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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 18 Dec 2010 19:54:43 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/18/t1292701968uiklwuhpr9kwk2m.htm/, Retrieved Tue, 30 Apr 2024 07:22:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112181, Retrieved Tue, 30 Apr 2024 07:22:42 +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] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
-  M D  [Exponential Smoothing] [exponential smoot...] [2010-11-29 09:42:21] [95e8426e0df851c9330605aa1e892ab5]
-    D      [Exponential Smoothing] [exponential smoot...] [2010-12-18 19:54:43] [dc77c696707133dea0955379c56a2acd] [Current]
-   P         [Exponential Smoothing] [ES faillissemten] [2010-12-19 20:22:31] [95e8426e0df851c9330605aa1e892ab5]
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Dataseries X:
46
62
66
59
58
61
41
27
58
70
49
59
44
36
72
45
56
54
53
35
61
52
47
51
52
63
74
45
51
64
36
30
55
64
39
40
63
45
59
55
40
64
27
28
45
57
45
69
60
56
58
50
51
53
37
22
55
70
62
58
39
49
58
47
42
62
39
40
72
70
54
65




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' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112181&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112181&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112181&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' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0440224583015312
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0440224583015312 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112181&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]0.0440224583015312[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112181&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112181&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
alpha0.0440224583015312
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2624616
36646.704359332824519.2956406671755
45947.553800869496611.4461991305034
55848.05769069343029.94230930656983
66148.495375590299612.5046244097004
74149.0458598969519-8.04585989695192
82748.6916613651384-21.6916613651384
95847.736741107200710.2632588927993
107048.188554993846721.8114450061533
114949.1487484221263-0.148748422126253
125949.14220015091589.85779984908422
134449.5761647337169-5.57616473371694
143649.3306882542444-13.3306882542444
157248.743838586441223.2561614135588
164549.7676319825233-4.7676319825233
175649.55774910237566.44225089762438
185449.84135282388434.15864717611571
195350.02442669578562.97557330421438
203550.1554187474935-15.1554187474935
216149.488239957639811.5117600423602
225249.99501593408182.00498406591819
234750.0832802615189-3.08328026151892
245149.94754668477431.05245331522573
255249.99387826695812.00612173304189
266350.082192677298712.9178073227013
277450.650866311509623.3491336884904
284551.678752575688-6.67875257568802
295151.3847374689185-0.384737468918544
306451.36780037973612.6321996202640
313651.9239008607757-15.9239008607757
323051.2228915991345-21.2228915991345
335550.28860773867374.71139226132631
346450.496014808040113.5039851919599
353951.0904934330576-12.0904934330576
364050.5582401900559-10.5582401900559
376350.093440501551612.9065594984484
384550.6616189788883-5.66161897888831
395950.4123805934718.58761940652897
405550.79042871070444.20957128929562
414050.9757443872547-10.9757443872547
426450.492565137638513.5074348623615
432751.0871956256275-24.0871956256275
442850.0268180605975-22.0268180605975
