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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 05:11:10 -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/2012/Dec/17/t13557391034tdgp5cugfvcr5v.htm/, Retrieved Thu, 31 Oct 2024 23:37:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200745, Retrieved Thu, 31 Oct 2024 23:37:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 oef 2] [2012-12-17 10:11:10] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
7.72
7.67
7.84
7.79
7.83
7.94
8.02
8.06
8.12
8.13
7.97
8.01
8
7.9
7.99
8.02
8.08
8.02
8.07
8.11
8.19
8.16
8.08
8.22
8.15
8.19
8.31
8.3
8.34
8.31
8.38
8.34
8.44
8.64
8.6
8.61
8.54
8.69
8.73
8.91
9.01
9.08
8.94
9.03
9.02
8.96
9.03
8.94
8.95
8.95
8.99
8.93
8.98
8.95
9.02
8.92
9.1
9.06
8.97
8.89
8.99
8.79
8.83
8.61
8.71
8.91
8.91
8.89
8.98
9
8.99
8.88




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=200745&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=200745&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200745&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
alpha0.81825522940517
beta0.111590999872759
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.81825522940517 \tabularnewline
beta & 0.111590999872759 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200745&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]0.81825522940517[/C][/ROW]
[ROW][C]beta[/C][C]0.111590999872759[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200745&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200745&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
alpha0.81825522940517
beta0.111590999872759
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
37.847.620.22
47.797.770104332693230.0198956673067672
57.837.758288920507820.0717110794921831
67.947.795419673181110.144580326818891
78.027.90537768650210.114622313497895
88.068.001288552944660.0587114470553356
98.128.056810998026790.0631890019732086
108.138.121767008499940.00823299150005674
117.978.14250672980484-0.172506729804843
128.017.999603653430760.0103963465692374
1388.00731126533928-0.00731126533928439
147.97.999861940156-0.0998619401559973
157.997.907564155632120.0824358443678852
168.027.971959696892330.0480403031076708
178.088.012597462843280.067402537156724
188.028.07523299827951-0.0552329982795126
198.078.032478044924040.037521955075956
208.118.069046443891150.0409535561088497
218.198.112162234247920.0778377657520775
228.168.19256608212931-0.0325660821293088
238.088.1796577978074-0.0996577978073958
248.228.102751620816640.117248379183366
258.158.21403599746846-0.0640359974684639
268.198.171136363160710.0188636368392867
278.318.197792225296680.112207774703325
288.38.31107309921603-0.0110730992160253
298.348.322467669570520.0175323304294839
308.318.35886965799674-0.048869657996736
318.388.336475587627270.0435244123727347
328.348.39365765908065-0.0536576590806455
338.448.366420515847730.073579484152269
348.648.450014367192480.189985632807524
358.68.6462057311902-0.0462057311902004
368.618.64491323487487-0.0349132348748711
378.548.64967295806715-0.109672958067147
