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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Dec 2013 05:19:30 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/16/t1387189235f0c521wg9ljgxdr.htm/, Retrieved Fri, 29 Mar 2024 02:35:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232380, Retrieved Fri, 29 Mar 2024 02:35:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-16 10:19:30] [996f793b29251b773cdee78c11137970] [Current]
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Dataseries X:
1,41
1,42
1,43
1,43
1,43
1,43
1,43
1,44
1,44
1,45
1,46
1,46
1,47
1,47
1,47
1,49
1,49
1,49
1,49
1,5
1,52
1,54
1,56
1,56
1,57
1,58
1,59
1,6
1,59
1,6
1,61
1,61
1,61
1,62
1,62
1,61
1,62
1,62
1,63
1,64
1,64
1,64
1,64
1,64
1,65
1,65
1,65
1,65
1,65
1,66
1,66
1,67
1,67
1,67
1,67
1,67
1,67
1,69
1,69
1,69
1,7
1,71
1,72
1,71
1,71
1,71
1,72
1,72
1,72
1,73
1,73
1,73
1,74
1,74
1,75
1,76
1,76
1,77
1,78
1,79
1,8
1,8
1,8
1,81




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232380&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232380&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232380&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0812546799739967
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0812546799739967 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232380&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0812546799739967[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232380&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232380&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
alpha1
beta0.0812546799739967
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31.431.430
41.431.44-0.01
51.431.43918745320026-0.00918745320026004
61.431.4384409296307-0.00844092963069687
71.431.43775506459487-0.00775506459487163
81.441.437124929303040.00287507069696247
91.441.44735854225242-0.00735854225242183
101.451.446760626256630.0032393737433738
111.461.457023840533460.00297615946653984
121.461.46726566741847-0.00726566741846546
131.471.466675297937580.00332470206241942
141.471.47694544553967-0.00694544553967136
151.471.47638109558507-0.0063810955850685
161.491.475862601705420.0141373982945796
171.491.49701133147951-0.00701133147951127
181.491.49644162798395-0.00644162798395209
191.491.4959182155636-0.00591821556360439
201.51.495437332851970.00456266714803344
211.521.505808070910910.0141919290890919
221.541.526961231567260.0130387684327442
231.561.548020692523510.0119793074764865
241.561.56899406731883-0.00899406731882557
251.571.568263257257170.00173674274283031
261.581.578404375732940.0015956242670645
271.591.588534027672110.00146597232788537
281.61.598653144784470.00134685521553224
291.591.60876258307398-0.018762583073977
301.61.597238035390820.00276196460918454
311.611.607462457941230.00253754205876566
321.611.61766864510914-0.00766864510913989
331.611.61704553180496-0.00704553180496248
341.621.61647304937290.00352695062709629
351.621.62675963061739-0.00675963061739249
361.611.62621037899483-0.0162103789948338
371.621.614893209837350.00510679016264848
