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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 14 Dec 2017 10:04:39 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/14/t1513242467s9b0nb237jtwo7a.htm/, Retrieved Mon, 13 May 2024 22:02:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309416, Retrieved Mon, 13 May 2024 22:02:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2017-12-14 09:04:39] [5c76e56d84d1440d36aad135bd2f9339] [Current]
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Dataseries X:
18142
8613
8347
7054
5179
6785
7887
6926
6355
7533
6727
8215
13880
10484
9847
6952
9393
12870
9330
14726
10176.66667
7815
6419
9900
9999.833333
14523
12419
8923
11857
12676
14873
11711
15243
9751
7631
8161
10435
15188
10237
11642
16513
18632
15526
14991
10365
10369
10912
14476.83333
19891
17448
17876
11414
9452
15509
11286
13318
9298.833333
6850
4497
4333
7301
4323
6033
4513
4442
7666
6260
5339
3686
4549
3675
7356
8341
20001
9554
6334
4313
4161
7835
9109
7691
5091
7407
11632
17611
9481
7603
4485
10381
8796
10132
10163
17969
6695




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309416&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309416&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309416&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.870420891732632
beta0.231095604177129
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.870420891732632 \tabularnewline
beta & 0.231095604177129 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309416&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]0.870420891732632[/C][/ROW]
[ROW][C]beta[/C][C]0.231095604177129[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309416&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309416&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
alpha0.870420891732632
beta0.231095604177129
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
38347-9169263
47054-519.0347369004387573.03473690044
55179-69.73126153116035248.73126153116
66785-587.7654773711047372.7654773711
778872226.039096539025660.96090346098
869264688.557993856612237.44200614339
963554621.236967886861733.76303211314
1075334464.250440190623068.74955980938
1167276086.54440630641640.455593693595
1282155724.028498712042490.97150128796
13138807473.300315724466406.69968427554
141048413919.6142219333-3435.61422193333
15984711107.8971623735-1260.8971623735
1669529935.46924370623-2983.46924370623
1793936663.552441274372729.44755872563
18128708913.307358890083956.69264110992
19933013027.1725085659-3697.17250856593
20147269735.265645716564990.73435428344
2110176.6666715009.3828423053-4832.71617230529
22781510760.8604781899-2945.86047818991
2364197562.13559306156-1143.13559306156
2499005702.597880341184197.40211965882
259999.8333339335.88505690615663.948276093852
261452310027.13367716994495.86632283011
271241914958.109318116-2539.10931811599
28892313254.9522270741-4331.95222707407
29118579119.893107873472737.10689212653
301267611688.4609916966987.539008303389
311487312932.81234581321940.18765418684
321171115396.638587725-3685.63858772496
331524312222.26030494963020.73969505043
34975115492.8769117774-5741.87691177744
3576319981.34787985004-2350.34787985004
3681616949.103057665581211.89694233442
37104357261.284155620273173.71584437973
38151889919.467756156875268.53224384313