388.698.583245917868880.106754082131124
398.738.703659141711230.0263408582887656
408.918.760679006273270.149320993726729
419.018.931962497642490.0780375023575051
429.089.052043497463460.0279565025365418
438.949.13369816327482-0.193698163274821
449.039.016296176026080.013703823973918
459.029.06985324449244-0.0498532444924429
468.969.06685231359406-0.106852313594056
479.039.00745492021140.0225450797886015
488.949.05599621004936-0.115996210049362
498.958.98058376042171-0.0305837604217096
508.958.97226789366524-0.0222678936652372
518.998.968723248797950.021276751202052
528.939.00275201573902-0.0727520157390167
538.988.953198271737240.0268017282627628
548.958.98755216301388-0.0375521630138849
559.028.965819261250240.054180738749757
568.929.02409452494067-0.10409452494067
579.18.943355363769380.156644636230615
589.069.09027059381462-0.0302705938146186
598.979.08147745394451-0.111477453944509
608.898.9960573787972-0.106057378797198
618.998.905388217794360.0846117822056378
628.798.97846098986499-0.188460989864994
638.838.810882180423660.0191178195763424
648.618.8149014638822-0.2049014638822
658.718.616906261052050.093093738947946
668.918.671247573056730.238752426943266
678.918.866575333034980.04342466696502
688.898.90604023479491-0.0160402347949073
698.988.895383037180630.0846169628193678
7098.974815485929530.0251845140704692
718.999.00791661863816-0.0179166186381643
728.889.00411405911448-0.124114059114476

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 7.84 & 7.62 & 0.22 \tabularnewline
4 & 7.79 & 7.77010433269323 & 0.0198956673067672 \tabularnewline
5 & 7.83 & 7.75828892050782 & 0.0717110794921831 \tabularnewline
6 & 7.94 & 7.79541967318111 & 0.144580326818891 \tabularnewline
7 & 8.02 & 7.9053776865021 & 0.114622313497895 \tabularnewline
8 & 8.06 & 8.00128855294466 & 0.0587114470553356 \tabularnewline
9 & 8.12 & 8.05681099802679 & 0.0631890019732086 \tabularnewline
10 & 8.13 & 8.12176700849994 & 0.00823299150005674 \tabularnewline
11 & 7.97 & 8.14250672980484 & -0.172506729804843 \tabularnewline
12 & 8.01 & 7.99960365343076 & 0.0103963465692374 \tabularnewline
13 & 8 & 8.00731126533928 & -0.00731126533928439 \tabularnewline
14 & 7.9 & 7.999861940156 & -0.0998619401559973 \tabularnewline
15 & 7.99 & 7.90756415563212 & 0.0824358443678852 \tabularnewline
16 & 8.02 & 7.97195969689233 & 0.0480403031076708 \tabularnewline
17 & 8.08 & 8.01259746284328 & 0.067402537156724 \tabularnewline
18 & 8.02 & 8.07523299827951 & -0.0552329982795126 \tabularnewline
19 & 8.07 & 8.03247804492404 & 0.037521955075956 \tabularnewline
20 & 8.11 & 8.06904644389115 & 0.0409535561088497 \tabularnewline
21 & 8.19 & 8.11216223424792 & 0.0778377657520775 \tabularnewline
22 & 8.16 & 8.19256608212931 & -0.0325660821293088 \tabularnewline
23 & 8.08 & 8.1796577978074 & -0.0996577978073958 \tabularnewline
24 & 8.22 & 8.10275162081664 & 0.117248379183366 \tabularnewline
25 & 8.15 & 8.21403599746846 & -0.0640359974684639 \tabularnewline
26 & 8.19 & 8.17113636316071 & 0.0188636368392867 \tabularnewline
