Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 17 Jan 2009 14:19:08 -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/Jan/17/t1232227383lnitr6p6ur7nxsf.htm/, Retrieved Mon, 29 Apr 2024 14:16:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36927, Retrieved Mon, 29 Apr 2024 14:16:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact205
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 - oefen...] [2009-01-17 21:19:08] [be6d97e5c18f42f870a86936f130440b] [Current]
Feedback Forum

Post a new message
Dataseries X:
0.7200
0.7400
0.7400
0.7400
0.7400
0.7400
0.7400
0.7400
0.7400
0.7400
0.7400
0.7400
0.7400
0.7500
0.7500
0.7500
0.7500
0.7500
0.7500
0.7500
0.7500
0.7500
0.7500
0.7500
0.7500
0.7600
0.7600
0.7600
0.7600
0.7600
0.7600
0.7600
0.7600
0.7600
0.7600
0.7600
0.7600
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.7800
0.8000
0.8000
0.8000
0.8000
0.8000
0.8000
0.8000
0.8000
0.8000
0.8000
0.8000
0.8000
0.8100
0.8100
0.8100
0.8100
0.8100
0.8100
0.8100
0.8100
0.8100
0.8100
0.8100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36927&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36927&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36927&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 time5 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999398485780202
beta0.00154973746659664
gamma0.00817138256199028

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999398485780202 \tabularnewline
beta & 0.00154973746659664 \tabularnewline
gamma & 0.00817138256199028 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36927&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]0.999398485780202[/C][/ROW]
[ROW][C]beta[/C][C]0.00154973746659664[/C][/ROW]
[ROW][C]gamma[/C][C]0.00817138256199028[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36927&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36927&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
alpha0.999398485780202
beta0.00154973746659664
gamma0.00817138256199028







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
130.740.7348424145299150.00515758547008516
140.750.75002091137562-2.0911375620436e-05
150.750.750023993927462-2.39939274615519e-05
160.750.750023958619739-2.39586197388064e-05
170.750.750023921491264-2.39214912640673e-05
180.750.750023884419199-2.38844191986498e-05
190.750.750440514071252-0.000440514071251785
200.750.749606749076060.000393250923939936
210.750.750023523290333-2.35232903325056e-05
220.750.750023737552953-2.37375529525963e-05
230.750.750023700916987-2.37009169874458e-05
240.750.750023664186845-2.36641868449627e-05
250.750.750023652864112-2.36528641124334e-05
260.760.76002356541968-2.35654196800716e-05
270.760.760023554307045-2.35543070453703e-05
280.760.760023517834651-2.35178346509324e-05
290.760.760023481388175-2.3481388174873e-05
300.760.760023444998153-2.34449981534324e-05
310.760.760440073283193-0.000440073283192954
320.760.7596063151158170.000393684884183121
330.760.760023083859663-2.30838596626537e-05
340.760.760023300847061-2.33008470613694e-05
350.760.76002326489034-2.32648903406574e-05
360.760.760023228835928-2.32288359277577e-05
370.760.76002321818775-2.32181877504178e-05
380.780.7700231314173270.009976868582673
390.780.780032593887485-3.25938874846665e-05
400.780.780038564255358-3.85642553576426e-05
410.780.780038508118105-3.85081181053515e-05
