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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 computationSun, 06 Jun 2010 13:58:50 +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/2010/Jun/06/t127583277059wbuwfdm273cta.htm/, Retrieved Sat, 27 Apr 2024 18:48:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77683, Retrieved Sat, 27 Apr 2024 18:48:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2010-06-06 13:58:50] [03859715711bd3369851d387eaa83ba4] [Current]
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Dataseries X:
1954
2302
3054
2414
2226
2725
2589
3470
2400
3180
4009
3924
2072
2434
2956
2828
2687
2629
3150
4119
3030
3055
3821
4001
2529
2472
3134
2789
2758
2993
3282
3437
2804
3076
3782
3889
2271
2452
3084
2522
2769
3438
2839
3746
2632
2851
3871
3618
2389
2344
2678
2492
2858
2246
2800
3869
3007
3023
3907
4209
2353
2570
2903
2910
3782
2759
2931
3641
2794
3070
3576
4106
2452
2206
2488
2416
2534
2521
3093
3903
2907
3025
3812
4209




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77683&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77683&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77683&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.369649244277171
beta0.00993226516517318
gamma0.570305179539606

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.369649244277171 \tabularnewline
beta & 0.00993226516517318 \tabularnewline
gamma & 0.570305179539606 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77683&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]0.369649244277171[/C][/ROW]
[ROW][C]beta[/C][C]0.00993226516517318[/C][/ROW]
[ROW][C]gamma[/C][C]0.570305179539606[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77683&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77683&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
alpha0.369649244277171
beta0.00993226516517318
gamma0.570305179539606







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1320722006.6844025824865.3155974175247
1424342364.8080898869969.1919101130079
1529562875.6573721808980.3426278191091
1628282782.8889043289645.1110956710413
1726872692.76062571217-5.76062571216744
1826292657.54308286388-28.5430828638755
1931502813.98415850912336.015841490876
2041193954.81928031406164.180719685939
2130302797.84170833199232.158291668007
2230553833.43262096272-778.432620962715
2338214448.03815236594-627.038152365939
2440014136.17590677012-135.175906770116
2525292184.31225076755344.687749232453
2624722686.94799112296-214.947991122958
2731343132.945759402541.05424059746383
2827892986.57353373055-197.573533730553
2927582781.72444066096-23.7244406609598
3029932728.01963951761264.980360482394
3132823137.64321765883144.356782341169
3234374182.95408726275-745.954087262747
3328042757.9016980364946.0983019635109
3430763298.86754297183-222.867542971832
3537824142.85719190746-360.857191907457
3638894102.49717875758-213.497178757575
3722712291.3499594395-20.3499594394980
3824522442.284475376889.71552462311502
3930843026.0353192735657.9646807264371
4025222831.01685839742-309.016858397422
4127692647.93666754506121.063332454938