381.621.62530816043771-0.00530816043771187
391.631.624876847560090.00512315243990491
401.641.635293127672060.00470687232794265
411.641.64567558307674-0.00567558307674276
421.641.64521441539018-0.00521441539017631
431.641.6447907197364-0.00479071973639589
441.641.64440145133737-0.00440145133737002
451.651.644043812817530.00595618718246915
461.651.65452778090091-0.00452778090090766
471.651.65415987751281-0.00415987751281199
481.651.65382186799678-0.00382186799677742
491.651.6535113233358-0.0035113233357964
501.661.653226011881860.00677398811813901
511.661.66377643011855-0.00377643011854811
521.671.663469577497820.00653042250217872
531.671.67400020488833-0.00400020488833075
541.671.6736751695203-0.003675169520299
551.671.67337654479708-0.00337654479707705
561.671.67310218473017-0.00310218473017265
571.671.6728501177027-0.00285011770270227
581.691.672618532300880.0173814676991191
591.691.69403085789625-0.00403085789625135
601.691.69370333182787-0.00370333182787075
611.71.693402418785360.00659758121464038
621.711.703938503135560.00606149686444235
631.721.714431028123440.0055689718765588
641.711.72488353315106-0.0148835331510553
651.711.71367417642798-0.00367417642798396
661.711.71337563239816-0.00337563239815997
671.721.713101346467940.00689865353206232
681.721.72366189435294-0.00366189435293696
691.721.72336434829919-0.00336434829919052
701.731.723090979254820.0069090207451814
711.731.7336523695244-0.00365236952440195
721.731.73335559740755-0.00335559740755009
731.741.733082939414080.00691706058592212
741.741.74364498295835-0.00364498295834781
751.751.743348811034560.00665118896544348
761.761.753889251265390.00611074873460971
771.761.76438577819822-0.00438577819822239
781.771.764029413194290.00597058680571094
791.781.774514551314440.005485448685556
801.791.78496026969190.00503973030809735
811.81.795369771365240.0046302286347577
821.81.80574599911117-0.00574599911116591
831.81.80527910979226-0.00527910979225732
841.811.804850157415540.00514984258446005

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.43 & 1.43 & 0 \tabularnewline
4 & 1.43 & 1.44 & -0.01 \tabularnewline
5 & 1.43 & 1.43918745320026 & -0.00918745320026004 \tabularnewline
6 & 1.43 & 1.4384409296307 & -0.00844092963069687 \tabularnewline
7 & 1.43 & 1.43775506459487 & -0.00775506459487163 \tabularnewline
8 & 1.44 & 1.43712492930304 & 0.00287507069696247 \tabularnewline
9 & 1.44 & 1.44735854225242 & -0.00735854225242183 \tabularnewline
10 & 1.45 & 1.44676062625663 & 0.0032393737433738 \tabularnewline
11 & 1.46 & 1.45702384053346 & 0.00297615946653984 \tabularnewline
12 & 1.46 & 1.46726566741847 & -0.00726566741846546 \tabularnewline
13 & 1.47 & 1.46667529793758 & 0.00332470206241942 \tabularnewline
14 & 1.47 & 1.47694544553967 & -0.00694544553967136 \tabularnewline
15 & 1.47 & 1.47638109558507 & -0.0063810955850685 \tabularnewline
16 & 1.49 & 1.47586260170542 & 0.0141373982945796 \tabularnewline
17 & 1.49 & 1.49701133147951 & -0.00701133147951127 \tabularnewline
18 & 1.49 & 1.49644162798395 & -0.00644162798395209 \tabularnewline
