Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 11 Dec 2016 12:28:06 +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/2016/Dec/11/t1481455791dcqrhq0ne6kz8av.htm/, Retrieved Wed, 01 May 2024 23:56:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298765, Retrieved Wed, 01 May 2024 23:56:13 +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] [] [2016-12-11 11:28:06] [1bf80170c5e6d32ce8f3ad7977dc404a] [Current]
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Dataseries X:
5682.5
5286.5
6608
6826
6994.5
7509
6599.5
7312.5
7791.5
7302.5
6168.5
5303
5631.5
5515.5
6676.5
6592.5
7101
7793
7177
7843
7858.5
7576.5
6229
5739.5
6559
6126.5
7486.5
7627.5
7602.5
7710
8102
7533.5
7736.5
8695
6885
6079.5
6874
5194
6980.5
7280.5
7313.5
7670.5
7251
7909.5
8434
8333.5
6898.5
6637
6683
5584
6510.5
7263
7114.5
8114.5
7228.5
8126
8071
8602.5
7371.5
6678
6440.5
6207.5
7067.5
7512
7474.5
8992
8265.5
7841
8758.5
9183.5
7792
7670.5
6530.5
6621.5
7870
7250.5
7779.5
9027.5
7891.5
9021
8559
8738
8051.5
7354
7182
6319.5
7353.5
7519.5
7854.5
8996.5
7684.5
8708.5
8371
8385.5
7916
6872
7492
6515
7875
7487
8195.5
8533
8688
8892.5
8221.5
8652.5
7410.5
6457
6400.5
6260.5
7220
7617
7922
8934
8395
8945
9738
9224
6923
6572.5
6962.5
7038
8564
8534
8420.5
8831




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298765&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298765&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298765&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.147006839672561
beta0
gamma0.176608877322796

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.147006839672561 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.176608877322796 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298765&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]0.147006839672561[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.176608877322796[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298765&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298765&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
alpha0.147006839672561
beta0
gamma0.176608877322796







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135631.55579.149973290652.3500267094005
145515.55442.6474315443272.8525684556816
156676.56607.4297369987569.0702630012529
166592.56537.3435176816455.1564823183562
1771017057.9827107717843.0172892282162
1877937753.5665261162339.4334738837661
1971776763.56099609293413.439003907073
2078437547.89100372507295.108996274926
217858.58075.84652423012-217.346524230123
227576.57579.7384115263-3.23841152629939
2362296468.52232248599-239.522322485988
245739.55569.50838243002169.991617569979
2565595912.95712323404646.042876765958
266126.55866.82012038549259.679879614507
277486.57058.49752860857428.002471391431
287627.57039.08074121129588.419258788714
297602.57636.28448690729-33.7844869072942
3077108320.03802782523-610.038027825231
3181027290.89824344423811.101756555772
327533.58115.86143381443-582.361433814427
337736.58437.62334089138-701.123340891381
3486957902.65129321111792.348706788887
3568856872.7966872207712.2033127792256
366079.56072.479841611357.02015838865191
3768746463.68595950446410.31404049554
3851946324.6911018255-1130.6911018255
396980.57337.33161892929-356.831618929293
407280.57226.7050259749653.7949740250415
417313.57651.58273738536-338.082737385357
427670.58203.79196851597-533.29196851597
4372517400.02363737802-149.02363737802
447909.57873.9219430216135.5780569783892
4584348268.63415596979165.365844030206
468333.58086.02778061106247.472219388936
476898.56858.5466929069239.9533070930829
4866376061.52846393402575.471536065979
4966836597.0554988361985.944501163809
5055846178.22958626812-594.229586268121
516510.57386.31257827015-875.812578270154
5272637261.251555865981.74844413402298
537114.57619.44319725964-504.943197259642
548114.58117.71527759068-3.21527759068158
557228.57449.7603957597-221.260395759699
5681267940.84894104369185.151058956312
5780718377.10144061953-306.10144061953
