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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 15 Dec 2016 12:28:58 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/15/t1481801399jnq74upgk6osamw.htm/, Retrieved Fri, 03 May 2024 09:12:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299879, Retrieved Fri, 03 May 2024 09:12:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [F1 exponential sm...] [2016-12-15 11:28:58] [e3cd721010e920ddac8a34a44b82c047] [Current]
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Dataseries X:
2473
2314
2789
2722
2732
2917
3100
3156
2589
2734
2551
2773
2624
2500
3160
2831
2913
3238
3340
3401
2898
3055
2807
2990
2764
2666
3246
3137
3248
3494
3582
3798
3189
3288
3075
3209
3013
2805
3525
3391
3544
3713
3919
4041
3238
3429
3166
3546
3346
3159
3901
3651
3776
3995
4325
4613
3656
3804
3579
3877
3545
3500
4341
4228
4305
4445
4844
4999
4020
4214
3910
4119
3861
3803
4591
4317
4449
4780
5058
5261
4364
4605
4295
4413
4104
3834
4674
4373
4537
5030
5200
5441
4501
4718
4473
4573
4323
4101
4958
4673
4771
5220
5488
5784
4758
4948
4608
4710
4242
3710
4414
4467
4737
5117
5446
5735
4738
4993
4517
4809
4352
4229
4929
4671
4935
5557




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299879&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299879&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299879&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.380470828344249
beta0
gamma0.836896644693645

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.380470828344249 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.836896644693645 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299879&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]0.380470828344249[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.836896644693645[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299879&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299879&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
alpha0.380470828344249
beta0
gamma0.836896644693645







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1326242515.57506033466108.424939665335
1425002437.0526624966362.9473375033731
1531603108.7212071792251.2787928207827
1628312797.6199895115133.3800104884908
1729132888.7937597774424.2062402225633
1832383222.7404156231615.2595843768395
1933403370.19026414008-30.1902641400766
2034013425.8852002465-24.8852002465032
2128982798.6998855457999.3001144542095
2230552994.3540521699460.645947830064
2328072822.31649858287-15.3164985828662
2429903059.44733996363-69.4473399636295
2527642928.77667298169-164.776672981694
2626662706.71765090311-40.7176509031146
2732463381.7397545011-135.739754501099
2831372970.10684910955166.893150890448
2932483111.13976700567136.86023299433
3034943509.09826601872-15.0982660187183
3135823629.17415403624-47.1741540362436
3237983684.81759638574113.182403614261
3331893119.1776730183569.8223269816472
3432883293.7758634177-5.77586341770075
3530753036.8921639245838.1078360754159
3632093282.77633148319-73.7763314831936
3730133084.15312345602-71.1531234560216
3828052950.64062981758-145.640629817581
3935253587.45961882635-62.4596188263454
4033913337.7486381520853.2513618479156
4135443421.82431827143122.175681728568
4237133753.08137614617-40.0813761461686
4339193852.8418363133266.1581636866758
4440414044.77551561245-3.77551561244582
4532383367.66772432143-129.667724321428
4634293430.94974508665-1.94974508664518
4731663187.36925444556-21.3692544455594
4835463357.67182525439188.328174745606
4933463247.3417432160498.6582567839591
5031593123.9740205236335.0259794763683
5139013952.73362192019-51.733621920187
5236513745.63295330757-94.6329533075727
5337763815.71139860749-39.7113986074933
5439954014.71083752342-19.7108375234152
5543254188.5043766667136.495623333303
5646134379.85559236659233.144407633407
5736563646.117073709689.88292629032276
5838043848.12371752861-44.1237175286124
