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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 computationMon, 30 Mar 2015 16:34:06 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Mar/30/t142772968028j1fy3o6fntm96.htm/, Retrieved Sun, 19 May 2024 13:58:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278479, Retrieved Sun, 19 May 2024 13:58:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact164
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-03-30 15:34:06] [a916b42d6b56a629542ed1ac6e46ec84] [Current]
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Dataseries X:
13671
15698
18150
16245
18479
18479
18819
18059
17004
16981
16578
21604
13419
14487
17349
15646
17419
17358
18221
19554
14386
16833
18067
19662
12192
15081
13698
18474
13871
15669
17597
15469
15374
16568
11619
16780
8700
8906
9612
10073
10275
9921
13237
9572
10425
11385
9970
15456
7708
8892
11145
11069
9893
10929
12240
10411
9747
9950
10079
14064
8368
9558
10432
10068
9915
9549
10433
10009
10327
9453
9494
13133
7082
7805
9064
8236
10182
16210
7451
8384
7143
8507
9833
17364
6260
7897
8933
6554
8333
7224
9659
9977
9289
9929
10576
15463




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278479&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278479&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278479&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.26016537213905
beta0
gamma0.142893319894312

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.26016537213905 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.142893319894312 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278479&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]0.26016537213905[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.142893319894312[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278479&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278479&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
alpha0.26016537213905
beta0
gamma0.142893319894312







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131341913793.1659492269-374.165949226872
141448714710.8813967835-223.881396783479
151734917544.4229556878-195.422955687824
161564615837.4562309625-191.456230962471
171741917467.267381653-48.2673816530005
181735817361.5343066764-3.53430667638531
191822118204.912959948416.0870400516142
201955417482.83275799312071.16724200694
211438617001.6921852337-2615.69218523367
221683316304.7917733685528.208226631486
231806716068.12235852151998.87764147852
241966221668.6712934686-2006.67129346858
251219213112.5919477879-920.591947787922
261508113842.38168010411238.6183198959
271369816965.8594314995-3267.85943149947
281847414584.91829997683889.08170002319
291387117272.5743703591-3401.57437035909
301566916301.4093973313-632.409397331316
311759716919.7957143646677.204285635395
321546916608.7602173188-1139.76021731878
331537414941.5485268869432.451473113106
341656815347.02948580121220.97051419876
351161915448.3452368372-3829.34523683718
361678018445.128612668-1665.12861266801
37870011191.2579827925-2491.25798279251
38890611521.4393824521-2615.4393824521