588602.58137.55516025679464.944839743206
597371.56910.78210700645460.717892993553
6066786256.29291721902421.707082780978
616440.56695.47015560704-254.970155607042
626207.56124.0618393467183.438160653287
637067.57389.34722746364-321.847227463644
6475127477.9241026300634.0758973699385
657474.57764.53694844432-290.036948444315
6689928369.98510391484622.014896085157
678265.57761.0956732635504.404326736495
6878418420.08622288856-579.086222888558
698758.58669.9853100827888.5146899172196
709183.58604.60546467289578.89453532711
7177927393.94702273698398.052977263016
727670.56724.36883280064946.131167199363
736530.57138.70116798084-608.201167980843
746621.56566.3453917659855.1546082340192
7578707766.41821501603103.58178498397
767250.57971.1545183882-720.654518388196
777779.58097.99047391934-318.490473919339
789027.58836.65287865317190.847121346827
797891.58146.66125490251-255.161254902513
8090218530.76677337186490.233226628139
8185599038.43465031038-479.434650310375
8287388963.43621011421-225.436210114211
838051.57607.29256015132444.207439848684
8473547027.06526900686326.934730993141
8571827116.2172884513965.7827115486098
866319.56742.87375568203-423.373755682031
877353.57879.89500488966-526.395004889658
887519.57867.85237364539-348.352373645394
897854.58110.00376164112-255.503761641119
908996.58934.6553990047261.8446009952786
917684.58158.51007125093-474.010071250934
928708.58622.7341364773985.7658635226144
9383718924.86579820322-553.865798203218
948385.58877.18936096366-491.689360963661
9579167582.78392412958333.216075870417
9668726968.57345955674-96.5734595567401
9774926956.12532827599535.874671724014
9865156578.19898334312-63.198983343118
9978757752.64863151627122.351368483727
10074877862.79759386898-375.797593868981
1018195.58114.901634044780.5983659552967
10285339036.76989660627-503.769896606273
10386888096.75091803232591.249081967678
1048892.58801.9034623080690.5965376919376
1058221.59008.38720970317-786.887209703173
1068652.58935.82167296975-283.321672969752
1077410.57796.3165514971-385.816551497095
10864577011.65722773807-554.657227738074
1096400.57027.14353455706-626.643534557056
1106260.56388.07091372238-127.570913722378
11172207581.0098966544-361.009896654396
11276177545.0572165160371.9427834839671
11379227931.73645535971-9.73645535971082
11489348752.29204396986181.707956030143
11583958078.00340725524316.996592744758
11689458667.41757432101277.582425678987
11797388769.19996529576968.800034704238
11892249030.59267845378193.407321546221
11969237945.72951952343-1022.72951952343
1206572.57042.00443291639-469.504432916388
1216962.57059.16432197911-96.6643219791113
12270386573.18564636819464.814353631813
12385647818.04262792018745.957372079823
12485348010.04436821303523.955631786966
1258420.58450.86792333344-30.3679233334424
12688319297.23091131247-466.230911312472

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5631.5 & 5579.1499732906 & 52.3500267094005 \tabularnewline
14 & 5515.5 & 5442.64743154432 & 72.8525684556816 \tabularnewline
15 & 6676.5 & 6607.42973699875 & 69.0702630012529 \tabularnewline
16 & 6592.5 & 6537.34351768164 & 55.1564823183562 \tabularnewline
17 & 7101 & 7057.98271077178 & 43.0172892282162 \tabularnewline
18 & 7793 & 7753.56652611623 & 39.4334738837661 \tabularnewline
19 & 7177 & 6763.56099609293 & 413.439003907073 \tabularnewline
20 & 7843 & 7547.89100372507 & 295.108996274926 \tabularnewline
21 & 7858.5 & 8075.84652423012 & -217.346524230123 \tabularnewline
22 & 7576.5 & 7579.7384115263 & -3.23841152629939 \tabularnewline
23 & 6229 & 6468.52232248599 & -239.522322485988 \tabularnewline
24 & 5739.5 & 5569.50838243002 & 169.991617569979 \tabularnewline
25 & 6559 & 5912.95712323404 & 646.042876765958 \tabularnewline
26 & 6126.5 & 5866.82012038549 & 259.679879614507 \tabularnewline
27 & 7486.5 & 7058.49752860857 & 428.002471391431 \tabularnewline
28 & 7627.5 & 7039.08074121129 & 588.419258788714 \tabularnewline
29 & 7602.5 & 7636.28448690729 & -33.7844869072942 \tabularnewline
30 & 7710 & 8320.03802782523 & -610.038027825231 \tabularnewline
