Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 27 Nov 2014 22:33:35 +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/Nov/27/t14171276337tu874e0jdu9ao9.htm/, Retrieved Fri, 17 May 2024 01:44:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260758, Retrieved Fri, 17 May 2024 01:44:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact45
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-27 22:33:35] [d67845bcf6d8dd3cd224f69460cf281c] [Current]
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Dataseries X:
11201
7804
8918
7874
8374
9099
7860
8000
7930
9079
8620
2513
13991
10095
11445
8792
8716
9607
7843
7221
8242
8839
6874
2478
11351
6480
6809
5464
4791
5179
4605
3809
5366
4402
4225
1719
7064
4820
6150
4971
4295
5713
4588
4253
5275
5114
5450
2088
9228
6060
7322
6147
6102
5988
5095
4971
5883
6211
6352
2581
9787
6187
7456
5127
5615
6243
5161
5439
4939
5349
4959
3080
7695
4965
6179
5166
5012
5094
4855
4272
4658
5146
5346
6009




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260758&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260758&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260758&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.436140159190146
beta0.195099885762931
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.436140159190146 \tabularnewline
beta & 0.195099885762931 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260758&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]0.436140159190146[/C][/ROW]
[ROW][C]beta[/C][C]0.195099885762931[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260758&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260758&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
alpha0.436140159190146
beta0.195099885762931
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131399113184.8266761368806.173323863241
14100959891.25247735576203.747522644237
151144511458.9641150456-13.9641150455918
1687928885.75640013737-93.7564001373685
1787168934.06916400532-218.069164005323
1896079897.21341737455-290.213417374551
1978438479.29152363998-636.29152363998
2072218124.61621835704-903.616218357036
2182427397.00288888254844.997111117461
2288398727.52459457217111.475405427835
2368748275.06457597245-1401.06457597245
2424782188.47509949309289.524900506911
251135113218.9556926377-1867.95569263774
2664808629.26910699428-2149.26910699428
2768098246.56941874261-1437.56941874261
2854645430.7403657035133.2596342964871
2947915021.71109811192-230.71109811192
3051795007.38344417348171.616555826521
3146053905.48769215978699.512307840222
3238093786.471427778122.5285722219023
3353663854.296764077731511.70323592227
3444024616.82891496915-214.828914969151
3542253612.54551064936612.454489350641
3617191297.09271075295421.907289247054
3770647211.77209370369-147.772093703691
3848204618.40841281035201.591587189647
3961505570.36781974148579.63218025852
4049715008.39693507704-37.396935077044
4142954818.27904096424-523.279040964237
4257135285.45671196462427.543288035376
4345884929.70717158232-341.707171582316
4442534222.2237950425930.7762049574058
4552755487.08832342485-212.088323424849
