Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 28 Jul 2012 03:19:36 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jul/28/t1343460019j38fclla2hnuw3f.htm/, Retrieved Mon, 06 May 2024 15:53:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=168899, Retrieved Mon, 06 May 2024 15:53:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Maele Karen
Estimated Impact169
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2012-07-28 07:19:36] [459538fe31c621d37110fb87514358a8] [Current]
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Dataseries X:
14724
14404
14058
13427
19946
19631
14724
11462
11778
11778
12093
12760
13742
13427
11462
11778
20929
22893
17666
14724
15387
15707
17351
18964
19315
16022
16369
12093
24222
27800
19631
17004
18649
20613
23555
27164
27164
24853
23871
17982
27800
32391
28462
24222
24853
27164
30426
34355
31724
30111
30111
24853
32391
37297
33373
29129
30426
35653
37964
41222
38595
34355
33373
25520
30742
36315
30111
26502
30111
33689
35653
40906
38280
31724
32391
26186
31409
36000
30742
27164
30426
34355
33689
41542
40244
35017
35333
28462
32706
39262
34355
31409
36315
39262
36982
47431
44835
38946
37297
29764
34035
37964
33053
33053
38595
41542
39924
51355
48413
42871
40560
32391
35333
40560
36631
35653
40244
44168
39924
50057




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time12 seconds
R Server'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 12 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168899&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]12 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168899&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168899&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time12 seconds
R Server'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.20403309369351
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.20403309369351 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168899&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]0.20403309369351[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168899&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168899&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
alpha0.20403309369351
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131374213610.9963300343131.00366996571
141342713239.9068014585187.09319854149
151146211242.8757523152219.124247684769
161177811485.7203055924292.279694407618
172092920230.2840525466698.715947453416
182289321852.92329837811040.07670162192
191766616082.11735174491583.8826482551
201472412978.59339360551745.40660639453
211538713987.53059097271399.46940902726
221570714597.07332064141109.92667935857
231735115395.6004437631955.39955623702
241896416605.12396546642358.87603453359
251931518365.158137745949.841862254987
261602218027.1165078794-2005.1165078794
271636914939.45756685991429.54243314014
281209315526.9281590739-3433.92815907391
292422226101.8951676827-1879.89516768266
302780027804.9038645905-4.90386459049478
311963120993.4730598489-1362.47305984887
321700416779.0146641708224.985335829184
331864917209.38391676941439.61608323058
342061317573.63720952263039.36279047736
352355519565.17535934833989.82464065171
362716421617.0975934985546.90240650197
372716422894.54586957454269.45413042547
382485320139.18848928354713.81151071647
392387121100.77421149492770.22578850505
401798216727.94531230511254.05468769486
412780034438.0605139476-6638.06051394756
423239137882.04810702-5491.04810702001
432846226251.40586456312210.59413543695
442422223012.21445803921209.78554196083
452485325022.3333381055-169.333338105465
462716426620.4728294818543.527170518213
473042629271.80707254721154.19292745275
483435532284.82863912952070.17136087054
493172431469.3140566699254.685943330052
503011127498.47090424322612.52909575683
513011126201.82130779323909.17869220677
