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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, 26 Apr 2016 17:12:10 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/26/t1461687198rbj0c04bvo4dhbv.htm/, Retrieved Fri, 03 May 2024 22:45:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294914, Retrieved Fri, 03 May 2024 22:45:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 16:12:10] [808bf237864283e5d6c581b9d5be65c1] [Current]
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Dataseries X:
4
7
9
6
9
13
18
8
15
4
8
14
8
3
5
6
12
7
3
11
6
9
6
10
10
6
13
10
9
15
8
12
13
9
6
7
8
7
6
8
3
7
8
8
7
12
7
5
9
9
8
11
9
8
9
11
8
9
9
5




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294914&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294914&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294914&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.274558999375664
beta0.676864733979293
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.274558999375664 \tabularnewline
beta & 0.676864733979293 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294914&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]0.274558999375664[/C][/ROW]
[ROW][C]beta[/C][C]0.676864733979293[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294914&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294914&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
alpha0.274558999375664
beta0.676864733979293
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3910-1
4612.5396016965503-6.53960169655031
5912.3429408661478-3.34294086614778
61312.40270223055840.597297769441584
71813.65529297385584.34470702614421
8816.7441859830687-8.74418598306872
91514.61439218694970.385607813050342
10415.062926527622-11.062926527622
11810.312236168486-2.31223616848598
12147.53442223779446.4655777622056
1388.36819458838407-0.368194588384071
1437.25726821436565-4.25726821436565
1554.287393914885240.712606085114762
1662.814473549029643.18552645097036
17122.612511743116819.38748825688319
1875.857918649463771.14208135053623
1937.05171848953851-4.05171848953851
20116.066545298165134.93345470183487
2168.46516205590201-2.46516205590201
2298.37429799897210.625702001027902
2369.24833850914782-3.24833850914782
24108.455057365372011.54494263462799
25109.264925760211090.735074239788915
2669.98904318410229-3.98904318410229
27138.674790645901974.32520935409803
281010.4470848614866-0.447084861486555
29910.8260168129933-1.82601681299328
301510.4870048939334.51299510606697
31812.7271176142014-4.72711761420136
321211.55178998417520.44821001582479
331311.88069016711021.11930983288985
34912.6018586046871-3.60185860468713
35611.3574208636909-5.3574208636909
3678.63535834058092-1.63535834058092
3786.631307723504451.36869227649555
3875.706403058081771.29359694191823
3965.001281448178140.998718551821862
4084.400799483188543.59920051681146
4135.18317616366807-2.18317616366807
4273.972229349814893.02777065018511
4384.754673669499213.24532633050079
4486.199959045832891.80004095416711
4577.58294667365528-0.582946673655277
46128.20332919871383.7966708012862
47710.7317457748496-3.73174577484964
48510.4996627911792-5.4996627911792
4998.760128774771540.239871225228462
5098.641012976355190.358987023644815
5188.62131539100762-0.621315391007622
52118.21700213573222.7829978642678
5399.26456410772154-0.26456410772154
5489.42622410448422-1.42622410448422
5599.00389139989006-0.00389139989005649
56118.97134976440112.0286502355989
5789.87386367453469-1.87386367453469
5899.35666974924725-0.356669749247255
