Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 May 2017 08:00:08 +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/2017/May/02/t14937084338snm7lvkljn16v6.htm/, Retrieved Fri, 17 May 2024 05:21:38 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 05:21:38 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
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
105308
102909
97849
93181
87470
86998
106716
115028
116828
108413
102628
99126




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 4 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0319143669934567
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0319143669934567 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.0319143669934567[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
beta0.0319143669934567
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3102304102887-583
49796898807.3939240428-839.393924042815
59246294444.6051982988-1982.60519829883
69228688875.33160839723410.66839160281
712009288808.180931139831283.8190688602
8126656117612.584213869043.41578613971
9124144124465.199104134-321.199104133571
10114045121942.948238046-7897.94823804629
11108120111591.890219482-3471.89021948195
12105698105556.087040856141.912959143592
13111203103138.6161031168064.38389688435
14110030108900.9858103771129.01418962306
15104009107764.017583565-3755.01758356539
1699772101623.178574337-1851.17857433661
179630197327.0993819448-1026.09938194479
189768093823.35206969763856.64793030235
1912156395325.434547109926237.5654528901
20134210120045.78983998814164.2101600117
21133111133144.831641207-33.8316412073036
22124527132044.751925794-7517.75192579383
23117589123220.827631868-5631.82763186828
24115699116103.091417981-404.091417980948
25117830114200.1950961693629.80490383141
26115874116447.038021984-573.038021984117
27111267114472.749876249-3205.74987624932
28107985109763.440398209-1778.44039820947
29102185106424.682598665-4239.68259866502
30102101100489.3758122751611.62418772455
31128932100456.80977805828475.190221942
32135782128196.577449017585.42255099042
33136971135288.6614081021682.33859189769
34126292136531.352179331-10239.3521793314
35119260125525.569736105-6265.56973610497
36117359118293.608044124-934.608044123815
37119818116362.7806200093455.21937999138
38116059118932.051759345-2873.05175934457
39110046115081.360131106-5035.36013110564
40104100108907.659799937-4807.65979993732
4197981102808.226380702-4827.22638070243
429752796535.1685064282991.831493571808
4312370096112.822180709727587.1778192903
44129678123166.2494979486511.7505020517
45130790129352.0678932411437.9321067594
46120961130509.958586207-9548.95858620739
47114232120376.209617482-6144.20961748186
48110518113451.121056865-2933.12105686481
49110959109643.512355021315.48764498021
50108443110126.495310497-1683.49531049705
51103977107556.767623326-3579.76762332609
5297126102976.521605644-5850.52160564395
539086095938.8059120183-5078.80591201829
549195989510.71903625362448.28096374639
5511373590687.854373433723047.1456265663
56119713113199.3894371126513.61056288843
57121905119385.2671950682519.73280493195
58112442121657.68287253-9215.6828725301
59106728111900.570187241-5172.57018724087
60104906106021.490883986-1115.49088398584
61105308104163.8906985361144.10930146354
62102909104602.404222664-1693.404222664
6397849102149.360298834-4300.36029883364
649318196952.1170220526-3771.11702205257
