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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 06 Jun 2009 03:02:15 -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/06/t124427896164cki81k0vc1118.htm/, Retrieved Mon, 29 Apr 2024 06:40:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41932, Retrieved Mon, 29 Apr 2024 06:40:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Quartiles] [k
- RMPD  [Classical Decomposition] [] [2009-06-04 15:14:57] [74be16979710d4c4e7c6647856088456]
- RMPD      [Exponential Smoothing] [] [2009-06-06 09:02:15] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
1,73
1,75
1,75
1,75
1,73
1,74
1,75
1,75
1,34
1,24
1,24
1,26
1,25
1,26
1,26
1,22
1,01
1,03
1,01
1,01
1
0,98
1
1,01
1
1
1
1,03
1,26
1,43
1,61
1,76
1,93
2,16
2,28
2,5
2,63
2,79
3
3,04
3,26
3,5
3,62
3,78
4
4,16
4,29
4,49
4,59
4,79
4,94
4,99
5,24
5,25
5,25
5,25
5,25
5,24
5,25
5,26
5,26
5,25
5,25
5,25
5,26
5,02
4,94
4,76
4,49
4,24
3,94
2,98
2,61
2,28
1,98
2
2,01
2
1,81
0,97
0,39
0,16
0,15
0,22




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=41932&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=41932&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41932&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
alpha0.932952155499902
beta0.189496457771257
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.932952155499902 \tabularnewline
beta & 0.189496457771257 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41932&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]0.932952155499902[/C][/ROW]
[ROW][C]beta[/C][C]0.189496457771257[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41932&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41932&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
alpha0.932952155499902
beta0.189496457771257
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131.251.55613514957265-0.306135149572649
141.261.241740261726990.0182597382730081
151.261.206551776803160.0534482231968443
161.221.153641636445760.066358363554239
171.010.950340942689850.0596590573101498
181.030.980920642147760.0490793578522398
191.011.22114011659760-0.211140116597604
201.010.9704262385880680.0395737614119325
2110.551029370096330.44897062990367
220.980.9046208836160970.0753791163839029
2311.03257908172319-0.0325790817231904
241.011.08155775357132-0.0715577535713181
2511.03182804490521-0.0318280449052057
2611.07706301749370-0.0770630174936968
2711.02041453445696-0.0204145344569628
281.030.9515135522036460.0784864477963538
291.260.813276724427980.44672327557202
301.431.32688711231420.103112887685801
311.611.73225041648978-0.122250416489781
321.761.729171397776620.0308286022233808
331.931.475414022055500.454585977944496
342.161.956537754955510.203462245044488
352.282.36673885446528-0.0867388544652825
362.52.52298648122298-0.0229864812229752
372.632.69023307474055-0.0602330747405508
382.792.86991068644488-0.0799106864448795
3932.977876260931490.0221237390685056
403.043.12628557745283-0.0862855774528297
413.263.000876613913430.259123386086571
423.53.425123743254580.0748762567454193
433.623.89273831067774-0.272738310677737
443.783.83662479299525-0.0566247929952528
4543.59132850592670.4086714940733
