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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 16 Dec 2016 18:28:04 +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/16/t148190932075qhtxwfl3pduhl.htm/, Retrieved Thu, 02 May 2024 18:10:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300464, Retrieved Thu, 02 May 2024 18:10:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact49
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [expsmoot] [2016-12-16 17:28:04] [ca14e1566745fb922befb698831e7d61] [Current]
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Dataseries X:
3795
3805
3860
3875
3885
3930
3960
3995
3875
4065
4165
4200
4240
4315
4355
4400
4440
4525
4525
4530
4565
4585
4685
4740
4780
4850
4905
4925
4950
4970
4985
5040
5105
5015
5045
5025
4960
4925
4955
4945
4935
4925
4995
4970
5005
5140
5190
5220
5250
5235
5255
5335
5360
5345
5325
5320
5350
5430
5440
5490
5505
5545
5530
5480
5535
5560
5575
5595
5595
5500
5450
5260
5240
5245
5205
5180
5155
5160
5150
5070
4855
4825
5015
5070
5075
5060
5070
5135
5135
5110
5015
5125
5185
5190
5230
5350
5415
5465
5560
5585
5615




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=300464&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=300464&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300464&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
alpha1
beta0.141861807305817
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.141861807305817 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300464&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.141861807305817[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300464&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300464&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
alpha1
beta0.141861807305817
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33860381545
438753876.38378132876-1.38378132876187
538853891.18747560855-6.18747560854763
639303900.3097091360629.6902908639418
739603949.5216274574510.4783725425473
839953981.0081083239613.991891676038
938754017.99302336475-142.993023364752
1040653877.70777463811187.292225361895
1141654094.2773882222770.7226117777277
1242004204.31022574645-4.31022574644794
1342404238.698769332161.30123066783926
1443154278.8833642664236.1166357335778
1543554359.00693548539-4.00693548539402
1644004398.438504375681.56149562432256
1744404443.66002096704-3.66002096704415
1845254483.1408037778841.859196222118
1945254574.07902500632-49.079025006321
2045304567.11658581812-37.1165858181166
2145654566.85115987294-1.85115987293739
2245854601.58855098775-16.5885509877498
2346854619.2352691640465.7647308359565
2447404728.5647727374111.4352272625874
2547804785.18699474384-5.18699474383629
2648504824.4511582949925.5488417050101
2749054898.075563153836.92443684616683
2849254954.0578762794-29.0578762794048
2949504969.93567343394-19.9356734339399
3049704992.10756277074-22.1075627707423
3149855008.97134396096-23.9713439609586
3250405020.5707257831119.4292742168927
3351055078.3269977381626.673002261844
3450155147.11087804529-132.110878045293
3550455038.369390121036.63060987897006
3650255069.310020422-44.310020422
3749605043.02412084318-83.0241208431771
3849254966.24616901039-41.2461690103873
3949554925.3949129301329.6050870698673
4049454959.59474408731-14.5947440873106
4149354947.52430731392-12.5243073139191
4249254935.74758644311-10.7475864431126
4349954924.2229144061270.7770855938825
4449705004.2634796843-34.263479684304
