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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 31 May 2008 10:28:22 -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/31/t12122513941o3im1928g1bnym.htm/, Retrieved Wed, 15 May 2024 05:38:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13614, Retrieved Wed, 15 May 2024 05:38:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [sven van roy - op...] [2008-05-31 16:28:22] [9ed44c8445a965e8d6beecda46dd06a5] [Current]
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Dataseries X:
7,1
7,1
7,3
7,1
7,4
7,3
7,4
7,6
7,8
7,7
8
8,1
7,7
7,9
8,1
8,1
8,2
8,1
8,3
8,3
8,3
8,5
8,7
8,7
8,4
8,4
8,6
8,7
8,7
8,6
8
8,1
8,1
8,5
8,6
8,6
8,3
8,3
8,5
9,2
9,2
9
7,4
7,3
7,4
8,6
8,7
8,7
8,5
8,4
8,6
8,4
8,4
8,2
7,7
7,6
7,7
8,1
8,2
8,3
8,1
8
8,2
7,6
7,7
7,6
6,9
6,9
7
7,4
7,4
7,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13614&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13614&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13614&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.759346220500825
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.759346220500825 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13614&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]0.759346220500825[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13614&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13614&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
alpha0.759346220500825
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137.77.372747162997980.327252837002016
147.97.754005839604880.145994160395121
158.18.013863735249590.0861362647504098
168.18.02524293564330.074757064356703
178.28.119139641694340.080860358305662
188.18.027507109709040.0724928902909596
198.38.227882946575410.0721170534245879
208.38.232874234189360.0671257658106406
218.38.242571162790.057428837210006
228.58.43959065685180.0604093431481942
238.78.638034776392360.061965223607638
248.78.642492994943660.0575070050563422
258.48.322284382729530.0777156172704654
268.48.47778538836818-0.0777853883681825
278.68.561970717357860.0380292826421424
288.78.530507629195890.169492370804109
298.78.70031868514656-0.000318685146565301
308.68.535447880779160.0645521192208385
3188.73826863996108-0.738268639961078
328.18.12734877532027-0.0273487753202684
338.18.063918400808860.0360815991911441
348.58.241493425700720.258506574299279
358.68.589536757229520.0104632427704807
368.68.554260066641010.0457399333589894
378.38.234430267129940.0655697328700562
388.38.34234278710195-0.0423427871019530
398.58.479452538464810.0205474615351875
409.28.466103192973550.733896807026447
419.29.023635944797630.176364055202370
4299.00060930513061-0.000609305130609528
437.48.94616870431184-1.54616870431184
447.37.8894016654441-0.589401665444092
457.47.41664253361104-0.0166425336110434
468.67.588882865584451.01111713441555
478.78.447171077459160.252828922540841
488.78.604220466921740.0957795330782574
498.58.323934656657220.176065343342783
508.48.49035250013043-0.0903525001304306
518.68.60883654246001-0.00883654246001164
528.48.73552077333166-0.335520773331657
