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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 01 Jun 2010 09:07:11 +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/2010/Jun/01/t1275383281jsz8rr6lm9bgs4i.htm/, Retrieved Sat, 27 Apr 2024 06:02:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76803, Retrieved Sat, 27 Apr 2024 06:02:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact181
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2010-06-01 09:07:11] [819ef9efcbdcdc4b312cf90f12d3a4d4] [Current]
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Dataseries X:
2
2.4
1.5
1.2
1.5
0.6
2.7
3.7
4.9
6.6
7.4
7.2
5.3
4.7
6.1
6.6
7
7.5
6.6
7.8
4.7
5.4
4.3
4.5
5.8
4.6
5.2
3.6
4.8
6.7
6.3
4.8
8.7
6.8
7.4
9
7.9
9.1
8.7
9.8
6.4
6.1
4.7
4.8
4.2
2.8
6.1
5.8
4.9
4.6
4.1
3.6
5.9
4.5
4.8
5.7
5
7
4.6
2.6
5
4.1
3.2
0
2.3
3.8
4.5
5.9
5
4.2
4.5
6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76803&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76803&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76803&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.694939004311082
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.694939004311082 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76803&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]0.694939004311082[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76803&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76803&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
alpha0.694939004311082
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
22.420.4
31.52.27797560172443-0.777975601724433
41.21.73733001168374-0.53733001168374
51.51.363918428377780.136081571622221
60.61.45848682026601-0.858486820266013
72.70.8618908441761631.83810915582384
83.72.139264590739461.56073540926054
94.93.223880502044031.67611949795597
106.64.388681317059942.21131868294006
117.45.92541292079681.4745870792032
127.26.950160997388260.249839002611741
135.37.12378386510134-1.82378386510134
144.75.8563653218092-1.15636532180920
156.15.052761956451251.04723804354875
166.65.78052851971170.819471480288296
1776.350011214284580.64998878571542
187.56.801713773843020.698286226156977
196.67.2869801085727-0.686980108572696
207.86.809570835939670.990429164060333
214.77.49785869305241-2.79785869305241
225.45.55351755869946-0.153517558699463
234.35.44683221931259-1.14683221931259
244.54.64985377871163-0.149853778711630
255.84.545714542941521.25428545705848
264.65.41736642959161-0.81736642959161
275.24.849346616853910.350653383146089
283.65.09302932979577-1.49302932979577
294.84.055465013940250.744534986059746
306.74.572871415827382.12712858417262
316.36.051096036153940.248903963846057
324.86.2240691089582-1.42406910895820
338.75.234427940308623.46557205969138
346.87.64278913683885-0.842789136838854
357.47.057102093239860.342897906760136
3697.29539522314411.70460477685589
377.98.47999156951626-0.579991569516256
389.18.07693280568781.02306719431219
398.78.78790210304646-0.0879021030464564
