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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 08:38:43 +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/2014/Dec/15/t1418632776htmw0pnfp50d13v.htm/, Retrieved Sun, 19 May 2024 14:38:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267957, Retrieved Sun, 19 May 2024 14:38:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-15 08:38:43] [6baf0af87d9d8aa2cb91b54f39a0a5b0] [Current]
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Dataseries X:
50
62
54
71
54
65
73
52
84
42
66
65
78
73
75
72
66
70
61
81
71
69
71
72
68
70
68
61
67
76
70
60
72
69
71
62
70
64
58
76
52
59
68
76
65
67
59
69
76
63
75
63
60
73
63
70
75
66
63
63
64
70
75
61
60
62
73
61
66
64
59
64
60
56
78
53
67
59
66
68
71
66
73
72
71
59
64
66
78
68
73
62
65
68
65
60
71
65
68
64
74
69
76
68
72
67
63
59
73
66
62
69
66




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267957&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267957&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267957&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.118883799046702
beta0.0730972973885657
gamma0.48557960533611

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.118883799046702 \tabularnewline
beta & 0.0730972973885657 \tabularnewline
gamma & 0.48557960533611 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267957&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]0.118883799046702[/C][/ROW]
[ROW][C]beta[/C][C]0.0730972973885657[/C][/ROW]
[ROW][C]gamma[/C][C]0.48557960533611[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267957&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267957&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
alpha0.118883799046702
beta0.0730972973885657
gamma0.48557960533611







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137873.77163461538464.22836538461536
147369.28440276902833.7155972309717
157571.81016661678743.18983338321262
167269.38447891562222.61552108437778
176663.16324388554112.8367561144589
187067.8262950997472.17370490025296
196180.5544099457191-19.5544099457191
208156.279474479592524.7205255204075
217190.7746016644141-19.7746016644141
226946.224802799395622.7751972006044
237173.3064040583332-2.30640405833319
247272.2194997608083-0.219499760808276
256888.1879019310077-20.1879019310077
267080.5784462810105-10.5784462810105
276881.0555780665149-13.0555780665149
286176.1873267178236-15.1873267178236
296767.5240424008656-0.524042400865611
307671.05442070194714.94557929805291
317074.3902951034268-4.39029510342682
326070.5676741054268-10.5676741054268
337281.2300415947923-9.23004159479225
346955.630239416590813.3697605834092
357170.27213825855210.727861741447867
366269.8748796433748-7.87487964337483
377075.7591676668446-5.75916766684459
386473.4713754906-9.47137549060002
395872.5247900273266-14.5247900273266
407666.06154845747119.93845154252894
415266.3691219312635-14.3691219312635
425970.1835120234484-11.1835120234484
436867.05714108898810.942858911011854
447660.721502329286315.2784976707137
456574.7494360877938-9.7494360877938
466758.47331094563178.52668905436828
475966.80455069365-7.80455069365003
486961.31204456437137.68795543562869
497669.68677430747516.31322569252491
506367.0858895210019-4.0858895210019
517564.504208769654410.4957912303456
526371.5863596317538-8.58635963175378
536059.23480813780160.765191862198442
547366.28613144183956.71386855816047
