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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 19 Jan 2014 12:36:19 -0500
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/Jan/19/t13901531412mzkopb4uavh03p.htm/, Retrieved Sun, 19 May 2024 07:20:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233141, Retrieved Sun, 19 May 2024 07:20:09 +0000
QR Codes:

Original text written by user:Uses Winters Multiplicative method using the historical data and zero (0) weeks of additional observed data.
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact191
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Beer Game Forecas...] [2014-01-19 17:36:19] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
21.8
18.8
27.2
17.7
34.6
41.8
32.2
38.3
22.4
22.3
19.8
35.2
21
22.8
28.2
25
32.3
40.3
34.7
38.7
23.7
22.7
16.8
33.3
20.3
23.9
28.5
18.7
31.2
37.4
34.8
37.6
24
19.4
20.4
32.5
20.8
23.4
27.7
21
31.7
39
31.8
40.7
22.1
15.7
20.8
31.1
19.8
19.5
27.5
21.2
31.3
37.9
32.2
40.8
25.2
18.7
19.6
34.4
22.5
21.8
29.6
22.3
31.2
40.7
33.9
40.2
26.5
21.1
19.9
36.5
21
21.7
28.1
20.9
32
39.5
33.2
39.3
23.9
19.9
19.5
33.8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233141&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233141&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233141&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.167835227221149
beta0.0145975367456994
gamma0.426123114058207

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.167835227221149 \tabularnewline
beta & 0.0145975367456994 \tabularnewline
gamma & 0.426123114058207 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233141&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]0.167835227221149[/C][/ROW]
[ROW][C]beta[/C][C]0.0145975367456994[/C][/ROW]
[ROW][C]gamma[/C][C]0.426123114058207[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233141&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233141&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
alpha0.167835227221149
beta0.0145975367456994
gamma0.426123114058207







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132120.59974191984750.400258080152476
1422.822.40468605335440.395313946645611
1528.227.80115500434320.398844995656788
162524.71356332397090.28643667602913
1732.332.20348089496220.0965191050377499
1840.340.6026727232346-0.3026727232346
1934.733.34851828653281.35148171346717
2038.739.8576517167864-1.15765171678642
2123.723.08889009917710.611109900822932
2222.722.8707020633886-0.170702063388571
2316.820.1898202755863-3.38982027558629
2433.335.1625225236309-1.86252252363086
2520.320.95228953107-0.652289531069979
2623.922.57071343479761.32928656520241
2728.528.15723486451540.342765135484584
2818.724.9872619799635-6.28726197996348
2931.231.00125055317080.198749446829186
3037.438.928318777283-1.52831877728298
3134.832.30992960495812.49007039504188
3237.637.8741883160299-0.274188316029921
332422.43957417552221.56042582447775
3419.422.1046899154051-2.7046899154051
3520.417.99413985283892.40586014716111
3632.534.4440085725439-1.94400857254391
3720.820.66833395019450.131666049805517
3823.423.11861130454560.281388695454428
3927.728.1465363756982-0.446536375698237
