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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 computationMon, 19 Dec 2016 23:43:23 +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/19/t1482187449sw3gjo3195zz9g9.htm/, Retrieved Fri, 17 May 2024 18:27:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301541, Retrieved Fri, 17 May 2024 18:27:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-19 22:43:23] [070714f07871aeb0c40d04255feda5cb] [Current]
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Dataseries X:
5276
4874
5374
5154
5384
5188
5368
5352
5220
5394
5218
5330
5392
4904
5394
5266
5352
5200
5354
5382
5270
5438
5262
5206
5498
5148
5376
5318
5552
5312
5508
5462
5396
5522
5388
5516
5418
5054
5638
5426
5662
5414
5548
5458
5372
5562
5342
5598
5664
5138
5588
5318
5480
5174
5368
5192
4996
5220
5048
5178
5258
4698
5248
5098
5168
4968
5116
5090
4924
5186
5038
5156
5114
4856
5192
4972
5102
4902
4984
5010
4736
4974
4814
4924
4922
4362
4696
4662
4846
4574
4616
4678
4528
4620
4522
4548
4678
4198
4608
4444
4544
4264
4448
4518
4334
4676
4432
4550
4650
4276
4678
4506
4594
4392
4556
4536
4420
4612
4396
4526
4564
4286
4556
4376
4444
4300




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=301541&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=301541&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301541&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
alpha0.486569439933574
beta0.040522379373557
gamma0.257385342811082

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.486569439933574 \tabularnewline
beta & 0.040522379373557 \tabularnewline
gamma & 0.257385342811082 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301541&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]0.486569439933574[/C][/ROW]
[ROW][C]beta[/C][C]0.040522379373557[/C][/ROW]
[ROW][C]gamma[/C][C]0.257385342811082[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301541&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301541&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
alpha0.486569439933574
beta0.040522379373557
gamma0.257385342811082







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1353925379.3012820512812.6987179487169
1449044899.175691581794.82430841821224
1553945390.647108065363.35289193464268
1652665262.885353728723.11464627127953
1753525349.319087662372.68091233763334
1852005204.59463933721-4.59463933720781
1953545397.23953762773-43.2395376277327
2053825355.8117908705326.1882091294665
2152705236.6818156164533.31818438355
2254385424.2613347852713.7386652147325
2352625254.751609539457.24839046054785
2452065374.39349777085-168.393497770849
2554985356.18133363545141.818666364552
2651484938.23643169703209.763568302971
2753765533.66682639807-157.66682639807
2853185328.78774015045-10.7877401504538
2955525409.38699361033142.613006389674
3053125335.53411332236-23.5341133223646
3155085517.22965758712-9.22965758712417
3254625505.56841157417-43.5684115741697
3353965356.1073216109139.8926783890893
3455225547.09609643086-25.0960964308633
3553885359.8649047508928.1350952491102
3655165468.9024879012947.0975120987132
3754185603.22872263278-185.228722632784
3850545035.3757394575418.6242605424641
3956385485.72345936945152.276540630545
4054265453.65009420008-27.6500942000766
4156625548.57075200163113.429247998371
4254145440.24055151975-26.2405515197515
4355485624.13505333591-76.1350533359091
4454585575.68816773758-117.688167737579
4553725400.03692581179-28.0369258117871
4655625546.8905472236615.1094527763353
4753425384.55490357491-42.5549035749109
4855985458.60725730213139.392742697872
4956645605.8640051467558.1359948532518
5051385186.88660689376-48.8866068937623
5155885624.23925612599-36.2392561259885
5253185475.13726573822-157.137265738223
5354805521.61851075115-41.6185107511519
5451745312.25396884395-138.253968843953
5553685425.70852229801-57.7085222980113
5651925371.75540615678-179.755406156784
5749965167.54693881946-171.546938819462