556370.7060303414797-7.70603034147975
567069.63082021353930.369179786460677
577571.20357035616233.79642964383771
586664.50056732765071.49943267234934
596365.0912185634773-2.09121856347733
606367.0382779636008-4.03827796360082
616473.4607079083262-9.46070790832619
627064.42813864386625.57186135613375
637569.21020029372045.78979970627964
646167.5044422220867-6.50444222208672
656059.35546427846710.644535721532876
666268.890535327025-6.89053532702499
677365.35822242670667.64177757329337
686169.5307018471921-8.53070184719212
696671.4025040008062-5.4025040008062
706462.43393025306021.56606974693979
715961.3076234607026-2.30762346070263
726462.205409298881.79459070112003
736066.8614699885041-6.86146998850413
745664.4524062481278-8.45240624812782
757867.421365550492510.5786344495075
765360.8273315173102-7.82733151731023
776755.370818239232511.6291817607675
785962.8743774440604-3.87437744406042
796665.83101483959840.168985160401633
806862.04343054216465.95656945783541
817166.9495948628444.05040513715596
826662.14213848981723.85786151018282
837359.7066378764913.29336212351
847264.42555967442327.57444032557676
857166.32675561066854.67324438933153
865964.9700529645682-5.9700529645682
876476.7599214064813-12.7599214064813
886659.69679440543566.30320559456441
897864.547991471030313.4520085289697
906865.95417524612442.04582475387555
917371.71518653233581.28481346766415
926270.9167793869938-8.91677938699375
936573.4902299061401-8.49022990614007
946867.25157857218430.748421427815714
956568.5984565218373-3.59845652183728
966068.8306132263219-8.8306132263219
977167.36592105880233.63407894119766
986561.14858100904553.85141899095449
996871.1030127892134-3.10301278921338
1006463.33006184547820.669938154521823
1017470.50715911998233.49284088001774
1026965.699628411913.30037158809003
1037671.14551525973244.85448474026755
1046866.29906296477691.70093703522312
1057270.30190813108781.69809186891216
1066769.3004166589587-2.30041665895874
1076368.4716793061619-5.4716793061619
1085966.2729355210739-7.27293552107393
1097370.37039089340652.62960910659355
1106664.16181682480611.83818317519389
1116270.9191361341714-8.91913613417142
1126964.03616116586054.96383883413947
1136672.9359867551221-6.9359867551221

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 78 & 73.7716346153846 & 4.22836538461536 \tabularnewline
14 & 73 & 69.2844027690283 & 3.7155972309717 \tabularnewline
15 & 75 & 71.8101666167874 & 3.18983338321262 \tabularnewline
16 & 72 & 69.3844789156222 & 2.61552108437778 \tabularnewline
17 & 66 & 63.1632438855411 & 2.8367561144589 \tabularnewline
18 & 70 & 67.826295099747 & 2.17370490025296 \tabularnewline
19 & 61 & 80.5544099457191 & -19.5544099457191 \tabularnewline
20 & 81 & 56.2794744795925 & 24.7205255204075 \tabularnewline
21 & 71 & 90.7746016644141 & -19.7746016644141 \tabularnewline
22 & 69 & 46.2248027993956 & 22.7751972006044 \tabularnewline
23 & 71 & 73.3064040583332 & -2.30640405833319 \tabularnewline
24 & 72 & 72.2194997608083 & -0.219499760808276 \tabularnewline
25 & 68 & 88.1879019310077 & -20.1879019310077 \tabularnewline
26 & 70 & 80.5784462810105 & -10.5784462810105 \tabularnewline
27 & 68 & 81.0555780665149 & -13.0555780665149 \tabularnewline
28 & 61 & 76.1873267178236 & -15.1873267178236 \tabularnewline
29 & 67 & 67.5240424008656 & -0.524042400865611 \tabularnewline
30 & 76 & 71.0544207019471 & 4.94557929805291 \tabularnewline
31 & 70 & 74.3902951034268 & -4.39029510342682 \tabularnewline