4234382744.35961559261693.640384407395
4328393273.33897787271-434.338977872713
4437463736.292016839369.70798316063838
4526322849.36695828950-217.366958289504
4628513188.29601732302-337.296017323021
4738713912.52244562161-41.5224456216129
4836184039.31927743104-421.319277431045
4923892245.53854743103143.461452568965
5023442467.71088386613-123.710883866128
5126783010.28585660102-332.285856601022
5224922552.69802575038-60.6980257503751
5328582610.56924010095247.430759899048
5422462933.04347847209-687.04347847209
5528002559.03307821820240.966921781798
5638693345.70983198529523.290168014706
5730072615.62594789321391.374052106793
5830233139.50463909946-116.504639099456
5939074099.96328287365-192.963282873648
6042094026.27903115901182.720968840985
6123532517.87690113672-164.876901136724
6225702531.3813606497738.6186393502262
6329033088.85754423609-185.857544236093
6429102760.56295689399149.437043106009
6537823026.60819327319755.391806726809
6627593154.27350131302-395.273501313020
6729313269.86980707291-338.869807072906
6836414051.65694382411-410.656943824106
6927942874.95772752598-80.957727525978
7030703035.0694812855134.9305187144878
7135764018.10535899468-442.105358994679
7241063979.73902662874126.260973371255
7324522376.6562476963875.3437523036196
7422062550.92778697610-344.927786976104
7524882857.33546422964-369.335464229642
7624162588.9893835527-172.989383552701
7725342878.32776861777-344.327768617773
7825212306.5684216494214.431578350598
7930932612.56512273000480.434877270003
8039033594.92481758455308.075182415454
8129072811.0375216359595.9624783640547
8230253079.33402369482-54.3340236948206
8338123848.93253200061-36.9325320006142
8442094175.3496011793333.6503988206687

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2072 & 2006.68440258248 & 65.3155974175247 \tabularnewline
14 & 2434 & 2364.80808988699 & 69.1919101130079 \tabularnewline
15 & 2956 & 2875.65737218089 & 80.3426278191091 \tabularnewline
16 & 2828 & 2782.88890432896 & 45.1110956710413 \tabularnewline
17 & 2687 & 2692.76062571217 & -5.76062571216744 \tabularnewline
18 & 2629 & 2657.54308286388 & -28.5430828638755 \tabularnewline
19 & 3150 & 2813.98415850912 & 336.015841490876 \tabularnewline
20 & 4119 & 3954.81928031406 & 164.180719685939 \tabularnewline
21 & 3030 & 2797.84170833199 & 232.158291668007 \tabularnewline
22 & 3055 & 3833.43262096272 & -778.432620962715 \tabularnewline
23 & 3821 & 4448.03815236594 & -627.038152365939 \tabularnewline
24 & 4001 & 4136.17590677012 & -135.175906770116 \tabularnewline
25 & 2529 & 2184.31225076755 & 344.687749232453 \tabularnewline
26 & 2472 & 2686.94799112296 & -214.947991122958 \tabularnewline
27 & 3134 & 3132.94575940254 & 1.05424059746383 \tabularnewline
28 & 2789 & 2986.57353373055 & -197.573533730553 \tabularnewline
29 & 2758 & 2781.72444066096 & -23.7244406609598 \tabularnewline
30 & 2993 & 2728.01963951761 & 264.980360482394 \tabularnewline
31 & 3282 & 3137.64321765883 & 144.356782341169 \tabularnewline
32 & 3437 & 4182.95408726275 & -745.954087262747 \tabularnewline
33 & 2804 & 2757.90169803649 & 46.0983019635109 \tabularnewline
34 & 3076 & 3298.86754297183 & -222.867542971832 \tabularnewline
