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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 09:36:38 -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/t1322491197he4yjsrscqk8jvn.htm/, Retrieved Sat, 20 Apr 2024 08:10:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147764, Retrieved Sat, 20 Apr 2024 08:10:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [HPC Retail Sales] [2008-03-02 16:19:32] [74be16979710d4c4e7c6647856088456]
- RM D    [Exponential Smoothing] [Tijdreeksanalyse-...] [2011-11-28 14:36:38] [c897fb90cb9e1f725365d7e541ad7850] [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 time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147764&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147764&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147764&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999925005630408
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999925005630408 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147764&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]0.999925005630408[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147764&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147764&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
alpha0.999925005630408
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23.273.270
33.273.270
43.273.270
53.273.270
63.283.270.00999999999999979
73.323.27999925005630.0400007499436961
83.343.319997000168970.0200029998310254
93.343.339998499887641.50011236232928e-06
103.353.33999999988750.0100000001125
113.353.34999925005637.49943704470013e-07
123.353.349999999943765.62416779814612e-11
133.353.353.99680288865056e-15
143.353.350
153.43.350.0499999999999998
163.423.399996250281520.0200037497184797
173.423.41999849983141.50016859956636e-06
183.423.41999999988751.12504228155785e-10
193.423.419999999999998.43769498715119e-15
203.423.420
213.423.420
223.423.420
233.423.420
243.423.420
253.423.420
263.423.420
273.433.420.0100000000000002
283.473.42999925005630.0400007499436961
293.513.469997000168970.040002999831025
303.523.509997000000250.0100029999997542
313.523.519999249831327.50168679175545e-07
323.523.519999999943745.62585533714355e-11
333.523.524.44089209850063e-15
343.523.520
353.523.520
363.523.520
373.523.520
383.523.520
393.583.520.0600000000000001
403.63.579995500337820.0200044996621753
413.613.599998499775160.010001500224841
423.613.60999924994387.50056204257277e-07
433.613.609999999943755.62501156764483e-11
443.633.610.020000000000004
453.683.629998500112610.0500014998873919
463.693.679996250169040.0100037498309624
473.693.689999249775097.50224911971742e-07
483.693.689999999943745.62625501743241e-11
493.693.694.44089209850063e-15
503.693.690
513.693.690
523.693.690
533.693.690
543.783.690.0899999999999999
553.793.779993250506740.0100067494932636
563.793.789999249550137.50449869801884e-07
573.83.789999999943720.0100000000562792
583.83.79999925005637.49943700029121e-07
593.83.799999999943765.62416779814612e-11
603.83.83.99680288865056e-15
613.813.80.0100000000000002
623.953.80999925005630.140000749943696
633.993.949989500732020.0400104992679844
6443.989996999437830.0100030005621696
654.063.999999249831280.060000750168721
664.164.059995500281570.100004499718435
