Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 14 Aug 2013 05:45:33 -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/2013/Aug/14/t1376473582mnvl0n23vaucoeg.htm/, Retrieved Sun, 05 May 2024 01:02:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211086, Retrieved Sun, 05 May 2024 01:02:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact181
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Notched Boxplots] [Box-plot maximump...] [2011-10-11 15:12:03] [102faec22d2a25d9aaa52ca244269a51]
- RMPD    [Exponential Smoothing] [] [2013-08-14 09:45:33] [4d26c4233714d8e4ecf99606d744931b] [Current]
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Dataseries X:
3207324
3178086
3148485
3087246
3693267
3661164
3207324
2905563
2934699
2934699
2967168
3025542
3207324
3148485
3239325
3388641
4238049
4238049
4056732
3874950
4024266
4205949
4238049
4328892
4601499
4419732
4419732
4692342
5448042
5509281
5357202
4993734
5266260
5266260
5295495
5448042
5568120
5629359
5629359
5811042
6508356
6689670
6718809
6264966
6508356
6417513
6235746
6628434
6718809
6566727
6598830
6809748
7597920
7990056
7990056
7808739
8080980
7808739
7656276
8233527
8323902
8110134
8654901
8868684
9504309
9926133
9867774
9835290
10078677
10049076
9686076
10230759
10412541
10230759
10986462
11349927
12196086
12529950
12439476
12257691
12409872
12591555
11985168
12468612
12773337
12650394
13438098
13710240
14861511
15072414
14800254
14952351
15043194
15134034
14556783
15101568
15403311
15101568
15980562
16252821
17433111
17614893
17673267
17977893
17977893
18097971
17553189
17825814
18007131
17673267
18642738
18824436
20034063
20247849
20549592
20822217
20851353
20883456
20338689
20883456




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211086&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211086&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211086&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.214234531513293
beta0.107870793542666
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.214234531513293 \tabularnewline
beta & 0.107870793542666 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211086&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]0.214234531513293[/C][/ROW]
[ROW][C]beta[/C][C]0.107870793542666[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211086&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211086&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
alpha0.214234531513293
beta0.107870793542666
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1332073243024589.7461559182734.253844095
1431484853000263.97374849148221.026251507
1532393253106130.84453269133194.155467313
1633886413256794.22176458131846.778235422
1742380494076401.79487787161647.205122134
1842380494081971.00595935156077.994040653
1940567323819517.04148672237214.958513284
2038749503587211.99199138287738.008008617
2140242663769565.12685425254700.873145752
2242059493896979.33795852308969.662041479
2342380494062721.12714081175327.872859194
2443288924225265.54928238103626.450717621
2546014994745548.48064813-144049.480648131
2644197324595867.58841893-176135.588418934
2744197324655247.97818401-235515.978184007
2846923424775677.89002496-83335.8900249638
2954480425894155.64312454-446113.643124539
3055092815733453.5749988-224172.574998799
3153572025346897.6380926910304.3619073126
3249937344996293.87938884-2559.8793888418
3352662605080735.39491208185524.605087921
3452662605226620.6435882239639.3564117784
3552954955186377.73523107109117.264768925
3654480425252577.70527234195464.294727658
3755681205624163.16767626-56043.1676762616
3856293595399638.39010221229720.609897791
3956293595482207.03003453147151.969965465
4058110425857121.58899021-46079.5889902124
4165083566880921.8696556-372565.869655596
4266896706918942.5005902-229272.500590201
4367188096662527.0843420556281.9156579496
4462649666209768.2543365755197.7456634287
4565083566498573.148209929782.85179008171
4664175136474575.76463398-57062.7646339787
