Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 01 Jun 2008 12:25:10 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Jun/01/t12123452251niyqcr49lnq4ce.htm/, Retrieved Sat, 18 May 2024 13:50:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13731, Retrieved Sat, 18 May 2024 13:50:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact206
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 oef 2] [2008-06-01 18:25:10] [2b08e9b5345c911f5a04c663d4ad43d5] [Current]
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Dataseries X:
78
69
78
74
81
80
76
71
72
69
70
68
62
57
49
57
57
58
53
55
62
54
62
68
73
74
79
77
76
83
77
84
78
74
75
79
79
82
88
81
69
62
62
68
57
67
72
75
81
80
79
81
83
84
90
84
90
92
93
85
93
94
94
102
96
96
92
90
84
86
70
67




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time8 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 & 8 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13731&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]8 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=13731&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13731&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 time8 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.690039354681511
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.690039354681511 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13731&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]0.690039354681511[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13731&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13731&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
alpha0.690039354681511
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136265.8847045912947-3.88470459129474
145759.6486145488604-2.64861454886037
154950.600721688916-1.60072168891604
165758.5915634346292-1.59156343462922
175758.4405615755904-1.44056157559039
185858.7912637201857-0.791263720185704
195352.80562904240350.194370957596519
205553.85951881967221.14048118032778
216259.6372771937682.362722806232
225451.61141925938072.38858074061930
236259.62413562201412.37586437798591
246865.35256903407322.64743096592683
257363.98702787876599.01297212123413
267466.58470403704397.41529596295612
277963.013697909860915.9863020901391
287787.7791692072488-10.7791692072488
297681.731326468887-5.73132646888706
308379.8828693472893.11713065271103
317774.7720147000372.22798529996304
328478.04859330619385.95140669380625
337890.1469770895449-12.1469770895449
347469.01088336665484.98911663334525
357580.9613005725973-5.96130057259728
367981.9926691848068-2.99266918480676
377978.20354114896920.796458851030806
388274.1348831525197.86511684748096
398872.283919870027715.7160801299723
408188.5253943469738-7.52539434697377
416986.4326655125165-17.4326655125165
426279.1258300697769-17.1258300697769
436261.18464490411230.81535509588769
446863.99349652734924.00650347265081
455768.3443836448818-11.3443836448818
466754.684893402779312.3151065972207
477267.46439616065074.53560383934929
487576.280351811562-1.280351811562
498174.87069284911826.12930715088179
508076.50333076811973.49666923188026
517973.6420507040935.35794929590706
528175.6232514730685.37674852693206
538378.50641321708464.49358678291539
548486.2025933492362-2.20259334923624
559083.91110758901356.08889241098647
568492.637590478116-8.63759047811602
579082.05437801672027.94562198327978
589289.05553956356052.94446043643946
599393.5452324173059-0.545232417305854
608598.1882770617686-13.1882770617686
619391.0702922639171.92970773608306
629488.47082058856855.52917941143147
639486.77600915819747.22399084180259
6410289.683905785882912.3160942141171
