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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 computationMon, 15 Dec 2014 08:15:44 +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/2014/Dec/15/t1418631355ke72pa1vm2czkqw.htm/, Retrieved Fri, 17 May 2024 00:07:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267952, Retrieved Fri, 17 May 2024 00:07:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-15 08:15:44] [6baf0af87d9d8aa2cb91b54f39a0a5b0] [Current]
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Dataseries X:
26
57
37
67
43
52
52
43
84
67
49
70
52
58
68
62
43
56
56
74
65
63
58
57
63
53
57
51
64
53
29
54
58
43
51
53
54
56
61
47
39
48
50
35
30
68
49
61
67
47
56
50
43
67
62
57
41
54
45
48
61
56
41
43
53
44
66
58
46
37
51
51
56
66
37
59
42
38
66
34
53
49
55
49
59
40
58
60
63
56
54
52
34
69
32
48
67
58
57
42
64
58
66
26
61
52
51
55
50
60
56
63
61




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267952&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267952&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267952&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0748389142941678
beta0.0722760522985544
gamma0.39530530549376

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0748389142941678 \tabularnewline
beta & 0.0722760522985544 \tabularnewline
gamma & 0.39530530549376 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267952&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]0.0748389142941678[/C][/ROW]
[ROW][C]beta[/C][C]0.0722760522985544[/C][/ROW]
[ROW][C]gamma[/C][C]0.39530530549376[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267952&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267952&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
alpha0.0748389142941678
beta0.0722760522985544
gamma0.39530530549376







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135249.70747396687762.29252603312245
145854.71548662224963.2845133777504
156864.42438258338783.57561741661223
166260.42542614409021.57457385590975
174342.19325867282380.806741327176162
185655.64299281570820.357007184291803
195656.7440138429038-0.744013842903819
207446.31389812241327.686101877587
216593.3323313866611-28.3323313866611
226372.0724527709792-9.07245277097915
235852.85267524616115.14732475383892
245776.5225001407897-19.5225001407897
256356.81118679907016.18881320092989
265363.1597586108316-10.1597586108316
275772.9709803875259-15.9709803875259
285166.2010916410362-15.2010916410362
296445.079931927776818.9200680722232
305360.8665718941286-7.86657189412855
312960.8828113444291-31.8828113444291
325457.8068333996353-3.80683339963528
335880.7177448410943-22.7177448410943
344366.6614396016519-23.6614396016519
355151.7057808480596-0.705780848059561
365364.2916108664255-11.2916108664255
375454.6767115029213-0.676711502921286
385653.98740266286942.01259733713058
396161.3242464989574-0.324246498957407
404755.8801905555823-8.88019055558231
413947.7219565870702-8.72195658707022
424850.5655585757858-2.56555857578581
435042.36852906881597.63147093118415
443551.4087833657452-16.4087833657452
453064.098219637411-34.098219637411
466849.82853613841218.171463861588
474946.58926614315312.41073385684692
486154.437030142126.56296985787998
496750.243666266755516.7563337332445
504751.7591443792178-4.75914437921784
515657.2223469907236-1.22234699072356
525049.01092127106240.989078728937571
534341.97539492178741.02460507821264
546747.562162444282219.4378375557178
