Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 24 Nov 2015 13:01:36 +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/Nov/24/t14483703446wyp1t0ibndffxx.htm/, Retrieved Tue, 14 May 2024 13:32:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284014, Retrieved Tue, 14 May 2024 13:32:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opdracht 10 oefen...] [2015-11-24 13:01:36] [cd0005da8c1be4acc9acd7984e542112] [Current]
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Dataseries X:
85.13
85.54
85.47
85.78
86.07
86.05
86.32
86.43
86.41
86.38
86.59
86.68
86.87
87.32
87.13
87.42
87.22
87.17
87.52
87.49
87.53
87.93
88.54
88.96
89.3
90.01
90.52
90.64
91.25
91.59
92.09
91.81
92.03
92.15
91.98
92.11
92.28
92.53
91.97
92.05
91.87
91.49
91.48
91.63
91.46
91.61
91.7
91.87
92.21
92.65
92.83
93.02
93.33
93.35
93.45
93.51
93.8
93.94
94.02
94.26
94.71
95.26
95.54
95.69
96.03
96.4
96.55
96.45
96.65
96.84
97.21
97.31
97.91
98.51
98.54
98.52
98.66
98.53
98.71
98.92
98.96
99.25
99.32
99.41
99.36
99.58
99.77
99.77
100.03
100.2
100.24
100.1
100.03
100.18
100.29
100.41
100.6
100.75
100.79
100.44
100.29
100.34
100.46
100.12
100.06
100.28
100.28
100.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284014&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284014&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284014&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.776244353974032
beta0.225573820484752
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.776244353974032 \tabularnewline
beta & 0.225573820484752 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284014&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]0.776244353974032[/C][/ROW]
[ROW][C]beta[/C][C]0.225573820484752[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284014&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284014&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
alpha0.776244353974032
beta0.225573820484752
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1386.8786.16851421246550.701485787534537
1487.3287.30619126312620.0138087368738411
1587.1387.2759985282948-0.145998528294825
1687.4287.5560276717539-0.136027671753865
1787.2287.2949330729636-0.0749330729636313
1887.1787.187834414369-0.0178344143690055
1987.5287.854710581972-0.33471058197199
2087.4987.673374207371-0.18337420737096
2187.5387.44931940884950.0806805911504824
2287.9387.44021940602890.489780593971062
2388.5488.09941578796980.440584212030203
2488.9688.69754293999980.262457060000202
2589.389.4656405755607-0.16564057556073
2690.0189.82288090139180.187119098608235
2790.5289.9527369010040.567263098995966
2890.6490.9916040923477-0.351604092347657
2991.2590.7221482893820.527851710617981
3091.5991.348940060580.241059939420012
3192.0992.4770756448052-0.387075644805194
3291.8192.5890872438108-0.779087243810821
3392.0392.1520517438329-0.122051743832898
3492.1592.2327755249438-0.0827755249438127
3591.9892.5000604441415-0.520060444141521
3692.1192.2023430831207-0.0923430831207099
3792.2892.4341028052127-0.154102805212688
3892.5392.7194396523294-0.189439652329369
3991.9792.3998651923734-0.429865192373427
4092.0592.04924143587970.000758564120317828
4191.8791.9001279471527-0.0301279471526641
4291.4991.5840010806421-0.0940010806421014
4391.4891.8069754358403-0.326975435840268
4491.6391.38429839181880.245701608181179
4591.4691.5756925444317-0.115692544431667
4691.6191.35796672528030.252033274719722
4791.791.53290948747690.167090512523117
4891.8791.73029508715710.139704912842888
4992.2192.03452707985120.17547292014882
