Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 18 Aug 2011 18:03:24 -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/2011/Aug/18/t1313705145cbs2z1mx58hdff5.htm/, Retrieved Wed, 15 May 2024 15:16:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124172, Retrieved Wed, 15 May 2024 15:16:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Tongelen Caroline
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS A - STA...] [2011-08-18 22:03:24] [7d6606cca1b3596736d7d387043cb02b] [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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124172&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124172&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124172&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.204033093693489
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.204033093693489 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124172&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]0.204033093693489[/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=124172&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124172&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
alpha0.204033093693489
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131374213610.9963300343131.003669965714
141342713239.9068014585187.093198541495
151146211242.8757523152219.124247684776
161177811485.7203055924292.279694407629
172092920230.2840525466698.715947453442
182289321852.9232983781040.07670162196
191766616082.11735174491583.88264825513
201472412978.59339360541745.40660639458
211538713987.53059097271399.46940902734
221570714597.07332064131109.92667935866
231735115395.60044376291955.39955623712
241896416605.12396546632358.87603453372
251931518365.1581377449949.841862255143
261602218027.1165078793-2005.11650787927
271636914939.45756685981429.54243314019
281209315526.9281590739-3433.92815907385
292422226101.8951676827-1879.89516768271
302780027804.9038645906-4.90386459060028
311963120993.473059849-1362.47305984896
321700416779.0146641709224.985335829071
331864917209.38391676951439.61608323048
342061317573.63720952273039.36279047731
352355519565.17535934833989.82464065171
362716421617.0975934985546.90240650203
372716422894.54586957444269.45413042565
382485320139.18848928334713.81151071675
392387121100.77421149472770.22578850534
401798216727.94531230481254.05468769517
412780034438.060513947-6638.06051394696
423239137882.0481070196-5491.04810701965
432846226251.40586456292210.59413543708
442422223012.21445803911209.78554196091
452485325022.3333381054-169.33333810544
462716426620.4728294819543.527170518115
473042629271.80707254741154.19292745256
483435532284.82863912972070.17136087026
493172431469.3140566702254.685943329812
503011127498.47090424342612.52909575663
513011126201.82130779333909.17869220669
522485320017.33352121114835.66647878895
533239133770.7342503827-1379.73425038274
543729740164.570648288-2867.57064828803
553337334149.799650329-776.799650328991
562912928590.3770677497538.622932250313
573042629459.279381563966.720618437015
583565332246.50276428823406.49723571182
593796436562.51396211381401.48603788617
604122241025.1425838211196.857416178878
613859537820.2898812773774.710118722716
623435535326.7509382633-971.750938263322
633337334062.0869671081-689.086967108073
642552026665.9064856929-1145.90648569291
653074234727.4623545746-3985.4623545746
663631539618.6772949454-3303.67729494541
673011135001.6882023544-4890.68820235442
682650229562.9722773953-3060.97227739534
693011130026.976917797984.0230822021222
703368934465.0438852324-776.043885232444
713565336254.3389658388-601.338965838804
724090639204.20564408731701.79435591265