4762357466451999.31753761-216253.317537612
4866284346514391.04830122114042.951698783
4967188096671318.0017340647490.9982659426
5065667276671060.34031653-104333.34031653
5165988306581380.2514960517449.7485039514
5268097486776755.6806443732992.3193556331
5375979207653487.76088564-55567.7608856428
5479900567884218.51270061105837.487299393
5579900567908519.18442981536.8155709989
5678087397360145.55385743448593.446142565
5780809807734675.46894099346304.531059008
5878087397712534.1160601196204.883939893
5976562767569818.5851939186457.4148060922
6082335278044640.2393224188886.760677597
6183239028192271.92017335131630.079826646
6281101348071816.3931828638317.6068171393
6386549018128397.29405094526503.705949057
6488686848519706.31776269348977.68223731
6595043099637122.66002308-132813.660023076
66992613310107981.7360995-181848.736099487
67986777410071958.2736964-204184.273696445
6898352909691983.37785294143306.622147059
69100786779974584.99759582104092.002404183
70100490769635844.85776256413231.142237436
7196860769518289.47357433167786.526425667
721023075910231732.9292816-973.929281555116
731041254110311968.4561434100572.543856595
741023075910060089.0568315170669.9431685
751098646210632148.2718542354313.72814578
761134992710875217.2590706474709.740929365
771219608611797118.0511072398967.948892755
781252995012468009.558193461940.4418065585
791243947612477299.1021865-37823.1021864843
801225769112407836.3919174-150145.391917353
811240987212665731.0344662-255859.034466222
821259155512463486.704415128068.295584951
831198516811990612.1839112-5444.18391120434
841246861212655555.4448367-186943.444836712
851277333712800973.3598185-27636.3598185256
861265039412511919.5386154138474.461384617
871343809813356256.011366581841.9886335414
881371024013664885.750857945354.2491420787
891486151114552925.9391922308585.060807783
901507241414964446.6767758107967.323224243
911480025414852371.3834719-52117.3834718633
921495235114627150.834574325200.165426034
931504319414919217.3932823123976.60671773
941513403415115413.779859818620.2201401573
951455678314375479.8290717181303.170928273
961510156815029779.972492471788.027507592
971540331115412414.8507475-9103.8507475052
981510156815219239.6912544-117671.691254418
991598056216105940.0128181-125378.012818113
1001625282116375618.2963931-122797.296393061
1011743311117619962.0936178-186851.093617789
1021761489317768921.9526423-154028.952642266
1031767326717391776.7392741281490.260725919
1041797789317518513.5605133459379.439486656
1051797789317665199.1593971312693.84060289
1061809797117811202.399882286768.600117985
1071755318917127857.5300106425331.469989352
1081782581417832554.3562844-6740.35628438741
1091800713118175349.2907438-168218.290743791
1101767326717796693.9695136-123426.969513647
1111864273818818972.596562-176234.596561983
1121882443619114430.7382189-289994.73821887
1132003406320460919.2835819-426856.283581864
1142024784920594632.5540044-346783.554004446
1152054959220488866.007766460725.992233593
1162082221720705222.1469039116994.853096124
1172085135320610824.5565057240528.44349432
1182088345620686103.3960731197352.603926931
1192033868919955191.316419383497.683581024
1202088345620305540.4912304577915.508769561

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3207324 & 3024589.7461559 & 182734.253844095 \tabularnewline
14 & 3148485 & 3000263.97374849 & 148221.026251507 \tabularnewline
15 & 3239325 & 3106130.84453269 & 133194.155467313 \tabularnewline
16 & 3388641 & 3256794.22176458 & 131846.778235422 \tabularnewline
17 & 4238049 & 4076401.79487787 & 161647.205122134 \tabularnewline
18 & 4238049 & 4081971.00595935 & 156077.994040653 \tabularnewline
19 & 4056732 & 3819517.04148672 & 237214.958513284 \tabularnewline
20 & 3874950 & 3587211.99199138 & 287738.008008617 \tabularnewline
21 & 4024266 & 3769565.12685425 & 254700.873145752 \tabularnewline
22 & 4205949 & 3896979.33795852 & 308969.662041479 \tabularnewline
23 & 4238049 & 4062721.12714081 & 175327.872859194 \tabularnewline
24 & 4328892 & 4225265.54928238 & 103626.450717621 \tabularnewline
