Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 22 Apr 2016 07:28:56 +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/22/t1461306675kh4nq1jqaek9fr9.htm/, Retrieved Mon, 06 May 2024 02:52:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294584, Retrieved Mon, 06 May 2024 02:52:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-22 06:28:56] [3fd8a2781b4a66a294f894c9e659cf7e] [Current]
Feedback Forum

Post a new message
Dataseries X:
97,78
97,73
97,61
97,69
97,68
97,67
97,67
97,96
98,27
99,52
99,59
99,75
99,75
99,8
99,99
100,25
100,08
100,08
100,08
100,06
101
101,81
101,82
101,96
101,96
101,93
102,03
102,11
102,07
102,34
102,34
102,33
102,77
103,08
103,38
103,44
99,1
99,15
99,21
99,01
99,08
99,11
100,11
100,31
100,55
101,38
101,49
101,5
100,69
100,8
100,58
100,34
100,38
100,33
101,06
101,15
101,36
101,98
102,24
102,34




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294584&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]2 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=294584&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294584&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999946824755918
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999946824755918 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294584&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]0.999946824755918[/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=294584&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294584&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
alpha0.999946824755918
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
297.7397.78-0.0499999999999972
397.6197.7300026587622-0.120002658762203
497.6997.61000638117070.0799936188293344
597.6897.6899957463198-0.00999574631977396
697.6797.6800005315263-0.0100005315262592
797.6797.6700005317807-5.31780699475348e-07
897.9697.67000000002830.289999999971712
998.2797.95998457917920.310015420820775
1099.5298.26998351485431.25001648514566
1199.5999.51993353006830.0700664699317031
1299.7599.58999627419840.160003725801644
1399.7599.74999149176288.50823717257754e-06
1499.899.74999999954760.0500000004524139
1599.9999.79999734123780.190002658762225
16100.2599.98998989656220.260010103437764
17100.08100.249986173899-0.169986173899289
18100.08100.080009039056-9.03905629456858e-06
19100.08100.080000000481-4.80653739032277e-10
20100.06100.08-0.0200000000000244
21101100.0600010635050.939998936495115
22101.81100.9999500153270.810049984672887
23101.82101.8099569253940.0100430746056475
24101.96101.8199994659570.14000053404294
25101.96101.9599925554377.44456256995818e-06
26101.93101.959999999604-0.0299999996041294
27102.03101.9300015952570.0999984047426921
28102.11102.029994682560.0800053174395714
29102.07102.109995745698-0.0399957456977234
30102.34102.0700021267840.269997873216468
31102.34102.3399856427971.43572028008521e-05
32102.33102.339999999237-0.00999999923655537
33102.77102.3300005317520.439999468247606
34103.08102.7699766029210.310023397079135
35103.38103.079983514430.300016485569799
36103.44103.379984046550.0600159534498488
3799.1103.439996808637-4.33999680863704
3899.1599.10023078038960.0497692196103969
3999.2199.14999735350960.0600026464903891
