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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 10:04:23 +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/Apr/25/t1461575083gp4yayuop8efvty.htm/, Retrieved Mon, 06 May 2024 05:05:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294668, Retrieved Mon, 06 May 2024 05:05:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 09:04:23] [133a6e874753017b0ae749fb238aa045] [Current]
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Dataseries X:
109337
109078
108293
106534
99197
103493
130676
137448
134704
123725
118277
121225
120528
118240
112514
107304
100001
102082
130455
135574
132540
119920
112454
109415
109843
106365
102304
97968
92462
92286
120092
126656
124144
114045
108120
105698
111203
110030
104009
99772
96301
97680
121563
134210
133111
124527
117589
115699
117830
115874
111267
107985
102185
102101
128932
135782
136971
126292
119260
117359
119818
116059
110046
104100
97981
97527
123700
129678
130790
120961
114232
110518
110959
108443
103977
97126
90860
91959
113735
119713
121905
112442
106728
104906




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294668&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294668&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294668&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294668&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]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294668&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294668&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2109078109337-259
3108293109078.017121703-785.017121702986
4106534108293.051895097-1759.05189509652
599197106534.116285576-7337.11628557566
610349399197.48503446274295.51496553727
7130676103492.71603655827183.2839634418
8137448130674.2029956986773.79700430238
9134704137447.552204863-2743.55220486323
10123725134704.1813679-10979.1813678996
11118277123725.725800318-5448.72580031837
12121225118277.3601987062947.63980129409
13120528121224.80514049-696.805140489581
14118240120528.04606367-2288.04606367048
15112514118240.151255773-5726.1512557727
16107304112514.37853846-5210.37853845976
17100001107304.344442293-7303.34444229267
18102082100001.4828019092080.51719809121
19130455102081.8624633328373.13753667
20135574130453.1243380935120.87566190657
21132540135573.661474471-3033.66147447054
22119920132540.200546142-12620.2005461418
23112454119920.83428311-7466.83428310975
24109415112454.493609725-3039.49360972538
25109843109415.200931687427.799068313412
26106365109842.971719504-3477.97171950352
27102304106365.229918142-4061.22991814204
2897968102304.268475569-4336.26847556925
299246297968.2866575325-5506.28665753253
309228692462.3640038793-176.364003879266
3112009292286.011658888427805.9883411116
32126656120090.1618306036565.83816939662
33124144126655.56595239-2511.56595238989
34114045124144.166031993-10099.1660319933
35108120114045.667625179-5925.66762517855
36105698108120.391727881-2422.39172788068
37111203105698.1601369565504.83986304367
38110030111202.636091764-1172.63609176392
39104009110030.077519409-6021.07751940879
4099772104009.398035139-4237.39803513887
419630199772.2801215081-3471.28012150814
429768096301.22947578081378.77052421917
4312156397679.908853670223883.0911463298
44134210121561.42116141712648.5788385834
45133111134209.163840888-1098.16384088754
46124527133111.072596275-8584.07259627458
47117589124527.567466955-6938.56746695536
48115699117589.458687611-1890.45868761138
