Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 24 May 2008 01:23:37 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/24/t1211613897tiz2vgbw9lww3w2.htm/, Retrieved Mon, 20 May 2024 01:08:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13053, Retrieved Mon, 20 May 2024 01:08:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordseigen cijferreeks
Estimated Impact208
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Stephanie De Coni...] [2008-05-24 07:23:37] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
68,64
68,61
68,61
68,61
68,58
68,75
68,54
68,5
68,47
68,47
68,47
68,59
68,32
67,86
67,91
67,91
68,05
68,15
68,25
68,25
68,31
68,31
69,65
69,65
70,18
70,08
70,08
70,09
70,04
70,14
70,26
70,23
70,54
70,54
70,57
70,61
70,63
70,45
70,4
70,4
70,33
70,51
70,45
70,39
70,59
70,59
70,32
70,94
70,44
70,57
70,61
70,61
70,68
69,96
70,11
70,22
70,49
70,49
70,58
70,85
70,69
70,7
70,7
70,7
70,67
70,64
70,98
70,75
70,88
70,88
70,92
70,89
71,02
71,01
71,02




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13053&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13053&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13053&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 time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.867742588299969
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.867742588299969 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13053&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]0.867742588299969[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13053&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13053&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
alpha0.867742588299969
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
368.6168.610
468.6168.610
568.5868.61-0.0300000000000011
668.7568.5839677223510.166032277648995
768.5468.7280410006995-0.188041000699471
868.568.564869816046-0.0648698160459986
968.4768.5085795139677-0.0385795139677043
1068.4768.475102426662-0.00510242666202032
1168.4768.4706748337437-0.000674833743701697
1268.5968.47008925176430.119910748235739
1368.3268.5741409148033-0.254140914803344
1467.8668.353612019599-0.493612019598956
1567.9167.9252838480962-0.015283848096189
1667.9167.91202140219-0.00202140219002445
1768.0567.91026734542170.139732654578339
1868.1568.03151932077550.118480679224518
1968.2568.13433005202930.115669947970687
2068.2568.23470179206990.0152982079300870
2168.3168.24797669861550.0620233013844853
2268.3168.30179695869380.00820304130620286
2369.6568.30891508698881.34108491301123
2469.6569.47263158053520.177368419464827
2570.1869.62654171192430.553458288075745
2670.0870.1068010393352-0.0268010393351830
2770.0870.0835446360933-0.00354463609333777
2870.0970.08046880439510.00953119560487892
2970.0470.0887394287389-0.0487394287388838
3070.1470.04644615069270.0935538493072556
3170.2670.1276268100360.132373189963957
3270.2370.2424926645169-0.0124926645168983
3370.5470.23165224747420.308347752525762
3470.5470.49921872434740.0407812756525772
3570.5770.53460637403640.0353936259636214
3670.6170.56531893063940.0446810693606352
3770.6370.60409059741440.0259094025856257
3870.4570.6265732894753-0.176573289475328
