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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 08:47:22 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/02/t12439540958rpufezk29qgyrf.htm/, Retrieved Fri, 10 May 2024 02:13:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41251, Retrieved Fri, 10 May 2024 02:13:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2009-06-02 14:47:22] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
8166
7102
6047
5854
5764
5209
5616
5597
6251
7024
7237
9230
9016
8201
7630
7107
6820
6082
6019
6576
8086
8323
7842
9077
10737
10176
10416
9807
9565
10439
9115
9535
10790
11340
11196
12132
12013
12692
13330
11926
11356
11221
9999
11772
12543
14176
2924
2322
15557
13381
13145
12448
12178
11836
9815
12382
12662
12767
13136
13533
17808
15892
16830
14444
15550
15092
16364
14314
15874
17846
18504
15130
19845
18137
18898
19573
17368
18938
16713
16379
19139
21461
19796
16668




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41251&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41251&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41251&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.105286354127589
beta0.0235096656309281
gamma0.357989297961511

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.105286354127589 \tabularnewline
beta & 0.0235096656309281 \tabularnewline
gamma & 0.357989297961511 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41251&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]0.105286354127589[/C][/ROW]
[ROW][C]beta[/C][C]0.0235096656309281[/C][/ROW]
[ROW][C]gamma[/C][C]0.357989297961511[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41251&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41251&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
alpha0.105286354127589
beta0.0235096656309281
gamma0.357989297961511







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1390168341.80493621812674.195063781877
1482017692.67196296991508.32803703009
1576307185.70804867018444.291951329816
1671076705.98981801135401.010181988650
1768206491.20256411012328.797435889876
1860825880.20373488518201.796265114823
1960196305.59531317355-286.595313173545
2065766256.22444562094319.775554379063
2180866996.0256132291089.974386771
2283237952.29768025301370.702319746989
2378428221.85319754435-379.853197544355
24907710443.1061170463-1366.10611704635
251073710364.0481378173372.951862182706
26101769455.23607663357720.763923366427
27104168816.912071469271599.08792853073
2898078315.30030146621491.69969853380
2995658117.625424429321447.37457557068
30104397407.058812030123031.94118796988
3191158042.873774447611072.12622555239
3295358383.909636833351151.09036316665
33107909764.11289270041025.8871072996
341134010678.1728122877661.827187712335
351119610732.2865452781463.713454721888
361213213374.3400349670-1242.34003496704
371201314077.9301818921-2064.93018189214
381269212753.1348944739-61.1348944738565
391333012165.01465368311164.98534631695
401192611360.2052048910565.794795109046
411135610932.0496986903423.950301309724
421122110472.1212611640748.878738836045
43999910156.8138772920-157.813877291954