19 & 1.49 & 1.4959182155636 & -0.00591821556360439 \tabularnewline
20 & 1.5 & 1.49543733285197 & 0.00456266714803344 \tabularnewline
21 & 1.52 & 1.50580807091091 & 0.0141919290890919 \tabularnewline
22 & 1.54 & 1.52696123156726 & 0.0130387684327442 \tabularnewline
23 & 1.56 & 1.54802069252351 & 0.0119793074764865 \tabularnewline
24 & 1.56 & 1.56899406731883 & -0.00899406731882557 \tabularnewline
25 & 1.57 & 1.56826325725717 & 0.00173674274283031 \tabularnewline
26 & 1.58 & 1.57840437573294 & 0.0015956242670645 \tabularnewline
27 & 1.59 & 1.58853402767211 & 0.00146597232788537 \tabularnewline
28 & 1.6 & 1.59865314478447 & 0.00134685521553224 \tabularnewline
29 & 1.59 & 1.60876258307398 & -0.018762583073977 \tabularnewline
30 & 1.6 & 1.59723803539082 & 0.00276196460918454 \tabularnewline
31 & 1.61 & 1.60746245794123 & 0.00253754205876566 \tabularnewline
32 & 1.61 & 1.61766864510914 & -0.00766864510913989 \tabularnewline
33 & 1.61 & 1.61704553180496 & -0.00704553180496248 \tabularnewline
34 & 1.62 & 1.6164730493729 & 0.00352695062709629 \tabularnewline
35 & 1.62 & 1.62675963061739 & -0.00675963061739249 \tabularnewline
36 & 1.61 & 1.62621037899483 & -0.0162103789948338 \tabularnewline
37 & 1.62 & 1.61489320983735 & 0.00510679016264848 \tabularnewline
38 & 1.62 & 1.62530816043771 & -0.00530816043771187 \tabularnewline
39 & 1.63 & 1.62487684756009 & 0.00512315243990491 \tabularnewline
40 & 1.64 & 1.63529312767206 & 0.00470687232794265 \tabularnewline
41 & 1.64 & 1.64567558307674 & -0.00567558307674276 \tabularnewline
42 & 1.64 & 1.64521441539018 & -0.00521441539017631 \tabularnewline
43 & 1.64 & 1.6447907197364 & -0.00479071973639589 \tabularnewline
44 & 1.64 & 1.64440145133737 & -0.00440145133737002 \tabularnewline
45 & 1.65 & 1.64404381281753 & 0.00595618718246915 \tabularnewline
46 & 1.65 & 1.65452778090091 & -0.00452778090090766 \tabularnewline
47 & 1.65 & 1.65415987751281 & -0.00415987751281199 \tabularnewline
48 & 1.65 & 1.65382186799678 & -0.00382186799677742 \tabularnewline
49 & 1.65 & 1.6535113233358 & -0.0035113233357964 \tabularnewline
50 & 1.66 & 1.65322601188186 & 0.00677398811813901 \tabularnewline
51 & 1.66 & 1.66377643011855 & -0.00377643011854811 \tabularnewline
52 & 1.67 & 1.66346957749782 & 0.00653042250217872 \tabularnewline
53 & 1.67 & 1.67400020488833 & -0.00400020488833075 \tabularnewline
54 & 1.67 & 1.6736751695203 & -0.003675169520299 \tabularnewline
55 & 1.67 & 1.67337654479708 & -0.00337654479707705 \tabularnewline
56 & 1.67 & 1.67310218473017 & -0.00310218473017265 \tabularnewline
57 & 1.67 & 1.6728501177027 & -0.00285011770270227 \tabularnewline
58 & 1.69 & 1.67261853230088 & 0.0173814676991191 \tabularnewline
59 & 1.69 & 1.69403085789625 & -0.00403085789625135 \tabularnewline
60 & 1.69 & 1.69370333182787 & -0.00370333182787075 \tabularnewline
61 & 1.7 & 1.69340241878536 & 0.00659758121464038 \tabularnewline
62 & 1.71 & 1.70393850313556 & 0.00606149686444235 \tabularnewline
63 & 1.72 & 1.71443102812344 & 0.0055689718765588 \tabularnewline