3970.470.4733531262414-0.0733531262413578
4070.470.4097014946168-0.0097014946167917
4170.3370.4012830945676-0.0712830945676473
4270.5170.33942771758550.170572282414525
4370.4570.4874405514201-0.0374405514200902
4470.3970.4549517904235-0.06495179042345
4570.5970.39859035568670.191409644313310
4670.5970.56468465586870.0253153441313003
4770.3270.5866518581089-0.266651858108915
4870.9470.35526668457850.584733315421516
4970.4470.8626646851676-0.422664685167575
5070.5770.49590053727730.074099462722728
5170.6170.56019979685190.0498002031480809
5270.6170.60341355402950.00658644597049829
5370.6870.60912889370360.0708711062963658
5469.9670.6706267709169-0.710626770916932
5570.1170.05398565740620.0560143425937838
5670.2270.10259168803050.117408311969527
5770.4970.20447188054680.285528119453161
5870.4970.45223678995350.0377632100464496
5970.5870.48500553558180.0949944644182352
6070.8570.56743627801020.282563721989789
6170.6970.8126288534893-0.122628853489303
6270.770.7062185747622-0.00621857476222942
6370.770.7008224526025-0.00082245260252023
6470.770.7001087754525-0.000108775452460463
6570.6770.7000143863598-0.0300143863597953
6670.6470.6739696250537-0.0339696250537145
6770.9870.6444927346860.335507265313979
6870.7570.935626677483-0.185626677483015
6970.8870.77455050390640.105449496093613
7070.8870.86605352258160.0139464774184148
7170.9270.87815547499430.0418445250057005
7270.8970.914465751429-0.0244657514289344
7371.0270.89323577695930.126764223040709
7471.0171.00323449196450.00676550803554221
7571.0271.00910521141840.0108947885816093

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 68.61 & 68.61 & 0 \tabularnewline
4 & 68.61 & 68.61 & 0 \tabularnewline
5 & 68.58 & 68.61 & -0.0300000000000011 \tabularnewline
6 & 68.75 & 68.583967722351 & 0.166032277648995 \tabularnewline
7 & 68.54 & 68.7280410006995 & -0.188041000699471 \tabularnewline
8 & 68.5 & 68.564869816046 & -0.0648698160459986 \tabularnewline
9 & 68.47 & 68.5085795139677 & -0.0385795139677043 \tabularnewline
10 & 68.47 & 68.475102426662 & -0.00510242666202032 \tabularnewline
11 & 68.47 & 68.4706748337437 & -0.000674833743701697 \tabularnewline
12 & 68.59 & 68.4700892517643 & 0.119910748235739 \tabularnewline
13 & 68.32 & 68.5741409148033 & -0.254140914803344 \tabularnewline
14 & 67.86 & 68.353612019599 & -0.493612019598956 \tabularnewline
15 & 67.91 & 67.9252838480962 & -0.015283848096189 \tabularnewline
16 & 67.91 & 67.91202140219 & -0.00202140219002445 \tabularnewline
17 & 68.05 & 67.9102673454217 & 0.139732654578339 \tabularnewline
18 & 68.15 & 68.0315193207755 & 0.118480679224518 \tabularnewline
19 & 68.25 & 68.1343300520293 & 0.115669947970687 \tabularnewline
20 & 68.25 & 68.2347017920699 & 0.0152982079300870 \tabularnewline
21 & 68.31 & 68.2479766986155 & 0.0620233013844853 \tabularnewline
22 & 68.31 & 68.3017969586938 & 0.00820304130620286 \tabularnewline
23 & 69.65 & 68.3089150869888 & 1.34108491301123 \tabularnewline
24 & 69.65 & 69.4726315805352 & 0.177368419464827 \tabularnewline
25 & 70.18 & 69.6265417119243 & 0.553458288075745 \tabularnewline
26 & 70.08 & 70.1068010393352 & -0.0268010393351830 \tabularnewline
27 & 70.08 & 70.0835446360933 & -0.00354463609333777 \tabularnewline
