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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 12 Jan 2014 07:53:44 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Jan/12/t1389531241a36eyrswx2agywl.htm/, Retrieved Sun, 19 May 2024 10:56:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232997, Retrieved Sun, 19 May 2024 10:56:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-01-12 12:53:44] [0a7dc2868d6127c6118dc8d5ca2cf9ea] [Current]
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Dataseries X:
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
286445
297584
300431
298522
292213
285383
277537
277891
302686
300653
296369
287224
279998
283495
285775
282329
277799
271980
266730
262433
285378
286692
282917
277686
274371
277466
290604
290770
283654
278601
274405
272817
294292
300562
298982
296917
295008
297295




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232997&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232997&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232997&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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.843381202464691
beta0.133839831386343
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.843381202464691 \tabularnewline
beta & 0.133839831386343 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232997&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]0.843381202464691[/C][/ROW]
[ROW][C]beta[/C][C]0.133839831386343[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232997&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232997&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
alpha0.843381202464691
beta0.133839831386343
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13269034282294.24732906-13260.2473290597
14264176264944.561023904-768.561023904127
15255198254189.6661726021008.33382739802
16253353252102.2730746621250.72692533821
17246057244441.4476437571615.55235624299
18235372233502.2111056531869.78889434741
19258556261904.617578382-3348.61757838179
20260993257480.2662104363512.73378956423
21254663260325.909967156-5662.90996715598
22250643239660.39531938310982.6046806175
23243422239664.4642593223757.53574067837
24247105239300.6889803717804.31101962854
25248541248414.977247058126.022752941644
26245039246811.420265229-1772.42026522887
27237080237874.838790213-794.838790212962
28237085236487.762857691597.237142308993
29225554230442.286070078-4888.28607007783
30226839215432.86354179911406.1364582012
31247934253512.400425402-5578.40042540157
32248333250482.069977979-2149.06997797915
33246969248676.444757917-1707.44475791717
34245098235961.2487814179136.75121858332
35246263235075.97493452511187.0250654747
36255765244249.51518978411515.484810216
37264319258347.7060782135971.29392178694
38268347265092.9442508513254.05574914906
39273046264832.4195353188213.58046468196
40273963276561.466394159-2598.4663941593
41267430271901.498717915-4471.4987179155
42271993264782.4872447157210.51275528513
43292710301176.710191525-8466.71019152482
44295881300434.798537943-4553.79853794305
45293299300586.063665343-7287.06366534327
46288576288149.537109023426.462890977156
47286445282542.0915248093902.9084751911
48297584287104.38152581510479.6184741854
49300431300824.284974074-393.284974074166
50298522302421.432711834-3899.43271183356
51292213296742.319980556-4529.31998055562
52285383294430.256157971-9047.25615797099
53277537281709.603665258-4172.60366525844
54277891274377.4912451093513.50875489105
55302686302486.266290419199.733709580614
56300653307932.440454532-7279.44045453175
57296369303315.339145849-6946.33914584894
58287224290371.18621872-3147.18621871964
59279998279887.812241687110.187758312561