556244.858304866274617.1416951337254
565745.834641791790511.1653582082095
574154.3583373416451-13.3583373416451
585461.7428939240467-7.7428939240467
594550.497568535412-5.49756853541201
604860.021080223466-12.021080223466
616158.17145175834912.82854824165094
625650.7494532559525.25054674404804
634158.6290892166909-17.6290892166909
644349.9790257712542-6.97902577125422
655342.372571890630810.6274281093692
664455.499596365819-11.499596365819
676649.514226981293816.4857730187062
685848.16703518915789.83296481084216
694647.4770491454124-1.47704914541244
703757.48021588306-20.48021588306
715146.38069844252264.61930155747744
725153.9336195341912-2.93361953419115
735658.0847598992321-2.08475989923213
746651.290688714509114.7093112854909
753751.3812699262628-14.3812699262628
765946.891391901810112.1086080981899
774247.1816482260649-5.18164822606487
783850.96674956518-12.96674956518
796654.927250726304911.0727492736951
803450.7525500336749-16.7525500336749
815344.09941567990228.90058432009784
824947.48932408226551.51067591773452
835547.20702451833737.79297548166274
844952.1892360279764-3.18923602797638
855956.58338788897662.41661211102344
864056.1988089830211-16.1988089830211
875843.683579284500914.3164207154991
886050.94971992875249.05028007124765
896344.770865500094418.2291344999056
905647.55274236385528.44725763614476
915463.0777602121242-9.07776021212421
925246.56729018312265.43270981687741
933451.5476493784833-17.5476493784833
946950.414244232092318.5857557679077
953254.0779777225652-22.0779777225652
964852.9115211176758-4.91152111767583
976759.55325683001217.44674316998793
985852.39443209170315.60556790829686
995752.74923239880214.25076760119789
1004257.719118218751-15.719118218751
1016452.762805043062311.2371949569377
1025851.34217267133216.65782732866795
1036660.33408693434995.6659130656501
1042649.9399327225585-23.9399327225585
1056144.096062057446416.9039379425536
1065259.1037455331738-7.10374553317378
1075145.6595329837845.340467016216
1085553.14232140079671.85767859920327
1095065.4920546716597-15.4920546716597
1106055.73194555960524.26805444039481
1115655.46616071406770.533839285932302
1126352.667234452420210.3327655475798
1136159.89051723452281.10948276547724

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 52 & 49.7074739668776 & 2.29252603312245 \tabularnewline
14 & 58 & 54.7154866222496 & 3.2845133777504 \tabularnewline
15 & 68 & 64.4243825833878 & 3.57561741661223 \tabularnewline
16 & 62 & 60.4254261440902 & 1.57457385590975 \tabularnewline
17 & 43 & 42.1932586728238 & 0.806741327176162 \tabularnewline
18 & 56 & 55.6429928157082 & 0.357007184291803 \tabularnewline
19 & 56 & 56.7440138429038 & -0.744013842903819 \tabularnewline
20 & 74 & 46.313898122413 & 27.686101877587 \tabularnewline
21 & 65 & 93.3323313866611 & -28.3323313866611 \tabularnewline
22 & 63 & 72.0724527709792 & -9.07245277097915 \tabularnewline
23 & 58 & 52.8526752461611 & 5.14732475383892 \tabularnewline
24 & 57 & 76.5225001407897 & -19.5225001407897 \tabularnewline
25 & 63 & 56.8111867990701 & 6.18881320092989 \tabularnewline
26 & 53 & 63.1597586108316 & -10.1597586108316 \tabularnewline
27 & 57 & 72.9709803875259 & -15.9709803875259 \tabularnewline
28 & 51 & 66.2010916410362 & -15.2010916410362 \tabularnewline
29 & 64 & 45.0799319277768 & 18.9200680722232 \tabularnewline
30 & 53 & 60.8665718941286 & -7.86657189412855 \tabularnewline
31 & 29 & 60.8828113444291 & -31.8828113444291 \tabularnewline