35 & 3782 & 4142.85719190746 & -360.857191907457 \tabularnewline
36 & 3889 & 4102.49717875758 & -213.497178757575 \tabularnewline
37 & 2271 & 2291.3499594395 & -20.3499594394980 \tabularnewline
38 & 2452 & 2442.28447537688 & 9.71552462311502 \tabularnewline
39 & 3084 & 3026.03531927356 & 57.9646807264371 \tabularnewline
40 & 2522 & 2831.01685839742 & -309.016858397422 \tabularnewline
41 & 2769 & 2647.93666754506 & 121.063332454938 \tabularnewline
42 & 3438 & 2744.35961559261 & 693.640384407395 \tabularnewline
43 & 2839 & 3273.33897787271 & -434.338977872713 \tabularnewline
44 & 3746 & 3736.29201683936 & 9.70798316063838 \tabularnewline
45 & 2632 & 2849.36695828950 & -217.366958289504 \tabularnewline
46 & 2851 & 3188.29601732302 & -337.296017323021 \tabularnewline
47 & 3871 & 3912.52244562161 & -41.5224456216129 \tabularnewline
48 & 3618 & 4039.31927743104 & -421.319277431045 \tabularnewline
49 & 2389 & 2245.53854743103 & 143.461452568965 \tabularnewline
50 & 2344 & 2467.71088386613 & -123.710883866128 \tabularnewline
51 & 2678 & 3010.28585660102 & -332.285856601022 \tabularnewline
52 & 2492 & 2552.69802575038 & -60.6980257503751 \tabularnewline
53 & 2858 & 2610.56924010095 & 247.430759899048 \tabularnewline
54 & 2246 & 2933.04347847209 & -687.04347847209 \tabularnewline
55 & 2800 & 2559.03307821820 & 240.966921781798 \tabularnewline
56 & 3869 & 3345.70983198529 & 523.290168014706 \tabularnewline
57 & 3007 & 2615.62594789321 & 391.374052106793 \tabularnewline
58 & 3023 & 3139.50463909946 & -116.504639099456 \tabularnewline
59 & 3907 & 4099.96328287365 & -192.963282873648 \tabularnewline
60 & 4209 & 4026.27903115901 & 182.720968840985 \tabularnewline
61 & 2353 & 2517.87690113672 & -164.876901136724 \tabularnewline
62 & 2570 & 2531.38136064977 & 38.6186393502262 \tabularnewline
63 & 2903 & 3088.85754423609 & -185.857544236093 \tabularnewline
64 & 2910 & 2760.56295689399 & 149.437043106009 \tabularnewline
65 & 3782 & 3026.60819327319 & 755.391806726809 \tabularnewline
66 & 2759 & 3154.27350131302 & -395.273501313020 \tabularnewline
67 & 2931 & 3269.86980707291 & -338.869807072906 \tabularnewline
68 & 3641 & 4051.65694382411 & -410.656943824106 \tabularnewline
69 & 2794 & 2874.95772752598 & -80.957727525978 \tabularnewline
70 & 3070 & 3035.06948128551 & 34.9305187144878 \tabularnewline
71 & 3576 & 4018.10535899468 & -442.105358994679 \tabularnewline
72 & 4106 & 3979.73902662874 & 126.260973371255 \tabularnewline
73 & 2452 & 2376.65624769638 & 75.3437523036196 \tabularnewline
74 & 2206 & 2550.92778697610 & -344.927786976104 \tabularnewline
75 & 2488 & 2857.33546422964 & -369.335464229642 \tabularnewline
76 & 2416 & 2588.9893835527 & -172.989383552701 \tabularnewline
77 & 2534 & 2878.32776861777 & -344.327768617773 \tabularnewline
78 & 2521 & 2306.5684216494 & 214.431578350598 \tabularnewline
79 & 3093 & 2612.56512273000 & 480.434877270003 \tabularnewline
80 & 3903 & 3594.92481758455 & 308.075182415454 \tabularnewline
81 & 2907 & 2811.03752163595 & 95.9624783640547 \tabularnewline
82 & 3025 & 3079.33402369482 & -54.3340236948206 \tabularnewline