420.780.780038448442761-3.84484427609078e-05
430.780.780455051428388-0.000455051428388198
440.780.7796212761934670.00037872380653281
450.780.780038015608657-3.8015608656905e-05
460.780.780038211499479-3.82114994789129e-05
470.780.780038152437614-3.81524376142917e-05
480.780.780038093311392-3.80933113920401e-05
490.780.780038059627034-3.80596270337374e-05
500.780.790037999008657-0.0100379990086565
510.780.780028394295395-2.83942953950289e-05
520.780.780022378583233-2.23785832327295e-05
530.780.780022340334259-2.23403342589634e-05
540.780.780022305710441-2.23057104408175e-05
550.780.780438931665105-0.000438931665104558
560.780.7796051875562370.000394812443763382
570.780.780021945761782-2.19457617823826e-05
580.780.780022168600366-2.21686003664123e-05
590.780.780022134403291-2.21344032913517e-05
600.780.780022100100842-2.21001008420263e-05
610.780.78002209120166-2.20912016595243e-05
620.80.7900220061782770.00997799382172326
630.80.800031470392236-3.14703922359438e-05
640.80.800037442500757-3.74425007569901e-05
650.80.800037388102172-3.73881021722422e-05
660.80.80003733016256-3.733016255969e-05
670.80.800453930785277-0.000453930785276779
680.80.7996201695762770.000379830423722916
690.80.800036898420833-3.68984208327650e-05
700.80.800037100130354-3.71001303544061e-05
710.80.800037042795801-3.70427958008568e-05
720.80.800036985389237-3.69853892373539e-05
730.80.80003695342162-3.69534216195788e-05
740.810.810036894518078-3.6894518078201e-05
750.810.81003676442704-3.67644270402590e-05
760.810.810036756592016-3.67565920158519e-05
770.810.81003669968837-3.66996883707227e-05
780.810.810036642813488-3.66428134876973e-05
790.810.810453242453454-0.000453242453453795
800.810.8096194884557370.000380511544263107
810.810.810036212213141-3.62122131412068e-05
820.810.81003641702972-3.64170297201261e-05
830.810.810036360756299-3.63607562987589e-05
840.810.81003630440672-3.63044067202001e-05

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.74 & 0.734842414529915 & 0.00515758547008516 \tabularnewline
14 & 0.75 & 0.75002091137562 & -2.0911375620436e-05 \tabularnewline
15 & 0.75 & 0.750023993927462 & -2.39939274615519e-05 \tabularnewline
16 & 0.75 & 0.750023958619739 & -2.39586197388064e-05 \tabularnewline
17 & 0.75 & 0.750023921491264 & -2.39214912640673e-05 \tabularnewline
18 & 0.75 & 0.750023884419199 & -2.38844191986498e-05 \tabularnewline
19 & 0.75 & 0.750440514071252 & -0.000440514071251785 \tabularnewline
20 & 0.75 & 0.74960674907606 & 0.000393250923939936 \tabularnewline
21 & 0.75 & 0.750023523290333 & -2.35232903325056e-05 \tabularnewline
22 & 0.75 & 0.750023737552953 & -2.37375529525963e-05 \tabularnewline
23 & 0.75 & 0.750023700916987 & -2.37009169874458e-05 \tabularnewline
24 & 0.75 & 0.750023664186845 & -2.36641868449627e-05 \tabularnewline
25 & 0.75 & 0.750023652864112 & -2.36528641124334e-05 \tabularnewline
26 & 0.76 & 0.76002356541968 & -2.35654196800716e-05 \tabularnewline
27 & 0.76 & 0.760023554307045 & -2.35543070453703e-05 \tabularnewline
28 & 0.76 & 0.760023517834651 & -2.35178346509324e-05 \tabularnewline
29 & 0.76 & 0.760023481388175 & -2.3481388174873e-05 \tabularnewline
30 & 0.76 & 0.760023444998153 & -2.34449981534324e-05 \tabularnewline
31 & 0.76 & 0.760440073283193 & -0.000440073283192954 \tabularnewline
32 & 0.76 & 0.759606315115817 & 0.000393684884183121 \tabularnewline
