Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 01 Dec 2014 20:52:25 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/01/t1417467159fk0uri827o9dv68.htm/, Retrieved Sun, 19 May 2024 14:40:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=262279, Retrieved Sun, 19 May 2024 14:40:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact49
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-01 20:52:25] [5cac5f97919544233533b60e31cabb24] [Current]
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Dataseries X:
8378669
7557530
8656721
7729873
7067002
7222189
6758161
6745665
8203660
8799755
7995151
6844694
7400186
6146183
6793027
5815146
5993505
5838016
5926815
5642890
7120621
7781743
7638921
5886070
7358890
6981189
8423532
6819313
6727221
6923349
7578240
7228898
8988846
8404694
9601659
8213138
8434646
8466539
9106270
8438555
7723821
7538413
7199881
8168314
9045790
8544483
9020709
7932021
8435986
7920357
8333659
7415547
7770392
8188878
8092465
7188528
8152373
9025069
9233973
6916290
8171721
7012501
8779456
7308709
8084547
8255978
7658071
7371877
8780827
10116778
9567175
7455902




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262279&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262279&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262279&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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.368636755124675
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.368636755124675 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262279&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]0.368636755124675[/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=262279&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262279&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
alpha0.368636755124675
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
275575308378669-821139
386567218075966.98353368580754.01646632
477298738290054.25968945-560181.259689447
570670028083550.85783588-1016548.85783588
672221897708813.58545756-486624.585457563
767581617529425.8773106-771264.877310596
867456657245109.29559719-499444.295597188
982036607060995.771102711142664.22889729
1087997557482223.804640451317531.19535955
1179951517967914.2292733327236.7707266724
1268446947977954.70405408-1133260.70405408
1374001867560193.15540128-160007.15540128
1461461837501208.63683742-1355025.63683742
1567930277001696.38296293-208669.382962929
1658151466924773.17873361-1109627.17873361
1759935056515723.8161671-522218.816167101
1858380166323214.76631021-485198.766310211
1959268156144352.66750712-217537.667507119
2056428906064160.2876399-421270.287639905
2171206215908864.575773891211756.42422611
2277817436355562.532002081426180.46799792
2376389216881305.07194703757615.928052973
2458860707160590.14929524-1274520.14929524
2573588906690755.17711803668134.822881971
2669811896937054.2302110444134.7697889619
2784235326953323.928534221470208.07146578
2868193137495296.66135747-675983.66135747
2967272217246104.23791736-518883.237917355
3069233497054824.80480292-131475.804802917
3175782407006357.99074296571882.009257035
3272288987217174.7189496611723.2810503421