409.88.72681550307851.0731844969215
416.49.47261326881122-3.07261326881122
426.17.33733446315053-1.23733446315053
434.76.47746248332891-1.77746248332891
444.85.24223447496401-0.442234474964015
454.24.93490848926049-0.734908489260488
462.84.42419191547404-1.62419191547404
476.13.29547760292442.8045223970756
485.85.244449605116250.555550394883752
494.95.63052324338139-0.73052324338139
504.65.12285414799983-0.522854147999825
514.14.75950240698891-0.659502406988908
523.64.30118846093527-0.701188460935274
535.93.813905250058492.08609474994151
544.55.26361385848142-0.763613858481420
554.84.73294880399020.0670511960098015
565.74.779545295383120.920454704616883
5755.41920517132302-0.419205171323025
5875.127883146961741.87211685303826
594.66.42889016876615-1.82889016876615
602.65.15792305588947-2.55792305588947
6153.380322554325281.61967744567472
624.14.50589958572759-0.405899585727588
633.24.22382413177178-1.02382413177178
6403.51232880904864-3.51232880904864
652.31.071474523675251.22852547632475
663.81.925224794963171.87477520503683
674.53.228079209258571.27192079074143
685.94.111986577138981.78801342286102
6955.35454684491687-0.354546844916869
704.25.1081584135287-0.908158413528704
714.54.477043709874330.0229562901256655
7264.492996931276941.50700306872306

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2.4 & 2 & 0.4 \tabularnewline
3 & 1.5 & 2.27797560172443 & -0.777975601724433 \tabularnewline
4 & 1.2 & 1.73733001168374 & -0.53733001168374 \tabularnewline
5 & 1.5 & 1.36391842837778 & 0.136081571622221 \tabularnewline
6 & 0.6 & 1.45848682026601 & -0.858486820266013 \tabularnewline
7 & 2.7 & 0.861890844176163 & 1.83810915582384 \tabularnewline
8 & 3.7 & 2.13926459073946 & 1.56073540926054 \tabularnewline
9 & 4.9 & 3.22388050204403 & 1.67611949795597 \tabularnewline
10 & 6.6 & 4.38868131705994 & 2.21131868294006 \tabularnewline
11 & 7.4 & 5.9254129207968 & 1.4745870792032 \tabularnewline
12 & 7.2 & 6.95016099738826 & 0.249839002611741 \tabularnewline
13 & 5.3 & 7.12378386510134 & -1.82378386510134 \tabularnewline
14 & 4.7 & 5.8563653218092 & -1.15636532180920 \tabularnewline
15 & 6.1 & 5.05276195645125 & 1.04723804354875 \tabularnewline
16 & 6.6 & 5.7805285197117 & 0.819471480288296 \tabularnewline
17 & 7 & 6.35001121428458 & 0.64998878571542 \tabularnewline
18 & 7.5 & 6.80171377384302 & 0.698286226156977 \tabularnewline
19 & 6.6 & 7.2869801085727 & -0.686980108572696 \tabularnewline
20 & 7.8 & 6.80957083593967 & 0.990429164060333 \tabularnewline
21 & 4.7 & 7.49785869305241 & -2.79785869305241 \tabularnewline
22 & 5.4 & 5.55351755869946 & -0.153517558699463 \tabularnewline
23 & 4.3 & 5.44683221931259 & -1.14683221931259 \tabularnewline
24 & 4.5 & 4.64985377871163 & -0.149853778711630 \tabularnewline
25 & 5.8 & 4.54571454294152 & 1.25428545705848 \tabularnewline
26 & 4.6 & 5.41736642959161 & -0.81736642959161 \tabularnewline
27 & 5.2 & 4.84934661685391 & 0.350653383146089 \tabularnewline
