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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 06 Jun 2010 22:35:04 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jun/07/t1275863782120dki9vk140wgp.htm/, Retrieved Sat, 04 May 2024 00:53:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77812, Retrieved Sat, 04 May 2024 00:53:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact201
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Blocked Bootstrap Plot - Central Tendency] [Bootstrap plot me...] [2010-06-06 21:44:12] [e634c4f3b95bc1f95d22c44d630e9c6e]
- RMPD    [Exponential Smoothing] [Exp smoothing meg...] [2010-06-06 22:35:04] [0291ee60c135beb64d296f3dc8feb2dc] [Current]
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Dataseries X:
93.2
96
95.2
77.1
70.9
64.8
70.1
77.3
79.5
100.6
100.7
107.1
95.9
82.8
83.3
80
80.4
67.5
75.7
71.1
89.3
101.1
105.2
114.1
96.3
84.4
91.2
81.9
80.5
70.4
74.8
75.9
86.3
98.7
100.9
113.8
89.8
84.4
87.2
85.6
72
69.2
77.5
78.1
94.3
97.7
100.2
116.4
97.1
93
96
80.5
76.1
69.9
73.6
92.6
94.2
93.5
108.5
109.4
105.1
92.5
97.1
81.4
79.1
72.1
78.7
87.1
91.4
109.9
116.3
113
100
84.8
94.3
87.1
90.3
72.4
84.9
92.7
92.2
114.9
112.5
118.3
106
91.2
96.6
96.3
88.2
70.2
86.5
88.2
102.8
119.1
119.2
125.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77812&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77812&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77812&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0248177025009365
beta0.0705169005484752
gamma0.299825872359443

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0248177025009365 \tabularnewline
beta & 0.0705169005484752 \tabularnewline
gamma & 0.299825872359443 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77812&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]0.0248177025009365[/C][/ROW]
[ROW][C]beta[/C][C]0.0705169005484752[/C][/ROW]
[ROW][C]gamma[/C][C]0.299825872359443[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77812&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77812&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
alpha0.0248177025009365
beta0.0705169005484752
gamma0.299825872359443







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1395.995.23283596705040.667164032949628
1482.882.38472054383180.415279456168221
1583.382.87135140618230.428648593817712
168079.32127150482320.67872849517677
1780.479.66303332246670.736966677533331
1867.566.62942188118120.870578118818798
1975.769.93229768408165.76770231591844
2071.177.7982686267752-6.69826862677525
2189.380.95180026333418.34819973666589
22101.1103.332512310900-2.23251231089969
23105.2102.9215545532682.27844544673231
24114.1109.0559535633785.04404643662184
2596.397.741984652808-1.44198465280812
2684.484.4835199637877-0.0835199637877224
2791.284.99454234949986.20545765050016
2881.981.60086745924240.299132540757626
2980.581.9883718385475-1.48837183854752
3070.468.62509539385021.77490460614980
3174.873.52720899117121.27279100882878
3275.977.751492159424-1.85149215942394
3386.385.65324035093240.646759649067619
3498.7105.237888480149-6.53788848014867
