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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 11 Jan 2014 05:28:13 -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/2014/Jan/11/t1389436147lpj7rwejl1aywyr.htm/, Retrieved Sun, 19 May 2024 06:42:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232893, Retrieved Sun, 19 May 2024 06:42:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-01-11 10:28:13] [4758dc02678b81fd9e5a152cd29d8108] [Current]
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Dataseries X:
104.78
105.56
107.95
107.11
107.47
107.06
99.71
99.6
107.19
107.26
113.24
113.52
110.48
111.41
115.5
118.32
118.42
117.5
110.23
109.19
118.41
118.3
116.1
114.11
113.41
114.33
116.61
123.64
123.77
123.39
116.03
114.95
123.4
123.53
114.45
114.26
114.35
112.77
115.31
114.93
116.38
115.07
105
103.43
114.52
115.04
117.16
115
116.22
112.92
116.56
114.32
113.22
111.56
103.87
102.85
112.27
112.76
118.55
122.73
115.44
116.97
119.84
116.37
117.23
115.58
109.82
108.46
116.54
117.49
122.87
127.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232893&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232893&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232893&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 time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232893&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]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232893&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232893&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2105.56104.780.780000000000001
3107.95105.559948436572.39005156342985
4107.11107.949842000954-0.839842000953666
5107.47107.1100555194030.359944480597306
6107.06107.469976205164-0.409976205164128
799.71107.060027102281-7.35002710228116
899.699.7104858879576-0.11048588795758
9107.1999.60000730388637.58999269611368
10107.26107.1894982486460.0705017513538309
11113.24107.2599953393435.98000466065655
12113.52113.2396046800630.280395319936986
13110.48113.519981463917-3.03998146391741
14111.41110.4802009639370.929799036062846
15115.5111.4099385338114.09006146618894
16118.32115.4997296184652.82027038153527
17118.42118.3198135604950.100186439505123
18117.5118.419993376979-0.919993376978923
19110.23117.500060817967-7.27006081796661
20109.19110.23048060163-1.04048060162953
21118.41109.1900687830119.21993121698908
22118.3118.409390498363-0.109390498363368
23116.1118.300007231473-2.20000723147345
24114.11116.100145435793-1.99014543579302
25113.41114.110131562467-0.700131562467405
26114.33113.410046283570.919953716429859
27116.61114.3299391846552.28006081534478
28123.64116.6098492721087.03015072789221
29123.77123.6395352580980.130464741902458
30123.39123.769991375372-0.379991375372342
31116.03123.390025120075-7.36002512007516
32114.95116.030486548896-1.08048654889616
33123.4114.9500714276838.44992857231748
34123.53123.3994414008980.130558599101548
35114.45123.529991369168-9.07999136916773
36114.26114.450600250639-0.190600250638511
37114.35114.2600126000030.0899873999965877
38112.77114.349994051206-1.57999405120643
39115.31112.7701044486062.53989555139432