522485320017.33352121114835.66647878889
533239133770.7342503832-1379.73425038322
543729740164.5706482887-2867.57064828866
553337334149.7996503293-776.799650329347
562912928590.3770677499538.622932250095
573042629459.2793815632966.72061843682
583565332246.50276428833406.49723571167
593796436562.5139621141401.48603788604
604122241025.1425838211196.857416178864
613859537820.2898812772774.710118722767
623435535326.7509382632-971.750938263169
633337334062.0869671078-689.086967107818
642552026665.9064856926-1145.90648569263
653074234727.4623545744-3985.4623545744
663631539618.6772949453-3303.67729494531
673011135001.6882023544-4890.68820235438
682650229562.9722773953-3060.97227739526
693011130026.976917797884.023082202235
703368934465.0438852323-776.043885232306
713565336254.3389658387-601.338965838673
724090639204.20564408721701.79435591277
733828036884.69757535141395.30242464865
743172433279.1808024148-1555.18080241477
753239132159.2666006519231.733399348061
762618624850.40859946341335.59140053664
773140930991.7739080546417.226091945377
783600037343.9316194407-1343.93161944068
793074231635.4168032464-893.416803246397
802716428274.2709432499-1110.27094324993
813042631839.5234701361-1413.52347013606
823435535454.4327135437-1099.43271354368
833368937401.7383848381-3712.73838483811
844154241668.0958059479-126.09580594788
854024438666.99616761921577.00383238075
863501732619.3128675462397.68713245399
873533333747.57837393131585.42162606867
882846227238.42839434311223.57160565693
893270632872.4635454833-166.463545483319
903926237908.44076506441353.55923493555
913435532786.9211086221568.07889137803
923140929479.11468004641929.88531995362
933631533750.3179018052564.68209819503
943926238923.3403238677338.659676132338
953698239003.0396996794-2021.03969967937
964743147584.0086961646-153.008696164565
974483545656.7060588895-821.706058889504
983894638972.8461389797-26.8461389796576
993729738925.811594511-1628.811594511
1002976430793.1558907558-1029.15589075577
1013403535167.8593378996-1132.85933789958
1023796441623.5671532351-3659.56715323507
1033305335415.6588134337-2362.65881343371
1043305331514.52070856831538.47929143171
1053859536235.85351877882359.14648122118
1064154239624.50420121521917.49579878481
1073992438091.45974048841832.5402595116
1085135549357.15123905571997.8487609443
1094841347204.33299346651208.66700653355
1104287141213.79019136981657.20980863023
1114056040123.8289220667436.171077933344
1123239132300.576758648890.4232413511781
1133533337187.7525561103-1854.75255611033
1144056041794.1807584359-1234.18075843588
1153663136652.943252462-21.9432524620279
1163565336270.3900896026-617.390089602573
1174024441635.0680656209-1391.06806562086
1184416844060.2483030534107.751696946645
1193992441942.7018485672-2018.70184856719
1205005752975.2835552999-2918.28355529987

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 13742 & 13610.9963300343 & 131.00366996571 \tabularnewline
14 & 13427 & 13239.9068014585 & 187.09319854149 \tabularnewline
15 & 11462 & 11242.8757523152 & 219.124247684769 \tabularnewline
16 & 11778 & 11485.7203055924 & 292.279694407618 \tabularnewline
17 & 20929 & 20230.2840525466 & 698.715947453416 \tabularnewline
18 & 22893 & 21852.9232983781 & 1040.07670162192 \tabularnewline
19 & 17666 & 16082.1173517449 & 1583.8826482551 \tabularnewline
20 & 14724 & 12978.5933936055 & 1745.40660639453 \tabularnewline
21 & 15387 & 13987.5305909727 & 1399.46940902726 \tabularnewline
22 & 15707 & 14597.0733206414 & 1109.92667935857 \tabularnewline
23 & 17351 & 15395.600443763 & 1955.39955623702 \tabularnewline
24 & 18964 & 16605.1239654664 & 2358.87603453359 \tabularnewline
25 & 19315 & 18365.158137745 & 949.841862254987 \tabularnewline
26 & 16022 & 18027.1165078794 & -2005.1165078794 \tabularnewline
27 & 16369 & 14939.4575668599 & 1429.54243314014 \tabularnewline