441177210423.51206771621348.48793228377
451254311998.1757629573544.824237042711
461417612852.92234478671323.07765521327
47292412883.0602369135-9959.06023691351
48232214014.7344942861-11692.7344942861
491555713296.02552951192260.97447048808
501338113018.8754885759362.124511424125
511314512823.4629621890321.537037811015
521244811686.6052026555761.394797344487
531217811194.8802035217983.119796478302
541183610861.2585869274974.741413072567
55981510242.7440794549-427.744079454931
561238210938.61806919591443.38193080409
571266212245.5709638898416.429036110152
581276713305.1729213711-538.172921371066
59131369269.79717294483866.20282705521
601353311083.93302865452449.06697134546
611780817593.1192915399214.880708460139
621589216238.0010641410-346.001064141023
631683015907.0315156117922.968484388324
641444414739.3692059401-295.369205940066
651555014097.88735548081452.11264451923
661509213713.96970941461378.03029058543
671636412425.78332474843938.21667525159
681431414557.304094364-243.304094364014
691587415581.7613180096292.238681990364
701784616515.60129634391330.39870365611
711850413330.0267619585173.97323804201
721513015075.559811257254.4401887427684
731984521975.8139573879-2130.81395738792
741813719841.2262186486-1704.22621864859
751889819799.9595923961-901.959592396102
761957317704.36343489581868.63656510418
771736817836.6883887206-468.688388720642
781893817104.46076277441833.5392372256
791671316506.8408255114206.15917448861
801637916963.8004058771-584.800405877104
811913918322.5238356449816.476164355106
822146119844.71503019051616.28496980948
831979617477.81128146792318.18871853211
841666817208.5259236055-540.52592360555

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9016 & 8341.80493621812 & 674.195063781877 \tabularnewline
14 & 8201 & 7692.67196296991 & 508.32803703009 \tabularnewline
15 & 7630 & 7185.70804867018 & 444.291951329816 \tabularnewline
16 & 7107 & 6705.98981801135 & 401.010181988650 \tabularnewline
17 & 6820 & 6491.20256411012 & 328.797435889876 \tabularnewline
18 & 6082 & 5880.20373488518 & 201.796265114823 \tabularnewline
19 & 6019 & 6305.59531317355 & -286.595313173545 \tabularnewline
20 & 6576 & 6256.22444562094 & 319.775554379063 \tabularnewline
21 & 8086 & 6996.025613229 & 1089.974386771 \tabularnewline
22 & 8323 & 7952.29768025301 & 370.702319746989 \tabularnewline
23 & 7842 & 8221.85319754435 & -379.853197544355 \tabularnewline
24 & 9077 & 10443.1061170463 & -1366.10611704635 \tabularnewline
25 & 10737 & 10364.0481378173 & 372.951862182706 \tabularnewline
26 & 10176 & 9455.23607663357 & 720.763923366427 \tabularnewline
27 & 10416 & 8816.91207146927 & 1599.08792853073 \tabularnewline
28 & 9807 & 8315.3003014662 & 1491.69969853380 \tabularnewline
29 & 9565 & 8117.62542442932 & 1447.37457557068 \tabularnewline
30 & 10439 & 7407.05881203012 & 3031.94118796988 \tabularnewline
31 & 9115 & 8042.87377444761 & 1072.12622555239 \tabularnewline
32 & 9535 & 8383.90963683335 & 1151.09036316665 \tabularnewline
33 & 10790 & 9764.1128927004 & 1025.8871072996 \tabularnewline
34 & 11340 & 10678.1728122877 & 661.827187712335 \tabularnewline