32 & 60 & 70.5676741054268 & -10.5676741054268 \tabularnewline
33 & 72 & 81.2300415947923 & -9.23004159479225 \tabularnewline
34 & 69 & 55.6302394165908 & 13.3697605834092 \tabularnewline
35 & 71 & 70.2721382585521 & 0.727861741447867 \tabularnewline
36 & 62 & 69.8748796433748 & -7.87487964337483 \tabularnewline
37 & 70 & 75.7591676668446 & -5.75916766684459 \tabularnewline
38 & 64 & 73.4713754906 & -9.47137549060002 \tabularnewline
39 & 58 & 72.5247900273266 & -14.5247900273266 \tabularnewline
40 & 76 & 66.0615484574711 & 9.93845154252894 \tabularnewline
41 & 52 & 66.3691219312635 & -14.3691219312635 \tabularnewline
42 & 59 & 70.1835120234484 & -11.1835120234484 \tabularnewline
43 & 68 & 67.0571410889881 & 0.942858911011854 \tabularnewline
44 & 76 & 60.7215023292863 & 15.2784976707137 \tabularnewline
45 & 65 & 74.7494360877938 & -9.7494360877938 \tabularnewline
46 & 67 & 58.4733109456317 & 8.52668905436828 \tabularnewline
47 & 59 & 66.80455069365 & -7.80455069365003 \tabularnewline
48 & 69 & 61.3120445643713 & 7.68795543562869 \tabularnewline
49 & 76 & 69.6867743074751 & 6.31322569252491 \tabularnewline
50 & 63 & 67.0858895210019 & -4.0858895210019 \tabularnewline
51 & 75 & 64.5042087696544 & 10.4957912303456 \tabularnewline
52 & 63 & 71.5863596317538 & -8.58635963175378 \tabularnewline
53 & 60 & 59.2348081378016 & 0.765191862198442 \tabularnewline
54 & 73 & 66.2861314418395 & 6.71386855816047 \tabularnewline
55 & 63 & 70.7060303414797 & -7.70603034147975 \tabularnewline
56 & 70 & 69.6308202135393 & 0.369179786460677 \tabularnewline
57 & 75 & 71.2035703561623 & 3.79642964383771 \tabularnewline
58 & 66 & 64.5005673276507 & 1.49943267234934 \tabularnewline
59 & 63 & 65.0912185634773 & -2.09121856347733 \tabularnewline
60 & 63 & 67.0382779636008 & -4.03827796360082 \tabularnewline
61 & 64 & 73.4607079083262 & -9.46070790832619 \tabularnewline
62 & 70 & 64.4281386438662 & 5.57186135613375 \tabularnewline
63 & 75 & 69.2102002937204 & 5.78979970627964 \tabularnewline
64 & 61 & 67.5044422220867 & -6.50444222208672 \tabularnewline
65 & 60 & 59.3554642784671 & 0.644535721532876 \tabularnewline
66 & 62 & 68.890535327025 & -6.89053532702499 \tabularnewline
67 & 73 & 65.3582224267066 & 7.64177757329337 \tabularnewline
68 & 61 & 69.5307018471921 & -8.53070184719212 \tabularnewline
69 & 66 & 71.4025040008062 & -5.4025040008062 \tabularnewline
70 & 64 & 62.4339302530602 & 1.56606974693979 \tabularnewline
71 & 59 & 61.3076234607026 & -2.30762346070263 \tabularnewline
72 & 64 & 62.20540929888 & 1.79459070112003 \tabularnewline
73 & 60 & 66.8614699885041 & -6.86146998850413 \tabularnewline
74 & 56 & 64.4524062481278 & -8.45240624812782 \tabularnewline
75 & 78 & 67.4213655504925 & 10.5786344495075 \tabularnewline
76 & 53 & 60.8273315173102 & -7.82733151731023 \tabularnewline
77 & 67 & 55.3708182392325 & 11.6291817607675 \tabularnewline
78 & 59 & 62.8743774440604 & -3.87437744406042 \tabularnewline
79 & 66 & 65.8310148395984 & 0.168985160401633 \tabularnewline
80 & 68 & 62.0434305421646 & 5.95656945783541 \tabularnewline
81 & 71 & 66.949594862844 & 4.05040513715596 \tabularnewline
82 & 66 & 62.1421384898172 & 3.85786151018282 \tabularnewline
83 & 73 & 59.70663787649 & 13.29336212351 \tabularnewline
84 & 72 & 64.4255596744232 & 7.57444032557676 \tabularnewline
85 & 71 & 66.3267556106685 & 4.67324438933153 \tabularnewline
86 & 59 & 64.9700529645682 & -5.9700529645682 \tabularnewline