5092.6592.53162983841230.11837016158772
5192.8392.41461116278080.415388837219226
5293.0292.98325540252560.0367445974743958
5393.3393.02565524844110.304344751558858
5493.3593.18020610860980.169793891390242
5593.4593.8378056872632-0.38780568726321
5693.5193.7631020549788-0.253102054978839
5793.893.66433273822480.135667261775239
5893.9493.9470262546781-0.00702625467805262
5994.0294.0785442220514-0.0585442220514523
6094.2694.23372137465390.0262786253461371
6194.7194.58036846081440.129631539185567
6295.2695.14706254914250.112937450857473
6395.5495.1947397137410.345260286258991
6495.6995.7210925906148-0.0310925906147759
6596.0395.85272832919260.1772716708074
6696.495.931396861380.468603138620054
6796.5596.8154972003536-0.265497200353593
6896.4597.0045389904477-0.554538990447696
6996.6596.8437755444924-0.193775544492382
7096.8496.8641339174598-0.024133917459821
7197.2196.9925736211210.217426378879011
7297.3197.4544360626095-0.144436062609529
7397.9197.73937519383360.170624806166444
7498.5198.39228226936860.117717730631426
7598.5498.53854385448240.00145614551762208
7698.5298.7003518510839-0.180351851083884
7798.6698.7242621221541-0.0642621221541333
7898.5398.593627317882-0.0636273178820375
7998.7198.7278010108062-0.0178010108062381
8098.9298.91527831133050.0047216886695054
8198.9699.2414614214962-0.281461421496189
8299.2599.18573053975850.0642694602414764
8399.3299.4061725415661-0.0861725415661283
8499.4199.4669845623066-0.0569845623065675
8599.3699.8270783299243-0.467078329924263
8699.5899.7963804574967-0.216380457496726
8799.7799.4156811324140.354318867586016
8899.7799.63207274237390.13792725762606
89100.0399.80734890930050.2226510906995
90100.299.82485214519120.375147854808802
91100.24100.315799187798-0.0757991877983812
92100.1100.45930940899-0.359309408989617
93100.03100.371591681777-0.34159168177699
94100.18100.269040610966-0.0890406109656681
95100.29100.2312009626850.0587990373150546
96100.41100.3309793479150.0790206520850205
97100.6100.649977323329-0.049977323329216
98100.75101.020004951475-0.270004951474775
99100.79100.7312254594410.058774540559412
100100.44100.623481267442-0.183481267442119
101100.29100.467352608851-0.177352608851237
102100.34100.0371503186640.302849681335587
103100.46100.1881664959240.271833504075531
104100.12100.415891152961-0.295891152960991
105100.06100.270312839557-0.21031283955665
106100.28100.2381796702170.0418203297833912
107100.28100.2698094904960.0101905095044259
108100.4100.2626672773090.13733272269107

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 86.87 & 86.1685142124655 & 0.701485787534537 \tabularnewline
14 & 87.32 & 87.3061912631262 & 0.0138087368738411 \tabularnewline
15 & 87.13 & 87.2759985282948 & -0.145998528294825 \tabularnewline
16 & 87.42 & 87.5560276717539 & -0.136027671753865 \tabularnewline
17 & 87.22 & 87.2949330729636 & -0.0749330729636313 \tabularnewline
18 & 87.17 & 87.187834414369 & -0.0178344143690055 \tabularnewline
19 & 87.52 & 87.854710581972 & -0.33471058197199 \tabularnewline
20 & 87.49 & 87.673374207371 & -0.18337420737096 \tabularnewline
21 & 87.53 & 87.4493194088495 & 0.0806805911504824 \tabularnewline
22 & 87.93 & 87.4402194060289 & 0.489780593971062 \tabularnewline
23 & 88.54 & 88.0994157879698 & 0.440584212030203 \tabularnewline
24 & 88.96 & 88.6975429399998 & 0.262457060000202 \tabularnewline
25 & 89.3 & 89.4656405755607 & -0.16564057556073 \tabularnewline
26 & 90.01 & 89.8228809013918 & 0.187119098608235 \tabularnewline
27 & 90.52 & 89.952736901004 & 0.567263098995966 \tabularnewline
