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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 23 Dec 2011 15:11:27 -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/2011/Dec/23/t1324671150vq6it00ezxyxc07.htm/, Retrieved Mon, 29 Apr 2024 21:00:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160692, Retrieved Mon, 29 Apr 2024 21:00:44 +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)
-     [Spectral Analysis] [] [2011-12-23 18:50:40] [2ba7ee2cbaa966a49160c7cfb7436069]
- RMP     [Exponential Smoothing] [] [2011-12-23 20:11:27] [393d554610c677f923bed472882d0fdb] [Current]
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Dataseries X:
302
262
218
175
100
77
43
47
49
69
152
205
246
294
242
181
107
56
49
47
47
71
151
244
280
230
185
148
98
61
46
45
55
48
115
185
276
220
181
151
83
55
49
42
46
74
103
200
237
247
215
182
80
46
65
40
44
63
85
185
247
231
167
117
79
45
40
38
41
69
152
232
282
255
161
107
53
40
39
34
35
56
97
210
260
257
210
125
80
42
35
31
32
50
92
189
256
250
198
136
73
39
32
30
31
45




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160692&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160692&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160692&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.044152333311505
beta0.0411060207296206
gamma0.391529447629937

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.044152333311505 \tabularnewline
beta & 0.0411060207296206 \tabularnewline
gamma & 0.391529447629937 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160692&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]0.044152333311505[/C][/ROW]
[ROW][C]beta[/C][C]0.0411060207296206[/C][/ROW]
[ROW][C]gamma[/C][C]0.391529447629937[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160692&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160692&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
alpha0.044152333311505
beta0.0411060207296206
gamma0.391529447629937







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13246244.8835470085471.116452991453
14294292.9232122818721.07678771812766
15242241.2964138649730.703586135027251
16181180.5710813513330.428918648667434
17107106.7927334165380.207266583462172
185654.46330853287661.53669146712342
194945.48703650887493.51296349112512
204750.8960639439936-3.89606394399364
214750.6375611263622-3.6375611263622
227169.46720323771591.53279676228412
23151152.236243961055-1.23624396105518
24244206.00578138321737.9942186167833
25280250.03588282329129.964117176709
26230299.458150625152-69.4581506251521
27185244.573141734302-59.5731417343023
28148180.970000477811-32.970000477811
2998105.459785803668-7.45978580366759
306153.10117992828457.89882007171549
314644.96877248176131.03122751823871
324547.3143050519288-2.31430505192876
335547.04410668481637.95589331518374
344868.1633592013522-20.1633592013522
35115148.741558965934-33.7415589659343
36185215.502010561893-30.5020105618933
37276253.12271564706722.8772843529332
38220264.631259509793-44.6312595097933
39181214.194080521376-33.1940805213758
40151161.411812963677-10.4118129636765
418396.1856933704142-13.1856933704142
425549.05281813300275.94718186699728
434937.991253778398311.0087462216017
444239.27054258264322.72945741735676
454642.82100296645053.17899703354955
467452.951675102482121.0483248975179