464.164.066300547302120.0936994526978783
474.294.38875739711791-0.0987573971179065
484.494.57005852830135-0.080058528301354
494.594.70346426753753-0.113464267537532
504.794.84465151794328-0.0546515179432818
514.944.99998060954632-0.0599806095463196
524.995.06696329871044-0.0769632987104432
535.244.977500010530910.262499989469089
545.255.39723043875835-0.147230438758349
555.255.59974324735948-0.349743247359479
565.255.438083932831-0.188083932830997
575.255.02990504056740.220094959432600
585.245.203052712181590.0369472878184061
595.255.34485212237757-0.094852122377568
605.265.41693425669915-0.156934256699154
615.265.34867173961789-0.0886717396178938
625.255.39360850247778-0.143608502477775
635.255.32653687580434-0.0765368758043357
645.255.234956903271190.0150430967288102
655.265.128379571594040.131620428405959
665.025.24968385364721-0.229683853647209
674.945.19826625598185-0.258266255981847
684.764.98553455906218-0.225534559062178
694.494.415907653486670.0740923465133312
704.244.26087436358426-0.0208743635842579
713.944.14998186561459-0.209981865614586
722.983.90022685977977-0.920226859779767
732.612.77921823239927-0.169218232399271
742.282.38587818868410-0.105878188684096
751.982.00572714136778-0.0257271413677773
7621.623896163937250.376103836062746
772.011.582025525826110.427974474173886
7821.728020086337940.271979913662062
791.812.00383490291067-0.193834902910672
800.971.72592056673923-0.75592056673923
810.390.460302090557214-0.0703020905572139
820.16-0.08259540904704050.242595409047040
830.15-0.1605671418129350.310567141812935
840.22-0.08047145515621550.300471455156215

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.25 & 1.55613514957265 & -0.306135149572649 \tabularnewline
14 & 1.26 & 1.24174026172699 & 0.0182597382730081 \tabularnewline
15 & 1.26 & 1.20655177680316 & 0.0534482231968443 \tabularnewline
16 & 1.22 & 1.15364163644576 & 0.066358363554239 \tabularnewline
17 & 1.01 & 0.95034094268985 & 0.0596590573101498 \tabularnewline
18 & 1.03 & 0.98092064214776 & 0.0490793578522398 \tabularnewline
19 & 1.01 & 1.22114011659760 & -0.211140116597604 \tabularnewline
20 & 1.01 & 0.970426238588068 & 0.0395737614119325 \tabularnewline
21 & 1 & 0.55102937009633 & 0.44897062990367 \tabularnewline
22 & 0.98 & 0.904620883616097 & 0.0753791163839029 \tabularnewline
23 & 1 & 1.03257908172319 & -0.0325790817231904 \tabularnewline
24 & 1.01 & 1.08155775357132 & -0.0715577535713181 \tabularnewline
25 & 1 & 1.03182804490521 & -0.0318280449052057 \tabularnewline
26 & 1 & 1.07706301749370 & -0.0770630174936968 \tabularnewline
27 & 1 & 1.02041453445696 & -0.0204145344569628 \tabularnewline
28 & 1.03 & 0.951513552203646 & 0.0784864477963538 \tabularnewline
29 & 1.26 & 0.81327672442798 & 0.44672327557202 \tabularnewline
30 & 1.43 & 1.3268871123142 & 0.103112887685801 \tabularnewline
31 & 1.61 & 1.73225041648978 & -0.122250416489781 \tabularnewline
32 & 1.76 & 1.72917139777662 & 0.0308286022233808 \tabularnewline
33 & 1.93 & 1.47541402205550 & 0.454585977944496 \tabularnewline
34 & 2.16 & 1.95653775495551 & 0.203462245044488 \tabularnewline
35 & 2.28 & 2.36673885446528 & -0.0867388544652825 \tabularnewline
