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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 19 Dec 2011 14:37:17 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/19/t1324323456wctot5d6eiamxce.htm/, Retrieved Wed, 15 May 2024 18:16:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157645, Retrieved Wed, 15 May 2024 18:16:09 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Exponential Smoothing] [] [2011-12-19 19:18:06] [2f0f353a58a70fd7baf0f5141860d820]
- R  D    [Exponential Smoothing] [] [2011-12-19 19:37:17] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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Histogram

Boxplots

3,32
3,32
3,32
3,32
3,32
3,32
3,32
3,33
3,41
3,42
3,42
3,42
3,43
3,43
3,43
3,43
3,43
3,43
3,43
3,43
3,5
3,52
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,58
3,58
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,61
3,71
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,98
3,98
3,98
3,98

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157645&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157645&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157645&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0
gamma	0.112439952533876

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.112439952533876 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157645&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]0.112439952533876[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157645&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157645&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
Parameter	Value
alpha	1
beta	0
gamma	0.112439952533876

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	3.43	3.37463786464421	0.0553621353557854
14	3.43	3.43007629875113	-7.62987511286894e-05
15	3.43	3.43090955720378	-0.000909557203775613
16	3.43	3.43090746246597	-0.000907462465972397
17	3.43	3.43007575448486	-7.57544848606351e-05
18	3.43	3.42966195168748	0.000338048312519046
19	3.43	3.42512550830276	0.00487449169724075
20	3.43	3.43969415279489	-0.0096941527948875
21	3.5	3.51178041783486	-0.0117804178348568
22	3.52	3.50967549050142	0.0103245094985791
23	3.53	3.51938685879749	0.0106131412025099
24	3.53	3.52936157897211	0.000638421027891578
25	3.53	3.53968306940357	-0.00968306940356811
26	3.53	3.52982057541942	0.000179424580580623
27	3.53	3.53067872255428	-0.000678722554280142
28	3.53	3.53067715943567	-0.00067715943566915
29	3.53	3.5298218553191	0.000178144680899717
30	3.53	3.52939666771304	0.000603332286955638
31	3.53	3.52472897935101	0.00527102064899099
32	3.53	3.5397222940693	-0.00972229406930314
33	3.58	3.61390479322839	-0.0339047932283911
34	3.58	3.58969284398665	-0.00969284398664527
35	3.59	3.579224835967	0.0107751640329998
36	3.59	3.58919999248661	0.000800007513385381
37	3.59	3.59969688430953	-0.00969688430953042
38	3.59	3.58966714142039	0.000332858579606743
39	3.59	3.59054022176458	-0.000540221764582238
40	3.59	3.59053897761749	-0.000538977617487557
41	3.59	3.58966951581964	0.000330484180355306
42	3.59	3.58923749732838	0.000762502671617149
43	3.59	3.58449106197996	0.00550893802004149
44	3.61	3.59973917883395	0.0102608211660473
45	3.71	3.69560429354322	0.0143957064567806
46	3.83	3.71972104340014	0.110278956599865
47	3.83	3.82854974083996	0.00145025916004071
48	3.83	3.82855364654464	0.00144635345536104