28 & 70.09 & 70.0804688043951 & 0.00953119560487892 \tabularnewline
29 & 70.04 & 70.0887394287389 & -0.0487394287388838 \tabularnewline
30 & 70.14 & 70.0464461506927 & 0.0935538493072556 \tabularnewline
31 & 70.26 & 70.127626810036 & 0.132373189963957 \tabularnewline
32 & 70.23 & 70.2424926645169 & -0.0124926645168983 \tabularnewline
33 & 70.54 & 70.2316522474742 & 0.308347752525762 \tabularnewline
34 & 70.54 & 70.4992187243474 & 0.0407812756525772 \tabularnewline
35 & 70.57 & 70.5346063740364 & 0.0353936259636214 \tabularnewline
36 & 70.61 & 70.5653189306394 & 0.0446810693606352 \tabularnewline
37 & 70.63 & 70.6040905974144 & 0.0259094025856257 \tabularnewline
38 & 70.45 & 70.6265732894753 & -0.176573289475328 \tabularnewline
39 & 70.4 & 70.4733531262414 & -0.0733531262413578 \tabularnewline
40 & 70.4 & 70.4097014946168 & -0.0097014946167917 \tabularnewline
41 & 70.33 & 70.4012830945676 & -0.0712830945676473 \tabularnewline
42 & 70.51 & 70.3394277175855 & 0.170572282414525 \tabularnewline
43 & 70.45 & 70.4874405514201 & -0.0374405514200902 \tabularnewline
44 & 70.39 & 70.4549517904235 & -0.06495179042345 \tabularnewline
45 & 70.59 & 70.3985903556867 & 0.191409644313310 \tabularnewline
46 & 70.59 & 70.5646846558687 & 0.0253153441313003 \tabularnewline
47 & 70.32 & 70.5866518581089 & -0.266651858108915 \tabularnewline
48 & 70.94 & 70.3552666845785 & 0.584733315421516 \tabularnewline
49 & 70.44 & 70.8626646851676 & -0.422664685167575 \tabularnewline
50 & 70.57 & 70.4959005372773 & 0.074099462722728 \tabularnewline
51 & 70.61 & 70.5601997968519 & 0.0498002031480809 \tabularnewline
52 & 70.61 & 70.6034135540295 & 0.00658644597049829 \tabularnewline
53 & 70.68 & 70.6091288937036 & 0.0708711062963658 \tabularnewline
54 & 69.96 & 70.6706267709169 & -0.710626770916932 \tabularnewline
55 & 70.11 & 70.0539856574062 & 0.0560143425937838 \tabularnewline
56 & 70.22 & 70.1025916880305 & 0.117408311969527 \tabularnewline
57 & 70.49 & 70.2044718805468 & 0.285528119453161 \tabularnewline
58 & 70.49 & 70.4522367899535 & 0.0377632100464496 \tabularnewline
59 & 70.58 & 70.4850055355818 & 0.0949944644182352 \tabularnewline
60 & 70.85 & 70.5674362780102 & 0.282563721989789 \tabularnewline
61 & 70.69 & 70.8126288534893 & -0.122628853489303 \tabularnewline
62 & 70.7 & 70.7062185747622 & -0.00621857476222942 \tabularnewline
63 & 70.7 & 70.7008224526025 & -0.00082245260252023 \tabularnewline
64 & 70.7 & 70.7001087754525 & -0.000108775452460463 \tabularnewline
65 & 70.67 & 70.7000143863598 & -0.0300143863597953 \tabularnewline
66 & 70.64 & 70.6739696250537 & -0.0339696250537145 \tabularnewline
67 & 70.98 & 70.644492734686 & 0.335507265313979 \tabularnewline
68 & 70.75 & 70.935626677483 & -0.185626677483015 \tabularnewline
69 & 70.88 & 70.7745505039064 & 0.105449496093613 \tabularnewline
70 & 70.88 & 70.8660535225816 & 0.0139464774184148 \tabularnewline
71 & 70.92 & 70.8781554749943 & 0.0418445250057005 \tabularnewline
72 & 70.89 & 70.914465751429 & -0.0244657514289344 \tabularnewline
73 & 71.02 & 70.8932357769593 & 0.126764223040709 \tabularnewline
74 & 71.01 & 71.0032344919645 & 0.00676550803554221 \tabularnewline