35 & 11196 & 10732.2865452781 & 463.713454721888 \tabularnewline
36 & 12132 & 13374.3400349670 & -1242.34003496704 \tabularnewline
37 & 12013 & 14077.9301818921 & -2064.93018189214 \tabularnewline
38 & 12692 & 12753.1348944739 & -61.1348944738565 \tabularnewline
39 & 13330 & 12165.0146536831 & 1164.98534631695 \tabularnewline
40 & 11926 & 11360.2052048910 & 565.794795109046 \tabularnewline
41 & 11356 & 10932.0496986903 & 423.950301309724 \tabularnewline
42 & 11221 & 10472.1212611640 & 748.878738836045 \tabularnewline
43 & 9999 & 10156.8138772920 & -157.813877291954 \tabularnewline
44 & 11772 & 10423.5120677162 & 1348.48793228377 \tabularnewline
45 & 12543 & 11998.1757629573 & 544.824237042711 \tabularnewline
46 & 14176 & 12852.9223447867 & 1323.07765521327 \tabularnewline
47 & 2924 & 12883.0602369135 & -9959.06023691351 \tabularnewline
48 & 2322 & 14014.7344942861 & -11692.7344942861 \tabularnewline
49 & 15557 & 13296.0255295119 & 2260.97447048808 \tabularnewline
50 & 13381 & 13018.8754885759 & 362.124511424125 \tabularnewline
51 & 13145 & 12823.4629621890 & 321.537037811015 \tabularnewline
52 & 12448 & 11686.6052026555 & 761.394797344487 \tabularnewline
53 & 12178 & 11194.8802035217 & 983.119796478302 \tabularnewline
54 & 11836 & 10861.2585869274 & 974.741413072567 \tabularnewline
55 & 9815 & 10242.7440794549 & -427.744079454931 \tabularnewline
56 & 12382 & 10938.6180691959 & 1443.38193080409 \tabularnewline
57 & 12662 & 12245.5709638898 & 416.429036110152 \tabularnewline
58 & 12767 & 13305.1729213711 & -538.172921371066 \tabularnewline
59 & 13136 & 9269.7971729448 & 3866.20282705521 \tabularnewline
60 & 13533 & 11083.9330286545 & 2449.06697134546 \tabularnewline
61 & 17808 & 17593.1192915399 & 214.880708460139 \tabularnewline
62 & 15892 & 16238.0010641410 & -346.001064141023 \tabularnewline
63 & 16830 & 15907.0315156117 & 922.968484388324 \tabularnewline
64 & 14444 & 14739.3692059401 & -295.369205940066 \tabularnewline
65 & 15550 & 14097.8873554808 & 1452.11264451923 \tabularnewline
66 & 15092 & 13713.9697094146 & 1378.03029058543 \tabularnewline
67 & 16364 & 12425.7833247484 & 3938.21667525159 \tabularnewline
68 & 14314 & 14557.304094364 & -243.304094364014 \tabularnewline
69 & 15874 & 15581.7613180096 & 292.238681990364 \tabularnewline
70 & 17846 & 16515.6012963439 & 1330.39870365611 \tabularnewline
71 & 18504 & 13330.026761958 & 5173.97323804201 \tabularnewline
72 & 15130 & 15075.5598112572 & 54.4401887427684 \tabularnewline
73 & 19845 & 21975.8139573879 & -2130.81395738792 \tabularnewline
74 & 18137 & 19841.2262186486 & -1704.22621864859 \tabularnewline
75 & 18898 & 19799.9595923961 & -901.959592396102 \tabularnewline
76 & 19573 & 17704.3634348958 & 1868.63656510418 \tabularnewline
77 & 17368 & 17836.6883887206 & -468.688388720642 \tabularnewline
78 & 18938 & 17104.4607627744 & 1833.5392372256 \tabularnewline
79 & 16713 & 16506.8408255114 & 206.15917448861 \tabularnewline
80 & 16379 & 16963.8004058771 & -584.800405877104 \tabularnewline
81 & 19139 & 18322.5238356449 & 816.476164355106 \tabularnewline
82 & 21461 & 19844.7150301905 & 1616.28496980948 \tabularnewline