40114.93115.309832095223-0.379832095222937
41116.38114.9300251095461.44997489045436
42115.07116.379904146566-1.30990414656596
43105115.070086593783-10.0700865937828
44103.43105.000665702825-1.57066570282525
45114.52103.43010383193711.0898961680631
46115.04114.5192668806630.520733119337393
47117.16115.0399655759162.12003442408418
48115117.159859850966-2.15985985096626
49116.22115.0001427817721.2198572182283
50112.92116.219919358946-3.29991935894601
51116.56112.9202181476423.63978185235847
52114.32116.559759385082-2.23975938508177
53113.22114.320148063687-1.1001480636871
54111.56113.220072727446-1.66007272744552
55103.87111.560109742364-7.69010974236363
56102.85103.870508369788-1.02050836978754
57112.27102.8500674627079.41993253729264
58112.76112.2693772768840.490622723116189
59118.55112.7599675664235.79003243357739
60122.73118.549617238554.18038276145032
61115.44122.729723647598-7.28972364759836
62116.97115.4404819014791.52951809852057
63119.84116.9698988882062.87010111179383
64116.37119.839810266337-3.46981026633672
65117.23116.3702293786130.859770621386829
66115.58117.229943163177-1.64994316317677
67109.82115.580109072729-5.76010907272892
68108.46109.820380783308-1.36038078330785
69116.54108.460089930648.07991006936015
70117.49116.5394658616970.950534138302672
71122.87117.4899371630765.38006283692356
72127.1122.8696443403944.23035565960602

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 105.56 & 104.78 & 0.780000000000001 \tabularnewline
3 & 107.95 & 105.55994843657 & 2.39005156342985 \tabularnewline
4 & 107.11 & 107.949842000954 & -0.839842000953666 \tabularnewline
5 & 107.47 & 107.110055519403 & 0.359944480597306 \tabularnewline
6 & 107.06 & 107.469976205164 & -0.409976205164128 \tabularnewline
7 & 99.71 & 107.060027102281 & -7.35002710228116 \tabularnewline
8 & 99.6 & 99.7104858879576 & -0.11048588795758 \tabularnewline
9 & 107.19 & 99.6000073038863 & 7.58999269611368 \tabularnewline
10 & 107.26 & 107.189498248646 & 0.0705017513538309 \tabularnewline
11 & 113.24 & 107.259995339343 & 5.98000466065655 \tabularnewline
12 & 113.52 & 113.239604680063 & 0.280395319936986 \tabularnewline
13 & 110.48 & 113.519981463917 & -3.03998146391741 \tabularnewline
14 & 111.41 & 110.480200963937 & 0.929799036062846 \tabularnewline
15 & 115.5 & 111.409938533811 & 4.09006146618894 \tabularnewline
16 & 118.32 & 115.499729618465 & 2.82027038153527 \tabularnewline
17 & 118.42 & 118.319813560495 & 0.100186439505123 \tabularnewline
18 & 117.5 & 118.419993376979 & -0.919993376978923 \tabularnewline
19 & 110.23 & 117.500060817967 & -7.27006081796661 \tabularnewline
20 & 109.19 & 110.23048060163 & -1.04048060162953 \tabularnewline
21 & 118.41 & 109.190068783011 & 9.21993121698908 \tabularnewline
22 & 118.3 & 118.409390498363 & -0.109390498363368 \tabularnewline
23 & 116.1 & 118.300007231473 & -2.20000723147345 \tabularnewline
24 & 114.11 & 116.100145435793 & -1.99014543579302 \tabularnewline
25 & 113.41 & 114.110131562467 & -0.700131562467405 \tabularnewline
26 & 114.33 & 113.41004628357 & 0.919953716429859 \tabularnewline
27 & 116.61 & 114.329939184655 & 2.28006081534478 \tabularnewline