83 & 3812 & 3848.93253200061 & -36.9325320006142 \tabularnewline
84 & 4209 & 4175.34960117933 & 33.6503988206687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77683&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]2072[/C][C]2006.68440258248[/C][C]65.3155974175247[/C][/ROW]
[ROW][C]14[/C][C]2434[/C][C]2364.80808988699[/C][C]69.1919101130079[/C][/ROW]
[ROW][C]15[/C][C]2956[/C][C]2875.65737218089[/C][C]80.3426278191091[/C][/ROW]
[ROW][C]16[/C][C]2828[/C][C]2782.88890432896[/C][C]45.1110956710413[/C][/ROW]
[ROW][C]17[/C][C]2687[/C][C]2692.76062571217[/C][C]-5.76062571216744[/C][/ROW]
[ROW][C]18[/C][C]2629[/C][C]2657.54308286388[/C][C]-28.5430828638755[/C][/ROW]
[ROW][C]19[/C][C]3150[/C][C]2813.98415850912[/C][C]336.015841490876[/C][/ROW]
[ROW][C]20[/C][C]4119[/C][C]3954.81928031406[/C][C]164.180719685939[/C][/ROW]
[ROW][C]21[/C][C]3030[/C][C]2797.84170833199[/C][C]232.158291668007[/C][/ROW]
[ROW][C]22[/C][C]3055[/C][C]3833.43262096272[/C][C]-778.432620962715[/C][/ROW]
[ROW][C]23[/C][C]3821[/C][C]4448.03815236594[/C][C]-627.038152365939[/C][/ROW]
[ROW][C]24[/C][C]4001[/C][C]4136.17590677012[/C][C]-135.175906770116[/C][/ROW]
[ROW][C]25[/C][C]2529[/C][C]2184.31225076755[/C][C]344.687749232453[/C][/ROW]
[ROW][C]26[/C][C]2472[/C][C]2686.94799112296[/C][C]-214.947991122958[/C][/ROW]
[ROW][C]27[/C][C]3134[/C][C]3132.94575940254[/C][C]1.05424059746383[/C][/ROW]
[ROW][C]28[/C][C]2789[/C][C]2986.57353373055[/C][C]-197.573533730553[/C][/ROW]
[ROW][C]29[/C][C]2758[/C][C]2781.72444066096[/C][C]-23.7244406609598[/C][/ROW]
[ROW][C]30[/C][C]2993[/C][C]2728.01963951761[/C][C]264.980360482394[/C][/ROW]
[ROW][C]31[/C][C]3282[/C][C]3137.64321765883[/C][C]144.356782341169[/C][/ROW]
[ROW][C]32[/C][C]3437[/C][C]4182.95408726275[/C][C]-745.954087262747[/C][/ROW]
[ROW][C]33[/C][C]2804[/C][C]2757.90169803649[/C][C]46.0983019635109[/C][/ROW]
[ROW][C]34[/C][C]3076[/C][C]3298.86754297183[/C][C]-222.867542971832[/C][/ROW]
[ROW][C]35[/C][C]3782[/C][C]4142.85719190746[/C][C]-360.857191907457[/C][/ROW]
[ROW][C]36[/C][C]3889[/C][C]4102.49717875758[/C][C]-213.497178757575[/C][/ROW]
[ROW][C]37[/C][C]2271[/C][C]2291.3499594395[/C][C]-20.3499594394980[/C][/ROW]
[ROW][C]38[/C][C]2452[/C][C]2442.28447537688[/C][C]9.71552462311502[/C][/ROW]
[ROW][C]39[/C][C]3084[/C][C]3026.03531927356[/C][C]57.9646807264371[/C][/ROW]
[ROW][C]40[/C][C]2522[/C][C]2831.01685839742[/C][C]-309.016858397422[/C][/ROW]
[ROW][C]41[/C][C]2769[/C][C]2647.93666754506[/C][C]121.063332454938[/C][/ROW]
[ROW][C]42[/C][C]3438[/C][C]2744.35961559261[/C][C]693.640384407395[/C][/ROW]
[ROW][C]43[/C][C]2839[/C][C]3273.33897787271[/C][C]-434.338977872713[/C][/ROW]
[ROW][C]44[/C][C]3746[/C][C]3736.29201683936[/C][C]9.70798316063838[/C][/ROW]
[ROW][C]45[/C][C]2632[/C][C]2849.36695828950[/C][C]-217.366958289504[/C][/ROW]
[ROW][C]46[/C][C]2851[/C][C]3188.29601732302[/C][C]-337.296017323021[/C][/ROW]
[ROW][C]47[/C][C]3871[/C][C]3912.52244562161[/C][C]-41.5224456216129[/C][/ROW]
[ROW][C]48[/C][C]3618[/C][C]4039.31927743104[/C][C]-421.319277431045[/C][/ROW]
[ROW][C]49[/C][C]2389[/C][C]2245.53854743103[/C][C]143.461452568965[/C][/ROW]
