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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 15:32:39 +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/t1461594783wgp5vc24i9fl80p.htm/, Retrieved Sun, 05 May 2024 23:14:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294718, Retrieved Sun, 05 May 2024 23:14:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 14:32:39] [c0f67b4e93ea0adf92c2b9d3976edd70] [Current]
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Dataseries X:
87.5
87.3
87.8
88.1
88.0
87.8
87.0
87.2
87.0
89.4
89.1
87.8
87.8
88.0
86.5
84.1
84.3
84.7
85.7
86.4
86.0
86.9
89.1
90.7
89.8
89.4
88.6
86.8
86.8
89.5
88.5
91.2
92.3
92.0
92.8
92.9
92.7
94.2
94.0
94.3
94.8
94.7
95.1
97.0
97.9
97.3
96.5
98.1
99.3
99.9
99.9
99.9
99.8
99.5
99.9
100.1
100.1
100.2
100.6
100.8
100.8
100.5
101.0
100.5
99.0
97.9
97.6
97.2
96.5
96.3
96.3
96.2
95.6
93.5
93.2
93.6
94.6
96.1
98.4
99.6
99.4
99.7
100.1
99.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294718&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294718&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294718&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.832646637647366
beta0.0234863353593083
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.832646637647366 \tabularnewline
beta & 0.0234863353593083 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294718&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]0.832646637647366[/C][/ROW]
[ROW][C]beta[/C][C]0.0234863353593083[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294718&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294718&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
alpha0.832646637647366
beta0.0234863353593083
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1387.889.1063568376068-1.30635683760684
148888.1304306447819-0.130430644781939
1586.586.41858476456130.081415235438655
1684.184.05555711907950.0444428809204709
1784.384.22094701715370.0790529828463349
1884.784.39170084598320.308299154016822
1985.785.49686477062850.203135229371512
2086.485.66010344929180.739896550708238
218685.95141058646040.0485894135396308
2286.988.4638866993533-1.56388669935329
2389.187.0031569146322.09684308536804
2490.787.59402695859783.10597304140217
2589.890.06726230223-0.267262302229994
2689.490.2461431241284-0.846143124128389
2788.688.05263167310310.547368326896944
2886.886.15931984690370.640680153096298
2986.886.9265457217242-0.126545721724213
3089.587.06004184705872.43995815294134
3188.590.0597795181783-1.55977951817829
3291.288.94774131629042.25225868370957
3392.390.51497394800941.7850260519906
349294.3697471527765-2.3697471527765
3592.893.0012088113275-0.201208811327504
3692.991.9531076786230.946892321377049
3792.792.12745957064260.572540429357417
3894.292.9885348179431.21146518205704
399492.86154420196491.13845579803512
4094.391.60762598863332.69237401136668
4194.894.12652314782450.673476852175469
4294.795.5430466498953-0.8430466498953
4395.195.2630082354153-0.163008235415319
449796.10243573406530.897564265934676
4597.996.58749288203891.31250711796109
4697.399.4682682453502-2.16826824535022
