Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 14 Dec 2015 19:30:35 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/14/t14501215751hc6k2fxi67rxy9.htm/, Retrieved Thu, 16 May 2024 20:01:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286392, Retrieved Thu, 16 May 2024 20:01:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [opgave 9 - 10 exp...] [2015-11-24 20:35:27] [1625b1453ed47b256ce4b6eedb089cd5]
- R P     [Exponential Smoothing] [oefening 10 kaas ...] [2015-12-14 19:30:35] [c4e632f9a17048eeb9519d4e8ae83546] [Current]
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Dataseries X:
79.58
80.08
80.41
80.34
80.32
80.39
81.01
81.54
82.48
84.68
88.26
90.6
92.46
93.31
93.58
93.92
93.92
93.67
93.76
93.95
93.89
94.07
93.93
93.35
93.58
93.55
93.44
93.38
93.17
92.95
93.37
94.13
94.07
94
94.47
94.81
94.18
94.14
93.96
93.23
93.13
92.51
92.49
92.73
92.75
92.83
92.85
93.27
93.98
94.34
94.57
94.62
94.82
95.07
95.72
96.06
96.54
96.38
96.8
97.02
97.29
97.45
97.95
97.69
97.63
97.35
97.38
98.06
98.34
98.53
98.79
98.77
99.2
99.76
99.84
99.83
99.88
99.48
99.66
99.58
99.89
100.7
101.19
100.99
101.52
101.75
101.56
102.57
102.66
102.62
102.76
102.73
102.26
101.72
101.48
100.93




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286392&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286392&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286392&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.777373911092591
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.777373911092591 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286392&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]0.777373911092591[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286392&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286392&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
beta0.777373911092591
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
380.4180.58-0.170000000000002
480.3480.7778464351143-0.437846435114253
580.3280.3674760393915-0.0474760393915545
680.3980.31056940496650.0794305950334575
781.0180.44231667728810.567683322711886
881.5481.50361888212670.0363811178733044
982.4882.06190061401780.418099385982217
1084.6883.32692016892421.35307983107582
1188.2686.57876912922811.6812308707719
1290.691.4657141466897-0.865714146689669
1392.4693.1327305545893-0.672730554589322
1493.3194.4697673722567-1.15976737225672
1593.5894.4181944741279-0.838194474127945
1693.9294.0366039575189-0.116603957518905
1793.9294.2859590830136-0.365959083013564
1893.6794.0014720393515-0.331472039351453
1993.7693.4937943237030.266205676297034
2093.9593.79073567144110.159264328558947
2193.8994.1045436054305-0.21454360543045
2294.0793.87776300377710.192236996222917
2393.9394.2072030293876-0.277203029387564
2493.3593.8517126262659-0.501712626265871
2593.5892.8816943197410.698305680258983
2693.5593.6545389375421-0.104538937542117
2793.4493.5432730948035-0.103273094803541
2893.3893.35299128518550.0270087148145279
2993.1793.3139871554544-0.143987155454425
3092.9592.9920552972717-0.0420552972717303
3193.3792.73936260634940.630637393650559
3294.1393.64960366353280.48039633646718
3394.0794.7830512424868-0.713051242486856
349494.1687438093054-0.168743809305411
3594.4793.9675667742930.502433225706994
3694.8194.8281452560237-0.0181452560237148
3794.1895.1540396073808-0.974039607380789
3894.1493.76684662823210.373153371767899
3993.9694.0169263242807-0.0569263242806954
