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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 computationMon, 07 Dec 2009 15:52:45 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/07/t1260226433sr14819w76bkq38.htm/, Retrieved Sat, 04 May 2024 21:48:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64659, Retrieved Sat, 04 May 2024 21:48:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsExponential Smoothing
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [Exponential Smoot...] [2009-12-07 22:52:45] [52b85b290d6f50b0921ad6729b8a5af2] [Current]
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Dataseries X:
220206
220115
218444
214912
210705
209673
237041
242081
241878
242621
238545
240337
244752
244576
241572
240541
236089
236997
264579
270349
269645
267037
258113
262813
267413
267366
264777
258863
254844
254868
277267
285351
286602
283042
276687
277915
277128
277103
275037
270150
267140
264993
287259
291186
292300
288186
281477
282656
280190
280408
276836
275216
274352
271311
289802
290726
292300
278506
269826
265861
269034
264176
255198
253353
246057
235372
258556
260993
254663
250643
243422
247105
248541
245039
237080
237085
225554
226839
247934
248333
246969
245098
246263
255765
264319
268347
273046
273963
267430
271993
292710
295881
293299
288576




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64659&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64659&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64659&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.94869489322508
beta0.175963834108314
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.94869489322508 \tabularnewline
beta & 0.175963834108314 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64659&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]0.94869489322508[/C][/ROW]
[ROW][C]beta[/C][C]0.175963834108314[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64659&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64659&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
alpha0.94869489322508
beta0.175963834108314
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13244752231608.73707040713143.2629295928
14244576245903.325396201-1327.32539620149
15241572243364.053924208-1792.05392420804
16240541242194.826493501-1653.82649350128
17236089237747.699578116-1658.69957811607
18236997238452.877674112-1455.87767411213
19264579264064.067305385514.932694614516
20270349270969.512147259-620.512147259142
21269645270902.763389931-1257.76338993129
22267037271021.465996317-3984.46599631675
23258113262498.400155499-4385.400155499
24262813259257.6072442433555.39275575674
25267413267640.15118384-227.151183839946
26267366265802.2000896921563.79991030786
27264777263606.7379374511170.26206254878
28258863263586.260963481-4723.26096348133
29254844253916.724584628927.275415371842
30254868255630.863548618-762.863548617752
31277267282406.233486272-5139.23348627193
32285351281661.7886772283689.2113227715
33286602283862.588459682739.41154032008
34283042286552.969876638-3510.96987663762
35276687277165.589420007-478.589420007367
36277915277811.580782719103.419217281102
37277128282081.067667089-4953.06766708888
38277103274147.2755011312955.72449886915
39275037271729.1640781053307.83592189493
40270150272344.444975788-2194.44497578795
41267140264574.1423564612565.85764353914
42264993267479.568305000-2486.56830500049
43287259292846.336443541-5587.33644354122
44291186291608.149839614-422.14983961446
45292300288468.7518503373831.24814966315
46288186290689.352216807-2503.35221680679