3389888467221496.351235471767349.64876453
3484046947873006.39092676531687.609073238
3596016598069005.985875521532653.01412448
3682131388633998.21973442-420860.219734419
3784346468478853.67397046-44207.6739704646
3884665398462557.100486383981.89951361716
3991062708464024.97500231642245.024997685
4084385558700780.09701243-262225.097012427
4177238218604114.28813751-880293.288137512
4275384138279605.82684047-741192.82684047
4371998818006374.90823231-806493.908232315
4481683147709071.61087374459242.389126264
4590457907878365.235016951167424.76498305
4685444838308720.91223249235762.087767514
4790207098395631.48324852625077.516751479
4879320218626058.03072518-694037.030725176
4984359868370210.4717822865775.528217718
5079203578394457.74907107-474100.749071073
5183336598219686.78733133113972.212668666
5274155478261701.13398389-846154.133983891
5377703927949777.61969674-179385.61969674
5481888787883649.4869357305228.513064295
5580924657996167.9355632696297.064436744
5671885288031666.57292525-843138.572925249
5781523737720854.70528164431518.294718364
5890250697879928.209223551145140.79077645
5992339738302069.19449628931903.805503717
6069162908645603.18944551-1729313.18944551
6181717218008114.78669401163606.213305986
6270125018068426.05028537-1055925.05028537
6387794567679173.266093311100282.73390669
6473087098084777.92284038-776068.922840379
6580845477798690.3933714285856.606628601
6682559787904067.64526992351910.354730083
6776580718033794.73653239-375723.736532388
6873718777895289.15747377-523412.15747377
6987808277702340.198149831078486.80185017
70101167788099910.073228672016867.92677133
7195671758843401.72126868723773.278731318
7274559029110211.15418614-1654309.15418614

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 7557530 & 8378669 & -821139 \tabularnewline
3 & 8656721 & 8075966.98353368 & 580754.01646632 \tabularnewline
4 & 7729873 & 8290054.25968945 & -560181.259689447 \tabularnewline
5 & 7067002 & 8083550.85783588 & -1016548.85783588 \tabularnewline
6 & 7222189 & 7708813.58545756 & -486624.585457563 \tabularnewline
7 & 6758161 & 7529425.8773106 & -771264.877310596 \tabularnewline
8 & 6745665 & 7245109.29559719 & -499444.295597188 \tabularnewline
9 & 8203660 & 7060995.77110271 & 1142664.22889729 \tabularnewline
10 & 8799755 & 7482223.80464045 & 1317531.19535955 \tabularnewline
11 & 7995151 & 7967914.22927333 & 27236.7707266724 \tabularnewline
12 & 6844694 & 7977954.70405408 & -1133260.70405408 \tabularnewline
13 & 7400186 & 7560193.15540128 & -160007.15540128 \tabularnewline
14 & 6146183 & 7501208.63683742 & -1355025.63683742 \tabularnewline
15 & 6793027 & 7001696.38296293 & -208669.382962929 \tabularnewline
16 & 5815146 & 6924773.17873361 & -1109627.17873361 \tabularnewline
17 & 5993505 & 6515723.8161671 & -522218.816167101 \tabularnewline
18 & 5838016 & 6323214.76631021 & -485198.766310211 \tabularnewline
19 & 5926815 & 6144352.66750712 & -217537.667507119 \tabularnewline
20 & 5642890 & 6064160.2876399 & -421270.287639905 \tabularnewline
21 & 7120621 & 5908864.57577389 & 1211756.42422611 \tabularnewline
22 & 7781743 & 6355562.53200208 & 1426180.46799792 \tabularnewline
23 & 7638921 & 6881305.07194703 & 757615.928052973 \tabularnewline
