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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 computationFri, 20 May 2011 07:31:36 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/20/t1305876603nzk4u5dqdxnftlb.htm/, Retrieved Mon, 13 May 2024 16:24:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122425, Retrieved Mon, 13 May 2024 16:24:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2011-05-20 07:31:36] [91b501704ec53ded4f914c1fb409b978] [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 time4 seconds
R Server'George Udny Yule' @ 216.218.223.82

\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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ 216.218.223.82 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122425&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 216.218.223.82[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122425&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122425&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 time4 seconds
R Server'George Udny Yule' @ 216.218.223.82







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.092298193665188
gamma0.433108278636975

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.092298193665188 \tabularnewline
gamma & 0.433108278636975 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122425&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]0.092298193665188[/C][/ROW]
[ROW][C]gamma[/C][C]0.433108278636975[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122425&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122425&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
beta0.092298193665188
gamma0.433108278636975







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310139796474.22628105124922.77371894875
149799498326.3999195871-332.399919587129
159404494389.11813641-345.118136410005
169115991555.113130523-396.113130523067
178723987704.6233374812-465.623337481185
188923589703.7044533642-468.704453364247
19118647117845.772628029801.22737197089
20125620127761.537998258-2141.53799825798
21125154125475.92083626-321.920836260309
22117529119486.218281916-1957.21828191556
23109459110229.333517975-770.333517974723
24108483108092.668042252390.331957748058
25107137107271.619819757-134.619819757208
26104699103305.305135241393.69486475992
27100804100428.855794712375.14420528803
289606697795.7866541242-1729.78665412424
299197192003.6665251494-32.6665251493687
309322894182.4737242576-954.47372425755
31120144122567.956055048-2423.95605504792
32127233128506.074067552-1273.07406755212
33127166126309.573889893856.426110106535
34118194120771.076124286-2577.07612428618
35109940110217.708812814-277.70881281422
36106683107989.967478556-1306.96747855567
37102834104784.426618019-1950.42661801871
389988298332.86085746741549.13914253261
399666695047.23162773841618.76837226162
409254093156.872132615-616.87213261491
418874488121.5113453721622.488654627887
428932190424.0899789227-1103.08997892265
43115870116820.025296034-950.02529603368
44122401123415.21156438-1014.21156438046
45122030121018.4985798321011.50142016841
46113802115442.722074415-1640.72207441457
47105791105773.50500239417.4949976061907
48103076103598.277304962-522.277304961812
4998658100997.683701832-2339.68370183161
509694594064.25539391452880.7446060855
519249792113.386475772383.613524228058
529068788901.04249918831785.95750081171
538879686338.37391360372457.62608639625
549001590629.9056220276-614.905622027596
55113228117986.74739014-4758.74739014011
56118711120499.859214844-1788.85921484396
57117460117195.414722752264.585277247563
58106556110890.555396165-4334.55539616494
