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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Nov 2014 17:34:19 +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/28/t141719610104b7xf73veldsj6.htm/, Retrieved Fri, 17 May 2024 03:20:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260996, Retrieved Fri, 17 May 2024 03:20:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-28 17:34:19] [0c3693ead1e3fa463b40b3108c1b2028] [Current]
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Dataseries X:
11236
10954
9580
10337
8961
10372
12782
15119
19940
13957
10849
9429
11816
11329
11334
9898
8961
10783
13149
16244
20067
13601
10573
8623
10962
11911
11677
9679
9116
11394
13240
18983
21545
14360
11839
9726
12347
12624
11918
10028
10228
11026
13878
22165
23533
13445
12164
9606
12177
13142
11210
9485
10082
10680
13579
21709
22205
14687
11222
8196
12794
12627
11080
10425
10865
10771
14771
20993
23882
14825
11648
10091




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260996&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260996&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260996&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0996673664868306
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0996673664868306 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260996&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]0.0996673664868306[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260996&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260996&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
alpha0.0996673664868306
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131181611647.5021504568168.49784954317
141132911150.8419751737178.158024826254
151133411150.0957864087183.904213591266
1698989781.86262090118116.137379098822
1789618904.3119262803856.6880737196243
181078310783.9982322339-0.998232233949238
191314913075.218830144173.7811698559217
201624415455.9745480349788.025451965081
212006720380.7179989138-313.71799891378
221360114209.24584152-608.245841520044
231057311037.704803605-464.704803605042
2486239559.43503731193-936.435037311931
251096212010.3294390765-1048.32943907649
261191111396.8085911138514.191408886169
271167711434.057799902242.94220009803
2896799994.46772913151-315.467729131511
2991169014.02527282957101.974727170431
301139410858.9754686318535.024531368153
311324013298.857470784-58.8574707840198
321898316338.48303112442644.5169688756
332154520539.90647097371005.09352902629
341436014048.5450693865311.454930613534
351183910990.3743388732848.625661126847
3697269120.56322158621605.436778413794
371234711772.1452559283574.854744071736
381262412793.9911919304-169.991191930381
391191812497.7668793169-579.766879316909
401002810342.6331818405-314.63318184052
41102289699.30109462831528.698905371693
421102612127.6934538618-1101.69345386177
431387813969.6144598164-91.6144598163773
442216519696.10505284942468.89494715058
452353322521.55166205851011.44833794153
461344515043.3693642109-1598.36936421092
471216412176.4754773064-12.475477306376
4896069935.92992433702-329.929924337021
491217712510.4224845696-333.422484569561
501314212773.764194466368.235805533974
511121012149.8641979198-939.864197919826
52948510174.8950982613-689.89509826131
531008210251.839319525-169.839319525045
541068011134.2447707563-454.244770756282
551357913966.231070646-387.231070646039
562170921969.647136522-260.647136521999
572220523194.6468282407-989.64682824073
581468713337.05795887981349.94204112023
591122212189.2660203843-967.266020384266
6081969581.64169283076-1385.64169283076
611279412003.3439470953790.656052904684
621262713002.4719766676-375.471976667626
631108011145.2859755309-65.2859755308946
64104259488.98152400809936.018475991912
651086510202.0359391949662.964060805129
661077110921.1694276935-150.169427693494
