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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 computationSat, 14 Jan 2012 16:19:45 -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/2012/Jan/14/t13265762381czwyopw6dzp95c.htm/, Retrieved Fri, 03 May 2024 16:35:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161050, Retrieved Fri, 03 May 2024 16:35:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact175
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Opgave 10 IKO - I...] [2011-05-18 12:30:16] [74be16979710d4c4e7c6647856088456]
- R PD    [Exponential Smoothing] [Exponential Smoot...] [2012-01-14 21:19:45] [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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161050&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161050&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161050&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.338261263337884
beta0.0217207423401571
gamma0.512815635756671

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.338261263337884 \tabularnewline
beta & 0.0217207423401571 \tabularnewline
gamma & 0.512815635756671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161050&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]0.338261263337884[/C][/ROW]
[ROW][C]beta[/C][C]0.0217207423401571[/C][/ROW]
[ROW][C]gamma[/C][C]0.512815635756671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161050&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161050&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
alpha0.338261263337884
beta0.0217207423401571
gamma0.512815635756671







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133124.85470085470096.14529914529914
145147.52518882260573.47481117739432
153936.56788458738732.43211541261269
163230.52574621239721.4742537876028
173028.87876545119931.1212345488007
184645.70394332025170.296056679748261
193144.9188373605294-13.9188373605294
203124.63978437587466.3602156241254
214033.89207979469286.10792020530715
222933.603910081461-4.60391008146099
234331.075183546521611.9248164534784
241737.475099964593-20.475099964593
255337.517017066035915.4829829339641
264762.510948181681-15.510948181681
274944.70926087071614.29073912928389
284438.91603107508525.08396892491477
294838.34206014416989.65793985583022
305157.8093523585176-6.80935235851756
314749.7792341201557-2.77923412015568
324440.21411552866843.78588447133161
333348.5552257367027-15.5552257367027
344737.1902560295519.80974397044902
354145.1380968447714-4.13809684477138
363634.9835860605011.01641393949897
374654.5294733247728-8.52947332477283
382460.7385537810068-36.7385537810068
391742.1755492661426-25.1755492661426
402226.1671582695281-4.16715826952811
413023.43105582350936.56894417649072
422435.6575791429703-11.6575791429703
431826.7117866076621-8.71178660766206
442416.68087247490487.31912752509521
452418.99278085583525.00721914416482
462822.6810137237365.31898627626398
471923.8337331717423-4.83373317174234
482214.6451149898757.35488501012498
492632.5942518187849-6.59425181878491
501429.3979976370585-15.3979976370585
511621.6471825377153-5.64718253771533
522119.18675959415721.81324040584278
531521.9739112886457-6.9739112886457
542323.1917586976378-0.191758697637834
552918.965823989031610.0341760109684
561720.6955253496344-3.69552534963439
572418.39562174028825.60437825971176
581822.2946005191612-4.29460051916123
592216.58240908052985.41759091947023
60814.9052615475889-6.90526154758891
612623.09996822242422.90003177757583