733828036884.69757535141395.30242464856
743172433279.1808024148-1555.18080241481
753239132159.266600652231.733399347966
762618624850.40859946351335.59140053655
773140930991.7739080546417.226091945373
783600037343.9316194406-1343.93161944063
793074231635.4168032463-893.416803246295
802716428274.2709432498-1110.27094324983
813042631839.523470136-1413.52347013602
823435535454.4327135437-1099.43271354369
833368937401.7383848382-3712.73838483816
844154241668.0958059481-126.095805948076
854024438666.99616761951577.00383238055
863501732619.31286754612397.6871324539
873533333747.57837393141585.42162606862
882846227238.42839434311223.57160565688
893270632872.4635454833-166.463545483341
903926237908.44076506441353.55923493556
913435532786.92110862191568.07889137811
923140929479.11468004631929.88531995374
933631533750.31790180482564.68209819523
943926238923.3403238674338.659676132615
953698239003.0396996791-2021.03969967907
964743147584.0086961644-153.008696164361
974483545656.7060588894-821.706058889446
983894638972.8461389797-26.8461389797158
993729738925.8115945111-1628.81159451109
1002976430793.1558907559-1029.1558907559
1013403535167.8593378997-1132.85933789972
1023796441623.5671532353-3659.56715323527
1033305335415.6588134339-2362.65881343393
1043305331514.52070856851538.47929143149
1053859536235.8535187792359.146481221
1064154239624.50420121521917.49579878477
1073992438091.45974048831832.5402595117
1085135549357.15123905551997.84876094451
1094841347204.33299346621208.66700653377
1104287141213.79019136961657.2098086304
1114056040123.8289220665436.171077933526
1123239132300.576758648790.4232413512946
1133533337187.7525561102-1854.75255611023
1144056041794.1807584358-1234.18075843579
1153663136652.943252462-21.9432524619842
1163565336270.3900896026-617.390089602624
1174024441635.068065621-1391.06806562102
1184416844060.2483030536107.75169694642
1193992441942.7018485674-2018.70184856737
1205005752975.2835553001-2918.28355530011

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 13742 & 13610.9963300343 & 131.003669965714 \tabularnewline
14 & 13427 & 13239.9068014585 & 187.093198541495 \tabularnewline
15 & 11462 & 11242.8757523152 & 219.124247684776 \tabularnewline
16 & 11778 & 11485.7203055924 & 292.279694407629 \tabularnewline
17 & 20929 & 20230.2840525466 & 698.715947453442 \tabularnewline
18 & 22893 & 21852.923298378 & 1040.07670162196 \tabularnewline
19 & 17666 & 16082.1173517449 & 1583.88264825513 \tabularnewline
20 & 14724 & 12978.5933936054 & 1745.40660639458 \tabularnewline
21 & 15387 & 13987.5305909727 & 1399.46940902734 \tabularnewline
22 & 15707 & 14597.0733206413 & 1109.92667935866 \tabularnewline
23 & 17351 & 15395.6004437629 & 1955.39955623712 \tabularnewline
24 & 18964 & 16605.1239654663 & 2358.87603453372 \tabularnewline
25 & 19315 & 18365.1581377449 & 949.841862255143 \tabularnewline
26 & 16022 & 18027.1165078793 & -2005.11650787927 \tabularnewline
27 & 16369 & 14939.4575668598 & 1429.54243314019 \tabularnewline
28 & 12093 & 15526.9281590739 & -3433.92815907385 \tabularnewline
29 & 24222 & 26101.8951676827 & -1879.89516768271 \tabularnewline
30 & 27800 & 27804.9038645906 & -4.90386459060028 \tabularnewline
31 & 19631 & 20993.473059849 & -1362.47305984896 \tabularnewline
32 & 17004 & 16779.0146641709 & 224.985335829071 \tabularnewline
33 & 18649 & 17209.3839167695 & 1439.61608323048 \tabularnewline
34 & 20613 & 17573.6372095227 & 3039.36279047731 \tabularnewline
35 & 23555 & 19565.1753593483 & 3989.82464065171 \tabularnewline
36 & 27164 & 21617.097593498 & 5546.90240650203 \tabularnewline
37 & 27164 & 22894.5458695744 & 4269.45413042565 \tabularnewline
38 & 24853 & 20139.1884892833 & 4713.81151071675 \tabularnewline
