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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 11 Dec 2009 05:54:10 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/11/t1260536095mudrt4t5ev04ag7.htm/, Retrieved Mon, 29 Apr 2024 00:29:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66146, Retrieved Mon, 29 Apr 2024 00:29:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD    [Exponential Smoothing] [ws 8 Ad hoc forec...] [2009-12-02 20:19:53] [616e2df490b611f6cb7080068870ecbd]
-   PD      [Exponential Smoothing] [Workshop 9] [2009-12-04 12:15:07] [4fe1472705bb0a32f118ba3ca90ffa8e]
-   PD          [Exponential Smoothing] [WS9] [2009-12-11 12:54:10] [ee8fc1691ecec7724e0ca78f0c288737] [Current]
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Dataseries X:
7.55
7.55
7.59
7.59
7.59
7.57
7.57
7.59
7.6
7.64
7.64
7.76
7.76
7.76
7.77
7.83
7.94
7.94
7.94
8.09
8.18
8.26
8.28
8.28
8.28
8.29
8.3
8.3
8.31
8.33
8.33
8.34
8.48
8.59
8.67
8.67
8.67
8.71
8.72
8.72
8.72
8.74
8.74
8.74
8.74
8.79
8.85
8.86
8.87
8.92
8.96
8.97
8.99
8.98
8.98
9.01
9.01
9.03
9.05
9.05




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66146&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66146&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66146&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.848800087938736
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.848800087938736 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66146&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]0.848800087938736[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66146&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66146&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
alpha0.848800087938736
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137.767.611976880966420.148023119033584
147.767.735081276175690.0249187238243094
157.777.754936108956190.0150638910438081
167.837.811423012455710.0185769875442885
177.947.918252314763190.0217476852368153
187.947.922073349214330.0179266507856743
197.947.96741586091488-0.0274158609148749
208.097.980289430440560.109710569559438
218.188.100265538692930.0797344613070692
228.268.22568016433890.0343198356610923
238.288.261804991763660.0181950082363436
248.288.40836139135682-0.128361391356817
258.288.32404003197007-0.0440400319700682
268.298.261787241691450.0282127583085447
278.38.280495663835110.0195043361648874
288.38.34201160340643-0.0420116034064311
298.318.40140676092787-0.0914067609278693
308.338.306247101132610.0237528988673894
318.338.34917362973838-0.0191736297383756
328.348.39073301192205-0.0507330119220519
338.488.369534760995030.11046523900497
348.598.514748954005710.075251045994289
358.678.582060113797460.0879398862025411
368.678.76881379003755-0.0988137900375463
378.678.72246943279367-0.0524694327936661
388.718.661691964196980.0483080358030215
398.728.694147103543740.0258528964562625
408.728.75183648926944-0.0318364892694394
418.728.81502799922603-0.0950279992260281
428.748.732480997820150.00751900217984769
438.748.75429194053674-0.0142919405367401
448.748.79615133617384-0.0561513361738371
458.748.79515626383475-0.0551562638347498
468.798.79477670626116-0.00477670626116122
478.858.795305006547020.0546949934529781
488.868.92645100310957-0.0664510031095702
498.878.91479209814778-0.0447920981477825
508.928.87490929804960.0450907019504001
