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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 25 May 2008 12:32:25 -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/25/t12117403882x5ko8vix6yn29e.htm/, Retrieved Sun, 19 May 2024 05:44:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13196, Retrieved Sun, 19 May 2024 05:44:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2008-05-25 18:32:25] [6461440fa2a8ea0ebac8d11789a457eb] [Current]
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Dataseries X:
48,04
48,06
48,04
48,09
48,12
48,16
48,16
48,16
48,08
48,13
48,16
48,15
48,15
48,15
48,27
48,47
48,51
48,53
48,53
48,53
48,68
48,64
48,67
48,66
48,66
48,67
48,71
48,96
49,01
49,04
49,04
49,04
49,06
49,13
49,19
49,26
49,26
49,26
49,29
49,43
49,43
49,45
49,45
49,46
49,57
49,68
49,71
49,7
49,7
49,8
49,84
50,09
50,2
50,16
50,16
50,29
50,36
51,02
51,03
51,04




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13196&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13196&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13196&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.641886638714992
beta0.220255401384085
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.641886638714992 \tabularnewline
beta & 0.220255401384085 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13196&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]0.641886638714992[/C][/ROW]
[ROW][C]beta[/C][C]0.220255401384085[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13196&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13196&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
alpha0.641886638714992
beta0.220255401384085
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1348.1547.94121420020610.208785799793937
1448.1548.11243316910760.0375668308924375
1548.2748.2894889364246-0.0194889364246436
1648.4748.5014620378868-0.0314620378868113
1748.5148.5450348788863-0.0350348788863499
1848.5348.5613471793674-0.0313471793674367
1948.5348.5555781352128-0.0255781352128324
2048.5348.5494716676626-0.0194716676625859
2148.6848.6974952763094-0.0174952763093756
2248.6448.6555254862202-0.0155254862201915
2348.6748.6801321428864-0.0101321428863912
2448.6648.6659297909034-0.00592979090337309
2548.6648.7202147708866-0.0602147708866454
2648.6748.62345074169950.0465492583005158
2748.7148.7547096337696-0.0447096337695783
2848.9648.91219052154520.0478094784548233
2949.0148.98110963777370.0288903622263064
3049.0449.02438514905090.0156148509490635
3149.0449.0418771340071-0.00187713400707423
3249.0449.047569435257-0.00756943525704656
3349.0649.2016115087932-0.14161150879319
3449.1349.05897599335390.071024006646148
3549.1949.13220649088290.0577935091170616
3649.2649.16342022849430.0965797715056667
3749.2649.2793112363648-0.0193112363647714
3849.2649.2674177178635-0.00741771786351819
3949.2949.345126988948-0.055126988948004
4049.4349.543328825983-0.113328825982990
4149.4349.491164915695-0.0611649156950378
4249.4549.44816323066670.00183676933328769
4349.4549.4247495688270.0252504311729567
4449.4649.4239130888320.0360869111679563
4549.5749.54301309250270.0269869074972533
4649.6849.59311309947870.0868869005212929
4749.7149.6822742049980.0277257950020555
4849.749.714040595124-0.0140405951239799
4949.749.7077549457867-0.00775494578667946
5049.849.69947109604880.100528903951229
5149.8449.83713320153980.00286679846015403