60283495279446.8579378314048.14206216898
61285775282479.130473353295.86952664953
62282329283494.393962477-1165.39396247733
63277799277186.959588041612.040411958762
64271980276248.268867342-4268.2688673418
65266730266605.869274875124.130725125142
66262433262870.620972857-437.620972856937
67285378285451.381817481-73.381817480782
68286692287788.301285024-1096.30128502351
69282917287428.518690137-4511.51869013679
70277686276398.1094277831287.89057221689
71274371269931.2275299084439.77247009159
72277466274013.1017951963452.89820480358
73290604276612.92743663113991.0725633691
74290770287344.2501126113425.74988738919
75283654287100.162631673-3446.16263167345
76278601283429.312580785-4828.31258078507
77274405275394.0993807-989.099380700151
78272817271897.918062768919.081937231589
79294292297099.010450708-2807.01045070839
80300562298080.7310833652481.26891663531
81298982301717.646251449-2735.64625144872
82296917294808.0574001112108.94259988872
83295008291334.7444836883673.25551631249
84297295296336.531981164958.468018835527

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 269034 & 282294.24732906 & -13260.2473290597 \tabularnewline
14 & 264176 & 264944.561023904 & -768.561023904127 \tabularnewline
15 & 255198 & 254189.666172602 & 1008.33382739802 \tabularnewline
16 & 253353 & 252102.273074662 & 1250.72692533821 \tabularnewline
17 & 246057 & 244441.447643757 & 1615.55235624299 \tabularnewline
18 & 235372 & 233502.211105653 & 1869.78889434741 \tabularnewline
19 & 258556 & 261904.617578382 & -3348.61757838179 \tabularnewline
20 & 260993 & 257480.266210436 & 3512.73378956423 \tabularnewline
21 & 254663 & 260325.909967156 & -5662.90996715598 \tabularnewline
22 & 250643 & 239660.395319383 & 10982.6046806175 \tabularnewline
23 & 243422 & 239664.464259322 & 3757.53574067837 \tabularnewline
24 & 247105 & 239300.688980371 & 7804.31101962854 \tabularnewline
25 & 248541 & 248414.977247058 & 126.022752941644 \tabularnewline
26 & 245039 & 246811.420265229 & -1772.42026522887 \tabularnewline
27 & 237080 & 237874.838790213 & -794.838790212962 \tabularnewline
28 & 237085 & 236487.762857691 & 597.237142308993 \tabularnewline
29 & 225554 & 230442.286070078 & -4888.28607007783 \tabularnewline
30 & 226839 & 215432.863541799 & 11406.1364582012 \tabularnewline
31 & 247934 & 253512.400425402 & -5578.40042540157 \tabularnewline
32 & 248333 & 250482.069977979 & -2149.06997797915 \tabularnewline
33 & 246969 & 248676.444757917 & -1707.44475791717 \tabularnewline
34 & 245098 & 235961.248781417 & 9136.75121858332 \tabularnewline
35 & 246263 & 235075.974934525 & 11187.0250654747 \tabularnewline
36 & 255765 & 244249.515189784 & 11515.484810216 \tabularnewline
37 & 264319 & 258347.706078213 & 5971.29392178694 \tabularnewline
38 & 268347 & 265092.944250851 & 3254.05574914906 \tabularnewline
39 & 273046 & 264832.419535318 & 8213.58046468196 \tabularnewline
40 & 273963 & 276561.466394159 & -2598.4663941593 \tabularnewline
41 & 267430 & 271901.498717915 & -4471.4987179155 \tabularnewline
42 & 271993 & 264782.487244715 & 7210.51275528513 \tabularnewline
43 & 292710 & 301176.710191525 & -8466.71019152482 \tabularnewline
44 & 295881 & 300434.798537943 & -4553.79853794305 \tabularnewline
45 & 293299 & 300586.063665343 & -7287.06366534327 \tabularnewline
46 & 288576 & 288149.537109023 & 426.462890977156 \tabularnewline
47 & 286445 & 282542.091524809 & 3902.9084751911 \tabularnewline
48 & 297584 & 287104.381525815 & 10479.6184741854 \tabularnewline
49 & 300431 & 300824.284974074 & -393.284974074166 \tabularnewline
50 & 298522 & 302421.432711834 & -3899.43271183356 \tabularnewline
51 & 292213 & 296742.319980556 & -4529.31998055562 \tabularnewline
52 & 285383 & 294430.256157971 & -9047.25615797099 \tabularnewline
