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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 25 May 2013 14:27:49 -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/2013/May/25/t1369506645586z9eu4odnb0je.htm/, Retrieved Thu, 02 May 2024 17:24:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210549, Retrieved Thu, 02 May 2024 17:24:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [verbetering oef 1...] [2013-05-25 18:27:49] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
68.906
39.556
50.669
36.432
40.891
48.428
36.222
33.425
39.401
37.967
34.801
12.657
69.116
41.519
51.321
38.529
41.547
52.073
38.401
40.898
40.439
41.888
37.898
8.771
68.184
50.530
47.221
41.756
45.633
48.138
39.486
39.341
41.117
41.629
29.722
7.054
56.676
34.870
35.117
30.169
30.936
35.699
33.228
27.733
33.666
35.429
27.438
8.170
63.410
38.040
45.389
37.353
37.024
50.957
37.994
36.454
46.080
43.373
37.395
10.963
76.058
50.179
57.452
47.568
50.050
50.856
41.992
39.284
44.521
43.832
41.153
17.100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210549&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210549&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210549&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.476038589911565
beta0
gamma0.358101133901473

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.476038589911565 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.358101133901473 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210549&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]0.476038589911565[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.358101133901473[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210549&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210549&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
alpha0.476038589911565
beta0
gamma0.358101133901473







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1369.11668.21502911324790.900970886752148
1441.51940.85957098293620.659429017063815
1551.32150.83567126824010.485328731759864
1638.52938.28289309922480.24610690077521
1741.54741.34044444044480.206555559555213
1852.07352.212459483628-0.139459483627967
1938.40138.5834663468994-0.182466346899375
2040.89835.82387528362255.07412471637747
2140.43944.3212077511831-3.88220775118308
2241.88841.13939700677360.748602993226406
2337.89838.4298642126135-0.531864212613463
248.77116.0682796153573-7.29727961535731
2568.18469.1946881024678-1.0106881024678
2650.5340.88388573769719.64611426230292
2747.22155.1053283540115-7.88432835401155
2841.75638.52338495459143.23261504540859
2945.63342.99520835711322.63779164288675
3048.13854.9596623880022-6.8216623880022
3139.48638.14161337488051.34438662511949
3239.34137.09516360548822.24583639451184
3341.11742.5656345032091-1.44863450320906
3441.62941.41118299772720.217817002272831
3529.72238.2087200224141-8.48672002241415
367.05410.7909142406349-3.73691424063494
3756.67666.7917545930674-10.1157545930674
3834.8736.1461375652863-1.27613756528628
3935.11741.8789092752823-6.76190927528233
4030.16927.91716582464672.25183417535334
4130.93631.8104922707989-0.8744922707989
4235.69940.3280751446805-4.62907514468046
4333.22826.08598764316587.14201235683422
4427.73327.9685715314346-0.235571531434552
4533.66631.56459858327912.10140141672087
