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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 computationTue, 02 Jun 2009 07:52:13 -0600
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/Jun/02/t12439510152utb6f71b5flsxk.htm/, Retrieved Fri, 10 May 2024 05:24:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41217, Retrieved Fri, 10 May 2024 05:24:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [cijferreeks - Ver...] [2009-06-02 13:52:13] [692360aaa1f674665b2fba1990ff39d8] [Current]
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Dataseries X:
53
59
73
72
62
58
55
56
52
52
43
37
43
55
68
68
64
65
57
59
54
57
43
42
52
51
58
60
61
58
62
61
49
51
47
40
45
50
58
52
50
50
46
46
38
37
34
29
30
40
46
46
47
47
43
46
37
41
39
36
48
55
56
53
52
53
52
56
51
48
42
42
44
50
60
66
58
59
55
57
57
56
53
51
45
58
74
65
65
55
52
59
54
57
45
40
47
47
60
58
63
64
64
63
55
54
44




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41217&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41217&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41217&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.571865347172465
beta0
gamma0.440257094572627

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.571865347172465 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.440257094572627 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41217&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]0.571865347172465[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.440257094572627[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41217&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41217&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
alpha0.571865347172465
beta0
gamma0.440257094572627







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134342.88114316239320.118856837606820
145554.83941047189220.160589528107792
156867.8215432609330.178456739066945
166867.73056035543870.269439644561288
176463.7749407541150.225059245885021
186564.79394154069460.20605845930541
195755.4687431025271.53125689747303
205958.02637972927450.973620270725512
215455.0567899595376-1.05678995953762
225754.92607893856882.0739210614312
234347.2940463958363-4.29404639583629
244238.56206059903723.43793940096275
255246.27413278855785.72586721144224
265161.4467211984748-10.4467211984748
275868.3662683347066-10.3662683347066
286062.2622718698977-2.26227186989774
296156.85048895332324.14951104667676
305860.1101662861139-2.11016628611392
316249.710184930052712.2898150699473
326158.31515961352052.68484038647953
334955.9414466891155-6.94144668911549
345153.0356099907569-2.03560999075687
354741.8531852009195.146814799081
364039.97749750120940.0225024987906295
374546.1676496343313-1.16764963433133
385054.3497144748269-4.34971447482686
395864.7710929832406-6.7710929832406
405262.250569488423-10.2505694884230
415053.4791085722009-3.4791085722009
425051.1963603847112-1.19636038471117
434644.03319562761241.96680437238761
444644.92436308389811.07563691610189
453839.8159501692132-1.81595016921322
463740.7659051327993-3.76590513279933
473429.94779486350934.05220513649071
482926.48025969664262.5197403033574
493033.8741646295526-3.87416462955262
504039.90868209998070.0913179000193196
514652.4133291447466-6.41332914474664
