Free Statistics

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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 computationMon, 28 Nov 2011 11:19:04 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/28/t1322497279kttu03m5umfp0rv.htm/, Retrieved Thu, 25 Apr 2024 17:58:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147842, Retrieved Thu, 25 Apr 2024 17:58:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-    D        [(Partial) Autocorrelation Function] [ACF van Y(t) (d=0...] [2009-11-26 00:58:58] [9717cb857c153ca3061376906953b329]
- RMPD            [Exponential Smoothing] [WS taak 2] [2011-11-28 16:19:04] [c98b04636162cea751932dfe577607eb] [Current]
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Dataseries X:
3.2700
3.2700
3.2700
3.2700
3.2700
3.2800
3.3200
3.3400
3.3400
3.3500
3.3500
3.3500
3.3500
3.3500
3.4000
3.4200
3.4200
3.4200
3.4200
3.4200
3.4200
3.4200
3.4200
3.4200
3.4200
3.4200
3.4300
3.4700
3.5100
3.5200
3.5200
3.5200
3.5200
3.5200
3.5200
3.5200
3.5200
3.5200
3.5800
3.6000
3.6100
3.6100
3.6100
3.6300
3.6800
3.6900
3.6900
3.6900
3.6900
3.6900
3.6900
3.6900
3.6900
3.7800
3.7900
3.7900
3.8000
3.8000
3.8000
3.8000
3.8100
3.9500
3.9900
4.0000
4.0600
4.1600
4.1900
4.2000
4.2000
4.2000
4.2000
4.2000
4.2300
4.3800
4.4300
4.4400
4.4400
4.4400
4.4400
4.4400
4.4500
4.4500
4.4500
4.4500
4.4500
4.4500
4.4500
4.4500
4.4600
4.4600
4.4600
4.4800
4.5800
4.6700
4.6800
4.6800




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147842&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147842&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147842&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0264298971176654
gamma0.0987822325018638

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0264298971176654 \tabularnewline
gamma & 0.0987822325018638 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147842&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0264298971176654[/C][/ROW]
[ROW][C]gamma[/C][C]0.0987822325018638[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147842&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147842&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0264298971176654
gamma0.0987822325018638







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133.353.283183760683760.0668162393162395
143.353.35325778782276-0.00325778782275865
153.43.40400501815911-0.00400501815910559
163.423.42431583260787-0.00431583260787294
173.423.42461843226274-0.00461843226273695
183.423.42449636757319-0.0044963675731875
193.423.42396086237416-0.00396086237415849
203.423.44343951052244-0.023439510522445
213.423.42073667333752-0.00073667333751537
223.423.42780053647033-0.00780053647032908
233.423.416761035760620.00323896423937819
243.423.41726330791890.00273669208109695
253.423.419418971742380.000581028257617078
263.423.42193432825945-0.00193432825945372
273.433.4727165374959-0.0427165374958975
283.473.452004210471330.0179957895286749
293.513.472896504003790.0371034959962131
303.523.513877145585670.00612285441432858
313.523.52362230533124-0.00362230533124253
323.523.54310990150734-0.0231099015073419
333.523.52041577585477-0.00041577585477004
343.523.52748812027504-0.00748812027503831