28 & 12093 & 15526.9281590739 & -3433.92815907391 \tabularnewline
29 & 24222 & 26101.8951676827 & -1879.89516768266 \tabularnewline
30 & 27800 & 27804.9038645905 & -4.90386459049478 \tabularnewline
31 & 19631 & 20993.4730598489 & -1362.47305984887 \tabularnewline
32 & 17004 & 16779.0146641708 & 224.985335829184 \tabularnewline
33 & 18649 & 17209.3839167694 & 1439.61608323058 \tabularnewline
34 & 20613 & 17573.6372095226 & 3039.36279047736 \tabularnewline
35 & 23555 & 19565.1753593483 & 3989.82464065171 \tabularnewline
36 & 27164 & 21617.097593498 & 5546.90240650197 \tabularnewline
37 & 27164 & 22894.5458695745 & 4269.45413042547 \tabularnewline
38 & 24853 & 20139.1884892835 & 4713.81151071647 \tabularnewline
39 & 23871 & 21100.7742114949 & 2770.22578850505 \tabularnewline
40 & 17982 & 16727.9453123051 & 1254.05468769486 \tabularnewline
41 & 27800 & 34438.0605139476 & -6638.06051394756 \tabularnewline
42 & 32391 & 37882.04810702 & -5491.04810702001 \tabularnewline
43 & 28462 & 26251.4058645631 & 2210.59413543695 \tabularnewline
44 & 24222 & 23012.2144580392 & 1209.78554196083 \tabularnewline
45 & 24853 & 25022.3333381055 & -169.333338105465 \tabularnewline
46 & 27164 & 26620.4728294818 & 543.527170518213 \tabularnewline
47 & 30426 & 29271.8070725472 & 1154.19292745275 \tabularnewline
48 & 34355 & 32284.8286391295 & 2070.17136087054 \tabularnewline
49 & 31724 & 31469.3140566699 & 254.685943330052 \tabularnewline
50 & 30111 & 27498.4709042432 & 2612.52909575683 \tabularnewline
51 & 30111 & 26201.8213077932 & 3909.17869220677 \tabularnewline
52 & 24853 & 20017.3335212111 & 4835.66647878889 \tabularnewline
53 & 32391 & 33770.7342503832 & -1379.73425038322 \tabularnewline
54 & 37297 & 40164.5706482887 & -2867.57064828866 \tabularnewline
55 & 33373 & 34149.7996503293 & -776.799650329347 \tabularnewline
56 & 29129 & 28590.3770677499 & 538.622932250095 \tabularnewline
57 & 30426 & 29459.2793815632 & 966.72061843682 \tabularnewline
58 & 35653 & 32246.5027642883 & 3406.49723571167 \tabularnewline
59 & 37964 & 36562.513962114 & 1401.48603788604 \tabularnewline
60 & 41222 & 41025.1425838211 & 196.857416178864 \tabularnewline
61 & 38595 & 37820.2898812772 & 774.710118722767 \tabularnewline
62 & 34355 & 35326.7509382632 & -971.750938263169 \tabularnewline
63 & 33373 & 34062.0869671078 & -689.086967107818 \tabularnewline
64 & 25520 & 26665.9064856926 & -1145.90648569263 \tabularnewline
65 & 30742 & 34727.4623545744 & -3985.4623545744 \tabularnewline
66 & 36315 & 39618.6772949453 & -3303.67729494531 \tabularnewline
67 & 30111 & 35001.6882023544 & -4890.68820235438 \tabularnewline
68 & 26502 & 29562.9722773953 & -3060.97227739526 \tabularnewline
69 & 30111 & 30026.9769177978 & 84.023082202235 \tabularnewline
70 & 33689 & 34465.0438852323 & -776.043885232306 \tabularnewline
71 & 35653 & 36254.3389658387 & -601.338965838673 \tabularnewline
72 & 40906 & 39204.2056440872 & 1701.79435591277 \tabularnewline
73 & 38280 & 36884.6975753514 & 1395.30242464865 \tabularnewline
74 & 31724 & 33279.1808024148 & -1555.18080241477 \tabularnewline
75 & 32391 & 32159.2666006519 & 231.733399348061 \tabularnewline
76 & 26186 & 24850.4085994634 & 1335.59140053664 \tabularnewline
77 & 31409 & 30991.7739080546 & 417.226091945377 \tabularnewline
78 & 36000 & 37343.9316194407 & -1343.93161944068 \tabularnewline
79 & 30742 & 31635.4168032464 & -893.416803246397 \tabularnewline
80 & 27164 & 28274.2709432499 & -1110.27094324993 \tabularnewline
81 & 30426 & 31839.5234701361 & -1413.52347013606 \tabularnewline
82 & 34355 & 35454.4327135437 & -1099.43271354368 \tabularnewline
83 & 33689 & 37401.7383848381 & -3712.73838483811 \tabularnewline
84 & 41542 & 41668.0958059479 & -126.09580594788 \tabularnewline
85 & 40244 & 38666.9961676192 & 1577.00383238075 \tabularnewline
86 & 35017 & 32619.312867546 & 2397.68713245399 \tabularnewline
