Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 14 Dec 2016 13:02:25 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/14/t14817169657xun2589btx2mtj.htm/, Retrieved Fri, 03 May 2024 18:06:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299332, Retrieved Fri, 03 May 2024 18:06:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-14 12:02:25] [349958aef20b862f8399a5ba04d6f6e3] [Current]
Feedback Forum

Post a new message
Dataseries X:
6830
6827
6841
6754
6869
6809
6836
6766
6759
6719
6702
6627
6630
6606
6512
6550
6578
6499
6371
6332
6291
6307
6252
6250
6164
6213
6174
6154
6091
6096
6046
6001
5979
5921
5863
5818
5758
5786
5734
5678
5610
5578
5589
5553
5533
5521
5464
5419
5346
5296
5255
5235
5164
5164
5172
5093
5070
5108
5051
5021
5001
4918
4886




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299332&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299332&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299332&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.646135953021989
beta0.129498833883744
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.646135953021989 \tabularnewline
beta & 0.129498833883744 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299332&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]0.646135953021989[/C][/ROW]
[ROW][C]beta[/C][C]0.129498833883744[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299332&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299332&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
alpha0.646135953021989
beta0.129498833883744
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
36841682417
467546833.40676669297-79.4067666929668
568696773.8773852314795.122614768532
668096835.07698762342-26.0769876234208
768366815.7832074033120.2167925966942
867666828.09311990539-62.0931199053875
967596782.02406809686-23.0240680968609
1067196759.27242283564-40.2724228356419
1167026722.0062466812-20.0062466811987
1266276696.1607758376-69.1607758376022
1366306632.76784789965-2.76784789965131
1466066612.04218123206-6.04218123205737
1565126588.69527749535-76.6952774953506
1665506513.279478738136.7205212618983
1765786514.2182526764563.7817473235482
1864996537.97912222043-38.9791222204331
1963716492.08096606707-121.080966067071
2063326383.0025459062-51.0025459061972
2162916314.93673304168-23.9367330416835
2263076262.3562362981144.6437637018889
2362526257.82357987333-5.82357987332671
2462506220.1948769480529.8051230519495
2561646208.08106941074-44.0810694107386
2662136144.5383035938168.4616964061852
2761746159.4419189070814.5580810929177
2861546140.7346010978613.2653989021428
2960916122.30200187973-31.302001879726
3060966072.4536435971223.5463564028814
3160466060.01499591645-14.0149959164473
3260016022.13391935778-21.1339193577769
3359795977.884693966891.11530603310985
3459215948.10481498039-27.1048149803919
3558635897.82293691917-34.822936919174
3658185839.64033349797-21.640333497965
3757585788.16475402962-30.1647540296235
3857865728.6572387993357.3427612006672
3957345730.489565058543.51043494145597
4056785697.83262150218-19.8326215021843
4156105648.43341807896-38.433418078961
4255785583.79969907927-5.79969907927261
4355895539.7665160411149.2334839588939
4455535535.4118064453517.5881935546477
4555335512.0816088878920.9183911121117
4655215492.6534940743128.3465059256941
4754645480.39681265916-16.3968126591608
4854195437.85787996579-18.8578799657853
4953465392.15085173708-46.1508517370776