33 & 0.76 & 0.760023083859663 & -2.30838596626537e-05 \tabularnewline
34 & 0.76 & 0.760023300847061 & -2.33008470613694e-05 \tabularnewline
35 & 0.76 & 0.76002326489034 & -2.32648903406574e-05 \tabularnewline
36 & 0.76 & 0.760023228835928 & -2.32288359277577e-05 \tabularnewline
37 & 0.76 & 0.76002321818775 & -2.32181877504178e-05 \tabularnewline
38 & 0.78 & 0.770023131417327 & 0.009976868582673 \tabularnewline
39 & 0.78 & 0.780032593887485 & -3.25938874846665e-05 \tabularnewline
40 & 0.78 & 0.780038564255358 & -3.85642553576426e-05 \tabularnewline
41 & 0.78 & 0.780038508118105 & -3.85081181053515e-05 \tabularnewline
42 & 0.78 & 0.780038448442761 & -3.84484427609078e-05 \tabularnewline
43 & 0.78 & 0.780455051428388 & -0.000455051428388198 \tabularnewline
44 & 0.78 & 0.779621276193467 & 0.00037872380653281 \tabularnewline
45 & 0.78 & 0.780038015608657 & -3.8015608656905e-05 \tabularnewline
46 & 0.78 & 0.780038211499479 & -3.82114994789129e-05 \tabularnewline
47 & 0.78 & 0.780038152437614 & -3.81524376142917e-05 \tabularnewline
48 & 0.78 & 0.780038093311392 & -3.80933113920401e-05 \tabularnewline
49 & 0.78 & 0.780038059627034 & -3.80596270337374e-05 \tabularnewline
50 & 0.78 & 0.790037999008657 & -0.0100379990086565 \tabularnewline
51 & 0.78 & 0.780028394295395 & -2.83942953950289e-05 \tabularnewline
52 & 0.78 & 0.780022378583233 & -2.23785832327295e-05 \tabularnewline
53 & 0.78 & 0.780022340334259 & -2.23403342589634e-05 \tabularnewline
54 & 0.78 & 0.780022305710441 & -2.23057104408175e-05 \tabularnewline
55 & 0.78 & 0.780438931665105 & -0.000438931665104558 \tabularnewline
56 & 0.78 & 0.779605187556237 & 0.000394812443763382 \tabularnewline
57 & 0.78 & 0.780021945761782 & -2.19457617823826e-05 \tabularnewline
58 & 0.78 & 0.780022168600366 & -2.21686003664123e-05 \tabularnewline
59 & 0.78 & 0.780022134403291 & -2.21344032913517e-05 \tabularnewline
60 & 0.78 & 0.780022100100842 & -2.21001008420263e-05 \tabularnewline
61 & 0.78 & 0.78002209120166 & -2.20912016595243e-05 \tabularnewline
62 & 0.8 & 0.790022006178277 & 0.00997799382172326 \tabularnewline
63 & 0.8 & 0.800031470392236 & -3.14703922359438e-05 \tabularnewline
64 & 0.8 & 0.800037442500757 & -3.74425007569901e-05 \tabularnewline
65 & 0.8 & 0.800037388102172 & -3.73881021722422e-05 \tabularnewline
66 & 0.8 & 0.80003733016256 & -3.733016255969e-05 \tabularnewline
67 & 0.8 & 0.800453930785277 & -0.000453930785276779 \tabularnewline
68 & 0.8 & 0.799620169576277 & 0.000379830423722916 \tabularnewline
69 & 0.8 & 0.800036898420833 & -3.68984208327650e-05 \tabularnewline
70 & 0.8 & 0.800037100130354 & -3.71001303544061e-05 \tabularnewline
71 & 0.8 & 0.800037042795801 & -3.70427958008568e-05 \tabularnewline
72 & 0.8 & 0.800036985389237 & -3.69853892373539e-05 \tabularnewline
73 & 0.8 & 0.80003695342162 & -3.69534216195788e-05 \tabularnewline
74 & 0.81 & 0.810036894518078 & -3.6894518078201e-05 \tabularnewline
75 & 0.81 & 0.81003676442704 & -3.67644270402590e-05 \tabularnewline
76 & 0.81 & 0.810036756592016 & -3.67565920158519e-05 \tabularnewline
77 & 0.81 & 0.81003669968837 & -3.66996883707227e-05 \tabularnewline
78 & 0.81 & 0.810036642813488 & -3.66428134876973e-05 \tabularnewline
79 & 0.81 & 0.810453242453454 & -0.000453242453453795 \tabularnewline
80 & 0.81 & 0.809619488455737 & 0.000380511544263107 \tabularnewline
81 & 0.81 & 0.810036212213141 & -3.62122131412068e-05 \tabularnewline
