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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Jan 2010 12:28:59 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/25/t12644479239syp6db4gaixxjx.htm/, Retrieved Mon, 06 May 2024 01:51:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72493, Retrieved Mon, 06 May 2024 01:51:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [niet werkende wer...] [2010-01-25 19:28:59] [8aa2720a1fbf81ca84b2e99ab4a134db] [Current]
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Dataseries X:
89507
87562
85209
82360
79054
79069
107551
115759
115585
110260
103444
102303
101397
97994
94044
91159
87239
89235
118647
125620
125154
117529
109459
108483
107137
104699
100804
96066
91971
93228
120144
127233
127166
118194
109940
106683
102834
99882
96666
92540
88744
89321
115870
122401
122030
113802
105791
103076
98658
96945
92497
90687
88796
90015
113228
118711
117460
106556
97347
92657
93118
89037
83570
81693
75956
73993
97088
102394
96549
89727
82336
82653
82303
79596
74472
73562
66618
69029
89899
93774
90305
83799
80320
82497




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72493&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72493&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72493&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0922981936893189
gamma0.433108278706043

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0922981936893189 \tabularnewline
gamma & 0.433108278706043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72493&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0922981936893189[/C][/ROW]
[ROW][C]gamma[/C][C]0.433108278706043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72493&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72493&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
alpha1
beta0.0922981936893189
gamma0.433108278706043







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310139796474.22628105124922.77371894875
149799498326.399919701-332.399919700954
159404494389.1181365008-345.118136500751
169115991555.1131305944-396.113130594356
178723987704.6233375337-465.623337533689
188923589703.7044534013-468.704453401326
19118647117845.772628058801.22737194167
20125620127761.537998307-2141.53799830689
21125154125475.920836253-321.920836253063
22117529119486.218281902-1957.21828190197
23109459110229.333517919-770.333517919251
24108483108092.668042184390.331957815768
25107137107271.619819706-134.619819706102
26104699103305.3051351931393.69486480746
27100804100428.855794703375.144205297096
289606697795.786654125-1729.78665412503
299197192003.6665251103-32.6665251103113
309322894182.4737242207-954.47372422066
31120144122567.956054974-2423.956054974
32127233128506.074067418-1273.07406741826
33127166126309.573889743856.426110257351
34118194120771.076124176-2577.07612417616
35109940110217.708812663-277.708812663244
36106683107989.967478415-1306.96747841456
37102834104784.426617862-1950.4266178619
389988298332.8608572861549.13914271408
399666695047.23162761711618.76837238288
409254093156.8721325465-616.872132546545
418874488121.5113452989622.488654701127
428932190424.0899788703-1103.08997887027