39 & 23871 & 21100.7742114947 & 2770.22578850534 \tabularnewline
40 & 17982 & 16727.9453123048 & 1254.05468769517 \tabularnewline
41 & 27800 & 34438.060513947 & -6638.06051394696 \tabularnewline
42 & 32391 & 37882.0481070196 & -5491.04810701965 \tabularnewline
43 & 28462 & 26251.4058645629 & 2210.59413543708 \tabularnewline
44 & 24222 & 23012.2144580391 & 1209.78554196091 \tabularnewline
45 & 24853 & 25022.3333381054 & -169.33333810544 \tabularnewline
46 & 27164 & 26620.4728294819 & 543.527170518115 \tabularnewline
47 & 30426 & 29271.8070725474 & 1154.19292745256 \tabularnewline
48 & 34355 & 32284.8286391297 & 2070.17136087026 \tabularnewline
49 & 31724 & 31469.3140566702 & 254.685943329812 \tabularnewline
50 & 30111 & 27498.4709042434 & 2612.52909575663 \tabularnewline
51 & 30111 & 26201.8213077933 & 3909.17869220669 \tabularnewline
52 & 24853 & 20017.3335212111 & 4835.66647878895 \tabularnewline
53 & 32391 & 33770.7342503827 & -1379.73425038274 \tabularnewline
54 & 37297 & 40164.570648288 & -2867.57064828803 \tabularnewline
55 & 33373 & 34149.799650329 & -776.799650328991 \tabularnewline
56 & 29129 & 28590.3770677497 & 538.622932250313 \tabularnewline
57 & 30426 & 29459.279381563 & 966.720618437015 \tabularnewline
58 & 35653 & 32246.5027642882 & 3406.49723571182 \tabularnewline
59 & 37964 & 36562.5139621138 & 1401.48603788617 \tabularnewline
60 & 41222 & 41025.1425838211 & 196.857416178878 \tabularnewline
61 & 38595 & 37820.2898812773 & 774.710118722716 \tabularnewline
62 & 34355 & 35326.7509382633 & -971.750938263322 \tabularnewline
63 & 33373 & 34062.0869671081 & -689.086967108073 \tabularnewline
64 & 25520 & 26665.9064856929 & -1145.90648569291 \tabularnewline
65 & 30742 & 34727.4623545746 & -3985.4623545746 \tabularnewline
66 & 36315 & 39618.6772949454 & -3303.67729494541 \tabularnewline
67 & 30111 & 35001.6882023544 & -4890.68820235442 \tabularnewline
68 & 26502 & 29562.9722773953 & -3060.97227739534 \tabularnewline
69 & 30111 & 30026.9769177979 & 84.0230822021222 \tabularnewline
70 & 33689 & 34465.0438852324 & -776.043885232444 \tabularnewline
71 & 35653 & 36254.3389658388 & -601.338965838804 \tabularnewline
72 & 40906 & 39204.2056440873 & 1701.79435591265 \tabularnewline
73 & 38280 & 36884.6975753514 & 1395.30242464856 \tabularnewline
74 & 31724 & 33279.1808024148 & -1555.18080241481 \tabularnewline
75 & 32391 & 32159.266600652 & 231.733399347966 \tabularnewline
76 & 26186 & 24850.4085994635 & 1335.59140053655 \tabularnewline
77 & 31409 & 30991.7739080546 & 417.226091945373 \tabularnewline
78 & 36000 & 37343.9316194406 & -1343.93161944063 \tabularnewline
79 & 30742 & 31635.4168032463 & -893.416803246295 \tabularnewline
80 & 27164 & 28274.2709432498 & -1110.27094324983 \tabularnewline
81 & 30426 & 31839.523470136 & -1413.52347013602 \tabularnewline
82 & 34355 & 35454.4327135437 & -1099.43271354369 \tabularnewline
83 & 33689 & 37401.7383848382 & -3712.73838483816 \tabularnewline
84 & 41542 & 41668.0958059481 & -126.095805948076 \tabularnewline
85 & 40244 & 38666.9961676195 & 1577.00383238055 \tabularnewline
86 & 35017 & 32619.3128675461 & 2397.6871324539 \tabularnewline
87 & 35333 & 33747.5783739314 & 1585.42162606862 \tabularnewline
88 & 28462 & 27238.4283943431 & 1223.57160565688 \tabularnewline
89 & 32706 & 32872.4635454833 & -166.463545483341 \tabularnewline
90 & 39262 & 37908.4407650644 & 1353.55923493556 \tabularnewline
91 & 34355 & 32786.9211086219 & 1568.07889137811 \tabularnewline
92 & 31409 & 29479.1146800463 & 1929.88531995374 \tabularnewline
93 & 36315 & 33750.3179018048 & 2564.68209819523 \tabularnewline
94 & 39262 & 38923.3403238674 & 338.659676132615 \tabularnewline