524649.4415542369943-3.44155423699426
534745.84028124369581.15971875630424
544746.64059130669590.359408693304104
554340.96333974237832.03666025762174
564641.72647981236364.2735201876364
573737.9017922463409-0.901792246340868
584139.00697676598131.99302323401865
593932.95582834188626.04417165811379
603630.33857654968665.66142345031345
614838.32391842380339.67608157619665
625552.85480324384162.14519675615836
635665.3079359462154-9.3079359462154
645361.2409835416346-8.2409835416346
655255.76237405281-3.76237405281
665353.5970599044756-0.597059904475628
675247.68898109747164.31101890252843
685650.17437226695105.82562773304895
695146.26179010835924.73820989164075
704851.1379382053022-3.13793820530225
714242.916168941332-0.916168941332018
724236.24639560700775.75360439299234
734445.0411727414269-1.04117274142691
745052.0237398541579-2.02373985415791
756059.93400899860850.0659910013915308
766661.42878971373064.57121028626941
775864.1211999459995-6.12119994599954
785961.2035829154875-2.20358291548752
795555.3019096977404-0.301909697740356
805755.43481443776151.56518556223854
815748.88086639037358.11913360962652
825654.20587781713061.79412218286937
835349.22336275339163.7766372466084
845146.49442368821404.50557631178595
854553.2947539003563-8.29475390035628
865855.94404590009082.05595409990919
877466.58124258841737.41875741158266
886573.130001331359-8.13000133135901
896566.543623656313-1.54362365631302
905566.9821928435083-11.9821928435083
915255.8469165529275-3.84691655292746
925954.30448222980704.69551777019305
935450.77601189717213.22398810282793
945752.10946214690384.89053785309622
954549.2713628183717-4.27136281837166
964042.0774486294968-2.07744862949677
974742.70044948193754.29955051806253
984754.5029856456102-7.5029856456102
996060.6845870783719-0.684587078371891
1005859.6685489748219-1.66854897482192
1016358.01871383318274.98128616681734
1026460.2210940511153.77890594888495
1036459.63245667578254.36754332421751
1046364.3977449246665-1.39774492466651
1055557.1073811817044-2.10738118170443
1065455.7061329110397-1.70613291103971
1074447.3687057535314-3.36870575353143

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 43 & 42.8811431623932 & 0.118856837606820 \tabularnewline
14 & 55 & 54.8394104718922 & 0.160589528107792 \tabularnewline
15 & 68 & 67.821543260933 & 0.178456739066945 \tabularnewline
16 & 68 & 67.7305603554387 & 0.269439644561288 \tabularnewline
17 & 64 & 63.774940754115 & 0.225059245885021 \tabularnewline
18 & 65 & 64.7939415406946 & 0.20605845930541 \tabularnewline
19 & 57 & 55.468743102527 & 1.53125689747303 \tabularnewline
20 & 59 & 58.0263797292745 & 0.973620270725512 \tabularnewline
21 & 54 & 55.0567899595376 & -1.05678995953762 \tabularnewline
22 & 57 & 54.9260789385688 & 2.0739210614312 \tabularnewline
23 & 43 & 47.2940463958363 & -4.29404639583629 \tabularnewline
24 & 42 & 38.5620605990372 & 3.43793940096275 \tabularnewline
25 & 52 & 46.2741327885578 & 5.72586721144224 \tabularnewline
26 & 51 & 61.4467211984748 & -10.4467211984748 \tabularnewline
27 & 58 & 68.3662683347066 & -10.3662683347066 \tabularnewline
28 & 60 & 62.2622718698977 & -2.26227186989774 \tabularnewline
29 & 61 & 56.8504889533232 & 4.14951104667676 \tabularnewline
30 & 58 & 60.1101662861139 & -2.11016628611392 \tabularnewline