24 & 5886070 & 7160590.14929524 & -1274520.14929524 \tabularnewline
25 & 7358890 & 6690755.17711803 & 668134.822881971 \tabularnewline
26 & 6981189 & 6937054.23021104 & 44134.7697889619 \tabularnewline
27 & 8423532 & 6953323.92853422 & 1470208.07146578 \tabularnewline
28 & 6819313 & 7495296.66135747 & -675983.66135747 \tabularnewline
29 & 6727221 & 7246104.23791736 & -518883.237917355 \tabularnewline
30 & 6923349 & 7054824.80480292 & -131475.804802917 \tabularnewline
31 & 7578240 & 7006357.99074296 & 571882.009257035 \tabularnewline
32 & 7228898 & 7217174.71894966 & 11723.2810503421 \tabularnewline
33 & 8988846 & 7221496.35123547 & 1767349.64876453 \tabularnewline
34 & 8404694 & 7873006.39092676 & 531687.609073238 \tabularnewline
35 & 9601659 & 8069005.98587552 & 1532653.01412448 \tabularnewline
36 & 8213138 & 8633998.21973442 & -420860.219734419 \tabularnewline
37 & 8434646 & 8478853.67397046 & -44207.6739704646 \tabularnewline
38 & 8466539 & 8462557.10048638 & 3981.89951361716 \tabularnewline
39 & 9106270 & 8464024.97500231 & 642245.024997685 \tabularnewline
40 & 8438555 & 8700780.09701243 & -262225.097012427 \tabularnewline
41 & 7723821 & 8604114.28813751 & -880293.288137512 \tabularnewline
42 & 7538413 & 8279605.82684047 & -741192.82684047 \tabularnewline
43 & 7199881 & 8006374.90823231 & -806493.908232315 \tabularnewline
44 & 8168314 & 7709071.61087374 & 459242.389126264 \tabularnewline
45 & 9045790 & 7878365.23501695 & 1167424.76498305 \tabularnewline
46 & 8544483 & 8308720.91223249 & 235762.087767514 \tabularnewline
47 & 9020709 & 8395631.48324852 & 625077.516751479 \tabularnewline
48 & 7932021 & 8626058.03072518 & -694037.030725176 \tabularnewline
49 & 8435986 & 8370210.47178228 & 65775.528217718 \tabularnewline
50 & 7920357 & 8394457.74907107 & -474100.749071073 \tabularnewline
51 & 8333659 & 8219686.78733133 & 113972.212668666 \tabularnewline
52 & 7415547 & 8261701.13398389 & -846154.133983891 \tabularnewline
53 & 7770392 & 7949777.61969674 & -179385.61969674 \tabularnewline
54 & 8188878 & 7883649.4869357 & 305228.513064295 \tabularnewline
55 & 8092465 & 7996167.93556326 & 96297.064436744 \tabularnewline
56 & 7188528 & 8031666.57292525 & -843138.572925249 \tabularnewline
57 & 8152373 & 7720854.70528164 & 431518.294718364 \tabularnewline
58 & 9025069 & 7879928.20922355 & 1145140.79077645 \tabularnewline
59 & 9233973 & 8302069.19449628 & 931903.805503717 \tabularnewline
60 & 6916290 & 8645603.18944551 & -1729313.18944551 \tabularnewline
61 & 8171721 & 8008114.78669401 & 163606.213305986 \tabularnewline
62 & 7012501 & 8068426.05028537 & -1055925.05028537 \tabularnewline
63 & 8779456 & 7679173.26609331 & 1100282.73390669 \tabularnewline
64 & 7308709 & 8084777.92284038 & -776068.922840379 \tabularnewline
65 & 8084547 & 7798690.3933714 & 285856.606628601 \tabularnewline
66 & 8255978 & 7904067.64526992 & 351910.354730083 \tabularnewline
67 & 7658071 & 8033794.73653239 & -375723.736532388 \tabularnewline
68 & 7371877 & 7895289.15747377 & -523412.15747377 \tabularnewline
69 & 8780827 & 7702340.19814983 & 1078486.80185017 \tabularnewline
70 & 10116778 & 8099910.07322867 & 2016867.92677133 \tabularnewline
