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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 computationWed, 28 Dec 2011 14:53:27 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/28/t1325102053ijtcr5e2yos14f1.htm/, Retrieved Fri, 03 May 2024 10:34:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160890, Retrieved Fri, 03 May 2024 10:34:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2011-12-28 19:53:27] [a9bbc2bac156539e6f87d9483eb06b77] [Current]
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Dataseries X:
43
30
42
23
19
19
36
20
27
24
23
26
31
51
39
32
30
46
31
31
40
29
43
17
53
47
49
44
48
51
47
44
33
47
41
36
46
24
17
22
30
24
18
24
24
28
19
22
26
14
16
21
15
23
29
17
24
18
22
8
26
22
34
25
20
35
38
24
14
25
31
17
32
27
30
19
36
27
28
38
26
25
30
27




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160890&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160890&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160890&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.348486060194574
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.348486060194574 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160890&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]0.348486060194574[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160890&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160890&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
alpha0.348486060194574
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23043-13
34238.46968121747053.53031878252946
42339.6999481012251-16.6999481012251
51933.8802489819753-14.8802489819753
61928.6946896395324-9.69468963953242
73625.316225442242610.6837745577574
82029.0393719458825-9.03937194588251
92725.88927682982861.11072317017145
102426.2763483713684-2.27634837136843
112325.4830726957999-2.48307269579991
122624.61775647486391.38224352513612
133125.0994490751685.90055092483198
145127.155708819940223.8442911800598
153935.46511191141153.53488808858854
163236.6969711346324-4.69697113463241
173035.0601421690767-5.06014216907672
184633.296753160550712.7032468394493
193137.7236576033096-6.72365760330959
203135.3805566550349-4.38055665503494
214033.85399372486276.14600627513731
222935.9957912376164-6.99579123761642
234333.55785551127589.44214448872425
241736.8483112439392-19.8483112439392
255329.931451457023123.0685485429769
264737.97051905317249.02948094682756
274941.11716729393447.88283270606565
284443.86422460684410.135775393155896
294843.91154043867644.08845956132363
305145.33631160346695.66368839653313
314747.3100280589444-0.310028058944432
324447.2019876021331-3.20198760213312
333346.0861395578739-13.0861395578739
344741.5258023401945.47419765980596
354143.4334839153862-2.43348391538618
363642.5854486931664-6.58544869316638
374640.29051162347135.70948837652868
382442.2801887335345-18.2801887335345
391735.9097977821718-18.9097977821718
402229.3199968539867-7.31999685398667
413026.76907998970423.23092001029582
422427.895010574896-3.89501057489598
431826.5376536852343-8.53765368523428
442423.56240038916130.437599610838706
452423.71489775348520.285102246514846
462823.81425191212574.18574808787427
471925.272926772236-6.27292677223601
482223.0868992354904-1.08689923549041
492622.70813000308593.29186999691414
501423.8553008089832-9.85530080898319