49	3.83	3.83975214393338	-0.00975214393337964
50	3.83	3.82905340542429	0.000946594575709891
51	3.83	3.82998621860579	1.37813942076015e-05
52	3.83	3.82998625034476	1.37496552397032e-05
53	3.83	3.82906015782182	0.000939842178178996
54	3.83	3.82860081578974	0.00139918421026408
55	3.83	3.82353939249576	0.0064606075042426
56	3.83	3.83980671789255	-0.0098067178925505
57	3.92	3.920277919409	-0.00027791940899613
58	3.92	3.92976659629885	-0.00976659629884935
59	3.92	3.91830670659422	0.00169329340577518
60	3.92	3.9183112668164	0.00168873318360241
61	3.92	3.92977286629232	-0.00977286629232355
62	3.92	3.91882325442575	0.00117674557424863
63	3.92	3.91977846742125	0.000221532578753791
64	3.92	3.91977897761749	0.000221022382512093
65	3.92	3.91883164857264	0.0011683514273626
66	3.92	3.91836206021274	0.00163793978725657
67	3.92	3.91318251643918	0.00681748356081879
68	3.92	3.92983204503952	-0.00983204503952484
69	3.98	4.01218985726318	-0.032189857263178
70	3.98	3.98977961141277	-0.00977961141276795
71	3.98	3.97814468376373	0.00185531623626511
72	3.98	3.9781496803309	0.00185031966909621

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3.43 & 3.37463786464421 & 0.0553621353557854 \tabularnewline
14 & 3.43 & 3.43007629875113 & -7.62987511286894e-05 \tabularnewline
15 & 3.43 & 3.43090955720378 & -0.000909557203775613 \tabularnewline
16 & 3.43 & 3.43090746246597 & -0.000907462465972397 \tabularnewline
17 & 3.43 & 3.43007575448486 & -7.57544848606351e-05 \tabularnewline
18 & 3.43 & 3.42966195168748 & 0.000338048312519046 \tabularnewline
19 & 3.43 & 3.42512550830276 & 0.00487449169724075 \tabularnewline
20 & 3.43 & 3.43969415279489 & -0.0096941527948875 \tabularnewline
21 & 3.5 & 3.51178041783486 & -0.0117804178348568 \tabularnewline
22 & 3.52 & 3.50967549050142 & 0.0103245094985791 \tabularnewline
23 & 3.53 & 3.51938685879749 & 0.0106131412025099 \tabularnewline
24 & 3.53 & 3.52936157897211 & 0.000638421027891578 \tabularnewline
25 & 3.53 & 3.53968306940357 & -0.00968306940356811 \tabularnewline
26 & 3.53 & 3.52982057541942 & 0.000179424580580623 \tabularnewline
27 & 3.53 & 3.53067872255428 & -0.000678722554280142 \tabularnewline
28 & 3.53 & 3.53067715943567 & -0.00067715943566915 \tabularnewline
29 & 3.53 & 3.5298218553191 & 0.000178144680899717 \tabularnewline
30 & 3.53 & 3.52939666771304 & 0.000603332286955638 \tabularnewline
31 & 3.53 & 3.52472897935101 & 0.00527102064899099 \tabularnewline
32 & 3.53 & 3.5397222940693 & -0.00972229406930314 \tabularnewline
33 & 3.58 & 3.61390479322839 & -0.0339047932283911 \tabularnewline
34 & 3.58 & 3.58969284398665 & -0.00969284398664527 \tabularnewline
35 & 3.59 & 3.579224835967 & 0.0107751640329998 \tabularnewline
36 & 3.59 & 3.58919999248661 & 0.000800007513385381 \tabularnewline
37 & 3.59 & 3.59969688430953 & -0.00969688430953042 \tabularnewline
38 & 3.59 & 3.58966714142039 & 0.000332858579606743 \tabularnewline
39 & 3.59 & 3.59054022176458 & -0.000540221764582238 \tabularnewline
40 & 3.59 & 3.59053897761749 & -0.000538977617487557 \tabularnewline
41 & 3.59 & 3.58966951581964 & 0.000330484180355306 \tabularnewline
42 & 3.59 & 3.58923749732838 & 0.000762502671617149 \tabularnewline
43 & 3.59 & 3.58449106197996 & 0.00550893802004149 \tabularnewline
44 & 3.61 & 3.59973917883395 & 0.0102608211660473 \tabularnewline
45 & 3.71 & 3.69560429354322 & 0.0143957064567806 \tabularnewline
