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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 03 Dec 2009 09:44:51 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/03/t1259858780sqqnkuffm6gymzp.htm/, Retrieved Fri, 29 Mar 2024 09:48:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62900, Retrieved Fri, 29 Mar 2024 09:48:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact174
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [Exponential smoot...] [2009-12-03 16:44:51] [6c304092df7982e5e12293b2743450a3] [Current]
-    D        [Exponential Smoothing] [Exponential smoot...] [2009-12-04 16:17:53] [34d27ebe78dc2d31581e8710befe8733]
-   PD          [Exponential Smoothing] [Exponential smoot...] [2009-12-16 22:59:52] [34d27ebe78dc2d31581e8710befe8733]
-    D        [Exponential Smoothing] [Exponential Smoot...] [2009-12-04 19:32:46] [4f1a20f787b3465111b61213cdeef1a9]
-    D          [Exponential Smoothing] [Experimental smoo...] [2009-12-11 16:09:28] [4f1a20f787b3465111b61213cdeef1a9]
-   PD          [Exponential Smoothing] [Exponential Smoot...] [2009-12-11 16:49:18] [4f1a20f787b3465111b61213cdeef1a9]
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Dataseries X:
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.4
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62900&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62900&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62900&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62900&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]1[/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=62900&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62900&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
alpha1
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
139.39.4006281885072-0.100628188507207
148.78.672696165550660.0273038344493415
158.28.14617848814480.0538215118552028
168.38.254020752915980.0459792470840252
178.58.49868078676950.00131921323049866
188.68.64507808414717-0.045078084147173
198.58.43089317979460.0691068202054073
208.27.645072103548580.554927896451415
218.17.87765860278460.222341397215402
227.98.35547852570824-0.455478525708243
238.69.4390561812499-0.839056181249903
248.79.12829638060467-0.428296380604673
258.78.71244853084964-0.0124485308496372
268.58.113915337705840.386084662294159
278.47.959159232863620.440840767136384
288.58.455072529953570.0449274700464297
298.78.70319974235725-0.00319974235724807
308.78.84822534501423-0.148225345014229
318.68.528797957133770.0712020428662257
328.57.734897014275110.765102985724888
338.38.165516169550180.134483830449824
3488.56154363891267-0.561543638912672
358.29.5583892456576-1.35838924565759
368.18.70430345736025-0.604303457360253
378.18.11244853084964-0.0124485308496372
3887.555134509861030.444865490138973
397.97.491611094660660.408388905339338
407.97.95244308735959-0.0524430873595847
4188.089642875594-0.0896428755940075
4288.13720993197953-0.137209931979534
437.97.84346451575950.0565354842405066
4487.106122639189420.893877360810585
457.77.685753558274210.0142464417257875
467.27.94334829929938-0.743348299299385
477.58.60372473039606-1.10372473039606
487.37.96231584168252-0.662315841682517