82 & 0.81 & 0.81003641702972 & -3.64170297201261e-05 \tabularnewline
83 & 0.81 & 0.810036360756299 & -3.63607562987589e-05 \tabularnewline
84 & 0.81 & 0.81003630440672 & -3.63044067202001e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36927&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]0.74[/C][C]0.734842414529915[/C][C]0.00515758547008516[/C][/ROW]
[ROW][C]14[/C][C]0.75[/C][C]0.75002091137562[/C][C]-2.0911375620436e-05[/C][/ROW]
[ROW][C]15[/C][C]0.75[/C][C]0.750023993927462[/C][C]-2.39939274615519e-05[/C][/ROW]
[ROW][C]16[/C][C]0.75[/C][C]0.750023958619739[/C][C]-2.39586197388064e-05[/C][/ROW]
[ROW][C]17[/C][C]0.75[/C][C]0.750023921491264[/C][C]-2.39214912640673e-05[/C][/ROW]
[ROW][C]18[/C][C]0.75[/C][C]0.750023884419199[/C][C]-2.38844191986498e-05[/C][/ROW]
[ROW][C]19[/C][C]0.75[/C][C]0.750440514071252[/C][C]-0.000440514071251785[/C][/ROW]
[ROW][C]20[/C][C]0.75[/C][C]0.74960674907606[/C][C]0.000393250923939936[/C][/ROW]
[ROW][C]21[/C][C]0.75[/C][C]0.750023523290333[/C][C]-2.35232903325056e-05[/C][/ROW]
[ROW][C]22[/C][C]0.75[/C][C]0.750023737552953[/C][C]-2.37375529525963e-05[/C][/ROW]
[ROW][C]23[/C][C]0.75[/C][C]0.750023700916987[/C][C]-2.37009169874458e-05[/C][/ROW]
[ROW][C]24[/C][C]0.75[/C][C]0.750023664186845[/C][C]-2.36641868449627e-05[/C][/ROW]
[ROW][C]25[/C][C]0.75[/C][C]0.750023652864112[/C][C]-2.36528641124334e-05[/C][/ROW]
[ROW][C]26[/C][C]0.76[/C][C]0.76002356541968[/C][C]-2.35654196800716e-05[/C][/ROW]
[ROW][C]27[/C][C]0.76[/C][C]0.760023554307045[/C][C]-2.35543070453703e-05[/C][/ROW]
[ROW][C]28[/C][C]0.76[/C][C]0.760023517834651[/C][C]-2.35178346509324e-05[/C][/ROW]
[ROW][C]29[/C][C]0.76[/C][C]0.760023481388175[/C][C]-2.3481388174873e-05[/C][/ROW]
[ROW][C]30[/C][C]0.76[/C][C]0.760023444998153[/C][C]-2.34449981534324e-05[/C][/ROW]
[ROW][C]31[/C][C]0.76[/C][C]0.760440073283193[/C][C]-0.000440073283192954[/C][/ROW]
[ROW][C]32[/C][C]0.76[/C][C]0.759606315115817[/C][C]0.000393684884183121[/C][/ROW]
[ROW][C]33[/C][C]0.76[/C][C]0.760023083859663[/C][C]-2.30838596626537e-05[/C][/ROW]
[ROW][C]34[/C][C]0.76[/C][C]0.760023300847061[/C][C]-2.33008470613694e-05[/C][/ROW]
[ROW][C]35[/C][C]0.76[/C][C]0.76002326489034[/C][C]-2.32648903406574e-05[/C][/ROW]
[ROW][C]36[/C][C]0.76[/C][C]0.760023228835928[/C][C]-2.32288359277577e-05[/C][/ROW]
[ROW][C]37[/C][C]0.76[/C][C]0.76002321818775[/C][C]-2.32181877504178e-05[/C][/ROW]
[ROW][C]38[/C][C]0.78[/C][C]0.770023131417327[/C][C]0.009976868582673[/C][/ROW]
[ROW][C]39[/C][C]0.78[/C][C]0.780032593887485[/C][C]-3.25938874846665e-05[/C][/ROW]
[ROW][C]40[/C][C]0.78[/C][C]0.780038564255358[/C][C]-3.85642553576426e-05[/C][/ROW]
[ROW][C]41[/C][C]0.78[/C][C]0.780038508118105[/C][C]-3.85081181053515e-05[/C][/ROW]
[ROW][C]42[/C][C]0.78[/C][C]0.780038448442761[/C][C]-3.84484427609078e-05[/C][/ROW]
[ROW][C]43[/C][C]0.78[/C][C]0.780455051428388[/C][C]-0.000455051428388198[/C][/ROW]
[ROW][C]44[/C][C]0.78[/C][C]0.779621276193467[/C][C]0.00037872380653281[/C][/ROW]
[ROW][C]45[/C][C]0.78[/C][C]0.780038015608657[/C][C]-3.8015608656905e-05[/C][/ROW]
[ROW][C]46[/C][C]0.78[/C][C]0.780038211499479[/C][C]-3.82114994789129e-05[/C][/ROW]
[ROW][C]47[/C][C]0.78[/C][C]0.780038152437614[/C][C]-3.81524376142917e-05[/C][/ROW]
[ROW][C]48[/C][C]0.78[/C][C]0.780038093311392[/C][C]-3.80933113920401e-05[/C][/ROW]