658747092163.7642094355-4693.76420943551
668699886302.9656958748695.034304125176
6710671685853.147275729720862.8527242703
68115028106236.9720141038791.02798589748
69116828114829.5321074941998.4678925058
70108413116693.31194524-8280.31194524028
71102628108014.051031-5386.05103099957
7299126102057.158621751-2931.15862175077

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 102304 & 102887 & -583 \tabularnewline
4 & 97968 & 98807.3939240428 & -839.393924042815 \tabularnewline
5 & 92462 & 94444.6051982988 & -1982.60519829883 \tabularnewline
6 & 92286 & 88875.3316083972 & 3410.66839160281 \tabularnewline
7 & 120092 & 88808.1809311398 & 31283.8190688602 \tabularnewline
8 & 126656 & 117612.58421386 & 9043.41578613971 \tabularnewline
9 & 124144 & 124465.199104134 & -321.199104133571 \tabularnewline
10 & 114045 & 121942.948238046 & -7897.94823804629 \tabularnewline
11 & 108120 & 111591.890219482 & -3471.89021948195 \tabularnewline
12 & 105698 & 105556.087040856 & 141.912959143592 \tabularnewline
13 & 111203 & 103138.616103116 & 8064.38389688435 \tabularnewline
14 & 110030 & 108900.985810377 & 1129.01418962306 \tabularnewline
15 & 104009 & 107764.017583565 & -3755.01758356539 \tabularnewline
16 & 99772 & 101623.178574337 & -1851.17857433661 \tabularnewline
17 & 96301 & 97327.0993819448 & -1026.09938194479 \tabularnewline
18 & 97680 & 93823.3520696976 & 3856.64793030235 \tabularnewline
19 & 121563 & 95325.4345471099 & 26237.5654528901 \tabularnewline
20 & 134210 & 120045.789839988 & 14164.2101600117 \tabularnewline
21 & 133111 & 133144.831641207 & -33.8316412073036 \tabularnewline
22 & 124527 & 132044.751925794 & -7517.75192579383 \tabularnewline
23 & 117589 & 123220.827631868 & -5631.82763186828 \tabularnewline
24 & 115699 & 116103.091417981 & -404.091417980948 \tabularnewline
25 & 117830 & 114200.195096169 & 3629.80490383141 \tabularnewline
26 & 115874 & 116447.038021984 & -573.038021984117 \tabularnewline
27 & 111267 & 114472.749876249 & -3205.74987624932 \tabularnewline
28 & 107985 & 109763.440398209 & -1778.44039820947 \tabularnewline
29 & 102185 & 106424.682598665 & -4239.68259866502 \tabularnewline
30 & 102101 & 100489.375812275 & 1611.62418772455 \tabularnewline
31 & 128932 & 100456.809778058 & 28475.190221942 \tabularnewline
32 & 135782 & 128196.57744901 & 7585.42255099042 \tabularnewline
33 & 136971 & 135288.661408102 & 1682.33859189769 \tabularnewline
34 & 126292 & 136531.352179331 & -10239.3521793314 \tabularnewline
35 & 119260 & 125525.569736105 & -6265.56973610497 \tabularnewline
36 & 117359 & 118293.608044124 & -934.608044123815 \tabularnewline
37 & 119818 & 116362.780620009 & 3455.21937999138 \tabularnewline
38 & 116059 & 118932.051759345 & -2873.05175934457 \tabularnewline
39 & 110046 & 115081.360131106 & -5035.36013110564 \tabularnewline
40 & 104100 & 108907.659799937 & -4807.65979993732 \tabularnewline
41 & 97981 & 102808.226380702 & -4827.22638070243 \tabularnewline
42 & 97527 & 96535.1685064282 & 991.831493571808 \tabularnewline
43 & 123700 & 96112.8221807097 & 27587.1778192903 \tabularnewline
44 & 129678 & 123166.249497948 & 6511.7505020517 \tabularnewline
45 & 130790 & 129352.067893241 & 1437.9321067594 \tabularnewline
46 & 120961 & 130509.958586207 & -9548.95858620739 \tabularnewline
47 & 114232 & 120376.209617482 & -6144.20961748186 \tabularnewline
48 & 110518 & 113451.121056865 & -2933.12105686481 \tabularnewline
