Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 08:39:13 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/19/t1305794203cmfmmwmmzvbhqfr.htm/, Retrieved Sun, 12 May 2024 02:18:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121966, Retrieved Sun, 12 May 2024 02:18:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact127
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [opdracht 10 axel ...] [2011-05-18 15:27:04] [6411650949db84072a7f54fa75041d5a]
-   P     [Exponential Smoothing] [opdracht 10 axel ...] [2011-05-19 08:39:13] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
8
8
8.2
8.5
8.7
8.7
8
8
8.3
8.5
8.7
8.6
8.3
7.9
7.9
8.1
8.3
8.1
7.4
7.3
7.7
8
8
7.7
6.9
6.6
6.9
7.5
7.9
7.7
6.5
6.1
6.4
6.8
7.1
7.3
7.2
7
7
7
7.3
7.5
7.2
7.7
8
7.9
8
8
7.9
7.9
8
8.1
8.1
8.2
8
8.3
8.5
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
7.9
8.1
8.2
8.5
8.6
8.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121966&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121966&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121966&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 time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.947401841274992
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.947401841274992 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121966&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]0.947401841274992[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121966&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121966&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
beta0.947401841274992
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
38.280.199999999999999
48.58.3894803682550.110519631745003
58.78.79418687086725-0.094186870867249
68.78.90495405598369-0.204954055983686
788.71078020596796-0.710780205967962
887.33738573009210.662614269907903
98.37.965147709457930.334852290542072
108.58.58238738607264-0.0823873860726376
118.78.70433342480959-0.00433342480958743
128.68.90022793016596-0.300227930165956
138.38.51579143632455-0.215791436324549
147.98.0113502322193-0.111350232219298
157.97.505856817188340.394143182811663
168.17.87926879431010.220731205689907
178.38.288389945007560.0116100549924418
188.18.4993893324847-0.399389332484704
197.47.9210071435031-0.521007143503104
207.36.727404016430840.57259598356916
217.77.169882505570930.530117494429073
2288.07211679588512-0.0721167958851172
2388.3037932106767-0.303793210676703
247.78.01597896351475-0.315978963514753
256.97.41661991167671-0.516619911676712
266.66.127173256114870.472826743885128
276.96.27513018387570.6248698161243
287.57.167132998229030.332867001770971
297.98.08249180860653-0.182491808606532
307.78.3095987331151-0.6095987331151
316.57.53206377092295-1.03206377092295
326.15.354284654037340.745715345962664
336.45.660776745869380.73922325413062
346.86.661118217946020.138881782053978
357.17.19269507398351-0.0926950739835126
367.37.40487559021441-0.104875590214411
377.27.50551626294048-0.305516262940476
3877.11606959289121-0.116069592891215
3976.806105046870040.193894953129961
4076.989801482479290.010198517520708
417.36.999463576756690.300536423243313
427.57.5841923375076-0.0841923375076021
437.27.70442836193165-0.504428361931654
447.76.926532003046280.773467996953723
4588.15931700752751-0.159317007527514
467.98.30837978124953-0.408379781249526
4787.821480024554250.178519975445753
4888.09061017799592-0.09061017799592
497.98.00476592852433-0.10476592852433
507.97.80551049493750.094489505062504