83 & 19796 & 17477.8112814679 & 2318.18871853211 \tabularnewline
84 & 16668 & 17208.5259236055 & -540.52592360555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41251&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]9016[/C][C]8341.80493621812[/C][C]674.195063781877[/C][/ROW]
[ROW][C]14[/C][C]8201[/C][C]7692.67196296991[/C][C]508.32803703009[/C][/ROW]
[ROW][C]15[/C][C]7630[/C][C]7185.70804867018[/C][C]444.291951329816[/C][/ROW]
[ROW][C]16[/C][C]7107[/C][C]6705.98981801135[/C][C]401.010181988650[/C][/ROW]
[ROW][C]17[/C][C]6820[/C][C]6491.20256411012[/C][C]328.797435889876[/C][/ROW]
[ROW][C]18[/C][C]6082[/C][C]5880.20373488518[/C][C]201.796265114823[/C][/ROW]
[ROW][C]19[/C][C]6019[/C][C]6305.59531317355[/C][C]-286.595313173545[/C][/ROW]
[ROW][C]20[/C][C]6576[/C][C]6256.22444562094[/C][C]319.775554379063[/C][/ROW]
[ROW][C]21[/C][C]8086[/C][C]6996.025613229[/C][C]1089.974386771[/C][/ROW]
[ROW][C]22[/C][C]8323[/C][C]7952.29768025301[/C][C]370.702319746989[/C][/ROW]
[ROW][C]23[/C][C]7842[/C][C]8221.85319754435[/C][C]-379.853197544355[/C][/ROW]
[ROW][C]24[/C][C]9077[/C][C]10443.1061170463[/C][C]-1366.10611704635[/C][/ROW]
[ROW][C]25[/C][C]10737[/C][C]10364.0481378173[/C][C]372.951862182706[/C][/ROW]
[ROW][C]26[/C][C]10176[/C][C]9455.23607663357[/C][C]720.763923366427[/C][/ROW]
[ROW][C]27[/C][C]10416[/C][C]8816.91207146927[/C][C]1599.08792853073[/C][/ROW]
[ROW][C]28[/C][C]9807[/C][C]8315.3003014662[/C][C]1491.69969853380[/C][/ROW]
[ROW][C]29[/C][C]9565[/C][C]8117.62542442932[/C][C]1447.37457557068[/C][/ROW]
[ROW][C]30[/C][C]10439[/C][C]7407.05881203012[/C][C]3031.94118796988[/C][/ROW]
[ROW][C]31[/C][C]9115[/C][C]8042.87377444761[/C][C]1072.12622555239[/C][/ROW]
[ROW][C]32[/C][C]9535[/C][C]8383.90963683335[/C][C]1151.09036316665[/C][/ROW]
[ROW][C]33[/C][C]10790[/C][C]9764.1128927004[/C][C]1025.8871072996[/C][/ROW]
[ROW][C]34[/C][C]11340[/C][C]10678.1728122877[/C][C]661.827187712335[/C][/ROW]
[ROW][C]35[/C][C]11196[/C][C]10732.2865452781[/C][C]463.713454721888[/C][/ROW]
[ROW][C]36[/C][C]12132[/C][C]13374.3400349670[/C][C]-1242.34003496704[/C][/ROW]
[ROW][C]37[/C][C]12013[/C][C]14077.9301818921[/C][C]-2064.93018189214[/C][/ROW]
[ROW][C]38[/C][C]12692[/C][C]12753.1348944739[/C][C]-61.1348944738565[/C][/ROW]
[ROW][C]39[/C][C]13330[/C][C]12165.0146536831[/C][C]1164.98534631695[/C][/ROW]
[ROW][C]40[/C][C]11926[/C][C]11360.2052048910[/C][C]565.794795109046[/C][/ROW]
[ROW][C]41[/C][C]11356[/C][C]10932.0496986903[/C][C]423.950301309724[/C][/ROW]
[ROW][C]42[/C][C]11221[/C][C]10472.1212611640[/C][C]748.878738836045[/C][/ROW]
[ROW][C]43[/C][C]9999[/C][C]10156.8138772920[/C][C]-157.813877291954[/C][/ROW]
[ROW][C]44[/C][C]11772[/C][C]10423.5120677162[/C][C]1348.48793228377[/C][/ROW]
[ROW][C]45[/C][C]12543[/C][C]11998.1757629573[/C][C]544.824237042711[/C][/ROW]
[ROW][C]46[/C][C]14176[/C][C]12852.9223447867[/C][C]1323.07765521327[/C][/ROW]
[ROW][C]47[/C][C]2924[/C][C]12883.0602369135[/C][C]-9959.06023691351[/C][/ROW]
[ROW][C]48[/C][C]2322[/C][C]14014.7344942861[/C][C]-11692.7344942861[/C][/ROW]
[ROW][C]49[/C][C]15557[/C][C]13296.0255295119[/C][C]2260.97447048808[/C][/ROW]
[ROW][C]50[/C][C]13381[/C][C]13018.8754885759[/C][C]362.124511424125[/C][/ROW]