4093.2393.7926732849305-0.562673284930469
4193.1392.62526575275680.504734247243221
4292.5192.9176329885986-0.407632988598593
4392.4991.98074973796140.509250262038634
4492.7392.35662760588730.373372394112749
4592.7592.8868775641927-0.136877564192702
4692.8392.80047251677540.0295274832246122
4792.8592.9034264118944-0.053426411894435
4893.2792.88189411312440.388105886875593
4993.9893.60359750432290.376402495677056
5094.3494.6062029845324-0.266202984532441
5194.5794.7592637293019-0.189263729301942
5294.6294.8421350438265-0.222135043826498
5394.8294.71945305601640.100546943983602
5495.0794.99761562710930.0723843728906672
5595.7295.30388535016530.416114649834668
5696.0696.2773620229702-0.217362022970235
5796.5496.44839045705090.0916095429491293
5896.3896.9996053257466-0.619605325746647
5996.896.35794031033720.442059689662827
6097.0297.1215859802267-0.101585980226744
6197.2997.26261568946570.0273843105343019
6297.4597.5539035380483-0.103903538048328
6397.9597.63313163829930.316868361700656
6497.6998.3794568359361-0.689456835936085
6597.6397.58349107885490.046508921145076
6697.3597.5596459007862-0.209645900786171
6797.3897.11667264694750.263327353052503
6898.0697.35137646128760.70862353871243
6998.3498.5822419130687-0.242241913068725
7098.5398.6739293696759-0.143929369675945
7198.7998.75204243264990.0379575673501478
7298.7799.0415496552364-0.271549655236413
7399.298.81045403768940.389545962310578
7499.7699.54327690596110.216723094038869
7599.84100.271751785198-0.431751785198216
7699.83100.016119211317-0.186119211317475
7799.8899.86143499208610.018565007913864
7899.4899.9258669448976-0.445866944897588
7999.6699.17926161411570.480738385884337
8099.5899.7329750933629-0.152975093362897
8199.8999.53405624673560.35594375326437
82100.7100.120757634340.579242365660278
83101.19101.381045537604-0.191045537603586
84100.99101.72253172084-0.732531720839901
85101.52100.9530806720110.566919327988799
86101.75101.923788967284-0.173788967283826
87101.56102.018689958082-0.458689958081663
88102.57101.4721163513891.09788364861116
89102.66103.335582457234-0.675582457234285
90102.62102.900402280189-0.280402280188525
91102.76102.6424248629590.117575137040902
92102.73102.873824707088-0.14382470708783
93102.26102.732019132027-0.472019132027214
94101.72101.895083773253-0.175083773252695
95101.48101.218978215670.261021784329614
96100.93101.181889741035-0.251889741035072

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 80.41 & 80.58 & -0.170000000000002 \tabularnewline
4 & 80.34 & 80.7778464351143 & -0.437846435114253 \tabularnewline
5 & 80.32 & 80.3674760393915 & -0.0474760393915545 \tabularnewline
6 & 80.39 & 80.3105694049665 & 0.0794305950334575 \tabularnewline
7 & 81.01 & 80.4423166772881 & 0.567683322711886 \tabularnewline
8 & 81.54 & 81.5036188821267 & 0.0363811178733044 \tabularnewline
9 & 82.48 & 82.0619006140178 & 0.418099385982217 \tabularnewline
10 & 84.68 & 83.3269201689242 & 1.35307983107582 \tabularnewline
11 & 88.26 & 86.5787691292281 & 1.6812308707719 \tabularnewline
12 & 90.6 & 91.4657141466897 & -0.865714146689669 \tabularnewline
13 & 92.46 & 93.1327305545893 & -0.672730554589322 \tabularnewline
14 & 93.31 & 94.4697673722567 & -1.15976737225672 \tabularnewline
15 & 93.58 & 94.4181944741279 & -0.838194474127945 \tabularnewline
16 & 93.92 & 94.0366039575189 & -0.116603957518905 \tabularnewline
17 & 93.92 & 94.2859590830136 & -0.365959083013564 \tabularnewline
18 & 93.67 & 94.0014720393515 & -0.331472039351453 \tabularnewline