538.48.356720769648680.0432792303513203
548.28.2076243241798-0.00762432417980641
557.77.76246074038417-0.0624607403841715
567.68.06849393088288-0.468493930882877
577.77.83174362246814-0.131743622468142
588.18.1599319666047-0.0599319666046956
598.28.026356074619680.173643925380317
608.38.089830149387270.210169850612727
618.17.932374426333460.167625573666543
6288.02972734991236-0.0297273499123598
638.28.2041951279071-0.00419512790709753
647.68.25093153080812-0.650931530808116
657.77.7262645662722-0.0262645662721974
667.67.52814705316680.0718529468331965
676.97.16412147444243-0.264121474442434
686.97.19014777554868-0.290147775548684
6977.15290119137087-0.152901191370868
707.47.44385958051969-0.0438595805196851
717.47.380792673912570.0192073260874306
727.57.340750954238050.159249045761952

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7.7 & 7.37274716299798 & 0.327252837002016 \tabularnewline
14 & 7.9 & 7.75400583960488 & 0.145994160395121 \tabularnewline
15 & 8.1 & 8.01386373524959 & 0.0861362647504098 \tabularnewline
16 & 8.1 & 8.0252429356433 & 0.074757064356703 \tabularnewline
17 & 8.2 & 8.11913964169434 & 0.080860358305662 \tabularnewline
18 & 8.1 & 8.02750710970904 & 0.0724928902909596 \tabularnewline
19 & 8.3 & 8.22788294657541 & 0.0721170534245879 \tabularnewline
20 & 8.3 & 8.23287423418936 & 0.0671257658106406 \tabularnewline
21 & 8.3 & 8.24257116279 & 0.057428837210006 \tabularnewline
22 & 8.5 & 8.4395906568518 & 0.0604093431481942 \tabularnewline
23 & 8.7 & 8.63803477639236 & 0.061965223607638 \tabularnewline
24 & 8.7 & 8.64249299494366 & 0.0575070050563422 \tabularnewline
25 & 8.4 & 8.32228438272953 & 0.0777156172704654 \tabularnewline
26 & 8.4 & 8.47778538836818 & -0.0777853883681825 \tabularnewline
27 & 8.6 & 8.56197071735786 & 0.0380292826421424 \tabularnewline
28 & 8.7 & 8.53050762919589 & 0.169492370804109 \tabularnewline
29 & 8.7 & 8.70031868514656 & -0.000318685146565301 \tabularnewline
30 & 8.6 & 8.53544788077916 & 0.0645521192208385 \tabularnewline
31 & 8 & 8.73826863996108 & -0.738268639961078 \tabularnewline
32 & 8.1 & 8.12734877532027 & -0.0273487753202684 \tabularnewline
33 & 8.1 & 8.06391840080886 & 0.0360815991911441 \tabularnewline
34 & 8.5 & 8.24149342570072 & 0.258506574299279 \tabularnewline
35 & 8.6 & 8.58953675722952 & 0.0104632427704807 \tabularnewline
36 & 8.6 & 8.55426006664101 & 0.0457399333589894 \tabularnewline
37 & 8.3 & 8.23443026712994 & 0.0655697328700562 \tabularnewline
38 & 8.3 & 8.34234278710195 & -0.0423427871019530 \tabularnewline
39 & 8.5 & 8.47945253846481 & 0.0205474615351875 \tabularnewline
40 & 9.2 & 8.46610319297355 & 0.733896807026447 \tabularnewline
41 & 9.2 & 9.02363594479763 & 0.176364055202370 \tabularnewline
42 & 9 & 9.00060930513061 & -0.000609305130609528 \tabularnewline
43 & 7.4 & 8.94616870431184 & -1.54616870431184 \tabularnewline
44 & 7.3 & 7.8894016654441 & -0.589401665444092 \tabularnewline
45 & 7.4 & 7.41664253361104 & -0.0166425336110434 \tabularnewline
46 & 8.6 & 7.58888286558445 & 1.01111713441555 \tabularnewline
47 & 8.7 & 8.44717107745916 & 0.252828922540841 \tabularnewline
