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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, 22 Dec 2016 20:57:26 +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/22/t1482436653wzlemcr1miw7svh.htm/, Retrieved Mon, 29 Apr 2024 05:20:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302664, Retrieved Mon, 29 Apr 2024 05:20:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact51
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-22 19:57:26] [037fdaa34a77b5f63489b3bcd360a80c] [Current]
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Dataseries X:
3455
3585
3675
3680
3735
3860
3765
3905
4110
4170
4110
4025
4145
4285
4370
4355
4385
4525
4375
4525
4610
4595
4500
4370
4390
4530
4590
4580
4595
4685
4490
4635
4710
4655
4665
4550
4590
4675
4645
4665
4635
4720
4565
4720
4830
4830
4765
4705
4675
4900
4945
4905
4955
5120
4860
5040
5140
5240
5145
5070
5085
5215
5255
5275
5315
5450
5205
5370
5500
5490
5440
5360
5380
5460
5450
5520
5475
5600
5250
5465
5515
5425
5325
5275
5160
5360
5435
5285
5415
5575
5265
5480
5565
5500
5280
5135
5050
5100
5070
5115
5140
5330
5080
5285
5405
5385
5255
5100
5040
5235
5310
5265
5380
5465
5225
5445




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302664&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302664&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302664&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.582325806328971
beta0.119665026828977
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.582325806328971 \tabularnewline
beta & 0.119665026828977 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302664&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]0.582325806328971[/C][/ROW]
[ROW][C]beta[/C][C]0.119665026828977[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302664&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302664&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
alpha0.582325806328971
beta0.119665026828977
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
336753715-40
436803818.91960641734-138.919606417339
537353855.55529479502-120.555294795021
638603894.48421657639-34.4842165763862
737653981.13154908894-216.131549088941
839053946.94003417822-41.9400341782161
941104011.2621829078898.7378170921152
1041704164.385124139235.61487586077237
1141104263.67144072641-153.67144072641
1240254259.49277878655-234.492778786546
1341454191.9093634013-46.9093634012979
1442854230.291777995854.7082220042021
1543704331.6610245092738.338975490733
1643554426.16965079017-71.1696507901734
1743854451.9491896609-66.9491896609043
1845254475.5211224042649.4788775957413
1943754570.3400110431-195.340011043101
2045254508.9824631286116.0175368713853
2146104571.8200362988738.1799637011254
2245954650.22389640253-55.2238964025282
2345004670.38805452466-170.388054524662
2443704611.61582455335-241.615824553347
2543904494.52906081817-104.529060818168
2645304449.9874507637680.0125492362395
2745904518.4847797259371.5152202740674
2845804587.01736373514-7.0173637351354
2945954609.32939923032-14.3293992303225
3046854626.3849174276358.6150825723716
3144904690.00242517013-200.002425170132
3246354589.0833085425445.9166914574553
3347104634.5689000505175.4310999494928
3446554702.49783655794-47.4978365579436
3546654695.53224017111-30.5322401711082
3645504696.31853874119-146.318538741189
3745904619.48342171769-29.4834217176867
3846754608.629884683566.3701153164966
3946454658.21927321393-13.2192732139301
4046654660.540534619134.45946538086991
4146354673.46733526525-38.4673352652489
4247204658.7161930428161.2838069571908
4345654706.32321798822-141.323217988217
4447204626.0989719448593.9010280551547
4548304689.39527700684140.604722993159
4648304789.6862530725740.3137469274343
4747654834.38443011412-69.3844301141207
4847054810.36754082289-105.367540822892
4946754758.05432235709-83.0543223570912
5049004712.94710666653187.052893333473
5149454838.16489318448106.835106815523
