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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 09 Aug 2011 12:46:00 -0400
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/Aug/09/t13129083958czcbokgwv62d9a.htm/, Retrieved Tue, 14 May 2024 20:41:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123510, Retrieved Tue, 14 May 2024 20:41:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsNick Verbeke
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS B - STA...] [2011-08-09 16:46:00] [af5734c86e7bdbdfefb37d9aed9dbb03] [Current]
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Dataseries X:
240
150
290
210
240
240
310
310
190
230
260
320
270
250
240
250
230
230
240
300
190
270
300
330
230
260
300
330
190
260
240
270
170
230
270
320
190
300
310
360
170
280
270
260
280
300
320
370
210
310
290
450
190
290
280
310
340
220
390
410
250
310
280
450
210
390
300
310
370
250
440
360
290
300
340
600
220
410
360
250
410
290
470
350
330
250
270
580
260
450
320
240
420
380
400
370
300
310
280
560
280
480
320
170
420
310
470
420




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123510&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123510&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123510&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0430483871777855
beta0.0448036711757159
gamma0.898503753214102

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0430483871777855 \tabularnewline
beta & 0.0448036711757159 \tabularnewline
gamma & 0.898503753214102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123510&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]0.0430483871777855[/C][/ROW]
[ROW][C]beta[/C][C]0.0448036711757159[/C][/ROW]
[ROW][C]gamma[/C][C]0.898503753214102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123510&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123510&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
alpha0.0430483871777855
beta0.0448036711757159
gamma0.898503753214102







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13270268.2045144408971.79548555910264
14250251.657731161184-1.65773116118379
15240241.875852425442-1.87585242544154
16250250.15370311025-0.153703110250206
17230227.0877977224482.9122022775519
18230225.3347903010494.66520969895055
19240313.039833199631-73.0398331996315
20300303.150119685592-3.15011968559173
21190184.1027680785125.89723192148824
22270223.40323401806746.5967659819326
23300253.53824033960446.4617596603964
24330315.58477147253614.4152285274644
25230271.922238623997-41.9222386239975
26260250.5443939107089.4556060892923
27300241.08228087139958.9177191286008
28330253.78460087996976.2153991200314
29190236.371753294665-46.3717532946652
30260234.20405142201325.7959485779867
31240256.146096590471-16.1460965904707
32270311.037839632958-41.0378396329584
33170195.042319012519-25.0423190125187
34230269.646661538361-39.646661538361
35270295.950028521385-25.9500285213848
36320327.116085596022-7.11608559602206
37190234.240901490662-44.2409014906622
38300256.60367480418543.3963251958152
39310290.44398462473619.5560153752638
40360315.04507460880744.9549253911935
41170192.568451949827-22.5684519498272
42280252.25485531967327.7451446803271
43270238.23765763334231.7623423666584
44260273.204753153959-13.2047531539591
45280172.496628823877107.503371176123
46300242.02881713858757.9711828614131
