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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 03:11:41 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/17/t135573197328c60tq4wxx3jx8.htm/, Retrieved Fri, 29 Mar 2024 06:18:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200698, Retrieved Fri, 29 Mar 2024 06:18:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2012-12-17 08:11:41] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
103,48
103,93
103,89
104,4
104,79
104,77
105,13
105,26
104,96
104,75
105,01
105,1
103,48
103,93
103,89
104,4
104,79
106,12
106,57
106,44
106,54
107,1
108,1
108,4
108,84
109,62
110,42
110,67
111,66
112,28
112,87
112,18
112,36
112,16
111,49
111,25
111,36
111,74
111,1
111,33
111,25
111,04
110,97
111,31
111,02
111,07
111,36
111,54
112,05
112,52
112,94
113,33
113,78
113,77
113,82
113,89
114,25
114,41
114,55
115
115,66
116,33
116,91
117,2
117,59
117,95
118,09
117,99
118,31
118,49
118,96
119,01




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200698&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]3 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=200698&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200698&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.806023377868737
beta0.0207897814954087
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.806023377868737 \tabularnewline
beta & 0.0207897814954087 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200698&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]0.806023377868737[/C][/ROW]
[ROW][C]beta[/C][C]0.0207897814954087[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200698&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200698&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
alpha0.806023377868737
beta0.0207897814954087
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13103.48103.2552056623930.224794337606838
14103.93103.8702887919020.0597112080975819
15103.89103.8574783100960.0325216899038026
16104.4104.3245474085740.0754525914264406
17104.79104.6445675134850.145432486515446
18106.12105.9238467359190.196153264080763
19106.57106.2468783741840.323121625815958
20106.44106.744330712133-0.304330712133307
21106.54106.3009421122660.23905788773412
22107.1106.3895433321140.710456667885794
23108.1107.3400081469030.759991853096594
24108.4108.116884700410.28311529958988
25108.84106.7877366269212.05226337307938
26109.62108.9204093585550.699590641444772
27110.42109.5054341247820.914565875217562
28110.67110.793911103266-0.123911103265769
29111.66111.0656051809090.594394819090908
30112.28112.822911776185-0.542911776185022
31112.87112.6687986502920.201201349707588
32112.18113.038156328382-0.858156328382449
33112.36112.3363825541560.0236174458440672
34112.16112.42177047261-0.261770472609925
35111.49112.660910881008-1.17091088100841
36111.25111.819280283477-0.569280283477269
37111.36110.1623196709281.19768032907179
38111.74111.3455361734530.394463826547309
39111.1111.722953308104-0.622953308103874
40111.33111.541580883532-0.211580883531553
41111.25111.851343797411-0.601343797410863
42111.04112.373607342803-1.33360734280257
43110.97111.662627051529-0.692627051528746
44111.31111.0271809867130.282819013286939
45111.02111.356356358713-0.33635635871272
46111.07111.0304591409070.0395408590925399