353.523.516456876693230.00354312330676931
363.523.516967187744370.00303281225562957
373.523.51913067799360.000869322006402662
383.523.52165365408479-0.00165365408478824
393.583.572443281510790.0075567184892078
403.63.60305967146968-0.00305967146967623
413.613.603395471334190.00660452866581362
423.613.61357002834733-0.00357002834733366
433.613.61305900619874-0.00305900619874011
443.633.63256149031296-0.00256149031295827
453.683.630410457054190.0495895429458146
463.693.688804436905690.00119556309431079
473.693.688002702181940.00199729781806424
483.693.688472157224450.00152784277555273
493.693.69059587128515-0.000595871285150817
503.693.69308012246839-0.00308012246838807
513.693.74383204848177-0.0538320484817723
523.693.71282593964543-0.0228259396454327
533.693.69263931907566-0.00263931907565684
543.783.692569562144030.0874304378559736
553.793.784463672954850.00553632704515428
563.793.81419333084239-0.0241933308423921
573.83.791470570263960.00852942973603943
583.83.80877933554769-0.00877933554769017
593.83.797713965279070.00228603472093081
603.83.798191051608220.00180894839178247
613.813.800322195261440.00967780473856283
623.953.8130779786450.136922021354998
633.994.00753014691589-0.0175301469158899
6444.01748349360311-0.0174834936031125
654.064.007438073332590.0525619266674076
664.164.068827279646720.0911727203532831
674.194.170820298598930.0191797014010735
684.24.22091054946704-0.0209105494670379
694.24.20827455246262-0.00827455246261621
704.24.21513919022567-0.0151391902256677
714.24.20390572965223-0.00390572965222535
724.24.20421916828601-0.00421916828601443
734.234.206190989435630.0238090105643733
744.384.239320259135320.140679740864684
754.434.44387174354624-0.0138717435462423
764.444.46392178145814-0.0239217814581387
774.444.453706197902-0.0137061979019961
784.444.45334394450157-0.0133439445015719
794.444.45257459875459-0.0125745987545853
804.444.47182558673654-0.0318255867365389
814.454.448901106420050.0010988935799503
824.454.46601348339764-0.0160134833976437
834.454.45475691534562-0.00475691534561573
844.454.4550478572291-0.00504785722910039
854.454.4569977762152-0.00699777621520425
864.454.45931282570978-0.00931282570978365
874.454.50990002201773-0.0599000220177324
884.454.47873353726512-0.0287335372651247
894.464.458390779498050.001609220501952
904.464.46843331103035-0.00843331103035361
914.464.46779375282079-0.00779375282079364
924.484.48717109806891-0.00717109806891258
934.584.48489823335140.095101766648602
944.674.594495096592960.0755049034070385
954.684.675657350088560.00434264991144406
964.684.6861887925456-0.00618879254559968

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3.35 & 3.28318376068376 & 0.0668162393162395 \tabularnewline
14 & 3.35 & 3.35325778782276 & -0.00325778782275865 \tabularnewline
15 & 3.4 & 3.40400501815911 & -0.00400501815910559 \tabularnewline
16 & 3.42 & 3.42431583260787 & -0.00431583260787294 \tabularnewline
17 & 3.42 & 3.42461843226274 & -0.00461843226273695 \tabularnewline
18 & 3.42 & 3.42449636757319 & -0.0044963675731875 \tabularnewline
19 & 3.42 & 3.42396086237416 & -0.00396086237415849 \tabularnewline
20 & 3.42 & 3.44343951052244 & -0.023439510522445 \tabularnewline
21 & 3.42 & 3.42073667333752 & -0.00073667333751537 \tabularnewline