518.968.900171014113460.0598289858865417
528.978.97779367639901-0.00779367639900919
538.999.05305911344782-0.0630591134478191
548.989.01251553925291-0.0325155392529144
558.988.99644891115725-0.0164489111572497
569.019.03049561520607-0.0204956152060696
579.019.06028623396056-0.0502862339605645
589.039.07230834976358-0.0423083497635783
599.059.049369183783320.000630816216675711
609.059.11698370075069-0.0669837007506882

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7.76 & 7.61197688096642 & 0.148023119033584 \tabularnewline
14 & 7.76 & 7.73508127617569 & 0.0249187238243094 \tabularnewline
15 & 7.77 & 7.75493610895619 & 0.0150638910438081 \tabularnewline
16 & 7.83 & 7.81142301245571 & 0.0185769875442885 \tabularnewline
17 & 7.94 & 7.91825231476319 & 0.0217476852368153 \tabularnewline
18 & 7.94 & 7.92207334921433 & 0.0179266507856743 \tabularnewline
19 & 7.94 & 7.96741586091488 & -0.0274158609148749 \tabularnewline
20 & 8.09 & 7.98028943044056 & 0.109710569559438 \tabularnewline
21 & 8.18 & 8.10026553869293 & 0.0797344613070692 \tabularnewline
22 & 8.26 & 8.2256801643389 & 0.0343198356610923 \tabularnewline
23 & 8.28 & 8.26180499176366 & 0.0181950082363436 \tabularnewline
24 & 8.28 & 8.40836139135682 & -0.128361391356817 \tabularnewline
25 & 8.28 & 8.32404003197007 & -0.0440400319700682 \tabularnewline
26 & 8.29 & 8.26178724169145 & 0.0282127583085447 \tabularnewline
27 & 8.3 & 8.28049566383511 & 0.0195043361648874 \tabularnewline
28 & 8.3 & 8.34201160340643 & -0.0420116034064311 \tabularnewline
29 & 8.31 & 8.40140676092787 & -0.0914067609278693 \tabularnewline
30 & 8.33 & 8.30624710113261 & 0.0237528988673894 \tabularnewline
31 & 8.33 & 8.34917362973838 & -0.0191736297383756 \tabularnewline
32 & 8.34 & 8.39073301192205 & -0.0507330119220519 \tabularnewline
33 & 8.48 & 8.36953476099503 & 0.11046523900497 \tabularnewline
34 & 8.59 & 8.51474895400571 & 0.075251045994289 \tabularnewline
35 & 8.67 & 8.58206011379746 & 0.0879398862025411 \tabularnewline
36 & 8.67 & 8.76881379003755 & -0.0988137900375463 \tabularnewline
37 & 8.67 & 8.72246943279367 & -0.0524694327936661 \tabularnewline
38 & 8.71 & 8.66169196419698 & 0.0483080358030215 \tabularnewline
39 & 8.72 & 8.69414710354374 & 0.0258528964562625 \tabularnewline
40 & 8.72 & 8.75183648926944 & -0.0318364892694394 \tabularnewline
41 & 8.72 & 8.81502799922603 & -0.0950279992260281 \tabularnewline
42 & 8.74 & 8.73248099782015 & 0.00751900217984769 \tabularnewline
43 & 8.74 & 8.75429194053674 & -0.0142919405367401 \tabularnewline
44 & 8.74 & 8.79615133617384 & -0.0561513361738371 \tabularnewline
45 & 8.74 & 8.79515626383475 & -0.0551562638347498 \tabularnewline
46 & 8.79 & 8.79477670626116 & -0.00477670626116122 \tabularnewline
47 & 8.85 & 8.79530500654702 & 0.0546949934529781 \tabularnewline
48 & 8.86 & 8.92645100310957 & -0.0664510031095702 \tabularnewline
49 & 8.87 & 8.91479209814778 & -0.0447920981477825 \tabularnewline
50 & 8.92 & 8.8749092980496 & 0.0450907019504001 \tabularnewline
51 & 8.96 & 8.90017101411346 & 0.0598289858865417 \tabularnewline
52 & 8.97 & 8.97779367639901 & -0.00779367639900919 \tabularnewline
53 & 8.99 & 9.05305911344782 & -0.0630591134478191 \tabularnewline
54 & 8.98 & 9.01251553925291 & -0.0325155392529144 \tabularnewline
55 & 8.98 & 8.99644891115725 & -0.0164489111572497 \tabularnewline