4099.0199.2099968093446-0.199996809344611
4199.0899.01001063487920.0699893651208328
4299.1199.07999627829840.0300037217015756
43100.1199.10999840454481.00000159545523
44100.31100.1099468246710.200053175328918
45100.55100.3099893621240.240010637876424
46101.38100.5499872373760.83001276262425
47101.49101.3799558638690.110044136131251
48101.5101.4899941483760.0100058516238022
49100.69101.499999467936-0.809999467936407
50100.8100.6900430719190.109956928080592
51100.58100.799994153014-0.219994153013516
52100.34100.580011698243-0.240011698242768
53100.38100.3400127626810.0399872373193517
54100.33100.379997873669-0.0499978736689002
55101.06100.3300026586490.729997341350867
56101.15101.0599611822130.0900388177868052
57101.36101.1499952121640.210004787836112
58101.98101.3599888329440.620011167055864
59102.24101.9799670307550.260032969245131
60102.34102.2399861726830.100013827316616

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 97.73 & 97.78 & -0.0499999999999972 \tabularnewline
3 & 97.61 & 97.7300026587622 & -0.120002658762203 \tabularnewline
4 & 97.69 & 97.6100063811707 & 0.0799936188293344 \tabularnewline
5 & 97.68 & 97.6899957463198 & -0.00999574631977396 \tabularnewline
6 & 97.67 & 97.6800005315263 & -0.0100005315262592 \tabularnewline
7 & 97.67 & 97.6700005317807 & -5.31780699475348e-07 \tabularnewline
8 & 97.96 & 97.6700000000283 & 0.289999999971712 \tabularnewline
9 & 98.27 & 97.9599845791792 & 0.310015420820775 \tabularnewline
10 & 99.52 & 98.2699835148543 & 1.25001648514566 \tabularnewline
11 & 99.59 & 99.5199335300683 & 0.0700664699317031 \tabularnewline
12 & 99.75 & 99.5899962741984 & 0.160003725801644 \tabularnewline
13 & 99.75 & 99.7499914917628 & 8.50823717257754e-06 \tabularnewline
14 & 99.8 & 99.7499999995476 & 0.0500000004524139 \tabularnewline
15 & 99.99 & 99.7999973412378 & 0.190002658762225 \tabularnewline
16 & 100.25 & 99.9899898965622 & 0.260010103437764 \tabularnewline
17 & 100.08 & 100.249986173899 & -0.169986173899289 \tabularnewline
18 & 100.08 & 100.080009039056 & -9.03905629456858e-06 \tabularnewline
19 & 100.08 & 100.080000000481 & -4.80653739032277e-10 \tabularnewline
20 & 100.06 & 100.08 & -0.0200000000000244 \tabularnewline
21 & 101 & 100.060001063505 & 0.939998936495115 \tabularnewline
22 & 101.81 & 100.999950015327 & 0.810049984672887 \tabularnewline
23 & 101.82 & 101.809956925394 & 0.0100430746056475 \tabularnewline
24 & 101.96 & 101.819999465957 & 0.14000053404294 \tabularnewline
25 & 101.96 & 101.959992555437 & 7.44456256995818e-06 \tabularnewline
26 & 101.93 & 101.959999999604 & -0.0299999996041294 \tabularnewline
27 & 102.03 & 101.930001595257 & 0.0999984047426921 \tabularnewline
28 & 102.11 & 102.02999468256 & 0.0800053174395714 \tabularnewline
29 & 102.07 & 102.109995745698 & -0.0399957456977234 \tabularnewline
30 & 102.34 & 102.070002126784 & 0.269997873216468 \tabularnewline
31 & 102.34 & 102.339985642797 & 1.43572028008521e-05 \tabularnewline
32 & 102.33 & 102.339999999237 & -0.00999999923655537 \tabularnewline
33 & 102.77 & 102.330000531752 & 0.439999468247606 \tabularnewline
34 & 103.08 & 102.769976602921 & 0.310023397079135 \tabularnewline
35 & 103.38 & 103.07998351443 & 0.300016485569799 \tabularnewline