[ROW][C]50[/C][C]2344[/C][C]2467.71088386613[/C][C]-123.710883866128[/C][/ROW]
[ROW][C]51[/C][C]2678[/C][C]3010.28585660102[/C][C]-332.285856601022[/C][/ROW]
[ROW][C]52[/C][C]2492[/C][C]2552.69802575038[/C][C]-60.6980257503751[/C][/ROW]
[ROW][C]53[/C][C]2858[/C][C]2610.56924010095[/C][C]247.430759899048[/C][/ROW]
[ROW][C]54[/C][C]2246[/C][C]2933.04347847209[/C][C]-687.04347847209[/C][/ROW]
[ROW][C]55[/C][C]2800[/C][C]2559.03307821820[/C][C]240.966921781798[/C][/ROW]
[ROW][C]56[/C][C]3869[/C][C]3345.70983198529[/C][C]523.290168014706[/C][/ROW]
[ROW][C]57[/C][C]3007[/C][C]2615.62594789321[/C][C]391.374052106793[/C][/ROW]
[ROW][C]58[/C][C]3023[/C][C]3139.50463909946[/C][C]-116.504639099456[/C][/ROW]
[ROW][C]59[/C][C]3907[/C][C]4099.96328287365[/C][C]-192.963282873648[/C][/ROW]
[ROW][C]60[/C][C]4209[/C][C]4026.27903115901[/C][C]182.720968840985[/C][/ROW]
[ROW][C]61[/C][C]2353[/C][C]2517.87690113672[/C][C]-164.876901136724[/C][/ROW]
[ROW][C]62[/C][C]2570[/C][C]2531.38136064977[/C][C]38.6186393502262[/C][/ROW]
[ROW][C]63[/C][C]2903[/C][C]3088.85754423609[/C][C]-185.857544236093[/C][/ROW]
[ROW][C]64[/C][C]2910[/C][C]2760.56295689399[/C][C]149.437043106009[/C][/ROW]
[ROW][C]65[/C][C]3782[/C][C]3026.60819327319[/C][C]755.391806726809[/C][/ROW]
[ROW][C]66[/C][C]2759[/C][C]3154.27350131302[/C][C]-395.273501313020[/C][/ROW]
[ROW][C]67[/C][C]2931[/C][C]3269.86980707291[/C][C]-338.869807072906[/C][/ROW]
[ROW][C]68[/C][C]3641[/C][C]4051.65694382411[/C][C]-410.656943824106[/C][/ROW]
[ROW][C]69[/C][C]2794[/C][C]2874.95772752598[/C][C]-80.957727525978[/C][/ROW]
[ROW][C]70[/C][C]3070[/C][C]3035.06948128551[/C][C]34.9305187144878[/C][/ROW]
[ROW][C]71[/C][C]3576[/C][C]4018.10535899468[/C][C]-442.105358994679[/C][/ROW]
[ROW][C]72[/C][C]4106[/C][C]3979.73902662874[/C][C]126.260973371255[/C][/ROW]
[ROW][C]73[/C][C]2452[/C][C]2376.65624769638[/C][C]75.3437523036196[/C][/ROW]
[ROW][C]74[/C][C]2206[/C][C]2550.92778697610[/C][C]-344.927786976104[/C][/ROW]
[ROW][C]75[/C][C]2488[/C][C]2857.33546422964[/C][C]-369.335464229642[/C][/ROW]
[ROW][C]76[/C][C]2416[/C][C]2588.9893835527[/C][C]-172.989383552701[/C][/ROW]
[ROW][C]77[/C][C]2534[/C][C]2878.32776861777[/C][C]-344.327768617773[/C][/ROW]
[ROW][C]78[/C][C]2521[/C][C]2306.5684216494[/C][C]214.431578350598[/C][/ROW]
[ROW][C]79[/C][C]3093[/C][C]2612.56512273000[/C][C]480.434877270003[/C][/ROW]
[ROW][C]80[/C][C]3903[/C][C]3594.92481758455[/C][C]308.075182415454[/C][/ROW]
[ROW][C]81[/C][C]2907[/C][C]2811.03752163595[/C][C]95.9624783640547[/C][/ROW]
[ROW][C]82[/C][C]3025[/C][C]3079.33402369482[/C][C]-54.3340236948206[/C][/ROW]
[ROW][C]83[/C][C]3812[/C][C]3848.93253200061[/C][C]-36.9325320006142[/C][/ROW]
[ROW][C]84[/C][C]4209[/C][C]4175.34960117933[/C][C]33.6503988206687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77683&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77683&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
1320722006.6844025824865.3155974175247
1424342364.8080898869969.1919101130079
1529562875.6573721808980.3426278191091
1628282782.8889043289645.1110956710413
1726872692.76062571217-5.76062571216744
1826292657.54308286388-28.5430828638755