47281477281330.075128912146.924871087947
48282656281752.933756179903.066243821231
49280190285843.824962593-5653.82496259286
50280408276783.2445517633624.75544823677
51276836274247.3278249892588.67217501142
52275216273063.1967176062152.80328239402
53274352269461.3376330154890.66236698517
54271311274586.638501698-3275.63850169827
55289802299879.632619517-10077.6326195168
56290726294123.130899924-3397.13089992350
57292300287324.5174908924975.48250910785
58278506289449.341261054-10943.3412610535
59269826270233.965110454-407.965110453952
60265861267864.81854471-2003.81854471005
61269034265899.3900213113134.60997868871
62264176264427.39238183-251.392381830257
63255198256578.07084208-1380.07084207979
64253353249372.6863474783980.31365252161
65246057245949.790026124107.20997387619
66235372243298.843766005-7926.8437660053
67258556256173.1315063512382.86849364921
68260993259995.073624063997.926375937037
69254663256667.881829140-2004.88182913963
70250643249270.7677572471372.23224275277
71243422242496.607111015925.392888984788
72247105241117.8279373005987.1720627005
73248541247958.652836620582.347163380327
74245039244818.258880736220.741119264363
75237080238556.846896415-1476.84689641459
76237085232533.7106649924551.28933500778
77225554230671.340467827-5117.34046782652
78226839222743.7332836714095.26671632929
79247934248819.419647614-885.419647614093
80248333250936.961365441-2603.96136544063
81246969245160.2662431381808.73375686168
82245098243276.9278373361821.07216266438
83246263238711.1546908357551.84530916536
84255765246658.4315318029106.56846819786
85264319259583.2400837984735.75991620217
86268347264185.238283594161.76171641017
87273046265592.3650822517453.63491774903
88273963273840.104030974122.895969025616
89267430271387.864162814-3957.86416281387
90271993270032.1892869581960.81071304181
91292710303696.52220238-10986.52220238
92295881300566.414224755-4685.41422475548
93293299296066.680917328-2767.68091732817
94288576291927.205471524-3351.20547152415

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 244752 & 231608.737070407 & 13143.2629295928 \tabularnewline
14 & 244576 & 245903.325396201 & -1327.32539620149 \tabularnewline
15 & 241572 & 243364.053924208 & -1792.05392420804 \tabularnewline
16 & 240541 & 242194.826493501 & -1653.82649350128 \tabularnewline
17 & 236089 & 237747.699578116 & -1658.69957811607 \tabularnewline
18 & 236997 & 238452.877674112 & -1455.87767411213 \tabularnewline
19 & 264579 & 264064.067305385 & 514.932694614516 \tabularnewline
20 & 270349 & 270969.512147259 & -620.512147259142 \tabularnewline
21 & 269645 & 270902.763389931 & -1257.76338993129 \tabularnewline
22 & 267037 & 271021.465996317 & -3984.46599631675 \tabularnewline
23 & 258113 & 262498.400155499 & -4385.400155499 \tabularnewline
24 & 262813 & 259257.607244243 & 3555.39275575674 \tabularnewline
25 & 267413 & 267640.15118384 & -227.151183839946 \tabularnewline
26 & 267366 & 265802.200089692 & 1563.79991030786 \tabularnewline
27 & 264777 & 263606.737937451 & 1170.26206254878 \tabularnewline
28 & 258863 & 263586.260963481 & -4723.26096348133 \tabularnewline
29 & 254844 & 253916.724584628 & 927.275415371842 \tabularnewline
30 & 254868 & 255630.863548618 & -762.863548617752 \tabularnewline
31 & 277267 & 282406.233486272 & -5139.23348627193 \tabularnewline
32 & 285351 & 281661.788677228 & 3689.2113227715 \tabularnewline
33 & 286602 & 283862.58845968 & 2739.41154032008 \tabularnewline
34 & 283042 & 286552.969876638 & -3510.96987663762 \tabularnewline
35 & 276687 & 277165.589420007 & -478.589420007367 \tabularnewline