47103130.088473867801-27.0884738678009
48200198.1876728142391.81232718576103
49237257.103202118011-20.1032021180114
50247241.2627535036225.73724649637796
51215197.23441840727917.7655815927213
52182155.22539812651626.7746018734844
538090.6676984903715-10.6676984903715
544650.8755607483303-4.87556074833033
556541.279984026638123.7200159733619
564040.0946976874145-0.0946976874144525
574443.7562306850860.243769314914047
586360.5069693560182.493030643982
5985118.838197336475-33.838197336475
60185197.471563380981-12.4715633809811
61247247.545053542196-0.545053542196484
62231242.264584377804-11.2645843778045
63167201.982083238645-34.9820832386445
64117160.914945841015-43.9149458410148
657978.99459796274480.00540203725520882
664541.63169822838613.3683017716139
674042.907081211191-2.90708121119104
683831.39063554242536.60936445757473
694135.24397197915695.75602802084309
706952.858997995064616.1410020049354
7115298.000034969397553.9999650306025
72232188.47129249053643.5287075094638
73282245.54569758610536.4543024138949
74255238.01924866679416.9807513332064
75161190.291128402667-29.2911284026666
76107146.325911371468-39.3259113714676
775381.2470783623455-28.2470783623455
784044.0460666540904-4.04606665409037
793942.7828772869157-3.78287728691575
803434.9249365638231-0.92493656382311
813538.2483019397091-3.24830193970914
825659.4579629762814-3.45796297628142
8397117.972221019114-20.9722210191138
84210201.1485506753818.85144932461907
85260253.9154528834876.08454711651328
86257237.57628099692219.4237190030777
87210172.45955610240337.5404438975968
88125127.631397992206-2.63139799220554
898068.327212903423311.6727870965767
904242.0265846457346-0.0265846457346299
913541.1274374064466-6.12743740644662
923134.3193625547326-3.31936255473261
933236.7469814055377-4.74698140553774
945057.8887632378853-7.88876323788527
9592109.721524723874-17.7215247238743
96189204.27727868341-15.2772786834099
97256254.9741702135441.02582978645646
98250243.4253694940566.5746305059435
99198184.51969597244913.4803040275514
100136123.54986829036812.4501317096322
1017370.24682655683932.75317344316068
1023939.1398103776277-0.139810377627725
1033235.9180960853078-3.91809608530775
1043030.2281101496311-0.228110149631149
1053132.2331901068143-1.23319010681435
1064552.3359537423806-7.33595374238064

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 246 & 244.883547008547 & 1.116452991453 \tabularnewline
14 & 294 & 292.923212281872 & 1.07678771812766 \tabularnewline
15 & 242 & 241.296413864973 & 0.703586135027251 \tabularnewline
16 & 181 & 180.571081351333 & 0.428918648667434 \tabularnewline
17 & 107 & 106.792733416538 & 0.207266583462172 \tabularnewline
18 & 56 & 54.4633085328766 & 1.53669146712342 \tabularnewline
19 & 49 & 45.4870365088749 & 3.51296349112512 \tabularnewline
20 & 47 & 50.8960639439936 & -3.89606394399364 \tabularnewline
21 & 47 & 50.6375611263622 & -3.6375611263622 \tabularnewline
22 & 71 & 69.4672032377159 & 1.53279676228412 \tabularnewline
23 & 151 & 152.236243961055 & -1.23624396105518 \tabularnewline
24 & 244 & 206.005781383217 & 37.9942186167833 \tabularnewline
25 & 280 & 250.035882823291 & 29.964117176709 \tabularnewline
26 & 230 & 299.458150625152 & -69.4581506251521 \tabularnewline
27 & 185 & 244.573141734302 & -59.5731417343023 \tabularnewline