25 & 4601499 & 4745548.48064813 & -144049.480648131 \tabularnewline
26 & 4419732 & 4595867.58841893 & -176135.588418934 \tabularnewline
27 & 4419732 & 4655247.97818401 & -235515.978184007 \tabularnewline
28 & 4692342 & 4775677.89002496 & -83335.8900249638 \tabularnewline
29 & 5448042 & 5894155.64312454 & -446113.643124539 \tabularnewline
30 & 5509281 & 5733453.5749988 & -224172.574998799 \tabularnewline
31 & 5357202 & 5346897.63809269 & 10304.3619073126 \tabularnewline
32 & 4993734 & 4996293.87938884 & -2559.8793888418 \tabularnewline
33 & 5266260 & 5080735.39491208 & 185524.605087921 \tabularnewline
34 & 5266260 & 5226620.64358822 & 39639.3564117784 \tabularnewline
35 & 5295495 & 5186377.73523107 & 109117.264768925 \tabularnewline
36 & 5448042 & 5252577.70527234 & 195464.294727658 \tabularnewline
37 & 5568120 & 5624163.16767626 & -56043.1676762616 \tabularnewline
38 & 5629359 & 5399638.39010221 & 229720.609897791 \tabularnewline
39 & 5629359 & 5482207.03003453 & 147151.969965465 \tabularnewline
40 & 5811042 & 5857121.58899021 & -46079.5889902124 \tabularnewline
41 & 6508356 & 6880921.8696556 & -372565.869655596 \tabularnewline
42 & 6689670 & 6918942.5005902 & -229272.500590201 \tabularnewline
43 & 6718809 & 6662527.08434205 & 56281.9156579496 \tabularnewline
44 & 6264966 & 6209768.25433657 & 55197.7456634287 \tabularnewline
45 & 6508356 & 6498573.14820992 & 9782.85179008171 \tabularnewline
46 & 6417513 & 6474575.76463398 & -57062.7646339787 \tabularnewline
47 & 6235746 & 6451999.31753761 & -216253.317537612 \tabularnewline
48 & 6628434 & 6514391.04830122 & 114042.951698783 \tabularnewline
49 & 6718809 & 6671318.00173406 & 47490.9982659426 \tabularnewline
50 & 6566727 & 6671060.34031653 & -104333.34031653 \tabularnewline
51 & 6598830 & 6581380.25149605 & 17449.7485039514 \tabularnewline
52 & 6809748 & 6776755.68064437 & 32992.3193556331 \tabularnewline
53 & 7597920 & 7653487.76088564 & -55567.7608856428 \tabularnewline
54 & 7990056 & 7884218.51270061 & 105837.487299393 \tabularnewline
55 & 7990056 & 7908519.184429 & 81536.8155709989 \tabularnewline
56 & 7808739 & 7360145.55385743 & 448593.446142565 \tabularnewline
57 & 8080980 & 7734675.46894099 & 346304.531059008 \tabularnewline
58 & 7808739 & 7712534.11606011 & 96204.883939893 \tabularnewline
59 & 7656276 & 7569818.58519391 & 86457.4148060922 \tabularnewline
60 & 8233527 & 8044640.2393224 & 188886.760677597 \tabularnewline
61 & 8323902 & 8192271.92017335 & 131630.079826646 \tabularnewline
62 & 8110134 & 8071816.39318286 & 38317.6068171393 \tabularnewline
63 & 8654901 & 8128397.29405094 & 526503.705949057 \tabularnewline
64 & 8868684 & 8519706.31776269 & 348977.68223731 \tabularnewline
65 & 9504309 & 9637122.66002308 & -132813.660023076 \tabularnewline
66 & 9926133 & 10107981.7360995 & -181848.736099487 \tabularnewline
67 & 9867774 & 10071958.2736964 & -204184.273696445 \tabularnewline
68 & 9835290 & 9691983.37785294 & 143306.622147059 \tabularnewline
69 & 10078677 & 9974584.99759582 & 104092.002404183 \tabularnewline
70 & 10049076 & 9635844.85776256 & 413231.142237436 \tabularnewline
71 & 9686076 & 9518289.47357433 & 167786.526425667 \tabularnewline
72 & 10230759 & 10231732.9292816 & -973.929281555116 \tabularnewline
73 & 10412541 & 10311968.4561434 & 100572.543856595 \tabularnewline
74 & 10230759 & 10060089.0568315 & 170669.9431685 \tabularnewline
75 & 10986462 & 10632148.2718542 & 354313.72814578 \tabularnewline
76 & 11349927 & 10875217.2590706 & 474709.740929365 \tabularnewline
77 & 12196086 & 11797118.0511072 & 398967.948892755 \tabularnewline
78 & 12529950 & 12468009.5581934 & 61940.4418065585 \tabularnewline
79 & 12439476 & 12477299.1021865 & -37823.1021864843 \tabularnewline
80 & 12257691 & 12407836.3919174 & -150145.391917353 \tabularnewline
81 & 12409872 & 12665731.0344662 & -255859.034466222 \tabularnewline
82 & 12591555 & 12463486.704415 & 128068.295584951 \tabularnewline
83 & 11985168 & 11990612.1839112 & -5444.18391120434 \tabularnewline