622220.00033294490111.99966705509891
633421.443859745961312.5561402540387
642527.8068021319259-2.80680213192594
652026.1495000119062-6.14950001190617
663530.05404157402744.94595842597261
673831.18022094080976.81977905919028
682427.2838782211329-3.28387822113285
691428.402601049555-14.402601049555
702522.15123871721892.8487612827811
713122.18014921557768.81985078442239
721717.5260396183558-0.52603961835576
733231.30683077570950.6931692242905
742727.2397609993172-0.239760999317181
753031.5762615519022-1.57626155190216
761927.9096576433508-8.90965764335076
773622.973123902999413.0268760970006
782737.189900910694-10.189900910694
792833.7812456086581-5.7812456086581
803822.050364486711715.9496355132883
812625.89979174761830.100208252381741
822530.5128636490419-5.51286364904187
833029.78266046671780.217339533282161
842719.02693288428857.97306711571149

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 31 & 24.8547008547009 & 6.14529914529914 \tabularnewline
14 & 51 & 47.5251888226057 & 3.47481117739432 \tabularnewline
15 & 39 & 36.5678845873873 & 2.43211541261269 \tabularnewline
16 & 32 & 30.5257462123972 & 1.4742537876028 \tabularnewline
17 & 30 & 28.8787654511993 & 1.1212345488007 \tabularnewline
18 & 46 & 45.7039433202517 & 0.296056679748261 \tabularnewline
19 & 31 & 44.9188373605294 & -13.9188373605294 \tabularnewline
20 & 31 & 24.6397843758746 & 6.3602156241254 \tabularnewline
21 & 40 & 33.8920797946928 & 6.10792020530715 \tabularnewline
22 & 29 & 33.603910081461 & -4.60391008146099 \tabularnewline
23 & 43 & 31.0751835465216 & 11.9248164534784 \tabularnewline
24 & 17 & 37.475099964593 & -20.475099964593 \tabularnewline
25 & 53 & 37.5170170660359 & 15.4829829339641 \tabularnewline
26 & 47 & 62.510948181681 & -15.510948181681 \tabularnewline
27 & 49 & 44.7092608707161 & 4.29073912928389 \tabularnewline
28 & 44 & 38.9160310750852 & 5.08396892491477 \tabularnewline
29 & 48 & 38.3420601441698 & 9.65793985583022 \tabularnewline
30 & 51 & 57.8093523585176 & -6.80935235851756 \tabularnewline
31 & 47 & 49.7792341201557 & -2.77923412015568 \tabularnewline
32 & 44 & 40.2141155286684 & 3.78588447133161 \tabularnewline
33 & 33 & 48.5552257367027 & -15.5552257367027 \tabularnewline
34 & 47 & 37.190256029551 & 9.80974397044902 \tabularnewline
35 & 41 & 45.1380968447714 & -4.13809684477138 \tabularnewline
36 & 36 & 34.983586060501 & 1.01641393949897 \tabularnewline
37 & 46 & 54.5294733247728 & -8.52947332477283 \tabularnewline
38 & 24 & 60.7385537810068 & -36.7385537810068 \tabularnewline
39 & 17 & 42.1755492661426 & -25.1755492661426 \tabularnewline
40 & 22 & 26.1671582695281 & -4.16715826952811 \tabularnewline
41 & 30 & 23.4310558235093 & 6.56894417649072 \tabularnewline
42 & 24 & 35.6575791429703 & -11.6575791429703 \tabularnewline
43 & 18 & 26.7117866076621 & -8.71178660766206 \tabularnewline
44 & 24 & 16.6808724749048 & 7.31912752509521 \tabularnewline
45 & 24 & 18.9927808558352 & 5.00721914416482 \tabularnewline
46 & 28 & 22.681013723736 & 5.31898627626398 \tabularnewline
47 & 19 & 23.8337331717423 & -4.83373317174234 \tabularnewline
48 & 22 & 14.645114989875 & 7.35488501012498 \tabularnewline
49 & 26 & 32.5942518187849 & -6.59425181878491 \tabularnewline
50 & 14 & 29.3979976370585 & -15.3979976370585 \tabularnewline
51 & 16 & 21.6471825377153 & -5.64718253771533 \tabularnewline
52 & 21 & 19.1867595941572 & 1.81324040584278 \tabularnewline
53 & 15 & 21.9739112886457 & -6.9739112886457 \tabularnewline
