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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 26 May 2013 15:26:54 -0400
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/May/26/t13695970197igws4jx70ilkse.htm/, Retrieved Fri, 01 Nov 2024 00:19:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210661, Retrieved Fri, 01 Nov 2024 00:19:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-05-26 19:26:54] [1f4ca98ed28755372cdf3133ccb2c2d2] [Current]
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Dataseries X:
9.11	
9.06	
9.11	
9.13	
9.13	
9.19	
9.2	
9.23	
9.24	
9.28	
9.32	
9.32	
9.32	
9.36	
9.37	
9.38	
9.41	
9.44	
9.44	
9.44	
9.47	
9.48	
9.56	
9.58	
9.56	
9.58	
9.7	
9.74	
9.76	
9.78	
9.84	
9.88	
9.96	
9.97	
9.96	
9.96	
9.96	
10.02	
10.08	
10.09	
10.12	
10.14	
10.17	
10.22	
10.25	
10.25	
10.26	
10.34	
10.33	
10.3	
10.33	
10.33	
10.37	
10.44	
10.45	
10.45	
10.44	
10.43	
10.4	
10.43	
10.47	
10.52	
10.55	
10.5	
10.44	
10.47	
10.5	
10.54	
10.55	
10.53	
10.54	
10.54	




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210661&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210661&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210661&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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.228398787427413
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.228398787427413 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210661&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]0.228398787427413[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210661&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210661&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
beta0.228398787427413
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
39.119.010.0999999999999979
49.139.082839878742740.0471601212572601
59.139.113611193252830.0163888067471696
69.199.117354376841270.0726456231587331
79.29.193946549082630.00605345091737064
89.239.205329149931910.0246708500680928
99.249.24096394217226-0.000963942172264254
109.289.250743778948970.0292562210510301
119.329.297425864361730.0225741356382692
129.329.34258176956873-0.0225817695687347
139.329.33742412078127-0.0174241207812713
149.369.333444472722840.0265555272771589
159.379.37950972295244-0.00950972295243879
169.389.38733771376133-0.00733771376132886
179.419.395661788835750.0143382111642456
189.449.428936618879550.0110633811204544
199.449.4614634817123-0.0214634817123045
209.449.45656124851524-0.0165612485152433
219.479.452778679436080.0172213205639231
229.489.48671200817078-0.00671200817077633
239.569.495178993643370.064821006356631
249.589.58998403289505-0.00998403289504779
259.569.60770369188818-0.0477036918881826
269.589.576808226505110.00319177349488875
279.79.597537223701090.102462776298912
289.749.7409395975642-0.000939597564203254
299.769.78072499461987-0.0207249946198704
309.789.79599143097925-0.0159914309792537
319.849.812339007534360.0276609924656377
329.889.878656744672550.00134325532744839
339.969.918963542560550.0410364574394535
349.9710.00833621968-0.0383362196800352
359.9610.0095802735906-0.0495802735905642