47111.36111.2753813802860.0846186197140355
48111.54111.5227479925980.0172520074016944
49112.05110.6514325298811.39856747011892
50112.52111.8142671766980.705732823301815
51112.94112.2239388468690.716061153130795
52113.33113.2027975332730.12720246672724
53113.78113.7168573820950.0631426179054273
54113.77114.650639863553-0.880639863553412
55113.82114.454656900469-0.634656900469238
56113.89114.081681032811-0.191681032811189
57114.25113.9268726741970.323127325803398
58114.41114.2350809435340.174919056465555
59114.55114.629764693319-0.0797646933192055
60115114.7607118718460.239288128154499
61115.66114.3691711984491.29082880155066
62116.33115.3418324306760.988167569323679
63116.91116.0169495319920.893050468008383
64117.2117.0629997122960.137000287703756
65117.59117.611453690742-0.0214536907416516
66117.95118.331483217357-0.381483217356688
67118.09118.631416902825-0.541416902824992
68117.99118.466953821027-0.476953821026854
69118.31118.2247215876530.0852784123471082
70118.49118.3511353619370.138864638063438
71118.96118.7054177774810.25458222251936
72119.01119.211409906399-0.201409906398538

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 103.48 & 103.255205662393 & 0.224794337606838 \tabularnewline
14 & 103.93 & 103.870288791902 & 0.0597112080975819 \tabularnewline
15 & 103.89 & 103.857478310096 & 0.0325216899038026 \tabularnewline
16 & 104.4 & 104.324547408574 & 0.0754525914264406 \tabularnewline
17 & 104.79 & 104.644567513485 & 0.145432486515446 \tabularnewline
18 & 106.12 & 105.923846735919 & 0.196153264080763 \tabularnewline
19 & 106.57 & 106.246878374184 & 0.323121625815958 \tabularnewline
20 & 106.44 & 106.744330712133 & -0.304330712133307 \tabularnewline
21 & 106.54 & 106.300942112266 & 0.23905788773412 \tabularnewline
22 & 107.1 & 106.389543332114 & 0.710456667885794 \tabularnewline
23 & 108.1 & 107.340008146903 & 0.759991853096594 \tabularnewline
24 & 108.4 & 108.11688470041 & 0.28311529958988 \tabularnewline
25 & 108.84 & 106.787736626921 & 2.05226337307938 \tabularnewline
26 & 109.62 & 108.920409358555 & 0.699590641444772 \tabularnewline
27 & 110.42 & 109.505434124782 & 0.914565875217562 \tabularnewline
28 & 110.67 & 110.793911103266 & -0.123911103265769 \tabularnewline
29 & 111.66 & 111.065605180909 & 0.594394819090908 \tabularnewline
30 & 112.28 & 112.822911776185 & -0.542911776185022 \tabularnewline
31 & 112.87 & 112.668798650292 & 0.201201349707588 \tabularnewline
32 & 112.18 & 113.038156328382 & -0.858156328382449 \tabularnewline
33 & 112.36 & 112.336382554156 & 0.0236174458440672 \tabularnewline
34 & 112.16 & 112.42177047261 & -0.261770472609925 \tabularnewline
35 & 111.49 & 112.660910881008 & -1.17091088100841 \tabularnewline
36 & 111.25 & 111.819280283477 & -0.569280283477269 \tabularnewline
37 & 111.36 & 110.162319670928 & 1.19768032907179 \tabularnewline
38 & 111.74 & 111.345536173453 & 0.394463826547309 \tabularnewline
39 & 111.1 & 111.722953308104 & -0.622953308103874 \tabularnewline
40 & 111.33 & 111.541580883532 & -0.211580883531553 \tabularnewline
41 & 111.25 & 111.851343797411 & -0.601343797410863 \tabularnewline
42 & 111.04 & 112.373607342803 & -1.33360734280257 \tabularnewline
43 & 110.97 & 111.662627051529 & -0.692627051528746 \tabularnewline
44 & 111.31 & 111.027180986713 & 0.282819013286939 \tabularnewline
