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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 May 2012 16:52:09 -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/2012/May/28/t13382384110947983qml35mne.htm/, Retrieved Thu, 02 May 2024 03:27:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167883, Retrieved Thu, 02 May 2024 03:27:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Smoothing Inschri...] [2012-05-28 20:46:57] [2f0f353a58a70fd7baf0f5141860d820]
- R PD    [Exponential Smoothing] [Smoothing Werkloo...] [2012-05-28 20:52:09] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
804,7
984,8
904,7
244,7
804,6
254,6
184,7
354,7
204,5
624,4
964,5
324,4
24,6
414,5
884,4
84,5
504,4
194,6
804,7
824,6
144,7
764,7
864,7
5
715
214,9
435,1
295
205,4
845,6
155,8
646,1
876,1
216,5
906,8
257,3
227,8
168,3
808,7
558,9
29,4
749,5
239,5
249,6
259,8
2710
829,9
259,9
179,7
319,8
469,8
789,9
309,6
689,4
269,5
279,6
379,5
469,5
619,8
419,4
419,1
959
148,9
149
659
729,1
739,1
659,1
619
598,9
498,7
398,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167883&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167883&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167883&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0760125846681286
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0760125846681286 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167883&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]0.0760125846681286[/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=167883&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167883&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
alpha0.0760125846681286
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2984.8804.7180.1
3904.7818.3898664987386.31013350127
4244.7824.950522829213-580.250522829213
5804.6780.84418083393123.7558191660687
6254.6782.649922049653-528.049922049653
7184.7742.511482640855-557.811482640855
8354.7700.110790087763-345.410790087763
9204.5673.855223160931-469.355223160931
10624.4638.178319520983-13.7783195209827
11964.5637.130993841809327.369006158191
12324.4662.01515814013-337.61515814013
1324.6636.35215734676-611.75215734676
14414.5589.851294690529-175.351294690529
15884.4576.522389556199307.877610443801
1684.5599.92496248748-515.42496248748
17504.4560.746178886333-56.346178886333
18194.6556.46316019301-361.86316019301
19804.7528.957006090562275.742993909438
20824.6549.916943761747274.683056238253
21144.7570.796312830957-426.096312830957
22764.7538.407630775117226.292369224883
23864.7555.608698650575309.091301349426
245579.10352736458-574.10352736458
25715535.464434382508179.535565617492
26214.9549.111396764948-334.211396764948
27435.1523.707124671299-88.6071246712991
28295516.971868105023-221.971868105023
29205.4500.099212686747-294.699212686747
30845.6477.698363830765367.901636169235
31155.8505.663518099622-349.863518099622
32646.1479.069487807785167.030512192215
33876.1491.765908757956384.334091242044
34216.5520.980136409341-304.480136409341
35906.8497.835814260762408.964185739238
36257.3528.922239055498-271.622239055498
37227.8508.275530611546-280.475530611546
38168.3486.955860593597-318.655860593597
39808.7462.734005010231345.965994989769
40558.9489.03177449668469.8682255033158
4129.4494.342638903367-464.942638903367
42749.5459.001147197902290.498852802098
43239.5481.082715842515-241.582715842515
44249.6462.71938920018-213.11938920018
45259.8446.519633584181-186.719633584181
462710432.3265916271622277.67340837284
47829.9605.458434427447224.441565572553
48259.9622.518817933578-362.618817933578