4651144673.74576471308440.254235286917
4754504568.52720158361881.472798416393
4820881854.28612844031233.713871559693
4992288362.23629746935865.763702530654
5060606085.71100307196-25.7110030719641
5173227672.50393811554-350.503938115544
5261476230.13936222505-83.139362225048
5361025734.21963783701367.78036216299
5459887837.43699616617-1849.43699616617
5550955866.95601946244-771.956019462439
5649715121.84615509207-150.846155092073
5758836372.43889841556-489.438898415558
5862115709.15855291913501.841447080869
5963525798.05902023725553.940979762749
6025812166.87737492211414.12262507789
6197879862.47024911462-75.4702491146236
6261876376.40157258651-189.401572586511
6374567639.56107060056-183.561070600563
6451276297.92080434324-1170.92080434324
6556155432.5612473316182.438752668404
6662435854.34489462546388.655105374539
6751615414.66510313591-253.665103135911
6854395259.37841993413179.621580065867
6949396593.50864396713-1654.50864396713
7053495922.11592295331-573.115922953313
7149595425.34075841788-466.340758417879
7230801873.288546270311206.71145372969
7376959058.50990977948-1363.50990977948
7449655312.69659154234-347.696591542336
7561796139.3636481263739.6363518736252
7651664511.42544992826654.574550071738
7750125216.84987475242-204.849874752423
7850945547.72548936966-453.725489369662
7948554462.89270527227392.107294727733
8042724811.46507427366-539.465074273657
8146584605.3243488139852.6756511860167
8251465295.55172631752-149.551726317519
8353465136.93034942685209.069650573151
8460092620.888223175313388.11177682469

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 13991 & 13184.8266761368 & 806.173323863241 \tabularnewline
14 & 10095 & 9891.25247735576 & 203.747522644237 \tabularnewline
15 & 11445 & 11458.9641150456 & -13.9641150455918 \tabularnewline
16 & 8792 & 8885.75640013737 & -93.7564001373685 \tabularnewline
17 & 8716 & 8934.06916400532 & -218.069164005323 \tabularnewline
18 & 9607 & 9897.21341737455 & -290.213417374551 \tabularnewline
19 & 7843 & 8479.29152363998 & -636.29152363998 \tabularnewline
20 & 7221 & 8124.61621835704 & -903.616218357036 \tabularnewline
21 & 8242 & 7397.00288888254 & 844.997111117461 \tabularnewline
22 & 8839 & 8727.52459457217 & 111.475405427835 \tabularnewline
23 & 6874 & 8275.06457597245 & -1401.06457597245 \tabularnewline
24 & 2478 & 2188.47509949309 & 289.524900506911 \tabularnewline
25 & 11351 & 13218.9556926377 & -1867.95569263774 \tabularnewline
26 & 6480 & 8629.26910699428 & -2149.26910699428 \tabularnewline
27 & 6809 & 8246.56941874261 & -1437.56941874261 \tabularnewline
28 & 5464 & 5430.74036570351 & 33.2596342964871 \tabularnewline
29 & 4791 & 5021.71109811192 & -230.71109811192 \tabularnewline
30 & 5179 & 5007.38344417348 & 171.616555826521 \tabularnewline
31 & 4605 & 3905.48769215978 & 699.512307840222 \tabularnewline
32 & 3809 & 3786.4714277781 & 22.5285722219023 \tabularnewline
33 & 5366 & 3854.29676407773 & 1511.70323592227 \tabularnewline
34 & 4402 & 4616.82891496915 & -214.828914969151 \tabularnewline
35 & 4225 & 3612.54551064936 & 612.454489350641 \tabularnewline