35100.9106.071178136997-5.1711781369971
36113.8112.9767618348120.82323816518823
3789.899.3696110725818-9.56961107258182
3884.486.0426835940844-1.64268359408436
3987.288.3698923658617-1.16989236586168
4085.682.9484104555162.65158954448397
417282.8390669991697-10.8390669991697
4269.269.9986789971331-0.798678997133095
4377.574.69766104430872.80233895569133
4478.178.03785980741170.0621401925883163
4594.386.76935006455557.53064993544446
4697.7104.602732780584-6.90273278058403
47100.2105.79895602503-5.59895602502995
48116.4114.5028042340351.89719576596470
4997.197.6451719437032-0.545171943703224
509386.69393654956156.30606345043854
519689.38828467412286.61171532587724
5280.585.2070359491507-4.70703594915069
5376.180.88964954136-4.7896495413600
5469.970.9717658399781-1.07176583997810
5573.676.8181494442719-3.21814944427189
5692.679.237428301689813.3625716983101
5794.290.70615967879053.49384032120948
5893.5104.472917853241-10.9729178532409
59108.5105.9815584750442.51844152495588
60109.4117.312514017756-7.91251401775617
61105.199.19173239494385.90826760505617
6292.590.24161072856182.25838927143825
6397.192.97369033079564.12630966920439
6481.485.286514512536-3.88651451253594
6579.180.8902705288784-1.79027052887841
6672.171.97773704630870.122262953691290
6778.777.3339513618121.36604863818798
6887.184.86862977467392.23137022532609
6991.493.3148786061067-1.91487860610665
70109.9102.8450047408477.05499525915283
71116.3108.8782793924397.4217206075613
72113117.481029004066-4.48102900406599
73100103.203314309358-3.20331430935849
7484.892.7650016690649-7.96500166906486
7594.395.839837380656-1.53983738065592
7687.185.49106720210261.60893279789741
7790.381.77508259834848.5249174016516
7872.473.517929041401-1.11792904140100
7984.979.33482296494145.5651770350586
8092.787.41624043297035.28375956702973
8192.294.9180146596084-2.71801465960839
82114.9107.3583147305797.5416852694213
83112.5113.677822389135-1.17782238913462
84118.3118.709212124037-0.409212124036799
85106104.6121834483031.3878165516971
8691.292.6327162683265-1.43271626832654
8796.697.9209706617054-1.32097066170536
8896.388.28299920593238.01700079406768
8988.286.73617632906431.46382367093568
9070.275.2051326429617-5.00513264296166
9186.583.10393995207393.39606004792611
9288.291.2696948551364-3.06969485513638
93102.896.34869099718226.45130900281777
94119.1112.4421433885166.65785661148428
95119.2116.3073060482542.89269395174632
96125.1121.8400644039803.25993559602045

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 95.9 & 95.2328359670504 & 0.667164032949628 \tabularnewline
14 & 82.8 & 82.3847205438318 & 0.415279456168221 \tabularnewline
15 & 83.3 & 82.8713514061823 & 0.428648593817712 \tabularnewline
16 & 80 & 79.3212715048232 & 0.67872849517677 \tabularnewline
17 & 80.4 & 79.6630333224667 & 0.736966677533331 \tabularnewline
18 & 67.5 & 66.6294218811812 & 0.870578118818798 \tabularnewline
19 & 75.7 & 69.9322976840816 & 5.76770231591844 \tabularnewline
20 & 71.1 & 77.7982686267752 & -6.69826862677525 \tabularnewline
21 & 89.3 & 80.9518002633341 & 8.34819973666589 \tabularnewline
