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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 02 Apr 2015 17:50:34 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Apr/02/t14279934486q41pbkzgk5b06s.htm/, Retrieved Thu, 09 May 2024 11:38:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278589, Retrieved Thu, 09 May 2024 11:38:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-04-02 16:50:34] [70effeb63bf28517d1b6107bc8921f07] [Current]
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Dataseries X:
15071
14236
14771
14804
15597
15418
16903
16350
16393
15685
14556
14850
15391
13704
15409
15098
15254
15522
16669
16238
16246
15424
14952
15008
14929
13905
14994
14753
15031
15386
16160
16116
16219
16064
15436
15404
15112
14119
14775
14289
15121
15371
15782
16104
15674
15105
14223
14385
14558
13804
14672
14244
15089
14580
15218
15696
15129
15110
14204
13655
14534
12746
14074
13699
14184
14110
15820
15362
14993
14437
13694
13688




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' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278589&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278589&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278589&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' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.728149673393151
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.728149673393151 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278589&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]0.728149673393151[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278589&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278589&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
alpha0.728149673393151
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21423615071-835
31477114462.9950227167308.004977283281
41480414687.268746329116.731253670994
51559714772.2665705643824.733429435686
61541815372.795947844345.2040521556792
71690315405.71126365751497.28873634247
81635016495.9615680005-145.961568000545
91639316389.6796999333.3203000670037
101568516392.0973753424-707.097375342353
111455615877.2246524297-1321.22465242966
121485014915.175353284-65.175353284023
131539114867.717941077523.282058923021
141370415248.7456013743-1544.74560137427
151540914123.93959625811285.06040374191
161509815059.655909533238.3440904667677
171525415087.5761464832166.423853516833
181552215208.7576210663313.242378933721
191666915436.84495697981232.15504302024
201623816334.0382491247-96.038249124671
211624616264.1080293913-18.108029391291
221542416250.9226737042-826.922673704228
231495215648.7991989251-696.799198925102
241500815141.4250898072-133.42508980718
251492915044.2716542416-115.271654241629
261390514960.3366368541-1055.3366368541
271499414191.893609409802.10639059104
281475314775.9471157444-22.9471157443859
291503114759.2381809098271.761819090205
301538614957.1214607211428.878539278943
311616015269.4092290224890.590770977649
321611615917.8926080367198.107391963318
331621916062.1444407915156.855559208459
341606416176.3587649991-112.35876499908
351543616094.5447669621-658.544766962143
361540415615.0256099839-211.025609983892
371511215461.3673809965-349.367380996531
381411915206.9756366297-1087.97563662969
391477514414.7665321581360.233467841927
401428914677.0704141125-388.070414112455
411512114394.4970688229726.502931177074
421537114923.4999408787447.500059121321
431578215249.3469627713532.653037228716
441610415637.1980978612466.801902138755
451567415977.0997504429-303.099750442881
461510515756.3977661524-651.397766152351
471422315282.0826954795-1059.08269547949
