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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 21:43:38 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/25/t1461617078sbjfod09pdttrl2.htm/, Retrieved Mon, 06 May 2024 06:07:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294790, Retrieved Mon, 06 May 2024 06:07:18 +0000
QR Codes:

Original text written by user:Benzine Exponential Smoothing
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 oef 2] [2016-04-25 20:43:38] [8fd6d867e46a5221be3e0a22eb2f8c7a] [Current]
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Dataseries X:
93,41
93
96,61
99,69
101,05
98
97,32
97,83
99,57
97,63
96,68
96,28
99,81
101,43
105,59
108,86
104,01
101,95
101,52
105,61
108,43
105,54
100,11
99,93
99,88
102,71
101,89
101,93
99,49
99,87
100,33
101,5
102,29
97,04
95,71
97,37
96,51
96,33
96,88
97,59
98,96
99,93
101,34
98,04
98,56
96,73
92,36
87,88
79,84
82,91
87,78
89,36
91,86
92,48
93,4
89,97
83,96
82,76
82,97
81,07




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294790&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294790&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294790&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294790&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]0.999933893038648[/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=294790&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294790&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
29393.41-0.409999999999997
396.6193.00002710385423.60997289614583
499.6996.60976135566133.08023864433872
5101.0599.6897963747831.36020362521701
698101.049910081072-3.04991008107152
797.3298.0002016202879-0.68020162028786
897.8397.32004496606220.509955033937786
999.5797.82996628842231.74003371157771
1097.6399.5698849716587-1.93988497165869
1196.6897.6301282399008-0.950128239900835
1296.2896.6800628100908-0.40006281009083
1399.8196.28002644693673.52997355306327
14101.4399.80976664417481.62023335582525
15105.59101.4298928912964.16010710870383
16108.86105.589724987963.27027501203986
17104.01108.859783812056-4.84978381205616
18101.95104.010320604471-2.06032060447103
19101.52101.950136201535-0.43013620153458
20105.61101.5200284349974.08997156500276
21108.43105.6097296244082.82027037559219
22105.54108.429813560495-2.88981356049527
23100.11105.540191036793-5.43019103679336
2499.93100.110358973429-0.180358973428994
2599.8899.9300119229837-0.0500119229836997
26102.7199.88000330613632.82999669386373
27101.89102.709812917518-0.819812917517922
28101.93101.8900541953410.0399458046591548
2999.49101.929997359304-2.43999735930426
3099.8799.49016130081110.37983869918888
31100.3399.86997489001780.460025109982212
32101.5100.3299695891381.17003041086218
33102.29101.4999226528450.790077347155162
3497.04102.289947770387-5.24994777038735
3595.7197.0403470580944-1.33034705809438
3697.3795.71008794520161.65991205479845
3796.5197.369890268258-0.859890268257956
3896.3396.5100568447327-0.180056844732732
3996.8896.33001190301090.549988096989125
4097.5996.87996364195810.710036358041876
4198.9697.58995306165391.37004693834608
4299.9398.959909430360.970090569640021
43101.3499.92993587026021.41006412973979
4498.04101.339906784945-3.29990678494507
4598.5698.04021814681030.519781853189698
4696.7398.5599656388011-1.82996563880111
4792.3696.7301209734678-4.37012097346776