31 & 62 & 49.7101849300527 & 12.2898150699473 \tabularnewline
32 & 61 & 58.3151596135205 & 2.68484038647953 \tabularnewline
33 & 49 & 55.9414466891155 & -6.94144668911549 \tabularnewline
34 & 51 & 53.0356099907569 & -2.03560999075687 \tabularnewline
35 & 47 & 41.853185200919 & 5.146814799081 \tabularnewline
36 & 40 & 39.9774975012094 & 0.0225024987906295 \tabularnewline
37 & 45 & 46.1676496343313 & -1.16764963433133 \tabularnewline
38 & 50 & 54.3497144748269 & -4.34971447482686 \tabularnewline
39 & 58 & 64.7710929832406 & -6.7710929832406 \tabularnewline
40 & 52 & 62.250569488423 & -10.2505694884230 \tabularnewline
41 & 50 & 53.4791085722009 & -3.4791085722009 \tabularnewline
42 & 50 & 51.1963603847112 & -1.19636038471117 \tabularnewline
43 & 46 & 44.0331956276124 & 1.96680437238761 \tabularnewline
44 & 46 & 44.9243630838981 & 1.07563691610189 \tabularnewline
45 & 38 & 39.8159501692132 & -1.81595016921322 \tabularnewline
46 & 37 & 40.7659051327993 & -3.76590513279933 \tabularnewline
47 & 34 & 29.9477948635093 & 4.05220513649071 \tabularnewline
48 & 29 & 26.4802596966426 & 2.5197403033574 \tabularnewline
49 & 30 & 33.8741646295526 & -3.87416462955262 \tabularnewline
50 & 40 & 39.9086820999807 & 0.0913179000193196 \tabularnewline
51 & 46 & 52.4133291447466 & -6.41332914474664 \tabularnewline
52 & 46 & 49.4415542369943 & -3.44155423699426 \tabularnewline
53 & 47 & 45.8402812436958 & 1.15971875630424 \tabularnewline
54 & 47 & 46.6405913066959 & 0.359408693304104 \tabularnewline
55 & 43 & 40.9633397423783 & 2.03666025762174 \tabularnewline
56 & 46 & 41.7264798123636 & 4.2735201876364 \tabularnewline
57 & 37 & 37.9017922463409 & -0.901792246340868 \tabularnewline
58 & 41 & 39.0069767659813 & 1.99302323401865 \tabularnewline
59 & 39 & 32.9558283418862 & 6.04417165811379 \tabularnewline
60 & 36 & 30.3385765496866 & 5.66142345031345 \tabularnewline
61 & 48 & 38.3239184238033 & 9.67608157619665 \tabularnewline
62 & 55 & 52.8548032438416 & 2.14519675615836 \tabularnewline
63 & 56 & 65.3079359462154 & -9.3079359462154 \tabularnewline
64 & 53 & 61.2409835416346 & -8.2409835416346 \tabularnewline
65 & 52 & 55.76237405281 & -3.76237405281 \tabularnewline
66 & 53 & 53.5970599044756 & -0.597059904475628 \tabularnewline
67 & 52 & 47.6889810974716 & 4.31101890252843 \tabularnewline
68 & 56 & 50.1743722669510 & 5.82562773304895 \tabularnewline
69 & 51 & 46.2617901083592 & 4.73820989164075 \tabularnewline
70 & 48 & 51.1379382053022 & -3.13793820530225 \tabularnewline
71 & 42 & 42.916168941332 & -0.916168941332018 \tabularnewline
72 & 42 & 36.2463956070077 & 5.75360439299234 \tabularnewline
73 & 44 & 45.0411727414269 & -1.04117274142691 \tabularnewline
74 & 50 & 52.0237398541579 & -2.02373985415791 \tabularnewline
75 & 60 & 59.9340089986085 & 0.0659910013915308 \tabularnewline
76 & 66 & 61.4287897137306 & 4.57121028626941 \tabularnewline
77 & 58 & 64.1211999459995 & -6.12119994599954 \tabularnewline
78 & 59 & 61.2035829154875 & -2.20358291548752 \tabularnewline
79 & 55 & 55.3019096977404 & -0.301909697740356 \tabularnewline
80 & 57 & 55.4348144377615 & 1.56518556223854 \tabularnewline
81 & 57 & 48.8808663903735 & 8.11913360962652 \tabularnewline
82 & 56 & 54.2058778171306 & 1.79412218286937 \tabularnewline