4550054974.402800531730.5971994682977
4651405013.74337454677126.256625453228
4751905166.654367617923.3456323820992
4852205219.966221220320.0337787796779594
4952505249.971013139060.0289868609443147
5052355279.97512526754-44.9751252675378
5152555258.59487271328-3.59487271327907
5253355278.0848975731456.9151024268613
5353605366.15897686641-6.15897686640892
5453455390.28525327699-45.2852532769857
5553255368.86100540281-43.8610054028104
5653205342.63880390612-22.6388039061176
5753505334.4272222687515.5727777312459
5854305366.6364046624863.3635953375197
5954405455.62527881446-15.6252788144557
6054905463.4086485221826.5913514778204
6155055517.18094570153-12.180945701527
6255455530.4529347296114.5470652703852
6355305572.51660769987-42.5166076998676
6454805551.48512489105-71.4851248910518
6555355491.3441158785243.6558841214755
6655605552.537218499537.46278150046965
6755755578.59590217072-3.59590217071582
6855955593.085780989881.91421901011654
6955955613.35733555824-18.3573355582375
7055005610.75313075863-110.753130758627
7154505500.04149146443-50.0414914644298
7252605442.94251504501-182.942515045008
7352405226.9899592276513.0100407723494
7452455208.8355871247436.1644128752614
7552055218.96593609538-13.9659360953774
7651805176.984703160173.01529683983063
7751555152.412458619432.58754138056884
7851605127.7795319161632.2204680838422
7951505137.3503857507712.6496142492297
8050705129.14488288989-59.1448828898874
8148555040.75448291024-185.754482910237
8248254799.4030162494325.5969837505663
8350154773.03425062587241.965749374133
8450704997.3599491381972.6400508618126
8550755062.6647980362312.3352019637696
8650605069.41469208029-9.41469208029321
8750705053.0791068465616.9208931534449
8851355065.4795353305369.5204646694683
8951355140.34183409328-5.34183409328216
9051105139.58403185448-29.5840318544815
9150155110.38718762821-95.3871876282119
9251255001.85538879745123.144611202545
9351855129.3249059026255.6750940973798
9451905197.2230753732-7.22307537319557
9552305201.1983968464528.8016031535517
9653505245.28424432312104.715755676884
9754155380.1394106768334.860589323167
9854655450.0847968819614.9152031180365
9955605502.2006945526257.7993054473782
10055855605.40020848441-20.4002084844078
10156155627.50619803939-12.5061980393939

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3860 & 3815 & 45 \tabularnewline
4 & 3875 & 3876.38378132876 & -1.38378132876187 \tabularnewline
5 & 3885 & 3891.18747560855 & -6.18747560854763 \tabularnewline
6 & 3930 & 3900.30970913606 & 29.6902908639418 \tabularnewline
7 & 3960 & 3949.52162745745 & 10.4783725425473 \tabularnewline
8 & 3995 & 3981.00810832396 & 13.991891676038 \tabularnewline
9 & 3875 & 4017.99302336475 & -142.993023364752 \tabularnewline
10 & 4065 & 3877.70777463811 & 187.292225361895 \tabularnewline
11 & 4165 & 4094.27738822227 & 70.7226117777277 \tabularnewline
12 & 4200 & 4204.31022574645 & -4.31022574644794 \tabularnewline
13 & 4240 & 4238.69876933216 & 1.30123066783926 \tabularnewline
14 & 4315 & 4278.88336426642 & 36.1166357335778 \tabularnewline
15 & 4355 & 4359.00693548539 & -4.00693548539402 \tabularnewline
16 & 4400 & 4398.43850437568 & 1.56149562432256 \tabularnewline
17 & 4440 & 4443.66002096704 & -3.66002096704415 \tabularnewline
18 & 4525 & 4483.14080377788 & 41.859196222118 \tabularnewline
19 & 4525 & 4574.07902500632 & -49.079025006321 \tabularnewline
20 & 4530 & 4567.11658581812 & -37.1165858181166 \tabularnewline
21 & 4565 & 4566.85115987294 & -1.85115987293739 \tabularnewline