659696.784093133400-0.78409313339992
669699.15076370676-3.15076370675992
679298.9489664716977-6.94896647169774
689093.919750225103-3.9197502251029
698491.6090946664054-7.60909466640538
708686.3084784684595-0.308478468459498
717087.3828854337043-17.3828854337043
726775.9415462386613-8.94154623866126

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 62 & 65.8847045912947 & -3.88470459129474 \tabularnewline
14 & 57 & 59.6486145488604 & -2.64861454886037 \tabularnewline
15 & 49 & 50.600721688916 & -1.60072168891604 \tabularnewline
16 & 57 & 58.5915634346292 & -1.59156343462922 \tabularnewline
17 & 57 & 58.4405615755904 & -1.44056157559039 \tabularnewline
18 & 58 & 58.7912637201857 & -0.791263720185704 \tabularnewline
19 & 53 & 52.8056290424035 & 0.194370957596519 \tabularnewline
20 & 55 & 53.8595188196722 & 1.14048118032778 \tabularnewline
21 & 62 & 59.637277193768 & 2.362722806232 \tabularnewline
22 & 54 & 51.6114192593807 & 2.38858074061930 \tabularnewline
23 & 62 & 59.6241356220141 & 2.37586437798591 \tabularnewline
24 & 68 & 65.3525690340732 & 2.64743096592683 \tabularnewline
25 & 73 & 63.9870278787659 & 9.01297212123413 \tabularnewline
26 & 74 & 66.5847040370439 & 7.41529596295612 \tabularnewline
27 & 79 & 63.0136979098609 & 15.9863020901391 \tabularnewline
28 & 77 & 87.7791692072488 & -10.7791692072488 \tabularnewline
29 & 76 & 81.731326468887 & -5.73132646888706 \tabularnewline
30 & 83 & 79.882869347289 & 3.11713065271103 \tabularnewline
31 & 77 & 74.772014700037 & 2.22798529996304 \tabularnewline
32 & 84 & 78.0485933061938 & 5.95140669380625 \tabularnewline
33 & 78 & 90.1469770895449 & -12.1469770895449 \tabularnewline
34 & 74 & 69.0108833666548 & 4.98911663334525 \tabularnewline
35 & 75 & 80.9613005725973 & -5.96130057259728 \tabularnewline
36 & 79 & 81.9926691848068 & -2.99266918480676 \tabularnewline
37 & 79 & 78.2035411489692 & 0.796458851030806 \tabularnewline
38 & 82 & 74.134883152519 & 7.86511684748096 \tabularnewline
39 & 88 & 72.2839198700277 & 15.7160801299723 \tabularnewline
40 & 81 & 88.5253943469738 & -7.52539434697377 \tabularnewline
41 & 69 & 86.4326655125165 & -17.4326655125165 \tabularnewline
42 & 62 & 79.1258300697769 & -17.1258300697769 \tabularnewline
43 & 62 & 61.1846449041123 & 0.81535509588769 \tabularnewline
44 & 68 & 63.9934965273492 & 4.00650347265081 \tabularnewline
45 & 57 & 68.3443836448818 & -11.3443836448818 \tabularnewline
46 & 67 & 54.6848934027793 & 12.3151065972207 \tabularnewline
47 & 72 & 67.4643961606507 & 4.53560383934929 \tabularnewline
48 & 75 & 76.280351811562 & -1.280351811562 \tabularnewline
49 & 81 & 74.8706928491182 & 6.12930715088179 \tabularnewline
50 & 80 & 76.5033307681197 & 3.49666923188026 \tabularnewline
51 & 79 & 73.642050704093 & 5.35794929590706 \tabularnewline
52 & 81 & 75.623251473068 & 5.37674852693206 \tabularnewline
53 & 83 & 78.5064132170846 & 4.49358678291539 \tabularnewline
54 & 84 & 86.2025933492362 & -2.20259334923624 \tabularnewline
55 & 90 & 83.9111075890135 & 6.08889241098647 \tabularnewline
56 & 84 & 92.637590478116 & -8.63759047811602 \tabularnewline
57 & 90 & 82.0543780167202 & 7.94562198327978 \tabularnewline
58 & 92 & 89.0555395635605 & 2.94446043643946 \tabularnewline
59 & 93 & 93.5452324173059 & -0.545232417305854 \tabularnewline
60 & 85 & 98.1882770617686 & -13.1882770617686 \tabularnewline
61 & 93 & 91.070292263917 & 1.92970773608306 \tabularnewline
62 & 94 & 88.4708205885685 & 5.52917941143147 \tabularnewline
63 & 94 & 86.7760091581974 & 7.22399084180259 \tabularnewline
64 & 102 & 89.6839057858829 & 12.3160942141171 \tabularnewline
65 & 96 & 96.784093133400 & -0.78409313339992 \tabularnewline