391023715460.7909039509-5223.79090395088
401164210818.6089325636823.391067436361
411651311605.64596222194907.35403777807
421863216934.5661154071697.43388459295
431552619810.9442823859-4284.94428238592
441499116618.2170748195-1627.21707481946
451036515411.5157196376-5046.51571963755
461036910213.4765220575155.523477942523
47109129574.684537971421337.31546202858
4814476.8333310233.55058261384243.28274738624
491989114275.36946271085615.63053728917
501744820641.2950937796-3193.29509377955
511787618697.4151027332-821.415102733179
521141418652.8409977082-7238.84099770817
53945211566.3092572834-2114.30925728343
54155098514.982762733036994.01723726697
551128614798.5835954373-3512.58359543728
561331811230.46181995612087.53818004388
579298.83333312956.712261423-3657.87892842304
5868508946.24765722734-2096.24765722734
5944975873.39839415708-1376.39839415708
6043333150.257823396811182.74217660319
6173012892.5557817414408.444218259
6243236329.33269007973-2006.33269007973
6360333778.979054461952254.02094553805
6445135390.32353861918-877.323538619181
6544424099.60634710385342.393652896149
6676663939.429115660183726.57088433982
6762607474.51182781102-1214.51182781102
6853396464.47332871439-1125.47332871439
6936865305.54634202367-1619.54634202367
7045493390.795420191031158.20457980897
7136754126.83029574782-451.830295747821
7273563370.571315564913985.42868443509
7383417278.265994650421062.73400534958
74200018855.7555796633811145.2444203366
75955421451.1437108186-11897.1437108186
76633411596.8401028614-5262.84010286139
7743136458.55034522059-2145.55034522059
7841613602.03631823332558.963681766682
7978353212.023593892654622.97640610735
8091097289.326195897681819.67380410232
8176919292.60383701142-1601.60383701142
8250917995.76662337714-2904.76662337714
8374074980.334205359422426.66579464058
84116327093.616843691574538.38315630843
851761111957.88016829055653.11983170945
86948118929.561135994-9448.56113599396
87760310855.8412416492-3252.84124164921
8844857520.69492959657-3035.69492959657
89103813763.925927666566617.07407233344
9087969740.15610157796-944.156101577955
91101328945.016147897331186.98385210267
921016310243.6272594415-80.6272594415423
931796910422.66496804247546.33503195765
94669518758.3186216612-12063.3186216612

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8347 & -916 & 9263 \tabularnewline
4 & 7054 & -519.034736900438 & 7573.03473690044 \tabularnewline
5 & 5179 & -69.7312615311603 & 5248.73126153116 \tabularnewline
6 & 6785 & -587.765477371104 & 7372.7654773711 \tabularnewline
7 & 7887 & 2226.03909653902 & 5660.96090346098 \tabularnewline
8 & 6926 & 4688.55799385661 & 2237.44200614339 \tabularnewline
9 & 6355 & 4621.23696788686 & 1733.76303211314 \tabularnewline
10 & 7533 & 4464.25044019062 & 3068.74955980938 \tabularnewline
11 & 6727 & 6086.54440630641 & 640.455593693595 \tabularnewline
12 & 8215 & 5724.02849871204 & 2490.97150128796 \tabularnewline
13 & 13880 & 7473.30031572446 & 6406.69968427554 \tabularnewline
14 & 10484 & 13919.6142219333 & -3435.61422193333 \tabularnewline
15 & 9847 & 11107.8971623735 & -1260.8971623735 \tabularnewline
16 & 6952 & 9935.46924370623 & -2983.46924370623 \tabularnewline
17 & 9393 & 6663.55244127437 & 2729.44755872563 \tabularnewline
18 & 12870 & 8913.30735889008 & 3956.69264110992 \tabularnewline