36 & 277915 & 277811.580782719 & 103.419217281102 \tabularnewline
37 & 277128 & 282081.067667089 & -4953.06766708888 \tabularnewline
38 & 277103 & 274147.275501131 & 2955.72449886915 \tabularnewline
39 & 275037 & 271729.164078105 & 3307.83592189493 \tabularnewline
40 & 270150 & 272344.444975788 & -2194.44497578795 \tabularnewline
41 & 267140 & 264574.142356461 & 2565.85764353914 \tabularnewline
42 & 264993 & 267479.568305000 & -2486.56830500049 \tabularnewline
43 & 287259 & 292846.336443541 & -5587.33644354122 \tabularnewline
44 & 291186 & 291608.149839614 & -422.14983961446 \tabularnewline
45 & 292300 & 288468.751850337 & 3831.24814966315 \tabularnewline
46 & 288186 & 290689.352216807 & -2503.35221680679 \tabularnewline
47 & 281477 & 281330.075128912 & 146.924871087947 \tabularnewline
48 & 282656 & 281752.933756179 & 903.066243821231 \tabularnewline
49 & 280190 & 285843.824962593 & -5653.82496259286 \tabularnewline
50 & 280408 & 276783.244551763 & 3624.75544823677 \tabularnewline
51 & 276836 & 274247.327824989 & 2588.67217501142 \tabularnewline
52 & 275216 & 273063.196717606 & 2152.80328239402 \tabularnewline
53 & 274352 & 269461.337633015 & 4890.66236698517 \tabularnewline
54 & 271311 & 274586.638501698 & -3275.63850169827 \tabularnewline
55 & 289802 & 299879.632619517 & -10077.6326195168 \tabularnewline
56 & 290726 & 294123.130899924 & -3397.13089992350 \tabularnewline
57 & 292300 & 287324.517490892 & 4975.48250910785 \tabularnewline
58 & 278506 & 289449.341261054 & -10943.3412610535 \tabularnewline
59 & 269826 & 270233.965110454 & -407.965110453952 \tabularnewline
60 & 265861 & 267864.81854471 & -2003.81854471005 \tabularnewline
61 & 269034 & 265899.390021311 & 3134.60997868871 \tabularnewline
62 & 264176 & 264427.39238183 & -251.392381830257 \tabularnewline
63 & 255198 & 256578.07084208 & -1380.07084207979 \tabularnewline
64 & 253353 & 249372.686347478 & 3980.31365252161 \tabularnewline
65 & 246057 & 245949.790026124 & 107.20997387619 \tabularnewline
66 & 235372 & 243298.843766005 & -7926.8437660053 \tabularnewline
67 & 258556 & 256173.131506351 & 2382.86849364921 \tabularnewline
68 & 260993 & 259995.073624063 & 997.926375937037 \tabularnewline
69 & 254663 & 256667.881829140 & -2004.88182913963 \tabularnewline
70 & 250643 & 249270.767757247 & 1372.23224275277 \tabularnewline
71 & 243422 & 242496.607111015 & 925.392888984788 \tabularnewline
72 & 247105 & 241117.827937300 & 5987.1720627005 \tabularnewline
73 & 248541 & 247958.652836620 & 582.347163380327 \tabularnewline
74 & 245039 & 244818.258880736 & 220.741119264363 \tabularnewline
75 & 237080 & 238556.846896415 & -1476.84689641459 \tabularnewline
76 & 237085 & 232533.710664992 & 4551.28933500778 \tabularnewline
77 & 225554 & 230671.340467827 & -5117.34046782652 \tabularnewline
78 & 226839 & 222743.733283671 & 4095.26671632929 \tabularnewline
79 & 247934 & 248819.419647614 & -885.419647614093 \tabularnewline
80 & 248333 & 250936.961365441 & -2603.96136544063 \tabularnewline
81 & 246969 & 245160.266243138 & 1808.73375686168 \tabularnewline
82 & 245098 & 243276.927837336 & 1821.07216266438 \tabularnewline
83 & 246263 & 238711.154690835 & 7551.84530916536 \tabularnewline
84 & 255765 & 246658.431531802 & 9106.56846819786 \tabularnewline
85 & 264319 & 259583.240083798 & 4735.75991620217 \tabularnewline
86 & 268347 & 264185.23828359 & 4161.76171641017 \tabularnewline
87 & 273046 & 265592.365082251 & 7453.63491774903 \tabularnewline
88 & 273963 & 273840.104030974 & 122.895969025616 \tabularnewline
89 & 267430 & 271387.864162814 & -3957.86416281387 \tabularnewline