5249054924.11449362071-19.1144936207065
5349554935.3884164173119.6115835826868
5451204970.58014758956149.419852410439
5548605091.77476153682-231.774761536818
5650404974.8389143624265.1610856375828
5751405035.35716107919104.642838920809
5852405126.15858667733113.841413322668
5951455230.2495083609-85.2495083609001
6050705212.4641189682-142.4641189682
6150855151.43371091846-66.4337109184644
6252155130.0484026220884.9515973779235
6352555202.7384359810152.2615640189897
6452755260.0340158694314.9659841305729
6553155296.654307262418.3456927375973
6654505336.52109205761113.478907942387
6752055439.69407109844-234.69407109844
6853705323.7625099262846.2374900737241
6955005374.64666143207125.353338567933
7054905480.337139416869.6628605831429
7154405519.33141362261-79.3314136226145
7253605500.97389247918-140.973892479182
7353805436.89673572233-56.8967357223346
7454605417.8150830445842.1849169554189
7554505459.37084881005-9.37084881005376
7655205470.251363165349.7486368347036
7754755519.02536533109-44.0253653310883
7856005510.1244810519689.8755189480362
7952505585.46042582846-335.460425828462
8054655389.7360381389775.2639618610274
8155155438.4317571096576.5682428903474
8254255493.22257656492-68.2225765649237
8353255458.94394103897-133.94394103897
8452755377.0603049133-102.060304913297
8551605306.63135922339-146.631359223392
8653605200.02967388364159.970326116363
8754355283.11743970329151.882560296708
8852855372.07928015054-87.0792801505386
8954155315.8194387251799.1805612748258
9055755374.93481117294200.065188827063
9152655506.73925497416-241.739254974158
9254805364.42420352067115.575796479332
9355655438.23671516163126.763284838367
9455005527.39736693605-27.3973669360485
9552805524.87713383353-244.877133833535
9651355378.64879377903-243.648793779031
9750505216.15731719322-166.157317193221
9851005087.2126151799112.7873848200907
9950705063.363107603626.63689239637915
10051155036.3944949977278.6055050022815
10151405056.8126113811683.1873886188396
10253305085.69570958958244.30429041042
10350805225.42544584005-145.425445840047
10452855128.07166757658156.928332423422
10554055217.7216961695187.278303830497
10653855338.0956038829146.9043961170864
10752555379.99465009757-124.994650097575
10851005313.08231426619-213.082314266186
10950405180.02582330051-140.025823300512
11052355079.754448219155.245551780999
11153105162.24535090798147.754649092016
11252655250.6702475268114.3297524731943
11353805262.39693858534117.603061414658
11454655342.45739818593122.542601814066
11552255433.93354237034-208.933542370335
11654455317.82324170276127.176758297241

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3675 & 3715 & -40 \tabularnewline
4 & 3680 & 3818.91960641734 & -138.919606417339 \tabularnewline
5 & 3735 & 3855.55529479502 & -120.555294795021 \tabularnewline
6 & 3860 & 3894.48421657639 & -34.4842165763862 \tabularnewline
7 & 3765 & 3981.13154908894 & -216.131549088941 \tabularnewline
8 & 3905 & 3946.94003417822 & -41.9400341782161 \tabularnewline
9 & 4110 & 4011.26218290788 & 98.7378170921152 \tabularnewline
10 & 4170 & 4164.38512413923 & 5.61487586077237 \tabularnewline
11 & 4110 & 4263.67144072641 & -153.67144072641 \tabularnewline
12 & 4025 & 4259.49277878655 & -234.492778786546 \tabularnewline
13 & 4145 & 4191.9093634013 & -46.9093634012979 \tabularnewline
14 & 4285 & 4230.2917779958 & 54.7082220042021 \tabularnewline
15 & 4370 & 4331.66102450927 & 38.338975490733 \tabularnewline
16 & 4355 & 4426.16965079017 & -71.1696507901734 \tabularnewline
17 & 4385 & 4451.9491896609 & -66.9491896609043 \tabularnewline
18 & 4525 & 4475.52112240426 & 49.4788775957413 \tabularnewline
19 & 4375 & 4570.3400110431 & -195.340011043101 \tabularnewline
20 & 4525 & 4508.98246312861 & 16.0175368713853 \tabularnewline
21 & 4610 & 4571.82003629887 & 38.1799637011254 \tabularnewline
22 & 4595 & 4650.22389640253 & -55.2238964025282 \tabularnewline