32 & 54 & 57.8068333996353 & -3.80683339963528 \tabularnewline
33 & 58 & 80.7177448410943 & -22.7177448410943 \tabularnewline
34 & 43 & 66.6614396016519 & -23.6614396016519 \tabularnewline
35 & 51 & 51.7057808480596 & -0.705780848059561 \tabularnewline
36 & 53 & 64.2916108664255 & -11.2916108664255 \tabularnewline
37 & 54 & 54.6767115029213 & -0.676711502921286 \tabularnewline
38 & 56 & 53.9874026628694 & 2.01259733713058 \tabularnewline
39 & 61 & 61.3242464989574 & -0.324246498957407 \tabularnewline
40 & 47 & 55.8801905555823 & -8.88019055558231 \tabularnewline
41 & 39 & 47.7219565870702 & -8.72195658707022 \tabularnewline
42 & 48 & 50.5655585757858 & -2.56555857578581 \tabularnewline
43 & 50 & 42.3685290688159 & 7.63147093118415 \tabularnewline
44 & 35 & 51.4087833657452 & -16.4087833657452 \tabularnewline
45 & 30 & 64.098219637411 & -34.098219637411 \tabularnewline
46 & 68 & 49.828536138412 & 18.171463861588 \tabularnewline
47 & 49 & 46.5892661431531 & 2.41073385684692 \tabularnewline
48 & 61 & 54.43703014212 & 6.56296985787998 \tabularnewline
49 & 67 & 50.2436662667555 & 16.7563337332445 \tabularnewline
50 & 47 & 51.7591443792178 & -4.75914437921784 \tabularnewline
51 & 56 & 57.2223469907236 & -1.22234699072356 \tabularnewline
52 & 50 & 49.0109212710624 & 0.989078728937571 \tabularnewline
53 & 43 & 41.9753949217874 & 1.02460507821264 \tabularnewline
54 & 67 & 47.5621624442822 & 19.4378375557178 \tabularnewline
55 & 62 & 44.8583048662746 & 17.1416951337254 \tabularnewline
56 & 57 & 45.8346417917905 & 11.1653582082095 \tabularnewline
57 & 41 & 54.3583373416451 & -13.3583373416451 \tabularnewline
58 & 54 & 61.7428939240467 & -7.7428939240467 \tabularnewline
59 & 45 & 50.497568535412 & -5.49756853541201 \tabularnewline
60 & 48 & 60.021080223466 & -12.021080223466 \tabularnewline
61 & 61 & 58.1714517583491 & 2.82854824165094 \tabularnewline
62 & 56 & 50.749453255952 & 5.25054674404804 \tabularnewline
63 & 41 & 58.6290892166909 & -17.6290892166909 \tabularnewline
64 & 43 & 49.9790257712542 & -6.97902577125422 \tabularnewline
65 & 53 & 42.3725718906308 & 10.6274281093692 \tabularnewline
66 & 44 & 55.499596365819 & -11.499596365819 \tabularnewline
67 & 66 & 49.5142269812938 & 16.4857730187062 \tabularnewline
68 & 58 & 48.1670351891578 & 9.83296481084216 \tabularnewline
69 & 46 & 47.4770491454124 & -1.47704914541244 \tabularnewline
70 & 37 & 57.48021588306 & -20.48021588306 \tabularnewline
71 & 51 & 46.3806984425226 & 4.61930155747744 \tabularnewline
72 & 51 & 53.9336195341912 & -2.93361953419115 \tabularnewline
73 & 56 & 58.0847598992321 & -2.08475989923213 \tabularnewline
74 & 66 & 51.2906887145091 & 14.7093112854909 \tabularnewline
75 & 37 & 51.3812699262628 & -14.3812699262628 \tabularnewline
76 & 59 & 46.8913919018101 & 12.1086080981899 \tabularnewline
77 & 42 & 47.1816482260649 & -5.18164822606487 \tabularnewline
78 & 38 & 50.96674956518 & -12.96674956518 \tabularnewline
79 & 66 & 54.9272507263049 & 11.0727492736951 \tabularnewline
80 & 34 & 50.7525500336749 & -16.7525500336749 \tabularnewline
81 & 53 & 44.0994156799022 & 8.90058432009784 \tabularnewline
82 & 49 & 47.4893240822655 & 1.51067591773452 \tabularnewline
83 & 55 & 47.2070245183373 & 7.79297548166274 \tabularnewline
84 & 49 & 52.1892360279764 & -3.18923602797638 \tabularnewline
85 & 59 & 56.5833878889766 & 2.41661211102344 \tabularnewline
86 & 40 & 56.1988089830211 & -16.1988089830211 \tabularnewline