674.194.159992500225590.0300074997744133
684.24.189997749606470.0100022503935282
694.24.199999249887547.50112462810648e-07
704.24.199999999943755.62545565685468e-11
714.24.24.44089209850063e-15
724.24.20
734.234.20.0300000000000002
744.384.229997750168910.150002249831087
754.434.379988750675840.0500112493241636
764.444.429996249437880.0100037505621167
774.444.439999249775037.50224966594715e-07
784.444.439999999943745.62625501743241e-11
794.444.444.44089209850063e-15
804.444.440
814.454.440.00999999999999979
824.454.44999925005637.49943695588229e-07
834.454.449999999943765.62412338922513e-11
844.454.454.44089209850063e-15
854.454.450
864.454.450
874.454.450
884.454.450
894.464.450.00999999999999979
904.464.45999925005637.49943695588229e-07
914.464.459999999943765.62412338922513e-11
924.484.460.0200000000000049
934.584.479998500112610.100001499887392
944.674.579992500450560.0900074995494418
954.684.669993249944310.0100067500556866
964.684.679999249550097.50449911990358e-07

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3.27 & 3.27 & 0 \tabularnewline
3 & 3.27 & 3.27 & 0 \tabularnewline
4 & 3.27 & 3.27 & 0 \tabularnewline
5 & 3.27 & 3.27 & 0 \tabularnewline
6 & 3.28 & 3.27 & 0.00999999999999979 \tabularnewline
7 & 3.32 & 3.2799992500563 & 0.0400007499436961 \tabularnewline
8 & 3.34 & 3.31999700016897 & 0.0200029998310254 \tabularnewline
9 & 3.34 & 3.33999849988764 & 1.50011236232928e-06 \tabularnewline
10 & 3.35 & 3.3399999998875 & 0.0100000001125 \tabularnewline
11 & 3.35 & 3.3499992500563 & 7.49943704470013e-07 \tabularnewline
12 & 3.35 & 3.34999999994376 & 5.62416779814612e-11 \tabularnewline
13 & 3.35 & 3.35 & 3.99680288865056e-15 \tabularnewline
14 & 3.35 & 3.35 & 0 \tabularnewline
15 & 3.4 & 3.35 & 0.0499999999999998 \tabularnewline
16 & 3.42 & 3.39999625028152 & 0.0200037497184797 \tabularnewline
17 & 3.42 & 3.4199984998314 & 1.50016859956636e-06 \tabularnewline
18 & 3.42 & 3.4199999998875 & 1.12504228155785e-10 \tabularnewline
19 & 3.42 & 3.41999999999999 & 8.43769498715119e-15 \tabularnewline
20 & 3.42 & 3.42 & 0 \tabularnewline
21 & 3.42 & 3.42 & 0 \tabularnewline
22 & 3.42 & 3.42 & 0 \tabularnewline
23 & 3.42 & 3.42 & 0 \tabularnewline
24 & 3.42 & 3.42 & 0 \tabularnewline
25 & 3.42 & 3.42 & 0 \tabularnewline
26 & 3.42 & 3.42 & 0 \tabularnewline
27 & 3.43 & 3.42 & 0.0100000000000002 \tabularnewline
28 & 3.47 & 3.4299992500563 & 0.0400007499436961 \tabularnewline
29 & 3.51 & 3.46999700016897 & 0.040002999831025 \tabularnewline
30 & 3.52 & 3.50999700000025 & 0.0100029999997542 \tabularnewline
31 & 3.52 & 3.51999924983132 & 7.50168679175545e-07 \tabularnewline
32 & 3.52 & 3.51999999994374 & 5.62585533714355e-11 \tabularnewline
33 & 3.52 & 3.52 & 4.44089209850063e-15 \tabularnewline
34 & 3.52 & 3.52 & 0 \tabularnewline
35 & 3.52 & 3.52 & 0 \tabularnewline
36 & 3.52 & 3.52 & 0 \tabularnewline
37 & 3.52 & 3.52 & 0 \tabularnewline
38 & 3.52 & 3.52 & 0 \tabularnewline
39 & 3.58 & 3.52 & 0.0600000000000001 \tabularnewline
40 & 3.6 & 3.57999550033782 & 0.0200044996621753 \tabularnewline
41 & 3.61 & 3.59999849977516 & 0.010001500224841 \tabularnewline
42 & 3.61 & 3.6099992499438 & 7.50056204257277e-07 \tabularnewline
43 & 3.61 & 3.60999999994375 & 5.62501156764483e-11 \tabularnewline