36 & 1719 & 1297.09271075295 & 421.907289247054 \tabularnewline
37 & 7064 & 7211.77209370369 & -147.772093703691 \tabularnewline
38 & 4820 & 4618.40841281035 & 201.591587189647 \tabularnewline
39 & 6150 & 5570.36781974148 & 579.63218025852 \tabularnewline
40 & 4971 & 5008.39693507704 & -37.396935077044 \tabularnewline
41 & 4295 & 4818.27904096424 & -523.279040964237 \tabularnewline
42 & 5713 & 5285.45671196462 & 427.543288035376 \tabularnewline
43 & 4588 & 4929.70717158232 & -341.707171582316 \tabularnewline
44 & 4253 & 4222.22379504259 & 30.7762049574058 \tabularnewline
45 & 5275 & 5487.08832342485 & -212.088323424849 \tabularnewline
46 & 5114 & 4673.74576471308 & 440.254235286917 \tabularnewline
47 & 5450 & 4568.52720158361 & 881.472798416393 \tabularnewline
48 & 2088 & 1854.28612844031 & 233.713871559693 \tabularnewline
49 & 9228 & 8362.23629746935 & 865.763702530654 \tabularnewline
50 & 6060 & 6085.71100307196 & -25.7110030719641 \tabularnewline
51 & 7322 & 7672.50393811554 & -350.503938115544 \tabularnewline
52 & 6147 & 6230.13936222505 & -83.139362225048 \tabularnewline
53 & 6102 & 5734.21963783701 & 367.78036216299 \tabularnewline
54 & 5988 & 7837.43699616617 & -1849.43699616617 \tabularnewline
55 & 5095 & 5866.95601946244 & -771.956019462439 \tabularnewline
56 & 4971 & 5121.84615509207 & -150.846155092073 \tabularnewline
57 & 5883 & 6372.43889841556 & -489.438898415558 \tabularnewline
58 & 6211 & 5709.15855291913 & 501.841447080869 \tabularnewline
59 & 6352 & 5798.05902023725 & 553.940979762749 \tabularnewline
60 & 2581 & 2166.87737492211 & 414.12262507789 \tabularnewline
61 & 9787 & 9862.47024911462 & -75.4702491146236 \tabularnewline
62 & 6187 & 6376.40157258651 & -189.401572586511 \tabularnewline
63 & 7456 & 7639.56107060056 & -183.561070600563 \tabularnewline
64 & 5127 & 6297.92080434324 & -1170.92080434324 \tabularnewline
65 & 5615 & 5432.5612473316 & 182.438752668404 \tabularnewline
66 & 6243 & 5854.34489462546 & 388.655105374539 \tabularnewline
67 & 5161 & 5414.66510313591 & -253.665103135911 \tabularnewline
68 & 5439 & 5259.37841993413 & 179.621580065867 \tabularnewline
69 & 4939 & 6593.50864396713 & -1654.50864396713 \tabularnewline
70 & 5349 & 5922.11592295331 & -573.115922953313 \tabularnewline
71 & 4959 & 5425.34075841788 & -466.340758417879 \tabularnewline
72 & 3080 & 1873.28854627031 & 1206.71145372969 \tabularnewline
73 & 7695 & 9058.50990977948 & -1363.50990977948 \tabularnewline
74 & 4965 & 5312.69659154234 & -347.696591542336 \tabularnewline
75 & 6179 & 6139.36364812637 & 39.6363518736252 \tabularnewline
76 & 5166 & 4511.42544992826 & 654.574550071738 \tabularnewline
77 & 5012 & 5216.84987475242 & -204.849874752423 \tabularnewline
78 & 5094 & 5547.72548936966 & -453.725489369662 \tabularnewline
79 & 4855 & 4462.89270527227 & 392.107294727733 \tabularnewline
80 & 4272 & 4811.46507427366 & -539.465074273657 \tabularnewline
81 & 4658 & 4605.32434881398 & 52.6756511860167 \tabularnewline
82 & 5146 & 5295.55172631752 & -149.551726317519 \tabularnewline
83 & 5346 & 5136.93034942685 & 209.069650573151 \tabularnewline