87 & 64 & 76.7599214064813 & -12.7599214064813 \tabularnewline
88 & 66 & 59.6967944054356 & 6.30320559456441 \tabularnewline
89 & 78 & 64.5479914710303 & 13.4520085289697 \tabularnewline
90 & 68 & 65.9541752461244 & 2.04582475387555 \tabularnewline
91 & 73 & 71.7151865323358 & 1.28481346766415 \tabularnewline
92 & 62 & 70.9167793869938 & -8.91677938699375 \tabularnewline
93 & 65 & 73.4902299061401 & -8.49022990614007 \tabularnewline
94 & 68 & 67.2515785721843 & 0.748421427815714 \tabularnewline
95 & 65 & 68.5984565218373 & -3.59845652183728 \tabularnewline
96 & 60 & 68.8306132263219 & -8.8306132263219 \tabularnewline
97 & 71 & 67.3659210588023 & 3.63407894119766 \tabularnewline
98 & 65 & 61.1485810090455 & 3.85141899095449 \tabularnewline
99 & 68 & 71.1030127892134 & -3.10301278921338 \tabularnewline
100 & 64 & 63.3300618454782 & 0.669938154521823 \tabularnewline
101 & 74 & 70.5071591199823 & 3.49284088001774 \tabularnewline
102 & 69 & 65.69962841191 & 3.30037158809003 \tabularnewline
103 & 76 & 71.1455152597324 & 4.85448474026755 \tabularnewline
104 & 68 & 66.2990629647769 & 1.70093703522312 \tabularnewline
105 & 72 & 70.3019081310878 & 1.69809186891216 \tabularnewline
106 & 67 & 69.3004166589587 & -2.30041665895874 \tabularnewline
107 & 63 & 68.4716793061619 & -5.4716793061619 \tabularnewline
108 & 59 & 66.2729355210739 & -7.27293552107393 \tabularnewline
109 & 73 & 70.3703908934065 & 2.62960910659355 \tabularnewline
110 & 66 & 64.1618168248061 & 1.83818317519389 \tabularnewline
111 & 62 & 70.9191361341714 & -8.91913613417142 \tabularnewline
112 & 69 & 64.0361611658605 & 4.96383883413947 \tabularnewline
113 & 66 & 72.9359867551221 & -6.9359867551221 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267957&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]78[/C][C]73.7716346153846[/C][C]4.22836538461536[/C][/ROW]
[ROW][C]14[/C][C]73[/C][C]69.2844027690283[/C][C]3.7155972309717[/C][/ROW]
[ROW][C]15[/C][C]75[/C][C]71.8101666167874[/C][C]3.18983338321262[/C][/ROW]
[ROW][C]16[/C][C]72[/C][C]69.3844789156222[/C][C]2.61552108437778[/C][/ROW]
[ROW][C]17[/C][C]66[/C][C]63.1632438855411[/C][C]2.8367561144589[/C][/ROW]
[ROW][C]18[/C][C]70[/C][C]67.826295099747[/C][C]2.17370490025296[/C][/ROW]
[ROW][C]19[/C][C]61[/C][C]80.5544099457191[/C][C]-19.5544099457191[/C][/ROW]
[ROW][C]20[/C][C]81[/C][C]56.2794744795925[/C][C]24.7205255204075[/C][/ROW]
[ROW][C]21[/C][C]71[/C][C]90.7746016644141[/C][C]-19.7746016644141[/C][/ROW]
[ROW][C]22[/C][C]69[/C][C]46.2248027993956[/C][C]22.7751972006044[/C][/ROW]
[ROW][C]23[/C][C]71[/C][C]73.3064040583332[/C][C]-2.30640405833319[/C][/ROW]
[ROW][C]24[/C][C]72[/C][C]72.2194997608083[/C][C]-0.219499760808276[/C][/ROW]
[ROW][C]25[/C][C]68[/C][C]88.1879019310077[/C][C]-20.1879019310077[/C][/ROW]
[ROW][C]26[/C][C]70[/C][C]80.5784462810105[/C][C]-10.5784462810105[/C][/ROW]
[ROW][C]27[/C][C]68[/C][C]81.0555780665149[/C][C]-13.0555780665149[/C][/ROW]
[ROW][C]28[/C][C]61[/C][C]76.1873267178236[/C][C]-15.1873267178236[/C][/ROW]
[ROW][C]29[/C][C]67[/C][C]67.5240424008656[/C][C]-0.524042400865611[/C][/ROW]
[ROW][C]30[/C][C]76[/C][C]71.0544207019471[/C][C]4.94557929805291[/C][/ROW]
[ROW][C]31[/C][C]70[/C][C]74.3902951034268[/C][C]-4.39029510342682[/C][/ROW]
[ROW][C]32[/C][C]60[/C][C]70.5676741054268[/C][C]-10.5676741054268[/C][/ROW]
[ROW][C]33[/C][C]72[/C][C]81.2300415947923[/C][C]-9.23004159479225[/C][/ROW]
[ROW][C]34[/C][C]69[/C][C]55.6302394165908[/C][C]13.3697605834092[/C][/ROW]