28 & 148 & 180.970000477811 & -32.970000477811 \tabularnewline
29 & 98 & 105.459785803668 & -7.45978580366759 \tabularnewline
30 & 61 & 53.1011799282845 & 7.89882007171549 \tabularnewline
31 & 46 & 44.9687724817613 & 1.03122751823871 \tabularnewline
32 & 45 & 47.3143050519288 & -2.31430505192876 \tabularnewline
33 & 55 & 47.0441066848163 & 7.95589331518374 \tabularnewline
34 & 48 & 68.1633592013522 & -20.1633592013522 \tabularnewline
35 & 115 & 148.741558965934 & -33.7415589659343 \tabularnewline
36 & 185 & 215.502010561893 & -30.5020105618933 \tabularnewline
37 & 276 & 253.122715647067 & 22.8772843529332 \tabularnewline
38 & 220 & 264.631259509793 & -44.6312595097933 \tabularnewline
39 & 181 & 214.194080521376 & -33.1940805213758 \tabularnewline
40 & 151 & 161.411812963677 & -10.4118129636765 \tabularnewline
41 & 83 & 96.1856933704142 & -13.1856933704142 \tabularnewline
42 & 55 & 49.0528181330027 & 5.94718186699728 \tabularnewline
43 & 49 & 37.9912537783983 & 11.0087462216017 \tabularnewline
44 & 42 & 39.2705425826432 & 2.72945741735676 \tabularnewline
45 & 46 & 42.8210029664505 & 3.17899703354955 \tabularnewline
46 & 74 & 52.9516751024821 & 21.0483248975179 \tabularnewline
47 & 103 & 130.088473867801 & -27.0884738678009 \tabularnewline
48 & 200 & 198.187672814239 & 1.81232718576103 \tabularnewline
49 & 237 & 257.103202118011 & -20.1032021180114 \tabularnewline
50 & 247 & 241.262753503622 & 5.73724649637796 \tabularnewline
51 & 215 & 197.234418407279 & 17.7655815927213 \tabularnewline
52 & 182 & 155.225398126516 & 26.7746018734844 \tabularnewline
53 & 80 & 90.6676984903715 & -10.6676984903715 \tabularnewline
54 & 46 & 50.8755607483303 & -4.87556074833033 \tabularnewline
55 & 65 & 41.2799840266381 & 23.7200159733619 \tabularnewline
56 & 40 & 40.0946976874145 & -0.0946976874144525 \tabularnewline
57 & 44 & 43.756230685086 & 0.243769314914047 \tabularnewline
58 & 63 & 60.506969356018 & 2.493030643982 \tabularnewline
59 & 85 & 118.838197336475 & -33.838197336475 \tabularnewline
60 & 185 & 197.471563380981 & -12.4715633809811 \tabularnewline
61 & 247 & 247.545053542196 & -0.545053542196484 \tabularnewline
62 & 231 & 242.264584377804 & -11.2645843778045 \tabularnewline
63 & 167 & 201.982083238645 & -34.9820832386445 \tabularnewline
64 & 117 & 160.914945841015 & -43.9149458410148 \tabularnewline
65 & 79 & 78.9945979627448 & 0.00540203725520882 \tabularnewline
66 & 45 & 41.6316982283861 & 3.3683017716139 \tabularnewline
67 & 40 & 42.907081211191 & -2.90708121119104 \tabularnewline
68 & 38 & 31.3906355424253 & 6.60936445757473 \tabularnewline
69 & 41 & 35.2439719791569 & 5.75602802084309 \tabularnewline
70 & 69 & 52.8589979950646 & 16.1410020049354 \tabularnewline
71 & 152 & 98.0000349693975 & 53.9999650306025 \tabularnewline
72 & 232 & 188.471292490536 & 43.5287075094638 \tabularnewline
73 & 282 & 245.545697586105 & 36.4543024138949 \tabularnewline
74 & 255 & 238.019248666794 & 16.9807513332064 \tabularnewline
75 & 161 & 190.291128402667 & -29.2911284026666 \tabularnewline
76 & 107 & 146.325911371468 & -39.3259113714676 \tabularnewline
77 & 53 & 81.2470783623455 & -28.2470783623455 \tabularnewline
78 & 40 & 44.0460666540904 & -4.04606665409037 \tabularnewline
79 & 39 & 42.7828772869157 & -3.78287728691575 \tabularnewline