22 & 101.1 & 103.332512310900 & -2.23251231089969 \tabularnewline
23 & 105.2 & 102.921554553268 & 2.27844544673231 \tabularnewline
24 & 114.1 & 109.055953563378 & 5.04404643662184 \tabularnewline
25 & 96.3 & 97.741984652808 & -1.44198465280812 \tabularnewline
26 & 84.4 & 84.4835199637877 & -0.0835199637877224 \tabularnewline
27 & 91.2 & 84.9945423494998 & 6.20545765050016 \tabularnewline
28 & 81.9 & 81.6008674592424 & 0.299132540757626 \tabularnewline
29 & 80.5 & 81.9883718385475 & -1.48837183854752 \tabularnewline
30 & 70.4 & 68.6250953938502 & 1.77490460614980 \tabularnewline
31 & 74.8 & 73.5272089911712 & 1.27279100882878 \tabularnewline
32 & 75.9 & 77.751492159424 & -1.85149215942394 \tabularnewline
33 & 86.3 & 85.6532403509324 & 0.646759649067619 \tabularnewline
34 & 98.7 & 105.237888480149 & -6.53788848014867 \tabularnewline
35 & 100.9 & 106.071178136997 & -5.1711781369971 \tabularnewline
36 & 113.8 & 112.976761834812 & 0.82323816518823 \tabularnewline
37 & 89.8 & 99.3696110725818 & -9.56961107258182 \tabularnewline
38 & 84.4 & 86.0426835940844 & -1.64268359408436 \tabularnewline
39 & 87.2 & 88.3698923658617 & -1.16989236586168 \tabularnewline
40 & 85.6 & 82.948410455516 & 2.65158954448397 \tabularnewline
41 & 72 & 82.8390669991697 & -10.8390669991697 \tabularnewline
42 & 69.2 & 69.9986789971331 & -0.798678997133095 \tabularnewline
43 & 77.5 & 74.6976610443087 & 2.80233895569133 \tabularnewline
44 & 78.1 & 78.0378598074117 & 0.0621401925883163 \tabularnewline
45 & 94.3 & 86.7693500645555 & 7.53064993544446 \tabularnewline
46 & 97.7 & 104.602732780584 & -6.90273278058403 \tabularnewline
47 & 100.2 & 105.79895602503 & -5.59895602502995 \tabularnewline
48 & 116.4 & 114.502804234035 & 1.89719576596470 \tabularnewline
49 & 97.1 & 97.6451719437032 & -0.545171943703224 \tabularnewline
50 & 93 & 86.6939365495615 & 6.30606345043854 \tabularnewline
51 & 96 & 89.3882846741228 & 6.61171532587724 \tabularnewline
52 & 80.5 & 85.2070359491507 & -4.70703594915069 \tabularnewline
53 & 76.1 & 80.88964954136 & -4.7896495413600 \tabularnewline
54 & 69.9 & 70.9717658399781 & -1.07176583997810 \tabularnewline
55 & 73.6 & 76.8181494442719 & -3.21814944427189 \tabularnewline
56 & 92.6 & 79.2374283016898 & 13.3625716983101 \tabularnewline
57 & 94.2 & 90.7061596787905 & 3.49384032120948 \tabularnewline
58 & 93.5 & 104.472917853241 & -10.9729178532409 \tabularnewline
59 & 108.5 & 105.981558475044 & 2.51844152495588 \tabularnewline
60 & 109.4 & 117.312514017756 & -7.91251401775617 \tabularnewline
61 & 105.1 & 99.1917323949438 & 5.90826760505617 \tabularnewline
62 & 92.5 & 90.2416107285618 & 2.25838927143825 \tabularnewline
63 & 97.1 & 92.9736903307956 & 4.12630966920439 \tabularnewline
64 & 81.4 & 85.286514512536 & -3.88651451253594 \tabularnewline
65 & 79.1 & 80.8902705288784 & -1.79027052887841 \tabularnewline
66 & 72.1 & 71.9777370463087 & 0.122262953691290 \tabularnewline
67 & 78.7 & 77.333951361812 & 1.36604863818798 \tabularnewline
68 & 87.1 & 84.8686297746739 & 2.23137022532609 \tabularnewline
69 & 91.4 & 93.3148786061067 & -1.91487860610665 \tabularnewline