36 & 2.5 & 2.52298648122298 & -0.0229864812229752 \tabularnewline
37 & 2.63 & 2.69023307474055 & -0.0602330747405508 \tabularnewline
38 & 2.79 & 2.86991068644488 & -0.0799106864448795 \tabularnewline
39 & 3 & 2.97787626093149 & 0.0221237390685056 \tabularnewline
40 & 3.04 & 3.12628557745283 & -0.0862855774528297 \tabularnewline
41 & 3.26 & 3.00087661391343 & 0.259123386086571 \tabularnewline
42 & 3.5 & 3.42512374325458 & 0.0748762567454193 \tabularnewline
43 & 3.62 & 3.89273831067774 & -0.272738310677737 \tabularnewline
44 & 3.78 & 3.83662479299525 & -0.0566247929952528 \tabularnewline
45 & 4 & 3.5913285059267 & 0.4086714940733 \tabularnewline
46 & 4.16 & 4.06630054730212 & 0.0936994526978783 \tabularnewline
47 & 4.29 & 4.38875739711791 & -0.0987573971179065 \tabularnewline
48 & 4.49 & 4.57005852830135 & -0.080058528301354 \tabularnewline
49 & 4.59 & 4.70346426753753 & -0.113464267537532 \tabularnewline
50 & 4.79 & 4.84465151794328 & -0.0546515179432818 \tabularnewline
51 & 4.94 & 4.99998060954632 & -0.0599806095463196 \tabularnewline
52 & 4.99 & 5.06696329871044 & -0.0769632987104432 \tabularnewline
53 & 5.24 & 4.97750001053091 & 0.262499989469089 \tabularnewline
54 & 5.25 & 5.39723043875835 & -0.147230438758349 \tabularnewline
55 & 5.25 & 5.59974324735948 & -0.349743247359479 \tabularnewline
56 & 5.25 & 5.438083932831 & -0.188083932830997 \tabularnewline
57 & 5.25 & 5.0299050405674 & 0.220094959432600 \tabularnewline
58 & 5.24 & 5.20305271218159 & 0.0369472878184061 \tabularnewline
59 & 5.25 & 5.34485212237757 & -0.094852122377568 \tabularnewline
60 & 5.26 & 5.41693425669915 & -0.156934256699154 \tabularnewline
61 & 5.26 & 5.34867173961789 & -0.0886717396178938 \tabularnewline
62 & 5.25 & 5.39360850247778 & -0.143608502477775 \tabularnewline
63 & 5.25 & 5.32653687580434 & -0.0765368758043357 \tabularnewline
64 & 5.25 & 5.23495690327119 & 0.0150430967288102 \tabularnewline
65 & 5.26 & 5.12837957159404 & 0.131620428405959 \tabularnewline
66 & 5.02 & 5.24968385364721 & -0.229683853647209 \tabularnewline
67 & 4.94 & 5.19826625598185 & -0.258266255981847 \tabularnewline
68 & 4.76 & 4.98553455906218 & -0.225534559062178 \tabularnewline
69 & 4.49 & 4.41590765348667 & 0.0740923465133312 \tabularnewline
70 & 4.24 & 4.26087436358426 & -0.0208743635842579 \tabularnewline
71 & 3.94 & 4.14998186561459 & -0.209981865614586 \tabularnewline
72 & 2.98 & 3.90022685977977 & -0.920226859779767 \tabularnewline
73 & 2.61 & 2.77921823239927 & -0.169218232399271 \tabularnewline
74 & 2.28 & 2.38587818868410 & -0.105878188684096 \tabularnewline
75 & 1.98 & 2.00572714136778 & -0.0257271413677773 \tabularnewline
76 & 2 & 1.62389616393725 & 0.376103836062746 \tabularnewline
77 & 2.01 & 1.58202552582611 & 0.427974474173886 \tabularnewline
78 & 2 & 1.72802008633794 & 0.271979913662062 \tabularnewline
79 & 1.81 & 2.00383490291067 & -0.193834902910672 \tabularnewline
80 & 0.97 & 1.72592056673923 & -0.75592056673923 \tabularnewline
81 & 0.39 & 0.460302090557214 & -0.0703020905572139 \tabularnewline
82 & 0.16 & -0.0825954090470405 & 0.242595409047040 \tabularnewline
83 & 0.15 & -0.160567141812935 & 0.310567141812935 \tabularnewline