39961212578.1057549183-2966.10575491833
401007311194.9257808994-1121.92578089936
411027511490.2103554365-1215.2103554365
42992111302.073759359-1381.07375935897
431323711552.33209637671684.66790362335
44957211498.8577614607-1926.85776146067
451042510163.6484602198261.351539780198
461138510468.7690027782916.230997221797
47997010164.2608913015-194.260891301508
481545613132.90330484592323.09669515406
4977088395.47783560602-687.477835606021
5088928965.83237655147-73.8323765514651
511114510361.5062831214783.493716878571
521106910175.7005625647893.29943743532
53989310960.0232489629-1067.02324896289
541092910782.9749453828146.02505461723
551224011750.3257682997489.674231700275
561041111014.7532180724-603.753218072434
57974710251.6421137068-504.642113706786
58995010419.7516875983-469.751687598264
59100799665.88610403639413.113895963612
601406412942.10671898041121.89328101962
6183687873.5212710068494.4787289932
6295588801.33690482966756.663095170345
631043210512.428893116-80.4288931159626
641006810116.2539928525-48.2539928524711
65991510430.5953423304-515.595342330396
66954910517.9764068914-968.976406891394
671043311177.2892978103-744.289297810263
681000910077.7759732344-68.7759732343948
69103279500.88192506575826.118074934255
70945310006.0056552182-553.005655218247
7194949341.81780629652152.182193703478
721313312475.8143626189657.185637381073
7370827504.04294009502-422.042940095015
7478058148.28826473726-343.288264737258
7590649319.12944422255-255.129444222548
7682368918.96369430784-682.963694307844
77101828974.267998727131207.73200127287
78162109438.963897129746771.03610287026
79745112235.2200072607-4784.22000726066
80838410149.9098590238-1765.90985902383
8171439239.19154603257-2096.19154603257
8285078815.4953926264-308.495392626395
8398338332.778025531041500.22197446896
841736411639.49507149875724.50492850134
8562607701.97055801319-1441.97055801319
8678978086.29503898329-189.295038983289
8789339308.68609164621-375.68609164621
8865548830.99463326608-2276.99463326608
8983338643.39899910431-310.398999104305
9072249127.10920026448-1903.10920026448
9196598440.636809754871218.36319024513
9299778306.355827115421670.64417288458
9392898277.207375321031011.79262467897
9499298853.690633883641075.30936611636
95105768906.710162219381669.28983778062
961546312809.18201485992653.81798514009

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 13419 & 13793.1659492269 & -374.165949226872 \tabularnewline
14 & 14487 & 14710.8813967835 & -223.881396783479 \tabularnewline
15 & 17349 & 17544.4229556878 & -195.422955687824 \tabularnewline
16 & 15646 & 15837.4562309625 & -191.456230962471 \tabularnewline
17 & 17419 & 17467.267381653 & -48.2673816530005 \tabularnewline
18 & 17358 & 17361.5343066764 & -3.53430667638531 \tabularnewline
19 & 18221 & 18204.9129599484 & 16.0870400516142 \tabularnewline
20 & 19554 & 17482.8327579931 & 2071.16724200694 \tabularnewline
21 & 14386 & 17001.6921852337 & -2615.69218523367 \tabularnewline
22 & 16833 & 16304.7917733685 & 528.208226631486 \tabularnewline
23 & 18067 & 16068.1223585215 & 1998.87764147852 \tabularnewline