5935793546.5158066033432.4841933966627
6038773876.621482433220.378517566778555
6135453623.09404820536-78.0940482053625
6235003383.06484694896116.935153051043
6343414262.3876260219878.6123739780232
6442284059.33531644465168.664683555353
6543054272.2784908606132.7215091393937
6644454536.13983746666-91.1398374666624
6748444792.8522907529351.147709247075
6849995018.3049596295-19.3049596294959
6940203984.7790741810135.2209258189869
7042144182.3782213267231.6217786732777
7139103922.47602371186-12.4760237118589
7241194245.66459130189-126.664591301889
7338613876.85643482358-15.8564348235823
7438033749.368537890653.6314621093989
7545914648.41607602373-57.4160760237264
7643174424.78879788166-107.788797881656
7744494464.34302501574-15.3430250157407
7847804651.32862399363128.671376006372
7950585084.17663411479-26.176634114795
8052615250.7032277312310.296772268769
8143644205.02613632614158.97386367386
8246054457.82649216564147.173507834356
8342954196.4336307008798.5663692991338
8444134522.35165209444-109.351652094439
8541044193.75243599222-89.7524359922245
8638344066.03723965232-232.037239652323
8746744836.57497251027-162.574972510266
8843734536.64444256026-163.644442560259
8945374606.48945767524-69.4894576752386
9050304853.9511023104176.048897689598
9152005233.54007759556-33.5400775955613
9254415421.5693190427819.4306809572199
9345014423.3539207011277.6460792988801
9447184642.1141810263175.8858189736893
9544734321.56195912181151.438040878192
9645734562.7857925210310.2142074789745
9743234279.9203708403343.0796291596653
9841014117.93559135664-16.9355913566424
9949585062.66133070322-104.661330703224
10046734764.57568360494-91.5756836049368
10147714922.80299020243-151.802990202429
10252205291.63598187968-71.6359818796791
10354885477.331738800110.6682611998995
10457845720.49727956563.502720434999
10547584713.0006284501944.9993715498131
10649484926.9911102970521.00888970295
10746084607.918663360370.0813366396305355
10847104721.37601417113-11.3760141711255
10942424438.09556363063-196.095563630627
11037104151.62157589583-441.621575895832
11144144863.19599944963-449.195999449633
11244674455.5964907038611.403509296144
11347374614.19966210131122.800337898687
11451175117.22299879428-0.222998794275554
11554465367.878966071778.1210339283034
11657355660.0346399480674.9653600519378
11747384663.5815225910574.4184774089472
11849934874.19412399974118.805876000262
11945174583.39414382029-66.3941438202928
12048094664.66670362591144.333296374089
12143524342.410425048479.58957495152845
12242293990.00923738658238.990762613419
12349295021.71313043903-92.7131304390268
12446714986.38972099262-315.389720992621
12549355094.82762088679-159.827620886788
12655575450.73852531711106.261474682887

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2624 & 2515.57506033466 & 108.424939665335 \tabularnewline
14 & 2500 & 2437.05266249663 & 62.9473375033731 \tabularnewline
15 & 3160 & 3108.72120717922 & 51.2787928207827 \tabularnewline
16 & 2831 & 2797.61998951151 & 33.3800104884908 \tabularnewline
17 & 2913 & 2888.79375977744 & 24.2062402225633 \tabularnewline
18 & 3238 & 3222.74041562316 & 15.2595843768395 \tabularnewline
19 & 3340 & 3370.19026414008 & -30.1902641400766 \tabularnewline
20 & 3401 & 3425.8852002465 & -24.8852002465032 \tabularnewline
21 & 2898 & 2798.69988554579 & 99.3001144542095 \tabularnewline
22 & 3055 & 2994.35405216994 & 60.645947830064 \tabularnewline
23 & 2807 & 2822.31649858287 & -15.3164985828662 \tabularnewline
24 & 2990 & 3059.44733996363 & -69.4473399636295 \tabularnewline
25 & 2764 & 2928.77667298169 & -164.776672981694 \tabularnewline
26 & 2666 & 2706.71765090311 & -40.7176509031146 \tabularnewline
27 & 3246 & 3381.7397545011 & -135.739754501099 \tabularnewline
28 & 3137 & 2970.10684910955 & 166.893150890448 \tabularnewline
29 & 3248 & 3111.13976700567 & 136.86023299433 \tabularnewline
30 & 3494 & 3509.09826601872 & -15.0982660187183 \tabularnewline
31 & 3582 & 3629.17415403624 & -47.1741540362436 \tabularnewline