48 & 8.7 & 8.60422046692174 & 0.0957795330782574 \tabularnewline
49 & 8.5 & 8.32393465665722 & 0.176065343342783 \tabularnewline
50 & 8.4 & 8.49035250013043 & -0.0903525001304306 \tabularnewline
51 & 8.6 & 8.60883654246001 & -0.00883654246001164 \tabularnewline
52 & 8.4 & 8.73552077333166 & -0.335520773331657 \tabularnewline
53 & 8.4 & 8.35672076964868 & 0.0432792303513203 \tabularnewline
54 & 8.2 & 8.2076243241798 & -0.00762432417980641 \tabularnewline
55 & 7.7 & 7.76246074038417 & -0.0624607403841715 \tabularnewline
56 & 7.6 & 8.06849393088288 & -0.468493930882877 \tabularnewline
57 & 7.7 & 7.83174362246814 & -0.131743622468142 \tabularnewline
58 & 8.1 & 8.1599319666047 & -0.0599319666046956 \tabularnewline
59 & 8.2 & 8.02635607461968 & 0.173643925380317 \tabularnewline
60 & 8.3 & 8.08983014938727 & 0.210169850612727 \tabularnewline
61 & 8.1 & 7.93237442633346 & 0.167625573666543 \tabularnewline
62 & 8 & 8.02972734991236 & -0.0297273499123598 \tabularnewline
63 & 8.2 & 8.2041951279071 & -0.00419512790709753 \tabularnewline
64 & 7.6 & 8.25093153080812 & -0.650931530808116 \tabularnewline
65 & 7.7 & 7.7262645662722 & -0.0262645662721974 \tabularnewline
66 & 7.6 & 7.5281470531668 & 0.0718529468331965 \tabularnewline
67 & 6.9 & 7.16412147444243 & -0.264121474442434 \tabularnewline
68 & 6.9 & 7.19014777554868 & -0.290147775548684 \tabularnewline
69 & 7 & 7.15290119137087 & -0.152901191370868 \tabularnewline
70 & 7.4 & 7.44385958051969 & -0.0438595805196851 \tabularnewline
71 & 7.4 & 7.38079267391257 & 0.0192073260874306 \tabularnewline
72 & 7.5 & 7.34075095423805 & 0.159249045761952 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13614&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]7.7[/C][C]7.37274716299798[/C][C]0.327252837002016[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]7.75400583960488[/C][C]0.145994160395121[/C][/ROW]
[ROW][C]15[/C][C]8.1[/C][C]8.01386373524959[/C][C]0.0861362647504098[/C][/ROW]
[ROW][C]16[/C][C]8.1[/C][C]8.0252429356433[/C][C]0.074757064356703[/C][/ROW]
[ROW][C]17[/C][C]8.2[/C][C]8.11913964169434[/C][C]0.080860358305662[/C][/ROW]
[ROW][C]18[/C][C]8.1[/C][C]8.02750710970904[/C][C]0.0724928902909596[/C][/ROW]
[ROW][C]19[/C][C]8.3[/C][C]8.22788294657541[/C][C]0.0721170534245879[/C][/ROW]
[ROW][C]20[/C][C]8.3[/C][C]8.23287423418936[/C][C]0.0671257658106406[/C][/ROW]
[ROW][C]21[/C][C]8.3[/C][C]8.24257116279[/C][C]0.057428837210006[/C][/ROW]
[ROW][C]22[/C][C]8.5[/C][C]8.4395906568518[/C][C]0.0604093431481942[/C][/ROW]
[ROW][C]23[/C][C]8.7[/C][C]8.63803477639236[/C][C]0.061965223607638[/C][/ROW]
[ROW][C]24[/C][C]8.7[/C][C]8.64249299494366[/C][C]0.0575070050563422[/C][/ROW]
[ROW][C]25[/C][C]8.4[/C][C]8.32228438272953[/C][C]0.0777156172704654[/C][/ROW]
[ROW][C]26[/C][C]8.4[/C][C]8.47778538836818[/C][C]-0.0777853883681825[/C][/ROW]
[ROW][C]27[/C][C]8.6[/C][C]8.56197071735786[/C][C]0.0380292826421424[/C][/ROW]
[ROW][C]28[/C][C]8.7[/C][C]8.53050762919589[/C][C]0.169492370804109[/C][/ROW]
[ROW][C]29[/C][C]8.7[/C][C]8.70031868514656[/C][C]-0.000318685146565301[/C][/ROW]