481438514510.9119766698-125.911976669762
491455814419.2292119814138.770788018612
501380414520.2751159536-716.275115953649
511467213998.7196242124673.280375787643
521424414488.9685099441-244.968509944147
531508914310.5947694367778.40523056329
541458014877.3902838389-297.390283838891
551521814660.8456457913557.154354208695
561569615066.5374068379629.462593162061
571512915524.8803884621-395.880388462099
581511015236.6202129007-126.620212900667
591420415144.4217462321-940.421746232076
601365514459.6539588614-804.653958861374
611453413873.745441522660.254558478042
621274614354.5095826341-1608.50958263408
631407413183.2738553893890.726144610679
641369913831.8558066703-132.855806670326
651418413735.1168944349448.883105565055
661411014061.970981143848.0290188561576
671582014096.94329553731723.05670446265
681536215351.586472129710.4135278702925
691499315359.1690790473-366.169079047331
701443715092.5431837323-655.543183732345
711369414615.2096286025-921.209628602532
721368813944.431138409-256.431138408972

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 14236 & 15071 & -835 \tabularnewline
3 & 14771 & 14462.9950227167 & 308.004977283281 \tabularnewline
4 & 14804 & 14687.268746329 & 116.731253670994 \tabularnewline
5 & 15597 & 14772.2665705643 & 824.733429435686 \tabularnewline
6 & 15418 & 15372.7959478443 & 45.2040521556792 \tabularnewline
7 & 16903 & 15405.7112636575 & 1497.28873634247 \tabularnewline
8 & 16350 & 16495.9615680005 & -145.961568000545 \tabularnewline
9 & 16393 & 16389.679699933 & 3.3203000670037 \tabularnewline
10 & 15685 & 16392.0973753424 & -707.097375342353 \tabularnewline
11 & 14556 & 15877.2246524297 & -1321.22465242966 \tabularnewline
12 & 14850 & 14915.175353284 & -65.175353284023 \tabularnewline
13 & 15391 & 14867.717941077 & 523.282058923021 \tabularnewline
14 & 13704 & 15248.7456013743 & -1544.74560137427 \tabularnewline
15 & 15409 & 14123.9395962581 & 1285.06040374191 \tabularnewline
16 & 15098 & 15059.6559095332 & 38.3440904667677 \tabularnewline
17 & 15254 & 15087.5761464832 & 166.423853516833 \tabularnewline
18 & 15522 & 15208.7576210663 & 313.242378933721 \tabularnewline
19 & 16669 & 15436.8449569798 & 1232.15504302024 \tabularnewline
20 & 16238 & 16334.0382491247 & -96.038249124671 \tabularnewline
21 & 16246 & 16264.1080293913 & -18.108029391291 \tabularnewline
22 & 15424 & 16250.9226737042 & -826.922673704228 \tabularnewline
23 & 14952 & 15648.7991989251 & -696.799198925102 \tabularnewline
24 & 15008 & 15141.4250898072 & -133.42508980718 \tabularnewline
25 & 14929 & 15044.2716542416 & -115.271654241629 \tabularnewline
26 & 13905 & 14960.3366368541 & -1055.3366368541 \tabularnewline
27 & 14994 & 14191.893609409 & 802.10639059104 \tabularnewline
28 & 14753 & 14775.9471157444 & -22.9471157443859 \tabularnewline
29 & 15031 & 14759.2381809098 & 271.761819090205 \tabularnewline
30 & 15386 & 14957.1214607211 & 428.878539278943 \tabularnewline
31 & 16160 & 15269.4092290224 & 890.590770977649 \tabularnewline
32 & 16116 & 15917.8926080367 & 198.107391963318 \tabularnewline
33 & 16219 & 16062.1444407915 & 156.855559208459 \tabularnewline
34 & 16064 & 16176.3587649991 & -112.35876499908 \tabularnewline
35 & 15436 & 16094.5447669621 & -658.544766962143 \tabularnewline
36 & 15404 & 15615.0256099839 & -211.025609983892 \tabularnewline
37 & 15112 & 15461.3673809965 & -349.367380996531 \tabularnewline
38 & 14119 & 15206.9756366297 & -1087.97563662969 \tabularnewline
39 & 14775 & 14414.7665321581 & 360.233467841927 \tabularnewline
40 & 14289 & 14677.0704141125 & -388.070414112455 \tabularnewline