84 & 0.22 & -0.0804714551562155 & 0.300471455156215 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41932&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]1.25[/C][C]1.55613514957265[/C][C]-0.306135149572649[/C][/ROW]
[ROW][C]14[/C][C]1.26[/C][C]1.24174026172699[/C][C]0.0182597382730081[/C][/ROW]
[ROW][C]15[/C][C]1.26[/C][C]1.20655177680316[/C][C]0.0534482231968443[/C][/ROW]
[ROW][C]16[/C][C]1.22[/C][C]1.15364163644576[/C][C]0.066358363554239[/C][/ROW]
[ROW][C]17[/C][C]1.01[/C][C]0.95034094268985[/C][C]0.0596590573101498[/C][/ROW]
[ROW][C]18[/C][C]1.03[/C][C]0.98092064214776[/C][C]0.0490793578522398[/C][/ROW]
[ROW][C]19[/C][C]1.01[/C][C]1.22114011659760[/C][C]-0.211140116597604[/C][/ROW]
[ROW][C]20[/C][C]1.01[/C][C]0.970426238588068[/C][C]0.0395737614119325[/C][/ROW]
[ROW][C]21[/C][C]1[/C][C]0.55102937009633[/C][C]0.44897062990367[/C][/ROW]
[ROW][C]22[/C][C]0.98[/C][C]0.904620883616097[/C][C]0.0753791163839029[/C][/ROW]
[ROW][C]23[/C][C]1[/C][C]1.03257908172319[/C][C]-0.0325790817231904[/C][/ROW]
[ROW][C]24[/C][C]1.01[/C][C]1.08155775357132[/C][C]-0.0715577535713181[/C][/ROW]
[ROW][C]25[/C][C]1[/C][C]1.03182804490521[/C][C]-0.0318280449052057[/C][/ROW]
[ROW][C]26[/C][C]1[/C][C]1.07706301749370[/C][C]-0.0770630174936968[/C][/ROW]
[ROW][C]27[/C][C]1[/C][C]1.02041453445696[/C][C]-0.0204145344569628[/C][/ROW]
[ROW][C]28[/C][C]1.03[/C][C]0.951513552203646[/C][C]0.0784864477963538[/C][/ROW]
[ROW][C]29[/C][C]1.26[/C][C]0.81327672442798[/C][C]0.44672327557202[/C][/ROW]
[ROW][C]30[/C][C]1.43[/C][C]1.3268871123142[/C][C]0.103112887685801[/C][/ROW]
[ROW][C]31[/C][C]1.61[/C][C]1.73225041648978[/C][C]-0.122250416489781[/C][/ROW]
[ROW][C]32[/C][C]1.76[/C][C]1.72917139777662[/C][C]0.0308286022233808[/C][/ROW]
[ROW][C]33[/C][C]1.93[/C][C]1.47541402205550[/C][C]0.454585977944496[/C][/ROW]
[ROW][C]34[/C][C]2.16[/C][C]1.95653775495551[/C][C]0.203462245044488[/C][/ROW]
[ROW][C]35[/C][C]2.28[/C][C]2.36673885446528[/C][C]-0.0867388544652825[/C][/ROW]
[ROW][C]36[/C][C]2.5[/C][C]2.52298648122298[/C][C]-0.0229864812229752[/C][/ROW]
[ROW][C]37[/C][C]2.63[/C][C]2.69023307474055[/C][C]-0.0602330747405508[/C][/ROW]
[ROW][C]38[/C][C]2.79[/C][C]2.86991068644488[/C][C]-0.0799106864448795[/C][/ROW]
[ROW][C]39[/C][C]3[/C][C]2.97787626093149[/C][C]0.0221237390685056[/C][/ROW]
[ROW][C]40[/C][C]3.04[/C][C]3.12628557745283[/C][C]-0.0862855774528297[/C][/ROW]
[ROW][C]41[/C][C]3.26[/C][C]3.00087661391343[/C][C]0.259123386086571[/C][/ROW]
[ROW][C]42[/C][C]3.5[/C][C]3.42512374325458[/C][C]0.0748762567454193[/C][/ROW]
[ROW][C]43[/C][C]3.62[/C][C]3.89273831067774[/C][C]-0.272738310677737[/C][/ROW]
[ROW][C]44[/C][C]3.78[/C][C]3.83662479299525[/C][C]-0.0566247929952528[/C][/ROW]
[ROW][C]45[/C][C]4[/C][C]3.5913285059267[/C][C]0.4086714940733[/C][/ROW]
[ROW][C]46[/C][C]4.16[/C][C]4.06630054730212[/C][C]0.0936994526978783[/C][/ROW]
[ROW][C]47[/C][C]4.29[/C][C]4.38875739711791[/C][C]-0.0987573971179065[/C][/ROW]
[ROW][C]48[/C][C]4.49[/C][C]4.57005852830135[/C][C]-0.080058528301354[/C][/ROW]
[ROW][C]49[/C][C]4.59[/C][C]4.70346426753753[/C][C]-0.113464267537532[/C][/ROW]
[ROW][C]50[/C][C]4.79[/C][C]4.84465151794328[/C][C]-0.0546515179432818[/C][/ROW]
[ROW][C]51[/C][C]4.94[/C][C]4.99998060954632[/C][C]-0.0599806095463196[/C][/ROW]