4977.31244853084964-0.312448530849637
5076.530702992145530.469297007854468
5176.556514818254750.443485181745245
527.27.047710090690410.152289909309589
537.37.3738265310369-0.073826531036894
547.17.42619451894484-0.326194518944841
556.86.96232151970685-0.162321519706847
566.46.11804862119760.281951378802395
576.16.15051320219113-0.0505132021911283
586.56.294827393663950.205172606336047
597.77.76839327954222-0.0683932795422235
607.98.17431230330473-0.274312303304727
617.57.91244853084964-0.412448530849637
626.96.99635368201621-0.0963536820162112
636.66.463005190614160.136994809385835
646.96.645606536615220.254393463384778
657.77.067048097655270.632951902344727
6687.832489040678950.167510959321048
6787.84346451575950.156535484240506
687.77.195947549915940.504052450084058
697.37.39789599150863-0.0978959915086346
707.47.53121807289053-0.131218072890525
718.18.84239085921145-0.742390859211447
728.38.59830522654915-0.298305226549147
738.28.31244853084964-0.112448530849639

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9.3 & 9.4006281885072 & -0.100628188507207 \tabularnewline
14 & 8.7 & 8.67269616555066 & 0.0273038344493415 \tabularnewline
15 & 8.2 & 8.1461784881448 & 0.0538215118552028 \tabularnewline
16 & 8.3 & 8.25402075291598 & 0.0459792470840252 \tabularnewline
17 & 8.5 & 8.4986807867695 & 0.00131921323049866 \tabularnewline
18 & 8.6 & 8.64507808414717 & -0.045078084147173 \tabularnewline
19 & 8.5 & 8.4308931797946 & 0.0691068202054073 \tabularnewline
20 & 8.2 & 7.64507210354858 & 0.554927896451415 \tabularnewline
21 & 8.1 & 7.8776586027846 & 0.222341397215402 \tabularnewline
22 & 7.9 & 8.35547852570824 & -0.455478525708243 \tabularnewline
23 & 8.6 & 9.4390561812499 & -0.839056181249903 \tabularnewline
24 & 8.7 & 9.12829638060467 & -0.428296380604673 \tabularnewline
25 & 8.7 & 8.71244853084964 & -0.0124485308496372 \tabularnewline
26 & 8.5 & 8.11391533770584 & 0.386084662294159 \tabularnewline
27 & 8.4 & 7.95915923286362 & 0.440840767136384 \tabularnewline
28 & 8.5 & 8.45507252995357 & 0.0449274700464297 \tabularnewline
29 & 8.7 & 8.70319974235725 & -0.00319974235724807 \tabularnewline
30 & 8.7 & 8.84822534501423 & -0.148225345014229 \tabularnewline
31 & 8.6 & 8.52879795713377 & 0.0712020428662257 \tabularnewline
32 & 8.5 & 7.73489701427511 & 0.765102985724888 \tabularnewline
33 & 8.3 & 8.16551616955018 & 0.134483830449824 \tabularnewline
34 & 8 & 8.56154363891267 & -0.561543638912672 \tabularnewline
35 & 8.2 & 9.5583892456576 & -1.35838924565759 \tabularnewline
36 & 8.1 & 8.70430345736025 & -0.604303457360253 \tabularnewline
37 & 8.1 & 8.11244853084964 & -0.0124485308496372 \tabularnewline
38 & 8 & 7.55513450986103 & 0.444865490138973 \tabularnewline
39 & 7.9 & 7.49161109466066 & 0.408388905339338 \tabularnewline
40 & 7.9 & 7.95244308735959 & -0.0524430873595847 \tabularnewline
41 & 8 & 8.089642875594 & -0.0896428755940075 \tabularnewline
42 & 8 & 8.13720993197953 & -0.137209931979534 \tabularnewline
43 & 7.9 & 7.8434645157595 & 0.0565354842405066 \tabularnewline
44 & 8 & 7.10612263918942 & 0.893877360810585 \tabularnewline
45 & 7.7 & 7.68575355827421 & 0.0142464417257875 \tabularnewline
46 & 7.2 & 7.94334829929938 & -0.743348299299385 \tabularnewline