454549.0571433810094-4.05714338100941
465748.87853795569568.12146204430441
474549.2360646798885-4.23606467988845
486949.049582699155519.9504173008445
496049.9278491128810.0721508871200
505650.3712499553155.62875004468498
515850.61904136944697.3809586305531
525050.9439693129858-0.943969312985757
535150.90241346326690.0975865367330826
545350.9067094625112.09329053748896
553750.9988612579106-13.9988612579106
562250.3825969719153-28.3825969719153
575549.133125280235.86687471976997
587049.391399527941420.6086004720586
596250.298640782875511.7013592171245
605850.81376338108267.18623661891737
613951.1301191829839-12.1301191829839
624950.5961215170583-1.59612151705834
635850.52585632412957.47414367587054
644750.8548865024401-3.85488650244013
654250.6851849221293-8.68518492212932
666250.302841731053811.6971582689462
673950.8177793931949-11.8177793931949
684050.2975316926413-10.2975316926413
697249.844209033093322.1557909669067
707050.819561417071419.1804385829286
715451.66393147479342.33606852520658
726551.766770954033813.2332290459662

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 62 & 46 & 16 \tabularnewline
3 & 66 & 46.7043593328245 & 19.2956406671755 \tabularnewline
4 & 59 & 47.5538008694966 & 11.4461991305034 \tabularnewline
5 & 58 & 48.0576906934302 & 9.94230930656983 \tabularnewline
6 & 61 & 48.4953755902996 & 12.5046244097004 \tabularnewline
7 & 41 & 49.0458598969519 & -8.04585989695192 \tabularnewline
8 & 27 & 48.6916613651384 & -21.6916613651384 \tabularnewline
9 & 58 & 47.7367411072007 & 10.2632588927993 \tabularnewline
10 & 70 & 48.1885549938467 & 21.8114450061533 \tabularnewline
11 & 49 & 49.1487484221263 & -0.148748422126253 \tabularnewline
12 & 59 & 49.1422001509158 & 9.85779984908422 \tabularnewline
13 & 44 & 49.5761647337169 & -5.57616473371694 \tabularnewline
14 & 36 & 49.3306882542444 & -13.3306882542444 \tabularnewline
15 & 72 & 48.7438385864412 & 23.2561614135588 \tabularnewline
16 & 45 & 49.7676319825233 & -4.7676319825233 \tabularnewline
17 & 56 & 49.5577491023756 & 6.44225089762438 \tabularnewline
18 & 54 & 49.8413528238843 & 4.15864717611571 \tabularnewline
19 & 53 & 50.0244266957856 & 2.97557330421438 \tabularnewline
20 & 35 & 50.1554187474935 & -15.1554187474935 \tabularnewline
21 & 61 & 49.4882399576398 & 11.5117600423602 \tabularnewline
22 & 52 & 49.9950159340818 & 2.00498406591819 \tabularnewline
23 & 47 & 50.0832802615189 & -3.08328026151892 \tabularnewline
24 & 51 & 49.9475466847743 & 1.05245331522573 \tabularnewline
25 & 52 & 49.9938782669581 & 2.00612173304189 \tabularnewline
26 & 63 & 50.0821926772987 & 12.9178073227013 \tabularnewline
27 & 74 & 50.6508663115096 & 23.3491336884904 \tabularnewline
28 & 45 & 51.678752575688 & -6.67875257568802 \tabularnewline
29 & 51 & 51.3847374689185 & -0.384737468918544 \tabularnewline
30 & 64 & 51.367800379736 & 12.6321996202640 \tabularnewline
31 & 36 & 51.9239008607757 & -15.9239008607757 \tabularnewline
32 & 30 & 51.2228915991345 & -21.2228915991345 \tabularnewline
33 & 55 & 50.2886077386737 & 4.71139226132631 \tabularnewline
34 & 64 & 50.4960148080401 & 13.5039851919599 \tabularnewline
35 & 39 & 51.0904934330576 & -12.0904934330576 \tabularnewline
36 & 40 & 50.5582401900559 & -10.5582401900559 \tabularnewline
37 & 63 & 50.0934405015516 & 12.9065594984484 \tabularnewline
38 & 45 & 50.6616189788883 & -5.66161897888831 \tabularnewline
39 & 59 & 50.412380593471 & 8.58761940652897 \tabularnewline
40 & 55 & 50.7904287107044 & 4.20957128929562 \tabularnewline
