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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 17 Nov 2013 14:20:42 -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/2013/Nov/17/t1384716060iau8xnz9e6j05kd.htm/, Retrieved Mon, 29 Apr 2024 05:37:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=225861, Retrieved Mon, 29 Apr 2024 05:37:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exp sm triple multi] [2013-11-17 19:20:42] [dbceeb23fcf622ba260f793fe955ad62] [Current]
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Dataseries X:
37
30
47
35
30
43
82
40
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8
7
10
7
10
3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225861&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225861&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225861&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.508264392434692
beta0.0121485853196825
gamma0.979025134159349

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.508264392434692 \tabularnewline
beta & 0.0121485853196825 \tabularnewline
gamma & 0.979025134159349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225861&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]0.508264392434692[/C][/ROW]
[ROW][C]beta[/C][C]0.0121485853196825[/C][/ROW]
[ROW][C]gamma[/C][C]0.979025134159349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225861&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225861&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
alpha0.508264392434692
beta0.0121485853196825
gamma0.979025134159349







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138062.085248919157717.9147510808423
144237.06931422146564.93068577853441
155450.26245732547593.73754267452414
166662.74498809362433.25501190637569
178180.99049500860130.00950499139865713
186368.9357142664024-5.93571426640243
19137127.6822835606699.31771643933099
207263.93989650363188.06010349636821
2110781.265344025510825.7346559744892
225838.103322458676119.8966775413239
2336127.400100077273-91.4001000772726
2452207.755430375571-155.755430375571
257983.9720467922422-4.97204679224224
267739.803295975167537.1967040248325
275471.8562522685251-17.8562522685251
288474.14213118137939.85786881862067
294896.3723303359829-48.3723303359829
309658.292609017279437.7073909827206
3183160.804925830847-77.8049258308473
326659.71642147546466.28357852453544
336180.2620666352148-19.2620666352148
345330.240309346132622.7596906538674
353042.1008083103332-12.1008083103332
367483.996295678302-9.99629567830202
3769118.499265778718-49.4992657787178
385960.7944264491956-1.79442644919558
394248.464872589241-6.46487258924104
406565.4427349518747-0.442734951874669
417050.608919588170419.3910804118296
4210089.009263193435410.9907368065646
4363109.593890953957-46.5938909539572
4410563.865629509893441.1343704901066
458289.0076172144281-7.00761721442814
468152.84815449656628.151845503434
477544.672478473206530.3275215267935
48102155.951624760774-53.9516247607736
49121151.815615614101-30.8156156141009
5098116.103656058154-18.1036560581542
517680.9242370425421-4.92423704254213
5277120.331036228097-43.331036228097
536387.587920514922-24.587920514922
5437100.646168372816-63.6461683728157
553555.3707922763374-20.3707922763374
562355.8437628857073-32.8437628857073
574032.27392055538887.72607944461116
582928.17245846794180.827541532058206
593719.81292182909317.187078170907