369.969.98825619922216-0.0282561992221595
379.969.98180251758251-0.0218025175825112
3810.029.97682284900380.0431771509961987
3910.0810.04668445793590.0333155420640985
4010.0910.1142936873458-0.0242936873458302
4110.1210.11874503861390.00125496138609726
4210.1410.1490316702728-0.00903167027275309
4310.1710.1669688477340.00303115226598649
4410.2210.19766115923610.0223388407639291
4510.2510.2527633233791-0.00276332337908869
4610.2510.28213218367-0.0321321836700346
4710.2610.2747932318824-0.014793231882404
4810.3410.28141447565830.0585855243416695
4910.3310.3747953383788-0.0447953383787656
5010.310.3545641374107-0.0545641374106545
5110.3310.3121017545890.0178982454109597
5210.3310.346189692138-0.0161896921379814
5310.3710.34249198608480.0275080139151562
5410.4410.38877478310760.0512252168923997
5510.4510.4704745605315-0.0204745605315306
5610.4510.475798195733-0.0257981957330209
5710.4410.4699059191098-0.0299059191097832
5810.4310.4530754434482-0.0230754434482066
5910.410.4378050401453-0.037805040145285
6010.4310.39917041481750.0308295851825413
6110.4710.436211854690.0337881453099591
6210.5210.48392902610830.0360709738917411
6310.5510.54216759280650.00783240719354517
6410.510.5739565051121-0.0739565051121005
6510.4410.5070649290221-0.067064929022127
6610.4710.43174738055460.0382526194454336
6710.510.47048423245180.0295157675481725
6810.5410.50722559796980.0327744020301797
6910.5510.5547112316522-0.0047112316521698
7010.5310.5636351920555-0.0336351920555273
7110.5410.53595295497520.00404704502484421
7210.5410.5468772951515-0.00687729515149371

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 9.11 & 9.01 & 0.0999999999999979 \tabularnewline
4 & 9.13 & 9.08283987874274 & 0.0471601212572601 \tabularnewline
5 & 9.13 & 9.11361119325283 & 0.0163888067471696 \tabularnewline
6 & 9.19 & 9.11735437684127 & 0.0726456231587331 \tabularnewline
7 & 9.2 & 9.19394654908263 & 0.00605345091737064 \tabularnewline
8 & 9.23 & 9.20532914993191 & 0.0246708500680928 \tabularnewline
9 & 9.24 & 9.24096394217226 & -0.000963942172264254 \tabularnewline
10 & 9.28 & 9.25074377894897 & 0.0292562210510301 \tabularnewline
11 & 9.32 & 9.29742586436173 & 0.0225741356382692 \tabularnewline
12 & 9.32 & 9.34258176956873 & -0.0225817695687347 \tabularnewline
13 & 9.32 & 9.33742412078127 & -0.0174241207812713 \tabularnewline
14 & 9.36 & 9.33344447272284 & 0.0265555272771589 \tabularnewline
15 & 9.37 & 9.37950972295244 & -0.00950972295243879 \tabularnewline
16 & 9.38 & 9.38733771376133 & -0.00733771376132886 \tabularnewline
17 & 9.41 & 9.39566178883575 & 0.0143382111642456 \tabularnewline
18 & 9.44 & 9.42893661887955 & 0.0110633811204544 \tabularnewline
19 & 9.44 & 9.4614634817123 & -0.0214634817123045 \tabularnewline
20 & 9.44 & 9.45656124851524 & -0.0165612485152433 \tabularnewline
21 & 9.47 & 9.45277867943608 & 0.0172213205639231 \tabularnewline
22 & 9.48 & 9.48671200817078 & -0.00671200817077633 \tabularnewline
23 & 9.56 & 9.49517899364337 & 0.064821006356631 \tabularnewline
24 & 9.58 & 9.58998403289505 & -0.00998403289504779 \tabularnewline
25 & 9.56 & 9.60770369188818 & -0.0477036918881826 \tabularnewline