84 & 12468612 & 12655555.4448367 & -186943.444836712 \tabularnewline
85 & 12773337 & 12800973.3598185 & -27636.3598185256 \tabularnewline
86 & 12650394 & 12511919.5386154 & 138474.461384617 \tabularnewline
87 & 13438098 & 13356256.0113665 & 81841.9886335414 \tabularnewline
88 & 13710240 & 13664885.7508579 & 45354.2491420787 \tabularnewline
89 & 14861511 & 14552925.9391922 & 308585.060807783 \tabularnewline
90 & 15072414 & 14964446.6767758 & 107967.323224243 \tabularnewline
91 & 14800254 & 14852371.3834719 & -52117.3834718633 \tabularnewline
92 & 14952351 & 14627150.834574 & 325200.165426034 \tabularnewline
93 & 15043194 & 14919217.3932823 & 123976.60671773 \tabularnewline
94 & 15134034 & 15115413.7798598 & 18620.2201401573 \tabularnewline
95 & 14556783 & 14375479.8290717 & 181303.170928273 \tabularnewline
96 & 15101568 & 15029779.9724924 & 71788.027507592 \tabularnewline
97 & 15403311 & 15412414.8507475 & -9103.8507475052 \tabularnewline
98 & 15101568 & 15219239.6912544 & -117671.691254418 \tabularnewline
99 & 15980562 & 16105940.0128181 & -125378.012818113 \tabularnewline
100 & 16252821 & 16375618.2963931 & -122797.296393061 \tabularnewline
101 & 17433111 & 17619962.0936178 & -186851.093617789 \tabularnewline
102 & 17614893 & 17768921.9526423 & -154028.952642266 \tabularnewline
103 & 17673267 & 17391776.7392741 & 281490.260725919 \tabularnewline
104 & 17977893 & 17518513.5605133 & 459379.439486656 \tabularnewline
105 & 17977893 & 17665199.1593971 & 312693.84060289 \tabularnewline
106 & 18097971 & 17811202.399882 & 286768.600117985 \tabularnewline
107 & 17553189 & 17127857.5300106 & 425331.469989352 \tabularnewline
108 & 17825814 & 17832554.3562844 & -6740.35628438741 \tabularnewline
109 & 18007131 & 18175349.2907438 & -168218.290743791 \tabularnewline
110 & 17673267 & 17796693.9695136 & -123426.969513647 \tabularnewline
111 & 18642738 & 18818972.596562 & -176234.596561983 \tabularnewline
112 & 18824436 & 19114430.7382189 & -289994.73821887 \tabularnewline
113 & 20034063 & 20460919.2835819 & -426856.283581864 \tabularnewline
114 & 20247849 & 20594632.5540044 & -346783.554004446 \tabularnewline
115 & 20549592 & 20488866.0077664 & 60725.992233593 \tabularnewline
116 & 20822217 & 20705222.1469039 & 116994.853096124 \tabularnewline
117 & 20851353 & 20610824.5565057 & 240528.44349432 \tabularnewline
118 & 20883456 & 20686103.3960731 & 197352.603926931 \tabularnewline
119 & 20338689 & 19955191.316419 & 383497.683581024 \tabularnewline
120 & 20883456 & 20305540.4912304 & 577915.508769561 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211086&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]3207324[/C][C]3024589.7461559[/C][C]182734.253844095[/C][/ROW]
[ROW][C]14[/C][C]3148485[/C][C]3000263.97374849[/C][C]148221.026251507[/C][/ROW]
[ROW][C]15[/C][C]3239325[/C][C]3106130.84453269[/C][C]133194.155467313[/C][/ROW]
[ROW][C]16[/C][C]3388641[/C][C]3256794.22176458[/C][C]131846.778235422[/C][/ROW]
[ROW][C]17[/C][C]4238049[/C][C]4076401.79487787[/C][C]161647.205122134[/C][/ROW]
[ROW][C]18[/C][C]4238049[/C][C]4081971.00595935[/C][C]156077.994040653[/C][/ROW]
[ROW][C]19[/C][C]4056732[/C][C]3819517.04148672[/C][C]237214.958513284[/C][/ROW]
[ROW][C]20[/C][C]3874950[/C][C]3587211.99199138[/C][C]287738.008008617[/C][/ROW]
[ROW][C]21[/C][C]4024266[/C][C]3769565.12685425[/C][C]254700.873145752[/C][/ROW]
[ROW][C]22[/C][C]4205949[/C][C]3896979.33795852[/C][C]308969.662041479[/C][/ROW]
[ROW][C]23[/C][C]4238049[/C][C]4062721.12714081[/C][C]175327.872859194[/C][/ROW]
[ROW][C]24[/C][C]4328892[/C][C]4225265.54928238[/C][C]103626.450717621[/C][/ROW]
[ROW][C]25[/C][C]4601499[/C][C]4745548.48064813[/C][C]-144049.480648131[/C][/ROW]
[ROW][C]26[/C][C]4419732[/C][C]4595867.58841893[/C][C]-176135.588418934[/C][/ROW]
[ROW][C]27[/C][C]4419732[/C][C]4655247.97818401[/C][C]-235515.978184007[/C][/ROW]
[ROW][C]28[/C][C]4692342[/C][C]4775677.89002496[/C][C]-83335.8900249638[/C][/ROW]
[ROW][C]29[/C][C]5448042[/C][C]5894155.64312454[/C][C]-446113.643124539[/C][/ROW]