28 & 3.6 & 5.09302932979577 & -1.49302932979577 \tabularnewline
29 & 4.8 & 4.05546501394025 & 0.744534986059746 \tabularnewline
30 & 6.7 & 4.57287141582738 & 2.12712858417262 \tabularnewline
31 & 6.3 & 6.05109603615394 & 0.248903963846057 \tabularnewline
32 & 4.8 & 6.2240691089582 & -1.42406910895820 \tabularnewline
33 & 8.7 & 5.23442794030862 & 3.46557205969138 \tabularnewline
34 & 6.8 & 7.64278913683885 & -0.842789136838854 \tabularnewline
35 & 7.4 & 7.05710209323986 & 0.342897906760136 \tabularnewline
36 & 9 & 7.2953952231441 & 1.70460477685589 \tabularnewline
37 & 7.9 & 8.47999156951626 & -0.579991569516256 \tabularnewline
38 & 9.1 & 8.0769328056878 & 1.02306719431219 \tabularnewline
39 & 8.7 & 8.78790210304646 & -0.0879021030464564 \tabularnewline
40 & 9.8 & 8.7268155030785 & 1.0731844969215 \tabularnewline
41 & 6.4 & 9.47261326881122 & -3.07261326881122 \tabularnewline
42 & 6.1 & 7.33733446315053 & -1.23733446315053 \tabularnewline
43 & 4.7 & 6.47746248332891 & -1.77746248332891 \tabularnewline
44 & 4.8 & 5.24223447496401 & -0.442234474964015 \tabularnewline
45 & 4.2 & 4.93490848926049 & -0.734908489260488 \tabularnewline
46 & 2.8 & 4.42419191547404 & -1.62419191547404 \tabularnewline
47 & 6.1 & 3.2954776029244 & 2.8045223970756 \tabularnewline
48 & 5.8 & 5.24444960511625 & 0.555550394883752 \tabularnewline
49 & 4.9 & 5.63052324338139 & -0.73052324338139 \tabularnewline
50 & 4.6 & 5.12285414799983 & -0.522854147999825 \tabularnewline
51 & 4.1 & 4.75950240698891 & -0.659502406988908 \tabularnewline
52 & 3.6 & 4.30118846093527 & -0.701188460935274 \tabularnewline
53 & 5.9 & 3.81390525005849 & 2.08609474994151 \tabularnewline
54 & 4.5 & 5.26361385848142 & -0.763613858481420 \tabularnewline
55 & 4.8 & 4.7329488039902 & 0.0670511960098015 \tabularnewline
56 & 5.7 & 4.77954529538312 & 0.920454704616883 \tabularnewline
57 & 5 & 5.41920517132302 & -0.419205171323025 \tabularnewline
58 & 7 & 5.12788314696174 & 1.87211685303826 \tabularnewline
59 & 4.6 & 6.42889016876615 & -1.82889016876615 \tabularnewline
60 & 2.6 & 5.15792305588947 & -2.55792305588947 \tabularnewline
61 & 5 & 3.38032255432528 & 1.61967744567472 \tabularnewline
62 & 4.1 & 4.50589958572759 & -0.405899585727588 \tabularnewline
63 & 3.2 & 4.22382413177178 & -1.02382413177178 \tabularnewline
64 & 0 & 3.51232880904864 & -3.51232880904864 \tabularnewline
65 & 2.3 & 1.07147452367525 & 1.22852547632475 \tabularnewline
66 & 3.8 & 1.92522479496317 & 1.87477520503683 \tabularnewline
67 & 4.5 & 3.22807920925857 & 1.27192079074143 \tabularnewline
68 & 5.9 & 4.11198657713898 & 1.78801342286102 \tabularnewline
69 & 5 & 5.35454684491687 & -0.354546844916869 \tabularnewline
70 & 4.2 & 5.1081584135287 & -0.908158413528704 \tabularnewline
71 & 4.5 & 4.47704370987433 & 0.0229562901256655 \tabularnewline
72 & 6 & 4.49299693127694 & 1.50700306872306 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76803&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]2[/C][C]2.4[/C][C]2[/C][C]0.4[/C][/ROW]