[ROW][C]35[/C][C]71[/C][C]70.2721382585521[/C][C]0.727861741447867[/C][/ROW]
[ROW][C]36[/C][C]62[/C][C]69.8748796433748[/C][C]-7.87487964337483[/C][/ROW]
[ROW][C]37[/C][C]70[/C][C]75.7591676668446[/C][C]-5.75916766684459[/C][/ROW]
[ROW][C]38[/C][C]64[/C][C]73.4713754906[/C][C]-9.47137549060002[/C][/ROW]
[ROW][C]39[/C][C]58[/C][C]72.5247900273266[/C][C]-14.5247900273266[/C][/ROW]
[ROW][C]40[/C][C]76[/C][C]66.0615484574711[/C][C]9.93845154252894[/C][/ROW]
[ROW][C]41[/C][C]52[/C][C]66.3691219312635[/C][C]-14.3691219312635[/C][/ROW]
[ROW][C]42[/C][C]59[/C][C]70.1835120234484[/C][C]-11.1835120234484[/C][/ROW]
[ROW][C]43[/C][C]68[/C][C]67.0571410889881[/C][C]0.942858911011854[/C][/ROW]
[ROW][C]44[/C][C]76[/C][C]60.7215023292863[/C][C]15.2784976707137[/C][/ROW]
[ROW][C]45[/C][C]65[/C][C]74.7494360877938[/C][C]-9.7494360877938[/C][/ROW]
[ROW][C]46[/C][C]67[/C][C]58.4733109456317[/C][C]8.52668905436828[/C][/ROW]
[ROW][C]47[/C][C]59[/C][C]66.80455069365[/C][C]-7.80455069365003[/C][/ROW]
[ROW][C]48[/C][C]69[/C][C]61.3120445643713[/C][C]7.68795543562869[/C][/ROW]
[ROW][C]49[/C][C]76[/C][C]69.6867743074751[/C][C]6.31322569252491[/C][/ROW]
[ROW][C]50[/C][C]63[/C][C]67.0858895210019[/C][C]-4.0858895210019[/C][/ROW]
[ROW][C]51[/C][C]75[/C][C]64.5042087696544[/C][C]10.4957912303456[/C][/ROW]
[ROW][C]52[/C][C]63[/C][C]71.5863596317538[/C][C]-8.58635963175378[/C][/ROW]
[ROW][C]53[/C][C]60[/C][C]59.2348081378016[/C][C]0.765191862198442[/C][/ROW]
[ROW][C]54[/C][C]73[/C][C]66.2861314418395[/C][C]6.71386855816047[/C][/ROW]
[ROW][C]55[/C][C]63[/C][C]70.7060303414797[/C][C]-7.70603034147975[/C][/ROW]
[ROW][C]56[/C][C]70[/C][C]69.6308202135393[/C][C]0.369179786460677[/C][/ROW]
[ROW][C]57[/C][C]75[/C][C]71.2035703561623[/C][C]3.79642964383771[/C][/ROW]
[ROW][C]58[/C][C]66[/C][C]64.5005673276507[/C][C]1.49943267234934[/C][/ROW]
[ROW][C]59[/C][C]63[/C][C]65.0912185634773[/C][C]-2.09121856347733[/C][/ROW]
[ROW][C]60[/C][C]63[/C][C]67.0382779636008[/C][C]-4.03827796360082[/C][/ROW]
[ROW][C]61[/C][C]64[/C][C]73.4607079083262[/C][C]-9.46070790832619[/C][/ROW]
[ROW][C]62[/C][C]70[/C][C]64.4281386438662[/C][C]5.57186135613375[/C][/ROW]
[ROW][C]63[/C][C]75[/C][C]69.2102002937204[/C][C]5.78979970627964[/C][/ROW]
[ROW][C]64[/C][C]61[/C][C]67.5044422220867[/C][C]-6.50444222208672[/C][/ROW]
[ROW][C]65[/C][C]60[/C][C]59.3554642784671[/C][C]0.644535721532876[/C][/ROW]
[ROW][C]66[/C][C]62[/C][C]68.890535327025[/C][C]-6.89053532702499[/C][/ROW]
[ROW][C]67[/C][C]73[/C][C]65.3582224267066[/C][C]7.64177757329337[/C][/ROW]
[ROW][C]68[/C][C]61[/C][C]69.5307018471921[/C][C]-8.53070184719212[/C][/ROW]
[ROW][C]69[/C][C]66[/C][C]71.4025040008062[/C][C]-5.4025040008062[/C][/ROW]
[ROW][C]70[/C][C]64[/C][C]62.4339302530602[/C][C]1.56606974693979[/C][/ROW]
[ROW][C]71[/C][C]59[/C][C]61.3076234607026[/C][C]-2.30762346070263[/C][/ROW]
[ROW][C]72[/C][C]64[/C][C]62.20540929888[/C][C]1.79459070112003[/C][/ROW]
[ROW][C]73[/C][C]60[/C][C]66.8614699885041[/C][C]-6.86146998850413[/C][/ROW]
[ROW][C]74[/C][C]56[/C][C]64.4524062481278[/C][C]-8.45240624812782[/C][/ROW]
[ROW][C]75[/C][C]78[/C][C]67.4213655504925[/C][C]10.5786344495075[/C][/ROW]
[ROW][C]76[/C][C]53[/C][C]60.8273315173102[/C][C]-7.82733151731023[/C][/ROW]
[ROW][C]77[/C][C]67[/C][C]55.3708182392325[/C][C]11.6291817607675[/C][/ROW]
[ROW][C]78[/C][C]59[/C][C]62.8743774440604[/C][C]-3.87437744406042[/C][/ROW]
[ROW][C]79[/C][C]66[/C][C]65.8310148395984[/C][C]0.168985160401633[/C][/ROW]