5999.18975181196121-0.189751811961207
6059.03339935183261-4.03339935183261

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 9 & 10 & -1 \tabularnewline
4 & 6 & 12.5396016965503 & -6.53960169655031 \tabularnewline
5 & 9 & 12.3429408661478 & -3.34294086614778 \tabularnewline
6 & 13 & 12.4027022305584 & 0.597297769441584 \tabularnewline
7 & 18 & 13.6552929738558 & 4.34470702614421 \tabularnewline
8 & 8 & 16.7441859830687 & -8.74418598306872 \tabularnewline
9 & 15 & 14.6143921869497 & 0.385607813050342 \tabularnewline
10 & 4 & 15.062926527622 & -11.062926527622 \tabularnewline
11 & 8 & 10.312236168486 & -2.31223616848598 \tabularnewline
12 & 14 & 7.5344222377944 & 6.4655777622056 \tabularnewline
13 & 8 & 8.36819458838407 & -0.368194588384071 \tabularnewline
14 & 3 & 7.25726821436565 & -4.25726821436565 \tabularnewline
15 & 5 & 4.28739391488524 & 0.712606085114762 \tabularnewline
16 & 6 & 2.81447354902964 & 3.18552645097036 \tabularnewline
17 & 12 & 2.61251174311681 & 9.38748825688319 \tabularnewline
18 & 7 & 5.85791864946377 & 1.14208135053623 \tabularnewline
19 & 3 & 7.05171848953851 & -4.05171848953851 \tabularnewline
20 & 11 & 6.06654529816513 & 4.93345470183487 \tabularnewline
21 & 6 & 8.46516205590201 & -2.46516205590201 \tabularnewline
22 & 9 & 8.3742979989721 & 0.625702001027902 \tabularnewline
23 & 6 & 9.24833850914782 & -3.24833850914782 \tabularnewline
24 & 10 & 8.45505736537201 & 1.54494263462799 \tabularnewline
25 & 10 & 9.26492576021109 & 0.735074239788915 \tabularnewline
26 & 6 & 9.98904318410229 & -3.98904318410229 \tabularnewline
27 & 13 & 8.67479064590197 & 4.32520935409803 \tabularnewline
28 & 10 & 10.4470848614866 & -0.447084861486555 \tabularnewline
29 & 9 & 10.8260168129933 & -1.82601681299328 \tabularnewline
30 & 15 & 10.487004893933 & 4.51299510606697 \tabularnewline
31 & 8 & 12.7271176142014 & -4.72711761420136 \tabularnewline
32 & 12 & 11.5517899841752 & 0.44821001582479 \tabularnewline
33 & 13 & 11.8806901671102 & 1.11930983288985 \tabularnewline
34 & 9 & 12.6018586046871 & -3.60185860468713 \tabularnewline
35 & 6 & 11.3574208636909 & -5.3574208636909 \tabularnewline
36 & 7 & 8.63535834058092 & -1.63535834058092 \tabularnewline
37 & 8 & 6.63130772350445 & 1.36869227649555 \tabularnewline
38 & 7 & 5.70640305808177 & 1.29359694191823 \tabularnewline
39 & 6 & 5.00128144817814 & 0.998718551821862 \tabularnewline
40 & 8 & 4.40079948318854 & 3.59920051681146 \tabularnewline
41 & 3 & 5.18317616366807 & -2.18317616366807 \tabularnewline
42 & 7 & 3.97222934981489 & 3.02777065018511 \tabularnewline
43 & 8 & 4.75467366949921 & 3.24532633050079 \tabularnewline
44 & 8 & 6.19995904583289 & 1.80004095416711 \tabularnewline
45 & 7 & 7.58294667365528 & -0.582946673655277 \tabularnewline
46 & 12 & 8.2033291987138 & 3.7966708012862 \tabularnewline
47 & 7 & 10.7317457748496 & -3.73174577484964 \tabularnewline
48 & 5 & 10.4996627911792 & -5.4996627911792 \tabularnewline
49 & 9 & 8.76012877477154 & 0.239871225228462 \tabularnewline
50 & 9 & 8.64101297635519 & 0.358987023644815 \tabularnewline
51 & 8 & 8.62131539100762 & -0.621315391007622 \tabularnewline
52 & 11 & 8.2170021357322 & 2.7829978642678 \tabularnewline
53 & 9 & 9.26456410772154 & -0.26456410772154 \tabularnewline
54 & 8 & 9.42622410448422 & -1.42622410448422 \tabularnewline
55 & 9 & 9.00389139989006 & -0.00389139989005649 \tabularnewline
56 & 11 & 8.9713497644011 & 2.0286502355989 \tabularnewline
57 & 8 & 9.87386367453469 & -1.87386367453469 \tabularnewline
58 & 9 & 9.35666974924725 & -0.356669749247255 \tabularnewline