[ROW][C]51[/C][C]13145[/C][C]12823.4629621890[/C][C]321.537037811015[/C][/ROW]
[ROW][C]52[/C][C]12448[/C][C]11686.6052026555[/C][C]761.394797344487[/C][/ROW]
[ROW][C]53[/C][C]12178[/C][C]11194.8802035217[/C][C]983.119796478302[/C][/ROW]
[ROW][C]54[/C][C]11836[/C][C]10861.2585869274[/C][C]974.741413072567[/C][/ROW]
[ROW][C]55[/C][C]9815[/C][C]10242.7440794549[/C][C]-427.744079454931[/C][/ROW]
[ROW][C]56[/C][C]12382[/C][C]10938.6180691959[/C][C]1443.38193080409[/C][/ROW]
[ROW][C]57[/C][C]12662[/C][C]12245.5709638898[/C][C]416.429036110152[/C][/ROW]
[ROW][C]58[/C][C]12767[/C][C]13305.1729213711[/C][C]-538.172921371066[/C][/ROW]
[ROW][C]59[/C][C]13136[/C][C]9269.7971729448[/C][C]3866.20282705521[/C][/ROW]
[ROW][C]60[/C][C]13533[/C][C]11083.9330286545[/C][C]2449.06697134546[/C][/ROW]
[ROW][C]61[/C][C]17808[/C][C]17593.1192915399[/C][C]214.880708460139[/C][/ROW]
[ROW][C]62[/C][C]15892[/C][C]16238.0010641410[/C][C]-346.001064141023[/C][/ROW]
[ROW][C]63[/C][C]16830[/C][C]15907.0315156117[/C][C]922.968484388324[/C][/ROW]
[ROW][C]64[/C][C]14444[/C][C]14739.3692059401[/C][C]-295.369205940066[/C][/ROW]
[ROW][C]65[/C][C]15550[/C][C]14097.8873554808[/C][C]1452.11264451923[/C][/ROW]
[ROW][C]66[/C][C]15092[/C][C]13713.9697094146[/C][C]1378.03029058543[/C][/ROW]
[ROW][C]67[/C][C]16364[/C][C]12425.7833247484[/C][C]3938.21667525159[/C][/ROW]
[ROW][C]68[/C][C]14314[/C][C]14557.304094364[/C][C]-243.304094364014[/C][/ROW]
[ROW][C]69[/C][C]15874[/C][C]15581.7613180096[/C][C]292.238681990364[/C][/ROW]
[ROW][C]70[/C][C]17846[/C][C]16515.6012963439[/C][C]1330.39870365611[/C][/ROW]
[ROW][C]71[/C][C]18504[/C][C]13330.026761958[/C][C]5173.97323804201[/C][/ROW]
[ROW][C]72[/C][C]15130[/C][C]15075.5598112572[/C][C]54.4401887427684[/C][/ROW]
[ROW][C]73[/C][C]19845[/C][C]21975.8139573879[/C][C]-2130.81395738792[/C][/ROW]
[ROW][C]74[/C][C]18137[/C][C]19841.2262186486[/C][C]-1704.22621864859[/C][/ROW]
[ROW][C]75[/C][C]18898[/C][C]19799.9595923961[/C][C]-901.959592396102[/C][/ROW]
[ROW][C]76[/C][C]19573[/C][C]17704.3634348958[/C][C]1868.63656510418[/C][/ROW]
[ROW][C]77[/C][C]17368[/C][C]17836.6883887206[/C][C]-468.688388720642[/C][/ROW]
[ROW][C]78[/C][C]18938[/C][C]17104.4607627744[/C][C]1833.5392372256[/C][/ROW]
[ROW][C]79[/C][C]16713[/C][C]16506.8408255114[/C][C]206.15917448861[/C][/ROW]
[ROW][C]80[/C][C]16379[/C][C]16963.8004058771[/C][C]-584.800405877104[/C][/ROW]
[ROW][C]81[/C][C]19139[/C][C]18322.5238356449[/C][C]816.476164355106[/C][/ROW]
[ROW][C]82[/C][C]21461[/C][C]19844.7150301905[/C][C]1616.28496980948[/C][/ROW]
[ROW][C]83[/C][C]19796[/C][C]17477.8112814679[/C][C]2318.18871853211[/C][/ROW]
[ROW][C]84[/C][C]16668[/C][C]17208.5259236055[/C][C]-540.52592360555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41251&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41251&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
1390168341.80493621812674.195063781877
1482017692.67196296991508.32803703009
1576307185.70804867018444.291951329816
1671076705.98981801135401.010181988650
1768206491.20256411012328.797435889876
1860825880.20373488518201.796265114823