32 & 3798 & 3684.81759638574 & 113.182403614261 \tabularnewline
33 & 3189 & 3119.17767301835 & 69.8223269816472 \tabularnewline
34 & 3288 & 3293.7758634177 & -5.77586341770075 \tabularnewline
35 & 3075 & 3036.89216392458 & 38.1078360754159 \tabularnewline
36 & 3209 & 3282.77633148319 & -73.7763314831936 \tabularnewline
37 & 3013 & 3084.15312345602 & -71.1531234560216 \tabularnewline
38 & 2805 & 2950.64062981758 & -145.640629817581 \tabularnewline
39 & 3525 & 3587.45961882635 & -62.4596188263454 \tabularnewline
40 & 3391 & 3337.74863815208 & 53.2513618479156 \tabularnewline
41 & 3544 & 3421.82431827143 & 122.175681728568 \tabularnewline
42 & 3713 & 3753.08137614617 & -40.0813761461686 \tabularnewline
43 & 3919 & 3852.84183631332 & 66.1581636866758 \tabularnewline
44 & 4041 & 4044.77551561245 & -3.77551561244582 \tabularnewline
45 & 3238 & 3367.66772432143 & -129.667724321428 \tabularnewline
46 & 3429 & 3430.94974508665 & -1.94974508664518 \tabularnewline
47 & 3166 & 3187.36925444556 & -21.3692544455594 \tabularnewline
48 & 3546 & 3357.67182525439 & 188.328174745606 \tabularnewline
49 & 3346 & 3247.34174321604 & 98.6582567839591 \tabularnewline
50 & 3159 & 3123.97402052363 & 35.0259794763683 \tabularnewline
51 & 3901 & 3952.73362192019 & -51.733621920187 \tabularnewline
52 & 3651 & 3745.63295330757 & -94.6329533075727 \tabularnewline
53 & 3776 & 3815.71139860749 & -39.7113986074933 \tabularnewline
54 & 3995 & 4014.71083752342 & -19.7108375234152 \tabularnewline
55 & 4325 & 4188.5043766667 & 136.495623333303 \tabularnewline
56 & 4613 & 4379.85559236659 & 233.144407633407 \tabularnewline
57 & 3656 & 3646.11707370968 & 9.88292629032276 \tabularnewline
58 & 3804 & 3848.12371752861 & -44.1237175286124 \tabularnewline
59 & 3579 & 3546.51580660334 & 32.4841933966627 \tabularnewline
60 & 3877 & 3876.62148243322 & 0.378517566778555 \tabularnewline
61 & 3545 & 3623.09404820536 & -78.0940482053625 \tabularnewline
62 & 3500 & 3383.06484694896 & 116.935153051043 \tabularnewline
63 & 4341 & 4262.38762602198 & 78.6123739780232 \tabularnewline
64 & 4228 & 4059.33531644465 & 168.664683555353 \tabularnewline
65 & 4305 & 4272.27849086061 & 32.7215091393937 \tabularnewline
66 & 4445 & 4536.13983746666 & -91.1398374666624 \tabularnewline
67 & 4844 & 4792.85229075293 & 51.147709247075 \tabularnewline
68 & 4999 & 5018.3049596295 & -19.3049596294959 \tabularnewline
69 & 4020 & 3984.77907418101 & 35.2209258189869 \tabularnewline
70 & 4214 & 4182.37822132672 & 31.6217786732777 \tabularnewline
71 & 3910 & 3922.47602371186 & -12.4760237118589 \tabularnewline
72 & 4119 & 4245.66459130189 & -126.664591301889 \tabularnewline
73 & 3861 & 3876.85643482358 & -15.8564348235823 \tabularnewline
74 & 3803 & 3749.3685378906 & 53.6314621093989 \tabularnewline
75 & 4591 & 4648.41607602373 & -57.4160760237264 \tabularnewline
76 & 4317 & 4424.78879788166 & -107.788797881656 \tabularnewline
77 & 4449 & 4464.34302501574 & -15.3430250157407 \tabularnewline
78 & 4780 & 4651.32862399363 & 128.671376006372 \tabularnewline
79 & 5058 & 5084.17663411479 & -26.176634114795 \tabularnewline
80 & 5261 & 5250.70322773123 & 10.296772268769 \tabularnewline
81 & 4364 & 4205.02613632614 & 158.97386367386 \tabularnewline
82 & 4605 & 4457.82649216564 & 147.173507834356 \tabularnewline
83 & 4295 & 4196.43363070087 & 98.5663692991338 \tabularnewline
84 & 4413 & 4522.35165209444 & -109.351652094439 \tabularnewline
85 & 4104 & 4193.75243599222 & -89.7524359922245 \tabularnewline
86 & 3834 & 4066.03723965232 & -232.037239652323 \tabularnewline
87 & 4674 & 4836.57497251027 & -162.574972510266 \tabularnewline
88 & 4373 & 4536.64444256026 & -163.644442560259 \tabularnewline
89 & 4537 & 4606.48945767524 & -69.4894576752386 \tabularnewline
90 & 5030 & 4853.9511023104 & 176.048897689598 \tabularnewline
91 & 5200 & 5233.54007759556 & -33.5400775955613 \tabularnewline
92 & 5441 & 5421.56931904278 & 19.4306809572199 \tabularnewline