[ROW][C]30[/C][C]8.6[/C][C]8.53544788077916[/C][C]0.0645521192208385[/C][/ROW]
[ROW][C]31[/C][C]8[/C][C]8.73826863996108[/C][C]-0.738268639961078[/C][/ROW]
[ROW][C]32[/C][C]8.1[/C][C]8.12734877532027[/C][C]-0.0273487753202684[/C][/ROW]
[ROW][C]33[/C][C]8.1[/C][C]8.06391840080886[/C][C]0.0360815991911441[/C][/ROW]
[ROW][C]34[/C][C]8.5[/C][C]8.24149342570072[/C][C]0.258506574299279[/C][/ROW]
[ROW][C]35[/C][C]8.6[/C][C]8.58953675722952[/C][C]0.0104632427704807[/C][/ROW]
[ROW][C]36[/C][C]8.6[/C][C]8.55426006664101[/C][C]0.0457399333589894[/C][/ROW]
[ROW][C]37[/C][C]8.3[/C][C]8.23443026712994[/C][C]0.0655697328700562[/C][/ROW]
[ROW][C]38[/C][C]8.3[/C][C]8.34234278710195[/C][C]-0.0423427871019530[/C][/ROW]
[ROW][C]39[/C][C]8.5[/C][C]8.47945253846481[/C][C]0.0205474615351875[/C][/ROW]
[ROW][C]40[/C][C]9.2[/C][C]8.46610319297355[/C][C]0.733896807026447[/C][/ROW]
[ROW][C]41[/C][C]9.2[/C][C]9.02363594479763[/C][C]0.176364055202370[/C][/ROW]
[ROW][C]42[/C][C]9[/C][C]9.00060930513061[/C][C]-0.000609305130609528[/C][/ROW]
[ROW][C]43[/C][C]7.4[/C][C]8.94616870431184[/C][C]-1.54616870431184[/C][/ROW]
[ROW][C]44[/C][C]7.3[/C][C]7.8894016654441[/C][C]-0.589401665444092[/C][/ROW]
[ROW][C]45[/C][C]7.4[/C][C]7.41664253361104[/C][C]-0.0166425336110434[/C][/ROW]
[ROW][C]46[/C][C]8.6[/C][C]7.58888286558445[/C][C]1.01111713441555[/C][/ROW]
[ROW][C]47[/C][C]8.7[/C][C]8.44717107745916[/C][C]0.252828922540841[/C][/ROW]
[ROW][C]48[/C][C]8.7[/C][C]8.60422046692174[/C][C]0.0957795330782574[/C][/ROW]
[ROW][C]49[/C][C]8.5[/C][C]8.32393465665722[/C][C]0.176065343342783[/C][/ROW]
[ROW][C]50[/C][C]8.4[/C][C]8.49035250013043[/C][C]-0.0903525001304306[/C][/ROW]
[ROW][C]51[/C][C]8.6[/C][C]8.60883654246001[/C][C]-0.00883654246001164[/C][/ROW]
[ROW][C]52[/C][C]8.4[/C][C]8.73552077333166[/C][C]-0.335520773331657[/C][/ROW]
[ROW][C]53[/C][C]8.4[/C][C]8.35672076964868[/C][C]0.0432792303513203[/C][/ROW]
[ROW][C]54[/C][C]8.2[/C][C]8.2076243241798[/C][C]-0.00762432417980641[/C][/ROW]
[ROW][C]55[/C][C]7.7[/C][C]7.76246074038417[/C][C]-0.0624607403841715[/C][/ROW]
[ROW][C]56[/C][C]7.6[/C][C]8.06849393088288[/C][C]-0.468493930882877[/C][/ROW]
[ROW][C]57[/C][C]7.7[/C][C]7.83174362246814[/C][C]-0.131743622468142[/C][/ROW]
[ROW][C]58[/C][C]8.1[/C][C]8.1599319666047[/C][C]-0.0599319666046956[/C][/ROW]
[ROW][C]59[/C][C]8.2[/C][C]8.02635607461968[/C][C]0.173643925380317[/C][/ROW]
[ROW][C]60[/C][C]8.3[/C][C]8.08983014938727[/C][C]0.210169850612727[/C][/ROW]
[ROW][C]61[/C][C]8.1[/C][C]7.93237442633346[/C][C]0.167625573666543[/C][/ROW]
[ROW][C]62[/C][C]8[/C][C]8.02972734991236[/C][C]-0.0297273499123598[/C][/ROW]
[ROW][C]63[/C][C]8.2[/C][C]8.2041951279071[/C][C]-0.00419512790709753[/C][/ROW]
[ROW][C]64[/C][C]7.6[/C][C]8.25093153080812[/C][C]-0.650931530808116[/C][/ROW]
[ROW][C]65[/C][C]7.7[/C][C]7.7262645662722[/C][C]-0.0262645662721974[/C][/ROW]
[ROW][C]66[/C][C]7.6[/C][C]7.5281470531668[/C][C]0.0718529468331965[/C][/ROW]
[ROW][C]67[/C][C]6.9[/C][C]7.16412147444243[/C][C]-0.264121474442434[/C][/ROW]
[ROW][C]68[/C][C]6.9[/C][C]7.19014777554868[/C][C]-0.290147775548684[/C][/ROW]
[ROW][C]69[/C][C]7[/C][C]7.15290119137087[/C][C]-0.152901191370868[/C][/ROW]