31 & 8102 & 7290.89824344423 & 811.101756555772 \tabularnewline
32 & 7533.5 & 8115.86143381443 & -582.361433814427 \tabularnewline
33 & 7736.5 & 8437.62334089138 & -701.123340891381 \tabularnewline
34 & 8695 & 7902.65129321111 & 792.348706788887 \tabularnewline
35 & 6885 & 6872.79668722077 & 12.2033127792256 \tabularnewline
36 & 6079.5 & 6072.47984161135 & 7.02015838865191 \tabularnewline
37 & 6874 & 6463.68595950446 & 410.31404049554 \tabularnewline
38 & 5194 & 6324.6911018255 & -1130.6911018255 \tabularnewline
39 & 6980.5 & 7337.33161892929 & -356.831618929293 \tabularnewline
40 & 7280.5 & 7226.70502597496 & 53.7949740250415 \tabularnewline
41 & 7313.5 & 7651.58273738536 & -338.082737385357 \tabularnewline
42 & 7670.5 & 8203.79196851597 & -533.29196851597 \tabularnewline
43 & 7251 & 7400.02363737802 & -149.02363737802 \tabularnewline
44 & 7909.5 & 7873.92194302161 & 35.5780569783892 \tabularnewline
45 & 8434 & 8268.63415596979 & 165.365844030206 \tabularnewline
46 & 8333.5 & 8086.02778061106 & 247.472219388936 \tabularnewline
47 & 6898.5 & 6858.54669290692 & 39.9533070930829 \tabularnewline
48 & 6637 & 6061.52846393402 & 575.471536065979 \tabularnewline
49 & 6683 & 6597.05549883619 & 85.944501163809 \tabularnewline
50 & 5584 & 6178.22958626812 & -594.229586268121 \tabularnewline
51 & 6510.5 & 7386.31257827015 & -875.812578270154 \tabularnewline
52 & 7263 & 7261.25155586598 & 1.74844413402298 \tabularnewline
53 & 7114.5 & 7619.44319725964 & -504.943197259642 \tabularnewline
54 & 8114.5 & 8117.71527759068 & -3.21527759068158 \tabularnewline
55 & 7228.5 & 7449.7603957597 & -221.260395759699 \tabularnewline
56 & 8126 & 7940.84894104369 & 185.151058956312 \tabularnewline
57 & 8071 & 8377.10144061953 & -306.10144061953 \tabularnewline
58 & 8602.5 & 8137.55516025679 & 464.944839743206 \tabularnewline
59 & 7371.5 & 6910.78210700645 & 460.717892993553 \tabularnewline
60 & 6678 & 6256.29291721902 & 421.707082780978 \tabularnewline
61 & 6440.5 & 6695.47015560704 & -254.970155607042 \tabularnewline
62 & 6207.5 & 6124.06183934671 & 83.438160653287 \tabularnewline
63 & 7067.5 & 7389.34722746364 & -321.847227463644 \tabularnewline
64 & 7512 & 7477.92410263006 & 34.0758973699385 \tabularnewline
65 & 7474.5 & 7764.53694844432 & -290.036948444315 \tabularnewline
66 & 8992 & 8369.98510391484 & 622.014896085157 \tabularnewline
67 & 8265.5 & 7761.0956732635 & 504.404326736495 \tabularnewline
68 & 7841 & 8420.08622288856 & -579.086222888558 \tabularnewline
69 & 8758.5 & 8669.98531008278 & 88.5146899172196 \tabularnewline
70 & 9183.5 & 8604.60546467289 & 578.89453532711 \tabularnewline
71 & 7792 & 7393.94702273698 & 398.052977263016 \tabularnewline
72 & 7670.5 & 6724.36883280064 & 946.131167199363 \tabularnewline
73 & 6530.5 & 7138.70116798084 & -608.201167980843 \tabularnewline
74 & 6621.5 & 6566.34539176598 & 55.1546082340192 \tabularnewline
75 & 7870 & 7766.41821501603 & 103.58178498397 \tabularnewline
76 & 7250.5 & 7971.1545183882 & -720.654518388196 \tabularnewline
77 & 7779.5 & 8097.99047391934 & -318.490473919339 \tabularnewline
78 & 9027.5 & 8836.65287865317 & 190.847121346827 \tabularnewline
79 & 7891.5 & 8146.66125490251 & -255.161254902513 \tabularnewline
80 & 9021 & 8530.76677337186 & 490.233226628139 \tabularnewline
81 & 8559 & 9038.43465031038 & -479.434650310375 \tabularnewline
82 & 8738 & 8963.43621011421 & -225.436210114211 \tabularnewline
83 & 8051.5 & 7607.29256015132 & 444.207439848684 \tabularnewline
84 & 7354 & 7027.06526900686 & 326.934730993141 \tabularnewline
85 & 7182 & 7116.21728845139 & 65.7827115486098 \tabularnewline
86 & 6319.5 & 6742.87375568203 & -423.373755682031 \tabularnewline
87 & 7353.5 & 7879.89500488966 & -526.395004889658 \tabularnewline
88 & 7519.5 & 7867.85237364539 & -348.352373645394 \tabularnewline
89 & 7854.5 & 8110.00376164112 & -255.503761641119 \tabularnewline
90 & 8996.5 & 8934.65539900472 & 61.8446009952786 \tabularnewline
91 & 7684.5 & 8158.51007125093 & -474.010071250934 \tabularnewline
