Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 18 Aug 2013 08:22:49 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Aug/18/t13768285930eh0lcxdqqvpcfu.htm/, Retrieved Mon, 06 May 2024 05:35:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211181, Retrieved Mon, 06 May 2024 05:35:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsDe Laere Dieter
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 2 - Sta...] [2013-08-18 12:22:49] [bc2cf5f41ec5ca561b7a550898b8dd0d] [Current]
Feedback Forum

Post a new message
Dataseries X:
4640
4880
4400
4120
4440
4640
4680
4360
4640
4840
5000
4800
4720
4840
3800
4280
4480
4880
4680
4480
4720
5000
4960
4920
4480
5320
3960
4440
4360
4840
4880
4880
4400
4800
5280
4720
4440
5200
4240
4520
4640
5040
4840
4760
4520
4680
5480
4680
4160
5360
4200
4520
4600
4880
4840
4600
4520
4600
5760
4640
4520
5400
4200
4600
4480
4680
4400
4480
4840
4680
5480
4680
4440
5280
4240
4600
4640
4920
4560
4400
5080
4640
5520
4600
4720
5480
4320
4640
4920
4840
4520
4440
5000
4840
5480
4320
4880
5440
4480
4600
4720
5000
4160
4720
5000
4480
5720
4600




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211181&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211181&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211181&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0
beta0
gamma0.80806834048429

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.80806834048429 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211181&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[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.80806834048429[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211181&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211181&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
beta0
gamma0.80806834048429







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1347204711.772891829618.22710817039388
1448404829.534398891610.4656011084016
1538003787.4607237746612.5392762253391
1642804259.4931112155720.5068887844254
1744804456.6806285682123.3193714317913
1848804854.3255194597425.6744805402577
1946804676.931908624173.06809137582968
2044804358.45272841655121.547271583454
2147204668.3361014558851.6638985441223
2250004892.27968712124107.720312878756
2349605048.15935542855-88.1593554285528
2449204837.1309872902582.8690127097498
2544804756.02459249678-276.02459249678
2653204876.52228587637443.477714123627
2739603827.8182336261132.181766373897
2844404310.07457190114129.925428098856
2943604511.09763394187-151.097633941875
3048404913.79574103269-73.7957410326944
3148804716.5558677243163.444132275703
3248804492.02448743012387.975512569876
3344004747.42287398061-347.422873980612
3448005018.77220017128-218.77220017128
3552805016.32264860841263.677351391585
3647204942.89473341105-222.894733411048
3744404568.8179681842-128.817968184196
3852005276.2450720647-76.2450720646993
3942403965.69845168438274.301548315618
4045204449.9021478711970.0978521288098
4146404423.61095189645216.389048103547
4250404892.41729186435147.582708135651
4348404886.81476294397-46.8147629439745
4447604843.35587391559-83.3558739155851
4545204501.81220964718.1877903529994
4646804880.04695098891-200.046950988907
4754805270.46765679443209.532343205574
4846804800.16664603541-120.166646035411
4941604499.74779288837-339.747792888367
5053605255.51333512206104.486664877935
5142004220.15766452533-20.157664525329