605147.77476297964643.22523702035363
612065.3647846084476-45.3647846084476
622837.4383425490998-9.43834254909981
631326.2915101865442-13.2915101865442
642224.6422453649333-2.64224536493332
652522.44042488096422.55957511903584
661321.0014091160599-8.00140911605987
671619.6310715708089-3.63107157080892
681316.931682936353-3.93168293635302
691622.854174141207-6.85417414120698
701713.98538386266433.01461613733571
71913.7656378268666-4.76563782686655
721715.40087577936521.59912422063484
732510.189803598944414.8101964010556
741427.8626917790874-13.8626917790874
75813.110021902923-5.11002190292302
76718.6370772937792-11.6370772937792
771013.7236343821601-3.72363438216008
7877.76991313461904-0.769913134619041
791010.0613597590645-0.0613597590644979
8039.29723138678188-6.29723138678188

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 80 & 62.0852489191577 & 17.9147510808423 \tabularnewline
14 & 42 & 37.0693142214656 & 4.93068577853441 \tabularnewline
15 & 54 & 50.2624573254759 & 3.73754267452414 \tabularnewline
16 & 66 & 62.7449880936243 & 3.25501190637569 \tabularnewline
17 & 81 & 80.9904950086013 & 0.00950499139865713 \tabularnewline
18 & 63 & 68.9357142664024 & -5.93571426640243 \tabularnewline
19 & 137 & 127.682283560669 & 9.31771643933099 \tabularnewline
20 & 72 & 63.9398965036318 & 8.06010349636821 \tabularnewline
21 & 107 & 81.2653440255108 & 25.7346559744892 \tabularnewline
22 & 58 & 38.1033224586761 & 19.8966775413239 \tabularnewline
23 & 36 & 127.400100077273 & -91.4001000772726 \tabularnewline
24 & 52 & 207.755430375571 & -155.755430375571 \tabularnewline
25 & 79 & 83.9720467922422 & -4.97204679224224 \tabularnewline
26 & 77 & 39.8032959751675 & 37.1967040248325 \tabularnewline
27 & 54 & 71.8562522685251 & -17.8562522685251 \tabularnewline
28 & 84 & 74.1421311813793 & 9.85786881862067 \tabularnewline
29 & 48 & 96.3723303359829 & -48.3723303359829 \tabularnewline
30 & 96 & 58.2926090172794 & 37.7073909827206 \tabularnewline
31 & 83 & 160.804925830847 & -77.8049258308473 \tabularnewline
32 & 66 & 59.7164214754646 & 6.28357852453544 \tabularnewline
33 & 61 & 80.2620666352148 & -19.2620666352148 \tabularnewline
34 & 53 & 30.2403093461326 & 22.7596906538674 \tabularnewline
35 & 30 & 42.1008083103332 & -12.1008083103332 \tabularnewline
36 & 74 & 83.996295678302 & -9.99629567830202 \tabularnewline
37 & 69 & 118.499265778718 & -49.4992657787178 \tabularnewline
38 & 59 & 60.7944264491956 & -1.79442644919558 \tabularnewline
39 & 42 & 48.464872589241 & -6.46487258924104 \tabularnewline
40 & 65 & 65.4427349518747 & -0.442734951874669 \tabularnewline
41 & 70 & 50.6089195881704 & 19.3910804118296 \tabularnewline
42 & 100 & 89.0092631934354 & 10.9907368065646 \tabularnewline
43 & 63 & 109.593890953957 & -46.5938909539572 \tabularnewline
44 & 105 & 63.8656295098934 & 41.1343704901066 \tabularnewline
45 & 82 & 89.0076172144281 & -7.00761721442814 \tabularnewline
46 & 81 & 52.848154496566 & 28.151845503434 \tabularnewline
47 & 75 & 44.6724784732065 & 30.3275215267935 \tabularnewline
48 & 102 & 155.951624760774 & -53.9516247607736 \tabularnewline
49 & 121 & 151.815615614101 & -30.8156156141009 \tabularnewline
50 & 98 & 116.103656058154 & -18.1036560581542 \tabularnewline
51 & 76 & 80.9242370425421 & -4.92423704254213 \tabularnewline
52 & 77 & 120.331036228097 & -43.331036228097 \tabularnewline
53 & 63 & 87.587920514922 & -24.587920514922 \tabularnewline
