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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 27 May 2013 04:15:29 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/27/t13696425534i8sxd0tqstbo33.htm/, Retrieved Thu, 02 May 2024 00:08:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210743, Retrieved Thu, 02 May 2024 00:08:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Eigen reeks] [2013-05-27 08:15:29] [1ea4354e3001d150961e77e2fcbe90b7] [Current]
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Dataseries X:
122,27
124,69
147,56
120,03
136,01
138,16
122,87
112,22
137,35
139,08
139,64
121,12
132,37
130,69
149,41
130,72
139,14
146,55
137,35
122,73
138,97
154,73
143,4
123,88
140,25
142,39
143,81
153,58
144,71
153,84
151,3
121,92
153,05
149,29
118,81
109,19
103,68
106,94
114,43
107,87
103,14
117,02
112,44
95,85
123,86
121,83
121,95
120,34
113,32
117,31
141,69
130,35
127,28
148,1
131,21
120,37
146,91
144,04
141,77
132,15
142,04
149,77
172,31
150,24
163,23
155,92
146,96
134,51
152,83
150,54
150,98
138,82




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210743&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210743&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210743&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.444066410335853
beta0.0444273937826881
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.444066410335853 \tabularnewline
beta & 0.0444273937826881 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210743&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]0.444066410335853[/C][/ROW]
[ROW][C]beta[/C][C]0.0444273937826881[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210743&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210743&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
alpha0.444066410335853
beta0.0444273937826881
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3147.56127.1120.45
4120.03139.014610277896-18.9846102778963
5136.01133.0330927938332.97690720616686
6138.16136.8626780931711.29732190682932
7122.87139.972010469707-17.1020104697072
8112.22134.573416704191-22.3534167041905
9137.35126.40184567397910.9481543260214
10139.08133.2343767473155.84562325268507
11139.64137.9163717883691.72362821163091
12121.12140.801932254905-19.6819322549046
13132.37133.793703125631-1.42370312563148
14130.69134.865252434126-4.17525243412609
15149.41134.63255876020114.7774412397993
16130.72143.107659633448-12.3876596334477
17139.14139.275259090411-0.135259090411182
18146.55140.8810695867055.66893041329504
19137.35145.176166383534-7.82616638353352
20122.73143.324143796016-20.5941437960156
21138.97135.3959953535373.57400464646292
22154.73138.27062034729716.4593796527029
23143.4147.191929947806-3.7919299478057
24123.88147.045503290707-23.1655032907072
25140.25137.8388978914932.41110210850684
26142.39140.0375717826672.35242821733345
27143.81142.2566009514121.55339904858783
28153.58144.1514546698759.42854533012536
29144.71149.729409395893-5.01940939589269
30153.84148.7924862412385.04751375876177
31151.3152.42552646671-1.12552646670966
32121.92153.295121689449-31.3751216894491