66 & 96 & 99.15076370676 & -3.15076370675992 \tabularnewline
67 & 92 & 98.9489664716977 & -6.94896647169774 \tabularnewline
68 & 90 & 93.919750225103 & -3.9197502251029 \tabularnewline
69 & 84 & 91.6090946664054 & -7.60909466640538 \tabularnewline
70 & 86 & 86.3084784684595 & -0.308478468459498 \tabularnewline
71 & 70 & 87.3828854337043 & -17.3828854337043 \tabularnewline
72 & 67 & 75.9415462386613 & -8.94154623866126 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13731&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]62[/C][C]65.8847045912947[/C][C]-3.88470459129474[/C][/ROW]
[ROW][C]14[/C][C]57[/C][C]59.6486145488604[/C][C]-2.64861454886037[/C][/ROW]
[ROW][C]15[/C][C]49[/C][C]50.600721688916[/C][C]-1.60072168891604[/C][/ROW]
[ROW][C]16[/C][C]57[/C][C]58.5915634346292[/C][C]-1.59156343462922[/C][/ROW]
[ROW][C]17[/C][C]57[/C][C]58.4405615755904[/C][C]-1.44056157559039[/C][/ROW]
[ROW][C]18[/C][C]58[/C][C]58.7912637201857[/C][C]-0.791263720185704[/C][/ROW]
[ROW][C]19[/C][C]53[/C][C]52.8056290424035[/C][C]0.194370957596519[/C][/ROW]
[ROW][C]20[/C][C]55[/C][C]53.8595188196722[/C][C]1.14048118032778[/C][/ROW]
[ROW][C]21[/C][C]62[/C][C]59.637277193768[/C][C]2.362722806232[/C][/ROW]
[ROW][C]22[/C][C]54[/C][C]51.6114192593807[/C][C]2.38858074061930[/C][/ROW]
[ROW][C]23[/C][C]62[/C][C]59.6241356220141[/C][C]2.37586437798591[/C][/ROW]
[ROW][C]24[/C][C]68[/C][C]65.3525690340732[/C][C]2.64743096592683[/C][/ROW]
[ROW][C]25[/C][C]73[/C][C]63.9870278787659[/C][C]9.01297212123413[/C][/ROW]
[ROW][C]26[/C][C]74[/C][C]66.5847040370439[/C][C]7.41529596295612[/C][/ROW]
[ROW][C]27[/C][C]79[/C][C]63.0136979098609[/C][C]15.9863020901391[/C][/ROW]
[ROW][C]28[/C][C]77[/C][C]87.7791692072488[/C][C]-10.7791692072488[/C][/ROW]
[ROW][C]29[/C][C]76[/C][C]81.731326468887[/C][C]-5.73132646888706[/C][/ROW]
[ROW][C]30[/C][C]83[/C][C]79.882869347289[/C][C]3.11713065271103[/C][/ROW]
[ROW][C]31[/C][C]77[/C][C]74.772014700037[/C][C]2.22798529996304[/C][/ROW]
[ROW][C]32[/C][C]84[/C][C]78.0485933061938[/C][C]5.95140669380625[/C][/ROW]
[ROW][C]33[/C][C]78[/C][C]90.1469770895449[/C][C]-12.1469770895449[/C][/ROW]
[ROW][C]34[/C][C]74[/C][C]69.0108833666548[/C][C]4.98911663334525[/C][/ROW]
[ROW][C]35[/C][C]75[/C][C]80.9613005725973[/C][C]-5.96130057259728[/C][/ROW]
[ROW][C]36[/C][C]79[/C][C]81.9926691848068[/C][C]-2.99266918480676[/C][/ROW]
[ROW][C]37[/C][C]79[/C][C]78.2035411489692[/C][C]0.796458851030806[/C][/ROW]
[ROW][C]38[/C][C]82[/C][C]74.134883152519[/C][C]7.86511684748096[/C][/ROW]
[ROW][C]39[/C][C]88[/C][C]72.2839198700277[/C][C]15.7160801299723[/C][/ROW]
[ROW][C]40[/C][C]81[/C][C]88.5253943469738[/C][C]-7.52539434697377[/C][/ROW]
[ROW][C]41[/C][C]69[/C][C]86.4326655125165[/C][C]-17.4326655125165[/C][/ROW]
[ROW][C]42[/C][C]62[/C][C]79.1258300697769[/C][C]-17.1258300697769[/C][/ROW]
[ROW][C]43[/C][C]62[/C][C]61.1846449041123[/C][C]0.81535509588769[/C][/ROW]
[ROW][C]44[/C][C]68[/C][C]63.9934965273492[/C][C]4.00650347265081[/C][/ROW]
[ROW][C]45[/C][C]57[/C][C]68.3443836448818[/C][C]-11.3443836448818[/C][/ROW]
[ROW][C]46[/C][C]67[/C][C]54.6848934027793[/C][C]12.3151065972207[/C][/ROW]
[ROW][C]47[/C][C]72[/C][C]67.4643961606507[/C][C]4.53560383934929[/C][/ROW]
[ROW][C]48[/C][C]75[/C][C]76.280351811562[/C][C]-1.280351811562[/C][/ROW]
[ROW][C]49[/C][C]81[/C][C]74.8706928491182[/C][C]6.12930715088179[/C][/ROW]
[ROW][C]50[/C][C]80[/C][C]76.5033307681197[/C][C]3.49666923188026[/C][/ROW]
[ROW][C]51[/C][C]79[/C][C]73.642050704093[/C][C]5.35794929590706[/C][/ROW]
[ROW][C]52[/C][C]81[/C][C]75.623251473068[/C][C]5.37674852693206[/C][/ROW]
[ROW][C]53[/C][C]83[/C][C]78.5064132170846[/C][C]4.49358678291539[/C][/ROW]