402122.4375477309824-1.43754773098241
4131.731.7767885114091-0.0767885114091413
423939.1928565061366-0.192856506136565
4331.834.0785397415072-2.27853974150718
4440.737.86103141050022.83896858949979
4522.123.3530086249195-1.25300862491947
4615.721.0154127407632-5.31541274076324
4720.818.29854493329332.50145506670668
4831.132.7920575863585-1.69205758635846
4919.820.1311866341023-0.331186634102284
5019.522.4613937487829-2.96139374878289
5127.526.39486311907151.1051368809285
5221.220.8564102063520.343589793648004
5331.330.596218491360.703781508639999
5437.937.83856210847510.0614378915249389
5532.232.18239659372310.0176034062768835
5640.838.00553798885192.79446201114805
5725.222.38703799625812.8129620037419
5818.719.1797093033272-0.479709303327169
5919.620.0783176706895-0.478317670689499
6034.432.83298800075031.56701199924971
6122.520.7640689313341.735931068666
6221.822.5742638428497-0.774263842849667
6329.628.76391978443640.836080215563616
6422.322.4957419023514-0.195741902351426
6531.232.9575258196221-1.75752581962215
6640.739.95519326690010.744806733099949
6733.934.0831221195584-0.183122119558391
6840.241.2571667174496-1.05716671744964
6926.524.32560209209252.17439790790753
7021.119.6765818263091.42341817369103
7119.920.9532501002127-1.0532501002127
7236.534.99151378642251.50848621357748
732122.3895963500908-1.38959635009076
7421.722.7972794826637-1.09727948266371
7528.129.6388447195997-1.53884471959969
7620.922.5594231623598-1.6594231623598
773232.1545022973318-0.154502297331788
7839.540.3201936950227-0.820193695022738
7933.233.8701648860084-0.670164886008415
8039.340.5891732762104-1.28917327621043
8123.924.8709870769614-0.970987076961393
8219.919.56509719586560.334902804134376
8319.519.7561061914571-0.256106191457121
8433.834.2974765009834-0.497476500983389

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 21 & 20.5997419198475 & 0.400258080152476 \tabularnewline
14 & 22.8 & 22.4046860533544 & 0.395313946645611 \tabularnewline
15 & 28.2 & 27.8011550043432 & 0.398844995656788 \tabularnewline
16 & 25 & 24.7135633239709 & 0.28643667602913 \tabularnewline
17 & 32.3 & 32.2034808949622 & 0.0965191050377499 \tabularnewline
18 & 40.3 & 40.6026727232346 & -0.3026727232346 \tabularnewline
19 & 34.7 & 33.3485182865328 & 1.35148171346717 \tabularnewline
20 & 38.7 & 39.8576517167864 & -1.15765171678642 \tabularnewline
21 & 23.7 & 23.0888900991771 & 0.611109900822932 \tabularnewline
22 & 22.7 & 22.8707020633886 & -0.170702063388571 \tabularnewline
23 & 16.8 & 20.1898202755863 & -3.38982027558629 \tabularnewline
24 & 33.3 & 35.1625225236309 & -1.86252252363086 \tabularnewline
25 & 20.3 & 20.95228953107 & -0.652289531069979 \tabularnewline
26 & 23.9 & 22.5707134347976 & 1.32928656520241 \tabularnewline
27 & 28.5 & 28.1572348645154 & 0.342765135484584 \tabularnewline
28 & 18.7 & 24.9872619799635 & -6.28726197996348 \tabularnewline
29 & 31.2 & 31.0012505531708 & 0.198749446829186 \tabularnewline
30 & 37.4 & 38.928318777283 & -1.52831877728298 \tabularnewline
31 & 34.8 & 32.3099296049581 & 2.49007039504188 \tabularnewline
32 & 37.6 & 37.8741883160299 & -0.274188316029921 \tabularnewline