19 & 9330 & 13027.1725085659 & -3697.17250856593 \tabularnewline
20 & 14726 & 9735.26564571656 & 4990.73435428344 \tabularnewline
21 & 10176.66667 & 15009.3828423053 & -4832.71617230529 \tabularnewline
22 & 7815 & 10760.8604781899 & -2945.86047818991 \tabularnewline
23 & 6419 & 7562.13559306156 & -1143.13559306156 \tabularnewline
24 & 9900 & 5702.59788034118 & 4197.40211965882 \tabularnewline
25 & 9999.833333 & 9335.88505690615 & 663.948276093852 \tabularnewline
26 & 14523 & 10027.1336771699 & 4495.86632283011 \tabularnewline
27 & 12419 & 14958.109318116 & -2539.10931811599 \tabularnewline
28 & 8923 & 13254.9522270741 & -4331.95222707407 \tabularnewline
29 & 11857 & 9119.89310787347 & 2737.10689212653 \tabularnewline
30 & 12676 & 11688.4609916966 & 987.539008303389 \tabularnewline
31 & 14873 & 12932.8123458132 & 1940.18765418684 \tabularnewline
32 & 11711 & 15396.638587725 & -3685.63858772496 \tabularnewline
33 & 15243 & 12222.2603049496 & 3020.73969505043 \tabularnewline
34 & 9751 & 15492.8769117774 & -5741.87691177744 \tabularnewline
35 & 7631 & 9981.34787985004 & -2350.34787985004 \tabularnewline
36 & 8161 & 6949.10305766558 & 1211.89694233442 \tabularnewline
37 & 10435 & 7261.28415562027 & 3173.71584437973 \tabularnewline
38 & 15188 & 9919.46775615687 & 5268.53224384313 \tabularnewline
39 & 10237 & 15460.7909039509 & -5223.79090395088 \tabularnewline
40 & 11642 & 10818.6089325636 & 823.391067436361 \tabularnewline
41 & 16513 & 11605.6459622219 & 4907.35403777807 \tabularnewline
42 & 18632 & 16934.566115407 & 1697.43388459295 \tabularnewline
43 & 15526 & 19810.9442823859 & -4284.94428238592 \tabularnewline
44 & 14991 & 16618.2170748195 & -1627.21707481946 \tabularnewline
45 & 10365 & 15411.5157196376 & -5046.51571963755 \tabularnewline
46 & 10369 & 10213.4765220575 & 155.523477942523 \tabularnewline
47 & 10912 & 9574.68453797142 & 1337.31546202858 \tabularnewline
48 & 14476.83333 & 10233.5505826138 & 4243.28274738624 \tabularnewline
49 & 19891 & 14275.3694627108 & 5615.63053728917 \tabularnewline
50 & 17448 & 20641.2950937796 & -3193.29509377955 \tabularnewline
51 & 17876 & 18697.4151027332 & -821.415102733179 \tabularnewline
52 & 11414 & 18652.8409977082 & -7238.84099770817 \tabularnewline
53 & 9452 & 11566.3092572834 & -2114.30925728343 \tabularnewline
54 & 15509 & 8514.98276273303 & 6994.01723726697 \tabularnewline
55 & 11286 & 14798.5835954373 & -3512.58359543728 \tabularnewline
56 & 13318 & 11230.4618199561 & 2087.53818004388 \tabularnewline
57 & 9298.833333 & 12956.712261423 & -3657.87892842304 \tabularnewline
58 & 6850 & 8946.24765722734 & -2096.24765722734 \tabularnewline
59 & 4497 & 5873.39839415708 & -1376.39839415708 \tabularnewline
60 & 4333 & 3150.25782339681 & 1182.74217660319 \tabularnewline
61 & 7301 & 2892.555781741 & 4408.444218259 \tabularnewline
62 & 4323 & 6329.33269007973 & -2006.33269007973 \tabularnewline
63 & 6033 & 3778.97905446195 & 2254.02094553805 \tabularnewline
64 & 4513 & 5390.32353861918 & -877.323538619181 \tabularnewline
65 & 4442 & 4099.60634710385 & 342.393652896149 \tabularnewline
66 & 7666 & 3939.42911566018 & 3726.57088433982 \tabularnewline
67 & 6260 & 7474.51182781102 & -1214.51182781102 \tabularnewline
68 & 5339 & 6464.47332871439 & -1125.47332871439 \tabularnewline
69 & 3686 & 5305.54634202367 & -1619.54634202367 \tabularnewline