54 & 23 & 23.1917586976378 & -0.191758697637834 \tabularnewline
55 & 29 & 18.9658239890316 & 10.0341760109684 \tabularnewline
56 & 17 & 20.6955253496344 & -3.69552534963439 \tabularnewline
57 & 24 & 18.3956217402882 & 5.60437825971176 \tabularnewline
58 & 18 & 22.2946005191612 & -4.29460051916123 \tabularnewline
59 & 22 & 16.5824090805298 & 5.41759091947023 \tabularnewline
60 & 8 & 14.9052615475889 & -6.90526154758891 \tabularnewline
61 & 26 & 23.0999682224242 & 2.90003177757583 \tabularnewline
62 & 22 & 20.0003329449011 & 1.99966705509891 \tabularnewline
63 & 34 & 21.4438597459613 & 12.5561402540387 \tabularnewline
64 & 25 & 27.8068021319259 & -2.80680213192594 \tabularnewline
65 & 20 & 26.1495000119062 & -6.14950001190617 \tabularnewline
66 & 35 & 30.0540415740274 & 4.94595842597261 \tabularnewline
67 & 38 & 31.1802209408097 & 6.81977905919028 \tabularnewline
68 & 24 & 27.2838782211329 & -3.28387822113285 \tabularnewline
69 & 14 & 28.402601049555 & -14.402601049555 \tabularnewline
70 & 25 & 22.1512387172189 & 2.8487612827811 \tabularnewline
71 & 31 & 22.1801492155776 & 8.81985078442239 \tabularnewline
72 & 17 & 17.5260396183558 & -0.52603961835576 \tabularnewline
73 & 32 & 31.3068307757095 & 0.6931692242905 \tabularnewline
74 & 27 & 27.2397609993172 & -0.239760999317181 \tabularnewline
75 & 30 & 31.5762615519022 & -1.57626155190216 \tabularnewline
76 & 19 & 27.9096576433508 & -8.90965764335076 \tabularnewline
77 & 36 & 22.9731239029994 & 13.0268760970006 \tabularnewline
78 & 27 & 37.189900910694 & -10.189900910694 \tabularnewline
79 & 28 & 33.7812456086581 & -5.7812456086581 \tabularnewline
80 & 38 & 22.0503644867117 & 15.9496355132883 \tabularnewline
81 & 26 & 25.8997917476183 & 0.100208252381741 \tabularnewline
82 & 25 & 30.5128636490419 & -5.51286364904187 \tabularnewline
83 & 30 & 29.7826604667178 & 0.217339533282161 \tabularnewline
84 & 27 & 19.0269328842885 & 7.97306711571149 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161050&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]31[/C][C]24.8547008547009[/C][C]6.14529914529914[/C][/ROW]
[ROW][C]14[/C][C]51[/C][C]47.5251888226057[/C][C]3.47481117739432[/C][/ROW]
[ROW][C]15[/C][C]39[/C][C]36.5678845873873[/C][C]2.43211541261269[/C][/ROW]
[ROW][C]16[/C][C]32[/C][C]30.5257462123972[/C][C]1.4742537876028[/C][/ROW]
[ROW][C]17[/C][C]30[/C][C]28.8787654511993[/C][C]1.1212345488007[/C][/ROW]
[ROW][C]18[/C][C]46[/C][C]45.7039433202517[/C][C]0.296056679748261[/C][/ROW]
[ROW][C]19[/C][C]31[/C][C]44.9188373605294[/C][C]-13.9188373605294[/C][/ROW]
[ROW][C]20[/C][C]31[/C][C]24.6397843758746[/C][C]6.3602156241254[/C][/ROW]
[ROW][C]21[/C][C]40[/C][C]33.8920797946928[/C][C]6.10792020530715[/C][/ROW]
[ROW][C]22[/C][C]29[/C][C]33.603910081461[/C][C]-4.60391008146099[/C][/ROW]
[ROW][C]23[/C][C]43[/C][C]31.0751835465216[/C][C]11.9248164534784[/C][/ROW]
[ROW][C]24[/C][C]17[/C][C]37.475099964593[/C][C]-20.475099964593[/C][/ROW]
[ROW][C]25[/C][C]53[/C][C]37.5170170660359[/C][C]15.4829829339641[/C][/ROW]
[ROW][C]26[/C][C]47[/C][C]62.510948181681[/C][C]-15.510948181681[/C][/ROW]
[ROW][C]27[/C][C]49[/C][C]44.7092608707161[/C][C]4.29073912928389[/C][/ROW]
[ROW][C]28[/C][C]44[/C][C]38.9160310750852[/C][C]5.08396892491477[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]38.3420601441698[/C][C]9.65793985583022[/C][/ROW]
[ROW][C]30[/C][C]51[/C][C]57.8093523585176[/C][C]-6.80935235851756[/C][/ROW]
[ROW][C]31[/C][C]47[/C][C]49.7792341201557[/C][C]-2.77923412015568[/C][/ROW]
[ROW][C]32[/C][C]44[/C][C]40.2141155286684[/C][C]3.78588447133161[/C][/ROW]