87 & 58 & 43.6835792845009 & 14.3164207154991 \tabularnewline
88 & 60 & 50.9497199287524 & 9.05028007124765 \tabularnewline
89 & 63 & 44.7708655000944 & 18.2291344999056 \tabularnewline
90 & 56 & 47.5527423638552 & 8.44725763614476 \tabularnewline
91 & 54 & 63.0777602121242 & -9.07776021212421 \tabularnewline
92 & 52 & 46.5672901831226 & 5.43270981687741 \tabularnewline
93 & 34 & 51.5476493784833 & -17.5476493784833 \tabularnewline
94 & 69 & 50.4142442320923 & 18.5857557679077 \tabularnewline
95 & 32 & 54.0779777225652 & -22.0779777225652 \tabularnewline
96 & 48 & 52.9115211176758 & -4.91152111767583 \tabularnewline
97 & 67 & 59.5532568300121 & 7.44674316998793 \tabularnewline
98 & 58 & 52.3944320917031 & 5.60556790829686 \tabularnewline
99 & 57 & 52.7492323988021 & 4.25076760119789 \tabularnewline
100 & 42 & 57.719118218751 & -15.719118218751 \tabularnewline
101 & 64 & 52.7628050430623 & 11.2371949569377 \tabularnewline
102 & 58 & 51.3421726713321 & 6.65782732866795 \tabularnewline
103 & 66 & 60.3340869343499 & 5.6659130656501 \tabularnewline
104 & 26 & 49.9399327225585 & -23.9399327225585 \tabularnewline
105 & 61 & 44.0960620574464 & 16.9039379425536 \tabularnewline
106 & 52 & 59.1037455331738 & -7.10374553317378 \tabularnewline
107 & 51 & 45.659532983784 & 5.340467016216 \tabularnewline
108 & 55 & 53.1423214007967 & 1.85767859920327 \tabularnewline
109 & 50 & 65.4920546716597 & -15.4920546716597 \tabularnewline
110 & 60 & 55.7319455596052 & 4.26805444039481 \tabularnewline
111 & 56 & 55.4661607140677 & 0.533839285932302 \tabularnewline
112 & 63 & 52.6672344524202 & 10.3327655475798 \tabularnewline
113 & 61 & 59.8905172345228 & 1.10948276547724 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267952&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]52[/C][C]49.7074739668776[/C][C]2.29252603312245[/C][/ROW]
[ROW][C]14[/C][C]58[/C][C]54.7154866222496[/C][C]3.2845133777504[/C][/ROW]
[ROW][C]15[/C][C]68[/C][C]64.4243825833878[/C][C]3.57561741661223[/C][/ROW]
[ROW][C]16[/C][C]62[/C][C]60.4254261440902[/C][C]1.57457385590975[/C][/ROW]
[ROW][C]17[/C][C]43[/C][C]42.1932586728238[/C][C]0.806741327176162[/C][/ROW]
[ROW][C]18[/C][C]56[/C][C]55.6429928157082[/C][C]0.357007184291803[/C][/ROW]
[ROW][C]19[/C][C]56[/C][C]56.7440138429038[/C][C]-0.744013842903819[/C][/ROW]
[ROW][C]20[/C][C]74[/C][C]46.313898122413[/C][C]27.686101877587[/C][/ROW]
[ROW][C]21[/C][C]65[/C][C]93.3323313866611[/C][C]-28.3323313866611[/C][/ROW]
[ROW][C]22[/C][C]63[/C][C]72.0724527709792[/C][C]-9.07245277097915[/C][/ROW]
[ROW][C]23[/C][C]58[/C][C]52.8526752461611[/C][C]5.14732475383892[/C][/ROW]
[ROW][C]24[/C][C]57[/C][C]76.5225001407897[/C][C]-19.5225001407897[/C][/ROW]
[ROW][C]25[/C][C]63[/C][C]56.8111867990701[/C][C]6.18881320092989[/C][/ROW]
[ROW][C]26[/C][C]53[/C][C]63.1597586108316[/C][C]-10.1597586108316[/C][/ROW]
[ROW][C]27[/C][C]57[/C][C]72.9709803875259[/C][C]-15.9709803875259[/C][/ROW]
[ROW][C]28[/C][C]51[/C][C]66.2010916410362[/C][C]-15.2010916410362[/C][/ROW]
[ROW][C]29[/C][C]64[/C][C]45.0799319277768[/C][C]18.9200680722232[/C][/ROW]
[ROW][C]30[/C][C]53[/C][C]60.8665718941286[/C][C]-7.86657189412855[/C][/ROW]
[ROW][C]31[/C][C]29[/C][C]60.8828113444291[/C][C]-31.8828113444291[/C][/ROW]
[ROW][C]32[/C][C]54[/C][C]57.8068333996353[/C][C]-3.80683339963528[/C][/ROW]
[ROW][C]33[/C][C]58[/C][C]80.7177448410943[/C][C]-22.7177448410943[/C][/ROW]
[ROW][C]34[/C][C]43[/C][C]66.6614396016519[/C][C]-23.6614396016519[/C][/ROW]