26 & 9.58 & 9.57680822650511 & 0.00319177349488875 \tabularnewline
27 & 9.7 & 9.59753722370109 & 0.102462776298912 \tabularnewline
28 & 9.74 & 9.7409395975642 & -0.000939597564203254 \tabularnewline
29 & 9.76 & 9.78072499461987 & -0.0207249946198704 \tabularnewline
30 & 9.78 & 9.79599143097925 & -0.0159914309792537 \tabularnewline
31 & 9.84 & 9.81233900753436 & 0.0276609924656377 \tabularnewline
32 & 9.88 & 9.87865674467255 & 0.00134325532744839 \tabularnewline
33 & 9.96 & 9.91896354256055 & 0.0410364574394535 \tabularnewline
34 & 9.97 & 10.00833621968 & -0.0383362196800352 \tabularnewline
35 & 9.96 & 10.0095802735906 & -0.0495802735905642 \tabularnewline
36 & 9.96 & 9.98825619922216 & -0.0282561992221595 \tabularnewline
37 & 9.96 & 9.98180251758251 & -0.0218025175825112 \tabularnewline
38 & 10.02 & 9.9768228490038 & 0.0431771509961987 \tabularnewline
39 & 10.08 & 10.0466844579359 & 0.0333155420640985 \tabularnewline
40 & 10.09 & 10.1142936873458 & -0.0242936873458302 \tabularnewline
41 & 10.12 & 10.1187450386139 & 0.00125496138609726 \tabularnewline
42 & 10.14 & 10.1490316702728 & -0.00903167027275309 \tabularnewline
43 & 10.17 & 10.166968847734 & 0.00303115226598649 \tabularnewline
44 & 10.22 & 10.1976611592361 & 0.0223388407639291 \tabularnewline
45 & 10.25 & 10.2527633233791 & -0.00276332337908869 \tabularnewline
46 & 10.25 & 10.28213218367 & -0.0321321836700346 \tabularnewline
47 & 10.26 & 10.2747932318824 & -0.014793231882404 \tabularnewline
48 & 10.34 & 10.2814144756583 & 0.0585855243416695 \tabularnewline
49 & 10.33 & 10.3747953383788 & -0.0447953383787656 \tabularnewline
50 & 10.3 & 10.3545641374107 & -0.0545641374106545 \tabularnewline
51 & 10.33 & 10.312101754589 & 0.0178982454109597 \tabularnewline
52 & 10.33 & 10.346189692138 & -0.0161896921379814 \tabularnewline
53 & 10.37 & 10.3424919860848 & 0.0275080139151562 \tabularnewline
54 & 10.44 & 10.3887747831076 & 0.0512252168923997 \tabularnewline
55 & 10.45 & 10.4704745605315 & -0.0204745605315306 \tabularnewline
56 & 10.45 & 10.475798195733 & -0.0257981957330209 \tabularnewline
57 & 10.44 & 10.4699059191098 & -0.0299059191097832 \tabularnewline
58 & 10.43 & 10.4530754434482 & -0.0230754434482066 \tabularnewline
59 & 10.4 & 10.4378050401453 & -0.037805040145285 \tabularnewline
60 & 10.43 & 10.3991704148175 & 0.0308295851825413 \tabularnewline
61 & 10.47 & 10.43621185469 & 0.0337881453099591 \tabularnewline
62 & 10.52 & 10.4839290261083 & 0.0360709738917411 \tabularnewline
63 & 10.55 & 10.5421675928065 & 0.00783240719354517 \tabularnewline
64 & 10.5 & 10.5739565051121 & -0.0739565051121005 \tabularnewline
65 & 10.44 & 10.5070649290221 & -0.067064929022127 \tabularnewline
66 & 10.47 & 10.4317473805546 & 0.0382526194454336 \tabularnewline
67 & 10.5 & 10.4704842324518 & 0.0295157675481725 \tabularnewline
68 & 10.54 & 10.5072255979698 & 0.0327744020301797 \tabularnewline
69 & 10.55 & 10.5547112316522 & -0.0047112316521698 \tabularnewline
70 & 10.53 & 10.5636351920555 & -0.0336351920555273 \tabularnewline
71 & 10.54 & 10.5359529549752 & 0.00404704502484421 \tabularnewline