[ROW][C]3[/C][C]1.5[/C][C]2.27797560172443[/C][C]-0.777975601724433[/C][/ROW]
[ROW][C]4[/C][C]1.2[/C][C]1.73733001168374[/C][C]-0.53733001168374[/C][/ROW]
[ROW][C]5[/C][C]1.5[/C][C]1.36391842837778[/C][C]0.136081571622221[/C][/ROW]
[ROW][C]6[/C][C]0.6[/C][C]1.45848682026601[/C][C]-0.858486820266013[/C][/ROW]
[ROW][C]7[/C][C]2.7[/C][C]0.861890844176163[/C][C]1.83810915582384[/C][/ROW]
[ROW][C]8[/C][C]3.7[/C][C]2.13926459073946[/C][C]1.56073540926054[/C][/ROW]
[ROW][C]9[/C][C]4.9[/C][C]3.22388050204403[/C][C]1.67611949795597[/C][/ROW]
[ROW][C]10[/C][C]6.6[/C][C]4.38868131705994[/C][C]2.21131868294006[/C][/ROW]
[ROW][C]11[/C][C]7.4[/C][C]5.9254129207968[/C][C]1.4745870792032[/C][/ROW]
[ROW][C]12[/C][C]7.2[/C][C]6.95016099738826[/C][C]0.249839002611741[/C][/ROW]
[ROW][C]13[/C][C]5.3[/C][C]7.12378386510134[/C][C]-1.82378386510134[/C][/ROW]
[ROW][C]14[/C][C]4.7[/C][C]5.8563653218092[/C][C]-1.15636532180920[/C][/ROW]
[ROW][C]15[/C][C]6.1[/C][C]5.05276195645125[/C][C]1.04723804354875[/C][/ROW]
[ROW][C]16[/C][C]6.6[/C][C]5.7805285197117[/C][C]0.819471480288296[/C][/ROW]
[ROW][C]17[/C][C]7[/C][C]6.35001121428458[/C][C]0.64998878571542[/C][/ROW]
[ROW][C]18[/C][C]7.5[/C][C]6.80171377384302[/C][C]0.698286226156977[/C][/ROW]
[ROW][C]19[/C][C]6.6[/C][C]7.2869801085727[/C][C]-0.686980108572696[/C][/ROW]
[ROW][C]20[/C][C]7.8[/C][C]6.80957083593967[/C][C]0.990429164060333[/C][/ROW]
[ROW][C]21[/C][C]4.7[/C][C]7.49785869305241[/C][C]-2.79785869305241[/C][/ROW]
[ROW][C]22[/C][C]5.4[/C][C]5.55351755869946[/C][C]-0.153517558699463[/C][/ROW]
[ROW][C]23[/C][C]4.3[/C][C]5.44683221931259[/C][C]-1.14683221931259[/C][/ROW]
[ROW][C]24[/C][C]4.5[/C][C]4.64985377871163[/C][C]-0.149853778711630[/C][/ROW]
[ROW][C]25[/C][C]5.8[/C][C]4.54571454294152[/C][C]1.25428545705848[/C][/ROW]
[ROW][C]26[/C][C]4.6[/C][C]5.41736642959161[/C][C]-0.81736642959161[/C][/ROW]
[ROW][C]27[/C][C]5.2[/C][C]4.84934661685391[/C][C]0.350653383146089[/C][/ROW]
[ROW][C]28[/C][C]3.6[/C][C]5.09302932979577[/C][C]-1.49302932979577[/C][/ROW]
[ROW][C]29[/C][C]4.8[/C][C]4.05546501394025[/C][C]0.744534986059746[/C][/ROW]
[ROW][C]30[/C][C]6.7[/C][C]4.57287141582738[/C][C]2.12712858417262[/C][/ROW]
[ROW][C]31[/C][C]6.3[/C][C]6.05109603615394[/C][C]0.248903963846057[/C][/ROW]
[ROW][C]32[/C][C]4.8[/C][C]6.2240691089582[/C][C]-1.42406910895820[/C][/ROW]
[ROW][C]33[/C][C]8.7[/C][C]5.23442794030862[/C][C]3.46557205969138[/C][/ROW]
[ROW][C]34[/C][C]6.8[/C][C]7.64278913683885[/C][C]-0.842789136838854[/C][/ROW]
[ROW][C]35[/C][C]7.4[/C][C]7.05710209323986[/C][C]0.342897906760136[/C][/ROW]
[ROW][C]36[/C][C]9[/C][C]7.2953952231441[/C][C]1.70460477685589[/C][/ROW]
[ROW][C]37[/C][C]7.9[/C][C]8.47999156951626[/C][C]-0.579991569516256[/C][/ROW]
[ROW][C]38[/C][C]9.1[/C][C]8.0769328056878[/C][C]1.02306719431219[/C][/ROW]
[ROW][C]39[/C][C]8.7[/C][C]8.78790210304646[/C][C]-0.0879021030464564[/C][/ROW]
[ROW][C]40[/C][C]9.8[/C][C]8.7268155030785[/C][C]1.0731844969215[/C][/ROW]
[ROW][C]41[/C][C]6.4[/C][C]9.47261326881122[/C][C]-3.07261326881122[/C][/ROW]