45 & 111.02 & 111.356356358713 & -0.33635635871272 \tabularnewline
46 & 111.07 & 111.030459140907 & 0.0395408590925399 \tabularnewline
47 & 111.36 & 111.275381380286 & 0.0846186197140355 \tabularnewline
48 & 111.54 & 111.522747992598 & 0.0172520074016944 \tabularnewline
49 & 112.05 & 110.651432529881 & 1.39856747011892 \tabularnewline
50 & 112.52 & 111.814267176698 & 0.705732823301815 \tabularnewline
51 & 112.94 & 112.223938846869 & 0.716061153130795 \tabularnewline
52 & 113.33 & 113.202797533273 & 0.12720246672724 \tabularnewline
53 & 113.78 & 113.716857382095 & 0.0631426179054273 \tabularnewline
54 & 113.77 & 114.650639863553 & -0.880639863553412 \tabularnewline
55 & 113.82 & 114.454656900469 & -0.634656900469238 \tabularnewline
56 & 113.89 & 114.081681032811 & -0.191681032811189 \tabularnewline
57 & 114.25 & 113.926872674197 & 0.323127325803398 \tabularnewline
58 & 114.41 & 114.235080943534 & 0.174919056465555 \tabularnewline
59 & 114.55 & 114.629764693319 & -0.0797646933192055 \tabularnewline
60 & 115 & 114.760711871846 & 0.239288128154499 \tabularnewline
61 & 115.66 & 114.369171198449 & 1.29082880155066 \tabularnewline
62 & 116.33 & 115.341832430676 & 0.988167569323679 \tabularnewline
63 & 116.91 & 116.016949531992 & 0.893050468008383 \tabularnewline
64 & 117.2 & 117.062999712296 & 0.137000287703756 \tabularnewline
65 & 117.59 & 117.611453690742 & -0.0214536907416516 \tabularnewline
66 & 117.95 & 118.331483217357 & -0.381483217356688 \tabularnewline
67 & 118.09 & 118.631416902825 & -0.541416902824992 \tabularnewline
68 & 117.99 & 118.466953821027 & -0.476953821026854 \tabularnewline
69 & 118.31 & 118.224721587653 & 0.0852784123471082 \tabularnewline
70 & 118.49 & 118.351135361937 & 0.138864638063438 \tabularnewline
71 & 118.96 & 118.705417777481 & 0.25458222251936 \tabularnewline
72 & 119.01 & 119.211409906399 & -0.201409906398538 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200698&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]103.48[/C][C]103.255205662393[/C][C]0.224794337606838[/C][/ROW]
[ROW][C]14[/C][C]103.93[/C][C]103.870288791902[/C][C]0.0597112080975819[/C][/ROW]
[ROW][C]15[/C][C]103.89[/C][C]103.857478310096[/C][C]0.0325216899038026[/C][/ROW]
[ROW][C]16[/C][C]104.4[/C][C]104.324547408574[/C][C]0.0754525914264406[/C][/ROW]
[ROW][C]17[/C][C]104.79[/C][C]104.644567513485[/C][C]0.145432486515446[/C][/ROW]
[ROW][C]18[/C][C]106.12[/C][C]105.923846735919[/C][C]0.196153264080763[/C][/ROW]
[ROW][C]19[/C][C]106.57[/C][C]106.246878374184[/C][C]0.323121625815958[/C][/ROW]
[ROW][C]20[/C][C]106.44[/C][C]106.744330712133[/C][C]-0.304330712133307[/C][/ROW]
[ROW][C]21[/C][C]106.54[/C][C]106.300942112266[/C][C]0.23905788773412[/C][/ROW]
[ROW][C]22[/C][C]107.1[/C][C]106.389543332114[/C][C]0.710456667885794[/C][/ROW]
[ROW][C]23[/C][C]108.1[/C][C]107.340008146903[/C][C]0.759991853096594[/C][/ROW]
[ROW][C]24[/C][C]108.4[/C][C]108.11688470041[/C][C]0.28311529958988[/C][/ROW]
[ROW][C]25[/C][C]108.84[/C][C]106.787736626921[/C][C]2.05226337307938[/C][/ROW]
[ROW][C]26[/C][C]109.62[/C][C]108.920409358555[/C][C]0.699590641444772[/C][/ROW]
[ROW][C]27[/C][C]110.42[/C][C]109.505434124782[/C][C]0.914565875217562[/C][/ROW]
[ROW][C]28[/C][C]110.67[/C][C]110.793911103266[/C][C]-0.123911103265769[/C][/ROW]