49117830115699.1249724792130.87502752061
50115874117829.859134327-1955.85913432691
51111267115874.129295904-4607.1292959042
52107985111267.304563318-3282.30456331831
53102185107985.216983181-5800.21698318092
54102101102185.38343472-84.3834347199445
55128932102101.00557833226830.9944216675
56135782128930.2262844896851.77371551127
57136971135781.547050061189.4529499402
58126292136970.92136888-10678.9213688798
59119260126292.705951042-7032.70595104221
60117359119260.464910821-1901.4649108205
61119818117359.1257000672458.87429993264
62116059119817.837451292-3758.83745129168
63110046116059.248485322-6013.24848532212
64104100110046.397517585-5946.39751758522
6597981104100.393098271-6119.39309827088
669752797981.4045344831-454.404534483052
6712370097527.03003930326172.969960697
68129678123698.2697844865979.73021551366
69130790129677.6046982061112.39530179425
70120961130789.926462927-9828.92646292679
71114232120961.649760462-6729.64976046182
72110518114232.444876697-3714.44487669662
73110959110518.245550664440.754449336091
74108443110958.970863063-2515.97086306266
75103977108443.166323189-4466.16632318861
7697126103977.295244685-6851.29524468452
779086097126.45291831-6266.45291830995
789195990860.41425616091098.58574383912
7911373591958.927375834721776.0726241653
80119713113733.5604500095979.43954999137
81121905119712.6047174212192.39528257924
82112442121904.85506741-9462.85506740979
83106728112442.625560594-5714.62556059421
84104906106728.377776531-1822.37777653108

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 109078 & 109337 & -259 \tabularnewline
3 & 108293 & 109078.017121703 & -785.017121702986 \tabularnewline
4 & 106534 & 108293.051895097 & -1759.05189509652 \tabularnewline
5 & 99197 & 106534.116285576 & -7337.11628557566 \tabularnewline
6 & 103493 & 99197.4850344627 & 4295.51496553727 \tabularnewline
7 & 130676 & 103492.716036558 & 27183.2839634418 \tabularnewline
8 & 137448 & 130674.202995698 & 6773.79700430238 \tabularnewline
9 & 134704 & 137447.552204863 & -2743.55220486323 \tabularnewline
10 & 123725 & 134704.1813679 & -10979.1813678996 \tabularnewline
11 & 118277 & 123725.725800318 & -5448.72580031837 \tabularnewline
12 & 121225 & 118277.360198706 & 2947.63980129409 \tabularnewline
13 & 120528 & 121224.80514049 & -696.805140489581 \tabularnewline
14 & 118240 & 120528.04606367 & -2288.04606367048 \tabularnewline
15 & 112514 & 118240.151255773 & -5726.1512557727 \tabularnewline
16 & 107304 & 112514.37853846 & -5210.37853845976 \tabularnewline
17 & 100001 & 107304.344442293 & -7303.34444229267 \tabularnewline
18 & 102082 & 100001.482801909 & 2080.51719809121 \tabularnewline
19 & 130455 & 102081.86246333 & 28373.13753667 \tabularnewline
20 & 135574 & 130453.124338093 & 5120.87566190657 \tabularnewline
21 & 132540 & 135573.661474471 & -3033.66147447054 \tabularnewline
22 & 119920 & 132540.200546142 & -12620.2005461418 \tabularnewline
23 & 112454 & 119920.83428311 & -7466.83428310975 \tabularnewline
24 & 109415 & 112454.493609725 & -3039.49360972538 \tabularnewline
25 & 109843 & 109415.200931687 & 427.799068313412 \tabularnewline
26 & 106365 & 109842.971719504 & -3477.97171950352 \tabularnewline
27 & 102304 & 106365.229918142 & -4061.22991814204 \tabularnewline
28 & 97968 & 102304.268475569 & -4336.26847556925 \tabularnewline
29 & 92462 & 97968.2866575325 & -5506.28665753253 \tabularnewline
30 & 92286 & 92462.3640038793 & -176.364003879266 \tabularnewline
31 & 120092 & 92286.0116588884 & 27805.9883411116 \tabularnewline