23 & 4500 & 4670.38805452466 & -170.388054524662 \tabularnewline
24 & 4370 & 4611.61582455335 & -241.615824553347 \tabularnewline
25 & 4390 & 4494.52906081817 & -104.529060818168 \tabularnewline
26 & 4530 & 4449.98745076376 & 80.0125492362395 \tabularnewline
27 & 4590 & 4518.48477972593 & 71.5152202740674 \tabularnewline
28 & 4580 & 4587.01736373514 & -7.0173637351354 \tabularnewline
29 & 4595 & 4609.32939923032 & -14.3293992303225 \tabularnewline
30 & 4685 & 4626.38491742763 & 58.6150825723716 \tabularnewline
31 & 4490 & 4690.00242517013 & -200.002425170132 \tabularnewline
32 & 4635 & 4589.08330854254 & 45.9166914574553 \tabularnewline
33 & 4710 & 4634.56890005051 & 75.4310999494928 \tabularnewline
34 & 4655 & 4702.49783655794 & -47.4978365579436 \tabularnewline
35 & 4665 & 4695.53224017111 & -30.5322401711082 \tabularnewline
36 & 4550 & 4696.31853874119 & -146.318538741189 \tabularnewline
37 & 4590 & 4619.48342171769 & -29.4834217176867 \tabularnewline
38 & 4675 & 4608.6298846835 & 66.3701153164966 \tabularnewline
39 & 4645 & 4658.21927321393 & -13.2192732139301 \tabularnewline
40 & 4665 & 4660.54053461913 & 4.45946538086991 \tabularnewline
41 & 4635 & 4673.46733526525 & -38.4673352652489 \tabularnewline
42 & 4720 & 4658.71619304281 & 61.2838069571908 \tabularnewline
43 & 4565 & 4706.32321798822 & -141.323217988217 \tabularnewline
44 & 4720 & 4626.09897194485 & 93.9010280551547 \tabularnewline
45 & 4830 & 4689.39527700684 & 140.604722993159 \tabularnewline
46 & 4830 & 4789.68625307257 & 40.3137469274343 \tabularnewline
47 & 4765 & 4834.38443011412 & -69.3844301141207 \tabularnewline
48 & 4705 & 4810.36754082289 & -105.367540822892 \tabularnewline
49 & 4675 & 4758.05432235709 & -83.0543223570912 \tabularnewline
50 & 4900 & 4712.94710666653 & 187.052893333473 \tabularnewline
51 & 4945 & 4838.16489318448 & 106.835106815523 \tabularnewline
52 & 4905 & 4924.11449362071 & -19.1144936207065 \tabularnewline
53 & 4955 & 4935.38841641731 & 19.6115835826868 \tabularnewline
54 & 5120 & 4970.58014758956 & 149.419852410439 \tabularnewline
55 & 4860 & 5091.77476153682 & -231.774761536818 \tabularnewline
56 & 5040 & 4974.83891436242 & 65.1610856375828 \tabularnewline
57 & 5140 & 5035.35716107919 & 104.642838920809 \tabularnewline
58 & 5240 & 5126.15858667733 & 113.841413322668 \tabularnewline
59 & 5145 & 5230.2495083609 & -85.2495083609001 \tabularnewline
60 & 5070 & 5212.4641189682 & -142.4641189682 \tabularnewline
61 & 5085 & 5151.43371091846 & -66.4337109184644 \tabularnewline
62 & 5215 & 5130.04840262208 & 84.9515973779235 \tabularnewline
63 & 5255 & 5202.73843598101 & 52.2615640189897 \tabularnewline
64 & 5275 & 5260.03401586943 & 14.9659841305729 \tabularnewline
65 & 5315 & 5296.6543072624 & 18.3456927375973 \tabularnewline
66 & 5450 & 5336.52109205761 & 113.478907942387 \tabularnewline
67 & 5205 & 5439.69407109844 & -234.69407109844 \tabularnewline
68 & 5370 & 5323.76250992628 & 46.2374900737241 \tabularnewline
69 & 5500 & 5374.64666143207 & 125.353338567933 \tabularnewline
70 & 5490 & 5480.33713941686 & 9.6628605831429 \tabularnewline
71 & 5440 & 5519.33141362261 & -79.3314136226145 \tabularnewline
72 & 5360 & 5500.97389247918 & -140.973892479182 \tabularnewline
73 & 5380 & 5436.89673572233 & -56.8967357223346 \tabularnewline
74 & 5460 & 5417.81508304458 & 42.1849169554189 \tabularnewline
75 & 5450 & 5459.37084881005 & -9.37084881005376 \tabularnewline
76 & 5520 & 5470.2513631653 & 49.7486368347036 \tabularnewline
77 & 5475 & 5519.02536533109 & -44.0253653310883 \tabularnewline
78 & 5600 & 5510.12448105196 & 89.8755189480362 \tabularnewline
79 & 5250 & 5585.46042582846 & -335.460425828462 \tabularnewline
80 & 5465 & 5389.73603813897 & 75.2639618610274 \tabularnewline
81 & 5515 & 5438.43175710965 & 76.5682428903474 \tabularnewline
82 & 5425 & 5493.22257656492 & -68.2225765649237 \tabularnewline
83 & 5325 & 5458.94394103897 & -133.94394103897 \tabularnewline