599734798582.3318795824-1235.33187958237
609265794764.2323705198-2107.23237051979
619311890080.18970497383037.81029502621
628903788579.115912196457.884087803948
638357084202.4301368743-632.430136874304
648169379848.96652547591844.0334745241
657595677346.4914324739-1390.49143247391
667399376760.1513257628-2767.15132576284
679708895723.33235305591364.66764694414
68102394102503.882472388-109.882472388155
6996549100407.271713753-3858.27171375277
708972790135.186238539-408.186238539056
718233682353.0623959294-17.0623959294317
728265379599.71774741763053.28225258237
738230380295.0255841422007.97441585804
747959678167.00595790821428.99404209181
757447275251.5873104586-779.587310458592
767356271113.65640496972448.3435950303
776661869682.3948192778-3064.39481927778
786902967174.8464723351854.15352766497
798989989683.663848974215.336151025942
809377495210.2299627812-1436.22996278122
819030592115.9084799295-1810.90847992947
828379984634.4137413744-835.413741374417
838032077177.46839073983142.5316092602
848249778247.5141704164249.48582958392

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 101397 & 96474.2262810512 & 4922.77371894875 \tabularnewline
14 & 97994 & 98326.3999195871 & -332.399919587129 \tabularnewline
15 & 94044 & 94389.11813641 & -345.118136410005 \tabularnewline
16 & 91159 & 91555.113130523 & -396.113130523067 \tabularnewline
17 & 87239 & 87704.6233374812 & -465.623337481185 \tabularnewline
18 & 89235 & 89703.7044533642 & -468.704453364247 \tabularnewline
19 & 118647 & 117845.772628029 & 801.22737197089 \tabularnewline
20 & 125620 & 127761.537998258 & -2141.53799825798 \tabularnewline
21 & 125154 & 125475.92083626 & -321.920836260309 \tabularnewline
22 & 117529 & 119486.218281916 & -1957.21828191556 \tabularnewline
23 & 109459 & 110229.333517975 & -770.333517974723 \tabularnewline
24 & 108483 & 108092.668042252 & 390.331957748058 \tabularnewline
25 & 107137 & 107271.619819757 & -134.619819757208 \tabularnewline
26 & 104699 & 103305.30513524 & 1393.69486475992 \tabularnewline
27 & 100804 & 100428.855794712 & 375.14420528803 \tabularnewline
28 & 96066 & 97795.7866541242 & -1729.78665412424 \tabularnewline
29 & 91971 & 92003.6665251494 & -32.6665251493687 \tabularnewline
30 & 93228 & 94182.4737242576 & -954.47372425755 \tabularnewline
31 & 120144 & 122567.956055048 & -2423.95605504792 \tabularnewline
32 & 127233 & 128506.074067552 & -1273.07406755212 \tabularnewline
33 & 127166 & 126309.573889893 & 856.426110106535 \tabularnewline
34 & 118194 & 120771.076124286 & -2577.07612428618 \tabularnewline
35 & 109940 & 110217.708812814 & -277.70881281422 \tabularnewline
36 & 106683 & 107989.967478556 & -1306.96747855567 \tabularnewline
37 & 102834 & 104784.426618019 & -1950.42661801871 \tabularnewline
38 & 99882 & 98332.8608574674 & 1549.13914253261 \tabularnewline
39 & 96666 & 95047.2316277384 & 1618.76837226162 \tabularnewline
40 & 92540 & 93156.872132615 & -616.87213261491 \tabularnewline
41 & 88744 & 88121.5113453721 & 622.488654627887 \tabularnewline
42 & 89321 & 90424.0899789227 & -1103.08997892265 \tabularnewline
43 & 115870 & 116820.025296034 & -950.02529603368 \tabularnewline
44 & 122401 & 123415.21156438 & -1014.21156438046 \tabularnewline
45 & 122030 & 121018.498579832 & 1011.50142016841 \tabularnewline
46 & 113802 & 115442.722074415 & -1640.72207441457 \tabularnewline
47 & 105791 & 105773.505002394 & 17.4949976061907 \tabularnewline
48 & 103076 & 103598.277304962 & -522.277304961812 \tabularnewline
49 & 98658 & 100997.683701832 & -2339.68370183161 \tabularnewline
50 & 96945 & 94064.2553939145 & 2880.7446060855 \tabularnewline
51 & 92497 & 92113.386475772 & 383.613524228058 \tabularnewline