28 & 123.64 & 116.609849272108 & 7.03015072789221 \tabularnewline
29 & 123.77 & 123.639535258098 & 0.130464741902458 \tabularnewline
30 & 123.39 & 123.769991375372 & -0.379991375372342 \tabularnewline
31 & 116.03 & 123.390025120075 & -7.36002512007516 \tabularnewline
32 & 114.95 & 116.030486548896 & -1.08048654889616 \tabularnewline
33 & 123.4 & 114.950071427683 & 8.44992857231748 \tabularnewline
34 & 123.53 & 123.399441400898 & 0.130558599101548 \tabularnewline
35 & 114.45 & 123.529991369168 & -9.07999136916773 \tabularnewline
36 & 114.26 & 114.450600250639 & -0.190600250638511 \tabularnewline
37 & 114.35 & 114.260012600003 & 0.0899873999965877 \tabularnewline
38 & 112.77 & 114.349994051206 & -1.57999405120643 \tabularnewline
39 & 115.31 & 112.770104448606 & 2.53989555139432 \tabularnewline
40 & 114.93 & 115.309832095223 & -0.379832095222937 \tabularnewline
41 & 116.38 & 114.930025109546 & 1.44997489045436 \tabularnewline
42 & 115.07 & 116.379904146566 & -1.30990414656596 \tabularnewline
43 & 105 & 115.070086593783 & -10.0700865937828 \tabularnewline
44 & 103.43 & 105.000665702825 & -1.57066570282525 \tabularnewline
45 & 114.52 & 103.430103831937 & 11.0898961680631 \tabularnewline
46 & 115.04 & 114.519266880663 & 0.520733119337393 \tabularnewline
47 & 117.16 & 115.039965575916 & 2.12003442408418 \tabularnewline
48 & 115 & 117.159859850966 & -2.15985985096626 \tabularnewline
49 & 116.22 & 115.000142781772 & 1.2198572182283 \tabularnewline
50 & 112.92 & 116.219919358946 & -3.29991935894601 \tabularnewline
51 & 116.56 & 112.920218147642 & 3.63978185235847 \tabularnewline
52 & 114.32 & 116.559759385082 & -2.23975938508177 \tabularnewline
53 & 113.22 & 114.320148063687 & -1.1001480636871 \tabularnewline
54 & 111.56 & 113.220072727446 & -1.66007272744552 \tabularnewline
55 & 103.87 & 111.560109742364 & -7.69010974236363 \tabularnewline
56 & 102.85 & 103.870508369788 & -1.02050836978754 \tabularnewline
57 & 112.27 & 102.850067462707 & 9.41993253729264 \tabularnewline
58 & 112.76 & 112.269377276884 & 0.490622723116189 \tabularnewline
59 & 118.55 & 112.759967566423 & 5.79003243357739 \tabularnewline
60 & 122.73 & 118.54961723855 & 4.18038276145032 \tabularnewline
61 & 115.44 & 122.729723647598 & -7.28972364759836 \tabularnewline
62 & 116.97 & 115.440481901479 & 1.52951809852057 \tabularnewline
63 & 119.84 & 116.969898888206 & 2.87010111179383 \tabularnewline
64 & 116.37 & 119.839810266337 & -3.46981026633672 \tabularnewline
65 & 117.23 & 116.370229378613 & 0.859770621386829 \tabularnewline
66 & 115.58 & 117.229943163177 & -1.64994316317677 \tabularnewline
67 & 109.82 & 115.580109072729 & -5.76010907272892 \tabularnewline
68 & 108.46 & 109.820380783308 & -1.36038078330785 \tabularnewline
69 & 116.54 & 108.46008993064 & 8.07991006936015 \tabularnewline
70 & 117.49 & 116.539465861697 & 0.950534138302672 \tabularnewline
71 & 122.87 & 117.489937163076 & 5.38006283692356 \tabularnewline
72 & 127.1 & 122.869644340394 & 4.23035565960602 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232893&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]2[/C][C]105.56[/C][C]104.78[/C][C]0.780000000000001[/C][/ROW]
