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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 27 Nov 2014 10:24:18 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/27/t1417083904wm2mfj2oa9xut8r.htm/, Retrieved Sun, 19 May 2024 19:18:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=259606, Retrieved Sun, 19 May 2024 19:18:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-27 10:24:18] [ee5b56c0207c42e2c93809919b6c628c] [Current]
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Dataseries X:
122.5
123.1
123.1
124.4
124.4
124.6
125.9
125.9
125.9
125.9
125.9
125.9
128.2
129.3
129.3
129.3
129.3
129.4
129.6
129.6
129.6
130
130
129.4
130.2
130.2
130.2
130.3
130.3
130.3
130.7
130.7
130.7
130.9
130.9
130.9
131.2
131.8
131.8
131.8
131.9
132
132.3
132.3
132.4
132.8
132.8
132.8
133
133.5
133.5
134.4
134.4
134.5
134.6
135.6
135.6
135.6
135.6
135.6
135.7
136.2
136.2
136.2
136.2
136.2
136.3
136.3
136.3
136.3
136.3
136.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259606&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259606&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259606&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.859211441588206
beta0.0302009590136069
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.859211441588206 \tabularnewline
beta & 0.0302009590136069 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259606&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]0.859211441588206[/C][/ROW]
[ROW][C]beta[/C][C]0.0302009590136069[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259606&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259606&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
alpha0.859211441588206
beta0.0302009590136069
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13128.2125.619845085472.58015491452991
14129.3129.0729415115690.227058488430714
15129.3129.410122508084-0.110122508084203
16129.3129.438069497829-0.138069497828809
17129.3129.421754680845-0.121754680845044
18129.4129.541298327907-0.141298327907435
19129.6130.598716631479-0.998716631479169
20129.6129.656015611005-0.0560156110054493
21129.6129.5010072103620.0989927896376059
22130129.5359192326030.464080767397348
23130129.9507281254440.049271874556382
24129.4130.014573694492-0.614573694492236
25130.2132.205344267406-2.00534426740626
26130.2131.300400142743-1.10040014274281
27130.2130.328257897407-0.128257897407053
28130.3130.2149331700710.0850668299288486
29130.3130.2766717785120.0233282214881285
30130.3130.405920750974-0.105920750974462
31130.7131.261739157221-0.561739157220671
32130.7130.72727280339-0.0272728033903036
33130.7130.5195869119290.180413088071163
34130.9130.578772123090.321227876909859
35130.9130.7116486677510.188351332248857
36130.9130.7043488474680.195651152531781
37131.2133.319311637444-2.11931163744387
38131.8132.364736225141-0.564736225141189
39131.8131.92449400196-0.124494001960471
40131.8131.7793195568650.0206804431350065
41131.9131.7102564118170.189743588182836
42132131.9018247652350.0981752347647955
43132.3132.811657020322-0.511657020321564
44132.3132.339594399881-0.0395943998809969
45132.4132.0943675566440.305632443355819
46132.8132.2280232075890.571976792411448
47132.8132.5112007041340.28879929586634