[ROW][C]35[/C][C]51[/C][C]51.7057808480596[/C][C]-0.705780848059561[/C][/ROW]
[ROW][C]36[/C][C]53[/C][C]64.2916108664255[/C][C]-11.2916108664255[/C][/ROW]
[ROW][C]37[/C][C]54[/C][C]54.6767115029213[/C][C]-0.676711502921286[/C][/ROW]
[ROW][C]38[/C][C]56[/C][C]53.9874026628694[/C][C]2.01259733713058[/C][/ROW]
[ROW][C]39[/C][C]61[/C][C]61.3242464989574[/C][C]-0.324246498957407[/C][/ROW]
[ROW][C]40[/C][C]47[/C][C]55.8801905555823[/C][C]-8.88019055558231[/C][/ROW]
[ROW][C]41[/C][C]39[/C][C]47.7219565870702[/C][C]-8.72195658707022[/C][/ROW]
[ROW][C]42[/C][C]48[/C][C]50.5655585757858[/C][C]-2.56555857578581[/C][/ROW]
[ROW][C]43[/C][C]50[/C][C]42.3685290688159[/C][C]7.63147093118415[/C][/ROW]
[ROW][C]44[/C][C]35[/C][C]51.4087833657452[/C][C]-16.4087833657452[/C][/ROW]
[ROW][C]45[/C][C]30[/C][C]64.098219637411[/C][C]-34.098219637411[/C][/ROW]
[ROW][C]46[/C][C]68[/C][C]49.828536138412[/C][C]18.171463861588[/C][/ROW]
[ROW][C]47[/C][C]49[/C][C]46.5892661431531[/C][C]2.41073385684692[/C][/ROW]
[ROW][C]48[/C][C]61[/C][C]54.43703014212[/C][C]6.56296985787998[/C][/ROW]
[ROW][C]49[/C][C]67[/C][C]50.2436662667555[/C][C]16.7563337332445[/C][/ROW]
[ROW][C]50[/C][C]47[/C][C]51.7591443792178[/C][C]-4.75914437921784[/C][/ROW]
[ROW][C]51[/C][C]56[/C][C]57.2223469907236[/C][C]-1.22234699072356[/C][/ROW]
[ROW][C]52[/C][C]50[/C][C]49.0109212710624[/C][C]0.989078728937571[/C][/ROW]
[ROW][C]53[/C][C]43[/C][C]41.9753949217874[/C][C]1.02460507821264[/C][/ROW]
[ROW][C]54[/C][C]67[/C][C]47.5621624442822[/C][C]19.4378375557178[/C][/ROW]
[ROW][C]55[/C][C]62[/C][C]44.8583048662746[/C][C]17.1416951337254[/C][/ROW]
[ROW][C]56[/C][C]57[/C][C]45.8346417917905[/C][C]11.1653582082095[/C][/ROW]
[ROW][C]57[/C][C]41[/C][C]54.3583373416451[/C][C]-13.3583373416451[/C][/ROW]
[ROW][C]58[/C][C]54[/C][C]61.7428939240467[/C][C]-7.7428939240467[/C][/ROW]
[ROW][C]59[/C][C]45[/C][C]50.497568535412[/C][C]-5.49756853541201[/C][/ROW]
[ROW][C]60[/C][C]48[/C][C]60.021080223466[/C][C]-12.021080223466[/C][/ROW]
[ROW][C]61[/C][C]61[/C][C]58.1714517583491[/C][C]2.82854824165094[/C][/ROW]
[ROW][C]62[/C][C]56[/C][C]50.749453255952[/C][C]5.25054674404804[/C][/ROW]
[ROW][C]63[/C][C]41[/C][C]58.6290892166909[/C][C]-17.6290892166909[/C][/ROW]
[ROW][C]64[/C][C]43[/C][C]49.9790257712542[/C][C]-6.97902577125422[/C][/ROW]
[ROW][C]65[/C][C]53[/C][C]42.3725718906308[/C][C]10.6274281093692[/C][/ROW]
[ROW][C]66[/C][C]44[/C][C]55.499596365819[/C][C]-11.499596365819[/C][/ROW]
[ROW][C]67[/C][C]66[/C][C]49.5142269812938[/C][C]16.4857730187062[/C][/ROW]
[ROW][C]68[/C][C]58[/C][C]48.1670351891578[/C][C]9.83296481084216[/C][/ROW]
[ROW][C]69[/C][C]46[/C][C]47.4770491454124[/C][C]-1.47704914541244[/C][/ROW]
[ROW][C]70[/C][C]37[/C][C]57.48021588306[/C][C]-20.48021588306[/C][/ROW]
[ROW][C]71[/C][C]51[/C][C]46.3806984425226[/C][C]4.61930155747744[/C][/ROW]
[ROW][C]72[/C][C]51[/C][C]53.9336195341912[/C][C]-2.93361953419115[/C][/ROW]
[ROW][C]73[/C][C]56[/C][C]58.0847598992321[/C][C]-2.08475989923213[/C][/ROW]
[ROW][C]74[/C][C]66[/C][C]51.2906887145091[/C][C]14.7093112854909[/C][/ROW]
[ROW][C]75[/C][C]37[/C][C]51.3812699262628[/C][C]-14.3812699262628[/C][/ROW]
[ROW][C]76[/C][C]59[/C][C]46.8913919018101[/C][C]12.1086080981899[/C][/ROW]
[ROW][C]77[/C][C]42[/C][C]47.1816482260649[/C][C]-5.18164822606487[/C][/ROW]
[ROW][C]78[/C][C]38[/C][C]50.96674956518[/C][C]-12.96674956518[/C][/ROW]
[ROW][C]79[/C][C]66[/C][C]54.9272507263049[/C][C]11.0727492736951[/C][/ROW]