22 & 3.42 & 3.42780053647033 & -0.00780053647032908 \tabularnewline
23 & 3.42 & 3.41676103576062 & 0.00323896423937819 \tabularnewline
24 & 3.42 & 3.4172633079189 & 0.00273669208109695 \tabularnewline
25 & 3.42 & 3.41941897174238 & 0.000581028257617078 \tabularnewline
26 & 3.42 & 3.42193432825945 & -0.00193432825945372 \tabularnewline
27 & 3.43 & 3.4727165374959 & -0.0427165374958975 \tabularnewline
28 & 3.47 & 3.45200421047133 & 0.0179957895286749 \tabularnewline
29 & 3.51 & 3.47289650400379 & 0.0371034959962131 \tabularnewline
30 & 3.52 & 3.51387714558567 & 0.00612285441432858 \tabularnewline
31 & 3.52 & 3.52362230533124 & -0.00362230533124253 \tabularnewline
32 & 3.52 & 3.54310990150734 & -0.0231099015073419 \tabularnewline
33 & 3.52 & 3.52041577585477 & -0.00041577585477004 \tabularnewline
34 & 3.52 & 3.52748812027504 & -0.00748812027503831 \tabularnewline
35 & 3.52 & 3.51645687669323 & 0.00354312330676931 \tabularnewline
36 & 3.52 & 3.51696718774437 & 0.00303281225562957 \tabularnewline
37 & 3.52 & 3.5191306779936 & 0.000869322006402662 \tabularnewline
38 & 3.52 & 3.52165365408479 & -0.00165365408478824 \tabularnewline
39 & 3.58 & 3.57244328151079 & 0.0075567184892078 \tabularnewline
40 & 3.6 & 3.60305967146968 & -0.00305967146967623 \tabularnewline
41 & 3.61 & 3.60339547133419 & 0.00660452866581362 \tabularnewline
42 & 3.61 & 3.61357002834733 & -0.00357002834733366 \tabularnewline
43 & 3.61 & 3.61305900619874 & -0.00305900619874011 \tabularnewline
44 & 3.63 & 3.63256149031296 & -0.00256149031295827 \tabularnewline
45 & 3.68 & 3.63041045705419 & 0.0495895429458146 \tabularnewline
46 & 3.69 & 3.68880443690569 & 0.00119556309431079 \tabularnewline
47 & 3.69 & 3.68800270218194 & 0.00199729781806424 \tabularnewline
48 & 3.69 & 3.68847215722445 & 0.00152784277555273 \tabularnewline
49 & 3.69 & 3.69059587128515 & -0.000595871285150817 \tabularnewline
50 & 3.69 & 3.69308012246839 & -0.00308012246838807 \tabularnewline
51 & 3.69 & 3.74383204848177 & -0.0538320484817723 \tabularnewline
52 & 3.69 & 3.71282593964543 & -0.0228259396454327 \tabularnewline
53 & 3.69 & 3.69263931907566 & -0.00263931907565684 \tabularnewline
54 & 3.78 & 3.69256956214403 & 0.0874304378559736 \tabularnewline
55 & 3.79 & 3.78446367295485 & 0.00553632704515428 \tabularnewline
56 & 3.79 & 3.81419333084239 & -0.0241933308423921 \tabularnewline
57 & 3.8 & 3.79147057026396 & 0.00852942973603943 \tabularnewline
58 & 3.8 & 3.80877933554769 & -0.00877933554769017 \tabularnewline
59 & 3.8 & 3.79771396527907 & 0.00228603472093081 \tabularnewline
60 & 3.8 & 3.79819105160822 & 0.00180894839178247 \tabularnewline
61 & 3.81 & 3.80032219526144 & 0.00967780473856283 \tabularnewline
62 & 3.95 & 3.813077978645 & 0.136922021354998 \tabularnewline
63 & 3.99 & 4.00753014691589 & -0.0175301469158899 \tabularnewline
64 & 4 & 4.01748349360311 & -0.0174834936031125 \tabularnewline
65 & 4.06 & 4.00743807333259 & 0.0525619266674076 \tabularnewline
66 & 4.16 & 4.06882727964672 & 0.0911727203532831 \tabularnewline
67 & 4.19 & 4.17082029859893 & 0.0191797014010735 \tabularnewline
68 & 4.2 & 4.22091054946704 & -0.0209105494670379 \tabularnewline
69 & 4.2 & 4.20827455246262 & -0.00827455246261621 \tabularnewline
