Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 15 May 2017 09:39:13 +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/2017/May/15/t1494837603psymmfbztxb7729.htm/, Retrieved Wed, 15 May 2024 22:26:07 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 22:26:07 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
91,46
92,17
91,91
92,06
92,33
92,73
93,35
93,28
93,22
93,31
93,21
93,14
93,82
94,18
94,44
94,35
94,38
94,72
95,25
95,16
94,9
95,09
95,22
95,39
96,57
97,05
97,11
97,08
97,5
97,92
98,44
98,44
98,06
98,2
98,19
98,36
98,41
98,97
99,45
98,95
99,7
100,12
100,62
100,75
100,47
100,71
100,85
101,03
101,13
101,38
101,73
101,89
102,02
102,11
102,77
102,49
102,52
102,69
102,32
102,6
103,03
103,7
103,17
103,88
104,09
104,32
104,88
105,06
104,66
105,41
105,41
105,48




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 time4 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.958441876333531
beta0.14699810426826
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.958441876333531 \tabularnewline
beta & 0.14699810426826 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.958441876333531[/C][/ROW]
[ROW][C]beta[/C][C]0.14699810426826[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.958441876333531
beta0.14699810426826
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
391.9192.88-0.970000000000013
492.0692.5236489152503-0.463648915250303
592.3392.5872828178429-0.257282817842921
692.7392.8124582753938-0.0824582753937477
793.3593.19357542002560.156424579974413
893.2893.8256864211515-0.545686421151458
993.2293.7079835469935-0.48798354699349
1093.3193.5768339420935-0.266833942093541
1193.2193.6200493751408-0.410049375140844
1293.1493.4682296364596-0.328229636459611
1393.8293.3485853708080.471414629192012
1494.1894.06177085668550.11822914331448
1594.4494.453105784976-0.0131057849760481
1694.3594.7167173554081-0.366717355408113
1794.3894.589746296369-0.209746296369033
1894.7294.58367189860830.136328101391669
1995.2594.92849684479760.321503155202436
2095.1695.4960976196926-0.33609761969258
2194.995.3860737698033-0.486073769803284
2295.0995.06382398234060.0261760176593953
2395.2295.2362237589122-0.0162237589122469
2495.3995.3657000626480.0242999373519694
2596.5795.53743957111541.03256042888458
2697.0596.82101470657950.228985293420493
2797.1197.3666713222389-0.256671322238859
2897.0897.4106920983684-0.330692098368402
2997.597.33717733796570.16282266203433
3097.9297.75960773516460.160392264835451
3198.4498.20230626598640.237693734013646
3298.4498.7525822274712-0.312582227471168
3398.0698.731411223074-0.671411223074017
3498.298.2717289338003-0.0717289338002729
3598.1998.3767014353467-0.186701435346706
3698.3698.3451752723320.0148247276680138
3798.4198.5088888662426-0.0988888662425751
3898.9798.54968222263190.420317777368126
3999.4599.14732317843440.302676821565626
4098.9599.6748559925709-0.724855992570852
4199.799.11543399173230.584566008267657
42100.1299.89337587180880.226624128191233
43100.62100.3601801429950.259819857005056