54 & 37 & 100.646168372816 & -63.6461683728157 \tabularnewline
55 & 35 & 55.3707922763374 & -20.3707922763374 \tabularnewline
56 & 23 & 55.8437628857073 & -32.8437628857073 \tabularnewline
57 & 40 & 32.2739205553888 & 7.72607944461116 \tabularnewline
58 & 29 & 28.1724584679418 & 0.827541532058206 \tabularnewline
59 & 37 & 19.812921829093 & 17.187078170907 \tabularnewline
60 & 51 & 47.7747629796464 & 3.22523702035363 \tabularnewline
61 & 20 & 65.3647846084476 & -45.3647846084476 \tabularnewline
62 & 28 & 37.4383425490998 & -9.43834254909981 \tabularnewline
63 & 13 & 26.2915101865442 & -13.2915101865442 \tabularnewline
64 & 22 & 24.6422453649333 & -2.64224536493332 \tabularnewline
65 & 25 & 22.4404248809642 & 2.55957511903584 \tabularnewline
66 & 13 & 21.0014091160599 & -8.00140911605987 \tabularnewline
67 & 16 & 19.6310715708089 & -3.63107157080892 \tabularnewline
68 & 13 & 16.931682936353 & -3.93168293635302 \tabularnewline
69 & 16 & 22.854174141207 & -6.85417414120698 \tabularnewline
70 & 17 & 13.9853838626643 & 3.01461613733571 \tabularnewline
71 & 9 & 13.7656378268666 & -4.76563782686655 \tabularnewline
72 & 17 & 15.4008757793652 & 1.59912422063484 \tabularnewline
73 & 25 & 10.1898035989444 & 14.8101964010556 \tabularnewline
74 & 14 & 27.8626917790874 & -13.8626917790874 \tabularnewline
75 & 8 & 13.110021902923 & -5.11002190292302 \tabularnewline
76 & 7 & 18.6370772937792 & -11.6370772937792 \tabularnewline
77 & 10 & 13.7236343821601 & -3.72363438216008 \tabularnewline
78 & 7 & 7.76991313461904 & -0.769913134619041 \tabularnewline
79 & 10 & 10.0613597590645 & -0.0613597590644979 \tabularnewline
80 & 3 & 9.29723138678188 & -6.29723138678188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225861&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[/C][C]62.0852489191577[/C][C]17.9147510808423[/C][/ROW]
[ROW][C]14[/C][C]42[/C][C]37.0693142214656[/C][C]4.93068577853441[/C][/ROW]
[ROW][C]15[/C][C]54[/C][C]50.2624573254759[/C][C]3.73754267452414[/C][/ROW]
[ROW][C]16[/C][C]66[/C][C]62.7449880936243[/C][C]3.25501190637569[/C][/ROW]
[ROW][C]17[/C][C]81[/C][C]80.9904950086013[/C][C]0.00950499139865713[/C][/ROW]
[ROW][C]18[/C][C]63[/C][C]68.9357142664024[/C][C]-5.93571426640243[/C][/ROW]
[ROW][C]19[/C][C]137[/C][C]127.682283560669[/C][C]9.31771643933099[/C][/ROW]
[ROW][C]20[/C][C]72[/C][C]63.9398965036318[/C][C]8.06010349636821[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]81.2653440255108[/C][C]25.7346559744892[/C][/ROW]
[ROW][C]22[/C][C]58[/C][C]38.1033224586761[/C][C]19.8966775413239[/C][/ROW]
[ROW][C]23[/C][C]36[/C][C]127.400100077273[/C][C]-91.4001000772726[/C][/ROW]
[ROW][C]24[/C][C]52[/C][C]207.755430375571[/C][C]-155.755430375571[/C][/ROW]
[ROW][C]25[/C][C]79[/C][C]83.9720467922422[/C][C]-4.97204679224224[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]39.8032959751675[/C][C]37.1967040248325[/C][/ROW]
[ROW][C]27[/C][C]54[/C][C]71.8562522685251[/C][C]-17.8562522685251[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]74.1421311813793[/C][C]9.85786881862067[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]96.3723303359829[/C][C]-48.3723303359829[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]58.2926090172794[/C][C]37.7073909827206[/C][/ROW]
[ROW][C]31[/C][C]83[/C][C]160.804925830847[/C][C]-77.8049258308473[/C][/ROW]
[ROW][C]32[/C][C]66[/C][C]59.7164214754646[/C][C]6.28357852453544[/C][/ROW]