4887.8892.3602888954183-4.4802888954183
4979.8487.8802961782849-8.04029617828485
5082.9179.84053151954873.06946848045128
5187.7882.90979708676584.87020291323421
5289.3687.77967804568421.58032195431575
5391.8689.35989552971762.50010447028235
5492.4891.85983472569040.620165274309599
5593.492.47995900275820.920040997241813
5689.9793.3999391788854-3.42993917888536
5783.9689.9702267428567-6.01022674285673
5882.7683.960397317827-1.20039731782698
5982.9782.76007935461910.209920645380905
6081.0782.969986122784-1.89998612278401

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 93 & 93.41 & -0.409999999999997 \tabularnewline
3 & 96.61 & 93.0000271038542 & 3.60997289614583 \tabularnewline
4 & 99.69 & 96.6097613556613 & 3.08023864433872 \tabularnewline
5 & 101.05 & 99.689796374783 & 1.36020362521701 \tabularnewline
6 & 98 & 101.049910081072 & -3.04991008107152 \tabularnewline
7 & 97.32 & 98.0002016202879 & -0.68020162028786 \tabularnewline
8 & 97.83 & 97.3200449660622 & 0.509955033937786 \tabularnewline
9 & 99.57 & 97.8299662884223 & 1.74003371157771 \tabularnewline
10 & 97.63 & 99.5698849716587 & -1.93988497165869 \tabularnewline
11 & 96.68 & 97.6301282399008 & -0.950128239900835 \tabularnewline
12 & 96.28 & 96.6800628100908 & -0.40006281009083 \tabularnewline
13 & 99.81 & 96.2800264469367 & 3.52997355306327 \tabularnewline
14 & 101.43 & 99.8097666441748 & 1.62023335582525 \tabularnewline
15 & 105.59 & 101.429892891296 & 4.16010710870383 \tabularnewline
16 & 108.86 & 105.58972498796 & 3.27027501203986 \tabularnewline
17 & 104.01 & 108.859783812056 & -4.84978381205616 \tabularnewline
18 & 101.95 & 104.010320604471 & -2.06032060447103 \tabularnewline
19 & 101.52 & 101.950136201535 & -0.43013620153458 \tabularnewline
20 & 105.61 & 101.520028434997 & 4.08997156500276 \tabularnewline
21 & 108.43 & 105.609729624408 & 2.82027037559219 \tabularnewline
22 & 105.54 & 108.429813560495 & -2.88981356049527 \tabularnewline
23 & 100.11 & 105.540191036793 & -5.43019103679336 \tabularnewline
24 & 99.93 & 100.110358973429 & -0.180358973428994 \tabularnewline
25 & 99.88 & 99.9300119229837 & -0.0500119229836997 \tabularnewline
26 & 102.71 & 99.8800033061363 & 2.82999669386373 \tabularnewline
27 & 101.89 & 102.709812917518 & -0.819812917517922 \tabularnewline
28 & 101.93 & 101.890054195341 & 0.0399458046591548 \tabularnewline
29 & 99.49 & 101.929997359304 & -2.43999735930426 \tabularnewline
30 & 99.87 & 99.4901613008111 & 0.37983869918888 \tabularnewline
31 & 100.33 & 99.8699748900178 & 0.460025109982212 \tabularnewline
32 & 101.5 & 100.329969589138 & 1.17003041086218 \tabularnewline
33 & 102.29 & 101.499922652845 & 0.790077347155162 \tabularnewline
34 & 97.04 & 102.289947770387 & -5.24994777038735 \tabularnewline
35 & 95.71 & 97.0403470580944 & -1.33034705809438 \tabularnewline
36 & 97.37 & 95.7100879452016 & 1.65991205479845 \tabularnewline
37 & 96.51 & 97.369890268258 & -0.859890268257956 \tabularnewline
38 & 96.33 & 96.5100568447327 & -0.180056844732732 \tabularnewline
39 & 96.88 & 96.3300119030109 & 0.549988096989125 \tabularnewline
40 & 97.59 & 96.8799636419581 & 0.710036358041876 \tabularnewline
41 & 98.96 & 97.5899530616539 & 1.37004693834608 \tabularnewline
42 & 99.93 & 98.95990943036 & 0.970090569640021 \tabularnewline
43 & 101.34 & 99.9299358702602 & 1.41006412973979 \tabularnewline
