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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 27 May 2012 17:04:02 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/27/t1338152816n26us1yb1016j30.htm/, Retrieved Wed, 08 May 2024 23:30:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167748, Retrieved Wed, 08 May 2024 23:30:14 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W101
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-27 21:04:02] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
162,32
162,76
163,39
162,58
162,66
162,66
162,66
162,89
163,03
162,38
162,44
162,51
162,51
162,42
162,07
161,45
162,22
162,21
162,21
162,21
162,41
163,96
163,79
163,86
163,86
164,39
164,74
164,27
165,2
165,42
165,42
165,5
165,71
165,74
165,29
164,88
164,88
164,57
164,53
165,03
165,92
165,92
165,92
165,92
166,12
166,34
165,48
165,61
165,61
165,94
165,88
166,23
166,32
166,43
166,43
166,2
166,21
168,02
168,68
168,65




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167748&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167748&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167748&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0968811902755698
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0968811902755698 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167748&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]0.0968811902755698[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167748&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167748&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
beta0.0968811902755698
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3163.39163.20.189999999999998
4162.58163.848407426152-1.26840742615232
5162.66162.915522604952-0.255522604952375
6162.66162.970767270842-0.310767270842234
7162.66162.940659767744-0.280659767744368
8162.89162.913469115383-0.0234691153828237
9163.03163.14119539955-0.111195399549814
10162.38163.270422656888-0.890422656888262
11162.44162.534157450041-0.0941574500405977
12162.51162.585035364207-0.0750353642073662
13162.51162.64776584881-0.137765848810176
14162.42162.634418929398-0.214418929398136
15162.07162.5236457683-0.453645768300419
16161.45162.129696026304-0.679696026304015
17162.22161.443846266250.776153733749908
18162.21162.289040963813-0.0790409638126164
19162.21162.271383381158-0.0613833811579241
20162.21162.265436486128-0.0554364861282011
21162.41162.2600657333670.149934266632584
22163.96162.4745915435821.48540845641816
23163.79164.168499682885-0.378499682885064
24163.86163.961830183088-0.101830183088197
25163.86164.021964753745-0.161964753744655
26164.39164.0062734156190.383726584380781
27164.74164.5734493038540.166550696145634
28164.27164.939584933538-0.669584933538175
29165.2164.4047147481860.795285251813567
30165.42165.4117629299910.00823707000927243
31165.42165.632560947138-0.212560947137604
32165.5165.611967789573-0.111967789572788
33165.71165.6811202168460.0288797831535419
34165.74165.893918124613-0.153918124613284
35165.29165.909006353496-0.619006353495791
36164.88165.399036281181-0.519036281180945
37164.88164.938751428464-0.0587514284639497
38164.57164.933059520144-0.363059520143963