28 & 90.64 & 90.9916040923477 & -0.351604092347657 \tabularnewline
29 & 91.25 & 90.722148289382 & 0.527851710617981 \tabularnewline
30 & 91.59 & 91.34894006058 & 0.241059939420012 \tabularnewline
31 & 92.09 & 92.4770756448052 & -0.387075644805194 \tabularnewline
32 & 91.81 & 92.5890872438108 & -0.779087243810821 \tabularnewline
33 & 92.03 & 92.1520517438329 & -0.122051743832898 \tabularnewline
34 & 92.15 & 92.2327755249438 & -0.0827755249438127 \tabularnewline
35 & 91.98 & 92.5000604441415 & -0.520060444141521 \tabularnewline
36 & 92.11 & 92.2023430831207 & -0.0923430831207099 \tabularnewline
37 & 92.28 & 92.4341028052127 & -0.154102805212688 \tabularnewline
38 & 92.53 & 92.7194396523294 & -0.189439652329369 \tabularnewline
39 & 91.97 & 92.3998651923734 & -0.429865192373427 \tabularnewline
40 & 92.05 & 92.0492414358797 & 0.000758564120317828 \tabularnewline
41 & 91.87 & 91.9001279471527 & -0.0301279471526641 \tabularnewline
42 & 91.49 & 91.5840010806421 & -0.0940010806421014 \tabularnewline
43 & 91.48 & 91.8069754358403 & -0.326975435840268 \tabularnewline
44 & 91.63 & 91.3842983918188 & 0.245701608181179 \tabularnewline
45 & 91.46 & 91.5756925444317 & -0.115692544431667 \tabularnewline
46 & 91.61 & 91.3579667252803 & 0.252033274719722 \tabularnewline
47 & 91.7 & 91.5329094874769 & 0.167090512523117 \tabularnewline
48 & 91.87 & 91.7302950871571 & 0.139704912842888 \tabularnewline
49 & 92.21 & 92.0345270798512 & 0.17547292014882 \tabularnewline
50 & 92.65 & 92.5316298384123 & 0.11837016158772 \tabularnewline
51 & 92.83 & 92.4146111627808 & 0.415388837219226 \tabularnewline
52 & 93.02 & 92.9832554025256 & 0.0367445974743958 \tabularnewline
53 & 93.33 & 93.0256552484411 & 0.304344751558858 \tabularnewline
54 & 93.35 & 93.1802061086098 & 0.169793891390242 \tabularnewline
55 & 93.45 & 93.8378056872632 & -0.38780568726321 \tabularnewline
56 & 93.51 & 93.7631020549788 & -0.253102054978839 \tabularnewline
57 & 93.8 & 93.6643327382248 & 0.135667261775239 \tabularnewline
58 & 93.94 & 93.9470262546781 & -0.00702625467805262 \tabularnewline
59 & 94.02 & 94.0785442220514 & -0.0585442220514523 \tabularnewline
60 & 94.26 & 94.2337213746539 & 0.0262786253461371 \tabularnewline
61 & 94.71 & 94.5803684608144 & 0.129631539185567 \tabularnewline
62 & 95.26 & 95.1470625491425 & 0.112937450857473 \tabularnewline
63 & 95.54 & 95.194739713741 & 0.345260286258991 \tabularnewline
64 & 95.69 & 95.7210925906148 & -0.0310925906147759 \tabularnewline
65 & 96.03 & 95.8527283291926 & 0.1772716708074 \tabularnewline
66 & 96.4 & 95.93139686138 & 0.468603138620054 \tabularnewline
67 & 96.55 & 96.8154972003536 & -0.265497200353593 \tabularnewline
68 & 96.45 & 97.0045389904477 & -0.554538990447696 \tabularnewline
69 & 96.65 & 96.8437755444924 & -0.193775544492382 \tabularnewline
70 & 96.84 & 96.8641339174598 & -0.024133917459821 \tabularnewline
71 & 97.21 & 96.992573621121 & 0.217426378879011 \tabularnewline
72 & 97.31 & 97.4544360626095 & -0.144436062609529 \tabularnewline
73 & 97.91 & 97.7393751938336 & 0.170624806166444 \tabularnewline
74 & 98.51 & 98.3922822693686 & 0.117717730631426 \tabularnewline
75 & 98.54 & 98.5385438544824 & 0.00145614551762208 \tabularnewline
76 & 98.52 & 98.7003518510839 & -0.180351851083884 \tabularnewline
77 & 98.66 & 98.7242621221541 & -0.0642621221541333 \tabularnewline
78 & 98.53 & 98.593627317882 & -0.0636273178820375 \tabularnewline
79 & 98.71 & 98.7278010108062 & -0.0178010108062381 \tabularnewline
80 & 98.92 & 98.9152783113305 & 0.0047216886695054 \tabularnewline