[ROW][C]33[/C][C]61[/C][C]80.2620666352148[/C][C]-19.2620666352148[/C][/ROW]
[ROW][C]34[/C][C]53[/C][C]30.2403093461326[/C][C]22.7596906538674[/C][/ROW]
[ROW][C]35[/C][C]30[/C][C]42.1008083103332[/C][C]-12.1008083103332[/C][/ROW]
[ROW][C]36[/C][C]74[/C][C]83.996295678302[/C][C]-9.99629567830202[/C][/ROW]
[ROW][C]37[/C][C]69[/C][C]118.499265778718[/C][C]-49.4992657787178[/C][/ROW]
[ROW][C]38[/C][C]59[/C][C]60.7944264491956[/C][C]-1.79442644919558[/C][/ROW]
[ROW][C]39[/C][C]42[/C][C]48.464872589241[/C][C]-6.46487258924104[/C][/ROW]
[ROW][C]40[/C][C]65[/C][C]65.4427349518747[/C][C]-0.442734951874669[/C][/ROW]
[ROW][C]41[/C][C]70[/C][C]50.6089195881704[/C][C]19.3910804118296[/C][/ROW]
[ROW][C]42[/C][C]100[/C][C]89.0092631934354[/C][C]10.9907368065646[/C][/ROW]
[ROW][C]43[/C][C]63[/C][C]109.593890953957[/C][C]-46.5938909539572[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]63.8656295098934[/C][C]41.1343704901066[/C][/ROW]
[ROW][C]45[/C][C]82[/C][C]89.0076172144281[/C][C]-7.00761721442814[/C][/ROW]
[ROW][C]46[/C][C]81[/C][C]52.848154496566[/C][C]28.151845503434[/C][/ROW]
[ROW][C]47[/C][C]75[/C][C]44.6724784732065[/C][C]30.3275215267935[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]155.951624760774[/C][C]-53.9516247607736[/C][/ROW]
[ROW][C]49[/C][C]121[/C][C]151.815615614101[/C][C]-30.8156156141009[/C][/ROW]
[ROW][C]50[/C][C]98[/C][C]116.103656058154[/C][C]-18.1036560581542[/C][/ROW]
[ROW][C]51[/C][C]76[/C][C]80.9242370425421[/C][C]-4.92423704254213[/C][/ROW]
[ROW][C]52[/C][C]77[/C][C]120.331036228097[/C][C]-43.331036228097[/C][/ROW]
[ROW][C]53[/C][C]63[/C][C]87.587920514922[/C][C]-24.587920514922[/C][/ROW]
[ROW][C]54[/C][C]37[/C][C]100.646168372816[/C][C]-63.6461683728157[/C][/ROW]
[ROW][C]55[/C][C]35[/C][C]55.3707922763374[/C][C]-20.3707922763374[/C][/ROW]
[ROW][C]56[/C][C]23[/C][C]55.8437628857073[/C][C]-32.8437628857073[/C][/ROW]
[ROW][C]57[/C][C]40[/C][C]32.2739205553888[/C][C]7.72607944461116[/C][/ROW]
[ROW][C]58[/C][C]29[/C][C]28.1724584679418[/C][C]0.827541532058206[/C][/ROW]
[ROW][C]59[/C][C]37[/C][C]19.812921829093[/C][C]17.187078170907[/C][/ROW]
[ROW][C]60[/C][C]51[/C][C]47.7747629796464[/C][C]3.22523702035363[/C][/ROW]
[ROW][C]61[/C][C]20[/C][C]65.3647846084476[/C][C]-45.3647846084476[/C][/ROW]
[ROW][C]62[/C][C]28[/C][C]37.4383425490998[/C][C]-9.43834254909981[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]26.2915101865442[/C][C]-13.2915101865442[/C][/ROW]
[ROW][C]64[/C][C]22[/C][C]24.6422453649333[/C][C]-2.64224536493332[/C][/ROW]
[ROW][C]65[/C][C]25[/C][C]22.4404248809642[/C][C]2.55957511903584[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]21.0014091160599[/C][C]-8.00140911605987[/C][/ROW]
[ROW][C]67[/C][C]16[/C][C]19.6310715708089[/C][C]-3.63107157080892[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]16.931682936353[/C][C]-3.93168293635302[/C][/ROW]
[ROW][C]69[/C][C]16[/C][C]22.854174141207[/C][C]-6.85417414120698[/C][/ROW]
[ROW][C]70[/C][C]17[/C][C]13.9853838626643[/C][C]3.01461613733571[/C][/ROW]
[ROW][C]71[/C][C]9[/C][C]13.7656378268666[/C][C]-4.76563782686655[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]15.4008757793652[/C][C]1.59912422063484[/C][/ROW]
[ROW][C]73[/C][C]25[/C][C]10.1898035989444[/C][C]14.8101964010556[/C][/ROW]
[ROW][C]74[/C][C]14[/C][C]27.8626917790874[/C][C]-13.8626917790874[/C][/ROW]
[ROW][C]75[/C][C]8[/C][C]13.110021902923[/C][C]-5.11002190292302[/C][/ROW]