39164.53164.587885881692-0.0578858816915329
40165.03164.5422778285730.487722171426896
41165.92165.0895289330650.830471066935246
42165.92166.059985958519-0.139985958518849
43165.92166.046423952236-0.126423952235683
44165.92166.034175849264-0.114175849263745
45166.12166.0231143570860.0968856429136622
46166.34166.2325007534920.107499246507558
47165.48166.462915408448-0.982915408447838
48165.61165.5076893937370.102310606262819
49165.61165.64760136705-0.0376013670497457
50165.94165.6439585018540.296041498145996
51165.88166.002639354565-0.122639354565337
52166.23165.930757907920.299242092079595
53166.32166.3097488379820.0102511620183634
54166.43166.400741982760.0292580172403234
55166.43166.513576534295-0.0835765342950197
56166.2166.505479540173-0.305479540173422
57166.21166.245884318717-0.0358843187165689
58168.02166.2524078032071.76759219679292
59168.68168.2336542391540.446345760845787
60168.65168.936896747739-0.286896747739405

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 163.39 & 163.2 & 0.189999999999998 \tabularnewline
4 & 162.58 & 163.848407426152 & -1.26840742615232 \tabularnewline
5 & 162.66 & 162.915522604952 & -0.255522604952375 \tabularnewline
6 & 162.66 & 162.970767270842 & -0.310767270842234 \tabularnewline
7 & 162.66 & 162.940659767744 & -0.280659767744368 \tabularnewline
8 & 162.89 & 162.913469115383 & -0.0234691153828237 \tabularnewline
9 & 163.03 & 163.14119539955 & -0.111195399549814 \tabularnewline
10 & 162.38 & 163.270422656888 & -0.890422656888262 \tabularnewline
11 & 162.44 & 162.534157450041 & -0.0941574500405977 \tabularnewline
12 & 162.51 & 162.585035364207 & -0.0750353642073662 \tabularnewline
13 & 162.51 & 162.64776584881 & -0.137765848810176 \tabularnewline
14 & 162.42 & 162.634418929398 & -0.214418929398136 \tabularnewline
15 & 162.07 & 162.5236457683 & -0.453645768300419 \tabularnewline
16 & 161.45 & 162.129696026304 & -0.679696026304015 \tabularnewline
17 & 162.22 & 161.44384626625 & 0.776153733749908 \tabularnewline
18 & 162.21 & 162.289040963813 & -0.0790409638126164 \tabularnewline
19 & 162.21 & 162.271383381158 & -0.0613833811579241 \tabularnewline
20 & 162.21 & 162.265436486128 & -0.0554364861282011 \tabularnewline
21 & 162.41 & 162.260065733367 & 0.149934266632584 \tabularnewline
22 & 163.96 & 162.474591543582 & 1.48540845641816 \tabularnewline
23 & 163.79 & 164.168499682885 & -0.378499682885064 \tabularnewline
24 & 163.86 & 163.961830183088 & -0.101830183088197 \tabularnewline
25 & 163.86 & 164.021964753745 & -0.161964753744655 \tabularnewline
26 & 164.39 & 164.006273415619 & 0.383726584380781 \tabularnewline
27 & 164.74 & 164.573449303854 & 0.166550696145634 \tabularnewline
28 & 164.27 & 164.939584933538 & -0.669584933538175 \tabularnewline
29 & 165.2 & 164.404714748186 & 0.795285251813567 \tabularnewline
30 & 165.42 & 165.411762929991 & 0.00823707000927243 \tabularnewline
31 & 165.42 & 165.632560947138 & -0.212560947137604 \tabularnewline
32 & 165.5 & 165.611967789573 & -0.111967789572788 \tabularnewline
33 & 165.71 & 165.681120216846 & 0.0288797831535419 \tabularnewline
34 & 165.74 & 165.893918124613 & -0.153918124613284 \tabularnewline
35 & 165.29 & 165.909006353496 & -0.619006353495791 \tabularnewline