[ROW][C]29[/C][C]111.66[/C][C]111.065605180909[/C][C]0.594394819090908[/C][/ROW]
[ROW][C]30[/C][C]112.28[/C][C]112.822911776185[/C][C]-0.542911776185022[/C][/ROW]
[ROW][C]31[/C][C]112.87[/C][C]112.668798650292[/C][C]0.201201349707588[/C][/ROW]
[ROW][C]32[/C][C]112.18[/C][C]113.038156328382[/C][C]-0.858156328382449[/C][/ROW]
[ROW][C]33[/C][C]112.36[/C][C]112.336382554156[/C][C]0.0236174458440672[/C][/ROW]
[ROW][C]34[/C][C]112.16[/C][C]112.42177047261[/C][C]-0.261770472609925[/C][/ROW]
[ROW][C]35[/C][C]111.49[/C][C]112.660910881008[/C][C]-1.17091088100841[/C][/ROW]
[ROW][C]36[/C][C]111.25[/C][C]111.819280283477[/C][C]-0.569280283477269[/C][/ROW]
[ROW][C]37[/C][C]111.36[/C][C]110.162319670928[/C][C]1.19768032907179[/C][/ROW]
[ROW][C]38[/C][C]111.74[/C][C]111.345536173453[/C][C]0.394463826547309[/C][/ROW]
[ROW][C]39[/C][C]111.1[/C][C]111.722953308104[/C][C]-0.622953308103874[/C][/ROW]
[ROW][C]40[/C][C]111.33[/C][C]111.541580883532[/C][C]-0.211580883531553[/C][/ROW]
[ROW][C]41[/C][C]111.25[/C][C]111.851343797411[/C][C]-0.601343797410863[/C][/ROW]
[ROW][C]42[/C][C]111.04[/C][C]112.373607342803[/C][C]-1.33360734280257[/C][/ROW]
[ROW][C]43[/C][C]110.97[/C][C]111.662627051529[/C][C]-0.692627051528746[/C][/ROW]
[ROW][C]44[/C][C]111.31[/C][C]111.027180986713[/C][C]0.282819013286939[/C][/ROW]
[ROW][C]45[/C][C]111.02[/C][C]111.356356358713[/C][C]-0.33635635871272[/C][/ROW]
[ROW][C]46[/C][C]111.07[/C][C]111.030459140907[/C][C]0.0395408590925399[/C][/ROW]
[ROW][C]47[/C][C]111.36[/C][C]111.275381380286[/C][C]0.0846186197140355[/C][/ROW]
[ROW][C]48[/C][C]111.54[/C][C]111.522747992598[/C][C]0.0172520074016944[/C][/ROW]
[ROW][C]49[/C][C]112.05[/C][C]110.651432529881[/C][C]1.39856747011892[/C][/ROW]
[ROW][C]50[/C][C]112.52[/C][C]111.814267176698[/C][C]0.705732823301815[/C][/ROW]
[ROW][C]51[/C][C]112.94[/C][C]112.223938846869[/C][C]0.716061153130795[/C][/ROW]
[ROW][C]52[/C][C]113.33[/C][C]113.202797533273[/C][C]0.12720246672724[/C][/ROW]
[ROW][C]53[/C][C]113.78[/C][C]113.716857382095[/C][C]0.0631426179054273[/C][/ROW]
[ROW][C]54[/C][C]113.77[/C][C]114.650639863553[/C][C]-0.880639863553412[/C][/ROW]
[ROW][C]55[/C][C]113.82[/C][C]114.454656900469[/C][C]-0.634656900469238[/C][/ROW]
[ROW][C]56[/C][C]113.89[/C][C]114.081681032811[/C][C]-0.191681032811189[/C][/ROW]
[ROW][C]57[/C][C]114.25[/C][C]113.926872674197[/C][C]0.323127325803398[/C][/ROW]
[ROW][C]58[/C][C]114.41[/C][C]114.235080943534[/C][C]0.174919056465555[/C][/ROW]
[ROW][C]59[/C][C]114.55[/C][C]114.629764693319[/C][C]-0.0797646933192055[/C][/ROW]
[ROW][C]60[/C][C]115[/C][C]114.760711871846[/C][C]0.239288128154499[/C][/ROW]
[ROW][C]61[/C][C]115.66[/C][C]114.369171198449[/C][C]1.29082880155066[/C][/ROW]
[ROW][C]62[/C][C]116.33[/C][C]115.341832430676[/C][C]0.988167569323679[/C][/ROW]
[ROW][C]63[/C][C]116.91[/C][C]116.016949531992[/C][C]0.893050468008383[/C][/ROW]
[ROW][C]64[/C][C]117.2[/C][C]117.062999712296[/C][C]0.137000287703756[/C][/ROW]
[ROW][C]65[/C][C]117.59[/C][C]117.611453690742[/C][C]-0.0214536907416516[/C][/ROW]
[ROW][C]66[/C][C]117.95[/C][C]118.331483217357[/C][C]-0.381483217356688[/C][/ROW]
[ROW][C]67[/C][C]118.09[/C][C]118.631416902825[/C][C]-0.541416902824992[/C][/ROW]
[ROW][C]68[/C][C]117.99[/C][C]118.466953821027[/C][C]-0.476953821026854[/C][/ROW]
[ROW][C]69[/C][C]118.31[/C][C]118.224721587653[/C][C]0.0852784123471082[/C][/ROW]