511620.4208658580282-4.42086585802824
522118.88025573251532.11974426748473
531519.6189570609111-4.61895706091106
542318.00931491254634.99068508745374
552919.74849909634489.25150090365517
561722.9725181971462-5.97251819714616
572420.89117886118233.10882113881771
581821.9745596916985-3.97455969169848
592220.58948104373031.41051895626968
60821.0810272376305-13.0810272376305
612616.52247159229079.47752840770927
622219.82525812747552.17474187252451
633420.583125354571713.4168746454283
642525.2587191398815-0.258719139881503
652025.1685591261273-5.16855912612727
663523.367388319380511.6326116806195
673827.42119133373310.578808666267
682431.1077586873926-7.10775868739258
691428.6308038656094-14.6308038656094
702523.53217266900361.46782733099638
713124.04369003262856.95630996737153
721726.46786708665-9.46786708665002
733223.16844738717758.83155261282253
742726.24612036262110.753879637378905
753026.50883690731223.49116309268782
761927.7254585789797-8.72545857897967
773624.684757895400111.3152421045999
782728.6279620365799-1.62796203657988
792828.0606399603058-0.0606399603058208
803828.03950777944859.96049222055151
812631.5106004709872-5.51060047098719
822529.5902330235465-4.5902330235465
833027.99060080179582.00939919820425
842728.6908484117361-1.69084841173608

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 30 & 43 & -13 \tabularnewline
3 & 42 & 38.4696812174705 & 3.53031878252946 \tabularnewline
4 & 23 & 39.6999481012251 & -16.6999481012251 \tabularnewline
5 & 19 & 33.8802489819753 & -14.8802489819753 \tabularnewline
6 & 19 & 28.6946896395324 & -9.69468963953242 \tabularnewline
7 & 36 & 25.3162254422426 & 10.6837745577574 \tabularnewline
8 & 20 & 29.0393719458825 & -9.03937194588251 \tabularnewline
9 & 27 & 25.8892768298286 & 1.11072317017145 \tabularnewline
10 & 24 & 26.2763483713684 & -2.27634837136843 \tabularnewline
11 & 23 & 25.4830726957999 & -2.48307269579991 \tabularnewline
12 & 26 & 24.6177564748639 & 1.38224352513612 \tabularnewline
13 & 31 & 25.099449075168 & 5.90055092483198 \tabularnewline
14 & 51 & 27.1557088199402 & 23.8442911800598 \tabularnewline
15 & 39 & 35.4651119114115 & 3.53488808858854 \tabularnewline
16 & 32 & 36.6969711346324 & -4.69697113463241 \tabularnewline
17 & 30 & 35.0601421690767 & -5.06014216907672 \tabularnewline
18 & 46 & 33.2967531605507 & 12.7032468394493 \tabularnewline
19 & 31 & 37.7236576033096 & -6.72365760330959 \tabularnewline
20 & 31 & 35.3805566550349 & -4.38055665503494 \tabularnewline
21 & 40 & 33.8539937248627 & 6.14600627513731 \tabularnewline
22 & 29 & 35.9957912376164 & -6.99579123761642 \tabularnewline
23 & 43 & 33.5578555112758 & 9.44214448872425 \tabularnewline
24 & 17 & 36.8483112439392 & -19.8483112439392 \tabularnewline
25 & 53 & 29.9314514570231 & 23.0685485429769 \tabularnewline
26 & 47 & 37.9705190531724 & 9.02948094682756 \tabularnewline
27 & 49 & 41.1171672939344 & 7.88283270606565 \tabularnewline
28 & 44 & 43.8642246068441 & 0.135775393155896 \tabularnewline
29 & 48 & 43.9115404386764 & 4.08845956132363 \tabularnewline
30 & 51 & 45.3363116034669 & 5.66368839653313 \tabularnewline
31 & 47 & 47.3100280589444 & -0.310028058944432 \tabularnewline
32 & 44 & 47.2019876021331 & -3.20198760213312 \tabularnewline
33 & 33 & 46.0861395578739 & -13.0861395578739 \tabularnewline