36 & 164.88 & 165.399036281181 & -0.519036281180945 \tabularnewline
37 & 164.88 & 164.938751428464 & -0.0587514284639497 \tabularnewline
38 & 164.57 & 164.933059520144 & -0.363059520143963 \tabularnewline
39 & 164.53 & 164.587885881692 & -0.0578858816915329 \tabularnewline
40 & 165.03 & 164.542277828573 & 0.487722171426896 \tabularnewline
41 & 165.92 & 165.089528933065 & 0.830471066935246 \tabularnewline
42 & 165.92 & 166.059985958519 & -0.139985958518849 \tabularnewline
43 & 165.92 & 166.046423952236 & -0.126423952235683 \tabularnewline
44 & 165.92 & 166.034175849264 & -0.114175849263745 \tabularnewline
45 & 166.12 & 166.023114357086 & 0.0968856429136622 \tabularnewline
46 & 166.34 & 166.232500753492 & 0.107499246507558 \tabularnewline
47 & 165.48 & 166.462915408448 & -0.982915408447838 \tabularnewline
48 & 165.61 & 165.507689393737 & 0.102310606262819 \tabularnewline
49 & 165.61 & 165.64760136705 & -0.0376013670497457 \tabularnewline
50 & 165.94 & 165.643958501854 & 0.296041498145996 \tabularnewline
51 & 165.88 & 166.002639354565 & -0.122639354565337 \tabularnewline
52 & 166.23 & 165.93075790792 & 0.299242092079595 \tabularnewline
53 & 166.32 & 166.309748837982 & 0.0102511620183634 \tabularnewline
54 & 166.43 & 166.40074198276 & 0.0292580172403234 \tabularnewline
55 & 166.43 & 166.513576534295 & -0.0835765342950197 \tabularnewline
56 & 166.2 & 166.505479540173 & -0.305479540173422 \tabularnewline
57 & 166.21 & 166.245884318717 & -0.0358843187165689 \tabularnewline
58 & 168.02 & 166.252407803207 & 1.76759219679292 \tabularnewline
59 & 168.68 & 168.233654239154 & 0.446345760845787 \tabularnewline
60 & 168.65 & 168.936896747739 & -0.286896747739405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167748&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]163.39[/C][C]163.2[/C][C]0.189999999999998[/C][/ROW]
[ROW][C]4[/C][C]162.58[/C][C]163.848407426152[/C][C]-1.26840742615232[/C][/ROW]
[ROW][C]5[/C][C]162.66[/C][C]162.915522604952[/C][C]-0.255522604952375[/C][/ROW]
[ROW][C]6[/C][C]162.66[/C][C]162.970767270842[/C][C]-0.310767270842234[/C][/ROW]
[ROW][C]7[/C][C]162.66[/C][C]162.940659767744[/C][C]-0.280659767744368[/C][/ROW]
[ROW][C]8[/C][C]162.89[/C][C]162.913469115383[/C][C]-0.0234691153828237[/C][/ROW]
[ROW][C]9[/C][C]163.03[/C][C]163.14119539955[/C][C]-0.111195399549814[/C][/ROW]
[ROW][C]10[/C][C]162.38[/C][C]163.270422656888[/C][C]-0.890422656888262[/C][/ROW]
[ROW][C]11[/C][C]162.44[/C][C]162.534157450041[/C][C]-0.0941574500405977[/C][/ROW]
[ROW][C]12[/C][C]162.51[/C][C]162.585035364207[/C][C]-0.0750353642073662[/C][/ROW]
[ROW][C]13[/C][C]162.51[/C][C]162.64776584881[/C][C]-0.137765848810176[/C][/ROW]
[ROW][C]14[/C][C]162.42[/C][C]162.634418929398[/C][C]-0.214418929398136[/C][/ROW]
[ROW][C]15[/C][C]162.07[/C][C]162.5236457683[/C][C]-0.453645768300419[/C][/ROW]
[ROW][C]16[/C][C]161.45[/C][C]162.129696026304[/C][C]-0.679696026304015[/C][/ROW]
[ROW][C]17[/C][C]162.22[/C][C]161.44384626625[/C][C]0.776153733749908[/C][/ROW]
[ROW][C]18[/C][C]162.21[/C][C]162.289040963813[/C][C]-0.0790409638126164[/C][/ROW]
[ROW][C]19[/C][C]162.21[/C][C]162.271383381158[/C][C]-0.0613833811579241[/C][/ROW]