49179.7594.955224333145-415.255224333145
50319.8563.390601434639-243.590601434639
51469.8544.874650218728-75.0746502187284
52789.9539.168032012547250.731967987453
53309.6558.2268169582-248.6268169582
54689.4539.328049983397150.071950016602
55269.5550.735406790346-281.235406790346
56279.6529.357976620019-249.757976620019
57379.5510.373227275649-130.873227275649
58469.5500.425215006568-30.9252150065677
59619.8498.074509482501121.725490517499
60419.4507.327178636732-87.9271786367318
61419.1500.643606525978-81.5436065259775
62959494.445266230777464.554733769223
63148.9529.75727226439-380.85727226439
64149500.807326609921-351.807326609921
65659474.065542409116184.934457590884
66729.1488.122888524798240.977111475202
67739.1506.440181613887232.659818386113
68659.1524.125255757833134.974744242167
69619534.385034932684.6149650674
70598.9540.81683712897658.0831628710235
71498.7545.231888464503-46.5318884645029
72398.5541.694879352827-143.194879352827

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 984.8 & 804.7 & 180.1 \tabularnewline
3 & 904.7 & 818.38986649873 & 86.31013350127 \tabularnewline
4 & 244.7 & 824.950522829213 & -580.250522829213 \tabularnewline
5 & 804.6 & 780.844180833931 & 23.7558191660687 \tabularnewline
6 & 254.6 & 782.649922049653 & -528.049922049653 \tabularnewline
7 & 184.7 & 742.511482640855 & -557.811482640855 \tabularnewline
8 & 354.7 & 700.110790087763 & -345.410790087763 \tabularnewline
9 & 204.5 & 673.855223160931 & -469.355223160931 \tabularnewline
10 & 624.4 & 638.178319520983 & -13.7783195209827 \tabularnewline
11 & 964.5 & 637.130993841809 & 327.369006158191 \tabularnewline
12 & 324.4 & 662.01515814013 & -337.61515814013 \tabularnewline
13 & 24.6 & 636.35215734676 & -611.75215734676 \tabularnewline
14 & 414.5 & 589.851294690529 & -175.351294690529 \tabularnewline
15 & 884.4 & 576.522389556199 & 307.877610443801 \tabularnewline
16 & 84.5 & 599.92496248748 & -515.42496248748 \tabularnewline
17 & 504.4 & 560.746178886333 & -56.346178886333 \tabularnewline
18 & 194.6 & 556.46316019301 & -361.86316019301 \tabularnewline
19 & 804.7 & 528.957006090562 & 275.742993909438 \tabularnewline
20 & 824.6 & 549.916943761747 & 274.683056238253 \tabularnewline
21 & 144.7 & 570.796312830957 & -426.096312830957 \tabularnewline
22 & 764.7 & 538.407630775117 & 226.292369224883 \tabularnewline
23 & 864.7 & 555.608698650575 & 309.091301349426 \tabularnewline
24 & 5 & 579.10352736458 & -574.10352736458 \tabularnewline
25 & 715 & 535.464434382508 & 179.535565617492 \tabularnewline
26 & 214.9 & 549.111396764948 & -334.211396764948 \tabularnewline
27 & 435.1 & 523.707124671299 & -88.6071246712991 \tabularnewline
28 & 295 & 516.971868105023 & -221.971868105023 \tabularnewline
29 & 205.4 & 500.099212686747 & -294.699212686747 \tabularnewline
30 & 845.6 & 477.698363830765 & 367.901636169235 \tabularnewline
31 & 155.8 & 505.663518099622 & -349.863518099622 \tabularnewline
32 & 646.1 & 479.069487807785 & 167.030512192215 \tabularnewline
33 & 876.1 & 491.765908757956 & 384.334091242044 \tabularnewline
34 & 216.5 & 520.980136409341 & -304.480136409341 \tabularnewline
35 & 906.8 & 497.835814260762 & 408.964185739238 \tabularnewline
36 & 257.3 & 528.922239055498 & -271.622239055498 \tabularnewline
37 & 227.8 & 508.275530611546 & -280.475530611546 \tabularnewline
38 & 168.3 & 486.955860593597 & -318.655860593597 \tabularnewline
39 & 808.7 & 462.734005010231 & 345.965994989769 \tabularnewline
40 & 558.9 & 489.031774496684 & 69.8682255033158 \tabularnewline
41 & 29.4 & 494.342638903367 & -464.942638903367 \tabularnewline