4635.42932.41277942543233.0162205745677
4727.43828.9092220302671-1.4712220302671
488.175.72227566040212.4477243395979
4963.4163.4703733307495-0.0603733307494991
5038.0439.2700935502257-1.23009355022573
5145.38943.99548219609471.39351780390527
5237.35335.6072960278141.74570397218599
5337.02438.6730886609846-1.64908866098459
5450.95746.11745696499514.83954303500485
5537.99438.5914200899485-0.597420089948514
5636.45435.40547073537741.04852926462258
5746.0840.05126829985826.02873170014177
5843.37342.94065850581440.432341494185572
5937.39537.36509082770310.0299091722969465
6010.96315.6280573512058-4.66505735120585
6176.05869.51959914202846.53840085797162
6250.17948.2411145421611.93788545783905
6357.45254.96685472920982.48514527079024
6447.56847.16440646557280.403593534427237
6550.0548.95433380755511.09566619244485
6650.85658.9227809313814-8.06678093138143
6741.99244.2326920144693-2.24069201446932
6839.28440.5733132216174-1.28931322161737
6944.52145.0406487805925-0.519648780592455
7043.83243.76269990578330.0693000942166648
7141.15337.93880166210783.21419833789219
7217.116.83669062413670.263309375863322

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 69.116 & 68.2150291132479 & 0.900970886752148 \tabularnewline
14 & 41.519 & 40.8595709829362 & 0.659429017063815 \tabularnewline
15 & 51.321 & 50.8356712682401 & 0.485328731759864 \tabularnewline
16 & 38.529 & 38.2828930992248 & 0.24610690077521 \tabularnewline
17 & 41.547 & 41.3404444404448 & 0.206555559555213 \tabularnewline
18 & 52.073 & 52.212459483628 & -0.139459483627967 \tabularnewline
19 & 38.401 & 38.5834663468994 & -0.182466346899375 \tabularnewline
20 & 40.898 & 35.8238752836225 & 5.07412471637747 \tabularnewline
21 & 40.439 & 44.3212077511831 & -3.88220775118308 \tabularnewline
22 & 41.888 & 41.1393970067736 & 0.748602993226406 \tabularnewline
23 & 37.898 & 38.4298642126135 & -0.531864212613463 \tabularnewline
24 & 8.771 & 16.0682796153573 & -7.29727961535731 \tabularnewline
25 & 68.184 & 69.1946881024678 & -1.0106881024678 \tabularnewline
26 & 50.53 & 40.8838857376971 & 9.64611426230292 \tabularnewline
27 & 47.221 & 55.1053283540115 & -7.88432835401155 \tabularnewline
28 & 41.756 & 38.5233849545914 & 3.23261504540859 \tabularnewline
29 & 45.633 & 42.9952083571132 & 2.63779164288675 \tabularnewline
30 & 48.138 & 54.9596623880022 & -6.8216623880022 \tabularnewline
31 & 39.486 & 38.1416133748805 & 1.34438662511949 \tabularnewline
32 & 39.341 & 37.0951636054882 & 2.24583639451184 \tabularnewline
33 & 41.117 & 42.5656345032091 & -1.44863450320906 \tabularnewline
34 & 41.629 & 41.4111829977272 & 0.217817002272831 \tabularnewline
35 & 29.722 & 38.2087200224141 & -8.48672002241415 \tabularnewline
36 & 7.054 & 10.7909142406349 & -3.73691424063494 \tabularnewline
37 & 56.676 & 66.7917545930674 & -10.1157545930674 \tabularnewline
38 & 34.87 & 36.1461375652863 & -1.27613756528628 \tabularnewline
39 & 35.117 & 41.8789092752823 & -6.76190927528233 \tabularnewline
40 & 30.169 & 27.9171658246467 & 2.25183417535334 \tabularnewline
41 & 30.936 & 31.8104922707989 & -0.8744922707989 \tabularnewline
42 & 35.699 & 40.3280751446805 & -4.62907514468046 \tabularnewline
43 & 33.228 & 26.0859876431658 & 7.14201235683422 \tabularnewline