[ROW][C]20[/C][C]162.21[/C][C]162.265436486128[/C][C]-0.0554364861282011[/C][/ROW]
[ROW][C]21[/C][C]162.41[/C][C]162.260065733367[/C][C]0.149934266632584[/C][/ROW]
[ROW][C]22[/C][C]163.96[/C][C]162.474591543582[/C][C]1.48540845641816[/C][/ROW]
[ROW][C]23[/C][C]163.79[/C][C]164.168499682885[/C][C]-0.378499682885064[/C][/ROW]
[ROW][C]24[/C][C]163.86[/C][C]163.961830183088[/C][C]-0.101830183088197[/C][/ROW]
[ROW][C]25[/C][C]163.86[/C][C]164.021964753745[/C][C]-0.161964753744655[/C][/ROW]
[ROW][C]26[/C][C]164.39[/C][C]164.006273415619[/C][C]0.383726584380781[/C][/ROW]
[ROW][C]27[/C][C]164.74[/C][C]164.573449303854[/C][C]0.166550696145634[/C][/ROW]
[ROW][C]28[/C][C]164.27[/C][C]164.939584933538[/C][C]-0.669584933538175[/C][/ROW]
[ROW][C]29[/C][C]165.2[/C][C]164.404714748186[/C][C]0.795285251813567[/C][/ROW]
[ROW][C]30[/C][C]165.42[/C][C]165.411762929991[/C][C]0.00823707000927243[/C][/ROW]
[ROW][C]31[/C][C]165.42[/C][C]165.632560947138[/C][C]-0.212560947137604[/C][/ROW]
[ROW][C]32[/C][C]165.5[/C][C]165.611967789573[/C][C]-0.111967789572788[/C][/ROW]
[ROW][C]33[/C][C]165.71[/C][C]165.681120216846[/C][C]0.0288797831535419[/C][/ROW]
[ROW][C]34[/C][C]165.74[/C][C]165.893918124613[/C][C]-0.153918124613284[/C][/ROW]
[ROW][C]35[/C][C]165.29[/C][C]165.909006353496[/C][C]-0.619006353495791[/C][/ROW]
[ROW][C]36[/C][C]164.88[/C][C]165.399036281181[/C][C]-0.519036281180945[/C][/ROW]
[ROW][C]37[/C][C]164.88[/C][C]164.938751428464[/C][C]-0.0587514284639497[/C][/ROW]
[ROW][C]38[/C][C]164.57[/C][C]164.933059520144[/C][C]-0.363059520143963[/C][/ROW]
[ROW][C]39[/C][C]164.53[/C][C]164.587885881692[/C][C]-0.0578858816915329[/C][/ROW]
[ROW][C]40[/C][C]165.03[/C][C]164.542277828573[/C][C]0.487722171426896[/C][/ROW]
[ROW][C]41[/C][C]165.92[/C][C]165.089528933065[/C][C]0.830471066935246[/C][/ROW]
[ROW][C]42[/C][C]165.92[/C][C]166.059985958519[/C][C]-0.139985958518849[/C][/ROW]
[ROW][C]43[/C][C]165.92[/C][C]166.046423952236[/C][C]-0.126423952235683[/C][/ROW]
[ROW][C]44[/C][C]165.92[/C][C]166.034175849264[/C][C]-0.114175849263745[/C][/ROW]
[ROW][C]45[/C][C]166.12[/C][C]166.023114357086[/C][C]0.0968856429136622[/C][/ROW]
[ROW][C]46[/C][C]166.34[/C][C]166.232500753492[/C][C]0.107499246507558[/C][/ROW]
[ROW][C]47[/C][C]165.48[/C][C]166.462915408448[/C][C]-0.982915408447838[/C][/ROW]
[ROW][C]48[/C][C]165.61[/C][C]165.507689393737[/C][C]0.102310606262819[/C][/ROW]
[ROW][C]49[/C][C]165.61[/C][C]165.64760136705[/C][C]-0.0376013670497457[/C][/ROW]
[ROW][C]50[/C][C]165.94[/C][C]165.643958501854[/C][C]0.296041498145996[/C][/ROW]
[ROW][C]51[/C][C]165.88[/C][C]166.002639354565[/C][C]-0.122639354565337[/C][/ROW]
[ROW][C]52[/C][C]166.23[/C][C]165.93075790792[/C][C]0.299242092079595[/C][/ROW]
[ROW][C]53[/C][C]166.32[/C][C]166.309748837982[/C][C]0.0102511620183634[/C][/ROW]
[ROW][C]54[/C][C]166.43[/C][C]166.40074198276[/C][C]0.0292580172403234[/C][/ROW]
[ROW][C]55[/C][C]166.43[/C][C]166.513576534295[/C][C]-0.0835765342950197[/C][/ROW]
[ROW][C]56[/C][C]166.2[/C][C]166.505479540173[/C][C]-0.305479540173422[/C][/ROW]
[ROW][C]57[/C][C]166.21[/C][C]166.245884318717[/C][C]-0.0358843187165689[/C][/ROW]
[ROW][C]58[/C][C]168.02[/C][C]166.252407803207[/C][C]1.76759219679292[/C][/ROW]