4796.598.7491016322559-2.24910163225586
4898.196.26661860388661.83338139611344
4999.397.21244020568152.08755979431848
5099.999.56753149228110.332468507718943
5199.998.80485343931861.09514656068143
5299.997.88250497968262.01749502031745
5399.899.5959769842240.204023015775988
5499.5100.453015262766-0.953015262766115
5599.9100.278267283566-0.378267283565563
56100.1101.194789582706-1.09478958270614
57100.1100.130239118523-0.0302391185228288
58100.2101.324080420369-1.12408042036873
59100.6101.494864035168-0.894864035167629
60100.8100.883721359778-0.0837213597781243
61100.8100.2988426041730.501157395826837
62100.5101.03130863956-0.531308639559811
6310199.65216211686051.34783788313948
64100.599.07463186983291.42536813016712
659999.9600587635619-0.960058763561932
6697.999.5999074355224-1.69990743552235
6797.698.8305555385099-1.2305555385099
6897.298.8319506094569-1.63195060945694
6996.597.4022264362377-0.902226436237697
7096.397.5738354989316-1.2738354989316
7196.397.5422406895367-1.24224068953667
7296.296.6547647359477-0.454764735947705
7395.695.7287246012602-0.128724601260245
7493.595.6215222035061-2.1215222035061
7593.293.05926062165370.140739378346268
7693.691.29250244103592.30749755896404
7794.692.33335661923142.26664338076861
7896.194.41932701280981.68067298719023
7998.496.49269686554081.90730313445918
8099.699.05035319822140.549646801778636
8199.499.6126220934628-0.212622093462755
8299.7100.363095169805-0.663095169804507
83100.1100.924119568794-0.824119568793861
8499.9100.603555039011-0.703555039010794

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 87.8 & 89.1063568376068 & -1.30635683760684 \tabularnewline
14 & 88 & 88.1304306447819 & -0.130430644781939 \tabularnewline
15 & 86.5 & 86.4185847645613 & 0.081415235438655 \tabularnewline
16 & 84.1 & 84.0555571190795 & 0.0444428809204709 \tabularnewline
17 & 84.3 & 84.2209470171537 & 0.0790529828463349 \tabularnewline
18 & 84.7 & 84.3917008459832 & 0.308299154016822 \tabularnewline
19 & 85.7 & 85.4968647706285 & 0.203135229371512 \tabularnewline
20 & 86.4 & 85.6601034492918 & 0.739896550708238 \tabularnewline
21 & 86 & 85.9514105864604 & 0.0485894135396308 \tabularnewline
22 & 86.9 & 88.4638866993533 & -1.56388669935329 \tabularnewline
23 & 89.1 & 87.003156914632 & 2.09684308536804 \tabularnewline
24 & 90.7 & 87.5940269585978 & 3.10597304140217 \tabularnewline
25 & 89.8 & 90.06726230223 & -0.267262302229994 \tabularnewline
26 & 89.4 & 90.2461431241284 & -0.846143124128389 \tabularnewline
27 & 88.6 & 88.0526316731031 & 0.547368326896944 \tabularnewline
28 & 86.8 & 86.1593198469037 & 0.640680153096298 \tabularnewline
29 & 86.8 & 86.9265457217242 & -0.126545721724213 \tabularnewline
30 & 89.5 & 87.0600418470587 & 2.43995815294134 \tabularnewline
31 & 88.5 & 90.0597795181783 & -1.55977951817829 \tabularnewline
32 & 91.2 & 88.9477413162904 & 2.25225868370957 \tabularnewline
33 & 92.3 & 90.5149739480094 & 1.7850260519906 \tabularnewline
34 & 92 & 94.3697471527765 & -2.3697471527765 \tabularnewline
35 & 92.8 & 93.0012088113275 & -0.201208811327504 \tabularnewline
36 & 92.9 & 91.953107678623 & 0.946892321377049 \tabularnewline