5187.895030026014880.104969973985124
528.18.094478772646970.00552122735302873
538.18.19970959360733-0.0997095936073276
548.28.105244541030960.0947554589690363
5588.29501603732908-0.295016037329084
568.37.815517300357860.484482699642142
578.58.5745171020647-0.0745171020647035
588.68.70391946236213-0.103919462362127
598.78.70546597237594-0.00546597237594071
608.78.80028750008261-0.100287500082615
618.58.70527493784748-0.205274937847479
628.48.310797083763170.0892029162368324
638.58.295308090853040.204691909146957
648.78.589233582472960.110766417527037
658.78.89417389038951-0.194173890389512
668.68.71021318910696-0.110213189106959
677.98.50579701081424-0.605797010814237
688.17.231863807329940.868136192670057
698.28.25433763474302-0.0543376347430158
708.58.302858059536950.197141940463046
718.68.78963069692417-0.189630696924169
728.58.70997422549595-0.20997422549595

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8.2 & 8 & 0.199999999999999 \tabularnewline
4 & 8.5 & 8.389480368255 & 0.110519631745003 \tabularnewline
5 & 8.7 & 8.79418687086725 & -0.094186870867249 \tabularnewline
6 & 8.7 & 8.90495405598369 & -0.204954055983686 \tabularnewline
7 & 8 & 8.71078020596796 & -0.710780205967962 \tabularnewline
8 & 8 & 7.3373857300921 & 0.662614269907903 \tabularnewline
9 & 8.3 & 7.96514770945793 & 0.334852290542072 \tabularnewline
10 & 8.5 & 8.58238738607264 & -0.0823873860726376 \tabularnewline
11 & 8.7 & 8.70433342480959 & -0.00433342480958743 \tabularnewline
12 & 8.6 & 8.90022793016596 & -0.300227930165956 \tabularnewline
13 & 8.3 & 8.51579143632455 & -0.215791436324549 \tabularnewline
14 & 7.9 & 8.0113502322193 & -0.111350232219298 \tabularnewline
15 & 7.9 & 7.50585681718834 & 0.394143182811663 \tabularnewline
16 & 8.1 & 7.8792687943101 & 0.220731205689907 \tabularnewline
17 & 8.3 & 8.28838994500756 & 0.0116100549924418 \tabularnewline
18 & 8.1 & 8.4993893324847 & -0.399389332484704 \tabularnewline
19 & 7.4 & 7.9210071435031 & -0.521007143503104 \tabularnewline
20 & 7.3 & 6.72740401643084 & 0.57259598356916 \tabularnewline
21 & 7.7 & 7.16988250557093 & 0.530117494429073 \tabularnewline
22 & 8 & 8.07211679588512 & -0.0721167958851172 \tabularnewline
23 & 8 & 8.3037932106767 & -0.303793210676703 \tabularnewline
24 & 7.7 & 8.01597896351475 & -0.315978963514753 \tabularnewline
25 & 6.9 & 7.41661991167671 & -0.516619911676712 \tabularnewline
26 & 6.6 & 6.12717325611487 & 0.472826743885128 \tabularnewline
27 & 6.9 & 6.2751301838757 & 0.6248698161243 \tabularnewline
28 & 7.5 & 7.16713299822903 & 0.332867001770971 \tabularnewline
29 & 7.9 & 8.08249180860653 & -0.182491808606532 \tabularnewline
30 & 7.7 & 8.3095987331151 & -0.6095987331151 \tabularnewline
31 & 6.5 & 7.53206377092295 & -1.03206377092295 \tabularnewline
32 & 6.1 & 5.35428465403734 & 0.745715345962664 \tabularnewline
33 & 6.4 & 5.66077674586938 & 0.73922325413062 \tabularnewline
34 & 6.8 & 6.66111821794602 & 0.138881782053978 \tabularnewline
35 & 7.1 & 7.19269507398351 & -0.0926950739835126 \tabularnewline
36 & 7.3 & 7.40487559021441 & -0.104875590214411 \tabularnewline
37 & 7.2 & 7.50551626294048 & -0.305516262940476 \tabularnewline
38 & 7 & 7.11606959289121 & -0.116069592891215 \tabularnewline
39 & 7 & 6.80610504687004 & 0.193894953129961 \tabularnewline
40 & 7 & 6.98980148247929 & 0.010198517520708 \tabularnewline
41 & 7.3 & 6.99946357675669 & 0.300536423243313 \tabularnewline
42 & 7.5 & 7.5841923375076 & -0.0841923375076021 \tabularnewline
43 & 7.2 & 7.70442836193165 & -0.504428361931654 \tabularnewline