70 & 4.2 & 4.21513919022567 & -0.0151391902256677 \tabularnewline
71 & 4.2 & 4.20390572965223 & -0.00390572965222535 \tabularnewline
72 & 4.2 & 4.20421916828601 & -0.00421916828601443 \tabularnewline
73 & 4.23 & 4.20619098943563 & 0.0238090105643733 \tabularnewline
74 & 4.38 & 4.23932025913532 & 0.140679740864684 \tabularnewline
75 & 4.43 & 4.44387174354624 & -0.0138717435462423 \tabularnewline
76 & 4.44 & 4.46392178145814 & -0.0239217814581387 \tabularnewline
77 & 4.44 & 4.453706197902 & -0.0137061979019961 \tabularnewline
78 & 4.44 & 4.45334394450157 & -0.0133439445015719 \tabularnewline
79 & 4.44 & 4.45257459875459 & -0.0125745987545853 \tabularnewline
80 & 4.44 & 4.47182558673654 & -0.0318255867365389 \tabularnewline
81 & 4.45 & 4.44890110642005 & 0.0010988935799503 \tabularnewline
82 & 4.45 & 4.46601348339764 & -0.0160134833976437 \tabularnewline
83 & 4.45 & 4.45475691534562 & -0.00475691534561573 \tabularnewline
84 & 4.45 & 4.4550478572291 & -0.00504785722910039 \tabularnewline
85 & 4.45 & 4.4569977762152 & -0.00699777621520425 \tabularnewline
86 & 4.45 & 4.45931282570978 & -0.00931282570978365 \tabularnewline
87 & 4.45 & 4.50990002201773 & -0.0599000220177324 \tabularnewline
88 & 4.45 & 4.47873353726512 & -0.0287335372651247 \tabularnewline
89 & 4.46 & 4.45839077949805 & 0.001609220501952 \tabularnewline
90 & 4.46 & 4.46843331103035 & -0.00843331103035361 \tabularnewline
91 & 4.46 & 4.46779375282079 & -0.00779375282079364 \tabularnewline
92 & 4.48 & 4.48717109806891 & -0.00717109806891258 \tabularnewline
93 & 4.58 & 4.4848982333514 & 0.095101766648602 \tabularnewline
94 & 4.67 & 4.59449509659296 & 0.0755049034070385 \tabularnewline
95 & 4.68 & 4.67565735008856 & 0.00434264991144406 \tabularnewline
96 & 4.68 & 4.6861887925456 & -0.00618879254559968 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147842&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]3.35[/C][C]3.28318376068376[/C][C]0.0668162393162395[/C][/ROW]
[ROW][C]14[/C][C]3.35[/C][C]3.35325778782276[/C][C]-0.00325778782275865[/C][/ROW]
[ROW][C]15[/C][C]3.4[/C][C]3.40400501815911[/C][C]-0.00400501815910559[/C][/ROW]
[ROW][C]16[/C][C]3.42[/C][C]3.42431583260787[/C][C]-0.00431583260787294[/C][/ROW]
[ROW][C]17[/C][C]3.42[/C][C]3.42461843226274[/C][C]-0.00461843226273695[/C][/ROW]
[ROW][C]18[/C][C]3.42[/C][C]3.42449636757319[/C][C]-0.0044963675731875[/C][/ROW]
[ROW][C]19[/C][C]3.42[/C][C]3.42396086237416[/C][C]-0.00396086237415849[/C][/ROW]
[ROW][C]20[/C][C]3.42[/C][C]3.44343951052244[/C][C]-0.023439510522445[/C][/ROW]
[ROW][C]21[/C][C]3.42[/C][C]3.42073667333752[/C][C]-0.00073667333751537[/C][/ROW]
[ROW][C]22[/C][C]3.42[/C][C]3.42780053647033[/C][C]-0.00780053647032908[/C][/ROW]
[ROW][C]23[/C][C]3.42[/C][C]3.41676103576062[/C][C]0.00323896423937819[/C][/ROW]
[ROW][C]24[/C][C]3.42[/C][C]3.4172633079189[/C][C]0.00273669208109695[/C][/ROW]
[ROW][C]25[/C][C]3.42[/C][C]3.41941897174238[/C][C]0.000581028257617078[/C][/ROW]
[ROW][C]26[/C][C]3.42[/C][C]3.42193432825945[/C][C]-0.00193432825945372[/C][/ROW]
[ROW][C]27[/C][C]3.43[/C][C]3.4727165374959[/C][C]-0.0427165374958975[/C][/ROW]
[ROW][C]28[/C][C]3.47[/C][C]3.45200421047133[/C][C]0.0179957895286749[/C][/ROW]