48132.8132.5474032917040.252596708296409
49133134.843020398586-1.84302039858571
50133.5134.309519812975-0.80951981297514
51133.5133.679401708528-0.17940170852836
52134.4133.4645279441210.935472055879245
53134.4134.1860434217210.213956578278896
54134.5134.3669294257390.133070574260813
55134.6135.203197600158-0.603197600157529
56135.6134.6988787430310.901121256968963
57135.6135.3148756456380.285124354361983
58135.6135.4722226848340.127777315165531
59135.6135.3261581562160.273841843783771
60135.6135.3363114881860.263688511814479
61135.7137.338606977893-1.63860697789286
62136.2137.123737215319-0.923737215319193
63136.2136.47872321864-0.278723218639612
64136.2136.327423038774-0.127423038773628
65136.2135.9984749832580.201525016742039
66136.2136.1213384541370.078661545862559
67136.3136.769834404225-0.469834404224997
68136.3136.557989027335-0.257989027334986
69136.3136.0273574450040.272642554996111
70136.3136.0875210755270.212478924473373
71136.3135.9726890350050.327310964994979
72136.3135.9666333272950.333366672705296

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 128.2 & 125.61984508547 & 2.58015491452991 \tabularnewline
14 & 129.3 & 129.072941511569 & 0.227058488430714 \tabularnewline
15 & 129.3 & 129.410122508084 & -0.110122508084203 \tabularnewline
16 & 129.3 & 129.438069497829 & -0.138069497828809 \tabularnewline
17 & 129.3 & 129.421754680845 & -0.121754680845044 \tabularnewline
18 & 129.4 & 129.541298327907 & -0.141298327907435 \tabularnewline
19 & 129.6 & 130.598716631479 & -0.998716631479169 \tabularnewline
20 & 129.6 & 129.656015611005 & -0.0560156110054493 \tabularnewline
21 & 129.6 & 129.501007210362 & 0.0989927896376059 \tabularnewline
22 & 130 & 129.535919232603 & 0.464080767397348 \tabularnewline
23 & 130 & 129.950728125444 & 0.049271874556382 \tabularnewline
24 & 129.4 & 130.014573694492 & -0.614573694492236 \tabularnewline
25 & 130.2 & 132.205344267406 & -2.00534426740626 \tabularnewline
26 & 130.2 & 131.300400142743 & -1.10040014274281 \tabularnewline
27 & 130.2 & 130.328257897407 & -0.128257897407053 \tabularnewline
28 & 130.3 & 130.214933170071 & 0.0850668299288486 \tabularnewline
29 & 130.3 & 130.276671778512 & 0.0233282214881285 \tabularnewline
30 & 130.3 & 130.405920750974 & -0.105920750974462 \tabularnewline
31 & 130.7 & 131.261739157221 & -0.561739157220671 \tabularnewline
32 & 130.7 & 130.72727280339 & -0.0272728033903036 \tabularnewline
33 & 130.7 & 130.519586911929 & 0.180413088071163 \tabularnewline
34 & 130.9 & 130.57877212309 & 0.321227876909859 \tabularnewline
35 & 130.9 & 130.711648667751 & 0.188351332248857 \tabularnewline
36 & 130.9 & 130.704348847468 & 0.195651152531781 \tabularnewline
37 & 131.2 & 133.319311637444 & -2.11931163744387 \tabularnewline
38 & 131.8 & 132.364736225141 & -0.564736225141189 \tabularnewline
39 & 131.8 & 131.92449400196 & -0.124494001960471 \tabularnewline
40 & 131.8 & 131.779319556865 & 0.0206804431350065 \tabularnewline
41 & 131.9 & 131.710256411817 & 0.189743588182836 \tabularnewline
42 & 132 & 131.901824765235 & 0.0981752347647955 \tabularnewline
43 & 132.3 & 132.811657020322 & -0.511657020321564 \tabularnewline
44 & 132.3 & 132.339594399881 & -0.0395943998809969 \tabularnewline
45 & 132.4 & 132.094367556644 & 0.305632443355819 \tabularnewline
