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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 May 2008 11:12:05 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/21/t1211389984mu5uendqkoyp8ru.htm/, Retrieved Wed, 15 May 2024 17:46:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12999, Retrieved Wed, 15 May 2024 17:46:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact212
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Elke Van Buggenho...] [2008-05-21 17:12:05] [ef244335fc0c3f0884149746f4e30bed] [Current]
-   PD    [Exponential Smoothing] [Goudprijs opgave ...] [2008-06-01 09:49:05] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
10.893
10.756
10.940
10.997
10.827
10.166
10.186
10.457
10.368
10.244
10.511
10.812
10.738
10.171
9.721
9.897
9.828
9.924
10.371
10.846
10.413
10.709
10.662
10.570
10.297
10.635
10.872
10.296
10.383
10.431
10.574
10.653
10.805
10.872
10.625
10.407
10.463
10.556
10.646
10.702
11.353
11.346
11.451
11.964
12.574
13.031
13.812
14.544
14.931
14.886
16.005
17.064
15.168
16.050
15.839
15.137
14.954
15.648
15.305
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032
17.696
17.745
19.394




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12999&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12999&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12999&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.994007474033322
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.994007474033322 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12999&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]0.994007474033322[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12999&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12999&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
alpha0.994007474033322
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
210.75610.893-0.137000000000000
310.9410.75682097605740.183179023942564
410.99710.93890229494250.0580977050575271
510.82710.9966518479938-0.169651847993839
610.16610.8280166431044-0.662016643104398
710.18610.16996715192420.0160328480758238
810.45710.18590392274160.271096077258415
910.36810.4553754497176-0.0873754497175643
1010.24410.3685235996513-0.124523599651283
1110.51110.24474621090440.266253789095625
1210.81210.50940446725510.302595532744881
1310.73810.8101866884126-0.072186688412625
1410.17110.7384325806048-0.567432580604761
159.72110.1744003544736-0.453400354473612
169.8979.723717013397480.173282986602516
179.8289.8959615972032-0.067961597203201
189.9249.828407261635980.0955927383640223
1910.3719.923427158033130.447572841966872
2010.84610.36831790812250.477682091877465
2110.41310.8431374776606-0.430137477660606
2210.70910.41557761000410.293422389995877
2310.66210.7072416587087-0.0452416587087434
2410.5710.6622711118146-0.092271111814588
2510.29710.5705529370335-0.273552937033523
2610.63510.29863927307840.336360726921566
2710.87210.63298434960980.239015650390249
2810.29610.8705676925086-0.574567692508595
2910.38310.29944311181700.0835568881830273
3010.43110.38249928317790.0485007168221312
3110.57410.43070935819500.143290641804960
3210.65310.57314132710820.079858672891799