84 & 5275 & 5377.0603049133 & -102.060304913297 \tabularnewline
85 & 5160 & 5306.63135922339 & -146.631359223392 \tabularnewline
86 & 5360 & 5200.02967388364 & 159.970326116363 \tabularnewline
87 & 5435 & 5283.11743970329 & 151.882560296708 \tabularnewline
88 & 5285 & 5372.07928015054 & -87.0792801505386 \tabularnewline
89 & 5415 & 5315.81943872517 & 99.1805612748258 \tabularnewline
90 & 5575 & 5374.93481117294 & 200.065188827063 \tabularnewline
91 & 5265 & 5506.73925497416 & -241.739254974158 \tabularnewline
92 & 5480 & 5364.42420352067 & 115.575796479332 \tabularnewline
93 & 5565 & 5438.23671516163 & 126.763284838367 \tabularnewline
94 & 5500 & 5527.39736693605 & -27.3973669360485 \tabularnewline
95 & 5280 & 5524.87713383353 & -244.877133833535 \tabularnewline
96 & 5135 & 5378.64879377903 & -243.648793779031 \tabularnewline
97 & 5050 & 5216.15731719322 & -166.157317193221 \tabularnewline
98 & 5100 & 5087.21261517991 & 12.7873848200907 \tabularnewline
99 & 5070 & 5063.36310760362 & 6.63689239637915 \tabularnewline
100 & 5115 & 5036.39449499772 & 78.6055050022815 \tabularnewline
101 & 5140 & 5056.81261138116 & 83.1873886188396 \tabularnewline
102 & 5330 & 5085.69570958958 & 244.30429041042 \tabularnewline
103 & 5080 & 5225.42544584005 & -145.425445840047 \tabularnewline
104 & 5285 & 5128.07166757658 & 156.928332423422 \tabularnewline
105 & 5405 & 5217.7216961695 & 187.278303830497 \tabularnewline
106 & 5385 & 5338.09560388291 & 46.9043961170864 \tabularnewline
107 & 5255 & 5379.99465009757 & -124.994650097575 \tabularnewline
108 & 5100 & 5313.08231426619 & -213.082314266186 \tabularnewline
109 & 5040 & 5180.02582330051 & -140.025823300512 \tabularnewline
110 & 5235 & 5079.754448219 & 155.245551780999 \tabularnewline
111 & 5310 & 5162.24535090798 & 147.754649092016 \tabularnewline
112 & 5265 & 5250.67024752681 & 14.3297524731943 \tabularnewline
113 & 5380 & 5262.39693858534 & 117.603061414658 \tabularnewline
114 & 5465 & 5342.45739818593 & 122.542601814066 \tabularnewline
115 & 5225 & 5433.93354237034 & -208.933542370335 \tabularnewline
116 & 5445 & 5317.82324170276 & 127.176758297241 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302664&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]3[/C][C]3675[/C][C]3715[/C][C]-40[/C][/ROW]
[ROW][C]4[/C][C]3680[/C][C]3818.91960641734[/C][C]-138.919606417339[/C][/ROW]
[ROW][C]5[/C][C]3735[/C][C]3855.55529479502[/C][C]-120.555294795021[/C][/ROW]
[ROW][C]6[/C][C]3860[/C][C]3894.48421657639[/C][C]-34.4842165763862[/C][/ROW]
[ROW][C]7[/C][C]3765[/C][C]3981.13154908894[/C][C]-216.131549088941[/C][/ROW]
[ROW][C]8[/C][C]3905[/C][C]3946.94003417822[/C][C]-41.9400341782161[/C][/ROW]
[ROW][C]9[/C][C]4110[/C][C]4011.26218290788[/C][C]98.7378170921152[/C][/ROW]
[ROW][C]10[/C][C]4170[/C][C]4164.38512413923[/C][C]5.61487586077237[/C][/ROW]
[ROW][C]11[/C][C]4110[/C][C]4263.67144072641[/C][C]-153.67144072641[/C][/ROW]
[ROW][C]12[/C][C]4025[/C][C]4259.49277878655[/C][C]-234.492778786546[/C][/ROW]
[ROW][C]13[/C][C]4145[/C][C]4191.9093634013[/C][C]-46.9093634012979[/C][/ROW]
[ROW][C]14[/C][C]4285[/C][C]4230.2917779958[/C][C]54.7082220042021[/C][/ROW]
[ROW][C]15[/C][C]4370[/C][C]4331.66102450927[/C][C]38.338975490733[/C][/ROW]
[ROW][C]16[/C][C]4355[/C][C]4426.16965079017[/C][C]-71.1696507901734[/C][/ROW]
[ROW][C]17[/C][C]4385[/C][C]4451.9491896609[/C][C]-66.9491896609043[/C][/ROW]
[ROW][C]18[/C][C]4525[/C][C]4475.52112240426[/C][C]49.4788775957413[/C][/ROW]
[ROW][C]19[/C][C]4375[/C][C]4570.3400110431[/C][C]-195.340011043101[/C][/ROW]
[ROW][C]20[/C][C]4525[/C][C]4508.98246312861[/C][C]16.0175368713853[/C][/ROW]
[ROW][C]21[/C][C]4610[/C][C]4571.82003629887[/C][C]38.1799637011254[/C][/ROW]
[ROW][C]22[/C][C]4595[/C][C]4650.22389640253[/C][C]-55.2238964025282[/C][/ROW]
[ROW][C]23[/C][C]4500[/C][C]4670.38805452466[/C][C]-170.388054524662[/C][/ROW]
[ROW][C]24[/C][C]4370[/C][C]4611.61582455335[/C][C]-241.615824553347[/C][/ROW]