27 & 8.31 & 8.19779222529668 & 0.112207774703325 \tabularnewline
28 & 8.3 & 8.31107309921603 & -0.0110730992160253 \tabularnewline
29 & 8.34 & 8.32246766957052 & 0.0175323304294839 \tabularnewline
30 & 8.31 & 8.35886965799674 & -0.048869657996736 \tabularnewline
31 & 8.38 & 8.33647558762727 & 0.0435244123727347 \tabularnewline
32 & 8.34 & 8.39365765908065 & -0.0536576590806455 \tabularnewline
33 & 8.44 & 8.36642051584773 & 0.073579484152269 \tabularnewline
34 & 8.64 & 8.45001436719248 & 0.189985632807524 \tabularnewline
35 & 8.6 & 8.6462057311902 & -0.0462057311902004 \tabularnewline
36 & 8.61 & 8.64491323487487 & -0.0349132348748711 \tabularnewline
37 & 8.54 & 8.64967295806715 & -0.109672958067147 \tabularnewline
38 & 8.69 & 8.58324591786888 & 0.106754082131124 \tabularnewline
39 & 8.73 & 8.70365914171123 & 0.0263408582887656 \tabularnewline
40 & 8.91 & 8.76067900627327 & 0.149320993726729 \tabularnewline
41 & 9.01 & 8.93196249764249 & 0.0780375023575051 \tabularnewline
42 & 9.08 & 9.05204349746346 & 0.0279565025365418 \tabularnewline
43 & 8.94 & 9.13369816327482 & -0.193698163274821 \tabularnewline
44 & 9.03 & 9.01629617602608 & 0.013703823973918 \tabularnewline
45 & 9.02 & 9.06985324449244 & -0.0498532444924429 \tabularnewline
46 & 8.96 & 9.06685231359406 & -0.106852313594056 \tabularnewline
47 & 9.03 & 9.0074549202114 & 0.0225450797886015 \tabularnewline
48 & 8.94 & 9.05599621004936 & -0.115996210049362 \tabularnewline
49 & 8.95 & 8.98058376042171 & -0.0305837604217096 \tabularnewline
50 & 8.95 & 8.97226789366524 & -0.0222678936652372 \tabularnewline
51 & 8.99 & 8.96872324879795 & 0.021276751202052 \tabularnewline
52 & 8.93 & 9.00275201573902 & -0.0727520157390167 \tabularnewline
53 & 8.98 & 8.95319827173724 & 0.0268017282627628 \tabularnewline
54 & 8.95 & 8.98755216301388 & -0.0375521630138849 \tabularnewline
55 & 9.02 & 8.96581926125024 & 0.054180738749757 \tabularnewline
56 & 8.92 & 9.02409452494067 & -0.10409452494067 \tabularnewline
57 & 9.1 & 8.94335536376938 & 0.156644636230615 \tabularnewline
58 & 9.06 & 9.09027059381462 & -0.0302705938146186 \tabularnewline
59 & 8.97 & 9.08147745394451 & -0.111477453944509 \tabularnewline
60 & 8.89 & 8.9960573787972 & -0.106057378797198 \tabularnewline
61 & 8.99 & 8.90538821779436 & 0.0846117822056378 \tabularnewline
62 & 8.79 & 8.97846098986499 & -0.188460989864994 \tabularnewline
63 & 8.83 & 8.81088218042366 & 0.0191178195763424 \tabularnewline
64 & 8.61 & 8.8149014638822 & -0.2049014638822 \tabularnewline
65 & 8.71 & 8.61690626105205 & 0.093093738947946 \tabularnewline
66 & 8.91 & 8.67124757305673 & 0.238752426943266 \tabularnewline
67 & 8.91 & 8.86657533303498 & 0.04342466696502 \tabularnewline
68 & 8.89 & 8.90604023479491 & -0.0160402347949073 \tabularnewline
69 & 8.98 & 8.89538303718063 & 0.0846169628193678 \tabularnewline
70 & 9 & 8.97481548592953 & 0.0251845140704692 \tabularnewline
71 & 8.99 & 9.00791661863816 & -0.0179166186381643 \tabularnewline
72 & 8.88 & 9.00411405911448 & -0.124114059114476 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200745&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]7.84[/C][C]7.62[/C][C]0.22[/C][/ROW]