33153.05140.11289696765112.9371030323487
34149.29146.8634752084272.42652479157337
35118.81148.994530911141-30.1845309111408
36109.19136.048610214922-26.8586102149217
37103.68124.049733363368-20.3697333633678
38106.94114.530480133327-7.59048013332675
39114.43110.5363136057333.89368639426732
40107.87111.718697106212-3.8486971062121
41103.14109.387018316489-6.24701831648909
42117.02105.8670800028811.1529199971203
43112.44110.2939025970922.14609740290798
4495.85110.763437553688-14.9134375536885
45123.86103.36318312662920.4968168733708
46121.83112.0918090952739.73819090472728
47121.95116.2350126260775.71498737392294
48120.34118.7043959541921.63560404580785
49113.32119.394530534663-6.07453053466276
50117.31116.5410106575630.76898934243728
51141.69116.74163925659924.9483607434009
52130.35128.1717135736932.17828642630718
53127.28129.533337514055-2.25333751405537
54148.1128.8825706695319.2174293304699
55131.21138.145385338006-6.93538533800569
56120.37135.657787247669-15.2877872476689
57146.91129.15955965236717.7504403476334
58144.04137.682692537346.35730746266029
59141.77141.2719392957520.498060704247848
60132.15142.269117475713-10.1191174757134
61142.04138.3519262861023.68807371389818
62149.77140.638805873739.13119412626978
63172.31145.52293911470626.7870608852939
64150.24158.775923972487-8.53592397248698
65163.23156.1747549455127.05524505448761
66155.92160.636291288069-4.71629128806947
67146.96159.777437384293-12.817437384293
68134.51155.068265066851-20.5582650668512
69152.83146.5160630703976.31393692960259
70150.54150.0214692036660.518530796333863
71150.98150.9635600843020.0164399156976458
72138.82151.683013608295-12.8630136082952

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 147.56 & 127.11 & 20.45 \tabularnewline
4 & 120.03 & 139.014610277896 & -18.9846102778963 \tabularnewline
5 & 136.01 & 133.033092793833 & 2.97690720616686 \tabularnewline
6 & 138.16 & 136.862678093171 & 1.29732190682932 \tabularnewline
7 & 122.87 & 139.972010469707 & -17.1020104697072 \tabularnewline
8 & 112.22 & 134.573416704191 & -22.3534167041905 \tabularnewline
9 & 137.35 & 126.401845673979 & 10.9481543260214 \tabularnewline
10 & 139.08 & 133.234376747315 & 5.84562325268507 \tabularnewline
11 & 139.64 & 137.916371788369 & 1.72362821163091 \tabularnewline
12 & 121.12 & 140.801932254905 & -19.6819322549046 \tabularnewline
13 & 132.37 & 133.793703125631 & -1.42370312563148 \tabularnewline
14 & 130.69 & 134.865252434126 & -4.17525243412609 \tabularnewline
15 & 149.41 & 134.632558760201 & 14.7774412397993 \tabularnewline
16 & 130.72 & 143.107659633448 & -12.3876596334477 \tabularnewline
17 & 139.14 & 139.275259090411 & -0.135259090411182 \tabularnewline
18 & 146.55 & 140.881069586705 & 5.66893041329504 \tabularnewline
19 & 137.35 & 145.176166383534 & -7.82616638353352 \tabularnewline
20 & 122.73 & 143.324143796016 & -20.5941437960156 \tabularnewline
21 & 138.97 & 135.395995353537 & 3.57400464646292 \tabularnewline
22 & 154.73 & 138.270620347297 & 16.4593796527029 \tabularnewline
23 & 143.4 & 147.191929947806 & -3.7919299478057 \tabularnewline
24 & 123.88 & 147.045503290707 & -23.1655032907072 \tabularnewline