44 & 27.733 & 27.9685715314346 & -0.235571531434552 \tabularnewline
45 & 33.666 & 31.5645985832791 & 2.10140141672087 \tabularnewline
46 & 35.429 & 32.4127794254323 & 3.0162205745677 \tabularnewline
47 & 27.438 & 28.9092220302671 & -1.4712220302671 \tabularnewline
48 & 8.17 & 5.7222756604021 & 2.4477243395979 \tabularnewline
49 & 63.41 & 63.4703733307495 & -0.0603733307494991 \tabularnewline
50 & 38.04 & 39.2700935502257 & -1.23009355022573 \tabularnewline
51 & 45.389 & 43.9954821960947 & 1.39351780390527 \tabularnewline
52 & 37.353 & 35.607296027814 & 1.74570397218599 \tabularnewline
53 & 37.024 & 38.6730886609846 & -1.64908866098459 \tabularnewline
54 & 50.957 & 46.1174569649951 & 4.83954303500485 \tabularnewline
55 & 37.994 & 38.5914200899485 & -0.597420089948514 \tabularnewline
56 & 36.454 & 35.4054707353774 & 1.04852926462258 \tabularnewline
57 & 46.08 & 40.0512682998582 & 6.02873170014177 \tabularnewline
58 & 43.373 & 42.9406585058144 & 0.432341494185572 \tabularnewline
59 & 37.395 & 37.3650908277031 & 0.0299091722969465 \tabularnewline
60 & 10.963 & 15.6280573512058 & -4.66505735120585 \tabularnewline
61 & 76.058 & 69.5195991420284 & 6.53840085797162 \tabularnewline
62 & 50.179 & 48.241114542161 & 1.93788545783905 \tabularnewline
63 & 57.452 & 54.9668547292098 & 2.48514527079024 \tabularnewline
64 & 47.568 & 47.1644064655728 & 0.403593534427237 \tabularnewline
65 & 50.05 & 48.9543338075551 & 1.09566619244485 \tabularnewline
66 & 50.856 & 58.9227809313814 & -8.06678093138143 \tabularnewline
67 & 41.992 & 44.2326920144693 & -2.24069201446932 \tabularnewline
68 & 39.284 & 40.5733132216174 & -1.28931322161737 \tabularnewline
69 & 44.521 & 45.0406487805925 & -0.519648780592455 \tabularnewline
70 & 43.832 & 43.7626999057833 & 0.0693000942166648 \tabularnewline
71 & 41.153 & 37.9388016621078 & 3.21419833789219 \tabularnewline
72 & 17.1 & 16.8366906241367 & 0.263309375863322 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210549&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]69.116[/C][C]68.2150291132479[/C][C]0.900970886752148[/C][/ROW]
[ROW][C]14[/C][C]41.519[/C][C]40.8595709829362[/C][C]0.659429017063815[/C][/ROW]
[ROW][C]15[/C][C]51.321[/C][C]50.8356712682401[/C][C]0.485328731759864[/C][/ROW]
[ROW][C]16[/C][C]38.529[/C][C]38.2828930992248[/C][C]0.24610690077521[/C][/ROW]
[ROW][C]17[/C][C]41.547[/C][C]41.3404444404448[/C][C]0.206555559555213[/C][/ROW]
[ROW][C]18[/C][C]52.073[/C][C]52.212459483628[/C][C]-0.139459483627967[/C][/ROW]
[ROW][C]19[/C][C]38.401[/C][C]38.5834663468994[/C][C]-0.182466346899375[/C][/ROW]
[ROW][C]20[/C][C]40.898[/C][C]35.8238752836225[/C][C]5.07412471637747[/C][/ROW]
[ROW][C]21[/C][C]40.439[/C][C]44.3212077511831[/C][C]-3.88220775118308[/C][/ROW]
[ROW][C]22[/C][C]41.888[/C][C]41.1393970067736[/C][C]0.748602993226406[/C][/ROW]
[ROW][C]23[/C][C]37.898[/C][C]38.4298642126135[/C][C]-0.531864212613463[/C][/ROW]
[ROW][C]24[/C][C]8.771[/C][C]16.0682796153573[/C][C]-7.29727961535731[/C][/ROW]
[ROW][C]25[/C][C]68.184[/C][C]69.1946881024678[/C][C]-1.0106881024678[/C][/ROW]
[ROW][C]26[/C][C]50.53[/C][C]40.8838857376971[/C][C]9.64611426230292[/C][/ROW]
[ROW][C]27[/C][C]47.221[/C][C]55.1053283540115[/C][C]-7.88432835401155[/C][/ROW]
[ROW][C]28[/C][C]41.756[/C][C]38.5233849545914[/C][C]3.23261504540859[/C][/ROW]