5052965324.94723362359-28.9472336235858
5152555266.43736514032-11.4373651403212
5252355218.2842438136516.7157561863496
5351645189.7205380826-25.7205380826035
5451645131.5850804029932.4149195970094
5551725113.72531327558.2746867250034
5650935117.45053896358-24.4505389635815
5750705065.678151323434.32184867656815
5851085032.8582635203375.1417364796716
5950515052.08504998658-1.08504998658373
6050215021.96817882119-0.968178821186484
6150014991.84581106589.15418893420156
6249184969.02983530103-51.0298353010257
6348864903.05693477097-17.0569347709688

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 6841 & 6824 & 17 \tabularnewline
4 & 6754 & 6833.40676669297 & -79.4067666929668 \tabularnewline
5 & 6869 & 6773.87738523147 & 95.122614768532 \tabularnewline
6 & 6809 & 6835.07698762342 & -26.0769876234208 \tabularnewline
7 & 6836 & 6815.78320740331 & 20.2167925966942 \tabularnewline
8 & 6766 & 6828.09311990539 & -62.0931199053875 \tabularnewline
9 & 6759 & 6782.02406809686 & -23.0240680968609 \tabularnewline
10 & 6719 & 6759.27242283564 & -40.2724228356419 \tabularnewline
11 & 6702 & 6722.0062466812 & -20.0062466811987 \tabularnewline
12 & 6627 & 6696.1607758376 & -69.1607758376022 \tabularnewline
13 & 6630 & 6632.76784789965 & -2.76784789965131 \tabularnewline
14 & 6606 & 6612.04218123206 & -6.04218123205737 \tabularnewline
15 & 6512 & 6588.69527749535 & -76.6952774953506 \tabularnewline
16 & 6550 & 6513.2794787381 & 36.7205212618983 \tabularnewline
17 & 6578 & 6514.21825267645 & 63.7817473235482 \tabularnewline
18 & 6499 & 6537.97912222043 & -38.9791222204331 \tabularnewline
19 & 6371 & 6492.08096606707 & -121.080966067071 \tabularnewline
20 & 6332 & 6383.0025459062 & -51.0025459061972 \tabularnewline
21 & 6291 & 6314.93673304168 & -23.9367330416835 \tabularnewline
22 & 6307 & 6262.35623629811 & 44.6437637018889 \tabularnewline
23 & 6252 & 6257.82357987333 & -5.82357987332671 \tabularnewline
24 & 6250 & 6220.19487694805 & 29.8051230519495 \tabularnewline
25 & 6164 & 6208.08106941074 & -44.0810694107386 \tabularnewline
26 & 6213 & 6144.53830359381 & 68.4616964061852 \tabularnewline
27 & 6174 & 6159.44191890708 & 14.5580810929177 \tabularnewline
28 & 6154 & 6140.73460109786 & 13.2653989021428 \tabularnewline
29 & 6091 & 6122.30200187973 & -31.302001879726 \tabularnewline
30 & 6096 & 6072.45364359712 & 23.5463564028814 \tabularnewline
31 & 6046 & 6060.01499591645 & -14.0149959164473 \tabularnewline
32 & 6001 & 6022.13391935778 & -21.1339193577769 \tabularnewline
33 & 5979 & 5977.88469396689 & 1.11530603310985 \tabularnewline
34 & 5921 & 5948.10481498039 & -27.1048149803919 \tabularnewline
35 & 5863 & 5897.82293691917 & -34.822936919174 \tabularnewline
36 & 5818 & 5839.64033349797 & -21.640333497965 \tabularnewline
37 & 5758 & 5788.16475402962 & -30.1647540296235 \tabularnewline
38 & 5786 & 5728.65723879933 & 57.3427612006672 \tabularnewline
39 & 5734 & 5730.48956505854 & 3.51043494145597 \tabularnewline
40 & 5678 & 5697.83262150218 & -19.8326215021843 \tabularnewline
41 & 5610 & 5648.43341807896 & -38.433418078961 \tabularnewline
42 & 5578 & 5583.79969907927 & -5.79969907927261 \tabularnewline
43 & 5589 & 5539.76651604111 & 49.2334839588939 \tabularnewline
44 & 5553 & 5535.41180644535 & 17.5881935546477 \tabularnewline
45 & 5533 & 5512.08160888789 & 20.9183911121117 \tabularnewline
46 & 5521 & 5492.65349407431 & 28.3465059256941 \tabularnewline