80 & 34 & 34.9249365638231 & -0.92493656382311 \tabularnewline
81 & 35 & 38.2483019397091 & -3.24830193970914 \tabularnewline
82 & 56 & 59.4579629762814 & -3.45796297628142 \tabularnewline
83 & 97 & 117.972221019114 & -20.9722210191138 \tabularnewline
84 & 210 & 201.148550675381 & 8.85144932461907 \tabularnewline
85 & 260 & 253.915452883487 & 6.08454711651328 \tabularnewline
86 & 257 & 237.576280996922 & 19.4237190030777 \tabularnewline
87 & 210 & 172.459556102403 & 37.5404438975968 \tabularnewline
88 & 125 & 127.631397992206 & -2.63139799220554 \tabularnewline
89 & 80 & 68.3272129034233 & 11.6727870965767 \tabularnewline
90 & 42 & 42.0265846457346 & -0.0265846457346299 \tabularnewline
91 & 35 & 41.1274374064466 & -6.12743740644662 \tabularnewline
92 & 31 & 34.3193625547326 & -3.31936255473261 \tabularnewline
93 & 32 & 36.7469814055377 & -4.74698140553774 \tabularnewline
94 & 50 & 57.8887632378853 & -7.88876323788527 \tabularnewline
95 & 92 & 109.721524723874 & -17.7215247238743 \tabularnewline
96 & 189 & 204.27727868341 & -15.2772786834099 \tabularnewline
97 & 256 & 254.974170213544 & 1.02582978645646 \tabularnewline
98 & 250 & 243.425369494056 & 6.5746305059435 \tabularnewline
99 & 198 & 184.519695972449 & 13.4803040275514 \tabularnewline
100 & 136 & 123.549868290368 & 12.4501317096322 \tabularnewline
101 & 73 & 70.2468265568393 & 2.75317344316068 \tabularnewline
102 & 39 & 39.1398103776277 & -0.139810377627725 \tabularnewline
103 & 32 & 35.9180960853078 & -3.91809608530775 \tabularnewline
104 & 30 & 30.2281101496311 & -0.228110149631149 \tabularnewline
105 & 31 & 32.2331901068143 & -1.23319010681435 \tabularnewline
106 & 45 & 52.3359537423806 & -7.33595374238064 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160692&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]246[/C][C]244.883547008547[/C][C]1.116452991453[/C][/ROW]
[ROW][C]14[/C][C]294[/C][C]292.923212281872[/C][C]1.07678771812766[/C][/ROW]
[ROW][C]15[/C][C]242[/C][C]241.296413864973[/C][C]0.703586135027251[/C][/ROW]
[ROW][C]16[/C][C]181[/C][C]180.571081351333[/C][C]0.428918648667434[/C][/ROW]
[ROW][C]17[/C][C]107[/C][C]106.792733416538[/C][C]0.207266583462172[/C][/ROW]
[ROW][C]18[/C][C]56[/C][C]54.4633085328766[/C][C]1.53669146712342[/C][/ROW]
[ROW][C]19[/C][C]49[/C][C]45.4870365088749[/C][C]3.51296349112512[/C][/ROW]
[ROW][C]20[/C][C]47[/C][C]50.8960639439936[/C][C]-3.89606394399364[/C][/ROW]
[ROW][C]21[/C][C]47[/C][C]50.6375611263622[/C][C]-3.6375611263622[/C][/ROW]
[ROW][C]22[/C][C]71[/C][C]69.4672032377159[/C][C]1.53279676228412[/C][/ROW]
[ROW][C]23[/C][C]151[/C][C]152.236243961055[/C][C]-1.23624396105518[/C][/ROW]
[ROW][C]24[/C][C]244[/C][C]206.005781383217[/C][C]37.9942186167833[/C][/ROW]
[ROW][C]25[/C][C]280[/C][C]250.035882823291[/C][C]29.964117176709[/C][/ROW]
[ROW][C]26[/C][C]230[/C][C]299.458150625152[/C][C]-69.4581506251521[/C][/ROW]
[ROW][C]27[/C][C]185[/C][C]244.573141734302[/C][C]-59.5731417343023[/C][/ROW]
[ROW][C]28[/C][C]148[/C][C]180.970000477811[/C][C]-32.970000477811[/C][/ROW]
[ROW][C]29[/C][C]98[/C][C]105.459785803668[/C][C]-7.45978580366759[/C][/ROW]
[ROW][C]30[/C][C]61[/C][C]53.1011799282845[/C][C]7.89882007171549[/C][/ROW]
[ROW][C]31[/C][C]46[/C][C]44.9687724817613[/C][C]1.03122751823871[/C][/ROW]
[ROW][C]32[/C][C]45[/C][C]47.3143050519288[/C][C]-2.31430505192876[/C][/ROW]