34 & 47 & 41.525802340194 & 5.47419765980596 \tabularnewline
35 & 41 & 43.4334839153862 & -2.43348391538618 \tabularnewline
36 & 36 & 42.5854486931664 & -6.58544869316638 \tabularnewline
37 & 46 & 40.2905116234713 & 5.70948837652868 \tabularnewline
38 & 24 & 42.2801887335345 & -18.2801887335345 \tabularnewline
39 & 17 & 35.9097977821718 & -18.9097977821718 \tabularnewline
40 & 22 & 29.3199968539867 & -7.31999685398667 \tabularnewline
41 & 30 & 26.7690799897042 & 3.23092001029582 \tabularnewline
42 & 24 & 27.895010574896 & -3.89501057489598 \tabularnewline
43 & 18 & 26.5376536852343 & -8.53765368523428 \tabularnewline
44 & 24 & 23.5624003891613 & 0.437599610838706 \tabularnewline
45 & 24 & 23.7148977534852 & 0.285102246514846 \tabularnewline
46 & 28 & 23.8142519121257 & 4.18574808787427 \tabularnewline
47 & 19 & 25.272926772236 & -6.27292677223601 \tabularnewline
48 & 22 & 23.0868992354904 & -1.08689923549041 \tabularnewline
49 & 26 & 22.7081300030859 & 3.29186999691414 \tabularnewline
50 & 14 & 23.8553008089832 & -9.85530080898319 \tabularnewline
51 & 16 & 20.4208658580282 & -4.42086585802824 \tabularnewline
52 & 21 & 18.8802557325153 & 2.11974426748473 \tabularnewline
53 & 15 & 19.6189570609111 & -4.61895706091106 \tabularnewline
54 & 23 & 18.0093149125463 & 4.99068508745374 \tabularnewline
55 & 29 & 19.7484990963448 & 9.25150090365517 \tabularnewline
56 & 17 & 22.9725181971462 & -5.97251819714616 \tabularnewline
57 & 24 & 20.8911788611823 & 3.10882113881771 \tabularnewline
58 & 18 & 21.9745596916985 & -3.97455969169848 \tabularnewline
59 & 22 & 20.5894810437303 & 1.41051895626968 \tabularnewline
60 & 8 & 21.0810272376305 & -13.0810272376305 \tabularnewline
61 & 26 & 16.5224715922907 & 9.47752840770927 \tabularnewline
62 & 22 & 19.8252581274755 & 2.17474187252451 \tabularnewline
63 & 34 & 20.5831253545717 & 13.4168746454283 \tabularnewline
64 & 25 & 25.2587191398815 & -0.258719139881503 \tabularnewline
65 & 20 & 25.1685591261273 & -5.16855912612727 \tabularnewline
66 & 35 & 23.3673883193805 & 11.6326116806195 \tabularnewline
67 & 38 & 27.421191333733 & 10.578808666267 \tabularnewline
68 & 24 & 31.1077586873926 & -7.10775868739258 \tabularnewline
69 & 14 & 28.6308038656094 & -14.6308038656094 \tabularnewline
70 & 25 & 23.5321726690036 & 1.46782733099638 \tabularnewline
71 & 31 & 24.0436900326285 & 6.95630996737153 \tabularnewline
72 & 17 & 26.46786708665 & -9.46786708665002 \tabularnewline
73 & 32 & 23.1684473871775 & 8.83155261282253 \tabularnewline
74 & 27 & 26.2461203626211 & 0.753879637378905 \tabularnewline
75 & 30 & 26.5088369073122 & 3.49116309268782 \tabularnewline
76 & 19 & 27.7254585789797 & -8.72545857897967 \tabularnewline
77 & 36 & 24.6847578954001 & 11.3152421045999 \tabularnewline
78 & 27 & 28.6279620365799 & -1.62796203657988 \tabularnewline
79 & 28 & 28.0606399603058 & -0.0606399603058208 \tabularnewline
80 & 38 & 28.0395077794485 & 9.96049222055151 \tabularnewline
81 & 26 & 31.5106004709872 & -5.51060047098719 \tabularnewline
82 & 25 & 29.5902330235465 & -4.5902330235465 \tabularnewline
83 & 30 & 27.9906008017958 & 2.00939919820425 \tabularnewline
84 & 27 & 28.6908484117361 & -1.69084841173608 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160890&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]30[/C][C]43[/C][C]-13[/C][/ROW]