83 & 53 & 49.2233627533916 & 3.7766372466084 \tabularnewline
84 & 51 & 46.4944236882140 & 4.50557631178595 \tabularnewline
85 & 45 & 53.2947539003563 & -8.29475390035628 \tabularnewline
86 & 58 & 55.9440459000908 & 2.05595409990919 \tabularnewline
87 & 74 & 66.5812425884173 & 7.41875741158266 \tabularnewline
88 & 65 & 73.130001331359 & -8.13000133135901 \tabularnewline
89 & 65 & 66.543623656313 & -1.54362365631302 \tabularnewline
90 & 55 & 66.9821928435083 & -11.9821928435083 \tabularnewline
91 & 52 & 55.8469165529275 & -3.84691655292746 \tabularnewline
92 & 59 & 54.3044822298070 & 4.69551777019305 \tabularnewline
93 & 54 & 50.7760118971721 & 3.22398810282793 \tabularnewline
94 & 57 & 52.1094621469038 & 4.89053785309622 \tabularnewline
95 & 45 & 49.2713628183717 & -4.27136281837166 \tabularnewline
96 & 40 & 42.0774486294968 & -2.07744862949677 \tabularnewline
97 & 47 & 42.7004494819375 & 4.29955051806253 \tabularnewline
98 & 47 & 54.5029856456102 & -7.5029856456102 \tabularnewline
99 & 60 & 60.6845870783719 & -0.684587078371891 \tabularnewline
100 & 58 & 59.6685489748219 & -1.66854897482192 \tabularnewline
101 & 63 & 58.0187138331827 & 4.98128616681734 \tabularnewline
102 & 64 & 60.221094051115 & 3.77890594888495 \tabularnewline
103 & 64 & 59.6324566757825 & 4.36754332421751 \tabularnewline
104 & 63 & 64.3977449246665 & -1.39774492466651 \tabularnewline
105 & 55 & 57.1073811817044 & -2.10738118170443 \tabularnewline
106 & 54 & 55.7061329110397 & -1.70613291103971 \tabularnewline
107 & 44 & 47.3687057535314 & -3.36870575353143 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41217&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]43[/C][C]42.8811431623932[/C][C]0.118856837606820[/C][/ROW]
[ROW][C]14[/C][C]55[/C][C]54.8394104718922[/C][C]0.160589528107792[/C][/ROW]
[ROW][C]15[/C][C]68[/C][C]67.821543260933[/C][C]0.178456739066945[/C][/ROW]
[ROW][C]16[/C][C]68[/C][C]67.7305603554387[/C][C]0.269439644561288[/C][/ROW]
[ROW][C]17[/C][C]64[/C][C]63.774940754115[/C][C]0.225059245885021[/C][/ROW]
[ROW][C]18[/C][C]65[/C][C]64.7939415406946[/C][C]0.20605845930541[/C][/ROW]
[ROW][C]19[/C][C]57[/C][C]55.468743102527[/C][C]1.53125689747303[/C][/ROW]
[ROW][C]20[/C][C]59[/C][C]58.0263797292745[/C][C]0.973620270725512[/C][/ROW]
[ROW][C]21[/C][C]54[/C][C]55.0567899595376[/C][C]-1.05678995953762[/C][/ROW]
[ROW][C]22[/C][C]57[/C][C]54.9260789385688[/C][C]2.0739210614312[/C][/ROW]
[ROW][C]23[/C][C]43[/C][C]47.2940463958363[/C][C]-4.29404639583629[/C][/ROW]
[ROW][C]24[/C][C]42[/C][C]38.5620605990372[/C][C]3.43793940096275[/C][/ROW]
[ROW][C]25[/C][C]52[/C][C]46.2741327885578[/C][C]5.72586721144224[/C][/ROW]
[ROW][C]26[/C][C]51[/C][C]61.4467211984748[/C][C]-10.4467211984748[/C][/ROW]
[ROW][C]27[/C][C]58[/C][C]68.3662683347066[/C][C]-10.3662683347066[/C][/ROW]
[ROW][C]28[/C][C]60[/C][C]62.2622718698977[/C][C]-2.26227186989774[/C][/ROW]
[ROW][C]29[/C][C]61[/C][C]56.8504889533232[/C][C]4.14951104667676[/C][/ROW]
[ROW][C]30[/C][C]58[/C][C]60.1101662861139[/C][C]-2.11016628611392[/C][/ROW]
[ROW][C]31[/C][C]62[/C][C]49.7101849300527[/C][C]12.2898150699473[/C][/ROW]
[ROW][C]32[/C][C]61[/C][C]58.3151596135205[/C][C]2.68484038647953[/C][/ROW]
[ROW][C]33[/C][C]49[/C][C]55.9414466891155[/C][C]-6.94144668911549[/C][/ROW]
[ROW][C]34[/C][C]51[/C][C]53.0356099907569[/C][C]-2.03560999075687[/C][/ROW]