22 & 4585 & 4601.58855098775 & -16.5885509877498 \tabularnewline
23 & 4685 & 4619.23526916404 & 65.7647308359565 \tabularnewline
24 & 4740 & 4728.56477273741 & 11.4352272625874 \tabularnewline
25 & 4780 & 4785.18699474384 & -5.18699474383629 \tabularnewline
26 & 4850 & 4824.45115829499 & 25.5488417050101 \tabularnewline
27 & 4905 & 4898.07556315383 & 6.92443684616683 \tabularnewline
28 & 4925 & 4954.0578762794 & -29.0578762794048 \tabularnewline
29 & 4950 & 4969.93567343394 & -19.9356734339399 \tabularnewline
30 & 4970 & 4992.10756277074 & -22.1075627707423 \tabularnewline
31 & 4985 & 5008.97134396096 & -23.9713439609586 \tabularnewline
32 & 5040 & 5020.57072578311 & 19.4292742168927 \tabularnewline
33 & 5105 & 5078.32699773816 & 26.673002261844 \tabularnewline
34 & 5015 & 5147.11087804529 & -132.110878045293 \tabularnewline
35 & 5045 & 5038.36939012103 & 6.63060987897006 \tabularnewline
36 & 5025 & 5069.310020422 & -44.310020422 \tabularnewline
37 & 4960 & 5043.02412084318 & -83.0241208431771 \tabularnewline
38 & 4925 & 4966.24616901039 & -41.2461690103873 \tabularnewline
39 & 4955 & 4925.39491293013 & 29.6050870698673 \tabularnewline
40 & 4945 & 4959.59474408731 & -14.5947440873106 \tabularnewline
41 & 4935 & 4947.52430731392 & -12.5243073139191 \tabularnewline
42 & 4925 & 4935.74758644311 & -10.7475864431126 \tabularnewline
43 & 4995 & 4924.22291440612 & 70.7770855938825 \tabularnewline
44 & 4970 & 5004.2634796843 & -34.263479684304 \tabularnewline
45 & 5005 & 4974.4028005317 & 30.5971994682977 \tabularnewline
46 & 5140 & 5013.74337454677 & 126.256625453228 \tabularnewline
47 & 5190 & 5166.6543676179 & 23.3456323820992 \tabularnewline
48 & 5220 & 5219.96622122032 & 0.0337787796779594 \tabularnewline
49 & 5250 & 5249.97101313906 & 0.0289868609443147 \tabularnewline
50 & 5235 & 5279.97512526754 & -44.9751252675378 \tabularnewline
51 & 5255 & 5258.59487271328 & -3.59487271327907 \tabularnewline
52 & 5335 & 5278.08489757314 & 56.9151024268613 \tabularnewline
53 & 5360 & 5366.15897686641 & -6.15897686640892 \tabularnewline
54 & 5345 & 5390.28525327699 & -45.2852532769857 \tabularnewline
55 & 5325 & 5368.86100540281 & -43.8610054028104 \tabularnewline
56 & 5320 & 5342.63880390612 & -22.6388039061176 \tabularnewline
57 & 5350 & 5334.42722226875 & 15.5727777312459 \tabularnewline
58 & 5430 & 5366.63640466248 & 63.3635953375197 \tabularnewline
59 & 5440 & 5455.62527881446 & -15.6252788144557 \tabularnewline
60 & 5490 & 5463.40864852218 & 26.5913514778204 \tabularnewline
61 & 5505 & 5517.18094570153 & -12.180945701527 \tabularnewline
62 & 5545 & 5530.45293472961 & 14.5470652703852 \tabularnewline
63 & 5530 & 5572.51660769987 & -42.5166076998676 \tabularnewline
64 & 5480 & 5551.48512489105 & -71.4851248910518 \tabularnewline
65 & 5535 & 5491.34411587852 & 43.6558841214755 \tabularnewline
66 & 5560 & 5552.53721849953 & 7.46278150046965 \tabularnewline
67 & 5575 & 5578.59590217072 & -3.59590217071582 \tabularnewline
68 & 5595 & 5593.08578098988 & 1.91421901011654 \tabularnewline
69 & 5595 & 5613.35733555824 & -18.3573355582375 \tabularnewline
70 & 5500 & 5610.75313075863 & -110.753130758627 \tabularnewline
71 & 5450 & 5500.04149146443 & -50.0414914644298 \tabularnewline
72 & 5260 & 5442.94251504501 & -182.942515045008 \tabularnewline
73 & 5240 & 5226.98995922765 & 13.0100407723494 \tabularnewline
74 & 5245 & 5208.83558712474 & 36.1644128752614 \tabularnewline