[ROW][C]80[/C][C]68[/C][C]62.0434305421646[/C][C]5.95656945783541[/C][/ROW]
[ROW][C]81[/C][C]71[/C][C]66.949594862844[/C][C]4.05040513715596[/C][/ROW]
[ROW][C]82[/C][C]66[/C][C]62.1421384898172[/C][C]3.85786151018282[/C][/ROW]
[ROW][C]83[/C][C]73[/C][C]59.70663787649[/C][C]13.29336212351[/C][/ROW]
[ROW][C]84[/C][C]72[/C][C]64.4255596744232[/C][C]7.57444032557676[/C][/ROW]
[ROW][C]85[/C][C]71[/C][C]66.3267556106685[/C][C]4.67324438933153[/C][/ROW]
[ROW][C]86[/C][C]59[/C][C]64.9700529645682[/C][C]-5.9700529645682[/C][/ROW]
[ROW][C]87[/C][C]64[/C][C]76.7599214064813[/C][C]-12.7599214064813[/C][/ROW]
[ROW][C]88[/C][C]66[/C][C]59.6967944054356[/C][C]6.30320559456441[/C][/ROW]
[ROW][C]89[/C][C]78[/C][C]64.5479914710303[/C][C]13.4520085289697[/C][/ROW]
[ROW][C]90[/C][C]68[/C][C]65.9541752461244[/C][C]2.04582475387555[/C][/ROW]
[ROW][C]91[/C][C]73[/C][C]71.7151865323358[/C][C]1.28481346766415[/C][/ROW]
[ROW][C]92[/C][C]62[/C][C]70.9167793869938[/C][C]-8.91677938699375[/C][/ROW]
[ROW][C]93[/C][C]65[/C][C]73.4902299061401[/C][C]-8.49022990614007[/C][/ROW]
[ROW][C]94[/C][C]68[/C][C]67.2515785721843[/C][C]0.748421427815714[/C][/ROW]
[ROW][C]95[/C][C]65[/C][C]68.5984565218373[/C][C]-3.59845652183728[/C][/ROW]
[ROW][C]96[/C][C]60[/C][C]68.8306132263219[/C][C]-8.8306132263219[/C][/ROW]
[ROW][C]97[/C][C]71[/C][C]67.3659210588023[/C][C]3.63407894119766[/C][/ROW]
[ROW][C]98[/C][C]65[/C][C]61.1485810090455[/C][C]3.85141899095449[/C][/ROW]
[ROW][C]99[/C][C]68[/C][C]71.1030127892134[/C][C]-3.10301278921338[/C][/ROW]
[ROW][C]100[/C][C]64[/C][C]63.3300618454782[/C][C]0.669938154521823[/C][/ROW]
[ROW][C]101[/C][C]74[/C][C]70.5071591199823[/C][C]3.49284088001774[/C][/ROW]
[ROW][C]102[/C][C]69[/C][C]65.69962841191[/C][C]3.30037158809003[/C][/ROW]
[ROW][C]103[/C][C]76[/C][C]71.1455152597324[/C][C]4.85448474026755[/C][/ROW]
[ROW][C]104[/C][C]68[/C][C]66.2990629647769[/C][C]1.70093703522312[/C][/ROW]
[ROW][C]105[/C][C]72[/C][C]70.3019081310878[/C][C]1.69809186891216[/C][/ROW]
[ROW][C]106[/C][C]67[/C][C]69.3004166589587[/C][C]-2.30041665895874[/C][/ROW]
[ROW][C]107[/C][C]63[/C][C]68.4716793061619[/C][C]-5.4716793061619[/C][/ROW]
[ROW][C]108[/C][C]59[/C][C]66.2729355210739[/C][C]-7.27293552107393[/C][/ROW]
[ROW][C]109[/C][C]73[/C][C]70.3703908934065[/C][C]2.62960910659355[/C][/ROW]
[ROW][C]110[/C][C]66[/C][C]64.1618168248061[/C][C]1.83818317519389[/C][/ROW]
[ROW][C]111[/C][C]62[/C][C]70.9191361341714[/C][C]-8.91913613417142[/C][/ROW]
[ROW][C]112[/C][C]69[/C][C]64.0361611658605[/C][C]4.96383883413947[/C][/ROW]
[ROW][C]113[/C][C]66[/C][C]72.9359867551221[/C][C]-6.9359867551221[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267957&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267957&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
137873.77163461538464.22836538461536
147369.28440276902833.7155972309717
157571.81016661678743.18983338321262
167269.38447891562222.61552108437778
176663.16324388554112.8367561144589
187067.8262950997472.17370490025296
196180.5544099457191-19.5544099457191
208156.279474479592524.7205255204075
217190.7746016644141-19.7746016644141
226946.224802799395622.7751972006044
237173.3064040583332-2.30640405833319
247272.2194997608083-0.219499760808276
256888.1879019310077-20.1879019310077
267080.5784462810105-10.5784462810105
276881.0555780665149-13.0555780665149
286176.1873267178236-15.1873267178236
296767.5240424008656-0.524042400865611