95 & 36982 & 39003.0396996791 & -2021.03969967907 \tabularnewline
96 & 47431 & 47584.0086961644 & -153.008696164361 \tabularnewline
97 & 44835 & 45656.7060588894 & -821.706058889446 \tabularnewline
98 & 38946 & 38972.8461389797 & -26.8461389797158 \tabularnewline
99 & 37297 & 38925.8115945111 & -1628.81159451109 \tabularnewline
100 & 29764 & 30793.1558907559 & -1029.1558907559 \tabularnewline
101 & 34035 & 35167.8593378997 & -1132.85933789972 \tabularnewline
102 & 37964 & 41623.5671532353 & -3659.56715323527 \tabularnewline
103 & 33053 & 35415.6588134339 & -2362.65881343393 \tabularnewline
104 & 33053 & 31514.5207085685 & 1538.47929143149 \tabularnewline
105 & 38595 & 36235.853518779 & 2359.146481221 \tabularnewline
106 & 41542 & 39624.5042012152 & 1917.49579878477 \tabularnewline
107 & 39924 & 38091.4597404883 & 1832.5402595117 \tabularnewline
108 & 51355 & 49357.1512390555 & 1997.84876094451 \tabularnewline
109 & 48413 & 47204.3329934662 & 1208.66700653377 \tabularnewline
110 & 42871 & 41213.7901913696 & 1657.2098086304 \tabularnewline
111 & 40560 & 40123.8289220665 & 436.171077933526 \tabularnewline
112 & 32391 & 32300.5767586487 & 90.4232413512946 \tabularnewline
113 & 35333 & 37187.7525561102 & -1854.75255611023 \tabularnewline
114 & 40560 & 41794.1807584358 & -1234.18075843579 \tabularnewline
115 & 36631 & 36652.943252462 & -21.9432524619842 \tabularnewline
116 & 35653 & 36270.3900896026 & -617.390089602624 \tabularnewline
117 & 40244 & 41635.068065621 & -1391.06806562102 \tabularnewline
118 & 44168 & 44060.2483030536 & 107.75169694642 \tabularnewline
119 & 39924 & 41942.7018485674 & -2018.70184856737 \tabularnewline
120 & 50057 & 52975.2835553001 & -2918.28355530011 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124172&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]131.003669965714[/C][/ROW]
[ROW][C]14[/C][C]13427[/C][C]13239.9068014585[/C][C]187.093198541495[/C][/ROW]
[ROW][C]15[/C][C]11462[/C][C]11242.8757523152[/C][C]219.124247684776[/C][/ROW]
[ROW][C]16[/C][C]11778[/C][C]11485.7203055924[/C][C]292.279694407629[/C][/ROW]
[ROW][C]17[/C][C]20929[/C][C]20230.2840525466[/C][C]698.715947453442[/C][/ROW]
[ROW][C]18[/C][C]22893[/C][C]21852.923298378[/C][C]1040.07670162196[/C][/ROW]
[ROW][C]19[/C][C]17666[/C][C]16082.1173517449[/C][C]1583.88264825513[/C][/ROW]
[ROW][C]20[/C][C]14724[/C][C]12978.5933936054[/C][C]1745.40660639458[/C][/ROW]
[ROW][C]21[/C][C]15387[/C][C]13987.5305909727[/C][C]1399.46940902734[/C][/ROW]
[ROW][C]22[/C][C]15707[/C][C]14597.0733206413[/C][C]1109.92667935866[/C][/ROW]
[ROW][C]23[/C][C]17351[/C][C]15395.6004437629[/C][C]1955.39955623712[/C][/ROW]
[ROW][C]24[/C][C]18964[/C][C]16605.1239654663[/C][C]2358.87603453372[/C][/ROW]
[ROW][C]25[/C][C]19315[/C][C]18365.1581377449[/C][C]949.841862255143[/C][/ROW]
[ROW][C]26[/C][C]16022[/C][C]18027.1165078793[/C][C]-2005.11650787927[/C][/ROW]
[ROW][C]27[/C][C]16369[/C][C]14939.4575668598[/C][C]1429.54243314019[/C][/ROW]
[ROW][C]28[/C][C]12093[/C][C]15526.9281590739[/C][C]-3433.92815907385[/C][/ROW]
[ROW][C]29[/C][C]24222[/C][C]26101.8951676827[/C][C]-1879.89516768271[/C][/ROW]
[ROW][C]30[/C][C]27800[/C][C]27804.9038645906[/C][C]-4.90386459060028[/C][/ROW]
[ROW][C]31[/C][C]19631[/C][C]20993.473059849[/C][C]-1362.47305984896[/C][/ROW]
[ROW][C]32[/C][C]17004[/C][C]16779.0146641709[/C][C]224.985335829071[/C][/ROW]
[ROW][C]33[/C][C]18649[/C][C]17209.3839167695[/C][C]1439.61608323048[/C][/ROW]
[ROW][C]34[/C][C]20613[/C][C]17573.6372095227[/C][C]3039.36279047731[/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]5546.90240650203[/C][/ROW]
[ROW][C]37[/C][C]27164[/C][C]22894.5458695744[/C][C]4269.45413042565[/C][/ROW]
[ROW][C]38[/C][C]24853[/C][C]20139.1884892833[/C][C]4713.81151071675[/C][/ROW]