19 & 93.76 & 93.493794323703 & 0.266205676297034 \tabularnewline
20 & 93.95 & 93.7907356714411 & 0.159264328558947 \tabularnewline
21 & 93.89 & 94.1045436054305 & -0.21454360543045 \tabularnewline
22 & 94.07 & 93.8777630037771 & 0.192236996222917 \tabularnewline
23 & 93.93 & 94.2072030293876 & -0.277203029387564 \tabularnewline
24 & 93.35 & 93.8517126262659 & -0.501712626265871 \tabularnewline
25 & 93.58 & 92.881694319741 & 0.698305680258983 \tabularnewline
26 & 93.55 & 93.6545389375421 & -0.104538937542117 \tabularnewline
27 & 93.44 & 93.5432730948035 & -0.103273094803541 \tabularnewline
28 & 93.38 & 93.3529912851855 & 0.0270087148145279 \tabularnewline
29 & 93.17 & 93.3139871554544 & -0.143987155454425 \tabularnewline
30 & 92.95 & 92.9920552972717 & -0.0420552972717303 \tabularnewline
31 & 93.37 & 92.7393626063494 & 0.630637393650559 \tabularnewline
32 & 94.13 & 93.6496036635328 & 0.48039633646718 \tabularnewline
33 & 94.07 & 94.7830512424868 & -0.713051242486856 \tabularnewline
34 & 94 & 94.1687438093054 & -0.168743809305411 \tabularnewline
35 & 94.47 & 93.967566774293 & 0.502433225706994 \tabularnewline
36 & 94.81 & 94.8281452560237 & -0.0181452560237148 \tabularnewline
37 & 94.18 & 95.1540396073808 & -0.974039607380789 \tabularnewline
38 & 94.14 & 93.7668466282321 & 0.373153371767899 \tabularnewline
39 & 93.96 & 94.0169263242807 & -0.0569263242806954 \tabularnewline
40 & 93.23 & 93.7926732849305 & -0.562673284930469 \tabularnewline
41 & 93.13 & 92.6252657527568 & 0.504734247243221 \tabularnewline
42 & 92.51 & 92.9176329885986 & -0.407632988598593 \tabularnewline
43 & 92.49 & 91.9807497379614 & 0.509250262038634 \tabularnewline
44 & 92.73 & 92.3566276058873 & 0.373372394112749 \tabularnewline
45 & 92.75 & 92.8868775641927 & -0.136877564192702 \tabularnewline
46 & 92.83 & 92.8004725167754 & 0.0295274832246122 \tabularnewline
47 & 92.85 & 92.9034264118944 & -0.053426411894435 \tabularnewline
48 & 93.27 & 92.8818941131244 & 0.388105886875593 \tabularnewline
49 & 93.98 & 93.6035975043229 & 0.376402495677056 \tabularnewline
50 & 94.34 & 94.6062029845324 & -0.266202984532441 \tabularnewline
51 & 94.57 & 94.7592637293019 & -0.189263729301942 \tabularnewline
52 & 94.62 & 94.8421350438265 & -0.222135043826498 \tabularnewline
53 & 94.82 & 94.7194530560164 & 0.100546943983602 \tabularnewline
54 & 95.07 & 94.9976156271093 & 0.0723843728906672 \tabularnewline
55 & 95.72 & 95.3038853501653 & 0.416114649834668 \tabularnewline
56 & 96.06 & 96.2773620229702 & -0.217362022970235 \tabularnewline
57 & 96.54 & 96.4483904570509 & 0.0916095429491293 \tabularnewline
58 & 96.38 & 96.9996053257466 & -0.619605325746647 \tabularnewline
59 & 96.8 & 96.3579403103372 & 0.442059689662827 \tabularnewline
60 & 97.02 & 97.1215859802267 & -0.101585980226744 \tabularnewline
61 & 97.29 & 97.2626156894657 & 0.0273843105343019 \tabularnewline
62 & 97.45 & 97.5539035380483 & -0.103903538048328 \tabularnewline
63 & 97.95 & 97.6331316382993 & 0.316868361700656 \tabularnewline
64 & 97.69 & 98.3794568359361 & -0.689456835936085 \tabularnewline
65 & 97.63 & 97.5834910788549 & 0.046508921145076 \tabularnewline
66 & 97.35 & 97.5596459007862 & -0.209645900786171 \tabularnewline
67 & 97.38 & 97.1166726469475 & 0.263327353052503 \tabularnewline
68 & 98.06 & 97.3513764612876 & 0.70862353871243 \tabularnewline
69 & 98.34 & 98.5822419130687 & -0.242241913068725 \tabularnewline