49 & 110959 & 109643.51235502 & 1315.48764498021 \tabularnewline
50 & 108443 & 110126.495310497 & -1683.49531049705 \tabularnewline
51 & 103977 & 107556.767623326 & -3579.76762332609 \tabularnewline
52 & 97126 & 102976.521605644 & -5850.52160564395 \tabularnewline
53 & 90860 & 95938.8059120183 & -5078.80591201829 \tabularnewline
54 & 91959 & 89510.7190362536 & 2448.28096374639 \tabularnewline
55 & 113735 & 90687.8543734337 & 23047.1456265663 \tabularnewline
56 & 119713 & 113199.389437112 & 6513.61056288843 \tabularnewline
57 & 121905 & 119385.267195068 & 2519.73280493195 \tabularnewline
58 & 112442 & 121657.68287253 & -9215.6828725301 \tabularnewline
59 & 106728 & 111900.570187241 & -5172.57018724087 \tabularnewline
60 & 104906 & 106021.490883986 & -1115.49088398584 \tabularnewline
61 & 105308 & 104163.890698536 & 1144.10930146354 \tabularnewline
62 & 102909 & 104602.404222664 & -1693.404222664 \tabularnewline
63 & 97849 & 102149.360298834 & -4300.36029883364 \tabularnewline
64 & 93181 & 96952.1170220526 & -3771.11702205257 \tabularnewline
65 & 87470 & 92163.7642094355 & -4693.76420943551 \tabularnewline
66 & 86998 & 86302.9656958748 & 695.034304125176 \tabularnewline
67 & 106716 & 85853.1472757297 & 20862.8527242703 \tabularnewline
68 & 115028 & 106236.972014103 & 8791.02798589748 \tabularnewline
69 & 116828 & 114829.532107494 & 1998.4678925058 \tabularnewline
70 & 108413 & 116693.31194524 & -8280.31194524028 \tabularnewline
71 & 102628 & 108014.051031 & -5386.05103099957 \tabularnewline
72 & 99126 & 102057.158621751 & -2931.15862175077 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]3[/C][C]102304[/C][C]102887[/C][C]-583[/C][/ROW]
[ROW][C]4[/C][C]97968[/C][C]98807.3939240428[/C][C]-839.393924042815[/C][/ROW]
[ROW][C]5[/C][C]92462[/C][C]94444.6051982988[/C][C]-1982.60519829883[/C][/ROW]
[ROW][C]6[/C][C]92286[/C][C]88875.3316083972[/C][C]3410.66839160281[/C][/ROW]
[ROW][C]7[/C][C]120092[/C][C]88808.1809311398[/C][C]31283.8190688602[/C][/ROW]
[ROW][C]8[/C][C]126656[/C][C]117612.58421386[/C][C]9043.41578613971[/C][/ROW]
[ROW][C]9[/C][C]124144[/C][C]124465.199104134[/C][C]-321.199104133571[/C][/ROW]
[ROW][C]10[/C][C]114045[/C][C]121942.948238046[/C][C]-7897.94823804629[/C][/ROW]
[ROW][C]11[/C][C]108120[/C][C]111591.890219482[/C][C]-3471.89021948195[/C][/ROW]
[ROW][C]12[/C][C]105698[/C][C]105556.087040856[/C][C]141.912959143592[/C][/ROW]
[ROW][C]13[/C][C]111203[/C][C]103138.616103116[/C][C]8064.38389688435[/C][/ROW]
[ROW][C]14[/C][C]110030[/C][C]108900.985810377[/C][C]1129.01418962306[/C][/ROW]
[ROW][C]15[/C][C]104009[/C][C]107764.017583565[/C][C]-3755.01758356539[/C][/ROW]
[ROW][C]16[/C][C]99772[/C][C]101623.178574337[/C][C]-1851.17857433661[/C][/ROW]
[ROW][C]17[/C][C]96301[/C][C]97327.0993819448[/C][C]-1026.09938194479[/C][/ROW]
[ROW][C]18[/C][C]97680[/C][C]93823.3520696976[/C][C]3856.64793030235[/C][/ROW]
[ROW][C]19[/C][C]121563[/C][C]95325.4345471099[/C][C]26237.5654528901[/C][/ROW]
[ROW][C]20[/C][C]134210[/C][C]120045.789839988[/C][C]14164.2101600117[/C][/ROW]
[ROW][C]21[/C][C]133111[/C][C]133144.831641207[/C][C]-33.8316412073036[/C][/ROW]
[ROW][C]22[/C][C]124527[/C][C]132044.751925794[/C][C]-7517.75192579383[/C][/ROW]
[ROW][C]23[/C][C]117589[/C][C]123220.827631868[/C][C]-5631.82763186828[/C][/ROW]
[ROW][C]24[/C][C]115699[/C][C]116103.091417981[/C][C]-404.091417980948[/C][/ROW]