75 & 5205 & 5218.96593609538 & -13.9659360953774 \tabularnewline
76 & 5180 & 5176.98470316017 & 3.01529683983063 \tabularnewline
77 & 5155 & 5152.41245861943 & 2.58754138056884 \tabularnewline
78 & 5160 & 5127.77953191616 & 32.2204680838422 \tabularnewline
79 & 5150 & 5137.35038575077 & 12.6496142492297 \tabularnewline
80 & 5070 & 5129.14488288989 & -59.1448828898874 \tabularnewline
81 & 4855 & 5040.75448291024 & -185.754482910237 \tabularnewline
82 & 4825 & 4799.40301624943 & 25.5969837505663 \tabularnewline
83 & 5015 & 4773.03425062587 & 241.965749374133 \tabularnewline
84 & 5070 & 4997.35994913819 & 72.6400508618126 \tabularnewline
85 & 5075 & 5062.66479803623 & 12.3352019637696 \tabularnewline
86 & 5060 & 5069.41469208029 & -9.41469208029321 \tabularnewline
87 & 5070 & 5053.07910684656 & 16.9208931534449 \tabularnewline
88 & 5135 & 5065.47953533053 & 69.5204646694683 \tabularnewline
89 & 5135 & 5140.34183409328 & -5.34183409328216 \tabularnewline
90 & 5110 & 5139.58403185448 & -29.5840318544815 \tabularnewline
91 & 5015 & 5110.38718762821 & -95.3871876282119 \tabularnewline
92 & 5125 & 5001.85538879745 & 123.144611202545 \tabularnewline
93 & 5185 & 5129.32490590262 & 55.6750940973798 \tabularnewline
94 & 5190 & 5197.2230753732 & -7.22307537319557 \tabularnewline
95 & 5230 & 5201.19839684645 & 28.8016031535517 \tabularnewline
96 & 5350 & 5245.28424432312 & 104.715755676884 \tabularnewline
97 & 5415 & 5380.13941067683 & 34.860589323167 \tabularnewline
98 & 5465 & 5450.08479688196 & 14.9152031180365 \tabularnewline
99 & 5560 & 5502.20069455262 & 57.7993054473782 \tabularnewline
100 & 5585 & 5605.40020848441 & -20.4002084844078 \tabularnewline
101 & 5615 & 5627.50619803939 & -12.5061980393939 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300464&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]3860[/C][C]3815[/C][C]45[/C][/ROW]
[ROW][C]4[/C][C]3875[/C][C]3876.38378132876[/C][C]-1.38378132876187[/C][/ROW]
[ROW][C]5[/C][C]3885[/C][C]3891.18747560855[/C][C]-6.18747560854763[/C][/ROW]
[ROW][C]6[/C][C]3930[/C][C]3900.30970913606[/C][C]29.6902908639418[/C][/ROW]
[ROW][C]7[/C][C]3960[/C][C]3949.52162745745[/C][C]10.4783725425473[/C][/ROW]
[ROW][C]8[/C][C]3995[/C][C]3981.00810832396[/C][C]13.991891676038[/C][/ROW]
[ROW][C]9[/C][C]3875[/C][C]4017.99302336475[/C][C]-142.993023364752[/C][/ROW]
[ROW][C]10[/C][C]4065[/C][C]3877.70777463811[/C][C]187.292225361895[/C][/ROW]
[ROW][C]11[/C][C]4165[/C][C]4094.27738822227[/C][C]70.7226117777277[/C][/ROW]
[ROW][C]12[/C][C]4200[/C][C]4204.31022574645[/C][C]-4.31022574644794[/C][/ROW]
[ROW][C]13[/C][C]4240[/C][C]4238.69876933216[/C][C]1.30123066783926[/C][/ROW]
[ROW][C]14[/C][C]4315[/C][C]4278.88336426642[/C][C]36.1166357335778[/C][/ROW]
[ROW][C]15[/C][C]4355[/C][C]4359.00693548539[/C][C]-4.00693548539402[/C][/ROW]
[ROW][C]16[/C][C]4400[/C][C]4398.43850437568[/C][C]1.56149562432256[/C][/ROW]
[ROW][C]17[/C][C]4440[/C][C]4443.66002096704[/C][C]-3.66002096704415[/C][/ROW]
[ROW][C]18[/C][C]4525[/C][C]4483.14080377788[/C][C]41.859196222118[/C][/ROW]
[ROW][C]19[/C][C]4525[/C][C]4574.07902500632[/C][C]-49.079025006321[/C][/ROW]
[ROW][C]20[/C][C]4530[/C][C]4567.11658581812[/C][C]-37.1165858181166[/C][/ROW]
[ROW][C]21[/C][C]4565[/C][C]4566.85115987294[/C][C]-1.85115987293739[/C][/ROW]
[ROW][C]22[/C][C]4585[/C][C]4601.58855098775[/C][C]-16.5885509877498[/C][/ROW]
[ROW][C]23[/C][C]4685[/C][C]4619.23526916404[/C][C]65.7647308359565[/C][/ROW]
[ROW][C]24[/C][C]4740[/C][C]4728.56477273741[/C][C]11.4352272625874[/C][/ROW]