81 & 98.96 & 99.2414614214962 & -0.281461421496189 \tabularnewline
82 & 99.25 & 99.1857305397585 & 0.0642694602414764 \tabularnewline
83 & 99.32 & 99.4061725415661 & -0.0861725415661283 \tabularnewline
84 & 99.41 & 99.4669845623066 & -0.0569845623065675 \tabularnewline
85 & 99.36 & 99.8270783299243 & -0.467078329924263 \tabularnewline
86 & 99.58 & 99.7963804574967 & -0.216380457496726 \tabularnewline
87 & 99.77 & 99.415681132414 & 0.354318867586016 \tabularnewline
88 & 99.77 & 99.6320727423739 & 0.13792725762606 \tabularnewline
89 & 100.03 & 99.8073489093005 & 0.2226510906995 \tabularnewline
90 & 100.2 & 99.8248521451912 & 0.375147854808802 \tabularnewline
91 & 100.24 & 100.315799187798 & -0.0757991877983812 \tabularnewline
92 & 100.1 & 100.45930940899 & -0.359309408989617 \tabularnewline
93 & 100.03 & 100.371591681777 & -0.34159168177699 \tabularnewline
94 & 100.18 & 100.269040610966 & -0.0890406109656681 \tabularnewline
95 & 100.29 & 100.231200962685 & 0.0587990373150546 \tabularnewline
96 & 100.41 & 100.330979347915 & 0.0790206520850205 \tabularnewline
97 & 100.6 & 100.649977323329 & -0.049977323329216 \tabularnewline
98 & 100.75 & 101.020004951475 & -0.270004951474775 \tabularnewline
99 & 100.79 & 100.731225459441 & 0.058774540559412 \tabularnewline
100 & 100.44 & 100.623481267442 & -0.183481267442119 \tabularnewline
101 & 100.29 & 100.467352608851 & -0.177352608851237 \tabularnewline
102 & 100.34 & 100.037150318664 & 0.302849681335587 \tabularnewline
103 & 100.46 & 100.188166495924 & 0.271833504075531 \tabularnewline
104 & 100.12 & 100.415891152961 & -0.295891152960991 \tabularnewline
105 & 100.06 & 100.270312839557 & -0.21031283955665 \tabularnewline
106 & 100.28 & 100.238179670217 & 0.0418203297833912 \tabularnewline
107 & 100.28 & 100.269809490496 & 0.0101905095044259 \tabularnewline
108 & 100.4 & 100.262667277309 & 0.13733272269107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284014&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]86.87[/C][C]86.1685142124655[/C][C]0.701485787534537[/C][/ROW]
[ROW][C]14[/C][C]87.32[/C][C]87.3061912631262[/C][C]0.0138087368738411[/C][/ROW]
[ROW][C]15[/C][C]87.13[/C][C]87.2759985282948[/C][C]-0.145998528294825[/C][/ROW]
[ROW][C]16[/C][C]87.42[/C][C]87.5560276717539[/C][C]-0.136027671753865[/C][/ROW]
[ROW][C]17[/C][C]87.22[/C][C]87.2949330729636[/C][C]-0.0749330729636313[/C][/ROW]
[ROW][C]18[/C][C]87.17[/C][C]87.187834414369[/C][C]-0.0178344143690055[/C][/ROW]
[ROW][C]19[/C][C]87.52[/C][C]87.854710581972[/C][C]-0.33471058197199[/C][/ROW]
[ROW][C]20[/C][C]87.49[/C][C]87.673374207371[/C][C]-0.18337420737096[/C][/ROW]
[ROW][C]21[/C][C]87.53[/C][C]87.4493194088495[/C][C]0.0806805911504824[/C][/ROW]
[ROW][C]22[/C][C]87.93[/C][C]87.4402194060289[/C][C]0.489780593971062[/C][/ROW]
[ROW][C]23[/C][C]88.54[/C][C]88.0994157879698[/C][C]0.440584212030203[/C][/ROW]
[ROW][C]24[/C][C]88.96[/C][C]88.6975429399998[/C][C]0.262457060000202[/C][/ROW]
[ROW][C]25[/C][C]89.3[/C][C]89.4656405755607[/C][C]-0.16564057556073[/C][/ROW]
[ROW][C]26[/C][C]90.01[/C][C]89.8228809013918[/C][C]0.187119098608235[/C][/ROW]
[ROW][C]27[/C][C]90.52[/C][C]89.952736901004[/C][C]0.567263098995966[/C][/ROW]
[ROW][C]28[/C][C]90.64[/C][C]90.9916040923477[/C][C]-0.351604092347657[/C][/ROW]
[ROW][C]29[/C][C]91.25[/C][C]90.722148289382[/C][C]0.527851710617981[/C][/ROW]
[ROW][C]30[/C][C]91.59[/C][C]91.34894006058[/C][C]0.241059939420012[/C][/ROW]
[ROW][C]31[/C][C]92.09[/C][C]92.4770756448052[/C][C]-0.387075644805194[/C][/ROW]