[ROW][C]76[/C][C]7[/C][C]18.6370772937792[/C][C]-11.6370772937792[/C][/ROW]
[ROW][C]77[/C][C]10[/C][C]13.7236343821601[/C][C]-3.72363438216008[/C][/ROW]
[ROW][C]78[/C][C]7[/C][C]7.76991313461904[/C][C]-0.769913134619041[/C][/ROW]
[ROW][C]79[/C][C]10[/C][C]10.0613597590645[/C][C]-0.0613597590644979[/C][/ROW]
[ROW][C]80[/C][C]3[/C][C]9.29723138678188[/C][C]-6.29723138678188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225861&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225861&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
138062.085248919157717.9147510808423
144237.06931422146564.93068577853441
155450.26245732547593.73754267452414
166662.74498809362433.25501190637569
178180.99049500860130.00950499139865713
186368.9357142664024-5.93571426640243
19137127.6822835606699.31771643933099
207263.93989650363188.06010349636821
2110781.265344025510825.7346559744892
225838.103322458676119.8966775413239
2336127.400100077273-91.4001000772726
2452207.755430375571-155.755430375571
257983.9720467922422-4.97204679224224
267739.803295975167537.1967040248325
275471.8562522685251-17.8562522685251
288474.14213118137939.85786881862067
294896.3723303359829-48.3723303359829
309658.292609017279437.7073909827206
3183160.804925830847-77.8049258308473
326659.71642147546466.28357852453544
336180.2620666352148-19.2620666352148
345330.240309346132622.7596906538674
353042.1008083103332-12.1008083103332
367483.996295678302-9.99629567830202
3769118.499265778718-49.4992657787178
385960.7944264491956-1.79442644919558
394248.464872589241-6.46487258924104
406565.4427349518747-0.442734951874669
417050.608919588170419.3910804118296
4210089.009263193435410.9907368065646
4363109.593890953957-46.5938909539572
4410563.865629509893441.1343704901066
458289.0076172144281-7.00761721442814
468152.84815449656628.151845503434
477544.672478473206530.3275215267935
48102155.951624760774-53.9516247607736
49121151.815615614101-30.8156156141009
5098116.103656058154-18.1036560581542
517680.9242370425421-4.92423704254213
5277120.331036228097-43.331036228097
536387.587920514922-24.587920514922
5437100.646168372816-63.6461683728157
553555.3707922763374-20.3707922763374
562355.8437628857073-32.8437628857073
574032.27392055538887.72607944461116
582928.17245846794180.827541532058206
593719.81292182909317.187078170907
605147.77476297964643.22523702035363
612065.3647846084476-45.3647846084476
622837.4383425490998-9.43834254909981
631326.2915101865442-13.2915101865442
642224.6422453649333-2.64224536493332
652522.44042488096422.55957511903584
661321.0014091160599-8.00140911605987
671619.6310715708089-3.63107157080892
681316.931682936353-3.93168293635302
691622.854174141207-6.85417414120698
701713.98538386266433.01461613733571
71913.7656378268666-4.76563782686655
721715.40087577936521.59912422063484
732510.189803598944414.8101964010556
741427.8626917790874-13.8626917790874
75813.110021902923-5.11002190292302
76718.6370772937792-11.6370772937792
771013.7236343821601-3.72363438216008
7877.76991313461904-0.769913134619041
791010.0613597590645-0.0613597590644979
8039.29723138678188-6.29723138678188







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
818.99905097450772-51.935306911655769.9334088606711
828.65140459553057-58.855928027993476.1587372190545
835.66441924524062-61.007434637605472.3362731280867
8410.1648195622737-84.1446639296237104.474303054171