47 & 5464 & 5480.39681265916 & -16.3968126591608 \tabularnewline
48 & 5419 & 5437.85787996579 & -18.8578799657853 \tabularnewline
49 & 5346 & 5392.15085173708 & -46.1508517370776 \tabularnewline
50 & 5296 & 5324.94723362359 & -28.9472336235858 \tabularnewline
51 & 5255 & 5266.43736514032 & -11.4373651403212 \tabularnewline
52 & 5235 & 5218.28424381365 & 16.7157561863496 \tabularnewline
53 & 5164 & 5189.7205380826 & -25.7205380826035 \tabularnewline
54 & 5164 & 5131.58508040299 & 32.4149195970094 \tabularnewline
55 & 5172 & 5113.725313275 & 58.2746867250034 \tabularnewline
56 & 5093 & 5117.45053896358 & -24.4505389635815 \tabularnewline
57 & 5070 & 5065.67815132343 & 4.32184867656815 \tabularnewline
58 & 5108 & 5032.85826352033 & 75.1417364796716 \tabularnewline
59 & 5051 & 5052.08504998658 & -1.08504998658373 \tabularnewline
60 & 5021 & 5021.96817882119 & -0.968178821186484 \tabularnewline
61 & 5001 & 4991.8458110658 & 9.15418893420156 \tabularnewline
62 & 4918 & 4969.02983530103 & -51.0298353010257 \tabularnewline
63 & 4886 & 4903.05693477097 & -17.0569347709688 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299332&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]6841[/C][C]6824[/C][C]17[/C][/ROW]
[ROW][C]4[/C][C]6754[/C][C]6833.40676669297[/C][C]-79.4067666929668[/C][/ROW]
[ROW][C]5[/C][C]6869[/C][C]6773.87738523147[/C][C]95.122614768532[/C][/ROW]
[ROW][C]6[/C][C]6809[/C][C]6835.07698762342[/C][C]-26.0769876234208[/C][/ROW]
[ROW][C]7[/C][C]6836[/C][C]6815.78320740331[/C][C]20.2167925966942[/C][/ROW]
[ROW][C]8[/C][C]6766[/C][C]6828.09311990539[/C][C]-62.0931199053875[/C][/ROW]
[ROW][C]9[/C][C]6759[/C][C]6782.02406809686[/C][C]-23.0240680968609[/C][/ROW]
[ROW][C]10[/C][C]6719[/C][C]6759.27242283564[/C][C]-40.2724228356419[/C][/ROW]
[ROW][C]11[/C][C]6702[/C][C]6722.0062466812[/C][C]-20.0062466811987[/C][/ROW]
[ROW][C]12[/C][C]6627[/C][C]6696.1607758376[/C][C]-69.1607758376022[/C][/ROW]
[ROW][C]13[/C][C]6630[/C][C]6632.76784789965[/C][C]-2.76784789965131[/C][/ROW]
[ROW][C]14[/C][C]6606[/C][C]6612.04218123206[/C][C]-6.04218123205737[/C][/ROW]
[ROW][C]15[/C][C]6512[/C][C]6588.69527749535[/C][C]-76.6952774953506[/C][/ROW]
[ROW][C]16[/C][C]6550[/C][C]6513.2794787381[/C][C]36.7205212618983[/C][/ROW]
[ROW][C]17[/C][C]6578[/C][C]6514.21825267645[/C][C]63.7817473235482[/C][/ROW]
[ROW][C]18[/C][C]6499[/C][C]6537.97912222043[/C][C]-38.9791222204331[/C][/ROW]
[ROW][C]19[/C][C]6371[/C][C]6492.08096606707[/C][C]-121.080966067071[/C][/ROW]
[ROW][C]20[/C][C]6332[/C][C]6383.0025459062[/C][C]-51.0025459061972[/C][/ROW]
[ROW][C]21[/C][C]6291[/C][C]6314.93673304168[/C][C]-23.9367330416835[/C][/ROW]
[ROW][C]22[/C][C]6307[/C][C]6262.35623629811[/C][C]44.6437637018889[/C][/ROW]
[ROW][C]23[/C][C]6252[/C][C]6257.82357987333[/C][C]-5.82357987332671[/C][/ROW]
[ROW][C]24[/C][C]6250[/C][C]6220.19487694805[/C][C]29.8051230519495[/C][/ROW]
[ROW][C]25[/C][C]6164[/C][C]6208.08106941074[/C][C]-44.0810694107386[/C][/ROW]
[ROW][C]26[/C][C]6213[/C][C]6144.53830359381[/C][C]68.4616964061852[/C][/ROW]
[ROW][C]27[/C][C]6174[/C][C]6159.44191890708[/C][C]14.5580810929177[/C][/ROW]
[ROW][C]28[/C][C]6154[/C][C]6140.73460109786[/C][C]13.2653989021428[/C][/ROW]
[ROW][C]29[/C][C]6091[/C][C]6122.30200187973[/C][C]-31.302001879726[/C][/ROW]
[ROW][C]30[/C][C]6096[/C][C]6072.45364359712[/C][C]23.5463564028814[/C][/ROW]
[ROW][C]31[/C][C]6046[/C][C]6060.01499591645[/C][C]-14.0149959164473[/C][/ROW]