[ROW][C]33[/C][C]33[/C][C]48.5552257367027[/C][C]-15.5552257367027[/C][/ROW]
[ROW][C]34[/C][C]47[/C][C]37.190256029551[/C][C]9.80974397044902[/C][/ROW]
[ROW][C]35[/C][C]41[/C][C]45.1380968447714[/C][C]-4.13809684477138[/C][/ROW]
[ROW][C]36[/C][C]36[/C][C]34.983586060501[/C][C]1.01641393949897[/C][/ROW]
[ROW][C]37[/C][C]46[/C][C]54.5294733247728[/C][C]-8.52947332477283[/C][/ROW]
[ROW][C]38[/C][C]24[/C][C]60.7385537810068[/C][C]-36.7385537810068[/C][/ROW]
[ROW][C]39[/C][C]17[/C][C]42.1755492661426[/C][C]-25.1755492661426[/C][/ROW]
[ROW][C]40[/C][C]22[/C][C]26.1671582695281[/C][C]-4.16715826952811[/C][/ROW]
[ROW][C]41[/C][C]30[/C][C]23.4310558235093[/C][C]6.56894417649072[/C][/ROW]
[ROW][C]42[/C][C]24[/C][C]35.6575791429703[/C][C]-11.6575791429703[/C][/ROW]
[ROW][C]43[/C][C]18[/C][C]26.7117866076621[/C][C]-8.71178660766206[/C][/ROW]
[ROW][C]44[/C][C]24[/C][C]16.6808724749048[/C][C]7.31912752509521[/C][/ROW]
[ROW][C]45[/C][C]24[/C][C]18.9927808558352[/C][C]5.00721914416482[/C][/ROW]
[ROW][C]46[/C][C]28[/C][C]22.681013723736[/C][C]5.31898627626398[/C][/ROW]
[ROW][C]47[/C][C]19[/C][C]23.8337331717423[/C][C]-4.83373317174234[/C][/ROW]
[ROW][C]48[/C][C]22[/C][C]14.645114989875[/C][C]7.35488501012498[/C][/ROW]
[ROW][C]49[/C][C]26[/C][C]32.5942518187849[/C][C]-6.59425181878491[/C][/ROW]
[ROW][C]50[/C][C]14[/C][C]29.3979976370585[/C][C]-15.3979976370585[/C][/ROW]
[ROW][C]51[/C][C]16[/C][C]21.6471825377153[/C][C]-5.64718253771533[/C][/ROW]
[ROW][C]52[/C][C]21[/C][C]19.1867595941572[/C][C]1.81324040584278[/C][/ROW]
[ROW][C]53[/C][C]15[/C][C]21.9739112886457[/C][C]-6.9739112886457[/C][/ROW]
[ROW][C]54[/C][C]23[/C][C]23.1917586976378[/C][C]-0.191758697637834[/C][/ROW]
[ROW][C]55[/C][C]29[/C][C]18.9658239890316[/C][C]10.0341760109684[/C][/ROW]
[ROW][C]56[/C][C]17[/C][C]20.6955253496344[/C][C]-3.69552534963439[/C][/ROW]
[ROW][C]57[/C][C]24[/C][C]18.3956217402882[/C][C]5.60437825971176[/C][/ROW]
[ROW][C]58[/C][C]18[/C][C]22.2946005191612[/C][C]-4.29460051916123[/C][/ROW]
[ROW][C]59[/C][C]22[/C][C]16.5824090805298[/C][C]5.41759091947023[/C][/ROW]
[ROW][C]60[/C][C]8[/C][C]14.9052615475889[/C][C]-6.90526154758891[/C][/ROW]
[ROW][C]61[/C][C]26[/C][C]23.0999682224242[/C][C]2.90003177757583[/C][/ROW]
[ROW][C]62[/C][C]22[/C][C]20.0003329449011[/C][C]1.99966705509891[/C][/ROW]
[ROW][C]63[/C][C]34[/C][C]21.4438597459613[/C][C]12.5561402540387[/C][/ROW]
[ROW][C]64[/C][C]25[/C][C]27.8068021319259[/C][C]-2.80680213192594[/C][/ROW]
[ROW][C]65[/C][C]20[/C][C]26.1495000119062[/C][C]-6.14950001190617[/C][/ROW]
[ROW][C]66[/C][C]35[/C][C]30.0540415740274[/C][C]4.94595842597261[/C][/ROW]
[ROW][C]67[/C][C]38[/C][C]31.1802209408097[/C][C]6.81977905919028[/C][/ROW]
[ROW][C]68[/C][C]24[/C][C]27.2838782211329[/C][C]-3.28387822113285[/C][/ROW]
[ROW][C]69[/C][C]14[/C][C]28.402601049555[/C][C]-14.402601049555[/C][/ROW]
[ROW][C]70[/C][C]25[/C][C]22.1512387172189[/C][C]2.8487612827811[/C][/ROW]
[ROW][C]71[/C][C]31[/C][C]22.1801492155776[/C][C]8.81985078442239[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]17.5260396183558[/C][C]-0.52603961835576[/C][/ROW]
[ROW][C]73[/C][C]32[/C][C]31.3068307757095[/C][C]0.6931692242905[/C][/ROW]
[ROW][C]74[/C][C]27[/C][C]27.2397609993172[/C][C]-0.239760999317181[/C][/ROW]
[ROW][C]75[/C][C]30[/C][C]31.5762615519022[/C][C]-1.57626155190216[/C][/ROW]
[ROW][C]76[/C][C]19[/C][C]27.9096576433508[/C][C]-8.90965764335076[/C][/ROW]
[ROW][C]77[/C][C]36[/C][C]22.9731239029994[/C][C]13.0268760970006[/C][/ROW]