5245204541.82842704324-21.828427043235
5346004634.44671332973-34.446713329733
5448805050.86022225685-170.860222256847
5548404886.87450715147-46.8745071514695
5646004813.29331180815-213.29331180815
5745204551.75463880728-31.7546388072842
5846004755.1923231192-155.192323119198
5957605482.17937544255277.820624557449
6046404739.69358826514-99.693588265136
6145204258.09504116285261.904958837154
6254005381.4819417505718.5180582494322
6342004236.54709138545-36.5470913854515
6446004559.3349658580140.6650341419927
6544804642.37394338113-162.373943381134
6646804950.90834117053-270.908341170526
6744004886.59229699321-486.592296993213
6844804676.89696294189-196.896962941887
6948404561.1414805172278.858519482802
7046804665.6128739766214.3871260233791
7154805750.80880010818-270.808800108182
7246804695.14157387731-15.1415738773112
7344404504.2533737887-64.2533737887006
7452805438.09753559092-158.097535590925
7542404239.464944824570.535055175434536
7646004627.59379274401-27.5937927440109
7746404545.9164585148294.0835414851781
7849204768.42543243688151.57456756312
7945604527.962931170132.0370688299026
8044004552.52666579586-152.526665795863
8150804823.25641716732256.743582832682
8246404713.15448154274-73.1544815427378
8355205574.42885181507-54.4288518150743
8446004718.81953149276-118.819531492759
8547204486.45555313857233.544446861431
8654805351.01716301665128.98283698335
8743204272.3510163456347.6489836543733
8846404640.52425701398-0.524257013978968
8949204657.27533643806262.724663561942
9048404928.27332230651-88.2733223065079
9145204588.61918922428-68.619189224275
9244404463.07018507818-23.0701850781779
9350005069.08294188473-69.0829418847334
9448404689.50602031305150.49397968695
9554805572.56374251465-92.5637425146479
9643204657.98788066913-337.98788066913
9748804710.73409778832169.265902211679
9854405496.70958281915-56.7095828191541
9944804343.60084387887136.399156121134
10046004675.32554010713-75.3255401071337
10147204906.51840008112-186.518400081119
10250004893.76690797946106.233092020543
10341604567.51817303745-407.518173037452
10447204478.08222382336241.917776176642
10550005051.19692268555-51.1969226855526
10644804847.50049639706-367.500496397058
10757205539.31771759051180.682282409493
10846004417.99031971424182.009680285758

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4720 & 4711.77289182961 & 8.22710817039388 \tabularnewline
14 & 4840 & 4829.5343988916 & 10.4656011084016 \tabularnewline
15 & 3800 & 3787.46072377466 & 12.5392762253391 \tabularnewline
16 & 4280 & 4259.49311121557 & 20.5068887844254 \tabularnewline
17 & 4480 & 4456.68062856821 & 23.3193714317913 \tabularnewline
18 & 4880 & 4854.32551945974 & 25.6744805402577 \tabularnewline
19 & 4680 & 4676.93190862417 & 3.06809137582968 \tabularnewline
20 & 4480 & 4358.45272841655 & 121.547271583454 \tabularnewline
21 & 4720 & 4668.33610145588 & 51.6638985441223 \tabularnewline
22 & 5000 & 4892.27968712124 & 107.720312878756 \tabularnewline
23 & 4960 & 5048.15935542855 & -88.1593554285528 \tabularnewline
24 & 4920 & 4837.13098729025 & 82.8690127097498 \tabularnewline
25 & 4480 & 4756.02459249678 & -276.02459249678 \tabularnewline
26 & 5320 & 4876.52228587637 & 443.477714123627 \tabularnewline
27 & 3960 & 3827.8182336261 & 132.181766373897 \tabularnewline
28 & 4440 & 4310.07457190114 & 129.925428098856 \tabularnewline
29 & 4360 & 4511.09763394187 & -151.097633941875 \tabularnewline