75 & 71.02 & 71.0091052114184 & 0.0108947885816093 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13053&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]68.61[/C][C]68.61[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]68.61[/C][C]68.61[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]68.58[/C][C]68.61[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]6[/C][C]68.75[/C][C]68.583967722351[/C][C]0.166032277648995[/C][/ROW]
[ROW][C]7[/C][C]68.54[/C][C]68.7280410006995[/C][C]-0.188041000699471[/C][/ROW]
[ROW][C]8[/C][C]68.5[/C][C]68.564869816046[/C][C]-0.0648698160459986[/C][/ROW]
[ROW][C]9[/C][C]68.47[/C][C]68.5085795139677[/C][C]-0.0385795139677043[/C][/ROW]
[ROW][C]10[/C][C]68.47[/C][C]68.475102426662[/C][C]-0.00510242666202032[/C][/ROW]
[ROW][C]11[/C][C]68.47[/C][C]68.4706748337437[/C][C]-0.000674833743701697[/C][/ROW]
[ROW][C]12[/C][C]68.59[/C][C]68.4700892517643[/C][C]0.119910748235739[/C][/ROW]
[ROW][C]13[/C][C]68.32[/C][C]68.5741409148033[/C][C]-0.254140914803344[/C][/ROW]
[ROW][C]14[/C][C]67.86[/C][C]68.353612019599[/C][C]-0.493612019598956[/C][/ROW]
[ROW][C]15[/C][C]67.91[/C][C]67.9252838480962[/C][C]-0.015283848096189[/C][/ROW]
[ROW][C]16[/C][C]67.91[/C][C]67.91202140219[/C][C]-0.00202140219002445[/C][/ROW]
[ROW][C]17[/C][C]68.05[/C][C]67.9102673454217[/C][C]0.139732654578339[/C][/ROW]
[ROW][C]18[/C][C]68.15[/C][C]68.0315193207755[/C][C]0.118480679224518[/C][/ROW]
[ROW][C]19[/C][C]68.25[/C][C]68.1343300520293[/C][C]0.115669947970687[/C][/ROW]
[ROW][C]20[/C][C]68.25[/C][C]68.2347017920699[/C][C]0.0152982079300870[/C][/ROW]
[ROW][C]21[/C][C]68.31[/C][C]68.2479766986155[/C][C]0.0620233013844853[/C][/ROW]
[ROW][C]22[/C][C]68.31[/C][C]68.3017969586938[/C][C]0.00820304130620286[/C][/ROW]
[ROW][C]23[/C][C]69.65[/C][C]68.3089150869888[/C][C]1.34108491301123[/C][/ROW]
[ROW][C]24[/C][C]69.65[/C][C]69.4726315805352[/C][C]0.177368419464827[/C][/ROW]
[ROW][C]25[/C][C]70.18[/C][C]69.6265417119243[/C][C]0.553458288075745[/C][/ROW]
[ROW][C]26[/C][C]70.08[/C][C]70.1068010393352[/C][C]-0.0268010393351830[/C][/ROW]
[ROW][C]27[/C][C]70.08[/C][C]70.0835446360933[/C][C]-0.00354463609333777[/C][/ROW]
[ROW][C]28[/C][C]70.09[/C][C]70.0804688043951[/C][C]0.00953119560487892[/C][/ROW]
[ROW][C]29[/C][C]70.04[/C][C]70.0887394287389[/C][C]-0.0487394287388838[/C][/ROW]
[ROW][C]30[/C][C]70.14[/C][C]70.0464461506927[/C][C]0.0935538493072556[/C][/ROW]
[ROW][C]31[/C][C]70.26[/C][C]70.127626810036[/C][C]0.132373189963957[/C][/ROW]
[ROW][C]32[/C][C]70.23[/C][C]70.2424926645169[/C][C]-0.0124926645168983[/C][/ROW]
[ROW][C]33[/C][C]70.54[/C][C]70.2316522474742[/C][C]0.308347752525762[/C][/ROW]
[ROW][C]34[/C][C]70.54[/C][C]70.4992187243474[/C][C]0.0407812756525772[/C][/ROW]
[ROW][C]35[/C][C]70.57[/C][C]70.5346063740364[/C][C]0.0353936259636214[/C][/ROW]
[ROW][C]36[/C][C]70.61[/C][C]70.5653189306394[/C][C]0.0446810693606352[/C][/ROW]
[ROW][C]37[/C][C]70.63[/C][C]70.6040905974144[/C][C]0.0259094025856257[/C][/ROW]
[ROW][C]38[/C][C]70.45[/C][C]70.6265732894753[/C][C]-0.176573289475328[/C][/ROW]
[ROW][C]39[/C][C]70.4[/C][C]70.4733531262414[/C][C]-0.0733531262413578[/C][/ROW]
[ROW][C]40[/C][C]70.4[/C][C]70.4097014946168[/C][C]-0.0097014946167917[/C][/ROW]