64 & 1.71 & 1.72488353315106 & -0.0148835331510553 \tabularnewline
65 & 1.71 & 1.71367417642798 & -0.00367417642798396 \tabularnewline
66 & 1.71 & 1.71337563239816 & -0.00337563239815997 \tabularnewline
67 & 1.72 & 1.71310134646794 & 0.00689865353206232 \tabularnewline
68 & 1.72 & 1.72366189435294 & -0.00366189435293696 \tabularnewline
69 & 1.72 & 1.72336434829919 & -0.00336434829919052 \tabularnewline
70 & 1.73 & 1.72309097925482 & 0.0069090207451814 \tabularnewline
71 & 1.73 & 1.7336523695244 & -0.00365236952440195 \tabularnewline
72 & 1.73 & 1.73335559740755 & -0.00335559740755009 \tabularnewline
73 & 1.74 & 1.73308293941408 & 0.00691706058592212 \tabularnewline
74 & 1.74 & 1.74364498295835 & -0.00364498295834781 \tabularnewline
75 & 1.75 & 1.74334881103456 & 0.00665118896544348 \tabularnewline
76 & 1.76 & 1.75388925126539 & 0.00611074873460971 \tabularnewline
77 & 1.76 & 1.76438577819822 & -0.00438577819822239 \tabularnewline
78 & 1.77 & 1.76402941319429 & 0.00597058680571094 \tabularnewline
79 & 1.78 & 1.77451455131444 & 0.005485448685556 \tabularnewline
80 & 1.79 & 1.7849602696919 & 0.00503973030809735 \tabularnewline
81 & 1.8 & 1.79536977136524 & 0.0046302286347577 \tabularnewline
82 & 1.8 & 1.80574599911117 & -0.00574599911116591 \tabularnewline
83 & 1.8 & 1.80527910979226 & -0.00527910979225732 \tabularnewline
84 & 1.81 & 1.80485015741554 & 0.00514984258446005 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232380&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]3[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]1.43[/C][C]1.44[/C][C]-0.01[/C][/ROW]
[ROW][C]5[/C][C]1.43[/C][C]1.43918745320026[/C][C]-0.00918745320026004[/C][/ROW]
[ROW][C]6[/C][C]1.43[/C][C]1.4384409296307[/C][C]-0.00844092963069687[/C][/ROW]
[ROW][C]7[/C][C]1.43[/C][C]1.43775506459487[/C][C]-0.00775506459487163[/C][/ROW]
[ROW][C]8[/C][C]1.44[/C][C]1.43712492930304[/C][C]0.00287507069696247[/C][/ROW]
[ROW][C]9[/C][C]1.44[/C][C]1.44735854225242[/C][C]-0.00735854225242183[/C][/ROW]
[ROW][C]10[/C][C]1.45[/C][C]1.44676062625663[/C][C]0.0032393737433738[/C][/ROW]
[ROW][C]11[/C][C]1.46[/C][C]1.45702384053346[/C][C]0.00297615946653984[/C][/ROW]
[ROW][C]12[/C][C]1.46[/C][C]1.46726566741847[/C][C]-0.00726566741846546[/C][/ROW]
[ROW][C]13[/C][C]1.47[/C][C]1.46667529793758[/C][C]0.00332470206241942[/C][/ROW]
[ROW][C]14[/C][C]1.47[/C][C]1.47694544553967[/C][C]-0.00694544553967136[/C][/ROW]
[ROW][C]15[/C][C]1.47[/C][C]1.47638109558507[/C][C]-0.0063810955850685[/C][/ROW]
[ROW][C]16[/C][C]1.49[/C][C]1.47586260170542[/C][C]0.0141373982945796[/C][/ROW]
[ROW][C]17[/C][C]1.49[/C][C]1.49701133147951[/C][C]-0.00701133147951127[/C][/ROW]
[ROW][C]18[/C][C]1.49[/C][C]1.49644162798395[/C][C]-0.00644162798395209[/C][/ROW]
[ROW][C]19[/C][C]1.49[/C][C]1.4959182155636[/C][C]-0.00591821556360439[/C][/ROW]
[ROW][C]20[/C][C]1.5[/C][C]1.49543733285197[/C][C]0.00456266714803344[/C][/ROW]
[ROW][C]21[/C][C]1.52[/C][C]1.50580807091091[/C][C]0.0141919290890919[/C][/ROW]
[ROW][C]22[/C][C]1.54[/C][C]1.52696123156726[/C][C]0.0130387684327442[/C][/ROW]