42 & 749.5 & 459.001147197902 & 290.498852802098 \tabularnewline
43 & 239.5 & 481.082715842515 & -241.582715842515 \tabularnewline
44 & 249.6 & 462.71938920018 & -213.11938920018 \tabularnewline
45 & 259.8 & 446.519633584181 & -186.719633584181 \tabularnewline
46 & 2710 & 432.326591627162 & 2277.67340837284 \tabularnewline
47 & 829.9 & 605.458434427447 & 224.441565572553 \tabularnewline
48 & 259.9 & 622.518817933578 & -362.618817933578 \tabularnewline
49 & 179.7 & 594.955224333145 & -415.255224333145 \tabularnewline
50 & 319.8 & 563.390601434639 & -243.590601434639 \tabularnewline
51 & 469.8 & 544.874650218728 & -75.0746502187284 \tabularnewline
52 & 789.9 & 539.168032012547 & 250.731967987453 \tabularnewline
53 & 309.6 & 558.2268169582 & -248.6268169582 \tabularnewline
54 & 689.4 & 539.328049983397 & 150.071950016602 \tabularnewline
55 & 269.5 & 550.735406790346 & -281.235406790346 \tabularnewline
56 & 279.6 & 529.357976620019 & -249.757976620019 \tabularnewline
57 & 379.5 & 510.373227275649 & -130.873227275649 \tabularnewline
58 & 469.5 & 500.425215006568 & -30.9252150065677 \tabularnewline
59 & 619.8 & 498.074509482501 & 121.725490517499 \tabularnewline
60 & 419.4 & 507.327178636732 & -87.9271786367318 \tabularnewline
61 & 419.1 & 500.643606525978 & -81.5436065259775 \tabularnewline
62 & 959 & 494.445266230777 & 464.554733769223 \tabularnewline
63 & 148.9 & 529.75727226439 & -380.85727226439 \tabularnewline
64 & 149 & 500.807326609921 & -351.807326609921 \tabularnewline
65 & 659 & 474.065542409116 & 184.934457590884 \tabularnewline
66 & 729.1 & 488.122888524798 & 240.977111475202 \tabularnewline
67 & 739.1 & 506.440181613887 & 232.659818386113 \tabularnewline
68 & 659.1 & 524.125255757833 & 134.974744242167 \tabularnewline
69 & 619 & 534.3850349326 & 84.6149650674 \tabularnewline
70 & 598.9 & 540.816837128976 & 58.0831628710235 \tabularnewline
71 & 498.7 & 545.231888464503 & -46.5318884645029 \tabularnewline
72 & 398.5 & 541.694879352827 & -143.194879352827 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167883&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]984.8[/C][C]804.7[/C][C]180.1[/C][/ROW]
[ROW][C]3[/C][C]904.7[/C][C]818.38986649873[/C][C]86.31013350127[/C][/ROW]
[ROW][C]4[/C][C]244.7[/C][C]824.950522829213[/C][C]-580.250522829213[/C][/ROW]
[ROW][C]5[/C][C]804.6[/C][C]780.844180833931[/C][C]23.7558191660687[/C][/ROW]
[ROW][C]6[/C][C]254.6[/C][C]782.649922049653[/C][C]-528.049922049653[/C][/ROW]
[ROW][C]7[/C][C]184.7[/C][C]742.511482640855[/C][C]-557.811482640855[/C][/ROW]
[ROW][C]8[/C][C]354.7[/C][C]700.110790087763[/C][C]-345.410790087763[/C][/ROW]
[ROW][C]9[/C][C]204.5[/C][C]673.855223160931[/C][C]-469.355223160931[/C][/ROW]
[ROW][C]10[/C][C]624.4[/C][C]638.178319520983[/C][C]-13.7783195209827[/C][/ROW]
[ROW][C]11[/C][C]964.5[/C][C]637.130993841809[/C][C]327.369006158191[/C][/ROW]
[ROW][C]12[/C][C]324.4[/C][C]662.01515814013[/C][C]-337.61515814013[/C][/ROW]
[ROW][C]13[/C][C]24.6[/C][C]636.35215734676[/C][C]-611.75215734676[/C][/ROW]
[ROW][C]14[/C][C]414.5[/C][C]589.851294690529[/C][C]-175.351294690529[/C][/ROW]
[ROW][C]15[/C][C]884.4[/C][C]576.522389556199[/C][C]307.877610443801[/C][/ROW]
[ROW][C]16[/C][C]84.5[/C][C]599.92496248748[/C][C]-515.42496248748[/C][/ROW]
[ROW][C]17[/C][C]504.4[/C][C]560.746178886333[/C][C]-56.346178886333[/C][/ROW]
[ROW][C]18[/C][C]194.6[/C][C]556.46316019301[/C][C]-361.86316019301[/C][/ROW]
[ROW][C]19[/C][C]804.7[/C][C]528.957006090562[/C][C]275.742993909438[/C][/ROW]
[ROW][C]20[/C][C]824.6[/C][C]549.916943761747[/C][C]274.683056238253[/C][/ROW]