44 & 3.63 & 3.61 & 0.020000000000004 \tabularnewline
45 & 3.68 & 3.62999850011261 & 0.0500014998873919 \tabularnewline
46 & 3.69 & 3.67999625016904 & 0.0100037498309624 \tabularnewline
47 & 3.69 & 3.68999924977509 & 7.50224911971742e-07 \tabularnewline
48 & 3.69 & 3.68999999994374 & 5.62625501743241e-11 \tabularnewline
49 & 3.69 & 3.69 & 4.44089209850063e-15 \tabularnewline
50 & 3.69 & 3.69 & 0 \tabularnewline
51 & 3.69 & 3.69 & 0 \tabularnewline
52 & 3.69 & 3.69 & 0 \tabularnewline
53 & 3.69 & 3.69 & 0 \tabularnewline
54 & 3.78 & 3.69 & 0.0899999999999999 \tabularnewline
55 & 3.79 & 3.77999325050674 & 0.0100067494932636 \tabularnewline
56 & 3.79 & 3.78999924955013 & 7.50449869801884e-07 \tabularnewline
57 & 3.8 & 3.78999999994372 & 0.0100000000562792 \tabularnewline
58 & 3.8 & 3.7999992500563 & 7.49943700029121e-07 \tabularnewline
59 & 3.8 & 3.79999999994376 & 5.62416779814612e-11 \tabularnewline
60 & 3.8 & 3.8 & 3.99680288865056e-15 \tabularnewline
61 & 3.81 & 3.8 & 0.0100000000000002 \tabularnewline
62 & 3.95 & 3.8099992500563 & 0.140000749943696 \tabularnewline
63 & 3.99 & 3.94998950073202 & 0.0400104992679844 \tabularnewline
64 & 4 & 3.98999699943783 & 0.0100030005621696 \tabularnewline
65 & 4.06 & 3.99999924983128 & 0.060000750168721 \tabularnewline
66 & 4.16 & 4.05999550028157 & 0.100004499718435 \tabularnewline
67 & 4.19 & 4.15999250022559 & 0.0300074997744133 \tabularnewline
68 & 4.2 & 4.18999774960647 & 0.0100022503935282 \tabularnewline
69 & 4.2 & 4.19999924988754 & 7.50112462810648e-07 \tabularnewline
70 & 4.2 & 4.19999999994375 & 5.62545565685468e-11 \tabularnewline
71 & 4.2 & 4.2 & 4.44089209850063e-15 \tabularnewline
72 & 4.2 & 4.2 & 0 \tabularnewline
73 & 4.23 & 4.2 & 0.0300000000000002 \tabularnewline
74 & 4.38 & 4.22999775016891 & 0.150002249831087 \tabularnewline
75 & 4.43 & 4.37998875067584 & 0.0500112493241636 \tabularnewline
76 & 4.44 & 4.42999624943788 & 0.0100037505621167 \tabularnewline
77 & 4.44 & 4.43999924977503 & 7.50224966594715e-07 \tabularnewline
78 & 4.44 & 4.43999999994374 & 5.62625501743241e-11 \tabularnewline
79 & 4.44 & 4.44 & 4.44089209850063e-15 \tabularnewline
80 & 4.44 & 4.44 & 0 \tabularnewline
81 & 4.45 & 4.44 & 0.00999999999999979 \tabularnewline
82 & 4.45 & 4.4499992500563 & 7.49943695588229e-07 \tabularnewline
83 & 4.45 & 4.44999999994376 & 5.62412338922513e-11 \tabularnewline
84 & 4.45 & 4.45 & 4.44089209850063e-15 \tabularnewline
85 & 4.45 & 4.45 & 0 \tabularnewline
86 & 4.45 & 4.45 & 0 \tabularnewline
87 & 4.45 & 4.45 & 0 \tabularnewline
88 & 4.45 & 4.45 & 0 \tabularnewline
89 & 4.46 & 4.45 & 0.00999999999999979 \tabularnewline
90 & 4.46 & 4.4599992500563 & 7.49943695588229e-07 \tabularnewline
91 & 4.46 & 4.45999999994376 & 5.62412338922513e-11 \tabularnewline
92 & 4.48 & 4.46 & 0.0200000000000049 \tabularnewline
93 & 4.58 & 4.47999850011261 & 0.100001499887392 \tabularnewline
94 & 4.67 & 4.57999250045056 & 0.0900074995494418 \tabularnewline
95 & 4.68 & 4.66999324994431 & 0.0100067500556866 \tabularnewline