[ROW][C]4[/C][C]7.79[/C][C]7.77010433269323[/C][C]0.0198956673067672[/C][/ROW]
[ROW][C]5[/C][C]7.83[/C][C]7.75828892050782[/C][C]0.0717110794921831[/C][/ROW]
[ROW][C]6[/C][C]7.94[/C][C]7.79541967318111[/C][C]0.144580326818891[/C][/ROW]
[ROW][C]7[/C][C]8.02[/C][C]7.9053776865021[/C][C]0.114622313497895[/C][/ROW]
[ROW][C]8[/C][C]8.06[/C][C]8.00128855294466[/C][C]0.0587114470553356[/C][/ROW]
[ROW][C]9[/C][C]8.12[/C][C]8.05681099802679[/C][C]0.0631890019732086[/C][/ROW]
[ROW][C]10[/C][C]8.13[/C][C]8.12176700849994[/C][C]0.00823299150005674[/C][/ROW]
[ROW][C]11[/C][C]7.97[/C][C]8.14250672980484[/C][C]-0.172506729804843[/C][/ROW]
[ROW][C]12[/C][C]8.01[/C][C]7.99960365343076[/C][C]0.0103963465692374[/C][/ROW]
[ROW][C]13[/C][C]8[/C][C]8.00731126533928[/C][C]-0.00731126533928439[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]7.999861940156[/C][C]-0.0998619401559973[/C][/ROW]
[ROW][C]15[/C][C]7.99[/C][C]7.90756415563212[/C][C]0.0824358443678852[/C][/ROW]
[ROW][C]16[/C][C]8.02[/C][C]7.97195969689233[/C][C]0.0480403031076708[/C][/ROW]
[ROW][C]17[/C][C]8.08[/C][C]8.01259746284328[/C][C]0.067402537156724[/C][/ROW]
[ROW][C]18[/C][C]8.02[/C][C]8.07523299827951[/C][C]-0.0552329982795126[/C][/ROW]
[ROW][C]19[/C][C]8.07[/C][C]8.03247804492404[/C][C]0.037521955075956[/C][/ROW]
[ROW][C]20[/C][C]8.11[/C][C]8.06904644389115[/C][C]0.0409535561088497[/C][/ROW]
[ROW][C]21[/C][C]8.19[/C][C]8.11216223424792[/C][C]0.0778377657520775[/C][/ROW]
[ROW][C]22[/C][C]8.16[/C][C]8.19256608212931[/C][C]-0.0325660821293088[/C][/ROW]
[ROW][C]23[/C][C]8.08[/C][C]8.1796577978074[/C][C]-0.0996577978073958[/C][/ROW]
[ROW][C]24[/C][C]8.22[/C][C]8.10275162081664[/C][C]0.117248379183366[/C][/ROW]
[ROW][C]25[/C][C]8.15[/C][C]8.21403599746846[/C][C]-0.0640359974684639[/C][/ROW]
[ROW][C]26[/C][C]8.19[/C][C]8.17113636316071[/C][C]0.0188636368392867[/C][/ROW]
[ROW][C]27[/C][C]8.31[/C][C]8.19779222529668[/C][C]0.112207774703325[/C][/ROW]
[ROW][C]28[/C][C]8.3[/C][C]8.31107309921603[/C][C]-0.0110730992160253[/C][/ROW]
[ROW][C]29[/C][C]8.34[/C][C]8.32246766957052[/C][C]0.0175323304294839[/C][/ROW]
[ROW][C]30[/C][C]8.31[/C][C]8.35886965799674[/C][C]-0.048869657996736[/C][/ROW]
[ROW][C]31[/C][C]8.38[/C][C]8.33647558762727[/C][C]0.0435244123727347[/C][/ROW]
[ROW][C]32[/C][C]8.34[/C][C]8.39365765908065[/C][C]-0.0536576590806455[/C][/ROW]
[ROW][C]33[/C][C]8.44[/C][C]8.36642051584773[/C][C]0.073579484152269[/C][/ROW]
[ROW][C]34[/C][C]8.64[/C][C]8.45001436719248[/C][C]0.189985632807524[/C][/ROW]
[ROW][C]35[/C][C]8.6[/C][C]8.6462057311902[/C][C]-0.0462057311902004[/C][/ROW]
[ROW][C]36[/C][C]8.61[/C][C]8.64491323487487[/C][C]-0.0349132348748711[/C][/ROW]
[ROW][C]37[/C][C]8.54[/C][C]8.64967295806715[/C][C]-0.109672958067147[/C][/ROW]
[ROW][C]38[/C][C]8.69[/C][C]8.58324591786888[/C][C]0.106754082131124[/C][/ROW]
[ROW][C]39[/C][C]8.73[/C][C]8.70365914171123[/C][C]0.0263408582887656[/C][/ROW]
[ROW][C]40[/C][C]8.91[/C][C]8.76067900627327[/C][C]0.149320993726729[/C][/ROW]