1960196305.59531317355-286.595313173545
2065766256.22444562094319.775554379063
2180866996.0256132291089.974386771
2283237952.29768025301370.702319746989
2378428221.85319754435-379.853197544355
24907710443.1061170463-1366.10611704635
251073710364.0481378173372.951862182706
26101769455.23607663357720.763923366427
27104168816.912071469271599.08792853073
2898078315.30030146621491.69969853380
2995658117.625424429321447.37457557068
30104397407.058812030123031.94118796988
3191158042.873774447611072.12622555239
3295358383.909636833351151.09036316665
33107909764.11289270041025.8871072996
341134010678.1728122877661.827187712335
351119610732.2865452781463.713454721888
361213213374.3400349670-1242.34003496704
371201314077.9301818921-2064.93018189214
381269212753.1348944739-61.1348944738565
391333012165.01465368311164.98534631695
401192611360.2052048910565.794795109046
411135610932.0496986903423.950301309724
421122110472.1212611640748.878738836045
43999910156.8138772920-157.813877291954
441177210423.51206771621348.48793228377
451254311998.1757629573544.824237042711
461417612852.92234478671323.07765521327
47292412883.0602369135-9959.06023691351
48232214014.7344942861-11692.7344942861
491555713296.02552951192260.97447048808
501338113018.8754885759362.124511424125
511314512823.4629621890321.537037811015
521244811686.6052026555761.394797344487
531217811194.8802035217983.119796478302
541183610861.2585869274974.741413072567
55981510242.7440794549-427.744079454931
561238210938.61806919591443.38193080409
571266212245.5709638898416.429036110152
581276713305.1729213711-538.172921371066
59131369269.79717294483866.20282705521
601353311083.93302865452449.06697134546
611780817593.1192915399214.880708460139
621589216238.0010641410-346.001064141023
631683015907.0315156117922.968484388324
641444414739.3692059401-295.369205940066
651555014097.88735548081452.11264451923
661509213713.96970941461378.03029058543
671636412425.78332474843938.21667525159
681431414557.304094364-243.304094364014
691587415581.7613180096292.238681990364
701784616515.60129634391330.39870365611
711850413330.0267619585173.97323804201
721513015075.559811257254.4401887427684
731984521975.8139573879-2130.81395738792
741813719841.2262186486-1704.22621864859
751889819799.9595923961-901.959592396102
761957317704.36343489581868.63656510418
771736817836.6883887206-468.688388720642
781893817104.46076277441833.5392372256
791671316506.8408255114206.15917448861
801637916963.8004058771-584.800405877104
811913918322.5238356449816.476164355106
822146119844.71503019051616.28496980948
831979617477.81128146792318.18871853211
841666817208.5259236055-540.52592360555







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8524162.008317781222257.255614406826066.7610211557
8622108.864035972620154.537068126924063.1910038183
8722553.635861858520536.068354483524571.2033692335
8821244.516667771519186.749291923123302.2840436198
8920299.304786996718200.366564336122398.2430096573
9020344.440857405718185.777439963722503.1042748476
9118839.837776162016664.361128245321015.3144240787
9219033.154843759216792.883732822321273.4259546961
9321147.646796792318765.943936307223529.3496572775