44100.75100.895406386707-0.14540638670708
45100.47101.021760648446-0.551760648446475
46100.71100.6809108864850.0290891135150275
47100.85100.900870200399-0.0508702003994159
48101.03101.037026100727-0.00702610072683285
49101.13101.21421412093-0.0842141209295733
50101.38101.305557055240.0744429447599515
51101.73101.5594517676660.170548232334099
52101.89101.92948620583-0.0394862058296752
53102.02102.092651665448-0.0726516654484186
54102.11102.213794129138-0.103794129138038
55102.77102.2904648860210.47953511397894
56102.49102.993784106465-0.503784106464877
57102.52102.683671299294-0.163671299294293
58102.69102.6764773407780.0135226592223603
59102.32102.84101868815-0.52101868814978
60102.6102.4198273492590.180172650741127
61103.03102.6960715224950.333928477505339
62103.7103.1667286144720.533271385527755
63103.17103.903576443541-0.733576443540883
64103.88103.322871308860.557128691139596
65104.09104.0577254067920.0322745932078732
66104.32104.2940844979450.0259155020546302
67104.88104.527999982610.352000017390182
68105.06105.124041501329-0.0640415013289299
69104.66105.31230865424-0.652308654239931
70105.41104.8448527287550.565147271245323
71105.41105.623880657227-0.213880657226696
72105.48105.6261221346-0.146122134599651

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 91.91 & 92.88 & -0.970000000000013 \tabularnewline
4 & 92.06 & 92.5236489152503 & -0.463648915250303 \tabularnewline
5 & 92.33 & 92.5872828178429 & -0.257282817842921 \tabularnewline
6 & 92.73 & 92.8124582753938 & -0.0824582753937477 \tabularnewline
7 & 93.35 & 93.1935754200256 & 0.156424579974413 \tabularnewline
8 & 93.28 & 93.8256864211515 & -0.545686421151458 \tabularnewline
9 & 93.22 & 93.7079835469935 & -0.48798354699349 \tabularnewline
10 & 93.31 & 93.5768339420935 & -0.266833942093541 \tabularnewline
11 & 93.21 & 93.6200493751408 & -0.410049375140844 \tabularnewline
12 & 93.14 & 93.4682296364596 & -0.328229636459611 \tabularnewline
13 & 93.82 & 93.348585370808 & 0.471414629192012 \tabularnewline
14 & 94.18 & 94.0617708566855 & 0.11822914331448 \tabularnewline
15 & 94.44 & 94.453105784976 & -0.0131057849760481 \tabularnewline
16 & 94.35 & 94.7167173554081 & -0.366717355408113 \tabularnewline
17 & 94.38 & 94.589746296369 & -0.209746296369033 \tabularnewline
18 & 94.72 & 94.5836718986083 & 0.136328101391669 \tabularnewline
19 & 95.25 & 94.9284968447976 & 0.321503155202436 \tabularnewline
20 & 95.16 & 95.4960976196926 & -0.33609761969258 \tabularnewline
21 & 94.9 & 95.3860737698033 & -0.486073769803284 \tabularnewline
22 & 95.09 & 95.0638239823406 & 0.0261760176593953 \tabularnewline
23 & 95.22 & 95.2362237589122 & -0.0162237589122469 \tabularnewline
24 & 95.39 & 95.365700062648 & 0.0242999373519694 \tabularnewline
25 & 96.57 & 95.5374395711154 & 1.03256042888458 \tabularnewline
26 & 97.05 & 96.8210147065795 & 0.228985293420493 \tabularnewline
27 & 97.11 & 97.3666713222389 & -0.256671322238859 \tabularnewline
28 & 97.08 & 97.4106920983684 & -0.330692098368402 \tabularnewline