[ROW][C]33[/C][C]55[/C][C]47.0441066848163[/C][C]7.95589331518374[/C][/ROW]
[ROW][C]34[/C][C]48[/C][C]68.1633592013522[/C][C]-20.1633592013522[/C][/ROW]
[ROW][C]35[/C][C]115[/C][C]148.741558965934[/C][C]-33.7415589659343[/C][/ROW]
[ROW][C]36[/C][C]185[/C][C]215.502010561893[/C][C]-30.5020105618933[/C][/ROW]
[ROW][C]37[/C][C]276[/C][C]253.122715647067[/C][C]22.8772843529332[/C][/ROW]
[ROW][C]38[/C][C]220[/C][C]264.631259509793[/C][C]-44.6312595097933[/C][/ROW]
[ROW][C]39[/C][C]181[/C][C]214.194080521376[/C][C]-33.1940805213758[/C][/ROW]
[ROW][C]40[/C][C]151[/C][C]161.411812963677[/C][C]-10.4118129636765[/C][/ROW]
[ROW][C]41[/C][C]83[/C][C]96.1856933704142[/C][C]-13.1856933704142[/C][/ROW]
[ROW][C]42[/C][C]55[/C][C]49.0528181330027[/C][C]5.94718186699728[/C][/ROW]
[ROW][C]43[/C][C]49[/C][C]37.9912537783983[/C][C]11.0087462216017[/C][/ROW]
[ROW][C]44[/C][C]42[/C][C]39.2705425826432[/C][C]2.72945741735676[/C][/ROW]
[ROW][C]45[/C][C]46[/C][C]42.8210029664505[/C][C]3.17899703354955[/C][/ROW]
[ROW][C]46[/C][C]74[/C][C]52.9516751024821[/C][C]21.0483248975179[/C][/ROW]
[ROW][C]47[/C][C]103[/C][C]130.088473867801[/C][C]-27.0884738678009[/C][/ROW]
[ROW][C]48[/C][C]200[/C][C]198.187672814239[/C][C]1.81232718576103[/C][/ROW]
[ROW][C]49[/C][C]237[/C][C]257.103202118011[/C][C]-20.1032021180114[/C][/ROW]
[ROW][C]50[/C][C]247[/C][C]241.262753503622[/C][C]5.73724649637796[/C][/ROW]
[ROW][C]51[/C][C]215[/C][C]197.234418407279[/C][C]17.7655815927213[/C][/ROW]
[ROW][C]52[/C][C]182[/C][C]155.225398126516[/C][C]26.7746018734844[/C][/ROW]
[ROW][C]53[/C][C]80[/C][C]90.6676984903715[/C][C]-10.6676984903715[/C][/ROW]
[ROW][C]54[/C][C]46[/C][C]50.8755607483303[/C][C]-4.87556074833033[/C][/ROW]
[ROW][C]55[/C][C]65[/C][C]41.2799840266381[/C][C]23.7200159733619[/C][/ROW]
[ROW][C]56[/C][C]40[/C][C]40.0946976874145[/C][C]-0.0946976874144525[/C][/ROW]
[ROW][C]57[/C][C]44[/C][C]43.756230685086[/C][C]0.243769314914047[/C][/ROW]
[ROW][C]58[/C][C]63[/C][C]60.506969356018[/C][C]2.493030643982[/C][/ROW]
[ROW][C]59[/C][C]85[/C][C]118.838197336475[/C][C]-33.838197336475[/C][/ROW]
[ROW][C]60[/C][C]185[/C][C]197.471563380981[/C][C]-12.4715633809811[/C][/ROW]
[ROW][C]61[/C][C]247[/C][C]247.545053542196[/C][C]-0.545053542196484[/C][/ROW]
[ROW][C]62[/C][C]231[/C][C]242.264584377804[/C][C]-11.2645843778045[/C][/ROW]
[ROW][C]63[/C][C]167[/C][C]201.982083238645[/C][C]-34.9820832386445[/C][/ROW]
[ROW][C]64[/C][C]117[/C][C]160.914945841015[/C][C]-43.9149458410148[/C][/ROW]
[ROW][C]65[/C][C]79[/C][C]78.9945979627448[/C][C]0.00540203725520882[/C][/ROW]
[ROW][C]66[/C][C]45[/C][C]41.6316982283861[/C][C]3.3683017716139[/C][/ROW]
[ROW][C]67[/C][C]40[/C][C]42.907081211191[/C][C]-2.90708121119104[/C][/ROW]
[ROW][C]68[/C][C]38[/C][C]31.3906355424253[/C][C]6.60936445757473[/C][/ROW]
[ROW][C]69[/C][C]41[/C][C]35.2439719791569[/C][C]5.75602802084309[/C][/ROW]
[ROW][C]70[/C][C]69[/C][C]52.8589979950646[/C][C]16.1410020049354[/C][/ROW]
[ROW][C]71[/C][C]152[/C][C]98.0000349693975[/C][C]53.9999650306025[/C][/ROW]
[ROW][C]72[/C][C]232[/C][C]188.471292490536[/C][C]43.5287075094638[/C][/ROW]
[ROW][C]73[/C][C]282[/C][C]245.545697586105[/C][C]36.4543024138949[/C][/ROW]
[ROW][C]74[/C][C]255[/C][C]238.019248666794[/C][C]16.9807513332064[/C][/ROW]
[ROW][C]75[/C][C]161[/C][C]190.291128402667[/C][C]-29.2911284026666[/C][/ROW]