[ROW][C]23[/C][C]1.56[/C][C]1.54802069252351[/C][C]0.0119793074764865[/C][/ROW]
[ROW][C]24[/C][C]1.56[/C][C]1.56899406731883[/C][C]-0.00899406731882557[/C][/ROW]
[ROW][C]25[/C][C]1.57[/C][C]1.56826325725717[/C][C]0.00173674274283031[/C][/ROW]
[ROW][C]26[/C][C]1.58[/C][C]1.57840437573294[/C][C]0.0015956242670645[/C][/ROW]
[ROW][C]27[/C][C]1.59[/C][C]1.58853402767211[/C][C]0.00146597232788537[/C][/ROW]
[ROW][C]28[/C][C]1.6[/C][C]1.59865314478447[/C][C]0.00134685521553224[/C][/ROW]
[ROW][C]29[/C][C]1.59[/C][C]1.60876258307398[/C][C]-0.018762583073977[/C][/ROW]
[ROW][C]30[/C][C]1.6[/C][C]1.59723803539082[/C][C]0.00276196460918454[/C][/ROW]
[ROW][C]31[/C][C]1.61[/C][C]1.60746245794123[/C][C]0.00253754205876566[/C][/ROW]
[ROW][C]32[/C][C]1.61[/C][C]1.61766864510914[/C][C]-0.00766864510913989[/C][/ROW]
[ROW][C]33[/C][C]1.61[/C][C]1.61704553180496[/C][C]-0.00704553180496248[/C][/ROW]
[ROW][C]34[/C][C]1.62[/C][C]1.6164730493729[/C][C]0.00352695062709629[/C][/ROW]
[ROW][C]35[/C][C]1.62[/C][C]1.62675963061739[/C][C]-0.00675963061739249[/C][/ROW]
[ROW][C]36[/C][C]1.61[/C][C]1.62621037899483[/C][C]-0.0162103789948338[/C][/ROW]
[ROW][C]37[/C][C]1.62[/C][C]1.61489320983735[/C][C]0.00510679016264848[/C][/ROW]
[ROW][C]38[/C][C]1.62[/C][C]1.62530816043771[/C][C]-0.00530816043771187[/C][/ROW]
[ROW][C]39[/C][C]1.63[/C][C]1.62487684756009[/C][C]0.00512315243990491[/C][/ROW]
[ROW][C]40[/C][C]1.64[/C][C]1.63529312767206[/C][C]0.00470687232794265[/C][/ROW]
[ROW][C]41[/C][C]1.64[/C][C]1.64567558307674[/C][C]-0.00567558307674276[/C][/ROW]
[ROW][C]42[/C][C]1.64[/C][C]1.64521441539018[/C][C]-0.00521441539017631[/C][/ROW]
[ROW][C]43[/C][C]1.64[/C][C]1.6447907197364[/C][C]-0.00479071973639589[/C][/ROW]
[ROW][C]44[/C][C]1.64[/C][C]1.64440145133737[/C][C]-0.00440145133737002[/C][/ROW]
[ROW][C]45[/C][C]1.65[/C][C]1.64404381281753[/C][C]0.00595618718246915[/C][/ROW]
[ROW][C]46[/C][C]1.65[/C][C]1.65452778090091[/C][C]-0.00452778090090766[/C][/ROW]
[ROW][C]47[/C][C]1.65[/C][C]1.65415987751281[/C][C]-0.00415987751281199[/C][/ROW]
[ROW][C]48[/C][C]1.65[/C][C]1.65382186799678[/C][C]-0.00382186799677742[/C][/ROW]
[ROW][C]49[/C][C]1.65[/C][C]1.6535113233358[/C][C]-0.0035113233357964[/C][/ROW]
[ROW][C]50[/C][C]1.66[/C][C]1.65322601188186[/C][C]0.00677398811813901[/C][/ROW]
[ROW][C]51[/C][C]1.66[/C][C]1.66377643011855[/C][C]-0.00377643011854811[/C][/ROW]
[ROW][C]52[/C][C]1.67[/C][C]1.66346957749782[/C][C]0.00653042250217872[/C][/ROW]
[ROW][C]53[/C][C]1.67[/C][C]1.67400020488833[/C][C]-0.00400020488833075[/C][/ROW]
[ROW][C]54[/C][C]1.67[/C][C]1.6736751695203[/C][C]-0.003675169520299[/C][/ROW]
[ROW][C]55[/C][C]1.67[/C][C]1.67337654479708[/C][C]-0.00337654479707705[/C][/ROW]
[ROW][C]56[/C][C]1.67[/C][C]1.67310218473017[/C][C]-0.00310218473017265[/C][/ROW]
[ROW][C]57[/C][C]1.67[/C][C]1.6728501177027[/C][C]-0.00285011770270227[/C][/ROW]
[ROW][C]58[/C][C]1.69[/C][C]1.67261853230088[/C][C]0.0173814676991191[/C][/ROW]
[ROW][C]59[/C][C]1.69[/C][C]1.69403085789625[/C][C]-0.00403085789625135[/C][/ROW]
[ROW][C]60[/C][C]1.69[/C][C]1.69370333182787[/C][C]-0.00370333182787075[/C][/ROW]