5250.0950.06940506979110.020594930208901
5350.250.15680460851360.043195391486428
5450.1650.2528716384357-0.0928716384357244
5550.1650.2126194865499-0.0526194865499079
5650.2950.19021969838170.099780301618317
5750.3650.3820976336702-0.0220976336702066
5851.0250.44965445291740.570345547082638
5951.0350.92266000000860.107339999991410
6051.0451.0958790705607-0.0558790705606853

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 48.15 & 47.9412142002061 & 0.208785799793937 \tabularnewline
14 & 48.15 & 48.1124331691076 & 0.0375668308924375 \tabularnewline
15 & 48.27 & 48.2894889364246 & -0.0194889364246436 \tabularnewline
16 & 48.47 & 48.5014620378868 & -0.0314620378868113 \tabularnewline
17 & 48.51 & 48.5450348788863 & -0.0350348788863499 \tabularnewline
18 & 48.53 & 48.5613471793674 & -0.0313471793674367 \tabularnewline
19 & 48.53 & 48.5555781352128 & -0.0255781352128324 \tabularnewline
20 & 48.53 & 48.5494716676626 & -0.0194716676625859 \tabularnewline
21 & 48.68 & 48.6974952763094 & -0.0174952763093756 \tabularnewline
22 & 48.64 & 48.6555254862202 & -0.0155254862201915 \tabularnewline
23 & 48.67 & 48.6801321428864 & -0.0101321428863912 \tabularnewline
24 & 48.66 & 48.6659297909034 & -0.00592979090337309 \tabularnewline
25 & 48.66 & 48.7202147708866 & -0.0602147708866454 \tabularnewline
26 & 48.67 & 48.6234507416995 & 0.0465492583005158 \tabularnewline
27 & 48.71 & 48.7547096337696 & -0.0447096337695783 \tabularnewline
28 & 48.96 & 48.9121905215452 & 0.0478094784548233 \tabularnewline
29 & 49.01 & 48.9811096377737 & 0.0288903622263064 \tabularnewline
30 & 49.04 & 49.0243851490509 & 0.0156148509490635 \tabularnewline
31 & 49.04 & 49.0418771340071 & -0.00187713400707423 \tabularnewline
32 & 49.04 & 49.047569435257 & -0.00756943525704656 \tabularnewline
33 & 49.06 & 49.2016115087932 & -0.14161150879319 \tabularnewline
34 & 49.13 & 49.0589759933539 & 0.071024006646148 \tabularnewline
35 & 49.19 & 49.1322064908829 & 0.0577935091170616 \tabularnewline
36 & 49.26 & 49.1634202284943 & 0.0965797715056667 \tabularnewline
37 & 49.26 & 49.2793112363648 & -0.0193112363647714 \tabularnewline
38 & 49.26 & 49.2674177178635 & -0.00741771786351819 \tabularnewline
39 & 49.29 & 49.345126988948 & -0.055126988948004 \tabularnewline
40 & 49.43 & 49.543328825983 & -0.113328825982990 \tabularnewline
41 & 49.43 & 49.491164915695 & -0.0611649156950378 \tabularnewline
42 & 49.45 & 49.4481632306667 & 0.00183676933328769 \tabularnewline
43 & 49.45 & 49.424749568827 & 0.0252504311729567 \tabularnewline
44 & 49.46 & 49.423913088832 & 0.0360869111679563 \tabularnewline
45 & 49.57 & 49.5430130925027 & 0.0269869074972533 \tabularnewline
46 & 49.68 & 49.5931130994787 & 0.0868869005212929 \tabularnewline
47 & 49.71 & 49.682274204998 & 0.0277257950020555 \tabularnewline
48 & 49.7 & 49.714040595124 & -0.0140405951239799 \tabularnewline
49 & 49.7 & 49.7077549457867 & -0.00775494578667946 \tabularnewline
50 & 49.8 & 49.6994710960488 & 0.100528903951229 \tabularnewline
51 & 49.84 & 49.8371332015398 & 0.00286679846015403 \tabularnewline
52 & 50.09 & 50.0694050697911 & 0.020594930208901 \tabularnewline
53 & 50.2 & 50.1568046085136 & 0.043195391486428 \tabularnewline
54 & 50.16 & 50.2528716384357 & -0.0928716384357244 \tabularnewline
55 & 50.16 & 50.2126194865499 & -0.0526194865499079 \tabularnewline
56 & 50.29 & 50.1902196983817 & 0.099780301618317 \tabularnewline