33 & 24 & 22.4395741755222 & 1.56042582447775 \tabularnewline
34 & 19.4 & 22.1046899154051 & -2.7046899154051 \tabularnewline
35 & 20.4 & 17.9941398528389 & 2.40586014716111 \tabularnewline
36 & 32.5 & 34.4440085725439 & -1.94400857254391 \tabularnewline
37 & 20.8 & 20.6683339501945 & 0.131666049805517 \tabularnewline
38 & 23.4 & 23.1186113045456 & 0.281388695454428 \tabularnewline
39 & 27.7 & 28.1465363756982 & -0.446536375698237 \tabularnewline
40 & 21 & 22.4375477309824 & -1.43754773098241 \tabularnewline
41 & 31.7 & 31.7767885114091 & -0.0767885114091413 \tabularnewline
42 & 39 & 39.1928565061366 & -0.192856506136565 \tabularnewline
43 & 31.8 & 34.0785397415072 & -2.27853974150718 \tabularnewline
44 & 40.7 & 37.8610314105002 & 2.83896858949979 \tabularnewline
45 & 22.1 & 23.3530086249195 & -1.25300862491947 \tabularnewline
46 & 15.7 & 21.0154127407632 & -5.31541274076324 \tabularnewline
47 & 20.8 & 18.2985449332933 & 2.50145506670668 \tabularnewline
48 & 31.1 & 32.7920575863585 & -1.69205758635846 \tabularnewline
49 & 19.8 & 20.1311866341023 & -0.331186634102284 \tabularnewline
50 & 19.5 & 22.4613937487829 & -2.96139374878289 \tabularnewline
51 & 27.5 & 26.3948631190715 & 1.1051368809285 \tabularnewline
52 & 21.2 & 20.856410206352 & 0.343589793648004 \tabularnewline
53 & 31.3 & 30.59621849136 & 0.703781508639999 \tabularnewline
54 & 37.9 & 37.8385621084751 & 0.0614378915249389 \tabularnewline
55 & 32.2 & 32.1823965937231 & 0.0176034062768835 \tabularnewline
56 & 40.8 & 38.0055379888519 & 2.79446201114805 \tabularnewline
57 & 25.2 & 22.3870379962581 & 2.8129620037419 \tabularnewline
58 & 18.7 & 19.1797093033272 & -0.479709303327169 \tabularnewline
59 & 19.6 & 20.0783176706895 & -0.478317670689499 \tabularnewline
60 & 34.4 & 32.8329880007503 & 1.56701199924971 \tabularnewline
61 & 22.5 & 20.764068931334 & 1.735931068666 \tabularnewline
62 & 21.8 & 22.5742638428497 & -0.774263842849667 \tabularnewline
63 & 29.6 & 28.7639197844364 & 0.836080215563616 \tabularnewline
64 & 22.3 & 22.4957419023514 & -0.195741902351426 \tabularnewline
65 & 31.2 & 32.9575258196221 & -1.75752581962215 \tabularnewline
66 & 40.7 & 39.9551932669001 & 0.744806733099949 \tabularnewline
67 & 33.9 & 34.0831221195584 & -0.183122119558391 \tabularnewline
68 & 40.2 & 41.2571667174496 & -1.05716671744964 \tabularnewline
69 & 26.5 & 24.3256020920925 & 2.17439790790753 \tabularnewline
70 & 21.1 & 19.676581826309 & 1.42341817369103 \tabularnewline
71 & 19.9 & 20.9532501002127 & -1.0532501002127 \tabularnewline
72 & 36.5 & 34.9915137864225 & 1.50848621357748 \tabularnewline
73 & 21 & 22.3895963500908 & -1.38959635009076 \tabularnewline
74 & 21.7 & 22.7972794826637 & -1.09727948266371 \tabularnewline
75 & 28.1 & 29.6388447195997 & -1.53884471959969 \tabularnewline
76 & 20.9 & 22.5594231623598 & -1.6594231623598 \tabularnewline
77 & 32 & 32.1545022973318 & -0.154502297331788 \tabularnewline
78 & 39.5 & 40.3201936950227 & -0.820193695022738 \tabularnewline
79 & 33.2 & 33.8701648860084 & -0.670164886008415 \tabularnewline
80 & 39.3 & 40.5891732762104 & -1.28917327621043 \tabularnewline
81 & 23.9 & 24.8709870769614 & -0.970987076961393 \tabularnewline