56 & 9.01 & 9.03049561520607 & -0.0204956152060696 \tabularnewline
57 & 9.01 & 9.06028623396056 & -0.0502862339605645 \tabularnewline
58 & 9.03 & 9.07230834976358 & -0.0423083497635783 \tabularnewline
59 & 9.05 & 9.04936918378332 & 0.000630816216675711 \tabularnewline
60 & 9.05 & 9.11698370075069 & -0.0669837007506882 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66146&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]7.76[/C][C]7.61197688096642[/C][C]0.148023119033584[/C][/ROW]
[ROW][C]14[/C][C]7.76[/C][C]7.73508127617569[/C][C]0.0249187238243094[/C][/ROW]
[ROW][C]15[/C][C]7.77[/C][C]7.75493610895619[/C][C]0.0150638910438081[/C][/ROW]
[ROW][C]16[/C][C]7.83[/C][C]7.81142301245571[/C][C]0.0185769875442885[/C][/ROW]
[ROW][C]17[/C][C]7.94[/C][C]7.91825231476319[/C][C]0.0217476852368153[/C][/ROW]
[ROW][C]18[/C][C]7.94[/C][C]7.92207334921433[/C][C]0.0179266507856743[/C][/ROW]
[ROW][C]19[/C][C]7.94[/C][C]7.96741586091488[/C][C]-0.0274158609148749[/C][/ROW]
[ROW][C]20[/C][C]8.09[/C][C]7.98028943044056[/C][C]0.109710569559438[/C][/ROW]
[ROW][C]21[/C][C]8.18[/C][C]8.10026553869293[/C][C]0.0797344613070692[/C][/ROW]
[ROW][C]22[/C][C]8.26[/C][C]8.2256801643389[/C][C]0.0343198356610923[/C][/ROW]
[ROW][C]23[/C][C]8.28[/C][C]8.26180499176366[/C][C]0.0181950082363436[/C][/ROW]
[ROW][C]24[/C][C]8.28[/C][C]8.40836139135682[/C][C]-0.128361391356817[/C][/ROW]
[ROW][C]25[/C][C]8.28[/C][C]8.32404003197007[/C][C]-0.0440400319700682[/C][/ROW]
[ROW][C]26[/C][C]8.29[/C][C]8.26178724169145[/C][C]0.0282127583085447[/C][/ROW]
[ROW][C]27[/C][C]8.3[/C][C]8.28049566383511[/C][C]0.0195043361648874[/C][/ROW]
[ROW][C]28[/C][C]8.3[/C][C]8.34201160340643[/C][C]-0.0420116034064311[/C][/ROW]
[ROW][C]29[/C][C]8.31[/C][C]8.40140676092787[/C][C]-0.0914067609278693[/C][/ROW]
[ROW][C]30[/C][C]8.33[/C][C]8.30624710113261[/C][C]0.0237528988673894[/C][/ROW]
[ROW][C]31[/C][C]8.33[/C][C]8.34917362973838[/C][C]-0.0191736297383756[/C][/ROW]
[ROW][C]32[/C][C]8.34[/C][C]8.39073301192205[/C][C]-0.0507330119220519[/C][/ROW]
[ROW][C]33[/C][C]8.48[/C][C]8.36953476099503[/C][C]0.11046523900497[/C][/ROW]
[ROW][C]34[/C][C]8.59[/C][C]8.51474895400571[/C][C]0.075251045994289[/C][/ROW]
[ROW][C]35[/C][C]8.67[/C][C]8.58206011379746[/C][C]0.0879398862025411[/C][/ROW]
[ROW][C]36[/C][C]8.67[/C][C]8.76881379003755[/C][C]-0.0988137900375463[/C][/ROW]
[ROW][C]37[/C][C]8.67[/C][C]8.72246943279367[/C][C]-0.0524694327936661[/C][/ROW]
[ROW][C]38[/C][C]8.71[/C][C]8.66169196419698[/C][C]0.0483080358030215[/C][/ROW]
[ROW][C]39[/C][C]8.72[/C][C]8.69414710354374[/C][C]0.0258528964562625[/C][/ROW]
[ROW][C]40[/C][C]8.72[/C][C]8.75183648926944[/C][C]-0.0318364892694394[/C][/ROW]
[ROW][C]41[/C][C]8.72[/C][C]8.81502799922603[/C][C]-0.0950279992260281[/C][/ROW]
[ROW][C]42[/C][C]8.74[/C][C]8.73248099782015[/C][C]0.00751900217984769[/C][/ROW]
[ROW][C]43[/C][C]8.74[/C][C]8.75429194053674[/C][C]-0.0142919405367401[/C][/ROW]
[ROW][C]44[/C][C]8.74[/C][C]8.79615133617384[/C][C]-0.0561513361738371[/C][/ROW]
[ROW][C]45[/C][C]8.74[/C][C]8.79515626383475[/C][C]-0.0551562638347498[/C][/ROW]
[ROW][C]46[/C][C]8.79[/C][C]8.79477670626116[/C][C]-0.00477670626116122[/C][/ROW]
[ROW][C]47[/C][C]8.85[/C][C]8.79530500654702[/C][C]0.0546949934529781[/C][/ROW]
[ROW][C]48[/C][C]8.86[/C][C]8.92645100310957[/C][C]-0.0664510031095702[/C][/ROW]