90 & 271993 & 270032.189286958 & 1960.81071304181 \tabularnewline
91 & 292710 & 303696.52220238 & -10986.52220238 \tabularnewline
92 & 295881 & 300566.414224755 & -4685.41422475548 \tabularnewline
93 & 293299 & 296066.680917328 & -2767.68091732817 \tabularnewline
94 & 288576 & 291927.205471524 & -3351.20547152415 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64659&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]244752[/C][C]231608.737070407[/C][C]13143.2629295928[/C][/ROW]
[ROW][C]14[/C][C]244576[/C][C]245903.325396201[/C][C]-1327.32539620149[/C][/ROW]
[ROW][C]15[/C][C]241572[/C][C]243364.053924208[/C][C]-1792.05392420804[/C][/ROW]
[ROW][C]16[/C][C]240541[/C][C]242194.826493501[/C][C]-1653.82649350128[/C][/ROW]
[ROW][C]17[/C][C]236089[/C][C]237747.699578116[/C][C]-1658.69957811607[/C][/ROW]
[ROW][C]18[/C][C]236997[/C][C]238452.877674112[/C][C]-1455.87767411213[/C][/ROW]
[ROW][C]19[/C][C]264579[/C][C]264064.067305385[/C][C]514.932694614516[/C][/ROW]
[ROW][C]20[/C][C]270349[/C][C]270969.512147259[/C][C]-620.512147259142[/C][/ROW]
[ROW][C]21[/C][C]269645[/C][C]270902.763389931[/C][C]-1257.76338993129[/C][/ROW]
[ROW][C]22[/C][C]267037[/C][C]271021.465996317[/C][C]-3984.46599631675[/C][/ROW]
[ROW][C]23[/C][C]258113[/C][C]262498.400155499[/C][C]-4385.400155499[/C][/ROW]
[ROW][C]24[/C][C]262813[/C][C]259257.607244243[/C][C]3555.39275575674[/C][/ROW]
[ROW][C]25[/C][C]267413[/C][C]267640.15118384[/C][C]-227.151183839946[/C][/ROW]
[ROW][C]26[/C][C]267366[/C][C]265802.200089692[/C][C]1563.79991030786[/C][/ROW]
[ROW][C]27[/C][C]264777[/C][C]263606.737937451[/C][C]1170.26206254878[/C][/ROW]
[ROW][C]28[/C][C]258863[/C][C]263586.260963481[/C][C]-4723.26096348133[/C][/ROW]
[ROW][C]29[/C][C]254844[/C][C]253916.724584628[/C][C]927.275415371842[/C][/ROW]
[ROW][C]30[/C][C]254868[/C][C]255630.863548618[/C][C]-762.863548617752[/C][/ROW]
[ROW][C]31[/C][C]277267[/C][C]282406.233486272[/C][C]-5139.23348627193[/C][/ROW]
[ROW][C]32[/C][C]285351[/C][C]281661.788677228[/C][C]3689.2113227715[/C][/ROW]
[ROW][C]33[/C][C]286602[/C][C]283862.58845968[/C][C]2739.41154032008[/C][/ROW]
[ROW][C]34[/C][C]283042[/C][C]286552.969876638[/C][C]-3510.96987663762[/C][/ROW]
[ROW][C]35[/C][C]276687[/C][C]277165.589420007[/C][C]-478.589420007367[/C][/ROW]
[ROW][C]36[/C][C]277915[/C][C]277811.580782719[/C][C]103.419217281102[/C][/ROW]
[ROW][C]37[/C][C]277128[/C][C]282081.067667089[/C][C]-4953.06766708888[/C][/ROW]
[ROW][C]38[/C][C]277103[/C][C]274147.275501131[/C][C]2955.72449886915[/C][/ROW]
[ROW][C]39[/C][C]275037[/C][C]271729.164078105[/C][C]3307.83592189493[/C][/ROW]
[ROW][C]40[/C][C]270150[/C][C]272344.444975788[/C][C]-2194.44497578795[/C][/ROW]
[ROW][C]41[/C][C]267140[/C][C]264574.142356461[/C][C]2565.85764353914[/C][/ROW]
[ROW][C]42[/C][C]264993[/C][C]267479.568305000[/C][C]-2486.56830500049[/C][/ROW]
[ROW][C]43[/C][C]287259[/C][C]292846.336443541[/C][C]-5587.33644354122[/C][/ROW]
[ROW][C]44[/C][C]291186[/C][C]291608.149839614[/C][C]-422.14983961446[/C][/ROW]
[ROW][C]45[/C][C]292300[/C][C]288468.751850337[/C][C]3831.24814966315[/C][/ROW]
[ROW][C]46[/C][C]288186[/C][C]290689.352216807[/C][C]-2503.35221680679[/C][/ROW]
[ROW][C]47[/C][C]281477[/C][C]281330.075128912[/C][C]146.924871087947[/C][/ROW]
[ROW][C]48[/C][C]282656[/C][C]281752.933756179[/C][C]903.066243821231[/C][/ROW]
[ROW][C]49[/C][C]280190[/C][C]285843.824962593[/C][C]-5653.82496259286[/C][/ROW]
[ROW][C]50[/C][C]280408[/C][C]276783.244551763[/C][C]3624.75544823677[/C][/ROW]
[ROW][C]51[/C][C]276836[/C][C]274247.327824989[/C][C]2588.67217501142[/C][/ROW]