53 & 277537 & 281709.603665258 & -4172.60366525844 \tabularnewline
54 & 277891 & 274377.491245109 & 3513.50875489105 \tabularnewline
55 & 302686 & 302486.266290419 & 199.733709580614 \tabularnewline
56 & 300653 & 307932.440454532 & -7279.44045453175 \tabularnewline
57 & 296369 & 303315.339145849 & -6946.33914584894 \tabularnewline
58 & 287224 & 290371.18621872 & -3147.18621871964 \tabularnewline
59 & 279998 & 279887.812241687 & 110.187758312561 \tabularnewline
60 & 283495 & 279446.857937831 & 4048.14206216898 \tabularnewline
61 & 285775 & 282479.13047335 & 3295.86952664953 \tabularnewline
62 & 282329 & 283494.393962477 & -1165.39396247733 \tabularnewline
63 & 277799 & 277186.959588041 & 612.040411958762 \tabularnewline
64 & 271980 & 276248.268867342 & -4268.2688673418 \tabularnewline
65 & 266730 & 266605.869274875 & 124.130725125142 \tabularnewline
66 & 262433 & 262870.620972857 & -437.620972856937 \tabularnewline
67 & 285378 & 285451.381817481 & -73.381817480782 \tabularnewline
68 & 286692 & 287788.301285024 & -1096.30128502351 \tabularnewline
69 & 282917 & 287428.518690137 & -4511.51869013679 \tabularnewline
70 & 277686 & 276398.109427783 & 1287.89057221689 \tabularnewline
71 & 274371 & 269931.227529908 & 4439.77247009159 \tabularnewline
72 & 277466 & 274013.101795196 & 3452.89820480358 \tabularnewline
73 & 290604 & 276612.927436631 & 13991.0725633691 \tabularnewline
74 & 290770 & 287344.250112611 & 3425.74988738919 \tabularnewline
75 & 283654 & 287100.162631673 & -3446.16263167345 \tabularnewline
76 & 278601 & 283429.312580785 & -4828.31258078507 \tabularnewline
77 & 274405 & 275394.0993807 & -989.099380700151 \tabularnewline
78 & 272817 & 271897.918062768 & 919.081937231589 \tabularnewline
79 & 294292 & 297099.010450708 & -2807.01045070839 \tabularnewline
80 & 300562 & 298080.731083365 & 2481.26891663531 \tabularnewline
81 & 298982 & 301717.646251449 & -2735.64625144872 \tabularnewline
82 & 296917 & 294808.057400111 & 2108.94259988872 \tabularnewline
83 & 295008 & 291334.744483688 & 3673.25551631249 \tabularnewline
84 & 297295 & 296336.531981164 & 958.468018835527 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232997&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]269034[/C][C]282294.24732906[/C][C]-13260.2473290597[/C][/ROW]
[ROW][C]14[/C][C]264176[/C][C]264944.561023904[/C][C]-768.561023904127[/C][/ROW]
[ROW][C]15[/C][C]255198[/C][C]254189.666172602[/C][C]1008.33382739802[/C][/ROW]
[ROW][C]16[/C][C]253353[/C][C]252102.273074662[/C][C]1250.72692533821[/C][/ROW]
[ROW][C]17[/C][C]246057[/C][C]244441.447643757[/C][C]1615.55235624299[/C][/ROW]
[ROW][C]18[/C][C]235372[/C][C]233502.211105653[/C][C]1869.78889434741[/C][/ROW]
[ROW][C]19[/C][C]258556[/C][C]261904.617578382[/C][C]-3348.61757838179[/C][/ROW]
[ROW][C]20[/C][C]260993[/C][C]257480.266210436[/C][C]3512.73378956423[/C][/ROW]
[ROW][C]21[/C][C]254663[/C][C]260325.909967156[/C][C]-5662.90996715598[/C][/ROW]
[ROW][C]22[/C][C]250643[/C][C]239660.395319383[/C][C]10982.6046806175[/C][/ROW]
[ROW][C]23[/C][C]243422[/C][C]239664.464259322[/C][C]3757.53574067837[/C][/ROW]
[ROW][C]24[/C][C]247105[/C][C]239300.688980371[/C][C]7804.31101962854[/C][/ROW]
[ROW][C]25[/C][C]248541[/C][C]248414.977247058[/C][C]126.022752941644[/C][/ROW]
[ROW][C]26[/C][C]245039[/C][C]246811.420265229[/C][C]-1772.42026522887[/C][/ROW]
[ROW][C]27[/C][C]237080[/C][C]237874.838790213[/C][C]-794.838790212962[/C][/ROW]
[ROW][C]28[/C][C]237085[/C][C]236487.762857691[/C][C]597.237142308993[/C][/ROW]
[ROW][C]29[/C][C]225554[/C][C]230442.286070078[/C][C]-4888.28607007783[/C][/ROW]
[ROW][C]30[/C][C]226839[/C][C]215432.863541799[/C][C]11406.1364582012[/C][/ROW]