[ROW][C]32[/C][C]6001[/C][C]6022.13391935778[/C][C]-21.1339193577769[/C][/ROW]
[ROW][C]33[/C][C]5979[/C][C]5977.88469396689[/C][C]1.11530603310985[/C][/ROW]
[ROW][C]34[/C][C]5921[/C][C]5948.10481498039[/C][C]-27.1048149803919[/C][/ROW]
[ROW][C]35[/C][C]5863[/C][C]5897.82293691917[/C][C]-34.822936919174[/C][/ROW]
[ROW][C]36[/C][C]5818[/C][C]5839.64033349797[/C][C]-21.640333497965[/C][/ROW]
[ROW][C]37[/C][C]5758[/C][C]5788.16475402962[/C][C]-30.1647540296235[/C][/ROW]
[ROW][C]38[/C][C]5786[/C][C]5728.65723879933[/C][C]57.3427612006672[/C][/ROW]
[ROW][C]39[/C][C]5734[/C][C]5730.48956505854[/C][C]3.51043494145597[/C][/ROW]
[ROW][C]40[/C][C]5678[/C][C]5697.83262150218[/C][C]-19.8326215021843[/C][/ROW]
[ROW][C]41[/C][C]5610[/C][C]5648.43341807896[/C][C]-38.433418078961[/C][/ROW]
[ROW][C]42[/C][C]5578[/C][C]5583.79969907927[/C][C]-5.79969907927261[/C][/ROW]
[ROW][C]43[/C][C]5589[/C][C]5539.76651604111[/C][C]49.2334839588939[/C][/ROW]
[ROW][C]44[/C][C]5553[/C][C]5535.41180644535[/C][C]17.5881935546477[/C][/ROW]
[ROW][C]45[/C][C]5533[/C][C]5512.08160888789[/C][C]20.9183911121117[/C][/ROW]
[ROW][C]46[/C][C]5521[/C][C]5492.65349407431[/C][C]28.3465059256941[/C][/ROW]
[ROW][C]47[/C][C]5464[/C][C]5480.39681265916[/C][C]-16.3968126591608[/C][/ROW]
[ROW][C]48[/C][C]5419[/C][C]5437.85787996579[/C][C]-18.8578799657853[/C][/ROW]
[ROW][C]49[/C][C]5346[/C][C]5392.15085173708[/C][C]-46.1508517370776[/C][/ROW]
[ROW][C]50[/C][C]5296[/C][C]5324.94723362359[/C][C]-28.9472336235858[/C][/ROW]
[ROW][C]51[/C][C]5255[/C][C]5266.43736514032[/C][C]-11.4373651403212[/C][/ROW]
[ROW][C]52[/C][C]5235[/C][C]5218.28424381365[/C][C]16.7157561863496[/C][/ROW]
[ROW][C]53[/C][C]5164[/C][C]5189.7205380826[/C][C]-25.7205380826035[/C][/ROW]
[ROW][C]54[/C][C]5164[/C][C]5131.58508040299[/C][C]32.4149195970094[/C][/ROW]
[ROW][C]55[/C][C]5172[/C][C]5113.725313275[/C][C]58.2746867250034[/C][/ROW]
[ROW][C]56[/C][C]5093[/C][C]5117.45053896358[/C][C]-24.4505389635815[/C][/ROW]
[ROW][C]57[/C][C]5070[/C][C]5065.67815132343[/C][C]4.32184867656815[/C][/ROW]
[ROW][C]58[/C][C]5108[/C][C]5032.85826352033[/C][C]75.1417364796716[/C][/ROW]
[ROW][C]59[/C][C]5051[/C][C]5052.08504998658[/C][C]-1.08504998658373[/C][/ROW]
[ROW][C]60[/C][C]5021[/C][C]5021.96817882119[/C][C]-0.968178821186484[/C][/ROW]
[ROW][C]61[/C][C]5001[/C][C]4991.8458110658[/C][C]9.15418893420156[/C][/ROW]
[ROW][C]62[/C][C]4918[/C][C]4969.02983530103[/C][C]-51.0298353010257[/C][/ROW]
[ROW][C]63[/C][C]4886[/C][C]4903.05693477097[/C][C]-17.0569347709688[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299332&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299332&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
36841682417
467546833.40676669297-79.4067666929668
568696773.8773852314795.122614768532
668096835.07698762342-26.0769876234208
768366815.7832074033120.2167925966942
867666828.09311990539-62.0931199053875
967596782.02406809686-23.0240680968609
1067196759.27242283564-40.2724228356419
1167026722.0062466812-20.0062466811987
1266276696.1607758376-69.1607758376022
1366306632.76784789965-2.76784789965131
1466066612.04218123206-6.04218123205737
1565126588.69527749535-76.6952774953506
1665506513.279478738136.7205212618983
1765786514.2182526764563.7817473235482
1864996537.97912222043-38.9791222204331
1963716492.08096606707-121.080966067071
2063326383.0025459062-51.0025459061972
2162916314.93673304168-23.9367330416835
2263076262.3562362981144.6437637018889
2362526257.82357987333-5.82357987332671