5852205237.24059517375-17.2405951737537
5950485037.8720957954310.1279042045662
6051785148.9693336553629.0306663446399
6152585216.9799747083941.0200252916111
6246984760.38475615212-62.3847561521161
6352485177.428088001570.5719119985006
6450985051.0136553267746.9863446732306
6551685202.79877131025-34.7987713102466
6649684974.83445751756-6.83445751756426
6751165156.32124051473-40.3212405147269
6850905088.486104732831.51389526716594
6949244970.92285790538-46.9228579053834
7051865121.4638699116564.5361300883505
7150384966.9321273222871.0678726777214
7251565112.8104003400643.1895996599415
7351145192.20542269505-78.2054226950504
7448564664.49378132904191.506218670963
7551925228.20874281755-36.20874281755
7649725050.1817797046-78.1817797045978
7751025131.24860935675-29.2486093567504
7849024910.78229722414-8.78229722414108
7949845087.95964619311-103.95964619311
8050104994.4973308540215.5026691459771
8147364877.42434867168-141.42434867168
8249744994.93443907348-20.934439073475
8348144796.2146431940717.7853568059254
8449244907.9687508238516.031249176147
8549224953.05715670167-31.0571567016714
8643624479.80839802807-117.808398028069
8746964852.70887853588-156.708878535881
8846624597.9085979777464.0914020222608
8948464744.87797939608101.122020603922
9045744583.3314313627-9.331431362697
9146164740.43390881063-124.433908810628
9246784645.1625977755432.8374022244552
9345284508.4943974688419.5056025311605
9446204716.11187108591-96.1118710859082
9545224480.3286717292941.6713282707069
9645484598.34295302845-50.3429530284466
9746784598.4740886248979.5259113751099
9841984163.3089966445134.6910033554941
9946084604.018628108763.98137189124463
10044444458.50056311225-14.5005631122522
10145444572.4900834442-28.4900834441996
10242644331.09333206081-67.0933320608065
10344484441.552464374756.44753562524875
10445184430.0005382337887.9994617662187
10543344318.7514958675415.2485041324626
10646764509.27564328321166.724356716792
10744324425.027669418026.97233058198344
10845504518.7538473947731.2461526052275
10946504582.1095523279767.8904476720263
11042764141.49237102304134.507628976957
11146784634.8138216489843.1861783510249
11245064514.8046001585-8.80460015849712
11345944638.7045621597-44.7045621597035
11443924392.98490912097-0.98490912096895
11545564555.30019347360.699806526400607
11645364561.58674139755-25.5867413975539
11744204393.0746444662226.9253555337837
11846124617.14660454956-5.14660454956265
11943964432.62030676415-36.62030676415
12045264511.9438830848814.0561169151224
12145644575.0395022-11.0395022000012
12242864106.52612357471179.473876425291
12345564612.25056618471-56.250566184709
12443764437.61919296372-61.6191929637243
12544444530.66696809658-86.6669680965806
12643004269.0697923305130.930207669493

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5392 & 5379.30128205128 & 12.6987179487169 \tabularnewline
14 & 4904 & 4899.17569158179 & 4.82430841821224 \tabularnewline
15 & 5394 & 5390.64710806536 & 3.35289193464268 \tabularnewline
16 & 5266 & 5262.88535372872 & 3.11464627127953 \tabularnewline
17 & 5352 & 5349.31908766237 & 2.68091233763334 \tabularnewline
18 & 5200 & 5204.59463933721 & -4.59463933720781 \tabularnewline
19 & 5354 & 5397.23953762773 & -43.2395376277327 \tabularnewline
20 & 5382 & 5355.81179087053 & 26.1882091294665 \tabularnewline
21 & 5270 & 5236.68181561645 & 33.31818438355 \tabularnewline
22 & 5438 & 5424.26133478527 & 13.7386652147325 \tabularnewline
23 & 5262 & 5254.75160953945 & 7.24839046054785 \tabularnewline
24 & 5206 & 5374.39349777085 & -168.393497770849 \tabularnewline
25 & 5498 & 5356.18133363545 & 141.818666364552 \tabularnewline
26 & 5148 & 4938.23643169703 & 209.763568302971 \tabularnewline
27 & 5376 & 5533.66682639807 & -157.66682639807 \tabularnewline
28 & 5318 & 5328.78774015045 & -10.7877401504538 \tabularnewline
29 & 5552 & 5409.38699361033 & 142.613006389674 \tabularnewline
30 & 5312 & 5335.53411332236 & -23.5341133223646 \tabularnewline