57 & 50.36 & 50.3820976336702 & -0.0220976336702066 \tabularnewline
58 & 51.02 & 50.4496544529174 & 0.570345547082638 \tabularnewline
59 & 51.03 & 50.9226600000086 & 0.107339999991410 \tabularnewline
60 & 51.04 & 51.0958790705607 & -0.0558790705606853 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13196&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]48.15[/C][C]47.9412142002061[/C][C]0.208785799793937[/C][/ROW]
[ROW][C]14[/C][C]48.15[/C][C]48.1124331691076[/C][C]0.0375668308924375[/C][/ROW]
[ROW][C]15[/C][C]48.27[/C][C]48.2894889364246[/C][C]-0.0194889364246436[/C][/ROW]
[ROW][C]16[/C][C]48.47[/C][C]48.5014620378868[/C][C]-0.0314620378868113[/C][/ROW]
[ROW][C]17[/C][C]48.51[/C][C]48.5450348788863[/C][C]-0.0350348788863499[/C][/ROW]
[ROW][C]18[/C][C]48.53[/C][C]48.5613471793674[/C][C]-0.0313471793674367[/C][/ROW]
[ROW][C]19[/C][C]48.53[/C][C]48.5555781352128[/C][C]-0.0255781352128324[/C][/ROW]
[ROW][C]20[/C][C]48.53[/C][C]48.5494716676626[/C][C]-0.0194716676625859[/C][/ROW]
[ROW][C]21[/C][C]48.68[/C][C]48.6974952763094[/C][C]-0.0174952763093756[/C][/ROW]
[ROW][C]22[/C][C]48.64[/C][C]48.6555254862202[/C][C]-0.0155254862201915[/C][/ROW]
[ROW][C]23[/C][C]48.67[/C][C]48.6801321428864[/C][C]-0.0101321428863912[/C][/ROW]
[ROW][C]24[/C][C]48.66[/C][C]48.6659297909034[/C][C]-0.00592979090337309[/C][/ROW]
[ROW][C]25[/C][C]48.66[/C][C]48.7202147708866[/C][C]-0.0602147708866454[/C][/ROW]
[ROW][C]26[/C][C]48.67[/C][C]48.6234507416995[/C][C]0.0465492583005158[/C][/ROW]
[ROW][C]27[/C][C]48.71[/C][C]48.7547096337696[/C][C]-0.0447096337695783[/C][/ROW]
[ROW][C]28[/C][C]48.96[/C][C]48.9121905215452[/C][C]0.0478094784548233[/C][/ROW]
[ROW][C]29[/C][C]49.01[/C][C]48.9811096377737[/C][C]0.0288903622263064[/C][/ROW]
[ROW][C]30[/C][C]49.04[/C][C]49.0243851490509[/C][C]0.0156148509490635[/C][/ROW]
[ROW][C]31[/C][C]49.04[/C][C]49.0418771340071[/C][C]-0.00187713400707423[/C][/ROW]
[ROW][C]32[/C][C]49.04[/C][C]49.047569435257[/C][C]-0.00756943525704656[/C][/ROW]
[ROW][C]33[/C][C]49.06[/C][C]49.2016115087932[/C][C]-0.14161150879319[/C][/ROW]
[ROW][C]34[/C][C]49.13[/C][C]49.0589759933539[/C][C]0.071024006646148[/C][/ROW]
[ROW][C]35[/C][C]49.19[/C][C]49.1322064908829[/C][C]0.0577935091170616[/C][/ROW]
[ROW][C]36[/C][C]49.26[/C][C]49.1634202284943[/C][C]0.0965797715056667[/C][/ROW]
[ROW][C]37[/C][C]49.26[/C][C]49.2793112363648[/C][C]-0.0193112363647714[/C][/ROW]
[ROW][C]38[/C][C]49.26[/C][C]49.2674177178635[/C][C]-0.00741771786351819[/C][/ROW]
[ROW][C]39[/C][C]49.29[/C][C]49.345126988948[/C][C]-0.055126988948004[/C][/ROW]
[ROW][C]40[/C][C]49.43[/C][C]49.543328825983[/C][C]-0.113328825982990[/C][/ROW]
[ROW][C]41[/C][C]49.43[/C][C]49.491164915695[/C][C]-0.0611649156950378[/C][/ROW]
[ROW][C]42[/C][C]49.45[/C][C]49.4481632306667[/C][C]0.00183676933328769[/C][/ROW]
[ROW][C]43[/C][C]49.45[/C][C]49.424749568827[/C][C]0.0252504311729567[/C][/ROW]
[ROW][C]44[/C][C]49.46[/C][C]49.423913088832[/C][C]0.0360869111679563[/C][/ROW]
[ROW][C]45[/C][C]49.57[/C][C]49.5430130925027[/C][C]0.0269869074972533[/C][/ROW]
[ROW][C]46[/C][C]49.68[/C][C]49.5931130994787[/C][C]0.0868869005212929[/C][/ROW]
[ROW][C]47[/C][C]49.71[/C][C]49.682274204998[/C][C]0.0277257950020555[/C][/ROW]
[ROW][C]48[/C][C]49.7[/C][C]49.714040595124[/C][C]-0.0140405951239799[/C][/ROW]
[ROW][C]49[/C][C]49.7[/C][C]49.7077549457867[/C][C]-0.00775494578667946[/C][/ROW]