82 & 19.9 & 19.5650971958656 & 0.334902804134376 \tabularnewline
83 & 19.5 & 19.7561061914571 & -0.256106191457121 \tabularnewline
84 & 33.8 & 34.2974765009834 & -0.497476500983389 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233141&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]21[/C][C]20.5997419198475[/C][C]0.400258080152476[/C][/ROW]
[ROW][C]14[/C][C]22.8[/C][C]22.4046860533544[/C][C]0.395313946645611[/C][/ROW]
[ROW][C]15[/C][C]28.2[/C][C]27.8011550043432[/C][C]0.398844995656788[/C][/ROW]
[ROW][C]16[/C][C]25[/C][C]24.7135633239709[/C][C]0.28643667602913[/C][/ROW]
[ROW][C]17[/C][C]32.3[/C][C]32.2034808949622[/C][C]0.0965191050377499[/C][/ROW]
[ROW][C]18[/C][C]40.3[/C][C]40.6026727232346[/C][C]-0.3026727232346[/C][/ROW]
[ROW][C]19[/C][C]34.7[/C][C]33.3485182865328[/C][C]1.35148171346717[/C][/ROW]
[ROW][C]20[/C][C]38.7[/C][C]39.8576517167864[/C][C]-1.15765171678642[/C][/ROW]
[ROW][C]21[/C][C]23.7[/C][C]23.0888900991771[/C][C]0.611109900822932[/C][/ROW]
[ROW][C]22[/C][C]22.7[/C][C]22.8707020633886[/C][C]-0.170702063388571[/C][/ROW]
[ROW][C]23[/C][C]16.8[/C][C]20.1898202755863[/C][C]-3.38982027558629[/C][/ROW]
[ROW][C]24[/C][C]33.3[/C][C]35.1625225236309[/C][C]-1.86252252363086[/C][/ROW]
[ROW][C]25[/C][C]20.3[/C][C]20.95228953107[/C][C]-0.652289531069979[/C][/ROW]
[ROW][C]26[/C][C]23.9[/C][C]22.5707134347976[/C][C]1.32928656520241[/C][/ROW]
[ROW][C]27[/C][C]28.5[/C][C]28.1572348645154[/C][C]0.342765135484584[/C][/ROW]
[ROW][C]28[/C][C]18.7[/C][C]24.9872619799635[/C][C]-6.28726197996348[/C][/ROW]
[ROW][C]29[/C][C]31.2[/C][C]31.0012505531708[/C][C]0.198749446829186[/C][/ROW]
[ROW][C]30[/C][C]37.4[/C][C]38.928318777283[/C][C]-1.52831877728298[/C][/ROW]
[ROW][C]31[/C][C]34.8[/C][C]32.3099296049581[/C][C]2.49007039504188[/C][/ROW]
[ROW][C]32[/C][C]37.6[/C][C]37.8741883160299[/C][C]-0.274188316029921[/C][/ROW]
[ROW][C]33[/C][C]24[/C][C]22.4395741755222[/C][C]1.56042582447775[/C][/ROW]
[ROW][C]34[/C][C]19.4[/C][C]22.1046899154051[/C][C]-2.7046899154051[/C][/ROW]
[ROW][C]35[/C][C]20.4[/C][C]17.9941398528389[/C][C]2.40586014716111[/C][/ROW]
[ROW][C]36[/C][C]32.5[/C][C]34.4440085725439[/C][C]-1.94400857254391[/C][/ROW]
[ROW][C]37[/C][C]20.8[/C][C]20.6683339501945[/C][C]0.131666049805517[/C][/ROW]
[ROW][C]38[/C][C]23.4[/C][C]23.1186113045456[/C][C]0.281388695454428[/C][/ROW]
[ROW][C]39[/C][C]27.7[/C][C]28.1465363756982[/C][C]-0.446536375698237[/C][/ROW]
[ROW][C]40[/C][C]21[/C][C]22.4375477309824[/C][C]-1.43754773098241[/C][/ROW]
[ROW][C]41[/C][C]31.7[/C][C]31.7767885114091[/C][C]-0.0767885114091413[/C][/ROW]
[ROW][C]42[/C][C]39[/C][C]39.1928565061366[/C][C]-0.192856506136565[/C][/ROW]
[ROW][C]43[/C][C]31.8[/C][C]34.0785397415072[/C][C]-2.27853974150718[/C][/ROW]
[ROW][C]44[/C][C]40.7[/C][C]37.8610314105002[/C][C]2.83896858949979[/C][/ROW]
[ROW][C]45[/C][C]22.1[/C][C]23.3530086249195[/C][C]-1.25300862491947[/C][/ROW]
[ROW][C]46[/C][C]15.7[/C][C]21.0154127407632[/C][C]-5.31541274076324[/C][/ROW]
[ROW][C]47[/C][C]20.8[/C][C]18.2985449332933[/C][C]2.50145506670668[/C][/ROW]
[ROW][C]48[/C][C]31.1[/C][C]32.7920575863585[/C][C]-1.69205758635846[/C][/ROW]
[ROW][C]49[/C][C]19.8[/C][C]20.1311866341023[/C][C]-0.331186634102284[/C][/ROW]