[ROW][C]25[/C][C]117830[/C][C]114200.195096169[/C][C]3629.80490383141[/C][/ROW]
[ROW][C]26[/C][C]115874[/C][C]116447.038021984[/C][C]-573.038021984117[/C][/ROW]
[ROW][C]27[/C][C]111267[/C][C]114472.749876249[/C][C]-3205.74987624932[/C][/ROW]
[ROW][C]28[/C][C]107985[/C][C]109763.440398209[/C][C]-1778.44039820947[/C][/ROW]
[ROW][C]29[/C][C]102185[/C][C]106424.682598665[/C][C]-4239.68259866502[/C][/ROW]
[ROW][C]30[/C][C]102101[/C][C]100489.375812275[/C][C]1611.62418772455[/C][/ROW]
[ROW][C]31[/C][C]128932[/C][C]100456.809778058[/C][C]28475.190221942[/C][/ROW]
[ROW][C]32[/C][C]135782[/C][C]128196.57744901[/C][C]7585.42255099042[/C][/ROW]
[ROW][C]33[/C][C]136971[/C][C]135288.661408102[/C][C]1682.33859189769[/C][/ROW]
[ROW][C]34[/C][C]126292[/C][C]136531.352179331[/C][C]-10239.3521793314[/C][/ROW]
[ROW][C]35[/C][C]119260[/C][C]125525.569736105[/C][C]-6265.56973610497[/C][/ROW]
[ROW][C]36[/C][C]117359[/C][C]118293.608044124[/C][C]-934.608044123815[/C][/ROW]
[ROW][C]37[/C][C]119818[/C][C]116362.780620009[/C][C]3455.21937999138[/C][/ROW]
[ROW][C]38[/C][C]116059[/C][C]118932.051759345[/C][C]-2873.05175934457[/C][/ROW]
[ROW][C]39[/C][C]110046[/C][C]115081.360131106[/C][C]-5035.36013110564[/C][/ROW]
[ROW][C]40[/C][C]104100[/C][C]108907.659799937[/C][C]-4807.65979993732[/C][/ROW]
[ROW][C]41[/C][C]97981[/C][C]102808.226380702[/C][C]-4827.22638070243[/C][/ROW]
[ROW][C]42[/C][C]97527[/C][C]96535.1685064282[/C][C]991.831493571808[/C][/ROW]
[ROW][C]43[/C][C]123700[/C][C]96112.8221807097[/C][C]27587.1778192903[/C][/ROW]
[ROW][C]44[/C][C]129678[/C][C]123166.249497948[/C][C]6511.7505020517[/C][/ROW]
[ROW][C]45[/C][C]130790[/C][C]129352.067893241[/C][C]1437.9321067594[/C][/ROW]
[ROW][C]46[/C][C]120961[/C][C]130509.958586207[/C][C]-9548.95858620739[/C][/ROW]
[ROW][C]47[/C][C]114232[/C][C]120376.209617482[/C][C]-6144.20961748186[/C][/ROW]
[ROW][C]48[/C][C]110518[/C][C]113451.121056865[/C][C]-2933.12105686481[/C][/ROW]
[ROW][C]49[/C][C]110959[/C][C]109643.51235502[/C][C]1315.48764498021[/C][/ROW]
[ROW][C]50[/C][C]108443[/C][C]110126.495310497[/C][C]-1683.49531049705[/C][/ROW]
[ROW][C]51[/C][C]103977[/C][C]107556.767623326[/C][C]-3579.76762332609[/C][/ROW]
[ROW][C]52[/C][C]97126[/C][C]102976.521605644[/C][C]-5850.52160564395[/C][/ROW]
[ROW][C]53[/C][C]90860[/C][C]95938.8059120183[/C][C]-5078.80591201829[/C][/ROW]
[ROW][C]54[/C][C]91959[/C][C]89510.7190362536[/C][C]2448.28096374639[/C][/ROW]
[ROW][C]55[/C][C]113735[/C][C]90687.8543734337[/C][C]23047.1456265663[/C][/ROW]
[ROW][C]56[/C][C]119713[/C][C]113199.389437112[/C][C]6513.61056288843[/C][/ROW]
[ROW][C]57[/C][C]121905[/C][C]119385.267195068[/C][C]2519.73280493195[/C][/ROW]
[ROW][C]58[/C][C]112442[/C][C]121657.68287253[/C][C]-9215.6828725301[/C][/ROW]
[ROW][C]59[/C][C]106728[/C][C]111900.570187241[/C][C]-5172.57018724087[/C][/ROW]
[ROW][C]60[/C][C]104906[/C][C]106021.490883986[/C][C]-1115.49088398584[/C][/ROW]
[ROW][C]61[/C][C]105308[/C][C]104163.890698536[/C][C]1144.10930146354[/C][/ROW]
[ROW][C]62[/C][C]102909[/C][C]104602.404222664[/C][C]-1693.404222664[/C][/ROW]
[ROW][C]63[/C][C]97849[/C][C]102149.360298834[/C][C]-4300.36029883364[/C][/ROW]
[ROW][C]64[/C][C]93181[/C][C]96952.1170220526[/C][C]-3771.11702205257[/C][/ROW]
[ROW][C]65[/C][C]87470[/C][C]92163.7642094355[/C][C]-4693.76420943551[/C][/ROW]
[ROW][C]66[/C][C]86998[/C][C]86302.9656958748[/C][C]695.034304125176[/C][/ROW]
[ROW][C]67[/C][C]106716[/C][C]85853.1472757297[/C][C]20862.8527242703[/C][/ROW]