44 & 98.04 & 101.339906784945 & -3.29990678494507 \tabularnewline
45 & 98.56 & 98.0402181468103 & 0.519781853189698 \tabularnewline
46 & 96.73 & 98.5599656388011 & -1.82996563880111 \tabularnewline
47 & 92.36 & 96.7301209734678 & -4.37012097346776 \tabularnewline
48 & 87.88 & 92.3602888954183 & -4.4802888954183 \tabularnewline
49 & 79.84 & 87.8802961782849 & -8.04029617828485 \tabularnewline
50 & 82.91 & 79.8405315195487 & 3.06946848045128 \tabularnewline
51 & 87.78 & 82.9097970867658 & 4.87020291323421 \tabularnewline
52 & 89.36 & 87.7796780456842 & 1.58032195431575 \tabularnewline
53 & 91.86 & 89.3598955297176 & 2.50010447028235 \tabularnewline
54 & 92.48 & 91.8598347256904 & 0.620165274309599 \tabularnewline
55 & 93.4 & 92.4799590027582 & 0.920040997241813 \tabularnewline
56 & 89.97 & 93.3999391788854 & -3.42993917888536 \tabularnewline
57 & 83.96 & 89.9702267428567 & -6.01022674285673 \tabularnewline
58 & 82.76 & 83.960397317827 & -1.20039731782698 \tabularnewline
59 & 82.97 & 82.7600793546191 & 0.209920645380905 \tabularnewline
60 & 81.07 & 82.969986122784 & -1.89998612278401 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294790&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]93[/C][C]93.41[/C][C]-0.409999999999997[/C][/ROW]
[ROW][C]3[/C][C]96.61[/C][C]93.0000271038542[/C][C]3.60997289614583[/C][/ROW]
[ROW][C]4[/C][C]99.69[/C][C]96.6097613556613[/C][C]3.08023864433872[/C][/ROW]
[ROW][C]5[/C][C]101.05[/C][C]99.689796374783[/C][C]1.36020362521701[/C][/ROW]
[ROW][C]6[/C][C]98[/C][C]101.049910081072[/C][C]-3.04991008107152[/C][/ROW]
[ROW][C]7[/C][C]97.32[/C][C]98.0002016202879[/C][C]-0.68020162028786[/C][/ROW]
[ROW][C]8[/C][C]97.83[/C][C]97.3200449660622[/C][C]0.509955033937786[/C][/ROW]
[ROW][C]9[/C][C]99.57[/C][C]97.8299662884223[/C][C]1.74003371157771[/C][/ROW]
[ROW][C]10[/C][C]97.63[/C][C]99.5698849716587[/C][C]-1.93988497165869[/C][/ROW]
[ROW][C]11[/C][C]96.68[/C][C]97.6301282399008[/C][C]-0.950128239900835[/C][/ROW]
[ROW][C]12[/C][C]96.28[/C][C]96.6800628100908[/C][C]-0.40006281009083[/C][/ROW]
[ROW][C]13[/C][C]99.81[/C][C]96.2800264469367[/C][C]3.52997355306327[/C][/ROW]
[ROW][C]14[/C][C]101.43[/C][C]99.8097666441748[/C][C]1.62023335582525[/C][/ROW]
[ROW][C]15[/C][C]105.59[/C][C]101.429892891296[/C][C]4.16010710870383[/C][/ROW]
[ROW][C]16[/C][C]108.86[/C][C]105.58972498796[/C][C]3.27027501203986[/C][/ROW]
[ROW][C]17[/C][C]104.01[/C][C]108.859783812056[/C][C]-4.84978381205616[/C][/ROW]
[ROW][C]18[/C][C]101.95[/C][C]104.010320604471[/C][C]-2.06032060447103[/C][/ROW]
[ROW][C]19[/C][C]101.52[/C][C]101.950136201535[/C][C]-0.43013620153458[/C][/ROW]
[ROW][C]20[/C][C]105.61[/C][C]101.520028434997[/C][C]4.08997156500276[/C][/ROW]
[ROW][C]21[/C][C]108.43[/C][C]105.609729624408[/C][C]2.82027037559219[/C][/ROW]
[ROW][C]22[/C][C]105.54[/C][C]108.429813560495[/C][C]-2.88981356049527[/C][/ROW]
[ROW][C]23[/C][C]100.11[/C][C]105.540191036793[/C][C]-5.43019103679336[/C][/ROW]
[ROW][C]24[/C][C]99.93[/C][C]100.110358973429[/C][C]-0.180358973428994[/C][/ROW]
[ROW][C]25[/C][C]99.88[/C][C]99.9300119229837[/C][C]-0.0500119229836997[/C][/ROW]
[ROW][C]26[/C][C]102.71[/C][C]99.8800033061363[/C][C]2.82999669386373[/C][/ROW]
[ROW][C]27[/C][C]101.89[/C][C]102.709812917518[/C][C]-0.819812917517922[/C][/ROW]
[ROW][C]28[/C][C]101.93[/C][C]101.890054195341[/C][C]0.0399458046591548[/C][/ROW]