[ROW][C]78[/C][C]27[/C][C]37.189900910694[/C][C]-10.189900910694[/C][/ROW]
[ROW][C]79[/C][C]28[/C][C]33.7812456086581[/C][C]-5.7812456086581[/C][/ROW]
[ROW][C]80[/C][C]38[/C][C]22.0503644867117[/C][C]15.9496355132883[/C][/ROW]
[ROW][C]81[/C][C]26[/C][C]25.8997917476183[/C][C]0.100208252381741[/C][/ROW]
[ROW][C]82[/C][C]25[/C][C]30.5128636490419[/C][C]-5.51286364904187[/C][/ROW]
[ROW][C]83[/C][C]30[/C][C]29.7826604667178[/C][C]0.217339533282161[/C][/ROW]
[ROW][C]84[/C][C]27[/C][C]19.0269328842885[/C][C]7.97306711571149[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161050&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161050&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
133124.85470085470096.14529914529914
145147.52518882260573.47481117739432
153936.56788458738732.43211541261269
163230.52574621239721.4742537876028
173028.87876545119931.1212345488007
184645.70394332025170.296056679748261
193144.9188373605294-13.9188373605294
203124.63978437587466.3602156241254
214033.89207979469286.10792020530715
222933.603910081461-4.60391008146099
234331.075183546521611.9248164534784
241737.475099964593-20.475099964593
255337.517017066035915.4829829339641
264762.510948181681-15.510948181681
274944.70926087071614.29073912928389
284438.91603107508525.08396892491477
294838.34206014416989.65793985583022
305157.8093523585176-6.80935235851756
314749.7792341201557-2.77923412015568
324440.21411552866843.78588447133161
333348.5552257367027-15.5552257367027
344737.1902560295519.80974397044902
354145.1380968447714-4.13809684477138
363634.9835860605011.01641393949897
374654.5294733247728-8.52947332477283
382460.7385537810068-36.7385537810068
391742.1755492661426-25.1755492661426
402226.1671582695281-4.16715826952811
413023.43105582350936.56894417649072
422435.6575791429703-11.6575791429703
431826.7117866076621-8.71178660766206
442416.68087247490487.31912752509521
452418.99278085583525.00721914416482
462822.6810137237365.31898627626398
471923.8337331717423-4.83373317174234
482214.6451149898757.35488501012498
492632.5942518187849-6.59425181878491
501429.3979976370585-15.3979976370585
511621.6471825377153-5.64718253771533
522119.18675959415721.81324040584278
531521.9739112886457-6.9739112886457
542323.1917586976378-0.191758697637834
552918.965823989031610.0341760109684
561720.6955253496344-3.69552534963439
572418.39562174028825.60437825971176
581822.2946005191612-4.29460051916123
592216.58240908052985.41759091947023
60814.9052615475889-6.90526154758891
612623.09996822242422.90003177757583
622220.00033294490111.99966705509891
633421.443859745961312.5561402540387
642527.8068021319259-2.80680213192594
652026.1495000119062-6.14950001190617
663530.05404157402744.94595842597261
673831.18022094080976.81977905919028
682427.2838782211329-3.28387822113285
691428.402601049555-14.402601049555
702522.15123871721892.8487612827811
713122.18014921557768.81985078442239
721717.5260396183558-0.52603961835576
733231.30683077570950.6931692242905
742727.2397609993172-0.239760999317181
753031.5762615519022-1.57626155190216
761927.9096576433508-8.90965764335076
773622.973123902999413.0268760970006
782737.189900910694-10.189900910694
792833.7812456086581-5.7812456086581
803822.050364486711715.9496355132883
812625.89979174761830.100208252381741
822530.5128636490419-5.51286364904187
833029.78266046671780.217339533282161
842719.02693288428857.97306711571149







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8536.138632448960617.626892865180354.6503720327409