[ROW][C]39[/C][C]23871[/C][C]21100.7742114947[/C][C]2770.22578850534[/C][/ROW]
[ROW][C]40[/C][C]17982[/C][C]16727.9453123048[/C][C]1254.05468769517[/C][/ROW]
[ROW][C]41[/C][C]27800[/C][C]34438.060513947[/C][C]-6638.06051394696[/C][/ROW]
[ROW][C]42[/C][C]32391[/C][C]37882.0481070196[/C][C]-5491.04810701965[/C][/ROW]
[ROW][C]43[/C][C]28462[/C][C]26251.4058645629[/C][C]2210.59413543708[/C][/ROW]
[ROW][C]44[/C][C]24222[/C][C]23012.2144580391[/C][C]1209.78554196091[/C][/ROW]
[ROW][C]45[/C][C]24853[/C][C]25022.3333381054[/C][C]-169.33333810544[/C][/ROW]
[ROW][C]46[/C][C]27164[/C][C]26620.4728294819[/C][C]543.527170518115[/C][/ROW]
[ROW][C]47[/C][C]30426[/C][C]29271.8070725474[/C][C]1154.19292745256[/C][/ROW]
[ROW][C]48[/C][C]34355[/C][C]32284.8286391297[/C][C]2070.17136087026[/C][/ROW]
[ROW][C]49[/C][C]31724[/C][C]31469.3140566702[/C][C]254.685943329812[/C][/ROW]
[ROW][C]50[/C][C]30111[/C][C]27498.4709042434[/C][C]2612.52909575663[/C][/ROW]
[ROW][C]51[/C][C]30111[/C][C]26201.8213077933[/C][C]3909.17869220669[/C][/ROW]
[ROW][C]52[/C][C]24853[/C][C]20017.3335212111[/C][C]4835.66647878895[/C][/ROW]
[ROW][C]53[/C][C]32391[/C][C]33770.7342503827[/C][C]-1379.73425038274[/C][/ROW]
[ROW][C]54[/C][C]37297[/C][C]40164.570648288[/C][C]-2867.57064828803[/C][/ROW]
[ROW][C]55[/C][C]33373[/C][C]34149.799650329[/C][C]-776.799650328991[/C][/ROW]
[ROW][C]56[/C][C]29129[/C][C]28590.3770677497[/C][C]538.622932250313[/C][/ROW]
[ROW][C]57[/C][C]30426[/C][C]29459.279381563[/C][C]966.720618437015[/C][/ROW]
[ROW][C]58[/C][C]35653[/C][C]32246.5027642882[/C][C]3406.49723571182[/C][/ROW]
[ROW][C]59[/C][C]37964[/C][C]36562.5139621138[/C][C]1401.48603788617[/C][/ROW]
[ROW][C]60[/C][C]41222[/C][C]41025.1425838211[/C][C]196.857416178878[/C][/ROW]
[ROW][C]61[/C][C]38595[/C][C]37820.2898812773[/C][C]774.710118722716[/C][/ROW]
[ROW][C]62[/C][C]34355[/C][C]35326.7509382633[/C][C]-971.750938263322[/C][/ROW]
[ROW][C]63[/C][C]33373[/C][C]34062.0869671081[/C][C]-689.086967108073[/C][/ROW]
[ROW][C]64[/C][C]25520[/C][C]26665.9064856929[/C][C]-1145.90648569291[/C][/ROW]
[ROW][C]65[/C][C]30742[/C][C]34727.4623545746[/C][C]-3985.4623545746[/C][/ROW]
[ROW][C]66[/C][C]36315[/C][C]39618.6772949454[/C][C]-3303.67729494541[/C][/ROW]
[ROW][C]67[/C][C]30111[/C][C]35001.6882023544[/C][C]-4890.68820235442[/C][/ROW]
[ROW][C]68[/C][C]26502[/C][C]29562.9722773953[/C][C]-3060.97227739534[/C][/ROW]
[ROW][C]69[/C][C]30111[/C][C]30026.9769177979[/C][C]84.0230822021222[/C][/ROW]
[ROW][C]70[/C][C]33689[/C][C]34465.0438852324[/C][C]-776.043885232444[/C][/ROW]
[ROW][C]71[/C][C]35653[/C][C]36254.3389658388[/C][C]-601.338965838804[/C][/ROW]
[ROW][C]72[/C][C]40906[/C][C]39204.2056440873[/C][C]1701.79435591265[/C][/ROW]
[ROW][C]73[/C][C]38280[/C][C]36884.6975753514[/C][C]1395.30242464856[/C][/ROW]
[ROW][C]74[/C][C]31724[/C][C]33279.1808024148[/C][C]-1555.18080241481[/C][/ROW]
[ROW][C]75[/C][C]32391[/C][C]32159.266600652[/C][C]231.733399347966[/C][/ROW]
[ROW][C]76[/C][C]26186[/C][C]24850.4085994635[/C][C]1335.59140053655[/C][/ROW]
[ROW][C]77[/C][C]31409[/C][C]30991.7739080546[/C][C]417.226091945373[/C][/ROW]
[ROW][C]78[/C][C]36000[/C][C]37343.9316194406[/C][C]-1343.93161944063[/C][/ROW]
[ROW][C]79[/C][C]30742[/C][C]31635.4168032463[/C][C]-893.416803246295[/C][/ROW]
[ROW][C]80[/C][C]27164[/C][C]28274.2709432498[/C][C]-1110.27094324983[/C][/ROW]
[ROW][C]81[/C][C]30426[/C][C]31839.523470136[/C][C]-1413.52347013602[/C][/ROW]
[ROW][C]82[/C][C]34355[/C][C]35454.4327135437[/C][C]-1099.43271354369[/C][/ROW]
[ROW][C]83[/C][C]33689[/C][C]37401.7383848382[/C][C]-3712.73838483816[/C][/ROW]
[ROW][C]84[/C][C]41542[/C][C]41668.0958059481[/C][C]-126.095805948076[/C][/ROW]