32 & 126656 & 120090.161830603 & 6565.83816939662 \tabularnewline
33 & 124144 & 126655.56595239 & -2511.56595238989 \tabularnewline
34 & 114045 & 124144.166031993 & -10099.1660319933 \tabularnewline
35 & 108120 & 114045.667625179 & -5925.66762517855 \tabularnewline
36 & 105698 & 108120.391727881 & -2422.39172788068 \tabularnewline
37 & 111203 & 105698.160136956 & 5504.83986304367 \tabularnewline
38 & 110030 & 111202.636091764 & -1172.63609176392 \tabularnewline
39 & 104009 & 110030.077519409 & -6021.07751940879 \tabularnewline
40 & 99772 & 104009.398035139 & -4237.39803513887 \tabularnewline
41 & 96301 & 99772.2801215081 & -3471.28012150814 \tabularnewline
42 & 97680 & 96301.2294757808 & 1378.77052421917 \tabularnewline
43 & 121563 & 97679.9088536702 & 23883.0911463298 \tabularnewline
44 & 134210 & 121561.421161417 & 12648.5788385834 \tabularnewline
45 & 133111 & 134209.163840888 & -1098.16384088754 \tabularnewline
46 & 124527 & 133111.072596275 & -8584.07259627458 \tabularnewline
47 & 117589 & 124527.567466955 & -6938.56746695536 \tabularnewline
48 & 115699 & 117589.458687611 & -1890.45868761138 \tabularnewline
49 & 117830 & 115699.124972479 & 2130.87502752061 \tabularnewline
50 & 115874 & 117829.859134327 & -1955.85913432691 \tabularnewline
51 & 111267 & 115874.129295904 & -4607.1292959042 \tabularnewline
52 & 107985 & 111267.304563318 & -3282.30456331831 \tabularnewline
53 & 102185 & 107985.216983181 & -5800.21698318092 \tabularnewline
54 & 102101 & 102185.38343472 & -84.3834347199445 \tabularnewline
55 & 128932 & 102101.005578332 & 26830.9944216675 \tabularnewline
56 & 135782 & 128930.226284489 & 6851.77371551127 \tabularnewline
57 & 136971 & 135781.54705006 & 1189.4529499402 \tabularnewline
58 & 126292 & 136970.92136888 & -10678.9213688798 \tabularnewline
59 & 119260 & 126292.705951042 & -7032.70595104221 \tabularnewline
60 & 117359 & 119260.464910821 & -1901.4649108205 \tabularnewline
61 & 119818 & 117359.125700067 & 2458.87429993264 \tabularnewline
62 & 116059 & 119817.837451292 & -3758.83745129168 \tabularnewline
63 & 110046 & 116059.248485322 & -6013.24848532212 \tabularnewline
64 & 104100 & 110046.397517585 & -5946.39751758522 \tabularnewline
65 & 97981 & 104100.393098271 & -6119.39309827088 \tabularnewline
66 & 97527 & 97981.4045344831 & -454.404534483052 \tabularnewline
67 & 123700 & 97527.030039303 & 26172.969960697 \tabularnewline
68 & 129678 & 123698.269784486 & 5979.73021551366 \tabularnewline
69 & 130790 & 129677.604698206 & 1112.39530179425 \tabularnewline
70 & 120961 & 130789.926462927 & -9828.92646292679 \tabularnewline
71 & 114232 & 120961.649760462 & -6729.64976046182 \tabularnewline
72 & 110518 & 114232.444876697 & -3714.44487669662 \tabularnewline
73 & 110959 & 110518.245550664 & 440.754449336091 \tabularnewline
74 & 108443 & 110958.970863063 & -2515.97086306266 \tabularnewline
75 & 103977 & 108443.166323189 & -4466.16632318861 \tabularnewline
76 & 97126 & 103977.295244685 & -6851.29524468452 \tabularnewline
77 & 90860 & 97126.45291831 & -6266.45291830995 \tabularnewline
78 & 91959 & 90860.4142561609 & 1098.58574383912 \tabularnewline
79 & 113735 & 91958.9273758347 & 21776.0726241653 \tabularnewline
80 & 119713 & 113733.560450009 & 5979.43954999137 \tabularnewline
81 & 121905 & 119712.604717421 & 2192.39528257924 \tabularnewline
82 & 112442 & 121904.85506741 & -9462.85506740979 \tabularnewline
83 & 106728 & 112442.625560594 & -5714.62556059421 \tabularnewline