92 & 8708.5 & 8622.73413647739 & 85.7658635226144 \tabularnewline
93 & 8371 & 8924.86579820322 & -553.865798203218 \tabularnewline
94 & 8385.5 & 8877.18936096366 & -491.689360963661 \tabularnewline
95 & 7916 & 7582.78392412958 & 333.216075870417 \tabularnewline
96 & 6872 & 6968.57345955674 & -96.5734595567401 \tabularnewline
97 & 7492 & 6956.12532827599 & 535.874671724014 \tabularnewline
98 & 6515 & 6578.19898334312 & -63.198983343118 \tabularnewline
99 & 7875 & 7752.64863151627 & 122.351368483727 \tabularnewline
100 & 7487 & 7862.79759386898 & -375.797593868981 \tabularnewline
101 & 8195.5 & 8114.9016340447 & 80.5983659552967 \tabularnewline
102 & 8533 & 9036.76989660627 & -503.769896606273 \tabularnewline
103 & 8688 & 8096.75091803232 & 591.249081967678 \tabularnewline
104 & 8892.5 & 8801.90346230806 & 90.5965376919376 \tabularnewline
105 & 8221.5 & 9008.38720970317 & -786.887209703173 \tabularnewline
106 & 8652.5 & 8935.82167296975 & -283.321672969752 \tabularnewline
107 & 7410.5 & 7796.3165514971 & -385.816551497095 \tabularnewline
108 & 6457 & 7011.65722773807 & -554.657227738074 \tabularnewline
109 & 6400.5 & 7027.14353455706 & -626.643534557056 \tabularnewline
110 & 6260.5 & 6388.07091372238 & -127.570913722378 \tabularnewline
111 & 7220 & 7581.0098966544 & -361.009896654396 \tabularnewline
112 & 7617 & 7545.05721651603 & 71.9427834839671 \tabularnewline
113 & 7922 & 7931.73645535971 & -9.73645535971082 \tabularnewline
114 & 8934 & 8752.29204396986 & 181.707956030143 \tabularnewline
115 & 8395 & 8078.00340725524 & 316.996592744758 \tabularnewline
116 & 8945 & 8667.41757432101 & 277.582425678987 \tabularnewline
117 & 9738 & 8769.19996529576 & 968.800034704238 \tabularnewline
118 & 9224 & 9030.59267845378 & 193.407321546221 \tabularnewline
119 & 6923 & 7945.72951952343 & -1022.72951952343 \tabularnewline
120 & 6572.5 & 7042.00443291639 & -469.504432916388 \tabularnewline
121 & 6962.5 & 7059.16432197911 & -96.6643219791113 \tabularnewline
122 & 7038 & 6573.18564636819 & 464.814353631813 \tabularnewline
123 & 8564 & 7818.04262792018 & 745.957372079823 \tabularnewline
124 & 8534 & 8010.04436821303 & 523.955631786966 \tabularnewline
125 & 8420.5 & 8450.86792333344 & -30.3679233334424 \tabularnewline
126 & 8831 & 9297.23091131247 & -466.230911312472 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298765&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]5631.5[/C][C]5579.1499732906[/C][C]52.3500267094005[/C][/ROW]
[ROW][C]14[/C][C]5515.5[/C][C]5442.64743154432[/C][C]72.8525684556816[/C][/ROW]
[ROW][C]15[/C][C]6676.5[/C][C]6607.42973699875[/C][C]69.0702630012529[/C][/ROW]
[ROW][C]16[/C][C]6592.5[/C][C]6537.34351768164[/C][C]55.1564823183562[/C][/ROW]
[ROW][C]17[/C][C]7101[/C][C]7057.98271077178[/C][C]43.0172892282162[/C][/ROW]
[ROW][C]18[/C][C]7793[/C][C]7753.56652611623[/C][C]39.4334738837661[/C][/ROW]
[ROW][C]19[/C][C]7177[/C][C]6763.56099609293[/C][C]413.439003907073[/C][/ROW]
[ROW][C]20[/C][C]7843[/C][C]7547.89100372507[/C][C]295.108996274926[/C][/ROW]
[ROW][C]21[/C][C]7858.5[/C][C]8075.84652423012[/C][C]-217.346524230123[/C][/ROW]
[ROW][C]22[/C][C]7576.5[/C][C]7579.7384115263[/C][C]-3.23841152629939[/C][/ROW]
[ROW][C]23[/C][C]6229[/C][C]6468.52232248599[/C][C]-239.522322485988[/C][/ROW]
[ROW][C]24[/C][C]5739.5[/C][C]5569.50838243002[/C][C]169.991617569979[/C][/ROW]
[ROW][C]25[/C][C]6559[/C][C]5912.95712323404[/C][C]646.042876765958[/C][/ROW]
[ROW][C]26[/C][C]6126.5[/C][C]5866.82012038549[/C][C]259.679879614507[/C][/ROW]
[ROW][C]27[/C][C]7486.5[/C][C]7058.49752860857[/C][C]428.002471391431[/C][/ROW]
[ROW][C]28[/C][C]7627.5[/C][C]7039.08074121129[/C][C]588.419258788714[/C][/ROW]
[ROW][C]29[/C][C]7602.5[/C][C]7636.28448690729[/C][C]-33.7844869072942[/C][/ROW]
[ROW][C]30[/C][C]7710[/C][C]8320.03802782523[/C][C]-610.038027825231[/C][/ROW]
[ROW][C]31[/C][C]8102[/C][C]7290.89824344423[/C][C]811.101756555772[/C][/ROW]
[ROW][C]32[/C][C]7533.5[/C][C]8115.86143381443[/C][C]-582.361433814427[/C][/ROW]