[ROW][C]41[/C][C]70.33[/C][C]70.4012830945676[/C][C]-0.0712830945676473[/C][/ROW]
[ROW][C]42[/C][C]70.51[/C][C]70.3394277175855[/C][C]0.170572282414525[/C][/ROW]
[ROW][C]43[/C][C]70.45[/C][C]70.4874405514201[/C][C]-0.0374405514200902[/C][/ROW]
[ROW][C]44[/C][C]70.39[/C][C]70.4549517904235[/C][C]-0.06495179042345[/C][/ROW]
[ROW][C]45[/C][C]70.59[/C][C]70.3985903556867[/C][C]0.191409644313310[/C][/ROW]
[ROW][C]46[/C][C]70.59[/C][C]70.5646846558687[/C][C]0.0253153441313003[/C][/ROW]
[ROW][C]47[/C][C]70.32[/C][C]70.5866518581089[/C][C]-0.266651858108915[/C][/ROW]
[ROW][C]48[/C][C]70.94[/C][C]70.3552666845785[/C][C]0.584733315421516[/C][/ROW]
[ROW][C]49[/C][C]70.44[/C][C]70.8626646851676[/C][C]-0.422664685167575[/C][/ROW]
[ROW][C]50[/C][C]70.57[/C][C]70.4959005372773[/C][C]0.074099462722728[/C][/ROW]
[ROW][C]51[/C][C]70.61[/C][C]70.5601997968519[/C][C]0.0498002031480809[/C][/ROW]
[ROW][C]52[/C][C]70.61[/C][C]70.6034135540295[/C][C]0.00658644597049829[/C][/ROW]
[ROW][C]53[/C][C]70.68[/C][C]70.6091288937036[/C][C]0.0708711062963658[/C][/ROW]
[ROW][C]54[/C][C]69.96[/C][C]70.6706267709169[/C][C]-0.710626770916932[/C][/ROW]
[ROW][C]55[/C][C]70.11[/C][C]70.0539856574062[/C][C]0.0560143425937838[/C][/ROW]
[ROW][C]56[/C][C]70.22[/C][C]70.1025916880305[/C][C]0.117408311969527[/C][/ROW]
[ROW][C]57[/C][C]70.49[/C][C]70.2044718805468[/C][C]0.285528119453161[/C][/ROW]
[ROW][C]58[/C][C]70.49[/C][C]70.4522367899535[/C][C]0.0377632100464496[/C][/ROW]
[ROW][C]59[/C][C]70.58[/C][C]70.4850055355818[/C][C]0.0949944644182352[/C][/ROW]
[ROW][C]60[/C][C]70.85[/C][C]70.5674362780102[/C][C]0.282563721989789[/C][/ROW]
[ROW][C]61[/C][C]70.69[/C][C]70.8126288534893[/C][C]-0.122628853489303[/C][/ROW]
[ROW][C]62[/C][C]70.7[/C][C]70.7062185747622[/C][C]-0.00621857476222942[/C][/ROW]
[ROW][C]63[/C][C]70.7[/C][C]70.7008224526025[/C][C]-0.00082245260252023[/C][/ROW]
[ROW][C]64[/C][C]70.7[/C][C]70.7001087754525[/C][C]-0.000108775452460463[/C][/ROW]
[ROW][C]65[/C][C]70.67[/C][C]70.7000143863598[/C][C]-0.0300143863597953[/C][/ROW]
[ROW][C]66[/C][C]70.64[/C][C]70.6739696250537[/C][C]-0.0339696250537145[/C][/ROW]
[ROW][C]67[/C][C]70.98[/C][C]70.644492734686[/C][C]0.335507265313979[/C][/ROW]
[ROW][C]68[/C][C]70.75[/C][C]70.935626677483[/C][C]-0.185626677483015[/C][/ROW]
[ROW][C]69[/C][C]70.88[/C][C]70.7745505039064[/C][C]0.105449496093613[/C][/ROW]
[ROW][C]70[/C][C]70.88[/C][C]70.8660535225816[/C][C]0.0139464774184148[/C][/ROW]
[ROW][C]71[/C][C]70.92[/C][C]70.8781554749943[/C][C]0.0418445250057005[/C][/ROW]
[ROW][C]72[/C][C]70.89[/C][C]70.914465751429[/C][C]-0.0244657514289344[/C][/ROW]
[ROW][C]73[/C][C]71.02[/C][C]70.8932357769593[/C][C]0.126764223040709[/C][/ROW]
[ROW][C]74[/C][C]71.01[/C][C]71.0032344919645[/C][C]0.00676550803554221[/C][/ROW]
[ROW][C]75[/C][C]71.02[/C][C]71.0091052114184[/C][C]0.0108947885816093[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13053&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13053&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
368.6168.610
468.6168.610
568.5868.61-0.0300000000000011
668.7568.5839677223510.166032277648995
768.5468.7280410006995-0.188041000699471
868.568.564869816046-0.0648698160459986
968.4768.5085795139677-0.0385795139677043