[ROW][C]59[/C][C]168.68[/C][C]168.233654239154[/C][C]0.446345760845787[/C][/ROW]
[ROW][C]60[/C][C]168.65[/C][C]168.936896747739[/C][C]-0.286896747739405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167748&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167748&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
3163.39163.20.189999999999998
4162.58163.848407426152-1.26840742615232
5162.66162.915522604952-0.255522604952375
6162.66162.970767270842-0.310767270842234
7162.66162.940659767744-0.280659767744368
8162.89162.913469115383-0.0234691153828237
9163.03163.14119539955-0.111195399549814
10162.38163.270422656888-0.890422656888262
11162.44162.534157450041-0.0941574500405977
12162.51162.585035364207-0.0750353642073662
13162.51162.64776584881-0.137765848810176
14162.42162.634418929398-0.214418929398136
15162.07162.5236457683-0.453645768300419
16161.45162.129696026304-0.679696026304015
17162.22161.443846266250.776153733749908
18162.21162.289040963813-0.0790409638126164
19162.21162.271383381158-0.0613833811579241
20162.21162.265436486128-0.0554364861282011
21162.41162.2600657333670.149934266632584
22163.96162.4745915435821.48540845641816
23163.79164.168499682885-0.378499682885064
24163.86163.961830183088-0.101830183088197
25163.86164.021964753745-0.161964753744655
26164.39164.0062734156190.383726584380781
27164.74164.5734493038540.166550696145634
28164.27164.939584933538-0.669584933538175
29165.2164.4047147481860.795285251813567
30165.42165.4117629299910.00823707000927243
31165.42165.632560947138-0.212560947137604
32165.5165.611967789573-0.111967789572788
33165.71165.6811202168460.0288797831535419
34165.74165.893918124613-0.153918124613284
35165.29165.909006353496-0.619006353495791
36164.88165.399036281181-0.519036281180945
37164.88164.938751428464-0.0587514284639497
38164.57164.933059520144-0.363059520143963
39164.53164.587885881692-0.0578858816915329
40165.03164.5422778285730.487722171426896
41165.92165.0895289330650.830471066935246
42165.92166.059985958519-0.139985958518849
43165.92166.046423952236-0.126423952235683
44165.92166.034175849264-0.114175849263745
45166.12166.0231143570860.0968856429136622
46166.34166.2325007534920.107499246507558
47165.48166.462915408448-0.982915408447838
48165.61165.5076893937370.102310606262819
49165.61165.64760136705-0.0376013670497457
50165.94165.6439585018540.296041498145996
51165.88166.002639354565-0.122639354565337
52166.23165.930757907920.299242092079595
53166.32166.3097488379820.0102511620183634
54166.43166.400741982760.0292580172403234
55166.43166.513576534295-0.0835765342950197
56166.2166.505479540173-0.305479540173422
57166.21166.245884318717-0.0358843187165689
58168.02166.2524078032071.76759219679292
59168.68168.2336542391540.446345760845787
60168.65168.936896747739-0.286896747739405







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61168.879101849332167.90131294546169.856890753204
62169.108203698664167.656871017462170.559536379867
63169.337305547997167.474825069292171.199786026702
64169.566407397329167.316647546321171.816167248337
65169.795509246661167.168329882199172.422688611123
66170.024611095993167.023155297271173.026066894716
67170.253712945326166.877418647774173.630007242877