[ROW][C]52[/C][C]275216[/C][C]273063.196717606[/C][C]2152.80328239402[/C][/ROW]
[ROW][C]53[/C][C]274352[/C][C]269461.337633015[/C][C]4890.66236698517[/C][/ROW]
[ROW][C]54[/C][C]271311[/C][C]274586.638501698[/C][C]-3275.63850169827[/C][/ROW]
[ROW][C]55[/C][C]289802[/C][C]299879.632619517[/C][C]-10077.6326195168[/C][/ROW]
[ROW][C]56[/C][C]290726[/C][C]294123.130899924[/C][C]-3397.13089992350[/C][/ROW]
[ROW][C]57[/C][C]292300[/C][C]287324.517490892[/C][C]4975.48250910785[/C][/ROW]
[ROW][C]58[/C][C]278506[/C][C]289449.341261054[/C][C]-10943.3412610535[/C][/ROW]
[ROW][C]59[/C][C]269826[/C][C]270233.965110454[/C][C]-407.965110453952[/C][/ROW]
[ROW][C]60[/C][C]265861[/C][C]267864.81854471[/C][C]-2003.81854471005[/C][/ROW]
[ROW][C]61[/C][C]269034[/C][C]265899.390021311[/C][C]3134.60997868871[/C][/ROW]
[ROW][C]62[/C][C]264176[/C][C]264427.39238183[/C][C]-251.392381830257[/C][/ROW]
[ROW][C]63[/C][C]255198[/C][C]256578.07084208[/C][C]-1380.07084207979[/C][/ROW]
[ROW][C]64[/C][C]253353[/C][C]249372.686347478[/C][C]3980.31365252161[/C][/ROW]
[ROW][C]65[/C][C]246057[/C][C]245949.790026124[/C][C]107.20997387619[/C][/ROW]
[ROW][C]66[/C][C]235372[/C][C]243298.843766005[/C][C]-7926.8437660053[/C][/ROW]
[ROW][C]67[/C][C]258556[/C][C]256173.131506351[/C][C]2382.86849364921[/C][/ROW]
[ROW][C]68[/C][C]260993[/C][C]259995.073624063[/C][C]997.926375937037[/C][/ROW]
[ROW][C]69[/C][C]254663[/C][C]256667.881829140[/C][C]-2004.88182913963[/C][/ROW]
[ROW][C]70[/C][C]250643[/C][C]249270.767757247[/C][C]1372.23224275277[/C][/ROW]
[ROW][C]71[/C][C]243422[/C][C]242496.607111015[/C][C]925.392888984788[/C][/ROW]
[ROW][C]72[/C][C]247105[/C][C]241117.827937300[/C][C]5987.1720627005[/C][/ROW]
[ROW][C]73[/C][C]248541[/C][C]247958.652836620[/C][C]582.347163380327[/C][/ROW]
[ROW][C]74[/C][C]245039[/C][C]244818.258880736[/C][C]220.741119264363[/C][/ROW]
[ROW][C]75[/C][C]237080[/C][C]238556.846896415[/C][C]-1476.84689641459[/C][/ROW]
[ROW][C]76[/C][C]237085[/C][C]232533.710664992[/C][C]4551.28933500778[/C][/ROW]
[ROW][C]77[/C][C]225554[/C][C]230671.340467827[/C][C]-5117.34046782652[/C][/ROW]
[ROW][C]78[/C][C]226839[/C][C]222743.733283671[/C][C]4095.26671632929[/C][/ROW]
[ROW][C]79[/C][C]247934[/C][C]248819.419647614[/C][C]-885.419647614093[/C][/ROW]
[ROW][C]80[/C][C]248333[/C][C]250936.961365441[/C][C]-2603.96136544063[/C][/ROW]
[ROW][C]81[/C][C]246969[/C][C]245160.266243138[/C][C]1808.73375686168[/C][/ROW]
[ROW][C]82[/C][C]245098[/C][C]243276.927837336[/C][C]1821.07216266438[/C][/ROW]
[ROW][C]83[/C][C]246263[/C][C]238711.154690835[/C][C]7551.84530916536[/C][/ROW]
[ROW][C]84[/C][C]255765[/C][C]246658.431531802[/C][C]9106.56846819786[/C][/ROW]
[ROW][C]85[/C][C]264319[/C][C]259583.240083798[/C][C]4735.75991620217[/C][/ROW]
[ROW][C]86[/C][C]268347[/C][C]264185.23828359[/C][C]4161.76171641017[/C][/ROW]
[ROW][C]87[/C][C]273046[/C][C]265592.365082251[/C][C]7453.63491774903[/C][/ROW]
[ROW][C]88[/C][C]273963[/C][C]273840.104030974[/C][C]122.895969025616[/C][/ROW]
[ROW][C]89[/C][C]267430[/C][C]271387.864162814[/C][C]-3957.86416281387[/C][/ROW]
[ROW][C]90[/C][C]271993[/C][C]270032.189286958[/C][C]1960.81071304181[/C][/ROW]
[ROW][C]91[/C][C]292710[/C][C]303696.52220238[/C][C]-10986.52220238[/C][/ROW]
[ROW][C]92[/C][C]295881[/C][C]300566.414224755[/C][C]-4685.41422475548[/C][/ROW]
[ROW][C]93[/C][C]293299[/C][C]296066.680917328[/C][C]-2767.68091732817[/C][/ROW]
[ROW][C]94[/C][C]288576[/C][C]291927.205471524[/C][C]-3351.20547152415[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64659&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64659&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