[ROW][C]80[/C][C]34[/C][C]50.7525500336749[/C][C]-16.7525500336749[/C][/ROW]
[ROW][C]81[/C][C]53[/C][C]44.0994156799022[/C][C]8.90058432009784[/C][/ROW]
[ROW][C]82[/C][C]49[/C][C]47.4893240822655[/C][C]1.51067591773452[/C][/ROW]
[ROW][C]83[/C][C]55[/C][C]47.2070245183373[/C][C]7.79297548166274[/C][/ROW]
[ROW][C]84[/C][C]49[/C][C]52.1892360279764[/C][C]-3.18923602797638[/C][/ROW]
[ROW][C]85[/C][C]59[/C][C]56.5833878889766[/C][C]2.41661211102344[/C][/ROW]
[ROW][C]86[/C][C]40[/C][C]56.1988089830211[/C][C]-16.1988089830211[/C][/ROW]
[ROW][C]87[/C][C]58[/C][C]43.6835792845009[/C][C]14.3164207154991[/C][/ROW]
[ROW][C]88[/C][C]60[/C][C]50.9497199287524[/C][C]9.05028007124765[/C][/ROW]
[ROW][C]89[/C][C]63[/C][C]44.7708655000944[/C][C]18.2291344999056[/C][/ROW]
[ROW][C]90[/C][C]56[/C][C]47.5527423638552[/C][C]8.44725763614476[/C][/ROW]
[ROW][C]91[/C][C]54[/C][C]63.0777602121242[/C][C]-9.07776021212421[/C][/ROW]
[ROW][C]92[/C][C]52[/C][C]46.5672901831226[/C][C]5.43270981687741[/C][/ROW]
[ROW][C]93[/C][C]34[/C][C]51.5476493784833[/C][C]-17.5476493784833[/C][/ROW]
[ROW][C]94[/C][C]69[/C][C]50.4142442320923[/C][C]18.5857557679077[/C][/ROW]
[ROW][C]95[/C][C]32[/C][C]54.0779777225652[/C][C]-22.0779777225652[/C][/ROW]
[ROW][C]96[/C][C]48[/C][C]52.9115211176758[/C][C]-4.91152111767583[/C][/ROW]
[ROW][C]97[/C][C]67[/C][C]59.5532568300121[/C][C]7.44674316998793[/C][/ROW]
[ROW][C]98[/C][C]58[/C][C]52.3944320917031[/C][C]5.60556790829686[/C][/ROW]
[ROW][C]99[/C][C]57[/C][C]52.7492323988021[/C][C]4.25076760119789[/C][/ROW]
[ROW][C]100[/C][C]42[/C][C]57.719118218751[/C][C]-15.719118218751[/C][/ROW]
[ROW][C]101[/C][C]64[/C][C]52.7628050430623[/C][C]11.2371949569377[/C][/ROW]
[ROW][C]102[/C][C]58[/C][C]51.3421726713321[/C][C]6.65782732866795[/C][/ROW]
[ROW][C]103[/C][C]66[/C][C]60.3340869343499[/C][C]5.6659130656501[/C][/ROW]
[ROW][C]104[/C][C]26[/C][C]49.9399327225585[/C][C]-23.9399327225585[/C][/ROW]
[ROW][C]105[/C][C]61[/C][C]44.0960620574464[/C][C]16.9039379425536[/C][/ROW]
[ROW][C]106[/C][C]52[/C][C]59.1037455331738[/C][C]-7.10374553317378[/C][/ROW]
[ROW][C]107[/C][C]51[/C][C]45.659532983784[/C][C]5.340467016216[/C][/ROW]
[ROW][C]108[/C][C]55[/C][C]53.1423214007967[/C][C]1.85767859920327[/C][/ROW]
[ROW][C]109[/C][C]50[/C][C]65.4920546716597[/C][C]-15.4920546716597[/C][/ROW]
[ROW][C]110[/C][C]60[/C][C]55.7319455596052[/C][C]4.26805444039481[/C][/ROW]
[ROW][C]111[/C][C]56[/C][C]55.4661607140677[/C][C]0.533839285932302[/C][/ROW]
[ROW][C]112[/C][C]63[/C][C]52.6672344524202[/C][C]10.3327655475798[/C][/ROW]
[ROW][C]113[/C][C]61[/C][C]59.8905172345228[/C][C]1.10948276547724[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267952&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267952&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
135249.70747396687762.29252603312245
145854.71548662224963.2845133777504
156864.42438258338783.57561741661223
166260.42542614409021.57457385590975
174342.19325867282380.806741327176162
185655.64299281570820.357007184291803
195656.7440138429038-0.744013842903819
207446.31389812241327.686101877587
216593.3323313866611-28.3323313866611
226372.0724527709792-9.07245277097915
235852.85267524616115.14732475383892
245776.5225001407897-19.5225001407897
256356.81118679907016.18881320092989
265363.1597586108316-10.1597586108316
275772.9709803875259-15.9709803875259
285166.2010916410362-15.2010916410362
296445.079931927776818.9200680722232
305360.8665718941286-7.86657189412855