24 & 19662 & 21668.6712934686 & -2006.67129346858 \tabularnewline
25 & 12192 & 13112.5919477879 & -920.591947787922 \tabularnewline
26 & 15081 & 13842.3816801041 & 1238.6183198959 \tabularnewline
27 & 13698 & 16965.8594314995 & -3267.85943149947 \tabularnewline
28 & 18474 & 14584.9182999768 & 3889.08170002319 \tabularnewline
29 & 13871 & 17272.5743703591 & -3401.57437035909 \tabularnewline
30 & 15669 & 16301.4093973313 & -632.409397331316 \tabularnewline
31 & 17597 & 16919.7957143646 & 677.204285635395 \tabularnewline
32 & 15469 & 16608.7602173188 & -1139.76021731878 \tabularnewline
33 & 15374 & 14941.5485268869 & 432.451473113106 \tabularnewline
34 & 16568 & 15347.0294858012 & 1220.97051419876 \tabularnewline
35 & 11619 & 15448.3452368372 & -3829.34523683718 \tabularnewline
36 & 16780 & 18445.128612668 & -1665.12861266801 \tabularnewline
37 & 8700 & 11191.2579827925 & -2491.25798279251 \tabularnewline
38 & 8906 & 11521.4393824521 & -2615.4393824521 \tabularnewline
39 & 9612 & 12578.1057549183 & -2966.10575491833 \tabularnewline
40 & 10073 & 11194.9257808994 & -1121.92578089936 \tabularnewline
41 & 10275 & 11490.2103554365 & -1215.2103554365 \tabularnewline
42 & 9921 & 11302.073759359 & -1381.07375935897 \tabularnewline
43 & 13237 & 11552.3320963767 & 1684.66790362335 \tabularnewline
44 & 9572 & 11498.8577614607 & -1926.85776146067 \tabularnewline
45 & 10425 & 10163.6484602198 & 261.351539780198 \tabularnewline
46 & 11385 & 10468.7690027782 & 916.230997221797 \tabularnewline
47 & 9970 & 10164.2608913015 & -194.260891301508 \tabularnewline
48 & 15456 & 13132.9033048459 & 2323.09669515406 \tabularnewline
49 & 7708 & 8395.47783560602 & -687.477835606021 \tabularnewline
50 & 8892 & 8965.83237655147 & -73.8323765514651 \tabularnewline
51 & 11145 & 10361.5062831214 & 783.493716878571 \tabularnewline
52 & 11069 & 10175.7005625647 & 893.29943743532 \tabularnewline
53 & 9893 & 10960.0232489629 & -1067.02324896289 \tabularnewline
54 & 10929 & 10782.9749453828 & 146.02505461723 \tabularnewline
55 & 12240 & 11750.3257682997 & 489.674231700275 \tabularnewline
56 & 10411 & 11014.7532180724 & -603.753218072434 \tabularnewline
57 & 9747 & 10251.6421137068 & -504.642113706786 \tabularnewline
58 & 9950 & 10419.7516875983 & -469.751687598264 \tabularnewline
59 & 10079 & 9665.88610403639 & 413.113895963612 \tabularnewline
60 & 14064 & 12942.1067189804 & 1121.89328101962 \tabularnewline
61 & 8368 & 7873.5212710068 & 494.4787289932 \tabularnewline
62 & 9558 & 8801.33690482966 & 756.663095170345 \tabularnewline
63 & 10432 & 10512.428893116 & -80.4288931159626 \tabularnewline
64 & 10068 & 10116.2539928525 & -48.2539928524711 \tabularnewline
65 & 9915 & 10430.5953423304 & -515.595342330396 \tabularnewline
66 & 9549 & 10517.9764068914 & -968.976406891394 \tabularnewline
67 & 10433 & 11177.2892978103 & -744.289297810263 \tabularnewline
68 & 10009 & 10077.7759732344 & -68.7759732343948 \tabularnewline
69 & 10327 & 9500.88192506575 & 826.118074934255 \tabularnewline
70 & 9453 & 10006.0056552182 & -553.005655218247 \tabularnewline
71 & 9494 & 9341.81780629652 & 152.182193703478 \tabularnewline