[ROW][C]31[/C][C]247934[/C][C]253512.400425402[/C][C]-5578.40042540157[/C][/ROW]
[ROW][C]32[/C][C]248333[/C][C]250482.069977979[/C][C]-2149.06997797915[/C][/ROW]
[ROW][C]33[/C][C]246969[/C][C]248676.444757917[/C][C]-1707.44475791717[/C][/ROW]
[ROW][C]34[/C][C]245098[/C][C]235961.248781417[/C][C]9136.75121858332[/C][/ROW]
[ROW][C]35[/C][C]246263[/C][C]235075.974934525[/C][C]11187.0250654747[/C][/ROW]
[ROW][C]36[/C][C]255765[/C][C]244249.515189784[/C][C]11515.484810216[/C][/ROW]
[ROW][C]37[/C][C]264319[/C][C]258347.706078213[/C][C]5971.29392178694[/C][/ROW]
[ROW][C]38[/C][C]268347[/C][C]265092.944250851[/C][C]3254.05574914906[/C][/ROW]
[ROW][C]39[/C][C]273046[/C][C]264832.419535318[/C][C]8213.58046468196[/C][/ROW]
[ROW][C]40[/C][C]273963[/C][C]276561.466394159[/C][C]-2598.4663941593[/C][/ROW]
[ROW][C]41[/C][C]267430[/C][C]271901.498717915[/C][C]-4471.4987179155[/C][/ROW]
[ROW][C]42[/C][C]271993[/C][C]264782.487244715[/C][C]7210.51275528513[/C][/ROW]
[ROW][C]43[/C][C]292710[/C][C]301176.710191525[/C][C]-8466.71019152482[/C][/ROW]
[ROW][C]44[/C][C]295881[/C][C]300434.798537943[/C][C]-4553.79853794305[/C][/ROW]
[ROW][C]45[/C][C]293299[/C][C]300586.063665343[/C][C]-7287.06366534327[/C][/ROW]
[ROW][C]46[/C][C]288576[/C][C]288149.537109023[/C][C]426.462890977156[/C][/ROW]
[ROW][C]47[/C][C]286445[/C][C]282542.091524809[/C][C]3902.9084751911[/C][/ROW]
[ROW][C]48[/C][C]297584[/C][C]287104.381525815[/C][C]10479.6184741854[/C][/ROW]
[ROW][C]49[/C][C]300431[/C][C]300824.284974074[/C][C]-393.284974074166[/C][/ROW]
[ROW][C]50[/C][C]298522[/C][C]302421.432711834[/C][C]-3899.43271183356[/C][/ROW]
[ROW][C]51[/C][C]292213[/C][C]296742.319980556[/C][C]-4529.31998055562[/C][/ROW]
[ROW][C]52[/C][C]285383[/C][C]294430.256157971[/C][C]-9047.25615797099[/C][/ROW]
[ROW][C]53[/C][C]277537[/C][C]281709.603665258[/C][C]-4172.60366525844[/C][/ROW]
[ROW][C]54[/C][C]277891[/C][C]274377.491245109[/C][C]3513.50875489105[/C][/ROW]
[ROW][C]55[/C][C]302686[/C][C]302486.266290419[/C][C]199.733709580614[/C][/ROW]
[ROW][C]56[/C][C]300653[/C][C]307932.440454532[/C][C]-7279.44045453175[/C][/ROW]
[ROW][C]57[/C][C]296369[/C][C]303315.339145849[/C][C]-6946.33914584894[/C][/ROW]
[ROW][C]58[/C][C]287224[/C][C]290371.18621872[/C][C]-3147.18621871964[/C][/ROW]
[ROW][C]59[/C][C]279998[/C][C]279887.812241687[/C][C]110.187758312561[/C][/ROW]
[ROW][C]60[/C][C]283495[/C][C]279446.857937831[/C][C]4048.14206216898[/C][/ROW]
[ROW][C]61[/C][C]285775[/C][C]282479.13047335[/C][C]3295.86952664953[/C][/ROW]
[ROW][C]62[/C][C]282329[/C][C]283494.393962477[/C][C]-1165.39396247733[/C][/ROW]
[ROW][C]63[/C][C]277799[/C][C]277186.959588041[/C][C]612.040411958762[/C][/ROW]
[ROW][C]64[/C][C]271980[/C][C]276248.268867342[/C][C]-4268.2688673418[/C][/ROW]
[ROW][C]65[/C][C]266730[/C][C]266605.869274875[/C][C]124.130725125142[/C][/ROW]
[ROW][C]66[/C][C]262433[/C][C]262870.620972857[/C][C]-437.620972856937[/C][/ROW]
[ROW][C]67[/C][C]285378[/C][C]285451.381817481[/C][C]-73.381817480782[/C][/ROW]
[ROW][C]68[/C][C]286692[/C][C]287788.301285024[/C][C]-1096.30128502351[/C][/ROW]
[ROW][C]69[/C][C]282917[/C][C]287428.518690137[/C][C]-4511.51869013679[/C][/ROW]
[ROW][C]70[/C][C]277686[/C][C]276398.109427783[/C][C]1287.89057221689[/C][/ROW]
[ROW][C]71[/C][C]274371[/C][C]269931.227529908[/C][C]4439.77247009159[/C][/ROW]
[ROW][C]72[/C][C]277466[/C][C]274013.101795196[/C][C]3452.89820480358[/C][/ROW]
[ROW][C]73[/C][C]290604[/C][C]276612.927436631[/C][C]13991.0725633691[/C][/ROW]
[ROW][C]74[/C][C]290770[/C][C]287344.250112611[/C][C]3425.74988738919[/C][/ROW]
[ROW][C]75[/C][C]283654[/C][C]287100.162631673[/C][C]-3446.16263167345[/C][/ROW]
[ROW][C]76[/C][C]278601[/C][C]283429.312580785[/C][C]-4828.31258078507[/C][/ROW]