[ROW][C]32[/C][C]91.81[/C][C]92.5890872438108[/C][C]-0.779087243810821[/C][/ROW]
[ROW][C]33[/C][C]92.03[/C][C]92.1520517438329[/C][C]-0.122051743832898[/C][/ROW]
[ROW][C]34[/C][C]92.15[/C][C]92.2327755249438[/C][C]-0.0827755249438127[/C][/ROW]
[ROW][C]35[/C][C]91.98[/C][C]92.5000604441415[/C][C]-0.520060444141521[/C][/ROW]
[ROW][C]36[/C][C]92.11[/C][C]92.2023430831207[/C][C]-0.0923430831207099[/C][/ROW]
[ROW][C]37[/C][C]92.28[/C][C]92.4341028052127[/C][C]-0.154102805212688[/C][/ROW]
[ROW][C]38[/C][C]92.53[/C][C]92.7194396523294[/C][C]-0.189439652329369[/C][/ROW]
[ROW][C]39[/C][C]91.97[/C][C]92.3998651923734[/C][C]-0.429865192373427[/C][/ROW]
[ROW][C]40[/C][C]92.05[/C][C]92.0492414358797[/C][C]0.000758564120317828[/C][/ROW]
[ROW][C]41[/C][C]91.87[/C][C]91.9001279471527[/C][C]-0.0301279471526641[/C][/ROW]
[ROW][C]42[/C][C]91.49[/C][C]91.5840010806421[/C][C]-0.0940010806421014[/C][/ROW]
[ROW][C]43[/C][C]91.48[/C][C]91.8069754358403[/C][C]-0.326975435840268[/C][/ROW]
[ROW][C]44[/C][C]91.63[/C][C]91.3842983918188[/C][C]0.245701608181179[/C][/ROW]
[ROW][C]45[/C][C]91.46[/C][C]91.5756925444317[/C][C]-0.115692544431667[/C][/ROW]
[ROW][C]46[/C][C]91.61[/C][C]91.3579667252803[/C][C]0.252033274719722[/C][/ROW]
[ROW][C]47[/C][C]91.7[/C][C]91.5329094874769[/C][C]0.167090512523117[/C][/ROW]
[ROW][C]48[/C][C]91.87[/C][C]91.7302950871571[/C][C]0.139704912842888[/C][/ROW]
[ROW][C]49[/C][C]92.21[/C][C]92.0345270798512[/C][C]0.17547292014882[/C][/ROW]
[ROW][C]50[/C][C]92.65[/C][C]92.5316298384123[/C][C]0.11837016158772[/C][/ROW]
[ROW][C]51[/C][C]92.83[/C][C]92.4146111627808[/C][C]0.415388837219226[/C][/ROW]
[ROW][C]52[/C][C]93.02[/C][C]92.9832554025256[/C][C]0.0367445974743958[/C][/ROW]
[ROW][C]53[/C][C]93.33[/C][C]93.0256552484411[/C][C]0.304344751558858[/C][/ROW]
[ROW][C]54[/C][C]93.35[/C][C]93.1802061086098[/C][C]0.169793891390242[/C][/ROW]
[ROW][C]55[/C][C]93.45[/C][C]93.8378056872632[/C][C]-0.38780568726321[/C][/ROW]
[ROW][C]56[/C][C]93.51[/C][C]93.7631020549788[/C][C]-0.253102054978839[/C][/ROW]
[ROW][C]57[/C][C]93.8[/C][C]93.6643327382248[/C][C]0.135667261775239[/C][/ROW]
[ROW][C]58[/C][C]93.94[/C][C]93.9470262546781[/C][C]-0.00702625467805262[/C][/ROW]
[ROW][C]59[/C][C]94.02[/C][C]94.0785442220514[/C][C]-0.0585442220514523[/C][/ROW]
[ROW][C]60[/C][C]94.26[/C][C]94.2337213746539[/C][C]0.0262786253461371[/C][/ROW]
[ROW][C]61[/C][C]94.71[/C][C]94.5803684608144[/C][C]0.129631539185567[/C][/ROW]
[ROW][C]62[/C][C]95.26[/C][C]95.1470625491425[/C][C]0.112937450857473[/C][/ROW]
[ROW][C]63[/C][C]95.54[/C][C]95.194739713741[/C][C]0.345260286258991[/C][/ROW]
[ROW][C]64[/C][C]95.69[/C][C]95.7210925906148[/C][C]-0.0310925906147759[/C][/ROW]
[ROW][C]65[/C][C]96.03[/C][C]95.8527283291926[/C][C]0.1772716708074[/C][/ROW]
[ROW][C]66[/C][C]96.4[/C][C]95.93139686138[/C][C]0.468603138620054[/C][/ROW]
[ROW][C]67[/C][C]96.55[/C][C]96.8154972003536[/C][C]-0.265497200353593[/C][/ROW]
[ROW][C]68[/C][C]96.45[/C][C]97.0045389904477[/C][C]-0.554538990447696[/C][/ROW]
[ROW][C]69[/C][C]96.65[/C][C]96.8437755444924[/C][C]-0.193775544492382[/C][/ROW]
[ROW][C]70[/C][C]96.84[/C][C]96.8641339174598[/C][C]-0.024133917459821[/C][/ROW]
[ROW][C]71[/C][C]97.21[/C][C]96.992573621121[/C][C]0.217426378879011[/C][/ROW]
[ROW][C]72[/C][C]97.31[/C][C]97.4544360626095[/C][C]-0.144436062609529[/C][/ROW]
[ROW][C]73[/C][C]97.91[/C][C]97.7393751938336[/C][C]0.170624806166444[/C][/ROW]
[ROW][C]74[/C][C]98.51[/C][C]98.3922822693686[/C][C]0.117717730631426[/C][/ROW]
[ROW][C]75[/C][C]98.54[/C][C]98.5385438544824[/C][C]0.00145614551762208[/C][/ROW]