[ROW][C]52[/C][C]4.99[/C][C]5.06696329871044[/C][C]-0.0769632987104432[/C][/ROW]
[ROW][C]53[/C][C]5.24[/C][C]4.97750001053091[/C][C]0.262499989469089[/C][/ROW]
[ROW][C]54[/C][C]5.25[/C][C]5.39723043875835[/C][C]-0.147230438758349[/C][/ROW]
[ROW][C]55[/C][C]5.25[/C][C]5.59974324735948[/C][C]-0.349743247359479[/C][/ROW]
[ROW][C]56[/C][C]5.25[/C][C]5.438083932831[/C][C]-0.188083932830997[/C][/ROW]
[ROW][C]57[/C][C]5.25[/C][C]5.0299050405674[/C][C]0.220094959432600[/C][/ROW]
[ROW][C]58[/C][C]5.24[/C][C]5.20305271218159[/C][C]0.0369472878184061[/C][/ROW]
[ROW][C]59[/C][C]5.25[/C][C]5.34485212237757[/C][C]-0.094852122377568[/C][/ROW]
[ROW][C]60[/C][C]5.26[/C][C]5.41693425669915[/C][C]-0.156934256699154[/C][/ROW]
[ROW][C]61[/C][C]5.26[/C][C]5.34867173961789[/C][C]-0.0886717396178938[/C][/ROW]
[ROW][C]62[/C][C]5.25[/C][C]5.39360850247778[/C][C]-0.143608502477775[/C][/ROW]
[ROW][C]63[/C][C]5.25[/C][C]5.32653687580434[/C][C]-0.0765368758043357[/C][/ROW]
[ROW][C]64[/C][C]5.25[/C][C]5.23495690327119[/C][C]0.0150430967288102[/C][/ROW]
[ROW][C]65[/C][C]5.26[/C][C]5.12837957159404[/C][C]0.131620428405959[/C][/ROW]
[ROW][C]66[/C][C]5.02[/C][C]5.24968385364721[/C][C]-0.229683853647209[/C][/ROW]
[ROW][C]67[/C][C]4.94[/C][C]5.19826625598185[/C][C]-0.258266255981847[/C][/ROW]
[ROW][C]68[/C][C]4.76[/C][C]4.98553455906218[/C][C]-0.225534559062178[/C][/ROW]
[ROW][C]69[/C][C]4.49[/C][C]4.41590765348667[/C][C]0.0740923465133312[/C][/ROW]
[ROW][C]70[/C][C]4.24[/C][C]4.26087436358426[/C][C]-0.0208743635842579[/C][/ROW]
[ROW][C]71[/C][C]3.94[/C][C]4.14998186561459[/C][C]-0.209981865614586[/C][/ROW]
[ROW][C]72[/C][C]2.98[/C][C]3.90022685977977[/C][C]-0.920226859779767[/C][/ROW]
[ROW][C]73[/C][C]2.61[/C][C]2.77921823239927[/C][C]-0.169218232399271[/C][/ROW]
[ROW][C]74[/C][C]2.28[/C][C]2.38587818868410[/C][C]-0.105878188684096[/C][/ROW]
[ROW][C]75[/C][C]1.98[/C][C]2.00572714136778[/C][C]-0.0257271413677773[/C][/ROW]
[ROW][C]76[/C][C]2[/C][C]1.62389616393725[/C][C]0.376103836062746[/C][/ROW]
[ROW][C]77[/C][C]2.01[/C][C]1.58202552582611[/C][C]0.427974474173886[/C][/ROW]
[ROW][C]78[/C][C]2[/C][C]1.72802008633794[/C][C]0.271979913662062[/C][/ROW]
[ROW][C]79[/C][C]1.81[/C][C]2.00383490291067[/C][C]-0.193834902910672[/C][/ROW]
[ROW][C]80[/C][C]0.97[/C][C]1.72592056673923[/C][C]-0.75592056673923[/C][/ROW]
[ROW][C]81[/C][C]0.39[/C][C]0.460302090557214[/C][C]-0.0703020905572139[/C][/ROW]
[ROW][C]82[/C][C]0.16[/C][C]-0.0825954090470405[/C][C]0.242595409047040[/C][/ROW]
[ROW][C]83[/C][C]0.15[/C][C]-0.160567141812935[/C][C]0.310567141812935[/C][/ROW]
[ROW][C]84[/C][C]0.22[/C][C]-0.0804714551562155[/C][C]0.300471455156215[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41932&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41932&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
131.251.55613514957265-0.306135149572649
141.261.241740261726990.0182597382730081
151.261.206551776803160.0534482231968443
161.221.153641636445760.066358363554239
171.010.950340942689850.0596590573101498
181.030.980920642147760.0490793578522398
191.011.22114011659760-0.211140116597604
201.010.9704262385880680.0395737614119325
2110.551029370096330.44897062990367