96 & 4.68 & 4.67999924955009 & 7.50449911990358e-07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147764&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]3.27[/C][C]3.27[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]3.27[/C][C]3.27[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]3.27[/C][C]3.27[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]3.27[/C][C]3.27[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]3.28[/C][C]3.27[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]7[/C][C]3.32[/C][C]3.2799992500563[/C][C]0.0400007499436961[/C][/ROW]
[ROW][C]8[/C][C]3.34[/C][C]3.31999700016897[/C][C]0.0200029998310254[/C][/ROW]
[ROW][C]9[/C][C]3.34[/C][C]3.33999849988764[/C][C]1.50011236232928e-06[/C][/ROW]
[ROW][C]10[/C][C]3.35[/C][C]3.3399999998875[/C][C]0.0100000001125[/C][/ROW]
[ROW][C]11[/C][C]3.35[/C][C]3.3499992500563[/C][C]7.49943704470013e-07[/C][/ROW]
[ROW][C]12[/C][C]3.35[/C][C]3.34999999994376[/C][C]5.62416779814612e-11[/C][/ROW]
[ROW][C]13[/C][C]3.35[/C][C]3.35[/C][C]3.99680288865056e-15[/C][/ROW]
[ROW][C]14[/C][C]3.35[/C][C]3.35[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]3.4[/C][C]3.35[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]16[/C][C]3.42[/C][C]3.39999625028152[/C][C]0.0200037497184797[/C][/ROW]
[ROW][C]17[/C][C]3.42[/C][C]3.4199984998314[/C][C]1.50016859956636e-06[/C][/ROW]
[ROW][C]18[/C][C]3.42[/C][C]3.4199999998875[/C][C]1.12504228155785e-10[/C][/ROW]
[ROW][C]19[/C][C]3.42[/C][C]3.41999999999999[/C][C]8.43769498715119e-15[/C][/ROW]
[ROW][C]20[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]3.43[/C][C]3.42[/C][C]0.0100000000000002[/C][/ROW]
[ROW][C]28[/C][C]3.47[/C][C]3.4299992500563[/C][C]0.0400007499436961[/C][/ROW]
[ROW][C]29[/C][C]3.51[/C][C]3.46999700016897[/C][C]0.040002999831025[/C][/ROW]
[ROW][C]30[/C][C]3.52[/C][C]3.50999700000025[/C][C]0.0100029999997542[/C][/ROW]
[ROW][C]31[/C][C]3.52[/C][C]3.51999924983132[/C][C]7.50168679175545e-07[/C][/ROW]
[ROW][C]32[/C][C]3.52[/C][C]3.51999999994374[/C][C]5.62585533714355e-11[/C][/ROW]
[ROW][C]33[/C][C]3.52[/C][C]3.52[/C][C]4.44089209850063e-15[/C][/ROW]
[ROW][C]34[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]35[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]36[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]39[/C][C]3.58[/C][C]3.52[/C][C]0.0600000000000001[/C][/ROW]
[ROW][C]40[/C][C]3.6[/C][C]3.57999550033782[/C][C]0.0200044996621753[/C][/ROW]
[ROW][C]41[/C][C]3.61[/C][C]3.59999849977516[/C][C]0.010001500224841[/C][/ROW]
[ROW][C]42[/C][C]3.61[/C][C]3.6099992499438[/C][C]7.50056204257277e-07[/C][/ROW]
[ROW][C]43[/C][C]3.61[/C][C]3.60999999994375[/C][C]5.62501156764483e-11[/C][/ROW]
[ROW][C]44[/C][C]3.63[/C][C]3.61[/C][C]0.020000000000004[/C][/ROW]
[ROW][C]45[/C][C]3.68[/C][C]3.62999850011261[/C][C]0.0500014998873919[/C][/ROW]
[ROW][C]46[/C][C]3.69[/C][C]3.67999625016904[/C][C]0.0100037498309624[/C][/ROW]
[ROW][C]47[/C][C]3.69[/C][C]3.68999924977509[/C][C]7.50224911971742e-07[/C][/ROW]
[ROW][C]48[/C][C]3.69[/C][C]3.68999999994374[/C][C]5.62625501743241e-11[/C][/ROW]
[ROW][C]49[/C][C]3.69[/C][C]3.69[/C][C]4.44089209850063e-15[/C][/ROW]
[ROW][C]50[/C][C]3.69[/C][C]3.69[/C][C]0[/C][/ROW]
[ROW][C]51[/C][C]3.69[/C][C]3.69[/C][C]0[/C][/ROW]
[ROW][C]52[/C][C]3.69[/C][C]3.69[/C][C]0[/C][/ROW]
[ROW][C]53[/C][C]3.69[/C][C]3.69[/C][C]0[/C][/ROW]
[ROW][C]54[/C][C]3.78[/C][C]3.69[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]55[/C][C]3.79[/C][C]3.77999325050674[/C][C]0.0100067494932636[/C][/ROW]