46 & 3.83 & 3.71972104340014 & 0.110278956599865 \tabularnewline
47 & 3.83 & 3.82854974083996 & 0.00145025916004071 \tabularnewline
48 & 3.83 & 3.82855364654464 & 0.00144635345536104 \tabularnewline
49 & 3.83 & 3.83975214393338 & -0.00975214393337964 \tabularnewline
50 & 3.83 & 3.82905340542429 & 0.000946594575709891 \tabularnewline
51 & 3.83 & 3.82998621860579 & 1.37813942076015e-05 \tabularnewline
52 & 3.83 & 3.82998625034476 & 1.37496552397032e-05 \tabularnewline
53 & 3.83 & 3.82906015782182 & 0.000939842178178996 \tabularnewline
54 & 3.83 & 3.82860081578974 & 0.00139918421026408 \tabularnewline
55 & 3.83 & 3.82353939249576 & 0.0064606075042426 \tabularnewline
56 & 3.83 & 3.83980671789255 & -0.0098067178925505 \tabularnewline
57 & 3.92 & 3.920277919409 & -0.00027791940899613 \tabularnewline
58 & 3.92 & 3.92976659629885 & -0.00976659629884935 \tabularnewline
59 & 3.92 & 3.91830670659422 & 0.00169329340577518 \tabularnewline
60 & 3.92 & 3.9183112668164 & 0.00168873318360241 \tabularnewline
61 & 3.92 & 3.92977286629232 & -0.00977286629232355 \tabularnewline
62 & 3.92 & 3.91882325442575 & 0.00117674557424863 \tabularnewline
63 & 3.92 & 3.91977846742125 & 0.000221532578753791 \tabularnewline
64 & 3.92 & 3.91977897761749 & 0.000221022382512093 \tabularnewline
65 & 3.92 & 3.91883164857264 & 0.0011683514273626 \tabularnewline
66 & 3.92 & 3.91836206021274 & 0.00163793978725657 \tabularnewline
67 & 3.92 & 3.91318251643918 & 0.00681748356081879 \tabularnewline
68 & 3.92 & 3.92983204503952 & -0.00983204503952484 \tabularnewline
69 & 3.98 & 4.01218985726318 & -0.032189857263178 \tabularnewline
70 & 3.98 & 3.98977961141277 & -0.00977961141276795 \tabularnewline
71 & 3.98 & 3.97814468376373 & 0.00185531623626511 \tabularnewline
72 & 3.98 & 3.9781496803309 & 0.00185031966909621 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157645&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]3.43[/C][C]3.37463786464421[/C][C]0.0553621353557854[/C][/ROW]
[ROW][C]14[/C][C]3.43[/C][C]3.43007629875113[/C][C]-7.62987511286894e-05[/C][/ROW]
[ROW][C]15[/C][C]3.43[/C][C]3.43090955720378[/C][C]-0.000909557203775613[/C][/ROW]
[ROW][C]16[/C][C]3.43[/C][C]3.43090746246597[/C][C]-0.000907462465972397[/C][/ROW]
[ROW][C]17[/C][C]3.43[/C][C]3.43007575448486[/C][C]-7.57544848606351e-05[/C][/ROW]
[ROW][C]18[/C][C]3.43[/C][C]3.42966195168748[/C][C]0.000338048312519046[/C][/ROW]
[ROW][C]19[/C][C]3.43[/C][C]3.42512550830276[/C][C]0.00487449169724075[/C][/ROW]
[ROW][C]20[/C][C]3.43[/C][C]3.43969415279489[/C][C]-0.0096941527948875[/C][/ROW]
[ROW][C]21[/C][C]3.5[/C][C]3.51178041783486[/C][C]-0.0117804178348568[/C][/ROW]
[ROW][C]22[/C][C]3.52[/C][C]3.50967549050142[/C][C]0.0103245094985791[/C][/ROW]
[ROW][C]23[/C][C]3.53[/C][C]3.51938685879749[/C][C]0.0106131412025099[/C][/ROW]
[ROW][C]24[/C][C]3.53[/C][C]3.52936157897211[/C][C]0.000638421027891578[/C][/ROW]
[ROW][C]25[/C][C]3.53[/C][C]3.53968306940357[/C][C]-0.00968306940356811[/C][/ROW]
[ROW][C]26[/C][C]3.53[/C][C]3.52982057541942[/C][C]0.000179424580580623[/C][/ROW]
[ROW][C]27[/C][C]3.53[/C][C]3.53067872255428[/C][C]-0.000678722554280142[/C][/ROW]
[ROW][C]28[/C][C]3.53[/C][C]3.53067715943567[/C][C]-0.00067715943566915[/C][/ROW]
[ROW][C]29[/C][C]3.53[/C][C]3.5298218553191[/C][C]0.000178144680899717[/C][/ROW]
[ROW][C]30[/C][C]3.53[/C][C]3.52939666771304[/C][C]0.000603332286955638[/C][/ROW]