[ROW][C]25[/C][C]4390[/C][C]4494.52906081817[/C][C]-104.529060818168[/C][/ROW]
[ROW][C]26[/C][C]4530[/C][C]4449.98745076376[/C][C]80.0125492362395[/C][/ROW]
[ROW][C]27[/C][C]4590[/C][C]4518.48477972593[/C][C]71.5152202740674[/C][/ROW]
[ROW][C]28[/C][C]4580[/C][C]4587.01736373514[/C][C]-7.0173637351354[/C][/ROW]
[ROW][C]29[/C][C]4595[/C][C]4609.32939923032[/C][C]-14.3293992303225[/C][/ROW]
[ROW][C]30[/C][C]4685[/C][C]4626.38491742763[/C][C]58.6150825723716[/C][/ROW]
[ROW][C]31[/C][C]4490[/C][C]4690.00242517013[/C][C]-200.002425170132[/C][/ROW]
[ROW][C]32[/C][C]4635[/C][C]4589.08330854254[/C][C]45.9166914574553[/C][/ROW]
[ROW][C]33[/C][C]4710[/C][C]4634.56890005051[/C][C]75.4310999494928[/C][/ROW]
[ROW][C]34[/C][C]4655[/C][C]4702.49783655794[/C][C]-47.4978365579436[/C][/ROW]
[ROW][C]35[/C][C]4665[/C][C]4695.53224017111[/C][C]-30.5322401711082[/C][/ROW]
[ROW][C]36[/C][C]4550[/C][C]4696.31853874119[/C][C]-146.318538741189[/C][/ROW]
[ROW][C]37[/C][C]4590[/C][C]4619.48342171769[/C][C]-29.4834217176867[/C][/ROW]
[ROW][C]38[/C][C]4675[/C][C]4608.6298846835[/C][C]66.3701153164966[/C][/ROW]
[ROW][C]39[/C][C]4645[/C][C]4658.21927321393[/C][C]-13.2192732139301[/C][/ROW]
[ROW][C]40[/C][C]4665[/C][C]4660.54053461913[/C][C]4.45946538086991[/C][/ROW]
[ROW][C]41[/C][C]4635[/C][C]4673.46733526525[/C][C]-38.4673352652489[/C][/ROW]
[ROW][C]42[/C][C]4720[/C][C]4658.71619304281[/C][C]61.2838069571908[/C][/ROW]
[ROW][C]43[/C][C]4565[/C][C]4706.32321798822[/C][C]-141.323217988217[/C][/ROW]
[ROW][C]44[/C][C]4720[/C][C]4626.09897194485[/C][C]93.9010280551547[/C][/ROW]
[ROW][C]45[/C][C]4830[/C][C]4689.39527700684[/C][C]140.604722993159[/C][/ROW]
[ROW][C]46[/C][C]4830[/C][C]4789.68625307257[/C][C]40.3137469274343[/C][/ROW]
[ROW][C]47[/C][C]4765[/C][C]4834.38443011412[/C][C]-69.3844301141207[/C][/ROW]
[ROW][C]48[/C][C]4705[/C][C]4810.36754082289[/C][C]-105.367540822892[/C][/ROW]
[ROW][C]49[/C][C]4675[/C][C]4758.05432235709[/C][C]-83.0543223570912[/C][/ROW]
[ROW][C]50[/C][C]4900[/C][C]4712.94710666653[/C][C]187.052893333473[/C][/ROW]
[ROW][C]51[/C][C]4945[/C][C]4838.16489318448[/C][C]106.835106815523[/C][/ROW]
[ROW][C]52[/C][C]4905[/C][C]4924.11449362071[/C][C]-19.1144936207065[/C][/ROW]
[ROW][C]53[/C][C]4955[/C][C]4935.38841641731[/C][C]19.6115835826868[/C][/ROW]
[ROW][C]54[/C][C]5120[/C][C]4970.58014758956[/C][C]149.419852410439[/C][/ROW]
[ROW][C]55[/C][C]4860[/C][C]5091.77476153682[/C][C]-231.774761536818[/C][/ROW]
[ROW][C]56[/C][C]5040[/C][C]4974.83891436242[/C][C]65.1610856375828[/C][/ROW]
[ROW][C]57[/C][C]5140[/C][C]5035.35716107919[/C][C]104.642838920809[/C][/ROW]
[ROW][C]58[/C][C]5240[/C][C]5126.15858667733[/C][C]113.841413322668[/C][/ROW]
[ROW][C]59[/C][C]5145[/C][C]5230.2495083609[/C][C]-85.2495083609001[/C][/ROW]
[ROW][C]60[/C][C]5070[/C][C]5212.4641189682[/C][C]-142.4641189682[/C][/ROW]
[ROW][C]61[/C][C]5085[/C][C]5151.43371091846[/C][C]-66.4337109184644[/C][/ROW]
[ROW][C]62[/C][C]5215[/C][C]5130.04840262208[/C][C]84.9515973779235[/C][/ROW]
[ROW][C]63[/C][C]5255[/C][C]5202.73843598101[/C][C]52.2615640189897[/C][/ROW]
[ROW][C]64[/C][C]5275[/C][C]5260.03401586943[/C][C]14.9659841305729[/C][/ROW]
[ROW][C]65[/C][C]5315[/C][C]5296.6543072624[/C][C]18.3456927375973[/C][/ROW]
[ROW][C]66[/C][C]5450[/C][C]5336.52109205761[/C][C]113.478907942387[/C][/ROW]
[ROW][C]67[/C][C]5205[/C][C]5439.69407109844[/C][C]-234.69407109844[/C][/ROW]
[ROW][C]68[/C][C]5370[/C][C]5323.76250992628[/C][C]46.2374900737241[/C][/ROW]
[ROW][C]69[/C][C]5500[/C][C]5374.64666143207[/C][C]125.353338567933[/C][/ROW]
[ROW][C]70[/C][C]5490[/C][C]5480.33713941686[/C][C]9.6628605831429[/C][/ROW]
[ROW][C]71[/C][C]5440[/C][C]5519.33141362261[/C][C]-79.3314136226145[/C][/ROW]
[ROW][C]72[/C][C]5360[/C][C]5500.97389247918[/C][C]-140.973892479182[/C][/ROW]
[ROW][C]73[/C][C]5380[/C][C]5436.89673572233[/C][C]-56.8967357223346[/C][/ROW]
[ROW][C]74[/C][C]5460[/C][C]5417.81508304458[/C][C]42.1849169554189[/C][/ROW]