[ROW][C]56[/C][C]3.79[/C][C]3.78999924955013[/C][C]7.50449869801884e-07[/C][/ROW]
[ROW][C]57[/C][C]3.8[/C][C]3.78999999994372[/C][C]0.0100000000562792[/C][/ROW]
[ROW][C]58[/C][C]3.8[/C][C]3.7999992500563[/C][C]7.49943700029121e-07[/C][/ROW]
[ROW][C]59[/C][C]3.8[/C][C]3.79999999994376[/C][C]5.62416779814612e-11[/C][/ROW]
[ROW][C]60[/C][C]3.8[/C][C]3.8[/C][C]3.99680288865056e-15[/C][/ROW]
[ROW][C]61[/C][C]3.81[/C][C]3.8[/C][C]0.0100000000000002[/C][/ROW]
[ROW][C]62[/C][C]3.95[/C][C]3.8099992500563[/C][C]0.140000749943696[/C][/ROW]
[ROW][C]63[/C][C]3.99[/C][C]3.94998950073202[/C][C]0.0400104992679844[/C][/ROW]
[ROW][C]64[/C][C]4[/C][C]3.98999699943783[/C][C]0.0100030005621696[/C][/ROW]
[ROW][C]65[/C][C]4.06[/C][C]3.99999924983128[/C][C]0.060000750168721[/C][/ROW]
[ROW][C]66[/C][C]4.16[/C][C]4.05999550028157[/C][C]0.100004499718435[/C][/ROW]
[ROW][C]67[/C][C]4.19[/C][C]4.15999250022559[/C][C]0.0300074997744133[/C][/ROW]
[ROW][C]68[/C][C]4.2[/C][C]4.18999774960647[/C][C]0.0100022503935282[/C][/ROW]
[ROW][C]69[/C][C]4.2[/C][C]4.19999924988754[/C][C]7.50112462810648e-07[/C][/ROW]
[ROW][C]70[/C][C]4.2[/C][C]4.19999999994375[/C][C]5.62545565685468e-11[/C][/ROW]
[ROW][C]71[/C][C]4.2[/C][C]4.2[/C][C]4.44089209850063e-15[/C][/ROW]
[ROW][C]72[/C][C]4.2[/C][C]4.2[/C][C]0[/C][/ROW]
[ROW][C]73[/C][C]4.23[/C][C]4.2[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]74[/C][C]4.38[/C][C]4.22999775016891[/C][C]0.150002249831087[/C][/ROW]
[ROW][C]75[/C][C]4.43[/C][C]4.37998875067584[/C][C]0.0500112493241636[/C][/ROW]
[ROW][C]76[/C][C]4.44[/C][C]4.42999624943788[/C][C]0.0100037505621167[/C][/ROW]
[ROW][C]77[/C][C]4.44[/C][C]4.43999924977503[/C][C]7.50224966594715e-07[/C][/ROW]
[ROW][C]78[/C][C]4.44[/C][C]4.43999999994374[/C][C]5.62625501743241e-11[/C][/ROW]
[ROW][C]79[/C][C]4.44[/C][C]4.44[/C][C]4.44089209850063e-15[/C][/ROW]
[ROW][C]80[/C][C]4.44[/C][C]4.44[/C][C]0[/C][/ROW]
[ROW][C]81[/C][C]4.45[/C][C]4.44[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]82[/C][C]4.45[/C][C]4.4499992500563[/C][C]7.49943695588229e-07[/C][/ROW]
[ROW][C]83[/C][C]4.45[/C][C]4.44999999994376[/C][C]5.62412338922513e-11[/C][/ROW]
[ROW][C]84[/C][C]4.45[/C][C]4.45[/C][C]4.44089209850063e-15[/C][/ROW]
[ROW][C]85[/C][C]4.45[/C][C]4.45[/C][C]0[/C][/ROW]
[ROW][C]86[/C][C]4.45[/C][C]4.45[/C][C]0[/C][/ROW]
[ROW][C]87[/C][C]4.45[/C][C]4.45[/C][C]0[/C][/ROW]
[ROW][C]88[/C][C]4.45[/C][C]4.45[/C][C]0[/C][/ROW]
[ROW][C]89[/C][C]4.46[/C][C]4.45[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]90[/C][C]4.46[/C][C]4.4599992500563[/C][C]7.49943695588229e-07[/C][/ROW]
[ROW][C]91[/C][C]4.46[/C][C]4.45999999994376[/C][C]5.62412338922513e-11[/C][/ROW]
[ROW][C]92[/C][C]4.48[/C][C]4.46[/C][C]0.0200000000000049[/C][/ROW]
[ROW][C]93[/C][C]4.58[/C][C]4.47999850011261[/C][C]0.100001499887392[/C][/ROW]
[ROW][C]94[/C][C]4.67[/C][C]4.57999250045056[/C][C]0.0900074995494418[/C][/ROW]
[ROW][C]95[/C][C]4.68[/C][C]4.66999324994431[/C][C]0.0100067500556866[/C][/ROW]
[ROW][C]96[/C][C]4.68[/C][C]4.67999924955009[/C][C]7.50449911990358e-07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147764&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147764&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
23.273.270
33.273.270
43.273.270
53.273.270
63.283.270.00999999999999979