31 & 5508 & 5517.22965758712 & -9.22965758712417 \tabularnewline
32 & 5462 & 5505.56841157417 & -43.5684115741697 \tabularnewline
33 & 5396 & 5356.10732161091 & 39.8926783890893 \tabularnewline
34 & 5522 & 5547.09609643086 & -25.0960964308633 \tabularnewline
35 & 5388 & 5359.86490475089 & 28.1350952491102 \tabularnewline
36 & 5516 & 5468.90248790129 & 47.0975120987132 \tabularnewline
37 & 5418 & 5603.22872263278 & -185.228722632784 \tabularnewline
38 & 5054 & 5035.37573945754 & 18.6242605424641 \tabularnewline
39 & 5638 & 5485.72345936945 & 152.276540630545 \tabularnewline
40 & 5426 & 5453.65009420008 & -27.6500942000766 \tabularnewline
41 & 5662 & 5548.57075200163 & 113.429247998371 \tabularnewline
42 & 5414 & 5440.24055151975 & -26.2405515197515 \tabularnewline
43 & 5548 & 5624.13505333591 & -76.1350533359091 \tabularnewline
44 & 5458 & 5575.68816773758 & -117.688167737579 \tabularnewline
45 & 5372 & 5400.03692581179 & -28.0369258117871 \tabularnewline
46 & 5562 & 5546.89054722366 & 15.1094527763353 \tabularnewline
47 & 5342 & 5384.55490357491 & -42.5549035749109 \tabularnewline
48 & 5598 & 5458.60725730213 & 139.392742697872 \tabularnewline
49 & 5664 & 5605.86400514675 & 58.1359948532518 \tabularnewline
50 & 5138 & 5186.88660689376 & -48.8866068937623 \tabularnewline
51 & 5588 & 5624.23925612599 & -36.2392561259885 \tabularnewline
52 & 5318 & 5475.13726573822 & -157.137265738223 \tabularnewline
53 & 5480 & 5521.61851075115 & -41.6185107511519 \tabularnewline
54 & 5174 & 5312.25396884395 & -138.253968843953 \tabularnewline
55 & 5368 & 5425.70852229801 & -57.7085222980113 \tabularnewline
56 & 5192 & 5371.75540615678 & -179.755406156784 \tabularnewline
57 & 4996 & 5167.54693881946 & -171.546938819462 \tabularnewline
58 & 5220 & 5237.24059517375 & -17.2405951737537 \tabularnewline
59 & 5048 & 5037.87209579543 & 10.1279042045662 \tabularnewline
60 & 5178 & 5148.96933365536 & 29.0306663446399 \tabularnewline
61 & 5258 & 5216.97997470839 & 41.0200252916111 \tabularnewline
62 & 4698 & 4760.38475615212 & -62.3847561521161 \tabularnewline
63 & 5248 & 5177.4280880015 & 70.5719119985006 \tabularnewline
64 & 5098 & 5051.01365532677 & 46.9863446732306 \tabularnewline
65 & 5168 & 5202.79877131025 & -34.7987713102466 \tabularnewline
66 & 4968 & 4974.83445751756 & -6.83445751756426 \tabularnewline
67 & 5116 & 5156.32124051473 & -40.3212405147269 \tabularnewline
68 & 5090 & 5088.48610473283 & 1.51389526716594 \tabularnewline
69 & 4924 & 4970.92285790538 & -46.9228579053834 \tabularnewline
70 & 5186 & 5121.46386991165 & 64.5361300883505 \tabularnewline
71 & 5038 & 4966.93212732228 & 71.0678726777214 \tabularnewline
72 & 5156 & 5112.81040034006 & 43.1895996599415 \tabularnewline
73 & 5114 & 5192.20542269505 & -78.2054226950504 \tabularnewline
74 & 4856 & 4664.49378132904 & 191.506218670963 \tabularnewline
75 & 5192 & 5228.20874281755 & -36.20874281755 \tabularnewline
76 & 4972 & 5050.1817797046 & -78.1817797045978 \tabularnewline
77 & 5102 & 5131.24860935675 & -29.2486093567504 \tabularnewline
78 & 4902 & 4910.78229722414 & -8.78229722414108 \tabularnewline
79 & 4984 & 5087.95964619311 & -103.95964619311 \tabularnewline
80 & 5010 & 4994.49733085402 & 15.5026691459771 \tabularnewline
81 & 4736 & 4877.42434867168 & -141.42434867168 \tabularnewline
82 & 4974 & 4994.93443907348 & -20.934439073475 \tabularnewline
83 & 4814 & 4796.21464319407 & 17.7853568059254 \tabularnewline
84 & 4924 & 4907.96875082385 & 16.031249176147 \tabularnewline
85 & 4922 & 4953.05715670167 & -31.0571567016714 \tabularnewline
86 & 4362 & 4479.80839802807 & -117.808398028069 \tabularnewline
87 & 4696 & 4852.70887853588 & -156.708878535881 \tabularnewline
88 & 4662 & 4597.90859797774 & 64.0914020222608 \tabularnewline
89 & 4846 & 4744.87797939608 & 101.122020603922 \tabularnewline
90 & 4574 & 4583.3314313627 & -9.331431362697 \tabularnewline
91 & 4616 & 4740.43390881063 & -124.433908810628 \tabularnewline