[ROW][C]35[/C][C]47[/C][C]41.853185200919[/C][C]5.146814799081[/C][/ROW]
[ROW][C]36[/C][C]40[/C][C]39.9774975012094[/C][C]0.0225024987906295[/C][/ROW]
[ROW][C]37[/C][C]45[/C][C]46.1676496343313[/C][C]-1.16764963433133[/C][/ROW]
[ROW][C]38[/C][C]50[/C][C]54.3497144748269[/C][C]-4.34971447482686[/C][/ROW]
[ROW][C]39[/C][C]58[/C][C]64.7710929832406[/C][C]-6.7710929832406[/C][/ROW]
[ROW][C]40[/C][C]52[/C][C]62.250569488423[/C][C]-10.2505694884230[/C][/ROW]
[ROW][C]41[/C][C]50[/C][C]53.4791085722009[/C][C]-3.4791085722009[/C][/ROW]
[ROW][C]42[/C][C]50[/C][C]51.1963603847112[/C][C]-1.19636038471117[/C][/ROW]
[ROW][C]43[/C][C]46[/C][C]44.0331956276124[/C][C]1.96680437238761[/C][/ROW]
[ROW][C]44[/C][C]46[/C][C]44.9243630838981[/C][C]1.07563691610189[/C][/ROW]
[ROW][C]45[/C][C]38[/C][C]39.8159501692132[/C][C]-1.81595016921322[/C][/ROW]
[ROW][C]46[/C][C]37[/C][C]40.7659051327993[/C][C]-3.76590513279933[/C][/ROW]
[ROW][C]47[/C][C]34[/C][C]29.9477948635093[/C][C]4.05220513649071[/C][/ROW]
[ROW][C]48[/C][C]29[/C][C]26.4802596966426[/C][C]2.5197403033574[/C][/ROW]
[ROW][C]49[/C][C]30[/C][C]33.8741646295526[/C][C]-3.87416462955262[/C][/ROW]
[ROW][C]50[/C][C]40[/C][C]39.9086820999807[/C][C]0.0913179000193196[/C][/ROW]
[ROW][C]51[/C][C]46[/C][C]52.4133291447466[/C][C]-6.41332914474664[/C][/ROW]
[ROW][C]52[/C][C]46[/C][C]49.4415542369943[/C][C]-3.44155423699426[/C][/ROW]
[ROW][C]53[/C][C]47[/C][C]45.8402812436958[/C][C]1.15971875630424[/C][/ROW]
[ROW][C]54[/C][C]47[/C][C]46.6405913066959[/C][C]0.359408693304104[/C][/ROW]
[ROW][C]55[/C][C]43[/C][C]40.9633397423783[/C][C]2.03666025762174[/C][/ROW]
[ROW][C]56[/C][C]46[/C][C]41.7264798123636[/C][C]4.2735201876364[/C][/ROW]
[ROW][C]57[/C][C]37[/C][C]37.9017922463409[/C][C]-0.901792246340868[/C][/ROW]
[ROW][C]58[/C][C]41[/C][C]39.0069767659813[/C][C]1.99302323401865[/C][/ROW]
[ROW][C]59[/C][C]39[/C][C]32.9558283418862[/C][C]6.04417165811379[/C][/ROW]
[ROW][C]60[/C][C]36[/C][C]30.3385765496866[/C][C]5.66142345031345[/C][/ROW]
[ROW][C]61[/C][C]48[/C][C]38.3239184238033[/C][C]9.67608157619665[/C][/ROW]
[ROW][C]62[/C][C]55[/C][C]52.8548032438416[/C][C]2.14519675615836[/C][/ROW]
[ROW][C]63[/C][C]56[/C][C]65.3079359462154[/C][C]-9.3079359462154[/C][/ROW]
[ROW][C]64[/C][C]53[/C][C]61.2409835416346[/C][C]-8.2409835416346[/C][/ROW]
[ROW][C]65[/C][C]52[/C][C]55.76237405281[/C][C]-3.76237405281[/C][/ROW]
[ROW][C]66[/C][C]53[/C][C]53.5970599044756[/C][C]-0.597059904475628[/C][/ROW]
[ROW][C]67[/C][C]52[/C][C]47.6889810974716[/C][C]4.31101890252843[/C][/ROW]
[ROW][C]68[/C][C]56[/C][C]50.1743722669510[/C][C]5.82562773304895[/C][/ROW]
[ROW][C]69[/C][C]51[/C][C]46.2617901083592[/C][C]4.73820989164075[/C][/ROW]
[ROW][C]70[/C][C]48[/C][C]51.1379382053022[/C][C]-3.13793820530225[/C][/ROW]
[ROW][C]71[/C][C]42[/C][C]42.916168941332[/C][C]-0.916168941332018[/C][/ROW]
[ROW][C]72[/C][C]42[/C][C]36.2463956070077[/C][C]5.75360439299234[/C][/ROW]
[ROW][C]73[/C][C]44[/C][C]45.0411727414269[/C][C]-1.04117274142691[/C][/ROW]
[ROW][C]74[/C][C]50[/C][C]52.0237398541579[/C][C]-2.02373985415791[/C][/ROW]
[ROW][C]75[/C][C]60[/C][C]59.9340089986085[/C][C]0.0659910013915308[/C][/ROW]
[ROW][C]76[/C][C]66[/C][C]61.4287897137306[/C][C]4.57121028626941[/C][/ROW]