8631.557658959296411.971527512293551.1437904062993
8735.560639967812314.913426262884956.2078536727398
8829.98913779771048.2913460534591751.6869295419616
8935.6265212608712.886386224654258.3666562970859
9037.578448984291713.802344247635561.3545537209478
9139.207838484623114.400593382991464.0150835862547
9236.944498145112811.109647676734262.7793486134913
9330.04068779919153.1806724971148556.9007031012681
9432.73474001741474.8510677798567160.6184122549727
9535.87404659907736.9674251603656364.780668037789
9627.7352878036709-2.1942657626998957.6648413700416

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 36.1386324489606 & 17.6268928651803 & 54.6503720327409 \tabularnewline
86 & 31.5576589592964 & 11.9715275122935 & 51.1437904062993 \tabularnewline
87 & 35.5606399678123 & 14.9134262628849 & 56.2078536727398 \tabularnewline
88 & 29.9891377977104 & 8.29134605345917 & 51.6869295419616 \tabularnewline
89 & 35.62652126087 & 12.8863862246542 & 58.3666562970859 \tabularnewline
90 & 37.5784489842917 & 13.8023442476355 & 61.3545537209478 \tabularnewline
91 & 39.2078384846231 & 14.4005933829914 & 64.0150835862547 \tabularnewline
92 & 36.9444981451128 & 11.1096476767342 & 62.7793486134913 \tabularnewline
93 & 30.0406877991915 & 3.18067249711485 & 56.9007031012681 \tabularnewline
94 & 32.7347400174147 & 4.85106777985671 & 60.6184122549727 \tabularnewline
95 & 35.8740465990773 & 6.96742516036563 & 64.780668037789 \tabularnewline
96 & 27.7352878036709 & -2.19426576269989 & 57.6648413700416 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161050&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]36.1386324489606[/C][C]17.6268928651803[/C][C]54.6503720327409[/C][/ROW]
[ROW][C]86[/C][C]31.5576589592964[/C][C]11.9715275122935[/C][C]51.1437904062993[/C][/ROW]
[ROW][C]87[/C][C]35.5606399678123[/C][C]14.9134262628849[/C][C]56.2078536727398[/C][/ROW]
[ROW][C]88[/C][C]29.9891377977104[/C][C]8.29134605345917[/C][C]51.6869295419616[/C][/ROW]
[ROW][C]89[/C][C]35.62652126087[/C][C]12.8863862246542[/C][C]58.3666562970859[/C][/ROW]
[ROW][C]90[/C][C]37.5784489842917[/C][C]13.8023442476355[/C][C]61.3545537209478[/C][/ROW]
[ROW][C]91[/C][C]39.2078384846231[/C][C]14.4005933829914[/C][C]64.0150835862547[/C][/ROW]
[ROW][C]92[/C][C]36.9444981451128[/C][C]11.1096476767342[/C][C]62.7793486134913[/C][/ROW]
[ROW][C]93[/C][C]30.0406877991915[/C][C]3.18067249711485[/C][C]56.9007031012681[/C][/ROW]
[ROW][C]94[/C][C]32.7347400174147[/C][C]4.85106777985671[/C][C]60.6184122549727[/C][/ROW]
[ROW][C]95[/C][C]35.8740465990773[/C][C]6.96742516036563[/C][C]64.780668037789[/C][/ROW]
[ROW][C]96[/C][C]27.7352878036709[/C][C]-2.19426576269989[/C][C]57.6648413700416[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161050&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161050&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
8536.138632448960617.626892865180354.6503720327409
8631.557658959296411.971527512293551.1437904062993
8735.560639967812314.913426262884956.2078536727398
8829.98913779771048.2913460534591751.6869295419616
8935.6265212608712.886386224654258.3666562970859
9037.578448984291713.802344247635561.3545537209478
9139.207838484623114.400593382991464.0150835862547
9236.944498145112811.109647676734262.7793486134913
9330.04068779919153.1806724971148556.9007031012681
9432.73474001741474.8510677798567160.6184122549727
9535.87404659907736.9674251603656364.780668037789
9627.7352878036709-2.1942657626998957.6648413700416



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')