70 & 4549 & 3390.79542019103 & 1158.20457980897 \tabularnewline
71 & 3675 & 4126.83029574782 & -451.830295747821 \tabularnewline
72 & 7356 & 3370.57131556491 & 3985.42868443509 \tabularnewline
73 & 8341 & 7278.26599465042 & 1062.73400534958 \tabularnewline
74 & 20001 & 8855.75557966338 & 11145.2444203366 \tabularnewline
75 & 9554 & 21451.1437108186 & -11897.1437108186 \tabularnewline
76 & 6334 & 11596.8401028614 & -5262.84010286139 \tabularnewline
77 & 4313 & 6458.55034522059 & -2145.55034522059 \tabularnewline
78 & 4161 & 3602.03631823332 & 558.963681766682 \tabularnewline
79 & 7835 & 3212.02359389265 & 4622.97640610735 \tabularnewline
80 & 9109 & 7289.32619589768 & 1819.67380410232 \tabularnewline
81 & 7691 & 9292.60383701142 & -1601.60383701142 \tabularnewline
82 & 5091 & 7995.76662337714 & -2904.76662337714 \tabularnewline
83 & 7407 & 4980.33420535942 & 2426.66579464058 \tabularnewline
84 & 11632 & 7093.61684369157 & 4538.38315630843 \tabularnewline
85 & 17611 & 11957.8801682905 & 5653.11983170945 \tabularnewline
86 & 9481 & 18929.561135994 & -9448.56113599396 \tabularnewline
87 & 7603 & 10855.8412416492 & -3252.84124164921 \tabularnewline
88 & 4485 & 7520.69492959657 & -3035.69492959657 \tabularnewline
89 & 10381 & 3763.92592766656 & 6617.07407233344 \tabularnewline
90 & 8796 & 9740.15610157796 & -944.156101577955 \tabularnewline
91 & 10132 & 8945.01614789733 & 1186.98385210267 \tabularnewline
92 & 10163 & 10243.6272594415 & -80.6272594415423 \tabularnewline
93 & 17969 & 10422.6649680424 & 7546.33503195765 \tabularnewline
94 & 6695 & 18758.3186216612 & -12063.3186216612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309416&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]8347[/C][C]-916[/C][C]9263[/C][/ROW]
[ROW][C]4[/C][C]7054[/C][C]-519.034736900438[/C][C]7573.03473690044[/C][/ROW]
[ROW][C]5[/C][C]5179[/C][C]-69.7312615311603[/C][C]5248.73126153116[/C][/ROW]
[ROW][C]6[/C][C]6785[/C][C]-587.765477371104[/C][C]7372.7654773711[/C][/ROW]
[ROW][C]7[/C][C]7887[/C][C]2226.03909653902[/C][C]5660.96090346098[/C][/ROW]
[ROW][C]8[/C][C]6926[/C][C]4688.55799385661[/C][C]2237.44200614339[/C][/ROW]
[ROW][C]9[/C][C]6355[/C][C]4621.23696788686[/C][C]1733.76303211314[/C][/ROW]
[ROW][C]10[/C][C]7533[/C][C]4464.25044019062[/C][C]3068.74955980938[/C][/ROW]
[ROW][C]11[/C][C]6727[/C][C]6086.54440630641[/C][C]640.455593693595[/C][/ROW]
[ROW][C]12[/C][C]8215[/C][C]5724.02849871204[/C][C]2490.97150128796[/C][/ROW]
[ROW][C]13[/C][C]13880[/C][C]7473.30031572446[/C][C]6406.69968427554[/C][/ROW]
[ROW][C]14[/C][C]10484[/C][C]13919.6142219333[/C][C]-3435.61422193333[/C][/ROW]
[ROW][C]15[/C][C]9847[/C][C]11107.8971623735[/C][C]-1260.8971623735[/C][/ROW]
[ROW][C]16[/C][C]6952[/C][C]9935.46924370623[/C][C]-2983.46924370623[/C][/ROW]
[ROW][C]17[/C][C]9393[/C][C]6663.55244127437[/C][C]2729.44755872563[/C][/ROW]
[ROW][C]18[/C][C]12870[/C][C]8913.30735889008[/C][C]3956.69264110992[/C][/ROW]
[ROW][C]19[/C][C]9330[/C][C]13027.1725085659[/C][C]-3697.17250856593[/C][/ROW]
[ROW][C]20[/C][C]14726[/C][C]9735.26564571656[/C][C]4990.73435428344[/C][/ROW]
[ROW][C]21[/C][C]10176.66667[/C][C]15009.3828423053[/C][C]-4832.71617230529[/C][/ROW]
[ROW][C]22[/C][C]7815[/C][C]10760.8604781899[/C][C]-2945.86047818991[/C][/ROW]
[ROW][C]23[/C][C]6419[/C][C]7562.13559306156[/C][C]-1143.13559306156[/C][/ROW]