671477113904.4591563393866.540843660696
682099322392.5697396158-1399.56973961578
692388222857.61297229821024.3870277018
701482515033.5396407359-208.539640735891
711164811561.858085331686.1419146684311
72100918573.559163396311517.44083660369

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 11816 & 11647.5021504568 & 168.49784954317 \tabularnewline
14 & 11329 & 11150.8419751737 & 178.158024826254 \tabularnewline
15 & 11334 & 11150.0957864087 & 183.904213591266 \tabularnewline
16 & 9898 & 9781.86262090118 & 116.137379098822 \tabularnewline
17 & 8961 & 8904.31192628038 & 56.6880737196243 \tabularnewline
18 & 10783 & 10783.9982322339 & -0.998232233949238 \tabularnewline
19 & 13149 & 13075.2188301441 & 73.7811698559217 \tabularnewline
20 & 16244 & 15455.9745480349 & 788.025451965081 \tabularnewline
21 & 20067 & 20380.7179989138 & -313.71799891378 \tabularnewline
22 & 13601 & 14209.24584152 & -608.245841520044 \tabularnewline
23 & 10573 & 11037.704803605 & -464.704803605042 \tabularnewline
24 & 8623 & 9559.43503731193 & -936.435037311931 \tabularnewline
25 & 10962 & 12010.3294390765 & -1048.32943907649 \tabularnewline
26 & 11911 & 11396.8085911138 & 514.191408886169 \tabularnewline
27 & 11677 & 11434.057799902 & 242.94220009803 \tabularnewline
28 & 9679 & 9994.46772913151 & -315.467729131511 \tabularnewline
29 & 9116 & 9014.02527282957 & 101.974727170431 \tabularnewline
30 & 11394 & 10858.9754686318 & 535.024531368153 \tabularnewline
31 & 13240 & 13298.857470784 & -58.8574707840198 \tabularnewline
32 & 18983 & 16338.4830311244 & 2644.5169688756 \tabularnewline
33 & 21545 & 20539.9064709737 & 1005.09352902629 \tabularnewline
34 & 14360 & 14048.5450693865 & 311.454930613534 \tabularnewline
35 & 11839 & 10990.3743388732 & 848.625661126847 \tabularnewline
36 & 9726 & 9120.56322158621 & 605.436778413794 \tabularnewline
37 & 12347 & 11772.1452559283 & 574.854744071736 \tabularnewline
38 & 12624 & 12793.9911919304 & -169.991191930381 \tabularnewline
39 & 11918 & 12497.7668793169 & -579.766879316909 \tabularnewline
40 & 10028 & 10342.6331818405 & -314.63318184052 \tabularnewline
41 & 10228 & 9699.30109462831 & 528.698905371693 \tabularnewline
42 & 11026 & 12127.6934538618 & -1101.69345386177 \tabularnewline
43 & 13878 & 13969.6144598164 & -91.6144598163773 \tabularnewline
44 & 22165 & 19696.1050528494 & 2468.89494715058 \tabularnewline
45 & 23533 & 22521.5516620585 & 1011.44833794153 \tabularnewline
46 & 13445 & 15043.3693642109 & -1598.36936421092 \tabularnewline
47 & 12164 & 12176.4754773064 & -12.475477306376 \tabularnewline
48 & 9606 & 9935.92992433702 & -329.929924337021 \tabularnewline
49 & 12177 & 12510.4224845696 & -333.422484569561 \tabularnewline
50 & 13142 & 12773.764194466 & 368.235805533974 \tabularnewline
51 & 11210 & 12149.8641979198 & -939.864197919826 \tabularnewline
52 & 9485 & 10174.8950982613 & -689.89509826131 \tabularnewline
53 & 10082 & 10251.839319525 & -169.839319525045 \tabularnewline
54 & 10680 & 11134.2447707563 & -454.244770756282 \tabularnewline
55 & 13579 & 13966.231070646 & -387.231070646039 \tabularnewline
56 & 21709 & 21969.647136522 & -260.647136521999 \tabularnewline
57 & 22205 & 23194.6468282407 & -989.64682824073 \tabularnewline
58 & 14687 & 13337.0579588798 & 1349.94204112023 \tabularnewline
59 & 11222 & 12189.2660203843 & -967.266020384266 \tabularnewline
60 & 8196 & 9581.64169283076 & -1385.64169283076 \tabularnewline
61 & 12794 & 12003.3439470953 & 790.656052904684 \tabularnewline
62 & 12627 & 13002.4719766676 & -375.471976667626 \tabularnewline
63 & 11080 & 11145.2859755309 & -65.2859755308946 \tabularnewline
64 & 10425 & 9488.98152400809 & 936.018475991912 \tabularnewline
65 & 10865 & 10202.0359391949 & 662.964060805129 \tabularnewline
66 & 10771 & 10921.1694276935 & -150.169427693494 \tabularnewline