[ROW][C]29[/C][C]3.51[/C][C]3.47289650400379[/C][C]0.0371034959962131[/C][/ROW]
[ROW][C]30[/C][C]3.52[/C][C]3.51387714558567[/C][C]0.00612285441432858[/C][/ROW]
[ROW][C]31[/C][C]3.52[/C][C]3.52362230533124[/C][C]-0.00362230533124253[/C][/ROW]
[ROW][C]32[/C][C]3.52[/C][C]3.54310990150734[/C][C]-0.0231099015073419[/C][/ROW]
[ROW][C]33[/C][C]3.52[/C][C]3.52041577585477[/C][C]-0.00041577585477004[/C][/ROW]
[ROW][C]34[/C][C]3.52[/C][C]3.52748812027504[/C][C]-0.00748812027503831[/C][/ROW]
[ROW][C]35[/C][C]3.52[/C][C]3.51645687669323[/C][C]0.00354312330676931[/C][/ROW]
[ROW][C]36[/C][C]3.52[/C][C]3.51696718774437[/C][C]0.00303281225562957[/C][/ROW]
[ROW][C]37[/C][C]3.52[/C][C]3.5191306779936[/C][C]0.000869322006402662[/C][/ROW]
[ROW][C]38[/C][C]3.52[/C][C]3.52165365408479[/C][C]-0.00165365408478824[/C][/ROW]
[ROW][C]39[/C][C]3.58[/C][C]3.57244328151079[/C][C]0.0075567184892078[/C][/ROW]
[ROW][C]40[/C][C]3.6[/C][C]3.60305967146968[/C][C]-0.00305967146967623[/C][/ROW]
[ROW][C]41[/C][C]3.61[/C][C]3.60339547133419[/C][C]0.00660452866581362[/C][/ROW]
[ROW][C]42[/C][C]3.61[/C][C]3.61357002834733[/C][C]-0.00357002834733366[/C][/ROW]
[ROW][C]43[/C][C]3.61[/C][C]3.61305900619874[/C][C]-0.00305900619874011[/C][/ROW]
[ROW][C]44[/C][C]3.63[/C][C]3.63256149031296[/C][C]-0.00256149031295827[/C][/ROW]
[ROW][C]45[/C][C]3.68[/C][C]3.63041045705419[/C][C]0.0495895429458146[/C][/ROW]
[ROW][C]46[/C][C]3.69[/C][C]3.68880443690569[/C][C]0.00119556309431079[/C][/ROW]
[ROW][C]47[/C][C]3.69[/C][C]3.68800270218194[/C][C]0.00199729781806424[/C][/ROW]
[ROW][C]48[/C][C]3.69[/C][C]3.68847215722445[/C][C]0.00152784277555273[/C][/ROW]
[ROW][C]49[/C][C]3.69[/C][C]3.69059587128515[/C][C]-0.000595871285150817[/C][/ROW]
[ROW][C]50[/C][C]3.69[/C][C]3.69308012246839[/C][C]-0.00308012246838807[/C][/ROW]
[ROW][C]51[/C][C]3.69[/C][C]3.74383204848177[/C][C]-0.0538320484817723[/C][/ROW]
[ROW][C]52[/C][C]3.69[/C][C]3.71282593964543[/C][C]-0.0228259396454327[/C][/ROW]
[ROW][C]53[/C][C]3.69[/C][C]3.69263931907566[/C][C]-0.00263931907565684[/C][/ROW]
[ROW][C]54[/C][C]3.78[/C][C]3.69256956214403[/C][C]0.0874304378559736[/C][/ROW]
[ROW][C]55[/C][C]3.79[/C][C]3.78446367295485[/C][C]0.00553632704515428[/C][/ROW]
[ROW][C]56[/C][C]3.79[/C][C]3.81419333084239[/C][C]-0.0241933308423921[/C][/ROW]
[ROW][C]57[/C][C]3.8[/C][C]3.79147057026396[/C][C]0.00852942973603943[/C][/ROW]
[ROW][C]58[/C][C]3.8[/C][C]3.80877933554769[/C][C]-0.00877933554769017[/C][/ROW]
[ROW][C]59[/C][C]3.8[/C][C]3.79771396527907[/C][C]0.00228603472093081[/C][/ROW]
[ROW][C]60[/C][C]3.8[/C][C]3.79819105160822[/C][C]0.00180894839178247[/C][/ROW]
[ROW][C]61[/C][C]3.81[/C][C]3.80032219526144[/C][C]0.00967780473856283[/C][/ROW]
[ROW][C]62[/C][C]3.95[/C][C]3.813077978645[/C][C]0.136922021354998[/C][/ROW]
[ROW][C]63[/C][C]3.99[/C][C]4.00753014691589[/C][C]-0.0175301469158899[/C][/ROW]
[ROW][C]64[/C][C]4[/C][C]4.01748349360311[/C][C]-0.0174834936031125[/C][/ROW]
[ROW][C]65[/C][C]4.06[/C][C]4.00743807333259[/C][C]0.0525619266674076[/C][/ROW]
[ROW][C]66[/C][C]4.16[/C][C]4.06882727964672[/C][C]0.0911727203532831[/C][/ROW]
[ROW][C]67[/C][C]4.19[/C][C]4.17082029859893[/C][C]0.0191797014010735[/C][/ROW]
[ROW][C]68[/C][C]4.2[/C][C]4.22091054946704[/C][C]-0.0209105494670379[/C][/ROW]