[ROW][C]77[/C][C]58[/C][C]64.1211999459995[/C][C]-6.12119994599954[/C][/ROW]
[ROW][C]78[/C][C]59[/C][C]61.2035829154875[/C][C]-2.20358291548752[/C][/ROW]
[ROW][C]79[/C][C]55[/C][C]55.3019096977404[/C][C]-0.301909697740356[/C][/ROW]
[ROW][C]80[/C][C]57[/C][C]55.4348144377615[/C][C]1.56518556223854[/C][/ROW]
[ROW][C]81[/C][C]57[/C][C]48.8808663903735[/C][C]8.11913360962652[/C][/ROW]
[ROW][C]82[/C][C]56[/C][C]54.2058778171306[/C][C]1.79412218286937[/C][/ROW]
[ROW][C]83[/C][C]53[/C][C]49.2233627533916[/C][C]3.7766372466084[/C][/ROW]
[ROW][C]84[/C][C]51[/C][C]46.4944236882140[/C][C]4.50557631178595[/C][/ROW]
[ROW][C]85[/C][C]45[/C][C]53.2947539003563[/C][C]-8.29475390035628[/C][/ROW]
[ROW][C]86[/C][C]58[/C][C]55.9440459000908[/C][C]2.05595409990919[/C][/ROW]
[ROW][C]87[/C][C]74[/C][C]66.5812425884173[/C][C]7.41875741158266[/C][/ROW]
[ROW][C]88[/C][C]65[/C][C]73.130001331359[/C][C]-8.13000133135901[/C][/ROW]
[ROW][C]89[/C][C]65[/C][C]66.543623656313[/C][C]-1.54362365631302[/C][/ROW]
[ROW][C]90[/C][C]55[/C][C]66.9821928435083[/C][C]-11.9821928435083[/C][/ROW]
[ROW][C]91[/C][C]52[/C][C]55.8469165529275[/C][C]-3.84691655292746[/C][/ROW]
[ROW][C]92[/C][C]59[/C][C]54.3044822298070[/C][C]4.69551777019305[/C][/ROW]
[ROW][C]93[/C][C]54[/C][C]50.7760118971721[/C][C]3.22398810282793[/C][/ROW]
[ROW][C]94[/C][C]57[/C][C]52.1094621469038[/C][C]4.89053785309622[/C][/ROW]
[ROW][C]95[/C][C]45[/C][C]49.2713628183717[/C][C]-4.27136281837166[/C][/ROW]
[ROW][C]96[/C][C]40[/C][C]42.0774486294968[/C][C]-2.07744862949677[/C][/ROW]
[ROW][C]97[/C][C]47[/C][C]42.7004494819375[/C][C]4.29955051806253[/C][/ROW]
[ROW][C]98[/C][C]47[/C][C]54.5029856456102[/C][C]-7.5029856456102[/C][/ROW]
[ROW][C]99[/C][C]60[/C][C]60.6845870783719[/C][C]-0.684587078371891[/C][/ROW]
[ROW][C]100[/C][C]58[/C][C]59.6685489748219[/C][C]-1.66854897482192[/C][/ROW]
[ROW][C]101[/C][C]63[/C][C]58.0187138331827[/C][C]4.98128616681734[/C][/ROW]
[ROW][C]102[/C][C]64[/C][C]60.221094051115[/C][C]3.77890594888495[/C][/ROW]
[ROW][C]103[/C][C]64[/C][C]59.6324566757825[/C][C]4.36754332421751[/C][/ROW]
[ROW][C]104[/C][C]63[/C][C]64.3977449246665[/C][C]-1.39774492466651[/C][/ROW]
[ROW][C]105[/C][C]55[/C][C]57.1073811817044[/C][C]-2.10738118170443[/C][/ROW]
[ROW][C]106[/C][C]54[/C][C]55.7061329110397[/C][C]-1.70613291103971[/C][/ROW]
[ROW][C]107[/C][C]44[/C][C]47.3687057535314[/C][C]-3.36870575353143[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41217&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41217&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
134342.88114316239320.118856837606820
145554.83941047189220.160589528107792
156867.8215432609330.178456739066945
166867.73056035543870.269439644561288
176463.7749407541150.225059245885021
186564.79394154069460.20605845930541
195755.4687431025271.53125689747303
205958.02637972927450.973620270725512
215455.0567899595376-1.05678995953762
225754.92607893856882.0739210614312
234347.2940463958363-4.29404639583629
244238.56206059903723.43793940096275
255246.27413278855785.72586721144224
265161.4467211984748-10.4467211984748
275868.3662683347066-10.3662683347066
286062.2622718698977-2.26227186989774
296156.85048895332324.14951104667676
305860.1101662861139-2.11016628611392
316249.710184930052712.2898150699473
326158.31515961352052.68484038647953
334955.9414466891155-6.94144668911549