1068.4768.475102426662-0.00510242666202032
1168.4768.4706748337437-0.000674833743701697
1268.5968.47008925176430.119910748235739
1368.3268.5741409148033-0.254140914803344
1467.8668.353612019599-0.493612019598956
1567.9167.9252838480962-0.015283848096189
1667.9167.91202140219-0.00202140219002445
1768.0567.91026734542170.139732654578339
1868.1568.03151932077550.118480679224518
1968.2568.13433005202930.115669947970687
2068.2568.23470179206990.0152982079300870
2168.3168.24797669861550.0620233013844853
2268.3168.30179695869380.00820304130620286
2369.6568.30891508698881.34108491301123
2469.6569.47263158053520.177368419464827
2570.1869.62654171192430.553458288075745
2670.0870.1068010393352-0.0268010393351830
2770.0870.0835446360933-0.00354463609333777
2870.0970.08046880439510.00953119560487892
2970.0470.0887394287389-0.0487394287388838
3070.1470.04644615069270.0935538493072556
3170.2670.1276268100360.132373189963957
3270.2370.2424926645169-0.0124926645168983
3370.5470.23165224747420.308347752525762
3470.5470.49921872434740.0407812756525772
3570.5770.53460637403640.0353936259636214
3670.6170.56531893063940.0446810693606352
3770.6370.60409059741440.0259094025856257
3870.4570.6265732894753-0.176573289475328
3970.470.4733531262414-0.0733531262413578
4070.470.4097014946168-0.0097014946167917
4170.3370.4012830945676-0.0712830945676473
4270.5170.33942771758550.170572282414525
4370.4570.4874405514201-0.0374405514200902
4470.3970.4549517904235-0.06495179042345
4570.5970.39859035568670.191409644313310
4670.5970.56468465586870.0253153441313003
4770.3270.5866518581089-0.266651858108915
4870.9470.35526668457850.584733315421516
4970.4470.8626646851676-0.422664685167575
5070.5770.49590053727730.074099462722728
5170.6170.56019979685190.0498002031480809
5270.6170.60341355402950.00658644597049829
5370.6870.60912889370360.0708711062963658
5469.9670.6706267709169-0.710626770916932
5570.1170.05398565740620.0560143425937838
5670.2270.10259168803050.117408311969527
5770.4970.20447188054680.285528119453161
5870.4970.45223678995350.0377632100464496
5970.5870.48500553558180.0949944644182352
6070.8570.56743627801020.282563721989789
6170.6970.8126288534893-0.122628853489303
6270.770.7062185747622-0.00621857476222942
6370.770.7008224526025-0.00082245260252023
6470.770.7001087754525-0.000108775452460463
6570.6770.7000143863598-0.0300143863597953
6670.6470.6739696250537-0.0339696250537145
6770.9870.6444927346860.335507265313979
6870.7570.935626677483-0.185626677483015
6970.8870.77455050390640.105449496093613
7070.8870.86605352258160.0139464774184148
7170.9270.87815547499430.0418445250057005
7270.8970.914465751429-0.0244657514289344
7371.0270.89323577695930.126764223040709
7471.0171.00323449196450.00676550803554221
7571.0271.00910521141840.0108947885816093







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7671.018559083461270.544577814776471.492540352146
7771.018559083461270.39100766900871.6461104979143
7871.018559083461270.268236944310171.7688812226122
7971.018559083461270.162903868308371.874214298614
8071.018559083461270.069186458020471.967931708902
8171.018559083461269.983923439065372.053194727857
8271.018559083461269.905170808252372.13194735867