[ROW][C]33[/C][C]7736.5[/C][C]8437.62334089138[/C][C]-701.123340891381[/C][/ROW]
[ROW][C]34[/C][C]8695[/C][C]7902.65129321111[/C][C]792.348706788887[/C][/ROW]
[ROW][C]35[/C][C]6885[/C][C]6872.79668722077[/C][C]12.2033127792256[/C][/ROW]
[ROW][C]36[/C][C]6079.5[/C][C]6072.47984161135[/C][C]7.02015838865191[/C][/ROW]
[ROW][C]37[/C][C]6874[/C][C]6463.68595950446[/C][C]410.31404049554[/C][/ROW]
[ROW][C]38[/C][C]5194[/C][C]6324.6911018255[/C][C]-1130.6911018255[/C][/ROW]
[ROW][C]39[/C][C]6980.5[/C][C]7337.33161892929[/C][C]-356.831618929293[/C][/ROW]
[ROW][C]40[/C][C]7280.5[/C][C]7226.70502597496[/C][C]53.7949740250415[/C][/ROW]
[ROW][C]41[/C][C]7313.5[/C][C]7651.58273738536[/C][C]-338.082737385357[/C][/ROW]
[ROW][C]42[/C][C]7670.5[/C][C]8203.79196851597[/C][C]-533.29196851597[/C][/ROW]
[ROW][C]43[/C][C]7251[/C][C]7400.02363737802[/C][C]-149.02363737802[/C][/ROW]
[ROW][C]44[/C][C]7909.5[/C][C]7873.92194302161[/C][C]35.5780569783892[/C][/ROW]
[ROW][C]45[/C][C]8434[/C][C]8268.63415596979[/C][C]165.365844030206[/C][/ROW]
[ROW][C]46[/C][C]8333.5[/C][C]8086.02778061106[/C][C]247.472219388936[/C][/ROW]
[ROW][C]47[/C][C]6898.5[/C][C]6858.54669290692[/C][C]39.9533070930829[/C][/ROW]
[ROW][C]48[/C][C]6637[/C][C]6061.52846393402[/C][C]575.471536065979[/C][/ROW]
[ROW][C]49[/C][C]6683[/C][C]6597.05549883619[/C][C]85.944501163809[/C][/ROW]
[ROW][C]50[/C][C]5584[/C][C]6178.22958626812[/C][C]-594.229586268121[/C][/ROW]
[ROW][C]51[/C][C]6510.5[/C][C]7386.31257827015[/C][C]-875.812578270154[/C][/ROW]
[ROW][C]52[/C][C]7263[/C][C]7261.25155586598[/C][C]1.74844413402298[/C][/ROW]
[ROW][C]53[/C][C]7114.5[/C][C]7619.44319725964[/C][C]-504.943197259642[/C][/ROW]
[ROW][C]54[/C][C]8114.5[/C][C]8117.71527759068[/C][C]-3.21527759068158[/C][/ROW]
[ROW][C]55[/C][C]7228.5[/C][C]7449.7603957597[/C][C]-221.260395759699[/C][/ROW]
[ROW][C]56[/C][C]8126[/C][C]7940.84894104369[/C][C]185.151058956312[/C][/ROW]
[ROW][C]57[/C][C]8071[/C][C]8377.10144061953[/C][C]-306.10144061953[/C][/ROW]
[ROW][C]58[/C][C]8602.5[/C][C]8137.55516025679[/C][C]464.944839743206[/C][/ROW]
[ROW][C]59[/C][C]7371.5[/C][C]6910.78210700645[/C][C]460.717892993553[/C][/ROW]
[ROW][C]60[/C][C]6678[/C][C]6256.29291721902[/C][C]421.707082780978[/C][/ROW]
[ROW][C]61[/C][C]6440.5[/C][C]6695.47015560704[/C][C]-254.970155607042[/C][/ROW]
[ROW][C]62[/C][C]6207.5[/C][C]6124.06183934671[/C][C]83.438160653287[/C][/ROW]
[ROW][C]63[/C][C]7067.5[/C][C]7389.34722746364[/C][C]-321.847227463644[/C][/ROW]
[ROW][C]64[/C][C]7512[/C][C]7477.92410263006[/C][C]34.0758973699385[/C][/ROW]
[ROW][C]65[/C][C]7474.5[/C][C]7764.53694844432[/C][C]-290.036948444315[/C][/ROW]
[ROW][C]66[/C][C]8992[/C][C]8369.98510391484[/C][C]622.014896085157[/C][/ROW]
[ROW][C]67[/C][C]8265.5[/C][C]7761.0956732635[/C][C]504.404326736495[/C][/ROW]
[ROW][C]68[/C][C]7841[/C][C]8420.08622288856[/C][C]-579.086222888558[/C][/ROW]
[ROW][C]69[/C][C]8758.5[/C][C]8669.98531008278[/C][C]88.5146899172196[/C][/ROW]
[ROW][C]70[/C][C]9183.5[/C][C]8604.60546467289[/C][C]578.89453532711[/C][/ROW]
[ROW][C]71[/C][C]7792[/C][C]7393.94702273698[/C][C]398.052977263016[/C][/ROW]
[ROW][C]72[/C][C]7670.5[/C][C]6724.36883280064[/C][C]946.131167199363[/C][/ROW]
[ROW][C]73[/C][C]6530.5[/C][C]7138.70116798084[/C][C]-608.201167980843[/C][/ROW]
[ROW][C]74[/C][C]6621.5[/C][C]6566.34539176598[/C][C]55.1546082340192[/C][/ROW]
[ROW][C]75[/C][C]7870[/C][C]7766.41821501603[/C][C]103.58178498397[/C][/ROW]
[ROW][C]76[/C][C]7250.5[/C][C]7971.1545183882[/C][C]-720.654518388196[/C][/ROW]
[ROW][C]77[/C][C]7779.5[/C][C]8097.99047391934[/C][C]-318.490473919339[/C][/ROW]
[ROW][C]78[/C][C]9027.5[/C][C]8836.65287865317[/C][C]190.847121346827[/C][/ROW]
[ROW][C]79[/C][C]7891.5[/C][C]8146.66125490251[/C][C]-255.161254902513[/C][/ROW]
[ROW][C]80[/C][C]9021[/C][C]8530.76677337186[/C][C]490.233226628139[/C][/ROW]
[ROW][C]81[/C][C]8559[/C][C]9038.43465031038[/C][C]-479.434650310375[/C][/ROW]
[ROW][C]82[/C][C]8738[/C][C]8963.43621011421[/C][C]-225.436210114211[/C][/ROW]