68170.482814794658166.728897170413174.236732418902
69170.71191664399166.576183667833174.847649620147
70170.941018493322166.41835560011175.463681386534
71171.170120342654166.254795122805176.085445562503
72171.399222191987166.085084287829176.713360096144

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 168.879101849332 & 167.90131294546 & 169.856890753204 \tabularnewline
62 & 169.108203698664 & 167.656871017462 & 170.559536379867 \tabularnewline
63 & 169.337305547997 & 167.474825069292 & 171.199786026702 \tabularnewline
64 & 169.566407397329 & 167.316647546321 & 171.816167248337 \tabularnewline
65 & 169.795509246661 & 167.168329882199 & 172.422688611123 \tabularnewline
66 & 170.024611095993 & 167.023155297271 & 173.026066894716 \tabularnewline
67 & 170.253712945326 & 166.877418647774 & 173.630007242877 \tabularnewline
68 & 170.482814794658 & 166.728897170413 & 174.236732418902 \tabularnewline
69 & 170.71191664399 & 166.576183667833 & 174.847649620147 \tabularnewline
70 & 170.941018493322 & 166.41835560011 & 175.463681386534 \tabularnewline
71 & 171.170120342654 & 166.254795122805 & 176.085445562503 \tabularnewline
72 & 171.399222191987 & 166.085084287829 & 176.713360096144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167748&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]61[/C][C]168.879101849332[/C][C]167.90131294546[/C][C]169.856890753204[/C][/ROW]
[ROW][C]62[/C][C]169.108203698664[/C][C]167.656871017462[/C][C]170.559536379867[/C][/ROW]
[ROW][C]63[/C][C]169.337305547997[/C][C]167.474825069292[/C][C]171.199786026702[/C][/ROW]
[ROW][C]64[/C][C]169.566407397329[/C][C]167.316647546321[/C][C]171.816167248337[/C][/ROW]
[ROW][C]65[/C][C]169.795509246661[/C][C]167.168329882199[/C][C]172.422688611123[/C][/ROW]
[ROW][C]66[/C][C]170.024611095993[/C][C]167.023155297271[/C][C]173.026066894716[/C][/ROW]
[ROW][C]67[/C][C]170.253712945326[/C][C]166.877418647774[/C][C]173.630007242877[/C][/ROW]
[ROW][C]68[/C][C]170.482814794658[/C][C]166.728897170413[/C][C]174.236732418902[/C][/ROW]
[ROW][C]69[/C][C]170.71191664399[/C][C]166.576183667833[/C][C]174.847649620147[/C][/ROW]
[ROW][C]70[/C][C]170.941018493322[/C][C]166.41835560011[/C][C]175.463681386534[/C][/ROW]
[ROW][C]71[/C][C]171.170120342654[/C][C]166.254795122805[/C][C]176.085445562503[/C][/ROW]
[ROW][C]72[/C][C]171.399222191987[/C][C]166.085084287829[/C][C]176.713360096144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167748&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167748&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
61168.879101849332167.90131294546169.856890753204
62169.108203698664167.656871017462170.559536379867
63169.337305547997167.474825069292171.199786026702
64169.566407397329167.316647546321171.816167248337
65169.795509246661167.168329882199172.422688611123
66170.024611095993167.023155297271173.026066894716
67170.253712945326166.877418647774173.630007242877
68170.482814794658166.728897170413174.236732418902
69170.71191664399166.576183667833174.847649620147
70170.941018493322166.41835560011175.463681386534
71171.170120342654166.254795122805176.085445562503
72171.399222191987166.085084287829176.713360096144



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