92 & 4678 & 4645.16259777554 & 32.8374022244552 \tabularnewline
93 & 4528 & 4508.49439746884 & 19.5056025311605 \tabularnewline
94 & 4620 & 4716.11187108591 & -96.1118710859082 \tabularnewline
95 & 4522 & 4480.32867172929 & 41.6713282707069 \tabularnewline
96 & 4548 & 4598.34295302845 & -50.3429530284466 \tabularnewline
97 & 4678 & 4598.47408862489 & 79.5259113751099 \tabularnewline
98 & 4198 & 4163.30899664451 & 34.6910033554941 \tabularnewline
99 & 4608 & 4604.01862810876 & 3.98137189124463 \tabularnewline
100 & 4444 & 4458.50056311225 & -14.5005631122522 \tabularnewline
101 & 4544 & 4572.4900834442 & -28.4900834441996 \tabularnewline
102 & 4264 & 4331.09333206081 & -67.0933320608065 \tabularnewline
103 & 4448 & 4441.55246437475 & 6.44753562524875 \tabularnewline
104 & 4518 & 4430.00053823378 & 87.9994617662187 \tabularnewline
105 & 4334 & 4318.75149586754 & 15.2485041324626 \tabularnewline
106 & 4676 & 4509.27564328321 & 166.724356716792 \tabularnewline
107 & 4432 & 4425.02766941802 & 6.97233058198344 \tabularnewline
108 & 4550 & 4518.75384739477 & 31.2461526052275 \tabularnewline
109 & 4650 & 4582.10955232797 & 67.8904476720263 \tabularnewline
110 & 4276 & 4141.49237102304 & 134.507628976957 \tabularnewline
111 & 4678 & 4634.81382164898 & 43.1861783510249 \tabularnewline
112 & 4506 & 4514.8046001585 & -8.80460015849712 \tabularnewline
113 & 4594 & 4638.7045621597 & -44.7045621597035 \tabularnewline
114 & 4392 & 4392.98490912097 & -0.98490912096895 \tabularnewline
115 & 4556 & 4555.3001934736 & 0.699806526400607 \tabularnewline
116 & 4536 & 4561.58674139755 & -25.5867413975539 \tabularnewline
117 & 4420 & 4393.07464446622 & 26.9253555337837 \tabularnewline
118 & 4612 & 4617.14660454956 & -5.14660454956265 \tabularnewline
119 & 4396 & 4432.62030676415 & -36.62030676415 \tabularnewline
120 & 4526 & 4511.94388308488 & 14.0561169151224 \tabularnewline
121 & 4564 & 4575.0395022 & -11.0395022000012 \tabularnewline
122 & 4286 & 4106.52612357471 & 179.473876425291 \tabularnewline
123 & 4556 & 4612.25056618471 & -56.250566184709 \tabularnewline
124 & 4376 & 4437.61919296372 & -61.6191929637243 \tabularnewline
125 & 4444 & 4530.66696809658 & -86.6669680965806 \tabularnewline
126 & 4300 & 4269.06979233051 & 30.930207669493 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301541&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]5392[/C][C]5379.30128205128[/C][C]12.6987179487169[/C][/ROW]
[ROW][C]14[/C][C]4904[/C][C]4899.17569158179[/C][C]4.82430841821224[/C][/ROW]
[ROW][C]15[/C][C]5394[/C][C]5390.64710806536[/C][C]3.35289193464268[/C][/ROW]
[ROW][C]16[/C][C]5266[/C][C]5262.88535372872[/C][C]3.11464627127953[/C][/ROW]
[ROW][C]17[/C][C]5352[/C][C]5349.31908766237[/C][C]2.68091233763334[/C][/ROW]
[ROW][C]18[/C][C]5200[/C][C]5204.59463933721[/C][C]-4.59463933720781[/C][/ROW]
[ROW][C]19[/C][C]5354[/C][C]5397.23953762773[/C][C]-43.2395376277327[/C][/ROW]
[ROW][C]20[/C][C]5382[/C][C]5355.81179087053[/C][C]26.1882091294665[/C][/ROW]
[ROW][C]21[/C][C]5270[/C][C]5236.68181561645[/C][C]33.31818438355[/C][/ROW]
[ROW][C]22[/C][C]5438[/C][C]5424.26133478527[/C][C]13.7386652147325[/C][/ROW]
[ROW][C]23[/C][C]5262[/C][C]5254.75160953945[/C][C]7.24839046054785[/C][/ROW]
[ROW][C]24[/C][C]5206[/C][C]5374.39349777085[/C][C]-168.393497770849[/C][/ROW]
[ROW][C]25[/C][C]5498[/C][C]5356.18133363545[/C][C]141.818666364552[/C][/ROW]
[ROW][C]26[/C][C]5148[/C][C]4938.23643169703[/C][C]209.763568302971[/C][/ROW]
[ROW][C]27[/C][C]5376[/C][C]5533.66682639807[/C][C]-157.66682639807[/C][/ROW]
[ROW][C]28[/C][C]5318[/C][C]5328.78774015045[/C][C]-10.7877401504538[/C][/ROW]
[ROW][C]29[/C][C]5552[/C][C]5409.38699361033[/C][C]142.613006389674[/C][/ROW]
[ROW][C]30[/C][C]5312[/C][C]5335.53411332236[/C][C]-23.5341133223646[/C][/ROW]
[ROW][C]31[/C][C]5508[/C][C]5517.22965758712[/C][C]-9.22965758712417[/C][/ROW]
[ROW][C]32[/C][C]5462[/C][C]5505.56841157417[/C][C]-43.5684115741697[/C][/ROW]