43115870116820.025295937-950.025295936648
44122401123415.211564262-1014.21156426215
45122030121018.4985797011011.50142029904
46113802115442.722074325-1640.72207432544
47105791105773.50500228217.4949977184733
48103076103598.277304862-522.277304862204
4998658100997.683701730-2339.68370173041
509694594064.25539377242880.7446062276
519249792113.3864757153383.613524284694
529068788901.04249914771785.95750085231
538879686338.37391360972457.6260863903
549001590629.9056220935-614.905622093458
55113228117986.747390199-4758.74739019891
56118711120499.859214778-1788.85921477847
57117460117195.414722651264.585277349222
58106556110890.555396084-4334.55539608361
599734798582.3318794162-1235.33187941618
609265794764.2323703424-2107.23237034245
619311890080.18970476573037.81029523433
628903788579.1159120853457.884087914703
638357084202.430136789-632.430136789088
648169379848.96652538671844.03347461326
657595677346.4914324392-1390.49143243923
667399376760.1513256966-2767.15132569664
679708895723.33235288991364.66764711009
68102394102503.882472263-109.882472262689
6996549100407.271713637-3858.27171363732
708972790135.1862383517-408.1862383517
718233682353.0623957618-17.0623957618373
728265379599.71774726793053.28225273211
738230380295.02558408082007.97441591919
747959678167.00595790151428.99404209854
757447275251.5873104856-779.587310485585
767356271113.65640497522448.34359502481
776661869682.3948193388-3064.39481933876
786902967174.84647231611854.15352768388
798989989683.6638490101215.336150989882
809377495210.2299628217-1436.22996282167
819030592115.9084799315-1810.90847993149
828379984634.4137413348-835.413741334778
838032077177.46839068753142.5316093125
848249778247.51417044394249.4858295561

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 101397 & 96474.2262810512 & 4922.77371894875 \tabularnewline
14 & 97994 & 98326.399919701 & -332.399919700954 \tabularnewline
15 & 94044 & 94389.1181365008 & -345.118136500751 \tabularnewline
16 & 91159 & 91555.1131305944 & -396.113130594356 \tabularnewline
17 & 87239 & 87704.6233375337 & -465.623337533689 \tabularnewline
18 & 89235 & 89703.7044534013 & -468.704453401326 \tabularnewline
19 & 118647 & 117845.772628058 & 801.22737194167 \tabularnewline
20 & 125620 & 127761.537998307 & -2141.53799830689 \tabularnewline
21 & 125154 & 125475.920836253 & -321.920836253063 \tabularnewline
22 & 117529 & 119486.218281902 & -1957.21828190197 \tabularnewline
23 & 109459 & 110229.333517919 & -770.333517919251 \tabularnewline
24 & 108483 & 108092.668042184 & 390.331957815768 \tabularnewline
25 & 107137 & 107271.619819706 & -134.619819706102 \tabularnewline
26 & 104699 & 103305.305135193 & 1393.69486480746 \tabularnewline
27 & 100804 & 100428.855794703 & 375.144205297096 \tabularnewline
28 & 96066 & 97795.786654125 & -1729.78665412503 \tabularnewline
29 & 91971 & 92003.6665251103 & -32.6665251103113 \tabularnewline
30 & 93228 & 94182.4737242207 & -954.47372422066 \tabularnewline
31 & 120144 & 122567.956054974 & -2423.956054974 \tabularnewline
32 & 127233 & 128506.074067418 & -1273.07406741826 \tabularnewline
33 & 127166 & 126309.573889743 & 856.426110257351 \tabularnewline
34 & 118194 & 120771.076124176 & -2577.07612417616 \tabularnewline