[ROW][C]24[/C][C]9900[/C][C]5702.59788034118[/C][C]4197.40211965882[/C][/ROW]
[ROW][C]25[/C][C]9999.833333[/C][C]9335.88505690615[/C][C]663.948276093852[/C][/ROW]
[ROW][C]26[/C][C]14523[/C][C]10027.1336771699[/C][C]4495.86632283011[/C][/ROW]
[ROW][C]27[/C][C]12419[/C][C]14958.109318116[/C][C]-2539.10931811599[/C][/ROW]
[ROW][C]28[/C][C]8923[/C][C]13254.9522270741[/C][C]-4331.95222707407[/C][/ROW]
[ROW][C]29[/C][C]11857[/C][C]9119.89310787347[/C][C]2737.10689212653[/C][/ROW]
[ROW][C]30[/C][C]12676[/C][C]11688.4609916966[/C][C]987.539008303389[/C][/ROW]
[ROW][C]31[/C][C]14873[/C][C]12932.8123458132[/C][C]1940.18765418684[/C][/ROW]
[ROW][C]32[/C][C]11711[/C][C]15396.638587725[/C][C]-3685.63858772496[/C][/ROW]
[ROW][C]33[/C][C]15243[/C][C]12222.2603049496[/C][C]3020.73969505043[/C][/ROW]
[ROW][C]34[/C][C]9751[/C][C]15492.8769117774[/C][C]-5741.87691177744[/C][/ROW]
[ROW][C]35[/C][C]7631[/C][C]9981.34787985004[/C][C]-2350.34787985004[/C][/ROW]
[ROW][C]36[/C][C]8161[/C][C]6949.10305766558[/C][C]1211.89694233442[/C][/ROW]
[ROW][C]37[/C][C]10435[/C][C]7261.28415562027[/C][C]3173.71584437973[/C][/ROW]
[ROW][C]38[/C][C]15188[/C][C]9919.46775615687[/C][C]5268.53224384313[/C][/ROW]
[ROW][C]39[/C][C]10237[/C][C]15460.7909039509[/C][C]-5223.79090395088[/C][/ROW]
[ROW][C]40[/C][C]11642[/C][C]10818.6089325636[/C][C]823.391067436361[/C][/ROW]
[ROW][C]41[/C][C]16513[/C][C]11605.6459622219[/C][C]4907.35403777807[/C][/ROW]
[ROW][C]42[/C][C]18632[/C][C]16934.566115407[/C][C]1697.43388459295[/C][/ROW]
[ROW][C]43[/C][C]15526[/C][C]19810.9442823859[/C][C]-4284.94428238592[/C][/ROW]
[ROW][C]44[/C][C]14991[/C][C]16618.2170748195[/C][C]-1627.21707481946[/C][/ROW]
[ROW][C]45[/C][C]10365[/C][C]15411.5157196376[/C][C]-5046.51571963755[/C][/ROW]
[ROW][C]46[/C][C]10369[/C][C]10213.4765220575[/C][C]155.523477942523[/C][/ROW]
[ROW][C]47[/C][C]10912[/C][C]9574.68453797142[/C][C]1337.31546202858[/C][/ROW]
[ROW][C]48[/C][C]14476.83333[/C][C]10233.5505826138[/C][C]4243.28274738624[/C][/ROW]
[ROW][C]49[/C][C]19891[/C][C]14275.3694627108[/C][C]5615.63053728917[/C][/ROW]
[ROW][C]50[/C][C]17448[/C][C]20641.2950937796[/C][C]-3193.29509377955[/C][/ROW]
[ROW][C]51[/C][C]17876[/C][C]18697.4151027332[/C][C]-821.415102733179[/C][/ROW]
[ROW][C]52[/C][C]11414[/C][C]18652.8409977082[/C][C]-7238.84099770817[/C][/ROW]
[ROW][C]53[/C][C]9452[/C][C]11566.3092572834[/C][C]-2114.30925728343[/C][/ROW]
[ROW][C]54[/C][C]15509[/C][C]8514.98276273303[/C][C]6994.01723726697[/C][/ROW]
[ROW][C]55[/C][C]11286[/C][C]14798.5835954373[/C][C]-3512.58359543728[/C][/ROW]
[ROW][C]56[/C][C]13318[/C][C]11230.4618199561[/C][C]2087.53818004388[/C][/ROW]
[ROW][C]57[/C][C]9298.833333[/C][C]12956.712261423[/C][C]-3657.87892842304[/C][/ROW]
[ROW][C]58[/C][C]6850[/C][C]8946.24765722734[/C][C]-2096.24765722734[/C][/ROW]
[ROW][C]59[/C][C]4497[/C][C]5873.39839415708[/C][C]-1376.39839415708[/C][/ROW]
[ROW][C]60[/C][C]4333[/C][C]3150.25782339681[/C][C]1182.74217660319[/C][/ROW]
[ROW][C]61[/C][C]7301[/C][C]2892.555781741[/C][C]4408.444218259[/C][/ROW]
[ROW][C]62[/C][C]4323[/C][C]6329.33269007973[/C][C]-2006.33269007973[/C][/ROW]
[ROW][C]63[/C][C]6033[/C][C]3778.97905446195[/C][C]2254.02094553805[/C][/ROW]
[ROW][C]64[/C][C]4513[/C][C]5390.32353861918[/C][C]-877.323538619181[/C][/ROW]