[ROW][C]85[/C][C]40244[/C][C]38666.9961676195[/C][C]1577.00383238055[/C][/ROW]
[ROW][C]86[/C][C]35017[/C][C]32619.3128675461[/C][C]2397.6871324539[/C][/ROW]
[ROW][C]87[/C][C]35333[/C][C]33747.5783739314[/C][C]1585.42162606862[/C][/ROW]
[ROW][C]88[/C][C]28462[/C][C]27238.4283943431[/C][C]1223.57160565688[/C][/ROW]
[ROW][C]89[/C][C]32706[/C][C]32872.4635454833[/C][C]-166.463545483341[/C][/ROW]
[ROW][C]90[/C][C]39262[/C][C]37908.4407650644[/C][C]1353.55923493556[/C][/ROW]
[ROW][C]91[/C][C]34355[/C][C]32786.9211086219[/C][C]1568.07889137811[/C][/ROW]
[ROW][C]92[/C][C]31409[/C][C]29479.1146800463[/C][C]1929.88531995374[/C][/ROW]
[ROW][C]93[/C][C]36315[/C][C]33750.3179018048[/C][C]2564.68209819523[/C][/ROW]
[ROW][C]94[/C][C]39262[/C][C]38923.3403238674[/C][C]338.659676132615[/C][/ROW]
[ROW][C]95[/C][C]36982[/C][C]39003.0396996791[/C][C]-2021.03969967907[/C][/ROW]
[ROW][C]96[/C][C]47431[/C][C]47584.0086961644[/C][C]-153.008696164361[/C][/ROW]
[ROW][C]97[/C][C]44835[/C][C]45656.7060588894[/C][C]-821.706058889446[/C][/ROW]
[ROW][C]98[/C][C]38946[/C][C]38972.8461389797[/C][C]-26.8461389797158[/C][/ROW]
[ROW][C]99[/C][C]37297[/C][C]38925.8115945111[/C][C]-1628.81159451109[/C][/ROW]
[ROW][C]100[/C][C]29764[/C][C]30793.1558907559[/C][C]-1029.1558907559[/C][/ROW]
[ROW][C]101[/C][C]34035[/C][C]35167.8593378997[/C][C]-1132.85933789972[/C][/ROW]
[ROW][C]102[/C][C]37964[/C][C]41623.5671532353[/C][C]-3659.56715323527[/C][/ROW]
[ROW][C]103[/C][C]33053[/C][C]35415.6588134339[/C][C]-2362.65881343393[/C][/ROW]
[ROW][C]104[/C][C]33053[/C][C]31514.5207085685[/C][C]1538.47929143149[/C][/ROW]
[ROW][C]105[/C][C]38595[/C][C]36235.853518779[/C][C]2359.146481221[/C][/ROW]
[ROW][C]106[/C][C]41542[/C][C]39624.5042012152[/C][C]1917.49579878477[/C][/ROW]
[ROW][C]107[/C][C]39924[/C][C]38091.4597404883[/C][C]1832.5402595117[/C][/ROW]
[ROW][C]108[/C][C]51355[/C][C]49357.1512390555[/C][C]1997.84876094451[/C][/ROW]
[ROW][C]109[/C][C]48413[/C][C]47204.3329934662[/C][C]1208.66700653377[/C][/ROW]
[ROW][C]110[/C][C]42871[/C][C]41213.7901913696[/C][C]1657.2098086304[/C][/ROW]
[ROW][C]111[/C][C]40560[/C][C]40123.8289220665[/C][C]436.171077933526[/C][/ROW]
[ROW][C]112[/C][C]32391[/C][C]32300.5767586487[/C][C]90.4232413512946[/C][/ROW]
[ROW][C]113[/C][C]35333[/C][C]37187.7525561102[/C][C]-1854.75255611023[/C][/ROW]
[ROW][C]114[/C][C]40560[/C][C]41794.1807584358[/C][C]-1234.18075843579[/C][/ROW]
[ROW][C]115[/C][C]36631[/C][C]36652.943252462[/C][C]-21.9432524619842[/C][/ROW]
[ROW][C]116[/C][C]35653[/C][C]36270.3900896026[/C][C]-617.390089602624[/C][/ROW]
[ROW][C]117[/C][C]40244[/C][C]41635.068065621[/C][C]-1391.06806562102[/C][/ROW]
[ROW][C]118[/C][C]44168[/C][C]44060.2483030536[/C][C]107.75169694642[/C][/ROW]
[ROW][C]119[/C][C]39924[/C][C]41942.7018485674[/C][C]-2018.70184856737[/C][/ROW]
[ROW][C]120[/C][C]50057[/C][C]52975.2835553001[/C][C]-2918.28355530011[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124172&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124172&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
131374213610.9963300343131.003669965714
141342713239.9068014585187.093198541495
151146211242.8757523152219.124247684776
161177811485.7203055924292.279694407629
172092920230.2840525466698.715947453442
182289321852.9232983781040.07670162196
191766616082.11735174491583.88264825513
201472412978.59339360541745.40660639458
211538713987.53059097271399.46940902734
221570714597.07332064131109.92667935866
231735115395.60044376291955.39955623712
241896416605.12396546632358.87603453372
251931518365.1581377449949.841862255143
261602218027.1165078793-2005.11650787927
271636914939.45756685981429.54243314019
281209315526.9281590739-3433.92815907385