35 & 109940 & 110217.708812663 & -277.708812663244 \tabularnewline
36 & 106683 & 107989.967478415 & -1306.96747841456 \tabularnewline
37 & 102834 & 104784.426617862 & -1950.4266178619 \tabularnewline
38 & 99882 & 98332.860857286 & 1549.13914271408 \tabularnewline
39 & 96666 & 95047.2316276171 & 1618.76837238288 \tabularnewline
40 & 92540 & 93156.8721325465 & -616.872132546545 \tabularnewline
41 & 88744 & 88121.5113452989 & 622.488654701127 \tabularnewline
42 & 89321 & 90424.0899788703 & -1103.08997887027 \tabularnewline
43 & 115870 & 116820.025295937 & -950.025295936648 \tabularnewline
44 & 122401 & 123415.211564262 & -1014.21156426215 \tabularnewline
45 & 122030 & 121018.498579701 & 1011.50142029904 \tabularnewline
46 & 113802 & 115442.722074325 & -1640.72207432544 \tabularnewline
47 & 105791 & 105773.505002282 & 17.4949977184733 \tabularnewline
48 & 103076 & 103598.277304862 & -522.277304862204 \tabularnewline
49 & 98658 & 100997.683701730 & -2339.68370173041 \tabularnewline
50 & 96945 & 94064.2553937724 & 2880.7446062276 \tabularnewline
51 & 92497 & 92113.3864757153 & 383.613524284694 \tabularnewline
52 & 90687 & 88901.0424991477 & 1785.95750085231 \tabularnewline
53 & 88796 & 86338.3739136097 & 2457.6260863903 \tabularnewline
54 & 90015 & 90629.9056220935 & -614.905622093458 \tabularnewline
55 & 113228 & 117986.747390199 & -4758.74739019891 \tabularnewline
56 & 118711 & 120499.859214778 & -1788.85921477847 \tabularnewline
57 & 117460 & 117195.414722651 & 264.585277349222 \tabularnewline
58 & 106556 & 110890.555396084 & -4334.55539608361 \tabularnewline
59 & 97347 & 98582.3318794162 & -1235.33187941618 \tabularnewline
60 & 92657 & 94764.2323703424 & -2107.23237034245 \tabularnewline
61 & 93118 & 90080.1897047657 & 3037.81029523433 \tabularnewline
62 & 89037 & 88579.1159120853 & 457.884087914703 \tabularnewline
63 & 83570 & 84202.430136789 & -632.430136789088 \tabularnewline
64 & 81693 & 79848.9665253867 & 1844.03347461326 \tabularnewline
65 & 75956 & 77346.4914324392 & -1390.49143243923 \tabularnewline
66 & 73993 & 76760.1513256966 & -2767.15132569664 \tabularnewline
67 & 97088 & 95723.3323528899 & 1364.66764711009 \tabularnewline
68 & 102394 & 102503.882472263 & -109.882472262689 \tabularnewline
69 & 96549 & 100407.271713637 & -3858.27171363732 \tabularnewline
70 & 89727 & 90135.1862383517 & -408.1862383517 \tabularnewline
71 & 82336 & 82353.0623957618 & -17.0623957618373 \tabularnewline
72 & 82653 & 79599.7177472679 & 3053.28225273211 \tabularnewline
73 & 82303 & 80295.0255840808 & 2007.97441591919 \tabularnewline
74 & 79596 & 78167.0059579015 & 1428.99404209854 \tabularnewline
75 & 74472 & 75251.5873104856 & -779.587310485585 \tabularnewline
76 & 73562 & 71113.6564049752 & 2448.34359502481 \tabularnewline
77 & 66618 & 69682.3948193388 & -3064.39481933876 \tabularnewline
78 & 69029 & 67174.8464723161 & 1854.15352768388 \tabularnewline
79 & 89899 & 89683.6638490101 & 215.336150989882 \tabularnewline
80 & 93774 & 95210.2299628217 & -1436.22996282167 \tabularnewline
81 & 90305 & 92115.9084799315 & -1810.90847993149 \tabularnewline
82 & 83799 & 84634.4137413348 & -835.413741334778 \tabularnewline