2462506220.1948769480529.8051230519495
2561646208.08106941074-44.0810694107386
2662136144.5383035938168.4616964061852
2761746159.4419189070814.5580810929177
2861546140.7346010978613.2653989021428
2960916122.30200187973-31.302001879726
3060966072.4536435971223.5463564028814
3160466060.01499591645-14.0149959164473
3260016022.13391935778-21.1339193577769
3359795977.884693966891.11530603310985
3459215948.10481498039-27.1048149803919
3558635897.82293691917-34.822936919174
3658185839.64033349797-21.640333497965
3757585788.16475402962-30.1647540296235
3857865728.6572387993357.3427612006672
3957345730.489565058543.51043494145597
4056785697.83262150218-19.8326215021843
4156105648.43341807896-38.433418078961
4255785583.79969907927-5.79969907927261
4355895539.7665160411149.2334839588939
4455535535.4118064453517.5881935546477
4555335512.0816088878920.9183911121117
4655215492.6534940743128.3465059256941
4754645480.39681265916-16.3968126591608
4854195437.85787996579-18.8578799657853
4953465392.15085173708-46.1508517370776
5052965324.94723362359-28.9472336235858
5152555266.43736514032-11.4373651403212
5252355218.2842438136516.7157561863496
5351645189.7205380826-25.7205380826035
5451645131.5850804029932.4149195970094
5551725113.72531327558.2746867250034
5650935117.45053896358-24.4505389635815
5750705065.678151323434.32184867656815
5851085032.8582635203375.1417364796716
5950515052.08504998658-1.08504998658373
6050215021.96817882119-0.968178821186484
6150014991.84581106589.15418893420156
6249184969.02983530103-51.0298353010257
6348864903.05693477097-17.0569347709688







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
644857.60792725864777.882233222414937.33362129479
654823.180018550114724.48030638314921.87973071712
664788.752109841624670.650986029224906.85323365402
674754.324201133124616.252059163534892.39634310272
684719.896292424634561.218129731644878.57445511763
694685.468383716144505.520036862874865.4167305694
704651.040475007654449.14727464254852.93367537279
714616.612566299154392.09946405834841.12566854001
724582.184657590664334.381879126764829.98743605456
734547.756748882174276.002964234474819.51053352987
744513.328840173674216.972899196644809.68478115071
754478.900931465184157.302745575794800.49911735457
764444.473022756694097.003929135334791.94211637805
774410.04511404824036.087923151554784.00230494484
784375.61720533973974.566054888874776.66835579054
794341.189296631213912.449389119974769.92920414245
804306.761387922723849.748660556674763.77411528877
814272.333479214233786.47423763274758.19272079575

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
64 & 4857.6079272586 & 4777.88223322241 & 4937.33362129479 \tabularnewline
65 & 4823.18001855011 & 4724.4803063831 & 4921.87973071712 \tabularnewline
66 & 4788.75210984162 & 4670.65098602922 & 4906.85323365402 \tabularnewline
67 & 4754.32420113312 & 4616.25205916353 & 4892.39634310272 \tabularnewline
68 & 4719.89629242463 & 4561.21812973164 & 4878.57445511763 \tabularnewline
69 & 4685.46838371614 & 4505.52003686287 & 4865.4167305694 \tabularnewline
70 & 4651.04047500765 & 4449.1472746425 & 4852.93367537279 \tabularnewline
71 & 4616.61256629915 & 4392.0994640583 & 4841.12566854001 \tabularnewline
72 & 4582.18465759066 & 4334.38187912676 & 4829.98743605456 \tabularnewline
73 & 4547.75674888217 & 4276.00296423447 & 4819.51053352987 \tabularnewline
74 & 4513.32884017367 & 4216.97289919664 & 4809.68478115071 \tabularnewline