70 & 109.9 & 102.845004740847 & 7.05499525915283 \tabularnewline
71 & 116.3 & 108.878279392439 & 7.4217206075613 \tabularnewline
72 & 113 & 117.481029004066 & -4.48102900406599 \tabularnewline
73 & 100 & 103.203314309358 & -3.20331430935849 \tabularnewline
74 & 84.8 & 92.7650016690649 & -7.96500166906486 \tabularnewline
75 & 94.3 & 95.839837380656 & -1.53983738065592 \tabularnewline
76 & 87.1 & 85.4910672021026 & 1.60893279789741 \tabularnewline
77 & 90.3 & 81.7750825983484 & 8.5249174016516 \tabularnewline
78 & 72.4 & 73.517929041401 & -1.11792904140100 \tabularnewline
79 & 84.9 & 79.3348229649414 & 5.5651770350586 \tabularnewline
80 & 92.7 & 87.4162404329703 & 5.28375956702973 \tabularnewline
81 & 92.2 & 94.9180146596084 & -2.71801465960839 \tabularnewline
82 & 114.9 & 107.358314730579 & 7.5416852694213 \tabularnewline
83 & 112.5 & 113.677822389135 & -1.17782238913462 \tabularnewline
84 & 118.3 & 118.709212124037 & -0.409212124036799 \tabularnewline
85 & 106 & 104.612183448303 & 1.3878165516971 \tabularnewline
86 & 91.2 & 92.6327162683265 & -1.43271626832654 \tabularnewline
87 & 96.6 & 97.9209706617054 & -1.32097066170536 \tabularnewline
88 & 96.3 & 88.2829992059323 & 8.01700079406768 \tabularnewline
89 & 88.2 & 86.7361763290643 & 1.46382367093568 \tabularnewline
90 & 70.2 & 75.2051326429617 & -5.00513264296166 \tabularnewline
91 & 86.5 & 83.1039399520739 & 3.39606004792611 \tabularnewline
92 & 88.2 & 91.2696948551364 & -3.06969485513638 \tabularnewline
93 & 102.8 & 96.3486909971822 & 6.45130900281777 \tabularnewline
94 & 119.1 & 112.442143388516 & 6.65785661148428 \tabularnewline
95 & 119.2 & 116.307306048254 & 2.89269395174632 \tabularnewline
96 & 125.1 & 121.840064403980 & 3.25993559602045 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77812&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]95.9[/C][C]95.2328359670504[/C][C]0.667164032949628[/C][/ROW]
[ROW][C]14[/C][C]82.8[/C][C]82.3847205438318[/C][C]0.415279456168221[/C][/ROW]
[ROW][C]15[/C][C]83.3[/C][C]82.8713514061823[/C][C]0.428648593817712[/C][/ROW]
[ROW][C]16[/C][C]80[/C][C]79.3212715048232[/C][C]0.67872849517677[/C][/ROW]
[ROW][C]17[/C][C]80.4[/C][C]79.6630333224667[/C][C]0.736966677533331[/C][/ROW]
[ROW][C]18[/C][C]67.5[/C][C]66.6294218811812[/C][C]0.870578118818798[/C][/ROW]
[ROW][C]19[/C][C]75.7[/C][C]69.9322976840816[/C][C]5.76770231591844[/C][/ROW]
[ROW][C]20[/C][C]71.1[/C][C]77.7982686267752[/C][C]-6.69826862677525[/C][/ROW]
[ROW][C]21[/C][C]89.3[/C][C]80.9518002633341[/C][C]8.34819973666589[/C][/ROW]
[ROW][C]22[/C][C]101.1[/C][C]103.332512310900[/C][C]-2.23251231089969[/C][/ROW]
[ROW][C]23[/C][C]105.2[/C][C]102.921554553268[/C][C]2.27844544673231[/C][/ROW]
[ROW][C]24[/C][C]114.1[/C][C]109.055953563378[/C][C]5.04404643662184[/C][/ROW]
[ROW][C]25[/C][C]96.3[/C][C]97.741984652808[/C][C]-1.44198465280812[/C][/ROW]
[ROW][C]26[/C][C]84.4[/C][C]84.4835199637877[/C][C]-0.0835199637877224[/C][/ROW]
[ROW][C]27[/C][C]91.2[/C][C]84.9945423494998[/C][C]6.20545765050016[/C][/ROW]
[ROW][C]28[/C][C]81.9[/C][C]81.6008674592424[/C][C]0.299132540757626[/C][/ROW]
[ROW][C]29[/C][C]80.5[/C][C]81.9883718385475[/C][C]-1.48837183854752[/C][/ROW]