[ROW][C]33[/C][C]5396[/C][C]5356.10732161091[/C][C]39.8926783890893[/C][/ROW]
[ROW][C]34[/C][C]5522[/C][C]5547.09609643086[/C][C]-25.0960964308633[/C][/ROW]
[ROW][C]35[/C][C]5388[/C][C]5359.86490475089[/C][C]28.1350952491102[/C][/ROW]
[ROW][C]36[/C][C]5516[/C][C]5468.90248790129[/C][C]47.0975120987132[/C][/ROW]
[ROW][C]37[/C][C]5418[/C][C]5603.22872263278[/C][C]-185.228722632784[/C][/ROW]
[ROW][C]38[/C][C]5054[/C][C]5035.37573945754[/C][C]18.6242605424641[/C][/ROW]
[ROW][C]39[/C][C]5638[/C][C]5485.72345936945[/C][C]152.276540630545[/C][/ROW]
[ROW][C]40[/C][C]5426[/C][C]5453.65009420008[/C][C]-27.6500942000766[/C][/ROW]
[ROW][C]41[/C][C]5662[/C][C]5548.57075200163[/C][C]113.429247998371[/C][/ROW]
[ROW][C]42[/C][C]5414[/C][C]5440.24055151975[/C][C]-26.2405515197515[/C][/ROW]
[ROW][C]43[/C][C]5548[/C][C]5624.13505333591[/C][C]-76.1350533359091[/C][/ROW]
[ROW][C]44[/C][C]5458[/C][C]5575.68816773758[/C][C]-117.688167737579[/C][/ROW]
[ROW][C]45[/C][C]5372[/C][C]5400.03692581179[/C][C]-28.0369258117871[/C][/ROW]
[ROW][C]46[/C][C]5562[/C][C]5546.89054722366[/C][C]15.1094527763353[/C][/ROW]
[ROW][C]47[/C][C]5342[/C][C]5384.55490357491[/C][C]-42.5549035749109[/C][/ROW]
[ROW][C]48[/C][C]5598[/C][C]5458.60725730213[/C][C]139.392742697872[/C][/ROW]
[ROW][C]49[/C][C]5664[/C][C]5605.86400514675[/C][C]58.1359948532518[/C][/ROW]
[ROW][C]50[/C][C]5138[/C][C]5186.88660689376[/C][C]-48.8866068937623[/C][/ROW]
[ROW][C]51[/C][C]5588[/C][C]5624.23925612599[/C][C]-36.2392561259885[/C][/ROW]
[ROW][C]52[/C][C]5318[/C][C]5475.13726573822[/C][C]-157.137265738223[/C][/ROW]
[ROW][C]53[/C][C]5480[/C][C]5521.61851075115[/C][C]-41.6185107511519[/C][/ROW]
[ROW][C]54[/C][C]5174[/C][C]5312.25396884395[/C][C]-138.253968843953[/C][/ROW]
[ROW][C]55[/C][C]5368[/C][C]5425.70852229801[/C][C]-57.7085222980113[/C][/ROW]
[ROW][C]56[/C][C]5192[/C][C]5371.75540615678[/C][C]-179.755406156784[/C][/ROW]
[ROW][C]57[/C][C]4996[/C][C]5167.54693881946[/C][C]-171.546938819462[/C][/ROW]
[ROW][C]58[/C][C]5220[/C][C]5237.24059517375[/C][C]-17.2405951737537[/C][/ROW]
[ROW][C]59[/C][C]5048[/C][C]5037.87209579543[/C][C]10.1279042045662[/C][/ROW]
[ROW][C]60[/C][C]5178[/C][C]5148.96933365536[/C][C]29.0306663446399[/C][/ROW]
[ROW][C]61[/C][C]5258[/C][C]5216.97997470839[/C][C]41.0200252916111[/C][/ROW]
[ROW][C]62[/C][C]4698[/C][C]4760.38475615212[/C][C]-62.3847561521161[/C][/ROW]
[ROW][C]63[/C][C]5248[/C][C]5177.4280880015[/C][C]70.5719119985006[/C][/ROW]
[ROW][C]64[/C][C]5098[/C][C]5051.01365532677[/C][C]46.9863446732306[/C][/ROW]
[ROW][C]65[/C][C]5168[/C][C]5202.79877131025[/C][C]-34.7987713102466[/C][/ROW]
[ROW][C]66[/C][C]4968[/C][C]4974.83445751756[/C][C]-6.83445751756426[/C][/ROW]
[ROW][C]67[/C][C]5116[/C][C]5156.32124051473[/C][C]-40.3212405147269[/C][/ROW]
[ROW][C]68[/C][C]5090[/C][C]5088.48610473283[/C][C]1.51389526716594[/C][/ROW]
[ROW][C]69[/C][C]4924[/C][C]4970.92285790538[/C][C]-46.9228579053834[/C][/ROW]
[ROW][C]70[/C][C]5186[/C][C]5121.46386991165[/C][C]64.5361300883505[/C][/ROW]
[ROW][C]71[/C][C]5038[/C][C]4966.93212732228[/C][C]71.0678726777214[/C][/ROW]
[ROW][C]72[/C][C]5156[/C][C]5112.81040034006[/C][C]43.1895996599415[/C][/ROW]
[ROW][C]73[/C][C]5114[/C][C]5192.20542269505[/C][C]-78.2054226950504[/C][/ROW]
[ROW][C]74[/C][C]4856[/C][C]4664.49378132904[/C][C]191.506218670963[/C][/ROW]
[ROW][C]75[/C][C]5192[/C][C]5228.20874281755[/C][C]-36.20874281755[/C][/ROW]
[ROW][C]76[/C][C]4972[/C][C]5050.1817797046[/C][C]-78.1817797045978[/C][/ROW]
[ROW][C]77[/C][C]5102[/C][C]5131.24860935675[/C][C]-29.2486093567504[/C][/ROW]
[ROW][C]78[/C][C]4902[/C][C]4910.78229722414[/C][C]-8.78229722414108[/C][/ROW]
[ROW][C]79[/C][C]4984[/C][C]5087.95964619311[/C][C]-103.95964619311[/C][/ROW]
[ROW][C]80[/C][C]5010[/C][C]4994.49733085402[/C][C]15.5026691459771[/C][/ROW]
[ROW][C]81[/C][C]4736[/C][C]4877.42434867168[/C][C]-141.42434867168[/C][/ROW]
[ROW][C]82[/C][C]4974[/C][C]4994.93443907348[/C][C]-20.934439073475[/C][/ROW]