[ROW][C]69[/C][C]4.2[/C][C]4.20827455246262[/C][C]-0.00827455246261621[/C][/ROW]
[ROW][C]70[/C][C]4.2[/C][C]4.21513919022567[/C][C]-0.0151391902256677[/C][/ROW]
[ROW][C]71[/C][C]4.2[/C][C]4.20390572965223[/C][C]-0.00390572965222535[/C][/ROW]
[ROW][C]72[/C][C]4.2[/C][C]4.20421916828601[/C][C]-0.00421916828601443[/C][/ROW]
[ROW][C]73[/C][C]4.23[/C][C]4.20619098943563[/C][C]0.0238090105643733[/C][/ROW]
[ROW][C]74[/C][C]4.38[/C][C]4.23932025913532[/C][C]0.140679740864684[/C][/ROW]
[ROW][C]75[/C][C]4.43[/C][C]4.44387174354624[/C][C]-0.0138717435462423[/C][/ROW]
[ROW][C]76[/C][C]4.44[/C][C]4.46392178145814[/C][C]-0.0239217814581387[/C][/ROW]
[ROW][C]77[/C][C]4.44[/C][C]4.453706197902[/C][C]-0.0137061979019961[/C][/ROW]
[ROW][C]78[/C][C]4.44[/C][C]4.45334394450157[/C][C]-0.0133439445015719[/C][/ROW]
[ROW][C]79[/C][C]4.44[/C][C]4.45257459875459[/C][C]-0.0125745987545853[/C][/ROW]
[ROW][C]80[/C][C]4.44[/C][C]4.47182558673654[/C][C]-0.0318255867365389[/C][/ROW]
[ROW][C]81[/C][C]4.45[/C][C]4.44890110642005[/C][C]0.0010988935799503[/C][/ROW]
[ROW][C]82[/C][C]4.45[/C][C]4.46601348339764[/C][C]-0.0160134833976437[/C][/ROW]
[ROW][C]83[/C][C]4.45[/C][C]4.45475691534562[/C][C]-0.00475691534561573[/C][/ROW]
[ROW][C]84[/C][C]4.45[/C][C]4.4550478572291[/C][C]-0.00504785722910039[/C][/ROW]
[ROW][C]85[/C][C]4.45[/C][C]4.4569977762152[/C][C]-0.00699777621520425[/C][/ROW]
[ROW][C]86[/C][C]4.45[/C][C]4.45931282570978[/C][C]-0.00931282570978365[/C][/ROW]
[ROW][C]87[/C][C]4.45[/C][C]4.50990002201773[/C][C]-0.0599000220177324[/C][/ROW]
[ROW][C]88[/C][C]4.45[/C][C]4.47873353726512[/C][C]-0.0287335372651247[/C][/ROW]
[ROW][C]89[/C][C]4.46[/C][C]4.45839077949805[/C][C]0.001609220501952[/C][/ROW]
[ROW][C]90[/C][C]4.46[/C][C]4.46843331103035[/C][C]-0.00843331103035361[/C][/ROW]
[ROW][C]91[/C][C]4.46[/C][C]4.46779375282079[/C][C]-0.00779375282079364[/C][/ROW]
[ROW][C]92[/C][C]4.48[/C][C]4.48717109806891[/C][C]-0.00717109806891258[/C][/ROW]
[ROW][C]93[/C][C]4.58[/C][C]4.4848982333514[/C][C]0.095101766648602[/C][/ROW]
[ROW][C]94[/C][C]4.67[/C][C]4.59449509659296[/C][C]0.0755049034070385[/C][/ROW]
[ROW][C]95[/C][C]4.68[/C][C]4.67565735008856[/C][C]0.00434264991144406[/C][/ROW]
[ROW][C]96[/C][C]4.68[/C][C]4.6861887925456[/C][C]-0.00618879254559968[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147842&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147842&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
133.353.283183760683760.0668162393162395
143.353.35325778782276-0.00325778782275865
153.43.40400501815911-0.00400501815910559
163.423.42431583260787-0.00431583260787294
173.423.42461843226274-0.00461843226273695
183.423.42449636757319-0.0044963675731875
193.423.42396086237416-0.00396086237415849
203.423.44343951052244-0.023439510522445
213.423.42073667333752-0.00073667333751537
223.423.42780053647033-0.00780053647032908
233.423.416761035760620.00323896423937819
243.423.41726330791890.00273669208109695
253.423.419418971742380.000581028257617078
263.423.42193432825945-0.00193432825945372
273.433.4727165374959-0.0427165374958975
283.473.452004210471330.0179957895286749
293.513.472896504003790.0371034959962131
303.523.513877145585670.00612285441432858
313.523.52362230533124-0.00362230533124253