8371.018559083461269.831631964346272.2054862025762
8471.018559083461269.762390893763372.274727273159
8571.018559083461269.696772014555372.340346152367
8671.018559083461269.634260130833972.4028580360884
8771.018559083461269.574451703463872.4626664634586

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 71.0185590834612 & 70.5445778147764 & 71.492540352146 \tabularnewline
77 & 71.0185590834612 & 70.391007669008 & 71.6461104979143 \tabularnewline
78 & 71.0185590834612 & 70.2682369443101 & 71.7688812226122 \tabularnewline
79 & 71.0185590834612 & 70.1629038683083 & 71.874214298614 \tabularnewline
80 & 71.0185590834612 & 70.0691864580204 & 71.967931708902 \tabularnewline
81 & 71.0185590834612 & 69.9839234390653 & 72.053194727857 \tabularnewline
82 & 71.0185590834612 & 69.9051708082523 & 72.13194735867 \tabularnewline
83 & 71.0185590834612 & 69.8316319643462 & 72.2054862025762 \tabularnewline
84 & 71.0185590834612 & 69.7623908937633 & 72.274727273159 \tabularnewline
85 & 71.0185590834612 & 69.6967720145553 & 72.340346152367 \tabularnewline
86 & 71.0185590834612 & 69.6342601308339 & 72.4028580360884 \tabularnewline
87 & 71.0185590834612 & 69.5744517034638 & 72.4626664634586 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13053&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]76[/C][C]71.0185590834612[/C][C]70.5445778147764[/C][C]71.492540352146[/C][/ROW]
[ROW][C]77[/C][C]71.0185590834612[/C][C]70.391007669008[/C][C]71.6461104979143[/C][/ROW]
[ROW][C]78[/C][C]71.0185590834612[/C][C]70.2682369443101[/C][C]71.7688812226122[/C][/ROW]
[ROW][C]79[/C][C]71.0185590834612[/C][C]70.1629038683083[/C][C]71.874214298614[/C][/ROW]
[ROW][C]80[/C][C]71.0185590834612[/C][C]70.0691864580204[/C][C]71.967931708902[/C][/ROW]
[ROW][C]81[/C][C]71.0185590834612[/C][C]69.9839234390653[/C][C]72.053194727857[/C][/ROW]
[ROW][C]82[/C][C]71.0185590834612[/C][C]69.9051708082523[/C][C]72.13194735867[/C][/ROW]
[ROW][C]83[/C][C]71.0185590834612[/C][C]69.8316319643462[/C][C]72.2054862025762[/C][/ROW]
[ROW][C]84[/C][C]71.0185590834612[/C][C]69.7623908937633[/C][C]72.274727273159[/C][/ROW]
[ROW][C]85[/C][C]71.0185590834612[/C][C]69.6967720145553[/C][C]72.340346152367[/C][/ROW]
[ROW][C]86[/C][C]71.0185590834612[/C][C]69.6342601308339[/C][C]72.4028580360884[/C][/ROW]
[ROW][C]87[/C][C]71.0185590834612[/C][C]69.5744517034638[/C][C]72.4626664634586[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13053&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13053&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
7671.018559083461270.544577814776471.492540352146
7771.018559083461270.39100766900871.6461104979143
7871.018559083461270.268236944310171.7688812226122
7971.018559083461270.162903868308371.874214298614
8071.018559083461270.069186458020471.967931708902
8171.018559083461269.983923439065372.053194727857
8271.018559083461269.905170808252372.13194735867
8371.018559083461269.831631964346272.2054862025762
8471.018559083461269.762390893763372.274727273159
8571.018559083461269.696772014555372.340346152367
8671.018559083461269.634260130833972.4028580360884
8771.018559083461269.574451703463872.4626664634586



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')