[ROW][C]65[/C][C]4442[/C][C]4099.60634710385[/C][C]342.393652896149[/C][/ROW]
[ROW][C]66[/C][C]7666[/C][C]3939.42911566018[/C][C]3726.57088433982[/C][/ROW]
[ROW][C]67[/C][C]6260[/C][C]7474.51182781102[/C][C]-1214.51182781102[/C][/ROW]
[ROW][C]68[/C][C]5339[/C][C]6464.47332871439[/C][C]-1125.47332871439[/C][/ROW]
[ROW][C]69[/C][C]3686[/C][C]5305.54634202367[/C][C]-1619.54634202367[/C][/ROW]
[ROW][C]70[/C][C]4549[/C][C]3390.79542019103[/C][C]1158.20457980897[/C][/ROW]
[ROW][C]71[/C][C]3675[/C][C]4126.83029574782[/C][C]-451.830295747821[/C][/ROW]
[ROW][C]72[/C][C]7356[/C][C]3370.57131556491[/C][C]3985.42868443509[/C][/ROW]
[ROW][C]73[/C][C]8341[/C][C]7278.26599465042[/C][C]1062.73400534958[/C][/ROW]
[ROW][C]74[/C][C]20001[/C][C]8855.75557966338[/C][C]11145.2444203366[/C][/ROW]
[ROW][C]75[/C][C]9554[/C][C]21451.1437108186[/C][C]-11897.1437108186[/C][/ROW]
[ROW][C]76[/C][C]6334[/C][C]11596.8401028614[/C][C]-5262.84010286139[/C][/ROW]
[ROW][C]77[/C][C]4313[/C][C]6458.55034522059[/C][C]-2145.55034522059[/C][/ROW]
[ROW][C]78[/C][C]4161[/C][C]3602.03631823332[/C][C]558.963681766682[/C][/ROW]
[ROW][C]79[/C][C]7835[/C][C]3212.02359389265[/C][C]4622.97640610735[/C][/ROW]
[ROW][C]80[/C][C]9109[/C][C]7289.32619589768[/C][C]1819.67380410232[/C][/ROW]
[ROW][C]81[/C][C]7691[/C][C]9292.60383701142[/C][C]-1601.60383701142[/C][/ROW]
[ROW][C]82[/C][C]5091[/C][C]7995.76662337714[/C][C]-2904.76662337714[/C][/ROW]
[ROW][C]83[/C][C]7407[/C][C]4980.33420535942[/C][C]2426.66579464058[/C][/ROW]
[ROW][C]84[/C][C]11632[/C][C]7093.61684369157[/C][C]4538.38315630843[/C][/ROW]
[ROW][C]85[/C][C]17611[/C][C]11957.8801682905[/C][C]5653.11983170945[/C][/ROW]
[ROW][C]86[/C][C]9481[/C][C]18929.561135994[/C][C]-9448.56113599396[/C][/ROW]
[ROW][C]87[/C][C]7603[/C][C]10855.8412416492[/C][C]-3252.84124164921[/C][/ROW]
[ROW][C]88[/C][C]4485[/C][C]7520.69492959657[/C][C]-3035.69492959657[/C][/ROW]
[ROW][C]89[/C][C]10381[/C][C]3763.92592766656[/C][C]6617.07407233344[/C][/ROW]
[ROW][C]90[/C][C]8796[/C][C]9740.15610157796[/C][C]-944.156101577955[/C][/ROW]
[ROW][C]91[/C][C]10132[/C][C]8945.01614789733[/C][C]1186.98385210267[/C][/ROW]
[ROW][C]92[/C][C]10163[/C][C]10243.6272594415[/C][C]-80.6272594415423[/C][/ROW]
[ROW][C]93[/C][C]17969[/C][C]10422.6649680424[/C][C]7546.33503195765[/C][/ROW]
[ROW][C]94[/C][C]6695[/C][C]18758.3186216612[/C][C]-12063.3186216612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309416&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309416&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
38347-9169263
47054-519.0347369004387573.03473690044
55179-69.73126153116035248.73126153116
66785-587.7654773711047372.7654773711
778872226.039096539025660.96090346098
869264688.557993856612237.44200614339
963554621.236967886861733.76303211314
1075334464.250440190623068.74955980938
1167276086.54440630641640.455593693595
1282155724.028498712042490.97150128796
13138807473.300315724466406.69968427554
141048413919.6142219333-3435.61422193333
15984711107.8971623735-1260.8971623735
1669529935.46924370623-2983.46924370623
1793936663.552441274372729.44755872563
18128708913.307358890083956.69264110992
19933013027.1725085659-3697.17250856593
20147269735.265645716564990.73435428344
2110176.6666715009.3828423053-4832.71617230529
22781510760.8604781899-2945.86047818991
2364197562.13559306156-1143.13559306156
2499005702.597880341184197.40211965882