[ROW][C]49[/C][C]0.78[/C][C]0.780038059627034[/C][C]-3.80596270337374e-05[/C][/ROW]
[ROW][C]50[/C][C]0.78[/C][C]0.790037999008657[/C][C]-0.0100379990086565[/C][/ROW]
[ROW][C]51[/C][C]0.78[/C][C]0.780028394295395[/C][C]-2.83942953950289e-05[/C][/ROW]
[ROW][C]52[/C][C]0.78[/C][C]0.780022378583233[/C][C]-2.23785832327295e-05[/C][/ROW]
[ROW][C]53[/C][C]0.78[/C][C]0.780022340334259[/C][C]-2.23403342589634e-05[/C][/ROW]
[ROW][C]54[/C][C]0.78[/C][C]0.780022305710441[/C][C]-2.23057104408175e-05[/C][/ROW]
[ROW][C]55[/C][C]0.78[/C][C]0.780438931665105[/C][C]-0.000438931665104558[/C][/ROW]
[ROW][C]56[/C][C]0.78[/C][C]0.779605187556237[/C][C]0.000394812443763382[/C][/ROW]
[ROW][C]57[/C][C]0.78[/C][C]0.780021945761782[/C][C]-2.19457617823826e-05[/C][/ROW]
[ROW][C]58[/C][C]0.78[/C][C]0.780022168600366[/C][C]-2.21686003664123e-05[/C][/ROW]
[ROW][C]59[/C][C]0.78[/C][C]0.780022134403291[/C][C]-2.21344032913517e-05[/C][/ROW]
[ROW][C]60[/C][C]0.78[/C][C]0.780022100100842[/C][C]-2.21001008420263e-05[/C][/ROW]
[ROW][C]61[/C][C]0.78[/C][C]0.78002209120166[/C][C]-2.20912016595243e-05[/C][/ROW]
[ROW][C]62[/C][C]0.8[/C][C]0.790022006178277[/C][C]0.00997799382172326[/C][/ROW]
[ROW][C]63[/C][C]0.8[/C][C]0.800031470392236[/C][C]-3.14703922359438e-05[/C][/ROW]
[ROW][C]64[/C][C]0.8[/C][C]0.800037442500757[/C][C]-3.74425007569901e-05[/C][/ROW]
[ROW][C]65[/C][C]0.8[/C][C]0.800037388102172[/C][C]-3.73881021722422e-05[/C][/ROW]
[ROW][C]66[/C][C]0.8[/C][C]0.80003733016256[/C][C]-3.733016255969e-05[/C][/ROW]
[ROW][C]67[/C][C]0.8[/C][C]0.800453930785277[/C][C]-0.000453930785276779[/C][/ROW]
[ROW][C]68[/C][C]0.8[/C][C]0.799620169576277[/C][C]0.000379830423722916[/C][/ROW]
[ROW][C]69[/C][C]0.8[/C][C]0.800036898420833[/C][C]-3.68984208327650e-05[/C][/ROW]
[ROW][C]70[/C][C]0.8[/C][C]0.800037100130354[/C][C]-3.71001303544061e-05[/C][/ROW]
[ROW][C]71[/C][C]0.8[/C][C]0.800037042795801[/C][C]-3.70427958008568e-05[/C][/ROW]
[ROW][C]72[/C][C]0.8[/C][C]0.800036985389237[/C][C]-3.69853892373539e-05[/C][/ROW]
[ROW][C]73[/C][C]0.8[/C][C]0.80003695342162[/C][C]-3.69534216195788e-05[/C][/ROW]
[ROW][C]74[/C][C]0.81[/C][C]0.810036894518078[/C][C]-3.6894518078201e-05[/C][/ROW]
[ROW][C]75[/C][C]0.81[/C][C]0.81003676442704[/C][C]-3.67644270402590e-05[/C][/ROW]
[ROW][C]76[/C][C]0.81[/C][C]0.810036756592016[/C][C]-3.67565920158519e-05[/C][/ROW]
[ROW][C]77[/C][C]0.81[/C][C]0.81003669968837[/C][C]-3.66996883707227e-05[/C][/ROW]
[ROW][C]78[/C][C]0.81[/C][C]0.810036642813488[/C][C]-3.66428134876973e-05[/C][/ROW]
[ROW][C]79[/C][C]0.81[/C][C]0.810453242453454[/C][C]-0.000453242453453795[/C][/ROW]
[ROW][C]80[/C][C]0.81[/C][C]0.809619488455737[/C][C]0.000380511544263107[/C][/ROW]
[ROW][C]81[/C][C]0.81[/C][C]0.810036212213141[/C][C]-3.62122131412068e-05[/C][/ROW]
[ROW][C]82[/C][C]0.81[/C][C]0.81003641702972[/C][C]-3.64170297201261e-05[/C][/ROW]
[ROW][C]83[/C][C]0.81[/C][C]0.810036360756299[/C][C]-3.63607562987589e-05[/C][/ROW]
[ROW][C]84[/C][C]0.81[/C][C]0.81003630440672[/C][C]-3.63044067202001e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36927&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36927&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
130.740.7348424145299150.00515758547008516
140.750.75002091137562-2.0911375620436e-05
150.750.750023993927462-2.39939274615519e-05
160.750.750023958619739-2.39586197388064e-05
170.750.750023921491264-2.39214912640673e-05