59 & 9 & 9.18975181196121 & -0.189751811961207 \tabularnewline
60 & 5 & 9.03339935183261 & -4.03339935183261 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294914&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]9[/C][C]10[/C][C]-1[/C][/ROW]
[ROW][C]4[/C][C]6[/C][C]12.5396016965503[/C][C]-6.53960169655031[/C][/ROW]
[ROW][C]5[/C][C]9[/C][C]12.3429408661478[/C][C]-3.34294086614778[/C][/ROW]
[ROW][C]6[/C][C]13[/C][C]12.4027022305584[/C][C]0.597297769441584[/C][/ROW]
[ROW][C]7[/C][C]18[/C][C]13.6552929738558[/C][C]4.34470702614421[/C][/ROW]
[ROW][C]8[/C][C]8[/C][C]16.7441859830687[/C][C]-8.74418598306872[/C][/ROW]
[ROW][C]9[/C][C]15[/C][C]14.6143921869497[/C][C]0.385607813050342[/C][/ROW]
[ROW][C]10[/C][C]4[/C][C]15.062926527622[/C][C]-11.062926527622[/C][/ROW]
[ROW][C]11[/C][C]8[/C][C]10.312236168486[/C][C]-2.31223616848598[/C][/ROW]
[ROW][C]12[/C][C]14[/C][C]7.5344222377944[/C][C]6.4655777622056[/C][/ROW]
[ROW][C]13[/C][C]8[/C][C]8.36819458838407[/C][C]-0.368194588384071[/C][/ROW]
[ROW][C]14[/C][C]3[/C][C]7.25726821436565[/C][C]-4.25726821436565[/C][/ROW]
[ROW][C]15[/C][C]5[/C][C]4.28739391488524[/C][C]0.712606085114762[/C][/ROW]
[ROW][C]16[/C][C]6[/C][C]2.81447354902964[/C][C]3.18552645097036[/C][/ROW]
[ROW][C]17[/C][C]12[/C][C]2.61251174311681[/C][C]9.38748825688319[/C][/ROW]
[ROW][C]18[/C][C]7[/C][C]5.85791864946377[/C][C]1.14208135053623[/C][/ROW]
[ROW][C]19[/C][C]3[/C][C]7.05171848953851[/C][C]-4.05171848953851[/C][/ROW]
[ROW][C]20[/C][C]11[/C][C]6.06654529816513[/C][C]4.93345470183487[/C][/ROW]
[ROW][C]21[/C][C]6[/C][C]8.46516205590201[/C][C]-2.46516205590201[/C][/ROW]
[ROW][C]22[/C][C]9[/C][C]8.3742979989721[/C][C]0.625702001027902[/C][/ROW]
[ROW][C]23[/C][C]6[/C][C]9.24833850914782[/C][C]-3.24833850914782[/C][/ROW]
[ROW][C]24[/C][C]10[/C][C]8.45505736537201[/C][C]1.54494263462799[/C][/ROW]
[ROW][C]25[/C][C]10[/C][C]9.26492576021109[/C][C]0.735074239788915[/C][/ROW]
[ROW][C]26[/C][C]6[/C][C]9.98904318410229[/C][C]-3.98904318410229[/C][/ROW]
[ROW][C]27[/C][C]13[/C][C]8.67479064590197[/C][C]4.32520935409803[/C][/ROW]
[ROW][C]28[/C][C]10[/C][C]10.4470848614866[/C][C]-0.447084861486555[/C][/ROW]
[ROW][C]29[/C][C]9[/C][C]10.8260168129933[/C][C]-1.82601681299328[/C][/ROW]
[ROW][C]30[/C][C]15[/C][C]10.487004893933[/C][C]4.51299510606697[/C][/ROW]
[ROW][C]31[/C][C]8[/C][C]12.7271176142014[/C][C]-4.72711761420136[/C][/ROW]
[ROW][C]32[/C][C]12[/C][C]11.5517899841752[/C][C]0.44821001582479[/C][/ROW]
[ROW][C]33[/C][C]13[/C][C]11.8806901671102[/C][C]1.11930983288985[/C][/ROW]
[ROW][C]34[/C][C]9[/C][C]12.6018586046871[/C][C]-3.60185860468713[/C][/ROW]
[ROW][C]35[/C][C]6[/C][C]11.3574208636909[/C][C]-5.3574208636909[/C][/ROW]
[ROW][C]36[/C][C]7[/C][C]8.63535834058092[/C][C]-1.63535834058092[/C][/ROW]
[ROW][C]37[/C][C]8[/C][C]6.63130772350445[/C][C]1.36869227649555[/C][/ROW]
[ROW][C]38[/C][C]7[/C][C]5.70640305808177[/C][C]1.29359694191823[/C][/ROW]
[ROW][C]39[/C][C]6[/C][C]5.00128144817814[/C][C]0.998718551821862[/C][/ROW]
[ROW][C]40[/C][C]8[/C][C]4.40079948318854[/C][C]3.59920051681146[/C][/ROW]
[ROW][C]41[/C][C]3[/C][C]5.18317616366807[/C][C]-2.18317616366807[/C][/ROW]
[ROW][C]42[/C][C]7[/C][C]3.97222934981489[/C][C]3.02777065018511[/C][/ROW]
[ROW][C]43[/C][C]8[/C][C]4.75467366949921[/C][C]3.24532633050079[/C][/ROW]
[ROW][C]44[/C][C]8[/C][C]6.19995904583289[/C][C]1.80004095416711[/C][/ROW]
[ROW][C]45[/C][C]7[/C][C]7.58294667365528[/C][C]-0.582946673655277[/C][/ROW]
[ROW][C]46[/C][C]12[/C][C]8.2033291987138[/C][C]3.7966708012862[/C][/ROW]