25 & 140.25 & 137.838897891493 & 2.41110210850684 \tabularnewline
26 & 142.39 & 140.037571782667 & 2.35242821733345 \tabularnewline
27 & 143.81 & 142.256600951412 & 1.55339904858783 \tabularnewline
28 & 153.58 & 144.151454669875 & 9.42854533012536 \tabularnewline
29 & 144.71 & 149.729409395893 & -5.01940939589269 \tabularnewline
30 & 153.84 & 148.792486241238 & 5.04751375876177 \tabularnewline
31 & 151.3 & 152.42552646671 & -1.12552646670966 \tabularnewline
32 & 121.92 & 153.295121689449 & -31.3751216894491 \tabularnewline
33 & 153.05 & 140.112896967651 & 12.9371030323487 \tabularnewline
34 & 149.29 & 146.863475208427 & 2.42652479157337 \tabularnewline
35 & 118.81 & 148.994530911141 & -30.1845309111408 \tabularnewline
36 & 109.19 & 136.048610214922 & -26.8586102149217 \tabularnewline
37 & 103.68 & 124.049733363368 & -20.3697333633678 \tabularnewline
38 & 106.94 & 114.530480133327 & -7.59048013332675 \tabularnewline
39 & 114.43 & 110.536313605733 & 3.89368639426732 \tabularnewline
40 & 107.87 & 111.718697106212 & -3.8486971062121 \tabularnewline
41 & 103.14 & 109.387018316489 & -6.24701831648909 \tabularnewline
42 & 117.02 & 105.86708000288 & 11.1529199971203 \tabularnewline
43 & 112.44 & 110.293902597092 & 2.14609740290798 \tabularnewline
44 & 95.85 & 110.763437553688 & -14.9134375536885 \tabularnewline
45 & 123.86 & 103.363183126629 & 20.4968168733708 \tabularnewline
46 & 121.83 & 112.091809095273 & 9.73819090472728 \tabularnewline
47 & 121.95 & 116.235012626077 & 5.71498737392294 \tabularnewline
48 & 120.34 & 118.704395954192 & 1.63560404580785 \tabularnewline
49 & 113.32 & 119.394530534663 & -6.07453053466276 \tabularnewline
50 & 117.31 & 116.541010657563 & 0.76898934243728 \tabularnewline
51 & 141.69 & 116.741639256599 & 24.9483607434009 \tabularnewline
52 & 130.35 & 128.171713573693 & 2.17828642630718 \tabularnewline
53 & 127.28 & 129.533337514055 & -2.25333751405537 \tabularnewline
54 & 148.1 & 128.88257066953 & 19.2174293304699 \tabularnewline
55 & 131.21 & 138.145385338006 & -6.93538533800569 \tabularnewline
56 & 120.37 & 135.657787247669 & -15.2877872476689 \tabularnewline
57 & 146.91 & 129.159559652367 & 17.7504403476334 \tabularnewline
58 & 144.04 & 137.68269253734 & 6.35730746266029 \tabularnewline
59 & 141.77 & 141.271939295752 & 0.498060704247848 \tabularnewline
60 & 132.15 & 142.269117475713 & -10.1191174757134 \tabularnewline
61 & 142.04 & 138.351926286102 & 3.68807371389818 \tabularnewline
62 & 149.77 & 140.63880587373 & 9.13119412626978 \tabularnewline
63 & 172.31 & 145.522939114706 & 26.7870608852939 \tabularnewline
64 & 150.24 & 158.775923972487 & -8.53592397248698 \tabularnewline
65 & 163.23 & 156.174754945512 & 7.05524505448761 \tabularnewline
66 & 155.92 & 160.636291288069 & -4.71629128806947 \tabularnewline
67 & 146.96 & 159.777437384293 & -12.817437384293 \tabularnewline
68 & 134.51 & 155.068265066851 & -20.5582650668512 \tabularnewline
69 & 152.83 & 146.516063070397 & 6.31393692960259 \tabularnewline
70 & 150.54 & 150.021469203666 & 0.518530796333863 \tabularnewline
71 & 150.98 & 150.963560084302 & 0.0164399156976458 \tabularnewline