345153.0356099907569-2.03560999075687
354741.8531852009195.146814799081
364039.97749750120940.0225024987906295
374546.1676496343313-1.16764963433133
385054.3497144748269-4.34971447482686
395864.7710929832406-6.7710929832406
405262.250569488423-10.2505694884230
415053.4791085722009-3.4791085722009
425051.1963603847112-1.19636038471117
434644.03319562761241.96680437238761
444644.92436308389811.07563691610189
453839.8159501692132-1.81595016921322
463740.7659051327993-3.76590513279933
473429.94779486350934.05220513649071
482926.48025969664262.5197403033574
493033.8741646295526-3.87416462955262
504039.90868209998070.0913179000193196
514652.4133291447466-6.41332914474664
524649.4415542369943-3.44155423699426
534745.84028124369581.15971875630424
544746.64059130669590.359408693304104
554340.96333974237832.03666025762174
564641.72647981236364.2735201876364
573737.9017922463409-0.901792246340868
584139.00697676598131.99302323401865
593932.95582834188626.04417165811379
603630.33857654968665.66142345031345
614838.32391842380339.67608157619665
625552.85480324384162.14519675615836
635665.3079359462154-9.3079359462154
645361.2409835416346-8.2409835416346
655255.76237405281-3.76237405281
665353.5970599044756-0.597059904475628
675247.68898109747164.31101890252843
685650.17437226695105.82562773304895
695146.26179010835924.73820989164075
704851.1379382053022-3.13793820530225
714242.916168941332-0.916168941332018
724236.24639560700775.75360439299234
734445.0411727414269-1.04117274142691
745052.0237398541579-2.02373985415791
756059.93400899860850.0659910013915308
766661.42878971373064.57121028626941
775864.1211999459995-6.12119994599954
785961.2035829154875-2.20358291548752
795555.3019096977404-0.301909697740356
805755.43481443776151.56518556223854
815748.88086639037358.11913360962652
825654.20587781713061.79412218286937
835349.22336275339163.7766372466084
845146.49442368821404.50557631178595
854553.2947539003563-8.29475390035628
865855.94404590009082.05595409990919
877466.58124258841737.41875741158266
886573.130001331359-8.13000133135901
896566.543623656313-1.54362365631302
905566.9821928435083-11.9821928435083
915255.8469165529275-3.84691655292746
925954.30448222980704.69551777019305
935450.77601189717213.22398810282793
945752.10946214690384.89053785309622
954549.2713628183717-4.27136281837166
964042.0774486294968-2.07744862949677
974742.70044948193754.29955051806253
984754.5029856456102-7.5029856456102
996060.6845870783719-0.684587078371891
1005859.6685489748219-1.66854897482192
1016358.01871383318274.98128616681734
1026460.2210940511153.77890594888495
1036459.63245667578254.36754332421751
1046364.3977449246665-1.39774492466651
1055557.1073811817044-2.10738118170443
1065455.7061329110397-1.70613291103971
1074447.3687057535314-3.36870575353143







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10841.104519250375931.848692549382950.360345951369
10944.117537206933133.455122229932654.7799521839336
11051.23665742473839.332714449206263.1406004002699
11162.994151646663849.966464837883776.0218384554439
11262.184138863222648.122226162220376.246051564225
11362.741911953263247.716794515001477.7670293915251
11461.8690314003845.938842473172977.799220327587
11559.23032052028242.443787689484076.01685335108