[ROW][C]42[/C][C]6.1[/C][C]7.33733446315053[/C][C]-1.23733446315053[/C][/ROW]
[ROW][C]43[/C][C]4.7[/C][C]6.47746248332891[/C][C]-1.77746248332891[/C][/ROW]
[ROW][C]44[/C][C]4.8[/C][C]5.24223447496401[/C][C]-0.442234474964015[/C][/ROW]
[ROW][C]45[/C][C]4.2[/C][C]4.93490848926049[/C][C]-0.734908489260488[/C][/ROW]
[ROW][C]46[/C][C]2.8[/C][C]4.42419191547404[/C][C]-1.62419191547404[/C][/ROW]
[ROW][C]47[/C][C]6.1[/C][C]3.2954776029244[/C][C]2.8045223970756[/C][/ROW]
[ROW][C]48[/C][C]5.8[/C][C]5.24444960511625[/C][C]0.555550394883752[/C][/ROW]
[ROW][C]49[/C][C]4.9[/C][C]5.63052324338139[/C][C]-0.73052324338139[/C][/ROW]
[ROW][C]50[/C][C]4.6[/C][C]5.12285414799983[/C][C]-0.522854147999825[/C][/ROW]
[ROW][C]51[/C][C]4.1[/C][C]4.75950240698891[/C][C]-0.659502406988908[/C][/ROW]
[ROW][C]52[/C][C]3.6[/C][C]4.30118846093527[/C][C]-0.701188460935274[/C][/ROW]
[ROW][C]53[/C][C]5.9[/C][C]3.81390525005849[/C][C]2.08609474994151[/C][/ROW]
[ROW][C]54[/C][C]4.5[/C][C]5.26361385848142[/C][C]-0.763613858481420[/C][/ROW]
[ROW][C]55[/C][C]4.8[/C][C]4.7329488039902[/C][C]0.0670511960098015[/C][/ROW]
[ROW][C]56[/C][C]5.7[/C][C]4.77954529538312[/C][C]0.920454704616883[/C][/ROW]
[ROW][C]57[/C][C]5[/C][C]5.41920517132302[/C][C]-0.419205171323025[/C][/ROW]
[ROW][C]58[/C][C]7[/C][C]5.12788314696174[/C][C]1.87211685303826[/C][/ROW]
[ROW][C]59[/C][C]4.6[/C][C]6.42889016876615[/C][C]-1.82889016876615[/C][/ROW]
[ROW][C]60[/C][C]2.6[/C][C]5.15792305588947[/C][C]-2.55792305588947[/C][/ROW]
[ROW][C]61[/C][C]5[/C][C]3.38032255432528[/C][C]1.61967744567472[/C][/ROW]
[ROW][C]62[/C][C]4.1[/C][C]4.50589958572759[/C][C]-0.405899585727588[/C][/ROW]
[ROW][C]63[/C][C]3.2[/C][C]4.22382413177178[/C][C]-1.02382413177178[/C][/ROW]
[ROW][C]64[/C][C]0[/C][C]3.51232880904864[/C][C]-3.51232880904864[/C][/ROW]
[ROW][C]65[/C][C]2.3[/C][C]1.07147452367525[/C][C]1.22852547632475[/C][/ROW]
[ROW][C]66[/C][C]3.8[/C][C]1.92522479496317[/C][C]1.87477520503683[/C][/ROW]
[ROW][C]67[/C][C]4.5[/C][C]3.22807920925857[/C][C]1.27192079074143[/C][/ROW]
[ROW][C]68[/C][C]5.9[/C][C]4.11198657713898[/C][C]1.78801342286102[/C][/ROW]
[ROW][C]69[/C][C]5[/C][C]5.35454684491687[/C][C]-0.354546844916869[/C][/ROW]
[ROW][C]70[/C][C]4.2[/C][C]5.1081584135287[/C][C]-0.908158413528704[/C][/ROW]
[ROW][C]71[/C][C]4.5[/C][C]4.47704370987433[/C][C]0.0229562901256655[/C][/ROW]
[ROW][C]72[/C][C]6[/C][C]4.49299693127694[/C][C]1.50700306872306[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76803&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76803&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
22.420.4
31.52.27797560172443-0.777975601724433
41.21.73733001168374-0.53733001168374
51.51.363918428377780.136081571622221
60.61.45848682026601-0.858486820266013
72.70.8618908441761631.83810915582384
83.72.139264590739461.56073540926054
94.93.223880502044031.67611949795597
106.64.388681317059942.21131868294006
117.45.92541292079681.4745870792032
127.26.950160997388260.249839002611741