323.523.54310990150734-0.0231099015073419
333.523.52041577585477-0.00041577585477004
343.523.52748812027504-0.00748812027503831
353.523.516456876693230.00354312330676931
363.523.516967187744370.00303281225562957
373.523.51913067799360.000869322006402662
383.523.52165365408479-0.00165365408478824
393.583.572443281510790.0075567184892078
403.63.60305967146968-0.00305967146967623
413.613.603395471334190.00660452866581362
423.613.61357002834733-0.00357002834733366
433.613.61305900619874-0.00305900619874011
443.633.63256149031296-0.00256149031295827
453.683.630410457054190.0495895429458146
463.693.688804436905690.00119556309431079
473.693.688002702181940.00199729781806424
483.693.688472157224450.00152784277555273
493.693.69059587128515-0.000595871285150817
503.693.69308012246839-0.00308012246838807
513.693.74383204848177-0.0538320484817723
523.693.71282593964543-0.0228259396454327
533.693.69263931907566-0.00263931907565684
543.783.692569562144030.0874304378559736
553.793.784463672954850.00553632704515428
563.793.81419333084239-0.0241933308423921
573.83.791470570263960.00852942973603943
583.83.80877933554769-0.00877933554769017
593.83.797713965279070.00228603472093081
603.83.798191051608220.00180894839178247
613.813.800322195261440.00967780473856283
623.953.8130779786450.136922021354998
633.994.00753014691589-0.0175301469158899
6444.01748349360311-0.0174834936031125
654.064.007438073332590.0525619266674076
664.164.068827279646720.0911727203532831
674.194.170820298598930.0191797014010735
684.24.22091054946704-0.0209105494670379
694.24.20827455246262-0.00827455246261621
704.24.21513919022567-0.0151391902256677
714.24.20390572965223-0.00390572965222535
724.24.20421916828601-0.00421916828601443
734.234.206190989435630.0238090105643733
744.384.239320259135320.140679740864684
754.434.44387174354624-0.0138717435462423
764.444.46392178145814-0.0239217814581387
774.444.453706197902-0.0137061979019961
784.444.45334394450157-0.0133439445015719
794.444.45257459875459-0.0125745987545853
804.444.47182558673654-0.0318255867365389
814.454.448901106420050.0010988935799503
824.454.46601348339764-0.0160134833976437
834.454.45475691534562-0.00475691534561573
844.454.4550478572291-0.00504785722910039
854.454.4569977762152-0.00699777621520425
864.454.45931282570978-0.00931282570978365
874.454.50990002201773-0.0599000220177324
884.454.47873353726512-0.0287335372651247
894.464.458390779498050.001609220501952
904.464.46843331103035-0.00843331103035361
914.464.46779375282079-0.00779375282079364
924.484.48717109806891-0.00717109806891258
934.584.48489823335140.095101766648602
944.674.594495096592960.0755049034070385
954.684.675657350088560.00434264991144406
964.684.6861887925456-0.00618879254559968







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
974.688108556728674.621242899734684.75497421372266
984.698717113457344.602897009398054.79453721751663
994.760159003519344.641257047553834.87906095948485
1004.792017560248014.652928341330624.93110677916541
1014.804292783643354.646774068043744.96181149924296
1024.816568007038694.64180266055934.99133335351807
1034.828426563767364.63726067015895.01959245737582
1044.859868453829364.652931724915265.06680518274346
1054.869227010558034.647000987383335.09145303373274