[ROW][C]50[/C][C]49.8[/C][C]49.6994710960488[/C][C]0.100528903951229[/C][/ROW]
[ROW][C]51[/C][C]49.84[/C][C]49.8371332015398[/C][C]0.00286679846015403[/C][/ROW]
[ROW][C]52[/C][C]50.09[/C][C]50.0694050697911[/C][C]0.020594930208901[/C][/ROW]
[ROW][C]53[/C][C]50.2[/C][C]50.1568046085136[/C][C]0.043195391486428[/C][/ROW]
[ROW][C]54[/C][C]50.16[/C][C]50.2528716384357[/C][C]-0.0928716384357244[/C][/ROW]
[ROW][C]55[/C][C]50.16[/C][C]50.2126194865499[/C][C]-0.0526194865499079[/C][/ROW]
[ROW][C]56[/C][C]50.29[/C][C]50.1902196983817[/C][C]0.099780301618317[/C][/ROW]
[ROW][C]57[/C][C]50.36[/C][C]50.3820976336702[/C][C]-0.0220976336702066[/C][/ROW]
[ROW][C]58[/C][C]51.02[/C][C]50.4496544529174[/C][C]0.570345547082638[/C][/ROW]
[ROW][C]59[/C][C]51.03[/C][C]50.9226600000086[/C][C]0.107339999991410[/C][/ROW]
[ROW][C]60[/C][C]51.04[/C][C]51.0958790705607[/C][C]-0.0558790705606853[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13196&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13196&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
1348.1547.94121420020610.208785799793937
1448.1548.11243316910760.0375668308924375
1548.2748.2894889364246-0.0194889364246436
1648.4748.5014620378868-0.0314620378868113
1748.5148.5450348788863-0.0350348788863499
1848.5348.5613471793674-0.0313471793674367
1948.5348.5555781352128-0.0255781352128324
2048.5348.5494716676626-0.0194716676625859
2148.6848.6974952763094-0.0174952763093756
2248.6448.6555254862202-0.0155254862201915
2348.6748.6801321428864-0.0101321428863912
2448.6648.6659297909034-0.00592979090337309
2548.6648.7202147708866-0.0602147708866454
2648.6748.62345074169950.0465492583005158
2748.7148.7547096337696-0.0447096337695783
2848.9648.91219052154520.0478094784548233
2949.0148.98110963777370.0288903622263064
3049.0449.02438514905090.0156148509490635
3149.0449.0418771340071-0.00187713400707423
3249.0449.047569435257-0.00756943525704656
3349.0649.2016115087932-0.14161150879319
3449.1349.05897599335390.071024006646148
3549.1949.13220649088290.0577935091170616
3649.2649.16342022849430.0965797715056667
3749.2649.2793112363648-0.0193112363647714
3849.2649.2674177178635-0.00741771786351819
3949.2949.345126988948-0.055126988948004
4049.4349.543328825983-0.113328825982990
4149.4349.491164915695-0.0611649156950378
4249.4549.44816323066670.00183676933328769
4349.4549.4247495688270.0252504311729567
4449.4649.4239130888320.0360869111679563
4549.5749.54301309250270.0269869074972533
4649.6849.59311309947870.0868869005212929
4749.7149.6822742049980.0277257950020555
4849.749.714040595124-0.0140405951239799
4949.749.7077549457867-0.00775494578667946
5049.849.69947109604880.100528903951229
5149.8449.83713320153980.00286679846015403
5250.0950.06940506979110.020594930208901
5350.250.15680460851360.043195391486428
5450.1650.2528716384357-0.0928716384357244
5550.1650.2126194865499-0.0526194865499079
5650.2950.19021969838170.099780301618317
5750.3650.3820976336702-0.0220976336702066
5851.0250.44965445291740.570345547082638
5951.0350.92266000000860.107339999991410
6051.0451.0958790705607-0.0558790705606853







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6151.164425811331450.963950046181551.3649015764813
6251.30119402706751.046567435875151.5558206182589
6351.426076674619751.111222401480751.7409309477587
6451.755735433531951.374279172017552.1371916950463