37 & 92.7 & 92.1274595706426 & 0.572540429357417 \tabularnewline
38 & 94.2 & 92.988534817943 & 1.21146518205704 \tabularnewline
39 & 94 & 92.8615442019649 & 1.13845579803512 \tabularnewline
40 & 94.3 & 91.6076259886333 & 2.69237401136668 \tabularnewline
41 & 94.8 & 94.1265231478245 & 0.673476852175469 \tabularnewline
42 & 94.7 & 95.5430466498953 & -0.8430466498953 \tabularnewline
43 & 95.1 & 95.2630082354153 & -0.163008235415319 \tabularnewline
44 & 97 & 96.1024357340653 & 0.897564265934676 \tabularnewline
45 & 97.9 & 96.5874928820389 & 1.31250711796109 \tabularnewline
46 & 97.3 & 99.4682682453502 & -2.16826824535022 \tabularnewline
47 & 96.5 & 98.7491016322559 & -2.24910163225586 \tabularnewline
48 & 98.1 & 96.2666186038866 & 1.83338139611344 \tabularnewline
49 & 99.3 & 97.2124402056815 & 2.08755979431848 \tabularnewline
50 & 99.9 & 99.5675314922811 & 0.332468507718943 \tabularnewline
51 & 99.9 & 98.8048534393186 & 1.09514656068143 \tabularnewline
52 & 99.9 & 97.8825049796826 & 2.01749502031745 \tabularnewline
53 & 99.8 & 99.595976984224 & 0.204023015775988 \tabularnewline
54 & 99.5 & 100.453015262766 & -0.953015262766115 \tabularnewline
55 & 99.9 & 100.278267283566 & -0.378267283565563 \tabularnewline
56 & 100.1 & 101.194789582706 & -1.09478958270614 \tabularnewline
57 & 100.1 & 100.130239118523 & -0.0302391185228288 \tabularnewline
58 & 100.2 & 101.324080420369 & -1.12408042036873 \tabularnewline
59 & 100.6 & 101.494864035168 & -0.894864035167629 \tabularnewline
60 & 100.8 & 100.883721359778 & -0.0837213597781243 \tabularnewline
61 & 100.8 & 100.298842604173 & 0.501157395826837 \tabularnewline
62 & 100.5 & 101.03130863956 & -0.531308639559811 \tabularnewline
63 & 101 & 99.6521621168605 & 1.34783788313948 \tabularnewline
64 & 100.5 & 99.0746318698329 & 1.42536813016712 \tabularnewline
65 & 99 & 99.9600587635619 & -0.960058763561932 \tabularnewline
66 & 97.9 & 99.5999074355224 & -1.69990743552235 \tabularnewline
67 & 97.6 & 98.8305555385099 & -1.2305555385099 \tabularnewline
68 & 97.2 & 98.8319506094569 & -1.63195060945694 \tabularnewline
69 & 96.5 & 97.4022264362377 & -0.902226436237697 \tabularnewline
70 & 96.3 & 97.5738354989316 & -1.2738354989316 \tabularnewline
71 & 96.3 & 97.5422406895367 & -1.24224068953667 \tabularnewline
72 & 96.2 & 96.6547647359477 & -0.454764735947705 \tabularnewline
73 & 95.6 & 95.7287246012602 & -0.128724601260245 \tabularnewline
74 & 93.5 & 95.6215222035061 & -2.1215222035061 \tabularnewline
75 & 93.2 & 93.0592606216537 & 0.140739378346268 \tabularnewline
76 & 93.6 & 91.2925024410359 & 2.30749755896404 \tabularnewline
77 & 94.6 & 92.3333566192314 & 2.26664338076861 \tabularnewline
78 & 96.1 & 94.4193270128098 & 1.68067298719023 \tabularnewline
79 & 98.4 & 96.4926968655408 & 1.90730313445918 \tabularnewline
80 & 99.6 & 99.0503531982214 & 0.549646801778636 \tabularnewline
81 & 99.4 & 99.6126220934628 & -0.212622093462755 \tabularnewline
82 & 99.7 & 100.363095169805 & -0.663095169804507 \tabularnewline
83 & 100.1 & 100.924119568794 & -0.824119568793861 \tabularnewline