[ROW][C]83[/C][C]8051.5[/C][C]7607.29256015132[/C][C]444.207439848684[/C][/ROW]
[ROW][C]84[/C][C]7354[/C][C]7027.06526900686[/C][C]326.934730993141[/C][/ROW]
[ROW][C]85[/C][C]7182[/C][C]7116.21728845139[/C][C]65.7827115486098[/C][/ROW]
[ROW][C]86[/C][C]6319.5[/C][C]6742.87375568203[/C][C]-423.373755682031[/C][/ROW]
[ROW][C]87[/C][C]7353.5[/C][C]7879.89500488966[/C][C]-526.395004889658[/C][/ROW]
[ROW][C]88[/C][C]7519.5[/C][C]7867.85237364539[/C][C]-348.352373645394[/C][/ROW]
[ROW][C]89[/C][C]7854.5[/C][C]8110.00376164112[/C][C]-255.503761641119[/C][/ROW]
[ROW][C]90[/C][C]8996.5[/C][C]8934.65539900472[/C][C]61.8446009952786[/C][/ROW]
[ROW][C]91[/C][C]7684.5[/C][C]8158.51007125093[/C][C]-474.010071250934[/C][/ROW]
[ROW][C]92[/C][C]8708.5[/C][C]8622.73413647739[/C][C]85.7658635226144[/C][/ROW]
[ROW][C]93[/C][C]8371[/C][C]8924.86579820322[/C][C]-553.865798203218[/C][/ROW]
[ROW][C]94[/C][C]8385.5[/C][C]8877.18936096366[/C][C]-491.689360963661[/C][/ROW]
[ROW][C]95[/C][C]7916[/C][C]7582.78392412958[/C][C]333.216075870417[/C][/ROW]
[ROW][C]96[/C][C]6872[/C][C]6968.57345955674[/C][C]-96.5734595567401[/C][/ROW]
[ROW][C]97[/C][C]7492[/C][C]6956.12532827599[/C][C]535.874671724014[/C][/ROW]
[ROW][C]98[/C][C]6515[/C][C]6578.19898334312[/C][C]-63.198983343118[/C][/ROW]
[ROW][C]99[/C][C]7875[/C][C]7752.64863151627[/C][C]122.351368483727[/C][/ROW]
[ROW][C]100[/C][C]7487[/C][C]7862.79759386898[/C][C]-375.797593868981[/C][/ROW]
[ROW][C]101[/C][C]8195.5[/C][C]8114.9016340447[/C][C]80.5983659552967[/C][/ROW]
[ROW][C]102[/C][C]8533[/C][C]9036.76989660627[/C][C]-503.769896606273[/C][/ROW]
[ROW][C]103[/C][C]8688[/C][C]8096.75091803232[/C][C]591.249081967678[/C][/ROW]
[ROW][C]104[/C][C]8892.5[/C][C]8801.90346230806[/C][C]90.5965376919376[/C][/ROW]
[ROW][C]105[/C][C]8221.5[/C][C]9008.38720970317[/C][C]-786.887209703173[/C][/ROW]
[ROW][C]106[/C][C]8652.5[/C][C]8935.82167296975[/C][C]-283.321672969752[/C][/ROW]
[ROW][C]107[/C][C]7410.5[/C][C]7796.3165514971[/C][C]-385.816551497095[/C][/ROW]
[ROW][C]108[/C][C]6457[/C][C]7011.65722773807[/C][C]-554.657227738074[/C][/ROW]
[ROW][C]109[/C][C]6400.5[/C][C]7027.14353455706[/C][C]-626.643534557056[/C][/ROW]
[ROW][C]110[/C][C]6260.5[/C][C]6388.07091372238[/C][C]-127.570913722378[/C][/ROW]
[ROW][C]111[/C][C]7220[/C][C]7581.0098966544[/C][C]-361.009896654396[/C][/ROW]
[ROW][C]112[/C][C]7617[/C][C]7545.05721651603[/C][C]71.9427834839671[/C][/ROW]
[ROW][C]113[/C][C]7922[/C][C]7931.73645535971[/C][C]-9.73645535971082[/C][/ROW]
[ROW][C]114[/C][C]8934[/C][C]8752.29204396986[/C][C]181.707956030143[/C][/ROW]
[ROW][C]115[/C][C]8395[/C][C]8078.00340725524[/C][C]316.996592744758[/C][/ROW]
[ROW][C]116[/C][C]8945[/C][C]8667.41757432101[/C][C]277.582425678987[/C][/ROW]
[ROW][C]117[/C][C]9738[/C][C]8769.19996529576[/C][C]968.800034704238[/C][/ROW]
[ROW][C]118[/C][C]9224[/C][C]9030.59267845378[/C][C]193.407321546221[/C][/ROW]
[ROW][C]119[/C][C]6923[/C][C]7945.72951952343[/C][C]-1022.72951952343[/C][/ROW]
[ROW][C]120[/C][C]6572.5[/C][C]7042.00443291639[/C][C]-469.504432916388[/C][/ROW]
[ROW][C]121[/C][C]6962.5[/C][C]7059.16432197911[/C][C]-96.6643219791113[/C][/ROW]
[ROW][C]122[/C][C]7038[/C][C]6573.18564636819[/C][C]464.814353631813[/C][/ROW]
[ROW][C]123[/C][C]8564[/C][C]7818.04262792018[/C][C]745.957372079823[/C][/ROW]
[ROW][C]124[/C][C]8534[/C][C]8010.04436821303[/C][C]523.955631786966[/C][/ROW]
[ROW][C]125[/C][C]8420.5[/C][C]8450.86792333344[/C][C]-30.3679233334424[/C][/ROW]
[ROW][C]126[/C][C]8831[/C][C]9297.23091131247[/C][C]-466.230911312472[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298765&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298765&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
135631.55579.149973290652.3500267094005
145515.55442.6474315443272.8525684556816
156676.56607.4297369987569.0702630012529
166592.56537.3435176816455.1564823183562
1771017057.9827107717843.0172892282162
1877937753.5665261162339.4334738837661
1971776763.56099609293413.439003907073
2078437547.89100372507295.108996274926
217858.58075.84652423012-217.346524230123