[ROW][C]29[/C][C]45.633[/C][C]42.9952083571132[/C][C]2.63779164288675[/C][/ROW]
[ROW][C]30[/C][C]48.138[/C][C]54.9596623880022[/C][C]-6.8216623880022[/C][/ROW]
[ROW][C]31[/C][C]39.486[/C][C]38.1416133748805[/C][C]1.34438662511949[/C][/ROW]
[ROW][C]32[/C][C]39.341[/C][C]37.0951636054882[/C][C]2.24583639451184[/C][/ROW]
[ROW][C]33[/C][C]41.117[/C][C]42.5656345032091[/C][C]-1.44863450320906[/C][/ROW]
[ROW][C]34[/C][C]41.629[/C][C]41.4111829977272[/C][C]0.217817002272831[/C][/ROW]
[ROW][C]35[/C][C]29.722[/C][C]38.2087200224141[/C][C]-8.48672002241415[/C][/ROW]
[ROW][C]36[/C][C]7.054[/C][C]10.7909142406349[/C][C]-3.73691424063494[/C][/ROW]
[ROW][C]37[/C][C]56.676[/C][C]66.7917545930674[/C][C]-10.1157545930674[/C][/ROW]
[ROW][C]38[/C][C]34.87[/C][C]36.1461375652863[/C][C]-1.27613756528628[/C][/ROW]
[ROW][C]39[/C][C]35.117[/C][C]41.8789092752823[/C][C]-6.76190927528233[/C][/ROW]
[ROW][C]40[/C][C]30.169[/C][C]27.9171658246467[/C][C]2.25183417535334[/C][/ROW]
[ROW][C]41[/C][C]30.936[/C][C]31.8104922707989[/C][C]-0.8744922707989[/C][/ROW]
[ROW][C]42[/C][C]35.699[/C][C]40.3280751446805[/C][C]-4.62907514468046[/C][/ROW]
[ROW][C]43[/C][C]33.228[/C][C]26.0859876431658[/C][C]7.14201235683422[/C][/ROW]
[ROW][C]44[/C][C]27.733[/C][C]27.9685715314346[/C][C]-0.235571531434552[/C][/ROW]
[ROW][C]45[/C][C]33.666[/C][C]31.5645985832791[/C][C]2.10140141672087[/C][/ROW]
[ROW][C]46[/C][C]35.429[/C][C]32.4127794254323[/C][C]3.0162205745677[/C][/ROW]
[ROW][C]47[/C][C]27.438[/C][C]28.9092220302671[/C][C]-1.4712220302671[/C][/ROW]
[ROW][C]48[/C][C]8.17[/C][C]5.7222756604021[/C][C]2.4477243395979[/C][/ROW]
[ROW][C]49[/C][C]63.41[/C][C]63.4703733307495[/C][C]-0.0603733307494991[/C][/ROW]
[ROW][C]50[/C][C]38.04[/C][C]39.2700935502257[/C][C]-1.23009355022573[/C][/ROW]
[ROW][C]51[/C][C]45.389[/C][C]43.9954821960947[/C][C]1.39351780390527[/C][/ROW]
[ROW][C]52[/C][C]37.353[/C][C]35.607296027814[/C][C]1.74570397218599[/C][/ROW]
[ROW][C]53[/C][C]37.024[/C][C]38.6730886609846[/C][C]-1.64908866098459[/C][/ROW]
[ROW][C]54[/C][C]50.957[/C][C]46.1174569649951[/C][C]4.83954303500485[/C][/ROW]
[ROW][C]55[/C][C]37.994[/C][C]38.5914200899485[/C][C]-0.597420089948514[/C][/ROW]
[ROW][C]56[/C][C]36.454[/C][C]35.4054707353774[/C][C]1.04852926462258[/C][/ROW]
[ROW][C]57[/C][C]46.08[/C][C]40.0512682998582[/C][C]6.02873170014177[/C][/ROW]
[ROW][C]58[/C][C]43.373[/C][C]42.9406585058144[/C][C]0.432341494185572[/C][/ROW]
[ROW][C]59[/C][C]37.395[/C][C]37.3650908277031[/C][C]0.0299091722969465[/C][/ROW]
[ROW][C]60[/C][C]10.963[/C][C]15.6280573512058[/C][C]-4.66505735120585[/C][/ROW]
[ROW][C]61[/C][C]76.058[/C][C]69.5195991420284[/C][C]6.53840085797162[/C][/ROW]
[ROW][C]62[/C][C]50.179[/C][C]48.241114542161[/C][C]1.93788545783905[/C][/ROW]
[ROW][C]63[/C][C]57.452[/C][C]54.9668547292098[/C][C]2.48514527079024[/C][/ROW]
[ROW][C]64[/C][C]47.568[/C][C]47.1644064655728[/C][C]0.403593534427237[/C][/ROW]
[ROW][C]65[/C][C]50.05[/C][C]48.9543338075551[/C][C]1.09566619244485[/C][/ROW]
[ROW][C]66[/C][C]50.856[/C][C]58.9227809313814[/C][C]-8.06678093138143[/C][/ROW]
[ROW][C]67[/C][C]41.992[/C][C]44.2326920144693[/C][C]-2.24069201446932[/C][/ROW]
[ROW][C]68[/C][C]39.284[/C][C]40.5733132216174[/C][C]-1.28931322161737[/C][/ROW]
[ROW][C]69[/C][C]44.521[/C][C]45.0406487805925[/C][C]-0.519648780592455[/C][/ROW]