[ROW][C]76[/C][C]98.52[/C][C]98.7003518510839[/C][C]-0.180351851083884[/C][/ROW]
[ROW][C]77[/C][C]98.66[/C][C]98.7242621221541[/C][C]-0.0642621221541333[/C][/ROW]
[ROW][C]78[/C][C]98.53[/C][C]98.593627317882[/C][C]-0.0636273178820375[/C][/ROW]
[ROW][C]79[/C][C]98.71[/C][C]98.7278010108062[/C][C]-0.0178010108062381[/C][/ROW]
[ROW][C]80[/C][C]98.92[/C][C]98.9152783113305[/C][C]0.0047216886695054[/C][/ROW]
[ROW][C]81[/C][C]98.96[/C][C]99.2414614214962[/C][C]-0.281461421496189[/C][/ROW]
[ROW][C]82[/C][C]99.25[/C][C]99.1857305397585[/C][C]0.0642694602414764[/C][/ROW]
[ROW][C]83[/C][C]99.32[/C][C]99.4061725415661[/C][C]-0.0861725415661283[/C][/ROW]
[ROW][C]84[/C][C]99.41[/C][C]99.4669845623066[/C][C]-0.0569845623065675[/C][/ROW]
[ROW][C]85[/C][C]99.36[/C][C]99.8270783299243[/C][C]-0.467078329924263[/C][/ROW]
[ROW][C]86[/C][C]99.58[/C][C]99.7963804574967[/C][C]-0.216380457496726[/C][/ROW]
[ROW][C]87[/C][C]99.77[/C][C]99.415681132414[/C][C]0.354318867586016[/C][/ROW]
[ROW][C]88[/C][C]99.77[/C][C]99.6320727423739[/C][C]0.13792725762606[/C][/ROW]
[ROW][C]89[/C][C]100.03[/C][C]99.8073489093005[/C][C]0.2226510906995[/C][/ROW]
[ROW][C]90[/C][C]100.2[/C][C]99.8248521451912[/C][C]0.375147854808802[/C][/ROW]
[ROW][C]91[/C][C]100.24[/C][C]100.315799187798[/C][C]-0.0757991877983812[/C][/ROW]
[ROW][C]92[/C][C]100.1[/C][C]100.45930940899[/C][C]-0.359309408989617[/C][/ROW]
[ROW][C]93[/C][C]100.03[/C][C]100.371591681777[/C][C]-0.34159168177699[/C][/ROW]
[ROW][C]94[/C][C]100.18[/C][C]100.269040610966[/C][C]-0.0890406109656681[/C][/ROW]
[ROW][C]95[/C][C]100.29[/C][C]100.231200962685[/C][C]0.0587990373150546[/C][/ROW]
[ROW][C]96[/C][C]100.41[/C][C]100.330979347915[/C][C]0.0790206520850205[/C][/ROW]
[ROW][C]97[/C][C]100.6[/C][C]100.649977323329[/C][C]-0.049977323329216[/C][/ROW]
[ROW][C]98[/C][C]100.75[/C][C]101.020004951475[/C][C]-0.270004951474775[/C][/ROW]
[ROW][C]99[/C][C]100.79[/C][C]100.731225459441[/C][C]0.058774540559412[/C][/ROW]
[ROW][C]100[/C][C]100.44[/C][C]100.623481267442[/C][C]-0.183481267442119[/C][/ROW]
[ROW][C]101[/C][C]100.29[/C][C]100.467352608851[/C][C]-0.177352608851237[/C][/ROW]
[ROW][C]102[/C][C]100.34[/C][C]100.037150318664[/C][C]0.302849681335587[/C][/ROW]
[ROW][C]103[/C][C]100.46[/C][C]100.188166495924[/C][C]0.271833504075531[/C][/ROW]
[ROW][C]104[/C][C]100.12[/C][C]100.415891152961[/C][C]-0.295891152960991[/C][/ROW]
[ROW][C]105[/C][C]100.06[/C][C]100.270312839557[/C][C]-0.21031283955665[/C][/ROW]
[ROW][C]106[/C][C]100.28[/C][C]100.238179670217[/C][C]0.0418203297833912[/C][/ROW]
[ROW][C]107[/C][C]100.28[/C][C]100.269809490496[/C][C]0.0101905095044259[/C][/ROW]
[ROW][C]108[/C][C]100.4[/C][C]100.262667277309[/C][C]0.13733272269107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284014&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284014&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
1386.8786.16851421246550.701485787534537
1487.3287.30619126312620.0138087368738411
1587.1387.2759985282948-0.145998528294825
1687.4287.5560276717539-0.136027671753865
1787.2287.2949330729636-0.0749330729636313
1887.1787.187834414369-0.0178344143690055
1987.5287.854710581972-0.33471058197199
2087.4987.673374207371-0.18337420737096
2187.5387.44931940884950.0806805911504824
2287.9387.44021940602890.489780593971062
2388.5488.09941578796980.440584212030203
2488.9688.69754293999980.262457060000202
2589.389.4656405755607-0.16564057556073
2690.0189.82288090139180.187119098608235
2790.5289.9527369010040.567263098995966