[ROW][C]3[/C][C]107.95[/C][C]105.55994843657[/C][C]2.39005156342985[/C][/ROW]
[ROW][C]4[/C][C]107.11[/C][C]107.949842000954[/C][C]-0.839842000953666[/C][/ROW]
[ROW][C]5[/C][C]107.47[/C][C]107.110055519403[/C][C]0.359944480597306[/C][/ROW]
[ROW][C]6[/C][C]107.06[/C][C]107.469976205164[/C][C]-0.409976205164128[/C][/ROW]
[ROW][C]7[/C][C]99.71[/C][C]107.060027102281[/C][C]-7.35002710228116[/C][/ROW]
[ROW][C]8[/C][C]99.6[/C][C]99.7104858879576[/C][C]-0.11048588795758[/C][/ROW]
[ROW][C]9[/C][C]107.19[/C][C]99.6000073038863[/C][C]7.58999269611368[/C][/ROW]
[ROW][C]10[/C][C]107.26[/C][C]107.189498248646[/C][C]0.0705017513538309[/C][/ROW]
[ROW][C]11[/C][C]113.24[/C][C]107.259995339343[/C][C]5.98000466065655[/C][/ROW]
[ROW][C]12[/C][C]113.52[/C][C]113.239604680063[/C][C]0.280395319936986[/C][/ROW]
[ROW][C]13[/C][C]110.48[/C][C]113.519981463917[/C][C]-3.03998146391741[/C][/ROW]
[ROW][C]14[/C][C]111.41[/C][C]110.480200963937[/C][C]0.929799036062846[/C][/ROW]
[ROW][C]15[/C][C]115.5[/C][C]111.409938533811[/C][C]4.09006146618894[/C][/ROW]
[ROW][C]16[/C][C]118.32[/C][C]115.499729618465[/C][C]2.82027038153527[/C][/ROW]
[ROW][C]17[/C][C]118.42[/C][C]118.319813560495[/C][C]0.100186439505123[/C][/ROW]
[ROW][C]18[/C][C]117.5[/C][C]118.419993376979[/C][C]-0.919993376978923[/C][/ROW]
[ROW][C]19[/C][C]110.23[/C][C]117.500060817967[/C][C]-7.27006081796661[/C][/ROW]
[ROW][C]20[/C][C]109.19[/C][C]110.23048060163[/C][C]-1.04048060162953[/C][/ROW]
[ROW][C]21[/C][C]118.41[/C][C]109.190068783011[/C][C]9.21993121698908[/C][/ROW]
[ROW][C]22[/C][C]118.3[/C][C]118.409390498363[/C][C]-0.109390498363368[/C][/ROW]
[ROW][C]23[/C][C]116.1[/C][C]118.300007231473[/C][C]-2.20000723147345[/C][/ROW]
[ROW][C]24[/C][C]114.11[/C][C]116.100145435793[/C][C]-1.99014543579302[/C][/ROW]
[ROW][C]25[/C][C]113.41[/C][C]114.110131562467[/C][C]-0.700131562467405[/C][/ROW]
[ROW][C]26[/C][C]114.33[/C][C]113.41004628357[/C][C]0.919953716429859[/C][/ROW]
[ROW][C]27[/C][C]116.61[/C][C]114.329939184655[/C][C]2.28006081534478[/C][/ROW]
[ROW][C]28[/C][C]123.64[/C][C]116.609849272108[/C][C]7.03015072789221[/C][/ROW]
[ROW][C]29[/C][C]123.77[/C][C]123.639535258098[/C][C]0.130464741902458[/C][/ROW]
[ROW][C]30[/C][C]123.39[/C][C]123.769991375372[/C][C]-0.379991375372342[/C][/ROW]
[ROW][C]31[/C][C]116.03[/C][C]123.390025120075[/C][C]-7.36002512007516[/C][/ROW]
[ROW][C]32[/C][C]114.95[/C][C]116.030486548896[/C][C]-1.08048654889616[/C][/ROW]
[ROW][C]33[/C][C]123.4[/C][C]114.950071427683[/C][C]8.44992857231748[/C][/ROW]
[ROW][C]34[/C][C]123.53[/C][C]123.399441400898[/C][C]0.130558599101548[/C][/ROW]
[ROW][C]35[/C][C]114.45[/C][C]123.529991369168[/C][C]-9.07999136916773[/C][/ROW]
[ROW][C]36[/C][C]114.26[/C][C]114.450600250639[/C][C]-0.190600250638511[/C][/ROW]
[ROW][C]37[/C][C]114.35[/C][C]114.260012600003[/C][C]0.0899873999965877[/C][/ROW]
[ROW][C]38[/C][C]112.77[/C][C]114.349994051206[/C][C]-1.57999405120643[/C][/ROW]
[ROW][C]39[/C][C]115.31[/C][C]112.770104448606[/C][C]2.53989555139432[/C][/ROW]
[ROW][C]40[/C][C]114.93[/C][C]115.309832095223[/C][C]-0.379832095222937[/C][/ROW]