[ROW][C]83[/C][C]4814[/C][C]4796.21464319407[/C][C]17.7853568059254[/C][/ROW]
[ROW][C]84[/C][C]4924[/C][C]4907.96875082385[/C][C]16.031249176147[/C][/ROW]
[ROW][C]85[/C][C]4922[/C][C]4953.05715670167[/C][C]-31.0571567016714[/C][/ROW]
[ROW][C]86[/C][C]4362[/C][C]4479.80839802807[/C][C]-117.808398028069[/C][/ROW]
[ROW][C]87[/C][C]4696[/C][C]4852.70887853588[/C][C]-156.708878535881[/C][/ROW]
[ROW][C]88[/C][C]4662[/C][C]4597.90859797774[/C][C]64.0914020222608[/C][/ROW]
[ROW][C]89[/C][C]4846[/C][C]4744.87797939608[/C][C]101.122020603922[/C][/ROW]
[ROW][C]90[/C][C]4574[/C][C]4583.3314313627[/C][C]-9.331431362697[/C][/ROW]
[ROW][C]91[/C][C]4616[/C][C]4740.43390881063[/C][C]-124.433908810628[/C][/ROW]
[ROW][C]92[/C][C]4678[/C][C]4645.16259777554[/C][C]32.8374022244552[/C][/ROW]
[ROW][C]93[/C][C]4528[/C][C]4508.49439746884[/C][C]19.5056025311605[/C][/ROW]
[ROW][C]94[/C][C]4620[/C][C]4716.11187108591[/C][C]-96.1118710859082[/C][/ROW]
[ROW][C]95[/C][C]4522[/C][C]4480.32867172929[/C][C]41.6713282707069[/C][/ROW]
[ROW][C]96[/C][C]4548[/C][C]4598.34295302845[/C][C]-50.3429530284466[/C][/ROW]
[ROW][C]97[/C][C]4678[/C][C]4598.47408862489[/C][C]79.5259113751099[/C][/ROW]
[ROW][C]98[/C][C]4198[/C][C]4163.30899664451[/C][C]34.6910033554941[/C][/ROW]
[ROW][C]99[/C][C]4608[/C][C]4604.01862810876[/C][C]3.98137189124463[/C][/ROW]
[ROW][C]100[/C][C]4444[/C][C]4458.50056311225[/C][C]-14.5005631122522[/C][/ROW]
[ROW][C]101[/C][C]4544[/C][C]4572.4900834442[/C][C]-28.4900834441996[/C][/ROW]
[ROW][C]102[/C][C]4264[/C][C]4331.09333206081[/C][C]-67.0933320608065[/C][/ROW]
[ROW][C]103[/C][C]4448[/C][C]4441.55246437475[/C][C]6.44753562524875[/C][/ROW]
[ROW][C]104[/C][C]4518[/C][C]4430.00053823378[/C][C]87.9994617662187[/C][/ROW]
[ROW][C]105[/C][C]4334[/C][C]4318.75149586754[/C][C]15.2485041324626[/C][/ROW]
[ROW][C]106[/C][C]4676[/C][C]4509.27564328321[/C][C]166.724356716792[/C][/ROW]
[ROW][C]107[/C][C]4432[/C][C]4425.02766941802[/C][C]6.97233058198344[/C][/ROW]
[ROW][C]108[/C][C]4550[/C][C]4518.75384739477[/C][C]31.2461526052275[/C][/ROW]
[ROW][C]109[/C][C]4650[/C][C]4582.10955232797[/C][C]67.8904476720263[/C][/ROW]
[ROW][C]110[/C][C]4276[/C][C]4141.49237102304[/C][C]134.507628976957[/C][/ROW]
[ROW][C]111[/C][C]4678[/C][C]4634.81382164898[/C][C]43.1861783510249[/C][/ROW]
[ROW][C]112[/C][C]4506[/C][C]4514.8046001585[/C][C]-8.80460015849712[/C][/ROW]
[ROW][C]113[/C][C]4594[/C][C]4638.7045621597[/C][C]-44.7045621597035[/C][/ROW]
[ROW][C]114[/C][C]4392[/C][C]4392.98490912097[/C][C]-0.98490912096895[/C][/ROW]
[ROW][C]115[/C][C]4556[/C][C]4555.3001934736[/C][C]0.699806526400607[/C][/ROW]
[ROW][C]116[/C][C]4536[/C][C]4561.58674139755[/C][C]-25.5867413975539[/C][/ROW]
[ROW][C]117[/C][C]4420[/C][C]4393.07464446622[/C][C]26.9253555337837[/C][/ROW]
[ROW][C]118[/C][C]4612[/C][C]4617.14660454956[/C][C]-5.14660454956265[/C][/ROW]
[ROW][C]119[/C][C]4396[/C][C]4432.62030676415[/C][C]-36.62030676415[/C][/ROW]
[ROW][C]120[/C][C]4526[/C][C]4511.94388308488[/C][C]14.0561169151224[/C][/ROW]
[ROW][C]121[/C][C]4564[/C][C]4575.0395022[/C][C]-11.0395022000012[/C][/ROW]
[ROW][C]122[/C][C]4286[/C][C]4106.52612357471[/C][C]179.473876425291[/C][/ROW]
[ROW][C]123[/C][C]4556[/C][C]4612.25056618471[/C][C]-56.250566184709[/C][/ROW]
[ROW][C]124[/C][C]4376[/C][C]4437.61919296372[/C][C]-61.6191929637243[/C][/ROW]
[ROW][C]125[/C][C]4444[/C][C]4530.66696809658[/C][C]-86.6669680965806[/C][/ROW]
[ROW][C]126[/C][C]4300[/C][C]4269.06979233051[/C][C]30.930207669493[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301541&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301541&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
1353925379.3012820512812.6987179487169
1449044899.175691581794.82430841821224
1553945390.647108065363.35289193464268
1652665262.885353728723.11464627127953
1753525349.319087662372.68091233763334
1852005204.59463933721-4.59463933720781
1953545397.23953762773-43.2395376277327
2053825355.8117908705326.1882091294665