41 & 15121 & 14394.4970688229 & 726.502931177074 \tabularnewline
42 & 15371 & 14923.4999408787 & 447.500059121321 \tabularnewline
43 & 15782 & 15249.3469627713 & 532.653037228716 \tabularnewline
44 & 16104 & 15637.1980978612 & 466.801902138755 \tabularnewline
45 & 15674 & 15977.0997504429 & -303.099750442881 \tabularnewline
46 & 15105 & 15756.3977661524 & -651.397766152351 \tabularnewline
47 & 14223 & 15282.0826954795 & -1059.08269547949 \tabularnewline
48 & 14385 & 14510.9119766698 & -125.911976669762 \tabularnewline
49 & 14558 & 14419.2292119814 & 138.770788018612 \tabularnewline
50 & 13804 & 14520.2751159536 & -716.275115953649 \tabularnewline
51 & 14672 & 13998.7196242124 & 673.280375787643 \tabularnewline
52 & 14244 & 14488.9685099441 & -244.968509944147 \tabularnewline
53 & 15089 & 14310.5947694367 & 778.40523056329 \tabularnewline
54 & 14580 & 14877.3902838389 & -297.390283838891 \tabularnewline
55 & 15218 & 14660.8456457913 & 557.154354208695 \tabularnewline
56 & 15696 & 15066.5374068379 & 629.462593162061 \tabularnewline
57 & 15129 & 15524.8803884621 & -395.880388462099 \tabularnewline
58 & 15110 & 15236.6202129007 & -126.620212900667 \tabularnewline
59 & 14204 & 15144.4217462321 & -940.421746232076 \tabularnewline
60 & 13655 & 14459.6539588614 & -804.653958861374 \tabularnewline
61 & 14534 & 13873.745441522 & 660.254558478042 \tabularnewline
62 & 12746 & 14354.5095826341 & -1608.50958263408 \tabularnewline
63 & 14074 & 13183.2738553893 & 890.726144610679 \tabularnewline
64 & 13699 & 13831.8558066703 & -132.855806670326 \tabularnewline
65 & 14184 & 13735.1168944349 & 448.883105565055 \tabularnewline
66 & 14110 & 14061.9709811438 & 48.0290188561576 \tabularnewline
67 & 15820 & 14096.9432955373 & 1723.05670446265 \tabularnewline
68 & 15362 & 15351.5864721297 & 10.4135278702925 \tabularnewline
69 & 14993 & 15359.1690790473 & -366.169079047331 \tabularnewline
70 & 14437 & 15092.5431837323 & -655.543183732345 \tabularnewline
71 & 13694 & 14615.2096286025 & -921.209628602532 \tabularnewline
72 & 13688 & 13944.431138409 & -256.431138408972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278589&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]2[/C][C]14236[/C][C]15071[/C][C]-835[/C][/ROW]
[ROW][C]3[/C][C]14771[/C][C]14462.9950227167[/C][C]308.004977283281[/C][/ROW]
[ROW][C]4[/C][C]14804[/C][C]14687.268746329[/C][C]116.731253670994[/C][/ROW]
[ROW][C]5[/C][C]15597[/C][C]14772.2665705643[/C][C]824.733429435686[/C][/ROW]
[ROW][C]6[/C][C]15418[/C][C]15372.7959478443[/C][C]45.2040521556792[/C][/ROW]
[ROW][C]7[/C][C]16903[/C][C]15405.7112636575[/C][C]1497.28873634247[/C][/ROW]
[ROW][C]8[/C][C]16350[/C][C]16495.9615680005[/C][C]-145.961568000545[/C][/ROW]
[ROW][C]9[/C][C]16393[/C][C]16389.679699933[/C][C]3.3203000670037[/C][/ROW]
[ROW][C]10[/C][C]15685[/C][C]16392.0973753424[/C][C]-707.097375342353[/C][/ROW]
[ROW][C]11[/C][C]14556[/C][C]15877.2246524297[/C][C]-1321.22465242966[/C][/ROW]
[ROW][C]12[/C][C]14850[/C][C]14915.175353284[/C][C]-65.175353284023[/C][/ROW]
[ROW][C]13[/C][C]15391[/C][C]14867.717941077[/C][C]523.282058923021[/C][/ROW]
[ROW][C]14[/C][C]13704[/C][C]15248.7456013743[/C][C]-1544.74560137427[/C][/ROW]
[ROW][C]15[/C][C]15409[/C][C]14123.9395962581[/C][C]1285.06040374191[/C][/ROW]
[ROW][C]16[/C][C]15098[/C][C]15059.6559095332[/C][C]38.3440904667677[/C][/ROW]
[ROW][C]17[/C][C]15254[/C][C]15087.5761464832[/C][C]166.423853516833[/C][/ROW]
[ROW][C]18[/C][C]15522[/C][C]15208.7576210663[/C][C]313.242378933721[/C][/ROW]
[ROW][C]19[/C][C]16669[/C][C]15436.8449569798[/C][C]1232.15504302024[/C][/ROW]
[ROW][C]20[/C][C]16238[/C][C]16334.0382491247[/C][C]-96.038249124671[/C][/ROW]