72 & 13133 & 12475.8143626189 & 657.185637381073 \tabularnewline
73 & 7082 & 7504.04294009502 & -422.042940095015 \tabularnewline
74 & 7805 & 8148.28826473726 & -343.288264737258 \tabularnewline
75 & 9064 & 9319.12944422255 & -255.129444222548 \tabularnewline
76 & 8236 & 8918.96369430784 & -682.963694307844 \tabularnewline
77 & 10182 & 8974.26799872713 & 1207.73200127287 \tabularnewline
78 & 16210 & 9438.96389712974 & 6771.03610287026 \tabularnewline
79 & 7451 & 12235.2200072607 & -4784.22000726066 \tabularnewline
80 & 8384 & 10149.9098590238 & -1765.90985902383 \tabularnewline
81 & 7143 & 9239.19154603257 & -2096.19154603257 \tabularnewline
82 & 8507 & 8815.4953926264 & -308.495392626395 \tabularnewline
83 & 9833 & 8332.77802553104 & 1500.22197446896 \tabularnewline
84 & 17364 & 11639.4950714987 & 5724.50492850134 \tabularnewline
85 & 6260 & 7701.97055801319 & -1441.97055801319 \tabularnewline
86 & 7897 & 8086.29503898329 & -189.295038983289 \tabularnewline
87 & 8933 & 9308.68609164621 & -375.68609164621 \tabularnewline
88 & 6554 & 8830.99463326608 & -2276.99463326608 \tabularnewline
89 & 8333 & 8643.39899910431 & -310.398999104305 \tabularnewline
90 & 7224 & 9127.10920026448 & -1903.10920026448 \tabularnewline
91 & 9659 & 8440.63680975487 & 1218.36319024513 \tabularnewline
92 & 9977 & 8306.35582711542 & 1670.64417288458 \tabularnewline
93 & 9289 & 8277.20737532103 & 1011.79262467897 \tabularnewline
94 & 9929 & 8853.69063388364 & 1075.30936611636 \tabularnewline
95 & 10576 & 8906.71016221938 & 1669.28983778062 \tabularnewline
96 & 15463 & 12809.1820148599 & 2653.81798514009 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278479&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]13419[/C][C]13793.1659492269[/C][C]-374.165949226872[/C][/ROW]
[ROW][C]14[/C][C]14487[/C][C]14710.8813967835[/C][C]-223.881396783479[/C][/ROW]
[ROW][C]15[/C][C]17349[/C][C]17544.4229556878[/C][C]-195.422955687824[/C][/ROW]
[ROW][C]16[/C][C]15646[/C][C]15837.4562309625[/C][C]-191.456230962471[/C][/ROW]
[ROW][C]17[/C][C]17419[/C][C]17467.267381653[/C][C]-48.2673816530005[/C][/ROW]
[ROW][C]18[/C][C]17358[/C][C]17361.5343066764[/C][C]-3.53430667638531[/C][/ROW]
[ROW][C]19[/C][C]18221[/C][C]18204.9129599484[/C][C]16.0870400516142[/C][/ROW]
[ROW][C]20[/C][C]19554[/C][C]17482.8327579931[/C][C]2071.16724200694[/C][/ROW]
[ROW][C]21[/C][C]14386[/C][C]17001.6921852337[/C][C]-2615.69218523367[/C][/ROW]
[ROW][C]22[/C][C]16833[/C][C]16304.7917733685[/C][C]528.208226631486[/C][/ROW]
[ROW][C]23[/C][C]18067[/C][C]16068.1223585215[/C][C]1998.87764147852[/C][/ROW]
[ROW][C]24[/C][C]19662[/C][C]21668.6712934686[/C][C]-2006.67129346858[/C][/ROW]
[ROW][C]25[/C][C]12192[/C][C]13112.5919477879[/C][C]-920.591947787922[/C][/ROW]
[ROW][C]26[/C][C]15081[/C][C]13842.3816801041[/C][C]1238.6183198959[/C][/ROW]
[ROW][C]27[/C][C]13698[/C][C]16965.8594314995[/C][C]-3267.85943149947[/C][/ROW]
[ROW][C]28[/C][C]18474[/C][C]14584.9182999768[/C][C]3889.08170002319[/C][/ROW]
[ROW][C]29[/C][C]13871[/C][C]17272.5743703591[/C][C]-3401.57437035909[/C][/ROW]
[ROW][C]30[/C][C]15669[/C][C]16301.4093973313[/C][C]-632.409397331316[/C][/ROW]