[ROW][C]54[/C][C]84[/C][C]86.2025933492362[/C][C]-2.20259334923624[/C][/ROW]
[ROW][C]55[/C][C]90[/C][C]83.9111075890135[/C][C]6.08889241098647[/C][/ROW]
[ROW][C]56[/C][C]84[/C][C]92.637590478116[/C][C]-8.63759047811602[/C][/ROW]
[ROW][C]57[/C][C]90[/C][C]82.0543780167202[/C][C]7.94562198327978[/C][/ROW]
[ROW][C]58[/C][C]92[/C][C]89.0555395635605[/C][C]2.94446043643946[/C][/ROW]
[ROW][C]59[/C][C]93[/C][C]93.5452324173059[/C][C]-0.545232417305854[/C][/ROW]
[ROW][C]60[/C][C]85[/C][C]98.1882770617686[/C][C]-13.1882770617686[/C][/ROW]
[ROW][C]61[/C][C]93[/C][C]91.070292263917[/C][C]1.92970773608306[/C][/ROW]
[ROW][C]62[/C][C]94[/C][C]88.4708205885685[/C][C]5.52917941143147[/C][/ROW]
[ROW][C]63[/C][C]94[/C][C]86.7760091581974[/C][C]7.22399084180259[/C][/ROW]
[ROW][C]64[/C][C]102[/C][C]89.6839057858829[/C][C]12.3160942141171[/C][/ROW]
[ROW][C]65[/C][C]96[/C][C]96.784093133400[/C][C]-0.78409313339992[/C][/ROW]
[ROW][C]66[/C][C]96[/C][C]99.15076370676[/C][C]-3.15076370675992[/C][/ROW]
[ROW][C]67[/C][C]92[/C][C]98.9489664716977[/C][C]-6.94896647169774[/C][/ROW]
[ROW][C]68[/C][C]90[/C][C]93.919750225103[/C][C]-3.9197502251029[/C][/ROW]
[ROW][C]69[/C][C]84[/C][C]91.6090946664054[/C][C]-7.60909466640538[/C][/ROW]
[ROW][C]70[/C][C]86[/C][C]86.3084784684595[/C][C]-0.308478468459498[/C][/ROW]
[ROW][C]71[/C][C]70[/C][C]87.3828854337043[/C][C]-17.3828854337043[/C][/ROW]
[ROW][C]72[/C][C]67[/C][C]75.9415462386613[/C][C]-8.94154623866126[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13731&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13731&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
136265.8847045912947-3.88470459129474
145759.6486145488604-2.64861454886037
154950.600721688916-1.60072168891604
165758.5915634346292-1.59156343462922
175758.4405615755904-1.44056157559039
185858.7912637201857-0.791263720185704
195352.80562904240350.194370957596519
205553.85951881967221.14048118032778
216259.6372771937682.362722806232
225451.61141925938072.38858074061930
236259.62413562201412.37586437798591
246865.35256903407322.64743096592683
257363.98702787876599.01297212123413
267466.58470403704397.41529596295612
277963.013697909860915.9863020901391
287787.7791692072488-10.7791692072488
297681.731326468887-5.73132646888706
308379.8828693472893.11713065271103
317774.7720147000372.22798529996304
328478.04859330619385.95140669380625
337890.1469770895449-12.1469770895449
347469.01088336665484.98911663334525
357580.9613005725973-5.96130057259728
367981.9926691848068-2.99266918480676
377978.20354114896920.796458851030806
388274.1348831525197.86511684748096
398872.283919870027715.7160801299723
408188.5253943469738-7.52539434697377
416986.4326655125165-17.4326655125165
426279.1258300697769-17.1258300697769
436261.18464490411230.81535509588769
446863.99349652734924.00650347265081
455768.3443836448818-11.3443836448818
466754.684893402779312.3151065972207
477267.46439616065074.53560383934929
487576.280351811562-1.280351811562
498174.87069284911826.12930715088179
508076.50333076811973.49666923188026
517973.6420507040935.35794929590706
528175.6232514730685.37674852693206
538378.50641321708464.49358678291539
548486.2025933492362-2.20259334923624
559083.91110758901356.08889241098647
568492.637590478116-8.63759047811602
579082.05437801672027.94562198327978
589289.05553956356052.94446043643946
599393.5452324173059-0.545232417305854
608598.1882770617686-13.1882770617686
619391.0702922639171.92970773608306
629488.47082058856855.52917941143147
639486.77600915819747.22399084180259
6410289.683905785882912.3160942141171
659696.784093133400-0.78409313339992
669699.15076370676-3.15076370675992