70 & 98.53 & 98.6739293696759 & -0.143929369675945 \tabularnewline
71 & 98.79 & 98.7520424326499 & 0.0379575673501478 \tabularnewline
72 & 98.77 & 99.0415496552364 & -0.271549655236413 \tabularnewline
73 & 99.2 & 98.8104540376894 & 0.389545962310578 \tabularnewline
74 & 99.76 & 99.5432769059611 & 0.216723094038869 \tabularnewline
75 & 99.84 & 100.271751785198 & -0.431751785198216 \tabularnewline
76 & 99.83 & 100.016119211317 & -0.186119211317475 \tabularnewline
77 & 99.88 & 99.8614349920861 & 0.018565007913864 \tabularnewline
78 & 99.48 & 99.9258669448976 & -0.445866944897588 \tabularnewline
79 & 99.66 & 99.1792616141157 & 0.480738385884337 \tabularnewline
80 & 99.58 & 99.7329750933629 & -0.152975093362897 \tabularnewline
81 & 99.89 & 99.5340562467356 & 0.35594375326437 \tabularnewline
82 & 100.7 & 100.12075763434 & 0.579242365660278 \tabularnewline
83 & 101.19 & 101.381045537604 & -0.191045537603586 \tabularnewline
84 & 100.99 & 101.72253172084 & -0.732531720839901 \tabularnewline
85 & 101.52 & 100.953080672011 & 0.566919327988799 \tabularnewline
86 & 101.75 & 101.923788967284 & -0.173788967283826 \tabularnewline
87 & 101.56 & 102.018689958082 & -0.458689958081663 \tabularnewline
88 & 102.57 & 101.472116351389 & 1.09788364861116 \tabularnewline
89 & 102.66 & 103.335582457234 & -0.675582457234285 \tabularnewline
90 & 102.62 & 102.900402280189 & -0.280402280188525 \tabularnewline
91 & 102.76 & 102.642424862959 & 0.117575137040902 \tabularnewline
92 & 102.73 & 102.873824707088 & -0.14382470708783 \tabularnewline
93 & 102.26 & 102.732019132027 & -0.472019132027214 \tabularnewline
94 & 101.72 & 101.895083773253 & -0.175083773252695 \tabularnewline
95 & 101.48 & 101.21897821567 & 0.261021784329614 \tabularnewline
96 & 100.93 & 101.181889741035 & -0.251889741035072 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286392&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]80.41[/C][C]80.58[/C][C]-0.170000000000002[/C][/ROW]
[ROW][C]4[/C][C]80.34[/C][C]80.7778464351143[/C][C]-0.437846435114253[/C][/ROW]
[ROW][C]5[/C][C]80.32[/C][C]80.3674760393915[/C][C]-0.0474760393915545[/C][/ROW]
[ROW][C]6[/C][C]80.39[/C][C]80.3105694049665[/C][C]0.0794305950334575[/C][/ROW]
[ROW][C]7[/C][C]81.01[/C][C]80.4423166772881[/C][C]0.567683322711886[/C][/ROW]
[ROW][C]8[/C][C]81.54[/C][C]81.5036188821267[/C][C]0.0363811178733044[/C][/ROW]
[ROW][C]9[/C][C]82.48[/C][C]82.0619006140178[/C][C]0.418099385982217[/C][/ROW]
[ROW][C]10[/C][C]84.68[/C][C]83.3269201689242[/C][C]1.35307983107582[/C][/ROW]
[ROW][C]11[/C][C]88.26[/C][C]86.5787691292281[/C][C]1.6812308707719[/C][/ROW]
[ROW][C]12[/C][C]90.6[/C][C]91.4657141466897[/C][C]-0.865714146689669[/C][/ROW]
[ROW][C]13[/C][C]92.46[/C][C]93.1327305545893[/C][C]-0.672730554589322[/C][/ROW]
[ROW][C]14[/C][C]93.31[/C][C]94.4697673722567[/C][C]-1.15976737225672[/C][/ROW]
[ROW][C]15[/C][C]93.58[/C][C]94.4181944741279[/C][C]-0.838194474127945[/C][/ROW]
[ROW][C]16[/C][C]93.92[/C][C]94.0366039575189[/C][C]-0.116603957518905[/C][/ROW]
[ROW][C]17[/C][C]93.92[/C][C]94.2859590830136[/C][C]-0.365959083013564[/C][/ROW]
[ROW][C]18[/C][C]93.67[/C][C]94.0014720393515[/C][C]-0.331472039351453[/C][/ROW]
[ROW][C]19[/C][C]93.76[/C][C]93.493794323703[/C][C]0.266205676297034[/C][/ROW]
[ROW][C]20[/C][C]93.95[/C][C]93.7907356714411[/C][C]0.159264328558947[/C][/ROW]
[ROW][C]21[/C][C]93.89[/C][C]94.1045436054305[/C][C]-0.21454360543045[/C][/ROW]
[ROW][C]22[/C][C]94.07[/C][C]93.8777630037771[/C][C]0.192236996222917[/C][/ROW]