292422226101.8951676827-1879.89516768271
302780027804.9038645906-4.90386459060028
311963120993.473059849-1362.47305984896
321700416779.0146641709224.985335829071
331864917209.38391676951439.61608323048
342061317573.63720952273039.36279047731
352355519565.17535934833989.82464065171
362716421617.0975934985546.90240650203
372716422894.54586957444269.45413042565
382485320139.18848928334713.81151071675
392387121100.77421149472770.22578850534
401798216727.94531230481254.05468769517
412780034438.060513947-6638.06051394696
423239137882.0481070196-5491.04810701965
432846226251.40586456292210.59413543708
442422223012.21445803911209.78554196091
452485325022.3333381054-169.33333810544
462716426620.4728294819543.527170518115
473042629271.80707254741154.19292745256
483435532284.82863912972070.17136087026
493172431469.3140566702254.685943329812
503011127498.47090424342612.52909575663
513011126201.82130779333909.17869220669
522485320017.33352121114835.66647878895
533239133770.7342503827-1379.73425038274
543729740164.570648288-2867.57064828803
553337334149.799650329-776.799650328991
562912928590.3770677497538.622932250313
573042629459.279381563966.720618437015
583565332246.50276428823406.49723571182
593796436562.51396211381401.48603788617
604122241025.1425838211196.857416178878
613859537820.2898812773774.710118722716
623435535326.7509382633-971.750938263322
633337334062.0869671081-689.086967108073
642552026665.9064856929-1145.90648569291
653074234727.4623545746-3985.4623545746
663631539618.6772949454-3303.67729494541
673011135001.6882023544-4890.68820235442
682650229562.9722773953-3060.97227739534
693011130026.976917797984.0230822021222
703368934465.0438852324-776.043885232444
713565336254.3389658388-601.338965838804
724090639204.20564408731701.79435591265
733828036884.69757535141395.30242464856
743172433279.1808024148-1555.18080241481
753239132159.266600652231.733399347966
762618624850.40859946351335.59140053655
773140930991.7739080546417.226091945373
783600037343.9316194406-1343.93161944063
793074231635.4168032463-893.416803246295
802716428274.2709432498-1110.27094324983
813042631839.523470136-1413.52347013602
823435535454.4327135437-1099.43271354369
833368937401.7383848382-3712.73838483816
844154241668.0958059481-126.095805948076
854024438666.99616761951577.00383238055
863501732619.31286754612397.6871324539
873533333747.57837393141585.42162606862
882846227238.42839434311223.57160565688
893270632872.4635454833-166.463545483341
903926237908.44076506441353.55923493556
913435532786.92110862191568.07889137811
923140929479.11468004631929.88531995374
933631533750.31790180482564.68209819523
943926238923.3403238674338.659676132615
953698239003.0396996791-2021.03969967907
964743147584.0086961644-153.008696164361
974483545656.7060588894-821.706058889446
983894638972.8461389797-26.8461389797158
993729738925.8115945111-1628.81159451109
1002976430793.1558907559-1029.1558907559
1013403535167.8593378997-1132.85933789972
1023796441623.5671532353-3659.56715323527
1033305335415.6588134339-2362.65881343393
1043305331514.52070856851538.47929143149
1053859536235.8535187792359.146481221
1064154239624.50420121521917.49579878477
1073992438091.45974048831832.5402595117
1085135549357.15123905551997.84876094451
1094841347204.33299346621208.66700653377
1104287141213.79019136961657.2098086304
1114056040123.8289220665436.171077933526
1123239132300.576758648790.4232413512946
1133533337187.7525561102-1854.75255611023
1144056041794.1807584358-1234.18075843579
1153663136652.943252462-21.9432524619842
1163565336270.3900896026-617.390089602624
1174024441635.068065621-1391.06806562102
1184416844060.2483030536107.75169694642
1193992441942.7018485674-2018.70184856737