44 & 7.7 & 6.92653200304628 & 0.773467996953723 \tabularnewline
45 & 8 & 8.15931700752751 & -0.159317007527514 \tabularnewline
46 & 7.9 & 8.30837978124953 & -0.408379781249526 \tabularnewline
47 & 8 & 7.82148002455425 & 0.178519975445753 \tabularnewline
48 & 8 & 8.09061017799592 & -0.09061017799592 \tabularnewline
49 & 7.9 & 8.00476592852433 & -0.10476592852433 \tabularnewline
50 & 7.9 & 7.8055104949375 & 0.094489505062504 \tabularnewline
51 & 8 & 7.89503002601488 & 0.104969973985124 \tabularnewline
52 & 8.1 & 8.09447877264697 & 0.00552122735302873 \tabularnewline
53 & 8.1 & 8.19970959360733 & -0.0997095936073276 \tabularnewline
54 & 8.2 & 8.10524454103096 & 0.0947554589690363 \tabularnewline
55 & 8 & 8.29501603732908 & -0.295016037329084 \tabularnewline
56 & 8.3 & 7.81551730035786 & 0.484482699642142 \tabularnewline
57 & 8.5 & 8.5745171020647 & -0.0745171020647035 \tabularnewline
58 & 8.6 & 8.70391946236213 & -0.103919462362127 \tabularnewline
59 & 8.7 & 8.70546597237594 & -0.00546597237594071 \tabularnewline
60 & 8.7 & 8.80028750008261 & -0.100287500082615 \tabularnewline
61 & 8.5 & 8.70527493784748 & -0.205274937847479 \tabularnewline
62 & 8.4 & 8.31079708376317 & 0.0892029162368324 \tabularnewline
63 & 8.5 & 8.29530809085304 & 0.204691909146957 \tabularnewline
64 & 8.7 & 8.58923358247296 & 0.110766417527037 \tabularnewline
65 & 8.7 & 8.89417389038951 & -0.194173890389512 \tabularnewline
66 & 8.6 & 8.71021318910696 & -0.110213189106959 \tabularnewline
67 & 7.9 & 8.50579701081424 & -0.605797010814237 \tabularnewline
68 & 8.1 & 7.23186380732994 & 0.868136192670057 \tabularnewline
69 & 8.2 & 8.25433763474302 & -0.0543376347430158 \tabularnewline
70 & 8.5 & 8.30285805953695 & 0.197141940463046 \tabularnewline
71 & 8.6 & 8.78963069692417 & -0.189630696924169 \tabularnewline
72 & 8.5 & 8.70997422549595 & -0.20997422549595 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121966&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]3[/C][C]8.2[/C][C]8[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]4[/C][C]8.5[/C][C]8.389480368255[/C][C]0.110519631745003[/C][/ROW]
[ROW][C]5[/C][C]8.7[/C][C]8.79418687086725[/C][C]-0.094186870867249[/C][/ROW]
[ROW][C]6[/C][C]8.7[/C][C]8.90495405598369[/C][C]-0.204954055983686[/C][/ROW]
[ROW][C]7[/C][C]8[/C][C]8.71078020596796[/C][C]-0.710780205967962[/C][/ROW]
[ROW][C]8[/C][C]8[/C][C]7.3373857300921[/C][C]0.662614269907903[/C][/ROW]
[ROW][C]9[/C][C]8.3[/C][C]7.96514770945793[/C][C]0.334852290542072[/C][/ROW]
[ROW][C]10[/C][C]8.5[/C][C]8.58238738607264[/C][C]-0.0823873860726376[/C][/ROW]
[ROW][C]11[/C][C]8.7[/C][C]8.70433342480959[/C][C]-0.00433342480958743[/C][/ROW]
[ROW][C]12[/C][C]8.6[/C][C]8.90022793016596[/C][C]-0.300227930165956[/C][/ROW]
[ROW][C]13[/C][C]8.3[/C][C]8.51579143632455[/C][C]-0.215791436324549[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]8.0113502322193[/C][C]-0.111350232219298[/C][/ROW]
[ROW][C]15[/C][C]7.9[/C][C]7.50585681718834[/C][C]0.394143182811663[/C][/ROW]
[ROW][C]16[/C][C]8.1[/C][C]7.8792687943101[/C][C]0.220731205689907[/C][/ROW]
[ROW][C]17[/C][C]8.3[/C][C]8.28838994500756[/C][C]0.0116100549924418[/C][/ROW]
[ROW][C]18[/C][C]8.1[/C][C]8.4993893324847[/C][C]-0.399389332484704[/C][/ROW]
[ROW][C]19[/C][C]7.4[/C][C]7.9210071435031[/C][C]-0.521007143503104[/C][/ROW]
[ROW][C]20[/C][C]7.3[/C][C]6.72740401643084[/C][C]0.57259598356916[/C][/ROW]
[ROW][C]21[/C][C]7.7[/C][C]7.16988250557093[/C][C]0.530117494429073[/C][/ROW]
[ROW][C]22[/C][C]8[/C][C]8.07211679588512[/C][C]-0.0721167958851172[/C][/ROW]