[ROW][C]50[/C][C]19.5[/C][C]22.4613937487829[/C][C]-2.96139374878289[/C][/ROW]
[ROW][C]51[/C][C]27.5[/C][C]26.3948631190715[/C][C]1.1051368809285[/C][/ROW]
[ROW][C]52[/C][C]21.2[/C][C]20.856410206352[/C][C]0.343589793648004[/C][/ROW]
[ROW][C]53[/C][C]31.3[/C][C]30.59621849136[/C][C]0.703781508639999[/C][/ROW]
[ROW][C]54[/C][C]37.9[/C][C]37.8385621084751[/C][C]0.0614378915249389[/C][/ROW]
[ROW][C]55[/C][C]32.2[/C][C]32.1823965937231[/C][C]0.0176034062768835[/C][/ROW]
[ROW][C]56[/C][C]40.8[/C][C]38.0055379888519[/C][C]2.79446201114805[/C][/ROW]
[ROW][C]57[/C][C]25.2[/C][C]22.3870379962581[/C][C]2.8129620037419[/C][/ROW]
[ROW][C]58[/C][C]18.7[/C][C]19.1797093033272[/C][C]-0.479709303327169[/C][/ROW]
[ROW][C]59[/C][C]19.6[/C][C]20.0783176706895[/C][C]-0.478317670689499[/C][/ROW]
[ROW][C]60[/C][C]34.4[/C][C]32.8329880007503[/C][C]1.56701199924971[/C][/ROW]
[ROW][C]61[/C][C]22.5[/C][C]20.764068931334[/C][C]1.735931068666[/C][/ROW]
[ROW][C]62[/C][C]21.8[/C][C]22.5742638428497[/C][C]-0.774263842849667[/C][/ROW]
[ROW][C]63[/C][C]29.6[/C][C]28.7639197844364[/C][C]0.836080215563616[/C][/ROW]
[ROW][C]64[/C][C]22.3[/C][C]22.4957419023514[/C][C]-0.195741902351426[/C][/ROW]
[ROW][C]65[/C][C]31.2[/C][C]32.9575258196221[/C][C]-1.75752581962215[/C][/ROW]
[ROW][C]66[/C][C]40.7[/C][C]39.9551932669001[/C][C]0.744806733099949[/C][/ROW]
[ROW][C]67[/C][C]33.9[/C][C]34.0831221195584[/C][C]-0.183122119558391[/C][/ROW]
[ROW][C]68[/C][C]40.2[/C][C]41.2571667174496[/C][C]-1.05716671744964[/C][/ROW]
[ROW][C]69[/C][C]26.5[/C][C]24.3256020920925[/C][C]2.17439790790753[/C][/ROW]
[ROW][C]70[/C][C]21.1[/C][C]19.676581826309[/C][C]1.42341817369103[/C][/ROW]
[ROW][C]71[/C][C]19.9[/C][C]20.9532501002127[/C][C]-1.0532501002127[/C][/ROW]
[ROW][C]72[/C][C]36.5[/C][C]34.9915137864225[/C][C]1.50848621357748[/C][/ROW]
[ROW][C]73[/C][C]21[/C][C]22.3895963500908[/C][C]-1.38959635009076[/C][/ROW]
[ROW][C]74[/C][C]21.7[/C][C]22.7972794826637[/C][C]-1.09727948266371[/C][/ROW]
[ROW][C]75[/C][C]28.1[/C][C]29.6388447195997[/C][C]-1.53884471959969[/C][/ROW]
[ROW][C]76[/C][C]20.9[/C][C]22.5594231623598[/C][C]-1.6594231623598[/C][/ROW]
[ROW][C]77[/C][C]32[/C][C]32.1545022973318[/C][C]-0.154502297331788[/C][/ROW]
[ROW][C]78[/C][C]39.5[/C][C]40.3201936950227[/C][C]-0.820193695022738[/C][/ROW]
[ROW][C]79[/C][C]33.2[/C][C]33.8701648860084[/C][C]-0.670164886008415[/C][/ROW]
[ROW][C]80[/C][C]39.3[/C][C]40.5891732762104[/C][C]-1.28917327621043[/C][/ROW]
[ROW][C]81[/C][C]23.9[/C][C]24.8709870769614[/C][C]-0.970987076961393[/C][/ROW]
[ROW][C]82[/C][C]19.9[/C][C]19.5650971958656[/C][C]0.334902804134376[/C][/ROW]
[ROW][C]83[/C][C]19.5[/C][C]19.7561061914571[/C][C]-0.256106191457121[/C][/ROW]
[ROW][C]84[/C][C]33.8[/C][C]34.2974765009834[/C][C]-0.497476500983389[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233141&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233141&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
132120.59974191984750.400258080152476
1422.822.40468605335440.395313946645611
1528.227.80115500434320.398844995656788
162524.71356332397090.28643667602913
1732.332.20348089496220.0965191050377499
1840.340.6026727232346-0.3026727232346