83 & 80320 & 77177.4683906875 & 3142.5316093125 \tabularnewline
84 & 82497 & 78247.5141704439 & 4249.4858295561 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72493&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]101397[/C][C]96474.2262810512[/C][C]4922.77371894875[/C][/ROW]
[ROW][C]14[/C][C]97994[/C][C]98326.399919701[/C][C]-332.399919700954[/C][/ROW]
[ROW][C]15[/C][C]94044[/C][C]94389.1181365008[/C][C]-345.118136500751[/C][/ROW]
[ROW][C]16[/C][C]91159[/C][C]91555.1131305944[/C][C]-396.113130594356[/C][/ROW]
[ROW][C]17[/C][C]87239[/C][C]87704.6233375337[/C][C]-465.623337533689[/C][/ROW]
[ROW][C]18[/C][C]89235[/C][C]89703.7044534013[/C][C]-468.704453401326[/C][/ROW]
[ROW][C]19[/C][C]118647[/C][C]117845.772628058[/C][C]801.22737194167[/C][/ROW]
[ROW][C]20[/C][C]125620[/C][C]127761.537998307[/C][C]-2141.53799830689[/C][/ROW]
[ROW][C]21[/C][C]125154[/C][C]125475.920836253[/C][C]-321.920836253063[/C][/ROW]
[ROW][C]22[/C][C]117529[/C][C]119486.218281902[/C][C]-1957.21828190197[/C][/ROW]
[ROW][C]23[/C][C]109459[/C][C]110229.333517919[/C][C]-770.333517919251[/C][/ROW]
[ROW][C]24[/C][C]108483[/C][C]108092.668042184[/C][C]390.331957815768[/C][/ROW]
[ROW][C]25[/C][C]107137[/C][C]107271.619819706[/C][C]-134.619819706102[/C][/ROW]
[ROW][C]26[/C][C]104699[/C][C]103305.305135193[/C][C]1393.69486480746[/C][/ROW]
[ROW][C]27[/C][C]100804[/C][C]100428.855794703[/C][C]375.144205297096[/C][/ROW]
[ROW][C]28[/C][C]96066[/C][C]97795.786654125[/C][C]-1729.78665412503[/C][/ROW]
[ROW][C]29[/C][C]91971[/C][C]92003.6665251103[/C][C]-32.6665251103113[/C][/ROW]
[ROW][C]30[/C][C]93228[/C][C]94182.4737242207[/C][C]-954.47372422066[/C][/ROW]
[ROW][C]31[/C][C]120144[/C][C]122567.956054974[/C][C]-2423.956054974[/C][/ROW]
[ROW][C]32[/C][C]127233[/C][C]128506.074067418[/C][C]-1273.07406741826[/C][/ROW]
[ROW][C]33[/C][C]127166[/C][C]126309.573889743[/C][C]856.426110257351[/C][/ROW]
[ROW][C]34[/C][C]118194[/C][C]120771.076124176[/C][C]-2577.07612417616[/C][/ROW]
[ROW][C]35[/C][C]109940[/C][C]110217.708812663[/C][C]-277.708812663244[/C][/ROW]
[ROW][C]36[/C][C]106683[/C][C]107989.967478415[/C][C]-1306.96747841456[/C][/ROW]
[ROW][C]37[/C][C]102834[/C][C]104784.426617862[/C][C]-1950.4266178619[/C][/ROW]
[ROW][C]38[/C][C]99882[/C][C]98332.860857286[/C][C]1549.13914271408[/C][/ROW]
[ROW][C]39[/C][C]96666[/C][C]95047.2316276171[/C][C]1618.76837238288[/C][/ROW]
[ROW][C]40[/C][C]92540[/C][C]93156.8721325465[/C][C]-616.872132546545[/C][/ROW]
[ROW][C]41[/C][C]88744[/C][C]88121.5113452989[/C][C]622.488654701127[/C][/ROW]
[ROW][C]42[/C][C]89321[/C][C]90424.0899788703[/C][C]-1103.08997887027[/C][/ROW]
[ROW][C]43[/C][C]115870[/C][C]116820.025295937[/C][C]-950.025295936648[/C][/ROW]
[ROW][C]44[/C][C]122401[/C][C]123415.211564262[/C][C]-1014.21156426215[/C][/ROW]
[ROW][C]45[/C][C]122030[/C][C]121018.498579701[/C][C]1011.50142029904[/C][/ROW]
[ROW][C]46[/C][C]113802[/C][C]115442.722074325[/C][C]-1640.72207432544[/C][/ROW]
[ROW][C]47[/C][C]105791[/C][C]105773.505002282[/C][C]17.4949977184733[/C][/ROW]
[ROW][C]48[/C][C]103076[/C][C]103598.277304862[/C][C]-522.277304862204[/C][/ROW]
[ROW][C]49[/C][C]98658[/C][C]100997.683701730[/C][C]-2339.68370173041[/C][/ROW]