[ROW][C]41[/C][C]9.01[/C][C]8.93196249764249[/C][C]0.0780375023575051[/C][/ROW]
[ROW][C]42[/C][C]9.08[/C][C]9.05204349746346[/C][C]0.0279565025365418[/C][/ROW]
[ROW][C]43[/C][C]8.94[/C][C]9.13369816327482[/C][C]-0.193698163274821[/C][/ROW]
[ROW][C]44[/C][C]9.03[/C][C]9.01629617602608[/C][C]0.013703823973918[/C][/ROW]
[ROW][C]45[/C][C]9.02[/C][C]9.06985324449244[/C][C]-0.0498532444924429[/C][/ROW]
[ROW][C]46[/C][C]8.96[/C][C]9.06685231359406[/C][C]-0.106852313594056[/C][/ROW]
[ROW][C]47[/C][C]9.03[/C][C]9.0074549202114[/C][C]0.0225450797886015[/C][/ROW]
[ROW][C]48[/C][C]8.94[/C][C]9.05599621004936[/C][C]-0.115996210049362[/C][/ROW]
[ROW][C]49[/C][C]8.95[/C][C]8.98058376042171[/C][C]-0.0305837604217096[/C][/ROW]
[ROW][C]50[/C][C]8.95[/C][C]8.97226789366524[/C][C]-0.0222678936652372[/C][/ROW]
[ROW][C]51[/C][C]8.99[/C][C]8.96872324879795[/C][C]0.021276751202052[/C][/ROW]
[ROW][C]52[/C][C]8.93[/C][C]9.00275201573902[/C][C]-0.0727520157390167[/C][/ROW]
[ROW][C]53[/C][C]8.98[/C][C]8.95319827173724[/C][C]0.0268017282627628[/C][/ROW]
[ROW][C]54[/C][C]8.95[/C][C]8.98755216301388[/C][C]-0.0375521630138849[/C][/ROW]
[ROW][C]55[/C][C]9.02[/C][C]8.96581926125024[/C][C]0.054180738749757[/C][/ROW]
[ROW][C]56[/C][C]8.92[/C][C]9.02409452494067[/C][C]-0.10409452494067[/C][/ROW]
[ROW][C]57[/C][C]9.1[/C][C]8.94335536376938[/C][C]0.156644636230615[/C][/ROW]
[ROW][C]58[/C][C]9.06[/C][C]9.09027059381462[/C][C]-0.0302705938146186[/C][/ROW]
[ROW][C]59[/C][C]8.97[/C][C]9.08147745394451[/C][C]-0.111477453944509[/C][/ROW]
[ROW][C]60[/C][C]8.89[/C][C]8.9960573787972[/C][C]-0.106057378797198[/C][/ROW]
[ROW][C]61[/C][C]8.99[/C][C]8.90538821779436[/C][C]0.0846117822056378[/C][/ROW]
[ROW][C]62[/C][C]8.79[/C][C]8.97846098986499[/C][C]-0.188460989864994[/C][/ROW]
[ROW][C]63[/C][C]8.83[/C][C]8.81088218042366[/C][C]0.0191178195763424[/C][/ROW]
[ROW][C]64[/C][C]8.61[/C][C]8.8149014638822[/C][C]-0.2049014638822[/C][/ROW]
[ROW][C]65[/C][C]8.71[/C][C]8.61690626105205[/C][C]0.093093738947946[/C][/ROW]
[ROW][C]66[/C][C]8.91[/C][C]8.67124757305673[/C][C]0.238752426943266[/C][/ROW]
[ROW][C]67[/C][C]8.91[/C][C]8.86657533303498[/C][C]0.04342466696502[/C][/ROW]
[ROW][C]68[/C][C]8.89[/C][C]8.90604023479491[/C][C]-0.0160402347949073[/C][/ROW]
[ROW][C]69[/C][C]8.98[/C][C]8.89538303718063[/C][C]0.0846169628193678[/C][/ROW]
[ROW][C]70[/C][C]9[/C][C]8.97481548592953[/C][C]0.0251845140704692[/C][/ROW]
[ROW][C]71[/C][C]8.99[/C][C]9.00791661863816[/C][C]-0.0179166186381643[/C][/ROW]
[ROW][C]72[/C][C]8.88[/C][C]9.00411405911448[/C][C]-0.124114059114476[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200745&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200745&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
37.847.620.22
47.797.770104332693230.0198956673067672
57.837.758288920507820.0717110794921831
67.947.795419673181110.144580326818891
78.027.90537768650210.114622313497895
88.068.001288552944660.0587114470553356
98.128.056810998026790.0631890019732086
108.138.121767008499940.00823299150005674
117.978.14250672980484-0.172506729804843