84 & 99.9 & 100.603555039011 & -0.703555039010794 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294718&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]87.8[/C][C]89.1063568376068[/C][C]-1.30635683760684[/C][/ROW]
[ROW][C]14[/C][C]88[/C][C]88.1304306447819[/C][C]-0.130430644781939[/C][/ROW]
[ROW][C]15[/C][C]86.5[/C][C]86.4185847645613[/C][C]0.081415235438655[/C][/ROW]
[ROW][C]16[/C][C]84.1[/C][C]84.0555571190795[/C][C]0.0444428809204709[/C][/ROW]
[ROW][C]17[/C][C]84.3[/C][C]84.2209470171537[/C][C]0.0790529828463349[/C][/ROW]
[ROW][C]18[/C][C]84.7[/C][C]84.3917008459832[/C][C]0.308299154016822[/C][/ROW]
[ROW][C]19[/C][C]85.7[/C][C]85.4968647706285[/C][C]0.203135229371512[/C][/ROW]
[ROW][C]20[/C][C]86.4[/C][C]85.6601034492918[/C][C]0.739896550708238[/C][/ROW]
[ROW][C]21[/C][C]86[/C][C]85.9514105864604[/C][C]0.0485894135396308[/C][/ROW]
[ROW][C]22[/C][C]86.9[/C][C]88.4638866993533[/C][C]-1.56388669935329[/C][/ROW]
[ROW][C]23[/C][C]89.1[/C][C]87.003156914632[/C][C]2.09684308536804[/C][/ROW]
[ROW][C]24[/C][C]90.7[/C][C]87.5940269585978[/C][C]3.10597304140217[/C][/ROW]
[ROW][C]25[/C][C]89.8[/C][C]90.06726230223[/C][C]-0.267262302229994[/C][/ROW]
[ROW][C]26[/C][C]89.4[/C][C]90.2461431241284[/C][C]-0.846143124128389[/C][/ROW]
[ROW][C]27[/C][C]88.6[/C][C]88.0526316731031[/C][C]0.547368326896944[/C][/ROW]
[ROW][C]28[/C][C]86.8[/C][C]86.1593198469037[/C][C]0.640680153096298[/C][/ROW]
[ROW][C]29[/C][C]86.8[/C][C]86.9265457217242[/C][C]-0.126545721724213[/C][/ROW]
[ROW][C]30[/C][C]89.5[/C][C]87.0600418470587[/C][C]2.43995815294134[/C][/ROW]
[ROW][C]31[/C][C]88.5[/C][C]90.0597795181783[/C][C]-1.55977951817829[/C][/ROW]
[ROW][C]32[/C][C]91.2[/C][C]88.9477413162904[/C][C]2.25225868370957[/C][/ROW]
[ROW][C]33[/C][C]92.3[/C][C]90.5149739480094[/C][C]1.7850260519906[/C][/ROW]
[ROW][C]34[/C][C]92[/C][C]94.3697471527765[/C][C]-2.3697471527765[/C][/ROW]
[ROW][C]35[/C][C]92.8[/C][C]93.0012088113275[/C][C]-0.201208811327504[/C][/ROW]
[ROW][C]36[/C][C]92.9[/C][C]91.953107678623[/C][C]0.946892321377049[/C][/ROW]
[ROW][C]37[/C][C]92.7[/C][C]92.1274595706426[/C][C]0.572540429357417[/C][/ROW]
[ROW][C]38[/C][C]94.2[/C][C]92.988534817943[/C][C]1.21146518205704[/C][/ROW]
[ROW][C]39[/C][C]94[/C][C]92.8615442019649[/C][C]1.13845579803512[/C][/ROW]
[ROW][C]40[/C][C]94.3[/C][C]91.6076259886333[/C][C]2.69237401136668[/C][/ROW]
[ROW][C]41[/C][C]94.8[/C][C]94.1265231478245[/C][C]0.673476852175469[/C][/ROW]
[ROW][C]42[/C][C]94.7[/C][C]95.5430466498953[/C][C]-0.8430466498953[/C][/ROW]
[ROW][C]43[/C][C]95.1[/C][C]95.2630082354153[/C][C]-0.163008235415319[/C][/ROW]
[ROW][C]44[/C][C]97[/C][C]96.1024357340653[/C][C]0.897564265934676[/C][/ROW]
[ROW][C]45[/C][C]97.9[/C][C]96.5874928820389[/C][C]1.31250711796109[/C][/ROW]
[ROW][C]46[/C][C]97.3[/C][C]99.4682682453502[/C][C]-2.16826824535022[/C][/ROW]
[ROW][C]47[/C][C]96.5[/C][C]98.7491016322559[/C][C]-2.24910163225586[/C][/ROW]
[ROW][C]48[/C][C]98.1[/C][C]96.2666186038866[/C][C]1.83338139611344[/C][/ROW]
[ROW][C]49[/C][C]99.3[/C][C]97.2124402056815[/C][C]2.08755979431848[/C][/ROW]
[ROW][C]50[/C][C]99.9[/C][C]99.5675314922811[/C][C]0.332468507718943[/C][/ROW]