220.980.9046208836160970.0753791163839029
2311.03257908172319-0.0325790817231904
241.011.08155775357132-0.0715577535713181
2511.03182804490521-0.0318280449052057
2611.07706301749370-0.0770630174936968
2711.02041453445696-0.0204145344569628
281.030.9515135522036460.0784864477963538
291.260.813276724427980.44672327557202
301.431.32688711231420.103112887685801
311.611.73225041648978-0.122250416489781
321.761.729171397776620.0308286022233808
331.931.475414022055500.454585977944496
342.161.956537754955510.203462245044488
352.282.36673885446528-0.0867388544652825
362.52.52298648122298-0.0229864812229752
372.632.69023307474055-0.0602330747405508
382.792.86991068644488-0.0799106864448795
3932.977876260931490.0221237390685056
403.043.12628557745283-0.0862855774528297
413.263.000876613913430.259123386086571
423.53.425123743254580.0748762567454193
433.623.89273831067774-0.272738310677737
443.783.83662479299525-0.0566247929952528
4543.59132850592670.4086714940733
464.164.066300547302120.0936994526978783
474.294.38875739711791-0.0987573971179065
484.494.57005852830135-0.080058528301354
494.594.70346426753753-0.113464267537532
504.794.84465151794328-0.0546515179432818
514.944.99998060954632-0.0599806095463196
524.995.06696329871044-0.0769632987104432
535.244.977500010530910.262499989469089
545.255.39723043875835-0.147230438758349
555.255.59974324735948-0.349743247359479
565.255.438083932831-0.188083932830997
575.255.02990504056740.220094959432600
585.245.203052712181590.0369472878184061
595.255.34485212237757-0.094852122377568
605.265.41693425669915-0.156934256699154
615.265.34867173961789-0.0886717396178938
625.255.39360850247778-0.143608502477775
635.255.32653687580434-0.0765368758043357
645.255.234956903271190.0150430967288102
655.265.128379571594040.131620428405959
665.025.24968385364721-0.229683853647209
674.945.19826625598185-0.258266255981847
684.764.98553455906218-0.225534559062178
694.494.415907653486670.0740923465133312
704.244.26087436358426-0.0208743635842579
713.944.14998186561459-0.209981865614586
722.983.90022685977977-0.920226859779767
732.612.77921823239927-0.169218232399271
742.282.38587818868410-0.105878188684096
751.982.00572714136778-0.0257271413677773
7621.623896163937250.376103836062746
772.011.582025525826110.427974474173886
7821.728020086337940.271979913662062
791.812.00383490291067-0.193834902910672
800.971.72592056673923-0.75592056673923
810.390.460302090557214-0.0703020905572139
820.16-0.08259540904704050.242595409047040
830.15-0.1605671418129350.310567141812935
840.22-0.08047145515621550.300471455156215







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
850.095358954104449-0.3691969504759110.55991485868481
860.0016869236061966-0.6922809480008630.695654795213256
87-0.118043874765269-1.033902727736840.797814978206305
88-0.288115419315582-1.428694547722220.852463709091057
89-0.583071609198795-1.954731844111140.788588625713548
90-0.828154427966192-2.438707456792270.782398600859889
91-0.866737945478451-2.724612803606880.991136912649974
92-0.996654140072004-3.110512236988631.11720395684462
93-1.37257951964057-3.751121661249441.00596262196830
94-1.67799450997325-4.329859787365620.973870767419127