[ROW][C]23[/C][C]93.93[/C][C]94.2072030293876[/C][C]-0.277203029387564[/C][/ROW]
[ROW][C]24[/C][C]93.35[/C][C]93.8517126262659[/C][C]-0.501712626265871[/C][/ROW]
[ROW][C]25[/C][C]93.58[/C][C]92.881694319741[/C][C]0.698305680258983[/C][/ROW]
[ROW][C]26[/C][C]93.55[/C][C]93.6545389375421[/C][C]-0.104538937542117[/C][/ROW]
[ROW][C]27[/C][C]93.44[/C][C]93.5432730948035[/C][C]-0.103273094803541[/C][/ROW]
[ROW][C]28[/C][C]93.38[/C][C]93.3529912851855[/C][C]0.0270087148145279[/C][/ROW]
[ROW][C]29[/C][C]93.17[/C][C]93.3139871554544[/C][C]-0.143987155454425[/C][/ROW]
[ROW][C]30[/C][C]92.95[/C][C]92.9920552972717[/C][C]-0.0420552972717303[/C][/ROW]
[ROW][C]31[/C][C]93.37[/C][C]92.7393626063494[/C][C]0.630637393650559[/C][/ROW]
[ROW][C]32[/C][C]94.13[/C][C]93.6496036635328[/C][C]0.48039633646718[/C][/ROW]
[ROW][C]33[/C][C]94.07[/C][C]94.7830512424868[/C][C]-0.713051242486856[/C][/ROW]
[ROW][C]34[/C][C]94[/C][C]94.1687438093054[/C][C]-0.168743809305411[/C][/ROW]
[ROW][C]35[/C][C]94.47[/C][C]93.967566774293[/C][C]0.502433225706994[/C][/ROW]
[ROW][C]36[/C][C]94.81[/C][C]94.8281452560237[/C][C]-0.0181452560237148[/C][/ROW]
[ROW][C]37[/C][C]94.18[/C][C]95.1540396073808[/C][C]-0.974039607380789[/C][/ROW]
[ROW][C]38[/C][C]94.14[/C][C]93.7668466282321[/C][C]0.373153371767899[/C][/ROW]
[ROW][C]39[/C][C]93.96[/C][C]94.0169263242807[/C][C]-0.0569263242806954[/C][/ROW]
[ROW][C]40[/C][C]93.23[/C][C]93.7926732849305[/C][C]-0.562673284930469[/C][/ROW]
[ROW][C]41[/C][C]93.13[/C][C]92.6252657527568[/C][C]0.504734247243221[/C][/ROW]
[ROW][C]42[/C][C]92.51[/C][C]92.9176329885986[/C][C]-0.407632988598593[/C][/ROW]
[ROW][C]43[/C][C]92.49[/C][C]91.9807497379614[/C][C]0.509250262038634[/C][/ROW]
[ROW][C]44[/C][C]92.73[/C][C]92.3566276058873[/C][C]0.373372394112749[/C][/ROW]
[ROW][C]45[/C][C]92.75[/C][C]92.8868775641927[/C][C]-0.136877564192702[/C][/ROW]
[ROW][C]46[/C][C]92.83[/C][C]92.8004725167754[/C][C]0.0295274832246122[/C][/ROW]
[ROW][C]47[/C][C]92.85[/C][C]92.9034264118944[/C][C]-0.053426411894435[/C][/ROW]
[ROW][C]48[/C][C]93.27[/C][C]92.8818941131244[/C][C]0.388105886875593[/C][/ROW]
[ROW][C]49[/C][C]93.98[/C][C]93.6035975043229[/C][C]0.376402495677056[/C][/ROW]
[ROW][C]50[/C][C]94.34[/C][C]94.6062029845324[/C][C]-0.266202984532441[/C][/ROW]
[ROW][C]51[/C][C]94.57[/C][C]94.7592637293019[/C][C]-0.189263729301942[/C][/ROW]
[ROW][C]52[/C][C]94.62[/C][C]94.8421350438265[/C][C]-0.222135043826498[/C][/ROW]
[ROW][C]53[/C][C]94.82[/C][C]94.7194530560164[/C][C]0.100546943983602[/C][/ROW]
[ROW][C]54[/C][C]95.07[/C][C]94.9976156271093[/C][C]0.0723843728906672[/C][/ROW]
[ROW][C]55[/C][C]95.72[/C][C]95.3038853501653[/C][C]0.416114649834668[/C][/ROW]
[ROW][C]56[/C][C]96.06[/C][C]96.2773620229702[/C][C]-0.217362022970235[/C][/ROW]
[ROW][C]57[/C][C]96.54[/C][C]96.4483904570509[/C][C]0.0916095429491293[/C][/ROW]
[ROW][C]58[/C][C]96.38[/C][C]96.9996053257466[/C][C]-0.619605325746647[/C][/ROW]
[ROW][C]59[/C][C]96.8[/C][C]96.3579403103372[/C][C]0.442059689662827[/C][/ROW]
[ROW][C]60[/C][C]97.02[/C][C]97.1215859802267[/C][C]-0.101585980226744[/C][/ROW]
[ROW][C]61[/C][C]97.29[/C][C]97.2626156894657[/C][C]0.0273843105343019[/C][/ROW]
[ROW][C]62[/C][C]97.45[/C][C]97.5539035380483[/C][C]-0.103903538048328[/C][/ROW]
[ROW][C]63[/C][C]97.95[/C][C]97.6331316382993[/C][C]0.316868361700656[/C][/ROW]
[ROW][C]64[/C][C]97.69[/C][C]98.3794568359361[/C][C]-0.689456835936085[/C][/ROW]