29 & 97.5 & 97.3371773379657 & 0.16282266203433 \tabularnewline
30 & 97.92 & 97.7596077351646 & 0.160392264835451 \tabularnewline
31 & 98.44 & 98.2023062659864 & 0.237693734013646 \tabularnewline
32 & 98.44 & 98.7525822274712 & -0.312582227471168 \tabularnewline
33 & 98.06 & 98.731411223074 & -0.671411223074017 \tabularnewline
34 & 98.2 & 98.2717289338003 & -0.0717289338002729 \tabularnewline
35 & 98.19 & 98.3767014353467 & -0.186701435346706 \tabularnewline
36 & 98.36 & 98.345175272332 & 0.0148247276680138 \tabularnewline
37 & 98.41 & 98.5088888662426 & -0.0988888662425751 \tabularnewline
38 & 98.97 & 98.5496822226319 & 0.420317777368126 \tabularnewline
39 & 99.45 & 99.1473231784344 & 0.302676821565626 \tabularnewline
40 & 98.95 & 99.6748559925709 & -0.724855992570852 \tabularnewline
41 & 99.7 & 99.1154339917323 & 0.584566008267657 \tabularnewline
42 & 100.12 & 99.8933758718088 & 0.226624128191233 \tabularnewline
43 & 100.62 & 100.360180142995 & 0.259819857005056 \tabularnewline
44 & 100.75 & 100.895406386707 & -0.14540638670708 \tabularnewline
45 & 100.47 & 101.021760648446 & -0.551760648446475 \tabularnewline
46 & 100.71 & 100.680910886485 & 0.0290891135150275 \tabularnewline
47 & 100.85 & 100.900870200399 & -0.0508702003994159 \tabularnewline
48 & 101.03 & 101.037026100727 & -0.00702610072683285 \tabularnewline
49 & 101.13 & 101.21421412093 & -0.0842141209295733 \tabularnewline
50 & 101.38 & 101.30555705524 & 0.0744429447599515 \tabularnewline
51 & 101.73 & 101.559451767666 & 0.170548232334099 \tabularnewline
52 & 101.89 & 101.92948620583 & -0.0394862058296752 \tabularnewline
53 & 102.02 & 102.092651665448 & -0.0726516654484186 \tabularnewline
54 & 102.11 & 102.213794129138 & -0.103794129138038 \tabularnewline
55 & 102.77 & 102.290464886021 & 0.47953511397894 \tabularnewline
56 & 102.49 & 102.993784106465 & -0.503784106464877 \tabularnewline
57 & 102.52 & 102.683671299294 & -0.163671299294293 \tabularnewline
58 & 102.69 & 102.676477340778 & 0.0135226592223603 \tabularnewline
59 & 102.32 & 102.84101868815 & -0.52101868814978 \tabularnewline
60 & 102.6 & 102.419827349259 & 0.180172650741127 \tabularnewline
61 & 103.03 & 102.696071522495 & 0.333928477505339 \tabularnewline
62 & 103.7 & 103.166728614472 & 0.533271385527755 \tabularnewline
63 & 103.17 & 103.903576443541 & -0.733576443540883 \tabularnewline
64 & 103.88 & 103.32287130886 & 0.557128691139596 \tabularnewline
65 & 104.09 & 104.057725406792 & 0.0322745932078732 \tabularnewline
66 & 104.32 & 104.294084497945 & 0.0259155020546302 \tabularnewline
67 & 104.88 & 104.52799998261 & 0.352000017390182 \tabularnewline
68 & 105.06 & 105.124041501329 & -0.0640415013289299 \tabularnewline
69 & 104.66 & 105.31230865424 & -0.652308654239931 \tabularnewline
70 & 105.41 & 104.844852728755 & 0.565147271245323 \tabularnewline
71 & 105.41 & 105.623880657227 & -0.213880657226696 \tabularnewline
72 & 105.48 & 105.6261221346 & -0.146122134599651 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]91.91[/C][C]92.88[/C][C]-0.970000000000013[/C][/ROW]
