 & 0.0973322905202592 \tabularnewline
64 & 2.13 & 2.20816771592389 & -0.0781677159238892 \tabularnewline
65 & 2.21 & 2.13065609879472 & 0.0793439012052808 \tabularnewline
66 & 2.18 & 2.20905461373201 & -0.0290546137320109 \tabularnewline
67 & 2.21 & 2.23415054641911 & -0.0241505464191061 \tabularnewline
68 & 2.23 & 2.18753905776586 & 0.0424609422341389 \tabularnewline
69 & 2.09 & 2.10722277233578 & -0.0172227723357832 \tabularnewline
70 & 2.16 & 2.15414150907782 & 0.0058584909221806 \tabularnewline
71 & 2.13 & 2.160472030872 & -0.0304720308719979 \tabularnewline
72 & 2.12 & 2.11923240315192 & 0.00076759684808092 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157617&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]2.17[/C][C]2.23286324786325[/C][C]-0.0628632478632474[/C][/ROW]
[ROW][C]14[/C][C]2.17[/C][C]2.19060193638328[/C][C]-0.0206019363832843[/C][/ROW]
[ROW][C]15[/C][C]2.08[/C][C]2.09408431912809[/C][C]-0.0140843191280933[/C][/ROW]
[ROW][C]16[/C][C]2.12[/C][C]2.134971679626[/C][C]-0.0149716796259973[/C][/ROW]
[ROW][C]17[/C][C]2.18[/C][C]2.19089703605644[/C][C]-0.010897036056444[/C][/ROW]
[ROW][C]18[/C][C]2.13[/C][C]2.13558802891069[/C][C]-0.00558802891068622[/C][/ROW]
[ROW][C]19[/C][C]2.21[/C][C]2.19451293022262[/C][C]0.0154870697773797[/C][/ROW]
[ROW][C]20[/C][C]2.06[/C][C]2.08455789258925[/C][C]-0.0245578925892507[/C][/ROW]
[ROW][C]21[/C][C]1.91[/C][C]2.05341770223942[/C][C]-0.14341770223942[/C][/ROW]
[ROW][C]22[/C][C]1.99[/C][C]1.95939608953435[/C][C]0.0306039104656453[/C][/ROW]
[ROW][C]23[/C][C]2.04[/C][C]1.98989072383383[/C][C]0.0501092761661737[/C][/ROW]
[ROW][C]24[/C][C]2.02[/C][C]1.93930373852079[/C][C]0.0806962614792064[/C][/ROW]
[ROW][C]25[/C][C]2.01[/C][C]1.93826005527593[/C][C]0.0717399447240687[/C][/ROW]
[ROW][C]26[/C][C]2.1[/C][C]1.99424388547181[/C][C]0.105756114528186[/C][/ROW]
[ROW][C]27[/C][C]2.01[/C][C]1.98408144967508[/C][C]0.0259185503249166[/C][/ROW]
[ROW][C]28[/C][C]2.07[/C][C]2.05356781522943[/C][C]0.01643218477057[/C][/ROW]
[ROW][C]29[/C][C]2.05[/C][C]2.13405374995918[/C][C]-0.0840537499591831[/C][/ROW]
[ROW][C]30[/C][C]2.1[/C][C]2.03400316125097[/C][C]0.0659968387490339[/C][/ROW]
[ROW][C]31[/C][C]2.15[/C][C]2.14774868212853[/C][C]0.00225131787147381[/C][/ROW]
[ROW][C]32[/C][C]2.15[/C][C]2.02264952969158[/C][C]0.127350470308421[/C][/ROW]
[ROW][C]33[/C][C]1.96[/C][C]2.06851798329439[/C][C]-0.108517983294385[/C][/ROW]
[ROW][C]34[/C][C]2.06[/C][C]2.04320839904107[/C][C]0.0167916009589342[/C][/ROW]
[ROW][C]35[/C][C]2.07[/C][C]2.07445731463281[/C][C]-0.00445731463280952[/C][/ROW]
[ROW][C]36[/C][C]2.05[/C][C]1.99969909407127[/C][C]0.0503009059287285[/C][/ROW]
[ROW][C]37[/C][C]2.08[/C][C]1.98072699902925[/C][C]0.0992730009707539[/C][/ROW]
[ROW][C]38[/C][C]2.14[/C][C]2.06711415387892[/C][C]0.0728858461210802[/C][/ROW]
[ROW][C]39[/C][C]2.16[/C][C]2.02088953919974[/C][C]0.139110460800264[/C][/ROW]
[ROW][C]40[/C][C]2.35[/C][C]2.16799194125411[/C][C]0.18200805874589[/C][/ROW]