13244752231608.73707040713143.2629295928
14244576245903.325396201-1327.32539620149
15241572243364.053924208-1792.05392420804
16240541242194.826493501-1653.82649350128
17236089237747.699578116-1658.69957811607
18236997238452.877674112-1455.87767411213
19264579264064.067305385514.932694614516
20270349270969.512147259-620.512147259142
21269645270902.763389931-1257.76338993129
22267037271021.465996317-3984.46599631675
23258113262498.400155499-4385.400155499
24262813259257.6072442433555.39275575674
25267413267640.15118384-227.151183839946
26267366265802.2000896921563.79991030786
27264777263606.7379374511170.26206254878
28258863263586.260963481-4723.26096348133
29254844253916.724584628927.275415371842
30254868255630.863548618-762.863548617752
31277267282406.233486272-5139.23348627193
32285351281661.7886772283689.2113227715
33286602283862.588459682739.41154032008
34283042286552.969876638-3510.96987663762
35276687277165.589420007-478.589420007367
36277915277811.580782719103.419217281102
37277128282081.067667089-4953.06766708888
38277103274147.2755011312955.72449886915
39275037271729.1640781053307.83592189493
40270150272344.444975788-2194.44497578795
41267140264574.1423564612565.85764353914
42264993267479.568305000-2486.56830500049
43287259292846.336443541-5587.33644354122
44291186291608.149839614-422.14983961446
45292300288468.7518503373831.24814966315
46288186290689.352216807-2503.35221680679
47281477281330.075128912146.924871087947
48282656281752.933756179903.066243821231
49280190285843.824962593-5653.82496259286
50280408276783.2445517633624.75544823677
51276836274247.3278249892588.67217501142
52275216273063.1967176062152.80328239402
53274352269461.3376330154890.66236698517
54271311274586.638501698-3275.63850169827
55289802299879.632619517-10077.6326195168
56290726294123.130899924-3397.13089992350
57292300287324.5174908924975.48250910785
58278506289449.341261054-10943.3412610535
59269826270233.965110454-407.965110453952
60265861267864.81854471-2003.81854471005
61269034265899.3900213113134.60997868871
62264176264427.39238183-251.392381830257
63255198256578.07084208-1380.07084207979
64253353249372.6863474783980.31365252161
65246057245949.790026124107.20997387619
66235372243298.843766005-7926.8437660053
67258556256173.1315063512382.86849364921
68260993259995.073624063997.926375937037
69254663256667.881829140-2004.88182913963
70250643249270.7677572471372.23224275277
71243422242496.607111015925.392888984788
72247105241117.8279373005987.1720627005
73248541247958.652836620582.347163380327
74245039244818.258880736220.741119264363
75237080238556.846896415-1476.84689641459
76237085232533.7106649924551.28933500778
77225554230671.340467827-5117.34046782652
78226839222743.7332836714095.26671632929
79247934248819.419647614-885.419647614093
80248333250936.961365441-2603.96136544063
81246969245160.2662431381808.73375686168
82245098243276.9278373361821.07216266438
83246263238711.1546908357551.84530916536
84255765246658.4315318029106.56846819786
85264319259583.2400837984735.75991620217
86268347264185.238283594161.76171641017
87273046265592.3650822517453.63491774903
88273963273840.104030974122.895969025616
89267430271387.864162814-3957.86416281387
90271993270032.1892869581960.81071304181
91292710303696.52220238-10986.52220238
92295881300566.414224755-4685.41422475548
93293299296066.680917328-2767.68091732817
94288576291927.205471524-3351.20547152415







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
95283461.88276079275236.469642982291687.295878599