259999.8333339335.88505690615663.948276093852
261452310027.13367716994495.86632283011
271241914958.109318116-2539.10931811599
28892313254.9522270741-4331.95222707407
29118579119.893107873472737.10689212653
301267611688.4609916966987.539008303389
311487312932.81234581321940.18765418684
321171115396.638587725-3685.63858772496
331524312222.26030494963020.73969505043
34975115492.8769117774-5741.87691177744
3576319981.34787985004-2350.34787985004
3681616949.103057665581211.89694233442
37104357261.284155620273173.71584437973
38151889919.467756156875268.53224384313
391023715460.7909039509-5223.79090395088
401164210818.6089325636823.391067436361
411651311605.64596222194907.35403777807
421863216934.5661154071697.43388459295
431552619810.9442823859-4284.94428238592
441499116618.2170748195-1627.21707481946
451036515411.5157196376-5046.51571963755
461036910213.4765220575155.523477942523
47109129574.684537971421337.31546202858
4814476.8333310233.55058261384243.28274738624
491989114275.36946271085615.63053728917
501744820641.2950937796-3193.29509377955
511787618697.4151027332-821.415102733179
521141418652.8409977082-7238.84099770817
53945211566.3092572834-2114.30925728343
54155098514.982762733036994.01723726697
551128614798.5835954373-3512.58359543728
561331811230.46181995612087.53818004388
579298.83333312956.712261423-3657.87892842304
5868508946.24765722734-2096.24765722734
5944975873.39839415708-1376.39839415708
6043333150.257823396811182.74217660319
6173012892.5557817414408.444218259
6243236329.33269007973-2006.33269007973
6360333778.979054461952254.02094553805
6445135390.32353861918-877.323538619181
6544424099.60634710385342.393652896149
6676663939.429115660183726.57088433982
6762607474.51182781102-1214.51182781102
6853396464.47332871439-1125.47332871439
6936865305.54634202367-1619.54634202367
7045493390.795420191031158.20457980897
7136754126.83029574782-451.830295747821
7273563370.571315564913985.42868443509
7383417278.265994650421062.73400534958
74200018855.7555796633811145.2444203366
75955421451.1437108186-11897.1437108186
76633411596.8401028614-5262.84010286139
7743136458.55034522059-2145.55034522059
7841613602.03631823332558.963681766682
7978353212.023593892654622.97640610735
8091097289.326195897681819.67380410232
8176919292.60383701142-1601.60383701142
8250917995.76662337714-2904.76662337714
8374074980.334205359422426.66579464058
84116327093.616843691574538.38315630843
851761111957.88016829055653.11983170945
86948118929.561135994-9448.56113599396
87760310855.8412416492-3252.84124164921
8844857520.69492959657-3035.69492959657
89103813763.925927666566617.07407233344
9087969740.15610157796-944.156101577955
91101328945.016147897331186.98385210267
921016310243.6272594415-80.6272594415423
931796910422.66496804247546.33503195765
94669518758.3186216612-12063.3186216612







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
957598.77818444351-920.14247779249216117.6988466795
966939.40229914704-5546.7466818462819425.5512801404
976280.02641385056-10256.525841230522816.5786689317
985620.65052855409-15142.434172914826383.7352300229
994961.27464325761-20232.395963148330154.9452496636
1004301.89875796113-25533.924712133734137.722228056
1013642.52287266466-31046.731970969738331.777716299
1022983.14698736818-36767.298315425842733.5922901622