84 & 6009 & 2620.88822317531 & 3388.11177682469 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260758&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]13[/C][C]13991[/C][C]13184.8266761368[/C][C]806.173323863241[/C][/ROW]
[ROW][C]14[/C][C]10095[/C][C]9891.25247735576[/C][C]203.747522644237[/C][/ROW]
[ROW][C]15[/C][C]11445[/C][C]11458.9641150456[/C][C]-13.9641150455918[/C][/ROW]
[ROW][C]16[/C][C]8792[/C][C]8885.75640013737[/C][C]-93.7564001373685[/C][/ROW]
[ROW][C]17[/C][C]8716[/C][C]8934.06916400532[/C][C]-218.069164005323[/C][/ROW]
[ROW][C]18[/C][C]9607[/C][C]9897.21341737455[/C][C]-290.213417374551[/C][/ROW]
[ROW][C]19[/C][C]7843[/C][C]8479.29152363998[/C][C]-636.29152363998[/C][/ROW]
[ROW][C]20[/C][C]7221[/C][C]8124.61621835704[/C][C]-903.616218357036[/C][/ROW]
[ROW][C]21[/C][C]8242[/C][C]7397.00288888254[/C][C]844.997111117461[/C][/ROW]
[ROW][C]22[/C][C]8839[/C][C]8727.52459457217[/C][C]111.475405427835[/C][/ROW]
[ROW][C]23[/C][C]6874[/C][C]8275.06457597245[/C][C]-1401.06457597245[/C][/ROW]
[ROW][C]24[/C][C]2478[/C][C]2188.47509949309[/C][C]289.524900506911[/C][/ROW]
[ROW][C]25[/C][C]11351[/C][C]13218.9556926377[/C][C]-1867.95569263774[/C][/ROW]
[ROW][C]26[/C][C]6480[/C][C]8629.26910699428[/C][C]-2149.26910699428[/C][/ROW]
[ROW][C]27[/C][C]6809[/C][C]8246.56941874261[/C][C]-1437.56941874261[/C][/ROW]
[ROW][C]28[/C][C]5464[/C][C]5430.74036570351[/C][C]33.2596342964871[/C][/ROW]
[ROW][C]29[/C][C]4791[/C][C]5021.71109811192[/C][C]-230.71109811192[/C][/ROW]
[ROW][C]30[/C][C]5179[/C][C]5007.38344417348[/C][C]171.616555826521[/C][/ROW]
[ROW][C]31[/C][C]4605[/C][C]3905.48769215978[/C][C]699.512307840222[/C][/ROW]
[ROW][C]32[/C][C]3809[/C][C]3786.4714277781[/C][C]22.5285722219023[/C][/ROW]
[ROW][C]33[/C][C]5366[/C][C]3854.29676407773[/C][C]1511.70323592227[/C][/ROW]
[ROW][C]34[/C][C]4402[/C][C]4616.82891496915[/C][C]-214.828914969151[/C][/ROW]
[ROW][C]35[/C][C]4225[/C][C]3612.54551064936[/C][C]612.454489350641[/C][/ROW]
[ROW][C]36[/C][C]1719[/C][C]1297.09271075295[/C][C]421.907289247054[/C][/ROW]
[ROW][C]37[/C][C]7064[/C][C]7211.77209370369[/C][C]-147.772093703691[/C][/ROW]
[ROW][C]38[/C][C]4820[/C][C]4618.40841281035[/C][C]201.591587189647[/C][/ROW]
[ROW][C]39[/C][C]6150[/C][C]5570.36781974148[/C][C]579.63218025852[/C][/ROW]
[ROW][C]40[/C][C]4971[/C][C]5008.39693507704[/C][C]-37.396935077044[/C][/ROW]
[ROW][C]41[/C][C]4295[/C][C]4818.27904096424[/C][C]-523.279040964237[/C][/ROW]
[ROW][C]42[/C][C]5713[/C][C]5285.45671196462[/C][C]427.543288035376[/C][/ROW]
[ROW][C]43[/C][C]4588[/C][C]4929.70717158232[/C][C]-341.707171582316[/C][/ROW]
[ROW][C]44[/C][C]4253[/C][C]4222.22379504259[/C][C]30.7762049574058[/C][/ROW]
[ROW][C]45[/C][C]5275[/C][C]5487.08832342485[/C][C]-212.088323424849[/C][/ROW]
[ROW][C]46[/C][C]5114[/C][C]4673.74576471308[/C][C]440.254235286917[/C][/ROW]
[ROW][C]47[/C][C]5450[/C][C]4568.52720158361[/C][C]881.472798416393[/C][/ROW]
[ROW][C]48[/C][C]2088[/C][C]1854.28612844031[/C][C]233.713871559693[/C][/ROW]
[ROW][C]49[/C][C]9228[/C][C]8362.23629746935[/C][C]865.763702530654[/C][/ROW]
[ROW][C]50[/C][C]6060[/C][C]6085.71100307196[/C][C]-25.7110030719641[/C][/ROW]