67 & 14771 & 13904.4591563393 & 866.540843660696 \tabularnewline
68 & 20993 & 22392.5697396158 & -1399.56973961578 \tabularnewline
69 & 23882 & 22857.6129722982 & 1024.3870277018 \tabularnewline
70 & 14825 & 15033.5396407359 & -208.539640735891 \tabularnewline
71 & 11648 & 11561.8580853316 & 86.1419146684311 \tabularnewline
72 & 10091 & 8573.55916339631 & 1517.44083660369 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260996&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]11816[/C][C]11647.5021504568[/C][C]168.49784954317[/C][/ROW]
[ROW][C]14[/C][C]11329[/C][C]11150.8419751737[/C][C]178.158024826254[/C][/ROW]
[ROW][C]15[/C][C]11334[/C][C]11150.0957864087[/C][C]183.904213591266[/C][/ROW]
[ROW][C]16[/C][C]9898[/C][C]9781.86262090118[/C][C]116.137379098822[/C][/ROW]
[ROW][C]17[/C][C]8961[/C][C]8904.31192628038[/C][C]56.6880737196243[/C][/ROW]
[ROW][C]18[/C][C]10783[/C][C]10783.9982322339[/C][C]-0.998232233949238[/C][/ROW]
[ROW][C]19[/C][C]13149[/C][C]13075.2188301441[/C][C]73.7811698559217[/C][/ROW]
[ROW][C]20[/C][C]16244[/C][C]15455.9745480349[/C][C]788.025451965081[/C][/ROW]
[ROW][C]21[/C][C]20067[/C][C]20380.7179989138[/C][C]-313.71799891378[/C][/ROW]
[ROW][C]22[/C][C]13601[/C][C]14209.24584152[/C][C]-608.245841520044[/C][/ROW]
[ROW][C]23[/C][C]10573[/C][C]11037.704803605[/C][C]-464.704803605042[/C][/ROW]
[ROW][C]24[/C][C]8623[/C][C]9559.43503731193[/C][C]-936.435037311931[/C][/ROW]
[ROW][C]25[/C][C]10962[/C][C]12010.3294390765[/C][C]-1048.32943907649[/C][/ROW]
[ROW][C]26[/C][C]11911[/C][C]11396.8085911138[/C][C]514.191408886169[/C][/ROW]
[ROW][C]27[/C][C]11677[/C][C]11434.057799902[/C][C]242.94220009803[/C][/ROW]
[ROW][C]28[/C][C]9679[/C][C]9994.46772913151[/C][C]-315.467729131511[/C][/ROW]
[ROW][C]29[/C][C]9116[/C][C]9014.02527282957[/C][C]101.974727170431[/C][/ROW]
[ROW][C]30[/C][C]11394[/C][C]10858.9754686318[/C][C]535.024531368153[/C][/ROW]
[ROW][C]31[/C][C]13240[/C][C]13298.857470784[/C][C]-58.8574707840198[/C][/ROW]
[ROW][C]32[/C][C]18983[/C][C]16338.4830311244[/C][C]2644.5169688756[/C][/ROW]
[ROW][C]33[/C][C]21545[/C][C]20539.9064709737[/C][C]1005.09352902629[/C][/ROW]
[ROW][C]34[/C][C]14360[/C][C]14048.5450693865[/C][C]311.454930613534[/C][/ROW]
[ROW][C]35[/C][C]11839[/C][C]10990.3743388732[/C][C]848.625661126847[/C][/ROW]
[ROW][C]36[/C][C]9726[/C][C]9120.56322158621[/C][C]605.436778413794[/C][/ROW]
[ROW][C]37[/C][C]12347[/C][C]11772.1452559283[/C][C]574.854744071736[/C][/ROW]
[ROW][C]38[/C][C]12624[/C][C]12793.9911919304[/C][C]-169.991191930381[/C][/ROW]
[ROW][C]39[/C][C]11918[/C][C]12497.7668793169[/C][C]-579.766879316909[/C][/ROW]
[ROW][C]40[/C][C]10028[/C][C]10342.6331818405[/C][C]-314.63318184052[/C][/ROW]
[ROW][C]41[/C][C]10228[/C][C]9699.30109462831[/C][C]528.698905371693[/C][/ROW]
[ROW][C]42[/C][C]11026[/C][C]12127.6934538618[/C][C]-1101.69345386177[/C][/ROW]
[ROW][C]43[/C][C]13878[/C][C]13969.6144598164[/C][C]-91.6144598163773[/C][/ROW]
[ROW][C]44[/C][C]22165[/C][C]19696.1050528494[/C][C]2468.89494715058[/C][/ROW]
[ROW][C]45[/C][C]23533[/C][C]22521.5516620585[/C][C]1011.44833794153[/C][/ROW]
[ROW][C]46[/C][C]13445[/C][C]15043.3693642109[/C][C]-1598.36936421092[/C][/ROW]
[ROW][C]47[/C][C]12164[/C][C]12176.4754773064[/C][C]-12.475477306376[/C][/ROW]
[ROW][C]48[/C][C]9606[/C][C]9935.92992433702[/C][C]-329.929924337021[/C][/ROW]
[ROW][C]49[/C][C]12177[/C][C]12510.4224845696[/C][C]-333.422484569561[/C][/ROW]
[ROW][C]50[/C][C]13142[/C][C]12773.764194466[/C][C]368.235805533974[/C][/ROW]
[ROW][C]51[/C][C]11210[/C][C]12149.8641979198[/C][C]-939.864197919826[/C][/ROW]
[ROW][C]52[/C][C]9485[/C][C]10174.8950982613[/C][C]-689.89509826131[/C][/ROW]
[ROW][C]53[/C][C]10082[/C][C]10251.839319525[/C][C]-169.839319525045[/C][/ROW]
[ROW][C]54[/C][C]10680[/C][C]11134.2447707563[/C][C]-454.244770756282[/C][/ROW]