87 & 35333 & 33747.5783739313 & 1585.42162606867 \tabularnewline
88 & 28462 & 27238.4283943431 & 1223.57160565693 \tabularnewline
89 & 32706 & 32872.4635454833 & -166.463545483319 \tabularnewline
90 & 39262 & 37908.4407650644 & 1353.55923493555 \tabularnewline
91 & 34355 & 32786.921108622 & 1568.07889137803 \tabularnewline
92 & 31409 & 29479.1146800464 & 1929.88531995362 \tabularnewline
93 & 36315 & 33750.317901805 & 2564.68209819503 \tabularnewline
94 & 39262 & 38923.3403238677 & 338.659676132338 \tabularnewline
95 & 36982 & 39003.0396996794 & -2021.03969967937 \tabularnewline
96 & 47431 & 47584.0086961646 & -153.008696164565 \tabularnewline
97 & 44835 & 45656.7060588895 & -821.706058889504 \tabularnewline
98 & 38946 & 38972.8461389797 & -26.8461389796576 \tabularnewline
99 & 37297 & 38925.811594511 & -1628.811594511 \tabularnewline
100 & 29764 & 30793.1558907558 & -1029.15589075577 \tabularnewline
101 & 34035 & 35167.8593378996 & -1132.85933789958 \tabularnewline
102 & 37964 & 41623.5671532351 & -3659.56715323507 \tabularnewline
103 & 33053 & 35415.6588134337 & -2362.65881343371 \tabularnewline
104 & 33053 & 31514.5207085683 & 1538.47929143171 \tabularnewline
105 & 38595 & 36235.8535187788 & 2359.14648122118 \tabularnewline
106 & 41542 & 39624.5042012152 & 1917.49579878481 \tabularnewline
107 & 39924 & 38091.4597404884 & 1832.5402595116 \tabularnewline
108 & 51355 & 49357.1512390557 & 1997.8487609443 \tabularnewline
109 & 48413 & 47204.3329934665 & 1208.66700653355 \tabularnewline
110 & 42871 & 41213.7901913698 & 1657.20980863023 \tabularnewline
111 & 40560 & 40123.8289220667 & 436.171077933344 \tabularnewline
112 & 32391 & 32300.5767586488 & 90.4232413511781 \tabularnewline
113 & 35333 & 37187.7525561103 & -1854.75255611033 \tabularnewline
114 & 40560 & 41794.1807584359 & -1234.18075843588 \tabularnewline
115 & 36631 & 36652.943252462 & -21.9432524620279 \tabularnewline
116 & 35653 & 36270.3900896026 & -617.390089602573 \tabularnewline
117 & 40244 & 41635.0680656209 & -1391.06806562086 \tabularnewline
118 & 44168 & 44060.2483030534 & 107.751696946645 \tabularnewline
119 & 39924 & 41942.7018485672 & -2018.70184856719 \tabularnewline
120 & 50057 & 52975.2835552999 & -2918.28355529987 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168899&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]13742[/C][C]13610.9963300343[/C][C]131.00366996571[/C][/ROW]
[ROW][C]14[/C][C]13427[/C][C]13239.9068014585[/C][C]187.09319854149[/C][/ROW]
[ROW][C]15[/C][C]11462[/C][C]11242.8757523152[/C][C]219.124247684769[/C][/ROW]
[ROW][C]16[/C][C]11778[/C][C]11485.7203055924[/C][C]292.279694407618[/C][/ROW]
[ROW][C]17[/C][C]20929[/C][C]20230.2840525466[/C][C]698.715947453416[/C][/ROW]
[ROW][C]18[/C][C]22893[/C][C]21852.9232983781[/C][C]1040.07670162192[/C][/ROW]
[ROW][C]19[/C][C]17666[/C][C]16082.1173517449[/C][C]1583.8826482551[/C][/ROW]
[ROW][C]20[/C][C]14724[/C][C]12978.5933936055[/C][C]1745.40660639453[/C][/ROW]
[ROW][C]21[/C][C]15387[/C][C]13987.5305909727[/C][C]1399.46940902726[/C][/ROW]
[ROW][C]22[/C][C]15707[/C][C]14597.0733206414[/C][C]1109.92667935857[/C][/ROW]
[ROW][C]23[/C][C]17351[/C][C]15395.600443763[/C][C]1955.39955623702[/C][/ROW]
[ROW][C]24[/C][C]18964[/C][C]16605.1239654664[/C][C]2358.87603453359[/C][/ROW]
[ROW][C]25[/C][C]19315[/C][C]18365.158137745[/C][C]949.841862254987[/C][/ROW]
[ROW][C]26[/C][C]16022[/C][C]18027.1165078794[/C][C]-2005.1165078794[/C][/ROW]
[ROW][C]27[/C][C]16369[/C][C]14939.4575668599[/C][C]1429.54243314014[/C][/ROW]
[ROW][C]28[/C][C]12093[/C][C]15526.9281590739[/C][C]-3433.92815907391[/C][/ROW]
[ROW][C]29[/C][C]24222[/C][C]26101.8951676827[/C][C]-1879.89516768266[/C][/ROW]
[ROW][C]30[/C][C]27800[/C][C]27804.9038645905[/C][C]-4.90386459049478[/C][/ROW]
[ROW][C]31[/C][C]19631[/C][C]20993.4730598489[/C][C]-1362.47305984887[/C][/ROW]