47320286.58239699360133.4176030063986
48370340.02315843640929.9768415635912
49210209.0037278892160.996272110783877
50310316.840473569586-6.84047356958558
51290329.588545768949-39.5885457689488
52450376.95784123313373.0421587668669
53190185.3792270244494.62077297555129
54290298.187849613402-8.18784961340231
55280285.6665268844-5.66652688440018
56310280.514320575729.4856794242997
57340283.73057556687956.2694244331207
58220309.72514768895-89.7251476889502
59390327.60572866153762.3942713384629
60410381.52843601830428.4715639816957
61250218.92367706315431.0763229368455
62310326.53818040339-16.5381804033899
63280309.998579725865-29.9985797258648
64450461.791097982977-11.7910979829771
65210197.26781582646312.7321841735371
66390303.95169179757786.048308202423
67300297.3504591135872.64954088641292
68310324.506671090642-14.5066710906422
69370350.03740421340519.962595786595
70250243.04051782076.95948217930024
71440405.58638422143234.4136157785676
72360430.74009923306-70.7400992330602
73290257.91704448330232.0829555166984
74300327.978345721439-27.9783457214393
75340298.01406706305841.985932936942
76600478.977566694663121.022433305337
77220223.70175817385-3.70175817385007
78410404.164282570895.83571742911016
79360317.68636263884942.3136373611515
80250332.84230231941-82.8423023194102
81410388.38556076208821.6144392379117
82290263.50437792439226.4956220756077
83470462.047494981847.95250501816048
84350391.415043018898-41.4150430188982
85330303.21404111916926.7859588808306
86250322.491006152532-72.4910061525325
87270352.33179464252-82.3317946425202
88580603.912062118518-23.9120621185178
89260225.77943529577634.2205647042238
90450421.6888584834928.3111415165103
91320365.292259935965-45.2922599359648
92240266.026753594784-26.0267535947841
93420417.4235185723742.57648142762633
94380292.69830959578287.3016904042179
95400483.373944331039-83.3739443310394
96370363.3440238996796.65597610032069
97300334.808730855513-34.8087308555132
98310263.99129855307846.008701446922
99280290.514365057172-10.5143650571725
100560608.714412836474-48.7144128364741
101280265.66778157594414.332218424056
102480462.6029270549217.3970729450797
103320337.825460835899-17.8254608358988
104170253.048511662432-83.0485116624315
105420431.458166115916-11.4581661159158
106310376.417576105605-66.4175761056055
107470412.84103193684257.1589680631578
108420375.27768757945144.7223124205489

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 270 & 268.204514440897 & 1.79548555910264 \tabularnewline
14 & 250 & 251.657731161184 & -1.65773116118379 \tabularnewline
15 & 240 & 241.875852425442 & -1.87585242544154 \tabularnewline
16 & 250 & 250.15370311025 & -0.153703110250206 \tabularnewline
17 & 230 & 227.087797722448 & 2.9122022775519 \tabularnewline
18 & 230 & 225.334790301049 & 4.66520969895055 \tabularnewline
19 & 240 & 313.039833199631 & -73.0398331996315 \tabularnewline
20 & 300 & 303.150119685592 & -3.15011968559173 \tabularnewline
21 & 190 & 184.102768078512 & 5.89723192148824 \tabularnewline
22 & 270 & 223.403234018067 & 46.5967659819326 \tabularnewline
23 & 300 & 253.538240339604 & 46.4617596603964 \tabularnewline
24 & 330 & 315.584771472536 & 14.4152285274644 \tabularnewline
25 & 230 & 271.922238623997 & -41.9222386239975 \tabularnewline
26 & 260 & 250.544393910708 & 9.4556060892923 \tabularnewline
27 & 300 & 241.082280871399 & 58.9177191286008 \tabularnewline