46 & 132.8 & 132.228023207589 & 0.571976792411448 \tabularnewline
47 & 132.8 & 132.511200704134 & 0.28879929586634 \tabularnewline
48 & 132.8 & 132.547403291704 & 0.252596708296409 \tabularnewline
49 & 133 & 134.843020398586 & -1.84302039858571 \tabularnewline
50 & 133.5 & 134.309519812975 & -0.80951981297514 \tabularnewline
51 & 133.5 & 133.679401708528 & -0.17940170852836 \tabularnewline
52 & 134.4 & 133.464527944121 & 0.935472055879245 \tabularnewline
53 & 134.4 & 134.186043421721 & 0.213956578278896 \tabularnewline
54 & 134.5 & 134.366929425739 & 0.133070574260813 \tabularnewline
55 & 134.6 & 135.203197600158 & -0.603197600157529 \tabularnewline
56 & 135.6 & 134.698878743031 & 0.901121256968963 \tabularnewline
57 & 135.6 & 135.314875645638 & 0.285124354361983 \tabularnewline
58 & 135.6 & 135.472222684834 & 0.127777315165531 \tabularnewline
59 & 135.6 & 135.326158156216 & 0.273841843783771 \tabularnewline
60 & 135.6 & 135.336311488186 & 0.263688511814479 \tabularnewline
61 & 135.7 & 137.338606977893 & -1.63860697789286 \tabularnewline
62 & 136.2 & 137.123737215319 & -0.923737215319193 \tabularnewline
63 & 136.2 & 136.47872321864 & -0.278723218639612 \tabularnewline
64 & 136.2 & 136.327423038774 & -0.127423038773628 \tabularnewline
65 & 136.2 & 135.998474983258 & 0.201525016742039 \tabularnewline
66 & 136.2 & 136.121338454137 & 0.078661545862559 \tabularnewline
67 & 136.3 & 136.769834404225 & -0.469834404224997 \tabularnewline
68 & 136.3 & 136.557989027335 & -0.257989027334986 \tabularnewline
69 & 136.3 & 136.027357445004 & 0.272642554996111 \tabularnewline
70 & 136.3 & 136.087521075527 & 0.212478924473373 \tabularnewline
71 & 136.3 & 135.972689035005 & 0.327310964994979 \tabularnewline
72 & 136.3 & 135.966633327295 & 0.333366672705296 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259606&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]128.2[/C][C]125.61984508547[/C][C]2.58015491452991[/C][/ROW]
[ROW][C]14[/C][C]129.3[/C][C]129.072941511569[/C][C]0.227058488430714[/C][/ROW]
[ROW][C]15[/C][C]129.3[/C][C]129.410122508084[/C][C]-0.110122508084203[/C][/ROW]
[ROW][C]16[/C][C]129.3[/C][C]129.438069497829[/C][C]-0.138069497828809[/C][/ROW]
[ROW][C]17[/C][C]129.3[/C][C]129.421754680845[/C][C]-0.121754680845044[/C][/ROW]
[ROW][C]18[/C][C]129.4[/C][C]129.541298327907[/C][C]-0.141298327907435[/C][/ROW]
[ROW][C]19[/C][C]129.6[/C][C]130.598716631479[/C][C]-0.998716631479169[/C][/ROW]
[ROW][C]20[/C][C]129.6[/C][C]129.656015611005[/C][C]-0.0560156110054493[/C][/ROW]
[ROW][C]21[/C][C]129.6[/C][C]129.501007210362[/C][C]0.0989927896376059[/C][/ROW]
[ROW][C]22[/C][C]130[/C][C]129.535919232603[/C][C]0.464080767397348[/C][/ROW]
[ROW][C]23[/C][C]130[/C][C]129.950728125444[/C][C]0.049271874556382[/C][/ROW]
[ROW][C]24[/C][C]129.4[/C][C]130.014573694492[/C][C]-0.614573694492236[/C][/ROW]
[ROW][C]25[/C][C]130.2[/C][C]132.205344267406[/C][C]-2.00534426740626[/C][/ROW]
[ROW][C]26[/C][C]130.2[/C][C]131.300400142743[/C][C]-1.10040014274281[/C][/ROW]
[ROW][C]27[/C][C]130.2[/C][C]130.328257897407[/C][C]-0.128257897407053[/C][/ROW]
[ROW][C]28[/C][C]130.3[/C][C]130.214933170071[/C][C]0.0850668299288486[/C][/ROW]
[ROW][C]29[/C][C]130.3[/C][C]130.276671778512[/C][C]0.0233282214881285[/C][/ROW]