[ROW][C]76[/C][C]107[/C][C]146.325911371468[/C][C]-39.3259113714676[/C][/ROW]
[ROW][C]77[/C][C]53[/C][C]81.2470783623455[/C][C]-28.2470783623455[/C][/ROW]
[ROW][C]78[/C][C]40[/C][C]44.0460666540904[/C][C]-4.04606665409037[/C][/ROW]
[ROW][C]79[/C][C]39[/C][C]42.7828772869157[/C][C]-3.78287728691575[/C][/ROW]
[ROW][C]80[/C][C]34[/C][C]34.9249365638231[/C][C]-0.92493656382311[/C][/ROW]
[ROW][C]81[/C][C]35[/C][C]38.2483019397091[/C][C]-3.24830193970914[/C][/ROW]
[ROW][C]82[/C][C]56[/C][C]59.4579629762814[/C][C]-3.45796297628142[/C][/ROW]
[ROW][C]83[/C][C]97[/C][C]117.972221019114[/C][C]-20.9722210191138[/C][/ROW]
[ROW][C]84[/C][C]210[/C][C]201.148550675381[/C][C]8.85144932461907[/C][/ROW]
[ROW][C]85[/C][C]260[/C][C]253.915452883487[/C][C]6.08454711651328[/C][/ROW]
[ROW][C]86[/C][C]257[/C][C]237.576280996922[/C][C]19.4237190030777[/C][/ROW]
[ROW][C]87[/C][C]210[/C][C]172.459556102403[/C][C]37.5404438975968[/C][/ROW]
[ROW][C]88[/C][C]125[/C][C]127.631397992206[/C][C]-2.63139799220554[/C][/ROW]
[ROW][C]89[/C][C]80[/C][C]68.3272129034233[/C][C]11.6727870965767[/C][/ROW]
[ROW][C]90[/C][C]42[/C][C]42.0265846457346[/C][C]-0.0265846457346299[/C][/ROW]
[ROW][C]91[/C][C]35[/C][C]41.1274374064466[/C][C]-6.12743740644662[/C][/ROW]
[ROW][C]92[/C][C]31[/C][C]34.3193625547326[/C][C]-3.31936255473261[/C][/ROW]
[ROW][C]93[/C][C]32[/C][C]36.7469814055377[/C][C]-4.74698140553774[/C][/ROW]
[ROW][C]94[/C][C]50[/C][C]57.8887632378853[/C][C]-7.88876323788527[/C][/ROW]
[ROW][C]95[/C][C]92[/C][C]109.721524723874[/C][C]-17.7215247238743[/C][/ROW]
[ROW][C]96[/C][C]189[/C][C]204.27727868341[/C][C]-15.2772786834099[/C][/ROW]
[ROW][C]97[/C][C]256[/C][C]254.974170213544[/C][C]1.02582978645646[/C][/ROW]
[ROW][C]98[/C][C]250[/C][C]243.425369494056[/C][C]6.5746305059435[/C][/ROW]
[ROW][C]99[/C][C]198[/C][C]184.519695972449[/C][C]13.4803040275514[/C][/ROW]
[ROW][C]100[/C][C]136[/C][C]123.549868290368[/C][C]12.4501317096322[/C][/ROW]
[ROW][C]101[/C][C]73[/C][C]70.2468265568393[/C][C]2.75317344316068[/C][/ROW]
[ROW][C]102[/C][C]39[/C][C]39.1398103776277[/C][C]-0.139810377627725[/C][/ROW]
[ROW][C]103[/C][C]32[/C][C]35.9180960853078[/C][C]-3.91809608530775[/C][/ROW]
[ROW][C]104[/C][C]30[/C][C]30.2281101496311[/C][C]-0.228110149631149[/C][/ROW]
[ROW][C]105[/C][C]31[/C][C]32.2331901068143[/C][C]-1.23319010681435[/C][/ROW]
[ROW][C]106[/C][C]45[/C][C]52.3359537423806[/C][C]-7.33595374238064[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160692&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160692&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
13246244.8835470085471.116452991453
14294292.9232122818721.07678771812766
15242241.2964138649730.703586135027251
16181180.5710813513330.428918648667434
17107106.7927334165380.207266583462172
185654.46330853287661.53669146712342
194945.48703650887493.51296349112512
204750.8960639439936-3.89606394399364
214750.6375611263622-3.6375611263622
227169.46720323771591.53279676228412
23151152.236243961055-1.23624396105518
24244206.00578138321737.9942186167833
25280250.03588282329129.964117176709
26230299.458150625152-69.4581506251521
27185244.573141734302-59.5731417343023
28148180.970000477811-32.970000477811
2998105.459785803668-7.45978580366759
306153.10117992828457.89882007171549
314644.96877248176131.03122751823871