41 & 40 & 50.9757443872547 & -10.9757443872547 \tabularnewline
42 & 64 & 50.4925651376385 & 13.5074348623615 \tabularnewline
43 & 27 & 51.0871956256275 & -24.0871956256275 \tabularnewline
44 & 28 & 50.0268180605975 & -22.0268180605975 \tabularnewline
45 & 45 & 49.0571433810094 & -4.05714338100941 \tabularnewline
46 & 57 & 48.8785379556956 & 8.12146204430441 \tabularnewline
47 & 45 & 49.2360646798885 & -4.23606467988845 \tabularnewline
48 & 69 & 49.0495826991555 & 19.9504173008445 \tabularnewline
49 & 60 & 49.92784911288 & 10.0721508871200 \tabularnewline
50 & 56 & 50.371249955315 & 5.62875004468498 \tabularnewline
51 & 58 & 50.6190413694469 & 7.3809586305531 \tabularnewline
52 & 50 & 50.9439693129858 & -0.943969312985757 \tabularnewline
53 & 51 & 50.9024134632669 & 0.0975865367330826 \tabularnewline
54 & 53 & 50.906709462511 & 2.09329053748896 \tabularnewline
55 & 37 & 50.9988612579106 & -13.9988612579106 \tabularnewline
56 & 22 & 50.3825969719153 & -28.3825969719153 \tabularnewline
57 & 55 & 49.13312528023 & 5.86687471976997 \tabularnewline
58 & 70 & 49.3913995279414 & 20.6086004720586 \tabularnewline
59 & 62 & 50.2986407828755 & 11.7013592171245 \tabularnewline
60 & 58 & 50.8137633810826 & 7.18623661891737 \tabularnewline
61 & 39 & 51.1301191829839 & -12.1301191829839 \tabularnewline
62 & 49 & 50.5961215170583 & -1.59612151705834 \tabularnewline
63 & 58 & 50.5258563241295 & 7.47414367587054 \tabularnewline
64 & 47 & 50.8548865024401 & -3.85488650244013 \tabularnewline
65 & 42 & 50.6851849221293 & -8.68518492212932 \tabularnewline
66 & 62 & 50.3028417310538 & 11.6971582689462 \tabularnewline
67 & 39 & 50.8177793931949 & -11.8177793931949 \tabularnewline
68 & 40 & 50.2975316926413 & -10.2975316926413 \tabularnewline
69 & 72 & 49.8442090330933 & 22.1557909669067 \tabularnewline
70 & 70 & 50.8195614170714 & 19.1804385829286 \tabularnewline
71 & 54 & 51.6639314747934 & 2.33606852520658 \tabularnewline
72 & 65 & 51.7667709540338 & 13.2332290459662 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112181&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]2[/C][C]62[/C][C]46[/C][C]16[/C][/ROW]
[ROW][C]3[/C][C]66[/C][C]46.7043593328245[/C][C]19.2956406671755[/C][/ROW]
[ROW][C]4[/C][C]59[/C][C]47.5538008694966[/C][C]11.4461991305034[/C][/ROW]
[ROW][C]5[/C][C]58[/C][C]48.0576906934302[/C][C]9.94230930656983[/C][/ROW]
[ROW][C]6[/C][C]61[/C][C]48.4953755902996[/C][C]12.5046244097004[/C][/ROW]
[ROW][C]7[/C][C]41[/C][C]49.0458598969519[/C][C]-8.04585989695192[/C][/ROW]
[ROW][C]8[/C][C]27[/C][C]48.6916613651384[/C][C]-21.6916613651384[/C][/ROW]
[ROW][C]9[/C][C]58[/C][C]47.7367411072007[/C][C]10.2632588927993[/C][/ROW]
[ROW][C]10[/C][C]70[/C][C]48.1885549938467[/C][C]21.8114450061533[/C][/ROW]
[ROW][C]11[/C][C]49[/C][C]49.1487484221263[/C][C]-0.148748422126253[/C][/ROW]
[ROW][C]12[/C][C]59[/C][C]49.1422001509158[/C][C]9.85779984908422[/C][/ROW]
[ROW][C]13[/C][C]44[/C][C]49.5761647337169[/C][C]-5.57616473371694[/C][/ROW]
[ROW][C]14[/C][C]36[/C][C]49.3306882542444[/C][C]-13.3306882542444[/C][/ROW]
[ROW][C]15[/C][C]72[/C][C]48.7438385864412[/C][C]23.2561614135588[/C][/ROW]
[ROW][C]16[/C][C]45[/C][C]49.7676319825233[/C][C]-4.7676319825233[/C][/ROW]
[ROW][C]17[/C][C]56[/C][C]49.5577491023756[/C][C]6.44225089762438[/C][/ROW]
[ROW][C]18[/C][C]54[/C][C]49.8413528238843[/C][C]4.15864717611571[/C][/ROW]
[ROW][C]19[/C][C]53[/C][C]50.0244266957856[/C][C]2.97557330421438[/C][/ROW]