[ROW][C]21[/C][C]144.7[/C][C]570.796312830957[/C][C]-426.096312830957[/C][/ROW]
[ROW][C]22[/C][C]764.7[/C][C]538.407630775117[/C][C]226.292369224883[/C][/ROW]
[ROW][C]23[/C][C]864.7[/C][C]555.608698650575[/C][C]309.091301349426[/C][/ROW]
[ROW][C]24[/C][C]5[/C][C]579.10352736458[/C][C]-574.10352736458[/C][/ROW]
[ROW][C]25[/C][C]715[/C][C]535.464434382508[/C][C]179.535565617492[/C][/ROW]
[ROW][C]26[/C][C]214.9[/C][C]549.111396764948[/C][C]-334.211396764948[/C][/ROW]
[ROW][C]27[/C][C]435.1[/C][C]523.707124671299[/C][C]-88.6071246712991[/C][/ROW]
[ROW][C]28[/C][C]295[/C][C]516.971868105023[/C][C]-221.971868105023[/C][/ROW]
[ROW][C]29[/C][C]205.4[/C][C]500.099212686747[/C][C]-294.699212686747[/C][/ROW]
[ROW][C]30[/C][C]845.6[/C][C]477.698363830765[/C][C]367.901636169235[/C][/ROW]
[ROW][C]31[/C][C]155.8[/C][C]505.663518099622[/C][C]-349.863518099622[/C][/ROW]
[ROW][C]32[/C][C]646.1[/C][C]479.069487807785[/C][C]167.030512192215[/C][/ROW]
[ROW][C]33[/C][C]876.1[/C][C]491.765908757956[/C][C]384.334091242044[/C][/ROW]
[ROW][C]34[/C][C]216.5[/C][C]520.980136409341[/C][C]-304.480136409341[/C][/ROW]
[ROW][C]35[/C][C]906.8[/C][C]497.835814260762[/C][C]408.964185739238[/C][/ROW]
[ROW][C]36[/C][C]257.3[/C][C]528.922239055498[/C][C]-271.622239055498[/C][/ROW]
[ROW][C]37[/C][C]227.8[/C][C]508.275530611546[/C][C]-280.475530611546[/C][/ROW]
[ROW][C]38[/C][C]168.3[/C][C]486.955860593597[/C][C]-318.655860593597[/C][/ROW]
[ROW][C]39[/C][C]808.7[/C][C]462.734005010231[/C][C]345.965994989769[/C][/ROW]
[ROW][C]40[/C][C]558.9[/C][C]489.031774496684[/C][C]69.8682255033158[/C][/ROW]
[ROW][C]41[/C][C]29.4[/C][C]494.342638903367[/C][C]-464.942638903367[/C][/ROW]
[ROW][C]42[/C][C]749.5[/C][C]459.001147197902[/C][C]290.498852802098[/C][/ROW]
[ROW][C]43[/C][C]239.5[/C][C]481.082715842515[/C][C]-241.582715842515[/C][/ROW]
[ROW][C]44[/C][C]249.6[/C][C]462.71938920018[/C][C]-213.11938920018[/C][/ROW]
[ROW][C]45[/C][C]259.8[/C][C]446.519633584181[/C][C]-186.719633584181[/C][/ROW]
[ROW][C]46[/C][C]2710[/C][C]432.326591627162[/C][C]2277.67340837284[/C][/ROW]
[ROW][C]47[/C][C]829.9[/C][C]605.458434427447[/C][C]224.441565572553[/C][/ROW]
[ROW][C]48[/C][C]259.9[/C][C]622.518817933578[/C][C]-362.618817933578[/C][/ROW]
[ROW][C]49[/C][C]179.7[/C][C]594.955224333145[/C][C]-415.255224333145[/C][/ROW]
[ROW][C]50[/C][C]319.8[/C][C]563.390601434639[/C][C]-243.590601434639[/C][/ROW]
[ROW][C]51[/C][C]469.8[/C][C]544.874650218728[/C][C]-75.0746502187284[/C][/ROW]
[ROW][C]52[/C][C]789.9[/C][C]539.168032012547[/C][C]250.731967987453[/C][/ROW]
[ROW][C]53[/C][C]309.6[/C][C]558.2268169582[/C][C]-248.6268169582[/C][/ROW]
[ROW][C]54[/C][C]689.4[/C][C]539.328049983397[/C][C]150.071950016602[/C][/ROW]
[ROW][C]55[/C][C]269.5[/C][C]550.735406790346[/C][C]-281.235406790346[/C][/ROW]
[ROW][C]56[/C][C]279.6[/C][C]529.357976620019[/C][C]-249.757976620019[/C][/ROW]
[ROW][C]57[/C][C]379.5[/C][C]510.373227275649[/C][C]-130.873227275649[/C][/ROW]
[ROW][C]58[/C][C]469.5[/C][C]500.425215006568[/C][C]-30.9252150065677[/C][/ROW]
[ROW][C]59[/C][C]619.8[/C][C]498.074509482501[/C][C]121.725490517499[/C][/ROW]
[ROW][C]60[/C][C]419.4[/C][C]507.327178636732[/C][C]-87.9271786367318[/C][/ROW]
[ROW][C]61[/C][C]419.1[/C][C]500.643606525978[/C][C]-81.5436065259775[/C][/ROW]
[ROW][C]62[/C][C]959[/C][C]494.445266230777[/C][C]464.554733769223[/C][/ROW]
[ROW][C]63[/C][C]148.9[/C][C]529.75727226439[/C][C]-380.85727226439[/C][/ROW]
[ROW][C]64[/C][C]149[/C][C]500.807326609921[/C][C]-351.807326609921[/C][/ROW]
[ROW][C]65[/C][C]659[/C][C]474.065542409116[/C][C]184.934457590884[/C][/ROW]