28 & 330 & 253.784600879969 & 76.2153991200314 \tabularnewline
29 & 190 & 236.371753294665 & -46.3717532946652 \tabularnewline
30 & 260 & 234.204051422013 & 25.7959485779867 \tabularnewline
31 & 240 & 256.146096590471 & -16.1460965904707 \tabularnewline
32 & 270 & 311.037839632958 & -41.0378396329584 \tabularnewline
33 & 170 & 195.042319012519 & -25.0423190125187 \tabularnewline
34 & 230 & 269.646661538361 & -39.646661538361 \tabularnewline
35 & 270 & 295.950028521385 & -25.9500285213848 \tabularnewline
36 & 320 & 327.116085596022 & -7.11608559602206 \tabularnewline
37 & 190 & 234.240901490662 & -44.2409014906622 \tabularnewline
38 & 300 & 256.603674804185 & 43.3963251958152 \tabularnewline
39 & 310 & 290.443984624736 & 19.5560153752638 \tabularnewline
40 & 360 & 315.045074608807 & 44.9549253911935 \tabularnewline
41 & 170 & 192.568451949827 & -22.5684519498272 \tabularnewline
42 & 280 & 252.254855319673 & 27.7451446803271 \tabularnewline
43 & 270 & 238.237657633342 & 31.7623423666584 \tabularnewline
44 & 260 & 273.204753153959 & -13.2047531539591 \tabularnewline
45 & 280 & 172.496628823877 & 107.503371176123 \tabularnewline
46 & 300 & 242.028817138587 & 57.9711828614131 \tabularnewline
47 & 320 & 286.582396993601 & 33.4176030063986 \tabularnewline
48 & 370 & 340.023158436409 & 29.9768415635912 \tabularnewline
49 & 210 & 209.003727889216 & 0.996272110783877 \tabularnewline
50 & 310 & 316.840473569586 & -6.84047356958558 \tabularnewline
51 & 290 & 329.588545768949 & -39.5885457689488 \tabularnewline
52 & 450 & 376.957841233133 & 73.0421587668669 \tabularnewline
53 & 190 & 185.379227024449 & 4.62077297555129 \tabularnewline
54 & 290 & 298.187849613402 & -8.18784961340231 \tabularnewline
55 & 280 & 285.6665268844 & -5.66652688440018 \tabularnewline
56 & 310 & 280.5143205757 & 29.4856794242997 \tabularnewline
57 & 340 & 283.730575566879 & 56.2694244331207 \tabularnewline
58 & 220 & 309.72514768895 & -89.7251476889502 \tabularnewline
59 & 390 & 327.605728661537 & 62.3942713384629 \tabularnewline
60 & 410 & 381.528436018304 & 28.4715639816957 \tabularnewline
61 & 250 & 218.923677063154 & 31.0763229368455 \tabularnewline
62 & 310 & 326.53818040339 & -16.5381804033899 \tabularnewline
63 & 280 & 309.998579725865 & -29.9985797258648 \tabularnewline
64 & 450 & 461.791097982977 & -11.7910979829771 \tabularnewline
65 & 210 & 197.267815826463 & 12.7321841735371 \tabularnewline
66 & 390 & 303.951691797577 & 86.048308202423 \tabularnewline
67 & 300 & 297.350459113587 & 2.64954088641292 \tabularnewline
68 & 310 & 324.506671090642 & -14.5066710906422 \tabularnewline
69 & 370 & 350.037404213405 & 19.962595786595 \tabularnewline
70 & 250 & 243.0405178207 & 6.95948217930024 \tabularnewline
71 & 440 & 405.586384221432 & 34.4136157785676 \tabularnewline
72 & 360 & 430.74009923306 & -70.7400992330602 \tabularnewline
73 & 290 & 257.917044483302 & 32.0829555166984 \tabularnewline
74 & 300 & 327.978345721439 & -27.9783457214393 \tabularnewline
75 & 340 & 298.014067063058 & 41.985932936942 \tabularnewline
76 & 600 & 478.977566694663 & 121.022433305337 \tabularnewline
77 & 220 & 223.70175817385 & -3.70175817385007 \tabularnewline
78 & 410 & 404.16428257089 & 5.83571742911016 \tabularnewline
79 & 360 & 317.686362638849 & 42.3136373611515 \tabularnewline
80 & 250 & 332.84230231941 & -82.8423023194102 \tabularnewline