[ROW][C]31[/C][C]3.53[/C][C]3.52472897935101[/C][C]0.00527102064899099[/C][/ROW]
[ROW][C]32[/C][C]3.53[/C][C]3.5397222940693[/C][C]-0.00972229406930314[/C][/ROW]
[ROW][C]33[/C][C]3.58[/C][C]3.61390479322839[/C][C]-0.0339047932283911[/C][/ROW]
[ROW][C]34[/C][C]3.58[/C][C]3.58969284398665[/C][C]-0.00969284398664527[/C][/ROW]
[ROW][C]35[/C][C]3.59[/C][C]3.579224835967[/C][C]0.0107751640329998[/C][/ROW]
[ROW][C]36[/C][C]3.59[/C][C]3.58919999248661[/C][C]0.000800007513385381[/C][/ROW]
[ROW][C]37[/C][C]3.59[/C][C]3.59969688430953[/C][C]-0.00969688430953042[/C][/ROW]
[ROW][C]38[/C][C]3.59[/C][C]3.58966714142039[/C][C]0.000332858579606743[/C][/ROW]
[ROW][C]39[/C][C]3.59[/C][C]3.59054022176458[/C][C]-0.000540221764582238[/C][/ROW]
[ROW][C]40[/C][C]3.59[/C][C]3.59053897761749[/C][C]-0.000538977617487557[/C][/ROW]
[ROW][C]41[/C][C]3.59[/C][C]3.58966951581964[/C][C]0.000330484180355306[/C][/ROW]
[ROW][C]42[/C][C]3.59[/C][C]3.58923749732838[/C][C]0.000762502671617149[/C][/ROW]
[ROW][C]43[/C][C]3.59[/C][C]3.58449106197996[/C][C]0.00550893802004149[/C][/ROW]
[ROW][C]44[/C][C]3.61[/C][C]3.59973917883395[/C][C]0.0102608211660473[/C][/ROW]
[ROW][C]45[/C][C]3.71[/C][C]3.69560429354322[/C][C]0.0143957064567806[/C][/ROW]
[ROW][C]46[/C][C]3.83[/C][C]3.71972104340014[/C][C]0.110278956599865[/C][/ROW]
[ROW][C]47[/C][C]3.83[/C][C]3.82854974083996[/C][C]0.00145025916004071[/C][/ROW]
[ROW][C]48[/C][C]3.83[/C][C]3.82855364654464[/C][C]0.00144635345536104[/C][/ROW]
[ROW][C]49[/C][C]3.83[/C][C]3.83975214393338[/C][C]-0.00975214393337964[/C][/ROW]
[ROW][C]50[/C][C]3.83[/C][C]3.82905340542429[/C][C]0.000946594575709891[/C][/ROW]
[ROW][C]51[/C][C]3.83[/C][C]3.82998621860579[/C][C]1.37813942076015e-05[/C][/ROW]
[ROW][C]52[/C][C]3.83[/C][C]3.82998625034476[/C][C]1.37496552397032e-05[/C][/ROW]
[ROW][C]53[/C][C]3.83[/C][C]3.82906015782182[/C][C]0.000939842178178996[/C][/ROW]
[ROW][C]54[/C][C]3.83[/C][C]3.82860081578974[/C][C]0.00139918421026408[/C][/ROW]
[ROW][C]55[/C][C]3.83[/C][C]3.82353939249576[/C][C]0.0064606075042426[/C][/ROW]
[ROW][C]56[/C][C]3.83[/C][C]3.83980671789255[/C][C]-0.0098067178925505[/C][/ROW]
[ROW][C]57[/C][C]3.92[/C][C]3.920277919409[/C][C]-0.00027791940899613[/C][/ROW]
[ROW][C]58[/C][C]3.92[/C][C]3.92976659629885[/C][C]-0.00976659629884935[/C][/ROW]
[ROW][C]59[/C][C]3.92[/C][C]3.91830670659422[/C][C]0.00169329340577518[/C][/ROW]
[ROW][C]60[/C][C]3.92[/C][C]3.9183112668164[/C][C]0.00168873318360241[/C][/ROW]
[ROW][C]61[/C][C]3.92[/C][C]3.92977286629232[/C][C]-0.00977286629232355[/C][/ROW]
[ROW][C]62[/C][C]3.92[/C][C]3.91882325442575[/C][C]0.00117674557424863[/C][/ROW]
[ROW][C]63[/C][C]3.92[/C][C]3.91977846742125[/C][C]0.000221532578753791[/C][/ROW]
[ROW][C]64[/C][C]3.92[/C][C]3.91977897761749[/C][C]0.000221022382512093[/C][/ROW]
[ROW][C]65[/C][C]3.92[/C][C]3.91883164857264[/C][C]0.0011683514273626[/C][/ROW]
[ROW][C]66[/C][C]3.92[/C][C]3.91836206021274[/C][C]0.00163793978725657[/C][/ROW]
[ROW][C]67[/C][C]3.92[/C][C]3.91318251643918[/C][C]0.00681748356081879[/C][/ROW]
[ROW][C]68[/C][C]3.92[/C][C]3.92983204503952[/C][C]-0.00983204503952484[/C][/ROW]
[ROW][C]69[/C][C]3.98[/C][C]4.01218985726318[/C][C]-0.032189857263178[/C][/ROW]
[ROW][C]70[/C][C]3.98[/C][C]3.98977961141277[/C][C]-0.00977961141276795[/C][/ROW]
[ROW][C]71[/C][C]3.98[/C][C]3.97814468376373[/C][C]0.00185531623626511[/C][/ROW]