[ROW][C]61[/C][C]1.7[/C][C]1.69340241878536[/C][C]0.00659758121464038[/C][/ROW]
[ROW][C]62[/C][C]1.71[/C][C]1.70393850313556[/C][C]0.00606149686444235[/C][/ROW]
[ROW][C]63[/C][C]1.72[/C][C]1.71443102812344[/C][C]0.0055689718765588[/C][/ROW]
[ROW][C]64[/C][C]1.71[/C][C]1.72488353315106[/C][C]-0.0148835331510553[/C][/ROW]
[ROW][C]65[/C][C]1.71[/C][C]1.71367417642798[/C][C]-0.00367417642798396[/C][/ROW]
[ROW][C]66[/C][C]1.71[/C][C]1.71337563239816[/C][C]-0.00337563239815997[/C][/ROW]
[ROW][C]67[/C][C]1.72[/C][C]1.71310134646794[/C][C]0.00689865353206232[/C][/ROW]
[ROW][C]68[/C][C]1.72[/C][C]1.72366189435294[/C][C]-0.00366189435293696[/C][/ROW]
[ROW][C]69[/C][C]1.72[/C][C]1.72336434829919[/C][C]-0.00336434829919052[/C][/ROW]
[ROW][C]70[/C][C]1.73[/C][C]1.72309097925482[/C][C]0.0069090207451814[/C][/ROW]
[ROW][C]71[/C][C]1.73[/C][C]1.7336523695244[/C][C]-0.00365236952440195[/C][/ROW]
[ROW][C]72[/C][C]1.73[/C][C]1.73335559740755[/C][C]-0.00335559740755009[/C][/ROW]
[ROW][C]73[/C][C]1.74[/C][C]1.73308293941408[/C][C]0.00691706058592212[/C][/ROW]
[ROW][C]74[/C][C]1.74[/C][C]1.74364498295835[/C][C]-0.00364498295834781[/C][/ROW]
[ROW][C]75[/C][C]1.75[/C][C]1.74334881103456[/C][C]0.00665118896544348[/C][/ROW]
[ROW][C]76[/C][C]1.76[/C][C]1.75388925126539[/C][C]0.00611074873460971[/C][/ROW]
[ROW][C]77[/C][C]1.76[/C][C]1.76438577819822[/C][C]-0.00438577819822239[/C][/ROW]
[ROW][C]78[/C][C]1.77[/C][C]1.76402941319429[/C][C]0.00597058680571094[/C][/ROW]
[ROW][C]79[/C][C]1.78[/C][C]1.77451455131444[/C][C]0.005485448685556[/C][/ROW]
[ROW][C]80[/C][C]1.79[/C][C]1.7849602696919[/C][C]0.00503973030809735[/C][/ROW]
[ROW][C]81[/C][C]1.8[/C][C]1.79536977136524[/C][C]0.0046302286347577[/C][/ROW]
[ROW][C]82[/C][C]1.8[/C][C]1.80574599911117[/C][C]-0.00574599911116591[/C][/ROW]
[ROW][C]83[/C][C]1.8[/C][C]1.80527910979226[/C][C]-0.00527910979225732[/C][/ROW]
[ROW][C]84[/C][C]1.81[/C][C]1.80485015741554[/C][C]0.00514984258446005[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232380&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232380&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
31.431.430
41.431.44-0.01
51.431.43918745320026-0.00918745320026004
61.431.4384409296307-0.00844092963069687
71.431.43775506459487-0.00775506459487163
81.441.437124929303040.00287507069696247
91.441.44735854225242-0.00735854225242183
101.451.446760626256630.0032393737433738
111.461.457023840533460.00297615946653984
121.461.46726566741847-0.00726566741846546
131.471.466675297937580.00332470206241942
141.471.47694544553967-0.00694544553967136
151.471.47638109558507-0.0063810955850685
161.491.475862601705420.0141373982945796
171.491.49701133147951-0.00701133147951127
181.491.49644162798395-0.00644162798395209
191.491.4959182155636-0.00591821556360439
201.51.495437332851970.00456266714803344
211.521.505808070910910.0141919290890919
221.541.526961231567260.0130387684327442
231.561.548020692523510.0119793074764865
241.561.56899406731883-0.00899406731882557
251.571.568263257257170.00173674274283031