[ROW][C]75[/C][C]5450[/C][C]5459.37084881005[/C][C]-9.37084881005376[/C][/ROW]
[ROW][C]76[/C][C]5520[/C][C]5470.2513631653[/C][C]49.7486368347036[/C][/ROW]
[ROW][C]77[/C][C]5475[/C][C]5519.02536533109[/C][C]-44.0253653310883[/C][/ROW]
[ROW][C]78[/C][C]5600[/C][C]5510.12448105196[/C][C]89.8755189480362[/C][/ROW]
[ROW][C]79[/C][C]5250[/C][C]5585.46042582846[/C][C]-335.460425828462[/C][/ROW]
[ROW][C]80[/C][C]5465[/C][C]5389.73603813897[/C][C]75.2639618610274[/C][/ROW]
[ROW][C]81[/C][C]5515[/C][C]5438.43175710965[/C][C]76.5682428903474[/C][/ROW]
[ROW][C]82[/C][C]5425[/C][C]5493.22257656492[/C][C]-68.2225765649237[/C][/ROW]
[ROW][C]83[/C][C]5325[/C][C]5458.94394103897[/C][C]-133.94394103897[/C][/ROW]
[ROW][C]84[/C][C]5275[/C][C]5377.0603049133[/C][C]-102.060304913297[/C][/ROW]
[ROW][C]85[/C][C]5160[/C][C]5306.63135922339[/C][C]-146.631359223392[/C][/ROW]
[ROW][C]86[/C][C]5360[/C][C]5200.02967388364[/C][C]159.970326116363[/C][/ROW]
[ROW][C]87[/C][C]5435[/C][C]5283.11743970329[/C][C]151.882560296708[/C][/ROW]
[ROW][C]88[/C][C]5285[/C][C]5372.07928015054[/C][C]-87.0792801505386[/C][/ROW]
[ROW][C]89[/C][C]5415[/C][C]5315.81943872517[/C][C]99.1805612748258[/C][/ROW]
[ROW][C]90[/C][C]5575[/C][C]5374.93481117294[/C][C]200.065188827063[/C][/ROW]
[ROW][C]91[/C][C]5265[/C][C]5506.73925497416[/C][C]-241.739254974158[/C][/ROW]
[ROW][C]92[/C][C]5480[/C][C]5364.42420352067[/C][C]115.575796479332[/C][/ROW]
[ROW][C]93[/C][C]5565[/C][C]5438.23671516163[/C][C]126.763284838367[/C][/ROW]
[ROW][C]94[/C][C]5500[/C][C]5527.39736693605[/C][C]-27.3973669360485[/C][/ROW]
[ROW][C]95[/C][C]5280[/C][C]5524.87713383353[/C][C]-244.877133833535[/C][/ROW]
[ROW][C]96[/C][C]5135[/C][C]5378.64879377903[/C][C]-243.648793779031[/C][/ROW]
[ROW][C]97[/C][C]5050[/C][C]5216.15731719322[/C][C]-166.157317193221[/C][/ROW]
[ROW][C]98[/C][C]5100[/C][C]5087.21261517991[/C][C]12.7873848200907[/C][/ROW]
[ROW][C]99[/C][C]5070[/C][C]5063.36310760362[/C][C]6.63689239637915[/C][/ROW]
[ROW][C]100[/C][C]5115[/C][C]5036.39449499772[/C][C]78.6055050022815[/C][/ROW]
[ROW][C]101[/C][C]5140[/C][C]5056.81261138116[/C][C]83.1873886188396[/C][/ROW]
[ROW][C]102[/C][C]5330[/C][C]5085.69570958958[/C][C]244.30429041042[/C][/ROW]
[ROW][C]103[/C][C]5080[/C][C]5225.42544584005[/C][C]-145.425445840047[/C][/ROW]
[ROW][C]104[/C][C]5285[/C][C]5128.07166757658[/C][C]156.928332423422[/C][/ROW]
[ROW][C]105[/C][C]5405[/C][C]5217.7216961695[/C][C]187.278303830497[/C][/ROW]
[ROW][C]106[/C][C]5385[/C][C]5338.09560388291[/C][C]46.9043961170864[/C][/ROW]
[ROW][C]107[/C][C]5255[/C][C]5379.99465009757[/C][C]-124.994650097575[/C][/ROW]
[ROW][C]108[/C][C]5100[/C][C]5313.08231426619[/C][C]-213.082314266186[/C][/ROW]
[ROW][C]109[/C][C]5040[/C][C]5180.02582330051[/C][C]-140.025823300512[/C][/ROW]
[ROW][C]110[/C][C]5235[/C][C]5079.754448219[/C][C]155.245551780999[/C][/ROW]
[ROW][C]111[/C][C]5310[/C][C]5162.24535090798[/C][C]147.754649092016[/C][/ROW]
[ROW][C]112[/C][C]5265[/C][C]5250.67024752681[/C][C]14.3297524731943[/C][/ROW]
[ROW][C]113[/C][C]5380[/C][C]5262.39693858534[/C][C]117.603061414658[/C][/ROW]
[ROW][C]114[/C][C]5465[/C][C]5342.45739818593[/C][C]122.542601814066[/C][/ROW]
[ROW][C]115[/C][C]5225[/C][C]5433.93354237034[/C][C]-208.933542370335[/C][/ROW]
[ROW][C]116[/C][C]5445[/C][C]5317.82324170276[/C][C]127.176758297241[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302664&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302664&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
336753715-40
436803818.91960641734-138.919606417339
537353855.55529479502-120.555294795021
638603894.48421657639-34.4842165763862
737653981.13154908894-216.131549088941
839053946.94003417822-41.9400341782161
941104011.2621829078898.7378170921152
1041704164.385124139235.61487586077237
1141104263.67144072641-153.67144072641
1240254259.49277878655-234.492778786546
1341454191.9093634013-46.9093634012979