[ROW][C]29[/C][C]99.49[/C][C]101.929997359304[/C][C]-2.43999735930426[/C][/ROW]
[ROW][C]30[/C][C]99.87[/C][C]99.4901613008111[/C][C]0.37983869918888[/C][/ROW]
[ROW][C]31[/C][C]100.33[/C][C]99.8699748900178[/C][C]0.460025109982212[/C][/ROW]
[ROW][C]32[/C][C]101.5[/C][C]100.329969589138[/C][C]1.17003041086218[/C][/ROW]
[ROW][C]33[/C][C]102.29[/C][C]101.499922652845[/C][C]0.790077347155162[/C][/ROW]
[ROW][C]34[/C][C]97.04[/C][C]102.289947770387[/C][C]-5.24994777038735[/C][/ROW]
[ROW][C]35[/C][C]95.71[/C][C]97.0403470580944[/C][C]-1.33034705809438[/C][/ROW]
[ROW][C]36[/C][C]97.37[/C][C]95.7100879452016[/C][C]1.65991205479845[/C][/ROW]
[ROW][C]37[/C][C]96.51[/C][C]97.369890268258[/C][C]-0.859890268257956[/C][/ROW]
[ROW][C]38[/C][C]96.33[/C][C]96.5100568447327[/C][C]-0.180056844732732[/C][/ROW]
[ROW][C]39[/C][C]96.88[/C][C]96.3300119030109[/C][C]0.549988096989125[/C][/ROW]
[ROW][C]40[/C][C]97.59[/C][C]96.8799636419581[/C][C]0.710036358041876[/C][/ROW]
[ROW][C]41[/C][C]98.96[/C][C]97.5899530616539[/C][C]1.37004693834608[/C][/ROW]
[ROW][C]42[/C][C]99.93[/C][C]98.95990943036[/C][C]0.970090569640021[/C][/ROW]
[ROW][C]43[/C][C]101.34[/C][C]99.9299358702602[/C][C]1.41006412973979[/C][/ROW]
[ROW][C]44[/C][C]98.04[/C][C]101.339906784945[/C][C]-3.29990678494507[/C][/ROW]
[ROW][C]45[/C][C]98.56[/C][C]98.0402181468103[/C][C]0.519781853189698[/C][/ROW]
[ROW][C]46[/C][C]96.73[/C][C]98.5599656388011[/C][C]-1.82996563880111[/C][/ROW]
[ROW][C]47[/C][C]92.36[/C][C]96.7301209734678[/C][C]-4.37012097346776[/C][/ROW]
[ROW][C]48[/C][C]87.88[/C][C]92.3602888954183[/C][C]-4.4802888954183[/C][/ROW]
[ROW][C]49[/C][C]79.84[/C][C]87.8802961782849[/C][C]-8.04029617828485[/C][/ROW]
[ROW][C]50[/C][C]82.91[/C][C]79.8405315195487[/C][C]3.06946848045128[/C][/ROW]
[ROW][C]51[/C][C]87.78[/C][C]82.9097970867658[/C][C]4.87020291323421[/C][/ROW]
[ROW][C]52[/C][C]89.36[/C][C]87.7796780456842[/C][C]1.58032195431575[/C][/ROW]
[ROW][C]53[/C][C]91.86[/C][C]89.3598955297176[/C][C]2.50010447028235[/C][/ROW]
[ROW][C]54[/C][C]92.48[/C][C]91.8598347256904[/C][C]0.620165274309599[/C][/ROW]
[ROW][C]55[/C][C]93.4[/C][C]92.4799590027582[/C][C]0.920040997241813[/C][/ROW]
[ROW][C]56[/C][C]89.97[/C][C]93.3999391788854[/C][C]-3.42993917888536[/C][/ROW]
[ROW][C]57[/C][C]83.96[/C][C]89.9702267428567[/C][C]-6.01022674285673[/C][/ROW]
[ROW][C]58[/C][C]82.76[/C][C]83.960397317827[/C][C]-1.20039731782698[/C][/ROW]
[ROW][C]59[/C][C]82.97[/C][C]82.7600793546191[/C][C]0.209920645380905[/C][/ROW]
[ROW][C]60[/C][C]81.07[/C][C]82.969986122784[/C][C]-1.89998612278401[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294790&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294790&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
29393.41-0.409999999999997
396.6193.00002710385423.60997289614583
499.6996.60976135566133.08023864433872
5101.0599.6897963747831.36020362521701
698101.049910081072-3.04991008107152
797.3298.0002016202879-0.68020162028786
897.8397.32004496606220.509955033937786
999.5797.82996628842231.74003371157771
1097.6399.5698849716587-1.93988497165869
1196.6897.6301282399008-0.950128239900835
1296.2896.6800628100908-0.40006281009083
1399.8196.28002644693673.52997355306327
14101.4399.80976664417481.62023335582525
15105.59101.4298928912964.16010710870383
16108.86105.589724987963.27027501203986
17104.01108.859783812056-4.84978381205616