[ROW][C]72[/C][C]3.98[/C][C]3.9781496803309[/C][C]0.00185031966909621[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157645&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157645&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
t	Observed	Fitted	Residuals
13	3.43	3.37463786464421	0.0553621353557854
14	3.43	3.43007629875113	-7.62987511286894e-05
15	3.43	3.43090955720378	-0.000909557203775613
16	3.43	3.43090746246597	-0.000907462465972397
17	3.43	3.43007575448486	-7.57544848606351e-05
18	3.43	3.42966195168748	0.000338048312519046
19	3.43	3.42512550830276	0.00487449169724075
20	3.43	3.43969415279489	-0.0096941527948875
21	3.5	3.51178041783486	-0.0117804178348568
22	3.52	3.50967549050142	0.0103245094985791
23	3.53	3.51938685879749	0.0106131412025099
24	3.53	3.52936157897211	0.000638421027891578
25	3.53	3.53968306940357	-0.00968306940356811
26	3.53	3.52982057541942	0.000179424580580623
27	3.53	3.53067872255428	-0.000678722554280142
28	3.53	3.53067715943567	-0.00067715943566915
29	3.53	3.5298218553191	0.000178144680899717
30	3.53	3.52939666771304	0.000603332286955638
31	3.53	3.52472897935101	0.00527102064899099
32	3.53	3.5397222940693	-0.00972229406930314
33	3.58	3.61390479322839	-0.0339047932283911
34	3.58	3.58969284398665	-0.00969284398664527
35	3.59	3.579224835967	0.0107751640329998
36	3.59	3.58919999248661	0.000800007513385381
37	3.59	3.59969688430953	-0.00969688430953042
38	3.59	3.58966714142039	0.000332858579606743
39	3.59	3.59054022176458	-0.000540221764582238
40	3.59	3.59053897761749	-0.000538977617487557
41	3.59	3.58966951581964	0.000330484180355306
42	3.59	3.58923749732838	0.000762502671617149
43	3.59	3.58449106197996	0.00550893802004149
44	3.61	3.59973917883395	0.0102608211660473
45	3.71	3.69560429354322	0.0143957064567806
46	3.83	3.71972104340014	0.110278956599865
47	3.83	3.82854974083996	0.00145025916004071
48	3.83	3.82855364654464	0.00144635345536104
49	3.83	3.83975214393338	-0.00975214393337964
50	3.83	3.82905340542429	0.000946594575709891
51	3.83	3.82998621860579	1.37813942076015e-05
52	3.83	3.82998625034476	1.37496552397032e-05
53	3.83	3.82906015782182	0.000939842178178996
54	3.83	3.82860081578974	0.00139918421026408
55	3.83	3.82353939249576	0.0064606075042426
56	3.83	3.83980671789255	-0.0098067178925505
57	3.92	3.920277919409	-0.00027791940899613
58	3.92	3.92976659629885	-0.00976659629884935
59	3.92	3.91830670659422	0.00169329340577518
60	3.92	3.9183112668164	0.00168873318360241
61	3.92	3.92977286629232	-0.00977286629232355
62	3.92	3.91882325442575	0.00117674557424863
63	3.92	3.91977846742125	0.000221532578753791
64	3.92	3.91977897761749	0.000221022382512093
65	3.92	3.91883164857264	0.0011683514273626
66	3.92	3.91836206021274	0.00163793978725657
67	3.92	3.91318251643918	0.00681748356081879
68	3.92	3.92983204503952	-0.00983204503952484
69	3.98	4.01218985726318	-0.032189857263178
70	3.98	3.98977961141277	-0.00977961141276795
71	3.98	3.97814468376373	0.00185531623626511
72	3.98	3.9781496803309	0.00185031966909621

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	3.98978668119829	3.95431015883787	4.0252632035587
74	3.98843147479779	3.93832420462682	4.03853874496875
75	3.98805197866404	3.92675153631481	4.04935242101326
76	3.98767423051248	3.9169703451581	4.05837811586687
77	3.98633405477841	3.90738932581878	4.06527878373804
78	3.98452014137424	3.89816140527339	4.07087887747509