2152705236.6818156164533.31818438355
2254385424.2613347852713.7386652147325
2352625254.751609539457.24839046054785
2452065374.39349777085-168.393497770849
2554985356.18133363545141.818666364552
2651484938.23643169703209.763568302971
2753765533.66682639807-157.66682639807
2853185328.78774015045-10.7877401504538
2955525409.38699361033142.613006389674
3053125335.53411332236-23.5341133223646
3155085517.22965758712-9.22965758712417
3254625505.56841157417-43.5684115741697
3353965356.1073216109139.8926783890893
3455225547.09609643086-25.0960964308633
3553885359.8649047508928.1350952491102
3655165468.9024879012947.0975120987132
3754185603.22872263278-185.228722632784
3850545035.3757394575418.6242605424641
3956385485.72345936945152.276540630545
4054265453.65009420008-27.6500942000766
4156625548.57075200163113.429247998371
4254145440.24055151975-26.2405515197515
4355485624.13505333591-76.1350533359091
4454585575.68816773758-117.688167737579
4553725400.03692581179-28.0369258117871
4655625546.8905472236615.1094527763353
4753425384.55490357491-42.5549035749109
4855985458.60725730213139.392742697872
4956645605.8640051467558.1359948532518
5051385186.88660689376-48.8866068937623
5155885624.23925612599-36.2392561259885
5253185475.13726573822-157.137265738223
5354805521.61851075115-41.6185107511519
5451745312.25396884395-138.253968843953
5553685425.70852229801-57.7085222980113
5651925371.75540615678-179.755406156784
5749965167.54693881946-171.546938819462
5852205237.24059517375-17.2405951737537
5950485037.8720957954310.1279042045662
6051785148.9693336553629.0306663446399
6152585216.9799747083941.0200252916111
6246984760.38475615212-62.3847561521161
6352485177.428088001570.5719119985006
6450985051.0136553267746.9863446732306
6551685202.79877131025-34.7987713102466
6649684974.83445751756-6.83445751756426
6751165156.32124051473-40.3212405147269
6850905088.486104732831.51389526716594
6949244970.92285790538-46.9228579053834
7051865121.4638699116564.5361300883505
7150384966.9321273222871.0678726777214
7251565112.8104003400643.1895996599415
7351145192.20542269505-78.2054226950504
7448564664.49378132904191.506218670963
7551925228.20874281755-36.20874281755
7649725050.1817797046-78.1817797045978
7751025131.24860935675-29.2486093567504
7849024910.78229722414-8.78229722414108
7949845087.95964619311-103.95964619311
8050104994.4973308540215.5026691459771
8147364877.42434867168-141.42434867168
8249744994.93443907348-20.934439073475
8348144796.2146431940717.7853568059254
8449244907.9687508238516.031249176147
8549224953.05715670167-31.0571567016714
8643624479.80839802807-117.808398028069
8746964852.70887853588-156.708878535881
8846624597.9085979777464.0914020222608
8948464744.87797939608101.122020603922
9045744583.3314313627-9.331431362697
9146164740.43390881063-124.433908810628
9246784645.1625977755432.8374022244552
9345284508.4943974688419.5056025311605
9446204716.11187108591-96.1118710859082
9545224480.3286717292941.6713282707069
9645484598.34295302845-50.3429530284466
9746784598.4740886248979.5259113751099
9841984163.3089966445134.6910033554941
9946084604.018628108763.98137189124463
10044444458.50056311225-14.5005631122522
10145444572.4900834442-28.4900834441996
10242644331.09333206081-67.0933320608065
10344484441.552464374756.44753562524875
10445184430.0005382337887.9994617662187
10543344318.7514958675415.2485041324626
10646764509.27564328321166.724356716792
10744324425.027669418026.97233058198344
10845504518.7538473947731.2461526052275
10946504582.1095523279767.8904476720263
11042764141.49237102304134.507628976957
11146784634.8138216489843.1861783510249
11245064514.8046001585-8.80460015849712
11345944638.7045621597-44.7045621597035
11443924392.98490912097-0.98490912096895
11545564555.30019347360.699806526400607
11645364561.58674139755-25.5867413975539
11744204393.0746444662226.9253555337837
11846124617.14660454956-5.14660454956265
11943964432.62030676415-36.62030676415
12045264511.9438830848814.0561169151224