[ROW][C]4[/C][C]92.06[/C][C]92.5236489152503[/C][C]-0.463648915250303[/C][/ROW]
[ROW][C]5[/C][C]92.33[/C][C]92.5872828178429[/C][C]-0.257282817842921[/C][/ROW]
[ROW][C]6[/C][C]92.73[/C][C]92.8124582753938[/C][C]-0.0824582753937477[/C][/ROW]
[ROW][C]7[/C][C]93.35[/C][C]93.1935754200256[/C][C]0.156424579974413[/C][/ROW]
[ROW][C]8[/C][C]93.28[/C][C]93.8256864211515[/C][C]-0.545686421151458[/C][/ROW]
[ROW][C]9[/C][C]93.22[/C][C]93.7079835469935[/C][C]-0.48798354699349[/C][/ROW]
[ROW][C]10[/C][C]93.31[/C][C]93.5768339420935[/C][C]-0.266833942093541[/C][/ROW]
[ROW][C]11[/C][C]93.21[/C][C]93.6200493751408[/C][C]-0.410049375140844[/C][/ROW]
[ROW][C]12[/C][C]93.14[/C][C]93.4682296364596[/C][C]-0.328229636459611[/C][/ROW]
[ROW][C]13[/C][C]93.82[/C][C]93.348585370808[/C][C]0.471414629192012[/C][/ROW]
[ROW][C]14[/C][C]94.18[/C][C]94.0617708566855[/C][C]0.11822914331448[/C][/ROW]
[ROW][C]15[/C][C]94.44[/C][C]94.453105784976[/C][C]-0.0131057849760481[/C][/ROW]
[ROW][C]16[/C][C]94.35[/C][C]94.7167173554081[/C][C]-0.366717355408113[/C][/ROW]
[ROW][C]17[/C][C]94.38[/C][C]94.589746296369[/C][C]-0.209746296369033[/C][/ROW]
[ROW][C]18[/C][C]94.72[/C][C]94.5836718986083[/C][C]0.136328101391669[/C][/ROW]
[ROW][C]19[/C][C]95.25[/C][C]94.9284968447976[/C][C]0.321503155202436[/C][/ROW]
[ROW][C]20[/C][C]95.16[/C][C]95.4960976196926[/C][C]-0.33609761969258[/C][/ROW]
[ROW][C]21[/C][C]94.9[/C][C]95.3860737698033[/C][C]-0.486073769803284[/C][/ROW]
[ROW][C]22[/C][C]95.09[/C][C]95.0638239823406[/C][C]0.0261760176593953[/C][/ROW]
[ROW][C]23[/C][C]95.22[/C][C]95.2362237589122[/C][C]-0.0162237589122469[/C][/ROW]
[ROW][C]24[/C][C]95.39[/C][C]95.365700062648[/C][C]0.0242999373519694[/C][/ROW]
[ROW][C]25[/C][C]96.57[/C][C]95.5374395711154[/C][C]1.03256042888458[/C][/ROW]
[ROW][C]26[/C][C]97.05[/C][C]96.8210147065795[/C][C]0.228985293420493[/C][/ROW]
[ROW][C]27[/C][C]97.11[/C][C]97.3666713222389[/C][C]-0.256671322238859[/C][/ROW]
[ROW][C]28[/C][C]97.08[/C][C]97.4106920983684[/C][C]-0.330692098368402[/C][/ROW]
[ROW][C]29[/C][C]97.5[/C][C]97.3371773379657[/C][C]0.16282266203433[/C][/ROW]
[ROW][C]30[/C][C]97.92[/C][C]97.7596077351646[/C][C]0.160392264835451[/C][/ROW]
[ROW][C]31[/C][C]98.44[/C][C]98.2023062659864[/C][C]0.237693734013646[/C][/ROW]
[ROW][C]32[/C][C]98.44[/C][C]98.7525822274712[/C][C]-0.312582227471168[/C][/ROW]
[ROW][C]33[/C][C]98.06[/C][C]98.731411223074[/C][C]-0.671411223074017[/C][/ROW]
[ROW][C]34[/C][C]98.2[/C][C]98.2717289338003[/C][C]-0.0717289338002729[/C][/ROW]
[ROW][C]35[/C][C]98.19[/C][C]98.3767014353467[/C][C]-0.186701435346706[/C][/ROW]
[ROW][C]36[/C][C]98.36[/C][C]98.345175272332[/C][C]0.0148247276680138[/C][/ROW]
[ROW][C]37[/C][C]98.41[/C][C]98.5088888662426[/C][C]-0.0988888662425751[/C][/ROW]
[ROW][C]38[/C][C]98.97[/C][C]98.5496822226319[/C][C]0.420317777368126[/C][/ROW]
[ROW][C]39[/C][C]99.45[/C][C]99.1473231784344[/C][C]0.302676821565626[/C][/ROW]
[ROW][C]40[/C][C]98.95[/C][C]99.6748559925709[/C][C]-0.724855992570852[/C][/ROW]