73.323.27999925005630.0400007499436961
83.343.319997000168970.0200029998310254
93.343.339998499887641.50011236232928e-06
103.353.33999999988750.0100000001125
113.353.34999925005637.49943704470013e-07
123.353.349999999943765.62416779814612e-11
133.353.353.99680288865056e-15
143.353.350
153.43.350.0499999999999998
163.423.399996250281520.0200037497184797
173.423.41999849983141.50016859956636e-06
183.423.41999999988751.12504228155785e-10
193.423.419999999999998.43769498715119e-15
203.423.420
213.423.420
223.423.420
233.423.420
243.423.420
253.423.420
263.423.420
273.433.420.0100000000000002
283.473.42999925005630.0400007499436961
293.513.469997000168970.040002999831025
303.523.509997000000250.0100029999997542
313.523.519999249831327.50168679175545e-07
323.523.519999999943745.62585533714355e-11
333.523.524.44089209850063e-15
343.523.520
353.523.520
363.523.520
373.523.520
383.523.520
393.583.520.0600000000000001
403.63.579995500337820.0200044996621753
413.613.599998499775160.010001500224841
423.613.60999924994387.50056204257277e-07
433.613.609999999943755.62501156764483e-11
443.633.610.020000000000004
453.683.629998500112610.0500014998873919
463.693.679996250169040.0100037498309624
473.693.689999249775097.50224911971742e-07
483.693.689999999943745.62625501743241e-11
493.693.694.44089209850063e-15
503.693.690
513.693.690
523.693.690
533.693.690
543.783.690.0899999999999999
553.793.779993250506740.0100067494932636
563.793.789999249550137.50449869801884e-07
573.83.789999999943720.0100000000562792
583.83.79999925005637.49943700029121e-07
593.83.799999999943765.62416779814612e-11
603.83.83.99680288865056e-15
613.813.80.0100000000000002
623.953.80999925005630.140000749943696
633.993.949989500732020.0400104992679844
6443.989996999437830.0100030005621696
654.063.999999249831280.060000750168721
664.164.059995500281570.100004499718435
674.194.159992500225590.0300074997744133
684.24.189997749606470.0100022503935282
694.24.199999249887547.50112462810648e-07
704.24.199999999943755.62545565685468e-11
714.24.24.44089209850063e-15
724.24.20
734.234.20.0300000000000002
744.384.229997750168910.150002249831087
754.434.379988750675840.0500112493241636
764.444.429996249437880.0100037505621167
774.444.439999249775037.50224966594715e-07
784.444.439999999943745.62625501743241e-11
794.444.444.44089209850063e-15
804.444.440
814.454.440.00999999999999979
824.454.44999925005637.49943695588229e-07
834.454.449999999943765.62412338922513e-11
844.454.454.44089209850063e-15
854.454.450
864.454.450
874.454.450
884.454.450
894.464.450.00999999999999979
904.464.45999925005637.49943695588229e-07
914.464.459999999943765.62412338922513e-11
924.484.460.0200000000000049
934.584.479998500112610.100001499887392
944.674.579992500450560.0900074995494418
954.684.669993249944310.0100067500556866
964.684.679999249550097.50449911990358e-07







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
974.679999999943724.621487778573624.73851222131382
984.679999999943724.597254325705564.76274567418188
994.679999999943724.578658926530264.78134107335718
1004.679999999943724.562982139272554.79701786061489
1014.679999999943724.549170545035734.81082945485171
1024.679999999943724.536683870959624.82331612892782
1034.679999999943724.525201164733474.83479883515398