[ROW][C]51[/C][C]99.9[/C][C]98.8048534393186[/C][C]1.09514656068143[/C][/ROW]
[ROW][C]52[/C][C]99.9[/C][C]97.8825049796826[/C][C]2.01749502031745[/C][/ROW]
[ROW][C]53[/C][C]99.8[/C][C]99.595976984224[/C][C]0.204023015775988[/C][/ROW]
[ROW][C]54[/C][C]99.5[/C][C]100.453015262766[/C][C]-0.953015262766115[/C][/ROW]
[ROW][C]55[/C][C]99.9[/C][C]100.278267283566[/C][C]-0.378267283565563[/C][/ROW]
[ROW][C]56[/C][C]100.1[/C][C]101.194789582706[/C][C]-1.09478958270614[/C][/ROW]
[ROW][C]57[/C][C]100.1[/C][C]100.130239118523[/C][C]-0.0302391185228288[/C][/ROW]
[ROW][C]58[/C][C]100.2[/C][C]101.324080420369[/C][C]-1.12408042036873[/C][/ROW]
[ROW][C]59[/C][C]100.6[/C][C]101.494864035168[/C][C]-0.894864035167629[/C][/ROW]
[ROW][C]60[/C][C]100.8[/C][C]100.883721359778[/C][C]-0.0837213597781243[/C][/ROW]
[ROW][C]61[/C][C]100.8[/C][C]100.298842604173[/C][C]0.501157395826837[/C][/ROW]
[ROW][C]62[/C][C]100.5[/C][C]101.03130863956[/C][C]-0.531308639559811[/C][/ROW]
[ROW][C]63[/C][C]101[/C][C]99.6521621168605[/C][C]1.34783788313948[/C][/ROW]
[ROW][C]64[/C][C]100.5[/C][C]99.0746318698329[/C][C]1.42536813016712[/C][/ROW]
[ROW][C]65[/C][C]99[/C][C]99.9600587635619[/C][C]-0.960058763561932[/C][/ROW]
[ROW][C]66[/C][C]97.9[/C][C]99.5999074355224[/C][C]-1.69990743552235[/C][/ROW]
[ROW][C]67[/C][C]97.6[/C][C]98.8305555385099[/C][C]-1.2305555385099[/C][/ROW]
[ROW][C]68[/C][C]97.2[/C][C]98.8319506094569[/C][C]-1.63195060945694[/C][/ROW]
[ROW][C]69[/C][C]96.5[/C][C]97.4022264362377[/C][C]-0.902226436237697[/C][/ROW]
[ROW][C]70[/C][C]96.3[/C][C]97.5738354989316[/C][C]-1.2738354989316[/C][/ROW]
[ROW][C]71[/C][C]96.3[/C][C]97.5422406895367[/C][C]-1.24224068953667[/C][/ROW]
[ROW][C]72[/C][C]96.2[/C][C]96.6547647359477[/C][C]-0.454764735947705[/C][/ROW]
[ROW][C]73[/C][C]95.6[/C][C]95.7287246012602[/C][C]-0.128724601260245[/C][/ROW]
[ROW][C]74[/C][C]93.5[/C][C]95.6215222035061[/C][C]-2.1215222035061[/C][/ROW]
[ROW][C]75[/C][C]93.2[/C][C]93.0592606216537[/C][C]0.140739378346268[/C][/ROW]
[ROW][C]76[/C][C]93.6[/C][C]91.2925024410359[/C][C]2.30749755896404[/C][/ROW]
[ROW][C]77[/C][C]94.6[/C][C]92.3333566192314[/C][C]2.26664338076861[/C][/ROW]
[ROW][C]78[/C][C]96.1[/C][C]94.4193270128098[/C][C]1.68067298719023[/C][/ROW]
[ROW][C]79[/C][C]98.4[/C][C]96.4926968655408[/C][C]1.90730313445918[/C][/ROW]
[ROW][C]80[/C][C]99.6[/C][C]99.0503531982214[/C][C]0.549646801778636[/C][/ROW]
[ROW][C]81[/C][C]99.4[/C][C]99.6126220934628[/C][C]-0.212622093462755[/C][/ROW]
[ROW][C]82[/C][C]99.7[/C][C]100.363095169805[/C][C]-0.663095169804507[/C][/ROW]
[ROW][C]83[/C][C]100.1[/C][C]100.924119568794[/C][C]-0.824119568793861[/C][/ROW]
[ROW][C]84[/C][C]99.9[/C][C]100.603555039011[/C][C]-0.703555039010794[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294718&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294718&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
1387.889.1063568376068-1.30635683760684
148888.1304306447819-0.130430644781939
1586.586.41858476456130.081415235438655
1684.184.05555711907950.0444428809204709
1784.384.22094701715370.0790529828463349
1884.784.39170084598320.308299154016822
1985.785.49686477062850.203135229371512