30 & 4840 & 4913.79574103269 & -73.7957410326944 \tabularnewline
31 & 4880 & 4716.5558677243 & 163.444132275703 \tabularnewline
32 & 4880 & 4492.02448743012 & 387.975512569876 \tabularnewline
33 & 4400 & 4747.42287398061 & -347.422873980612 \tabularnewline
34 & 4800 & 5018.77220017128 & -218.77220017128 \tabularnewline
35 & 5280 & 5016.32264860841 & 263.677351391585 \tabularnewline
36 & 4720 & 4942.89473341105 & -222.894733411048 \tabularnewline
37 & 4440 & 4568.8179681842 & -128.817968184196 \tabularnewline
38 & 5200 & 5276.2450720647 & -76.2450720646993 \tabularnewline
39 & 4240 & 3965.69845168438 & 274.301548315618 \tabularnewline
40 & 4520 & 4449.90214787119 & 70.0978521288098 \tabularnewline
41 & 4640 & 4423.61095189645 & 216.389048103547 \tabularnewline
42 & 5040 & 4892.41729186435 & 147.582708135651 \tabularnewline
43 & 4840 & 4886.81476294397 & -46.8147629439745 \tabularnewline
44 & 4760 & 4843.35587391559 & -83.3558739155851 \tabularnewline
45 & 4520 & 4501.812209647 & 18.1877903529994 \tabularnewline
46 & 4680 & 4880.04695098891 & -200.046950988907 \tabularnewline
47 & 5480 & 5270.46765679443 & 209.532343205574 \tabularnewline
48 & 4680 & 4800.16664603541 & -120.166646035411 \tabularnewline
49 & 4160 & 4499.74779288837 & -339.747792888367 \tabularnewline
50 & 5360 & 5255.51333512206 & 104.486664877935 \tabularnewline
51 & 4200 & 4220.15766452533 & -20.157664525329 \tabularnewline
52 & 4520 & 4541.82842704324 & -21.828427043235 \tabularnewline
53 & 4600 & 4634.44671332973 & -34.446713329733 \tabularnewline
54 & 4880 & 5050.86022225685 & -170.860222256847 \tabularnewline
55 & 4840 & 4886.87450715147 & -46.8745071514695 \tabularnewline
56 & 4600 & 4813.29331180815 & -213.29331180815 \tabularnewline
57 & 4520 & 4551.75463880728 & -31.7546388072842 \tabularnewline
58 & 4600 & 4755.1923231192 & -155.192323119198 \tabularnewline
59 & 5760 & 5482.17937544255 & 277.820624557449 \tabularnewline
60 & 4640 & 4739.69358826514 & -99.693588265136 \tabularnewline
61 & 4520 & 4258.09504116285 & 261.904958837154 \tabularnewline
62 & 5400 & 5381.48194175057 & 18.5180582494322 \tabularnewline
63 & 4200 & 4236.54709138545 & -36.5470913854515 \tabularnewline
64 & 4600 & 4559.33496585801 & 40.6650341419927 \tabularnewline
65 & 4480 & 4642.37394338113 & -162.373943381134 \tabularnewline
66 & 4680 & 4950.90834117053 & -270.908341170526 \tabularnewline
67 & 4400 & 4886.59229699321 & -486.592296993213 \tabularnewline
68 & 4480 & 4676.89696294189 & -196.896962941887 \tabularnewline
69 & 4840 & 4561.1414805172 & 278.858519482802 \tabularnewline
70 & 4680 & 4665.61287397662 & 14.3871260233791 \tabularnewline
71 & 5480 & 5750.80880010818 & -270.808800108182 \tabularnewline
72 & 4680 & 4695.14157387731 & -15.1415738773112 \tabularnewline
73 & 4440 & 4504.2533737887 & -64.2533737887006 \tabularnewline
74 & 5280 & 5438.09753559092 & -158.097535590925 \tabularnewline
75 & 4240 & 4239.46494482457 & 0.535055175434536 \tabularnewline
76 & 4600 & 4627.59379274401 & -27.5937927440109 \tabularnewline
77 & 4640 & 4545.91645851482 & 94.0835414851781 \tabularnewline
78 & 4920 & 4768.42543243688 & 151.57456756312 \tabularnewline
79 & 4560 & 4527.9629311701 & 32.0370688299026 \tabularnewline
80 & 4400 & 4552.52666579586 & -152.526665795863 \tabularnewline
81 & 5080 & 4823.25641716732 & 256.743582832682 \tabularnewline
82 & 4640 & 4713.15448154274 & -73.1544815427378 \tabularnewline