1934.733.34851828653281.35148171346717
2038.739.8576517167864-1.15765171678642
2123.723.08889009917710.611109900822932
2222.722.8707020633886-0.170702063388571
2316.820.1898202755863-3.38982027558629
2433.335.1625225236309-1.86252252363086
2520.320.95228953107-0.652289531069979
2623.922.57071343479761.32928656520241
2728.528.15723486451540.342765135484584
2818.724.9872619799635-6.28726197996348
2931.231.00125055317080.198749446829186
3037.438.928318777283-1.52831877728298
3134.832.30992960495812.49007039504188
3237.637.8741883160299-0.274188316029921
332422.43957417552221.56042582447775
3419.422.1046899154051-2.7046899154051
3520.417.99413985283892.40586014716111
3632.534.4440085725439-1.94400857254391
3720.820.66833395019450.131666049805517
3823.423.11861130454560.281388695454428
3927.728.1465363756982-0.446536375698237
402122.4375477309824-1.43754773098241
4131.731.7767885114091-0.0767885114091413
423939.1928565061366-0.192856506136565
4331.834.0785397415072-2.27853974150718
4440.737.86103141050022.83896858949979
4522.123.3530086249195-1.25300862491947
4615.721.0154127407632-5.31541274076324
4720.818.29854493329332.50145506670668
4831.132.7920575863585-1.69205758635846
4919.820.1311866341023-0.331186634102284
5019.522.4613937487829-2.96139374878289
5127.526.39486311907151.1051368809285
5221.220.8564102063520.343589793648004
5331.330.596218491360.703781508639999
5437.937.83856210847510.0614378915249389
5532.232.18239659372310.0176034062768835
5640.838.00553798885192.79446201114805
5725.222.38703799625812.8129620037419
5818.719.1797093033272-0.479709303327169
5919.620.0783176706895-0.478317670689499
6034.432.83298800075031.56701199924971
6122.520.7640689313341.735931068666
6221.822.5742638428497-0.774263842849667
6329.628.76391978443640.836080215563616
6422.322.4957419023514-0.195741902351426
6531.232.9575258196221-1.75752581962215
6640.739.95519326690010.744806733099949
6733.934.0831221195584-0.183122119558391
6840.241.2571667174496-1.05716671744964
6926.524.32560209209252.17439790790753
7021.119.6765818263091.42341817369103
7119.920.9532501002127-1.0532501002127
7236.534.99151378642251.50848621357748
732122.3895963500908-1.38959635009076
7421.722.7972794826637-1.09727948266371
7528.129.6388447195997-1.53884471959969
7620.922.5594231623598-1.6594231623598
773232.1545022973318-0.154502297331788
7839.540.3201936950227-0.820193695022738
7933.233.8701648860084-0.670164886008415
8039.340.5891732762104-1.28917327621043
8123.924.8709870769614-0.970987076961393
8219.919.56509719586560.334902804134376
8319.519.7561061914571-0.256106191457121
8433.834.2974765009834-0.497476500983389







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8520.916507215685119.194710728240922.6383037031293
8621.617481745480319.800808025708923.4341554652517
8728.278078632301726.255135257362130.3010220072413
8821.529495858683219.575559061171923.4834326561945
8931.848945736957729.489083274243134.2088081996722
9039.736283298664736.976915236975142.4956513603542
9133.492585875588430.92808001453536.0570917366418
9240.088782462715437.135400478616943.0421644468139
9324.627675901324722.323036912133626.9323148905158