18101.95104.010320604471-2.06032060447103
19101.52101.950136201535-0.43013620153458
20105.61101.5200284349974.08997156500276
21108.43105.6097296244082.82027037559219
22105.54108.429813560495-2.88981356049527
23100.11105.540191036793-5.43019103679336
2499.93100.110358973429-0.180358973428994
2599.8899.9300119229837-0.0500119229836997
26102.7199.88000330613632.82999669386373
27101.89102.709812917518-0.819812917517922
28101.93101.8900541953410.0399458046591548
2999.49101.929997359304-2.43999735930426
3099.8799.49016130081110.37983869918888
31100.3399.86997489001780.460025109982212
32101.5100.3299695891381.17003041086218
33102.29101.4999226528450.790077347155162
3497.04102.289947770387-5.24994777038735
3595.7197.0403470580944-1.33034705809438
3697.3795.71008794520161.65991205479845
3796.5197.369890268258-0.859890268257956
3896.3396.5100568447327-0.180056844732732
3996.8896.33001190301090.549988096989125
4097.5996.87996364195810.710036358041876
4198.9697.58995306165391.37004693834608
4299.9398.959909430360.970090569640021
43101.3499.92993587026021.41006412973979
4498.04101.339906784945-3.29990678494507
4598.5698.04021814681030.519781853189698
4696.7398.5599656388011-1.82996563880111
4792.3696.7301209734678-4.37012097346776
4887.8892.3602888954183-4.4802888954183
4979.8487.8802961782849-8.04029617828485
5082.9179.84053151954873.06946848045128
5187.7882.90979708676584.87020291323421
5289.3687.77967804568421.58032195431575
5391.8689.35989552971762.50010447028235
5492.4891.85983472569040.620165274309599
5593.492.47995900275820.920040997241813
5689.9793.3999391788854-3.42993917888536
5783.9689.9702267428567-6.01022674285673
5882.7683.960397317827-1.20039731782698
5982.9782.76007935461910.209920645380905
6081.0782.969986122784-1.89998612278401







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6181.070125602309275.651503813772786.4887473908457
6281.070125602309273.407290467149488.732960737469
6381.070125602309271.685210976694590.4550402279239
6481.070125602309270.233419333727791.9068318708907

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 81.0701256023092 & 75.6515038137727 & 86.4887473908457 \tabularnewline
62 & 81.0701256023092 & 73.4072904671494 & 88.732960737469 \tabularnewline
63 & 81.0701256023092 & 71.6852109766945 & 90.4550402279239 \tabularnewline
64 & 81.0701256023092 & 70.2334193337277 & 91.9068318708907 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294790&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]81.0701256023092[/C][C]75.6515038137727[/C][C]86.4887473908457[/C][/ROW]
[ROW][C]62[/C][C]81.0701256023092[/C][C]73.4072904671494[/C][C]88.732960737469[/C][/ROW]
[ROW][C]63[/C][C]81.0701256023092[/C][C]71.6852109766945[/C][C]90.4550402279239[/C][/ROW]
[ROW][C]64[/C][C]81.0701256023092[/C][C]70.2334193337277[/C][C]91.9068318708907[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294790&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294790&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
6181.070125602309275.651503813772786.4887473908457
6281.070125602309273.407290467149488.732960737469
6381.070125602309271.685210976694590.4550402279239
6481.070125602309270.233419333727791.9068318708907



Parameters (Session):
par1 = 4 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 4 ; 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')