3310.80510.65252144482900.152478555170967
3410.87210.80408626829880.067913731701223
3510.62510.8715930251993-0.246593025199287
3610.40710.6264777151067-0.219477715106708
3710.46310.40831522590690.0546847740931149
3810.55610.46267230007130.093327699928734
3910.64610.55544073133480.0905592686652348
4010.70210.6454573212310.0565426787689987
4111.35310.70166116652930.651338833470749
4211.34611.3490968351273-0.00309683512732128
4311.45111.34601855786490.104981442135086
4411.96411.45037089598200.513629104018014
4512.57411.96092206425690.613077935743069
4613.03112.57032611455050.460673885449538
4713.81213.02823939977930.783760600220726
4814.54413.80730329425150.736696705748482
4914.93114.53958532586120.391414674138762
5014.88614.9286544374015-0.0426544374014846
5116.00514.88625560782371.11874439217628
5217.06415.99829589517981.06570410482019
5315.16817.0576137404791-1.88961374047907
5416.0515.17932355940680.87067644059319
5515.83916.0447824488212-0.205782448821170
5615.13715.8402331566680-0.703233156668047
5714.95415.1412141429520-0.187214142951962
5815.64814.95512188561300.69287811438703
5915.30515.6438479099078-0.338847909907793
6015.57915.30703055489890.271969445101124
6116.34815.57737021603810.77062978396191
6215.92816.3433819810089-0.41538198100891
6316.17115.93048918730730.240510812692712
6415.93716.1695587327097-0.232558732709672
6515.71315.9383936142445-0.22539361424454
6615.59415.7143506770861-0.120350677086083
6715.68315.59472120455750.088278795442454
6816.43815.6824709870260.755529012973994
6917.03216.43347247277120.598527527228825
7017.69617.02841330825130.667586691748692
7117.74517.69199946941470.0530005305853116
7219.39417.74468239294421.64931760705578

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 10.756 & 10.893 & -0.137000000000000 \tabularnewline
3 & 10.94 & 10.7568209760574 & 0.183179023942564 \tabularnewline
4 & 10.997 & 10.9389022949425 & 0.0580977050575271 \tabularnewline
5 & 10.827 & 10.9966518479938 & -0.169651847993839 \tabularnewline
6 & 10.166 & 10.8280166431044 & -0.662016643104398 \tabularnewline
7 & 10.186 & 10.1699671519242 & 0.0160328480758238 \tabularnewline
8 & 10.457 & 10.1859039227416 & 0.271096077258415 \tabularnewline
9 & 10.368 & 10.4553754497176 & -0.0873754497175643 \tabularnewline
10 & 10.244 & 10.3685235996513 & -0.124523599651283 \tabularnewline
11 & 10.511 & 10.2447462109044 & 0.266253789095625 \tabularnewline
12 & 10.812 & 10.5094044672551 & 0.302595532744881 \tabularnewline
13 & 10.738 & 10.8101866884126 & -0.072186688412625 \tabularnewline
14 & 10.171 & 10.7384325806048 & -0.567432580604761 \tabularnewline
15 & 9.721 & 10.1744003544736 & -0.453400354473612 \tabularnewline
16 & 9.897 & 9.72371701339748 & 0.173282986602516 \tabularnewline
17 & 9.828 & 9.8959615972032 & -0.067961597203201 \tabularnewline
18 & 9.924 & 9.82840726163598 & 0.0955927383640223 \tabularnewline
19 & 10.371 & 9.92342715803313 & 0.447572841966872 \tabularnewline
20 & 10.846 & 10.3683179081225 & 0.477682091877465 \tabularnewline
21 & 10.413 & 10.8431374776606 & -0.430137477660606 \tabularnewline
22 & 10.709 & 10.4155776100041 & 0.293422389995877 \tabularnewline
23 & 10.662 & 10.7072416587087 & -0.0452416587087434 \tabularnewline