[ROW][C]65[/C][C]97.63[/C][C]97.5834910788549[/C][C]0.046508921145076[/C][/ROW]
[ROW][C]66[/C][C]97.35[/C][C]97.5596459007862[/C][C]-0.209645900786171[/C][/ROW]
[ROW][C]67[/C][C]97.38[/C][C]97.1166726469475[/C][C]0.263327353052503[/C][/ROW]
[ROW][C]68[/C][C]98.06[/C][C]97.3513764612876[/C][C]0.70862353871243[/C][/ROW]
[ROW][C]69[/C][C]98.34[/C][C]98.5822419130687[/C][C]-0.242241913068725[/C][/ROW]
[ROW][C]70[/C][C]98.53[/C][C]98.6739293696759[/C][C]-0.143929369675945[/C][/ROW]
[ROW][C]71[/C][C]98.79[/C][C]98.7520424326499[/C][C]0.0379575673501478[/C][/ROW]
[ROW][C]72[/C][C]98.77[/C][C]99.0415496552364[/C][C]-0.271549655236413[/C][/ROW]
[ROW][C]73[/C][C]99.2[/C][C]98.8104540376894[/C][C]0.389545962310578[/C][/ROW]
[ROW][C]74[/C][C]99.76[/C][C]99.5432769059611[/C][C]0.216723094038869[/C][/ROW]
[ROW][C]75[/C][C]99.84[/C][C]100.271751785198[/C][C]-0.431751785198216[/C][/ROW]
[ROW][C]76[/C][C]99.83[/C][C]100.016119211317[/C][C]-0.186119211317475[/C][/ROW]
[ROW][C]77[/C][C]99.88[/C][C]99.8614349920861[/C][C]0.018565007913864[/C][/ROW]
[ROW][C]78[/C][C]99.48[/C][C]99.9258669448976[/C][C]-0.445866944897588[/C][/ROW]
[ROW][C]79[/C][C]99.66[/C][C]99.1792616141157[/C][C]0.480738385884337[/C][/ROW]
[ROW][C]80[/C][C]99.58[/C][C]99.7329750933629[/C][C]-0.152975093362897[/C][/ROW]
[ROW][C]81[/C][C]99.89[/C][C]99.5340562467356[/C][C]0.35594375326437[/C][/ROW]
[ROW][C]82[/C][C]100.7[/C][C]100.12075763434[/C][C]0.579242365660278[/C][/ROW]
[ROW][C]83[/C][C]101.19[/C][C]101.381045537604[/C][C]-0.191045537603586[/C][/ROW]
[ROW][C]84[/C][C]100.99[/C][C]101.72253172084[/C][C]-0.732531720839901[/C][/ROW]
[ROW][C]85[/C][C]101.52[/C][C]100.953080672011[/C][C]0.566919327988799[/C][/ROW]
[ROW][C]86[/C][C]101.75[/C][C]101.923788967284[/C][C]-0.173788967283826[/C][/ROW]
[ROW][C]87[/C][C]101.56[/C][C]102.018689958082[/C][C]-0.458689958081663[/C][/ROW]
[ROW][C]88[/C][C]102.57[/C][C]101.472116351389[/C][C]1.09788364861116[/C][/ROW]
[ROW][C]89[/C][C]102.66[/C][C]103.335582457234[/C][C]-0.675582457234285[/C][/ROW]
[ROW][C]90[/C][C]102.62[/C][C]102.900402280189[/C][C]-0.280402280188525[/C][/ROW]
[ROW][C]91[/C][C]102.76[/C][C]102.642424862959[/C][C]0.117575137040902[/C][/ROW]
[ROW][C]92[/C][C]102.73[/C][C]102.873824707088[/C][C]-0.14382470708783[/C][/ROW]
[ROW][C]93[/C][C]102.26[/C][C]102.732019132027[/C][C]-0.472019132027214[/C][/ROW]
[ROW][C]94[/C][C]101.72[/C][C]101.895083773253[/C][C]-0.175083773252695[/C][/ROW]
[ROW][C]95[/C][C]101.48[/C][C]101.21897821567[/C][C]0.261021784329614[/C][/ROW]
[ROW][C]96[/C][C]100.93[/C][C]101.181889741035[/C][C]-0.251889741035072[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286392&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286392&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
380.4180.58-0.170000000000002
480.3480.7778464351143-0.437846435114253
580.3280.3674760393915-0.0474760393915545
680.3980.31056940496650.0794305950334575
781.0180.44231667728810.567683322711886
881.5481.50361888212670.0363811178733044
982.4882.06190061401780.418099385982217
1084.6883.32692016892421.35307983107582
1188.2686.57876912922811.6812308707719
1290.691.4657141466897-0.865714146689669
1392.4693.1327305545893-0.672730554589322
1493.3194.4697673722567-1.15976737225672
1593.5894.4181944741279-0.838194474127945
1693.9294.0366039575189-0.116603957518905
1793.9294.2859590830136-0.365959083013564
1893.6794.0014720393515-0.331472039351453
1993.7693.4937943237030.266205676297034