11660.411266837707442.810004107368878.0125295680461
11753.786466126990135.406552772315272.166379481665
11853.665987140448134.539095596124872.7928786847714
11945.990861050662526.145087057914065.836635043411

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
108 & 41.1045192503759 & 31.8486925493829 & 50.360345951369 \tabularnewline
109 & 44.1175372069331 & 33.4551222299326 & 54.7799521839336 \tabularnewline
110 & 51.236657424738 & 39.3327144492062 & 63.1406004002699 \tabularnewline
111 & 62.9941516466638 & 49.9664648378837 & 76.0218384554439 \tabularnewline
112 & 62.1841388632226 & 48.1222261622203 & 76.246051564225 \tabularnewline
113 & 62.7419119532632 & 47.7167945150014 & 77.7670293915251 \tabularnewline
114 & 61.86903140038 & 45.9388424731729 & 77.799220327587 \tabularnewline
115 & 59.230320520282 & 42.4437876894840 & 76.01685335108 \tabularnewline
116 & 60.4112668377074 & 42.8100041073688 & 78.0125295680461 \tabularnewline
117 & 53.7864661269901 & 35.4065527723152 & 72.166379481665 \tabularnewline
118 & 53.6659871404481 & 34.5390955961248 & 72.7928786847714 \tabularnewline
119 & 45.9908610506625 & 26.1450870579140 & 65.836635043411 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41217&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]108[/C][C]41.1045192503759[/C][C]31.8486925493829[/C][C]50.360345951369[/C][/ROW]
[ROW][C]109[/C][C]44.1175372069331[/C][C]33.4551222299326[/C][C]54.7799521839336[/C][/ROW]
[ROW][C]110[/C][C]51.236657424738[/C][C]39.3327144492062[/C][C]63.1406004002699[/C][/ROW]
[ROW][C]111[/C][C]62.9941516466638[/C][C]49.9664648378837[/C][C]76.0218384554439[/C][/ROW]
[ROW][C]112[/C][C]62.1841388632226[/C][C]48.1222261622203[/C][C]76.246051564225[/C][/ROW]
[ROW][C]113[/C][C]62.7419119532632[/C][C]47.7167945150014[/C][C]77.7670293915251[/C][/ROW]
[ROW][C]114[/C][C]61.86903140038[/C][C]45.9388424731729[/C][C]77.799220327587[/C][/ROW]
[ROW][C]115[/C][C]59.230320520282[/C][C]42.4437876894840[/C][C]76.01685335108[/C][/ROW]
[ROW][C]116[/C][C]60.4112668377074[/C][C]42.8100041073688[/C][C]78.0125295680461[/C][/ROW]
[ROW][C]117[/C][C]53.7864661269901[/C][C]35.4065527723152[/C][C]72.166379481665[/C][/ROW]
[ROW][C]118[/C][C]53.6659871404481[/C][C]34.5390955961248[/C][C]72.7928786847714[/C][/ROW]
[ROW][C]119[/C][C]45.9908610506625[/C][C]26.1450870579140[/C][C]65.836635043411[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41217&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41217&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
10841.104519250375931.848692549382950.360345951369
10944.117537206933133.455122229932654.7799521839336
11051.23665742473839.332714449206263.1406004002699
11162.994151646663849.966464837883776.0218384554439
11262.184138863222648.122226162220376.246051564225
11362.741911953263247.716794515001477.7670293915251
11461.8690314003845.938842473172977.799220327587
11559.23032052028242.443787689484076.01685335108
11660.411266837707442.810004107368878.0125295680461
11753.786466126990135.406552772315272.166379481665
11853.665987140448134.539095596124872.7928786847714
11945.990861050662526.145087057914065.836635043411



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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=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')