83 & 5520 & 5574.42885181507 & -54.4288518150743 \tabularnewline
84 & 4600 & 4718.81953149276 & -118.819531492759 \tabularnewline
85 & 4720 & 4486.45555313857 & 233.544446861431 \tabularnewline
86 & 5480 & 5351.01716301665 & 128.98283698335 \tabularnewline
87 & 4320 & 4272.35101634563 & 47.6489836543733 \tabularnewline
88 & 4640 & 4640.52425701398 & -0.524257013978968 \tabularnewline
89 & 4920 & 4657.27533643806 & 262.724663561942 \tabularnewline
90 & 4840 & 4928.27332230651 & -88.2733223065079 \tabularnewline
91 & 4520 & 4588.61918922428 & -68.619189224275 \tabularnewline
92 & 4440 & 4463.07018507818 & -23.0701850781779 \tabularnewline
93 & 5000 & 5069.08294188473 & -69.0829418847334 \tabularnewline
94 & 4840 & 4689.50602031305 & 150.49397968695 \tabularnewline
95 & 5480 & 5572.56374251465 & -92.5637425146479 \tabularnewline
96 & 4320 & 4657.98788066913 & -337.98788066913 \tabularnewline
97 & 4880 & 4710.73409778832 & 169.265902211679 \tabularnewline
98 & 5440 & 5496.70958281915 & -56.7095828191541 \tabularnewline
99 & 4480 & 4343.60084387887 & 136.399156121134 \tabularnewline
100 & 4600 & 4675.32554010713 & -75.3255401071337 \tabularnewline
101 & 4720 & 4906.51840008112 & -186.518400081119 \tabularnewline
102 & 5000 & 4893.76690797946 & 106.233092020543 \tabularnewline
103 & 4160 & 4567.51817303745 & -407.518173037452 \tabularnewline
104 & 4720 & 4478.08222382336 & 241.917776176642 \tabularnewline
105 & 5000 & 5051.19692268555 & -51.1969226855526 \tabularnewline
106 & 4480 & 4847.50049639706 & -367.500496397058 \tabularnewline
107 & 5720 & 5539.31771759051 & 180.682282409493 \tabularnewline
108 & 4600 & 4417.99031971424 & 182.009680285758 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211181&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]4720[/C][C]4711.77289182961[/C][C]8.22710817039388[/C][/ROW]
[ROW][C]14[/C][C]4840[/C][C]4829.5343988916[/C][C]10.4656011084016[/C][/ROW]
[ROW][C]15[/C][C]3800[/C][C]3787.46072377466[/C][C]12.5392762253391[/C][/ROW]
[ROW][C]16[/C][C]4280[/C][C]4259.49311121557[/C][C]20.5068887844254[/C][/ROW]
[ROW][C]17[/C][C]4480[/C][C]4456.68062856821[/C][C]23.3193714317913[/C][/ROW]
[ROW][C]18[/C][C]4880[/C][C]4854.32551945974[/C][C]25.6744805402577[/C][/ROW]
[ROW][C]19[/C][C]4680[/C][C]4676.93190862417[/C][C]3.06809137582968[/C][/ROW]
[ROW][C]20[/C][C]4480[/C][C]4358.45272841655[/C][C]121.547271583454[/C][/ROW]
[ROW][C]21[/C][C]4720[/C][C]4668.33610145588[/C][C]51.6638985441223[/C][/ROW]
[ROW][C]22[/C][C]5000[/C][C]4892.27968712124[/C][C]107.720312878756[/C][/ROW]
[ROW][C]23[/C][C]4960[/C][C]5048.15935542855[/C][C]-88.1593554285528[/C][/ROW]
[ROW][C]24[/C][C]4920[/C][C]4837.13098729025[/C][C]82.8690127097498[/C][/ROW]
[ROW][C]25[/C][C]4480[/C][C]4756.02459249678[/C][C]-276.02459249678[/C][/ROW]
[ROW][C]26[/C][C]5320[/C][C]4876.52228587637[/C][C]443.477714123627[/C][/ROW]
[ROW][C]27[/C][C]3960[/C][C]3827.8182336261[/C][C]132.181766373897[/C][/ROW]
[ROW][C]28[/C][C]4440[/C][C]4310.07457190114[/C][C]129.925428098856[/C][/ROW]
[ROW][C]29[/C][C]4360[/C][C]4511.09763394187[/C][C]-151.097633941875[/C][/ROW]
[ROW][C]30[/C][C]4840[/C][C]4913.79574103269[/C][C]-73.7957410326944[/C][/ROW]
[ROW][C]31[/C][C]4880[/C][C]4716.5558677243[/C][C]163.444132275703[/C][/ROW]
[ROW][C]32[/C][C]4880[/C][C]4492.02448743012[/C][C]387.975512569876[/C][/ROW]