36 & 103.44 & 103.37998404655 & 0.0600159534498488 \tabularnewline
37 & 99.1 & 103.439996808637 & -4.33999680863704 \tabularnewline
38 & 99.15 & 99.1002307803896 & 0.0497692196103969 \tabularnewline
39 & 99.21 & 99.1499973535096 & 0.0600026464903891 \tabularnewline
40 & 99.01 & 99.2099968093446 & -0.199996809344611 \tabularnewline
41 & 99.08 & 99.0100106348792 & 0.0699893651208328 \tabularnewline
42 & 99.11 & 99.0799962782984 & 0.0300037217015756 \tabularnewline
43 & 100.11 & 99.1099984045448 & 1.00000159545523 \tabularnewline
44 & 100.31 & 100.109946824671 & 0.200053175328918 \tabularnewline
45 & 100.55 & 100.309989362124 & 0.240010637876424 \tabularnewline
46 & 101.38 & 100.549987237376 & 0.83001276262425 \tabularnewline
47 & 101.49 & 101.379955863869 & 0.110044136131251 \tabularnewline
48 & 101.5 & 101.489994148376 & 0.0100058516238022 \tabularnewline
49 & 100.69 & 101.499999467936 & -0.809999467936407 \tabularnewline
50 & 100.8 & 100.690043071919 & 0.109956928080592 \tabularnewline
51 & 100.58 & 100.799994153014 & -0.219994153013516 \tabularnewline
52 & 100.34 & 100.580011698243 & -0.240011698242768 \tabularnewline
53 & 100.38 & 100.340012762681 & 0.0399872373193517 \tabularnewline
54 & 100.33 & 100.379997873669 & -0.0499978736689002 \tabularnewline
55 & 101.06 & 100.330002658649 & 0.729997341350867 \tabularnewline
56 & 101.15 & 101.059961182213 & 0.0900388177868052 \tabularnewline
57 & 101.36 & 101.149995212164 & 0.210004787836112 \tabularnewline
58 & 101.98 & 101.359988832944 & 0.620011167055864 \tabularnewline
59 & 102.24 & 101.979967030755 & 0.260032969245131 \tabularnewline
60 & 102.34 & 102.239986172683 & 0.100013827316616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294584&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]97.73[/C][C]97.78[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]3[/C][C]97.61[/C][C]97.7300026587622[/C][C]-0.120002658762203[/C][/ROW]
[ROW][C]4[/C][C]97.69[/C][C]97.6100063811707[/C][C]0.0799936188293344[/C][/ROW]
[ROW][C]5[/C][C]97.68[/C][C]97.6899957463198[/C][C]-0.00999574631977396[/C][/ROW]
[ROW][C]6[/C][C]97.67[/C][C]97.6800005315263[/C][C]-0.0100005315262592[/C][/ROW]
[ROW][C]7[/C][C]97.67[/C][C]97.6700005317807[/C][C]-5.31780699475348e-07[/C][/ROW]
[ROW][C]8[/C][C]97.96[/C][C]97.6700000000283[/C][C]0.289999999971712[/C][/ROW]
[ROW][C]9[/C][C]98.27[/C][C]97.9599845791792[/C][C]0.310015420820775[/C][/ROW]
[ROW][C]10[/C][C]99.52[/C][C]98.2699835148543[/C][C]1.25001648514566[/C][/ROW]
[ROW][C]11[/C][C]99.59[/C][C]99.5199335300683[/C][C]0.0700664699317031[/C][/ROW]
[ROW][C]12[/C][C]99.75[/C][C]99.5899962741984[/C][C]0.160003725801644[/C][/ROW]
[ROW][C]13[/C][C]99.75[/C][C]99.7499914917628[/C][C]8.50823717257754e-06[/C][/ROW]
[ROW][C]14[/C][C]99.8[/C][C]99.7499999995476[/C][C]0.0500000004524139[/C][/ROW]
[ROW][C]15[/C][C]99.99[/C][C]99.7999973412378[/C][C]0.190002658762225[/C][/ROW]
[ROW][C]16[/C][C]100.25[/C][C]99.9899898965622[/C][C]0.260010103437764[/C][/ROW]
[ROW][C]17[/C][C]100.08[/C][C]100.249986173899[/C][C]-0.169986173899289[/C][/ROW]
[ROW][C]18[/C][C]100.08[/C][C]100.080009039056[/C][C]-9.03905629456858e-06[/C][/ROW]
[ROW][C]19[/C][C]100.08[/C][C]100.080000000481[/C][C]-4.80653739032277e-10[/C][/ROW]