[ROW][C]51[/C][C]7322[/C][C]7672.50393811554[/C][C]-350.503938115544[/C][/ROW]
[ROW][C]52[/C][C]6147[/C][C]6230.13936222505[/C][C]-83.139362225048[/C][/ROW]
[ROW][C]53[/C][C]6102[/C][C]5734.21963783701[/C][C]367.78036216299[/C][/ROW]
[ROW][C]54[/C][C]5988[/C][C]7837.43699616617[/C][C]-1849.43699616617[/C][/ROW]
[ROW][C]55[/C][C]5095[/C][C]5866.95601946244[/C][C]-771.956019462439[/C][/ROW]
[ROW][C]56[/C][C]4971[/C][C]5121.84615509207[/C][C]-150.846155092073[/C][/ROW]
[ROW][C]57[/C][C]5883[/C][C]6372.43889841556[/C][C]-489.438898415558[/C][/ROW]
[ROW][C]58[/C][C]6211[/C][C]5709.15855291913[/C][C]501.841447080869[/C][/ROW]
[ROW][C]59[/C][C]6352[/C][C]5798.05902023725[/C][C]553.940979762749[/C][/ROW]
[ROW][C]60[/C][C]2581[/C][C]2166.87737492211[/C][C]414.12262507789[/C][/ROW]
[ROW][C]61[/C][C]9787[/C][C]9862.47024911462[/C][C]-75.4702491146236[/C][/ROW]
[ROW][C]62[/C][C]6187[/C][C]6376.40157258651[/C][C]-189.401572586511[/C][/ROW]
[ROW][C]63[/C][C]7456[/C][C]7639.56107060056[/C][C]-183.561070600563[/C][/ROW]
[ROW][C]64[/C][C]5127[/C][C]6297.92080434324[/C][C]-1170.92080434324[/C][/ROW]
[ROW][C]65[/C][C]5615[/C][C]5432.5612473316[/C][C]182.438752668404[/C][/ROW]
[ROW][C]66[/C][C]6243[/C][C]5854.34489462546[/C][C]388.655105374539[/C][/ROW]
[ROW][C]67[/C][C]5161[/C][C]5414.66510313591[/C][C]-253.665103135911[/C][/ROW]
[ROW][C]68[/C][C]5439[/C][C]5259.37841993413[/C][C]179.621580065867[/C][/ROW]
[ROW][C]69[/C][C]4939[/C][C]6593.50864396713[/C][C]-1654.50864396713[/C][/ROW]
[ROW][C]70[/C][C]5349[/C][C]5922.11592295331[/C][C]-573.115922953313[/C][/ROW]
[ROW][C]71[/C][C]4959[/C][C]5425.34075841788[/C][C]-466.340758417879[/C][/ROW]
[ROW][C]72[/C][C]3080[/C][C]1873.28854627031[/C][C]1206.71145372969[/C][/ROW]
[ROW][C]73[/C][C]7695[/C][C]9058.50990977948[/C][C]-1363.50990977948[/C][/ROW]
[ROW][C]74[/C][C]4965[/C][C]5312.69659154234[/C][C]-347.696591542336[/C][/ROW]
[ROW][C]75[/C][C]6179[/C][C]6139.36364812637[/C][C]39.6363518736252[/C][/ROW]
[ROW][C]76[/C][C]5166[/C][C]4511.42544992826[/C][C]654.574550071738[/C][/ROW]
[ROW][C]77[/C][C]5012[/C][C]5216.84987475242[/C][C]-204.849874752423[/C][/ROW]
[ROW][C]78[/C][C]5094[/C][C]5547.72548936966[/C][C]-453.725489369662[/C][/ROW]
[ROW][C]79[/C][C]4855[/C][C]4462.89270527227[/C][C]392.107294727733[/C][/ROW]
[ROW][C]80[/C][C]4272[/C][C]4811.46507427366[/C][C]-539.465074273657[/C][/ROW]
[ROW][C]81[/C][C]4658[/C][C]4605.32434881398[/C][C]52.6756511860167[/C][/ROW]
[ROW][C]82[/C][C]5146[/C][C]5295.55172631752[/C][C]-149.551726317519[/C][/ROW]
[ROW][C]83[/C][C]5346[/C][C]5136.93034942685[/C][C]209.069650573151[/C][/ROW]
[ROW][C]84[/C][C]6009[/C][C]2620.88822317531[/C][C]3388.11177682469[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260758&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260758&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
131399113184.8266761368806.173323863241
14100959891.25247735576203.747522644237
151144511458.9641150456-13.9641150455918
1687928885.75640013737-93.7564001373685
1787168934.06916400532-218.069164005323
1896079897.21341737455-290.213417374551
1978438479.29152363998-636.29152363998