[ROW][C]77[/C][C]274405[/C][C]275394.0993807[/C][C]-989.099380700151[/C][/ROW]
[ROW][C]78[/C][C]272817[/C][C]271897.918062768[/C][C]919.081937231589[/C][/ROW]
[ROW][C]79[/C][C]294292[/C][C]297099.010450708[/C][C]-2807.01045070839[/C][/ROW]
[ROW][C]80[/C][C]300562[/C][C]298080.731083365[/C][C]2481.26891663531[/C][/ROW]
[ROW][C]81[/C][C]298982[/C][C]301717.646251449[/C][C]-2735.64625144872[/C][/ROW]
[ROW][C]82[/C][C]296917[/C][C]294808.057400111[/C][C]2108.94259988872[/C][/ROW]
[ROW][C]83[/C][C]295008[/C][C]291334.744483688[/C][C]3673.25551631249[/C][/ROW]
[ROW][C]84[/C][C]297295[/C][C]296336.531981164[/C][C]958.468018835527[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232997&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232997&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
13269034282294.24732906-13260.2473290597
14264176264944.561023904-768.561023904127
15255198254189.6661726021008.33382739802
16253353252102.2730746621250.72692533821
17246057244441.4476437571615.55235624299
18235372233502.2111056531869.78889434741
19258556261904.617578382-3348.61757838179
20260993257480.2662104363512.73378956423
21254663260325.909967156-5662.90996715598
22250643239660.39531938310982.6046806175
23243422239664.4642593223757.53574067837
24247105239300.6889803717804.31101962854
25248541248414.977247058126.022752941644
26245039246811.420265229-1772.42026522887
27237080237874.838790213-794.838790212962
28237085236487.762857691597.237142308993
29225554230442.286070078-4888.28607007783
30226839215432.86354179911406.1364582012
31247934253512.400425402-5578.40042540157
32248333250482.069977979-2149.06997797915
33246969248676.444757917-1707.44475791717
34245098235961.2487814179136.75121858332
35246263235075.97493452511187.0250654747
36255765244249.51518978411515.484810216
37264319258347.7060782135971.29392178694
38268347265092.9442508513254.05574914906
39273046264832.4195353188213.58046468196
40273963276561.466394159-2598.4663941593
41267430271901.498717915-4471.4987179155
42271993264782.4872447157210.51275528513
43292710301176.710191525-8466.71019152482
44295881300434.798537943-4553.79853794305
45293299300586.063665343-7287.06366534327
46288576288149.537109023426.462890977156
47286445282542.0915248093902.9084751911
48297584287104.38152581510479.6184741854
49300431300824.284974074-393.284974074166
50298522302421.432711834-3899.43271183356
51292213296742.319980556-4529.31998055562
52285383294430.256157971-9047.25615797099
53277537281709.603665258-4172.60366525844
54277891274377.4912451093513.50875489105
55302686302486.266290419199.733709580614
56300653307932.440454532-7279.44045453175
57296369303315.339145849-6946.33914584894
58287224290371.18621872-3147.18621871964
59279998279887.812241687110.187758312561
60283495279446.8579378314048.14206216898
61285775282479.130473353295.86952664953
62282329283494.393962477-1165.39396247733
63277799277186.959588041612.040411958762
64271980276248.268867342-4268.2688673418
65266730266605.869274875124.130725125142
66262433262870.620972857-437.620972856937
67285378285451.381817481-73.381817480782
68286692287788.301285024-1096.30128502351
69282917287428.518690137-4511.51869013679
70277686276398.1094277831287.89057221689
71274371269931.2275299084439.77247009159
72277466274013.1017951963452.89820480358
73290604276612.92743663113991.0725633691
74290770287344.2501126113425.74988738919
75283654287100.162631673-3446.16263167345
76278601283429.312580785-4828.31258078507
77274405275394.0993807-989.099380700151
78272817271897.918062768919.081937231589
79294292297099.010450708-2807.01045070839
80300562298080.7310833652481.26891663531
81298982301717.646251449-2735.64625144872
82296917294808.0574001112108.94259988872