[ROW][C]30[/C][C]5509281[/C][C]5733453.5749988[/C][C]-224172.574998799[/C][/ROW]
[ROW][C]31[/C][C]5357202[/C][C]5346897.63809269[/C][C]10304.3619073126[/C][/ROW]
[ROW][C]32[/C][C]4993734[/C][C]4996293.87938884[/C][C]-2559.8793888418[/C][/ROW]
[ROW][C]33[/C][C]5266260[/C][C]5080735.39491208[/C][C]185524.605087921[/C][/ROW]
[ROW][C]34[/C][C]5266260[/C][C]5226620.64358822[/C][C]39639.3564117784[/C][/ROW]
[ROW][C]35[/C][C]5295495[/C][C]5186377.73523107[/C][C]109117.264768925[/C][/ROW]
[ROW][C]36[/C][C]5448042[/C][C]5252577.70527234[/C][C]195464.294727658[/C][/ROW]
[ROW][C]37[/C][C]5568120[/C][C]5624163.16767626[/C][C]-56043.1676762616[/C][/ROW]
[ROW][C]38[/C][C]5629359[/C][C]5399638.39010221[/C][C]229720.609897791[/C][/ROW]
[ROW][C]39[/C][C]5629359[/C][C]5482207.03003453[/C][C]147151.969965465[/C][/ROW]
[ROW][C]40[/C][C]5811042[/C][C]5857121.58899021[/C][C]-46079.5889902124[/C][/ROW]
[ROW][C]41[/C][C]6508356[/C][C]6880921.8696556[/C][C]-372565.869655596[/C][/ROW]
[ROW][C]42[/C][C]6689670[/C][C]6918942.5005902[/C][C]-229272.500590201[/C][/ROW]
[ROW][C]43[/C][C]6718809[/C][C]6662527.08434205[/C][C]56281.9156579496[/C][/ROW]
[ROW][C]44[/C][C]6264966[/C][C]6209768.25433657[/C][C]55197.7456634287[/C][/ROW]
[ROW][C]45[/C][C]6508356[/C][C]6498573.14820992[/C][C]9782.85179008171[/C][/ROW]
[ROW][C]46[/C][C]6417513[/C][C]6474575.76463398[/C][C]-57062.7646339787[/C][/ROW]
[ROW][C]47[/C][C]6235746[/C][C]6451999.31753761[/C][C]-216253.317537612[/C][/ROW]
[ROW][C]48[/C][C]6628434[/C][C]6514391.04830122[/C][C]114042.951698783[/C][/ROW]
[ROW][C]49[/C][C]6718809[/C][C]6671318.00173406[/C][C]47490.9982659426[/C][/ROW]
[ROW][C]50[/C][C]6566727[/C][C]6671060.34031653[/C][C]-104333.34031653[/C][/ROW]
[ROW][C]51[/C][C]6598830[/C][C]6581380.25149605[/C][C]17449.7485039514[/C][/ROW]
[ROW][C]52[/C][C]6809748[/C][C]6776755.68064437[/C][C]32992.3193556331[/C][/ROW]
[ROW][C]53[/C][C]7597920[/C][C]7653487.76088564[/C][C]-55567.7608856428[/C][/ROW]
[ROW][C]54[/C][C]7990056[/C][C]7884218.51270061[/C][C]105837.487299393[/C][/ROW]
[ROW][C]55[/C][C]7990056[/C][C]7908519.184429[/C][C]81536.8155709989[/C][/ROW]
[ROW][C]56[/C][C]7808739[/C][C]7360145.55385743[/C][C]448593.446142565[/C][/ROW]
[ROW][C]57[/C][C]8080980[/C][C]7734675.46894099[/C][C]346304.531059008[/C][/ROW]
[ROW][C]58[/C][C]7808739[/C][C]7712534.11606011[/C][C]96204.883939893[/C][/ROW]
[ROW][C]59[/C][C]7656276[/C][C]7569818.58519391[/C][C]86457.4148060922[/C][/ROW]
[ROW][C]60[/C][C]8233527[/C][C]8044640.2393224[/C][C]188886.760677597[/C][/ROW]
[ROW][C]61[/C][C]8323902[/C][C]8192271.92017335[/C][C]131630.079826646[/C][/ROW]
[ROW][C]62[/C][C]8110134[/C][C]8071816.39318286[/C][C]38317.6068171393[/C][/ROW]
[ROW][C]63[/C][C]8654901[/C][C]8128397.29405094[/C][C]526503.705949057[/C][/ROW]
[ROW][C]64[/C][C]8868684[/C][C]8519706.31776269[/C][C]348977.68223731[/C][/ROW]
[ROW][C]65[/C][C]9504309[/C][C]9637122.66002308[/C][C]-132813.660023076[/C][/ROW]
[ROW][C]66[/C][C]9926133[/C][C]10107981.7360995[/C][C]-181848.736099487[/C][/ROW]
[ROW][C]67[/C][C]9867774[/C][C]10071958.2736964[/C][C]-204184.273696445[/C][/ROW]
[ROW][C]68[/C][C]9835290[/C][C]9691983.37785294[/C][C]143306.622147059[/C][/ROW]
[ROW][C]69[/C][C]10078677[/C][C]9974584.99759582[/C][C]104092.002404183[/C][/ROW]
[ROW][C]70[/C][C]10049076[/C][C]9635844.85776256[/C][C]413231.142237436[/C][/ROW]
[ROW][C]71[/C][C]9686076[/C][C]9518289.47357433[/C][C]167786.526425667[/C][/ROW]
[ROW][C]72[/C][C]10230759[/C][C]10231732.9292816[/C][C]-973.929281555116[/C][/ROW]
[ROW][C]73[/C][C]10412541[/C][C]10311968.4561434[/C][C]100572.543856595[/C][/ROW]
[ROW][C]74[/C][C]10230759[/C][C]10060089.0568315[/C][C]170669.9431685[/C][/ROW]
[ROW][C]75[/C][C]10986462[/C][C]10632148.2718542[/C][C]354313.72814578[/C][/ROW]
[ROW][C]76[/C][C]11349927[/C][C]10875217.2590706[/C][C]474709.740929365[/C][/ROW]
[ROW][C]77[/C][C]12196086[/C][C]11797118.0511072[/C][C]398967.948892755[/C][/ROW]
[ROW][C]78[/C][C]12529950[/C][C]12468009.5581934[/C][C]61940.4418065585[/C][/ROW]