[ROW][C]25[/C][C]4780[/C][C]4785.18699474384[/C][C]-5.18699474383629[/C][/ROW]
[ROW][C]26[/C][C]4850[/C][C]4824.45115829499[/C][C]25.5488417050101[/C][/ROW]
[ROW][C]27[/C][C]4905[/C][C]4898.07556315383[/C][C]6.92443684616683[/C][/ROW]
[ROW][C]28[/C][C]4925[/C][C]4954.0578762794[/C][C]-29.0578762794048[/C][/ROW]
[ROW][C]29[/C][C]4950[/C][C]4969.93567343394[/C][C]-19.9356734339399[/C][/ROW]
[ROW][C]30[/C][C]4970[/C][C]4992.10756277074[/C][C]-22.1075627707423[/C][/ROW]
[ROW][C]31[/C][C]4985[/C][C]5008.97134396096[/C][C]-23.9713439609586[/C][/ROW]
[ROW][C]32[/C][C]5040[/C][C]5020.57072578311[/C][C]19.4292742168927[/C][/ROW]
[ROW][C]33[/C][C]5105[/C][C]5078.32699773816[/C][C]26.673002261844[/C][/ROW]
[ROW][C]34[/C][C]5015[/C][C]5147.11087804529[/C][C]-132.110878045293[/C][/ROW]
[ROW][C]35[/C][C]5045[/C][C]5038.36939012103[/C][C]6.63060987897006[/C][/ROW]
[ROW][C]36[/C][C]5025[/C][C]5069.310020422[/C][C]-44.310020422[/C][/ROW]
[ROW][C]37[/C][C]4960[/C][C]5043.02412084318[/C][C]-83.0241208431771[/C][/ROW]
[ROW][C]38[/C][C]4925[/C][C]4966.24616901039[/C][C]-41.2461690103873[/C][/ROW]
[ROW][C]39[/C][C]4955[/C][C]4925.39491293013[/C][C]29.6050870698673[/C][/ROW]
[ROW][C]40[/C][C]4945[/C][C]4959.59474408731[/C][C]-14.5947440873106[/C][/ROW]
[ROW][C]41[/C][C]4935[/C][C]4947.52430731392[/C][C]-12.5243073139191[/C][/ROW]
[ROW][C]42[/C][C]4925[/C][C]4935.74758644311[/C][C]-10.7475864431126[/C][/ROW]
[ROW][C]43[/C][C]4995[/C][C]4924.22291440612[/C][C]70.7770855938825[/C][/ROW]
[ROW][C]44[/C][C]4970[/C][C]5004.2634796843[/C][C]-34.263479684304[/C][/ROW]
[ROW][C]45[/C][C]5005[/C][C]4974.4028005317[/C][C]30.5971994682977[/C][/ROW]
[ROW][C]46[/C][C]5140[/C][C]5013.74337454677[/C][C]126.256625453228[/C][/ROW]
[ROW][C]47[/C][C]5190[/C][C]5166.6543676179[/C][C]23.3456323820992[/C][/ROW]
[ROW][C]48[/C][C]5220[/C][C]5219.96622122032[/C][C]0.0337787796779594[/C][/ROW]
[ROW][C]49[/C][C]5250[/C][C]5249.97101313906[/C][C]0.0289868609443147[/C][/ROW]
[ROW][C]50[/C][C]5235[/C][C]5279.97512526754[/C][C]-44.9751252675378[/C][/ROW]
[ROW][C]51[/C][C]5255[/C][C]5258.59487271328[/C][C]-3.59487271327907[/C][/ROW]
[ROW][C]52[/C][C]5335[/C][C]5278.08489757314[/C][C]56.9151024268613[/C][/ROW]
[ROW][C]53[/C][C]5360[/C][C]5366.15897686641[/C][C]-6.15897686640892[/C][/ROW]
[ROW][C]54[/C][C]5345[/C][C]5390.28525327699[/C][C]-45.2852532769857[/C][/ROW]
[ROW][C]55[/C][C]5325[/C][C]5368.86100540281[/C][C]-43.8610054028104[/C][/ROW]
[ROW][C]56[/C][C]5320[/C][C]5342.63880390612[/C][C]-22.6388039061176[/C][/ROW]
[ROW][C]57[/C][C]5350[/C][C]5334.42722226875[/C][C]15.5727777312459[/C][/ROW]
[ROW][C]58[/C][C]5430[/C][C]5366.63640466248[/C][C]63.3635953375197[/C][/ROW]
[ROW][C]59[/C][C]5440[/C][C]5455.62527881446[/C][C]-15.6252788144557[/C][/ROW]
[ROW][C]60[/C][C]5490[/C][C]5463.40864852218[/C][C]26.5913514778204[/C][/ROW]
[ROW][C]61[/C][C]5505[/C][C]5517.18094570153[/C][C]-12.180945701527[/C][/ROW]
[ROW][C]62[/C][C]5545[/C][C]5530.45293472961[/C][C]14.5470652703852[/C][/ROW]
[ROW][C]63[/C][C]5530[/C][C]5572.51660769987[/C][C]-42.5166076998676[/C][/ROW]
[ROW][C]64[/C][C]5480[/C][C]5551.48512489105[/C][C]-71.4851248910518[/C][/ROW]
[ROW][C]65[/C][C]5535[/C][C]5491.34411587852[/C][C]43.6558841214755[/C][/ROW]
[ROW][C]66[/C][C]5560[/C][C]5552.53721849953[/C][C]7.46278150046965[/C][/ROW]
[ROW][C]67[/C][C]5575[/C][C]5578.59590217072[/C][C]-3.59590217071582[/C][/ROW]
[ROW][C]68[/C][C]5595[/C][C]5593.08578098988[/C][C]1.91421901011654[/C][/ROW]