679298.9489664716977-6.94896647169774
689093.919750225103-3.9197502251029
698491.6090946664054-7.60909466640538
708686.3084784684595-0.308478468459498
717087.3828854337043-17.3828854337043
726775.9415462386613-8.94154623866126







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7375.238172753341760.385641655687390.0907038509962
7472.90319609218455.168091882450490.6383003019175
7568.942785612244348.544789799237789.3407814252508
7668.33474727620146.203255671781290.4662388806207
7764.676619976007339.941823567486989.4114163845278
7866.126626643540139.220127674197493.0331256128829
7966.598720082976737.652642871527995.5447972944255
8067.082831005894136.609007987278597.5566540245098
8166.417352475890633.598277420308399.236427531473
8268.166837632206235.3571637951204100.976511469292
8364.312713697067528.767052140727999.8583752534072
8467NANA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 75.2381727533417 & 60.3856416556873 & 90.0907038509962 \tabularnewline
74 & 72.903196092184 & 55.1680918824504 & 90.6383003019175 \tabularnewline
75 & 68.9427856122443 & 48.5447897992377 & 89.3407814252508 \tabularnewline
76 & 68.334747276201 & 46.2032556717812 & 90.4662388806207 \tabularnewline
77 & 64.6766199760073 & 39.9418235674869 & 89.4114163845278 \tabularnewline
78 & 66.1266266435401 & 39.2201276741974 & 93.0331256128829 \tabularnewline
79 & 66.5987200829767 & 37.6526428715279 & 95.5447972944255 \tabularnewline
80 & 67.0828310058941 & 36.6090079872785 & 97.5566540245098 \tabularnewline
81 & 66.4173524758906 & 33.5982774203083 & 99.236427531473 \tabularnewline
82 & 68.1668376322062 & 35.3571637951204 & 100.976511469292 \tabularnewline
83 & 64.3127136970675 & 28.7670521407279 & 99.8583752534072 \tabularnewline
84 & 67 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13731&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]75.2381727533417[/C][C]60.3856416556873[/C][C]90.0907038509962[/C][/ROW]
[ROW][C]74[/C][C]72.903196092184[/C][C]55.1680918824504[/C][C]90.6383003019175[/C][/ROW]
[ROW][C]75[/C][C]68.9427856122443[/C][C]48.5447897992377[/C][C]89.3407814252508[/C][/ROW]
[ROW][C]76[/C][C]68.334747276201[/C][C]46.2032556717812[/C][C]90.4662388806207[/C][/ROW]
[ROW][C]77[/C][C]64.6766199760073[/C][C]39.9418235674869[/C][C]89.4114163845278[/C][/ROW]
[ROW][C]78[/C][C]66.1266266435401[/C][C]39.2201276741974[/C][C]93.0331256128829[/C][/ROW]
[ROW][C]79[/C][C]66.5987200829767[/C][C]37.6526428715279[/C][C]95.5447972944255[/C][/ROW]
[ROW][C]80[/C][C]67.0828310058941[/C][C]36.6090079872785[/C][C]97.5566540245098[/C][/ROW]
[ROW][C]81[/C][C]66.4173524758906[/C][C]33.5982774203083[/C][C]99.236427531473[/C][/ROW]
[ROW][C]82[/C][C]68.1668376322062[/C][C]35.3571637951204[/C][C]100.976511469292[/C][/ROW]
[ROW][C]83[/C][C]64.3127136970675[/C][C]28.7670521407279[/C][C]99.8583752534072[/C][/ROW]
[ROW][C]84[/C][C]67[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13731&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13731&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
7375.238172753341760.385641655687390.0907038509962
7472.90319609218455.168091882450490.6383003019175
7568.942785612244348.544789799237789.3407814252508
7668.33474727620146.203255671781290.4662388806207
7764.676619976007339.941823567486989.4114163845278
7866.126626643540139.220127674197493.0331256128829
7966.598720082976737.652642871527995.5447972944255
8067.082831005894136.609007987278597.5566540245098
8166.417352475890633.598277420308399.236427531473
8268.166837632206235.3571637951204100.976511469292
8364.312713697067528.767052140727999.8583752534072
8467NANA



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')