[ROW][C]33[/C][C]4400[/C][C]4747.42287398061[/C][C]-347.422873980612[/C][/ROW]
[ROW][C]34[/C][C]4800[/C][C]5018.77220017128[/C][C]-218.77220017128[/C][/ROW]
[ROW][C]35[/C][C]5280[/C][C]5016.32264860841[/C][C]263.677351391585[/C][/ROW]
[ROW][C]36[/C][C]4720[/C][C]4942.89473341105[/C][C]-222.894733411048[/C][/ROW]
[ROW][C]37[/C][C]4440[/C][C]4568.8179681842[/C][C]-128.817968184196[/C][/ROW]
[ROW][C]38[/C][C]5200[/C][C]5276.2450720647[/C][C]-76.2450720646993[/C][/ROW]
[ROW][C]39[/C][C]4240[/C][C]3965.69845168438[/C][C]274.301548315618[/C][/ROW]
[ROW][C]40[/C][C]4520[/C][C]4449.90214787119[/C][C]70.0978521288098[/C][/ROW]
[ROW][C]41[/C][C]4640[/C][C]4423.61095189645[/C][C]216.389048103547[/C][/ROW]
[ROW][C]42[/C][C]5040[/C][C]4892.41729186435[/C][C]147.582708135651[/C][/ROW]
[ROW][C]43[/C][C]4840[/C][C]4886.81476294397[/C][C]-46.8147629439745[/C][/ROW]
[ROW][C]44[/C][C]4760[/C][C]4843.35587391559[/C][C]-83.3558739155851[/C][/ROW]
[ROW][C]45[/C][C]4520[/C][C]4501.812209647[/C][C]18.1877903529994[/C][/ROW]
[ROW][C]46[/C][C]4680[/C][C]4880.04695098891[/C][C]-200.046950988907[/C][/ROW]
[ROW][C]47[/C][C]5480[/C][C]5270.46765679443[/C][C]209.532343205574[/C][/ROW]
[ROW][C]48[/C][C]4680[/C][C]4800.16664603541[/C][C]-120.166646035411[/C][/ROW]
[ROW][C]49[/C][C]4160[/C][C]4499.74779288837[/C][C]-339.747792888367[/C][/ROW]
[ROW][C]50[/C][C]5360[/C][C]5255.51333512206[/C][C]104.486664877935[/C][/ROW]
[ROW][C]51[/C][C]4200[/C][C]4220.15766452533[/C][C]-20.157664525329[/C][/ROW]
[ROW][C]52[/C][C]4520[/C][C]4541.82842704324[/C][C]-21.828427043235[/C][/ROW]
[ROW][C]53[/C][C]4600[/C][C]4634.44671332973[/C][C]-34.446713329733[/C][/ROW]
[ROW][C]54[/C][C]4880[/C][C]5050.86022225685[/C][C]-170.860222256847[/C][/ROW]
[ROW][C]55[/C][C]4840[/C][C]4886.87450715147[/C][C]-46.8745071514695[/C][/ROW]
[ROW][C]56[/C][C]4600[/C][C]4813.29331180815[/C][C]-213.29331180815[/C][/ROW]
[ROW][C]57[/C][C]4520[/C][C]4551.75463880728[/C][C]-31.7546388072842[/C][/ROW]
[ROW][C]58[/C][C]4600[/C][C]4755.1923231192[/C][C]-155.192323119198[/C][/ROW]
[ROW][C]59[/C][C]5760[/C][C]5482.17937544255[/C][C]277.820624557449[/C][/ROW]
[ROW][C]60[/C][C]4640[/C][C]4739.69358826514[/C][C]-99.693588265136[/C][/ROW]
[ROW][C]61[/C][C]4520[/C][C]4258.09504116285[/C][C]261.904958837154[/C][/ROW]
[ROW][C]62[/C][C]5400[/C][C]5381.48194175057[/C][C]18.5180582494322[/C][/ROW]
[ROW][C]63[/C][C]4200[/C][C]4236.54709138545[/C][C]-36.5470913854515[/C][/ROW]
[ROW][C]64[/C][C]4600[/C][C]4559.33496585801[/C][C]40.6650341419927[/C][/ROW]
[ROW][C]65[/C][C]4480[/C][C]4642.37394338113[/C][C]-162.373943381134[/C][/ROW]
[ROW][C]66[/C][C]4680[/C][C]4950.90834117053[/C][C]-270.908341170526[/C][/ROW]
[ROW][C]67[/C][C]4400[/C][C]4886.59229699321[/C][C]-486.592296993213[/C][/ROW]
[ROW][C]68[/C][C]4480[/C][C]4676.89696294189[/C][C]-196.896962941887[/C][/ROW]
[ROW][C]69[/C][C]4840[/C][C]4561.1414805172[/C][C]278.858519482802[/C][/ROW]
[ROW][C]70[/C][C]4680[/C][C]4665.61287397662[/C][C]14.3871260233791[/C][/ROW]
[ROW][C]71[/C][C]5480[/C][C]5750.80880010818[/C][C]-270.808800108182[/C][/ROW]
[ROW][C]72[/C][C]4680[/C][C]4695.14157387731[/C][C]-15.1415738773112[/C][/ROW]
[ROW][C]73[/C][C]4440[/C][C]4504.2533737887[/C][C]-64.2533737887006[/C][/ROW]
[ROW][C]74[/C][C]5280[/C][C]5438.09753559092[/C][C]-158.097535590925[/C][/ROW]
[ROW][C]75[/C][C]4240[/C][C]4239.46494482457[/C][C]0.535055175434536[/C][/ROW]
[ROW][C]76[/C][C]4600[/C][C]4627.59379274401[/C][C]-27.5937927440109[/C][/ROW]