227576.57579.7384115263-3.23841152629939
2362296468.52232248599-239.522322485988
245739.55569.50838243002169.991617569979
2565595912.95712323404646.042876765958
266126.55866.82012038549259.679879614507
277486.57058.49752860857428.002471391431
287627.57039.08074121129588.419258788714
297602.57636.28448690729-33.7844869072942
3077108320.03802782523-610.038027825231
3181027290.89824344423811.101756555772
327533.58115.86143381443-582.361433814427
337736.58437.62334089138-701.123340891381
3486957902.65129321111792.348706788887
3568856872.7966872207712.2033127792256
366079.56072.479841611357.02015838865191
3768746463.68595950446410.31404049554
3851946324.6911018255-1130.6911018255
396980.57337.33161892929-356.831618929293
407280.57226.7050259749653.7949740250415
417313.57651.58273738536-338.082737385357
427670.58203.79196851597-533.29196851597
4372517400.02363737802-149.02363737802
447909.57873.9219430216135.5780569783892
4584348268.63415596979165.365844030206
468333.58086.02778061106247.472219388936
476898.56858.5466929069239.9533070930829
4866376061.52846393402575.471536065979
4966836597.0554988361985.944501163809
5055846178.22958626812-594.229586268121
516510.57386.31257827015-875.812578270154
5272637261.251555865981.74844413402298
537114.57619.44319725964-504.943197259642
548114.58117.71527759068-3.21527759068158
557228.57449.7603957597-221.260395759699
5681267940.84894104369185.151058956312
5780718377.10144061953-306.10144061953
588602.58137.55516025679464.944839743206
597371.56910.78210700645460.717892993553
6066786256.29291721902421.707082780978
616440.56695.47015560704-254.970155607042
626207.56124.0618393467183.438160653287
637067.57389.34722746364-321.847227463644
6475127477.9241026300634.0758973699385
657474.57764.53694844432-290.036948444315
6689928369.98510391484622.014896085157
678265.57761.0956732635504.404326736495
6878418420.08622288856-579.086222888558
698758.58669.9853100827888.5146899172196
709183.58604.60546467289578.89453532711
7177927393.94702273698398.052977263016
727670.56724.36883280064946.131167199363
736530.57138.70116798084-608.201167980843
746621.56566.3453917659855.1546082340192
7578707766.41821501603103.58178498397
767250.57971.1545183882-720.654518388196
777779.58097.99047391934-318.490473919339
789027.58836.65287865317190.847121346827
797891.58146.66125490251-255.161254902513
8090218530.76677337186490.233226628139
8185599038.43465031038-479.434650310375
8287388963.43621011421-225.436210114211
838051.57607.29256015132444.207439848684
8473547027.06526900686326.934730993141
8571827116.2172884513965.7827115486098
866319.56742.87375568203-423.373755682031
877353.57879.89500488966-526.395004889658
887519.57867.85237364539-348.352373645394
897854.58110.00376164112-255.503761641119
908996.58934.6553990047261.8446009952786
917684.58158.51007125093-474.010071250934
928708.58622.7341364773985.7658635226144
9383718924.86579820322-553.865798203218
948385.58877.18936096366-491.689360963661
9579167582.78392412958333.216075870417
9668726968.57345955674-96.5734595567401
9774926956.12532827599535.874671724014
9865156578.19898334312-63.198983343118
9978757752.64863151627122.351368483727
10074877862.79759386898-375.797593868981
1018195.58114.901634044780.5983659552967
10285339036.76989660627-503.769896606273
10386888096.75091803232591.249081967678
1048892.58801.9034623080690.5965376919376
1058221.59008.38720970317-786.887209703173
1068652.58935.82167296975-283.321672969752
1077410.57796.3165514971-385.816551497095
10864577011.65722773807-554.657227738074
1096400.57027.14353455706-626.643534557056
1106260.56388.07091372238-127.570913722378
11172207581.0098966544-361.009896654396
11276177545.0572165160371.9427834839671
11379227931.73645535971-9.73645535971082
11489348752.29204396986181.707956030143
11583958078.00340725524316.996592744758
11689458667.41757432101277.582425678987
11797388769.19996529576968.800034704238
11892249030.59267845378193.407321546221
11969237945.72951952343-1022.72951952343