1032323.77110207171-42690.777739081747338.3199432251
1041664.39521677523-48811.859231783152140.6496653335
1051005.01933147876-55125.174092933957135.2127558914
106345.643446182281-61625.490190650662316.7770830151

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
95 & 7598.77818444351 & -920.142477792492 & 16117.6988466795 \tabularnewline
96 & 6939.40229914704 & -5546.74668184628 & 19425.5512801404 \tabularnewline
97 & 6280.02641385056 & -10256.5258412305 & 22816.5786689317 \tabularnewline
98 & 5620.65052855409 & -15142.4341729148 & 26383.7352300229 \tabularnewline
99 & 4961.27464325761 & -20232.3959631483 & 30154.9452496636 \tabularnewline
100 & 4301.89875796113 & -25533.9247121337 & 34137.722228056 \tabularnewline
101 & 3642.52287266466 & -31046.7319709697 & 38331.777716299 \tabularnewline
102 & 2983.14698736818 & -36767.2983154258 & 42733.5922901622 \tabularnewline
103 & 2323.77110207171 & -42690.7777390817 & 47338.3199432251 \tabularnewline
104 & 1664.39521677523 & -48811.8592317831 & 52140.6496653335 \tabularnewline
105 & 1005.01933147876 & -55125.1740929339 & 57135.2127558914 \tabularnewline
106 & 345.643446182281 & -61625.4901906506 & 62316.7770830151 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309416&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]95[/C][C]7598.77818444351[/C][C]-920.142477792492[/C][C]16117.6988466795[/C][/ROW]
[ROW][C]96[/C][C]6939.40229914704[/C][C]-5546.74668184628[/C][C]19425.5512801404[/C][/ROW]
[ROW][C]97[/C][C]6280.02641385056[/C][C]-10256.5258412305[/C][C]22816.5786689317[/C][/ROW]
[ROW][C]98[/C][C]5620.65052855409[/C][C]-15142.4341729148[/C][C]26383.7352300229[/C][/ROW]
[ROW][C]99[/C][C]4961.27464325761[/C][C]-20232.3959631483[/C][C]30154.9452496636[/C][/ROW]
[ROW][C]100[/C][C]4301.89875796113[/C][C]-25533.9247121337[/C][C]34137.722228056[/C][/ROW]
[ROW][C]101[/C][C]3642.52287266466[/C][C]-31046.7319709697[/C][C]38331.777716299[/C][/ROW]
[ROW][C]102[/C][C]2983.14698736818[/C][C]-36767.2983154258[/C][C]42733.5922901622[/C][/ROW]
[ROW][C]103[/C][C]2323.77110207171[/C][C]-42690.7777390817[/C][C]47338.3199432251[/C][/ROW]
[ROW][C]104[/C][C]1664.39521677523[/C][C]-48811.8592317831[/C][C]52140.6496653335[/C][/ROW]
[ROW][C]105[/C][C]1005.01933147876[/C][C]-55125.1740929339[/C][C]57135.2127558914[/C][/ROW]
[ROW][C]106[/C][C]345.643446182281[/C][C]-61625.4901906506[/C][C]62316.7770830151[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309416&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309416&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
957598.77818444351-920.14247779249216117.6988466795
966939.40229914704-5546.7466818462819425.5512801404
976280.02641385056-10256.525841230522816.5786689317
985620.65052855409-15142.434172914826383.7352300229
994961.27464325761-20232.395963148330154.9452496636
1004301.89875796113-25533.924712133734137.722228056
1013642.52287266466-31046.731970969738331.777716299
1022983.14698736818-36767.298315425842733.5922901622
1032323.77110207171-42690.777739081747338.3199432251
1041664.39521677523-48811.859231783152140.6496653335
1051005.01933147876-55125.174092933957135.2127558914
106345.643446182281-61625.490190650662316.7770830151



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'multiplicative'
par2 <- 'Double'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')