[ROW][C]55[/C][C]13579[/C][C]13966.231070646[/C][C]-387.231070646039[/C][/ROW]
[ROW][C]56[/C][C]21709[/C][C]21969.647136522[/C][C]-260.647136521999[/C][/ROW]
[ROW][C]57[/C][C]22205[/C][C]23194.6468282407[/C][C]-989.64682824073[/C][/ROW]
[ROW][C]58[/C][C]14687[/C][C]13337.0579588798[/C][C]1349.94204112023[/C][/ROW]
[ROW][C]59[/C][C]11222[/C][C]12189.2660203843[/C][C]-967.266020384266[/C][/ROW]
[ROW][C]60[/C][C]8196[/C][C]9581.64169283076[/C][C]-1385.64169283076[/C][/ROW]
[ROW][C]61[/C][C]12794[/C][C]12003.3439470953[/C][C]790.656052904684[/C][/ROW]
[ROW][C]62[/C][C]12627[/C][C]13002.4719766676[/C][C]-375.471976667626[/C][/ROW]
[ROW][C]63[/C][C]11080[/C][C]11145.2859755309[/C][C]-65.2859755308946[/C][/ROW]
[ROW][C]64[/C][C]10425[/C][C]9488.98152400809[/C][C]936.018475991912[/C][/ROW]
[ROW][C]65[/C][C]10865[/C][C]10202.0359391949[/C][C]662.964060805129[/C][/ROW]
[ROW][C]66[/C][C]10771[/C][C]10921.1694276935[/C][C]-150.169427693494[/C][/ROW]
[ROW][C]67[/C][C]14771[/C][C]13904.4591563393[/C][C]866.540843660696[/C][/ROW]
[ROW][C]68[/C][C]20993[/C][C]22392.5697396158[/C][C]-1399.56973961578[/C][/ROW]
[ROW][C]69[/C][C]23882[/C][C]22857.6129722982[/C][C]1024.3870277018[/C][/ROW]
[ROW][C]70[/C][C]14825[/C][C]15033.5396407359[/C][C]-208.539640735891[/C][/ROW]
[ROW][C]71[/C][C]11648[/C][C]11561.8580853316[/C][C]86.1419146684311[/C][/ROW]
[ROW][C]72[/C][C]10091[/C][C]8573.55916339631[/C][C]1517.44083660369[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260996&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260996&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
131181611647.5021504568168.49784954317
141132911150.8419751737178.158024826254
151133411150.0957864087183.904213591266
1698989781.86262090118116.137379098822
1789618904.3119262803856.6880737196243
181078310783.9982322339-0.998232233949238
191314913075.218830144173.7811698559217
201624415455.9745480349788.025451965081
212006720380.7179989138-313.71799891378
221360114209.24584152-608.245841520044
231057311037.704803605-464.704803605042
2486239559.43503731193-936.435037311931
251096212010.3294390765-1048.32943907649
261191111396.8085911138514.191408886169
271167711434.057799902242.94220009803
2896799994.46772913151-315.467729131511
2991169014.02527282957101.974727170431
301139410858.9754686318535.024531368153
311324013298.857470784-58.8574707840198
321898316338.48303112442644.5169688756
332154520539.90647097371005.09352902629
341436014048.5450693865311.454930613534
351183910990.3743388732848.625661126847
3697269120.56322158621605.436778413794
371234711772.1452559283574.854744071736
381262412793.9911919304-169.991191930381
391191812497.7668793169-579.766879316909
401002810342.6331818405-314.63318184052
41102289699.30109462831528.698905371693
421102612127.6934538618-1101.69345386177
431387813969.6144598164-91.6144598163773
442216519696.10505284942468.89494715058
452353322521.55166205851011.44833794153
461344515043.3693642109-1598.36936421092
471216412176.4754773064-12.475477306376
4896069935.92992433702-329.929924337021
491217712510.4224845696-333.422484569561
501314212773.764194466368.235805533974
511121012149.8641979198-939.864197919826
52948510174.8950982613-689.89509826131
531008210251.839319525-169.839319525045
541068011134.2447707563-454.244770756282
551357913966.231070646-387.231070646039
562170921969.647136522-260.647136521999
572220523194.6468282407-989.64682824073
581468713337.05795887981349.94204112023
591122212189.2660203843-967.266020384266
6081969581.64169283076-1385.64169283076
611279412003.3439470953790.656052904684
621262713002.4719766676-375.471976667626
631108011145.2859755309-65.2859755308946
64104259488.98152400809936.018475991912
651086510202.0359391949662.964060805129
661077110921.1694276935-150.169427693494
671477113904.4591563393866.540843660696