324547.3143050519288-2.31430505192876
335547.04410668481637.95589331518374
344868.1633592013522-20.1633592013522
35115148.741558965934-33.7415589659343
36185215.502010561893-30.5020105618933
37276253.12271564706722.8772843529332
38220264.631259509793-44.6312595097933
39181214.194080521376-33.1940805213758
40151161.411812963677-10.4118129636765
418396.1856933704142-13.1856933704142
425549.05281813300275.94718186699728
434937.991253778398311.0087462216017
444239.27054258264322.72945741735676
454642.82100296645053.17899703354955
467452.951675102482121.0483248975179
47103130.088473867801-27.0884738678009
48200198.1876728142391.81232718576103
49237257.103202118011-20.1032021180114
50247241.2627535036225.73724649637796
51215197.23441840727917.7655815927213
52182155.22539812651626.7746018734844
538090.6676984903715-10.6676984903715
544650.8755607483303-4.87556074833033
556541.279984026638123.7200159733619
564040.0946976874145-0.0946976874144525
574443.7562306850860.243769314914047
586360.5069693560182.493030643982
5985118.838197336475-33.838197336475
60185197.471563380981-12.4715633809811
61247247.545053542196-0.545053542196484
62231242.264584377804-11.2645843778045
63167201.982083238645-34.9820832386445
64117160.914945841015-43.9149458410148
657978.99459796274480.00540203725520882
664541.63169822838613.3683017716139
674042.907081211191-2.90708121119104
683831.39063554242536.60936445757473
694135.24397197915695.75602802084309
706952.858997995064616.1410020049354
7115298.000034969397553.9999650306025
72232188.47129249053643.5287075094638
73282245.54569758610536.4543024138949
74255238.01924866679416.9807513332064
75161190.291128402667-29.2911284026666
76107146.325911371468-39.3259113714676
775381.2470783623455-28.2470783623455
784044.0460666540904-4.04606665409037
793942.7828772869157-3.78287728691575
803434.9249365638231-0.92493656382311
813538.2483019397091-3.24830193970914
825659.4579629762814-3.45796297628142
8397117.972221019114-20.9722210191138
84210201.1485506753818.85144932461907
85260253.9154528834876.08454711651328
86257237.57628099692219.4237190030777
87210172.45955610240337.5404438975968
88125127.631397992206-2.63139799220554
898068.327212903423311.6727870965767
904242.0265846457346-0.0265846457346299
913541.1274374064466-6.12743740644662
923134.3193625547326-3.31936255473261
933236.7469814055377-4.74698140553774
945057.8887632378853-7.88876323788527
9592109.721524723874-17.7215247238743
96189204.27727868341-15.2772786834099
97256254.9741702135441.02582978645646
98250243.4253694940566.5746305059435
99198184.51969597244913.4803040275514
100136123.54986829036812.4501317096322
1017370.24682655683932.75317344316068
1023939.1398103776277-0.139810377627725
1033235.9180960853078-3.91809608530775
1043030.2281101496311-0.228110149631149
1053132.2331901068143-1.23319010681435
1064552.3359537423806-7.33595374238064







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
107100.49591707185460.0372900899317140.954544053776
108196.763653080239156.262304337266237.265001823212
109254.278910081635213.731450004584294.826370158686
110244.802073633741204.204991384778285.399155882703
111188.219238894046147.56890385172228.869573936372
112126.27295177304685.5656151095006166.980288436592
11368.772859317357428.0046556721995109.541062962515