47 & 7.5 & 8.60372473039606 & -1.10372473039606 \tabularnewline
48 & 7.3 & 7.96231584168252 & -0.662315841682517 \tabularnewline
49 & 7 & 7.31244853084964 & -0.312448530849637 \tabularnewline
50 & 7 & 6.53070299214553 & 0.469297007854468 \tabularnewline
51 & 7 & 6.55651481825475 & 0.443485181745245 \tabularnewline
52 & 7.2 & 7.04771009069041 & 0.152289909309589 \tabularnewline
53 & 7.3 & 7.3738265310369 & -0.073826531036894 \tabularnewline
54 & 7.1 & 7.42619451894484 & -0.326194518944841 \tabularnewline
55 & 6.8 & 6.96232151970685 & -0.162321519706847 \tabularnewline
56 & 6.4 & 6.1180486211976 & 0.281951378802395 \tabularnewline
57 & 6.1 & 6.15051320219113 & -0.0505132021911283 \tabularnewline
58 & 6.5 & 6.29482739366395 & 0.205172606336047 \tabularnewline
59 & 7.7 & 7.76839327954222 & -0.0683932795422235 \tabularnewline
60 & 7.9 & 8.17431230330473 & -0.274312303304727 \tabularnewline
61 & 7.5 & 7.91244853084964 & -0.412448530849637 \tabularnewline
62 & 6.9 & 6.99635368201621 & -0.0963536820162112 \tabularnewline
63 & 6.6 & 6.46300519061416 & 0.136994809385835 \tabularnewline
64 & 6.9 & 6.64560653661522 & 0.254393463384778 \tabularnewline
65 & 7.7 & 7.06704809765527 & 0.632951902344727 \tabularnewline
66 & 8 & 7.83248904067895 & 0.167510959321048 \tabularnewline
67 & 8 & 7.8434645157595 & 0.156535484240506 \tabularnewline
68 & 7.7 & 7.19594754991594 & 0.504052450084058 \tabularnewline
69 & 7.3 & 7.39789599150863 & -0.0978959915086346 \tabularnewline
70 & 7.4 & 7.53121807289053 & -0.131218072890525 \tabularnewline
71 & 8.1 & 8.84239085921145 & -0.742390859211447 \tabularnewline
72 & 8.3 & 8.59830522654915 & -0.298305226549147 \tabularnewline
73 & 8.2 & 8.31244853084964 & -0.112448530849639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62900&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]9.3[/C][C]9.4006281885072[/C][C]-0.100628188507207[/C][/ROW]
[ROW][C]14[/C][C]8.7[/C][C]8.67269616555066[/C][C]0.0273038344493415[/C][/ROW]
[ROW][C]15[/C][C]8.2[/C][C]8.1461784881448[/C][C]0.0538215118552028[/C][/ROW]
[ROW][C]16[/C][C]8.3[/C][C]8.25402075291598[/C][C]0.0459792470840252[/C][/ROW]
[ROW][C]17[/C][C]8.5[/C][C]8.4986807867695[/C][C]0.00131921323049866[/C][/ROW]
[ROW][C]18[/C][C]8.6[/C][C]8.64507808414717[/C][C]-0.045078084147173[/C][/ROW]
[ROW][C]19[/C][C]8.5[/C][C]8.4308931797946[/C][C]0.0691068202054073[/C][/ROW]
[ROW][C]20[/C][C]8.2[/C][C]7.64507210354858[/C][C]0.554927896451415[/C][/ROW]
[ROW][C]21[/C][C]8.1[/C][C]7.8776586027846[/C][C]0.222341397215402[/C][/ROW]
[ROW][C]22[/C][C]7.9[/C][C]8.35547852570824[/C][C]-0.455478525708243[/C][/ROW]
[ROW][C]23[/C][C]8.6[/C][C]9.4390561812499[/C][C]-0.839056181249903[/C][/ROW]
[ROW][C]24[/C][C]8.7[/C][C]9.12829638060467[/C][C]-0.428296380604673[/C][/ROW]
[ROW][C]25[/C][C]8.7[/C][C]8.71244853084964[/C][C]-0.0124485308496372[/C][/ROW]
[ROW][C]26[/C][C]8.5[/C][C]8.11391533770584[/C][C]0.386084662294159[/C][/ROW]
[ROW][C]27[/C][C]8.4[/C][C]7.95915923286362[/C][C]0.440840767136384[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]8.45507252995357[/C][C]0.0449274700464297[/C][/ROW]
[ROW][C]29[/C][C]8.7[/C][C]8.70319974235725[/C][C]-0.00319974235724807[/C][/ROW]