[ROW][C]23[/C][C]8[/C][C]8.3037932106767[/C][C]-0.303793210676703[/C][/ROW]
[ROW][C]24[/C][C]7.7[/C][C]8.01597896351475[/C][C]-0.315978963514753[/C][/ROW]
[ROW][C]25[/C][C]6.9[/C][C]7.41661991167671[/C][C]-0.516619911676712[/C][/ROW]
[ROW][C]26[/C][C]6.6[/C][C]6.12717325611487[/C][C]0.472826743885128[/C][/ROW]
[ROW][C]27[/C][C]6.9[/C][C]6.2751301838757[/C][C]0.6248698161243[/C][/ROW]
[ROW][C]28[/C][C]7.5[/C][C]7.16713299822903[/C][C]0.332867001770971[/C][/ROW]
[ROW][C]29[/C][C]7.9[/C][C]8.08249180860653[/C][C]-0.182491808606532[/C][/ROW]
[ROW][C]30[/C][C]7.7[/C][C]8.3095987331151[/C][C]-0.6095987331151[/C][/ROW]
[ROW][C]31[/C][C]6.5[/C][C]7.53206377092295[/C][C]-1.03206377092295[/C][/ROW]
[ROW][C]32[/C][C]6.1[/C][C]5.35428465403734[/C][C]0.745715345962664[/C][/ROW]
[ROW][C]33[/C][C]6.4[/C][C]5.66077674586938[/C][C]0.73922325413062[/C][/ROW]
[ROW][C]34[/C][C]6.8[/C][C]6.66111821794602[/C][C]0.138881782053978[/C][/ROW]
[ROW][C]35[/C][C]7.1[/C][C]7.19269507398351[/C][C]-0.0926950739835126[/C][/ROW]
[ROW][C]36[/C][C]7.3[/C][C]7.40487559021441[/C][C]-0.104875590214411[/C][/ROW]
[ROW][C]37[/C][C]7.2[/C][C]7.50551626294048[/C][C]-0.305516262940476[/C][/ROW]
[ROW][C]38[/C][C]7[/C][C]7.11606959289121[/C][C]-0.116069592891215[/C][/ROW]
[ROW][C]39[/C][C]7[/C][C]6.80610504687004[/C][C]0.193894953129961[/C][/ROW]
[ROW][C]40[/C][C]7[/C][C]6.98980148247929[/C][C]0.010198517520708[/C][/ROW]
[ROW][C]41[/C][C]7.3[/C][C]6.99946357675669[/C][C]0.300536423243313[/C][/ROW]
[ROW][C]42[/C][C]7.5[/C][C]7.5841923375076[/C][C]-0.0841923375076021[/C][/ROW]
[ROW][C]43[/C][C]7.2[/C][C]7.70442836193165[/C][C]-0.504428361931654[/C][/ROW]
[ROW][C]44[/C][C]7.7[/C][C]6.92653200304628[/C][C]0.773467996953723[/C][/ROW]
[ROW][C]45[/C][C]8[/C][C]8.15931700752751[/C][C]-0.159317007527514[/C][/ROW]
[ROW][C]46[/C][C]7.9[/C][C]8.30837978124953[/C][C]-0.408379781249526[/C][/ROW]
[ROW][C]47[/C][C]8[/C][C]7.82148002455425[/C][C]0.178519975445753[/C][/ROW]
[ROW][C]48[/C][C]8[/C][C]8.09061017799592[/C][C]-0.09061017799592[/C][/ROW]
[ROW][C]49[/C][C]7.9[/C][C]8.00476592852433[/C][C]-0.10476592852433[/C][/ROW]
[ROW][C]50[/C][C]7.9[/C][C]7.8055104949375[/C][C]0.094489505062504[/C][/ROW]
[ROW][C]51[/C][C]8[/C][C]7.89503002601488[/C][C]0.104969973985124[/C][/ROW]
[ROW][C]52[/C][C]8.1[/C][C]8.09447877264697[/C][C]0.00552122735302873[/C][/ROW]
[ROW][C]53[/C][C]8.1[/C][C]8.19970959360733[/C][C]-0.0997095936073276[/C][/ROW]
[ROW][C]54[/C][C]8.2[/C][C]8.10524454103096[/C][C]0.0947554589690363[/C][/ROW]
[ROW][C]55[/C][C]8[/C][C]8.29501603732908[/C][C]-0.295016037329084[/C][/ROW]
[ROW][C]56[/C][C]8.3[/C][C]7.81551730035786[/C][C]0.484482699642142[/C][/ROW]
[ROW][C]57[/C][C]8.5[/C][C]8.5745171020647[/C][C]-0.0745171020647035[/C][/ROW]
[ROW][C]58[/C][C]8.6[/C][C]8.70391946236213[/C][C]-0.103919462362127[/C][/ROW]
[ROW][C]59[/C][C]8.7[/C][C]8.70546597237594[/C][C]-0.00546597237594071[/C][/ROW]
[ROW][C]60[/C][C]8.7[/C][C]8.80028750008261[/C][C]-0.100287500082615[/C][/ROW]
[ROW][C]61[/C][C]8.5[/C][C]8.70527493784748[/C][C]-0.205274937847479[/C][/ROW]
[ROW][C]62[/C][C]8.4[/C][C]8.31079708376317[/C][C]0.0892029162368324[/C][/ROW]
[ROW][C]63[/C][C]8.5[/C][C]8.29530809085304[/C][C]0.204691909146957[/C][/ROW]
[ROW][C]64[/C][C]8.7[/C][C]8.58923358247296[/C][C]0.110766417527037[/C][/ROW]
[ROW][C]65[/C][C]8.7[/C][C]8.89417389038951[/C][C]-0.194173890389512[/C][/ROW]
[ROW][C]66[/C][C]8.6[/C][C]8.71021318910696[/C][C]-0.110213189106959[/C][/ROW]