[ROW][C]79[/C][C]12439476[/C][C]12477299.1021865[/C][C]-37823.1021864843[/C][/ROW]
[ROW][C]80[/C][C]12257691[/C][C]12407836.3919174[/C][C]-150145.391917353[/C][/ROW]
[ROW][C]81[/C][C]12409872[/C][C]12665731.0344662[/C][C]-255859.034466222[/C][/ROW]
[ROW][C]82[/C][C]12591555[/C][C]12463486.704415[/C][C]128068.295584951[/C][/ROW]
[ROW][C]83[/C][C]11985168[/C][C]11990612.1839112[/C][C]-5444.18391120434[/C][/ROW]
[ROW][C]84[/C][C]12468612[/C][C]12655555.4448367[/C][C]-186943.444836712[/C][/ROW]
[ROW][C]85[/C][C]12773337[/C][C]12800973.3598185[/C][C]-27636.3598185256[/C][/ROW]
[ROW][C]86[/C][C]12650394[/C][C]12511919.5386154[/C][C]138474.461384617[/C][/ROW]
[ROW][C]87[/C][C]13438098[/C][C]13356256.0113665[/C][C]81841.9886335414[/C][/ROW]
[ROW][C]88[/C][C]13710240[/C][C]13664885.7508579[/C][C]45354.2491420787[/C][/ROW]
[ROW][C]89[/C][C]14861511[/C][C]14552925.9391922[/C][C]308585.060807783[/C][/ROW]
[ROW][C]90[/C][C]15072414[/C][C]14964446.6767758[/C][C]107967.323224243[/C][/ROW]
[ROW][C]91[/C][C]14800254[/C][C]14852371.3834719[/C][C]-52117.3834718633[/C][/ROW]
[ROW][C]92[/C][C]14952351[/C][C]14627150.834574[/C][C]325200.165426034[/C][/ROW]
[ROW][C]93[/C][C]15043194[/C][C]14919217.3932823[/C][C]123976.60671773[/C][/ROW]
[ROW][C]94[/C][C]15134034[/C][C]15115413.7798598[/C][C]18620.2201401573[/C][/ROW]
[ROW][C]95[/C][C]14556783[/C][C]14375479.8290717[/C][C]181303.170928273[/C][/ROW]
[ROW][C]96[/C][C]15101568[/C][C]15029779.9724924[/C][C]71788.027507592[/C][/ROW]
[ROW][C]97[/C][C]15403311[/C][C]15412414.8507475[/C][C]-9103.8507475052[/C][/ROW]
[ROW][C]98[/C][C]15101568[/C][C]15219239.6912544[/C][C]-117671.691254418[/C][/ROW]
[ROW][C]99[/C][C]15980562[/C][C]16105940.0128181[/C][C]-125378.012818113[/C][/ROW]
[ROW][C]100[/C][C]16252821[/C][C]16375618.2963931[/C][C]-122797.296393061[/C][/ROW]
[ROW][C]101[/C][C]17433111[/C][C]17619962.0936178[/C][C]-186851.093617789[/C][/ROW]
[ROW][C]102[/C][C]17614893[/C][C]17768921.9526423[/C][C]-154028.952642266[/C][/ROW]
[ROW][C]103[/C][C]17673267[/C][C]17391776.7392741[/C][C]281490.260725919[/C][/ROW]
[ROW][C]104[/C][C]17977893[/C][C]17518513.5605133[/C][C]459379.439486656[/C][/ROW]
[ROW][C]105[/C][C]17977893[/C][C]17665199.1593971[/C][C]312693.84060289[/C][/ROW]
[ROW][C]106[/C][C]18097971[/C][C]17811202.399882[/C][C]286768.600117985[/C][/ROW]
[ROW][C]107[/C][C]17553189[/C][C]17127857.5300106[/C][C]425331.469989352[/C][/ROW]
[ROW][C]108[/C][C]17825814[/C][C]17832554.3562844[/C][C]-6740.35628438741[/C][/ROW]
[ROW][C]109[/C][C]18007131[/C][C]18175349.2907438[/C][C]-168218.290743791[/C][/ROW]
[ROW][C]110[/C][C]17673267[/C][C]17796693.9695136[/C][C]-123426.969513647[/C][/ROW]
[ROW][C]111[/C][C]18642738[/C][C]18818972.596562[/C][C]-176234.596561983[/C][/ROW]
[ROW][C]112[/C][C]18824436[/C][C]19114430.7382189[/C][C]-289994.73821887[/C][/ROW]
[ROW][C]113[/C][C]20034063[/C][C]20460919.2835819[/C][C]-426856.283581864[/C][/ROW]
[ROW][C]114[/C][C]20247849[/C][C]20594632.5540044[/C][C]-346783.554004446[/C][/ROW]
[ROW][C]115[/C][C]20549592[/C][C]20488866.0077664[/C][C]60725.992233593[/C][/ROW]
[ROW][C]116[/C][C]20822217[/C][C]20705222.1469039[/C][C]116994.853096124[/C][/ROW]
[ROW][C]117[/C][C]20851353[/C][C]20610824.5565057[/C][C]240528.44349432[/C][/ROW]
[ROW][C]118[/C][C]20883456[/C][C]20686103.3960731[/C][C]197352.603926931[/C][/ROW]
[ROW][C]119[/C][C]20338689[/C][C]19955191.316419[/C][C]383497.683581024[/C][/ROW]
[ROW][C]120[/C][C]20883456[/C][C]20305540.4912304[/C][C]577915.508769561[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211086&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211086&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
1332073243024589.7461559182734.253844095
1431484853000263.97374849148221.026251507
1532393253106130.84453269133194.155467313
1633886413256794.22176458131846.778235422
1742380494076401.79487787161647.205122134
1842380494081971.00595935156077.994040653
1940567323819517.04148672237214.958513284
2038749503587211.99199138287738.008008617