[ROW][C]49[/C][C]8.87[/C][C]8.91479209814778[/C][C]-0.0447920981477825[/C][/ROW]
[ROW][C]50[/C][C]8.92[/C][C]8.8749092980496[/C][C]0.0450907019504001[/C][/ROW]
[ROW][C]51[/C][C]8.96[/C][C]8.90017101411346[/C][C]0.0598289858865417[/C][/ROW]
[ROW][C]52[/C][C]8.97[/C][C]8.97779367639901[/C][C]-0.00779367639900919[/C][/ROW]
[ROW][C]53[/C][C]8.99[/C][C]9.05305911344782[/C][C]-0.0630591134478191[/C][/ROW]
[ROW][C]54[/C][C]8.98[/C][C]9.01251553925291[/C][C]-0.0325155392529144[/C][/ROW]
[ROW][C]55[/C][C]8.98[/C][C]8.99644891115725[/C][C]-0.0164489111572497[/C][/ROW]
[ROW][C]56[/C][C]9.01[/C][C]9.03049561520607[/C][C]-0.0204956152060696[/C][/ROW]
[ROW][C]57[/C][C]9.01[/C][C]9.06028623396056[/C][C]-0.0502862339605645[/C][/ROW]
[ROW][C]58[/C][C]9.03[/C][C]9.07230834976358[/C][C]-0.0423083497635783[/C][/ROW]
[ROW][C]59[/C][C]9.05[/C][C]9.04936918378332[/C][C]0.000630816216675711[/C][/ROW]
[ROW][C]60[/C][C]9.05[/C][C]9.11698370075069[/C][C]-0.0669837007506882[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66146&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66146&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
137.767.611976880966420.148023119033584
147.767.735081276175690.0249187238243094
157.777.754936108956190.0150638910438081
167.837.811423012455710.0185769875442885
177.947.918252314763190.0217476852368153
187.947.922073349214330.0179266507856743
197.947.96741586091488-0.0274158609148749
208.097.980289430440560.109710569559438
218.188.100265538692930.0797344613070692
228.268.22568016433890.0343198356610923
238.288.261804991763660.0181950082363436
248.288.40836139135682-0.128361391356817
258.288.32404003197007-0.0440400319700682
268.298.261787241691450.0282127583085447
278.38.280495663835110.0195043361648874
288.38.34201160340643-0.0420116034064311
298.318.40140676092787-0.0914067609278693
308.338.306247101132610.0237528988673894
318.338.34917362973838-0.0191736297383756
328.348.39073301192205-0.0507330119220519
338.488.369534760995030.11046523900497
348.598.514748954005710.075251045994289
358.678.582060113797460.0879398862025411
368.678.76881379003755-0.0988137900375463
378.678.72246943279367-0.0524694327936661
388.718.661691964196980.0483080358030215
398.728.694147103543740.0258528964562625
408.728.75183648926944-0.0318364892694394
418.728.81502799922603-0.0950279992260281
428.748.732480997820150.00751900217984769
438.748.75429194053674-0.0142919405367401
448.748.79615133617384-0.0561513361738371
458.748.79515626383475-0.0551562638347498
468.798.79477670626116-0.00477670626116122
478.858.795305006547020.0546949934529781
488.868.92645100310957-0.0664510031095702
498.878.91479209814778-0.0447920981477825
508.928.87490929804960.0450907019504001
518.968.900171014113460.0598289858865417
528.978.97779367639901-0.00779367639900919
538.999.05305911344782-0.0630591134478191
548.989.01251553925291-0.0325155392529144
558.988.99644891115725-0.0164489111572497
569.019.03049561520607-0.0204956152060696
579.019.06028623396056-0.0502862339605645
589.039.07230834976358-0.0423083497635783
599.059.049369183783320.000630816216675711
609.059.11698370075069-0.0669837007506882







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
619.108442107179988.992462453719899.22442176064008
629.119551629611448.967582370731469.2715208884914
639.107727604705698.927188277568049.28826693184334
649.124066080206628.918693333277279.32943882713597