81 & 410 & 388.385560762088 & 21.6144392379117 \tabularnewline
82 & 290 & 263.504377924392 & 26.4956220756077 \tabularnewline
83 & 470 & 462.04749498184 & 7.95250501816048 \tabularnewline
84 & 350 & 391.415043018898 & -41.4150430188982 \tabularnewline
85 & 330 & 303.214041119169 & 26.7859588808306 \tabularnewline
86 & 250 & 322.491006152532 & -72.4910061525325 \tabularnewline
87 & 270 & 352.33179464252 & -82.3317946425202 \tabularnewline
88 & 580 & 603.912062118518 & -23.9120621185178 \tabularnewline
89 & 260 & 225.779435295776 & 34.2205647042238 \tabularnewline
90 & 450 & 421.68885848349 & 28.3111415165103 \tabularnewline
91 & 320 & 365.292259935965 & -45.2922599359648 \tabularnewline
92 & 240 & 266.026753594784 & -26.0267535947841 \tabularnewline
93 & 420 & 417.423518572374 & 2.57648142762633 \tabularnewline
94 & 380 & 292.698309595782 & 87.3016904042179 \tabularnewline
95 & 400 & 483.373944331039 & -83.3739443310394 \tabularnewline
96 & 370 & 363.344023899679 & 6.65597610032069 \tabularnewline
97 & 300 & 334.808730855513 & -34.8087308555132 \tabularnewline
98 & 310 & 263.991298553078 & 46.008701446922 \tabularnewline
99 & 280 & 290.514365057172 & -10.5143650571725 \tabularnewline
100 & 560 & 608.714412836474 & -48.7144128364741 \tabularnewline
101 & 280 & 265.667781575944 & 14.332218424056 \tabularnewline
102 & 480 & 462.60292705492 & 17.3970729450797 \tabularnewline
103 & 320 & 337.825460835899 & -17.8254608358988 \tabularnewline
104 & 170 & 253.048511662432 & -83.0485116624315 \tabularnewline
105 & 420 & 431.458166115916 & -11.4581661159158 \tabularnewline
106 & 310 & 376.417576105605 & -66.4175761056055 \tabularnewline
107 & 470 & 412.841031936842 & 57.1589680631578 \tabularnewline
108 & 420 & 375.277687579451 & 44.7223124205489 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123510&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]270[/C][C]268.204514440897[/C][C]1.79548555910264[/C][/ROW]
[ROW][C]14[/C][C]250[/C][C]251.657731161184[/C][C]-1.65773116118379[/C][/ROW]
[ROW][C]15[/C][C]240[/C][C]241.875852425442[/C][C]-1.87585242544154[/C][/ROW]
[ROW][C]16[/C][C]250[/C][C]250.15370311025[/C][C]-0.153703110250206[/C][/ROW]
[ROW][C]17[/C][C]230[/C][C]227.087797722448[/C][C]2.9122022775519[/C][/ROW]
[ROW][C]18[/C][C]230[/C][C]225.334790301049[/C][C]4.66520969895055[/C][/ROW]
[ROW][C]19[/C][C]240[/C][C]313.039833199631[/C][C]-73.0398331996315[/C][/ROW]
[ROW][C]20[/C][C]300[/C][C]303.150119685592[/C][C]-3.15011968559173[/C][/ROW]
[ROW][C]21[/C][C]190[/C][C]184.102768078512[/C][C]5.89723192148824[/C][/ROW]
[ROW][C]22[/C][C]270[/C][C]223.403234018067[/C][C]46.5967659819326[/C][/ROW]
[ROW][C]23[/C][C]300[/C][C]253.538240339604[/C][C]46.4617596603964[/C][/ROW]
[ROW][C]24[/C][C]330[/C][C]315.584771472536[/C][C]14.4152285274644[/C][/ROW]
[ROW][C]25[/C][C]230[/C][C]271.922238623997[/C][C]-41.9222386239975[/C][/ROW]
[ROW][C]26[/C][C]260[/C][C]250.544393910708[/C][C]9.4556060892923[/C][/ROW]
[ROW][C]27[/C][C]300[/C][C]241.082280871399[/C][C]58.9177191286008[/C][/ROW]
[ROW][C]28[/C][C]330[/C][C]253.784600879969[/C][C]76.2153991200314[/C][/ROW]
[ROW][C]29[/C][C]190[/C][C]236.371753294665[/C][C]-46.3717532946652[/C][/ROW]
[ROW][C]30[/C][C]260[/C][C]234.204051422013[/C][C]25.7959485779867[/C][/ROW]
[ROW][C]31[/C][C]240[/C][C]256.146096590471[/C][C]-16.1460965904707[/C][/ROW]