2890.6490.9916040923477-0.351604092347657
2991.2590.7221482893820.527851710617981
3091.5991.348940060580.241059939420012
3192.0992.4770756448052-0.387075644805194
3291.8192.5890872438108-0.779087243810821
3392.0392.1520517438329-0.122051743832898
3492.1592.2327755249438-0.0827755249438127
3591.9892.5000604441415-0.520060444141521
3692.1192.2023430831207-0.0923430831207099
3792.2892.4341028052127-0.154102805212688
3892.5392.7194396523294-0.189439652329369
3991.9792.3998651923734-0.429865192373427
4092.0592.04924143587970.000758564120317828
4191.8791.9001279471527-0.0301279471526641
4291.4991.5840010806421-0.0940010806421014
4391.4891.8069754358403-0.326975435840268
4491.6391.38429839181880.245701608181179
4591.4691.5756925444317-0.115692544431667
4691.6191.35796672528030.252033274719722
4791.791.53290948747690.167090512523117
4891.8791.73029508715710.139704912842888
4992.2192.03452707985120.17547292014882
5092.6592.53162983841230.11837016158772
5192.8392.41461116278080.415388837219226
5293.0292.98325540252560.0367445974743958
5393.3393.02565524844110.304344751558858
5493.3593.18020610860980.169793891390242
5593.4593.8378056872632-0.38780568726321
5693.5193.7631020549788-0.253102054978839
5793.893.66433273822480.135667261775239
5893.9493.9470262546781-0.00702625467805262
5994.0294.0785442220514-0.0585442220514523
6094.2694.23372137465390.0262786253461371
6194.7194.58036846081440.129631539185567
6295.2695.14706254914250.112937450857473
6395.5495.1947397137410.345260286258991
6495.6995.7210925906148-0.0310925906147759
6596.0395.85272832919260.1772716708074
6696.495.931396861380.468603138620054
6796.5596.8154972003536-0.265497200353593
6896.4597.0045389904477-0.554538990447696
6996.6596.8437755444924-0.193775544492382
7096.8496.8641339174598-0.024133917459821
7197.2196.9925736211210.217426378879011
7297.3197.4544360626095-0.144436062609529
7397.9197.73937519383360.170624806166444
7498.5198.39228226936860.117717730631426
7598.5498.53854385448240.00145614551762208
7698.5298.7003518510839-0.180351851083884
7798.6698.7242621221541-0.0642621221541333
7898.5398.593627317882-0.0636273178820375
7998.7198.7278010108062-0.0178010108062381
8098.9298.91527831133050.0047216886695054
8198.9699.2414614214962-0.281461421496189
8299.2599.18573053975850.0642694602414764
8399.3299.4061725415661-0.0861725415661283
8499.4199.4669845623066-0.0569845623065675
8599.3699.8270783299243-0.467078329924263
8699.5899.7963804574967-0.216380457496726
8799.7799.4156811324140.354318867586016
8899.7799.63207274237390.13792725762606
89100.0399.80734890930050.2226510906995
90100.299.82485214519120.375147854808802
91100.24100.315799187798-0.0757991877983812
92100.1100.45930940899-0.359309408989617
93100.03100.371591681777-0.34159168177699
94100.18100.269040610966-0.0890406109656681
95100.29100.2312009626850.0587990373150546
96100.41100.3309793479150.0790206520850205
97100.6100.649977323329-0.049977323329216
98100.75101.020004951475-0.270004951474775
99100.79100.7312254594410.058774540559412
100100.44100.623481267442-0.183481267442119
101100.29100.467352608851-0.177352608851237
102100.34100.0371503186640.302849681335587
103100.46100.1881664959240.271833504075531
104100.12100.415891152961-0.295891152960991
105100.06100.270312839557-0.21031283955665
106100.28100.2381796702170.0418203297833912
107100.28100.2698094904960.0101905095044259
108100.4100.2626672773090.13733272269107







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109100.534409707435100.017459394881101.051360019988
110100.838686289926100.124193604718101.553178975133