[ROW][C]70[/C][C]118.49[/C][C]118.351135361937[/C][C]0.138864638063438[/C][/ROW]
[ROW][C]71[/C][C]118.96[/C][C]118.705417777481[/C][C]0.25458222251936[/C][/ROW]
[ROW][C]72[/C][C]119.01[/C][C]119.211409906399[/C][C]-0.201409906398538[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200698&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200698&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
13103.48103.2552056623930.224794337606838
14103.93103.8702887919020.0597112080975819
15103.89103.8574783100960.0325216899038026
16104.4104.3245474085740.0754525914264406
17104.79104.6445675134850.145432486515446
18106.12105.9238467359190.196153264080763
19106.57106.2468783741840.323121625815958
20106.44106.744330712133-0.304330712133307
21106.54106.3009421122660.23905788773412
22107.1106.3895433321140.710456667885794
23108.1107.3400081469030.759991853096594
24108.4108.116884700410.28311529958988
25108.84106.7877366269212.05226337307938
26109.62108.9204093585550.699590641444772
27110.42109.5054341247820.914565875217562
28110.67110.793911103266-0.123911103265769
29111.66111.0656051809090.594394819090908
30112.28112.822911776185-0.542911776185022
31112.87112.6687986502920.201201349707588
32112.18113.038156328382-0.858156328382449
33112.36112.3363825541560.0236174458440672
34112.16112.42177047261-0.261770472609925
35111.49112.660910881008-1.17091088100841
36111.25111.819280283477-0.569280283477269
37111.36110.1623196709281.19768032907179
38111.74111.3455361734530.394463826547309
39111.1111.722953308104-0.622953308103874
40111.33111.541580883532-0.211580883531553
41111.25111.851343797411-0.601343797410863
42111.04112.373607342803-1.33360734280257
43110.97111.662627051529-0.692627051528746
44111.31111.0271809867130.282819013286939
45111.02111.356356358713-0.33635635871272
46111.07111.0304591409070.0395408590925399
47111.36111.2753813802860.0846186197140355
48111.54111.5227479925980.0172520074016944
49112.05110.6514325298811.39856747011892
50112.52111.8142671766980.705732823301815
51112.94112.2239388468690.716061153130795
52113.33113.2027975332730.12720246672724
53113.78113.7168573820950.0631426179054273
54113.77114.650639863553-0.880639863553412
55113.82114.454656900469-0.634656900469238
56113.89114.081681032811-0.191681032811189
57114.25113.9268726741970.323127325803398
58114.41114.2350809435340.174919056465555
59114.55114.629764693319-0.0797646933192055
60115114.7607118718460.239288128154499
61115.66114.3691711984491.29082880155066
62116.33115.3418324306760.988167569323679
63116.91116.0169495319920.893050468008383
64117.2117.0629997122960.137000287703756
65117.59117.611453690742-0.0214536907416516
66117.95118.331483217357-0.381483217356688
67118.09118.631416902825-0.541416902824992
68117.99118.466953821027-0.476953821026854
69118.31118.2247215876530.0852784123471082
70118.49118.3511353619370.138864638063438
71118.96118.7054177774810.25458222251936
72119.01119.211409906399-0.201409906398538







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73118.704910554789117.476594668219119.933226441359
74118.593073842372117.002431976301120.183715708444
75118.451344963977116.555678721356120.347011206597
76118.614045314487116.446135236821120.781955392153
77119.002167555283116.583523375971121.420811734594