[ROW][C]32[/C][C]17004[/C][C]16779.0146641708[/C][C]224.985335829184[/C][/ROW]
[ROW][C]33[/C][C]18649[/C][C]17209.3839167694[/C][C]1439.61608323058[/C][/ROW]
[ROW][C]34[/C][C]20613[/C][C]17573.6372095226[/C][C]3039.36279047736[/C][/ROW]
[ROW][C]35[/C][C]23555[/C][C]19565.1753593483[/C][C]3989.82464065171[/C][/ROW]
[ROW][C]36[/C][C]27164[/C][C]21617.097593498[/C][C]5546.90240650197[/C][/ROW]
[ROW][C]37[/C][C]27164[/C][C]22894.5458695745[/C][C]4269.45413042547[/C][/ROW]
[ROW][C]38[/C][C]24853[/C][C]20139.1884892835[/C][C]4713.81151071647[/C][/ROW]
[ROW][C]39[/C][C]23871[/C][C]21100.7742114949[/C][C]2770.22578850505[/C][/ROW]
[ROW][C]40[/C][C]17982[/C][C]16727.9453123051[/C][C]1254.05468769486[/C][/ROW]
[ROW][C]41[/C][C]27800[/C][C]34438.0605139476[/C][C]-6638.06051394756[/C][/ROW]
[ROW][C]42[/C][C]32391[/C][C]37882.04810702[/C][C]-5491.04810702001[/C][/ROW]
[ROW][C]43[/C][C]28462[/C][C]26251.4058645631[/C][C]2210.59413543695[/C][/ROW]
[ROW][C]44[/C][C]24222[/C][C]23012.2144580392[/C][C]1209.78554196083[/C][/ROW]
[ROW][C]45[/C][C]24853[/C][C]25022.3333381055[/C][C]-169.333338105465[/C][/ROW]
[ROW][C]46[/C][C]27164[/C][C]26620.4728294818[/C][C]543.527170518213[/C][/ROW]
[ROW][C]47[/C][C]30426[/C][C]29271.8070725472[/C][C]1154.19292745275[/C][/ROW]
[ROW][C]48[/C][C]34355[/C][C]32284.8286391295[/C][C]2070.17136087054[/C][/ROW]
[ROW][C]49[/C][C]31724[/C][C]31469.3140566699[/C][C]254.685943330052[/C][/ROW]
[ROW][C]50[/C][C]30111[/C][C]27498.4709042432[/C][C]2612.52909575683[/C][/ROW]
[ROW][C]51[/C][C]30111[/C][C]26201.8213077932[/C][C]3909.17869220677[/C][/ROW]
[ROW][C]52[/C][C]24853[/C][C]20017.3335212111[/C][C]4835.66647878889[/C][/ROW]
[ROW][C]53[/C][C]32391[/C][C]33770.7342503832[/C][C]-1379.73425038322[/C][/ROW]
[ROW][C]54[/C][C]37297[/C][C]40164.5706482887[/C][C]-2867.57064828866[/C][/ROW]
[ROW][C]55[/C][C]33373[/C][C]34149.7996503293[/C][C]-776.799650329347[/C][/ROW]
[ROW][C]56[/C][C]29129[/C][C]28590.3770677499[/C][C]538.622932250095[/C][/ROW]
[ROW][C]57[/C][C]30426[/C][C]29459.2793815632[/C][C]966.72061843682[/C][/ROW]
[ROW][C]58[/C][C]35653[/C][C]32246.5027642883[/C][C]3406.49723571167[/C][/ROW]
[ROW][C]59[/C][C]37964[/C][C]36562.513962114[/C][C]1401.48603788604[/C][/ROW]
[ROW][C]60[/C][C]41222[/C][C]41025.1425838211[/C][C]196.857416178864[/C][/ROW]
[ROW][C]61[/C][C]38595[/C][C]37820.2898812772[/C][C]774.710118722767[/C][/ROW]
[ROW][C]62[/C][C]34355[/C][C]35326.7509382632[/C][C]-971.750938263169[/C][/ROW]
[ROW][C]63[/C][C]33373[/C][C]34062.0869671078[/C][C]-689.086967107818[/C][/ROW]
[ROW][C]64[/C][C]25520[/C][C]26665.9064856926[/C][C]-1145.90648569263[/C][/ROW]
[ROW][C]65[/C][C]30742[/C][C]34727.4623545744[/C][C]-3985.4623545744[/C][/ROW]
[ROW][C]66[/C][C]36315[/C][C]39618.6772949453[/C][C]-3303.67729494531[/C][/ROW]
[ROW][C]67[/C][C]30111[/C][C]35001.6882023544[/C][C]-4890.68820235438[/C][/ROW]
[ROW][C]68[/C][C]26502[/C][C]29562.9722773953[/C][C]-3060.97227739526[/C][/ROW]
[ROW][C]69[/C][C]30111[/C][C]30026.9769177978[/C][C]84.023082202235[/C][/ROW]
[ROW][C]70[/C][C]33689[/C][C]34465.0438852323[/C][C]-776.043885232306[/C][/ROW]
[ROW][C]71[/C][C]35653[/C][C]36254.3389658387[/C][C]-601.338965838673[/C][/ROW]
[ROW][C]72[/C][C]40906[/C][C]39204.2056440872[/C][C]1701.79435591277[/C][/ROW]
[ROW][C]73[/C][C]38280[/C][C]36884.6975753514[/C][C]1395.30242464865[/C][/ROW]
[ROW][C]74[/C][C]31724[/C][C]33279.1808024148[/C][C]-1555.18080241477[/C][/ROW]
[ROW][C]75[/C][C]32391[/C][C]32159.2666006519[/C][C]231.733399348061[/C][/ROW]
[ROW][C]76[/C][C]26186[/C][C]24850.4085994634[/C][C]1335.59140053664[/C][/ROW]
[ROW][C]77[/C][C]31409[/C][C]30991.7739080546[/C][C]417.226091945377[/C][/ROW]
[ROW][C]78[/C][C]36000[/C][C]37343.9316194407[/C][C]-1343.93161944068[/C][/ROW]
[ROW][C]79[/C][C]30742[/C][C]31635.4168032464[/C][C]-893.416803246397[/C][/ROW]