[ROW][C]20[/C][C]35[/C][C]50.1554187474935[/C][C]-15.1554187474935[/C][/ROW]
[ROW][C]21[/C][C]61[/C][C]49.4882399576398[/C][C]11.5117600423602[/C][/ROW]
[ROW][C]22[/C][C]52[/C][C]49.9950159340818[/C][C]2.00498406591819[/C][/ROW]
[ROW][C]23[/C][C]47[/C][C]50.0832802615189[/C][C]-3.08328026151892[/C][/ROW]
[ROW][C]24[/C][C]51[/C][C]49.9475466847743[/C][C]1.05245331522573[/C][/ROW]
[ROW][C]25[/C][C]52[/C][C]49.9938782669581[/C][C]2.00612173304189[/C][/ROW]
[ROW][C]26[/C][C]63[/C][C]50.0821926772987[/C][C]12.9178073227013[/C][/ROW]
[ROW][C]27[/C][C]74[/C][C]50.6508663115096[/C][C]23.3491336884904[/C][/ROW]
[ROW][C]28[/C][C]45[/C][C]51.678752575688[/C][C]-6.67875257568802[/C][/ROW]
[ROW][C]29[/C][C]51[/C][C]51.3847374689185[/C][C]-0.384737468918544[/C][/ROW]
[ROW][C]30[/C][C]64[/C][C]51.367800379736[/C][C]12.6321996202640[/C][/ROW]
[ROW][C]31[/C][C]36[/C][C]51.9239008607757[/C][C]-15.9239008607757[/C][/ROW]
[ROW][C]32[/C][C]30[/C][C]51.2228915991345[/C][C]-21.2228915991345[/C][/ROW]
[ROW][C]33[/C][C]55[/C][C]50.2886077386737[/C][C]4.71139226132631[/C][/ROW]
[ROW][C]34[/C][C]64[/C][C]50.4960148080401[/C][C]13.5039851919599[/C][/ROW]
[ROW][C]35[/C][C]39[/C][C]51.0904934330576[/C][C]-12.0904934330576[/C][/ROW]
[ROW][C]36[/C][C]40[/C][C]50.5582401900559[/C][C]-10.5582401900559[/C][/ROW]
[ROW][C]37[/C][C]63[/C][C]50.0934405015516[/C][C]12.9065594984484[/C][/ROW]
[ROW][C]38[/C][C]45[/C][C]50.6616189788883[/C][C]-5.66161897888831[/C][/ROW]
[ROW][C]39[/C][C]59[/C][C]50.412380593471[/C][C]8.58761940652897[/C][/ROW]
[ROW][C]40[/C][C]55[/C][C]50.7904287107044[/C][C]4.20957128929562[/C][/ROW]
[ROW][C]41[/C][C]40[/C][C]50.9757443872547[/C][C]-10.9757443872547[/C][/ROW]
[ROW][C]42[/C][C]64[/C][C]50.4925651376385[/C][C]13.5074348623615[/C][/ROW]
[ROW][C]43[/C][C]27[/C][C]51.0871956256275[/C][C]-24.0871956256275[/C][/ROW]
[ROW][C]44[/C][C]28[/C][C]50.0268180605975[/C][C]-22.0268180605975[/C][/ROW]
[ROW][C]45[/C][C]45[/C][C]49.0571433810094[/C][C]-4.05714338100941[/C][/ROW]
[ROW][C]46[/C][C]57[/C][C]48.8785379556956[/C][C]8.12146204430441[/C][/ROW]
[ROW][C]47[/C][C]45[/C][C]49.2360646798885[/C][C]-4.23606467988845[/C][/ROW]
[ROW][C]48[/C][C]69[/C][C]49.0495826991555[/C][C]19.9504173008445[/C][/ROW]
[ROW][C]49[/C][C]60[/C][C]49.92784911288[/C][C]10.0721508871200[/C][/ROW]
[ROW][C]50[/C][C]56[/C][C]50.371249955315[/C][C]5.62875004468498[/C][/ROW]
[ROW][C]51[/C][C]58[/C][C]50.6190413694469[/C][C]7.3809586305531[/C][/ROW]
[ROW][C]52[/C][C]50[/C][C]50.9439693129858[/C][C]-0.943969312985757[/C][/ROW]
[ROW][C]53[/C][C]51[/C][C]50.9024134632669[/C][C]0.0975865367330826[/C][/ROW]
[ROW][C]54[/C][C]53[/C][C]50.906709462511[/C][C]2.09329053748896[/C][/ROW]
[ROW][C]55[/C][C]37[/C][C]50.9988612579106[/C][C]-13.9988612579106[/C][/ROW]
[ROW][C]56[/C][C]22[/C][C]50.3825969719153[/C][C]-28.3825969719153[/C][/ROW]
[ROW][C]57[/C][C]55[/C][C]49.13312528023[/C][C]5.86687471976997[/C][/ROW]
[ROW][C]58[/C][C]70[/C][C]49.3913995279414[/C][C]20.6086004720586[/C][/ROW]
[ROW][C]59[/C][C]62[/C][C]50.2986407828755[/C][C]11.7013592171245[/C][/ROW]
[ROW][C]60[/C][C]58[/C][C]50.8137633810826[/C][C]7.18623661891737[/C][/ROW]
[ROW][C]61[/C][C]39[/C][C]51.1301191829839[/C][C]-12.1301191829839[/C][/ROW]
[ROW][C]62[/C][C]49[/C][C]50.5961215170583[/C][C]-1.59612151705834[/C][/ROW]
[ROW][C]63[/C][C]58[/C][C]50.5258563241295[/C][C]7.47414367587054[/C][/ROW]
[ROW][C]64[/C][C]47[/C][C]50.8548865024401[/C][C]-3.85488650244013[/C][/ROW]
[ROW][C]65[/C][C]42[/C][C]50.6851849221293[/C][C]-8.68518492212932[/C][/ROW]