[ROW][C]30[/C][C]8.7[/C][C]8.84822534501423[/C][C]-0.148225345014229[/C][/ROW]
[ROW][C]31[/C][C]8.6[/C][C]8.52879795713377[/C][C]0.0712020428662257[/C][/ROW]
[ROW][C]32[/C][C]8.5[/C][C]7.73489701427511[/C][C]0.765102985724888[/C][/ROW]
[ROW][C]33[/C][C]8.3[/C][C]8.16551616955018[/C][C]0.134483830449824[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]8.56154363891267[/C][C]-0.561543638912672[/C][/ROW]
[ROW][C]35[/C][C]8.2[/C][C]9.5583892456576[/C][C]-1.35838924565759[/C][/ROW]
[ROW][C]36[/C][C]8.1[/C][C]8.70430345736025[/C][C]-0.604303457360253[/C][/ROW]
[ROW][C]37[/C][C]8.1[/C][C]8.11244853084964[/C][C]-0.0124485308496372[/C][/ROW]
[ROW][C]38[/C][C]8[/C][C]7.55513450986103[/C][C]0.444865490138973[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]7.49161109466066[/C][C]0.408388905339338[/C][/ROW]
[ROW][C]40[/C][C]7.9[/C][C]7.95244308735959[/C][C]-0.0524430873595847[/C][/ROW]
[ROW][C]41[/C][C]8[/C][C]8.089642875594[/C][C]-0.0896428755940075[/C][/ROW]
[ROW][C]42[/C][C]8[/C][C]8.13720993197953[/C][C]-0.137209931979534[/C][/ROW]
[ROW][C]43[/C][C]7.9[/C][C]7.8434645157595[/C][C]0.0565354842405066[/C][/ROW]
[ROW][C]44[/C][C]8[/C][C]7.10612263918942[/C][C]0.893877360810585[/C][/ROW]
[ROW][C]45[/C][C]7.7[/C][C]7.68575355827421[/C][C]0.0142464417257875[/C][/ROW]
[ROW][C]46[/C][C]7.2[/C][C]7.94334829929938[/C][C]-0.743348299299385[/C][/ROW]
[ROW][C]47[/C][C]7.5[/C][C]8.60372473039606[/C][C]-1.10372473039606[/C][/ROW]
[ROW][C]48[/C][C]7.3[/C][C]7.96231584168252[/C][C]-0.662315841682517[/C][/ROW]
[ROW][C]49[/C][C]7[/C][C]7.31244853084964[/C][C]-0.312448530849637[/C][/ROW]
[ROW][C]50[/C][C]7[/C][C]6.53070299214553[/C][C]0.469297007854468[/C][/ROW]
[ROW][C]51[/C][C]7[/C][C]6.55651481825475[/C][C]0.443485181745245[/C][/ROW]
[ROW][C]52[/C][C]7.2[/C][C]7.04771009069041[/C][C]0.152289909309589[/C][/ROW]
[ROW][C]53[/C][C]7.3[/C][C]7.3738265310369[/C][C]-0.073826531036894[/C][/ROW]
[ROW][C]54[/C][C]7.1[/C][C]7.42619451894484[/C][C]-0.326194518944841[/C][/ROW]
[ROW][C]55[/C][C]6.8[/C][C]6.96232151970685[/C][C]-0.162321519706847[/C][/ROW]
[ROW][C]56[/C][C]6.4[/C][C]6.1180486211976[/C][C]0.281951378802395[/C][/ROW]
[ROW][C]57[/C][C]6.1[/C][C]6.15051320219113[/C][C]-0.0505132021911283[/C][/ROW]
[ROW][C]58[/C][C]6.5[/C][C]6.29482739366395[/C][C]0.205172606336047[/C][/ROW]
[ROW][C]59[/C][C]7.7[/C][C]7.76839327954222[/C][C]-0.0683932795422235[/C][/ROW]
[ROW][C]60[/C][C]7.9[/C][C]8.17431230330473[/C][C]-0.274312303304727[/C][/ROW]
[ROW][C]61[/C][C]7.5[/C][C]7.91244853084964[/C][C]-0.412448530849637[/C][/ROW]
[ROW][C]62[/C][C]6.9[/C][C]6.99635368201621[/C][C]-0.0963536820162112[/C][/ROW]
[ROW][C]63[/C][C]6.6[/C][C]6.46300519061416[/C][C]0.136994809385835[/C][/ROW]
[ROW][C]64[/C][C]6.9[/C][C]6.64560653661522[/C][C]0.254393463384778[/C][/ROW]
[ROW][C]65[/C][C]7.7[/C][C]7.06704809765527[/C][C]0.632951902344727[/C][/ROW]
[ROW][C]66[/C][C]8[/C][C]7.83248904067895[/C][C]0.167510959321048[/C][/ROW]
[ROW][C]67[/C][C]8[/C][C]7.8434645157595[/C][C]0.156535484240506[/C][/ROW]
[ROW][C]68[/C][C]7.7[/C][C]7.19594754991594[/C][C]0.504052450084058[/C][/ROW]
[ROW][C]69[/C][C]7.3[/C][C]7.39789599150863[/C][C]-0.0978959915086346[/C][/ROW]
[ROW][C]70[/C][C]7.4[/C][C]7.53121807289053[/C][C]-0.131218072890525[/C][/ROW]