[ROW][C]80[/C][C]27164[/C][C]28274.2709432499[/C][C]-1110.27094324993[/C][/ROW]
[ROW][C]81[/C][C]30426[/C][C]31839.5234701361[/C][C]-1413.52347013606[/C][/ROW]
[ROW][C]82[/C][C]34355[/C][C]35454.4327135437[/C][C]-1099.43271354368[/C][/ROW]
[ROW][C]83[/C][C]33689[/C][C]37401.7383848381[/C][C]-3712.73838483811[/C][/ROW]
[ROW][C]84[/C][C]41542[/C][C]41668.0958059479[/C][C]-126.09580594788[/C][/ROW]
[ROW][C]85[/C][C]40244[/C][C]38666.9961676192[/C][C]1577.00383238075[/C][/ROW]
[ROW][C]86[/C][C]35017[/C][C]32619.312867546[/C][C]2397.68713245399[/C][/ROW]
[ROW][C]87[/C][C]35333[/C][C]33747.5783739313[/C][C]1585.42162606867[/C][/ROW]
[ROW][C]88[/C][C]28462[/C][C]27238.4283943431[/C][C]1223.57160565693[/C][/ROW]
[ROW][C]89[/C][C]32706[/C][C]32872.4635454833[/C][C]-166.463545483319[/C][/ROW]
[ROW][C]90[/C][C]39262[/C][C]37908.4407650644[/C][C]1353.55923493555[/C][/ROW]
[ROW][C]91[/C][C]34355[/C][C]32786.921108622[/C][C]1568.07889137803[/C][/ROW]
[ROW][C]92[/C][C]31409[/C][C]29479.1146800464[/C][C]1929.88531995362[/C][/ROW]
[ROW][C]93[/C][C]36315[/C][C]33750.317901805[/C][C]2564.68209819503[/C][/ROW]
[ROW][C]94[/C][C]39262[/C][C]38923.3403238677[/C][C]338.659676132338[/C][/ROW]
[ROW][C]95[/C][C]36982[/C][C]39003.0396996794[/C][C]-2021.03969967937[/C][/ROW]
[ROW][C]96[/C][C]47431[/C][C]47584.0086961646[/C][C]-153.008696164565[/C][/ROW]
[ROW][C]97[/C][C]44835[/C][C]45656.7060588895[/C][C]-821.706058889504[/C][/ROW]
[ROW][C]98[/C][C]38946[/C][C]38972.8461389797[/C][C]-26.8461389796576[/C][/ROW]
[ROW][C]99[/C][C]37297[/C][C]38925.811594511[/C][C]-1628.811594511[/C][/ROW]
[ROW][C]100[/C][C]29764[/C][C]30793.1558907558[/C][C]-1029.15589075577[/C][/ROW]
[ROW][C]101[/C][C]34035[/C][C]35167.8593378996[/C][C]-1132.85933789958[/C][/ROW]
[ROW][C]102[/C][C]37964[/C][C]41623.5671532351[/C][C]-3659.56715323507[/C][/ROW]
[ROW][C]103[/C][C]33053[/C][C]35415.6588134337[/C][C]-2362.65881343371[/C][/ROW]
[ROW][C]104[/C][C]33053[/C][C]31514.5207085683[/C][C]1538.47929143171[/C][/ROW]
[ROW][C]105[/C][C]38595[/C][C]36235.8535187788[/C][C]2359.14648122118[/C][/ROW]
[ROW][C]106[/C][C]41542[/C][C]39624.5042012152[/C][C]1917.49579878481[/C][/ROW]
[ROW][C]107[/C][C]39924[/C][C]38091.4597404884[/C][C]1832.5402595116[/C][/ROW]
[ROW][C]108[/C][C]51355[/C][C]49357.1512390557[/C][C]1997.8487609443[/C][/ROW]
[ROW][C]109[/C][C]48413[/C][C]47204.3329934665[/C][C]1208.66700653355[/C][/ROW]
[ROW][C]110[/C][C]42871[/C][C]41213.7901913698[/C][C]1657.20980863023[/C][/ROW]
[ROW][C]111[/C][C]40560[/C][C]40123.8289220667[/C][C]436.171077933344[/C][/ROW]
[ROW][C]112[/C][C]32391[/C][C]32300.5767586488[/C][C]90.4232413511781[/C][/ROW]
[ROW][C]113[/C][C]35333[/C][C]37187.7525561103[/C][C]-1854.75255611033[/C][/ROW]
[ROW][C]114[/C][C]40560[/C][C]41794.1807584359[/C][C]-1234.18075843588[/C][/ROW]
[ROW][C]115[/C][C]36631[/C][C]36652.943252462[/C][C]-21.9432524620279[/C][/ROW]
[ROW][C]116[/C][C]35653[/C][C]36270.3900896026[/C][C]-617.390089602573[/C][/ROW]
[ROW][C]117[/C][C]40244[/C][C]41635.0680656209[/C][C]-1391.06806562086[/C][/ROW]
[ROW][C]118[/C][C]44168[/C][C]44060.2483030534[/C][C]107.751696946645[/C][/ROW]
[ROW][C]119[/C][C]39924[/C][C]41942.7018485672[/C][C]-2018.70184856719[/C][/ROW]
[ROW][C]120[/C][C]50057[/C][C]52975.2835552999[/C][C]-2918.28355529987[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168899&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168899&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
131374213610.9963300343131.00366996571
141342713239.9068014585187.09319854149
151146211242.8757523152219.124247684769
161177811485.7203055924292.279694407618
172092920230.2840525466698.715947453416
182289321852.92329837811040.07670162192
191766616082.11735174491583.8826482551
201472412978.59339360551745.40660639453
211538713987.53059097271399.46940902726
221570714597.07332064141109.92667935857