52 & 90687 & 88901.0424991883 & 1785.95750081171 \tabularnewline
53 & 88796 & 86338.3739136037 & 2457.62608639625 \tabularnewline
54 & 90015 & 90629.9056220276 & -614.905622027596 \tabularnewline
55 & 113228 & 117986.74739014 & -4758.74739014011 \tabularnewline
56 & 118711 & 120499.859214844 & -1788.85921484396 \tabularnewline
57 & 117460 & 117195.414722752 & 264.585277247563 \tabularnewline
58 & 106556 & 110890.555396165 & -4334.55539616494 \tabularnewline
59 & 97347 & 98582.3318795824 & -1235.33187958237 \tabularnewline
60 & 92657 & 94764.2323705198 & -2107.23237051979 \tabularnewline
61 & 93118 & 90080.1897049738 & 3037.81029502621 \tabularnewline
62 & 89037 & 88579.115912196 & 457.884087803948 \tabularnewline
63 & 83570 & 84202.4301368743 & -632.430136874304 \tabularnewline
64 & 81693 & 79848.9665254759 & 1844.0334745241 \tabularnewline
65 & 75956 & 77346.4914324739 & -1390.49143247391 \tabularnewline
66 & 73993 & 76760.1513257628 & -2767.15132576284 \tabularnewline
67 & 97088 & 95723.3323530559 & 1364.66764694414 \tabularnewline
68 & 102394 & 102503.882472388 & -109.882472388155 \tabularnewline
69 & 96549 & 100407.271713753 & -3858.27171375277 \tabularnewline
70 & 89727 & 90135.186238539 & -408.186238539056 \tabularnewline
71 & 82336 & 82353.0623959294 & -17.0623959294317 \tabularnewline
72 & 82653 & 79599.7177474176 & 3053.28225258237 \tabularnewline
73 & 82303 & 80295.025584142 & 2007.97441585804 \tabularnewline
74 & 79596 & 78167.0059579082 & 1428.99404209181 \tabularnewline
75 & 74472 & 75251.5873104586 & -779.587310458592 \tabularnewline
76 & 73562 & 71113.6564049697 & 2448.3435950303 \tabularnewline
77 & 66618 & 69682.3948192778 & -3064.39481927778 \tabularnewline
78 & 69029 & 67174.846472335 & 1854.15352766497 \tabularnewline
79 & 89899 & 89683.663848974 & 215.336151025942 \tabularnewline
80 & 93774 & 95210.2299627812 & -1436.22996278122 \tabularnewline
81 & 90305 & 92115.9084799295 & -1810.90847992947 \tabularnewline
82 & 83799 & 84634.4137413744 & -835.413741374417 \tabularnewline
83 & 80320 & 77177.4683907398 & 3142.5316092602 \tabularnewline
84 & 82497 & 78247.514170416 & 4249.48582958392 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122425&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]98326.3999195871[/C][C]-332.399919587129[/C][/ROW]
[ROW][C]15[/C][C]94044[/C][C]94389.11813641[/C][C]-345.118136410005[/C][/ROW]
[ROW][C]16[/C][C]91159[/C][C]91555.113130523[/C][C]-396.113130523067[/C][/ROW]
[ROW][C]17[/C][C]87239[/C][C]87704.6233374812[/C][C]-465.623337481185[/C][/ROW]
[ROW][C]18[/C][C]89235[/C][C]89703.7044533642[/C][C]-468.704453364247[/C][/ROW]
[ROW][C]19[/C][C]118647[/C][C]117845.772628029[/C][C]801.22737197089[/C][/ROW]
[ROW][C]20[/C][C]125620[/C][C]127761.537998258[/C][C]-2141.53799825798[/C][/ROW]
[ROW][C]21[/C][C]125154[/C][C]125475.92083626[/C][C]-321.920836260309[/C][/ROW]
[ROW][C]22[/C][C]117529[/C][C]119486.218281916[/C][C]-1957.21828191556[/C][/ROW]
[ROW][C]23[/C][C]109459[/C][C]110229.333517975[/C][C]-770.333517974723[/C][/ROW]
[ROW][C]24[/C][C]108483[/C][C]108092.668042252[/C][C]390.331957748058[/C][/ROW]
[ROW][C]25[/C][C]107137[/C][C]107271.619819757[/C][C]-134.619819757208[/C][/ROW]
[ROW][C]26[/C][C]104699[/C][C]103305.30513524[/C][C]1393.69486475992[/C][/ROW]
[ROW][C]27[/C][C]100804[/C][C]100428.855794712[/C][C]375.14420528803[/C][/ROW]
[ROW][C]28[/C][C]96066[/C][C]97795.7866541242[/C][C]-1729.78665412424[/C][/ROW]
[ROW][C]29[/C][C]91971[/C][C]92003.6665251494[/C][C]-32.6665251493687[/C][/ROW]
[ROW][C]30[/C][C]93228[/C][C]94182.4737242576[/C][C]-954.47372425755[/C][/ROW]
[ROW][C]31[/C][C]120144[/C][C]122567.956055048[/C][C]-2423.95605504792[/C][/ROW]