72 & 10.54 & 10.5468772951515 & -0.00687729515149371 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210661&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]9.11[/C][C]9.01[/C][C]0.0999999999999979[/C][/ROW]
[ROW][C]4[/C][C]9.13[/C][C]9.08283987874274[/C][C]0.0471601212572601[/C][/ROW]
[ROW][C]5[/C][C]9.13[/C][C]9.11361119325283[/C][C]0.0163888067471696[/C][/ROW]
[ROW][C]6[/C][C]9.19[/C][C]9.11735437684127[/C][C]0.0726456231587331[/C][/ROW]
[ROW][C]7[/C][C]9.2[/C][C]9.19394654908263[/C][C]0.00605345091737064[/C][/ROW]
[ROW][C]8[/C][C]9.23[/C][C]9.20532914993191[/C][C]0.0246708500680928[/C][/ROW]
[ROW][C]9[/C][C]9.24[/C][C]9.24096394217226[/C][C]-0.000963942172264254[/C][/ROW]
[ROW][C]10[/C][C]9.28[/C][C]9.25074377894897[/C][C]0.0292562210510301[/C][/ROW]
[ROW][C]11[/C][C]9.32[/C][C]9.29742586436173[/C][C]0.0225741356382692[/C][/ROW]
[ROW][C]12[/C][C]9.32[/C][C]9.34258176956873[/C][C]-0.0225817695687347[/C][/ROW]
[ROW][C]13[/C][C]9.32[/C][C]9.33742412078127[/C][C]-0.0174241207812713[/C][/ROW]
[ROW][C]14[/C][C]9.36[/C][C]9.33344447272284[/C][C]0.0265555272771589[/C][/ROW]
[ROW][C]15[/C][C]9.37[/C][C]9.37950972295244[/C][C]-0.00950972295243879[/C][/ROW]
[ROW][C]16[/C][C]9.38[/C][C]9.38733771376133[/C][C]-0.00733771376132886[/C][/ROW]
[ROW][C]17[/C][C]9.41[/C][C]9.39566178883575[/C][C]0.0143382111642456[/C][/ROW]
[ROW][C]18[/C][C]9.44[/C][C]9.42893661887955[/C][C]0.0110633811204544[/C][/ROW]
[ROW][C]19[/C][C]9.44[/C][C]9.4614634817123[/C][C]-0.0214634817123045[/C][/ROW]
[ROW][C]20[/C][C]9.44[/C][C]9.45656124851524[/C][C]-0.0165612485152433[/C][/ROW]
[ROW][C]21[/C][C]9.47[/C][C]9.45277867943608[/C][C]0.0172213205639231[/C][/ROW]
[ROW][C]22[/C][C]9.48[/C][C]9.48671200817078[/C][C]-0.00671200817077633[/C][/ROW]
[ROW][C]23[/C][C]9.56[/C][C]9.49517899364337[/C][C]0.064821006356631[/C][/ROW]
[ROW][C]24[/C][C]9.58[/C][C]9.58998403289505[/C][C]-0.00998403289504779[/C][/ROW]
[ROW][C]25[/C][C]9.56[/C][C]9.60770369188818[/C][C]-0.0477036918881826[/C][/ROW]
[ROW][C]26[/C][C]9.58[/C][C]9.57680822650511[/C][C]0.00319177349488875[/C][/ROW]
[ROW][C]27[/C][C]9.7[/C][C]9.59753722370109[/C][C]0.102462776298912[/C][/ROW]
[ROW][C]28[/C][C]9.74[/C][C]9.7409395975642[/C][C]-0.000939597564203254[/C][/ROW]
[ROW][C]29[/C][C]9.76[/C][C]9.78072499461987[/C][C]-0.0207249946198704[/C][/ROW]
[ROW][C]30[/C][C]9.78[/C][C]9.79599143097925[/C][C]-0.0159914309792537[/C][/ROW]
[ROW][C]31[/C][C]9.84[/C][C]9.81233900753436[/C][C]0.0276609924656377[/C][/ROW]
[ROW][C]32[/C][C]9.88[/C][C]9.87865674467255[/C][C]0.00134325532744839[/C][/ROW]
[ROW][C]33[/C][C]9.96[/C][C]9.91896354256055[/C][C]0.0410364574394535[/C][/ROW]
[ROW][C]34[/C][C]9.97[/C][C]10.00833621968[/C][C]-0.0383362196800352[/C][/ROW]
[ROW][C]35[/C][C]9.96[/C][C]10.0095802735906[/C][C]-0.0495802735905642[/C][/ROW]
[ROW][C]36[/C][C]9.96[/C][C]9.98825619922216[/C][C]-0.0282561992221595[/C][/ROW]
[ROW][C]37[/C][C]9.96[/C][C]9.98180251758251[/C][C]-0.0218025175825112[/C][/ROW]
[ROW][C]38[/C][C]10.02[/C][C]9.9768228490038[/C][C]0.0431771509961987[/C][/ROW]
[ROW][C]39[/C][C]10.08[/C][C]10.0466844579359[/C][C]0.0333155420640985[/C][/ROW]