6551.92300811505651.470890190136752.3751260399754
6652.019056773910651.492469516918452.5456440309028
6752.143239219483951.537949927499552.7485285114683
6852.308531629588751.620270691919852.9967925672575
6952.478187730166451.703201470329253.2531739900036
7052.868531062365951.999844943034753.7372171816972
7152.809521703122551.850846103493853.7681973027512
7252.843561121879251.157848570272354.5292736734862

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 51.1644258113314 & 50.9639500461815 & 51.3649015764813 \tabularnewline
62 & 51.301194027067 & 51.0465674358751 & 51.5558206182589 \tabularnewline
63 & 51.4260766746197 & 51.1112224014807 & 51.7409309477587 \tabularnewline
64 & 51.7557354335319 & 51.3742791720175 & 52.1371916950463 \tabularnewline
65 & 51.923008115056 & 51.4708901901367 & 52.3751260399754 \tabularnewline
66 & 52.0190567739106 & 51.4924695169184 & 52.5456440309028 \tabularnewline
67 & 52.1432392194839 & 51.5379499274995 & 52.7485285114683 \tabularnewline
68 & 52.3085316295887 & 51.6202706919198 & 52.9967925672575 \tabularnewline
69 & 52.4781877301664 & 51.7032014703292 & 53.2531739900036 \tabularnewline
70 & 52.8685310623659 & 51.9998449430347 & 53.7372171816972 \tabularnewline
71 & 52.8095217031225 & 51.8508461034938 & 53.7681973027512 \tabularnewline
72 & 52.8435611218792 & 51.1578485702723 & 54.5292736734862 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13196&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]51.1644258113314[/C][C]50.9639500461815[/C][C]51.3649015764813[/C][/ROW]
[ROW][C]62[/C][C]51.301194027067[/C][C]51.0465674358751[/C][C]51.5558206182589[/C][/ROW]
[ROW][C]63[/C][C]51.4260766746197[/C][C]51.1112224014807[/C][C]51.7409309477587[/C][/ROW]
[ROW][C]64[/C][C]51.7557354335319[/C][C]51.3742791720175[/C][C]52.1371916950463[/C][/ROW]
[ROW][C]65[/C][C]51.923008115056[/C][C]51.4708901901367[/C][C]52.3751260399754[/C][/ROW]
[ROW][C]66[/C][C]52.0190567739106[/C][C]51.4924695169184[/C][C]52.5456440309028[/C][/ROW]
[ROW][C]67[/C][C]52.1432392194839[/C][C]51.5379499274995[/C][C]52.7485285114683[/C][/ROW]
[ROW][C]68[/C][C]52.3085316295887[/C][C]51.6202706919198[/C][C]52.9967925672575[/C][/ROW]
[ROW][C]69[/C][C]52.4781877301664[/C][C]51.7032014703292[/C][C]53.2531739900036[/C][/ROW]
[ROW][C]70[/C][C]52.8685310623659[/C][C]51.9998449430347[/C][C]53.7372171816972[/C][/ROW]
[ROW][C]71[/C][C]52.8095217031225[/C][C]51.8508461034938[/C][C]53.7681973027512[/C][/ROW]
[ROW][C]72[/C][C]52.8435611218792[/C][C]51.1578485702723[/C][C]54.5292736734862[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13196&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13196&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
6151.164425811331450.963950046181551.3649015764813
6251.30119402706751.046567435875151.5558206182589
6351.426076674619751.111222401480751.7409309477587
6451.755735433531951.374279172017552.1371916950463
6551.92300811505651.470890190136752.3751260399754
6652.019056773910651.492469516918452.5456440309028
6752.143239219483951.537949927499552.7485285114683
6852.308531629588751.620270691919852.9967925672575
6952.478187730166451.703201470329253.2531739900036
7052.868531062365951.999844943034753.7372171816972
7152.809521703122551.850846103493853.7681973027512
7252.843561121879251.157848570272354.5292736734862



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')