[ROW][C]32[/C][C]127233[/C][C]128506.074067552[/C][C]-1273.07406755212[/C][/ROW]
[ROW][C]33[/C][C]127166[/C][C]126309.573889893[/C][C]856.426110106535[/C][/ROW]
[ROW][C]34[/C][C]118194[/C][C]120771.076124286[/C][C]-2577.07612428618[/C][/ROW]
[ROW][C]35[/C][C]109940[/C][C]110217.708812814[/C][C]-277.70881281422[/C][/ROW]
[ROW][C]36[/C][C]106683[/C][C]107989.967478556[/C][C]-1306.96747855567[/C][/ROW]
[ROW][C]37[/C][C]102834[/C][C]104784.426618019[/C][C]-1950.42661801871[/C][/ROW]
[ROW][C]38[/C][C]99882[/C][C]98332.8608574674[/C][C]1549.13914253261[/C][/ROW]
[ROW][C]39[/C][C]96666[/C][C]95047.2316277384[/C][C]1618.76837226162[/C][/ROW]
[ROW][C]40[/C][C]92540[/C][C]93156.872132615[/C][C]-616.87213261491[/C][/ROW]
[ROW][C]41[/C][C]88744[/C][C]88121.5113453721[/C][C]622.488654627887[/C][/ROW]
[ROW][C]42[/C][C]89321[/C][C]90424.0899789227[/C][C]-1103.08997892265[/C][/ROW]
[ROW][C]43[/C][C]115870[/C][C]116820.025296034[/C][C]-950.02529603368[/C][/ROW]
[ROW][C]44[/C][C]122401[/C][C]123415.21156438[/C][C]-1014.21156438046[/C][/ROW]
[ROW][C]45[/C][C]122030[/C][C]121018.498579832[/C][C]1011.50142016841[/C][/ROW]
[ROW][C]46[/C][C]113802[/C][C]115442.722074415[/C][C]-1640.72207441457[/C][/ROW]
[ROW][C]47[/C][C]105791[/C][C]105773.505002394[/C][C]17.4949976061907[/C][/ROW]
[ROW][C]48[/C][C]103076[/C][C]103598.277304962[/C][C]-522.277304961812[/C][/ROW]
[ROW][C]49[/C][C]98658[/C][C]100997.683701832[/C][C]-2339.68370183161[/C][/ROW]
[ROW][C]50[/C][C]96945[/C][C]94064.2553939145[/C][C]2880.7446060855[/C][/ROW]
[ROW][C]51[/C][C]92497[/C][C]92113.386475772[/C][C]383.613524228058[/C][/ROW]
[ROW][C]52[/C][C]90687[/C][C]88901.0424991883[/C][C]1785.95750081171[/C][/ROW]
[ROW][C]53[/C][C]88796[/C][C]86338.3739136037[/C][C]2457.62608639625[/C][/ROW]
[ROW][C]54[/C][C]90015[/C][C]90629.9056220276[/C][C]-614.905622027596[/C][/ROW]
[ROW][C]55[/C][C]113228[/C][C]117986.74739014[/C][C]-4758.74739014011[/C][/ROW]
[ROW][C]56[/C][C]118711[/C][C]120499.859214844[/C][C]-1788.85921484396[/C][/ROW]
[ROW][C]57[/C][C]117460[/C][C]117195.414722752[/C][C]264.585277247563[/C][/ROW]
[ROW][C]58[/C][C]106556[/C][C]110890.555396165[/C][C]-4334.55539616494[/C][/ROW]
[ROW][C]59[/C][C]97347[/C][C]98582.3318795824[/C][C]-1235.33187958237[/C][/ROW]
[ROW][C]60[/C][C]92657[/C][C]94764.2323705198[/C][C]-2107.23237051979[/C][/ROW]
[ROW][C]61[/C][C]93118[/C][C]90080.1897049738[/C][C]3037.81029502621[/C][/ROW]
[ROW][C]62[/C][C]89037[/C][C]88579.115912196[/C][C]457.884087803948[/C][/ROW]
[ROW][C]63[/C][C]83570[/C][C]84202.4301368743[/C][C]-632.430136874304[/C][/ROW]
[ROW][C]64[/C][C]81693[/C][C]79848.9665254759[/C][C]1844.0334745241[/C][/ROW]
[ROW][C]65[/C][C]75956[/C][C]77346.4914324739[/C][C]-1390.49143247391[/C][/ROW]
[ROW][C]66[/C][C]73993[/C][C]76760.1513257628[/C][C]-2767.15132576284[/C][/ROW]
[ROW][C]67[/C][C]97088[/C][C]95723.3323530559[/C][C]1364.66764694414[/C][/ROW]
[ROW][C]68[/C][C]102394[/C][C]102503.882472388[/C][C]-109.882472388155[/C][/ROW]
[ROW][C]69[/C][C]96549[/C][C]100407.271713753[/C][C]-3858.27171375277[/C][/ROW]
[ROW][C]70[/C][C]89727[/C][C]90135.186238539[/C][C]-408.186238539056[/C][/ROW]
[ROW][C]71[/C][C]82336[/C][C]82353.0623959294[/C][C]-17.0623959294317[/C][/ROW]
[ROW][C]72[/C][C]82653[/C][C]79599.7177474176[/C][C]3053.28225258237[/C][/ROW]
[ROW][C]73[/C][C]82303[/C][C]80295.025584142[/C][C]2007.97441585804[/C][/ROW]
[ROW][C]74[/C][C]79596[/C][C]78167.0059579082[/C][C]1428.99404209181[/C][/ROW]
[ROW][C]75[/C][C]74472[/C][C]75251.5873104586[/C][C]-779.587310458592[/C][/ROW]
[ROW][C]76[/C][C]73562[/C][C]71113.6564049697[/C][C]2448.3435950303[/C][/ROW]