2086.485.66010344929180.739896550708238
218685.95141058646040.0485894135396308
2286.988.4638866993533-1.56388669935329
2389.187.0031569146322.09684308536804
2490.787.59402695859783.10597304140217
2589.890.06726230223-0.267262302229994
2689.490.2461431241284-0.846143124128389
2788.688.05263167310310.547368326896944
2886.886.15931984690370.640680153096298
2986.886.9265457217242-0.126545721724213
3089.587.06004184705872.43995815294134
3188.590.0597795181783-1.55977951817829
3291.288.94774131629042.25225868370957
3392.390.51497394800941.7850260519906
349294.3697471527765-2.3697471527765
3592.893.0012088113275-0.201208811327504
3692.991.9531076786230.946892321377049
3792.792.12745957064260.572540429357417
3894.292.9885348179431.21146518205704
399492.86154420196491.13845579803512
4094.391.60762598863332.69237401136668
4194.894.12652314782450.673476852175469
4294.795.5430466498953-0.8430466498953
4395.195.2630082354153-0.163008235415319
449796.10243573406530.897564265934676
4597.996.58749288203891.31250711796109
4697.399.4682682453502-2.16826824535022
4796.598.7491016322559-2.24910163225586
4898.196.26661860388661.83338139611344
4999.397.21244020568152.08755979431848
5099.999.56753149228110.332468507718943
5199.998.80485343931861.09514656068143
5299.997.88250497968262.01749502031745
5399.899.5959769842240.204023015775988
5499.5100.453015262766-0.953015262766115
5599.9100.278267283566-0.378267283565563
56100.1101.194789582706-1.09478958270614
57100.1100.130239118523-0.0302391185228288
58100.2101.324080420369-1.12408042036873
59100.6101.494864035168-0.894864035167629
60100.8100.883721359778-0.0837213597781243
61100.8100.2988426041730.501157395826837
62100.5101.03130863956-0.531308639559811
6310199.65216211686051.34783788313948
64100.599.07463186983291.42536813016712
659999.9600587635619-0.960058763561932
6697.999.5999074355224-1.69990743552235
6797.698.8305555385099-1.2305555385099
6897.298.8319506094569-1.63195060945694
6996.597.4022264362377-0.902226436237697
7096.397.5738354989316-1.2738354989316
7196.397.5422406895367-1.24224068953667
7296.296.6547647359477-0.454764735947705
7395.695.7287246012602-0.128724601260245
7493.595.6215222035061-2.1215222035061
7593.293.05926062165370.140739378346268
7693.691.29250244103592.30749755896404
7794.692.33335661923142.26664338076861
7896.194.41932701280981.68067298719023
7998.496.49269686554081.90730313445918
8099.699.05035319822140.549646801778636
8199.499.6126220934628-0.212622093462755
8299.7100.363095169805-0.663095169804507
83100.1100.924119568794-0.824119568793861
8499.9100.603555039011-0.703555039010794







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8599.60703663975797.0238255061132102.190247773401
8699.358144516053195.9641461644197102.752142867686
8799.067075995191294.9939397202633103.140212270119
8897.669111286951192.9902517500195102.347970823883
8996.860038670133991.6228456182101102.097231722058
9096.994546265485791.2321737940025102.756918736969
9197.707484095387891.4443325905204103.970635600255
9298.41357103248991.6682255426576105.15891652232
9398.343609809284291.1305731804761105.556646438092