79	3.97744681677316	3.88440173478314	4.07049189876318
80	3.98729502807903	3.88769159337345	4.08689846278462
81	4.0809144843598	3.97318604318374	4.18864292553585
82	4.09071598599773	3.97727421201691	4.20415775997855
83	4.08856169447094	3.96999436770667	4.2071290212352
84	4.08641900642403	0.0483421410524381	8.12449587179561

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 3.98978668119829 & 3.95431015883787 & 4.0252632035587 \tabularnewline
74 & 3.98843147479779 & 3.93832420462682 & 4.03853874496875 \tabularnewline
75 & 3.98805197866404 & 3.92675153631481 & 4.04935242101326 \tabularnewline
76 & 3.98767423051248 & 3.9169703451581 & 4.05837811586687 \tabularnewline
77 & 3.98633405477841 & 3.90738932581878 & 4.06527878373804 \tabularnewline
78 & 3.98452014137424 & 3.89816140527339 & 4.07087887747509 \tabularnewline
79 & 3.97744681677316 & 3.88440173478314 & 4.07049189876318 \tabularnewline
80 & 3.98729502807903 & 3.88769159337345 & 4.08689846278462 \tabularnewline
81 & 4.0809144843598 & 3.97318604318374 & 4.18864292553585 \tabularnewline
82 & 4.09071598599773 & 3.97727421201691 & 4.20415775997855 \tabularnewline
83 & 4.08856169447094 & 3.96999436770667 & 4.2071290212352 \tabularnewline
84 & 4.08641900642403 & 0.0483421410524381 & 8.12449587179561 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157645&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]3.98978668119829[/C][C]3.95431015883787[/C][C]4.0252632035587[/C][/ROW]
[ROW][C]74[/C][C]3.98843147479779[/C][C]3.93832420462682[/C][C]4.03853874496875[/C][/ROW]
[ROW][C]75[/C][C]3.98805197866404[/C][C]3.92675153631481[/C][C]4.04935242101326[/C][/ROW]
[ROW][C]76[/C][C]3.98767423051248[/C][C]3.9169703451581[/C][C]4.05837811586687[/C][/ROW]
[ROW][C]77[/C][C]3.98633405477841[/C][C]3.90738932581878[/C][C]4.06527878373804[/C][/ROW]
[ROW][C]78[/C][C]3.98452014137424[/C][C]3.89816140527339[/C][C]4.07087887747509[/C][/ROW]
[ROW][C]79[/C][C]3.97744681677316[/C][C]3.88440173478314[/C][C]4.07049189876318[/C][/ROW]
[ROW][C]80[/C][C]3.98729502807903[/C][C]3.88769159337345[/C][C]4.08689846278462[/C][/ROW]
[ROW][C]81[/C][C]4.0809144843598[/C][C]3.97318604318374[/C][C]4.18864292553585[/C][/ROW]
[ROW][C]82[/C][C]4.09071598599773[/C][C]3.97727421201691[/C][C]4.20415775997855[/C][/ROW]
[ROW][C]83[/C][C]4.08856169447094[/C][C]3.96999436770667[/C][C]4.2071290212352[/C][/ROW]
[ROW][C]84[/C][C]4.08641900642403[/C][C]0.0483421410524381[/C][C]8.12449587179561[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157645&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157645&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
t	Forecast	95% Lower Bound	95% Upper Bound
73	3.98978668119829	3.95431015883787	4.0252632035587
74	3.98843147479779	3.93832420462682	4.03853874496875
75	3.98805197866404	3.92675153631481	4.04935242101326
76	3.98767423051248	3.9169703451581	4.05837811586687
77	3.98633405477841	3.90738932581878	4.06527878373804
78	3.98452014137424	3.89816140527339	4.07087887747509
79	3.97744681677316	3.88440173478314	4.07049189876318
80	3.98729502807903	3.88769159337345	4.08689846278462
81	4.0809144843598	3.97318604318374	4.18864292553585
82	4.09071598599773	3.97727421201691	4.20415775997855
83	4.08856169447094	3.96999436770667	4.2071290212352
84	4.08641900642403	0.0483421410524381	8.12449587179561

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code