[ROW][C]21[/C][C]16246[/C][C]16264.1080293913[/C][C]-18.108029391291[/C][/ROW]
[ROW][C]22[/C][C]15424[/C][C]16250.9226737042[/C][C]-826.922673704228[/C][/ROW]
[ROW][C]23[/C][C]14952[/C][C]15648.7991989251[/C][C]-696.799198925102[/C][/ROW]
[ROW][C]24[/C][C]15008[/C][C]15141.4250898072[/C][C]-133.42508980718[/C][/ROW]
[ROW][C]25[/C][C]14929[/C][C]15044.2716542416[/C][C]-115.271654241629[/C][/ROW]
[ROW][C]26[/C][C]13905[/C][C]14960.3366368541[/C][C]-1055.3366368541[/C][/ROW]
[ROW][C]27[/C][C]14994[/C][C]14191.893609409[/C][C]802.10639059104[/C][/ROW]
[ROW][C]28[/C][C]14753[/C][C]14775.9471157444[/C][C]-22.9471157443859[/C][/ROW]
[ROW][C]29[/C][C]15031[/C][C]14759.2381809098[/C][C]271.761819090205[/C][/ROW]
[ROW][C]30[/C][C]15386[/C][C]14957.1214607211[/C][C]428.878539278943[/C][/ROW]
[ROW][C]31[/C][C]16160[/C][C]15269.4092290224[/C][C]890.590770977649[/C][/ROW]
[ROW][C]32[/C][C]16116[/C][C]15917.8926080367[/C][C]198.107391963318[/C][/ROW]
[ROW][C]33[/C][C]16219[/C][C]16062.1444407915[/C][C]156.855559208459[/C][/ROW]
[ROW][C]34[/C][C]16064[/C][C]16176.3587649991[/C][C]-112.35876499908[/C][/ROW]
[ROW][C]35[/C][C]15436[/C][C]16094.5447669621[/C][C]-658.544766962143[/C][/ROW]
[ROW][C]36[/C][C]15404[/C][C]15615.0256099839[/C][C]-211.025609983892[/C][/ROW]
[ROW][C]37[/C][C]15112[/C][C]15461.3673809965[/C][C]-349.367380996531[/C][/ROW]
[ROW][C]38[/C][C]14119[/C][C]15206.9756366297[/C][C]-1087.97563662969[/C][/ROW]
[ROW][C]39[/C][C]14775[/C][C]14414.7665321581[/C][C]360.233467841927[/C][/ROW]
[ROW][C]40[/C][C]14289[/C][C]14677.0704141125[/C][C]-388.070414112455[/C][/ROW]
[ROW][C]41[/C][C]15121[/C][C]14394.4970688229[/C][C]726.502931177074[/C][/ROW]
[ROW][C]42[/C][C]15371[/C][C]14923.4999408787[/C][C]447.500059121321[/C][/ROW]
[ROW][C]43[/C][C]15782[/C][C]15249.3469627713[/C][C]532.653037228716[/C][/ROW]
[ROW][C]44[/C][C]16104[/C][C]15637.1980978612[/C][C]466.801902138755[/C][/ROW]
[ROW][C]45[/C][C]15674[/C][C]15977.0997504429[/C][C]-303.099750442881[/C][/ROW]
[ROW][C]46[/C][C]15105[/C][C]15756.3977661524[/C][C]-651.397766152351[/C][/ROW]
[ROW][C]47[/C][C]14223[/C][C]15282.0826954795[/C][C]-1059.08269547949[/C][/ROW]
[ROW][C]48[/C][C]14385[/C][C]14510.9119766698[/C][C]-125.911976669762[/C][/ROW]
[ROW][C]49[/C][C]14558[/C][C]14419.2292119814[/C][C]138.770788018612[/C][/ROW]
[ROW][C]50[/C][C]13804[/C][C]14520.2751159536[/C][C]-716.275115953649[/C][/ROW]
[ROW][C]51[/C][C]14672[/C][C]13998.7196242124[/C][C]673.280375787643[/C][/ROW]
[ROW][C]52[/C][C]14244[/C][C]14488.9685099441[/C][C]-244.968509944147[/C][/ROW]
[ROW][C]53[/C][C]15089[/C][C]14310.5947694367[/C][C]778.40523056329[/C][/ROW]
[ROW][C]54[/C][C]14580[/C][C]14877.3902838389[/C][C]-297.390283838891[/C][/ROW]
[ROW][C]55[/C][C]15218[/C][C]14660.8456457913[/C][C]557.154354208695[/C][/ROW]
[ROW][C]56[/C][C]15696[/C][C]15066.5374068379[/C][C]629.462593162061[/C][/ROW]
[ROW][C]57[/C][C]15129[/C][C]15524.8803884621[/C][C]-395.880388462099[/C][/ROW]
[ROW][C]58[/C][C]15110[/C][C]15236.6202129007[/C][C]-126.620212900667[/C][/ROW]
[ROW][C]59[/C][C]14204[/C][C]15144.4217462321[/C][C]-940.421746232076[/C][/ROW]
[ROW][C]60[/C][C]13655[/C][C]14459.6539588614[/C][C]-804.653958861374[/C][/ROW]
[ROW][C]61[/C][C]14534[/C][C]13873.745441522[/C][C]660.254558478042[/C][/ROW]
[ROW][C]62[/C][C]12746[/C][C]14354.5095826341[/C][C]-1608.50958263408[/C][/ROW]
[ROW][C]63[/C][C]14074[/C][C]13183.2738553893[/C][C]890.726144610679[/C][/ROW]
[ROW][C]64[/C][C]13699[/C][C]13831.8558066703[/C][C]-132.855806670326[/C][/ROW]
[ROW][C]65[/C][C]14184[/C][C]13735.1168944349[/C][C]448.883105565055[/C][/ROW]