93 & 4501 & 4423.35392070112 & 77.6460792988801 \tabularnewline
94 & 4718 & 4642.11418102631 & 75.8858189736893 \tabularnewline
95 & 4473 & 4321.56195912181 & 151.438040878192 \tabularnewline
96 & 4573 & 4562.78579252103 & 10.2142074789745 \tabularnewline
97 & 4323 & 4279.92037084033 & 43.0796291596653 \tabularnewline
98 & 4101 & 4117.93559135664 & -16.9355913566424 \tabularnewline
99 & 4958 & 5062.66133070322 & -104.661330703224 \tabularnewline
100 & 4673 & 4764.57568360494 & -91.5756836049368 \tabularnewline
101 & 4771 & 4922.80299020243 & -151.802990202429 \tabularnewline
102 & 5220 & 5291.63598187968 & -71.6359818796791 \tabularnewline
103 & 5488 & 5477.3317388001 & 10.6682611998995 \tabularnewline
104 & 5784 & 5720.497279565 & 63.502720434999 \tabularnewline
105 & 4758 & 4713.00062845019 & 44.9993715498131 \tabularnewline
106 & 4948 & 4926.99111029705 & 21.00888970295 \tabularnewline
107 & 4608 & 4607.91866336037 & 0.0813366396305355 \tabularnewline
108 & 4710 & 4721.37601417113 & -11.3760141711255 \tabularnewline
109 & 4242 & 4438.09556363063 & -196.095563630627 \tabularnewline
110 & 3710 & 4151.62157589583 & -441.621575895832 \tabularnewline
111 & 4414 & 4863.19599944963 & -449.195999449633 \tabularnewline
112 & 4467 & 4455.59649070386 & 11.403509296144 \tabularnewline
113 & 4737 & 4614.19966210131 & 122.800337898687 \tabularnewline
114 & 5117 & 5117.22299879428 & -0.222998794275554 \tabularnewline
115 & 5446 & 5367.8789660717 & 78.1210339283034 \tabularnewline
116 & 5735 & 5660.03463994806 & 74.9653600519378 \tabularnewline
117 & 4738 & 4663.58152259105 & 74.4184774089472 \tabularnewline
118 & 4993 & 4874.19412399974 & 118.805876000262 \tabularnewline
119 & 4517 & 4583.39414382029 & -66.3941438202928 \tabularnewline
120 & 4809 & 4664.66670362591 & 144.333296374089 \tabularnewline
121 & 4352 & 4342.41042504847 & 9.58957495152845 \tabularnewline
122 & 4229 & 3990.00923738658 & 238.990762613419 \tabularnewline
123 & 4929 & 5021.71313043903 & -92.7131304390268 \tabularnewline
124 & 4671 & 4986.38972099262 & -315.389720992621 \tabularnewline
125 & 4935 & 5094.82762088679 & -159.827620886788 \tabularnewline
126 & 5557 & 5450.73852531711 & 106.261474682887 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299879&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]2624[/C][C]2515.57506033466[/C][C]108.424939665335[/C][/ROW]
[ROW][C]14[/C][C]2500[/C][C]2437.05266249663[/C][C]62.9473375033731[/C][/ROW]
[ROW][C]15[/C][C]3160[/C][C]3108.72120717922[/C][C]51.2787928207827[/C][/ROW]
[ROW][C]16[/C][C]2831[/C][C]2797.61998951151[/C][C]33.3800104884908[/C][/ROW]
[ROW][C]17[/C][C]2913[/C][C]2888.79375977744[/C][C]24.2062402225633[/C][/ROW]
[ROW][C]18[/C][C]3238[/C][C]3222.74041562316[/C][C]15.2595843768395[/C][/ROW]
[ROW][C]19[/C][C]3340[/C][C]3370.19026414008[/C][C]-30.1902641400766[/C][/ROW]
[ROW][C]20[/C][C]3401[/C][C]3425.8852002465[/C][C]-24.8852002465032[/C][/ROW]
[ROW][C]21[/C][C]2898[/C][C]2798.69988554579[/C][C]99.3001144542095[/C][/ROW]
[ROW][C]22[/C][C]3055[/C][C]2994.35405216994[/C][C]60.645947830064[/C][/ROW]
[ROW][C]23[/C][C]2807[/C][C]2822.31649858287[/C][C]-15.3164985828662[/C][/ROW]
[ROW][C]24[/C][C]2990[/C][C]3059.44733996363[/C][C]-69.4473399636295[/C][/ROW]
[ROW][C]25[/C][C]2764[/C][C]2928.77667298169[/C][C]-164.776672981694[/C][/ROW]
[ROW][C]26[/C][C]2666[/C][C]2706.71765090311[/C][C]-40.7176509031146[/C][/ROW]
[ROW][C]27[/C][C]3246[/C][C]3381.7397545011[/C][C]-135.739754501099[/C][/ROW]
[ROW][C]28[/C][C]3137[/C][C]2970.10684910955[/C][C]166.893150890448[/C][/ROW]
[ROW][C]29[/C][C]3248[/C][C]3111.13976700567[/C][C]136.86023299433[/C][/ROW]
[ROW][C]30[/C][C]3494[/C][C]3509.09826601872[/C][C]-15.0982660187183[/C][/ROW]
[ROW][C]31[/C][C]3582[/C][C]3629.17415403624[/C][C]-47.1741540362436[/C][/ROW]
[ROW][C]32[/C][C]3798[/C][C]3684.81759638574[/C][C]113.182403614261[/C][/ROW]
[ROW][C]33[/C][C]3189[/C][C]3119.17767301835[/C][C]69.8223269816472[/C][/ROW]