[ROW][C]41[/C][C]2.31[/C][C]2.34169671004787[/C][C]-0.0316967100478656[/C][/ROW]
[ROW][C]42[/C][C]2.2[/C][C]2.31948335777815[/C][C]-0.119483357778149[/C][/ROW]
[ROW][C]43[/C][C]2.3[/C][C]2.30293297327076[/C][C]-0.00293297327076303[/C][/ROW]
[ROW][C]44[/C][C]2.22[/C][C]2.20944388913186[/C][C]0.0105561108681429[/C][/ROW]
[ROW][C]45[/C][C]2.14[/C][C]2.12839278682005[/C][C]0.0116072131799463[/C][/ROW]
[ROW][C]46[/C][C]2.17[/C][C]2.21693600517702[/C][C]-0.0469360051770216[/C][/ROW]
[ROW][C]47[/C][C]2.12[/C][C]2.2066215991408[/C][C]-0.0866215991407979[/C][/ROW]
[ROW][C]48[/C][C]2.1[/C][C]2.09466525110437[/C][C]0.00533474889563434[/C][/ROW]
[ROW][C]49[/C][C]2.17[/C][C]2.06089695191257[/C][C]0.10910304808743[/C][/ROW]
[ROW][C]50[/C][C]2.29[/C][C]2.1510762246868[/C][C]0.1389237753132[/C][/ROW]
[ROW][C]51[/C][C]2.17[/C][C]2.16790682368662[/C][C]0.00209317631337758[/C][/ROW]
[ROW][C]52[/C][C]2.25[/C][C]2.23758804251692[/C][C]0.0124119574830823[/C][/ROW]
[ROW][C]53[/C][C]2.13[/C][C]2.25059647379867[/C][C]-0.120596473798669[/C][/ROW]
[ROW][C]54[/C][C]2.23[/C][C]2.14851516998384[/C][C]0.081484830016155[/C][/ROW]
[ROW][C]55[/C][C]2.17[/C][C]2.29236634676109[/C][C]-0.122366346761093[/C][/ROW]
[ROW][C]56[/C][C]2.24[/C][C]2.12363920535288[/C][C]0.116360794647122[/C][/ROW]
[ROW][C]57[/C][C]2.13[/C][C]2.11363019089422[/C][C]0.0163698091057789[/C][/ROW]
[ROW][C]58[/C][C]2.16[/C][C]2.19322739720009[/C][C]-0.0332273972000876[/C][/ROW]
[ROW][C]59[/C][C]2.1[/C][C]2.18439963306795[/C][C]-0.0843996330679526[/C][/ROW]
[ROW][C]60[/C][C]2.05[/C][C]2.09695531054366[/C][C]-0.0469553105436584[/C][/ROW]
[ROW][C]61[/C][C]2.03[/C][C]2.05395648043144[/C][C]-0.0239564804314387[/C][/ROW]
[ROW][C]62[/C][C]2.24[/C][C]2.06291214977812[/C][C]0.177087850221883[/C][/ROW]
[ROW][C]63[/C][C]2.17[/C][C]2.07266770947974[/C][C]0.0973322905202592[/C][/ROW]
[ROW][C]64[/C][C]2.13[/C][C]2.20816771592389[/C][C]-0.0781677159238892[/C][/ROW]
[ROW][C]65[/C][C]2.21[/C][C]2.13065609879472[/C][C]0.0793439012052808[/C][/ROW]
[ROW][C]66[/C][C]2.18[/C][C]2.20905461373201[/C][C]-0.0290546137320109[/C][/ROW]
[ROW][C]67[/C][C]2.21[/C][C]2.23415054641911[/C][C]-0.0241505464191061[/C][/ROW]
[ROW][C]68[/C][C]2.23[/C][C]2.18753905776586[/C][C]0.0424609422341389[/C][/ROW]
[ROW][C]69[/C][C]2.09[/C][C]2.10722277233578[/C][C]-0.0172227723357832[/C][/ROW]
[ROW][C]70[/C][C]2.16[/C][C]2.15414150907782[/C][C]0.0058584909221806[/C][/ROW]
[ROW][C]71[/C][C]2.13[/C][C]2.160472030872[/C][C]-0.0304720308719979[/C][/ROW]
[ROW][C]72[/C][C]2.12[/C][C]2.11923240315192[/C][C]0.00076759684808092[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157617&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157617&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132.172.23286324786325-0.0628632478632474
142.172.19060193638328-0.0206019363832843
152.082.09408431912809-0.0140843191280933
162.122.134971679626-0.0149716796259973
172.182.19089703605644-0.010897036056444