9499.152891477444291.4836799428362106.822103012052
95100.2092169385792.0930901446545108.325343732486
96100.58127108178992.0257391274789109.136803036098

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 99.607036639757 & 97.0238255061132 & 102.190247773401 \tabularnewline
86 & 99.3581445160531 & 95.9641461644197 & 102.752142867686 \tabularnewline
87 & 99.0670759951912 & 94.9939397202633 & 103.140212270119 \tabularnewline
88 & 97.6691112869511 & 92.9902517500195 & 102.347970823883 \tabularnewline
89 & 96.8600386701339 & 91.6228456182101 & 102.097231722058 \tabularnewline
90 & 96.9945462654857 & 91.2321737940025 & 102.756918736969 \tabularnewline
91 & 97.7074840953878 & 91.4443325905204 & 103.970635600255 \tabularnewline
92 & 98.413571032489 & 91.6682255426576 & 105.15891652232 \tabularnewline
93 & 98.3436098092842 & 91.1305731804761 & 105.556646438092 \tabularnewline
94 & 99.1528914774442 & 91.4836799428362 & 106.822103012052 \tabularnewline
95 & 100.20921693857 & 92.0930901446545 & 108.325343732486 \tabularnewline
96 & 100.581271081789 & 92.0257391274789 & 109.136803036098 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294718&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]99.607036639757[/C][C]97.0238255061132[/C][C]102.190247773401[/C][/ROW]
[ROW][C]86[/C][C]99.3581445160531[/C][C]95.9641461644197[/C][C]102.752142867686[/C][/ROW]
[ROW][C]87[/C][C]99.0670759951912[/C][C]94.9939397202633[/C][C]103.140212270119[/C][/ROW]
[ROW][C]88[/C][C]97.6691112869511[/C][C]92.9902517500195[/C][C]102.347970823883[/C][/ROW]
[ROW][C]89[/C][C]96.8600386701339[/C][C]91.6228456182101[/C][C]102.097231722058[/C][/ROW]
[ROW][C]90[/C][C]96.9945462654857[/C][C]91.2321737940025[/C][C]102.756918736969[/C][/ROW]
[ROW][C]91[/C][C]97.7074840953878[/C][C]91.4443325905204[/C][C]103.970635600255[/C][/ROW]
[ROW][C]92[/C][C]98.413571032489[/C][C]91.6682255426576[/C][C]105.15891652232[/C][/ROW]
[ROW][C]93[/C][C]98.3436098092842[/C][C]91.1305731804761[/C][C]105.556646438092[/C][/ROW]
[ROW][C]94[/C][C]99.1528914774442[/C][C]91.4836799428362[/C][C]106.822103012052[/C][/ROW]
[ROW][C]95[/C][C]100.20921693857[/C][C]92.0930901446545[/C][C]108.325343732486[/C][/ROW]
[ROW][C]96[/C][C]100.581271081789[/C][C]92.0257391274789[/C][C]109.136803036098[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294718&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294718&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
8599.60703663975797.0238255061132102.190247773401
8699.358144516053195.9641461644197102.752142867686
8799.067075995191294.9939397202633103.140212270119
8897.669111286951192.9902517500195102.347970823883
8996.860038670133991.6228456182101102.097231722058
9096.994546265485791.2321737940025102.756918736969
9197.707484095387891.4443325905204103.970635600255
9298.41357103248991.6682255426576105.15891652232
9398.343609809284291.1305731804761105.556646438092
9499.152891477444291.4836799428362106.822103012052
95100.2092169385792.0930901446545108.325343732486
96100.58127108178992.0257391274789109.136803036098



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')