[ROW][C]66[/C][C]729.1[/C][C]488.122888524798[/C][C]240.977111475202[/C][/ROW]
[ROW][C]67[/C][C]739.1[/C][C]506.440181613887[/C][C]232.659818386113[/C][/ROW]
[ROW][C]68[/C][C]659.1[/C][C]524.125255757833[/C][C]134.974744242167[/C][/ROW]
[ROW][C]69[/C][C]619[/C][C]534.3850349326[/C][C]84.6149650674[/C][/ROW]
[ROW][C]70[/C][C]598.9[/C][C]540.816837128976[/C][C]58.0831628710235[/C][/ROW]
[ROW][C]71[/C][C]498.7[/C][C]545.231888464503[/C][C]-46.5318884645029[/C][/ROW]
[ROW][C]72[/C][C]398.5[/C][C]541.694879352827[/C][C]-143.194879352827[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167883&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167883&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
2984.8804.7180.1
3904.7818.3898664987386.31013350127
4244.7824.950522829213-580.250522829213
5804.6780.84418083393123.7558191660687
6254.6782.649922049653-528.049922049653
7184.7742.511482640855-557.811482640855
8354.7700.110790087763-345.410790087763
9204.5673.855223160931-469.355223160931
10624.4638.178319520983-13.7783195209827
11964.5637.130993841809327.369006158191
12324.4662.01515814013-337.61515814013
1324.6636.35215734676-611.75215734676
14414.5589.851294690529-175.351294690529
15884.4576.522389556199307.877610443801
1684.5599.92496248748-515.42496248748
17504.4560.746178886333-56.346178886333
18194.6556.46316019301-361.86316019301
19804.7528.957006090562275.742993909438
20824.6549.916943761747274.683056238253
21144.7570.796312830957-426.096312830957
22764.7538.407630775117226.292369224883
23864.7555.608698650575309.091301349426
245579.10352736458-574.10352736458
25715535.464434382508179.535565617492
26214.9549.111396764948-334.211396764948
27435.1523.707124671299-88.6071246712991
28295516.971868105023-221.971868105023
29205.4500.099212686747-294.699212686747
30845.6477.698363830765367.901636169235
31155.8505.663518099622-349.863518099622
32646.1479.069487807785167.030512192215
33876.1491.765908757956384.334091242044
34216.5520.980136409341-304.480136409341
35906.8497.835814260762408.964185739238
36257.3528.922239055498-271.622239055498
37227.8508.275530611546-280.475530611546
38168.3486.955860593597-318.655860593597
39808.7462.734005010231345.965994989769
40558.9489.03177449668469.8682255033158
4129.4494.342638903367-464.942638903367
42749.5459.001147197902290.498852802098
43239.5481.082715842515-241.582715842515
44249.6462.71938920018-213.11938920018
45259.8446.519633584181-186.719633584181
462710432.3265916271622277.67340837284
47829.9605.458434427447224.441565572553
48259.9622.518817933578-362.618817933578
49179.7594.955224333145-415.255224333145
50319.8563.390601434639-243.590601434639
51469.8544.874650218728-75.0746502187284
52789.9539.168032012547250.731967987453
53309.6558.2268169582-248.6268169582
54689.4539.328049983397150.071950016602
55269.5550.735406790346-281.235406790346
56279.6529.357976620019-249.757976620019
57379.5510.373227275649-130.873227275649
58469.5500.425215006568-30.9252150065677
59619.8498.074509482501121.725490517499
60419.4507.327178636732-87.9271786367318
61419.1500.643606525978-81.5436065259775
62959494.445266230777464.554733769223
63148.9529.75727226439-380.85727226439
64149500.807326609921-351.807326609921
65659474.065542409116184.934457590884
66729.1488.122888524798240.977111475202
67739.1506.440181613887232.659818386113
68659.1524.125255757833134.974744242167
69619534.385034932684.6149650674
70598.9540.81683712897658.0831628710235
71498.7545.231888464503-46.5318884645029
72398.5541.694879352827-143.194879352827







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73530.810266461978-262.8676835862151324.48821651017