[ROW][C]20[/C][C]100.06[/C][C]100.08[/C][C]-0.0200000000000244[/C][/ROW]
[ROW][C]21[/C][C]101[/C][C]100.060001063505[/C][C]0.939998936495115[/C][/ROW]
[ROW][C]22[/C][C]101.81[/C][C]100.999950015327[/C][C]0.810049984672887[/C][/ROW]
[ROW][C]23[/C][C]101.82[/C][C]101.809956925394[/C][C]0.0100430746056475[/C][/ROW]
[ROW][C]24[/C][C]101.96[/C][C]101.819999465957[/C][C]0.14000053404294[/C][/ROW]
[ROW][C]25[/C][C]101.96[/C][C]101.959992555437[/C][C]7.44456256995818e-06[/C][/ROW]
[ROW][C]26[/C][C]101.93[/C][C]101.959999999604[/C][C]-0.0299999996041294[/C][/ROW]
[ROW][C]27[/C][C]102.03[/C][C]101.930001595257[/C][C]0.0999984047426921[/C][/ROW]
[ROW][C]28[/C][C]102.11[/C][C]102.02999468256[/C][C]0.0800053174395714[/C][/ROW]
[ROW][C]29[/C][C]102.07[/C][C]102.109995745698[/C][C]-0.0399957456977234[/C][/ROW]
[ROW][C]30[/C][C]102.34[/C][C]102.070002126784[/C][C]0.269997873216468[/C][/ROW]
[ROW][C]31[/C][C]102.34[/C][C]102.339985642797[/C][C]1.43572028008521e-05[/C][/ROW]
[ROW][C]32[/C][C]102.33[/C][C]102.339999999237[/C][C]-0.00999999923655537[/C][/ROW]
[ROW][C]33[/C][C]102.77[/C][C]102.330000531752[/C][C]0.439999468247606[/C][/ROW]
[ROW][C]34[/C][C]103.08[/C][C]102.769976602921[/C][C]0.310023397079135[/C][/ROW]
[ROW][C]35[/C][C]103.38[/C][C]103.07998351443[/C][C]0.300016485569799[/C][/ROW]
[ROW][C]36[/C][C]103.44[/C][C]103.37998404655[/C][C]0.0600159534498488[/C][/ROW]
[ROW][C]37[/C][C]99.1[/C][C]103.439996808637[/C][C]-4.33999680863704[/C][/ROW]
[ROW][C]38[/C][C]99.15[/C][C]99.1002307803896[/C][C]0.0497692196103969[/C][/ROW]
[ROW][C]39[/C][C]99.21[/C][C]99.1499973535096[/C][C]0.0600026464903891[/C][/ROW]
[ROW][C]40[/C][C]99.01[/C][C]99.2099968093446[/C][C]-0.199996809344611[/C][/ROW]
[ROW][C]41[/C][C]99.08[/C][C]99.0100106348792[/C][C]0.0699893651208328[/C][/ROW]
[ROW][C]42[/C][C]99.11[/C][C]99.0799962782984[/C][C]0.0300037217015756[/C][/ROW]
[ROW][C]43[/C][C]100.11[/C][C]99.1099984045448[/C][C]1.00000159545523[/C][/ROW]
[ROW][C]44[/C][C]100.31[/C][C]100.109946824671[/C][C]0.200053175328918[/C][/ROW]
[ROW][C]45[/C][C]100.55[/C][C]100.309989362124[/C][C]0.240010637876424[/C][/ROW]
[ROW][C]46[/C][C]101.38[/C][C]100.549987237376[/C][C]0.83001276262425[/C][/ROW]
[ROW][C]47[/C][C]101.49[/C][C]101.379955863869[/C][C]0.110044136131251[/C][/ROW]
[ROW][C]48[/C][C]101.5[/C][C]101.489994148376[/C][C]0.0100058516238022[/C][/ROW]
[ROW][C]49[/C][C]100.69[/C][C]101.499999467936[/C][C]-0.809999467936407[/C][/ROW]
[ROW][C]50[/C][C]100.8[/C][C]100.690043071919[/C][C]0.109956928080592[/C][/ROW]
[ROW][C]51[/C][C]100.58[/C][C]100.799994153014[/C][C]-0.219994153013516[/C][/ROW]
[ROW][C]52[/C][C]100.34[/C][C]100.580011698243[/C][C]-0.240011698242768[/C][/ROW]
[ROW][C]53[/C][C]100.38[/C][C]100.340012762681[/C][C]0.0399872373193517[/C][/ROW]
[ROW][C]54[/C][C]100.33[/C][C]100.379997873669[/C][C]-0.0499978736689002[/C][/ROW]
[ROW][C]55[/C][C]101.06[/C][C]100.330002658649[/C][C]0.729997341350867[/C][/ROW]
[ROW][C]56[/C][C]101.15[/C][C]101.059961182213[/C][C]0.0900388177868052[/C][/ROW]
[ROW][C]57[/C][C]101.36[/C][C]101.149995212164[/C][C]0.210004787836112[/C][/ROW]
[ROW][C]58[/C][C]101.98[/C][C]101.359988832944[/C][C]0.620011167055864[/C][/ROW]