2093.9593.79073567144110.159264328558947
2193.8994.1045436054305-0.21454360543045
2294.0793.87776300377710.192236996222917
2393.9394.2072030293876-0.277203029387564
2493.3593.8517126262659-0.501712626265871
2593.5892.8816943197410.698305680258983
2693.5593.6545389375421-0.104538937542117
2793.4493.5432730948035-0.103273094803541
2893.3893.35299128518550.0270087148145279
2993.1793.3139871554544-0.143987155454425
3092.9592.9920552972717-0.0420552972717303
3193.3792.73936260634940.630637393650559
3294.1393.64960366353280.48039633646718
3394.0794.7830512424868-0.713051242486856
349494.1687438093054-0.168743809305411
3594.4793.9675667742930.502433225706994
3694.8194.8281452560237-0.0181452560237148
3794.1895.1540396073808-0.974039607380789
3894.1493.76684662823210.373153371767899
3993.9694.0169263242807-0.0569263242806954
4093.2393.7926732849305-0.562673284930469
4193.1392.62526575275680.504734247243221
4292.5192.9176329885986-0.407632988598593
4392.4991.98074973796140.509250262038634
4492.7392.35662760588730.373372394112749
4592.7592.8868775641927-0.136877564192702
4692.8392.80047251677540.0295274832246122
4792.8592.9034264118944-0.053426411894435
4893.2792.88189411312440.388105886875593
4993.9893.60359750432290.376402495677056
5094.3494.6062029845324-0.266202984532441
5194.5794.7592637293019-0.189263729301942
5294.6294.8421350438265-0.222135043826498
5394.8294.71945305601640.100546943983602
5495.0794.99761562710930.0723843728906672
5595.7295.30388535016530.416114649834668
5696.0696.2773620229702-0.217362022970235
5796.5496.44839045705090.0916095429491293
5896.3896.9996053257466-0.619605325746647
5996.896.35794031033720.442059689662827
6097.0297.1215859802267-0.101585980226744
6197.2997.26261568946570.0273843105343019
6297.4597.5539035380483-0.103903538048328
6397.9597.63313163829930.316868361700656
6497.6998.3794568359361-0.689456835936085
6597.6397.58349107885490.046508921145076
6697.3597.5596459007862-0.209645900786171
6797.3897.11667264694750.263327353052503
6898.0697.35137646128760.70862353871243
6998.3498.5822419130687-0.242241913068725
7098.5398.6739293696759-0.143929369675945
7198.7998.75204243264990.0379575673501478
7298.7799.0415496552364-0.271549655236413
7399.298.81045403768940.389545962310578
7499.7699.54327690596110.216723094038869
7599.84100.271751785198-0.431751785198216
7699.83100.016119211317-0.186119211317475
7799.8899.86143499208610.018565007913864
7899.4899.9258669448976-0.445866944897588
7999.6699.17926161411570.480738385884337
8099.5899.7329750933629-0.152975093362897
8199.8999.53405624673560.35594375326437
82100.7100.120757634340.579242365660278
83101.19101.381045537604-0.191045537603586
84100.99101.72253172084-0.732531720839901
85101.52100.9530806720110.566919327988799
86101.75101.923788967284-0.173788967283826
87101.56102.018689958082-0.458689958081663
88102.57101.4721163513891.09788364861116
89102.66103.335582457234-0.675582457234285
90102.62102.900402280189-0.280402280188525
91102.76102.6424248629590.117575137040902
92102.73102.873824707088-0.14382470708783
93102.26102.732019132027-0.472019132027214
94101.72101.895083773253-0.175083773252695
95101.48101.218978215670.261021784329614
96100.93101.181889741035-0.251889741035072







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97100.43607722788399.5079361102846101.36421834548
9899.942154455765198.0493249279982101.834983983532
9999.448231683647696.4142187986189102.482244568676