[ROW][C]41[/C][C]116.38[/C][C]114.930025109546[/C][C]1.44997489045436[/C][/ROW]
[ROW][C]42[/C][C]115.07[/C][C]116.379904146566[/C][C]-1.30990414656596[/C][/ROW]
[ROW][C]43[/C][C]105[/C][C]115.070086593783[/C][C]-10.0700865937828[/C][/ROW]
[ROW][C]44[/C][C]103.43[/C][C]105.000665702825[/C][C]-1.57066570282525[/C][/ROW]
[ROW][C]45[/C][C]114.52[/C][C]103.430103831937[/C][C]11.0898961680631[/C][/ROW]
[ROW][C]46[/C][C]115.04[/C][C]114.519266880663[/C][C]0.520733119337393[/C][/ROW]
[ROW][C]47[/C][C]117.16[/C][C]115.039965575916[/C][C]2.12003442408418[/C][/ROW]
[ROW][C]48[/C][C]115[/C][C]117.159859850966[/C][C]-2.15985985096626[/C][/ROW]
[ROW][C]49[/C][C]116.22[/C][C]115.000142781772[/C][C]1.2198572182283[/C][/ROW]
[ROW][C]50[/C][C]112.92[/C][C]116.219919358946[/C][C]-3.29991935894601[/C][/ROW]
[ROW][C]51[/C][C]116.56[/C][C]112.920218147642[/C][C]3.63978185235847[/C][/ROW]
[ROW][C]52[/C][C]114.32[/C][C]116.559759385082[/C][C]-2.23975938508177[/C][/ROW]
[ROW][C]53[/C][C]113.22[/C][C]114.320148063687[/C][C]-1.1001480636871[/C][/ROW]
[ROW][C]54[/C][C]111.56[/C][C]113.220072727446[/C][C]-1.66007272744552[/C][/ROW]
[ROW][C]55[/C][C]103.87[/C][C]111.560109742364[/C][C]-7.69010974236363[/C][/ROW]
[ROW][C]56[/C][C]102.85[/C][C]103.870508369788[/C][C]-1.02050836978754[/C][/ROW]
[ROW][C]57[/C][C]112.27[/C][C]102.850067462707[/C][C]9.41993253729264[/C][/ROW]
[ROW][C]58[/C][C]112.76[/C][C]112.269377276884[/C][C]0.490622723116189[/C][/ROW]
[ROW][C]59[/C][C]118.55[/C][C]112.759967566423[/C][C]5.79003243357739[/C][/ROW]
[ROW][C]60[/C][C]122.73[/C][C]118.54961723855[/C][C]4.18038276145032[/C][/ROW]
[ROW][C]61[/C][C]115.44[/C][C]122.729723647598[/C][C]-7.28972364759836[/C][/ROW]
[ROW][C]62[/C][C]116.97[/C][C]115.440481901479[/C][C]1.52951809852057[/C][/ROW]
[ROW][C]63[/C][C]119.84[/C][C]116.969898888206[/C][C]2.87010111179383[/C][/ROW]
[ROW][C]64[/C][C]116.37[/C][C]119.839810266337[/C][C]-3.46981026633672[/C][/ROW]
[ROW][C]65[/C][C]117.23[/C][C]116.370229378613[/C][C]0.859770621386829[/C][/ROW]
[ROW][C]66[/C][C]115.58[/C][C]117.229943163177[/C][C]-1.64994316317677[/C][/ROW]
[ROW][C]67[/C][C]109.82[/C][C]115.580109072729[/C][C]-5.76010907272892[/C][/ROW]
[ROW][C]68[/C][C]108.46[/C][C]109.820380783308[/C][C]-1.36038078330785[/C][/ROW]
[ROW][C]69[/C][C]116.54[/C][C]108.46008993064[/C][C]8.07991006936015[/C][/ROW]
[ROW][C]70[/C][C]117.49[/C][C]116.539465861697[/C][C]0.950534138302672[/C][/ROW]
[ROW][C]71[/C][C]122.87[/C][C]117.489937163076[/C][C]5.38006283692356[/C][/ROW]
[ROW][C]72[/C][C]127.1[/C][C]122.869644340394[/C][C]4.23035565960602[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232893&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232893&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
2105.56104.780.780000000000001
3107.95105.559948436572.39005156342985
4107.11107.949842000954-0.839842000953666
5107.47107.1100555194030.359944480597306
6107.06107.469976205164-0.409976205164128
799.71107.060027102281-7.35002710228116
899.699.7104858879576-0.11048588795758
9107.1999.60000730388637.58999269611368
10107.26107.1894982486460.0705017513538309
11113.24107.2599953393435.98000466065655