312960.8828113444291-31.8828113444291
325457.8068333996353-3.80683339963528
335880.7177448410943-22.7177448410943
344366.6614396016519-23.6614396016519
355151.7057808480596-0.705780848059561
365364.2916108664255-11.2916108664255
375454.6767115029213-0.676711502921286
385653.98740266286942.01259733713058
396161.3242464989574-0.324246498957407
404755.8801905555823-8.88019055558231
413947.7219565870702-8.72195658707022
424850.5655585757858-2.56555857578581
435042.36852906881597.63147093118415
443551.4087833657452-16.4087833657452
453064.098219637411-34.098219637411
466849.82853613841218.171463861588
474946.58926614315312.41073385684692
486154.437030142126.56296985787998
496750.243666266755516.7563337332445
504751.7591443792178-4.75914437921784
515657.2223469907236-1.22234699072356
525049.01092127106240.989078728937571
534341.97539492178741.02460507821264
546747.562162444282219.4378375557178
556244.858304866274617.1416951337254
565745.834641791790511.1653582082095
574154.3583373416451-13.3583373416451
585461.7428939240467-7.7428939240467
594550.497568535412-5.49756853541201
604860.021080223466-12.021080223466
616158.17145175834912.82854824165094
625650.7494532559525.25054674404804
634158.6290892166909-17.6290892166909
644349.9790257712542-6.97902577125422
655342.372571890630810.6274281093692
664455.499596365819-11.499596365819
676649.514226981293816.4857730187062
685848.16703518915789.83296481084216
694647.4770491454124-1.47704914541244
703757.48021588306-20.48021588306
715146.38069844252264.61930155747744
725153.9336195341912-2.93361953419115
735658.0847598992321-2.08475989923213
746651.290688714509114.7093112854909
753751.3812699262628-14.3812699262628
765946.891391901810112.1086080981899
774247.1816482260649-5.18164822606487
783850.96674956518-12.96674956518
796654.927250726304911.0727492736951
803450.7525500336749-16.7525500336749
815344.09941567990228.90058432009784
824947.48932408226551.51067591773452
835547.20702451833737.79297548166274
844952.1892360279764-3.18923602797638
855956.58338788897662.41661211102344
864056.1988089830211-16.1988089830211
875843.683579284500914.3164207154991
886050.94971992875249.05028007124765
896344.770865500094418.2291344999056
905647.55274236385528.44725763614476
915463.0777602121242-9.07776021212421
925246.56729018312265.43270981687741
933451.5476493784833-17.5476493784833
946950.414244232092318.5857557679077
953254.0779777225652-22.0779777225652
964852.9115211176758-4.91152111767583
976759.55325683001217.44674316998793
985852.39443209170315.60556790829686
995752.74923239880214.25076760119789
1004257.719118218751-15.719118218751
1016452.762805043062311.2371949569377
1025851.34217267133216.65782732866795
1036660.33408693434995.6659130656501
1042649.9399327225585-23.9399327225585
1056144.096062057446416.9039379425536
1065259.1037455331738-7.10374553317378
1075145.6595329837845.340467016216
1085553.14232140079671.85767859920327
1095065.4920546716597-15.4920546716597
1106055.73194555960524.26805444039481
1115655.46616071406770.533839285932302
1126352.667234452420210.3327655475798
1136159.89051723452281.10948276547724







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
11455.915382555356845.11447456583566.7162905448787
11564.298479967048753.264451247648175.3325086864492
11641.807115947157530.819601618434352.7946302758806
11753.305510442595741.887450666180264.7235702190112
11858.437356310277646.61207662781470.2626359927412
11949.742128174295937.983317900312561.5009384482792