[ROW][C]30[/C][C]130.3[/C][C]130.405920750974[/C][C]-0.105920750974462[/C][/ROW]
[ROW][C]31[/C][C]130.7[/C][C]131.261739157221[/C][C]-0.561739157220671[/C][/ROW]
[ROW][C]32[/C][C]130.7[/C][C]130.72727280339[/C][C]-0.0272728033903036[/C][/ROW]
[ROW][C]33[/C][C]130.7[/C][C]130.519586911929[/C][C]0.180413088071163[/C][/ROW]
[ROW][C]34[/C][C]130.9[/C][C]130.57877212309[/C][C]0.321227876909859[/C][/ROW]
[ROW][C]35[/C][C]130.9[/C][C]130.711648667751[/C][C]0.188351332248857[/C][/ROW]
[ROW][C]36[/C][C]130.9[/C][C]130.704348847468[/C][C]0.195651152531781[/C][/ROW]
[ROW][C]37[/C][C]131.2[/C][C]133.319311637444[/C][C]-2.11931163744387[/C][/ROW]
[ROW][C]38[/C][C]131.8[/C][C]132.364736225141[/C][C]-0.564736225141189[/C][/ROW]
[ROW][C]39[/C][C]131.8[/C][C]131.92449400196[/C][C]-0.124494001960471[/C][/ROW]
[ROW][C]40[/C][C]131.8[/C][C]131.779319556865[/C][C]0.0206804431350065[/C][/ROW]
[ROW][C]41[/C][C]131.9[/C][C]131.710256411817[/C][C]0.189743588182836[/C][/ROW]
[ROW][C]42[/C][C]132[/C][C]131.901824765235[/C][C]0.0981752347647955[/C][/ROW]
[ROW][C]43[/C][C]132.3[/C][C]132.811657020322[/C][C]-0.511657020321564[/C][/ROW]
[ROW][C]44[/C][C]132.3[/C][C]132.339594399881[/C][C]-0.0395943998809969[/C][/ROW]
[ROW][C]45[/C][C]132.4[/C][C]132.094367556644[/C][C]0.305632443355819[/C][/ROW]
[ROW][C]46[/C][C]132.8[/C][C]132.228023207589[/C][C]0.571976792411448[/C][/ROW]
[ROW][C]47[/C][C]132.8[/C][C]132.511200704134[/C][C]0.28879929586634[/C][/ROW]
[ROW][C]48[/C][C]132.8[/C][C]132.547403291704[/C][C]0.252596708296409[/C][/ROW]
[ROW][C]49[/C][C]133[/C][C]134.843020398586[/C][C]-1.84302039858571[/C][/ROW]
[ROW][C]50[/C][C]133.5[/C][C]134.309519812975[/C][C]-0.80951981297514[/C][/ROW]
[ROW][C]51[/C][C]133.5[/C][C]133.679401708528[/C][C]-0.17940170852836[/C][/ROW]
[ROW][C]52[/C][C]134.4[/C][C]133.464527944121[/C][C]0.935472055879245[/C][/ROW]
[ROW][C]53[/C][C]134.4[/C][C]134.186043421721[/C][C]0.213956578278896[/C][/ROW]
[ROW][C]54[/C][C]134.5[/C][C]134.366929425739[/C][C]0.133070574260813[/C][/ROW]
[ROW][C]55[/C][C]134.6[/C][C]135.203197600158[/C][C]-0.603197600157529[/C][/ROW]
[ROW][C]56[/C][C]135.6[/C][C]134.698878743031[/C][C]0.901121256968963[/C][/ROW]
[ROW][C]57[/C][C]135.6[/C][C]135.314875645638[/C][C]0.285124354361983[/C][/ROW]
[ROW][C]58[/C][C]135.6[/C][C]135.472222684834[/C][C]0.127777315165531[/C][/ROW]
[ROW][C]59[/C][C]135.6[/C][C]135.326158156216[/C][C]0.273841843783771[/C][/ROW]
[ROW][C]60[/C][C]135.6[/C][C]135.336311488186[/C][C]0.263688511814479[/C][/ROW]
[ROW][C]61[/C][C]135.7[/C][C]137.338606977893[/C][C]-1.63860697789286[/C][/ROW]
[ROW][C]62[/C][C]136.2[/C][C]137.123737215319[/C][C]-0.923737215319193[/C][/ROW]
[ROW][C]63[/C][C]136.2[/C][C]136.47872321864[/C][C]-0.278723218639612[/C][/ROW]
[ROW][C]64[/C][C]136.2[/C][C]136.327423038774[/C][C]-0.127423038773628[/C][/ROW]
[ROW][C]65[/C][C]136.2[/C][C]135.998474983258[/C][C]0.201525016742039[/C][/ROW]
[ROW][C]66[/C][C]136.2[/C][C]136.121338454137[/C][C]0.078661545862559[/C][/ROW]
[ROW][C]67[/C][C]136.3[/C][C]136.769834404225[/C][C]-0.469834404224997[/C][/ROW]
[ROW][C]68[/C][C]136.3[/C][C]136.557989027335[/C][C]-0.257989027334986[/C][/ROW]
[ROW][C]69[/C][C]136.3[/C][C]136.027357445004[/C][C]0.272642554996111[/C][/ROW]