[ROW][C]31[/C][C]17597[/C][C]16919.7957143646[/C][C]677.204285635395[/C][/ROW]
[ROW][C]32[/C][C]15469[/C][C]16608.7602173188[/C][C]-1139.76021731878[/C][/ROW]
[ROW][C]33[/C][C]15374[/C][C]14941.5485268869[/C][C]432.451473113106[/C][/ROW]
[ROW][C]34[/C][C]16568[/C][C]15347.0294858012[/C][C]1220.97051419876[/C][/ROW]
[ROW][C]35[/C][C]11619[/C][C]15448.3452368372[/C][C]-3829.34523683718[/C][/ROW]
[ROW][C]36[/C][C]16780[/C][C]18445.128612668[/C][C]-1665.12861266801[/C][/ROW]
[ROW][C]37[/C][C]8700[/C][C]11191.2579827925[/C][C]-2491.25798279251[/C][/ROW]
[ROW][C]38[/C][C]8906[/C][C]11521.4393824521[/C][C]-2615.4393824521[/C][/ROW]
[ROW][C]39[/C][C]9612[/C][C]12578.1057549183[/C][C]-2966.10575491833[/C][/ROW]
[ROW][C]40[/C][C]10073[/C][C]11194.9257808994[/C][C]-1121.92578089936[/C][/ROW]
[ROW][C]41[/C][C]10275[/C][C]11490.2103554365[/C][C]-1215.2103554365[/C][/ROW]
[ROW][C]42[/C][C]9921[/C][C]11302.073759359[/C][C]-1381.07375935897[/C][/ROW]
[ROW][C]43[/C][C]13237[/C][C]11552.3320963767[/C][C]1684.66790362335[/C][/ROW]
[ROW][C]44[/C][C]9572[/C][C]11498.8577614607[/C][C]-1926.85776146067[/C][/ROW]
[ROW][C]45[/C][C]10425[/C][C]10163.6484602198[/C][C]261.351539780198[/C][/ROW]
[ROW][C]46[/C][C]11385[/C][C]10468.7690027782[/C][C]916.230997221797[/C][/ROW]
[ROW][C]47[/C][C]9970[/C][C]10164.2608913015[/C][C]-194.260891301508[/C][/ROW]
[ROW][C]48[/C][C]15456[/C][C]13132.9033048459[/C][C]2323.09669515406[/C][/ROW]
[ROW][C]49[/C][C]7708[/C][C]8395.47783560602[/C][C]-687.477835606021[/C][/ROW]
[ROW][C]50[/C][C]8892[/C][C]8965.83237655147[/C][C]-73.8323765514651[/C][/ROW]
[ROW][C]51[/C][C]11145[/C][C]10361.5062831214[/C][C]783.493716878571[/C][/ROW]
[ROW][C]52[/C][C]11069[/C][C]10175.7005625647[/C][C]893.29943743532[/C][/ROW]
[ROW][C]53[/C][C]9893[/C][C]10960.0232489629[/C][C]-1067.02324896289[/C][/ROW]
[ROW][C]54[/C][C]10929[/C][C]10782.9749453828[/C][C]146.02505461723[/C][/ROW]
[ROW][C]55[/C][C]12240[/C][C]11750.3257682997[/C][C]489.674231700275[/C][/ROW]
[ROW][C]56[/C][C]10411[/C][C]11014.7532180724[/C][C]-603.753218072434[/C][/ROW]
[ROW][C]57[/C][C]9747[/C][C]10251.6421137068[/C][C]-504.642113706786[/C][/ROW]
[ROW][C]58[/C][C]9950[/C][C]10419.7516875983[/C][C]-469.751687598264[/C][/ROW]
[ROW][C]59[/C][C]10079[/C][C]9665.88610403639[/C][C]413.113895963612[/C][/ROW]
[ROW][C]60[/C][C]14064[/C][C]12942.1067189804[/C][C]1121.89328101962[/C][/ROW]
[ROW][C]61[/C][C]8368[/C][C]7873.5212710068[/C][C]494.4787289932[/C][/ROW]
[ROW][C]62[/C][C]9558[/C][C]8801.33690482966[/C][C]756.663095170345[/C][/ROW]
[ROW][C]63[/C][C]10432[/C][C]10512.428893116[/C][C]-80.4288931159626[/C][/ROW]
[ROW][C]64[/C][C]10068[/C][C]10116.2539928525[/C][C]-48.2539928524711[/C][/ROW]
[ROW][C]65[/C][C]9915[/C][C]10430.5953423304[/C][C]-515.595342330396[/C][/ROW]
[ROW][C]66[/C][C]9549[/C][C]10517.9764068914[/C][C]-968.976406891394[/C][/ROW]
[ROW][C]67[/C][C]10433[/C][C]11177.2892978103[/C][C]-744.289297810263[/C][/ROW]
[ROW][C]68[/C][C]10009[/C][C]10077.7759732344[/C][C]-68.7759732343948[/C][/ROW]
[ROW][C]69[/C][C]10327[/C][C]9500.88192506575[/C][C]826.118074934255[/C][/ROW]