1044.679999999943724.514513305802124.84548669408532
1054.679999999943724.504475037350424.85552496253703
1064.679999999943724.494980598126384.86501940176106
1074.679999999943724.485950146544374.87404985334307
1084.679999999943724.477321653394874.88267834649257

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 4.67999999994372 & 4.62148777857362 & 4.73851222131382 \tabularnewline
98 & 4.67999999994372 & 4.59725432570556 & 4.76274567418188 \tabularnewline
99 & 4.67999999994372 & 4.57865892653026 & 4.78134107335718 \tabularnewline
100 & 4.67999999994372 & 4.56298213927255 & 4.79701786061489 \tabularnewline
101 & 4.67999999994372 & 4.54917054503573 & 4.81082945485171 \tabularnewline
102 & 4.67999999994372 & 4.53668387095962 & 4.82331612892782 \tabularnewline
103 & 4.67999999994372 & 4.52520116473347 & 4.83479883515398 \tabularnewline
104 & 4.67999999994372 & 4.51451330580212 & 4.84548669408532 \tabularnewline
105 & 4.67999999994372 & 4.50447503735042 & 4.85552496253703 \tabularnewline
106 & 4.67999999994372 & 4.49498059812638 & 4.86501940176106 \tabularnewline
107 & 4.67999999994372 & 4.48595014654437 & 4.87404985334307 \tabularnewline
108 & 4.67999999994372 & 4.47732165339487 & 4.88267834649257 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147764&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]4.67999999994372[/C][C]4.62148777857362[/C][C]4.73851222131382[/C][/ROW]
[ROW][C]98[/C][C]4.67999999994372[/C][C]4.59725432570556[/C][C]4.76274567418188[/C][/ROW]
[ROW][C]99[/C][C]4.67999999994372[/C][C]4.57865892653026[/C][C]4.78134107335718[/C][/ROW]
[ROW][C]100[/C][C]4.67999999994372[/C][C]4.56298213927255[/C][C]4.79701786061489[/C][/ROW]
[ROW][C]101[/C][C]4.67999999994372[/C][C]4.54917054503573[/C][C]4.81082945485171[/C][/ROW]
[ROW][C]102[/C][C]4.67999999994372[/C][C]4.53668387095962[/C][C]4.82331612892782[/C][/ROW]
[ROW][C]103[/C][C]4.67999999994372[/C][C]4.52520116473347[/C][C]4.83479883515398[/C][/ROW]
[ROW][C]104[/C][C]4.67999999994372[/C][C]4.51451330580212[/C][C]4.84548669408532[/C][/ROW]
[ROW][C]105[/C][C]4.67999999994372[/C][C]4.50447503735042[/C][C]4.85552496253703[/C][/ROW]
[ROW][C]106[/C][C]4.67999999994372[/C][C]4.49498059812638[/C][C]4.86501940176106[/C][/ROW]
[ROW][C]107[/C][C]4.67999999994372[/C][C]4.48595014654437[/C][C]4.87404985334307[/C][/ROW]
[ROW][C]108[/C][C]4.67999999994372[/C][C]4.47732165339487[/C][C]4.88267834649257[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147764&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147764&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
974.679999999943724.621487778573624.73851222131382
984.679999999943724.597254325705564.76274567418188
994.679999999943724.578658926530264.78134107335718
1004.679999999943724.562982139272554.79701786061489
1014.679999999943724.549170545035734.81082945485171
1024.679999999943724.536683870959624.82331612892782
1034.679999999943724.525201164733474.83479883515398
1044.679999999943724.514513305802124.84548669408532
1054.679999999943724.504475037350424.85552496253703
1064.679999999943724.494980598126384.86501940176106
1074.679999999943724.485950146544374.87404985334307
1084.679999999943724.477321653394874.88267834649257



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