261.581.578404375732940.0015956242670645
271.591.588534027672110.00146597232788537
281.61.598653144784470.00134685521553224
291.591.60876258307398-0.018762583073977
301.61.597238035390820.00276196460918454
311.611.607462457941230.00253754205876566
321.611.61766864510914-0.00766864510913989
331.611.61704553180496-0.00704553180496248
341.621.61647304937290.00352695062709629
351.621.62675963061739-0.00675963061739249
361.611.62621037899483-0.0162103789948338
371.621.614893209837350.00510679016264848
381.621.62530816043771-0.00530816043771187
391.631.624876847560090.00512315243990491
401.641.635293127672060.00470687232794265
411.641.64567558307674-0.00567558307674276
421.641.64521441539018-0.00521441539017631
431.641.6447907197364-0.00479071973639589
441.641.64440145133737-0.00440145133737002
451.651.644043812817530.00595618718246915
461.651.65452778090091-0.00452778090090766
471.651.65415987751281-0.00415987751281199
481.651.65382186799678-0.00382186799677742
491.651.6535113233358-0.0035113233357964
501.661.653226011881860.00677398811813901
511.661.66377643011855-0.00377643011854811
521.671.663469577497820.00653042250217872
531.671.67400020488833-0.00400020488833075
541.671.6736751695203-0.003675169520299
551.671.67337654479708-0.00337654479707705
561.671.67310218473017-0.00310218473017265
571.671.6728501177027-0.00285011770270227
581.691.672618532300880.0173814676991191
591.691.69403085789625-0.00403085789625135
601.691.69370333182787-0.00370333182787075
611.71.693402418785360.00659758121464038
621.711.703938503135560.00606149686444235
631.721.714431028123440.0055689718765588
641.711.72488353315106-0.0148835331510553
651.711.71367417642798-0.00367417642798396
661.711.71337563239816-0.00337563239815997
671.721.713101346467940.00689865353206232
681.721.72366189435294-0.00366189435293696
691.721.72336434829919-0.00336434829919052
701.731.723090979254820.0069090207451814
711.731.7336523695244-0.00365236952440195
721.731.73335559740755-0.00335559740755009
731.741.733082939414080.00691706058592212
741.741.74364498295835-0.00364498295834781
751.751.743348811034560.00665118896544348
761.761.753889251265390.00611074873460971
771.761.76438577819822-0.00438577819822239
781.771.764029413194290.00597058680571094
791.781.774514551314440.005485448685556
801.791.78496026969190.00503973030809735
811.81.795369771365240.0046302286347577
821.81.80574599911117-0.00574599911116591
831.81.80527910979226-0.00527910979225732
841.811.804850157415540.00514984258446005







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
851.815268606226661.801636263283871.82890094916944
861.820537212453311.800459628079371.84061479682725
871.825805818679971.800227315553521.85138432180642
881.831074424906631.800386544245971.86176230556729
891.836343031133281.800733735328791.87195232693778
901.841611637359941.801169807918391.88205346680149
911.84688024358661.801639124637741.89212136253545
921.852148849813251.80210758948911.90219011013741
931.857417456039911.802553057715721.9122818543641
941.862686062266571.802960555057981.92241156947515