[ROW][C]66[/C][C]62[/C][C]50.3028417310538[/C][C]11.6971582689462[/C][/ROW]
[ROW][C]67[/C][C]39[/C][C]50.8177793931949[/C][C]-11.8177793931949[/C][/ROW]
[ROW][C]68[/C][C]40[/C][C]50.2975316926413[/C][C]-10.2975316926413[/C][/ROW]
[ROW][C]69[/C][C]72[/C][C]49.8442090330933[/C][C]22.1557909669067[/C][/ROW]
[ROW][C]70[/C][C]70[/C][C]50.8195614170714[/C][C]19.1804385829286[/C][/ROW]
[ROW][C]71[/C][C]54[/C][C]51.6639314747934[/C][C]2.33606852520658[/C][/ROW]
[ROW][C]72[/C][C]65[/C][C]51.7667709540338[/C][C]13.2332290459662[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112181&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112181&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
2624616
36646.704359332824519.2956406671755
45947.553800869496611.4461991305034
55848.05769069343029.94230930656983
66148.495375590299612.5046244097004
74149.0458598969519-8.04585989695192
82748.6916613651384-21.6916613651384
95847.736741107200710.2632588927993
107048.188554993846721.8114450061533
114949.1487484221263-0.148748422126253
125949.14220015091589.85779984908422
134449.5761647337169-5.57616473371694
143649.3306882542444-13.3306882542444
157248.743838586441223.2561614135588
164549.7676319825233-4.7676319825233
175649.55774910237566.44225089762438
185449.84135282388434.15864717611571
195350.02442669578562.97557330421438
203550.1554187474935-15.1554187474935
216149.488239957639811.5117600423602
225249.99501593408182.00498406591819
234750.0832802615189-3.08328026151892
245149.94754668477431.05245331522573
255249.99387826695812.00612173304189
266350.082192677298712.9178073227013
277450.650866311509623.3491336884904
284551.678752575688-6.67875257568802
295151.3847374689185-0.384737468918544
306451.36780037973612.6321996202640
313651.9239008607757-15.9239008607757
323051.2228915991345-21.2228915991345
335550.28860773867374.71139226132631
346450.496014808040113.5039851919599
353951.0904934330576-12.0904934330576
364050.5582401900559-10.5582401900559
376350.093440501551612.9065594984484
384550.6616189788883-5.66161897888831
395950.4123805934718.58761940652897
405550.79042871070444.20957128929562
414050.9757443872547-10.9757443872547
426450.492565137638513.5074348623615
432751.0871956256275-24.0871956256275
442850.0268180605975-22.0268180605975
454549.0571433810094-4.05714338100941
465748.87853795569568.12146204430441
474549.2360646798885-4.23606467988845
486949.049582699155519.9504173008445
496049.9278491128810.0721508871200
505650.3712499553155.62875004468498
515850.61904136944697.3809586305531
525050.9439693129858-0.943969312985757
535150.90241346326690.0975865367330826
545350.9067094625112.09329053748896
553750.9988612579106-13.9988612579106
562250.3825969719153-28.3825969719153
575549.133125280235.86687471976997
587049.391399527941420.6086004720586
596250.298640782875511.7013592171245
605850.81376338108267.18623661891737
613951.1301191829839-12.1301191829839
624950.5961215170583-1.59612151705834
635850.52585632412957.47414367587054
644750.8548865024401-3.85488650244013
654250.6851849221293-8.68518492212932
666250.302841731053811.6971582689462
673950.8177793931949-11.8177793931949
684050.2975316926413-10.2975316926413
697249.844209033093322.1557909669067
707050.819561417071419.1804385829286
715451.66393147479342.33606852520658
726551.766770954033813.2332290459662







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7352.349330227904527.829983417588576.8686770382205
7452.349330227904527.806235954465176.8924245013439