1931502813.98415850912336.015841490876
2041193954.81928031406164.180719685939
2130302797.84170833199232.158291668007
2230553833.43262096272-778.432620962715
2338214448.03815236594-627.038152365939
2440014136.17590677012-135.175906770116
2525292184.31225076755344.687749232453
2624722686.94799112296-214.947991122958
2731343132.945759402541.05424059746383
2827892986.57353373055-197.573533730553
2927582781.72444066096-23.7244406609598
3029932728.01963951761264.980360482394
3132823137.64321765883144.356782341169
3234374182.95408726275-745.954087262747
3328042757.9016980364946.0983019635109
3430763298.86754297183-222.867542971832
3537824142.85719190746-360.857191907457
3638894102.49717875758-213.497178757575
3722712291.3499594395-20.3499594394980
3824522442.284475376889.71552462311502
3930843026.0353192735657.9646807264371
4025222831.01685839742-309.016858397422
4127692647.93666754506121.063332454938
4234382744.35961559261693.640384407395
4328393273.33897787271-434.338977872713
4437463736.292016839369.70798316063838
4526322849.36695828950-217.366958289504
4628513188.29601732302-337.296017323021
4738713912.52244562161-41.5224456216129
4836184039.31927743104-421.319277431045
4923892245.53854743103143.461452568965
5023442467.71088386613-123.710883866128
5126783010.28585660102-332.285856601022
5224922552.69802575038-60.6980257503751
5328582610.56924010095247.430759899048
5422462933.04347847209-687.04347847209
5528002559.03307821820240.966921781798
5638693345.70983198529523.290168014706
5730072615.62594789321391.374052106793
5830233139.50463909946-116.504639099456
5939074099.96328287365-192.963282873648
6042094026.27903115901182.720968840985
6123532517.87690113672-164.876901136724
6225702531.3813606497738.6186393502262
6329033088.85754423609-185.857544236093
6429102760.56295689399149.437043106009
6537823026.60819327319755.391806726809
6627593154.27350131302-395.273501313020
6729313269.86980707291-338.869807072906
6836414051.65694382411-410.656943824106
6927942874.95772752598-80.957727525978
7030703035.0694812855134.9305187144878
7135764018.10535899468-442.105358994679
7241063979.73902662874126.260973371255
7324522376.6562476963875.3437523036196
7422062550.92778697610-344.927786976104
7524882857.33546422964-369.335464229642
7624162588.9893835527-172.989383552701
7725342878.32776861777-344.327768617773
7825212306.5684216494214.431578350598
7930932612.56512273000480.434877270003
8039033594.92481758455308.075182415454
8129072811.0375216359595.9624783640547
8230253079.33402369482-54.3340236948206
8338123848.93253200061-36.9325320006142
8442094175.3496011793333.6503988206687







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
852471.074810345462034.359489044202907.79013164672
862458.750446045261969.060479739082948.44041235143
872905.901909724032332.080999696883479.72281975118
882835.857044276512226.480884421403445.23320413161
893166.128630700042473.221364808563859.03589659151
902871.164137400442184.090319205123558.23795559576
913235.361157117072451.275958839664019.44635539448
924042.713599854933074.533457241375010.89374246849
933010.762219902532212.788593664893808.73584614017