[ROW][C]66[/C][C]14110[/C][C]14061.9709811438[/C][C]48.0290188561576[/C][/ROW]
[ROW][C]67[/C][C]15820[/C][C]14096.9432955373[/C][C]1723.05670446265[/C][/ROW]
[ROW][C]68[/C][C]15362[/C][C]15351.5864721297[/C][C]10.4135278702925[/C][/ROW]
[ROW][C]69[/C][C]14993[/C][C]15359.1690790473[/C][C]-366.169079047331[/C][/ROW]
[ROW][C]70[/C][C]14437[/C][C]15092.5431837323[/C][C]-655.543183732345[/C][/ROW]
[ROW][C]71[/C][C]13694[/C][C]14615.2096286025[/C][C]-921.209628602532[/C][/ROW]
[ROW][C]72[/C][C]13688[/C][C]13944.431138409[/C][C]-256.431138408972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278589&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278589&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
21423615071-835
31477114462.9950227167308.004977283281
41480414687.268746329116.731253670994
51559714772.2665705643824.733429435686
61541815372.795947844345.2040521556792
71690315405.71126365751497.28873634247
81635016495.9615680005-145.961568000545
91639316389.6796999333.3203000670037
101568516392.0973753424-707.097375342353
111455615877.2246524297-1321.22465242966
121485014915.175353284-65.175353284023
131539114867.717941077523.282058923021
141370415248.7456013743-1544.74560137427
151540914123.93959625811285.06040374191
161509815059.655909533238.3440904667677
171525415087.5761464832166.423853516833
181552215208.7576210663313.242378933721
191666915436.84495697981232.15504302024
201623816334.0382491247-96.038249124671
211624616264.1080293913-18.108029391291
221542416250.9226737042-826.922673704228
231495215648.7991989251-696.799198925102
241500815141.4250898072-133.42508980718
251492915044.2716542416-115.271654241629
261390514960.3366368541-1055.3366368541
271499414191.893609409802.10639059104
281475314775.9471157444-22.9471157443859
291503114759.2381809098271.761819090205
301538614957.1214607211428.878539278943
311616015269.4092290224890.590770977649
321611615917.8926080367198.107391963318
331621916062.1444407915156.855559208459
341606416176.3587649991-112.35876499908
351543616094.5447669621-658.544766962143
361540415615.0256099839-211.025609983892
371511215461.3673809965-349.367380996531
381411915206.9756366297-1087.97563662969
391477514414.7665321581360.233467841927
401428914677.0704141125-388.070414112455
411512114394.4970688229726.502931177074
421537114923.4999408787447.500059121321
431578215249.3469627713532.653037228716
441610415637.1980978612466.801902138755
451567415977.0997504429-303.099750442881
461510515756.3977661524-651.397766152351
471422315282.0826954795-1059.08269547949
481438514510.9119766698-125.911976669762
491455814419.2292119814138.770788018612
501380414520.2751159536-716.275115953649
511467213998.7196242124673.280375787643
521424414488.9685099441-244.968509944147
531508914310.5947694367778.40523056329
541458014877.3902838389-297.390283838891
551521814660.8456457913557.154354208695
561569615066.5374068379629.462593162061
571512915524.8803884621-395.880388462099
581511015236.6202129007-126.620212900667
591420415144.4217462321-940.421746232076
601365514459.6539588614-804.653958861374
611453413873.745441522660.254558478042
621274614354.5095826341-1608.50958263408
631407413183.2738553893890.726144610679
641369913831.8558066703-132.855806670326
651418413735.1168944349448.883105565055
661411014061.970981143848.0290188561576
671582014096.94329553731723.05670446265
681536215351.586472129710.4135278702925
691499315359.1690790473-366.169079047331
701443715092.5431837323-655.543183732345
711369414615.2096286025-921.209628602532
721368813944.431138409-256.431138408972