[ROW][C]71[/C][C]8.1[/C][C]8.84239085921145[/C][C]-0.742390859211447[/C][/ROW]
[ROW][C]72[/C][C]8.3[/C][C]8.59830522654915[/C][C]-0.298305226549147[/C][/ROW]
[ROW][C]73[/C][C]8.2[/C][C]8.31244853084964[/C][C]-0.112448530849639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62900&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62900&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
139.39.4006281885072-0.100628188507207
148.78.672696165550660.0273038344493415
158.28.14617848814480.0538215118552028
168.38.254020752915980.0459792470840252
178.58.49868078676950.00131921323049866
188.68.64507808414717-0.045078084147173
198.58.43089317979460.0691068202054073
208.27.645072103548580.554927896451415
218.17.87765860278460.222341397215402
227.98.35547852570824-0.455478525708243
238.69.4390561812499-0.839056181249903
248.79.12829638060467-0.428296380604673
258.78.71244853084964-0.0124485308496372
268.58.113915337705840.386084662294159
278.47.959159232863620.440840767136384
288.58.455072529953570.0449274700464297
298.78.70319974235725-0.00319974235724807
308.78.84822534501423-0.148225345014229
318.68.528797957133770.0712020428662257
328.57.734897014275110.765102985724888
338.38.165516169550180.134483830449824
3488.56154363891267-0.561543638912672
358.29.5583892456576-1.35838924565759
368.18.70430345736025-0.604303457360253
378.18.11244853084964-0.0124485308496372
3887.555134509861030.444865490138973
397.97.491611094660660.408388905339338
407.97.95244308735959-0.0524430873595847
4188.089642875594-0.0896428755940075
4288.13720993197953-0.137209931979534
437.97.84346451575950.0565354842405066
4487.106122639189420.893877360810585
457.77.685753558274210.0142464417257875
467.27.94334829929938-0.743348299299385
477.58.60372473039606-1.10372473039606
487.37.96231584168252-0.662315841682517
4977.31244853084964-0.312448530849637
5076.530702992145530.469297007854468
5176.556514818254750.443485181745245
527.27.047710090690410.152289909309589
537.37.3738265310369-0.073826531036894
547.17.42619451894484-0.326194518944841
556.86.96232151970685-0.162321519706847
566.46.11804862119760.281951378802395
576.16.15051320219113-0.0505132021911283
586.56.294827393663950.205172606336047
597.77.76839327954222-0.0683932795422235
607.98.17431230330473-0.274312303304727
617.57.91244853084964-0.412448530849637
626.96.99635368201621-0.0963536820162112
636.66.463005190614160.136994809385835
646.96.645606536615220.254393463384778
657.77.067048097655270.632951902344727
6687.832489040678950.167510959321048
6787.84346451575950.156535484240506
687.77.195947549915940.504052450084058
697.37.39789599150863-0.0978959915086346
707.47.53121807289053-0.131218072890525
718.18.84239085921145-0.742390859211447
728.38.59830522654915-0.298305226549147
738.28.31244853084964-0.112448530849639







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
747.648264647835166.816249874747068.48027942092327
757.1627046765716.023602294656438.30180705848557
767.211270412475055.795824870737158.62671595421294
777.385351595979095.715832462154519.05487072980367
787.512889233613765.623985752833569.40179271439396
797.366559804533865.33868949313749.39443011593032
806.626960459832534.624404605836738.62951631382834