12113.52113.2396046800630.280395319936986
13110.48113.519981463917-3.03998146391741
14111.41110.4802009639370.929799036062846
15115.5111.4099385338114.09006146618894
16118.32115.4997296184652.82027038153527
17118.42118.3198135604950.100186439505123
18117.5118.419993376979-0.919993376978923
19110.23117.500060817967-7.27006081796661
20109.19110.23048060163-1.04048060162953
21118.41109.1900687830119.21993121698908
22118.3118.409390498363-0.109390498363368
23116.1118.300007231473-2.20000723147345
24114.11116.100145435793-1.99014543579302
25113.41114.110131562467-0.700131562467405
26114.33113.410046283570.919953716429859
27116.61114.3299391846552.28006081534478
28123.64116.6098492721087.03015072789221
29123.77123.6395352580980.130464741902458
30123.39123.769991375372-0.379991375372342
31116.03123.390025120075-7.36002512007516
32114.95116.030486548896-1.08048654889616
33123.4114.9500714276838.44992857231748
34123.53123.3994414008980.130558599101548
35114.45123.529991369168-9.07999136916773
36114.26114.450600250639-0.190600250638511
37114.35114.2600126000030.0899873999965877
38112.77114.349994051206-1.57999405120643
39115.31112.7701044486062.53989555139432
40114.93115.309832095223-0.379832095222937
41116.38114.9300251095461.44997489045436
42115.07116.379904146566-1.30990414656596
43105115.070086593783-10.0700865937828
44103.43105.000665702825-1.57066570282525
45114.52103.43010383193711.0898961680631
46115.04114.5192668806630.520733119337393
47117.16115.0399655759162.12003442408418
48115117.159859850966-2.15985985096626
49116.22115.0001427817721.2198572182283
50112.92116.219919358946-3.29991935894601
51116.56112.9202181476423.63978185235847
52114.32116.559759385082-2.23975938508177
53113.22114.320148063687-1.1001480636871
54111.56113.220072727446-1.66007272744552
55103.87111.560109742364-7.69010974236363
56102.85103.870508369788-1.02050836978754
57112.27102.8500674627079.41993253729264
58112.76112.2693772768840.490622723116189
59118.55112.7599675664235.79003243357739
60122.73118.549617238554.18038276145032
61115.44122.729723647598-7.28972364759836
62116.97115.4404819014791.52951809852057
63119.84116.9698988882062.87010111179383
64116.37119.839810266337-3.46981026633672
65117.23116.3702293786130.859770621386829
66115.58117.229943163177-1.64994316317677
67109.82115.580109072729-5.76010907272892
68108.46109.820380783308-1.36038078330785
69116.54108.460089930648.07991006936015
70117.49116.5394658616970.950534138302672
71122.87117.4899371630765.38006283692356
72127.1122.8696443403944.23035565960602







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73127.099720344042118.628032757443135.571407930641
74127.099720344042115.119340862672139.080099825412
75127.099720344042112.426973686707141.772467001377
76127.099720344042110.157185220188144.042255467896
77127.099720344042108.157452835221146.041987852863
78127.099720344042106.349551662115147.849889025969
79127.099720344042104.687011844596149.512428843488
80127.099720344042103.139555398161151.059885289923
81127.099720344042101.686151012157152.513289675927
82127.099720344042100.311485834481153.887954853603