[ROW][C]34[/C][C]3288[/C][C]3293.7758634177[/C][C]-5.77586341770075[/C][/ROW]
[ROW][C]35[/C][C]3075[/C][C]3036.89216392458[/C][C]38.1078360754159[/C][/ROW]
[ROW][C]36[/C][C]3209[/C][C]3282.77633148319[/C][C]-73.7763314831936[/C][/ROW]
[ROW][C]37[/C][C]3013[/C][C]3084.15312345602[/C][C]-71.1531234560216[/C][/ROW]
[ROW][C]38[/C][C]2805[/C][C]2950.64062981758[/C][C]-145.640629817581[/C][/ROW]
[ROW][C]39[/C][C]3525[/C][C]3587.45961882635[/C][C]-62.4596188263454[/C][/ROW]
[ROW][C]40[/C][C]3391[/C][C]3337.74863815208[/C][C]53.2513618479156[/C][/ROW]
[ROW][C]41[/C][C]3544[/C][C]3421.82431827143[/C][C]122.175681728568[/C][/ROW]
[ROW][C]42[/C][C]3713[/C][C]3753.08137614617[/C][C]-40.0813761461686[/C][/ROW]
[ROW][C]43[/C][C]3919[/C][C]3852.84183631332[/C][C]66.1581636866758[/C][/ROW]
[ROW][C]44[/C][C]4041[/C][C]4044.77551561245[/C][C]-3.77551561244582[/C][/ROW]
[ROW][C]45[/C][C]3238[/C][C]3367.66772432143[/C][C]-129.667724321428[/C][/ROW]
[ROW][C]46[/C][C]3429[/C][C]3430.94974508665[/C][C]-1.94974508664518[/C][/ROW]
[ROW][C]47[/C][C]3166[/C][C]3187.36925444556[/C][C]-21.3692544455594[/C][/ROW]
[ROW][C]48[/C][C]3546[/C][C]3357.67182525439[/C][C]188.328174745606[/C][/ROW]
[ROW][C]49[/C][C]3346[/C][C]3247.34174321604[/C][C]98.6582567839591[/C][/ROW]
[ROW][C]50[/C][C]3159[/C][C]3123.97402052363[/C][C]35.0259794763683[/C][/ROW]
[ROW][C]51[/C][C]3901[/C][C]3952.73362192019[/C][C]-51.733621920187[/C][/ROW]
[ROW][C]52[/C][C]3651[/C][C]3745.63295330757[/C][C]-94.6329533075727[/C][/ROW]
[ROW][C]53[/C][C]3776[/C][C]3815.71139860749[/C][C]-39.7113986074933[/C][/ROW]
[ROW][C]54[/C][C]3995[/C][C]4014.71083752342[/C][C]-19.7108375234152[/C][/ROW]
[ROW][C]55[/C][C]4325[/C][C]4188.5043766667[/C][C]136.495623333303[/C][/ROW]
[ROW][C]56[/C][C]4613[/C][C]4379.85559236659[/C][C]233.144407633407[/C][/ROW]
[ROW][C]57[/C][C]3656[/C][C]3646.11707370968[/C][C]9.88292629032276[/C][/ROW]
[ROW][C]58[/C][C]3804[/C][C]3848.12371752861[/C][C]-44.1237175286124[/C][/ROW]
[ROW][C]59[/C][C]3579[/C][C]3546.51580660334[/C][C]32.4841933966627[/C][/ROW]
[ROW][C]60[/C][C]3877[/C][C]3876.62148243322[/C][C]0.378517566778555[/C][/ROW]
[ROW][C]61[/C][C]3545[/C][C]3623.09404820536[/C][C]-78.0940482053625[/C][/ROW]
[ROW][C]62[/C][C]3500[/C][C]3383.06484694896[/C][C]116.935153051043[/C][/ROW]
[ROW][C]63[/C][C]4341[/C][C]4262.38762602198[/C][C]78.6123739780232[/C][/ROW]
[ROW][C]64[/C][C]4228[/C][C]4059.33531644465[/C][C]168.664683555353[/C][/ROW]
[ROW][C]65[/C][C]4305[/C][C]4272.27849086061[/C][C]32.7215091393937[/C][/ROW]
[ROW][C]66[/C][C]4445[/C][C]4536.13983746666[/C][C]-91.1398374666624[/C][/ROW]
[ROW][C]67[/C][C]4844[/C][C]4792.85229075293[/C][C]51.147709247075[/C][/ROW]
[ROW][C]68[/C][C]4999[/C][C]5018.3049596295[/C][C]-19.3049596294959[/C][/ROW]
[ROW][C]69[/C][C]4020[/C][C]3984.77907418101[/C][C]35.2209258189869[/C][/ROW]
[ROW][C]70[/C][C]4214[/C][C]4182.37822132672[/C][C]31.6217786732777[/C][/ROW]
[ROW][C]71[/C][C]3910[/C][C]3922.47602371186[/C][C]-12.4760237118589[/C][/ROW]
[ROW][C]72[/C][C]4119[/C][C]4245.66459130189[/C][C]-126.664591301889[/C][/ROW]
[ROW][C]73[/C][C]3861[/C][C]3876.85643482358[/C][C]-15.8564348235823[/C][/ROW]
[ROW][C]74[/C][C]3803[/C][C]3749.3685378906[/C][C]53.6314621093989[/C][/ROW]
[ROW][C]75[/C][C]4591[/C][C]4648.41607602373[/C][C]-57.4160760237264[/C][/ROW]
[ROW][C]76[/C][C]4317[/C][C]4424.78879788166[/C][C]-107.788797881656[/C][/ROW]
[ROW][C]77[/C][C]4449[/C][C]4464.34302501574[/C][C]-15.3430250157407[/C][/ROW]
[ROW][C]78[/C][C]4780[/C][C]4651.32862399363[/C][C]128.671376006372[/C][/ROW]
[ROW][C]79[/C][C]5058[/C][C]5084.17663411479[/C][C]-26.176634114795[/C][/ROW]
[ROW][C]80[/C][C]5261[/C][C]5250.70322773123[/C][C]10.296772268769[/C][/ROW]
[ROW][C]81[/C][C]4364[/C][C]4205.02613632614[/C][C]158.97386367386[/C][/ROW]
[ROW][C]82[/C][C]4605[/C][C]4457.82649216564[/C][C]147.173507834356[/C][/ROW]
[ROW][C]83[/C][C]4295[/C][C]4196.43363070087[/C][C]98.5663692991338[/C][/ROW]