83295008291334.7444836883673.25551631249
84297295296336.531981164958.468018835527







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85299922.4542869289338.885565534310506.023008266
86297059.332965403282415.590993798311703.074937008
87292323.161698759273817.084343625310829.239053893
88291204.665656597268866.951486556313542.379826638
89288250.259626739262043.594601055314456.924652422
90286406.176900292256260.252824476316552.100976107
91310663.86632347276490.920866215344836.811780725
92315573.3700547277276.058565247353870.681544153
93316752.641305903274228.380892527359276.901719279
94313669.871658133266813.382700779360526.360615486
95309185.736683448257890.591148312360480.882218585
96310772.572724247254932.163476838366612.981971656

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 299922.4542869 & 289338.885565534 & 310506.023008266 \tabularnewline
86 & 297059.332965403 & 282415.590993798 & 311703.074937008 \tabularnewline
87 & 292323.161698759 & 273817.084343625 & 310829.239053893 \tabularnewline
88 & 291204.665656597 & 268866.951486556 & 313542.379826638 \tabularnewline
89 & 288250.259626739 & 262043.594601055 & 314456.924652422 \tabularnewline
90 & 286406.176900292 & 256260.252824476 & 316552.100976107 \tabularnewline
91 & 310663.86632347 & 276490.920866215 & 344836.811780725 \tabularnewline
92 & 315573.3700547 & 277276.058565247 & 353870.681544153 \tabularnewline
93 & 316752.641305903 & 274228.380892527 & 359276.901719279 \tabularnewline
94 & 313669.871658133 & 266813.382700779 & 360526.360615486 \tabularnewline
95 & 309185.736683448 & 257890.591148312 & 360480.882218585 \tabularnewline
96 & 310772.572724247 & 254932.163476838 & 366612.981971656 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232997&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]85[/C][C]299922.4542869[/C][C]289338.885565534[/C][C]310506.023008266[/C][/ROW]
[ROW][C]86[/C][C]297059.332965403[/C][C]282415.590993798[/C][C]311703.074937008[/C][/ROW]
[ROW][C]87[/C][C]292323.161698759[/C][C]273817.084343625[/C][C]310829.239053893[/C][/ROW]
[ROW][C]88[/C][C]291204.665656597[/C][C]268866.951486556[/C][C]313542.379826638[/C][/ROW]
[ROW][C]89[/C][C]288250.259626739[/C][C]262043.594601055[/C][C]314456.924652422[/C][/ROW]
[ROW][C]90[/C][C]286406.176900292[/C][C]256260.252824476[/C][C]316552.100976107[/C][/ROW]
[ROW][C]91[/C][C]310663.86632347[/C][C]276490.920866215[/C][C]344836.811780725[/C][/ROW]
[ROW][C]92[/C][C]315573.3700547[/C][C]277276.058565247[/C][C]353870.681544153[/C][/ROW]
[ROW][C]93[/C][C]316752.641305903[/C][C]274228.380892527[/C][C]359276.901719279[/C][/ROW]
[ROW][C]94[/C][C]313669.871658133[/C][C]266813.382700779[/C][C]360526.360615486[/C][/ROW]
[ROW][C]95[/C][C]309185.736683448[/C][C]257890.591148312[/C][C]360480.882218585[/C][/ROW]
[ROW][C]96[/C][C]310772.572724247[/C][C]254932.163476838[/C][C]366612.981971656[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232997&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232997&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
85299922.4542869289338.885565534310506.023008266
86297059.332965403282415.590993798311703.074937008
87292323.161698759273817.084343625310829.239053893
88291204.665656597268866.951486556313542.379826638
89288250.259626739262043.594601055314456.924652422
90286406.176900292256260.252824476316552.100976107
91310663.86632347276490.920866215344836.811780725
92315573.3700547277276.058565247353870.681544153
93316752.641305903274228.380892527359276.901719279
94313669.871658133266813.382700779360526.360615486
95309185.736683448257890.591148312360480.882218585
96310772.572724247254932.163476838366612.981971656



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')