78119.650841511819116.996709920707122.304973102931
79120.214818291064117.336553895457123.09308268667
80120.49590886943117.402260333144123.589557405716
81120.751819462887117.44969471906124.053944206715
82120.823109291074117.31806251251124.328156069638
83121.088801079289117.3853589142124.792243244377
84121.297767136527117.399656313294125.19587795976

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 118.704910554789 & 117.476594668219 & 119.933226441359 \tabularnewline
74 & 118.593073842372 & 117.002431976301 & 120.183715708444 \tabularnewline
75 & 118.451344963977 & 116.555678721356 & 120.347011206597 \tabularnewline
76 & 118.614045314487 & 116.446135236821 & 120.781955392153 \tabularnewline
77 & 119.002167555283 & 116.583523375971 & 121.420811734594 \tabularnewline
78 & 119.650841511819 & 116.996709920707 & 122.304973102931 \tabularnewline
79 & 120.214818291064 & 117.336553895457 & 123.09308268667 \tabularnewline
80 & 120.49590886943 & 117.402260333144 & 123.589557405716 \tabularnewline
81 & 120.751819462887 & 117.44969471906 & 124.053944206715 \tabularnewline
82 & 120.823109291074 & 117.31806251251 & 124.328156069638 \tabularnewline
83 & 121.088801079289 & 117.3853589142 & 124.792243244377 \tabularnewline
84 & 121.297767136527 & 117.399656313294 & 125.19587795976 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200698&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]118.704910554789[/C][C]117.476594668219[/C][C]119.933226441359[/C][/ROW]
[ROW][C]74[/C][C]118.593073842372[/C][C]117.002431976301[/C][C]120.183715708444[/C][/ROW]
[ROW][C]75[/C][C]118.451344963977[/C][C]116.555678721356[/C][C]120.347011206597[/C][/ROW]
[ROW][C]76[/C][C]118.614045314487[/C][C]116.446135236821[/C][C]120.781955392153[/C][/ROW]
[ROW][C]77[/C][C]119.002167555283[/C][C]116.583523375971[/C][C]121.420811734594[/C][/ROW]
[ROW][C]78[/C][C]119.650841511819[/C][C]116.996709920707[/C][C]122.304973102931[/C][/ROW]
[ROW][C]79[/C][C]120.214818291064[/C][C]117.336553895457[/C][C]123.09308268667[/C][/ROW]
[ROW][C]80[/C][C]120.49590886943[/C][C]117.402260333144[/C][C]123.589557405716[/C][/ROW]
[ROW][C]81[/C][C]120.751819462887[/C][C]117.44969471906[/C][C]124.053944206715[/C][/ROW]
[ROW][C]82[/C][C]120.823109291074[/C][C]117.31806251251[/C][C]124.328156069638[/C][/ROW]
[ROW][C]83[/C][C]121.088801079289[/C][C]117.3853589142[/C][C]124.792243244377[/C][/ROW]
[ROW][C]84[/C][C]121.297767136527[/C][C]117.399656313294[/C][C]125.19587795976[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200698&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200698&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
73118.704910554789117.476594668219119.933226441359
74118.593073842372117.002431976301120.183715708444
75118.451344963977116.555678721356120.347011206597
76118.614045314487116.446135236821120.781955392153
77119.002167555283116.583523375971121.420811734594
78119.650841511819116.996709920707122.304973102931
79120.214818291064117.336553895457123.09308268667
80120.49590886943117.402260333144123.589557405716
81120.751819462887117.44969471906124.053944206715
82120.823109291074117.31806251251124.328156069638
83121.088801079289117.3853589142124.792243244377
84121.297767136527117.399656313294125.19587795976



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