943196.653477156772327.884920308644065.4220340049
954032.755119713342947.963723075365117.54651635131
964417.442553527663296.431425531095538.45368152422

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 2471.07481034546 & 2034.35948904420 & 2907.79013164672 \tabularnewline
86 & 2458.75044604526 & 1969.06047973908 & 2948.44041235143 \tabularnewline
87 & 2905.90190972403 & 2332.08099969688 & 3479.72281975118 \tabularnewline
88 & 2835.85704427651 & 2226.48088442140 & 3445.23320413161 \tabularnewline
89 & 3166.12863070004 & 2473.22136480856 & 3859.03589659151 \tabularnewline
90 & 2871.16413740044 & 2184.09031920512 & 3558.23795559576 \tabularnewline
91 & 3235.36115711707 & 2451.27595883966 & 4019.44635539448 \tabularnewline
92 & 4042.71359985493 & 3074.53345724137 & 5010.89374246849 \tabularnewline
93 & 3010.76221990253 & 2212.78859366489 & 3808.73584614017 \tabularnewline
94 & 3196.65347715677 & 2327.88492030864 & 4065.4220340049 \tabularnewline
95 & 4032.75511971334 & 2947.96372307536 & 5117.54651635131 \tabularnewline
96 & 4417.44255352766 & 3296.43142553109 & 5538.45368152422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77683&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]2471.07481034546[/C][C]2034.35948904420[/C][C]2907.79013164672[/C][/ROW]
[ROW][C]86[/C][C]2458.75044604526[/C][C]1969.06047973908[/C][C]2948.44041235143[/C][/ROW]
[ROW][C]87[/C][C]2905.90190972403[/C][C]2332.08099969688[/C][C]3479.72281975118[/C][/ROW]
[ROW][C]88[/C][C]2835.85704427651[/C][C]2226.48088442140[/C][C]3445.23320413161[/C][/ROW]
[ROW][C]89[/C][C]3166.12863070004[/C][C]2473.22136480856[/C][C]3859.03589659151[/C][/ROW]
[ROW][C]90[/C][C]2871.16413740044[/C][C]2184.09031920512[/C][C]3558.23795559576[/C][/ROW]
[ROW][C]91[/C][C]3235.36115711707[/C][C]2451.27595883966[/C][C]4019.44635539448[/C][/ROW]
[ROW][C]92[/C][C]4042.71359985493[/C][C]3074.53345724137[/C][C]5010.89374246849[/C][/ROW]
[ROW][C]93[/C][C]3010.76221990253[/C][C]2212.78859366489[/C][C]3808.73584614017[/C][/ROW]
[ROW][C]94[/C][C]3196.65347715677[/C][C]2327.88492030864[/C][C]4065.4220340049[/C][/ROW]
[ROW][C]95[/C][C]4032.75511971334[/C][C]2947.96372307536[/C][C]5117.54651635131[/C][/ROW]
[ROW][C]96[/C][C]4417.44255352766[/C][C]3296.43142553109[/C][C]5538.45368152422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77683&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77683&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
852471.074810345462034.359489044202907.79013164672
862458.750446045261969.060479739082948.44041235143
872905.901909724032332.080999696883479.72281975118
882835.857044276512226.480884421403445.23320413161
893166.128630700042473.221364808563859.03589659151
902871.164137400442184.090319205123558.23795559576
913235.361157117072451.275958839664019.44635539448
924042.713599854933074.533457241375010.89374246849
933010.762219902532212.788593664893808.73584614017
943196.653477156772327.884920308644065.4220340049
954032.755119713342947.963723075365117.54651635131
964417.442553527663296.431425531095538.45368152422



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')