[ROW][C]50[/C][C]96945[/C][C]94064.2553937724[/C][C]2880.7446062276[/C][/ROW]
[ROW][C]51[/C][C]92497[/C][C]92113.3864757153[/C][C]383.613524284694[/C][/ROW]
[ROW][C]52[/C][C]90687[/C][C]88901.0424991477[/C][C]1785.95750085231[/C][/ROW]
[ROW][C]53[/C][C]88796[/C][C]86338.3739136097[/C][C]2457.6260863903[/C][/ROW]
[ROW][C]54[/C][C]90015[/C][C]90629.9056220935[/C][C]-614.905622093458[/C][/ROW]
[ROW][C]55[/C][C]113228[/C][C]117986.747390199[/C][C]-4758.74739019891[/C][/ROW]
[ROW][C]56[/C][C]118711[/C][C]120499.859214778[/C][C]-1788.85921477847[/C][/ROW]
[ROW][C]57[/C][C]117460[/C][C]117195.414722651[/C][C]264.585277349222[/C][/ROW]
[ROW][C]58[/C][C]106556[/C][C]110890.555396084[/C][C]-4334.55539608361[/C][/ROW]
[ROW][C]59[/C][C]97347[/C][C]98582.3318794162[/C][C]-1235.33187941618[/C][/ROW]
[ROW][C]60[/C][C]92657[/C][C]94764.2323703424[/C][C]-2107.23237034245[/C][/ROW]
[ROW][C]61[/C][C]93118[/C][C]90080.1897047657[/C][C]3037.81029523433[/C][/ROW]
[ROW][C]62[/C][C]89037[/C][C]88579.1159120853[/C][C]457.884087914703[/C][/ROW]
[ROW][C]63[/C][C]83570[/C][C]84202.430136789[/C][C]-632.430136789088[/C][/ROW]
[ROW][C]64[/C][C]81693[/C][C]79848.9665253867[/C][C]1844.03347461326[/C][/ROW]
[ROW][C]65[/C][C]75956[/C][C]77346.4914324392[/C][C]-1390.49143243923[/C][/ROW]
[ROW][C]66[/C][C]73993[/C][C]76760.1513256966[/C][C]-2767.15132569664[/C][/ROW]
[ROW][C]67[/C][C]97088[/C][C]95723.3323528899[/C][C]1364.66764711009[/C][/ROW]
[ROW][C]68[/C][C]102394[/C][C]102503.882472263[/C][C]-109.882472262689[/C][/ROW]
[ROW][C]69[/C][C]96549[/C][C]100407.271713637[/C][C]-3858.27171363732[/C][/ROW]
[ROW][C]70[/C][C]89727[/C][C]90135.1862383517[/C][C]-408.1862383517[/C][/ROW]
[ROW][C]71[/C][C]82336[/C][C]82353.0623957618[/C][C]-17.0623957618373[/C][/ROW]
[ROW][C]72[/C][C]82653[/C][C]79599.7177472679[/C][C]3053.28225273211[/C][/ROW]
[ROW][C]73[/C][C]82303[/C][C]80295.0255840808[/C][C]2007.97441591919[/C][/ROW]
[ROW][C]74[/C][C]79596[/C][C]78167.0059579015[/C][C]1428.99404209854[/C][/ROW]
[ROW][C]75[/C][C]74472[/C][C]75251.5873104856[/C][C]-779.587310485585[/C][/ROW]
[ROW][C]76[/C][C]73562[/C][C]71113.6564049752[/C][C]2448.34359502481[/C][/ROW]
[ROW][C]77[/C][C]66618[/C][C]69682.3948193388[/C][C]-3064.39481933876[/C][/ROW]
[ROW][C]78[/C][C]69029[/C][C]67174.8464723161[/C][C]1854.15352768388[/C][/ROW]
[ROW][C]79[/C][C]89899[/C][C]89683.6638490101[/C][C]215.336150989882[/C][/ROW]
[ROW][C]80[/C][C]93774[/C][C]95210.2299628217[/C][C]-1436.22996282167[/C][/ROW]
[ROW][C]81[/C][C]90305[/C][C]92115.9084799315[/C][C]-1810.90847993149[/C][/ROW]
[ROW][C]82[/C][C]83799[/C][C]84634.4137413348[/C][C]-835.413741334778[/C][/ROW]
[ROW][C]83[/C][C]80320[/C][C]77177.4683906875[/C][C]3142.5316093125[/C][/ROW]
[ROW][C]84[/C][C]82497[/C][C]78247.5141704439[/C][C]4249.4858295561[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72493&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72493&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
1310139796474.22628105124922.77371894875
149799498326.399919701-332.399919700954
159404494389.1181365008-345.118136500751
169115991555.1131305944-396.113130594356
178723987704.6233375337-465.623337533689