24 & 10.57 & 10.6622711118146 & -0.092271111814588 \tabularnewline
25 & 10.297 & 10.5705529370335 & -0.273552937033523 \tabularnewline
26 & 10.635 & 10.2986392730784 & 0.336360726921566 \tabularnewline
27 & 10.872 & 10.6329843496098 & 0.239015650390249 \tabularnewline
28 & 10.296 & 10.8705676925086 & -0.574567692508595 \tabularnewline
29 & 10.383 & 10.2994431118170 & 0.0835568881830273 \tabularnewline
30 & 10.431 & 10.3824992831779 & 0.0485007168221312 \tabularnewline
31 & 10.574 & 10.4307093581950 & 0.143290641804960 \tabularnewline
32 & 10.653 & 10.5731413271082 & 0.079858672891799 \tabularnewline
33 & 10.805 & 10.6525214448290 & 0.152478555170967 \tabularnewline
34 & 10.872 & 10.8040862682988 & 0.067913731701223 \tabularnewline
35 & 10.625 & 10.8715930251993 & -0.246593025199287 \tabularnewline
36 & 10.407 & 10.6264777151067 & -0.219477715106708 \tabularnewline
37 & 10.463 & 10.4083152259069 & 0.0546847740931149 \tabularnewline
38 & 10.556 & 10.4626723000713 & 0.093327699928734 \tabularnewline
39 & 10.646 & 10.5554407313348 & 0.0905592686652348 \tabularnewline
40 & 10.702 & 10.645457321231 & 0.0565426787689987 \tabularnewline
41 & 11.353 & 10.7016611665293 & 0.651338833470749 \tabularnewline
42 & 11.346 & 11.3490968351273 & -0.00309683512732128 \tabularnewline
43 & 11.451 & 11.3460185578649 & 0.104981442135086 \tabularnewline
44 & 11.964 & 11.4503708959820 & 0.513629104018014 \tabularnewline
45 & 12.574 & 11.9609220642569 & 0.613077935743069 \tabularnewline
46 & 13.031 & 12.5703261145505 & 0.460673885449538 \tabularnewline
47 & 13.812 & 13.0282393997793 & 0.783760600220726 \tabularnewline
48 & 14.544 & 13.8073032942515 & 0.736696705748482 \tabularnewline
49 & 14.931 & 14.5395853258612 & 0.391414674138762 \tabularnewline
50 & 14.886 & 14.9286544374015 & -0.0426544374014846 \tabularnewline
51 & 16.005 & 14.8862556078237 & 1.11874439217628 \tabularnewline
52 & 17.064 & 15.9982958951798 & 1.06570410482019 \tabularnewline
53 & 15.168 & 17.0576137404791 & -1.88961374047907 \tabularnewline
54 & 16.05 & 15.1793235594068 & 0.87067644059319 \tabularnewline
55 & 15.839 & 16.0447824488212 & -0.205782448821170 \tabularnewline
56 & 15.137 & 15.8402331566680 & -0.703233156668047 \tabularnewline
57 & 14.954 & 15.1412141429520 & -0.187214142951962 \tabularnewline
58 & 15.648 & 14.9551218856130 & 0.69287811438703 \tabularnewline
59 & 15.305 & 15.6438479099078 & -0.338847909907793 \tabularnewline
60 & 15.579 & 15.3070305548989 & 0.271969445101124 \tabularnewline
61 & 16.348 & 15.5773702160381 & 0.77062978396191 \tabularnewline
62 & 15.928 & 16.3433819810089 & -0.41538198100891 \tabularnewline
63 & 16.171 & 15.9304891873073 & 0.240510812692712 \tabularnewline
64 & 15.937 & 16.1695587327097 & -0.232558732709672 \tabularnewline
65 & 15.713 & 15.9383936142445 & -0.22539361424454 \tabularnewline
66 & 15.594 & 15.7143506770861 & -0.120350677086083 \tabularnewline
67 & 15.683 & 15.5947212045575 & 0.088278795442454 \tabularnewline
68 & 16.438 & 15.682470987026 & 0.755529012973994 \tabularnewline
69 & 17.032 & 16.4334724727712 & 0.598527527228825 \tabularnewline
70 & 17.696 & 17.0284133082513 & 0.667586691748692 \tabularnewline