128.017.999603653430760.0103963465692374
1388.00731126533928-0.00731126533928439
147.97.999861940156-0.0998619401559973
157.997.907564155632120.0824358443678852
168.027.971959696892330.0480403031076708
178.088.012597462843280.067402537156724
188.028.07523299827951-0.0552329982795126
198.078.032478044924040.037521955075956
208.118.069046443891150.0409535561088497
218.198.112162234247920.0778377657520775
228.168.19256608212931-0.0325660821293088
238.088.1796577978074-0.0996577978073958
248.228.102751620816640.117248379183366
258.158.21403599746846-0.0640359974684639
268.198.171136363160710.0188636368392867
278.318.197792225296680.112207774703325
288.38.31107309921603-0.0110730992160253
298.348.322467669570520.0175323304294839
308.318.35886965799674-0.048869657996736
318.388.336475587627270.0435244123727347
328.348.39365765908065-0.0536576590806455
338.448.366420515847730.073579484152269
348.648.450014367192480.189985632807524
358.68.6462057311902-0.0462057311902004
368.618.64491323487487-0.0349132348748711
378.548.64967295806715-0.109672958067147
388.698.583245917868880.106754082131124
398.738.703659141711230.0263408582887656
408.918.760679006273270.149320993726729
419.018.931962497642490.0780375023575051
429.089.052043497463460.0279565025365418
438.949.13369816327482-0.193698163274821
449.039.016296176026080.013703823973918
459.029.06985324449244-0.0498532444924429
468.969.06685231359406-0.106852313594056
479.039.00745492021140.0225450797886015
488.949.05599621004936-0.115996210049362
498.958.98058376042171-0.0305837604217096
508.958.97226789366524-0.0222678936652372
518.998.968723248797950.021276751202052
528.939.00275201573902-0.0727520157390167
538.988.953198271737240.0268017282627628
548.958.98755216301388-0.0375521630138849
559.028.965819261250240.054180738749757
568.929.02409452494067-0.10409452494067
579.18.943355363769380.156644636230615
589.069.09027059381462-0.0302705938146186
598.979.08147745394451-0.111477453944509
608.898.9960573787972-0.106057378797198
618.998.905388217794360.0846117822056378
628.798.97846098986499-0.188460989864994
638.838.810882180423660.0191178195763424
648.618.8149014638822-0.2049014638822
658.718.616906261052050.093093738947946
668.918.671247573056730.238752426943266
678.918.866575333034980.04342466696502
688.898.90604023479491-0.0160402347949073
698.988.895383037180630.0846169628193678
7098.974815485929530.0251845140704692
718.999.00791661863816-0.0179166186381643
728.889.00411405911448-0.124114059114476







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
738.902082043862228.716490698151779.08767338957268
748.901607006523098.65072836528449.15248564776178
758.901131969183968.588970875296329.21329306307159
768.900656931844828.528458232789389.27285563090027
778.900181894505698.468005520778519.33235826823288
788.899706857166568.407007614139689.39240610019343
798.899231819827428.345124784999079.45333885465578
808.898756782488298.282155647099359.51535791787723
818.898281745149168.217977428917749.57858606138058
828.897806707810028.152514838901829.64309857671823