188923589703.7044534013-468.704453401326
19118647117845.772628058801.22737194167
20125620127761.537998307-2141.53799830689
21125154125475.920836253-321.920836253063
22117529119486.218281902-1957.21828190197
23109459110229.333517919-770.333517919251
24108483108092.668042184390.331957815768
25107137107271.619819706-134.619819706102
26104699103305.3051351931393.69486480746
27100804100428.855794703375.144205297096
289606697795.786654125-1729.78665412503
299197192003.6665251103-32.6665251103113
309322894182.4737242207-954.47372422066
31120144122567.956054974-2423.956054974
32127233128506.074067418-1273.07406741826
33127166126309.573889743856.426110257351
34118194120771.076124176-2577.07612417616
35109940110217.708812663-277.708812663244
36106683107989.967478415-1306.96747841456
37102834104784.426617862-1950.4266178619
389988298332.8608572861549.13914271408
399666695047.23162761711618.76837238288
409254093156.8721325465-616.872132546545
418874488121.5113452989622.488654701127
428932190424.0899788703-1103.08997887027
43115870116820.025295937-950.025295936648
44122401123415.211564262-1014.21156426215
45122030121018.4985797011011.50142029904
46113802115442.722074325-1640.72207432544
47105791105773.50500228217.4949977184733
48103076103598.277304862-522.277304862204
4998658100997.683701730-2339.68370173041
509694594064.25539377242880.7446062276
519249792113.3864757153383.613524284694
529068788901.04249914771785.95750085231
538879686338.37391360972457.6260863903
549001590629.9056220935-614.905622093458
55113228117986.747390199-4758.74739019891
56118711120499.859214778-1788.85921477847
57117460117195.414722651264.585277349222
58106556110890.555396084-4334.55539608361
599734798582.3318794162-1235.33187941618
609265794764.2323703424-2107.23237034245
619311890080.18970476573037.81029523433
628903788579.1159120853457.884087914703
638357084202.430136789-632.430136789088
648169379848.96652538671844.03347461326
657595677346.4914324392-1390.49143243923
667399376760.1513256966-2767.15132569664
679708895723.33235288991364.66764711009
68102394102503.882472263-109.882472262689
6996549100407.271713637-3858.27171363732
708972790135.1862383517-408.1862383517
718233682353.0623957618-17.0623957618373
728265379599.71774726793053.28225273211
738230380295.02558408082007.97441591919
747959678167.00595790151428.99404209854
757447275251.5873104856-779.587310485585
767356271113.65640497522448.34359502481
776661869682.3948193388-3064.39481933876
786902967174.84647231611854.15352768388
798989989683.6638490101215.336150989882
809377495210.2299628217-1436.22996282167
819030592115.9084799315-1810.90847993149
828379984634.4137413348-835.413741334778
838032077177.46839068753142.5316093125
848249778247.51417044394249.4858295561







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8580865.730334580777154.217445836384577.2432233252
8677305.92686199271933.200753375782678.6529706083
8773436.891709611866745.944542711480127.8388765123
8870538.597352594262627.283348536478449.911356652
8966990.45714558458042.192503147175938.7217880208
9068031.400016790357533.420306831278529.3797267493
9188779.367422185573558.2529477566104000.481896614
9294422.523673677676648.7716941604112196.275653195