182.132.13558802891069-0.00558802891068622
192.212.194512930222620.0154870697773797
202.062.08455789258925-0.0245578925892507
211.912.05341770223942-0.14341770223942
221.991.959396089534350.0306039104656453
232.041.989890723833830.0501092761661737
242.021.939303738520790.0806962614792064
252.011.938260055275930.0717399447240687
262.11.994243885471810.105756114528186
272.011.984081449675080.0259185503249166
282.072.053567815229430.01643218477057
292.052.13405374995918-0.0840537499591831
302.12.034003161250970.0659968387490339
312.152.147748682128530.00225131787147381
322.152.022649529691580.127350470308421
331.962.06851798329439-0.108517983294385
342.062.043208399041070.0167916009589342
352.072.07445731463281-0.00445731463280952
362.051.999699094071270.0503009059287285
372.081.980726999029250.0992730009707539
382.142.067114153878920.0728858461210802
392.162.020889539199740.139110460800264
402.352.167991941254110.18200805874589
412.312.34169671004787-0.0316967100478656
422.22.31948335777815-0.119483357778149
432.32.30293297327076-0.00293297327076303
442.222.209443889131860.0105561108681429
452.142.128392786820050.0116072131799463
462.172.21693600517702-0.0469360051770216
472.122.2066215991408-0.0866215991407979
482.12.094665251104370.00533474889563434
492.172.060896951912570.10910304808743
502.292.15107622468680.1389237753132
512.172.167906823686620.00209317631337758
522.252.237588042516920.0124119574830823
532.132.25059647379867-0.120596473798669
542.232.148515169983840.081484830016155
552.172.29236634676109-0.122366346761093
562.242.123639205352880.116360794647122
572.132.113630190894220.0163698091057789
582.162.19322739720009-0.0332273972000876
592.12.18439963306795-0.0843996330679526
602.052.09695531054366-0.0469553105436584
612.032.05395648043144-0.0239564804314387
622.242.062912149778120.177087850221883
632.172.072667709479740.0973322905202592
642.132.20816771592389-0.0781677159238892
652.212.130656098794720.0793439012052808
662.182.20905461373201-0.0290546137320109
672.212.23415054641911-0.0241505464191061
682.232.187539057765860.0424609422341389
692.092.10722277233578-0.0172227723357832
702.162.154141509077820.0058584909221806
712.132.160472030872-0.0304720308719979
722.122.119232403151920.00076759684808092






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
732.115702279333041.968811095726562.26259346293951
742.190171736426562.013373381104962.36697009174816
752.066011095978851.862651468673162.26937072328454
762.096289492960451.868521530329172.32405745559172
772.106935532022751.856264901406152.35760616263936
782.107446688191451.8349829565962.37991041978689
792.152401687732081.858992091767332.44581128369682
802.13708707287951.823395075498322.45077907026069
812.014510763212141.681065556401862.34795597002242
822.077731438681361.724960851139142.43050202622358
832.071373653621011.699626965739572.44312034150246
842.057364375881061.666928683670412.4478000680917