1442854230.291777995854.7082220042021
1543704331.6610245092738.338975490733
1643554426.16965079017-71.1696507901734
1743854451.9491896609-66.9491896609043
1845254475.5211224042649.4788775957413
1943754570.3400110431-195.340011043101
2045254508.9824631286116.0175368713853
2146104571.8200362988738.1799637011254
2245954650.22389640253-55.2238964025282
2345004670.38805452466-170.388054524662
2443704611.61582455335-241.615824553347
2543904494.52906081817-104.529060818168
2645304449.9874507637680.0125492362395
2745904518.4847797259371.5152202740674
2845804587.01736373514-7.0173637351354
2945954609.32939923032-14.3293992303225
3046854626.3849174276358.6150825723716
3144904690.00242517013-200.002425170132
3246354589.0833085425445.9166914574553
3347104634.5689000505175.4310999494928
3446554702.49783655794-47.4978365579436
3546654695.53224017111-30.5322401711082
3645504696.31853874119-146.318538741189
3745904619.48342171769-29.4834217176867
3846754608.629884683566.3701153164966
3946454658.21927321393-13.2192732139301
4046654660.540534619134.45946538086991
4146354673.46733526525-38.4673352652489
4247204658.7161930428161.2838069571908
4345654706.32321798822-141.323217988217
4447204626.0989719448593.9010280551547
4548304689.39527700684140.604722993159
4648304789.6862530725740.3137469274343
4747654834.38443011412-69.3844301141207
4847054810.36754082289-105.367540822892
4946754758.05432235709-83.0543223570912
5049004712.94710666653187.052893333473
5149454838.16489318448106.835106815523
5249054924.11449362071-19.1144936207065
5349554935.3884164173119.6115835826868
5451204970.58014758956149.419852410439
5548605091.77476153682-231.774761536818
5650404974.8389143624265.1610856375828
5751405035.35716107919104.642838920809
5852405126.15858667733113.841413322668
5951455230.2495083609-85.2495083609001
6050705212.4641189682-142.4641189682
6150855151.43371091846-66.4337109184644
6252155130.0484026220884.9515973779235
6352555202.7384359810152.2615640189897
6452755260.0340158694314.9659841305729
6553155296.654307262418.3456927375973
6654505336.52109205761113.478907942387
6752055439.69407109844-234.69407109844
6853705323.7625099262846.2374900737241
6955005374.64666143207125.353338567933
7054905480.337139416869.6628605831429
7154405519.33141362261-79.3314136226145
7253605500.97389247918-140.973892479182
7353805436.89673572233-56.8967357223346
7454605417.8150830445842.1849169554189
7554505459.37084881005-9.37084881005376
7655205470.251363165349.7486368347036
7754755519.02536533109-44.0253653310883
7856005510.1244810519689.8755189480362
7952505585.46042582846-335.460425828462
8054655389.7360381389775.2639618610274
8155155438.4317571096576.5682428903474
8254255493.22257656492-68.2225765649237
8353255458.94394103897-133.94394103897
8452755377.0603049133-102.060304913297
8551605306.63135922339-146.631359223392
8653605200.02967388364159.970326116363
8754355283.11743970329151.882560296708
8852855372.07928015054-87.0792801505386
8954155315.8194387251799.1805612748258
9055755374.93481117294200.065188827063
9152655506.73925497416-241.739254974158
9254805364.42420352067115.575796479332
9355655438.23671516163126.763284838367
9455005527.39736693605-27.3973669360485
9552805524.87713383353-244.877133833535
9651355378.64879377903-243.648793779031
9750505216.15731719322-166.157317193221
9851005087.2126151799112.7873848200907
9950705063.363107603626.63689239637915
10051155036.3944949977278.6055050022815
10151405056.8126113811683.1873886188396
10253305085.69570958958244.30429041042
10350805225.42544584005-145.425445840047
10452855128.07166757658156.928332423422
10554055217.7216961695187.278303830497
10653855338.0956038829146.9043961170864
10752555379.99465009757-124.994650097575
10851005313.08231426619-213.082314266186
10950405180.02582330051-140.025823300512
11052355079.754448219155.245551780999
11153105162.24535090798147.754649092016
11252655250.6702475268114.3297524731943