[ROW][C]84[/C][C]4413[/C][C]4522.35165209444[/C][C]-109.351652094439[/C][/ROW]
[ROW][C]85[/C][C]4104[/C][C]4193.75243599222[/C][C]-89.7524359922245[/C][/ROW]
[ROW][C]86[/C][C]3834[/C][C]4066.03723965232[/C][C]-232.037239652323[/C][/ROW]
[ROW][C]87[/C][C]4674[/C][C]4836.57497251027[/C][C]-162.574972510266[/C][/ROW]
[ROW][C]88[/C][C]4373[/C][C]4536.64444256026[/C][C]-163.644442560259[/C][/ROW]
[ROW][C]89[/C][C]4537[/C][C]4606.48945767524[/C][C]-69.4894576752386[/C][/ROW]
[ROW][C]90[/C][C]5030[/C][C]4853.9511023104[/C][C]176.048897689598[/C][/ROW]
[ROW][C]91[/C][C]5200[/C][C]5233.54007759556[/C][C]-33.5400775955613[/C][/ROW]
[ROW][C]92[/C][C]5441[/C][C]5421.56931904278[/C][C]19.4306809572199[/C][/ROW]
[ROW][C]93[/C][C]4501[/C][C]4423.35392070112[/C][C]77.6460792988801[/C][/ROW]
[ROW][C]94[/C][C]4718[/C][C]4642.11418102631[/C][C]75.8858189736893[/C][/ROW]
[ROW][C]95[/C][C]4473[/C][C]4321.56195912181[/C][C]151.438040878192[/C][/ROW]
[ROW][C]96[/C][C]4573[/C][C]4562.78579252103[/C][C]10.2142074789745[/C][/ROW]
[ROW][C]97[/C][C]4323[/C][C]4279.92037084033[/C][C]43.0796291596653[/C][/ROW]
[ROW][C]98[/C][C]4101[/C][C]4117.93559135664[/C][C]-16.9355913566424[/C][/ROW]
[ROW][C]99[/C][C]4958[/C][C]5062.66133070322[/C][C]-104.661330703224[/C][/ROW]
[ROW][C]100[/C][C]4673[/C][C]4764.57568360494[/C][C]-91.5756836049368[/C][/ROW]
[ROW][C]101[/C][C]4771[/C][C]4922.80299020243[/C][C]-151.802990202429[/C][/ROW]
[ROW][C]102[/C][C]5220[/C][C]5291.63598187968[/C][C]-71.6359818796791[/C][/ROW]
[ROW][C]103[/C][C]5488[/C][C]5477.3317388001[/C][C]10.6682611998995[/C][/ROW]
[ROW][C]104[/C][C]5784[/C][C]5720.497279565[/C][C]63.502720434999[/C][/ROW]
[ROW][C]105[/C][C]4758[/C][C]4713.00062845019[/C][C]44.9993715498131[/C][/ROW]
[ROW][C]106[/C][C]4948[/C][C]4926.99111029705[/C][C]21.00888970295[/C][/ROW]
[ROW][C]107[/C][C]4608[/C][C]4607.91866336037[/C][C]0.0813366396305355[/C][/ROW]
[ROW][C]108[/C][C]4710[/C][C]4721.37601417113[/C][C]-11.3760141711255[/C][/ROW]
[ROW][C]109[/C][C]4242[/C][C]4438.09556363063[/C][C]-196.095563630627[/C][/ROW]
[ROW][C]110[/C][C]3710[/C][C]4151.62157589583[/C][C]-441.621575895832[/C][/ROW]
[ROW][C]111[/C][C]4414[/C][C]4863.19599944963[/C][C]-449.195999449633[/C][/ROW]
[ROW][C]112[/C][C]4467[/C][C]4455.59649070386[/C][C]11.403509296144[/C][/ROW]
[ROW][C]113[/C][C]4737[/C][C]4614.19966210131[/C][C]122.800337898687[/C][/ROW]
[ROW][C]114[/C][C]5117[/C][C]5117.22299879428[/C][C]-0.222998794275554[/C][/ROW]
[ROW][C]115[/C][C]5446[/C][C]5367.8789660717[/C][C]78.1210339283034[/C][/ROW]
[ROW][C]116[/C][C]5735[/C][C]5660.03463994806[/C][C]74.9653600519378[/C][/ROW]
[ROW][C]117[/C][C]4738[/C][C]4663.58152259105[/C][C]74.4184774089472[/C][/ROW]
[ROW][C]118[/C][C]4993[/C][C]4874.19412399974[/C][C]118.805876000262[/C][/ROW]
[ROW][C]119[/C][C]4517[/C][C]4583.39414382029[/C][C]-66.3941438202928[/C][/ROW]
[ROW][C]120[/C][C]4809[/C][C]4664.66670362591[/C][C]144.333296374089[/C][/ROW]
[ROW][C]121[/C][C]4352[/C][C]4342.41042504847[/C][C]9.58957495152845[/C][/ROW]
[ROW][C]122[/C][C]4229[/C][C]3990.00923738658[/C][C]238.990762613419[/C][/ROW]
[ROW][C]123[/C][C]4929[/C][C]5021.71313043903[/C][C]-92.7131304390268[/C][/ROW]
[ROW][C]124[/C][C]4671[/C][C]4986.38972099262[/C][C]-315.389720992621[/C][/ROW]
[ROW][C]125[/C][C]4935[/C][C]5094.82762088679[/C][C]-159.827620886788[/C][/ROW]
[ROW][C]126[/C][C]5557[/C][C]5450.73852531711[/C][C]106.261474682887[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299879&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299879&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
1326242515.57506033466108.424939665335
1425002437.0526624966362.9473375033731
1531603108.7212071792251.2787928207827
1628312797.6199895115133.3800104884908
1729132888.7937597774424.2062402225633
1832383222.7404156231615.2595843768395
1933403370.19026414008-30.1902641400766
2034013425.8852002465-24.8852002465032
2128982798.6998855457999.3001144542095