74530.810266461978-265.1572821581781326.77781508213
75530.810266461978-267.4403135691671329.06084649312
76530.810266461978-269.7168340060431331.33736693
77530.810266461978-271.9868988590111333.60743178297
78530.810266461978-274.2505627373411335.8710956613
79530.810266461978-276.5078794846951338.12841240865
80530.810266461978-278.7589021940741340.37943511803
81530.810266461978-281.0036832223881342.62421614634
82530.810266461978-283.242274204661344.86280712862
83530.810266461978-285.4747260678911347.09525899185
84530.810266461978-287.701089044571349.32162196853

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 530.810266461978 & -262.867683586215 & 1324.48821651017 \tabularnewline
74 & 530.810266461978 & -265.157282158178 & 1326.77781508213 \tabularnewline
75 & 530.810266461978 & -267.440313569167 & 1329.06084649312 \tabularnewline
76 & 530.810266461978 & -269.716834006043 & 1331.33736693 \tabularnewline
77 & 530.810266461978 & -271.986898859011 & 1333.60743178297 \tabularnewline
78 & 530.810266461978 & -274.250562737341 & 1335.8710956613 \tabularnewline
79 & 530.810266461978 & -276.507879484695 & 1338.12841240865 \tabularnewline
80 & 530.810266461978 & -278.758902194074 & 1340.37943511803 \tabularnewline
81 & 530.810266461978 & -281.003683222388 & 1342.62421614634 \tabularnewline
82 & 530.810266461978 & -283.24227420466 & 1344.86280712862 \tabularnewline
83 & 530.810266461978 & -285.474726067891 & 1347.09525899185 \tabularnewline
84 & 530.810266461978 & -287.70108904457 & 1349.32162196853 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167883&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]530.810266461978[/C][C]-262.867683586215[/C][C]1324.48821651017[/C][/ROW]
[ROW][C]74[/C][C]530.810266461978[/C][C]-265.157282158178[/C][C]1326.77781508213[/C][/ROW]
[ROW][C]75[/C][C]530.810266461978[/C][C]-267.440313569167[/C][C]1329.06084649312[/C][/ROW]
[ROW][C]76[/C][C]530.810266461978[/C][C]-269.716834006043[/C][C]1331.33736693[/C][/ROW]
[ROW][C]77[/C][C]530.810266461978[/C][C]-271.986898859011[/C][C]1333.60743178297[/C][/ROW]
[ROW][C]78[/C][C]530.810266461978[/C][C]-274.250562737341[/C][C]1335.8710956613[/C][/ROW]
[ROW][C]79[/C][C]530.810266461978[/C][C]-276.507879484695[/C][C]1338.12841240865[/C][/ROW]
[ROW][C]80[/C][C]530.810266461978[/C][C]-278.758902194074[/C][C]1340.37943511803[/C][/ROW]
[ROW][C]81[/C][C]530.810266461978[/C][C]-281.003683222388[/C][C]1342.62421614634[/C][/ROW]
[ROW][C]82[/C][C]530.810266461978[/C][C]-283.24227420466[/C][C]1344.86280712862[/C][/ROW]
[ROW][C]83[/C][C]530.810266461978[/C][C]-285.474726067891[/C][C]1347.09525899185[/C][/ROW]
[ROW][C]84[/C][C]530.810266461978[/C][C]-287.70108904457[/C][C]1349.32162196853[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167883&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167883&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
73530.810266461978-262.8676835862151324.48821651017
74530.810266461978-265.1572821581781326.77781508213
75530.810266461978-267.4403135691671329.06084649312
76530.810266461978-269.7168340060431331.33736693
77530.810266461978-271.9868988590111333.60743178297
78530.810266461978-274.2505627373411335.8710956613
79530.810266461978-276.5078794846951338.12841240865
80530.810266461978-278.7589021940741340.37943511803
81530.810266461978-281.0036832223881342.62421614634
82530.810266461978-283.242274204661344.86280712862
83530.810266461978-285.4747260678911347.09525899185
84530.810266461978-287.701089044571349.32162196853



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')