951.867954668493221.803319664663921.93258967232252
961.873223274719881.80362299676651.94282355267326

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1.81526860622666 & 1.80163626328387 & 1.82890094916944 \tabularnewline
86 & 1.82053721245331 & 1.80045962807937 & 1.84061479682725 \tabularnewline
87 & 1.82580581867997 & 1.80022731555352 & 1.85138432180642 \tabularnewline
88 & 1.83107442490663 & 1.80038654424597 & 1.86176230556729 \tabularnewline
89 & 1.83634303113328 & 1.80073373532879 & 1.87195232693778 \tabularnewline
90 & 1.84161163735994 & 1.80116980791839 & 1.88205346680149 \tabularnewline
91 & 1.8468802435866 & 1.80163912463774 & 1.89212136253545 \tabularnewline
92 & 1.85214884981325 & 1.8021075894891 & 1.90219011013741 \tabularnewline
93 & 1.85741745603991 & 1.80255305771572 & 1.9122818543641 \tabularnewline
94 & 1.86268606226657 & 1.80296055505798 & 1.92241156947515 \tabularnewline
95 & 1.86795466849322 & 1.80331966466392 & 1.93258967232252 \tabularnewline
96 & 1.87322327471988 & 1.8036229967665 & 1.94282355267326 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232380&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]1.81526860622666[/C][C]1.80163626328387[/C][C]1.82890094916944[/C][/ROW]
[ROW][C]86[/C][C]1.82053721245331[/C][C]1.80045962807937[/C][C]1.84061479682725[/C][/ROW]
[ROW][C]87[/C][C]1.82580581867997[/C][C]1.80022731555352[/C][C]1.85138432180642[/C][/ROW]
[ROW][C]88[/C][C]1.83107442490663[/C][C]1.80038654424597[/C][C]1.86176230556729[/C][/ROW]
[ROW][C]89[/C][C]1.83634303113328[/C][C]1.80073373532879[/C][C]1.87195232693778[/C][/ROW]
[ROW][C]90[/C][C]1.84161163735994[/C][C]1.80116980791839[/C][C]1.88205346680149[/C][/ROW]
[ROW][C]91[/C][C]1.8468802435866[/C][C]1.80163912463774[/C][C]1.89212136253545[/C][/ROW]
[ROW][C]92[/C][C]1.85214884981325[/C][C]1.8021075894891[/C][C]1.90219011013741[/C][/ROW]
[ROW][C]93[/C][C]1.85741745603991[/C][C]1.80255305771572[/C][C]1.9122818543641[/C][/ROW]
[ROW][C]94[/C][C]1.86268606226657[/C][C]1.80296055505798[/C][C]1.92241156947515[/C][/ROW]
[ROW][C]95[/C][C]1.86795466849322[/C][C]1.80331966466392[/C][C]1.93258967232252[/C][/ROW]
[ROW][C]96[/C][C]1.87322327471988[/C][C]1.8036229967665[/C][C]1.94282355267326[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232380&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232380&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
851.815268606226661.801636263283871.82890094916944
861.820537212453311.800459628079371.84061479682725
871.825805818679971.800227315553521.85138432180642
881.831074424906631.800386544245971.86176230556729
891.836343031133281.800733735328791.87195232693778
901.841611637359941.801169807918391.88205346680149
911.84688024358661.801639124637741.89212136253545
921.852148849813251.80210758948911.90219011013741
931.857417456039911.802553057715721.9122818543641
941.862686062266571.802960555057981.92241156947515
951.867954668493221.803319664663921.93258967232252
961.873223274719881.80362299676651.94282355267326



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