[ROW][C]70[/C][C]7.4[/C][C]7.44385958051969[/C][C]-0.0438595805196851[/C][/ROW]
[ROW][C]71[/C][C]7.4[/C][C]7.38079267391257[/C][C]0.0192073260874306[/C][/ROW]
[ROW][C]72[/C][C]7.5[/C][C]7.34075095423805[/C][C]0.159249045761952[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13614&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13614&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
137.77.372747162997980.327252837002016
147.97.754005839604880.145994160395121
158.18.013863735249590.0861362647504098
168.18.02524293564330.074757064356703
178.28.119139641694340.080860358305662
188.18.027507109709040.0724928902909596
198.38.227882946575410.0721170534245879
208.38.232874234189360.0671257658106406
218.38.242571162790.057428837210006
228.58.43959065685180.0604093431481942
238.78.638034776392360.061965223607638
248.78.642492994943660.0575070050563422
258.48.322284382729530.0777156172704654
268.48.47778538836818-0.0777853883681825
278.68.561970717357860.0380292826421424
288.78.530507629195890.169492370804109
298.78.70031868514656-0.000318685146565301
308.68.535447880779160.0645521192208385
3188.73826863996108-0.738268639961078
328.18.12734877532027-0.0273487753202684
338.18.063918400808860.0360815991911441
348.58.241493425700720.258506574299279
358.68.589536757229520.0104632427704807
368.68.554260066641010.0457399333589894
378.38.234430267129940.0655697328700562
388.38.34234278710195-0.0423427871019530
398.58.479452538464810.0205474615351875
409.28.466103192973550.733896807026447
419.29.023635944797630.176364055202370
4299.00060930513061-0.000609305130609528
437.48.94616870431184-1.54616870431184
447.37.8894016654441-0.589401665444092
457.47.41664253361104-0.0166425336110434
468.67.588882865584451.01111713441555
478.78.447171077459160.252828922540841
488.78.604220466921740.0957795330782574
498.58.323934656657220.176065343342783
508.48.49035250013043-0.0903525001304306
518.68.60883654246001-0.00883654246001164
528.48.73552077333166-0.335520773331657
538.48.356720769648680.0432792303513203
548.28.2076243241798-0.00762432417980641
557.77.76246074038417-0.0624607403841715
567.68.06849393088288-0.468493930882877
577.77.83174362246814-0.131743622468142
588.18.1599319666047-0.0599319666046956
598.28.026356074619680.173643925380317
608.38.089830149387270.210169850612727
618.17.932374426333460.167625573666543
6288.02972734991236-0.0297273499123598
638.28.2041951279071-0.00419512790709753
647.68.25093153080812-0.650931530808116
657.77.7262645662722-0.0262645662721974
667.67.52814705316680.0718529468331965
676.97.16412147444243-0.264121474442434
686.97.19014777554868-0.290147775548684
6977.15290119137087-0.152901191370868
707.47.44385958051969-0.0438595805196851
717.47.380792673912570.0192073260874306
727.57.340750954238050.159249045761952







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
737.166874345473546.522234201634097.811514489313
747.09834945552096.281341348695227.91535756234659
757.278634366353746.333465683363288.2238030493442
767.175934730598326.100863256247968.25100620494868
777.289170547535616.124515457010848.45382563806038