[ROW][C]70[/C][C]43.832[/C][C]43.7626999057833[/C][C]0.0693000942166648[/C][/ROW]
[ROW][C]71[/C][C]41.153[/C][C]37.9388016621078[/C][C]3.21419833789219[/C][/ROW]
[ROW][C]72[/C][C]17.1[/C][C]16.8366906241367[/C][C]0.263309375863322[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210549&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210549&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
1369.11668.21502911324790.900970886752148
1441.51940.85957098293620.659429017063815
1551.32150.83567126824010.485328731759864
1638.52938.28289309922480.24610690077521
1741.54741.34044444044480.206555559555213
1852.07352.212459483628-0.139459483627967
1938.40138.5834663468994-0.182466346899375
2040.89835.82387528362255.07412471637747
2140.43944.3212077511831-3.88220775118308
2241.88841.13939700677360.748602993226406
2337.89838.4298642126135-0.531864212613463
248.77116.0682796153573-7.29727961535731
2568.18469.1946881024678-1.0106881024678
2650.5340.88388573769719.64611426230292
2747.22155.1053283540115-7.88432835401155
2841.75638.52338495459143.23261504540859
2945.63342.99520835711322.63779164288675
3048.13854.9596623880022-6.8216623880022
3139.48638.14161337488051.34438662511949
3239.34137.09516360548822.24583639451184
3341.11742.5656345032091-1.44863450320906
3441.62941.41118299772720.217817002272831
3529.72238.2087200224141-8.48672002241415
367.05410.7909142406349-3.73691424063494
3756.67666.7917545930674-10.1157545930674
3834.8736.1461375652863-1.27613756528628
3935.11741.8789092752823-6.76190927528233
4030.16927.91716582464672.25183417535334
4130.93631.8104922707989-0.8744922707989
4235.69940.3280751446805-4.62907514468046
4333.22826.08598764316587.14201235683422
4427.73327.9685715314346-0.235571531434552
4533.66631.56459858327912.10140141672087
4635.42932.41277942543233.0162205745677
4727.43828.9092220302671-1.4712220302671
488.175.72227566040212.4477243395979
4963.4163.4703733307495-0.0603733307494991
5038.0439.2700935502257-1.23009355022573
5145.38943.99548219609471.39351780390527
5237.35335.6072960278141.74570397218599
5337.02438.6730886609846-1.64908866098459
5450.95746.11745696499514.83954303500485
5537.99438.5914200899485-0.597420089948514
5636.45435.40547073537741.04852926462258
5746.0840.05126829985826.02873170014177
5843.37342.94065850581440.432341494185572
5937.39537.36509082770310.0299091722969465
6010.96315.6280573512058-4.66505735120585
6176.05869.51959914202846.53840085797162
6250.17948.2411145421611.93788545783905
6357.45254.96685472920982.48514527079024
6447.56847.16440646557280.403593534427237
6550.0548.95433380755511.09566619244485
6650.85658.9227809313814-8.06678093138143
6741.99244.2326920144693-2.24069201446932
6839.28440.5733132216174-1.28931322161737
6944.52145.0406487805925-0.519648780592455
7043.83243.76269990578330.0693000942166648
7141.15337.93880166210783.21419833789219
7217.116.83669062413670.263309375863322







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7375.176443190952767.571581388109482.781304993796
7449.922227355910341.499648964909858.3448057469107
7555.828142283973746.660496432134164.9957881358132
7646.452104971634736.59555211696256.3086578263073
7748.179760622650837.679401681683258.6801195636184
7855.907467636821544.800558003563467.0143772700796