[ROW][C]77[/C][C]4640[/C][C]4545.91645851482[/C][C]94.0835414851781[/C][/ROW]
[ROW][C]78[/C][C]4920[/C][C]4768.42543243688[/C][C]151.57456756312[/C][/ROW]
[ROW][C]79[/C][C]4560[/C][C]4527.9629311701[/C][C]32.0370688299026[/C][/ROW]
[ROW][C]80[/C][C]4400[/C][C]4552.52666579586[/C][C]-152.526665795863[/C][/ROW]
[ROW][C]81[/C][C]5080[/C][C]4823.25641716732[/C][C]256.743582832682[/C][/ROW]
[ROW][C]82[/C][C]4640[/C][C]4713.15448154274[/C][C]-73.1544815427378[/C][/ROW]
[ROW][C]83[/C][C]5520[/C][C]5574.42885181507[/C][C]-54.4288518150743[/C][/ROW]
[ROW][C]84[/C][C]4600[/C][C]4718.81953149276[/C][C]-118.819531492759[/C][/ROW]
[ROW][C]85[/C][C]4720[/C][C]4486.45555313857[/C][C]233.544446861431[/C][/ROW]
[ROW][C]86[/C][C]5480[/C][C]5351.01716301665[/C][C]128.98283698335[/C][/ROW]
[ROW][C]87[/C][C]4320[/C][C]4272.35101634563[/C][C]47.6489836543733[/C][/ROW]
[ROW][C]88[/C][C]4640[/C][C]4640.52425701398[/C][C]-0.524257013978968[/C][/ROW]
[ROW][C]89[/C][C]4920[/C][C]4657.27533643806[/C][C]262.724663561942[/C][/ROW]
[ROW][C]90[/C][C]4840[/C][C]4928.27332230651[/C][C]-88.2733223065079[/C][/ROW]
[ROW][C]91[/C][C]4520[/C][C]4588.61918922428[/C][C]-68.619189224275[/C][/ROW]
[ROW][C]92[/C][C]4440[/C][C]4463.07018507818[/C][C]-23.0701850781779[/C][/ROW]
[ROW][C]93[/C][C]5000[/C][C]5069.08294188473[/C][C]-69.0829418847334[/C][/ROW]
[ROW][C]94[/C][C]4840[/C][C]4689.50602031305[/C][C]150.49397968695[/C][/ROW]
[ROW][C]95[/C][C]5480[/C][C]5572.56374251465[/C][C]-92.5637425146479[/C][/ROW]
[ROW][C]96[/C][C]4320[/C][C]4657.98788066913[/C][C]-337.98788066913[/C][/ROW]
[ROW][C]97[/C][C]4880[/C][C]4710.73409778832[/C][C]169.265902211679[/C][/ROW]
[ROW][C]98[/C][C]5440[/C][C]5496.70958281915[/C][C]-56.7095828191541[/C][/ROW]
[ROW][C]99[/C][C]4480[/C][C]4343.60084387887[/C][C]136.399156121134[/C][/ROW]
[ROW][C]100[/C][C]4600[/C][C]4675.32554010713[/C][C]-75.3255401071337[/C][/ROW]
[ROW][C]101[/C][C]4720[/C][C]4906.51840008112[/C][C]-186.518400081119[/C][/ROW]
[ROW][C]102[/C][C]5000[/C][C]4893.76690797946[/C][C]106.233092020543[/C][/ROW]
[ROW][C]103[/C][C]4160[/C][C]4567.51817303745[/C][C]-407.518173037452[/C][/ROW]
[ROW][C]104[/C][C]4720[/C][C]4478.08222382336[/C][C]241.917776176642[/C][/ROW]
[ROW][C]105[/C][C]5000[/C][C]5051.19692268555[/C][C]-51.1969226855526[/C][/ROW]
[ROW][C]106[/C][C]4480[/C][C]4847.50049639706[/C][C]-367.500496397058[/C][/ROW]
[ROW][C]107[/C][C]5720[/C][C]5539.31771759051[/C][C]180.682282409493[/C][/ROW]
[ROW][C]108[/C][C]4600[/C][C]4417.99031971424[/C][C]182.009680285758[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211181&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211181&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
1347204711.772891829618.22710817039388
1448404829.534398891610.4656011084016
1538003787.4607237746612.5392762253391
1642804259.4931112155720.5068887844254
1744804456.6806285682123.3193714317913
1848804854.3255194597425.6744805402577
1946804676.931908624173.06809137582968
2044804358.45272841655121.547271583454
2147204668.3361014558851.6638985441223
2250004892.27968712124107.720312878756
2349605048.15935542855-88.1593554285528
2449204837.1309872902582.8690127097498
2544804756.02459249678-276.02459249678
2653204876.52228587637443.477714123627
2739603827.8182336261132.181766373897
2844404310.07457190114129.925428098856
2943604511.09763394187-151.097633941875
3048404913.79574103269-73.7957410326944