[ROW][C]47[/C][C]7[/C][C]10.7317457748496[/C][C]-3.73174577484964[/C][/ROW]
[ROW][C]48[/C][C]5[/C][C]10.4996627911792[/C][C]-5.4996627911792[/C][/ROW]
[ROW][C]49[/C][C]9[/C][C]8.76012877477154[/C][C]0.239871225228462[/C][/ROW]
[ROW][C]50[/C][C]9[/C][C]8.64101297635519[/C][C]0.358987023644815[/C][/ROW]
[ROW][C]51[/C][C]8[/C][C]8.62131539100762[/C][C]-0.621315391007622[/C][/ROW]
[ROW][C]52[/C][C]11[/C][C]8.2170021357322[/C][C]2.7829978642678[/C][/ROW]
[ROW][C]53[/C][C]9[/C][C]9.26456410772154[/C][C]-0.26456410772154[/C][/ROW]
[ROW][C]54[/C][C]8[/C][C]9.42622410448422[/C][C]-1.42622410448422[/C][/ROW]
[ROW][C]55[/C][C]9[/C][C]9.00389139989006[/C][C]-0.00389139989005649[/C][/ROW]
[ROW][C]56[/C][C]11[/C][C]8.9713497644011[/C][C]2.0286502355989[/C][/ROW]
[ROW][C]57[/C][C]8[/C][C]9.87386367453469[/C][C]-1.87386367453469[/C][/ROW]
[ROW][C]58[/C][C]9[/C][C]9.35666974924725[/C][C]-0.356669749247255[/C][/ROW]
[ROW][C]59[/C][C]9[/C][C]9.18975181196121[/C][C]-0.189751811961207[/C][/ROW]
[ROW][C]60[/C][C]5[/C][C]9.03339935183261[/C][C]-4.03339935183261[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294914&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294914&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
3910-1
4612.5396016965503-6.53960169655031
5912.3429408661478-3.34294086614778
61312.40270223055840.597297769441584
71813.65529297385584.34470702614421
8816.7441859830687-8.74418598306872
91514.61439218694970.385607813050342
10415.062926527622-11.062926527622
11810.312236168486-2.31223616848598
12147.53442223779446.4655777622056
1388.36819458838407-0.368194588384071
1437.25726821436565-4.25726821436565
1554.287393914885240.712606085114762
1662.814473549029643.18552645097036
17122.612511743116819.38748825688319
1875.857918649463771.14208135053623
1937.05171848953851-4.05171848953851
20116.066545298165134.93345470183487
2168.46516205590201-2.46516205590201
2298.37429799897210.625702001027902
2369.24833850914782-3.24833850914782
24108.455057365372011.54494263462799
25109.264925760211090.735074239788915
2669.98904318410229-3.98904318410229
27138.674790645901974.32520935409803
281010.4470848614866-0.447084861486555
29910.8260168129933-1.82601681299328
301510.4870048939334.51299510606697
31812.7271176142014-4.72711761420136
321211.55178998417520.44821001582479
331311.88069016711021.11930983288985
34912.6018586046871-3.60185860468713
35611.3574208636909-5.3574208636909
3678.63535834058092-1.63535834058092
3786.631307723504451.36869227649555
3875.706403058081771.29359694191823
3965.001281448178140.998718551821862
4084.400799483188543.59920051681146
4135.18317616366807-2.18317616366807
4273.972229349814893.02777065018511
4384.754673669499213.24532633050079
4486.199959045832891.80004095416711
4577.58294667365528-0.582946673655277
46128.20332919871383.7966708012862
47710.7317457748496-3.73174577484964
48510.4996627911792-5.4996627911792
4998.760128774771540.239871225228462
5098.641012976355190.358987023644815
5188.62131539100762-0.621315391007622
52118.21700213573222.7829978642678
5399.26456410772154-0.26456410772154
5489.42622410448422-1.42622410448422
5599.00389139989006-0.00389139989005649
56118.97134976440112.0286502355989
5789.87386367453469-1.87386367453469
5899.35666974924725-0.356669749247255
5999.18975181196121-0.189751811961207
6059.03339935183261-4.03339935183261







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
617.07217474060697-0.071581598444420414.2159310796584
626.21835621950295-1.6461590224986314.0828714615045