135.37.12378386510134-1.82378386510134
144.75.8563653218092-1.15636532180920
156.15.052761956451251.04723804354875
166.65.78052851971170.819471480288296
1776.350011214284580.64998878571542
187.56.801713773843020.698286226156977
196.67.2869801085727-0.686980108572696
207.86.809570835939670.990429164060333
214.77.49785869305241-2.79785869305241
225.45.55351755869946-0.153517558699463
234.35.44683221931259-1.14683221931259
244.54.64985377871163-0.149853778711630
255.84.545714542941521.25428545705848
264.65.41736642959161-0.81736642959161
275.24.849346616853910.350653383146089
283.65.09302932979577-1.49302932979577
294.84.055465013940250.744534986059746
306.74.572871415827382.12712858417262
316.36.051096036153940.248903963846057
324.86.2240691089582-1.42406910895820
338.75.234427940308623.46557205969138
346.87.64278913683885-0.842789136838854
357.47.057102093239860.342897906760136
3697.29539522314411.70460477685589
377.98.47999156951626-0.579991569516256
389.18.07693280568781.02306719431219
398.78.78790210304646-0.0879021030464564
409.88.72681550307851.0731844969215
416.49.47261326881122-3.07261326881122
426.17.33733446315053-1.23733446315053
434.76.47746248332891-1.77746248332891
444.85.24223447496401-0.442234474964015
454.24.93490848926049-0.734908489260488
462.84.42419191547404-1.62419191547404
476.13.29547760292442.8045223970756
485.85.244449605116250.555550394883752
494.95.63052324338139-0.73052324338139
504.65.12285414799983-0.522854147999825
514.14.75950240698891-0.659502406988908
523.64.30118846093527-0.701188460935274
535.93.813905250058492.08609474994151
544.55.26361385848142-0.763613858481420
554.84.73294880399020.0670511960098015
565.74.779545295383120.920454704616883
5755.41920517132302-0.419205171323025
5875.127883146961741.87211685303826
594.66.42889016876615-1.82889016876615
602.65.15792305588947-2.55792305588947
6153.380322554325281.61967744567472
624.14.50589958572759-0.405899585727588
633.24.22382413177178-1.02382413177178
6403.51232880904864-3.51232880904864
652.31.071474523675251.22852547632475
663.81.925224794963171.87477520503683
674.53.228079209258571.27192079074143
685.94.111986577138981.78801342286102
6955.35454684491687-0.354546844916869
704.25.1081584135287-0.908158413528704
714.54.477043709874330.0229562901256655
7264.492996931276941.50700306872306







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
735.540272143349092.75633132937198.32421295732628
745.540272143349092.150099460858748.93044482583943
755.540272143349091.636912669962159.44363161673603
765.540272143349091.183764420429809.89677986626837
775.540272143349090.7735013389961910.3070429477020
785.540272143349090.39585300581694210.6846912808812
795.540272143349090.044092322420484111.0364519642777
805.54027214334909-0.28647111385373711.3670154005519
815.54027214334909-0.59926215061282411.679806437311
825.54027214334909-0.89687207657562911.9774163632738
835.54027214334909-1.1813177035164612.2618619902146
845.54027214334909-1.4542052803661212.5347495670643