231735115395.6004437631955.39955623702
241896416605.12396546642358.87603453359
251931518365.158137745949.841862254987
261602218027.1165078794-2005.1165078794
271636914939.45756685991429.54243314014
281209315526.9281590739-3433.92815907391
292422226101.8951676827-1879.89516768266
302780027804.9038645905-4.90386459049478
311963120993.4730598489-1362.47305984887
321700416779.0146641708224.985335829184
331864917209.38391676941439.61608323058
342061317573.63720952263039.36279047736
352355519565.17535934833989.82464065171
362716421617.0975934985546.90240650197
372716422894.54586957454269.45413042547
382485320139.18848928354713.81151071647
392387121100.77421149492770.22578850505
401798216727.94531230511254.05468769486
412780034438.0605139476-6638.06051394756
423239137882.04810702-5491.04810702001
432846226251.40586456312210.59413543695
442422223012.21445803921209.78554196083
452485325022.3333381055-169.333338105465
462716426620.4728294818543.527170518213
473042629271.80707254721154.19292745275
483435532284.82863912952070.17136087054
493172431469.3140566699254.685943330052
503011127498.47090424322612.52909575683
513011126201.82130779323909.17869220677
522485320017.33352121114835.66647878889
533239133770.7342503832-1379.73425038322
543729740164.5706482887-2867.57064828866
553337334149.7996503293-776.799650329347
562912928590.3770677499538.622932250095
573042629459.2793815632966.72061843682
583565332246.50276428833406.49723571167
593796436562.5139621141401.48603788604
604122241025.1425838211196.857416178864
613859537820.2898812772774.710118722767
623435535326.7509382632-971.750938263169
633337334062.0869671078-689.086967107818
642552026665.9064856926-1145.90648569263
653074234727.4623545744-3985.4623545744
663631539618.6772949453-3303.67729494531
673011135001.6882023544-4890.68820235438
682650229562.9722773953-3060.97227739526
693011130026.976917797884.023082202235
703368934465.0438852323-776.043885232306
713565336254.3389658387-601.338965838673
724090639204.20564408721701.79435591277
733828036884.69757535141395.30242464865
743172433279.1808024148-1555.18080241477
753239132159.2666006519231.733399348061
762618624850.40859946341335.59140053664
773140930991.7739080546417.226091945377
783600037343.9316194407-1343.93161944068
793074231635.4168032464-893.416803246397
802716428274.2709432499-1110.27094324993
813042631839.5234701361-1413.52347013606
823435535454.4327135437-1099.43271354368
833368937401.7383848381-3712.73838483811
844154241668.0958059479-126.09580594788
854024438666.99616761921577.00383238075
863501732619.3128675462397.68713245399
873533333747.57837393131585.42162606867
882846227238.42839434311223.57160565693
893270632872.4635454833-166.463545483319
903926237908.44076506441353.55923493555
913435532786.9211086221568.07889137803
923140929479.11468004641929.88531995362
933631533750.3179018052564.68209819503
943926238923.3403238677338.659676132338
953698239003.0396996794-2021.03969967937
964743147584.0086961646-153.008696164565
974483545656.7060588895-821.706058889504
983894638972.8461389797-26.8461389796576
993729738925.811594511-1628.811594511
1002976430793.1558907558-1029.15589075577
1013403535167.8593378996-1132.85933789958
1023796441623.5671532351-3659.56715323507
1033305335415.6588134337-2362.65881343371
1043305331514.52070856831538.47929143171
1053859536235.85351877882359.14648122118
1064154239624.50420121521917.49579878481
1073992438091.45974048841832.5402595116
1085135549357.15123905571997.8487609443
1094841347204.33299346651208.66700653355
1104287141213.79019136981657.20980863023
1114056040123.8289220667436.171077933344
1123239132300.576758648890.4232413511781
1133533337187.7525561103-1854.75255611033
1144056041794.1807584359-1234.18075843588
1153663136652.943252462-21.9432524620279
1163565336270.3900896026-617.390089602573