307671.05442070194714.94557929805291
317074.3902951034268-4.39029510342682
326070.5676741054268-10.5676741054268
337281.2300415947923-9.23004159479225
346955.630239416590813.3697605834092
357170.27213825855210.727861741447867
366269.8748796433748-7.87487964337483
377075.7591676668446-5.75916766684459
386473.4713754906-9.47137549060002
395872.5247900273266-14.5247900273266
407666.06154845747119.93845154252894
415266.3691219312635-14.3691219312635
425970.1835120234484-11.1835120234484
436867.05714108898810.942858911011854
447660.721502329286315.2784976707137
456574.7494360877938-9.7494360877938
466758.47331094563178.52668905436828
475966.80455069365-7.80455069365003
486961.31204456437137.68795543562869
497669.68677430747516.31322569252491
506367.0858895210019-4.0858895210019
517564.504208769654410.4957912303456
526371.5863596317538-8.58635963175378
536059.23480813780160.765191862198442
547366.28613144183956.71386855816047
556370.7060303414797-7.70603034147975
567069.63082021353930.369179786460677
577571.20357035616233.79642964383771
586664.50056732765071.49943267234934
596365.0912185634773-2.09121856347733
606367.0382779636008-4.03827796360082
616473.4607079083262-9.46070790832619
627064.42813864386625.57186135613375
637569.21020029372045.78979970627964
646167.5044422220867-6.50444222208672
656059.35546427846710.644535721532876
666268.890535327025-6.89053532702499
677365.35822242670667.64177757329337
686169.5307018471921-8.53070184719212
696671.4025040008062-5.4025040008062
706462.43393025306021.56606974693979
715961.3076234607026-2.30762346070263
726462.205409298881.79459070112003
736066.8614699885041-6.86146998850413
745664.4524062481278-8.45240624812782
757867.421365550492510.5786344495075
765360.8273315173102-7.82733151731023
776755.370818239232511.6291817607675
785962.8743774440604-3.87437744406042
796665.83101483959840.168985160401633
806862.04343054216465.95656945783541
817166.9495948628444.05040513715596
826662.14213848981723.85786151018282
837359.7066378764913.29336212351
847264.42555967442327.57444032557676
857166.32675561066854.67324438933153
865964.9700529645682-5.9700529645682
876476.7599214064813-12.7599214064813
886659.69679440543566.30320559456441
897864.547991471030313.4520085289697
906865.95417524612442.04582475387555
917371.71518653233581.28481346766415
926270.9167793869938-8.91677938699375
936573.4902299061401-8.49022990614007
946867.25157857218430.748421427815714
956568.5984565218373-3.59845652183728
966068.8306132263219-8.8306132263219
977167.36592105880233.63407894119766
986561.14858100904553.85141899095449
996871.1030127892134-3.10301278921338
1006463.33006184547820.669938154521823
1017470.50715911998233.49284088001774
1026965.699628411913.30037158809003
1037671.14551525973244.85448474026755
1046866.29906296477691.70093703522312
1057270.30190813108781.69809186891216
1066769.3004166589587-2.30041665895874
1076368.4716793061619-5.4716793061619
1085966.2729355210739-7.27293552107393
1097370.37039089340652.62960910659355
1106664.16181682480611.83818317519389
1116270.9191361341714-8.91913613417142
1126964.03616116586054.96383883413947
1136672.9359867551221-6.9359867551221







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
11466.720129974313150.130841576810983.3094183718152
11572.323747069542655.600007387549289.0474867515361
11665.393897882179248.518074055038882.2697217093197
11769.021505163866751.975217070463186.0677932572702