[ROW][C]41[/C][C]99.7[/C][C]99.1154339917323[/C][C]0.584566008267657[/C][/ROW]
[ROW][C]42[/C][C]100.12[/C][C]99.8933758718088[/C][C]0.226624128191233[/C][/ROW]
[ROW][C]43[/C][C]100.62[/C][C]100.360180142995[/C][C]0.259819857005056[/C][/ROW]
[ROW][C]44[/C][C]100.75[/C][C]100.895406386707[/C][C]-0.14540638670708[/C][/ROW]
[ROW][C]45[/C][C]100.47[/C][C]101.021760648446[/C][C]-0.551760648446475[/C][/ROW]
[ROW][C]46[/C][C]100.71[/C][C]100.680910886485[/C][C]0.0290891135150275[/C][/ROW]
[ROW][C]47[/C][C]100.85[/C][C]100.900870200399[/C][C]-0.0508702003994159[/C][/ROW]
[ROW][C]48[/C][C]101.03[/C][C]101.037026100727[/C][C]-0.00702610072683285[/C][/ROW]
[ROW][C]49[/C][C]101.13[/C][C]101.21421412093[/C][C]-0.0842141209295733[/C][/ROW]
[ROW][C]50[/C][C]101.38[/C][C]101.30555705524[/C][C]0.0744429447599515[/C][/ROW]
[ROW][C]51[/C][C]101.73[/C][C]101.559451767666[/C][C]0.170548232334099[/C][/ROW]
[ROW][C]52[/C][C]101.89[/C][C]101.92948620583[/C][C]-0.0394862058296752[/C][/ROW]
[ROW][C]53[/C][C]102.02[/C][C]102.092651665448[/C][C]-0.0726516654484186[/C][/ROW]
[ROW][C]54[/C][C]102.11[/C][C]102.213794129138[/C][C]-0.103794129138038[/C][/ROW]
[ROW][C]55[/C][C]102.77[/C][C]102.290464886021[/C][C]0.47953511397894[/C][/ROW]
[ROW][C]56[/C][C]102.49[/C][C]102.993784106465[/C][C]-0.503784106464877[/C][/ROW]
[ROW][C]57[/C][C]102.52[/C][C]102.683671299294[/C][C]-0.163671299294293[/C][/ROW]
[ROW][C]58[/C][C]102.69[/C][C]102.676477340778[/C][C]0.0135226592223603[/C][/ROW]
[ROW][C]59[/C][C]102.32[/C][C]102.84101868815[/C][C]-0.52101868814978[/C][/ROW]
[ROW][C]60[/C][C]102.6[/C][C]102.419827349259[/C][C]0.180172650741127[/C][/ROW]
[ROW][C]61[/C][C]103.03[/C][C]102.696071522495[/C][C]0.333928477505339[/C][/ROW]
[ROW][C]62[/C][C]103.7[/C][C]103.166728614472[/C][C]0.533271385527755[/C][/ROW]
[ROW][C]63[/C][C]103.17[/C][C]103.903576443541[/C][C]-0.733576443540883[/C][/ROW]
[ROW][C]64[/C][C]103.88[/C][C]103.32287130886[/C][C]0.557128691139596[/C][/ROW]
[ROW][C]65[/C][C]104.09[/C][C]104.057725406792[/C][C]0.0322745932078732[/C][/ROW]
[ROW][C]66[/C][C]104.32[/C][C]104.294084497945[/C][C]0.0259155020546302[/C][/ROW]
[ROW][C]67[/C][C]104.88[/C][C]104.52799998261[/C][C]0.352000017390182[/C][/ROW]
[ROW][C]68[/C][C]105.06[/C][C]105.124041501329[/C][C]-0.0640415013289299[/C][/ROW]
[ROW][C]69[/C][C]104.66[/C][C]105.31230865424[/C][C]-0.652308654239931[/C][/ROW]
[ROW][C]70[/C][C]105.41[/C][C]104.844852728755[/C][C]0.565147271245323[/C][/ROW]
[ROW][C]71[/C][C]105.41[/C][C]105.623880657227[/C][C]-0.213880657226696[/C][/ROW]
[ROW][C]72[/C][C]105.48[/C][C]105.6261221346[/C][C]-0.146122134599651[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
391.9192.88-0.970000000000013
492.0692.5236489152503-0.463648915250303
592.3392.5872828178429-0.257282817842921
692.7392.8124582753938-0.0824582753937477
793.3593.19357542002560.156424579974413
893.2893.8256864211515-0.545686421151458
993.2293.7079835469935-0.48798354699349
1093.3193.5768339420935-0.266833942093541
1193.2193.6200493751408-0.410049375140844