72 & 138.82 & 151.683013608295 & -12.8630136082952 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210743&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]147.56[/C][C]127.11[/C][C]20.45[/C][/ROW]
[ROW][C]4[/C][C]120.03[/C][C]139.014610277896[/C][C]-18.9846102778963[/C][/ROW]
[ROW][C]5[/C][C]136.01[/C][C]133.033092793833[/C][C]2.97690720616686[/C][/ROW]
[ROW][C]6[/C][C]138.16[/C][C]136.862678093171[/C][C]1.29732190682932[/C][/ROW]
[ROW][C]7[/C][C]122.87[/C][C]139.972010469707[/C][C]-17.1020104697072[/C][/ROW]
[ROW][C]8[/C][C]112.22[/C][C]134.573416704191[/C][C]-22.3534167041905[/C][/ROW]
[ROW][C]9[/C][C]137.35[/C][C]126.401845673979[/C][C]10.9481543260214[/C][/ROW]
[ROW][C]10[/C][C]139.08[/C][C]133.234376747315[/C][C]5.84562325268507[/C][/ROW]
[ROW][C]11[/C][C]139.64[/C][C]137.916371788369[/C][C]1.72362821163091[/C][/ROW]
[ROW][C]12[/C][C]121.12[/C][C]140.801932254905[/C][C]-19.6819322549046[/C][/ROW]
[ROW][C]13[/C][C]132.37[/C][C]133.793703125631[/C][C]-1.42370312563148[/C][/ROW]
[ROW][C]14[/C][C]130.69[/C][C]134.865252434126[/C][C]-4.17525243412609[/C][/ROW]
[ROW][C]15[/C][C]149.41[/C][C]134.632558760201[/C][C]14.7774412397993[/C][/ROW]
[ROW][C]16[/C][C]130.72[/C][C]143.107659633448[/C][C]-12.3876596334477[/C][/ROW]
[ROW][C]17[/C][C]139.14[/C][C]139.275259090411[/C][C]-0.135259090411182[/C][/ROW]
[ROW][C]18[/C][C]146.55[/C][C]140.881069586705[/C][C]5.66893041329504[/C][/ROW]
[ROW][C]19[/C][C]137.35[/C][C]145.176166383534[/C][C]-7.82616638353352[/C][/ROW]
[ROW][C]20[/C][C]122.73[/C][C]143.324143796016[/C][C]-20.5941437960156[/C][/ROW]
[ROW][C]21[/C][C]138.97[/C][C]135.395995353537[/C][C]3.57400464646292[/C][/ROW]
[ROW][C]22[/C][C]154.73[/C][C]138.270620347297[/C][C]16.4593796527029[/C][/ROW]
[ROW][C]23[/C][C]143.4[/C][C]147.191929947806[/C][C]-3.7919299478057[/C][/ROW]
[ROW][C]24[/C][C]123.88[/C][C]147.045503290707[/C][C]-23.1655032907072[/C][/ROW]
[ROW][C]25[/C][C]140.25[/C][C]137.838897891493[/C][C]2.41110210850684[/C][/ROW]
[ROW][C]26[/C][C]142.39[/C][C]140.037571782667[/C][C]2.35242821733345[/C][/ROW]
[ROW][C]27[/C][C]143.81[/C][C]142.256600951412[/C][C]1.55339904858783[/C][/ROW]
[ROW][C]28[/C][C]153.58[/C][C]144.151454669875[/C][C]9.42854533012536[/C][/ROW]
[ROW][C]29[/C][C]144.71[/C][C]149.729409395893[/C][C]-5.01940939589269[/C][/ROW]
[ROW][C]30[/C][C]153.84[/C][C]148.792486241238[/C][C]5.04751375876177[/C][/ROW]
[ROW][C]31[/C][C]151.3[/C][C]152.42552646671[/C][C]-1.12552646670966[/C][/ROW]
[ROW][C]32[/C][C]121.92[/C][C]153.295121689449[/C][C]-31.3751216894491[/C][/ROW]
[ROW][C]33[/C][C]153.05[/C][C]140.112896967651[/C][C]12.9371030323487[/C][/ROW]
[ROW][C]34[/C][C]149.29[/C][C]146.863475208427[/C][C]2.42652479157337[/C][/ROW]
[ROW][C]35[/C][C]118.81[/C][C]148.994530911141[/C][C]-30.1845309111408[/C][/ROW]
[ROW][C]36[/C][C]109.19[/C][C]136.048610214922[/C][C]-26.8586102149217[/C][/ROW]
[ROW][C]37[/C][C]103.68[/C][C]124.049733363368[/C][C]-20.3697333633678[/C][/ROW]
[ROW][C]38[/C][C]106.94[/C][C]114.530480133327[/C][C]-7.59048013332675[/C][/ROW]
[ROW][C]39[/C][C]114.43[/C][C]110.536313605733[/C][C]3.89368639426732[/C][/ROW]