[ROW][C]77[/C][C]66618[/C][C]69682.3948192778[/C][C]-3064.39481927778[/C][/ROW]
[ROW][C]78[/C][C]69029[/C][C]67174.846472335[/C][C]1854.15352766497[/C][/ROW]
[ROW][C]79[/C][C]89899[/C][C]89683.663848974[/C][C]215.336151025942[/C][/ROW]
[ROW][C]80[/C][C]93774[/C][C]95210.2299627812[/C][C]-1436.22996278122[/C][/ROW]
[ROW][C]81[/C][C]90305[/C][C]92115.9084799295[/C][C]-1810.90847992947[/C][/ROW]
[ROW][C]82[/C][C]83799[/C][C]84634.4137413744[/C][C]-835.413741374417[/C][/ROW]
[ROW][C]83[/C][C]80320[/C][C]77177.4683907398[/C][C]3142.5316092602[/C][/ROW]
[ROW][C]84[/C][C]82497[/C][C]78247.514170416[/C][C]4249.48582958392[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122425&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122425&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
149799498326.3999195871-332.399919587129
159404494389.11813641-345.118136410005
169115991555.113130523-396.113130523067
178723987704.6233374812-465.623337481185
188923589703.7044533642-468.704453364247
19118647117845.772628029801.22737197089
20125620127761.537998258-2141.53799825798
21125154125475.92083626-321.920836260309
22117529119486.218281916-1957.21828191556
23109459110229.333517975-770.333517974723
24108483108092.668042252390.331957748058
25107137107271.619819757-134.619819757208
26104699103305.305135241393.69486475992
27100804100428.855794712375.14420528803
289606697795.7866541242-1729.78665412424
299197192003.6665251494-32.6665251493687
309322894182.4737242576-954.47372425755
31120144122567.956055048-2423.95605504792
32127233128506.074067552-1273.07406755212
33127166126309.573889893856.426110106535
34118194120771.076124286-2577.07612428618
35109940110217.708812814-277.70881281422
36106683107989.967478556-1306.96747855567
37102834104784.426618019-1950.42661801871
389988298332.86085746741549.13914253261
399666695047.23162773841618.76837226162
409254093156.872132615-616.87213261491
418874488121.5113453721622.488654627887
428932190424.0899789227-1103.08997892265
43115870116820.025296034-950.02529603368
44122401123415.21156438-1014.21156438046
45122030121018.4985798321011.50142016841
46113802115442.722074415-1640.72207441457
47105791105773.50500239417.4949976061907
48103076103598.277304962-522.277304961812
4998658100997.683701832-2339.68370183161
509694594064.25539391452880.7446060855
519249792113.386475772383.613524228058
529068788901.04249918831785.95750081171
538879686338.37391360372457.62608639625
549001590629.9056220276-614.905622027596
55113228117986.74739014-4758.74739014011
56118711120499.859214844-1788.85921484396
57117460117195.414722752264.585277247563
58106556110890.555396165-4334.55539616494
599734798582.3318795824-1235.33187958237
609265794764.2323705198-2107.23237051979
619311890080.18970497383037.81029502621
628903788579.115912196457.884087803948
638357084202.4301368743-632.430136874304
648169379848.96652547591844.0334745241
657595677346.4914324739-1390.49143247391
667399376760.1513257628-2767.15132576284
679708895723.33235305591364.66764694414
68102394102503.882472388-109.882472388155
6996549100407.271713753-3858.27171375277
708972790135.186238539-408.186238539056
718233682353.0623959294-17.0623959294317
728265379599.71774741763053.28225258237
738230380295.0255841422007.97441585804
747959678167.00595790821428.99404209181
757447275251.5873104586-779.587310458592
767356271113.65640496972448.3435950303
776661869682.3948192778-3064.39481927778
786902967174.8464723351854.15352766497
798989989683.663848974215.336151025942
809377495210.2299627812-1436.22996278122
819030592115.9084799295-1810.90847992947
828379984634.4137413744-835.413741374417
838032077177.46839073983142.5316092602