11865.92080470083248.685011761312483.1565976403517
11963.842145908179346.397236711976881.2870551043817
12061.404201859879943.730085216053279.0783185037065
12170.54729484105152.623490818786788.4710988633152
12263.608817428196545.41454698726981.8030878691239
12365.450419164993546.964691063730783.9361472662563
12465.550506251674346.752200055524984.3488124478237
12568.70857265441949.576516840792187.8406284680459

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
114 & 66.7201299743131 & 50.1308415768109 & 83.3094183718152 \tabularnewline
115 & 72.3237470695426 & 55.6000073875492 & 89.0474867515361 \tabularnewline
116 & 65.3938978821792 & 48.5180740550388 & 82.2697217093197 \tabularnewline
117 & 69.0215051638667 & 51.9752170704631 & 86.0677932572702 \tabularnewline
118 & 65.920804700832 & 48.6850117613124 & 83.1565976403517 \tabularnewline
119 & 63.8421459081793 & 46.3972367119768 & 81.2870551043817 \tabularnewline
120 & 61.4042018598799 & 43.7300852160532 & 79.0783185037065 \tabularnewline
121 & 70.547294841051 & 52.6234908187867 & 88.4710988633152 \tabularnewline
122 & 63.6088174281965 & 45.414546987269 & 81.8030878691239 \tabularnewline
123 & 65.4504191649935 & 46.9646910637307 & 83.9361472662563 \tabularnewline
124 & 65.5505062516743 & 46.7522000555249 & 84.3488124478237 \tabularnewline
125 & 68.708572654419 & 49.5765168407921 & 87.8406284680459 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267957&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]66.7201299743131[/C][C]50.1308415768109[/C][C]83.3094183718152[/C][/ROW]
[ROW][C]115[/C][C]72.3237470695426[/C][C]55.6000073875492[/C][C]89.0474867515361[/C][/ROW]
[ROW][C]116[/C][C]65.3938978821792[/C][C]48.5180740550388[/C][C]82.2697217093197[/C][/ROW]
[ROW][C]117[/C][C]69.0215051638667[/C][C]51.9752170704631[/C][C]86.0677932572702[/C][/ROW]
[ROW][C]118[/C][C]65.920804700832[/C][C]48.6850117613124[/C][C]83.1565976403517[/C][/ROW]
[ROW][C]119[/C][C]63.8421459081793[/C][C]46.3972367119768[/C][C]81.2870551043817[/C][/ROW]
[ROW][C]120[/C][C]61.4042018598799[/C][C]43.7300852160532[/C][C]79.0783185037065[/C][/ROW]
[ROW][C]121[/C][C]70.547294841051[/C][C]52.6234908187867[/C][C]88.4710988633152[/C][/ROW]
[ROW][C]122[/C][C]63.6088174281965[/C][C]45.414546987269[/C][C]81.8030878691239[/C][/ROW]
[ROW][C]123[/C][C]65.4504191649935[/C][C]46.9646910637307[/C][C]83.9361472662563[/C][/ROW]
[ROW][C]124[/C][C]65.5505062516743[/C][C]46.7522000555249[/C][C]84.3488124478237[/C][/ROW]
[ROW][C]125[/C][C]68.708572654419[/C][C]49.5765168407921[/C][C]87.8406284680459[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267957&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267957&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
11466.720129974313150.130841576810983.3094183718152
11572.323747069542655.600007387549289.0474867515361
11665.393897882179248.518074055038882.2697217093197
11769.021505163866751.975217070463186.0677932572702
11865.92080470083248.685011761312483.1565976403517
11963.842145908179346.397236711976881.2870551043817
12061.404201859879943.730085216053279.0783185037065
12170.54729484105152.623490818786788.4710988633152
12263.608817428196545.41454698726981.8030878691239
12365.450419164993546.964691063730783.9361472662563
12465.550506251674346.752200055524984.3488124478237
12568.70857265441949.576516840792187.8406284680459



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=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')