[ROW][C]70[/C][C]9453[/C][C]10006.0056552182[/C][C]-553.005655218247[/C][/ROW]
[ROW][C]71[/C][C]9494[/C][C]9341.81780629652[/C][C]152.182193703478[/C][/ROW]
[ROW][C]72[/C][C]13133[/C][C]12475.8143626189[/C][C]657.185637381073[/C][/ROW]
[ROW][C]73[/C][C]7082[/C][C]7504.04294009502[/C][C]-422.042940095015[/C][/ROW]
[ROW][C]74[/C][C]7805[/C][C]8148.28826473726[/C][C]-343.288264737258[/C][/ROW]
[ROW][C]75[/C][C]9064[/C][C]9319.12944422255[/C][C]-255.129444222548[/C][/ROW]
[ROW][C]76[/C][C]8236[/C][C]8918.96369430784[/C][C]-682.963694307844[/C][/ROW]
[ROW][C]77[/C][C]10182[/C][C]8974.26799872713[/C][C]1207.73200127287[/C][/ROW]
[ROW][C]78[/C][C]16210[/C][C]9438.96389712974[/C][C]6771.03610287026[/C][/ROW]
[ROW][C]79[/C][C]7451[/C][C]12235.2200072607[/C][C]-4784.22000726066[/C][/ROW]
[ROW][C]80[/C][C]8384[/C][C]10149.9098590238[/C][C]-1765.90985902383[/C][/ROW]
[ROW][C]81[/C][C]7143[/C][C]9239.19154603257[/C][C]-2096.19154603257[/C][/ROW]
[ROW][C]82[/C][C]8507[/C][C]8815.4953926264[/C][C]-308.495392626395[/C][/ROW]
[ROW][C]83[/C][C]9833[/C][C]8332.77802553104[/C][C]1500.22197446896[/C][/ROW]
[ROW][C]84[/C][C]17364[/C][C]11639.4950714987[/C][C]5724.50492850134[/C][/ROW]
[ROW][C]85[/C][C]6260[/C][C]7701.97055801319[/C][C]-1441.97055801319[/C][/ROW]
[ROW][C]86[/C][C]7897[/C][C]8086.29503898329[/C][C]-189.295038983289[/C][/ROW]
[ROW][C]87[/C][C]8933[/C][C]9308.68609164621[/C][C]-375.68609164621[/C][/ROW]
[ROW][C]88[/C][C]6554[/C][C]8830.99463326608[/C][C]-2276.99463326608[/C][/ROW]
[ROW][C]89[/C][C]8333[/C][C]8643.39899910431[/C][C]-310.398999104305[/C][/ROW]
[ROW][C]90[/C][C]7224[/C][C]9127.10920026448[/C][C]-1903.10920026448[/C][/ROW]
[ROW][C]91[/C][C]9659[/C][C]8440.63680975487[/C][C]1218.36319024513[/C][/ROW]
[ROW][C]92[/C][C]9977[/C][C]8306.35582711542[/C][C]1670.64417288458[/C][/ROW]
[ROW][C]93[/C][C]9289[/C][C]8277.20737532103[/C][C]1011.79262467897[/C][/ROW]
[ROW][C]94[/C][C]9929[/C][C]8853.69063388364[/C][C]1075.30936611636[/C][/ROW]
[ROW][C]95[/C][C]10576[/C][C]8906.71016221938[/C][C]1669.28983778062[/C][/ROW]
[ROW][C]96[/C][C]15463[/C][C]12809.1820148599[/C][C]2653.81798514009[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278479&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278479&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
131341913793.1659492269-374.165949226872
141448714710.8813967835-223.881396783479
151734917544.4229556878-195.422955687824
161564615837.4562309625-191.456230962471
171741917467.267381653-48.2673816530005
181735817361.5343066764-3.53430667638531
191822118204.912959948416.0870400516142
201955417482.83275799312071.16724200694
211438617001.6921852337-2615.69218523367
221683316304.7917733685528.208226631486
231806716068.12235852151998.87764147852
241966221668.6712934686-2006.67129346858
251219213112.5919477879-920.591947787922
261508113842.38168010411238.6183198959
271369816965.8594314995-3267.85943149947
281847414584.91829997683889.08170002319
291387117272.5743703591-3401.57437035909
301566916301.4093973313-632.409397331316
311759716919.7957143646677.204285635395
321546916608.7602173188-1139.76021731878