71 & 17.745 & 17.6919994694147 & 0.0530005305853116 \tabularnewline
72 & 19.394 & 17.7446823929442 & 1.64931760705578 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12999&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]10.756[/C][C]10.893[/C][C]-0.137000000000000[/C][/ROW]
[ROW][C]3[/C][C]10.94[/C][C]10.7568209760574[/C][C]0.183179023942564[/C][/ROW]
[ROW][C]4[/C][C]10.997[/C][C]10.9389022949425[/C][C]0.0580977050575271[/C][/ROW]
[ROW][C]5[/C][C]10.827[/C][C]10.9966518479938[/C][C]-0.169651847993839[/C][/ROW]
[ROW][C]6[/C][C]10.166[/C][C]10.8280166431044[/C][C]-0.662016643104398[/C][/ROW]
[ROW][C]7[/C][C]10.186[/C][C]10.1699671519242[/C][C]0.0160328480758238[/C][/ROW]
[ROW][C]8[/C][C]10.457[/C][C]10.1859039227416[/C][C]0.271096077258415[/C][/ROW]
[ROW][C]9[/C][C]10.368[/C][C]10.4553754497176[/C][C]-0.0873754497175643[/C][/ROW]
[ROW][C]10[/C][C]10.244[/C][C]10.3685235996513[/C][C]-0.124523599651283[/C][/ROW]
[ROW][C]11[/C][C]10.511[/C][C]10.2447462109044[/C][C]0.266253789095625[/C][/ROW]
[ROW][C]12[/C][C]10.812[/C][C]10.5094044672551[/C][C]0.302595532744881[/C][/ROW]
[ROW][C]13[/C][C]10.738[/C][C]10.8101866884126[/C][C]-0.072186688412625[/C][/ROW]
[ROW][C]14[/C][C]10.171[/C][C]10.7384325806048[/C][C]-0.567432580604761[/C][/ROW]
[ROW][C]15[/C][C]9.721[/C][C]10.1744003544736[/C][C]-0.453400354473612[/C][/ROW]
[ROW][C]16[/C][C]9.897[/C][C]9.72371701339748[/C][C]0.173282986602516[/C][/ROW]
[ROW][C]17[/C][C]9.828[/C][C]9.8959615972032[/C][C]-0.067961597203201[/C][/ROW]
[ROW][C]18[/C][C]9.924[/C][C]9.82840726163598[/C][C]0.0955927383640223[/C][/ROW]
[ROW][C]19[/C][C]10.371[/C][C]9.92342715803313[/C][C]0.447572841966872[/C][/ROW]
[ROW][C]20[/C][C]10.846[/C][C]10.3683179081225[/C][C]0.477682091877465[/C][/ROW]
[ROW][C]21[/C][C]10.413[/C][C]10.8431374776606[/C][C]-0.430137477660606[/C][/ROW]
[ROW][C]22[/C][C]10.709[/C][C]10.4155776100041[/C][C]0.293422389995877[/C][/ROW]
[ROW][C]23[/C][C]10.662[/C][C]10.7072416587087[/C][C]-0.0452416587087434[/C][/ROW]
[ROW][C]24[/C][C]10.57[/C][C]10.6622711118146[/C][C]-0.092271111814588[/C][/ROW]
[ROW][C]25[/C][C]10.297[/C][C]10.5705529370335[/C][C]-0.273552937033523[/C][/ROW]
[ROW][C]26[/C][C]10.635[/C][C]10.2986392730784[/C][C]0.336360726921566[/C][/ROW]
[ROW][C]27[/C][C]10.872[/C][C]10.6329843496098[/C][C]0.239015650390249[/C][/ROW]
[ROW][C]28[/C][C]10.296[/C][C]10.8705676925086[/C][C]-0.574567692508595[/C][/ROW]
[ROW][C]29[/C][C]10.383[/C][C]10.2994431118170[/C][C]0.0835568881830273[/C][/ROW]
[ROW][C]30[/C][C]10.431[/C][C]10.3824992831779[/C][C]0.0485007168221312[/C][/ROW]
[ROW][C]31[/C][C]10.574[/C][C]10.4307093581950[/C][C]0.143290641804960[/C][/ROW]
[ROW][C]32[/C][C]10.653[/C][C]10.5731413271082[/C][C]0.079858672891799[/C][/ROW]
[ROW][C]33[/C][C]10.805[/C][C]10.6525214448290[/C][C]0.152478555170967[/C][/ROW]
[ROW][C]34[/C][C]10.872[/C][C]10.8040862682988[/C][C]0.067913731701223[/C][/ROW]
[ROW][C]35[/C][C]10.625[/C][C]10.8715930251993[/C][C]-0.246593025199287[/C][/ROW]
[ROW][C]36[/C][C]10.407[/C][C]10.6264777151067[/C][C]-0.219477715106708[/C][/ROW]
[ROW][C]37[/C][C]10.463[/C][C]10.4083152259069[/C][C]0.0546847740931149[/C][/ROW]
[ROW][C]38[/C][C]10.556[/C][C]10.4626723000713[/C][C]0.093327699928734[/C][/ROW]