71 & 9567175 & 8843401.72126868 & 723773.278731318 \tabularnewline
72 & 7455902 & 9110211.15418614 & -1654309.15418614 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262279&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]7557530[/C][C]8378669[/C][C]-821139[/C][/ROW]
[ROW][C]3[/C][C]8656721[/C][C]8075966.98353368[/C][C]580754.01646632[/C][/ROW]
[ROW][C]4[/C][C]7729873[/C][C]8290054.25968945[/C][C]-560181.259689447[/C][/ROW]
[ROW][C]5[/C][C]7067002[/C][C]8083550.85783588[/C][C]-1016548.85783588[/C][/ROW]
[ROW][C]6[/C][C]7222189[/C][C]7708813.58545756[/C][C]-486624.585457563[/C][/ROW]
[ROW][C]7[/C][C]6758161[/C][C]7529425.8773106[/C][C]-771264.877310596[/C][/ROW]
[ROW][C]8[/C][C]6745665[/C][C]7245109.29559719[/C][C]-499444.295597188[/C][/ROW]
[ROW][C]9[/C][C]8203660[/C][C]7060995.77110271[/C][C]1142664.22889729[/C][/ROW]
[ROW][C]10[/C][C]8799755[/C][C]7482223.80464045[/C][C]1317531.19535955[/C][/ROW]
[ROW][C]11[/C][C]7995151[/C][C]7967914.22927333[/C][C]27236.7707266724[/C][/ROW]
[ROW][C]12[/C][C]6844694[/C][C]7977954.70405408[/C][C]-1133260.70405408[/C][/ROW]
[ROW][C]13[/C][C]7400186[/C][C]7560193.15540128[/C][C]-160007.15540128[/C][/ROW]
[ROW][C]14[/C][C]6146183[/C][C]7501208.63683742[/C][C]-1355025.63683742[/C][/ROW]
[ROW][C]15[/C][C]6793027[/C][C]7001696.38296293[/C][C]-208669.382962929[/C][/ROW]
[ROW][C]16[/C][C]5815146[/C][C]6924773.17873361[/C][C]-1109627.17873361[/C][/ROW]
[ROW][C]17[/C][C]5993505[/C][C]6515723.8161671[/C][C]-522218.816167101[/C][/ROW]
[ROW][C]18[/C][C]5838016[/C][C]6323214.76631021[/C][C]-485198.766310211[/C][/ROW]
[ROW][C]19[/C][C]5926815[/C][C]6144352.66750712[/C][C]-217537.667507119[/C][/ROW]
[ROW][C]20[/C][C]5642890[/C][C]6064160.2876399[/C][C]-421270.287639905[/C][/ROW]
[ROW][C]21[/C][C]7120621[/C][C]5908864.57577389[/C][C]1211756.42422611[/C][/ROW]
[ROW][C]22[/C][C]7781743[/C][C]6355562.53200208[/C][C]1426180.46799792[/C][/ROW]
[ROW][C]23[/C][C]7638921[/C][C]6881305.07194703[/C][C]757615.928052973[/C][/ROW]
[ROW][C]24[/C][C]5886070[/C][C]7160590.14929524[/C][C]-1274520.14929524[/C][/ROW]
[ROW][C]25[/C][C]7358890[/C][C]6690755.17711803[/C][C]668134.822881971[/C][/ROW]
[ROW][C]26[/C][C]6981189[/C][C]6937054.23021104[/C][C]44134.7697889619[/C][/ROW]
[ROW][C]27[/C][C]8423532[/C][C]6953323.92853422[/C][C]1470208.07146578[/C][/ROW]
[ROW][C]28[/C][C]6819313[/C][C]7495296.66135747[/C][C]-675983.66135747[/C][/ROW]
[ROW][C]29[/C][C]6727221[/C][C]7246104.23791736[/C][C]-518883.237917355[/C][/ROW]
[ROW][C]30[/C][C]6923349[/C][C]7054824.80480292[/C][C]-131475.804802917[/C][/ROW]
[ROW][C]31[/C][C]7578240[/C][C]7006357.99074296[/C][C]571882.009257035[/C][/ROW]
[ROW][C]32[/C][C]7228898[/C][C]7217174.71894966[/C][C]11723.2810503421[/C][/ROW]
[ROW][C]33[/C][C]8988846[/C][C]7221496.35123547[/C][C]1767349.64876453[/C][/ROW]
[ROW][C]34[/C][C]8404694[/C][C]7873006.39092676[/C][C]531687.609073238[/C][/ROW]
[ROW][C]35[/C][C]9601659[/C][C]8069005.98587552[/C][C]1532653.01412448[/C][/ROW]
[ROW][C]36[/C][C]8213138[/C][C]8633998.21973442[/C][C]-420860.219734419[/C][/ROW]
[ROW][C]37[/C][C]8434646[/C][C]8478853.67397046[/C][C]-44207.6739704646[/C][/ROW]
[ROW][C]38[/C][C]8466539[/C][C]8462557.10048638[/C][C]3981.89951361716[/C][/ROW]