[ROW][C]40[/C][C]10.09[/C][C]10.1142936873458[/C][C]-0.0242936873458302[/C][/ROW]
[ROW][C]41[/C][C]10.12[/C][C]10.1187450386139[/C][C]0.00125496138609726[/C][/ROW]
[ROW][C]42[/C][C]10.14[/C][C]10.1490316702728[/C][C]-0.00903167027275309[/C][/ROW]
[ROW][C]43[/C][C]10.17[/C][C]10.166968847734[/C][C]0.00303115226598649[/C][/ROW]
[ROW][C]44[/C][C]10.22[/C][C]10.1976611592361[/C][C]0.0223388407639291[/C][/ROW]
[ROW][C]45[/C][C]10.25[/C][C]10.2527633233791[/C][C]-0.00276332337908869[/C][/ROW]
[ROW][C]46[/C][C]10.25[/C][C]10.28213218367[/C][C]-0.0321321836700346[/C][/ROW]
[ROW][C]47[/C][C]10.26[/C][C]10.2747932318824[/C][C]-0.014793231882404[/C][/ROW]
[ROW][C]48[/C][C]10.34[/C][C]10.2814144756583[/C][C]0.0585855243416695[/C][/ROW]
[ROW][C]49[/C][C]10.33[/C][C]10.3747953383788[/C][C]-0.0447953383787656[/C][/ROW]
[ROW][C]50[/C][C]10.3[/C][C]10.3545641374107[/C][C]-0.0545641374106545[/C][/ROW]
[ROW][C]51[/C][C]10.33[/C][C]10.312101754589[/C][C]0.0178982454109597[/C][/ROW]
[ROW][C]52[/C][C]10.33[/C][C]10.346189692138[/C][C]-0.0161896921379814[/C][/ROW]
[ROW][C]53[/C][C]10.37[/C][C]10.3424919860848[/C][C]0.0275080139151562[/C][/ROW]
[ROW][C]54[/C][C]10.44[/C][C]10.3887747831076[/C][C]0.0512252168923997[/C][/ROW]
[ROW][C]55[/C][C]10.45[/C][C]10.4704745605315[/C][C]-0.0204745605315306[/C][/ROW]
[ROW][C]56[/C][C]10.45[/C][C]10.475798195733[/C][C]-0.0257981957330209[/C][/ROW]
[ROW][C]57[/C][C]10.44[/C][C]10.4699059191098[/C][C]-0.0299059191097832[/C][/ROW]
[ROW][C]58[/C][C]10.43[/C][C]10.4530754434482[/C][C]-0.0230754434482066[/C][/ROW]
[ROW][C]59[/C][C]10.4[/C][C]10.4378050401453[/C][C]-0.037805040145285[/C][/ROW]
[ROW][C]60[/C][C]10.43[/C][C]10.3991704148175[/C][C]0.0308295851825413[/C][/ROW]
[ROW][C]61[/C][C]10.47[/C][C]10.43621185469[/C][C]0.0337881453099591[/C][/ROW]
[ROW][C]62[/C][C]10.52[/C][C]10.4839290261083[/C][C]0.0360709738917411[/C][/ROW]
[ROW][C]63[/C][C]10.55[/C][C]10.5421675928065[/C][C]0.00783240719354517[/C][/ROW]
[ROW][C]64[/C][C]10.5[/C][C]10.5739565051121[/C][C]-0.0739565051121005[/C][/ROW]
[ROW][C]65[/C][C]10.44[/C][C]10.5070649290221[/C][C]-0.067064929022127[/C][/ROW]
[ROW][C]66[/C][C]10.47[/C][C]10.4317473805546[/C][C]0.0382526194454336[/C][/ROW]
[ROW][C]67[/C][C]10.5[/C][C]10.4704842324518[/C][C]0.0295157675481725[/C][/ROW]
[ROW][C]68[/C][C]10.54[/C][C]10.5072255979698[/C][C]0.0327744020301797[/C][/ROW]
[ROW][C]69[/C][C]10.55[/C][C]10.5547112316522[/C][C]-0.0047112316521698[/C][/ROW]
[ROW][C]70[/C][C]10.53[/C][C]10.5636351920555[/C][C]-0.0336351920555273[/C][/ROW]
[ROW][C]71[/C][C]10.54[/C][C]10.5359529549752[/C][C]0.00404704502484421[/C][/ROW]
[ROW][C]72[/C][C]10.54[/C][C]10.5468772951515[/C][C]-0.00687729515149371[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210661&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210661&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
39.119.010.0999999999999979
49.139.082839878742740.0471601212572601
59.139.113611193252830.0163888067471696
69.199.117354376841270.0726456231587331
79.29.193946549082630.00605345091737064
89.239.205329149931910.0246708500680928
99.249.24096394217226-0.000963942172264254
109.289.250743778948970.0292562210510301