[ROW][C]67[/C][C]7.9[/C][C]8.50579701081424[/C][C]-0.605797010814237[/C][/ROW]
[ROW][C]68[/C][C]8.1[/C][C]7.23186380732994[/C][C]0.868136192670057[/C][/ROW]
[ROW][C]69[/C][C]8.2[/C][C]8.25433763474302[/C][C]-0.0543376347430158[/C][/ROW]
[ROW][C]70[/C][C]8.5[/C][C]8.30285805953695[/C][C]0.197141940463046[/C][/ROW]
[ROW][C]71[/C][C]8.6[/C][C]8.78963069692417[/C][C]-0.189630696924169[/C][/ROW]
[ROW][C]72[/C][C]8.5[/C][C]8.70997422549595[/C][C]-0.20997422549595[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121966&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121966&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
38.280.199999999999999
48.58.3894803682550.110519631745003
58.78.79418687086725-0.094186870867249
68.78.90495405598369-0.204954055983686
788.71078020596796-0.710780205967962
887.33738573009210.662614269907903
98.37.965147709457930.334852290542072
108.58.58238738607264-0.0823873860726376
118.78.70433342480959-0.00433342480958743
128.68.90022793016596-0.300227930165956
138.38.51579143632455-0.215791436324549
147.98.0113502322193-0.111350232219298
157.97.505856817188340.394143182811663
168.17.87926879431010.220731205689907
178.38.288389945007560.0116100549924418
188.18.4993893324847-0.399389332484704
197.47.9210071435031-0.521007143503104
207.36.727404016430840.57259598356916
217.77.169882505570930.530117494429073
2288.07211679588512-0.0721167958851172
2388.3037932106767-0.303793210676703
247.78.01597896351475-0.315978963514753
256.97.41661991167671-0.516619911676712
266.66.127173256114870.472826743885128
276.96.27513018387570.6248698161243
287.57.167132998229030.332867001770971
297.98.08249180860653-0.182491808606532
307.78.3095987331151-0.6095987331151
316.57.53206377092295-1.03206377092295
326.15.354284654037340.745715345962664
336.45.660776745869380.73922325413062
346.86.661118217946020.138881782053978
357.17.19269507398351-0.0926950739835126
367.37.40487559021441-0.104875590214411
377.27.50551626294048-0.305516262940476
3877.11606959289121-0.116069592891215
3976.806105046870040.193894953129961
4076.989801482479290.010198517520708
417.36.999463576756690.300536423243313
427.57.5841923375076-0.0841923375076021
437.27.70442836193165-0.504428361931654
447.76.926532003046280.773467996953723
4588.15931700752751-0.159317007527514
467.98.30837978124953-0.408379781249526
4787.821480024554250.178519975445753
4888.09061017799592-0.09061017799592
497.98.00476592852433-0.10476592852433
507.97.80551049493750.094489505062504
5187.895030026014880.104969973985124
528.18.094478772646970.00552122735302873
538.18.19970959360733-0.0997095936073276
548.28.105244541030960.0947554589690363
5588.29501603732908-0.295016037329084
568.37.815517300357860.484482699642142
578.58.5745171020647-0.0745171020647035
588.68.70391946236213-0.103919462362127
598.78.70546597237594-0.00546597237594071
608.78.80028750008261-0.100287500082615
618.58.70527493784748-0.205274937847479
628.48.310797083763170.0892029162368324
638.58.295308090853040.204691909146957
648.78.589233582472960.110766417527037
658.78.89417389038951-0.194173890389512
668.68.71021318910696-0.110213189106959
677.98.50579701081424-0.605797010814237
688.17.231863807329940.868136192670057
698.28.25433763474302-0.0543376347430158
708.58.302858059536950.197141940463046
718.68.78963069692417-0.189630696924169
728.58.70997422549595-0.20997422549595







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
738.41104425764087.684502594726119.13758592055548
748.32208851528166.731580463012659.91259656755054