[ROW][C]39[/C][C]9106270[/C][C]8464024.97500231[/C][C]642245.024997685[/C][/ROW]
[ROW][C]40[/C][C]8438555[/C][C]8700780.09701243[/C][C]-262225.097012427[/C][/ROW]
[ROW][C]41[/C][C]7723821[/C][C]8604114.28813751[/C][C]-880293.288137512[/C][/ROW]
[ROW][C]42[/C][C]7538413[/C][C]8279605.82684047[/C][C]-741192.82684047[/C][/ROW]
[ROW][C]43[/C][C]7199881[/C][C]8006374.90823231[/C][C]-806493.908232315[/C][/ROW]
[ROW][C]44[/C][C]8168314[/C][C]7709071.61087374[/C][C]459242.389126264[/C][/ROW]
[ROW][C]45[/C][C]9045790[/C][C]7878365.23501695[/C][C]1167424.76498305[/C][/ROW]
[ROW][C]46[/C][C]8544483[/C][C]8308720.91223249[/C][C]235762.087767514[/C][/ROW]
[ROW][C]47[/C][C]9020709[/C][C]8395631.48324852[/C][C]625077.516751479[/C][/ROW]
[ROW][C]48[/C][C]7932021[/C][C]8626058.03072518[/C][C]-694037.030725176[/C][/ROW]
[ROW][C]49[/C][C]8435986[/C][C]8370210.47178228[/C][C]65775.528217718[/C][/ROW]
[ROW][C]50[/C][C]7920357[/C][C]8394457.74907107[/C][C]-474100.749071073[/C][/ROW]
[ROW][C]51[/C][C]8333659[/C][C]8219686.78733133[/C][C]113972.212668666[/C][/ROW]
[ROW][C]52[/C][C]7415547[/C][C]8261701.13398389[/C][C]-846154.133983891[/C][/ROW]
[ROW][C]53[/C][C]7770392[/C][C]7949777.61969674[/C][C]-179385.61969674[/C][/ROW]
[ROW][C]54[/C][C]8188878[/C][C]7883649.4869357[/C][C]305228.513064295[/C][/ROW]
[ROW][C]55[/C][C]8092465[/C][C]7996167.93556326[/C][C]96297.064436744[/C][/ROW]
[ROW][C]56[/C][C]7188528[/C][C]8031666.57292525[/C][C]-843138.572925249[/C][/ROW]
[ROW][C]57[/C][C]8152373[/C][C]7720854.70528164[/C][C]431518.294718364[/C][/ROW]
[ROW][C]58[/C][C]9025069[/C][C]7879928.20922355[/C][C]1145140.79077645[/C][/ROW]
[ROW][C]59[/C][C]9233973[/C][C]8302069.19449628[/C][C]931903.805503717[/C][/ROW]
[ROW][C]60[/C][C]6916290[/C][C]8645603.18944551[/C][C]-1729313.18944551[/C][/ROW]
[ROW][C]61[/C][C]8171721[/C][C]8008114.78669401[/C][C]163606.213305986[/C][/ROW]
[ROW][C]62[/C][C]7012501[/C][C]8068426.05028537[/C][C]-1055925.05028537[/C][/ROW]
[ROW][C]63[/C][C]8779456[/C][C]7679173.26609331[/C][C]1100282.73390669[/C][/ROW]
[ROW][C]64[/C][C]7308709[/C][C]8084777.92284038[/C][C]-776068.922840379[/C][/ROW]
[ROW][C]65[/C][C]8084547[/C][C]7798690.3933714[/C][C]285856.606628601[/C][/ROW]
[ROW][C]66[/C][C]8255978[/C][C]7904067.64526992[/C][C]351910.354730083[/C][/ROW]
[ROW][C]67[/C][C]7658071[/C][C]8033794.73653239[/C][C]-375723.736532388[/C][/ROW]
[ROW][C]68[/C][C]7371877[/C][C]7895289.15747377[/C][C]-523412.15747377[/C][/ROW]
[ROW][C]69[/C][C]8780827[/C][C]7702340.19814983[/C][C]1078486.80185017[/C][/ROW]
[ROW][C]70[/C][C]10116778[/C][C]8099910.07322867[/C][C]2016867.92677133[/C][/ROW]
[ROW][C]71[/C][C]9567175[/C][C]8843401.72126868[/C][C]723773.278731318[/C][/ROW]
[ROW][C]72[/C][C]7455902[/C][C]9110211.15418614[/C][C]-1654309.15418614[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262279&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262279&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
275575308378669-821139
386567218075966.98353368580754.01646632
477298738290054.25968945-560181.259689447
570670028083550.85783588-1016548.85783588
672221897708813.58545756-486624.585457563
767581617529425.8773106-771264.877310596