[ROW][C]30[/C][C]70.4[/C][C]68.6250953938502[/C][C]1.77490460614980[/C][/ROW]
[ROW][C]31[/C][C]74.8[/C][C]73.5272089911712[/C][C]1.27279100882878[/C][/ROW]
[ROW][C]32[/C][C]75.9[/C][C]77.751492159424[/C][C]-1.85149215942394[/C][/ROW]
[ROW][C]33[/C][C]86.3[/C][C]85.6532403509324[/C][C]0.646759649067619[/C][/ROW]
[ROW][C]34[/C][C]98.7[/C][C]105.237888480149[/C][C]-6.53788848014867[/C][/ROW]
[ROW][C]35[/C][C]100.9[/C][C]106.071178136997[/C][C]-5.1711781369971[/C][/ROW]
[ROW][C]36[/C][C]113.8[/C][C]112.976761834812[/C][C]0.82323816518823[/C][/ROW]
[ROW][C]37[/C][C]89.8[/C][C]99.3696110725818[/C][C]-9.56961107258182[/C][/ROW]
[ROW][C]38[/C][C]84.4[/C][C]86.0426835940844[/C][C]-1.64268359408436[/C][/ROW]
[ROW][C]39[/C][C]87.2[/C][C]88.3698923658617[/C][C]-1.16989236586168[/C][/ROW]
[ROW][C]40[/C][C]85.6[/C][C]82.948410455516[/C][C]2.65158954448397[/C][/ROW]
[ROW][C]41[/C][C]72[/C][C]82.8390669991697[/C][C]-10.8390669991697[/C][/ROW]
[ROW][C]42[/C][C]69.2[/C][C]69.9986789971331[/C][C]-0.798678997133095[/C][/ROW]
[ROW][C]43[/C][C]77.5[/C][C]74.6976610443087[/C][C]2.80233895569133[/C][/ROW]
[ROW][C]44[/C][C]78.1[/C][C]78.0378598074117[/C][C]0.0621401925883163[/C][/ROW]
[ROW][C]45[/C][C]94.3[/C][C]86.7693500645555[/C][C]7.53064993544446[/C][/ROW]
[ROW][C]46[/C][C]97.7[/C][C]104.602732780584[/C][C]-6.90273278058403[/C][/ROW]
[ROW][C]47[/C][C]100.2[/C][C]105.79895602503[/C][C]-5.59895602502995[/C][/ROW]
[ROW][C]48[/C][C]116.4[/C][C]114.502804234035[/C][C]1.89719576596470[/C][/ROW]
[ROW][C]49[/C][C]97.1[/C][C]97.6451719437032[/C][C]-0.545171943703224[/C][/ROW]
[ROW][C]50[/C][C]93[/C][C]86.6939365495615[/C][C]6.30606345043854[/C][/ROW]
[ROW][C]51[/C][C]96[/C][C]89.3882846741228[/C][C]6.61171532587724[/C][/ROW]
[ROW][C]52[/C][C]80.5[/C][C]85.2070359491507[/C][C]-4.70703594915069[/C][/ROW]
[ROW][C]53[/C][C]76.1[/C][C]80.88964954136[/C][C]-4.7896495413600[/C][/ROW]
[ROW][C]54[/C][C]69.9[/C][C]70.9717658399781[/C][C]-1.07176583997810[/C][/ROW]
[ROW][C]55[/C][C]73.6[/C][C]76.8181494442719[/C][C]-3.21814944427189[/C][/ROW]
[ROW][C]56[/C][C]92.6[/C][C]79.2374283016898[/C][C]13.3625716983101[/C][/ROW]
[ROW][C]57[/C][C]94.2[/C][C]90.7061596787905[/C][C]3.49384032120948[/C][/ROW]
[ROW][C]58[/C][C]93.5[/C][C]104.472917853241[/C][C]-10.9729178532409[/C][/ROW]
[ROW][C]59[/C][C]108.5[/C][C]105.981558475044[/C][C]2.51844152495588[/C][/ROW]
[ROW][C]60[/C][C]109.4[/C][C]117.312514017756[/C][C]-7.91251401775617[/C][/ROW]
[ROW][C]61[/C][C]105.1[/C][C]99.1917323949438[/C][C]5.90826760505617[/C][/ROW]
[ROW][C]62[/C][C]92.5[/C][C]90.2416107285618[/C][C]2.25838927143825[/C][/ROW]
[ROW][C]63[/C][C]97.1[/C][C]92.9736903307956[/C][C]4.12630966920439[/C][/ROW]
[ROW][C]64[/C][C]81.4[/C][C]85.286514512536[/C][C]-3.88651451253594[/C][/ROW]
[ROW][C]65[/C][C]79.1[/C][C]80.8902705288784[/C][C]-1.79027052887841[/C][/ROW]
[ROW][C]66[/C][C]72.1[/C][C]71.9777370463087[/C][C]0.122262953691290[/C][/ROW]
[ROW][C]67[/C][C]78.7[/C][C]77.333951361812[/C][C]1.36604863818798[/C][/ROW]
[ROW][C]68[/C][C]87.1[/C][C]84.8686297746739[/C][C]2.23137022532609[/C][/ROW]