[ROW][C]59[/C][C]102.24[/C][C]101.979967030755[/C][C]0.260032969245131[/C][/ROW]
[ROW][C]60[/C][C]102.34[/C][C]102.239986172683[/C][C]0.100013827316616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294584&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294584&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
297.7397.78-0.0499999999999972
397.6197.7300026587622-0.120002658762203
497.6997.61000638117070.0799936188293344
597.6897.6899957463198-0.00999574631977396
697.6797.6800005315263-0.0100005315262592
797.6797.6700005317807-5.31780699475348e-07
897.9697.67000000002830.289999999971712
998.2797.95998457917920.310015420820775
1099.5298.26998351485431.25001648514566
1199.5999.51993353006830.0700664699317031
1299.7599.58999627419840.160003725801644
1399.7599.74999149176288.50823717257754e-06
1499.899.74999999954760.0500000004524139
1599.9999.79999734123780.190002658762225
16100.2599.98998989656220.260010103437764
17100.08100.249986173899-0.169986173899289
18100.08100.080009039056-9.03905629456858e-06
19100.08100.080000000481-4.80653739032277e-10
20100.06100.08-0.0200000000000244
21101100.0600010635050.939998936495115
22101.81100.9999500153270.810049984672887
23101.82101.8099569253940.0100430746056475
24101.96101.8199994659570.14000053404294
25101.96101.9599925554377.44456256995818e-06
26101.93101.959999999604-0.0299999996041294
27102.03101.9300015952570.0999984047426921
28102.11102.029994682560.0800053174395714
29102.07102.109995745698-0.0399957456977234
30102.34102.0700021267840.269997873216468
31102.34102.3399856427971.43572028008521e-05
32102.33102.339999999237-0.00999999923655537
33102.77102.3300005317520.439999468247606
34103.08102.7699766029210.310023397079135
35103.38103.079983514430.300016485569799
36103.44103.379984046550.0600159534498488
3799.1103.439996808637-4.33999680863704
3899.1599.10023078038960.0497692196103969
3999.2199.14999735350960.0600026464903891
4099.0199.2099968093446-0.199996809344611
4199.0899.01001063487920.0699893651208328
4299.1199.07999627829840.0300037217015756
43100.1199.10999840454481.00000159545523
44100.31100.1099468246710.200053175328918
45100.55100.3099893621240.240010637876424
46101.38100.5499872373760.83001276262425
47101.49101.3799558638690.110044136131251
48101.5101.4899941483760.0100058516238022
49100.69101.499999467936-0.809999467936407
50100.8100.6900430719190.109956928080592
51100.58100.799994153014-0.219994153013516
52100.34100.580011698243-0.240011698242768
53100.38100.3400127626810.0399872373193517
54100.33100.379997873669-0.0499978736689002
55101.06100.3300026586490.729997341350867
56101.15101.0599611822130.0900388177868052
57101.36101.1499952121640.210004787836112
58101.98101.3599888329440.620011167055864
59102.24101.9799670307550.260032969245131
60102.34102.2399861726830.100013827316616







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61102.33999468174101.024552770005103.655436593475
62102.33999468174100.479728350366104.200261013114
63102.33999468174100.061663225578104.618326137903
64102.3399946817499.70921578099104.970773582491
65102.3399946817499.3987022744596105.281287089021
66102.3399946817499.1179759937712105.562013369709
67102.3399946817498.8598211478319105.820168215649