858.61507856005386-80.194575840704997.4247329608126
866.66563071424487-74.771411351288488.1026727797781
874.7837821187888-70.171899912597479.7394641501749
886.23643494044997-85.296832179082197.769702059982
8910.1808474630549-124.218650414004144.580345340114
907.44390546148555-100.018195959591114.906006882562
9110.5878982292271-133.626573696938154.802370155392
924.91873234704401-62.534219594703372.3716842887913

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 8.99905097450772 & -51.9353069116557 & 69.9334088606711 \tabularnewline
82 & 8.65140459553057 & -58.8559280279934 & 76.1587372190545 \tabularnewline
83 & 5.66441924524062 & -61.0074346376054 & 72.3362731280867 \tabularnewline
84 & 10.1648195622737 & -84.1446639296237 & 104.474303054171 \tabularnewline
85 & 8.61507856005386 & -80.1945758407049 & 97.4247329608126 \tabularnewline
86 & 6.66563071424487 & -74.7714113512884 & 88.1026727797781 \tabularnewline
87 & 4.7837821187888 & -70.1718999125974 & 79.7394641501749 \tabularnewline
88 & 6.23643494044997 & -85.2968321790821 & 97.769702059982 \tabularnewline
89 & 10.1808474630549 & -124.218650414004 & 144.580345340114 \tabularnewline
90 & 7.44390546148555 & -100.018195959591 & 114.906006882562 \tabularnewline
91 & 10.5878982292271 & -133.626573696938 & 154.802370155392 \tabularnewline
92 & 4.91873234704401 & -62.5342195947033 & 72.3716842887913 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225861&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]81[/C][C]8.99905097450772[/C][C]-51.9353069116557[/C][C]69.9334088606711[/C][/ROW]
[ROW][C]82[/C][C]8.65140459553057[/C][C]-58.8559280279934[/C][C]76.1587372190545[/C][/ROW]
[ROW][C]83[/C][C]5.66441924524062[/C][C]-61.0074346376054[/C][C]72.3362731280867[/C][/ROW]
[ROW][C]84[/C][C]10.1648195622737[/C][C]-84.1446639296237[/C][C]104.474303054171[/C][/ROW]
[ROW][C]85[/C][C]8.61507856005386[/C][C]-80.1945758407049[/C][C]97.4247329608126[/C][/ROW]
[ROW][C]86[/C][C]6.66563071424487[/C][C]-74.7714113512884[/C][C]88.1026727797781[/C][/ROW]
[ROW][C]87[/C][C]4.7837821187888[/C][C]-70.1718999125974[/C][C]79.7394641501749[/C][/ROW]
[ROW][C]88[/C][C]6.23643494044997[/C][C]-85.2968321790821[/C][C]97.769702059982[/C][/ROW]
[ROW][C]89[/C][C]10.1808474630549[/C][C]-124.218650414004[/C][C]144.580345340114[/C][/ROW]
[ROW][C]90[/C][C]7.44390546148555[/C][C]-100.018195959591[/C][C]114.906006882562[/C][/ROW]
[ROW][C]91[/C][C]10.5878982292271[/C][C]-133.626573696938[/C][C]154.802370155392[/C][/ROW]
[ROW][C]92[/C][C]4.91873234704401[/C][C]-62.5342195947033[/C][C]72.3716842887913[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225861&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225861&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
818.99905097450772-51.935306911655769.9334088606711
828.65140459553057-58.855928027993476.1587372190545
835.66441924524062-61.007434637605472.3362731280867
8410.1648195622737-84.1446639296237104.474303054171
858.61507856005386-80.194575840704997.4247329608126
866.66563071424487-74.771411351288488.1026727797781
874.7837821187888-70.171899912597479.7394641501749
886.23643494044997-85.296832179082197.769702059982
8910.1808474630549-124.218650414004144.580345340114
907.44390546148555-100.018195959591114.906006882562
9110.5878982292271-133.626573696938154.802370155392
924.91873234704401-62.534219594703372.3716842887913



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')