9419.896047933792117.718937902009222.0731579655751
9519.818989850440917.56466735965422.0733123412277
9634.4610675651465-35.9164501933037104.838585323597

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 20.9165072156851 & 19.1947107282409 & 22.6383037031293 \tabularnewline
86 & 21.6174817454803 & 19.8008080257089 & 23.4341554652517 \tabularnewline
87 & 28.2780786323017 & 26.2551352573621 & 30.3010220072413 \tabularnewline
88 & 21.5294958586832 & 19.5755590611719 & 23.4834326561945 \tabularnewline
89 & 31.8489457369577 & 29.4890832742431 & 34.2088081996722 \tabularnewline
90 & 39.7362832986647 & 36.9769152369751 & 42.4956513603542 \tabularnewline
91 & 33.4925858755884 & 30.928080014535 & 36.0570917366418 \tabularnewline
92 & 40.0887824627154 & 37.1354004786169 & 43.0421644468139 \tabularnewline
93 & 24.6276759013247 & 22.3230369121336 & 26.9323148905158 \tabularnewline
94 & 19.8960479337921 & 17.7189379020092 & 22.0731579655751 \tabularnewline
95 & 19.8189898504409 & 17.564667359654 & 22.0733123412277 \tabularnewline
96 & 34.4610675651465 & -35.9164501933037 & 104.838585323597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233141&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]85[/C][C]20.9165072156851[/C][C]19.1947107282409[/C][C]22.6383037031293[/C][/ROW]
[ROW][C]86[/C][C]21.6174817454803[/C][C]19.8008080257089[/C][C]23.4341554652517[/C][/ROW]
[ROW][C]87[/C][C]28.2780786323017[/C][C]26.2551352573621[/C][C]30.3010220072413[/C][/ROW]
[ROW][C]88[/C][C]21.5294958586832[/C][C]19.5755590611719[/C][C]23.4834326561945[/C][/ROW]
[ROW][C]89[/C][C]31.8489457369577[/C][C]29.4890832742431[/C][C]34.2088081996722[/C][/ROW]
[ROW][C]90[/C][C]39.7362832986647[/C][C]36.9769152369751[/C][C]42.4956513603542[/C][/ROW]
[ROW][C]91[/C][C]33.4925858755884[/C][C]30.928080014535[/C][C]36.0570917366418[/C][/ROW]
[ROW][C]92[/C][C]40.0887824627154[/C][C]37.1354004786169[/C][C]43.0421644468139[/C][/ROW]
[ROW][C]93[/C][C]24.6276759013247[/C][C]22.3230369121336[/C][C]26.9323148905158[/C][/ROW]
[ROW][C]94[/C][C]19.8960479337921[/C][C]17.7189379020092[/C][C]22.0731579655751[/C][/ROW]
[ROW][C]95[/C][C]19.8189898504409[/C][C]17.564667359654[/C][C]22.0733123412277[/C][/ROW]
[ROW][C]96[/C][C]34.4610675651465[/C][C]-35.9164501933037[/C][C]104.838585323597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233141&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233141&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
8520.916507215685119.194710728240922.6383037031293
8621.617481745480319.800808025708923.4341554652517
8728.278078632301726.255135257362130.3010220072413
8821.529495858683219.575559061171923.4834326561945
8931.848945736957729.489083274243134.2088081996722
9039.736283298664736.976915236975142.4956513603542
9133.492585875588430.92808001453536.0570917366418
9240.088782462715437.135400478616943.0421644468139
9324.627675901324722.323036912133626.9323148905158
9419.896047933792117.718937902009222.0731579655751
9519.818989850440917.56466735965422.0733123412277
9634.4610675651465-35.9164501933037104.838585323597



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=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')