9423044.750018386220516.789057077125572.7109796953
9520422.613411341017966.384704637822878.8421180443
9618823.655907277617310.632395259720336.6794192954

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 24162.0083177812 & 22257.2556144068 & 26066.7610211557 \tabularnewline
86 & 22108.8640359726 & 20154.5370681269 & 24063.1910038183 \tabularnewline
87 & 22553.6358618585 & 20536.0683544835 & 24571.2033692335 \tabularnewline
88 & 21244.5166677715 & 19186.7492919231 & 23302.2840436198 \tabularnewline
89 & 20299.3047869967 & 18200.3665643361 & 22398.2430096573 \tabularnewline
90 & 20344.4408574057 & 18185.7774399637 & 22503.1042748476 \tabularnewline
91 & 18839.8377761620 & 16664.3611282453 & 21015.3144240787 \tabularnewline
92 & 19033.1548437592 & 16792.8837328223 & 21273.4259546961 \tabularnewline
93 & 21147.6467967923 & 18765.9439363072 & 23529.3496572775 \tabularnewline
94 & 23044.7500183862 & 20516.7890570771 & 25572.7109796953 \tabularnewline
95 & 20422.6134113410 & 17966.3847046378 & 22878.8421180443 \tabularnewline
96 & 18823.6559072776 & 17310.6323952597 & 20336.6794192954 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41251&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]85[/C][C]24162.0083177812[/C][C]22257.2556144068[/C][C]26066.7610211557[/C][/ROW]
[ROW][C]86[/C][C]22108.8640359726[/C][C]20154.5370681269[/C][C]24063.1910038183[/C][/ROW]
[ROW][C]87[/C][C]22553.6358618585[/C][C]20536.0683544835[/C][C]24571.2033692335[/C][/ROW]
[ROW][C]88[/C][C]21244.5166677715[/C][C]19186.7492919231[/C][C]23302.2840436198[/C][/ROW]
[ROW][C]89[/C][C]20299.3047869967[/C][C]18200.3665643361[/C][C]22398.2430096573[/C][/ROW]
[ROW][C]90[/C][C]20344.4408574057[/C][C]18185.7774399637[/C][C]22503.1042748476[/C][/ROW]
[ROW][C]91[/C][C]18839.8377761620[/C][C]16664.3611282453[/C][C]21015.3144240787[/C][/ROW]
[ROW][C]92[/C][C]19033.1548437592[/C][C]16792.8837328223[/C][C]21273.4259546961[/C][/ROW]
[ROW][C]93[/C][C]21147.6467967923[/C][C]18765.9439363072[/C][C]23529.3496572775[/C][/ROW]
[ROW][C]94[/C][C]23044.7500183862[/C][C]20516.7890570771[/C][C]25572.7109796953[/C][/ROW]
[ROW][C]95[/C][C]20422.6134113410[/C][C]17966.3847046378[/C][C]22878.8421180443[/C][/ROW]
[ROW][C]96[/C][C]18823.6559072776[/C][C]17310.6323952597[/C][C]20336.6794192954[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41251&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41251&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
8524162.008317781222257.255614406826066.7610211557
8622108.864035972620154.537068126924063.1910038183
8722553.635861858520536.068354483524571.2033692335
8821244.516667771519186.749291923123302.2840436198
8920299.304786996718200.366564336122398.2430096573
9020344.440857405718185.777439963722503.1042748476
9118839.837776162016664.361128245321015.3144240787
9219033.154843759216792.883732822321273.4259546961
9321147.646796792318765.943936307223529.3496572775
9423044.750018386220516.789057077125572.7109796953
9520422.613411341017966.384704637822878.8421180443
9618823.655907277617310.632395259720336.6794192954



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')