[ROW][C]70[/C][C]136.3[/C][C]136.087521075527[/C][C]0.212478924473373[/C][/ROW]
[ROW][C]71[/C][C]136.3[/C][C]135.972689035005[/C][C]0.327310964994979[/C][/ROW]
[ROW][C]72[/C][C]136.3[/C][C]135.966633327295[/C][C]0.333366672705296[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259606&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259606&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
13128.2125.619845085472.58015491452991
14129.3129.0729415115690.227058488430714
15129.3129.410122508084-0.110122508084203
16129.3129.438069497829-0.138069497828809
17129.3129.421754680845-0.121754680845044
18129.4129.541298327907-0.141298327907435
19129.6130.598716631479-0.998716631479169
20129.6129.656015611005-0.0560156110054493
21129.6129.5010072103620.0989927896376059
22130129.5359192326030.464080767397348
23130129.9507281254440.049271874556382
24129.4130.014573694492-0.614573694492236
25130.2132.205344267406-2.00534426740626
26130.2131.300400142743-1.10040014274281
27130.2130.328257897407-0.128257897407053
28130.3130.2149331700710.0850668299288486
29130.3130.2766717785120.0233282214881285
30130.3130.405920750974-0.105920750974462
31130.7131.261739157221-0.561739157220671
32130.7130.72727280339-0.0272728033903036
33130.7130.5195869119290.180413088071163
34130.9130.578772123090.321227876909859
35130.9130.7116486677510.188351332248857
36130.9130.7043488474680.195651152531781
37131.2133.319311637444-2.11931163744387
38131.8132.364736225141-0.564736225141189
39131.8131.92449400196-0.124494001960471
40131.8131.7793195568650.0206804431350065
41131.9131.7102564118170.189743588182836
42132131.9018247652350.0981752347647955
43132.3132.811657020322-0.511657020321564
44132.3132.339594399881-0.0395943998809969
45132.4132.0943675566440.305632443355819
46132.8132.2280232075890.571976792411448
47132.8132.5112007041340.28879929586634
48132.8132.5474032917040.252596708296409
49133134.843020398586-1.84302039858571
50133.5134.309519812975-0.80951981297514
51133.5133.679401708528-0.17940170852836
52134.4133.4645279441210.935472055879245
53134.4134.1860434217210.213956578278896
54134.5134.3669294257390.133070574260813
55134.6135.203197600158-0.603197600157529
56135.6134.6988787430310.901121256968963
57135.6135.3148756456380.285124354361983
58135.6135.4722226848340.127777315165531
59135.6135.3261581562160.273841843783771
60135.6135.3363114881860.263688511814479
61135.7137.338606977893-1.63860697789286
62136.2137.123737215319-0.923737215319193
63136.2136.47872321864-0.278723218639612
64136.2136.327423038774-0.127423038773628
65136.2135.9984749832580.201525016742039
66136.2136.1213384541370.078661545862559
67136.3136.769834404225-0.469834404224997
68136.3136.557989027335-0.257989027334986
69136.3136.0273574450040.272642554996111
70136.3136.0875210755270.212478924473373
71136.3135.9726890350050.327310964994979
72136.3135.9666333272950.333366672705296







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73137.702062882235136.303482939952139.100642824518
74138.979355926582137.111579236521140.847132616643
75139.226415630802136.965370114792141.487461146812
76139.350709080824136.737306849275141.964111312373
77139.195673099507136.255629367956142.135716831057
78139.140973443542135.891832208005142.390114679079