83127.09972034404299.0039998497755155.195440838308
84127.09972034404297.7547120454463156.444728642637

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 127.099720344042 & 118.628032757443 & 135.571407930641 \tabularnewline
74 & 127.099720344042 & 115.119340862672 & 139.080099825412 \tabularnewline
75 & 127.099720344042 & 112.426973686707 & 141.772467001377 \tabularnewline
76 & 127.099720344042 & 110.157185220188 & 144.042255467896 \tabularnewline
77 & 127.099720344042 & 108.157452835221 & 146.041987852863 \tabularnewline
78 & 127.099720344042 & 106.349551662115 & 147.849889025969 \tabularnewline
79 & 127.099720344042 & 104.687011844596 & 149.512428843488 \tabularnewline
80 & 127.099720344042 & 103.139555398161 & 151.059885289923 \tabularnewline
81 & 127.099720344042 & 101.686151012157 & 152.513289675927 \tabularnewline
82 & 127.099720344042 & 100.311485834481 & 153.887954853603 \tabularnewline
83 & 127.099720344042 & 99.0039998497755 & 155.195440838308 \tabularnewline
84 & 127.099720344042 & 97.7547120454463 & 156.444728642637 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232893&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]127.099720344042[/C][C]118.628032757443[/C][C]135.571407930641[/C][/ROW]
[ROW][C]74[/C][C]127.099720344042[/C][C]115.119340862672[/C][C]139.080099825412[/C][/ROW]
[ROW][C]75[/C][C]127.099720344042[/C][C]112.426973686707[/C][C]141.772467001377[/C][/ROW]
[ROW][C]76[/C][C]127.099720344042[/C][C]110.157185220188[/C][C]144.042255467896[/C][/ROW]
[ROW][C]77[/C][C]127.099720344042[/C][C]108.157452835221[/C][C]146.041987852863[/C][/ROW]
[ROW][C]78[/C][C]127.099720344042[/C][C]106.349551662115[/C][C]147.849889025969[/C][/ROW]
[ROW][C]79[/C][C]127.099720344042[/C][C]104.687011844596[/C][C]149.512428843488[/C][/ROW]
[ROW][C]80[/C][C]127.099720344042[/C][C]103.139555398161[/C][C]151.059885289923[/C][/ROW]
[ROW][C]81[/C][C]127.099720344042[/C][C]101.686151012157[/C][C]152.513289675927[/C][/ROW]
[ROW][C]82[/C][C]127.099720344042[/C][C]100.311485834481[/C][C]153.887954853603[/C][/ROW]
[ROW][C]83[/C][C]127.099720344042[/C][C]99.0039998497755[/C][C]155.195440838308[/C][/ROW]
[ROW][C]84[/C][C]127.099720344042[/C][C]97.7547120454463[/C][C]156.444728642637[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232893&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232893&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
73127.099720344042118.628032757443135.571407930641
74127.099720344042115.119340862672139.080099825412
75127.099720344042112.426973686707141.772467001377
76127.099720344042110.157185220188144.042255467896
77127.099720344042108.157452835221146.041987852863
78127.099720344042106.349551662115147.849889025969
79127.099720344042104.687011844596149.512428843488
80127.099720344042103.139555398161151.059885289923
81127.099720344042101.686151012157152.513289675927
82127.099720344042100.311485834481153.887954853603
83127.09972034404299.0039998497755155.195440838308
84127.09972034404297.7547120454463156.444728642637



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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')