1174024441635.0680656209-1391.06806562086
1184416844060.2483030534107.751696946645
1193992441942.7018485672-2018.70184856719
1205005752975.2835552999-2918.28355529987







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12149118.341892842644887.440344216453349.2434414688
12243138.991484150138841.263374751147436.719593549
12340722.147435747136356.07950138845088.2153701063
12432501.379369730228130.425991877736872.3327475826
12535817.384704863131317.5166651940317.2527445362
12641362.907240647236673.372745517746052.4417357767
12737357.623188062532687.191488293842028.0548878311
12836483.950511318731761.011624836241206.8893978013
12941460.63338381236511.115877126646410.1508904974
13045474.929138626640311.476661998950638.3816152543
13141507.994686536736432.984004563846583.0053685096
13252626.127247368548922.914587852956329.3399068842

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 49118.3418928426 & 44887.4403442164 & 53349.2434414688 \tabularnewline
122 & 43138.9914841501 & 38841.2633747511 & 47436.719593549 \tabularnewline
123 & 40722.1474357471 & 36356.079501388 & 45088.2153701063 \tabularnewline
124 & 32501.3793697302 & 28130.4259918777 & 36872.3327475826 \tabularnewline
125 & 35817.3847048631 & 31317.51666519 & 40317.2527445362 \tabularnewline
126 & 41362.9072406472 & 36673.3727455177 & 46052.4417357767 \tabularnewline
127 & 37357.6231880625 & 32687.1914882938 & 42028.0548878311 \tabularnewline
128 & 36483.9505113187 & 31761.0116248362 & 41206.8893978013 \tabularnewline
129 & 41460.633383812 & 36511.1158771266 & 46410.1508904974 \tabularnewline
130 & 45474.9291386266 & 40311.4766619989 & 50638.3816152543 \tabularnewline
131 & 41507.9946865367 & 36432.9840045638 & 46583.0053685096 \tabularnewline
132 & 52626.1272473685 & 48922.9145878529 & 56329.3399068842 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168899&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]121[/C][C]49118.3418928426[/C][C]44887.4403442164[/C][C]53349.2434414688[/C][/ROW]
[ROW][C]122[/C][C]43138.9914841501[/C][C]38841.2633747511[/C][C]47436.719593549[/C][/ROW]
[ROW][C]123[/C][C]40722.1474357471[/C][C]36356.079501388[/C][C]45088.2153701063[/C][/ROW]
[ROW][C]124[/C][C]32501.3793697302[/C][C]28130.4259918777[/C][C]36872.3327475826[/C][/ROW]
[ROW][C]125[/C][C]35817.3847048631[/C][C]31317.51666519[/C][C]40317.2527445362[/C][/ROW]
[ROW][C]126[/C][C]41362.9072406472[/C][C]36673.3727455177[/C][C]46052.4417357767[/C][/ROW]
[ROW][C]127[/C][C]37357.6231880625[/C][C]32687.1914882938[/C][C]42028.0548878311[/C][/ROW]
[ROW][C]128[/C][C]36483.9505113187[/C][C]31761.0116248362[/C][C]41206.8893978013[/C][/ROW]
[ROW][C]129[/C][C]41460.633383812[/C][C]36511.1158771266[/C][C]46410.1508904974[/C][/ROW]
[ROW][C]130[/C][C]45474.9291386266[/C][C]40311.4766619989[/C][C]50638.3816152543[/C][/ROW]
[ROW][C]131[/C][C]41507.9946865367[/C][C]36432.9840045638[/C][C]46583.0053685096[/C][/ROW]
[ROW][C]132[/C][C]52626.1272473685[/C][C]48922.9145878529[/C][C]56329.3399068842[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168899&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168899&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
12149118.341892842644887.440344216453349.2434414688
12243138.991484150138841.263374751147436.719593549
12340722.147435747136356.07950138845088.2153701063
12432501.379369730228130.425991877736872.3327475826
12535817.384704863131317.5166651940317.2527445362
12641362.907240647236673.372745517746052.4417357767
12737357.623188062532687.191488293842028.0548878311
12836483.950511318731761.011624836241206.8893978013
12941460.63338381236511.115877126646410.1508904974
13045474.929138626640311.476661998950638.3816152543
13141507.994686536736432.984004563846583.0053685096
13252626.127247368548922.914587852956329.3399068842



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')