84 & 104906 & 106728.377776531 & -1822.37777653108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294668&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]2[/C][C]109078[/C][C]109337[/C][C]-259[/C][/ROW]
[ROW][C]3[/C][C]108293[/C][C]109078.017121703[/C][C]-785.017121702986[/C][/ROW]
[ROW][C]4[/C][C]106534[/C][C]108293.051895097[/C][C]-1759.05189509652[/C][/ROW]
[ROW][C]5[/C][C]99197[/C][C]106534.116285576[/C][C]-7337.11628557566[/C][/ROW]
[ROW][C]6[/C][C]103493[/C][C]99197.4850344627[/C][C]4295.51496553727[/C][/ROW]
[ROW][C]7[/C][C]130676[/C][C]103492.716036558[/C][C]27183.2839634418[/C][/ROW]
[ROW][C]8[/C][C]137448[/C][C]130674.202995698[/C][C]6773.79700430238[/C][/ROW]
[ROW][C]9[/C][C]134704[/C][C]137447.552204863[/C][C]-2743.55220486323[/C][/ROW]
[ROW][C]10[/C][C]123725[/C][C]134704.1813679[/C][C]-10979.1813678996[/C][/ROW]
[ROW][C]11[/C][C]118277[/C][C]123725.725800318[/C][C]-5448.72580031837[/C][/ROW]
[ROW][C]12[/C][C]121225[/C][C]118277.360198706[/C][C]2947.63980129409[/C][/ROW]
[ROW][C]13[/C][C]120528[/C][C]121224.80514049[/C][C]-696.805140489581[/C][/ROW]
[ROW][C]14[/C][C]118240[/C][C]120528.04606367[/C][C]-2288.04606367048[/C][/ROW]
[ROW][C]15[/C][C]112514[/C][C]118240.151255773[/C][C]-5726.1512557727[/C][/ROW]
[ROW][C]16[/C][C]107304[/C][C]112514.37853846[/C][C]-5210.37853845976[/C][/ROW]
[ROW][C]17[/C][C]100001[/C][C]107304.344442293[/C][C]-7303.34444229267[/C][/ROW]
[ROW][C]18[/C][C]102082[/C][C]100001.482801909[/C][C]2080.51719809121[/C][/ROW]
[ROW][C]19[/C][C]130455[/C][C]102081.86246333[/C][C]28373.13753667[/C][/ROW]
[ROW][C]20[/C][C]135574[/C][C]130453.124338093[/C][C]5120.87566190657[/C][/ROW]
[ROW][C]21[/C][C]132540[/C][C]135573.661474471[/C][C]-3033.66147447054[/C][/ROW]
[ROW][C]22[/C][C]119920[/C][C]132540.200546142[/C][C]-12620.2005461418[/C][/ROW]
[ROW][C]23[/C][C]112454[/C][C]119920.83428311[/C][C]-7466.83428310975[/C][/ROW]
[ROW][C]24[/C][C]109415[/C][C]112454.493609725[/C][C]-3039.49360972538[/C][/ROW]
[ROW][C]25[/C][C]109843[/C][C]109415.200931687[/C][C]427.799068313412[/C][/ROW]
[ROW][C]26[/C][C]106365[/C][C]109842.971719504[/C][C]-3477.97171950352[/C][/ROW]
[ROW][C]27[/C][C]102304[/C][C]106365.229918142[/C][C]-4061.22991814204[/C][/ROW]
[ROW][C]28[/C][C]97968[/C][C]102304.268475569[/C][C]-4336.26847556925[/C][/ROW]
[ROW][C]29[/C][C]92462[/C][C]97968.2866575325[/C][C]-5506.28665753253[/C][/ROW]
[ROW][C]30[/C][C]92286[/C][C]92462.3640038793[/C][C]-176.364003879266[/C][/ROW]
[ROW][C]31[/C][C]120092[/C][C]92286.0116588884[/C][C]27805.9883411116[/C][/ROW]
[ROW][C]32[/C][C]126656[/C][C]120090.161830603[/C][C]6565.83816939662[/C][/ROW]
[ROW][C]33[/C][C]124144[/C][C]126655.56595239[/C][C]-2511.56595238989[/C][/ROW]
[ROW][C]34[/C][C]114045[/C][C]124144.166031993[/C][C]-10099.1660319933[/C][/ROW]
[ROW][C]35[/C][C]108120[/C][C]114045.667625179[/C][C]-5925.66762517855[/C][/ROW]
[ROW][C]36[/C][C]105698[/C][C]108120.391727881[/C][C]-2422.39172788068[/C][/ROW]
[ROW][C]37[/C][C]111203[/C][C]105698.160136956[/C][C]5504.83986304367[/C][/ROW]
[ROW][C]38[/C][C]110030[/C][C]111202.636091764[/C][C]-1172.63609176392[/C][/ROW]
[ROW][C]39[/C][C]104009[/C][C]110030.077519409[/C][C]-6021.07751940879[/C][/ROW]
[ROW][C]40[/C][C]99772[/C][C]104009.398035139[/C][C]-4237.39803513887[/C][/ROW]
[ROW][C]41[/C][C]96301[/C][C]99772.2801215081[/C][C]-3471.28012150814[/C][/ROW]
[ROW][C]42[/C][C]97680[/C][C]96301.2294757808[/C][C]1378.77052421917[/C][/ROW]
[ROW][C]43[/C][C]121563[/C][C]97679.9088536702[/C][C]23883.0911463298[/C][/ROW]
[ROW][C]44[/C][C]134210[/C][C]121561.421161417[/C][C]12648.5788385834[/C][/ROW]