[ROW][C]40[/C][C]107.87[/C][C]111.718697106212[/C][C]-3.8486971062121[/C][/ROW]
[ROW][C]41[/C][C]103.14[/C][C]109.387018316489[/C][C]-6.24701831648909[/C][/ROW]
[ROW][C]42[/C][C]117.02[/C][C]105.86708000288[/C][C]11.1529199971203[/C][/ROW]
[ROW][C]43[/C][C]112.44[/C][C]110.293902597092[/C][C]2.14609740290798[/C][/ROW]
[ROW][C]44[/C][C]95.85[/C][C]110.763437553688[/C][C]-14.9134375536885[/C][/ROW]
[ROW][C]45[/C][C]123.86[/C][C]103.363183126629[/C][C]20.4968168733708[/C][/ROW]
[ROW][C]46[/C][C]121.83[/C][C]112.091809095273[/C][C]9.73819090472728[/C][/ROW]
[ROW][C]47[/C][C]121.95[/C][C]116.235012626077[/C][C]5.71498737392294[/C][/ROW]
[ROW][C]48[/C][C]120.34[/C][C]118.704395954192[/C][C]1.63560404580785[/C][/ROW]
[ROW][C]49[/C][C]113.32[/C][C]119.394530534663[/C][C]-6.07453053466276[/C][/ROW]
[ROW][C]50[/C][C]117.31[/C][C]116.541010657563[/C][C]0.76898934243728[/C][/ROW]
[ROW][C]51[/C][C]141.69[/C][C]116.741639256599[/C][C]24.9483607434009[/C][/ROW]
[ROW][C]52[/C][C]130.35[/C][C]128.171713573693[/C][C]2.17828642630718[/C][/ROW]
[ROW][C]53[/C][C]127.28[/C][C]129.533337514055[/C][C]-2.25333751405537[/C][/ROW]
[ROW][C]54[/C][C]148.1[/C][C]128.88257066953[/C][C]19.2174293304699[/C][/ROW]
[ROW][C]55[/C][C]131.21[/C][C]138.145385338006[/C][C]-6.93538533800569[/C][/ROW]
[ROW][C]56[/C][C]120.37[/C][C]135.657787247669[/C][C]-15.2877872476689[/C][/ROW]
[ROW][C]57[/C][C]146.91[/C][C]129.159559652367[/C][C]17.7504403476334[/C][/ROW]
[ROW][C]58[/C][C]144.04[/C][C]137.68269253734[/C][C]6.35730746266029[/C][/ROW]
[ROW][C]59[/C][C]141.77[/C][C]141.271939295752[/C][C]0.498060704247848[/C][/ROW]
[ROW][C]60[/C][C]132.15[/C][C]142.269117475713[/C][C]-10.1191174757134[/C][/ROW]
[ROW][C]61[/C][C]142.04[/C][C]138.351926286102[/C][C]3.68807371389818[/C][/ROW]
[ROW][C]62[/C][C]149.77[/C][C]140.63880587373[/C][C]9.13119412626978[/C][/ROW]
[ROW][C]63[/C][C]172.31[/C][C]145.522939114706[/C][C]26.7870608852939[/C][/ROW]
[ROW][C]64[/C][C]150.24[/C][C]158.775923972487[/C][C]-8.53592397248698[/C][/ROW]
[ROW][C]65[/C][C]163.23[/C][C]156.174754945512[/C][C]7.05524505448761[/C][/ROW]
[ROW][C]66[/C][C]155.92[/C][C]160.636291288069[/C][C]-4.71629128806947[/C][/ROW]
[ROW][C]67[/C][C]146.96[/C][C]159.777437384293[/C][C]-12.817437384293[/C][/ROW]
[ROW][C]68[/C][C]134.51[/C][C]155.068265066851[/C][C]-20.5582650668512[/C][/ROW]
[ROW][C]69[/C][C]152.83[/C][C]146.516063070397[/C][C]6.31393692960259[/C][/ROW]
[ROW][C]70[/C][C]150.54[/C][C]150.021469203666[/C][C]0.518530796333863[/C][/ROW]
[ROW][C]71[/C][C]150.98[/C][C]150.963560084302[/C][C]0.0164399156976458[/C][/ROW]
[ROW][C]72[/C][C]138.82[/C][C]151.683013608295[/C][C]-12.8630136082952[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210743&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210743&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
3147.56127.1120.45
4120.03139.014610277896-18.9846102778963
5136.01133.0330927938332.97690720616686
6138.16136.8626780931711.29732190682932
7122.87139.972010469707-17.1020104697072
8112.22134.573416704191-22.3534167041905
9137.35126.40184567397910.9481543260214