682099322392.5697396158-1399.56973961578
692388222857.61297229821024.3870277018
701482515033.5396407359-208.539640735891
711164811561.858085331686.1419146684311
72100918573.559163396311517.44083660369







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7313528.994932025211893.580076255115164.4097877953
7413389.504999182111746.182815916215032.827182448
7511754.626868319310106.934942437513402.318794201
7610950.83068332599297.8310467572212603.8303198945
7711338.51853766419675.773339178713001.2637361495
7811254.93829742819584.8635593648712925.0130354914
7915338.103633395513624.706510230617051.5007565604
8021934.075003343220128.308452023523739.841554663
8124839.570762384922980.118573847926699.0229509218
8215439.630608275813711.566813862317167.6944026892
8312120.990848325910423.272125958313818.7095706935
8410317.97292732929904.2058748758810731.7399797826

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 13528.9949320252 & 11893.5800762551 & 15164.4097877953 \tabularnewline
74 & 13389.5049991821 & 11746.1828159162 & 15032.827182448 \tabularnewline
75 & 11754.6268683193 & 10106.9349424375 & 13402.318794201 \tabularnewline
76 & 10950.8306833259 & 9297.83104675722 & 12603.8303198945 \tabularnewline
77 & 11338.5185376641 & 9675.7733391787 & 13001.2637361495 \tabularnewline
78 & 11254.9382974281 & 9584.86355936487 & 12925.0130354914 \tabularnewline
79 & 15338.1036333955 & 13624.7065102306 & 17051.5007565604 \tabularnewline
80 & 21934.0750033432 & 20128.3084520235 & 23739.841554663 \tabularnewline
81 & 24839.5707623849 & 22980.1185738479 & 26699.0229509218 \tabularnewline
82 & 15439.6306082758 & 13711.5668138623 & 17167.6944026892 \tabularnewline
83 & 12120.9908483259 & 10423.2721259583 & 13818.7095706935 \tabularnewline
84 & 10317.9729273292 & 9904.20587487588 & 10731.7399797826 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260996&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]13528.9949320252[/C][C]11893.5800762551[/C][C]15164.4097877953[/C][/ROW]
[ROW][C]74[/C][C]13389.5049991821[/C][C]11746.1828159162[/C][C]15032.827182448[/C][/ROW]
[ROW][C]75[/C][C]11754.6268683193[/C][C]10106.9349424375[/C][C]13402.318794201[/C][/ROW]
[ROW][C]76[/C][C]10950.8306833259[/C][C]9297.83104675722[/C][C]12603.8303198945[/C][/ROW]
[ROW][C]77[/C][C]11338.5185376641[/C][C]9675.7733391787[/C][C]13001.2637361495[/C][/ROW]
[ROW][C]78[/C][C]11254.9382974281[/C][C]9584.86355936487[/C][C]12925.0130354914[/C][/ROW]
[ROW][C]79[/C][C]15338.1036333955[/C][C]13624.7065102306[/C][C]17051.5007565604[/C][/ROW]
[ROW][C]80[/C][C]21934.0750033432[/C][C]20128.3084520235[/C][C]23739.841554663[/C][/ROW]
[ROW][C]81[/C][C]24839.5707623849[/C][C]22980.1185738479[/C][C]26699.0229509218[/C][/ROW]
[ROW][C]82[/C][C]15439.6306082758[/C][C]13711.5668138623[/C][C]17167.6944026892[/C][/ROW]
[ROW][C]83[/C][C]12120.9908483259[/C][C]10423.2721259583[/C][C]13818.7095706935[/C][/ROW]
[ROW][C]84[/C][C]10317.9729273292[/C][C]9904.20587487588[/C][C]10731.7399797826[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260996&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260996&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
7313528.994932025211893.580076255115164.4097877953
7413389.504999182111746.182815916215032.827182448
7511754.626868319310106.934942437513402.318794201
7610950.83068332599297.8310467572212603.8303198945
7711338.51853766419675.773339178713001.2637361495
7811254.93829742819584.8635593648712925.0130354914
7915338.103633395513624.706510230617051.5007565604
8021934.075003343220128.308452023523739.841554663
8124839.570762384922980.118573847926699.0229509218
8215439.630608275813711.566813862317167.6944026892
8312120.990848325910423.272125958313818.7095706935
8410317.97292732929904.2058748758810731.7399797826



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')