[ROW][C]45[/C][C]133111[/C][C]134209.163840888[/C][C]-1098.16384088754[/C][/ROW]
[ROW][C]46[/C][C]124527[/C][C]133111.072596275[/C][C]-8584.07259627458[/C][/ROW]
[ROW][C]47[/C][C]117589[/C][C]124527.567466955[/C][C]-6938.56746695536[/C][/ROW]
[ROW][C]48[/C][C]115699[/C][C]117589.458687611[/C][C]-1890.45868761138[/C][/ROW]
[ROW][C]49[/C][C]117830[/C][C]115699.124972479[/C][C]2130.87502752061[/C][/ROW]
[ROW][C]50[/C][C]115874[/C][C]117829.859134327[/C][C]-1955.85913432691[/C][/ROW]
[ROW][C]51[/C][C]111267[/C][C]115874.129295904[/C][C]-4607.1292959042[/C][/ROW]
[ROW][C]52[/C][C]107985[/C][C]111267.304563318[/C][C]-3282.30456331831[/C][/ROW]
[ROW][C]53[/C][C]102185[/C][C]107985.216983181[/C][C]-5800.21698318092[/C][/ROW]
[ROW][C]54[/C][C]102101[/C][C]102185.38343472[/C][C]-84.3834347199445[/C][/ROW]
[ROW][C]55[/C][C]128932[/C][C]102101.005578332[/C][C]26830.9944216675[/C][/ROW]
[ROW][C]56[/C][C]135782[/C][C]128930.226284489[/C][C]6851.77371551127[/C][/ROW]
[ROW][C]57[/C][C]136971[/C][C]135781.54705006[/C][C]1189.4529499402[/C][/ROW]
[ROW][C]58[/C][C]126292[/C][C]136970.92136888[/C][C]-10678.9213688798[/C][/ROW]
[ROW][C]59[/C][C]119260[/C][C]126292.705951042[/C][C]-7032.70595104221[/C][/ROW]
[ROW][C]60[/C][C]117359[/C][C]119260.464910821[/C][C]-1901.4649108205[/C][/ROW]
[ROW][C]61[/C][C]119818[/C][C]117359.125700067[/C][C]2458.87429993264[/C][/ROW]
[ROW][C]62[/C][C]116059[/C][C]119817.837451292[/C][C]-3758.83745129168[/C][/ROW]
[ROW][C]63[/C][C]110046[/C][C]116059.248485322[/C][C]-6013.24848532212[/C][/ROW]
[ROW][C]64[/C][C]104100[/C][C]110046.397517585[/C][C]-5946.39751758522[/C][/ROW]
[ROW][C]65[/C][C]97981[/C][C]104100.393098271[/C][C]-6119.39309827088[/C][/ROW]
[ROW][C]66[/C][C]97527[/C][C]97981.4045344831[/C][C]-454.404534483052[/C][/ROW]
[ROW][C]67[/C][C]123700[/C][C]97527.030039303[/C][C]26172.969960697[/C][/ROW]
[ROW][C]68[/C][C]129678[/C][C]123698.269784486[/C][C]5979.73021551366[/C][/ROW]
[ROW][C]69[/C][C]130790[/C][C]129677.604698206[/C][C]1112.39530179425[/C][/ROW]
[ROW][C]70[/C][C]120961[/C][C]130789.926462927[/C][C]-9828.92646292679[/C][/ROW]
[ROW][C]71[/C][C]114232[/C][C]120961.649760462[/C][C]-6729.64976046182[/C][/ROW]
[ROW][C]72[/C][C]110518[/C][C]114232.444876697[/C][C]-3714.44487669662[/C][/ROW]
[ROW][C]73[/C][C]110959[/C][C]110518.245550664[/C][C]440.754449336091[/C][/ROW]
[ROW][C]74[/C][C]108443[/C][C]110958.970863063[/C][C]-2515.97086306266[/C][/ROW]
[ROW][C]75[/C][C]103977[/C][C]108443.166323189[/C][C]-4466.16632318861[/C][/ROW]
[ROW][C]76[/C][C]97126[/C][C]103977.295244685[/C][C]-6851.29524468452[/C][/ROW]
[ROW][C]77[/C][C]90860[/C][C]97126.45291831[/C][C]-6266.45291830995[/C][/ROW]
[ROW][C]78[/C][C]91959[/C][C]90860.4142561609[/C][C]1098.58574383912[/C][/ROW]
[ROW][C]79[/C][C]113735[/C][C]91958.9273758347[/C][C]21776.0726241653[/C][/ROW]
[ROW][C]80[/C][C]119713[/C][C]113733.560450009[/C][C]5979.43954999137[/C][/ROW]
[ROW][C]81[/C][C]121905[/C][C]119712.604717421[/C][C]2192.39528257924[/C][/ROW]
[ROW][C]82[/C][C]112442[/C][C]121904.85506741[/C][C]-9462.85506740979[/C][/ROW]
[ROW][C]83[/C][C]106728[/C][C]112442.625560594[/C][C]-5714.62556059421[/C][/ROW]
[ROW][C]84[/C][C]104906[/C][C]106728.377776531[/C][C]-1822.37777653108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294668&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294668&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
2109078109337-259
3108293109078.017121703-785.017121702986
4106534108293.051895097-1759.05189509652