[ROW][C]32[/C][C]270[/C][C]311.037839632958[/C][C]-41.0378396329584[/C][/ROW]
[ROW][C]33[/C][C]170[/C][C]195.042319012519[/C][C]-25.0423190125187[/C][/ROW]
[ROW][C]34[/C][C]230[/C][C]269.646661538361[/C][C]-39.646661538361[/C][/ROW]
[ROW][C]35[/C][C]270[/C][C]295.950028521385[/C][C]-25.9500285213848[/C][/ROW]
[ROW][C]36[/C][C]320[/C][C]327.116085596022[/C][C]-7.11608559602206[/C][/ROW]
[ROW][C]37[/C][C]190[/C][C]234.240901490662[/C][C]-44.2409014906622[/C][/ROW]
[ROW][C]38[/C][C]300[/C][C]256.603674804185[/C][C]43.3963251958152[/C][/ROW]
[ROW][C]39[/C][C]310[/C][C]290.443984624736[/C][C]19.5560153752638[/C][/ROW]
[ROW][C]40[/C][C]360[/C][C]315.045074608807[/C][C]44.9549253911935[/C][/ROW]
[ROW][C]41[/C][C]170[/C][C]192.568451949827[/C][C]-22.5684519498272[/C][/ROW]
[ROW][C]42[/C][C]280[/C][C]252.254855319673[/C][C]27.7451446803271[/C][/ROW]
[ROW][C]43[/C][C]270[/C][C]238.237657633342[/C][C]31.7623423666584[/C][/ROW]
[ROW][C]44[/C][C]260[/C][C]273.204753153959[/C][C]-13.2047531539591[/C][/ROW]
[ROW][C]45[/C][C]280[/C][C]172.496628823877[/C][C]107.503371176123[/C][/ROW]
[ROW][C]46[/C][C]300[/C][C]242.028817138587[/C][C]57.9711828614131[/C][/ROW]
[ROW][C]47[/C][C]320[/C][C]286.582396993601[/C][C]33.4176030063986[/C][/ROW]
[ROW][C]48[/C][C]370[/C][C]340.023158436409[/C][C]29.9768415635912[/C][/ROW]
[ROW][C]49[/C][C]210[/C][C]209.003727889216[/C][C]0.996272110783877[/C][/ROW]
[ROW][C]50[/C][C]310[/C][C]316.840473569586[/C][C]-6.84047356958558[/C][/ROW]
[ROW][C]51[/C][C]290[/C][C]329.588545768949[/C][C]-39.5885457689488[/C][/ROW]
[ROW][C]52[/C][C]450[/C][C]376.957841233133[/C][C]73.0421587668669[/C][/ROW]
[ROW][C]53[/C][C]190[/C][C]185.379227024449[/C][C]4.62077297555129[/C][/ROW]
[ROW][C]54[/C][C]290[/C][C]298.187849613402[/C][C]-8.18784961340231[/C][/ROW]
[ROW][C]55[/C][C]280[/C][C]285.6665268844[/C][C]-5.66652688440018[/C][/ROW]
[ROW][C]56[/C][C]310[/C][C]280.5143205757[/C][C]29.4856794242997[/C][/ROW]
[ROW][C]57[/C][C]340[/C][C]283.730575566879[/C][C]56.2694244331207[/C][/ROW]
[ROW][C]58[/C][C]220[/C][C]309.72514768895[/C][C]-89.7251476889502[/C][/ROW]
[ROW][C]59[/C][C]390[/C][C]327.605728661537[/C][C]62.3942713384629[/C][/ROW]
[ROW][C]60[/C][C]410[/C][C]381.528436018304[/C][C]28.4715639816957[/C][/ROW]
[ROW][C]61[/C][C]250[/C][C]218.923677063154[/C][C]31.0763229368455[/C][/ROW]
[ROW][C]62[/C][C]310[/C][C]326.53818040339[/C][C]-16.5381804033899[/C][/ROW]
[ROW][C]63[/C][C]280[/C][C]309.998579725865[/C][C]-29.9985797258648[/C][/ROW]
[ROW][C]64[/C][C]450[/C][C]461.791097982977[/C][C]-11.7910979829771[/C][/ROW]
[ROW][C]65[/C][C]210[/C][C]197.267815826463[/C][C]12.7321841735371[/C][/ROW]
[ROW][C]66[/C][C]390[/C][C]303.951691797577[/C][C]86.048308202423[/C][/ROW]
[ROW][C]67[/C][C]300[/C][C]297.350459113587[/C][C]2.64954088641292[/C][/ROW]
[ROW][C]68[/C][C]310[/C][C]324.506671090642[/C][C]-14.5066710906422[/C][/ROW]
[ROW][C]69[/C][C]370[/C][C]350.037404213405[/C][C]19.962595786595[/C][/ROW]
[ROW][C]70[/C][C]250[/C][C]243.0405178207[/C][C]6.95948217930024[/C][/ROW]
[ROW][C]71[/C][C]440[/C][C]405.586384221432[/C][C]34.4136157785676[/C][/ROW]
[ROW][C]72[/C][C]360[/C][C]430.74009923306[/C][C]-70.7400992330602[/C][/ROW]
[ROW][C]73[/C][C]290[/C][C]257.917044483302[/C][C]32.0829555166984[/C][/ROW]
[ROW][C]74[/C][C]300[/C][C]327.978345721439[/C][C]-27.9783457214393[/C][/ROW]
[ROW][C]75[/C][C]340[/C][C]298.014067063058[/C][C]41.985932936942[/C][/ROW]