12145644575.0395022-11.0395022000012
12242864106.52612357471179.473876425291
12345564612.25056618471-56.250566184709
12443764437.61919296372-61.6191929637243
12544444530.66696809658-86.6669680965806
12643004269.0697923305130.930207669493







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1274446.528471632024291.845697762474601.21124550157
1284448.378802966564275.001153885824621.75645204729
1294299.138414458944107.618562381934490.65826653596
1304505.22267454224295.925045324944714.52030375947
1314318.494447242654091.656742666634545.33215181868
1324422.508374638824178.278980316344666.73776896131
1334475.346364344094213.8084903284736.88423836018
1344037.496404375833758.684397557674316.30841119399
1354421.320484738714125.231262878244717.40970659918
1364271.035555020013957.636864116194584.43424592383
1374389.656336386054058.892863390164720.41980938193
1384186.378916212683838.176909363754534.58092306161

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 4446.52847163202 & 4291.84569776247 & 4601.21124550157 \tabularnewline
128 & 4448.37880296656 & 4275.00115388582 & 4621.75645204729 \tabularnewline
129 & 4299.13841445894 & 4107.61856238193 & 4490.65826653596 \tabularnewline
130 & 4505.2226745422 & 4295.92504532494 & 4714.52030375947 \tabularnewline
131 & 4318.49444724265 & 4091.65674266663 & 4545.33215181868 \tabularnewline
132 & 4422.50837463882 & 4178.27898031634 & 4666.73776896131 \tabularnewline
133 & 4475.34636434409 & 4213.808490328 & 4736.88423836018 \tabularnewline
134 & 4037.49640437583 & 3758.68439755767 & 4316.30841119399 \tabularnewline
135 & 4421.32048473871 & 4125.23126287824 & 4717.40970659918 \tabularnewline
136 & 4271.03555502001 & 3957.63686411619 & 4584.43424592383 \tabularnewline
137 & 4389.65633638605 & 4058.89286339016 & 4720.41980938193 \tabularnewline
138 & 4186.37891621268 & 3838.17690936375 & 4534.58092306161 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301541&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]4446.52847163202[/C][C]4291.84569776247[/C][C]4601.21124550157[/C][/ROW]
[ROW][C]128[/C][C]4448.37880296656[/C][C]4275.00115388582[/C][C]4621.75645204729[/C][/ROW]
[ROW][C]129[/C][C]4299.13841445894[/C][C]4107.61856238193[/C][C]4490.65826653596[/C][/ROW]
[ROW][C]130[/C][C]4505.2226745422[/C][C]4295.92504532494[/C][C]4714.52030375947[/C][/ROW]
[ROW][C]131[/C][C]4318.49444724265[/C][C]4091.65674266663[/C][C]4545.33215181868[/C][/ROW]
[ROW][C]132[/C][C]4422.50837463882[/C][C]4178.27898031634[/C][C]4666.73776896131[/C][/ROW]
[ROW][C]133[/C][C]4475.34636434409[/C][C]4213.808490328[/C][C]4736.88423836018[/C][/ROW]
[ROW][C]134[/C][C]4037.49640437583[/C][C]3758.68439755767[/C][C]4316.30841119399[/C][/ROW]
[ROW][C]135[/C][C]4421.32048473871[/C][C]4125.23126287824[/C][C]4717.40970659918[/C][/ROW]
[ROW][C]136[/C][C]4271.03555502001[/C][C]3957.63686411619[/C][C]4584.43424592383[/C][/ROW]
[ROW][C]137[/C][C]4389.65633638605[/C][C]4058.89286339016[/C][C]4720.41980938193[/C][/ROW]
[ROW][C]138[/C][C]4186.37891621268[/C][C]3838.17690936375[/C][C]4534.58092306161[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301541&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301541&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
1274446.528471632024291.845697762474601.21124550157
1284448.378802966564275.001153885824621.75645204729
1294299.138414458944107.618562381934490.65826653596
1304505.22267454224295.925045324944714.52030375947
1314318.494447242654091.656742666634545.33215181868
1324422.508374638824178.278980316344666.73776896131
1334475.346364344094213.8084903284736.88423836018
1344037.496404375833758.684397557674316.30841119399
1354421.320484738714125.231262878244717.40970659918
1364271.035555020013957.636864116194584.43424592383
1374389.656336386054058.892863390164720.41980938193
1384186.378916212683838.176909363754534.58092306161



Parameters (Session):
par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')