75 & 4478.90093146518 & 4157.30274557579 & 4800.49911735457 \tabularnewline
76 & 4444.47302275669 & 4097.00392913533 & 4791.94211637805 \tabularnewline
77 & 4410.0451140482 & 4036.08792315155 & 4784.00230494484 \tabularnewline
78 & 4375.6172053397 & 3974.56605488887 & 4776.66835579054 \tabularnewline
79 & 4341.18929663121 & 3912.44938911997 & 4769.92920414245 \tabularnewline
80 & 4306.76138792272 & 3849.74866055667 & 4763.77411528877 \tabularnewline
81 & 4272.33347921423 & 3786.4742376327 & 4758.19272079575 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299332&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]64[/C][C]4857.6079272586[/C][C]4777.88223322241[/C][C]4937.33362129479[/C][/ROW]
[ROW][C]65[/C][C]4823.18001855011[/C][C]4724.4803063831[/C][C]4921.87973071712[/C][/ROW]
[ROW][C]66[/C][C]4788.75210984162[/C][C]4670.65098602922[/C][C]4906.85323365402[/C][/ROW]
[ROW][C]67[/C][C]4754.32420113312[/C][C]4616.25205916353[/C][C]4892.39634310272[/C][/ROW]
[ROW][C]68[/C][C]4719.89629242463[/C][C]4561.21812973164[/C][C]4878.57445511763[/C][/ROW]
[ROW][C]69[/C][C]4685.46838371614[/C][C]4505.52003686287[/C][C]4865.4167305694[/C][/ROW]
[ROW][C]70[/C][C]4651.04047500765[/C][C]4449.1472746425[/C][C]4852.93367537279[/C][/ROW]
[ROW][C]71[/C][C]4616.61256629915[/C][C]4392.0994640583[/C][C]4841.12566854001[/C][/ROW]
[ROW][C]72[/C][C]4582.18465759066[/C][C]4334.38187912676[/C][C]4829.98743605456[/C][/ROW]
[ROW][C]73[/C][C]4547.75674888217[/C][C]4276.00296423447[/C][C]4819.51053352987[/C][/ROW]
[ROW][C]74[/C][C]4513.32884017367[/C][C]4216.97289919664[/C][C]4809.68478115071[/C][/ROW]
[ROW][C]75[/C][C]4478.90093146518[/C][C]4157.30274557579[/C][C]4800.49911735457[/C][/ROW]
[ROW][C]76[/C][C]4444.47302275669[/C][C]4097.00392913533[/C][C]4791.94211637805[/C][/ROW]
[ROW][C]77[/C][C]4410.0451140482[/C][C]4036.08792315155[/C][C]4784.00230494484[/C][/ROW]
[ROW][C]78[/C][C]4375.6172053397[/C][C]3974.56605488887[/C][C]4776.66835579054[/C][/ROW]
[ROW][C]79[/C][C]4341.18929663121[/C][C]3912.44938911997[/C][C]4769.92920414245[/C][/ROW]
[ROW][C]80[/C][C]4306.76138792272[/C][C]3849.74866055667[/C][C]4763.77411528877[/C][/ROW]
[ROW][C]81[/C][C]4272.33347921423[/C][C]3786.4742376327[/C][C]4758.19272079575[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299332&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299332&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
644857.60792725864777.882233222414937.33362129479
654823.180018550114724.48030638314921.87973071712
664788.752109841624670.650986029224906.85323365402
674754.324201133124616.252059163534892.39634310272
684719.896292424634561.218129731644878.57445511763
694685.468383716144505.520036862874865.4167305694
704651.040475007654449.14727464254852.93367537279
714616.612566299154392.09946405834841.12566854001
724582.184657590664334.381879126764829.98743605456
734547.756748882174276.002964234474819.51053352987
744513.328840173674216.972899196644809.68478115071
754478.900931465184157.302745575794800.49911735457
764444.473022756694097.003929135334791.94211637805
774410.04511404824036.087923151554784.00230494484
784375.61720533973974.566054888874776.66835579054
794341.189296631213912.449389119974769.92920414245
804306.761387922723849.748660556674763.77411528877
814272.333479214233786.47423763274758.19272079575



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 18 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')