[ROW][C]68[/C][C]115028[/C][C]106236.972014103[/C][C]8791.02798589748[/C][/ROW]
[ROW][C]69[/C][C]116828[/C][C]114829.532107494[/C][C]1998.4678925058[/C][/ROW]
[ROW][C]70[/C][C]108413[/C][C]116693.31194524[/C][C]-8280.31194524028[/C][/ROW]
[ROW][C]71[/C][C]102628[/C][C]108014.051031[/C][C]-5386.05103099957[/C][/ROW]
[ROW][C]72[/C][C]99126[/C][C]102057.158621751[/C][C]-2931.15862175077[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
3102304102887-583
49796898807.3939240428-839.393924042815
59246294444.6051982988-1982.60519829883
69228688875.33160839723410.66839160281
712009288808.180931139831283.8190688602
8126656117612.584213869043.41578613971
9124144124465.199104134-321.199104133571
10114045121942.948238046-7897.94823804629
11108120111591.890219482-3471.89021948195
12105698105556.087040856141.912959143592
13111203103138.6161031168064.38389688435
14110030108900.9858103771129.01418962306
15104009107764.017583565-3755.01758356539
1699772101623.178574337-1851.17857433661
179630197327.0993819448-1026.09938194479
189768093823.35206969763856.64793030235
1912156395325.434547109926237.5654528901
20134210120045.78983998814164.2101600117
21133111133144.831641207-33.8316412073036
22124527132044.751925794-7517.75192579383
23117589123220.827631868-5631.82763186828
24115699116103.091417981-404.091417980948
25117830114200.1950961693629.80490383141
26115874116447.038021984-573.038021984117
27111267114472.749876249-3205.74987624932
28107985109763.440398209-1778.44039820947
29102185106424.682598665-4239.68259866502
30102101100489.3758122751611.62418772455
31128932100456.80977805828475.190221942
32135782128196.577449017585.42255099042
33136971135288.6614081021682.33859189769
34126292136531.352179331-10239.3521793314
35119260125525.569736105-6265.56973610497
36117359118293.608044124-934.608044123815
37119818116362.7806200093455.21937999138
38116059118932.051759345-2873.05175934457
39110046115081.360131106-5035.36013110564
40104100108907.659799937-4807.65979993732
4197981102808.226380702-4827.22638070243
429752796535.1685064282991.831493571808
4312370096112.822180709727587.1778192903
44129678123166.2494979486511.7505020517
45130790129352.0678932411437.9321067594
46120961130509.958586207-9548.95858620739
47114232120376.209617482-6144.20961748186
48110518113451.121056865-2933.12105686481
49110959109643.512355021315.48764498021
50108443110126.495310497-1683.49531049705
51103977107556.767623326-3579.76762332609
5297126102976.521605644-5850.52160564395
539086095938.8059120183-5078.80591201829
549195989510.71903625362448.28096374639
5511373590687.854373433723047.1456265663
56119713113199.3894371126513.61056288843
57121905119385.2671950682519.73280493195
58112442121657.68287253-9215.6828725301
59106728111900.570187241-5172.57018724087
60104906106021.490883986-1115.49088398584
61105308104163.8906985361144.10930146354
62102909104602.404222664-1693.404222664
6397849102149.360298834-4300.36029883364
649318196952.1170220526-3771.11702205257
658747092163.7642094355-4693.76420943551
668699886302.9656958748695.034304125176
6710671685853.147275729720862.8527242703
68115028106236.9720141038791.02798589748
69116828114829.5321074941998.4678925058
70108413116693.31194524-8280.31194524028
71102628108014.051031-5386.05103099957
7299126102057.158621751-2931.15862175077