95-1.86971259109484-4.803424694972061.06399951278237
96-2.02691739513862-5.250856749537831.19702195926059

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 0.095358954104449 & -0.369196950475911 & 0.55991485868481 \tabularnewline
86 & 0.0016869236061966 & -0.692280948000863 & 0.695654795213256 \tabularnewline
87 & -0.118043874765269 & -1.03390272773684 & 0.797814978206305 \tabularnewline
88 & -0.288115419315582 & -1.42869454772222 & 0.852463709091057 \tabularnewline
89 & -0.583071609198795 & -1.95473184411114 & 0.788588625713548 \tabularnewline
90 & -0.828154427966192 & -2.43870745679227 & 0.782398600859889 \tabularnewline
91 & -0.866737945478451 & -2.72461280360688 & 0.991136912649974 \tabularnewline
92 & -0.996654140072004 & -3.11051223698863 & 1.11720395684462 \tabularnewline
93 & -1.37257951964057 & -3.75112166124944 & 1.00596262196830 \tabularnewline
94 & -1.67799450997325 & -4.32985978736562 & 0.973870767419127 \tabularnewline
95 & -1.86971259109484 & -4.80342469497206 & 1.06399951278237 \tabularnewline
96 & -2.02691739513862 & -5.25085674953783 & 1.19702195926059 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41932&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]85[/C][C]0.095358954104449[/C][C]-0.369196950475911[/C][C]0.55991485868481[/C][/ROW]
[ROW][C]86[/C][C]0.0016869236061966[/C][C]-0.692280948000863[/C][C]0.695654795213256[/C][/ROW]
[ROW][C]87[/C][C]-0.118043874765269[/C][C]-1.03390272773684[/C][C]0.797814978206305[/C][/ROW]
[ROW][C]88[/C][C]-0.288115419315582[/C][C]-1.42869454772222[/C][C]0.852463709091057[/C][/ROW]
[ROW][C]89[/C][C]-0.583071609198795[/C][C]-1.95473184411114[/C][C]0.788588625713548[/C][/ROW]
[ROW][C]90[/C][C]-0.828154427966192[/C][C]-2.43870745679227[/C][C]0.782398600859889[/C][/ROW]
[ROW][C]91[/C][C]-0.866737945478451[/C][C]-2.72461280360688[/C][C]0.991136912649974[/C][/ROW]
[ROW][C]92[/C][C]-0.996654140072004[/C][C]-3.11051223698863[/C][C]1.11720395684462[/C][/ROW]
[ROW][C]93[/C][C]-1.37257951964057[/C][C]-3.75112166124944[/C][C]1.00596262196830[/C][/ROW]
[ROW][C]94[/C][C]-1.67799450997325[/C][C]-4.32985978736562[/C][C]0.973870767419127[/C][/ROW]
[ROW][C]95[/C][C]-1.86971259109484[/C][C]-4.80342469497206[/C][C]1.06399951278237[/C][/ROW]
[ROW][C]96[/C][C]-2.02691739513862[/C][C]-5.25085674953783[/C][C]1.19702195926059[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41932&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41932&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
850.095358954104449-0.3691969504759110.55991485868481
860.0016869236061966-0.6922809480008630.695654795213256
87-0.118043874765269-1.033902727736840.797814978206305
88-0.288115419315582-1.428694547722220.852463709091057
89-0.583071609198795-1.954731844111140.788588625713548
90-0.828154427966192-2.438707456792270.782398600859889
91-0.866737945478451-2.724612803606880.991136912649974
92-0.996654140072004-3.110512236988631.11720395684462
93-1.37257951964057-3.751121661249441.00596262196830
94-1.67799450997325-4.329859787365620.973870767419127
95-1.86971259109484-4.803424694972061.06399951278237
96-2.02691739513862-5.250856749537831.19702195926059



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')