79139.655506594353136.109848646485143.201164542221
80139.900211510927136.067352803359143.733070218495
81139.695686260423135.582670369442143.808702151404
82139.535779485373135.14800031939143.923558651357
83139.27169408961134.613308218258143.930079960962
84138.993912165145134.068123633886143.919700696405

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 137.702062882235 & 136.303482939952 & 139.100642824518 \tabularnewline
74 & 138.979355926582 & 137.111579236521 & 140.847132616643 \tabularnewline
75 & 139.226415630802 & 136.965370114792 & 141.487461146812 \tabularnewline
76 & 139.350709080824 & 136.737306849275 & 141.964111312373 \tabularnewline
77 & 139.195673099507 & 136.255629367956 & 142.135716831057 \tabularnewline
78 & 139.140973443542 & 135.891832208005 & 142.390114679079 \tabularnewline
79 & 139.655506594353 & 136.109848646485 & 143.201164542221 \tabularnewline
80 & 139.900211510927 & 136.067352803359 & 143.733070218495 \tabularnewline
81 & 139.695686260423 & 135.582670369442 & 143.808702151404 \tabularnewline
82 & 139.535779485373 & 135.14800031939 & 143.923558651357 \tabularnewline
83 & 139.27169408961 & 134.613308218258 & 143.930079960962 \tabularnewline
84 & 138.993912165145 & 134.068123633886 & 143.919700696405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259606&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]137.702062882235[/C][C]136.303482939952[/C][C]139.100642824518[/C][/ROW]
[ROW][C]74[/C][C]138.979355926582[/C][C]137.111579236521[/C][C]140.847132616643[/C][/ROW]
[ROW][C]75[/C][C]139.226415630802[/C][C]136.965370114792[/C][C]141.487461146812[/C][/ROW]
[ROW][C]76[/C][C]139.350709080824[/C][C]136.737306849275[/C][C]141.964111312373[/C][/ROW]
[ROW][C]77[/C][C]139.195673099507[/C][C]136.255629367956[/C][C]142.135716831057[/C][/ROW]
[ROW][C]78[/C][C]139.140973443542[/C][C]135.891832208005[/C][C]142.390114679079[/C][/ROW]
[ROW][C]79[/C][C]139.655506594353[/C][C]136.109848646485[/C][C]143.201164542221[/C][/ROW]
[ROW][C]80[/C][C]139.900211510927[/C][C]136.067352803359[/C][C]143.733070218495[/C][/ROW]
[ROW][C]81[/C][C]139.695686260423[/C][C]135.582670369442[/C][C]143.808702151404[/C][/ROW]
[ROW][C]82[/C][C]139.535779485373[/C][C]135.14800031939[/C][C]143.923558651357[/C][/ROW]
[ROW][C]83[/C][C]139.27169408961[/C][C]134.613308218258[/C][C]143.930079960962[/C][/ROW]
[ROW][C]84[/C][C]138.993912165145[/C][C]134.068123633886[/C][C]143.919700696405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259606&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259606&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
73137.702062882235136.303482939952139.100642824518
74138.979355926582137.111579236521140.847132616643
75139.226415630802136.965370114792141.487461146812
76139.350709080824136.737306849275141.964111312373
77139.195673099507136.255629367956142.135716831057
78139.140973443542135.891832208005142.390114679079
79139.655506594353136.109848646485143.201164542221
80139.900211510927136.067352803359143.733070218495
81139.695686260423135.582670369442143.808702151404
82139.535779485373135.14800031939143.923558651357
83139.27169408961134.613308218258143.930079960962
84138.993912165145134.068123633886143.919700696405



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')