2140242663769565.12685425254700.873145752
2242059493896979.33795852308969.662041479
2342380494062721.12714081175327.872859194
2443288924225265.54928238103626.450717621
2546014994745548.48064813-144049.480648131
2644197324595867.58841893-176135.588418934
2744197324655247.97818401-235515.978184007
2846923424775677.89002496-83335.8900249638
2954480425894155.64312454-446113.643124539
3055092815733453.5749988-224172.574998799
3153572025346897.6380926910304.3619073126
3249937344996293.87938884-2559.8793888418
3352662605080735.39491208185524.605087921
3452662605226620.6435882239639.3564117784
3552954955186377.73523107109117.264768925
3654480425252577.70527234195464.294727658
3755681205624163.16767626-56043.1676762616
3856293595399638.39010221229720.609897791
3956293595482207.03003453147151.969965465
4058110425857121.58899021-46079.5889902124
4165083566880921.8696556-372565.869655596
4266896706918942.5005902-229272.500590201
4367188096662527.0843420556281.9156579496
4462649666209768.2543365755197.7456634287
4565083566498573.148209929782.85179008171
4664175136474575.76463398-57062.7646339787
4762357466451999.31753761-216253.317537612
4866284346514391.04830122114042.951698783
4967188096671318.0017340647490.9982659426
5065667276671060.34031653-104333.34031653
5165988306581380.2514960517449.7485039514
5268097486776755.6806443732992.3193556331
5375979207653487.76088564-55567.7608856428
5479900567884218.51270061105837.487299393
5579900567908519.18442981536.8155709989
5678087397360145.55385743448593.446142565
5780809807734675.46894099346304.531059008
5878087397712534.1160601196204.883939893
5976562767569818.5851939186457.4148060922
6082335278044640.2393224188886.760677597
6183239028192271.92017335131630.079826646
6281101348071816.3931828638317.6068171393
6386549018128397.29405094526503.705949057
6488686848519706.31776269348977.68223731
6595043099637122.66002308-132813.660023076
66992613310107981.7360995-181848.736099487
67986777410071958.2736964-204184.273696445
6898352909691983.37785294143306.622147059
69100786779974584.99759582104092.002404183
70100490769635844.85776256413231.142237436
7196860769518289.47357433167786.526425667
721023075910231732.9292816-973.929281555116
731041254110311968.4561434100572.543856595
741023075910060089.0568315170669.9431685
751098646210632148.2718542354313.72814578
761134992710875217.2590706474709.740929365
771219608611797118.0511072398967.948892755
781252995012468009.558193461940.4418065585
791243947612477299.1021865-37823.1021864843
801225769112407836.3919174-150145.391917353
811240987212665731.0344662-255859.034466222
821259155512463486.704415128068.295584951
831198516811990612.1839112-5444.18391120434
841246861212655555.4448367-186943.444836712
851277333712800973.3598185-27636.3598185256
861265039412511919.5386154138474.461384617
871343809813356256.011366581841.9886335414
881371024013664885.750857945354.2491420787
891486151114552925.9391922308585.060807783
901507241414964446.6767758107967.323224243
911480025414852371.3834719-52117.3834718633
921495235114627150.834574325200.165426034
931504319414919217.3932823123976.60671773
941513403415115413.779859818620.2201401573
951455678314375479.8290717181303.170928273
961510156815029779.972492471788.027507592
971540331115412414.8507475-9103.8507475052
981510156815219239.6912544-117671.691254418
991598056216105940.0128181-125378.012818113
1001625282116375618.2963931-122797.296393061
1011743311117619962.0936178-186851.093617789
1021761489317768921.9526423-154028.952642266
1031767326717391776.7392741281490.260725919
1041797789317518513.5605133459379.439486656
1051797789317665199.1593971312693.84060289
1061809797117811202.399882286768.600117985
1071755318917127857.5300106425331.469989352
1081782581417832554.3562844-6740.35628438741
1091800713118175349.2907438-168218.290743791
1101767326717796693.9695136-123426.969513647
1111864273818818972.596562-176234.596561983
1121882443619114430.7382189-289994.73821887
1132003406320460919.2835819-426856.283581864