867456657245109.29559719-499444.295597188
982036607060995.771102711142664.22889729
1087997557482223.804640451317531.19535955
1179951517967914.2292733327236.7707266724
1268446947977954.70405408-1133260.70405408
1374001867560193.15540128-160007.15540128
1461461837501208.63683742-1355025.63683742
1567930277001696.38296293-208669.382962929
1658151466924773.17873361-1109627.17873361
1759935056515723.8161671-522218.816167101
1858380166323214.76631021-485198.766310211
1959268156144352.66750712-217537.667507119
2056428906064160.2876399-421270.287639905
2171206215908864.575773891211756.42422611
2277817436355562.532002081426180.46799792
2376389216881305.07194703757615.928052973
2458860707160590.14929524-1274520.14929524
2573588906690755.17711803668134.822881971
2669811896937054.2302110444134.7697889619
2784235326953323.928534221470208.07146578
2868193137495296.66135747-675983.66135747
2967272217246104.23791736-518883.237917355
3069233497054824.80480292-131475.804802917
3175782407006357.99074296571882.009257035
3272288987217174.7189496611723.2810503421
3389888467221496.351235471767349.64876453
3484046947873006.39092676531687.609073238
3596016598069005.985875521532653.01412448
3682131388633998.21973442-420860.219734419
3784346468478853.67397046-44207.6739704646
3884665398462557.100486383981.89951361716
3991062708464024.97500231642245.024997685
4084385558700780.09701243-262225.097012427
4177238218604114.28813751-880293.288137512
4275384138279605.82684047-741192.82684047
4371998818006374.90823231-806493.908232315
4481683147709071.61087374459242.389126264
4590457907878365.235016951167424.76498305
4685444838308720.91223249235762.087767514
4790207098395631.48324852625077.516751479
4879320218626058.03072518-694037.030725176
4984359868370210.4717822865775.528217718
5079203578394457.74907107-474100.749071073
5183336598219686.78733133113972.212668666
5274155478261701.13398389-846154.133983891
5377703927949777.61969674-179385.61969674
5481888787883649.4869357305228.513064295
5580924657996167.9355632696297.064436744
5671885288031666.57292525-843138.572925249
5781523737720854.70528164431518.294718364
5890250697879928.209223551145140.79077645
5992339738302069.19449628931903.805503717
6069162908645603.18944551-1729313.18944551
6181717218008114.78669401163606.213305986
6270125018068426.05028537-1055925.05028537
6387794567679173.266093311100282.73390669
6473087098084777.92284038-776068.922840379
6580845477798690.3933714285856.606628601
6682559787904067.64526992351910.354730083
6776580718033794.73653239-375723.736532388
6873718777895289.15747377-523412.15747377
6987808277702340.198149831078486.80185017
70101167788099910.073228672016867.92677133
7195671758843401.72126868723773.278731318
7274559029110211.15418614-1654309.15418614







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
738500371.995613926825212.3164993610175531.6747285
748500371.995613926715015.5591335110285728.4320943
758500371.995613926611235.8808691710389508.1103587
768500371.995613926512867.8032199210487876.1880079
778500371.995613926419143.855900610581600.1353272
788500371.995613926329462.4571288610671281.534099
798500371.995613926243341.6725929210757402.3186349