[ROW][C]3[/C][C]42[/C][C]38.4696812174705[/C][C]3.53031878252946[/C][/ROW]
[ROW][C]4[/C][C]23[/C][C]39.6999481012251[/C][C]-16.6999481012251[/C][/ROW]
[ROW][C]5[/C][C]19[/C][C]33.8802489819753[/C][C]-14.8802489819753[/C][/ROW]
[ROW][C]6[/C][C]19[/C][C]28.6946896395324[/C][C]-9.69468963953242[/C][/ROW]
[ROW][C]7[/C][C]36[/C][C]25.3162254422426[/C][C]10.6837745577574[/C][/ROW]
[ROW][C]8[/C][C]20[/C][C]29.0393719458825[/C][C]-9.03937194588251[/C][/ROW]
[ROW][C]9[/C][C]27[/C][C]25.8892768298286[/C][C]1.11072317017145[/C][/ROW]
[ROW][C]10[/C][C]24[/C][C]26.2763483713684[/C][C]-2.27634837136843[/C][/ROW]
[ROW][C]11[/C][C]23[/C][C]25.4830726957999[/C][C]-2.48307269579991[/C][/ROW]
[ROW][C]12[/C][C]26[/C][C]24.6177564748639[/C][C]1.38224352513612[/C][/ROW]
[ROW][C]13[/C][C]31[/C][C]25.099449075168[/C][C]5.90055092483198[/C][/ROW]
[ROW][C]14[/C][C]51[/C][C]27.1557088199402[/C][C]23.8442911800598[/C][/ROW]
[ROW][C]15[/C][C]39[/C][C]35.4651119114115[/C][C]3.53488808858854[/C][/ROW]
[ROW][C]16[/C][C]32[/C][C]36.6969711346324[/C][C]-4.69697113463241[/C][/ROW]
[ROW][C]17[/C][C]30[/C][C]35.0601421690767[/C][C]-5.06014216907672[/C][/ROW]
[ROW][C]18[/C][C]46[/C][C]33.2967531605507[/C][C]12.7032468394493[/C][/ROW]
[ROW][C]19[/C][C]31[/C][C]37.7236576033096[/C][C]-6.72365760330959[/C][/ROW]
[ROW][C]20[/C][C]31[/C][C]35.3805566550349[/C][C]-4.38055665503494[/C][/ROW]
[ROW][C]21[/C][C]40[/C][C]33.8539937248627[/C][C]6.14600627513731[/C][/ROW]
[ROW][C]22[/C][C]29[/C][C]35.9957912376164[/C][C]-6.99579123761642[/C][/ROW]
[ROW][C]23[/C][C]43[/C][C]33.5578555112758[/C][C]9.44214448872425[/C][/ROW]
[ROW][C]24[/C][C]17[/C][C]36.8483112439392[/C][C]-19.8483112439392[/C][/ROW]
[ROW][C]25[/C][C]53[/C][C]29.9314514570231[/C][C]23.0685485429769[/C][/ROW]
[ROW][C]26[/C][C]47[/C][C]37.9705190531724[/C][C]9.02948094682756[/C][/ROW]
[ROW][C]27[/C][C]49[/C][C]41.1171672939344[/C][C]7.88283270606565[/C][/ROW]
[ROW][C]28[/C][C]44[/C][C]43.8642246068441[/C][C]0.135775393155896[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]43.9115404386764[/C][C]4.08845956132363[/C][/ROW]
[ROW][C]30[/C][C]51[/C][C]45.3363116034669[/C][C]5.66368839653313[/C][/ROW]
[ROW][C]31[/C][C]47[/C][C]47.3100280589444[/C][C]-0.310028058944432[/C][/ROW]
[ROW][C]32[/C][C]44[/C][C]47.2019876021331[/C][C]-3.20198760213312[/C][/ROW]
[ROW][C]33[/C][C]33[/C][C]46.0861395578739[/C][C]-13.0861395578739[/C][/ROW]
[ROW][C]34[/C][C]47[/C][C]41.525802340194[/C][C]5.47419765980596[/C][/ROW]
[ROW][C]35[/C][C]41[/C][C]43.4334839153862[/C][C]-2.43348391538618[/C][/ROW]
[ROW][C]36[/C][C]36[/C][C]42.5854486931664[/C][C]-6.58544869316638[/C][/ROW]
[ROW][C]37[/C][C]46[/C][C]40.2905116234713[/C][C]5.70948837652868[/C][/ROW]
[ROW][C]38[/C][C]24[/C][C]42.2801887335345[/C][C]-18.2801887335345[/C][/ROW]
[ROW][C]39[/C][C]17[/C][C]35.9097977821718[/C][C]-18.9097977821718[/C][/ROW]
[ROW][C]40[/C][C]22[/C][C]29.3199968539867[/C][C]-7.31999685398667[/C][/ROW]
[ROW][C]41[/C][C]30[/C][C]26.7690799897042[/C][C]3.23092001029582[/C][/ROW]
[ROW][C]42[/C][C]24[/C][C]27.895010574896[/C][C]-3.89501057489598[/C][/ROW]
[ROW][C]43[/C][C]18[/C][C]26.5376536852343[/C][C]-8.53765368523428[/C][/ROW]
[ROW][C]44[/C][C]24[/C][C]23.5624003891613[/C][C]0.437599610838706[/C][/ROW]
[ROW][C]45[/C][C]24[/C][C]23.7148977534852[/C][C]0.285102246514846[/C][/ROW]