7552.349330227904527.782511446765776.9161490090433
7652.349330227904527.758809828049476.9398506277596
7752.349330227904527.735131032194976.963529423614
7852.349330227904527.711474993399176.98718546241
7952.349330227904527.687841646174077.010818809635
8052.349330227904527.664230925345477.0344295304636
8152.349330227904527.640642766050577.0580176897585
8252.349330227904527.617077103735677.0815833520734
8352.349330227904527.593533874154577.1051265816545
8452.349330227904527.570013013366177.1286474424429

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 52.3493302279045 & 27.8299834175885 & 76.8686770382205 \tabularnewline
74 & 52.3493302279045 & 27.8062359544651 & 76.8924245013439 \tabularnewline
75 & 52.3493302279045 & 27.7825114467657 & 76.9161490090433 \tabularnewline
76 & 52.3493302279045 & 27.7588098280494 & 76.9398506277596 \tabularnewline
77 & 52.3493302279045 & 27.7351310321949 & 76.963529423614 \tabularnewline
78 & 52.3493302279045 & 27.7114749933991 & 76.98718546241 \tabularnewline
79 & 52.3493302279045 & 27.6878416461740 & 77.010818809635 \tabularnewline
80 & 52.3493302279045 & 27.6642309253454 & 77.0344295304636 \tabularnewline
81 & 52.3493302279045 & 27.6406427660505 & 77.0580176897585 \tabularnewline
82 & 52.3493302279045 & 27.6170771037356 & 77.0815833520734 \tabularnewline
83 & 52.3493302279045 & 27.5935338741545 & 77.1051265816545 \tabularnewline
84 & 52.3493302279045 & 27.5700130133661 & 77.1286474424429 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112181&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]73[/C][C]52.3493302279045[/C][C]27.8299834175885[/C][C]76.8686770382205[/C][/ROW]
[ROW][C]74[/C][C]52.3493302279045[/C][C]27.8062359544651[/C][C]76.8924245013439[/C][/ROW]
[ROW][C]75[/C][C]52.3493302279045[/C][C]27.7825114467657[/C][C]76.9161490090433[/C][/ROW]
[ROW][C]76[/C][C]52.3493302279045[/C][C]27.7588098280494[/C][C]76.9398506277596[/C][/ROW]
[ROW][C]77[/C][C]52.3493302279045[/C][C]27.7351310321949[/C][C]76.963529423614[/C][/ROW]
[ROW][C]78[/C][C]52.3493302279045[/C][C]27.7114749933991[/C][C]76.98718546241[/C][/ROW]
[ROW][C]79[/C][C]52.3493302279045[/C][C]27.6878416461740[/C][C]77.010818809635[/C][/ROW]
[ROW][C]80[/C][C]52.3493302279045[/C][C]27.6642309253454[/C][C]77.0344295304636[/C][/ROW]
[ROW][C]81[/C][C]52.3493302279045[/C][C]27.6406427660505[/C][C]77.0580176897585[/C][/ROW]
[ROW][C]82[/C][C]52.3493302279045[/C][C]27.6170771037356[/C][C]77.0815833520734[/C][/ROW]
[ROW][C]83[/C][C]52.3493302279045[/C][C]27.5935338741545[/C][C]77.1051265816545[/C][/ROW]
[ROW][C]84[/C][C]52.3493302279045[/C][C]27.5700130133661[/C][C]77.1286474424429[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112181&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112181&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
7352.349330227904527.829983417588576.8686770382205
7452.349330227904527.806235954465176.8924245013439
7552.349330227904527.782511446765776.9161490090433
7652.349330227904527.758809828049476.9398506277596
7752.349330227904527.735131032194976.963529423614
7852.349330227904527.711474993399176.98718546241
7952.349330227904527.687841646174077.010818809635
8052.349330227904527.664230925345477.0344295304636
8152.349330227904527.640642766050577.0580176897585
8252.349330227904527.617077103735677.0815833520734
8352.349330227904527.593533874154577.1051265816545
8452.349330227904527.570013013366177.1286474424429



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