9393291.493801789374135.0657599713112447.921843607
9488125.508563053668462.6563421975107788.360783910
9581897.511731033962096.8385146462101698.184947422
9680188.023869528659597.0776465497100778.970092507

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 80865.7303345807 & 77154.2174458363 & 84577.2432233252 \tabularnewline
86 & 77305.926861992 & 71933.2007533757 & 82678.6529706083 \tabularnewline
87 & 73436.8917096118 & 66745.9445427114 & 80127.8388765123 \tabularnewline
88 & 70538.5973525942 & 62627.2833485364 & 78449.911356652 \tabularnewline
89 & 66990.457145584 & 58042.1925031471 & 75938.7217880208 \tabularnewline
90 & 68031.4000167903 & 57533.4203068312 & 78529.3797267493 \tabularnewline
91 & 88779.3674221855 & 73558.2529477566 & 104000.481896614 \tabularnewline
92 & 94422.5236736776 & 76648.7716941604 & 112196.275653195 \tabularnewline
93 & 93291.4938017893 & 74135.0657599713 & 112447.921843607 \tabularnewline
94 & 88125.5085630536 & 68462.6563421975 & 107788.360783910 \tabularnewline
95 & 81897.5117310339 & 62096.8385146462 & 101698.184947422 \tabularnewline
96 & 80188.0238695286 & 59597.0776465497 & 100778.970092507 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72493&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]80865.7303345807[/C][C]77154.2174458363[/C][C]84577.2432233252[/C][/ROW]
[ROW][C]86[/C][C]77305.926861992[/C][C]71933.2007533757[/C][C]82678.6529706083[/C][/ROW]
[ROW][C]87[/C][C]73436.8917096118[/C][C]66745.9445427114[/C][C]80127.8388765123[/C][/ROW]
[ROW][C]88[/C][C]70538.5973525942[/C][C]62627.2833485364[/C][C]78449.911356652[/C][/ROW]
[ROW][C]89[/C][C]66990.457145584[/C][C]58042.1925031471[/C][C]75938.7217880208[/C][/ROW]
[ROW][C]90[/C][C]68031.4000167903[/C][C]57533.4203068312[/C][C]78529.3797267493[/C][/ROW]
[ROW][C]91[/C][C]88779.3674221855[/C][C]73558.2529477566[/C][C]104000.481896614[/C][/ROW]
[ROW][C]92[/C][C]94422.5236736776[/C][C]76648.7716941604[/C][C]112196.275653195[/C][/ROW]
[ROW][C]93[/C][C]93291.4938017893[/C][C]74135.0657599713[/C][C]112447.921843607[/C][/ROW]
[ROW][C]94[/C][C]88125.5085630536[/C][C]68462.6563421975[/C][C]107788.360783910[/C][/ROW]
[ROW][C]95[/C][C]81897.5117310339[/C][C]62096.8385146462[/C][C]101698.184947422[/C][/ROW]
[ROW][C]96[/C][C]80188.0238695286[/C][C]59597.0776465497[/C][C]100778.970092507[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72493&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72493&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
8580865.730334580777154.217445836384577.2432233252
8677305.92686199271933.200753375782678.6529706083
8773436.891709611866745.944542711480127.8388765123
8870538.597352594262627.283348536478449.911356652
8966990.45714558458042.192503147175938.7217880208
9068031.400016790357533.420306831278529.3797267493
9188779.367422185573558.2529477566104000.481896614
9294422.523673677676648.7716941604112196.275653195
9393291.493801789374135.0657599713112447.921843607
9488125.508563053668462.6563421975107788.360783910
9581897.511731033962096.8385146462101698.184947422
9680188.023869528659597.0776465497100778.970092507



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')