[ROW][C]46[/C][C]28[/C][C]23.8142519121257[/C][C]4.18574808787427[/C][/ROW]
[ROW][C]47[/C][C]19[/C][C]25.272926772236[/C][C]-6.27292677223601[/C][/ROW]
[ROW][C]48[/C][C]22[/C][C]23.0868992354904[/C][C]-1.08689923549041[/C][/ROW]
[ROW][C]49[/C][C]26[/C][C]22.7081300030859[/C][C]3.29186999691414[/C][/ROW]
[ROW][C]50[/C][C]14[/C][C]23.8553008089832[/C][C]-9.85530080898319[/C][/ROW]
[ROW][C]51[/C][C]16[/C][C]20.4208658580282[/C][C]-4.42086585802824[/C][/ROW]
[ROW][C]52[/C][C]21[/C][C]18.8802557325153[/C][C]2.11974426748473[/C][/ROW]
[ROW][C]53[/C][C]15[/C][C]19.6189570609111[/C][C]-4.61895706091106[/C][/ROW]
[ROW][C]54[/C][C]23[/C][C]18.0093149125463[/C][C]4.99068508745374[/C][/ROW]
[ROW][C]55[/C][C]29[/C][C]19.7484990963448[/C][C]9.25150090365517[/C][/ROW]
[ROW][C]56[/C][C]17[/C][C]22.9725181971462[/C][C]-5.97251819714616[/C][/ROW]
[ROW][C]57[/C][C]24[/C][C]20.8911788611823[/C][C]3.10882113881771[/C][/ROW]
[ROW][C]58[/C][C]18[/C][C]21.9745596916985[/C][C]-3.97455969169848[/C][/ROW]
[ROW][C]59[/C][C]22[/C][C]20.5894810437303[/C][C]1.41051895626968[/C][/ROW]
[ROW][C]60[/C][C]8[/C][C]21.0810272376305[/C][C]-13.0810272376305[/C][/ROW]
[ROW][C]61[/C][C]26[/C][C]16.5224715922907[/C][C]9.47752840770927[/C][/ROW]
[ROW][C]62[/C][C]22[/C][C]19.8252581274755[/C][C]2.17474187252451[/C][/ROW]
[ROW][C]63[/C][C]34[/C][C]20.5831253545717[/C][C]13.4168746454283[/C][/ROW]
[ROW][C]64[/C][C]25[/C][C]25.2587191398815[/C][C]-0.258719139881503[/C][/ROW]
[ROW][C]65[/C][C]20[/C][C]25.1685591261273[/C][C]-5.16855912612727[/C][/ROW]
[ROW][C]66[/C][C]35[/C][C]23.3673883193805[/C][C]11.6326116806195[/C][/ROW]
[ROW][C]67[/C][C]38[/C][C]27.421191333733[/C][C]10.578808666267[/C][/ROW]
[ROW][C]68[/C][C]24[/C][C]31.1077586873926[/C][C]-7.10775868739258[/C][/ROW]
[ROW][C]69[/C][C]14[/C][C]28.6308038656094[/C][C]-14.6308038656094[/C][/ROW]
[ROW][C]70[/C][C]25[/C][C]23.5321726690036[/C][C]1.46782733099638[/C][/ROW]
[ROW][C]71[/C][C]31[/C][C]24.0436900326285[/C][C]6.95630996737153[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]26.46786708665[/C][C]-9.46786708665002[/C][/ROW]
[ROW][C]73[/C][C]32[/C][C]23.1684473871775[/C][C]8.83155261282253[/C][/ROW]
[ROW][C]74[/C][C]27[/C][C]26.2461203626211[/C][C]0.753879637378905[/C][/ROW]
[ROW][C]75[/C][C]30[/C][C]26.5088369073122[/C][C]3.49116309268782[/C][/ROW]
[ROW][C]76[/C][C]19[/C][C]27.7254585789797[/C][C]-8.72545857897967[/C][/ROW]
[ROW][C]77[/C][C]36[/C][C]24.6847578954001[/C][C]11.3152421045999[/C][/ROW]
[ROW][C]78[/C][C]27[/C][C]28.6279620365799[/C][C]-1.62796203657988[/C][/ROW]
[ROW][C]79[/C][C]28[/C][C]28.0606399603058[/C][C]-0.0606399603058208[/C][/ROW]
[ROW][C]80[/C][C]38[/C][C]28.0395077794485[/C][C]9.96049222055151[/C][/ROW]
[ROW][C]81[/C][C]26[/C][C]31.5106004709872[/C][C]-5.51060047098719[/C][/ROW]
[ROW][C]82[/C][C]25[/C][C]29.5902330235465[/C][C]-4.5902330235465[/C][/ROW]
[ROW][C]83[/C][C]30[/C][C]27.9906008017958[/C][C]2.00939919820425[/C][/ROW]
[ROW][C]84[/C][C]27[/C][C]28.6908484117361[/C][C]-1.69084841173608[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160890&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160890&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
23043-13
34238.46968121747053.53031878252946
42339.6999481012251-16.6999481012251
51933.8802489819753-14.8802489819753