1064.885668900620044.648528790034365.12280901120571
1074.891277457348714.639519366806165.14303554789125
1084.897302680744044.631162183912925.16344317757516

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 4.68810855672867 & 4.62124289973468 & 4.75497421372266 \tabularnewline
98 & 4.69871711345734 & 4.60289700939805 & 4.79453721751663 \tabularnewline
99 & 4.76015900351934 & 4.64125704755383 & 4.87906095948485 \tabularnewline
100 & 4.79201756024801 & 4.65292834133062 & 4.93110677916541 \tabularnewline
101 & 4.80429278364335 & 4.64677406804374 & 4.96181149924296 \tabularnewline
102 & 4.81656800703869 & 4.6418026605593 & 4.99133335351807 \tabularnewline
103 & 4.82842656376736 & 4.6372606701589 & 5.01959245737582 \tabularnewline
104 & 4.85986845382936 & 4.65293172491526 & 5.06680518274346 \tabularnewline
105 & 4.86922701055803 & 4.64700098738333 & 5.09145303373274 \tabularnewline
106 & 4.88566890062004 & 4.64852879003436 & 5.12280901120571 \tabularnewline
107 & 4.89127745734871 & 4.63951936680616 & 5.14303554789125 \tabularnewline
108 & 4.89730268074404 & 4.63116218391292 & 5.16344317757516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147842&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]97[/C][C]4.68810855672867[/C][C]4.62124289973468[/C][C]4.75497421372266[/C][/ROW]
[ROW][C]98[/C][C]4.69871711345734[/C][C]4.60289700939805[/C][C]4.79453721751663[/C][/ROW]
[ROW][C]99[/C][C]4.76015900351934[/C][C]4.64125704755383[/C][C]4.87906095948485[/C][/ROW]
[ROW][C]100[/C][C]4.79201756024801[/C][C]4.65292834133062[/C][C]4.93110677916541[/C][/ROW]
[ROW][C]101[/C][C]4.80429278364335[/C][C]4.64677406804374[/C][C]4.96181149924296[/C][/ROW]
[ROW][C]102[/C][C]4.81656800703869[/C][C]4.6418026605593[/C][C]4.99133335351807[/C][/ROW]
[ROW][C]103[/C][C]4.82842656376736[/C][C]4.6372606701589[/C][C]5.01959245737582[/C][/ROW]
[ROW][C]104[/C][C]4.85986845382936[/C][C]4.65293172491526[/C][C]5.06680518274346[/C][/ROW]
[ROW][C]105[/C][C]4.86922701055803[/C][C]4.64700098738333[/C][C]5.09145303373274[/C][/ROW]
[ROW][C]106[/C][C]4.88566890062004[/C][C]4.64852879003436[/C][C]5.12280901120571[/C][/ROW]
[ROW][C]107[/C][C]4.89127745734871[/C][C]4.63951936680616[/C][C]5.14303554789125[/C][/ROW]
[ROW][C]108[/C][C]4.89730268074404[/C][C]4.63116218391292[/C][C]5.16344317757516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147842&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147842&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
974.688108556728674.621242899734684.75497421372266
984.698717113457344.602897009398054.79453721751663
994.760159003519344.641257047553834.87906095948485
1004.792017560248014.652928341330624.93110677916541
1014.804292783643354.646774068043744.96181149924296
1024.816568007038694.64180266055934.99133335351807
1034.828426563767364.63726067015895.01959245737582
1044.859868453829364.652931724915265.06680518274346
1054.869227010558034.647000987383335.09145303373274
1064.885668900620044.648528790034365.12280901120571
1074.891277457348714.639519366806165.14303554789125
1084.897302680744044.631162183912925.16344317757516



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=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')