[ROW][C]39[/C][C]10.646[/C][C]10.5554407313348[/C][C]0.0905592686652348[/C][/ROW]
[ROW][C]40[/C][C]10.702[/C][C]10.645457321231[/C][C]0.0565426787689987[/C][/ROW]
[ROW][C]41[/C][C]11.353[/C][C]10.7016611665293[/C][C]0.651338833470749[/C][/ROW]
[ROW][C]42[/C][C]11.346[/C][C]11.3490968351273[/C][C]-0.00309683512732128[/C][/ROW]
[ROW][C]43[/C][C]11.451[/C][C]11.3460185578649[/C][C]0.104981442135086[/C][/ROW]
[ROW][C]44[/C][C]11.964[/C][C]11.4503708959820[/C][C]0.513629104018014[/C][/ROW]
[ROW][C]45[/C][C]12.574[/C][C]11.9609220642569[/C][C]0.613077935743069[/C][/ROW]
[ROW][C]46[/C][C]13.031[/C][C]12.5703261145505[/C][C]0.460673885449538[/C][/ROW]
[ROW][C]47[/C][C]13.812[/C][C]13.0282393997793[/C][C]0.783760600220726[/C][/ROW]
[ROW][C]48[/C][C]14.544[/C][C]13.8073032942515[/C][C]0.736696705748482[/C][/ROW]
[ROW][C]49[/C][C]14.931[/C][C]14.5395853258612[/C][C]0.391414674138762[/C][/ROW]
[ROW][C]50[/C][C]14.886[/C][C]14.9286544374015[/C][C]-0.0426544374014846[/C][/ROW]
[ROW][C]51[/C][C]16.005[/C][C]14.8862556078237[/C][C]1.11874439217628[/C][/ROW]
[ROW][C]52[/C][C]17.064[/C][C]15.9982958951798[/C][C]1.06570410482019[/C][/ROW]
[ROW][C]53[/C][C]15.168[/C][C]17.0576137404791[/C][C]-1.88961374047907[/C][/ROW]
[ROW][C]54[/C][C]16.05[/C][C]15.1793235594068[/C][C]0.87067644059319[/C][/ROW]
[ROW][C]55[/C][C]15.839[/C][C]16.0447824488212[/C][C]-0.205782448821170[/C][/ROW]
[ROW][C]56[/C][C]15.137[/C][C]15.8402331566680[/C][C]-0.703233156668047[/C][/ROW]
[ROW][C]57[/C][C]14.954[/C][C]15.1412141429520[/C][C]-0.187214142951962[/C][/ROW]
[ROW][C]58[/C][C]15.648[/C][C]14.9551218856130[/C][C]0.69287811438703[/C][/ROW]
[ROW][C]59[/C][C]15.305[/C][C]15.6438479099078[/C][C]-0.338847909907793[/C][/ROW]
[ROW][C]60[/C][C]15.579[/C][C]15.3070305548989[/C][C]0.271969445101124[/C][/ROW]
[ROW][C]61[/C][C]16.348[/C][C]15.5773702160381[/C][C]0.77062978396191[/C][/ROW]
[ROW][C]62[/C][C]15.928[/C][C]16.3433819810089[/C][C]-0.41538198100891[/C][/ROW]
[ROW][C]63[/C][C]16.171[/C][C]15.9304891873073[/C][C]0.240510812692712[/C][/ROW]
[ROW][C]64[/C][C]15.937[/C][C]16.1695587327097[/C][C]-0.232558732709672[/C][/ROW]
[ROW][C]65[/C][C]15.713[/C][C]15.9383936142445[/C][C]-0.22539361424454[/C][/ROW]
[ROW][C]66[/C][C]15.594[/C][C]15.7143506770861[/C][C]-0.120350677086083[/C][/ROW]
[ROW][C]67[/C][C]15.683[/C][C]15.5947212045575[/C][C]0.088278795442454[/C][/ROW]
[ROW][C]68[/C][C]16.438[/C][C]15.682470987026[/C][C]0.755529012973994[/C][/ROW]
[ROW][C]69[/C][C]17.032[/C][C]16.4334724727712[/C][C]0.598527527228825[/C][/ROW]
[ROW][C]70[/C][C]17.696[/C][C]17.0284133082513[/C][C]0.667586691748692[/C][/ROW]
[ROW][C]71[/C][C]17.745[/C][C]17.6919994694147[/C][C]0.0530005305853116[/C][/ROW]
[ROW][C]72[/C][C]19.394[/C][C]17.7446823929442[/C][C]1.64931760705578[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12999&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12999&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
210.75610.893-0.137000000000000
310.9410.75682097605740.183179023942564
410.99710.93890229494250.0580977050575271
510.82710.9966518479938-0.169651847993839
610.16610.8280166431044-0.662016643104398
710.18610.16996715192420.0160328480758238