[ROW][C]76[/C][C]600[/C][C]478.977566694663[/C][C]121.022433305337[/C][/ROW]
[ROW][C]77[/C][C]220[/C][C]223.70175817385[/C][C]-3.70175817385007[/C][/ROW]
[ROW][C]78[/C][C]410[/C][C]404.16428257089[/C][C]5.83571742911016[/C][/ROW]
[ROW][C]79[/C][C]360[/C][C]317.686362638849[/C][C]42.3136373611515[/C][/ROW]
[ROW][C]80[/C][C]250[/C][C]332.84230231941[/C][C]-82.8423023194102[/C][/ROW]
[ROW][C]81[/C][C]410[/C][C]388.385560762088[/C][C]21.6144392379117[/C][/ROW]
[ROW][C]82[/C][C]290[/C][C]263.504377924392[/C][C]26.4956220756077[/C][/ROW]
[ROW][C]83[/C][C]470[/C][C]462.04749498184[/C][C]7.95250501816048[/C][/ROW]
[ROW][C]84[/C][C]350[/C][C]391.415043018898[/C][C]-41.4150430188982[/C][/ROW]
[ROW][C]85[/C][C]330[/C][C]303.214041119169[/C][C]26.7859588808306[/C][/ROW]
[ROW][C]86[/C][C]250[/C][C]322.491006152532[/C][C]-72.4910061525325[/C][/ROW]
[ROW][C]87[/C][C]270[/C][C]352.33179464252[/C][C]-82.3317946425202[/C][/ROW]
[ROW][C]88[/C][C]580[/C][C]603.912062118518[/C][C]-23.9120621185178[/C][/ROW]
[ROW][C]89[/C][C]260[/C][C]225.779435295776[/C][C]34.2205647042238[/C][/ROW]
[ROW][C]90[/C][C]450[/C][C]421.68885848349[/C][C]28.3111415165103[/C][/ROW]
[ROW][C]91[/C][C]320[/C][C]365.292259935965[/C][C]-45.2922599359648[/C][/ROW]
[ROW][C]92[/C][C]240[/C][C]266.026753594784[/C][C]-26.0267535947841[/C][/ROW]
[ROW][C]93[/C][C]420[/C][C]417.423518572374[/C][C]2.57648142762633[/C][/ROW]
[ROW][C]94[/C][C]380[/C][C]292.698309595782[/C][C]87.3016904042179[/C][/ROW]
[ROW][C]95[/C][C]400[/C][C]483.373944331039[/C][C]-83.3739443310394[/C][/ROW]
[ROW][C]96[/C][C]370[/C][C]363.344023899679[/C][C]6.65597610032069[/C][/ROW]
[ROW][C]97[/C][C]300[/C][C]334.808730855513[/C][C]-34.8087308555132[/C][/ROW]
[ROW][C]98[/C][C]310[/C][C]263.991298553078[/C][C]46.008701446922[/C][/ROW]
[ROW][C]99[/C][C]280[/C][C]290.514365057172[/C][C]-10.5143650571725[/C][/ROW]
[ROW][C]100[/C][C]560[/C][C]608.714412836474[/C][C]-48.7144128364741[/C][/ROW]
[ROW][C]101[/C][C]280[/C][C]265.667781575944[/C][C]14.332218424056[/C][/ROW]
[ROW][C]102[/C][C]480[/C][C]462.60292705492[/C][C]17.3970729450797[/C][/ROW]
[ROW][C]103[/C][C]320[/C][C]337.825460835899[/C][C]-17.8254608358988[/C][/ROW]
[ROW][C]104[/C][C]170[/C][C]253.048511662432[/C][C]-83.0485116624315[/C][/ROW]
[ROW][C]105[/C][C]420[/C][C]431.458166115916[/C][C]-11.4581661159158[/C][/ROW]
[ROW][C]106[/C][C]310[/C][C]376.417576105605[/C][C]-66.4175761056055[/C][/ROW]
[ROW][C]107[/C][C]470[/C][C]412.841031936842[/C][C]57.1589680631578[/C][/ROW]
[ROW][C]108[/C][C]420[/C][C]375.277687579451[/C][C]44.7223124205489[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123510&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123510&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
13270268.2045144408971.79548555910264
14250251.657731161184-1.65773116118379
15240241.875852425442-1.87585242544154
16250250.15370311025-0.153703110250206
17230227.0877977224482.9122022775519
18230225.3347903010494.66520969895055
19240313.039833199631-73.0398331996315
20300303.150119685592-3.15011968559173
21190184.1027680785125.89723192148824
22270223.40323401806746.5967659819326
23300253.53824033960446.4617596603964
24330315.58477147253614.4152285274644
25230271.922238623997-41.9222386239975
26260250.5443939107089.4556060892923
27300241.08228087139958.9177191286008
28330253.78460087996976.2153991200314