2072218124.61621835704-903.616218357036
2182427397.00288888254844.997111117461
2288398727.52459457217111.475405427835
2368748275.06457597245-1401.06457597245
2424782188.47509949309289.524900506911
251135113218.9556926377-1867.95569263774
2664808629.26910699428-2149.26910699428
2768098246.56941874261-1437.56941874261
2854645430.7403657035133.2596342964871
2947915021.71109811192-230.71109811192
3051795007.38344417348171.616555826521
3146053905.48769215978699.512307840222
3238093786.471427778122.5285722219023
3353663854.296764077731511.70323592227
3444024616.82891496915-214.828914969151
3542253612.54551064936612.454489350641
3617191297.09271075295421.907289247054
3770647211.77209370369-147.772093703691
3848204618.40841281035201.591587189647
3961505570.36781974148579.63218025852
4049715008.39693507704-37.396935077044
4142954818.27904096424-523.279040964237
4257135285.45671196462427.543288035376
4345884929.70717158232-341.707171582316
4442534222.2237950425930.7762049574058
4552755487.08832342485-212.088323424849
4651144673.74576471308440.254235286917
4754504568.52720158361881.472798416393
4820881854.28612844031233.713871559693
4992288362.23629746935865.763702530654
5060606085.71100307196-25.7110030719641
5173227672.50393811554-350.503938115544
5261476230.13936222505-83.139362225048
5361025734.21963783701367.78036216299
5459887837.43699616617-1849.43699616617
5550955866.95601946244-771.956019462439
5649715121.84615509207-150.846155092073
5758836372.43889841556-489.438898415558
5862115709.15855291913501.841447080869
5963525798.05902023725553.940979762749
6025812166.87737492211414.12262507789
6197879862.47024911462-75.4702491146236
6261876376.40157258651-189.401572586511
6374567639.56107060056-183.561070600563
6451276297.92080434324-1170.92080434324
6556155432.5612473316182.438752668404
6662435854.34489462546388.655105374539
6751615414.66510313591-253.665103135911
6854395259.37841993413179.621580065867
6949396593.50864396713-1654.50864396713
7053495922.11592295331-573.115922953313
7149595425.34075841788-466.340758417879
7230801873.288546270311206.71145372969
7376959058.50990977948-1363.50990977948
7449655312.69659154234-347.696591542336
7561796139.3636481263739.6363518736252
7651664511.42544992826654.574550071738
7750125216.84987475242-204.849874752423
7850945547.72548936966-453.725489369662
7948554462.89270527227392.107294727733
8042724811.46507427366-539.465074273657
8146584605.3243488139852.6756511860167
8251465295.55172631752-149.551726317519
8353465136.93034942685209.069650573151
8460092620.888223175313388.11177682469







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8511564.29555694489962.7340969030713165.8570169866
868182.566524104336486.863926389829878.26912181884
8710847.52883178868768.4219186823512926.6357448948
889080.822254581066963.2765263242111198.3679828379
899403.144984040757022.8319659165411783.458002165
9010406.99625107087619.2804936477613194.7120084938
9110083.25266800157116.0466737026713050.4586623002
929754.181562457486618.8840107774412889.4791141375
9311158.5683052567394.3549908336114922.7816196785