787.142738035326545.940468728073268.3450073425798
796.671626511488075.342493055297318.00075996767882
806.882522793316815.430930746800848.33411483983279
817.097474767902295.487136793705528.70781274209906
827.536765030042885.856503585538089.21702647454767
837.521901178382085.776192173918689.26761018284548
847.5NANA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 7.16687434547354 & 6.52223420163409 & 7.811514489313 \tabularnewline
74 & 7.0983494555209 & 6.28134134869522 & 7.91535756234659 \tabularnewline
75 & 7.27863436635374 & 6.33346568336328 & 8.2238030493442 \tabularnewline
76 & 7.17593473059832 & 6.10086325624796 & 8.25100620494868 \tabularnewline
77 & 7.28917054753561 & 6.12451545701084 & 8.45382563806038 \tabularnewline
78 & 7.14273803532654 & 5.94046872807326 & 8.3450073425798 \tabularnewline
79 & 6.67162651148807 & 5.34249305529731 & 8.00075996767882 \tabularnewline
80 & 6.88252279331681 & 5.43093074680084 & 8.33411483983279 \tabularnewline
81 & 7.09747476790229 & 5.48713679370552 & 8.70781274209906 \tabularnewline
82 & 7.53676503004288 & 5.85650358553808 & 9.21702647454767 \tabularnewline
83 & 7.52190117838208 & 5.77619217391868 & 9.26761018284548 \tabularnewline
84 & 7.5 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13614&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]7.16687434547354[/C][C]6.52223420163409[/C][C]7.811514489313[/C][/ROW]
[ROW][C]74[/C][C]7.0983494555209[/C][C]6.28134134869522[/C][C]7.91535756234659[/C][/ROW]
[ROW][C]75[/C][C]7.27863436635374[/C][C]6.33346568336328[/C][C]8.2238030493442[/C][/ROW]
[ROW][C]76[/C][C]7.17593473059832[/C][C]6.10086325624796[/C][C]8.25100620494868[/C][/ROW]
[ROW][C]77[/C][C]7.28917054753561[/C][C]6.12451545701084[/C][C]8.45382563806038[/C][/ROW]
[ROW][C]78[/C][C]7.14273803532654[/C][C]5.94046872807326[/C][C]8.3450073425798[/C][/ROW]
[ROW][C]79[/C][C]6.67162651148807[/C][C]5.34249305529731[/C][C]8.00075996767882[/C][/ROW]
[ROW][C]80[/C][C]6.88252279331681[/C][C]5.43093074680084[/C][C]8.33411483983279[/C][/ROW]
[ROW][C]81[/C][C]7.09747476790229[/C][C]5.48713679370552[/C][C]8.70781274209906[/C][/ROW]
[ROW][C]82[/C][C]7.53676503004288[/C][C]5.85650358553808[/C][C]9.21702647454767[/C][/ROW]
[ROW][C]83[/C][C]7.52190117838208[/C][C]5.77619217391868[/C][C]9.26761018284548[/C][/ROW]
[ROW][C]84[/C][C]7.5[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13614&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13614&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
737.166874345473546.522234201634097.811514489313
747.09834945552096.281341348695227.91535756234659
757.278634366353746.333465683363288.2238030493442
767.175934730598326.100863256247968.25100620494868
777.289170547535616.124515457010848.45382563806038
787.142738035326545.940468728073268.3450073425798
796.671626511488075.342493055297318.00075996767882
806.882522793316815.430930746800848.33411483983279
817.097474767902295.487136793705528.70781274209906
827.536765030042885.856503585538089.21702647454767
837.521901178382085.776192173918689.26761018284548
847.5NANA



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