7946.150633649171434.468624176757657.8326431215851
8043.736419044156131.506323009137955.9665150791743
8148.961930494585936.207278294781761.7165826943901
8248.041859661977834.783388541589461.3003307823662
8342.775052852117429.031219319860956.5188863843738
8419.58918060622375.376550171480833.8018110409666

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 75.1764431909527 & 67.5715813881094 & 82.781304993796 \tabularnewline
74 & 49.9222273559103 & 41.4996489649098 & 58.3448057469107 \tabularnewline
75 & 55.8281422839737 & 46.6604964321341 & 64.9957881358132 \tabularnewline
76 & 46.4521049716347 & 36.595552116962 & 56.3086578263073 \tabularnewline
77 & 48.1797606226508 & 37.6794016816832 & 58.6801195636184 \tabularnewline
78 & 55.9074676368215 & 44.8005580035634 & 67.0143772700796 \tabularnewline
79 & 46.1506336491714 & 34.4686241767576 & 57.8326431215851 \tabularnewline
80 & 43.7364190441561 & 31.5063230091379 & 55.9665150791743 \tabularnewline
81 & 48.9619304945859 & 36.2072782947817 & 61.7165826943901 \tabularnewline
82 & 48.0418596619778 & 34.7833885415894 & 61.3003307823662 \tabularnewline
83 & 42.7750528521174 & 29.0312193198609 & 56.5188863843738 \tabularnewline
84 & 19.5891806062237 & 5.3765501714808 & 33.8018110409666 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210549&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]75.1764431909527[/C][C]67.5715813881094[/C][C]82.781304993796[/C][/ROW]
[ROW][C]74[/C][C]49.9222273559103[/C][C]41.4996489649098[/C][C]58.3448057469107[/C][/ROW]
[ROW][C]75[/C][C]55.8281422839737[/C][C]46.6604964321341[/C][C]64.9957881358132[/C][/ROW]
[ROW][C]76[/C][C]46.4521049716347[/C][C]36.595552116962[/C][C]56.3086578263073[/C][/ROW]
[ROW][C]77[/C][C]48.1797606226508[/C][C]37.6794016816832[/C][C]58.6801195636184[/C][/ROW]
[ROW][C]78[/C][C]55.9074676368215[/C][C]44.8005580035634[/C][C]67.0143772700796[/C][/ROW]
[ROW][C]79[/C][C]46.1506336491714[/C][C]34.4686241767576[/C][C]57.8326431215851[/C][/ROW]
[ROW][C]80[/C][C]43.7364190441561[/C][C]31.5063230091379[/C][C]55.9665150791743[/C][/ROW]
[ROW][C]81[/C][C]48.9619304945859[/C][C]36.2072782947817[/C][C]61.7165826943901[/C][/ROW]
[ROW][C]82[/C][C]48.0418596619778[/C][C]34.7833885415894[/C][C]61.3003307823662[/C][/ROW]
[ROW][C]83[/C][C]42.7750528521174[/C][C]29.0312193198609[/C][C]56.5188863843738[/C][/ROW]
[ROW][C]84[/C][C]19.5891806062237[/C][C]5.3765501714808[/C][C]33.8018110409666[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210549&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210549&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
7375.176443190952767.571581388109482.781304993796
7449.922227355910341.499648964909858.3448057469107
7555.828142283973746.660496432134164.9957881358132
7646.452104971634736.59555211696256.3086578263073
7748.179760622650837.679401681683258.6801195636184
7855.907467636821544.800558003563467.0143772700796
7946.150633649171434.468624176757657.8326431215851
8043.736419044156131.506323009137955.9665150791743
8148.961930494585936.207278294781761.7165826943901
8248.041859661977834.783388541589461.3003307823662
8342.775052852117429.031219319860956.5188863843738
8419.58918060622375.376550171480833.8018110409666



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