61928.6946896395324-9.69468963953242
73625.316225442242610.6837745577574
82029.0393719458825-9.03937194588251
92725.88927682982861.11072317017145
102426.2763483713684-2.27634837136843
112325.4830726957999-2.48307269579991
122624.61775647486391.38224352513612
133125.0994490751685.90055092483198
145127.155708819940223.8442911800598
153935.46511191141153.53488808858854
163236.6969711346324-4.69697113463241
173035.0601421690767-5.06014216907672
184633.296753160550712.7032468394493
193137.7236576033096-6.72365760330959
203135.3805566550349-4.38055665503494
214033.85399372486276.14600627513731
222935.9957912376164-6.99579123761642
234333.55785551127589.44214448872425
241736.8483112439392-19.8483112439392
255329.931451457023123.0685485429769
264737.97051905317249.02948094682756
274941.11716729393447.88283270606565
284443.86422460684410.135775393155896
294843.91154043867644.08845956132363
305145.33631160346695.66368839653313
314747.3100280589444-0.310028058944432
324447.2019876021331-3.20198760213312
333346.0861395578739-13.0861395578739
344741.5258023401945.47419765980596
354143.4334839153862-2.43348391538618
363642.5854486931664-6.58544869316638
374640.29051162347135.70948837652868
382442.2801887335345-18.2801887335345
391735.9097977821718-18.9097977821718
402229.3199968539867-7.31999685398667
413026.76907998970423.23092001029582
422427.895010574896-3.89501057489598
431826.5376536852343-8.53765368523428
442423.56240038916130.437599610838706
452423.71489775348520.285102246514846
462823.81425191212574.18574808787427
471925.272926772236-6.27292677223601
482223.0868992354904-1.08689923549041
492622.70813000308593.29186999691414
501423.8553008089832-9.85530080898319
511620.4208658580282-4.42086585802824
522118.88025573251532.11974426748473
531519.6189570609111-4.61895706091106
542318.00931491254634.99068508745374
552919.74849909634489.25150090365517
561722.9725181971462-5.97251819714616
572420.89117886118233.10882113881771
581821.9745596916985-3.97455969169848
592220.58948104373031.41051895626968
60821.0810272376305-13.0810272376305
612616.52247159229079.47752840770927
622219.82525812747552.17474187252451
633420.583125354571713.4168746454283
642525.2587191398815-0.258719139881503
652025.1685591261273-5.16855912612727
663523.367388319380511.6326116806195
673827.42119133373310.578808666267
682431.1077586873926-7.10775868739258
691428.6308038656094-14.6308038656094
702523.53217266900361.46782733099638
713124.04369003262856.95630996737153
721726.46786708665-9.46786708665002
733223.16844738717758.83155261282253
742726.24612036262110.753879637378905
753026.50883690731223.49116309268782
761927.7254585789797-8.72545857897967
773624.684757895400111.3152421045999
782728.6279620365799-1.62796203657988
792828.0606399603058-0.0606399603058208
803828.03950777944859.96049222055151
812631.5106004709872-5.51060047098719
822529.5902330235465-4.5902330235465
833027.99060080179582.00939919820425
842728.6908484117361-1.69084841173608







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8528.101611310343910.990409291118345.2128133295695
8628.10161131034399.9811591380724546.2220634826154
8728.10161131034399.0252295959724547.1779930247154
8828.10161131034398.1149684782614348.0882541424264
8928.10161131034397.2443956744527648.9588269462351