180.750.750023884419199-2.38844191986498e-05
190.750.750440514071252-0.000440514071251785
200.750.749606749076060.000393250923939936
210.750.750023523290333-2.35232903325056e-05
220.750.750023737552953-2.37375529525963e-05
230.750.750023700916987-2.37009169874458e-05
240.750.750023664186845-2.36641868449627e-05
250.750.750023652864112-2.36528641124334e-05
260.760.76002356541968-2.35654196800716e-05
270.760.760023554307045-2.35543070453703e-05
280.760.760023517834651-2.35178346509324e-05
290.760.760023481388175-2.3481388174873e-05
300.760.760023444998153-2.34449981534324e-05
310.760.760440073283193-0.000440073283192954
320.760.7596063151158170.000393684884183121
330.760.760023083859663-2.30838596626537e-05
340.760.760023300847061-2.33008470613694e-05
350.760.76002326489034-2.32648903406574e-05
360.760.760023228835928-2.32288359277577e-05
370.760.76002321818775-2.32181877504178e-05
380.780.7700231314173270.009976868582673
390.780.780032593887485-3.25938874846665e-05
400.780.780038564255358-3.85642553576426e-05
410.780.780038508118105-3.85081181053515e-05
420.780.780038448442761-3.84484427609078e-05
430.780.780455051428388-0.000455051428388198
440.780.7796212761934670.00037872380653281
450.780.780038015608657-3.8015608656905e-05
460.780.780038211499479-3.82114994789129e-05
470.780.780038152437614-3.81524376142917e-05
480.780.780038093311392-3.80933113920401e-05
490.780.780038059627034-3.80596270337374e-05
500.780.790037999008657-0.0100379990086565
510.780.780028394295395-2.83942953950289e-05
520.780.780022378583233-2.23785832327295e-05
530.780.780022340334259-2.23403342589634e-05
540.780.780022305710441-2.23057104408175e-05
550.780.780438931665105-0.000438931665104558
560.780.7796051875562370.000394812443763382
570.780.780021945761782-2.19457617823826e-05
580.780.780022168600366-2.21686003664123e-05
590.780.780022134403291-2.21344032913517e-05
600.780.780022100100842-2.21001008420263e-05
610.780.78002209120166-2.20912016595243e-05
620.80.7900220061782770.00997799382172326
630.80.800031470392236-3.14703922359438e-05
640.80.800037442500757-3.74425007569901e-05
650.80.800037388102172-3.73881021722422e-05
660.80.80003733016256-3.733016255969e-05
670.80.800453930785277-0.000453930785276779
680.80.7996201695762770.000379830423722916
690.80.800036898420833-3.68984208327650e-05
700.80.800037100130354-3.71001303544061e-05
710.80.800037042795801-3.70427958008568e-05
720.80.800036985389237-3.69853892373539e-05
730.80.80003695342162-3.69534216195788e-05
740.810.810036894518078-3.6894518078201e-05
750.810.81003676442704-3.67644270402590e-05
760.810.810036756592016-3.67565920158519e-05
770.810.81003669968837-3.66996883707227e-05
780.810.810036642813488-3.66428134876973e-05
790.810.810453242453454-0.000453242453453795
800.810.8096194884557370.000380511544263107
810.810.810036212213141-3.62122131412068e-05
820.810.81003641702972-3.64170297201261e-05
830.810.810036360756299-3.63607562987589e-05
840.810.81003630440672-3.63044067202001e-05







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
850.8100362734943220.8058348901585020.814237656830142
860.8200725235005020.8141280553025810.826016991698424
870.820108700593850.8128233348263250.827394066361375
880.8201449268707630.8117264196841280.828563434057397
890.8201811531777880.8107619752149380.829600331140637
900.8202173794848290.8098914127124060.830543346257252