2230552994.3540521699460.645947830064
2328072822.31649858287-15.3164985828662
2429903059.44733996363-69.4473399636295
2527642928.77667298169-164.776672981694
2626662706.71765090311-40.7176509031146
2732463381.7397545011-135.739754501099
2831372970.10684910955166.893150890448
2932483111.13976700567136.86023299433
3034943509.09826601872-15.0982660187183
3135823629.17415403624-47.1741540362436
3237983684.81759638574113.182403614261
3331893119.1776730183569.8223269816472
3432883293.7758634177-5.77586341770075
3530753036.8921639245838.1078360754159
3632093282.77633148319-73.7763314831936
3730133084.15312345602-71.1531234560216
3828052950.64062981758-145.640629817581
3935253587.45961882635-62.4596188263454
4033913337.7486381520853.2513618479156
4135443421.82431827143122.175681728568
4237133753.08137614617-40.0813761461686
4339193852.8418363133266.1581636866758
4440414044.77551561245-3.77551561244582
4532383367.66772432143-129.667724321428
4634293430.94974508665-1.94974508664518
4731663187.36925444556-21.3692544455594
4835463357.67182525439188.328174745606
4933463247.3417432160498.6582567839591
5031593123.9740205236335.0259794763683
5139013952.73362192019-51.733621920187
5236513745.63295330757-94.6329533075727
5337763815.71139860749-39.7113986074933
5439954014.71083752342-19.7108375234152
5543254188.5043766667136.495623333303
5646134379.85559236659233.144407633407
5736563646.117073709689.88292629032276
5838043848.12371752861-44.1237175286124
5935793546.5158066033432.4841933966627
6038773876.621482433220.378517566778555
6135453623.09404820536-78.0940482053625
6235003383.06484694896116.935153051043
6343414262.3876260219878.6123739780232
6442284059.33531644465168.664683555353
6543054272.2784908606132.7215091393937
6644454536.13983746666-91.1398374666624
6748444792.8522907529351.147709247075
6849995018.3049596295-19.3049596294959
6940203984.7790741810135.2209258189869
7042144182.3782213267231.6217786732777
7139103922.47602371186-12.4760237118589
7241194245.66459130189-126.664591301889
7338613876.85643482358-15.8564348235823
7438033749.368537890653.6314621093989
7545914648.41607602373-57.4160760237264
7643174424.78879788166-107.788797881656
7744494464.34302501574-15.3430250157407
7847804651.32862399363128.671376006372
7950585084.17663411479-26.176634114795
8052615250.7032277312310.296772268769
8143644205.02613632614158.97386367386
8246054457.82649216564147.173507834356
8342954196.4336307008798.5663692991338
8444134522.35165209444-109.351652094439
8541044193.75243599222-89.7524359922245
8638344066.03723965232-232.037239652323
8746744836.57497251027-162.574972510266
8843734536.64444256026-163.644442560259
8945374606.48945767524-69.4894576752386
9050304853.9511023104176.048897689598
9152005233.54007759556-33.5400775955613
9254415421.5693190427819.4306809572199
9345014423.3539207011277.6460792988801
9447184642.1141810263175.8858189736893
9544734321.56195912181151.438040878192
9645734562.7857925210310.2142074789745
9743234279.9203708403343.0796291596653
9841014117.93559135664-16.9355913566424
9949585062.66133070322-104.661330703224
10046734764.57568360494-91.5756836049368
10147714922.80299020243-151.802990202429
10252205291.63598187968-71.6359818796791
10354885477.331738800110.6682611998995
10457845720.49727956563.502720434999
10547584713.0006284501944.9993715498131
10649484926.9911102970521.00888970295
10746084607.918663360370.0813366396305355
10847104721.37601417113-11.3760141711255
10942424438.09556363063-196.095563630627
11037104151.62157589583-441.621575895832
11144144863.19599944963-449.195999449633
11244674455.5964907038611.403509296144
11347374614.19966210131122.800337898687
11451175117.22299879428-0.222998794275554
11554465367.878966071778.1210339283034
11657355660.0346399480674.9653600519378
11747384663.5815225910574.4184774089472
11849934874.19412399974118.805876000262
11945174583.39414382029-66.3941438202928
12048094664.66670362591144.333296374089