[ROW][C]69[/C][C]5595[/C][C]5613.35733555824[/C][C]-18.3573355582375[/C][/ROW]
[ROW][C]70[/C][C]5500[/C][C]5610.75313075863[/C][C]-110.753130758627[/C][/ROW]
[ROW][C]71[/C][C]5450[/C][C]5500.04149146443[/C][C]-50.0414914644298[/C][/ROW]
[ROW][C]72[/C][C]5260[/C][C]5442.94251504501[/C][C]-182.942515045008[/C][/ROW]
[ROW][C]73[/C][C]5240[/C][C]5226.98995922765[/C][C]13.0100407723494[/C][/ROW]
[ROW][C]74[/C][C]5245[/C][C]5208.83558712474[/C][C]36.1644128752614[/C][/ROW]
[ROW][C]75[/C][C]5205[/C][C]5218.96593609538[/C][C]-13.9659360953774[/C][/ROW]
[ROW][C]76[/C][C]5180[/C][C]5176.98470316017[/C][C]3.01529683983063[/C][/ROW]
[ROW][C]77[/C][C]5155[/C][C]5152.41245861943[/C][C]2.58754138056884[/C][/ROW]
[ROW][C]78[/C][C]5160[/C][C]5127.77953191616[/C][C]32.2204680838422[/C][/ROW]
[ROW][C]79[/C][C]5150[/C][C]5137.35038575077[/C][C]12.6496142492297[/C][/ROW]
[ROW][C]80[/C][C]5070[/C][C]5129.14488288989[/C][C]-59.1448828898874[/C][/ROW]
[ROW][C]81[/C][C]4855[/C][C]5040.75448291024[/C][C]-185.754482910237[/C][/ROW]
[ROW][C]82[/C][C]4825[/C][C]4799.40301624943[/C][C]25.5969837505663[/C][/ROW]
[ROW][C]83[/C][C]5015[/C][C]4773.03425062587[/C][C]241.965749374133[/C][/ROW]
[ROW][C]84[/C][C]5070[/C][C]4997.35994913819[/C][C]72.6400508618126[/C][/ROW]
[ROW][C]85[/C][C]5075[/C][C]5062.66479803623[/C][C]12.3352019637696[/C][/ROW]
[ROW][C]86[/C][C]5060[/C][C]5069.41469208029[/C][C]-9.41469208029321[/C][/ROW]
[ROW][C]87[/C][C]5070[/C][C]5053.07910684656[/C][C]16.9208931534449[/C][/ROW]
[ROW][C]88[/C][C]5135[/C][C]5065.47953533053[/C][C]69.5204646694683[/C][/ROW]
[ROW][C]89[/C][C]5135[/C][C]5140.34183409328[/C][C]-5.34183409328216[/C][/ROW]
[ROW][C]90[/C][C]5110[/C][C]5139.58403185448[/C][C]-29.5840318544815[/C][/ROW]
[ROW][C]91[/C][C]5015[/C][C]5110.38718762821[/C][C]-95.3871876282119[/C][/ROW]
[ROW][C]92[/C][C]5125[/C][C]5001.85538879745[/C][C]123.144611202545[/C][/ROW]
[ROW][C]93[/C][C]5185[/C][C]5129.32490590262[/C][C]55.6750940973798[/C][/ROW]
[ROW][C]94[/C][C]5190[/C][C]5197.2230753732[/C][C]-7.22307537319557[/C][/ROW]
[ROW][C]95[/C][C]5230[/C][C]5201.19839684645[/C][C]28.8016031535517[/C][/ROW]
[ROW][C]96[/C][C]5350[/C][C]5245.28424432312[/C][C]104.715755676884[/C][/ROW]
[ROW][C]97[/C][C]5415[/C][C]5380.13941067683[/C][C]34.860589323167[/C][/ROW]
[ROW][C]98[/C][C]5465[/C][C]5450.08479688196[/C][C]14.9152031180365[/C][/ROW]
[ROW][C]99[/C][C]5560[/C][C]5502.20069455262[/C][C]57.7993054473782[/C][/ROW]
[ROW][C]100[/C][C]5585[/C][C]5605.40020848441[/C][C]-20.4002084844078[/C][/ROW]
[ROW][C]101[/C][C]5615[/C][C]5627.50619803939[/C][C]-12.5061980393939[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300464&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300464&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
33860381545
438753876.38378132876-1.38378132876187
538853891.18747560855-6.18747560854763
639303900.3097091360629.6902908639418
739603949.5216274574510.4783725425473
839953981.0081083239613.991891676038
938754017.99302336475-142.993023364752
1040653877.70777463811187.292225361895
1141654094.2773882222770.7226117777277
1242004204.31022574645-4.31022574644794
1342404238.698769332161.30123066783926
1443154278.8833642664236.1166357335778
1543554359.00693548539-4.00693548539402
1644004398.438504375681.56149562432256
1744404443.66002096704-3.66002096704415
1845254483.1408037778841.859196222118
1945254574.07902500632-49.079025006321
2045304567.11658581812-37.1165858181166
2145654566.85115987294-1.85115987293739