816.368287487922434.27438639406088.46218858178405
826.571250851514284.258974352489028.88352735053955
837.85341910407084.971398547669710.7354396604719
848.336933839346025.1707679575419611.5030997211501
858.34938237019565-76.194320788434592.8930855288258

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 7.64826464783516 & 6.81624987474706 & 8.48027942092327 \tabularnewline
75 & 7.162704676571 & 6.02360229465643 & 8.30180705848557 \tabularnewline
76 & 7.21127041247505 & 5.79582487073715 & 8.62671595421294 \tabularnewline
77 & 7.38535159597909 & 5.71583246215451 & 9.05487072980367 \tabularnewline
78 & 7.51288923361376 & 5.62398575283356 & 9.40179271439396 \tabularnewline
79 & 7.36655980453386 & 5.3386894931374 & 9.39443011593032 \tabularnewline
80 & 6.62696045983253 & 4.62440460583673 & 8.62951631382834 \tabularnewline
81 & 6.36828748792243 & 4.2743863940608 & 8.46218858178405 \tabularnewline
82 & 6.57125085151428 & 4.25897435248902 & 8.88352735053955 \tabularnewline
83 & 7.8534191040708 & 4.9713985476697 & 10.7354396604719 \tabularnewline
84 & 8.33693383934602 & 5.17076795754196 & 11.5030997211501 \tabularnewline
85 & 8.34938237019565 & -76.1943207884345 & 92.8930855288258 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62900&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]74[/C][C]7.64826464783516[/C][C]6.81624987474706[/C][C]8.48027942092327[/C][/ROW]
[ROW][C]75[/C][C]7.162704676571[/C][C]6.02360229465643[/C][C]8.30180705848557[/C][/ROW]
[ROW][C]76[/C][C]7.21127041247505[/C][C]5.79582487073715[/C][C]8.62671595421294[/C][/ROW]
[ROW][C]77[/C][C]7.38535159597909[/C][C]5.71583246215451[/C][C]9.05487072980367[/C][/ROW]
[ROW][C]78[/C][C]7.51288923361376[/C][C]5.62398575283356[/C][C]9.40179271439396[/C][/ROW]
[ROW][C]79[/C][C]7.36655980453386[/C][C]5.3386894931374[/C][C]9.39443011593032[/C][/ROW]
[ROW][C]80[/C][C]6.62696045983253[/C][C]4.62440460583673[/C][C]8.62951631382834[/C][/ROW]
[ROW][C]81[/C][C]6.36828748792243[/C][C]4.2743863940608[/C][C]8.46218858178405[/C][/ROW]
[ROW][C]82[/C][C]6.57125085151428[/C][C]4.25897435248902[/C][C]8.88352735053955[/C][/ROW]
[ROW][C]83[/C][C]7.8534191040708[/C][C]4.9713985476697[/C][C]10.7354396604719[/C][/ROW]
[ROW][C]84[/C][C]8.33693383934602[/C][C]5.17076795754196[/C][C]11.5030997211501[/C][/ROW]
[ROW][C]85[/C][C]8.34938237019565[/C][C]-76.1943207884345[/C][C]92.8930855288258[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62900&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62900&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
747.648264647835166.816249874747068.48027942092327
757.1627046765716.023602294656438.30180705848557
767.211270412475055.795824870737158.62671595421294
777.385351595979095.715832462154519.05487072980367
787.512889233613765.623985752833569.40179271439396
797.366559804533865.33868949313749.39443011593032
806.626960459832534.624404605836738.62951631382834
816.368287487922434.27438639406088.46218858178405
826.571250851514284.258974352489028.88352735053955
837.85341910407084.971398547669710.7354396604719
848.336933839346025.1707679575419611.5030997211501
858.34938237019565-76.194320788434592.8930855288258



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')