599197106534.116285576-7337.11628557566
610349399197.48503446274295.51496553727
7130676103492.71603655827183.2839634418
8137448130674.2029956986773.79700430238
9134704137447.552204863-2743.55220486323
10123725134704.1813679-10979.1813678996
11118277123725.725800318-5448.72580031837
12121225118277.3601987062947.63980129409
13120528121224.80514049-696.805140489581
14118240120528.04606367-2288.04606367048
15112514118240.151255773-5726.1512557727
16107304112514.37853846-5210.37853845976
17100001107304.344442293-7303.34444229267
18102082100001.4828019092080.51719809121
19130455102081.8624633328373.13753667
20135574130453.1243380935120.87566190657
21132540135573.661474471-3033.66147447054
22119920132540.200546142-12620.2005461418
23112454119920.83428311-7466.83428310975
24109415112454.493609725-3039.49360972538
25109843109415.200931687427.799068313412
26106365109842.971719504-3477.97171950352
27102304106365.229918142-4061.22991814204
2897968102304.268475569-4336.26847556925
299246297968.2866575325-5506.28665753253
309228692462.3640038793-176.364003879266
3112009292286.011658888427805.9883411116
32126656120090.1618306036565.83816939662
33124144126655.56595239-2511.56595238989
34114045124144.166031993-10099.1660319933
35108120114045.667625179-5925.66762517855
36105698108120.391727881-2422.39172788068
37111203105698.1601369565504.83986304367
38110030111202.636091764-1172.63609176392
39104009110030.077519409-6021.07751940879
4099772104009.398035139-4237.39803513887
419630199772.2801215081-3471.28012150814
429768096301.22947578081378.77052421917
4312156397679.908853670223883.0911463298
44134210121561.42116141712648.5788385834
45133111134209.163840888-1098.16384088754
46124527133111.072596275-8584.07259627458
47117589124527.567466955-6938.56746695536
48115699117589.458687611-1890.45868761138
49117830115699.1249724792130.87502752061
50115874117829.859134327-1955.85913432691
51111267115874.129295904-4607.1292959042
52107985111267.304563318-3282.30456331831
53102185107985.216983181-5800.21698318092
54102101102185.38343472-84.3834347199445
55128932102101.00557833226830.9944216675
56135782128930.2262844896851.77371551127
57136971135781.547050061189.4529499402
58126292136970.92136888-10678.9213688798
59119260126292.705951042-7032.70595104221
60117359119260.464910821-1901.4649108205
61119818117359.1257000672458.87429993264
62116059119817.837451292-3758.83745129168
63110046116059.248485322-6013.24848532212
64104100110046.397517585-5946.39751758522
6597981104100.393098271-6119.39309827088
669752797981.4045344831-454.404534483052
6712370097527.03003930326172.969960697
68129678123698.2697844865979.73021551366
69130790129677.6046982061112.39530179425
70120961130789.926462927-9828.92646292679
71114232120961.649760462-6729.64976046182
72110518114232.444876697-3714.44487669662
73110959110518.245550664440.754449336091
74108443110958.970863063-2515.97086306266
75103977108443.166323189-4466.16632318861
7697126103977.295244685-6851.29524468452
779086097126.45291831-6266.45291830995
789195990860.41425616091098.58574383912
7911373591958.927375834721776.0726241653
80119713113733.5604500095979.43954999137
81121905119712.6047174212192.39528257924
82112442121904.85506741-9462.85506740979
83106728112442.625560594-5714.62556059421
84104906106728.377776531-1822.37777653108







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85104906.12047185786815.308246609122996.932697105
86104906.12047185779322.6941038302130489.546839884