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 5.54027214334909 & 2.7563313293719 & 8.32421295732628 \tabularnewline
74 & 5.54027214334909 & 2.15009946085874 & 8.93044482583943 \tabularnewline
75 & 5.54027214334909 & 1.63691266996215 & 9.44363161673603 \tabularnewline
76 & 5.54027214334909 & 1.18376442042980 & 9.89677986626837 \tabularnewline
77 & 5.54027214334909 & 0.77350133899619 & 10.3070429477020 \tabularnewline
78 & 5.54027214334909 & 0.395853005816942 & 10.6846912808812 \tabularnewline
79 & 5.54027214334909 & 0.0440923224204841 & 11.0364519642777 \tabularnewline
80 & 5.54027214334909 & -0.286471113853737 & 11.3670154005519 \tabularnewline
81 & 5.54027214334909 & -0.599262150612824 & 11.679806437311 \tabularnewline
82 & 5.54027214334909 & -0.896872076575629 & 11.9774163632738 \tabularnewline
83 & 5.54027214334909 & -1.18131770351646 & 12.2618619902146 \tabularnewline
84 & 5.54027214334909 & -1.45420528036612 & 12.5347495670643 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76803&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]5.54027214334909[/C][C]2.7563313293719[/C][C]8.32421295732628[/C][/ROW]
[ROW][C]74[/C][C]5.54027214334909[/C][C]2.15009946085874[/C][C]8.93044482583943[/C][/ROW]
[ROW][C]75[/C][C]5.54027214334909[/C][C]1.63691266996215[/C][C]9.44363161673603[/C][/ROW]
[ROW][C]76[/C][C]5.54027214334909[/C][C]1.18376442042980[/C][C]9.89677986626837[/C][/ROW]
[ROW][C]77[/C][C]5.54027214334909[/C][C]0.77350133899619[/C][C]10.3070429477020[/C][/ROW]
[ROW][C]78[/C][C]5.54027214334909[/C][C]0.395853005816942[/C][C]10.6846912808812[/C][/ROW]
[ROW][C]79[/C][C]5.54027214334909[/C][C]0.0440923224204841[/C][C]11.0364519642777[/C][/ROW]
[ROW][C]80[/C][C]5.54027214334909[/C][C]-0.286471113853737[/C][C]11.3670154005519[/C][/ROW]
[ROW][C]81[/C][C]5.54027214334909[/C][C]-0.599262150612824[/C][C]11.679806437311[/C][/ROW]
[ROW][C]82[/C][C]5.54027214334909[/C][C]-0.896872076575629[/C][C]11.9774163632738[/C][/ROW]
[ROW][C]83[/C][C]5.54027214334909[/C][C]-1.18131770351646[/C][C]12.2618619902146[/C][/ROW]
[ROW][C]84[/C][C]5.54027214334909[/C][C]-1.45420528036612[/C][C]12.5347495670643[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76803&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76803&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
735.540272143349092.75633132937198.32421295732628
745.540272143349092.150099460858748.93044482583943
755.540272143349091.636912669962159.44363161673603
765.540272143349091.183764420429809.89677986626837
775.540272143349090.7735013389961910.3070429477020
785.540272143349090.39585300581694210.6846912808812
795.540272143349090.044092322420484111.0364519642777
805.54027214334909-0.28647111385373711.3670154005519
815.54027214334909-0.59926215061282411.679806437311
825.54027214334909-0.89687207657562911.9774163632738
835.54027214334909-1.1813177035164612.2618619902146
845.54027214334909-1.4542052803661212.5347495670643



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