2245854601.58855098775-16.5885509877498
2346854619.2352691640465.7647308359565
2447404728.5647727374111.4352272625874
2547804785.18699474384-5.18699474383629
2648504824.4511582949925.5488417050101
2749054898.075563153836.92443684616683
2849254954.0578762794-29.0578762794048
2949504969.93567343394-19.9356734339399
3049704992.10756277074-22.1075627707423
3149855008.97134396096-23.9713439609586
3250405020.5707257831119.4292742168927
3351055078.3269977381626.673002261844
3450155147.11087804529-132.110878045293
3550455038.369390121036.63060987897006
3650255069.310020422-44.310020422
3749605043.02412084318-83.0241208431771
3849254966.24616901039-41.2461690103873
3949554925.3949129301329.6050870698673
4049454959.59474408731-14.5947440873106
4149354947.52430731392-12.5243073139191
4249254935.74758644311-10.7475864431126
4349954924.2229144061270.7770855938825
4449705004.2634796843-34.263479684304
4550054974.402800531730.5971994682977
4651405013.74337454677126.256625453228
4751905166.654367617923.3456323820992
4852205219.966221220320.0337787796779594
4952505249.971013139060.0289868609443147
5052355279.97512526754-44.9751252675378
5152555258.59487271328-3.59487271327907
5253355278.0848975731456.9151024268613
5353605366.15897686641-6.15897686640892
5453455390.28525327699-45.2852532769857
5553255368.86100540281-43.8610054028104
5653205342.63880390612-22.6388039061176
5753505334.4272222687515.5727777312459
5854305366.6364046624863.3635953375197
5954405455.62527881446-15.6252788144557
6054905463.4086485221826.5913514778204
6155055517.18094570153-12.180945701527
6255455530.4529347296114.5470652703852
6355305572.51660769987-42.5166076998676
6454805551.48512489105-71.4851248910518
6555355491.3441158785243.6558841214755
6655605552.537218499537.46278150046965
6755755578.59590217072-3.59590217071582
6855955593.085780989881.91421901011654
6955955613.35733555824-18.3573355582375
7055005610.75313075863-110.753130758627
7154505500.04149146443-50.0414914644298
7252605442.94251504501-182.942515045008
7352405226.9899592276513.0100407723494
7452455208.8355871247436.1644128752614
7552055218.96593609538-13.9659360953774
7651805176.984703160173.01529683983063
7751555152.412458619432.58754138056884
7851605127.7795319161632.2204680838422
7951505137.3503857507712.6496142492297
8050705129.14488288989-59.1448828898874
8148555040.75448291024-185.754482910237
8248254799.4030162494325.5969837505663
8350154773.03425062587241.965749374133
8450704997.3599491381972.6400508618126
8550755062.6647980362312.3352019637696
8650605069.41469208029-9.41469208029321
8750705053.0791068465616.9208931534449
8851355065.4795353305369.5204646694683
8951355140.34183409328-5.34183409328216
9051105139.58403185448-29.5840318544815
9150155110.38718762821-95.3871876282119
9251255001.85538879745123.144611202545
9351855129.3249059026255.6750940973798
9451905197.2230753732-7.22307537319557
9552305201.1983968464528.8016031535517
9653505245.28424432312104.715755676884
9754155380.1394106768334.860589323167
9854655450.0847968819614.9152031180365
9955605502.2006945526257.7993054473782
10055855605.40020848441-20.4002084844078
10156155627.50619803939-12.5061980393939







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1025655.7320461835536.756984802275774.70710756373
1035696.4640923665515.878588520735877.04959621127
1045737.1961385495500.684168795135973.70810830287
1055777.9281847325486.88667038176068.96969908231
1065818.660230915015472.997660124086164.32280170593