808500371.995613926160388.3346053410840355.6566225
818500371.995613926080276.7106017910920467.280626
828500371.995613926002733.3421476510998010.6490802
838500371.995613925927526.003713211073217.9875146
848500371.995613925854455.490357111146288.5008707

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 8500371.99561392 & 6825212.31649936 & 10175531.6747285 \tabularnewline
74 & 8500371.99561392 & 6715015.55913351 & 10285728.4320943 \tabularnewline
75 & 8500371.99561392 & 6611235.88086917 & 10389508.1103587 \tabularnewline
76 & 8500371.99561392 & 6512867.80321992 & 10487876.1880079 \tabularnewline
77 & 8500371.99561392 & 6419143.8559006 & 10581600.1353272 \tabularnewline
78 & 8500371.99561392 & 6329462.45712886 & 10671281.534099 \tabularnewline
79 & 8500371.99561392 & 6243341.67259292 & 10757402.3186349 \tabularnewline
80 & 8500371.99561392 & 6160388.33460534 & 10840355.6566225 \tabularnewline
81 & 8500371.99561392 & 6080276.71060179 & 10920467.280626 \tabularnewline
82 & 8500371.99561392 & 6002733.34214765 & 10998010.6490802 \tabularnewline
83 & 8500371.99561392 & 5927526.0037132 & 11073217.9875146 \tabularnewline
84 & 8500371.99561392 & 5854455.4903571 & 11146288.5008707 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262279&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]8500371.99561392[/C][C]6825212.31649936[/C][C]10175531.6747285[/C][/ROW]
[ROW][C]74[/C][C]8500371.99561392[/C][C]6715015.55913351[/C][C]10285728.4320943[/C][/ROW]
[ROW][C]75[/C][C]8500371.99561392[/C][C]6611235.88086917[/C][C]10389508.1103587[/C][/ROW]
[ROW][C]76[/C][C]8500371.99561392[/C][C]6512867.80321992[/C][C]10487876.1880079[/C][/ROW]
[ROW][C]77[/C][C]8500371.99561392[/C][C]6419143.8559006[/C][C]10581600.1353272[/C][/ROW]
[ROW][C]78[/C][C]8500371.99561392[/C][C]6329462.45712886[/C][C]10671281.534099[/C][/ROW]
[ROW][C]79[/C][C]8500371.99561392[/C][C]6243341.67259292[/C][C]10757402.3186349[/C][/ROW]
[ROW][C]80[/C][C]8500371.99561392[/C][C]6160388.33460534[/C][C]10840355.6566225[/C][/ROW]
[ROW][C]81[/C][C]8500371.99561392[/C][C]6080276.71060179[/C][C]10920467.280626[/C][/ROW]
[ROW][C]82[/C][C]8500371.99561392[/C][C]6002733.34214765[/C][C]10998010.6490802[/C][/ROW]
[ROW][C]83[/C][C]8500371.99561392[/C][C]5927526.0037132[/C][C]11073217.9875146[/C][/ROW]
[ROW][C]84[/C][C]8500371.99561392[/C][C]5854455.4903571[/C][C]11146288.5008707[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262279&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262279&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
738500371.995613926825212.3164993610175531.6747285
748500371.995613926715015.5591335110285728.4320943
758500371.995613926611235.8808691710389508.1103587
768500371.995613926512867.8032199210487876.1880079
778500371.995613926419143.855900610581600.1353272
788500371.995613926329462.4571288610671281.534099
798500371.995613926243341.6725929210757402.3186349
808500371.995613926160388.3346053410840355.6566225
818500371.995613926080276.7106017910920467.280626
828500371.995613926002733.3421476510998010.6490802
838500371.995613925927526.003713211073217.9875146
848500371.995613925854455.490357111146288.5008707



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')