810.45710.18590392274160.271096077258415
910.36810.4553754497176-0.0873754497175643
1010.24410.3685235996513-0.124523599651283
1110.51110.24474621090440.266253789095625
1210.81210.50940446725510.302595532744881
1310.73810.8101866884126-0.072186688412625
1410.17110.7384325806048-0.567432580604761
159.72110.1744003544736-0.453400354473612
169.8979.723717013397480.173282986602516
179.8289.8959615972032-0.067961597203201
189.9249.828407261635980.0955927383640223
1910.3719.923427158033130.447572841966872
2010.84610.36831790812250.477682091877465
2110.41310.8431374776606-0.430137477660606
2210.70910.41557761000410.293422389995877
2310.66210.7072416587087-0.0452416587087434
2410.5710.6622711118146-0.092271111814588
2510.29710.5705529370335-0.273552937033523
2610.63510.29863927307840.336360726921566
2710.87210.63298434960980.239015650390249
2810.29610.8705676925086-0.574567692508595
2910.38310.29944311181700.0835568881830273
3010.43110.38249928317790.0485007168221312
3110.57410.43070935819500.143290641804960
3210.65310.57314132710820.079858672891799
3310.80510.65252144482900.152478555170967
3410.87210.80408626829880.067913731701223
3510.62510.8715930251993-0.246593025199287
3610.40710.6264777151067-0.219477715106708
3710.46310.40831522590690.0546847740931149
3810.55610.46267230007130.093327699928734
3910.64610.55544073133480.0905592686652348
4010.70210.6454573212310.0565426787689987
4111.35310.70166116652930.651338833470749
4211.34611.3490968351273-0.00309683512732128
4311.45111.34601855786490.104981442135086
4411.96411.45037089598200.513629104018014
4512.57411.96092206425690.613077935743069
4613.03112.57032611455050.460673885449538
4713.81213.02823939977930.783760600220726
4814.54413.80730329425150.736696705748482
4914.93114.53958532586120.391414674138762
5014.88614.9286544374015-0.0426544374014846
5116.00514.88625560782371.11874439217628
5217.06415.99829589517981.06570410482019
5315.16817.0576137404791-1.88961374047907
5416.0515.17932355940680.87067644059319
5515.83916.0447824488212-0.205782448821170
5615.13715.8402331566680-0.703233156668047
5714.95415.1412141429520-0.187214142951962
5815.64814.95512188561300.69287811438703
5915.30515.6438479099078-0.338847909907793
6015.57915.30703055489890.271969445101124
6116.34815.57737021603810.77062978396191
6215.92816.3433819810089-0.41538198100891
6316.17115.93048918730730.240510812692712
6415.93716.1695587327097-0.232558732709672
6515.71315.9383936142445-0.22539361424454
6615.59415.7143506770861-0.120350677086083
6715.68315.59472120455750.088278795442454
6816.43815.6824709870260.755529012973994
6917.03216.43347247277120.598527527228825
7017.69617.02841330825130.667586691748692
7117.74517.69199946941470.0530005305853116
7219.39417.74468239294421.64931760705578







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7319.384116421412418.406441369244920.3617914735800
7419.384116421412418.005611635012220.7626212078127
7519.384116421412417.697491867865921.0707409749589
7619.384116421412417.437547819198921.3306850236260
7719.384116421412417.208442672519621.5597901703052
7819.384116421412417.001264516631321.7669683261935
7919.384116421412416.810712034493021.9575208083319
8019.384116421412416.633327974964022.1349048678608