3148804716.5558677243163.444132275703
3248804492.02448743012387.975512569876
3344004747.42287398061-347.422873980612
3448005018.77220017128-218.77220017128
3552805016.32264860841263.677351391585
3647204942.89473341105-222.894733411048
3744404568.8179681842-128.817968184196
3852005276.2450720647-76.2450720646993
3942403965.69845168438274.301548315618
4045204449.9021478711970.0978521288098
4146404423.61095189645216.389048103547
4250404892.41729186435147.582708135651
4348404886.81476294397-46.8147629439745
4447604843.35587391559-83.3558739155851
4545204501.81220964718.1877903529994
4646804880.04695098891-200.046950988907
4754805270.46765679443209.532343205574
4846804800.16664603541-120.166646035411
4941604499.74779288837-339.747792888367
5053605255.51333512206104.486664877935
5142004220.15766452533-20.157664525329
5245204541.82842704324-21.828427043235
5346004634.44671332973-34.446713329733
5448805050.86022225685-170.860222256847
5548404886.87450715147-46.8745071514695
5646004813.29331180815-213.29331180815
5745204551.75463880728-31.7546388072842
5846004755.1923231192-155.192323119198
5957605482.17937544255277.820624557449
6046404739.69358826514-99.693588265136
6145204258.09504116285261.904958837154
6254005381.4819417505718.5180582494322
6342004236.54709138545-36.5470913854515
6446004559.3349658580140.6650341419927
6544804642.37394338113-162.373943381134
6646804950.90834117053-270.908341170526
6744004886.59229699321-486.592296993213
6844804676.89696294189-196.896962941887
6948404561.1414805172278.858519482802
7046804665.6128739766214.3871260233791
7154805750.80880010818-270.808800108182
7246804695.14157387731-15.1415738773112
7344404504.2533737887-64.2533737887006
7452805438.09753559092-158.097535590925
7542404239.464944824570.535055175434536
7646004627.59379274401-27.5937927440109
7746404545.9164585148294.0835414851781
7849204768.42543243688151.57456756312
7945604527.962931170132.0370688299026
8044004552.52666579586-152.526665795863
8150804823.25641716732256.743582832682
8246404713.15448154274-73.1544815427378
8355205574.42885181507-54.4288518150743
8446004718.81953149276-118.819531492759
8547204486.45555313857233.544446861431
8654805351.01716301665128.98283698335
8743204272.3510163456347.6489836543733
8846404640.52425701398-0.524257013978968
8949204657.27533643806262.724663561942
9048404928.27332230651-88.2733223065079
9145204588.61918922428-68.619189224275
9244404463.07018507818-23.0701850781779
9350005069.08294188473-69.0829418847334
9448404689.50602031305150.49397968695
9554805572.56374251465-92.5637425146479
9643204657.98788066913-337.98788066913
9748804710.73409778832169.265902211679
9854405496.70958281915-56.7095828191541
9944804343.60084387887136.399156121134
10046004675.32554010713-75.3255401071337
10147204906.51840008112-186.518400081119
10250004893.76690797946106.233092020543
10341604567.51817303745-407.518173037452
10447204478.08222382336241.917776176642
10550005051.19692268555-51.1969226855526
10644804847.50049639706-367.500496397058
10757205539.31771759051180.682282409493
10846004417.99031971424182.009680285758







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1094884.103648548374600.537521937515167.66977515923
1105492.004145871815208.438019260955775.57027248267
1114487.39781792694203.831691316044770.96394453776
1124649.223680378494365.657553767634932.78980698934