659.198220453779278.96972050101559.42672040654304
669.215437309706998.96697684718079.46389777223328
679.228886407350848.96210297512729.49566983957449
689.276664333663258.991928557709989.5614001096165
699.319583403997999.018048243197869.6211185647981
709.3762372439299.058357482671649.69411700518637
719.395164244094149.062843891338889.7274845968494
729.452842139932265.9652656477190112.9404186321455

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 9.10844210717998 & 8.99246245371989 & 9.22442176064008 \tabularnewline
62 & 9.11955162961144 & 8.96758237073146 & 9.2715208884914 \tabularnewline
63 & 9.10772760470569 & 8.92718827756804 & 9.28826693184334 \tabularnewline
64 & 9.12406608020662 & 8.91869333327727 & 9.32943882713597 \tabularnewline
65 & 9.19822045377927 & 8.9697205010155 & 9.42672040654304 \tabularnewline
66 & 9.21543730970699 & 8.9669768471807 & 9.46389777223328 \tabularnewline
67 & 9.22888640735084 & 8.9621029751272 & 9.49566983957449 \tabularnewline
68 & 9.27666433366325 & 8.99192855770998 & 9.5614001096165 \tabularnewline
69 & 9.31958340399799 & 9.01804824319786 & 9.6211185647981 \tabularnewline
70 & 9.376237243929 & 9.05835748267164 & 9.69411700518637 \tabularnewline
71 & 9.39516424409414 & 9.06284389133888 & 9.7274845968494 \tabularnewline
72 & 9.45284213993226 & 5.96526564771901 & 12.9404186321455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66146&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]9.10844210717998[/C][C]8.99246245371989[/C][C]9.22442176064008[/C][/ROW]
[ROW][C]62[/C][C]9.11955162961144[/C][C]8.96758237073146[/C][C]9.2715208884914[/C][/ROW]
[ROW][C]63[/C][C]9.10772760470569[/C][C]8.92718827756804[/C][C]9.28826693184334[/C][/ROW]
[ROW][C]64[/C][C]9.12406608020662[/C][C]8.91869333327727[/C][C]9.32943882713597[/C][/ROW]
[ROW][C]65[/C][C]9.19822045377927[/C][C]8.9697205010155[/C][C]9.42672040654304[/C][/ROW]
[ROW][C]66[/C][C]9.21543730970699[/C][C]8.9669768471807[/C][C]9.46389777223328[/C][/ROW]
[ROW][C]67[/C][C]9.22888640735084[/C][C]8.9621029751272[/C][C]9.49566983957449[/C][/ROW]
[ROW][C]68[/C][C]9.27666433366325[/C][C]8.99192855770998[/C][C]9.5614001096165[/C][/ROW]
[ROW][C]69[/C][C]9.31958340399799[/C][C]9.01804824319786[/C][C]9.6211185647981[/C][/ROW]
[ROW][C]70[/C][C]9.376237243929[/C][C]9.05835748267164[/C][C]9.69411700518637[/C][/ROW]
[ROW][C]71[/C][C]9.39516424409414[/C][C]9.06284389133888[/C][C]9.7274845968494[/C][/ROW]
[ROW][C]72[/C][C]9.45284213993226[/C][C]5.96526564771901[/C][C]12.9404186321455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66146&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66146&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
619.108442107179988.992462453719899.22442176064008
629.119551629611448.967582370731469.2715208884914
639.107727604705698.927188277568049.28826693184334
649.124066080206628.918693333277279.32943882713597
659.198220453779278.96972050101559.42672040654304
669.215437309706998.96697684718079.46389777223328
679.228886407350848.96210297512729.49566983957449
689.276664333663258.991928557709989.5614001096165
699.319583403997999.018048243197869.6211185647981
709.3762372439299.058357482671649.69411700518637
719.395164244094149.062843891338889.7274845968494
729.452842139932265.9652656477190112.9404186321455



Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')