910.8206702601706790.8095084781980350.831832042143323
920.820289844398250.80834830516580.8322313836307
930.8203260584134720.8076504668384630.83300164998848
940.8203622847129480.8069908132494530.833733756176443
950.8203985110199740.8063636499272040.834433372112744
960.8204347373270030.805764565656410.835104908997596

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 0.810036273494322 & 0.805834890158502 & 0.814237656830142 \tabularnewline
86 & 0.820072523500502 & 0.814128055302581 & 0.826016991698424 \tabularnewline
87 & 0.82010870059385 & 0.812823334826325 & 0.827394066361375 \tabularnewline
88 & 0.820144926870763 & 0.811726419684128 & 0.828563434057397 \tabularnewline
89 & 0.820181153177788 & 0.810761975214938 & 0.829600331140637 \tabularnewline
90 & 0.820217379484829 & 0.809891412712406 & 0.830543346257252 \tabularnewline
91 & 0.820670260170679 & 0.809508478198035 & 0.831832042143323 \tabularnewline
92 & 0.82028984439825 & 0.8083483051658 & 0.8322313836307 \tabularnewline
93 & 0.820326058413472 & 0.807650466838463 & 0.83300164998848 \tabularnewline
94 & 0.820362284712948 & 0.806990813249453 & 0.833733756176443 \tabularnewline
95 & 0.820398511019974 & 0.806363649927204 & 0.834433372112744 \tabularnewline
96 & 0.820434737327003 & 0.80576456565641 & 0.835104908997596 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36927&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]85[/C][C]0.810036273494322[/C][C]0.805834890158502[/C][C]0.814237656830142[/C][/ROW]
[ROW][C]86[/C][C]0.820072523500502[/C][C]0.814128055302581[/C][C]0.826016991698424[/C][/ROW]
[ROW][C]87[/C][C]0.82010870059385[/C][C]0.812823334826325[/C][C]0.827394066361375[/C][/ROW]
[ROW][C]88[/C][C]0.820144926870763[/C][C]0.811726419684128[/C][C]0.828563434057397[/C][/ROW]
[ROW][C]89[/C][C]0.820181153177788[/C][C]0.810761975214938[/C][C]0.829600331140637[/C][/ROW]
[ROW][C]90[/C][C]0.820217379484829[/C][C]0.809891412712406[/C][C]0.830543346257252[/C][/ROW]
[ROW][C]91[/C][C]0.820670260170679[/C][C]0.809508478198035[/C][C]0.831832042143323[/C][/ROW]
[ROW][C]92[/C][C]0.82028984439825[/C][C]0.8083483051658[/C][C]0.8322313836307[/C][/ROW]
[ROW][C]93[/C][C]0.820326058413472[/C][C]0.807650466838463[/C][C]0.83300164998848[/C][/ROW]
[ROW][C]94[/C][C]0.820362284712948[/C][C]0.806990813249453[/C][C]0.833733756176443[/C][/ROW]
[ROW][C]95[/C][C]0.820398511019974[/C][C]0.806363649927204[/C][C]0.834433372112744[/C][/ROW]
[ROW][C]96[/C][C]0.820434737327003[/C][C]0.80576456565641[/C][C]0.835104908997596[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36927&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36927&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
850.8100362734943220.8058348901585020.814237656830142
860.8200725235005020.8141280553025810.826016991698424
870.820108700593850.8128233348263250.827394066361375
880.8201449268707630.8117264196841280.828563434057397
890.8201811531777880.8107619752149380.829600331140637
900.8202173794848290.8098914127124060.830543346257252
910.8206702601706790.8095084781980350.831832042143323
920.820289844398250.80834830516580.8322313836307
930.8203260584134720.8076504668384630.83300164998848
940.8203622847129480.8069908132494530.833733756176443
950.8203985110199740.8063636499272040.834433372112744
960.8204347373270030.805764565656410.835104908997596



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