[ROW][C]69[/C][C]91.4[/C][C]93.3148786061067[/C][C]-1.91487860610665[/C][/ROW]
[ROW][C]70[/C][C]109.9[/C][C]102.845004740847[/C][C]7.05499525915283[/C][/ROW]
[ROW][C]71[/C][C]116.3[/C][C]108.878279392439[/C][C]7.4217206075613[/C][/ROW]
[ROW][C]72[/C][C]113[/C][C]117.481029004066[/C][C]-4.48102900406599[/C][/ROW]
[ROW][C]73[/C][C]100[/C][C]103.203314309358[/C][C]-3.20331430935849[/C][/ROW]
[ROW][C]74[/C][C]84.8[/C][C]92.7650016690649[/C][C]-7.96500166906486[/C][/ROW]
[ROW][C]75[/C][C]94.3[/C][C]95.839837380656[/C][C]-1.53983738065592[/C][/ROW]
[ROW][C]76[/C][C]87.1[/C][C]85.4910672021026[/C][C]1.60893279789741[/C][/ROW]
[ROW][C]77[/C][C]90.3[/C][C]81.7750825983484[/C][C]8.5249174016516[/C][/ROW]
[ROW][C]78[/C][C]72.4[/C][C]73.517929041401[/C][C]-1.11792904140100[/C][/ROW]
[ROW][C]79[/C][C]84.9[/C][C]79.3348229649414[/C][C]5.5651770350586[/C][/ROW]
[ROW][C]80[/C][C]92.7[/C][C]87.4162404329703[/C][C]5.28375956702973[/C][/ROW]
[ROW][C]81[/C][C]92.2[/C][C]94.9180146596084[/C][C]-2.71801465960839[/C][/ROW]
[ROW][C]82[/C][C]114.9[/C][C]107.358314730579[/C][C]7.5416852694213[/C][/ROW]
[ROW][C]83[/C][C]112.5[/C][C]113.677822389135[/C][C]-1.17782238913462[/C][/ROW]
[ROW][C]84[/C][C]118.3[/C][C]118.709212124037[/C][C]-0.409212124036799[/C][/ROW]
[ROW][C]85[/C][C]106[/C][C]104.612183448303[/C][C]1.3878165516971[/C][/ROW]
[ROW][C]86[/C][C]91.2[/C][C]92.6327162683265[/C][C]-1.43271626832654[/C][/ROW]
[ROW][C]87[/C][C]96.6[/C][C]97.9209706617054[/C][C]-1.32097066170536[/C][/ROW]
[ROW][C]88[/C][C]96.3[/C][C]88.2829992059323[/C][C]8.01700079406768[/C][/ROW]
[ROW][C]89[/C][C]88.2[/C][C]86.7361763290643[/C][C]1.46382367093568[/C][/ROW]
[ROW][C]90[/C][C]70.2[/C][C]75.2051326429617[/C][C]-5.00513264296166[/C][/ROW]
[ROW][C]91[/C][C]86.5[/C][C]83.1039399520739[/C][C]3.39606004792611[/C][/ROW]
[ROW][C]92[/C][C]88.2[/C][C]91.2696948551364[/C][C]-3.06969485513638[/C][/ROW]
[ROW][C]93[/C][C]102.8[/C][C]96.3486909971822[/C][C]6.45130900281777[/C][/ROW]
[ROW][C]94[/C][C]119.1[/C][C]112.442143388516[/C][C]6.65785661148428[/C][/ROW]
[ROW][C]95[/C][C]119.2[/C][C]116.307306048254[/C][C]2.89269395174632[/C][/ROW]
[ROW][C]96[/C][C]125.1[/C][C]121.840064403980[/C][C]3.25993559602045[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77812&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77812&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
1395.995.23283596705040.667164032949628
1482.882.38472054383180.415279456168221
1583.382.87135140618230.428648593817712
168079.32127150482320.67872849517677
1780.479.66303332246670.736966677533331
1867.566.62942188118120.870578118818798
1975.769.93229768408165.76770231591844
2071.177.7982686267752-6.69826862677525
2189.380.95180026333418.34819973666589
22101.1103.332512310900-2.23251231089969
23105.2102.9215545532682.27844544673231
24114.1109.0559535633785.04404643662184
2596.397.741984652808-1.44198465280812
2684.484.4835199637877-0.0835199637877224
2791.284.99454234949986.20545765050016
2881.981.60086745924240.299132540757626
2980.581.9883718385475-1.48837183854752
3070.468.62509539385021.77490460614980
3174.873.52720899117121.27279100882878