635.36453769839893-3.7548517113439914.4839271081418
644.5107191772949-6.3748785759018315.3963169304916
653.65690065619088-9.4341084673787416.7479097797605
662.80308213508686-12.859711410815918.4658756809896
671.94926361398284-16.594386996861420.4929142248271
681.09544509287881-20.596284736435322.787174922193
690.241626571774791-24.835067605535525.318320749085
70-0.612191949329231-29.288319926591628.0639360279331
71-1.46601047043325-33.939004047773831.0069831069073
72-2.31982899153728-38.773780400780434.1341224177058

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 7.07217474060697 & -0.0715815984444204 & 14.2159310796584 \tabularnewline
62 & 6.21835621950295 & -1.64615902249863 & 14.0828714615045 \tabularnewline
63 & 5.36453769839893 & -3.75485171134399 & 14.4839271081418 \tabularnewline
64 & 4.5107191772949 & -6.37487857590183 & 15.3963169304916 \tabularnewline
65 & 3.65690065619088 & -9.43410846737874 & 16.7479097797605 \tabularnewline
66 & 2.80308213508686 & -12.8597114108159 & 18.4658756809896 \tabularnewline
67 & 1.94926361398284 & -16.5943869968614 & 20.4929142248271 \tabularnewline
68 & 1.09544509287881 & -20.5962847364353 & 22.787174922193 \tabularnewline
69 & 0.241626571774791 & -24.8350676055355 & 25.318320749085 \tabularnewline
70 & -0.612191949329231 & -29.2883199265916 & 28.0639360279331 \tabularnewline
71 & -1.46601047043325 & -33.9390040477738 & 31.0069831069073 \tabularnewline
72 & -2.31982899153728 & -38.7737804007804 & 34.1341224177058 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294914&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]61[/C][C]7.07217474060697[/C][C]-0.0715815984444204[/C][C]14.2159310796584[/C][/ROW]
[ROW][C]62[/C][C]6.21835621950295[/C][C]-1.64615902249863[/C][C]14.0828714615045[/C][/ROW]
[ROW][C]63[/C][C]5.36453769839893[/C][C]-3.75485171134399[/C][C]14.4839271081418[/C][/ROW]
[ROW][C]64[/C][C]4.5107191772949[/C][C]-6.37487857590183[/C][C]15.3963169304916[/C][/ROW]
[ROW][C]65[/C][C]3.65690065619088[/C][C]-9.43410846737874[/C][C]16.7479097797605[/C][/ROW]
[ROW][C]66[/C][C]2.80308213508686[/C][C]-12.8597114108159[/C][C]18.4658756809896[/C][/ROW]
[ROW][C]67[/C][C]1.94926361398284[/C][C]-16.5943869968614[/C][C]20.4929142248271[/C][/ROW]
[ROW][C]68[/C][C]1.09544509287881[/C][C]-20.5962847364353[/C][C]22.787174922193[/C][/ROW]
[ROW][C]69[/C][C]0.241626571774791[/C][C]-24.8350676055355[/C][C]25.318320749085[/C][/ROW]
[ROW][C]70[/C][C]-0.612191949329231[/C][C]-29.2883199265916[/C][C]28.0639360279331[/C][/ROW]
[ROW][C]71[/C][C]-1.46601047043325[/C][C]-33.9390040477738[/C][C]31.0069831069073[/C][/ROW]
[ROW][C]72[/C][C]-2.31982899153728[/C][C]-38.7737804007804[/C][C]34.1341224177058[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294914&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294914&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
617.07217474060697-0.071581598444420414.2159310796584
626.21835621950295-1.6461590224986314.0828714615045
635.36453769839893-3.7548517113439914.4839271081418
644.5107191772949-6.3748785759018315.3963169304916
653.65690065619088-9.4341084673787416.7479097797605
662.80308213508686-12.859711410815918.4658756809896
671.94926361398284-16.594386996861420.4929142248271
681.09544509287881-20.596284736435322.787174922193
690.241626571774791-24.835067605535525.318320749085
70-0.612191949329231-29.288319926591628.0639360279331
71-1.46601047043325-33.939004047773831.0069831069073
72-2.31982899153728-38.773780400780434.1341224177058



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')