87104906.12047185773573.2954717502136238.945471964
88104906.12047185768726.2898994734141085.951044241
89104906.12047185764455.9738960354145356.267047679
90104906.12047185760595.3026531288149216.938290586
91104906.12047185757045.0424070705152767.198536644
92104906.12047185753740.5362253866156071.704718328
93104906.12047185750636.8729273984159175.368016316
94104906.12047185747701.3527789383162110.888164776
95104906.12047185744909.2900175749164902.95092614
96104906.12047185742241.5061961835167570.734747531

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 104906.120471857 & 86815.308246609 & 122996.932697105 \tabularnewline
86 & 104906.120471857 & 79322.6941038302 & 130489.546839884 \tabularnewline
87 & 104906.120471857 & 73573.2954717502 & 136238.945471964 \tabularnewline
88 & 104906.120471857 & 68726.2898994734 & 141085.951044241 \tabularnewline
89 & 104906.120471857 & 64455.9738960354 & 145356.267047679 \tabularnewline
90 & 104906.120471857 & 60595.3026531288 & 149216.938290586 \tabularnewline
91 & 104906.120471857 & 57045.0424070705 & 152767.198536644 \tabularnewline
92 & 104906.120471857 & 53740.5362253866 & 156071.704718328 \tabularnewline
93 & 104906.120471857 & 50636.8729273984 & 159175.368016316 \tabularnewline
94 & 104906.120471857 & 47701.3527789383 & 162110.888164776 \tabularnewline
95 & 104906.120471857 & 44909.2900175749 & 164902.95092614 \tabularnewline
96 & 104906.120471857 & 42241.5061961835 & 167570.734747531 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294668&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]104906.120471857[/C][C]86815.308246609[/C][C]122996.932697105[/C][/ROW]
[ROW][C]86[/C][C]104906.120471857[/C][C]79322.6941038302[/C][C]130489.546839884[/C][/ROW]
[ROW][C]87[/C][C]104906.120471857[/C][C]73573.2954717502[/C][C]136238.945471964[/C][/ROW]
[ROW][C]88[/C][C]104906.120471857[/C][C]68726.2898994734[/C][C]141085.951044241[/C][/ROW]
[ROW][C]89[/C][C]104906.120471857[/C][C]64455.9738960354[/C][C]145356.267047679[/C][/ROW]
[ROW][C]90[/C][C]104906.120471857[/C][C]60595.3026531288[/C][C]149216.938290586[/C][/ROW]
[ROW][C]91[/C][C]104906.120471857[/C][C]57045.0424070705[/C][C]152767.198536644[/C][/ROW]
[ROW][C]92[/C][C]104906.120471857[/C][C]53740.5362253866[/C][C]156071.704718328[/C][/ROW]
[ROW][C]93[/C][C]104906.120471857[/C][C]50636.8729273984[/C][C]159175.368016316[/C][/ROW]
[ROW][C]94[/C][C]104906.120471857[/C][C]47701.3527789383[/C][C]162110.888164776[/C][/ROW]
[ROW][C]95[/C][C]104906.120471857[/C][C]44909.2900175749[/C][C]164902.95092614[/C][/ROW]
[ROW][C]96[/C][C]104906.120471857[/C][C]42241.5061961835[/C][C]167570.734747531[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294668&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294668&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
85104906.12047185786815.308246609122996.932697105
86104906.12047185779322.6941038302130489.546839884
87104906.12047185773573.2954717502136238.945471964
88104906.12047185768726.2898994734141085.951044241
89104906.12047185764455.9738960354145356.267047679
90104906.12047185760595.3026531288149216.938290586
91104906.12047185757045.0424070705152767.198536644
92104906.12047185753740.5362253866156071.704718328
93104906.12047185750636.8729273984159175.368016316
94104906.12047185747701.3527789383162110.888164776
95104906.12047185744909.2900175749164902.95092614
96104906.12047185742241.5061961835167570.734747531



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
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')