3275.977.751492159424-1.85149215942394
3386.385.65324035093240.646759649067619
3498.7105.237888480149-6.53788848014867
35100.9106.071178136997-5.1711781369971
36113.8112.9767618348120.82323816518823
3789.899.3696110725818-9.56961107258182
3884.486.0426835940844-1.64268359408436
3987.288.3698923658617-1.16989236586168
4085.682.9484104555162.65158954448397
417282.8390669991697-10.8390669991697
4269.269.9986789971331-0.798678997133095
4377.574.69766104430872.80233895569133
4478.178.03785980741170.0621401925883163
4594.386.76935006455557.53064993544446
4697.7104.602732780584-6.90273278058403
47100.2105.79895602503-5.59895602502995
48116.4114.5028042340351.89719576596470
4997.197.6451719437032-0.545171943703224
509386.69393654956156.30606345043854
519689.38828467412286.61171532587724
5280.585.2070359491507-4.70703594915069
5376.180.88964954136-4.7896495413600
5469.970.9717658399781-1.07176583997810
5573.676.8181494442719-3.21814944427189
5692.679.237428301689813.3625716983101
5794.290.70615967879053.49384032120948
5893.5104.472917853241-10.9729178532409
59108.5105.9815584750442.51844152495588
60109.4117.312514017756-7.91251401775617
61105.199.19173239494385.90826760505617
6292.590.24161072856182.25838927143825
6397.192.97369033079564.12630966920439
6481.485.286514512536-3.88651451253594
6579.180.8902705288784-1.79027052887841
6672.171.97773704630870.122262953691290
6778.777.3339513618121.36604863818798
6887.184.86862977467392.23137022532609
6991.493.3148786061067-1.91487860610665
70109.9102.8450047408477.05499525915283
71116.3108.8782793924397.4217206075613
72113117.481029004066-4.48102900406599
73100103.203314309358-3.20331430935849
7484.892.7650016690649-7.96500166906486
7594.395.839837380656-1.53983738065592
7687.185.49106720210261.60893279789741
7790.381.77508259834848.5249174016516
7872.473.517929041401-1.11792904140100
7984.979.33482296494145.5651770350586
8092.787.41624043297035.28375956702973
8192.294.9180146596084-2.71801465960839
82114.9107.3583147305797.5416852694213
83112.5113.677822389135-1.17782238913462
84118.3118.709212124037-0.409212124036799
85106104.6121834483031.3878165516971
8691.292.6327162683265-1.43271626832654
8796.697.9209706617054-1.32097066170536
8896.388.28299920593238.01700079406768
8988.286.73617632906431.46382367093568
9070.275.2051326429617-5.00513264296166
9186.583.10393995207393.39606004792611
9288.291.2696948551364-3.06969485513638
93102.896.34869099718226.45130900281777
94119.1112.4421433885166.65785661148428
95119.2116.3073060482542.89269395174632
96125.1121.8400644039803.25993559602045







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97108.011178298607105.045621419736110.976735177477
9894.838385029740891.864853153498697.811916905983
99100.38101399375797.3938105159789103.368217471535
10093.329178099093790.33364735405596.3247088441323
10189.582535617105286.576547421988492.588523812222
10275.765158480445872.759875173623478.7704417872683
10386.572202711955983.535724507811389.6086809161005
10492.956355434532689.888523299318896.0241875697463
105101.15141620781998.0404853469597104.262347068678