11353805262.39693858534117.603061414658
11454655342.45739818593122.542601814066
11552255433.93354237034-208.933542370335
11654455317.82324170276127.176758297241







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1175406.300832339145166.199281901775646.4023827765
1185420.720114653765134.091068062445707.34916124509
1195435.139396968395100.203424568985770.07536936781
1205449.558679283025064.479064951065834.63829361499
1215463.977961597655026.909670903455901.04625229185
1225478.397243912284987.511189154385969.28329867019
1235492.816526226914946.311757235736039.32129521809
1245507.235808541544903.345428478186111.1261886049
1255521.655090856174858.648775920616184.66140579173
1265536.07437317084812.259010565156259.88973577645
1275550.493655485434764.212931626976336.77437934388
1285564.912937800064714.546348953536415.27952664658

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 5406.30083233914 & 5166.19928190177 & 5646.4023827765 \tabularnewline
118 & 5420.72011465376 & 5134.09106806244 & 5707.34916124509 \tabularnewline
119 & 5435.13939696839 & 5100.20342456898 & 5770.07536936781 \tabularnewline
120 & 5449.55867928302 & 5064.47906495106 & 5834.63829361499 \tabularnewline
121 & 5463.97796159765 & 5026.90967090345 & 5901.04625229185 \tabularnewline
122 & 5478.39724391228 & 4987.51118915438 & 5969.28329867019 \tabularnewline
123 & 5492.81652622691 & 4946.31175723573 & 6039.32129521809 \tabularnewline
124 & 5507.23580854154 & 4903.34542847818 & 6111.1261886049 \tabularnewline
125 & 5521.65509085617 & 4858.64877592061 & 6184.66140579173 \tabularnewline
126 & 5536.0743731708 & 4812.25901056515 & 6259.88973577645 \tabularnewline
127 & 5550.49365548543 & 4764.21293162697 & 6336.77437934388 \tabularnewline
128 & 5564.91293780006 & 4714.54634895353 & 6415.27952664658 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302664&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]117[/C][C]5406.30083233914[/C][C]5166.19928190177[/C][C]5646.4023827765[/C][/ROW]
[ROW][C]118[/C][C]5420.72011465376[/C][C]5134.09106806244[/C][C]5707.34916124509[/C][/ROW]
[ROW][C]119[/C][C]5435.13939696839[/C][C]5100.20342456898[/C][C]5770.07536936781[/C][/ROW]
[ROW][C]120[/C][C]5449.55867928302[/C][C]5064.47906495106[/C][C]5834.63829361499[/C][/ROW]
[ROW][C]121[/C][C]5463.97796159765[/C][C]5026.90967090345[/C][C]5901.04625229185[/C][/ROW]
[ROW][C]122[/C][C]5478.39724391228[/C][C]4987.51118915438[/C][C]5969.28329867019[/C][/ROW]
[ROW][C]123[/C][C]5492.81652622691[/C][C]4946.31175723573[/C][C]6039.32129521809[/C][/ROW]
[ROW][C]124[/C][C]5507.23580854154[/C][C]4903.34542847818[/C][C]6111.1261886049[/C][/ROW]
[ROW][C]125[/C][C]5521.65509085617[/C][C]4858.64877592061[/C][C]6184.66140579173[/C][/ROW]
[ROW][C]126[/C][C]5536.0743731708[/C][C]4812.25901056515[/C][C]6259.88973577645[/C][/ROW]
[ROW][C]127[/C][C]5550.49365548543[/C][C]4764.21293162697[/C][C]6336.77437934388[/C][/ROW]
[ROW][C]128[/C][C]5564.91293780006[/C][C]4714.54634895353[/C][C]6415.27952664658[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302664&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302664&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
1175406.300832339145166.199281901775646.4023827765
1185420.720114653765134.091068062445707.34916124509
1195435.139396968395100.203424568985770.07536936781
1205449.558679283025064.479064951065834.63829361499
1215463.977961597655026.909670903455901.04625229185
1225478.397243912284987.511189154385969.28329867019
1235492.816526226914946.311757235736039.32129521809
1245507.235808541544903.345428478186111.1261886049
1255521.655090856174858.648775920616184.66140579173
1265536.07437317084812.259010565156259.88973577645
1275550.493655485434764.212931626976336.77437934388
1285564.912937800064714.546348953536415.27952664658



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; 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')