10098.954308911530294.6218847915176103.286733031543
10198.460386139412792.6882151046882104.232557174137
10297.966463367295290.6254433831684105.307483351422
10397.472540595177888.4432046428021106.501876547553
10496.978617823060386.1493002277478107.807935418373
10596.484695050942983.7501997311163109.219190370769
10695.990772278825481.2513753007273110.730169256923
10795.496849506707978.6575313082926112.336167705123
10895.002926734590575.9727671318777114.033086337303

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 100.436077227883 & 99.5079361102846 & 101.36421834548 \tabularnewline
98 & 99.9421544557651 & 98.0493249279982 & 101.834983983532 \tabularnewline
99 & 99.4482316836476 & 96.4142187986189 & 102.482244568676 \tabularnewline
100 & 98.9543089115302 & 94.6218847915176 & 103.286733031543 \tabularnewline
101 & 98.4603861394127 & 92.6882151046882 & 104.232557174137 \tabularnewline
102 & 97.9664633672952 & 90.6254433831684 & 105.307483351422 \tabularnewline
103 & 97.4725405951778 & 88.4432046428021 & 106.501876547553 \tabularnewline
104 & 96.9786178230603 & 86.1493002277478 & 107.807935418373 \tabularnewline
105 & 96.4846950509429 & 83.7501997311163 & 109.219190370769 \tabularnewline
106 & 95.9907722788254 & 81.2513753007273 & 110.730169256923 \tabularnewline
107 & 95.4968495067079 & 78.6575313082926 & 112.336167705123 \tabularnewline
108 & 95.0029267345905 & 75.9727671318777 & 114.033086337303 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286392&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]97[/C][C]100.436077227883[/C][C]99.5079361102846[/C][C]101.36421834548[/C][/ROW]
[ROW][C]98[/C][C]99.9421544557651[/C][C]98.0493249279982[/C][C]101.834983983532[/C][/ROW]
[ROW][C]99[/C][C]99.4482316836476[/C][C]96.4142187986189[/C][C]102.482244568676[/C][/ROW]
[ROW][C]100[/C][C]98.9543089115302[/C][C]94.6218847915176[/C][C]103.286733031543[/C][/ROW]
[ROW][C]101[/C][C]98.4603861394127[/C][C]92.6882151046882[/C][C]104.232557174137[/C][/ROW]
[ROW][C]102[/C][C]97.9664633672952[/C][C]90.6254433831684[/C][C]105.307483351422[/C][/ROW]
[ROW][C]103[/C][C]97.4725405951778[/C][C]88.4432046428021[/C][C]106.501876547553[/C][/ROW]
[ROW][C]104[/C][C]96.9786178230603[/C][C]86.1493002277478[/C][C]107.807935418373[/C][/ROW]
[ROW][C]105[/C][C]96.4846950509429[/C][C]83.7501997311163[/C][C]109.219190370769[/C][/ROW]
[ROW][C]106[/C][C]95.9907722788254[/C][C]81.2513753007273[/C][C]110.730169256923[/C][/ROW]
[ROW][C]107[/C][C]95.4968495067079[/C][C]78.6575313082926[/C][C]112.336167705123[/C][/ROW]
[ROW][C]108[/C][C]95.0029267345905[/C][C]75.9727671318777[/C][C]114.033086337303[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286392&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286392&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
97100.43607722788399.5079361102846101.36421834548
9899.942154455765198.0493249279982101.834983983532
9999.448231683647696.4142187986189102.482244568676
10098.954308911530294.6218847915176103.286733031543
10198.460386139412792.6882151046882104.232557174137
10297.966463367295290.6254433831684105.307483351422
10397.472540595177888.4432046428021106.501876547553
10496.978617823060386.1493002277478107.807935418373
10596.484695050942983.7501997311163109.219190370769
10695.990772278825481.2513753007273110.730169256923
10795.496849506707978.6575313082926112.336167705123
10895.002926734590575.9727671318777114.033086337303



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')