96284760.263821161272429.52429436297091.003347962
97287916.972938466271595.978121189304237.967755742
98285852.314594405265795.920499146305908.708689664
99280557.074910050256977.311817304304136.838002797
100277528.933204777250236.452854669304821.413554886
101271010.202892415240329.884257648301690.521527182
102270727.860029076235942.025856382305513.69420177
103298107.574925040255284.997019572340930.152830509
104303992.394017023255614.335110779352370.452923267
105302952.803588062249934.329966301355971.277209823
106300745.422996905243823.839403356357667.006590455

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
95 & 283461.88276079 & 275236.469642982 & 291687.295878599 \tabularnewline
96 & 284760.263821161 & 272429.52429436 & 297091.003347962 \tabularnewline
97 & 287916.972938466 & 271595.978121189 & 304237.967755742 \tabularnewline
98 & 285852.314594405 & 265795.920499146 & 305908.708689664 \tabularnewline
99 & 280557.074910050 & 256977.311817304 & 304136.838002797 \tabularnewline
100 & 277528.933204777 & 250236.452854669 & 304821.413554886 \tabularnewline
101 & 271010.202892415 & 240329.884257648 & 301690.521527182 \tabularnewline
102 & 270727.860029076 & 235942.025856382 & 305513.69420177 \tabularnewline
103 & 298107.574925040 & 255284.997019572 & 340930.152830509 \tabularnewline
104 & 303992.394017023 & 255614.335110779 & 352370.452923267 \tabularnewline
105 & 302952.803588062 & 249934.329966301 & 355971.277209823 \tabularnewline
106 & 300745.422996905 & 243823.839403356 & 357667.006590455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64659&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]95[/C][C]283461.88276079[/C][C]275236.469642982[/C][C]291687.295878599[/C][/ROW]
[ROW][C]96[/C][C]284760.263821161[/C][C]272429.52429436[/C][C]297091.003347962[/C][/ROW]
[ROW][C]97[/C][C]287916.972938466[/C][C]271595.978121189[/C][C]304237.967755742[/C][/ROW]
[ROW][C]98[/C][C]285852.314594405[/C][C]265795.920499146[/C][C]305908.708689664[/C][/ROW]
[ROW][C]99[/C][C]280557.074910050[/C][C]256977.311817304[/C][C]304136.838002797[/C][/ROW]
[ROW][C]100[/C][C]277528.933204777[/C][C]250236.452854669[/C][C]304821.413554886[/C][/ROW]
[ROW][C]101[/C][C]271010.202892415[/C][C]240329.884257648[/C][C]301690.521527182[/C][/ROW]
[ROW][C]102[/C][C]270727.860029076[/C][C]235942.025856382[/C][C]305513.69420177[/C][/ROW]
[ROW][C]103[/C][C]298107.574925040[/C][C]255284.997019572[/C][C]340930.152830509[/C][/ROW]
[ROW][C]104[/C][C]303992.394017023[/C][C]255614.335110779[/C][C]352370.452923267[/C][/ROW]
[ROW][C]105[/C][C]302952.803588062[/C][C]249934.329966301[/C][C]355971.277209823[/C][/ROW]
[ROW][C]106[/C][C]300745.422996905[/C][C]243823.839403356[/C][C]357667.006590455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64659&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64659&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
95283461.88276079275236.469642982291687.295878599
96284760.263821161272429.52429436297091.003347962
97287916.972938466271595.978121189304237.967755742
98285852.314594405265795.920499146305908.708689664
99280557.074910050256977.311817304304136.838002797
100277528.933204777250236.452854669304821.413554886
101271010.202892415240329.884257648301690.521527182
102270727.860029076235942.025856382305513.69420177
103298107.574925040255284.997019572340930.152830509
104303992.394017023255614.335110779352370.452923267
105302952.803588062249934.329966301355971.277209823
106300745.422996905243823.839403356357667.006590455



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