68102.3399946817498.6195362117919106.060453151689
69102.3399946817498.3938554765036106.286133886977
70102.3399946817498.1804011886691106.499588174812
71102.3399946817497.9773783305016106.702611032979
72102.3399946817497.7833923479186106.896597015562

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 102.33999468174 & 101.024552770005 & 103.655436593475 \tabularnewline
62 & 102.33999468174 & 100.479728350366 & 104.200261013114 \tabularnewline
63 & 102.33999468174 & 100.061663225578 & 104.618326137903 \tabularnewline
64 & 102.33999468174 & 99.70921578099 & 104.970773582491 \tabularnewline
65 & 102.33999468174 & 99.3987022744596 & 105.281287089021 \tabularnewline
66 & 102.33999468174 & 99.1179759937712 & 105.562013369709 \tabularnewline
67 & 102.33999468174 & 98.8598211478319 & 105.820168215649 \tabularnewline
68 & 102.33999468174 & 98.6195362117919 & 106.060453151689 \tabularnewline
69 & 102.33999468174 & 98.3938554765036 & 106.286133886977 \tabularnewline
70 & 102.33999468174 & 98.1804011886691 & 106.499588174812 \tabularnewline
71 & 102.33999468174 & 97.9773783305016 & 106.702611032979 \tabularnewline
72 & 102.33999468174 & 97.7833923479186 & 106.896597015562 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294584&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]61[/C][C]102.33999468174[/C][C]101.024552770005[/C][C]103.655436593475[/C][/ROW]
[ROW][C]62[/C][C]102.33999468174[/C][C]100.479728350366[/C][C]104.200261013114[/C][/ROW]
[ROW][C]63[/C][C]102.33999468174[/C][C]100.061663225578[/C][C]104.618326137903[/C][/ROW]
[ROW][C]64[/C][C]102.33999468174[/C][C]99.70921578099[/C][C]104.970773582491[/C][/ROW]
[ROW][C]65[/C][C]102.33999468174[/C][C]99.3987022744596[/C][C]105.281287089021[/C][/ROW]
[ROW][C]66[/C][C]102.33999468174[/C][C]99.1179759937712[/C][C]105.562013369709[/C][/ROW]
[ROW][C]67[/C][C]102.33999468174[/C][C]98.8598211478319[/C][C]105.820168215649[/C][/ROW]
[ROW][C]68[/C][C]102.33999468174[/C][C]98.6195362117919[/C][C]106.060453151689[/C][/ROW]
[ROW][C]69[/C][C]102.33999468174[/C][C]98.3938554765036[/C][C]106.286133886977[/C][/ROW]
[ROW][C]70[/C][C]102.33999468174[/C][C]98.1804011886691[/C][C]106.499588174812[/C][/ROW]
[ROW][C]71[/C][C]102.33999468174[/C][C]97.9773783305016[/C][C]106.702611032979[/C][/ROW]
[ROW][C]72[/C][C]102.33999468174[/C][C]97.7833923479186[/C][C]106.896597015562[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294584&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294584&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
61102.33999468174101.024552770005103.655436593475
62102.33999468174100.479728350366104.200261013114
63102.33999468174100.061663225578104.618326137903
64102.3399946817499.70921578099104.970773582491
65102.3399946817499.3987022744596105.281287089021
66102.3399946817499.1179759937712105.562013369709
67102.3399946817498.8598211478319105.820168215649
68102.3399946817498.6195362117919106.060453151689
69102.3399946817498.3938554765036106.286133886977
70102.3399946817498.1804011886691106.499588174812
71102.3399946817497.9773783305016106.702611032979
72102.3399946817497.7833923479186106.896597015562



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')