331537414941.5485268869432.451473113106
341656815347.02948580121220.97051419876
351161915448.3452368372-3829.34523683718
361678018445.128612668-1665.12861266801
37870011191.2579827925-2491.25798279251
38890611521.4393824521-2615.4393824521
39961212578.1057549183-2966.10575491833
401007311194.9257808994-1121.92578089936
411027511490.2103554365-1215.2103554365
42992111302.073759359-1381.07375935897
431323711552.33209637671684.66790362335
44957211498.8577614607-1926.85776146067
451042510163.6484602198261.351539780198
461138510468.7690027782916.230997221797
47997010164.2608913015-194.260891301508
481545613132.90330484592323.09669515406
4977088395.47783560602-687.477835606021
5088928965.83237655147-73.8323765514651
511114510361.5062831214783.493716878571
521106910175.7005625647893.29943743532
53989310960.0232489629-1067.02324896289
541092910782.9749453828146.02505461723
551224011750.3257682997489.674231700275
561041111014.7532180724-603.753218072434
57974710251.6421137068-504.642113706786
58995010419.7516875983-469.751687598264
59100799665.88610403639413.113895963612
601406412942.10671898041121.89328101962
6183687873.5212710068494.4787289932
6295588801.33690482966756.663095170345
631043210512.428893116-80.4288931159626
641006810116.2539928525-48.2539928524711
65991510430.5953423304-515.595342330396
66954910517.9764068914-968.976406891394
671043311177.2892978103-744.289297810263
681000910077.7759732344-68.7759732343948
69103279500.88192506575826.118074934255
70945310006.0056552182-553.005655218247
7194949341.81780629652152.182193703478
721313312475.8143626189657.185637381073
7370827504.04294009502-422.042940095015
7478058148.28826473726-343.288264737258
7590649319.12944422255-255.129444222548
7682368918.96369430784-682.963694307844
77101828974.267998727131207.73200127287
78162109438.963897129746771.03610287026
79745112235.2200072607-4784.22000726066
80838410149.9098590238-1765.90985902383
8171439239.19154603257-2096.19154603257
8285078815.4953926264-308.495392626395
8398338332.778025531041500.22197446896
841736411639.49507149875724.50492850134
8562607701.97055801319-1441.97055801319
8678978086.29503898329-189.295038983289
8789339308.68609164621-375.68609164621
8865548830.99463326608-2276.99463326608
8983338643.39899910431-310.398999104305
9072249127.10920026448-1903.10920026448
9196598440.636809754871218.36319024513
9299778306.355827115421670.64417288458
9392898277.207375321031011.79262467897
9499298853.690633883641075.30936611636
95105768906.710162219381669.28983778062
961546312809.18201485992653.81798514009







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
977412.387122533166119.643701673288705.13054339305
988335.143267987226676.714441746469993.57209422797
999638.245822297667571.8307049336911704.6609396616
1009011.848772737236841.0006219734111182.6969235011
1019708.158870209647212.6742240695412203.6435163497
10210153.01948922187389.0578124451612916.9811659984
10310325.24104957197360.3867743811813290.0953247627
1049854.536075287356854.3540081598812854.7181424148
1059266.471902251036270.6454794962312262.2983250058
1069609.212143554566364.8544165427212853.5698705664