758.233132772922395.5962506942117810.870014851633
768.144177030563194.3041582345271411.9841958265992
778.055221288203982.8730310656371113.2374115107709
787.966265545844781.3157927497363114.6167383419532
797.87730980348558-0.3576407700469616.1122603770181
807.78835406112638-2.139362241275917.7160703635286
817.69939831876717-4.0228794623229519.4216760998573
827.61044257640797-6.002739821715221.2236249745311
837.52148683404877-8.0742803715573423.1172540396549
847.43253109168956-10.23345440093425.0985165843131

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 8.4110442576408 & 7.68450259472611 & 9.13758592055548 \tabularnewline
74 & 8.3220885152816 & 6.73158046301265 & 9.91259656755054 \tabularnewline
75 & 8.23313277292239 & 5.59625069421178 & 10.870014851633 \tabularnewline
76 & 8.14417703056319 & 4.30415823452714 & 11.9841958265992 \tabularnewline
77 & 8.05522128820398 & 2.87303106563711 & 13.2374115107709 \tabularnewline
78 & 7.96626554584478 & 1.31579274973631 & 14.6167383419532 \tabularnewline
79 & 7.87730980348558 & -0.35764077004696 & 16.1122603770181 \tabularnewline
80 & 7.78835406112638 & -2.1393622412759 & 17.7160703635286 \tabularnewline
81 & 7.69939831876717 & -4.02287946232295 & 19.4216760998573 \tabularnewline
82 & 7.61044257640797 & -6.0027398217152 & 21.2236249745311 \tabularnewline
83 & 7.52148683404877 & -8.07428037155734 & 23.1172540396549 \tabularnewline
84 & 7.43253109168956 & -10.233454400934 & 25.0985165843131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121966&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]8.4110442576408[/C][C]7.68450259472611[/C][C]9.13758592055548[/C][/ROW]
[ROW][C]74[/C][C]8.3220885152816[/C][C]6.73158046301265[/C][C]9.91259656755054[/C][/ROW]
[ROW][C]75[/C][C]8.23313277292239[/C][C]5.59625069421178[/C][C]10.870014851633[/C][/ROW]
[ROW][C]76[/C][C]8.14417703056319[/C][C]4.30415823452714[/C][C]11.9841958265992[/C][/ROW]
[ROW][C]77[/C][C]8.05522128820398[/C][C]2.87303106563711[/C][C]13.2374115107709[/C][/ROW]
[ROW][C]78[/C][C]7.96626554584478[/C][C]1.31579274973631[/C][C]14.6167383419532[/C][/ROW]
[ROW][C]79[/C][C]7.87730980348558[/C][C]-0.35764077004696[/C][C]16.1122603770181[/C][/ROW]
[ROW][C]80[/C][C]7.78835406112638[/C][C]-2.1393622412759[/C][C]17.7160703635286[/C][/ROW]
[ROW][C]81[/C][C]7.69939831876717[/C][C]-4.02287946232295[/C][C]19.4216760998573[/C][/ROW]
[ROW][C]82[/C][C]7.61044257640797[/C][C]-6.0027398217152[/C][C]21.2236249745311[/C][/ROW]
[ROW][C]83[/C][C]7.52148683404877[/C][C]-8.07428037155734[/C][C]23.1172540396549[/C][/ROW]
[ROW][C]84[/C][C]7.43253109168956[/C][C]-10.233454400934[/C][C]25.0985165843131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121966&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121966&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
738.41104425764087.684502594726119.13758592055548
748.32208851528166.731580463012659.91259656755054
758.233132772922395.5962506942117810.870014851633
768.144177030563194.3041582345271411.9841958265992
778.055221288203982.8730310656371113.2374115107709
787.966265545844781.3157927497363114.6167383419532
797.87730980348558-0.3576407700469616.1122603770181
807.78835406112638-2.139362241275917.7160703635286
817.69939831876717-4.0228794623229519.4216760998573
827.61044257640797-6.002739821715221.2236249745311
837.52148683404877-8.0742803715573423.1172540396549
847.43253109168956-10.23345440093425.0985165843131



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
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')