29190236.371753294665-46.3717532946652
30260234.20405142201325.7959485779867
31240256.146096590471-16.1460965904707
32270311.037839632958-41.0378396329584
33170195.042319012519-25.0423190125187
34230269.646661538361-39.646661538361
35270295.950028521385-25.9500285213848
36320327.116085596022-7.11608559602206
37190234.240901490662-44.2409014906622
38300256.60367480418543.3963251958152
39310290.44398462473619.5560153752638
40360315.04507460880744.9549253911935
41170192.568451949827-22.5684519498272
42280252.25485531967327.7451446803271
43270238.23765763334231.7623423666584
44260273.204753153959-13.2047531539591
45280172.496628823877107.503371176123
46300242.02881713858757.9711828614131
47320286.58239699360133.4176030063986
48370340.02315843640929.9768415635912
49210209.0037278892160.996272110783877
50310316.840473569586-6.84047356958558
51290329.588545768949-39.5885457689488
52450376.95784123313373.0421587668669
53190185.3792270244494.62077297555129
54290298.187849613402-8.18784961340231
55280285.6665268844-5.66652688440018
56310280.514320575729.4856794242997
57340283.73057556687956.2694244331207
58220309.72514768895-89.7251476889502
59390327.60572866153762.3942713384629
60410381.52843601830428.4715639816957
61250218.92367706315431.0763229368455
62310326.53818040339-16.5381804033899
63280309.998579725865-29.9985797258648
64450461.791097982977-11.7910979829771
65210197.26781582646312.7321841735371
66390303.95169179757786.048308202423
67300297.3504591135872.64954088641292
68310324.506671090642-14.5066710906422
69370350.03740421340519.962595786595
70250243.04051782076.95948217930024
71440405.58638422143234.4136157785676
72360430.74009923306-70.7400992330602
73290257.91704448330232.0829555166984
74300327.978345721439-27.9783457214393
75340298.01406706305841.985932936942
76600478.977566694663121.022433305337
77220223.70175817385-3.70175817385007
78410404.164282570895.83571742911016
79360317.68636263884942.3136373611515
80250332.84230231941-82.8423023194102
81410388.38556076208821.6144392379117
82290263.50437792439226.4956220756077
83470462.047494981847.95250501816048
84350391.415043018898-41.4150430188982
85330303.21404111916926.7859588808306
86250322.491006152532-72.4910061525325
87270352.33179464252-82.3317946425202
88580603.912062118518-23.9120621185178
89260225.77943529577634.2205647042238
90450421.6888584834928.3111415165103
91320365.292259935965-45.2922599359648
92240266.026753594784-26.0267535947841
93420417.4235185723742.57648142762633
94380292.69830959578287.3016904042179
95400483.373944331039-83.3739443310394
96370363.3440238996796.65597610032069
97300334.808730855513-34.8087308555132
98310263.99129855307846.008701446922
99280290.514365057172-10.5143650571725
100560608.714412836474-48.7144128364741
101280265.66778157594414.332218424056
102480462.6029270549217.3970729450797
103320337.825460835899-17.8254608358988
104170253.048511662432-83.0485116624315
105420431.458166115916-11.4581661159158
106310376.417576105605-66.4175761056055
107470412.84103193684257.1589680631578
108420375.27768757945144.7223124205489







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109311.031416154049234.09072996171387.972102346388
110310.77319828177233.737729172609387.808667390931
111286.080205911497208.972217401944363.18819442105
112576.504937412472498.45166941922654.558205405724
113283.612065973486206.356461998862360.867669948111