9413126.90259932568488.3884169921517765.4167816591
9514108.99903540648842.0736141137519375.9244566991
9610625.94407199866604.3676805911614647.5204634061

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 11564.2955569448 & 9962.73409690307 & 13165.8570169866 \tabularnewline
86 & 8182.56652410433 & 6486.86392638982 & 9878.26912181884 \tabularnewline
87 & 10847.5288317886 & 8768.42191868235 & 12926.6357448948 \tabularnewline
88 & 9080.82225458106 & 6963.27652632421 & 11198.3679828379 \tabularnewline
89 & 9403.14498404075 & 7022.83196591654 & 11783.458002165 \tabularnewline
90 & 10406.9962510708 & 7619.28049364776 & 13194.7120084938 \tabularnewline
91 & 10083.2526680015 & 7116.04667370267 & 13050.4586623002 \tabularnewline
92 & 9754.18156245748 & 6618.88401077744 & 12889.4791141375 \tabularnewline
93 & 11158.568305256 & 7394.35499083361 & 14922.7816196785 \tabularnewline
94 & 13126.9025993256 & 8488.38841699215 & 17765.4167816591 \tabularnewline
95 & 14108.9990354064 & 8842.07361411375 & 19375.9244566991 \tabularnewline
96 & 10625.9440719986 & 6604.36768059116 & 14647.5204634061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260758&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]85[/C][C]11564.2955569448[/C][C]9962.73409690307[/C][C]13165.8570169866[/C][/ROW]
[ROW][C]86[/C][C]8182.56652410433[/C][C]6486.86392638982[/C][C]9878.26912181884[/C][/ROW]
[ROW][C]87[/C][C]10847.5288317886[/C][C]8768.42191868235[/C][C]12926.6357448948[/C][/ROW]
[ROW][C]88[/C][C]9080.82225458106[/C][C]6963.27652632421[/C][C]11198.3679828379[/C][/ROW]
[ROW][C]89[/C][C]9403.14498404075[/C][C]7022.83196591654[/C][C]11783.458002165[/C][/ROW]
[ROW][C]90[/C][C]10406.9962510708[/C][C]7619.28049364776[/C][C]13194.7120084938[/C][/ROW]
[ROW][C]91[/C][C]10083.2526680015[/C][C]7116.04667370267[/C][C]13050.4586623002[/C][/ROW]
[ROW][C]92[/C][C]9754.18156245748[/C][C]6618.88401077744[/C][C]12889.4791141375[/C][/ROW]
[ROW][C]93[/C][C]11158.568305256[/C][C]7394.35499083361[/C][C]14922.7816196785[/C][/ROW]
[ROW][C]94[/C][C]13126.9025993256[/C][C]8488.38841699215[/C][C]17765.4167816591[/C][/ROW]
[ROW][C]95[/C][C]14108.9990354064[/C][C]8842.07361411375[/C][C]19375.9244566991[/C][/ROW]
[ROW][C]96[/C][C]10625.9440719986[/C][C]6604.36768059116[/C][C]14647.5204634061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260758&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260758&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
8511564.29555694489962.7340969030713165.8570169866
868182.566524104336486.863926389829878.26912181884
8710847.52883178868768.4219186823512926.6357448948
889080.822254581066963.2765263242111198.3679828379
899403.144984040757022.8319659165411783.458002165
9010406.99625107087619.2804936477613194.7120084938
9110083.25266800157116.0466737026713050.4586623002
929754.181562457486618.8840107774412889.4791141375
9311158.5683052567394.3549908336114922.7816196785
9413126.90259932568488.3884169921517765.4167816591
9514108.99903540648842.0736141137519375.9244566991
9610625.94407199866604.3676805911614647.5204634061



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')