1205005752975.2835553001-2918.28355530011







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12149118.341892842844887.440344216753349.243441469
12243138.991484150238841.263374751347436.7195935492
12340722.147435747336356.079501388245088.2153701064
12432501.379369730228130.425991877836872.3327475827
12535817.384704863131317.516665190140317.2527445361
12641362.907240647236673.372745517846052.4417357765
12737357.623188062532687.191488293942028.054887831
12836483.950511318731761.011624836341206.8893978012
12941460.63338381236511.115877126746410.1508904973
13045474.929138626740311.476661999150638.3816152542
13141507.994686536736432.98400456446583.0053685095
13252626.127247368648922.914587853356329.3399068839

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 49118.3418928428 & 44887.4403442167 & 53349.243441469 \tabularnewline
122 & 43138.9914841502 & 38841.2633747513 & 47436.7195935492 \tabularnewline
123 & 40722.1474357473 & 36356.0795013882 & 45088.2153701064 \tabularnewline
124 & 32501.3793697302 & 28130.4259918778 & 36872.3327475827 \tabularnewline
125 & 35817.3847048631 & 31317.5166651901 & 40317.2527445361 \tabularnewline
126 & 41362.9072406472 & 36673.3727455178 & 46052.4417357765 \tabularnewline
127 & 37357.6231880625 & 32687.1914882939 & 42028.054887831 \tabularnewline
128 & 36483.9505113187 & 31761.0116248363 & 41206.8893978012 \tabularnewline
129 & 41460.633383812 & 36511.1158771267 & 46410.1508904973 \tabularnewline
130 & 45474.9291386267 & 40311.4766619991 & 50638.3816152542 \tabularnewline
131 & 41507.9946865367 & 36432.984004564 & 46583.0053685095 \tabularnewline
132 & 52626.1272473686 & 48922.9145878533 & 56329.3399068839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124172&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]49118.3418928428[/C][C]44887.4403442167[/C][C]53349.243441469[/C][/ROW]
[ROW][C]122[/C][C]43138.9914841502[/C][C]38841.2633747513[/C][C]47436.7195935492[/C][/ROW]
[ROW][C]123[/C][C]40722.1474357473[/C][C]36356.0795013882[/C][C]45088.2153701064[/C][/ROW]
[ROW][C]124[/C][C]32501.3793697302[/C][C]28130.4259918778[/C][C]36872.3327475827[/C][/ROW]
[ROW][C]125[/C][C]35817.3847048631[/C][C]31317.5166651901[/C][C]40317.2527445361[/C][/ROW]
[ROW][C]126[/C][C]41362.9072406472[/C][C]36673.3727455178[/C][C]46052.4417357765[/C][/ROW]
[ROW][C]127[/C][C]37357.6231880625[/C][C]32687.1914882939[/C][C]42028.054887831[/C][/ROW]
[ROW][C]128[/C][C]36483.9505113187[/C][C]31761.0116248363[/C][C]41206.8893978012[/C][/ROW]
[ROW][C]129[/C][C]41460.633383812[/C][C]36511.1158771267[/C][C]46410.1508904973[/C][/ROW]
[ROW][C]130[/C][C]45474.9291386267[/C][C]40311.4766619991[/C][C]50638.3816152542[/C][/ROW]
[ROW][C]131[/C][C]41507.9946865367[/C][C]36432.984004564[/C][C]46583.0053685095[/C][/ROW]
[ROW][C]132[/C][C]52626.1272473686[/C][C]48922.9145878533[/C][C]56329.3399068839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124172&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124172&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
12149118.341892842844887.440344216753349.243441469
12243138.991484150238841.263374751347436.7195935492
12340722.147435747336356.079501388245088.2153701064
12432501.379369730228130.425991877836872.3327475827
12535817.384704863131317.516665190140317.2527445361
12641362.907240647236673.372745517846052.4417357765
12737357.623188062532687.191488293942028.054887831
12836483.950511318731761.011624836341206.8893978012
12941460.63338381236511.115877126746410.1508904973
13045474.929138626740311.476661999150638.3816152542
13141507.994686536736432.98400456446583.0053685095
13252626.127247368648922.914587853356329.3399068839



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')