119.329.297425864361730.0225741356382692
129.329.34258176956873-0.0225817695687347
139.329.33742412078127-0.0174241207812713
149.369.333444472722840.0265555272771589
159.379.37950972295244-0.00950972295243879
169.389.38733771376133-0.00733771376132886
179.419.395661788835750.0143382111642456
189.449.428936618879550.0110633811204544
199.449.4614634817123-0.0214634817123045
209.449.45656124851524-0.0165612485152433
219.479.452778679436080.0172213205639231
229.489.48671200817078-0.00671200817077633
239.569.495178993643370.064821006356631
249.589.58998403289505-0.00998403289504779
259.569.60770369188818-0.0477036918881826
269.589.576808226505110.00319177349488875
279.79.597537223701090.102462776298912
289.749.7409395975642-0.000939597564203254
299.769.78072499461987-0.0207249946198704
309.789.79599143097925-0.0159914309792537
319.849.812339007534360.0276609924656377
329.889.878656744672550.00134325532744839
339.969.918963542560550.0410364574394535
349.9710.00833621968-0.0383362196800352
359.9610.0095802735906-0.0495802735905642
369.969.98825619922216-0.0282561992221595
379.969.98180251758251-0.0218025175825112
3810.029.97682284900380.0431771509961987
3910.0810.04668445793590.0333155420640985
4010.0910.1142936873458-0.0242936873458302
4110.1210.11874503861390.00125496138609726
4210.1410.1490316702728-0.00903167027275309
4310.1710.1669688477340.00303115226598649
4410.2210.19766115923610.0223388407639291
4510.2510.2527633233791-0.00276332337908869
4610.2510.28213218367-0.0321321836700346
4710.2610.2747932318824-0.014793231882404
4810.3410.28141447565830.0585855243416695
4910.3310.3747953383788-0.0447953383787656
5010.310.3545641374107-0.0545641374106545
5110.3310.3121017545890.0178982454109597
5210.3310.346189692138-0.0161896921379814
5310.3710.34249198608480.0275080139151562
5410.4410.38877478310760.0512252168923997
5510.4510.4704745605315-0.0204745605315306
5610.4510.475798195733-0.0257981957330209
5710.4410.4699059191098-0.0299059191097832
5810.4310.4530754434482-0.0230754434482066
5910.410.4378050401453-0.037805040145285
6010.4310.39917041481750.0308295851825413
6110.4710.436211854690.0337881453099591
6210.5210.48392902610830.0360709738917411
6310.5510.54216759280650.00783240719354517
6410.510.5739565051121-0.0739565051121005
6510.4410.5070649290221-0.067064929022127
6610.4710.43174738055460.0382526194454336
6710.510.47048423245180.0295157675481725
6810.5410.50722559796980.0327744020301797
6910.5510.5547112316522-0.0047112316521698
7010.5310.5636351920555-0.0336351920555273
7110.5410.53595295497520.00404704502484421
7210.5410.5468772951515-0.00687729515149371







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7310.545306529278110.475623273532710.6149897850235
7410.550613058556210.440236814321510.660989302791
7510.555919587834310.405959298796910.7058798768718
7610.561226117112410.370758571505210.7516936627197
7710.566532646390610.334026906625610.7990383861555
7810.571839175668710.295546218143310.848132133194
7910.577145704946810.255243336516610.8990480733769
8010.582452234224910.213107491335410.9517969771143
8110.58775876350310.169156778219411.0063607487866