1206572.57042.00443291639-469.504432916388
1216962.57059.16432197911-96.6643219791113
12270386573.18564636819464.814353631813
12385647818.04262792018745.957372079823
12485348010.04436821303523.955631786966
1258420.58450.86792333344-30.3679233334424
12688319297.23091131247-466.230911312472







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1278548.071543618047701.829546063619394.31354117247
1289084.947450305588229.610256669719940.28464394146
1299250.052607704558385.7159191341310114.389296275
1309252.215151337738378.9717101365710125.4585925389
1317955.713442793177073.65318181738837.77370376905
1327285.677828043546394.888009744758176.46764634234
1337428.025012652266528.590358674118327.4596666304
1347040.841262403066132.844074539157948.83845026696
1358259.720472172887343.240745413619176.20019893215
1368308.617665998497383.733194319619233.50213767737
1378588.909442140567655.695917621829522.1229666593
1389374.075635209178432.6067410142210315.5445294041

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 8548.07154361804 & 7701.82954606361 & 9394.31354117247 \tabularnewline
128 & 9084.94745030558 & 8229.61025666971 & 9940.28464394146 \tabularnewline
129 & 9250.05260770455 & 8385.71591913413 & 10114.389296275 \tabularnewline
130 & 9252.21515133773 & 8378.97171013657 & 10125.4585925389 \tabularnewline
131 & 7955.71344279317 & 7073.6531818173 & 8837.77370376905 \tabularnewline
132 & 7285.67782804354 & 6394.88800974475 & 8176.46764634234 \tabularnewline
133 & 7428.02501265226 & 6528.59035867411 & 8327.4596666304 \tabularnewline
134 & 7040.84126240306 & 6132.84407453915 & 7948.83845026696 \tabularnewline
135 & 8259.72047217288 & 7343.24074541361 & 9176.20019893215 \tabularnewline
136 & 8308.61766599849 & 7383.73319431961 & 9233.50213767737 \tabularnewline
137 & 8588.90944214056 & 7655.69591762182 & 9522.1229666593 \tabularnewline
138 & 9374.07563520917 & 8432.60674101422 & 10315.5445294041 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298765&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]127[/C][C]8548.07154361804[/C][C]7701.82954606361[/C][C]9394.31354117247[/C][/ROW]
[ROW][C]128[/C][C]9084.94745030558[/C][C]8229.61025666971[/C][C]9940.28464394146[/C][/ROW]
[ROW][C]129[/C][C]9250.05260770455[/C][C]8385.71591913413[/C][C]10114.389296275[/C][/ROW]
[ROW][C]130[/C][C]9252.21515133773[/C][C]8378.97171013657[/C][C]10125.4585925389[/C][/ROW]
[ROW][C]131[/C][C]7955.71344279317[/C][C]7073.6531818173[/C][C]8837.77370376905[/C][/ROW]
[ROW][C]132[/C][C]7285.67782804354[/C][C]6394.88800974475[/C][C]8176.46764634234[/C][/ROW]
[ROW][C]133[/C][C]7428.02501265226[/C][C]6528.59035867411[/C][C]8327.4596666304[/C][/ROW]
[ROW][C]134[/C][C]7040.84126240306[/C][C]6132.84407453915[/C][C]7948.83845026696[/C][/ROW]
[ROW][C]135[/C][C]8259.72047217288[/C][C]7343.24074541361[/C][C]9176.20019893215[/C][/ROW]
[ROW][C]136[/C][C]8308.61766599849[/C][C]7383.73319431961[/C][C]9233.50213767737[/C][/ROW]
[ROW][C]137[/C][C]8588.90944214056[/C][C]7655.69591762182[/C][C]9522.1229666593[/C][/ROW]
[ROW][C]138[/C][C]9374.07563520917[/C][C]8432.60674101422[/C][C]10315.5445294041[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298765&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298765&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
1278548.071543618047701.829546063619394.31354117247
1289084.947450305588229.610256669719940.28464394146
1299250.052607704558385.7159191341310114.389296275
1309252.215151337738378.9717101365710125.4585925389
1317955.713442793177073.65318181738837.77370376905
1327285.677828043546394.888009744758176.46764634234
1337428.025012652266528.590358674118327.4596666304
1347040.841262403066132.844074539157948.83845026696
1358259.720472172887343.240745413619176.20019893215
1368308.617665998497383.733194319619233.50213767737
1378588.909442140567655.695917621829522.1229666593
1389374.075635209178432.6067410142210315.5445294041



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
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')