10139.08133.2343767473155.84562325268507
11139.64137.9163717883691.72362821163091
12121.12140.801932254905-19.6819322549046
13132.37133.793703125631-1.42370312563148
14130.69134.865252434126-4.17525243412609
15149.41134.63255876020114.7774412397993
16130.72143.107659633448-12.3876596334477
17139.14139.275259090411-0.135259090411182
18146.55140.8810695867055.66893041329504
19137.35145.176166383534-7.82616638353352
20122.73143.324143796016-20.5941437960156
21138.97135.3959953535373.57400464646292
22154.73138.27062034729716.4593796527029
23143.4147.191929947806-3.7919299478057
24123.88147.045503290707-23.1655032907072
25140.25137.8388978914932.41110210850684
26142.39140.0375717826672.35242821733345
27143.81142.2566009514121.55339904858783
28153.58144.1514546698759.42854533012536
29144.71149.729409395893-5.01940939589269
30153.84148.7924862412385.04751375876177
31151.3152.42552646671-1.12552646670966
32121.92153.295121689449-31.3751216894491
33153.05140.11289696765112.9371030323487
34149.29146.8634752084272.42652479157337
35118.81148.994530911141-30.1845309111408
36109.19136.048610214922-26.8586102149217
37103.68124.049733363368-20.3697333633678
38106.94114.530480133327-7.59048013332675
39114.43110.5363136057333.89368639426732
40107.87111.718697106212-3.8486971062121
41103.14109.387018316489-6.24701831648909
42117.02105.8670800028811.1529199971203
43112.44110.2939025970922.14609740290798
4495.85110.763437553688-14.9134375536885
45123.86103.36318312662920.4968168733708
46121.83112.0918090952739.73819090472728
47121.95116.2350126260775.71498737392294
48120.34118.7043959541921.63560404580785
49113.32119.394530534663-6.07453053466276
50117.31116.5410106575630.76898934243728
51141.69116.74163925659924.9483607434009
52130.35128.1717135736932.17828642630718
53127.28129.533337514055-2.25333751405537
54148.1128.8825706695319.2174293304699
55131.21138.145385338006-6.93538533800569
56120.37135.657787247669-15.2877872476689
57146.91129.15955965236717.7504403476334
58144.04137.682692537346.35730746266029
59141.77141.2719392957520.498060704247848
60132.15142.269117475713-10.1191174757134
61142.04138.3519262861023.68807371389818
62149.77140.638805873739.13119412626978
63172.31145.52293911470626.7870608852939
64150.24158.775923972487-8.53592397248698
65163.23156.1747549455127.05524505448761
66155.92160.636291288069-4.71629128806947
67146.96159.777437384293-12.817437384293
68134.51155.068265066851-20.5582650668512
69152.83146.5160630703976.31393692960259
70150.54150.0214692036660.518530796333863
71150.98150.9635600843020.0164399156976458
72138.82151.683013608295-12.8630136082952







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73146.429363731436120.965259028319171.893468434554
74146.887746133715118.818194267186174.957298000243
75147.346128535993116.694906083037177.997350988948
76147.804510938271114.582252206165181.026769670376
77148.262893340549112.470888458063184.054898223035
78148.721275742827110.353977011896187.088574473758
79149.179658145105108.226401500758190.132914789453
80149.638040547383106.084266584282193.191814510484
81150.096422949661103.924566140834196.268279758488