8119.384116421412416.466709350808222.3015234920166
8219.384116421412416.309105697185722.4591271456391
8319.384116421412416.159195043672122.6090377991528
8419.384116421412416.015950031356222.7522828114686

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 19.3841164214124 & 18.4064413692449 & 20.3617914735800 \tabularnewline
74 & 19.3841164214124 & 18.0056116350122 & 20.7626212078127 \tabularnewline
75 & 19.3841164214124 & 17.6974918678659 & 21.0707409749589 \tabularnewline
76 & 19.3841164214124 & 17.4375478191989 & 21.3306850236260 \tabularnewline
77 & 19.3841164214124 & 17.2084426725196 & 21.5597901703052 \tabularnewline
78 & 19.3841164214124 & 17.0012645166313 & 21.7669683261935 \tabularnewline
79 & 19.3841164214124 & 16.8107120344930 & 21.9575208083319 \tabularnewline
80 & 19.3841164214124 & 16.6333279749640 & 22.1349048678608 \tabularnewline
81 & 19.3841164214124 & 16.4667093508082 & 22.3015234920166 \tabularnewline
82 & 19.3841164214124 & 16.3091056971857 & 22.4591271456391 \tabularnewline
83 & 19.3841164214124 & 16.1591950436721 & 22.6090377991528 \tabularnewline
84 & 19.3841164214124 & 16.0159500313562 & 22.7522828114686 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12999&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]19.3841164214124[/C][C]18.4064413692449[/C][C]20.3617914735800[/C][/ROW]
[ROW][C]74[/C][C]19.3841164214124[/C][C]18.0056116350122[/C][C]20.7626212078127[/C][/ROW]
[ROW][C]75[/C][C]19.3841164214124[/C][C]17.6974918678659[/C][C]21.0707409749589[/C][/ROW]
[ROW][C]76[/C][C]19.3841164214124[/C][C]17.4375478191989[/C][C]21.3306850236260[/C][/ROW]
[ROW][C]77[/C][C]19.3841164214124[/C][C]17.2084426725196[/C][C]21.5597901703052[/C][/ROW]
[ROW][C]78[/C][C]19.3841164214124[/C][C]17.0012645166313[/C][C]21.7669683261935[/C][/ROW]
[ROW][C]79[/C][C]19.3841164214124[/C][C]16.8107120344930[/C][C]21.9575208083319[/C][/ROW]
[ROW][C]80[/C][C]19.3841164214124[/C][C]16.6333279749640[/C][C]22.1349048678608[/C][/ROW]
[ROW][C]81[/C][C]19.3841164214124[/C][C]16.4667093508082[/C][C]22.3015234920166[/C][/ROW]
[ROW][C]82[/C][C]19.3841164214124[/C][C]16.3091056971857[/C][C]22.4591271456391[/C][/ROW]
[ROW][C]83[/C][C]19.3841164214124[/C][C]16.1591950436721[/C][C]22.6090377991528[/C][/ROW]
[ROW][C]84[/C][C]19.3841164214124[/C][C]16.0159500313562[/C][C]22.7522828114686[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12999&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12999&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
7319.384116421412418.406441369244920.3617914735800
7419.384116421412418.005611635012220.7626212078127
7519.384116421412417.697491867865921.0707409749589
7619.384116421412417.437547819198921.3306850236260
7719.384116421412417.208442672519621.5597901703052
7819.384116421412417.001264516631321.7669683261935
7919.384116421412416.810712034493021.9575208083319
8019.384116421412416.633327974964022.1349048678608
8119.384116421412416.466709350808222.3015234920166
8219.384116421412416.309105697185722.4591271456391
8319.384116421412416.159195043672122.6090377991528
8419.384116421412416.015950031356222.7522828114686



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')