11436.4382754088359-4.3947753400512377.2713261577231
11531.785661519383-9.1163293493994272.6876523881653
11627.633651891176-13.341483043631868.6087868259838
11729.2571074306278-11.795484386634970.3096992478905
11847.11709149375625.982623261341488.251559726171

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
107 & 100.495917071854 & 60.0372900899317 & 140.954544053776 \tabularnewline
108 & 196.763653080239 & 156.262304337266 & 237.265001823212 \tabularnewline
109 & 254.278910081635 & 213.731450004584 & 294.826370158686 \tabularnewline
110 & 244.802073633741 & 204.204991384778 & 285.399155882703 \tabularnewline
111 & 188.219238894046 & 147.56890385172 & 228.869573936372 \tabularnewline
112 & 126.272951773046 & 85.5656151095006 & 166.980288436592 \tabularnewline
113 & 68.7728593173574 & 28.0046556721995 & 109.541062962515 \tabularnewline
114 & 36.4382754088359 & -4.39477534005123 & 77.2713261577231 \tabularnewline
115 & 31.785661519383 & -9.11632934939942 & 72.6876523881653 \tabularnewline
116 & 27.633651891176 & -13.3414830436318 & 68.6087868259838 \tabularnewline
117 & 29.2571074306278 & -11.7954843866349 & 70.3096992478905 \tabularnewline
118 & 47.1170914937562 & 5.9826232613414 & 88.251559726171 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160692&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]107[/C][C]100.495917071854[/C][C]60.0372900899317[/C][C]140.954544053776[/C][/ROW]
[ROW][C]108[/C][C]196.763653080239[/C][C]156.262304337266[/C][C]237.265001823212[/C][/ROW]
[ROW][C]109[/C][C]254.278910081635[/C][C]213.731450004584[/C][C]294.826370158686[/C][/ROW]
[ROW][C]110[/C][C]244.802073633741[/C][C]204.204991384778[/C][C]285.399155882703[/C][/ROW]
[ROW][C]111[/C][C]188.219238894046[/C][C]147.56890385172[/C][C]228.869573936372[/C][/ROW]
[ROW][C]112[/C][C]126.272951773046[/C][C]85.5656151095006[/C][C]166.980288436592[/C][/ROW]
[ROW][C]113[/C][C]68.7728593173574[/C][C]28.0046556721995[/C][C]109.541062962515[/C][/ROW]
[ROW][C]114[/C][C]36.4382754088359[/C][C]-4.39477534005123[/C][C]77.2713261577231[/C][/ROW]
[ROW][C]115[/C][C]31.785661519383[/C][C]-9.11632934939942[/C][C]72.6876523881653[/C][/ROW]
[ROW][C]116[/C][C]27.633651891176[/C][C]-13.3414830436318[/C][C]68.6087868259838[/C][/ROW]
[ROW][C]117[/C][C]29.2571074306278[/C][C]-11.7954843866349[/C][C]70.3096992478905[/C][/ROW]
[ROW][C]118[/C][C]47.1170914937562[/C][C]5.9826232613414[/C][C]88.251559726171[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160692&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160692&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
107100.49591707185460.0372900899317140.954544053776
108196.763653080239156.262304337266237.265001823212
109254.278910081635213.731450004584294.826370158686
110244.802073633741204.204991384778285.399155882703
111188.219238894046147.56890385172228.869573936372
112126.27295177304685.5656151095006166.980288436592
11368.772859317357428.0046556721995109.541062962515
11436.4382754088359-4.3947753400512377.2713261577231
11531.785661519383-9.1163293493994272.6876523881653
11627.633651891176-13.341483043631868.6087868259838
11729.2571074306278-11.795484386634970.3096992478905
11847.11709149375625.982623261341488.251559726171



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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')