111100.82528579775199.9034221881265101.747149407375
112100.59957334023699.4602085995388101.738938080932
113100.60128402550399.2303547691256101.972213281881
114100.46064924402198.8481813412825102.07311714676
115100.361408786598.4956142138367102.227203359162
116100.19562340389998.0669771973635102.324269610434
117100.29514410259897.8874336518599102.702854553337
118100.51631903261397.8153048320552103.21733323317
119100.53425028631497.5343985918197103.534101980808
120100.57172686214264.33190019808136.811553526204

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 100.534409707435 & 100.017459394881 & 101.051360019988 \tabularnewline
110 & 100.838686289926 & 100.124193604718 & 101.553178975133 \tabularnewline
111 & 100.825285797751 & 99.9034221881265 & 101.747149407375 \tabularnewline
112 & 100.599573340236 & 99.4602085995388 & 101.738938080932 \tabularnewline
113 & 100.601284025503 & 99.2303547691256 & 101.972213281881 \tabularnewline
114 & 100.460649244021 & 98.8481813412825 & 102.07311714676 \tabularnewline
115 & 100.3614087865 & 98.4956142138367 & 102.227203359162 \tabularnewline
116 & 100.195623403899 & 98.0669771973635 & 102.324269610434 \tabularnewline
117 & 100.295144102598 & 97.8874336518599 & 102.702854553337 \tabularnewline
118 & 100.516319032613 & 97.8153048320552 & 103.21733323317 \tabularnewline
119 & 100.534250286314 & 97.5343985918197 & 103.534101980808 \tabularnewline
120 & 100.571726862142 & 64.33190019808 & 136.811553526204 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284014&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]109[/C][C]100.534409707435[/C][C]100.017459394881[/C][C]101.051360019988[/C][/ROW]
[ROW][C]110[/C][C]100.838686289926[/C][C]100.124193604718[/C][C]101.553178975133[/C][/ROW]
[ROW][C]111[/C][C]100.825285797751[/C][C]99.9034221881265[/C][C]101.747149407375[/C][/ROW]
[ROW][C]112[/C][C]100.599573340236[/C][C]99.4602085995388[/C][C]101.738938080932[/C][/ROW]
[ROW][C]113[/C][C]100.601284025503[/C][C]99.2303547691256[/C][C]101.972213281881[/C][/ROW]
[ROW][C]114[/C][C]100.460649244021[/C][C]98.8481813412825[/C][C]102.07311714676[/C][/ROW]
[ROW][C]115[/C][C]100.3614087865[/C][C]98.4956142138367[/C][C]102.227203359162[/C][/ROW]
[ROW][C]116[/C][C]100.195623403899[/C][C]98.0669771973635[/C][C]102.324269610434[/C][/ROW]
[ROW][C]117[/C][C]100.295144102598[/C][C]97.8874336518599[/C][C]102.702854553337[/C][/ROW]
[ROW][C]118[/C][C]100.516319032613[/C][C]97.8153048320552[/C][C]103.21733323317[/C][/ROW]
[ROW][C]119[/C][C]100.534250286314[/C][C]97.5343985918197[/C][C]103.534101980808[/C][/ROW]
[ROW][C]120[/C][C]100.571726862142[/C][C]64.33190019808[/C][C]136.811553526204[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284014&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284014&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
109100.534409707435100.017459394881101.051360019988
110100.838686289926100.124193604718101.553178975133
111100.82528579775199.9034221881265101.747149407375
112100.59957334023699.4602085995388101.738938080932
113100.60128402550399.2303547691256101.972213281881
114100.46064924402198.8481813412825102.07311714676
115100.361408786598.4956142138367102.227203359162
116100.19562340389998.0669771973635102.324269610434
117100.29514410259897.8874336518599102.702854553337
118100.51631903261397.8153048320552103.21733323317
119100.53425028631497.5343985918197103.534101980808
120100.57172686214264.33190019808136.811553526204



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