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7313757.710888728612399.981340528215115.4404369291
7413757.710888728612078.181356485915437.2404209714
7513757.710888728611808.811359944615706.6104175127
7613757.710888728611572.396426937415943.0253505199
7713757.710888728611359.171912490616156.2498649667
7813757.710888728611163.413460878116352.0083165792
7913757.710888728610981.423967718616533.9978097386
8013757.710888728610810.651508364816704.7702690924
8113757.710888728610649.246812209616866.1749652477
8213757.710888728610495.818977792817019.6027996645
8313757.710888728610349.290615017117166.1311624401
8413757.710888728610208.807017690917306.6147597664

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 13757.7108887286 & 12399.9813405282 & 15115.4404369291 \tabularnewline
74 & 13757.7108887286 & 12078.1813564859 & 15437.2404209714 \tabularnewline
75 & 13757.7108887286 & 11808.8113599446 & 15706.6104175127 \tabularnewline
76 & 13757.7108887286 & 11572.3964269374 & 15943.0253505199 \tabularnewline
77 & 13757.7108887286 & 11359.1719124906 & 16156.2498649667 \tabularnewline
78 & 13757.7108887286 & 11163.4134608781 & 16352.0083165792 \tabularnewline
79 & 13757.7108887286 & 10981.4239677186 & 16533.9978097386 \tabularnewline
80 & 13757.7108887286 & 10810.6515083648 & 16704.7702690924 \tabularnewline
81 & 13757.7108887286 & 10649.2468122096 & 16866.1749652477 \tabularnewline
82 & 13757.7108887286 & 10495.8189777928 & 17019.6027996645 \tabularnewline
83 & 13757.7108887286 & 10349.2906150171 & 17166.1311624401 \tabularnewline
84 & 13757.7108887286 & 10208.8070176909 & 17306.6147597664 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278589&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]73[/C][C]13757.7108887286[/C][C]12399.9813405282[/C][C]15115.4404369291[/C][/ROW]
[ROW][C]74[/C][C]13757.7108887286[/C][C]12078.1813564859[/C][C]15437.2404209714[/C][/ROW]
[ROW][C]75[/C][C]13757.7108887286[/C][C]11808.8113599446[/C][C]15706.6104175127[/C][/ROW]
[ROW][C]76[/C][C]13757.7108887286[/C][C]11572.3964269374[/C][C]15943.0253505199[/C][/ROW]
[ROW][C]77[/C][C]13757.7108887286[/C][C]11359.1719124906[/C][C]16156.2498649667[/C][/ROW]
[ROW][C]78[/C][C]13757.7108887286[/C][C]11163.4134608781[/C][C]16352.0083165792[/C][/ROW]
[ROW][C]79[/C][C]13757.7108887286[/C][C]10981.4239677186[/C][C]16533.9978097386[/C][/ROW]
[ROW][C]80[/C][C]13757.7108887286[/C][C]10810.6515083648[/C][C]16704.7702690924[/C][/ROW]
[ROW][C]81[/C][C]13757.7108887286[/C][C]10649.2468122096[/C][C]16866.1749652477[/C][/ROW]
[ROW][C]82[/C][C]13757.7108887286[/C][C]10495.8189777928[/C][C]17019.6027996645[/C][/ROW]
[ROW][C]83[/C][C]13757.7108887286[/C][C]10349.2906150171[/C][C]17166.1311624401[/C][/ROW]
[ROW][C]84[/C][C]13757.7108887286[/C][C]10208.8070176909[/C][C]17306.6147597664[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278589&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278589&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
7313757.710888728612399.981340528215115.4404369291
7413757.710888728612078.181356485915437.2404209714
7513757.710888728611808.811359944615706.6104175127
7613757.710888728611572.396426937415943.0253505199
7713757.710888728611359.171912490616156.2498649667
7813757.710888728611163.413460878116352.0083165792
7913757.710888728610981.423967718616533.9978097386
8013757.710888728610810.651508364816704.7702690924
8113757.710888728610649.246812209616866.1749652477
8213757.710888728610495.818977792817019.6027996645
8313757.710888728610349.290615017117166.1311624401
8413757.710888728610208.807017690917306.6147597664



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