838.897331670470898.08572256631459.70894077462729
848.896856633131768.017574867596059.77613839866747

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 8.90208204386222 & 8.71649069815177 & 9.08767338957268 \tabularnewline
74 & 8.90160700652309 & 8.6507283652844 & 9.15248564776178 \tabularnewline
75 & 8.90113196918396 & 8.58897087529632 & 9.21329306307159 \tabularnewline
76 & 8.90065693184482 & 8.52845823278938 & 9.27285563090027 \tabularnewline
77 & 8.90018189450569 & 8.46800552077851 & 9.33235826823288 \tabularnewline
78 & 8.89970685716656 & 8.40700761413968 & 9.39240610019343 \tabularnewline
79 & 8.89923181982742 & 8.34512478499907 & 9.45333885465578 \tabularnewline
80 & 8.89875678248829 & 8.28215564709935 & 9.51535791787723 \tabularnewline
81 & 8.89828174514916 & 8.21797742891774 & 9.57858606138058 \tabularnewline
82 & 8.89780670781002 & 8.15251483890182 & 9.64309857671823 \tabularnewline
83 & 8.89733167047089 & 8.0857225663145 & 9.70894077462729 \tabularnewline
84 & 8.89685663313176 & 8.01757486759605 & 9.77613839866747 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200745&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]8.90208204386222[/C][C]8.71649069815177[/C][C]9.08767338957268[/C][/ROW]
[ROW][C]74[/C][C]8.90160700652309[/C][C]8.6507283652844[/C][C]9.15248564776178[/C][/ROW]
[ROW][C]75[/C][C]8.90113196918396[/C][C]8.58897087529632[/C][C]9.21329306307159[/C][/ROW]
[ROW][C]76[/C][C]8.90065693184482[/C][C]8.52845823278938[/C][C]9.27285563090027[/C][/ROW]
[ROW][C]77[/C][C]8.90018189450569[/C][C]8.46800552077851[/C][C]9.33235826823288[/C][/ROW]
[ROW][C]78[/C][C]8.89970685716656[/C][C]8.40700761413968[/C][C]9.39240610019343[/C][/ROW]
[ROW][C]79[/C][C]8.89923181982742[/C][C]8.34512478499907[/C][C]9.45333885465578[/C][/ROW]
[ROW][C]80[/C][C]8.89875678248829[/C][C]8.28215564709935[/C][C]9.51535791787723[/C][/ROW]
[ROW][C]81[/C][C]8.89828174514916[/C][C]8.21797742891774[/C][C]9.57858606138058[/C][/ROW]
[ROW][C]82[/C][C]8.89780670781002[/C][C]8.15251483890182[/C][C]9.64309857671823[/C][/ROW]
[ROW][C]83[/C][C]8.89733167047089[/C][C]8.0857225663145[/C][C]9.70894077462729[/C][/ROW]
[ROW][C]84[/C][C]8.89685663313176[/C][C]8.01757486759605[/C][C]9.77613839866747[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200745&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200745&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
738.902082043862228.716490698151779.08767338957268
748.901607006523098.65072836528449.15248564776178
758.901131969183968.588970875296329.21329306307159
768.900656931844828.528458232789389.27285563090027
778.900181894505698.468005520778519.33235826823288
788.899706857166568.407007614139689.39240610019343
798.899231819827428.345124784999079.45333885465578
808.898756782488298.282155647099359.51535791787723
818.898281745149168.217977428917749.57858606138058
828.897806707810028.152514838901829.64309857671823
838.897331670470898.08572256631459.70894077462729
848.896856633131768.017574867596059.77613839866747



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')