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 2.11570227933304 & 1.96881109572656 & 2.26259346293951 \tabularnewline
74 & 2.19017173642656 & 2.01337338110496 & 2.36697009174816 \tabularnewline
75 & 2.06601109597885 & 1.86265146867316 & 2.26937072328454 \tabularnewline
76 & 2.09628949296045 & 1.86852153032917 & 2.32405745559172 \tabularnewline
77 & 2.10693553202275 & 1.85626490140615 & 2.35760616263936 \tabularnewline
78 & 2.10744668819145 & 1.834982956596 & 2.37991041978689 \tabularnewline
79 & 2.15240168773208 & 1.85899209176733 & 2.44581128369682 \tabularnewline
80 & 2.1370870728795 & 1.82339507549832 & 2.45077907026069 \tabularnewline
81 & 2.01451076321214 & 1.68106555640186 & 2.34795597002242 \tabularnewline
82 & 2.07773143868136 & 1.72496085113914 & 2.43050202622358 \tabularnewline
83 & 2.07137365362101 & 1.69962696573957 & 2.44312034150246 \tabularnewline
84 & 2.05736437588106 & 1.66692868367041 & 2.4478000680917 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157617&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]2.11570227933304[/C][C]1.96881109572656[/C][C]2.26259346293951[/C][/ROW]
[ROW][C]74[/C][C]2.19017173642656[/C][C]2.01337338110496[/C][C]2.36697009174816[/C][/ROW]
[ROW][C]75[/C][C]2.06601109597885[/C][C]1.86265146867316[/C][C]2.26937072328454[/C][/ROW]
[ROW][C]76[/C][C]2.09628949296045[/C][C]1.86852153032917[/C][C]2.32405745559172[/C][/ROW]
[ROW][C]77[/C][C]2.10693553202275[/C][C]1.85626490140615[/C][C]2.35760616263936[/C][/ROW]
[ROW][C]78[/C][C]2.10744668819145[/C][C]1.834982956596[/C][C]2.37991041978689[/C][/ROW]
[ROW][C]79[/C][C]2.15240168773208[/C][C]1.85899209176733[/C][C]2.44581128369682[/C][/ROW]
[ROW][C]80[/C][C]2.1370870728795[/C][C]1.82339507549832[/C][C]2.45077907026069[/C][/ROW]
[ROW][C]81[/C][C]2.01451076321214[/C][C]1.68106555640186[/C][C]2.34795597002242[/C][/ROW]
[ROW][C]82[/C][C]2.07773143868136[/C][C]1.72496085113914[/C][C]2.43050202622358[/C][/ROW]
[ROW][C]83[/C][C]2.07137365362101[/C][C]1.69962696573957[/C][C]2.44312034150246[/C][/ROW]
[ROW][C]84[/C][C]2.05736437588106[/C][C]1.66692868367041[/C][C]2.4478000680917[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157617&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157617&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
732.115702279333041.968811095726562.26259346293951
742.190171736426562.013373381104962.36697009174816
752.066011095978851.862651468673162.26937072328454
762.096289492960451.868521530329172.32405745559172
772.106935532022751.856264901406152.35760616263936
782.107446688191451.8349829565962.37991041978689
792.152401687732081.858992091767332.44581128369682
802.13708707287951.823395075498322.45077907026069
812.014510763212141.681065556401862.34795597002242
822.077731438681361.724960851139142.43050202622358
832.071373653621011.699626965739572.44312034150246
842.057364375881061.666928683670412.4478000680917


Figures (Output of Computation)

Input Parameters & R Code

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')