8210.593065292781110.123422881409611.0627077041526
8310.598371822059210.075943580733911.1208000633846
8410.603678351337310.026758901831911.1805978008428

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 10.5453065292781 & 10.4756232735327 & 10.6149897850235 \tabularnewline
74 & 10.5506130585562 & 10.4402368143215 & 10.660989302791 \tabularnewline
75 & 10.5559195878343 & 10.4059592987969 & 10.7058798768718 \tabularnewline
76 & 10.5612261171124 & 10.3707585715052 & 10.7516936627197 \tabularnewline
77 & 10.5665326463906 & 10.3340269066256 & 10.7990383861555 \tabularnewline
78 & 10.5718391756687 & 10.2955462181433 & 10.848132133194 \tabularnewline
79 & 10.5771457049468 & 10.2552433365166 & 10.8990480733769 \tabularnewline
80 & 10.5824522342249 & 10.2131074913354 & 10.9517969771143 \tabularnewline
81 & 10.587758763503 & 10.1691567782194 & 11.0063607487866 \tabularnewline
82 & 10.5930652927811 & 10.1234228814096 & 11.0627077041526 \tabularnewline
83 & 10.5983718220592 & 10.0759435807339 & 11.1208000633846 \tabularnewline
84 & 10.6036783513373 & 10.0267589018319 & 11.1805978008428 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210661&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]10.5453065292781[/C][C]10.4756232735327[/C][C]10.6149897850235[/C][/ROW]
[ROW][C]74[/C][C]10.5506130585562[/C][C]10.4402368143215[/C][C]10.660989302791[/C][/ROW]
[ROW][C]75[/C][C]10.5559195878343[/C][C]10.4059592987969[/C][C]10.7058798768718[/C][/ROW]
[ROW][C]76[/C][C]10.5612261171124[/C][C]10.3707585715052[/C][C]10.7516936627197[/C][/ROW]
[ROW][C]77[/C][C]10.5665326463906[/C][C]10.3340269066256[/C][C]10.7990383861555[/C][/ROW]
[ROW][C]78[/C][C]10.5718391756687[/C][C]10.2955462181433[/C][C]10.848132133194[/C][/ROW]
[ROW][C]79[/C][C]10.5771457049468[/C][C]10.2552433365166[/C][C]10.8990480733769[/C][/ROW]
[ROW][C]80[/C][C]10.5824522342249[/C][C]10.2131074913354[/C][C]10.9517969771143[/C][/ROW]
[ROW][C]81[/C][C]10.587758763503[/C][C]10.1691567782194[/C][C]11.0063607487866[/C][/ROW]
[ROW][C]82[/C][C]10.5930652927811[/C][C]10.1234228814096[/C][C]11.0627077041526[/C][/ROW]
[ROW][C]83[/C][C]10.5983718220592[/C][C]10.0759435807339[/C][C]11.1208000633846[/C][/ROW]
[ROW][C]84[/C][C]10.6036783513373[/C][C]10.0267589018319[/C][C]11.1805978008428[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210661&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210661&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
7310.545306529278110.475623273532710.6149897850235
7410.550613058556210.440236814321510.660989302791
7510.555919587834310.405959298796910.7058798768718
7610.561226117112410.370758571505210.7516936627197
7710.566532646390610.334026906625610.7990383861555
7810.571839175668710.295546218143310.848132133194
7910.577145704946810.255243336516610.8990480733769
8010.582452234224910.213107491335410.9517969771143
8110.58775876350310.169156778219411.0063607487866
8210.593065292781110.123422881409611.0627077041526
8310.598371822059210.075943580733911.1208000633846
8410.603678351337310.026758901831911.1805978008428



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')