1293.1493.4682296364596-0.328229636459611
1393.8293.3485853708080.471414629192012
1494.1894.06177085668550.11822914331448
1594.4494.453105784976-0.0131057849760481
1694.3594.7167173554081-0.366717355408113
1794.3894.589746296369-0.209746296369033
1894.7294.58367189860830.136328101391669
1995.2594.92849684479760.321503155202436
2095.1695.4960976196926-0.33609761969258
2194.995.3860737698033-0.486073769803284
2295.0995.06382398234060.0261760176593953
2395.2295.2362237589122-0.0162237589122469
2495.3995.3657000626480.0242999373519694
2596.5795.53743957111541.03256042888458
2697.0596.82101470657950.228985293420493
2797.1197.3666713222389-0.256671322238859
2897.0897.4106920983684-0.330692098368402
2997.597.33717733796570.16282266203433
3097.9297.75960773516460.160392264835451
3198.4498.20230626598640.237693734013646
3298.4498.7525822274712-0.312582227471168
3398.0698.731411223074-0.671411223074017
3498.298.2717289338003-0.0717289338002729
3598.1998.3767014353467-0.186701435346706
3698.3698.3451752723320.0148247276680138
3798.4198.5088888662426-0.0988888662425751
3898.9798.54968222263190.420317777368126
3999.4599.14732317843440.302676821565626
4098.9599.6748559925709-0.724855992570852
4199.799.11543399173230.584566008267657
42100.1299.89337587180880.226624128191233
43100.62100.3601801429950.259819857005056
44100.75100.895406386707-0.14540638670708
45100.47101.021760648446-0.551760648446475
46100.71100.6809108864850.0290891135150275
47100.85100.900870200399-0.0508702003994159
48101.03101.037026100727-0.00702610072683285
49101.13101.21421412093-0.0842141209295733
50101.38101.305557055240.0744429447599515
51101.73101.5594517676660.170548232334099
52101.89101.92948620583-0.0394862058296752
53102.02102.092651665448-0.0726516654484186
54102.11102.213794129138-0.103794129138038
55102.77102.2904648860210.47953511397894
56102.49102.993784106465-0.503784106464877
57102.52102.683671299294-0.163671299294293
58102.69102.6764773407780.0135226592223603
59102.32102.84101868815-0.52101868814978
60102.6102.4198273492590.180172650741127
61103.03102.6960715224950.333928477505339
62103.7103.1667286144720.533271385527755
63103.17103.903576443541-0.733576443540883
64103.88103.322871308860.557128691139596
65104.09104.0577254067920.0322745932078732
66104.32104.2940844979450.0259155020546302
67104.88104.527999982610.352000017390182
68105.06105.124041501329-0.0640415013289299
69104.66105.31230865424-0.652308654239931
70105.41104.8448527287550.565147271245323
71105.41105.623880657227-0.213880657226696
72105.48105.6261221346-0.146122134599651







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73105.672719195823104.946565837463106.398872554183
74105.859365829906104.780220657983106.938511001829
75106.046012463989104.640446135351107.451578792627
76106.232659098071104.505980378575107.959337817568
77106.419305732154104.369209177178108.469402287131
78106.605952366237104.226671035362108.985233697112
79106.79259900032104.076608537396109.508589463243
80106.979245634403103.918085232103110.040406036702