848249778247.5141704164249.48582958392







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8580865.730334455277154.217445722484577.243223188
8677305.926861751371933.200753213982678.6529702888
8773436.891709268166745.944542535880127.8388760004
8870538.59735215362627.283348370378449.9113559356
8966990.457145058958042.192503011475938.7217871064
9068031.400016148957533.420306739178529.3797255587
9188779.367421206773558.2529477385104000.481894675
9294422.52367248576648.7716942669112196.275650703
9393291.493800460674135.0657602118112447.921840709
9488125.508561655768462.6563425604107788.360780751
9581897.511729601562096.8385151165101698.184944086
9680188.023867994959597.0776471834100778.970088806

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 80865.7303344552 & 77154.2174457224 & 84577.243223188 \tabularnewline
86 & 77305.9268617513 & 71933.2007532139 & 82678.6529702888 \tabularnewline
87 & 73436.8917092681 & 66745.9445425358 & 80127.8388760004 \tabularnewline
88 & 70538.597352153 & 62627.2833483703 & 78449.9113559356 \tabularnewline
89 & 66990.4571450589 & 58042.1925030114 & 75938.7217871064 \tabularnewline
90 & 68031.4000161489 & 57533.4203067391 & 78529.3797255587 \tabularnewline
91 & 88779.3674212067 & 73558.2529477385 & 104000.481894675 \tabularnewline
92 & 94422.523672485 & 76648.7716942669 & 112196.275650703 \tabularnewline
93 & 93291.4938004606 & 74135.0657602118 & 112447.921840709 \tabularnewline
94 & 88125.5085616557 & 68462.6563425604 & 107788.360780751 \tabularnewline
95 & 81897.5117296015 & 62096.8385151165 & 101698.184944086 \tabularnewline
96 & 80188.0238679949 & 59597.0776471834 & 100778.970088806 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122425&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]80865.7303344552[/C][C]77154.2174457224[/C][C]84577.243223188[/C][/ROW]
[ROW][C]86[/C][C]77305.9268617513[/C][C]71933.2007532139[/C][C]82678.6529702888[/C][/ROW]
[ROW][C]87[/C][C]73436.8917092681[/C][C]66745.9445425358[/C][C]80127.8388760004[/C][/ROW]
[ROW][C]88[/C][C]70538.597352153[/C][C]62627.2833483703[/C][C]78449.9113559356[/C][/ROW]
[ROW][C]89[/C][C]66990.4571450589[/C][C]58042.1925030114[/C][C]75938.7217871064[/C][/ROW]
[ROW][C]90[/C][C]68031.4000161489[/C][C]57533.4203067391[/C][C]78529.3797255587[/C][/ROW]
[ROW][C]91[/C][C]88779.3674212067[/C][C]73558.2529477385[/C][C]104000.481894675[/C][/ROW]
[ROW][C]92[/C][C]94422.523672485[/C][C]76648.7716942669[/C][C]112196.275650703[/C][/ROW]
[ROW][C]93[/C][C]93291.4938004606[/C][C]74135.0657602118[/C][C]112447.921840709[/C][/ROW]
[ROW][C]94[/C][C]88125.5085616557[/C][C]68462.6563425604[/C][C]107788.360780751[/C][/ROW]
[ROW][C]95[/C][C]81897.5117296015[/C][C]62096.8385151165[/C][C]101698.184944086[/C][/ROW]
[ROW][C]96[/C][C]80188.0238679949[/C][C]59597.0776471834[/C][C]100778.970088806[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122425&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122425&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
8580865.730334455277154.217445722484577.243223188
8677305.926861751371933.200753213982678.6529702888
8773436.891709268166745.944542535880127.8388760004
8870538.59735215362627.283348370378449.9113559356
8966990.457145058958042.192503011475938.7217871064
9068031.400016148957533.420306739178529.3797255587
9188779.367421206773558.2529477385104000.481894675
9294422.52367248576648.7716942669112196.275650703
9393291.493800460674135.0657602118112447.921840709
9488125.508561655768462.6563425604107788.360780751
9581897.511729601562096.8385151165101698.184944086
9680188.023867994959597.0776471834100778.970088806



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')