1075859.392277098015458.34365650496260.44089769111
1085900.124323281015442.579737794316357.6689087677
1095940.856369464015425.518128438936456.19461048908
1105981.588415647015407.054608221486556.12222307254
1116022.320461830015387.132645294066657.50827836596
1126063.052508013015365.724294904826760.38072112121
1136103.784554196015342.819341870836864.7497665212

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
102 & 5655.732046183 & 5536.75698480227 & 5774.70710756373 \tabularnewline
103 & 5696.464092366 & 5515.87858852073 & 5877.04959621127 \tabularnewline
104 & 5737.196138549 & 5500.68416879513 & 5973.70810830287 \tabularnewline
105 & 5777.928184732 & 5486.8866703817 & 6068.96969908231 \tabularnewline
106 & 5818.66023091501 & 5472.99766012408 & 6164.32280170593 \tabularnewline
107 & 5859.39227709801 & 5458.3436565049 & 6260.44089769111 \tabularnewline
108 & 5900.12432328101 & 5442.57973779431 & 6357.6689087677 \tabularnewline
109 & 5940.85636946401 & 5425.51812843893 & 6456.19461048908 \tabularnewline
110 & 5981.58841564701 & 5407.05460822148 & 6556.12222307254 \tabularnewline
111 & 6022.32046183001 & 5387.13264529406 & 6657.50827836596 \tabularnewline
112 & 6063.05250801301 & 5365.72429490482 & 6760.38072112121 \tabularnewline
113 & 6103.78455419601 & 5342.81934187083 & 6864.7497665212 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300464&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]102[/C][C]5655.732046183[/C][C]5536.75698480227[/C][C]5774.70710756373[/C][/ROW]
[ROW][C]103[/C][C]5696.464092366[/C][C]5515.87858852073[/C][C]5877.04959621127[/C][/ROW]
[ROW][C]104[/C][C]5737.196138549[/C][C]5500.68416879513[/C][C]5973.70810830287[/C][/ROW]
[ROW][C]105[/C][C]5777.928184732[/C][C]5486.8866703817[/C][C]6068.96969908231[/C][/ROW]
[ROW][C]106[/C][C]5818.66023091501[/C][C]5472.99766012408[/C][C]6164.32280170593[/C][/ROW]
[ROW][C]107[/C][C]5859.39227709801[/C][C]5458.3436565049[/C][C]6260.44089769111[/C][/ROW]
[ROW][C]108[/C][C]5900.12432328101[/C][C]5442.57973779431[/C][C]6357.6689087677[/C][/ROW]
[ROW][C]109[/C][C]5940.85636946401[/C][C]5425.51812843893[/C][C]6456.19461048908[/C][/ROW]
[ROW][C]110[/C][C]5981.58841564701[/C][C]5407.05460822148[/C][C]6556.12222307254[/C][/ROW]
[ROW][C]111[/C][C]6022.32046183001[/C][C]5387.13264529406[/C][C]6657.50827836596[/C][/ROW]
[ROW][C]112[/C][C]6063.05250801301[/C][C]5365.72429490482[/C][C]6760.38072112121[/C][/ROW]
[ROW][C]113[/C][C]6103.78455419601[/C][C]5342.81934187083[/C][C]6864.7497665212[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300464&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300464&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
1025655.7320461835536.756984802275774.70710756373
1035696.4640923665515.878588520735877.04959621127
1045737.1961385495500.684168795135973.70810830287
1055777.9281847325486.88667038176068.96969908231
1065818.660230915015472.997660124086164.32280170593
1075859.392277098015458.34365650496260.44089769111
1085900.124323281015442.579737794316357.6689087677
1095940.856369464015425.518128438936456.19461048908
1105981.588415647015407.054608221486556.12222307254
1116022.320461830015387.132645294066657.50827836596
1126063.052508013015365.724294904826760.38072112121
1136103.784554196015342.819341870836864.7497665212



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):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Triple'
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')