1079432.265242551926098.274674072912766.2558110309
10812957.7112242258527.6501346802117387.7723137698

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 7412.38712253316 & 6119.64370167328 & 8705.13054339305 \tabularnewline
98 & 8335.14326798722 & 6676.71444174646 & 9993.57209422797 \tabularnewline
99 & 9638.24582229766 & 7571.83070493369 & 11704.6609396616 \tabularnewline
100 & 9011.84877273723 & 6841.00062197341 & 11182.6969235011 \tabularnewline
101 & 9708.15887020964 & 7212.67422406954 & 12203.6435163497 \tabularnewline
102 & 10153.0194892218 & 7389.05781244516 & 12916.9811659984 \tabularnewline
103 & 10325.2410495719 & 7360.38677438118 & 13290.0953247627 \tabularnewline
104 & 9854.53607528735 & 6854.35400815988 & 12854.7181424148 \tabularnewline
105 & 9266.47190225103 & 6270.64547949623 & 12262.2983250058 \tabularnewline
106 & 9609.21214355456 & 6364.85441654272 & 12853.5698705664 \tabularnewline
107 & 9432.26524255192 & 6098.2746740729 & 12766.2558110309 \tabularnewline
108 & 12957.711224225 & 8527.65013468021 & 17387.7723137698 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278479&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]97[/C][C]7412.38712253316[/C][C]6119.64370167328[/C][C]8705.13054339305[/C][/ROW]
[ROW][C]98[/C][C]8335.14326798722[/C][C]6676.71444174646[/C][C]9993.57209422797[/C][/ROW]
[ROW][C]99[/C][C]9638.24582229766[/C][C]7571.83070493369[/C][C]11704.6609396616[/C][/ROW]
[ROW][C]100[/C][C]9011.84877273723[/C][C]6841.00062197341[/C][C]11182.6969235011[/C][/ROW]
[ROW][C]101[/C][C]9708.15887020964[/C][C]7212.67422406954[/C][C]12203.6435163497[/C][/ROW]
[ROW][C]102[/C][C]10153.0194892218[/C][C]7389.05781244516[/C][C]12916.9811659984[/C][/ROW]
[ROW][C]103[/C][C]10325.2410495719[/C][C]7360.38677438118[/C][C]13290.0953247627[/C][/ROW]
[ROW][C]104[/C][C]9854.53607528735[/C][C]6854.35400815988[/C][C]12854.7181424148[/C][/ROW]
[ROW][C]105[/C][C]9266.47190225103[/C][C]6270.64547949623[/C][C]12262.2983250058[/C][/ROW]
[ROW][C]106[/C][C]9609.21214355456[/C][C]6364.85441654272[/C][C]12853.5698705664[/C][/ROW]
[ROW][C]107[/C][C]9432.26524255192[/C][C]6098.2746740729[/C][C]12766.2558110309[/C][/ROW]
[ROW][C]108[/C][C]12957.711224225[/C][C]8527.65013468021[/C][C]17387.7723137698[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278479&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278479&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
977412.387122533166119.643701673288705.13054339305
988335.143267987226676.714441746469993.57209422797
999638.245822297667571.8307049336911704.6609396616
1009011.848772737236841.0006219734111182.6969235011
1019708.158870209647212.6742240695412203.6435163497
10210153.01948922187389.0578124451612916.9811659984
10310325.24104957197360.3867743811813290.0953247627
1049854.536075287356854.3540081598812854.7181424148
1059266.471902251036270.6454794962312262.2983250058
1069609.212143554566364.8544165427212853.5698705664
1079432.265242551926098.274674072912766.2558110309
10812957.7112242258527.6501346802117387.7723137698



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')