1134791.607525000024508.041398389165075.17365161088
1145017.080922290274733.514795679415300.64704890112
1154270.087244942383986.521118331524553.65337155324
1164708.691789775274425.125663164414992.25791638613
1175047.453309584274763.887182973415331.01943619513
1184584.691029987584301.124903376734868.25715659844
1195727.968364259375444.402237648516011.53449087022
1204599.288891417644512.561868864444686.01591397084

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 4884.10364854837 & 4600.53752193751 & 5167.66977515923 \tabularnewline
110 & 5492.00414587181 & 5208.43801926095 & 5775.57027248267 \tabularnewline
111 & 4487.3978179269 & 4203.83169131604 & 4770.96394453776 \tabularnewline
112 & 4649.22368037849 & 4365.65755376763 & 4932.78980698934 \tabularnewline
113 & 4791.60752500002 & 4508.04139838916 & 5075.17365161088 \tabularnewline
114 & 5017.08092229027 & 4733.51479567941 & 5300.64704890112 \tabularnewline
115 & 4270.08724494238 & 3986.52111833152 & 4553.65337155324 \tabularnewline
116 & 4708.69178977527 & 4425.12566316441 & 4992.25791638613 \tabularnewline
117 & 5047.45330958427 & 4763.88718297341 & 5331.01943619513 \tabularnewline
118 & 4584.69102998758 & 4301.12490337673 & 4868.25715659844 \tabularnewline
119 & 5727.96836425937 & 5444.40223764851 & 6011.53449087022 \tabularnewline
120 & 4599.28889141764 & 4512.56186886444 & 4686.01591397084 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211181&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]109[/C][C]4884.10364854837[/C][C]4600.53752193751[/C][C]5167.66977515923[/C][/ROW]
[ROW][C]110[/C][C]5492.00414587181[/C][C]5208.43801926095[/C][C]5775.57027248267[/C][/ROW]
[ROW][C]111[/C][C]4487.3978179269[/C][C]4203.83169131604[/C][C]4770.96394453776[/C][/ROW]
[ROW][C]112[/C][C]4649.22368037849[/C][C]4365.65755376763[/C][C]4932.78980698934[/C][/ROW]
[ROW][C]113[/C][C]4791.60752500002[/C][C]4508.04139838916[/C][C]5075.17365161088[/C][/ROW]
[ROW][C]114[/C][C]5017.08092229027[/C][C]4733.51479567941[/C][C]5300.64704890112[/C][/ROW]
[ROW][C]115[/C][C]4270.08724494238[/C][C]3986.52111833152[/C][C]4553.65337155324[/C][/ROW]
[ROW][C]116[/C][C]4708.69178977527[/C][C]4425.12566316441[/C][C]4992.25791638613[/C][/ROW]
[ROW][C]117[/C][C]5047.45330958427[/C][C]4763.88718297341[/C][C]5331.01943619513[/C][/ROW]
[ROW][C]118[/C][C]4584.69102998758[/C][C]4301.12490337673[/C][C]4868.25715659844[/C][/ROW]
[ROW][C]119[/C][C]5727.96836425937[/C][C]5444.40223764851[/C][C]6011.53449087022[/C][/ROW]
[ROW][C]120[/C][C]4599.28889141764[/C][C]4512.56186886444[/C][C]4686.01591397084[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211181&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211181&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
1094884.103648548374600.537521937515167.66977515923
1105492.004145871815208.438019260955775.57027248267
1114487.39781792694203.831691316044770.96394453776
1124649.223680378494365.657553767634932.78980698934
1134791.607525000024508.041398389165075.17365161088
1145017.080922290274733.514795679415300.64704890112
1154270.087244942383986.521118331524553.65337155324
1164708.691789775274425.125663164414992.25791638613
1175047.453309584274763.887182973415331.01943619513
1184584.691029987584301.124903376734868.25715659844
1195727.968364259375444.402237648516011.53449087022
1204599.288891417644512.561868864444686.01591397084



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')