1142024784920594632.5540044-346783.554004446
1152054959220488866.007766460725.992233593
1162082221720705222.1469039116994.853096124
1172085135320610824.5565057240528.44349432
1182088345620686103.3960731197352.603926931
1192033868919955191.316419383497.683581024
1202088345620305540.4912304577915.508769561







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12120645989.065124420233608.826484521058369.3037643
12220266320.370541119843140.485426420689500.2556558
12321396145.479613720957577.474654721834713.4845727
12421654662.319635221200442.119182322108882.5200882
12523135407.103769422657176.803989923613637.4035489
12623462889.753769322963822.696066823961956.8114718
12723801674.032528723279620.885029224323727.1800281
12824091012.147083223544432.380402324637591.9137641
12924064421.520494923495044.289449924633798.7515399
13024046396.385384723453113.606386724639679.1643826
13123312901.193039522704919.761041123920882.6250379
13223772702.466264723282581.591574124262823.3409554

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 20645989.0651244 & 20233608.8264845 & 21058369.3037643 \tabularnewline
122 & 20266320.3705411 & 19843140.4854264 & 20689500.2556558 \tabularnewline
123 & 21396145.4796137 & 20957577.4746547 & 21834713.4845727 \tabularnewline
124 & 21654662.3196352 & 21200442.1191823 & 22108882.5200882 \tabularnewline
125 & 23135407.1037694 & 22657176.8039899 & 23613637.4035489 \tabularnewline
126 & 23462889.7537693 & 22963822.6960668 & 23961956.8114718 \tabularnewline
127 & 23801674.0325287 & 23279620.8850292 & 24323727.1800281 \tabularnewline
128 & 24091012.1470832 & 23544432.3804023 & 24637591.9137641 \tabularnewline
129 & 24064421.5204949 & 23495044.2894499 & 24633798.7515399 \tabularnewline
130 & 24046396.3853847 & 23453113.6063867 & 24639679.1643826 \tabularnewline
131 & 23312901.1930395 & 22704919.7610411 & 23920882.6250379 \tabularnewline
132 & 23772702.4662647 & 23282581.5915741 & 24262823.3409554 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211086&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]20645989.0651244[/C][C]20233608.8264845[/C][C]21058369.3037643[/C][/ROW]
[ROW][C]122[/C][C]20266320.3705411[/C][C]19843140.4854264[/C][C]20689500.2556558[/C][/ROW]
[ROW][C]123[/C][C]21396145.4796137[/C][C]20957577.4746547[/C][C]21834713.4845727[/C][/ROW]
[ROW][C]124[/C][C]21654662.3196352[/C][C]21200442.1191823[/C][C]22108882.5200882[/C][/ROW]
[ROW][C]125[/C][C]23135407.1037694[/C][C]22657176.8039899[/C][C]23613637.4035489[/C][/ROW]
[ROW][C]126[/C][C]23462889.7537693[/C][C]22963822.6960668[/C][C]23961956.8114718[/C][/ROW]
[ROW][C]127[/C][C]23801674.0325287[/C][C]23279620.8850292[/C][C]24323727.1800281[/C][/ROW]
[ROW][C]128[/C][C]24091012.1470832[/C][C]23544432.3804023[/C][C]24637591.9137641[/C][/ROW]
[ROW][C]129[/C][C]24064421.5204949[/C][C]23495044.2894499[/C][C]24633798.7515399[/C][/ROW]
[ROW][C]130[/C][C]24046396.3853847[/C][C]23453113.6063867[/C][C]24639679.1643826[/C][/ROW]
[ROW][C]131[/C][C]23312901.1930395[/C][C]22704919.7610411[/C][C]23920882.6250379[/C][/ROW]
[ROW][C]132[/C][C]23772702.4662647[/C][C]23282581.5915741[/C][C]24262823.3409554[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211086&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211086&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
12120645989.065124420233608.826484521058369.3037643
12220266320.370541119843140.485426420689500.2556558
12321396145.479613720957577.474654721834713.4845727
12421654662.319635221200442.119182322108882.5200882
12523135407.103769422657176.803989923613637.4035489
12623462889.753769322963822.696066823961956.8114718
12723801674.032528723279620.885029224323727.1800281
12824091012.147083223544432.380402324637591.9137641
12924064421.520494923495044.289449924633798.7515399
13024046396.385384723453113.606386724639679.1643826
13123312901.193039522704919.761041123920882.6250379
13223772702.466264723282581.591574124262823.3409554



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')