81107.165892268486103.750601711687110.581182825284
82107.352538902568103.573907215689111.131170589448
83107.539185536651103.387898987162111.690472086141
84107.725832170734103.192565042695112.259099298773

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 105.672719195823 & 104.946565837463 & 106.398872554183 \tabularnewline
74 & 105.859365829906 & 104.780220657983 & 106.938511001829 \tabularnewline
75 & 106.046012463989 & 104.640446135351 & 107.451578792627 \tabularnewline
76 & 106.232659098071 & 104.505980378575 & 107.959337817568 \tabularnewline
77 & 106.419305732154 & 104.369209177178 & 108.469402287131 \tabularnewline
78 & 106.605952366237 & 104.226671035362 & 108.985233697112 \tabularnewline
79 & 106.79259900032 & 104.076608537396 & 109.508589463243 \tabularnewline
80 & 106.979245634403 & 103.918085232103 & 110.040406036702 \tabularnewline
81 & 107.165892268486 & 103.750601711687 & 110.581182825284 \tabularnewline
82 & 107.352538902568 & 103.573907215689 & 111.131170589448 \tabularnewline
83 & 107.539185536651 & 103.387898987162 & 111.690472086141 \tabularnewline
84 & 107.725832170734 & 103.192565042695 & 112.259099298773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]73[/C][C]105.672719195823[/C][C]104.946565837463[/C][C]106.398872554183[/C][/ROW]
[ROW][C]74[/C][C]105.859365829906[/C][C]104.780220657983[/C][C]106.938511001829[/C][/ROW]
[ROW][C]75[/C][C]106.046012463989[/C][C]104.640446135351[/C][C]107.451578792627[/C][/ROW]
[ROW][C]76[/C][C]106.232659098071[/C][C]104.505980378575[/C][C]107.959337817568[/C][/ROW]
[ROW][C]77[/C][C]106.419305732154[/C][C]104.369209177178[/C][C]108.469402287131[/C][/ROW]
[ROW][C]78[/C][C]106.605952366237[/C][C]104.226671035362[/C][C]108.985233697112[/C][/ROW]
[ROW][C]79[/C][C]106.79259900032[/C][C]104.076608537396[/C][C]109.508589463243[/C][/ROW]
[ROW][C]80[/C][C]106.979245634403[/C][C]103.918085232103[/C][C]110.040406036702[/C][/ROW]
[ROW][C]81[/C][C]107.165892268486[/C][C]103.750601711687[/C][C]110.581182825284[/C][/ROW]
[ROW][C]82[/C][C]107.352538902568[/C][C]103.573907215689[/C][C]111.131170589448[/C][/ROW]
[ROW][C]83[/C][C]107.539185536651[/C][C]103.387898987162[/C][C]111.690472086141[/C][/ROW]
[ROW][C]84[/C][C]107.725832170734[/C][C]103.192565042695[/C][C]112.259099298773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
73105.672719195823104.946565837463106.398872554183
74105.859365829906104.780220657983106.938511001829
75106.046012463989104.640446135351107.451578792627
76106.232659098071104.505980378575107.959337817568
77106.419305732154104.369209177178108.469402287131
78106.605952366237104.226671035362108.985233697112
79106.79259900032104.076608537396109.508589463243
80106.979245634403103.918085232103110.040406036702
81107.165892268486103.750601711687110.581182825284
82107.352538902568103.573907215689111.131170589448
83107.539185536651103.387898987162111.690472086141
84107.725832170734103.192565042695112.259099298773



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')