106117.606294843281114.412876470844120.799713215718
107120.278326729567117.041626761403123.51502669773
108125.99020071115108.028689666140143.951711756160

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 108.011178298607 & 105.045621419736 & 110.976735177477 \tabularnewline
98 & 94.8383850297408 & 91.8648531534986 & 97.811916905983 \tabularnewline
99 & 100.381013993757 & 97.3938105159789 & 103.368217471535 \tabularnewline
100 & 93.3291780990937 & 90.333647354055 & 96.3247088441323 \tabularnewline
101 & 89.5825356171052 & 86.5765474219884 & 92.588523812222 \tabularnewline
102 & 75.7651584804458 & 72.7598751736234 & 78.7704417872683 \tabularnewline
103 & 86.5722027119559 & 83.5357245078113 & 89.6086809161005 \tabularnewline
104 & 92.9563554345326 & 89.8885232993188 & 96.0241875697463 \tabularnewline
105 & 101.151416207819 & 98.0404853469597 & 104.262347068678 \tabularnewline
106 & 117.606294843281 & 114.412876470844 & 120.799713215718 \tabularnewline
107 & 120.278326729567 & 117.041626761403 & 123.51502669773 \tabularnewline
108 & 125.99020071115 & 108.028689666140 & 143.951711756160 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77812&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]97[/C][C]108.011178298607[/C][C]105.045621419736[/C][C]110.976735177477[/C][/ROW]
[ROW][C]98[/C][C]94.8383850297408[/C][C]91.8648531534986[/C][C]97.811916905983[/C][/ROW]
[ROW][C]99[/C][C]100.381013993757[/C][C]97.3938105159789[/C][C]103.368217471535[/C][/ROW]
[ROW][C]100[/C][C]93.3291780990937[/C][C]90.333647354055[/C][C]96.3247088441323[/C][/ROW]
[ROW][C]101[/C][C]89.5825356171052[/C][C]86.5765474219884[/C][C]92.588523812222[/C][/ROW]
[ROW][C]102[/C][C]75.7651584804458[/C][C]72.7598751736234[/C][C]78.7704417872683[/C][/ROW]
[ROW][C]103[/C][C]86.5722027119559[/C][C]83.5357245078113[/C][C]89.6086809161005[/C][/ROW]
[ROW][C]104[/C][C]92.9563554345326[/C][C]89.8885232993188[/C][C]96.0241875697463[/C][/ROW]
[ROW][C]105[/C][C]101.151416207819[/C][C]98.0404853469597[/C][C]104.262347068678[/C][/ROW]
[ROW][C]106[/C][C]117.606294843281[/C][C]114.412876470844[/C][C]120.799713215718[/C][/ROW]
[ROW][C]107[/C][C]120.278326729567[/C][C]117.041626761403[/C][C]123.51502669773[/C][/ROW]
[ROW][C]108[/C][C]125.99020071115[/C][C]108.028689666140[/C][C]143.951711756160[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77812&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77812&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
97108.011178298607105.045621419736110.976735177477
9894.838385029740891.864853153498697.811916905983
99100.38101399375797.3938105159789103.368217471535
10093.329178099093790.33364735405596.3247088441323
10189.582535617105286.576547421988492.588523812222
10275.765158480445872.759875173623478.7704417872683
10386.572202711955983.535724507811389.6086809161005
10492.956355434532689.888523299318896.0241875697463
105101.15141620781998.0404853469597104.262347068678
106117.606294843281114.412876470844120.799713215718
107120.278326729567117.041626761403123.51502669773
108125.99020071115108.028689666140143.951711756160



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')