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7398461.612549780280685.3854364502116237.83966311
7497797.225099560472253.5397284604123340.91047066
7597132.837649340565350.7588454373128914.916453244
7696468.450199120759192.4530977375133744.447300504
7795804.062748900953480.0525420392138128.072955763
7895139.675298681148063.0370308474142216.313566515
7994475.287848461242853.5119300519146097.063766871
8093810.900398241437795.1957044783149826.605092004
8193146.512948021632849.681870891153443.344025152
8292482.125497801827989.5100831338156974.74091247
8391817.738047581923194.3332587058160441.142836458
8491153.350597362118448.6446935254163858.056501199

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 98461.6125497802 & 80685.3854364502 & 116237.83966311 \tabularnewline
74 & 97797.2250995604 & 72253.5397284604 & 123340.91047066 \tabularnewline
75 & 97132.8376493405 & 65350.7588454373 & 128914.916453244 \tabularnewline
76 & 96468.4501991207 & 59192.4530977375 & 133744.447300504 \tabularnewline
77 & 95804.0627489009 & 53480.0525420392 & 138128.072955763 \tabularnewline
78 & 95139.6752986811 & 48063.0370308474 & 142216.313566515 \tabularnewline
79 & 94475.2878484612 & 42853.5119300519 & 146097.063766871 \tabularnewline
80 & 93810.9003982414 & 37795.1957044783 & 149826.605092004 \tabularnewline
81 & 93146.5129480216 & 32849.681870891 & 153443.344025152 \tabularnewline
82 & 92482.1254978018 & 27989.5100831338 & 156974.74091247 \tabularnewline
83 & 91817.7380475819 & 23194.3332587058 & 160441.142836458 \tabularnewline
84 & 91153.3505973621 & 18448.6446935254 & 163858.056501199 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]73[/C][C]98461.6125497802[/C][C]80685.3854364502[/C][C]116237.83966311[/C][/ROW]
[ROW][C]74[/C][C]97797.2250995604[/C][C]72253.5397284604[/C][C]123340.91047066[/C][/ROW]
[ROW][C]75[/C][C]97132.8376493405[/C][C]65350.7588454373[/C][C]128914.916453244[/C][/ROW]
[ROW][C]76[/C][C]96468.4501991207[/C][C]59192.4530977375[/C][C]133744.447300504[/C][/ROW]
[ROW][C]77[/C][C]95804.0627489009[/C][C]53480.0525420392[/C][C]138128.072955763[/C][/ROW]
[ROW][C]78[/C][C]95139.6752986811[/C][C]48063.0370308474[/C][C]142216.313566515[/C][/ROW]
[ROW][C]79[/C][C]94475.2878484612[/C][C]42853.5119300519[/C][C]146097.063766871[/C][/ROW]
[ROW][C]80[/C][C]93810.9003982414[/C][C]37795.1957044783[/C][C]149826.605092004[/C][/ROW]
[ROW][C]81[/C][C]93146.5129480216[/C][C]32849.681870891[/C][C]153443.344025152[/C][/ROW]
[ROW][C]82[/C][C]92482.1254978018[/C][C]27989.5100831338[/C][C]156974.74091247[/C][/ROW]
[ROW][C]83[/C][C]91817.7380475819[/C][C]23194.3332587058[/C][C]160441.142836458[/C][/ROW]
[ROW][C]84[/C][C]91153.3505973621[/C][C]18448.6446935254[/C][C]163858.056501199[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
7398461.612549780280685.3854364502116237.83966311
7497797.225099560472253.5397284604123340.91047066
7597132.837649340565350.7588454373128914.916453244
7696468.450199120759192.4530977375133744.447300504
7795804.062748900953480.0525420392138128.072955763
7895139.675298681148063.0370308474142216.313566515
7994475.287848461242853.5119300519146097.063766871
8093810.900398241437795.1957044783149826.605092004
8193146.512948021632849.681870891153443.344025152
8292482.125497801827989.5100831338156974.74091247
8391817.738047581923194.3332587058160441.142836458
8491153.350597362118448.6446935254163858.056501199



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