9028.10161131034396.4087323758435349.7944902448443
9128.10161131034395.6040881388541550.5991344818337
9228.10161131034394.8272455566537151.3759770640341
9328.10161131034394.0755077223424852.1277148983454
9428.10161131034393.3465874564631952.8566351642247
9528.10161131034392.6385251189367253.5646975017511
9628.10161131034391.9496264759979754.2535961446899

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 28.1016113103439 & 10.9904092911183 & 45.2128133295695 \tabularnewline
86 & 28.1016113103439 & 9.98115913807245 & 46.2220634826154 \tabularnewline
87 & 28.1016113103439 & 9.02522959597245 & 47.1779930247154 \tabularnewline
88 & 28.1016113103439 & 8.11496847826143 & 48.0882541424264 \tabularnewline
89 & 28.1016113103439 & 7.24439567445276 & 48.9588269462351 \tabularnewline
90 & 28.1016113103439 & 6.40873237584353 & 49.7944902448443 \tabularnewline
91 & 28.1016113103439 & 5.60408813885415 & 50.5991344818337 \tabularnewline
92 & 28.1016113103439 & 4.82724555665371 & 51.3759770640341 \tabularnewline
93 & 28.1016113103439 & 4.07550772234248 & 52.1277148983454 \tabularnewline
94 & 28.1016113103439 & 3.34658745646319 & 52.8566351642247 \tabularnewline
95 & 28.1016113103439 & 2.63852511893672 & 53.5646975017511 \tabularnewline
96 & 28.1016113103439 & 1.94962647599797 & 54.2535961446899 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160890&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]28.1016113103439[/C][C]10.9904092911183[/C][C]45.2128133295695[/C][/ROW]
[ROW][C]86[/C][C]28.1016113103439[/C][C]9.98115913807245[/C][C]46.2220634826154[/C][/ROW]
[ROW][C]87[/C][C]28.1016113103439[/C][C]9.02522959597245[/C][C]47.1779930247154[/C][/ROW]
[ROW][C]88[/C][C]28.1016113103439[/C][C]8.11496847826143[/C][C]48.0882541424264[/C][/ROW]
[ROW][C]89[/C][C]28.1016113103439[/C][C]7.24439567445276[/C][C]48.9588269462351[/C][/ROW]
[ROW][C]90[/C][C]28.1016113103439[/C][C]6.40873237584353[/C][C]49.7944902448443[/C][/ROW]
[ROW][C]91[/C][C]28.1016113103439[/C][C]5.60408813885415[/C][C]50.5991344818337[/C][/ROW]
[ROW][C]92[/C][C]28.1016113103439[/C][C]4.82724555665371[/C][C]51.3759770640341[/C][/ROW]
[ROW][C]93[/C][C]28.1016113103439[/C][C]4.07550772234248[/C][C]52.1277148983454[/C][/ROW]
[ROW][C]94[/C][C]28.1016113103439[/C][C]3.34658745646319[/C][C]52.8566351642247[/C][/ROW]
[ROW][C]95[/C][C]28.1016113103439[/C][C]2.63852511893672[/C][C]53.5646975017511[/C][/ROW]
[ROW][C]96[/C][C]28.1016113103439[/C][C]1.94962647599797[/C][C]54.2535961446899[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160890&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160890&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
8528.101611310343910.990409291118345.2128133295695
8628.10161131034399.9811591380724546.2220634826154
8728.10161131034399.0252295959724547.1779930247154
8828.10161131034398.1149684782614348.0882541424264
8928.10161131034397.2443956744527648.9588269462351
9028.10161131034396.4087323758435349.7944902448443
9128.10161131034395.6040881388541550.5991344818337
9228.10161131034394.8272455566537151.3759770640341
9328.10161131034394.0755077223424852.1277148983454
9428.10161131034393.3465874564631952.8566351642247
9528.10161131034392.6385251189367253.5646975017511
9628.10161131034391.9496264759979754.2535961446899



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