82150.554805351939101.744956004408199.36465469947
83151.01318775421899.5435939904863202.482781517949
84151.47157015649697.3190246289546205.624115684037

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 146.429363731436 & 120.965259028319 & 171.893468434554 \tabularnewline
74 & 146.887746133715 & 118.818194267186 & 174.957298000243 \tabularnewline
75 & 147.346128535993 & 116.694906083037 & 177.997350988948 \tabularnewline
76 & 147.804510938271 & 114.582252206165 & 181.026769670376 \tabularnewline
77 & 148.262893340549 & 112.470888458063 & 184.054898223035 \tabularnewline
78 & 148.721275742827 & 110.353977011896 & 187.088574473758 \tabularnewline
79 & 149.179658145105 & 108.226401500758 & 190.132914789453 \tabularnewline
80 & 149.638040547383 & 106.084266584282 & 193.191814510484 \tabularnewline
81 & 150.096422949661 & 103.924566140834 & 196.268279758488 \tabularnewline
82 & 150.554805351939 & 101.744956004408 & 199.36465469947 \tabularnewline
83 & 151.013187754218 & 99.5435939904863 & 202.482781517949 \tabularnewline
84 & 151.471570156496 & 97.3190246289546 & 205.624115684037 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210743&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]146.429363731436[/C][C]120.965259028319[/C][C]171.893468434554[/C][/ROW]
[ROW][C]74[/C][C]146.887746133715[/C][C]118.818194267186[/C][C]174.957298000243[/C][/ROW]
[ROW][C]75[/C][C]147.346128535993[/C][C]116.694906083037[/C][C]177.997350988948[/C][/ROW]
[ROW][C]76[/C][C]147.804510938271[/C][C]114.582252206165[/C][C]181.026769670376[/C][/ROW]
[ROW][C]77[/C][C]148.262893340549[/C][C]112.470888458063[/C][C]184.054898223035[/C][/ROW]
[ROW][C]78[/C][C]148.721275742827[/C][C]110.353977011896[/C][C]187.088574473758[/C][/ROW]
[ROW][C]79[/C][C]149.179658145105[/C][C]108.226401500758[/C][C]190.132914789453[/C][/ROW]
[ROW][C]80[/C][C]149.638040547383[/C][C]106.084266584282[/C][C]193.191814510484[/C][/ROW]
[ROW][C]81[/C][C]150.096422949661[/C][C]103.924566140834[/C][C]196.268279758488[/C][/ROW]
[ROW][C]82[/C][C]150.554805351939[/C][C]101.744956004408[/C][C]199.36465469947[/C][/ROW]
[ROW][C]83[/C][C]151.013187754218[/C][C]99.5435939904863[/C][C]202.482781517949[/C][/ROW]
[ROW][C]84[/C][C]151.471570156496[/C][C]97.3190246289546[/C][C]205.624115684037[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210743&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210743&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
73146.429363731436120.965259028319171.893468434554
74146.887746133715118.818194267186174.957298000243
75147.346128535993116.694906083037177.997350988948
76147.804510938271114.582252206165181.026769670376
77148.262893340549112.470888458063184.054898223035
78148.721275742827110.353977011896187.088574473758
79149.179658145105108.226401500758190.132914789453
80149.638040547383106.084266584282193.191814510484
81150.096422949661103.924566140834196.268279758488
82150.554805351939101.744956004408199.36465469947
83151.01318775421899.5435939904863202.482781517949
84151.47157015649697.3190246289546205.624115684037



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