114485.819758217216407.614461712781564.025054721651
115327.307100009493249.704090170653404.910109848333
116183.643232696212106.448477017384260.83798837504
117434.811694207352355.837142295627513.786246119077
118329.271390350912251.020544846982407.522235854843
119480.594156615235400.504428715837560.683884514634
120427.9733452614308.904814153046547.041876369754

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 311.031416154049 & 234.09072996171 & 387.972102346388 \tabularnewline
110 & 310.77319828177 & 233.737729172609 & 387.808667390931 \tabularnewline
111 & 286.080205911497 & 208.972217401944 & 363.18819442105 \tabularnewline
112 & 576.504937412472 & 498.45166941922 & 654.558205405724 \tabularnewline
113 & 283.612065973486 & 206.356461998862 & 360.867669948111 \tabularnewline
114 & 485.819758217216 & 407.614461712781 & 564.025054721651 \tabularnewline
115 & 327.307100009493 & 249.704090170653 & 404.910109848333 \tabularnewline
116 & 183.643232696212 & 106.448477017384 & 260.83798837504 \tabularnewline
117 & 434.811694207352 & 355.837142295627 & 513.786246119077 \tabularnewline
118 & 329.271390350912 & 251.020544846982 & 407.522235854843 \tabularnewline
119 & 480.594156615235 & 400.504428715837 & 560.683884514634 \tabularnewline
120 & 427.9733452614 & 308.904814153046 & 547.041876369754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123510&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]109[/C][C]311.031416154049[/C][C]234.09072996171[/C][C]387.972102346388[/C][/ROW]
[ROW][C]110[/C][C]310.77319828177[/C][C]233.737729172609[/C][C]387.808667390931[/C][/ROW]
[ROW][C]111[/C][C]286.080205911497[/C][C]208.972217401944[/C][C]363.18819442105[/C][/ROW]
[ROW][C]112[/C][C]576.504937412472[/C][C]498.45166941922[/C][C]654.558205405724[/C][/ROW]
[ROW][C]113[/C][C]283.612065973486[/C][C]206.356461998862[/C][C]360.867669948111[/C][/ROW]
[ROW][C]114[/C][C]485.819758217216[/C][C]407.614461712781[/C][C]564.025054721651[/C][/ROW]
[ROW][C]115[/C][C]327.307100009493[/C][C]249.704090170653[/C][C]404.910109848333[/C][/ROW]
[ROW][C]116[/C][C]183.643232696212[/C][C]106.448477017384[/C][C]260.83798837504[/C][/ROW]
[ROW][C]117[/C][C]434.811694207352[/C][C]355.837142295627[/C][C]513.786246119077[/C][/ROW]
[ROW][C]118[/C][C]329.271390350912[/C][C]251.020544846982[/C][C]407.522235854843[/C][/ROW]
[ROW][C]119[/C][C]480.594156615235[/C][C]400.504428715837[/C][C]560.683884514634[/C][/ROW]
[ROW][C]120[/C][C]427.9733452614[/C][C]308.904814153046[/C][C]547.041876369754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123510&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123510&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
109311.031416154049234.09072996171387.972102346388
110310.77319828177233.737729172609387.808667390931
111286.080205911497208.972217401944363.18819442105
112576.504937412472498.45166941922654.558205405724
113283.612065973486206.356461998862360.867669948111
114485.819758217216407.614461712781564.025054721651
115327.307100009493249.704090170653404.910109848333
116183.643232696212106.448477017384260.83798837504
117434.811694207352355.837142295627513.786246119077
118329.271390350912251.020544846982407.522235854843
119480.594156615235400.504428715837560.683884514634
120427.9733452614308.904814153046547.041876369754



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')