12143524342.410425048479.58957495152845
12242293990.00923738658238.990762613419
12349295021.71313043903-92.7131304390268
12446714986.38972099262-315.389720992621
12549355094.82762088679-159.827620886788
12655575450.73852531711106.261474682887







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1275801.828247467355598.114303383596005.54219155111
1286078.176019166115855.486255623736300.8657827085
1294988.622206051474760.869482110525216.37492999242
1305203.375148934984956.976576334185449.77372153578
1314750.994832248624498.937860257465003.05180423978
1324975.695606571534704.481921587785246.90929155528
1334511.063307393024239.592062062354782.5345527237
1344261.736855897843984.996375592874538.47733620281
1355040.310864962984723.299709968235357.32201995774
1364917.901479627044595.045166225240.75779303407
1375239.121310904394891.988621910935586.25399989785
1385824.289283727395498.572857485266150.00570996952

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 5801.82824746735 & 5598.11430338359 & 6005.54219155111 \tabularnewline
128 & 6078.17601916611 & 5855.48625562373 & 6300.8657827085 \tabularnewline
129 & 4988.62220605147 & 4760.86948211052 & 5216.37492999242 \tabularnewline
130 & 5203.37514893498 & 4956.97657633418 & 5449.77372153578 \tabularnewline
131 & 4750.99483224862 & 4498.93786025746 & 5003.05180423978 \tabularnewline
132 & 4975.69560657153 & 4704.48192158778 & 5246.90929155528 \tabularnewline
133 & 4511.06330739302 & 4239.59206206235 & 4782.5345527237 \tabularnewline
134 & 4261.73685589784 & 3984.99637559287 & 4538.47733620281 \tabularnewline
135 & 5040.31086496298 & 4723.29970996823 & 5357.32201995774 \tabularnewline
136 & 4917.90147962704 & 4595.04516622 & 5240.75779303407 \tabularnewline
137 & 5239.12131090439 & 4891.98862191093 & 5586.25399989785 \tabularnewline
138 & 5824.28928372739 & 5498.57285748526 & 6150.00570996952 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299879&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]127[/C][C]5801.82824746735[/C][C]5598.11430338359[/C][C]6005.54219155111[/C][/ROW]
[ROW][C]128[/C][C]6078.17601916611[/C][C]5855.48625562373[/C][C]6300.8657827085[/C][/ROW]
[ROW][C]129[/C][C]4988.62220605147[/C][C]4760.86948211052[/C][C]5216.37492999242[/C][/ROW]
[ROW][C]130[/C][C]5203.37514893498[/C][C]4956.97657633418[/C][C]5449.77372153578[/C][/ROW]
[ROW][C]131[/C][C]4750.99483224862[/C][C]4498.93786025746[/C][C]5003.05180423978[/C][/ROW]
[ROW][C]132[/C][C]4975.69560657153[/C][C]4704.48192158778[/C][C]5246.90929155528[/C][/ROW]
[ROW][C]133[/C][C]4511.06330739302[/C][C]4239.59206206235[/C][C]4782.5345527237[/C][/ROW]
[ROW][C]134[/C][C]4261.73685589784[/C][C]3984.99637559287[/C][C]4538.47733620281[/C][/ROW]
[ROW][C]135[/C][C]5040.31086496298[/C][C]4723.29970996823[/C][C]5357.32201995774[/C][/ROW]
[ROW][C]136[/C][C]4917.90147962704[/C][C]4595.04516622[/C][C]5240.75779303407[/C][/ROW]
[ROW][C]137[/C][C]5239.12131090439[/C][C]4891.98862191093[/C][C]5586.25399989785[/C][/ROW]
[ROW][C]138[/C][C]5824.28928372739[/C][C]5498.57285748526[/C][C]6150.00570996952[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299879&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299879&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
1275801.828247467355598.114303383596005.54219155111
1286078.176019166115855.486255623736300.8657827085
1294988.622206051474760.869482110525216.37492999242
1305203.375148934984956.976576334185449.77372153578
1314750.994832248624498.937860257465003.05180423978
1324975.695606571534704.481921587785246.90929155528
1334511.063307393024239.592062062354782.5345527237
1344261.736855897843984.996375592874538.47733620281
1355040.310864962984723.299709968235357.32201995774
1364917.901479627044595.045166225240.75779303407
1375239.121310904394891.988621910935586.25399989785
1385824.289283727395498.572857485266150.00570996952



Parameters (Session):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')