12055.782832302369543.461046605690368.1046179990486
12161.755908887291348.743687780602774.7681299939798
12260.390594081860447.118568003065973.6626201606549
12358.408990319875844.92934630245771.8886343372947
12459.193732475741245.260996763602673.1264681878799
12562.3766625162506-4.62571988510053129.379044917602

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
114 & 55.9153825553568 & 45.114474565835 & 66.7162905448787 \tabularnewline
115 & 64.2984799670487 & 53.2644512476481 & 75.3325086864492 \tabularnewline
116 & 41.8071159471575 & 30.8196016184343 & 52.7946302758806 \tabularnewline
117 & 53.3055104425957 & 41.8874506661802 & 64.7235702190112 \tabularnewline
118 & 58.4373563102776 & 46.612076627814 & 70.2626359927412 \tabularnewline
119 & 49.7421281742959 & 37.9833179003125 & 61.5009384482792 \tabularnewline
120 & 55.7828323023695 & 43.4610466056903 & 68.1046179990486 \tabularnewline
121 & 61.7559088872913 & 48.7436877806027 & 74.7681299939798 \tabularnewline
122 & 60.3905940818604 & 47.1185680030659 & 73.6626201606549 \tabularnewline
123 & 58.4089903198758 & 44.929346302457 & 71.8886343372947 \tabularnewline
124 & 59.1937324757412 & 45.2609967636026 & 73.1264681878799 \tabularnewline
125 & 62.3766625162506 & -4.62571988510053 & 129.379044917602 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267952&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]114[/C][C]55.9153825553568[/C][C]45.114474565835[/C][C]66.7162905448787[/C][/ROW]
[ROW][C]115[/C][C]64.2984799670487[/C][C]53.2644512476481[/C][C]75.3325086864492[/C][/ROW]
[ROW][C]116[/C][C]41.8071159471575[/C][C]30.8196016184343[/C][C]52.7946302758806[/C][/ROW]
[ROW][C]117[/C][C]53.3055104425957[/C][C]41.8874506661802[/C][C]64.7235702190112[/C][/ROW]
[ROW][C]118[/C][C]58.4373563102776[/C][C]46.612076627814[/C][C]70.2626359927412[/C][/ROW]
[ROW][C]119[/C][C]49.7421281742959[/C][C]37.9833179003125[/C][C]61.5009384482792[/C][/ROW]
[ROW][C]120[/C][C]55.7828323023695[/C][C]43.4610466056903[/C][C]68.1046179990486[/C][/ROW]
[ROW][C]121[/C][C]61.7559088872913[/C][C]48.7436877806027[/C][C]74.7681299939798[/C][/ROW]
[ROW][C]122[/C][C]60.3905940818604[/C][C]47.1185680030659[/C][C]73.6626201606549[/C][/ROW]
[ROW][C]123[/C][C]58.4089903198758[/C][C]44.929346302457[/C][C]71.8886343372947[/C][/ROW]
[ROW][C]124[/C][C]59.1937324757412[/C][C]45.2609967636026[/C][C]73.1264681878799[/C][/ROW]
[ROW][C]125[/C][C]62.3766625162506[/C][C]-4.62571988510053[/C][C]129.379044917602[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267952&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267952&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
11455.915382555356845.11447456583566.7162905448787
11564.298479967048753.264451247648175.3325086864492
11641.807115947157530.819601618434352.7946302758806
11753.305510442595741.887450666180264.7235702190112
11858.437356310277646.61207662781470.2626359927412
11949.742128174295937.983317900312561.5009384482792
12055.782832302369543.461046605690368.1046179990486
12161.755908887291348.743687780602774.7681299939798
12260.390594081860447.118568003065973.6626201606549
12358.408990319875844.92934630245771.8886343372947
12459.193732475741245.260996763602673.1264681878799
12562.3766625162506-4.62571988510053129.379044917602



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):
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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')