Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 14 Dec 2014 21:53:13 +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/2014/Dec/14/t1418594025gd553enzqnnwnpj.htm/, Retrieved Thu, 16 May 2024 23:27:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267906, Retrieved Thu, 16 May 2024 23:27:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [KUL paper CD vrou...] [2014-12-14 20:44:21] [bb1b6762b7e5624d262776d3f7139d34]
- RMPD  [Spectral Analysis] [KUl paper SP vrou...] [2014-12-14 20:50:58] [bb1b6762b7e5624d262776d3f7139d34]
- R       [Spectral Analysis] [KUL paper vrouw s...] [2014-12-14 20:52:17] [bb1b6762b7e5624d262776d3f7139d34]
- R P       [Spectral Analysis] [KUl paper SP vrou...] [2014-12-14 21:20:19] [bb1b6762b7e5624d262776d3f7139d34]
- RMP         [Classical Decomposition] [KUl paper CD test ] [2014-12-14 21:36:33] [bb1b6762b7e5624d262776d3f7139d34]
- RM            [Exponential Smoothing] [Kul paper ES2 vrouw] [2014-12-14 21:52:03] [bb1b6762b7e5624d262776d3f7139d34]
- R                 [Exponential Smoothing] [Kul paper ES2 vrouw2] [2014-12-14 21:53:13] [8568a324fefbb8dbb43f697bfa8d1be6] [Current]
Feedback Forum

Post a new message
Dataseries X:
7.5
NA
6.5
NA
NA
NA
8.5
NA
NA
NA
NA
NA
NA
5
2.5
5
NA
3.5
NA
4
NA
NA
4.5
NA
NA
NA
NA
7
NA
5.5
2.5
5.5
NA
NA
NA
NA
4.5
NA
NA
5
NA
NA
NA
NA
NA
4.5
NA
NA
7.5
NA
NA
NA
NA
NA
NA
NA
0
NA
3.5
NA
NA
6
1.5
NA
3.5
NA
4
NA
NA
6
5
5.5
3.5
NA
6.5
6.5
NA
7
3.5
NA
4
7.5
4.5
NA
3.5
NA
NA
4.5
2.5
7.5
NA
NA
NA
3
NA
3.5
NA
NA
NA
NA
NA
4.5
NA
NA
NA
2.5
7
0
1
3.5
5.5
NA
NA
NA
NA
NA
8.5
NA
NA
10
NA
8.5
9
NA
NA
NA
NA
NA
NA
NA
NA
7.5
NA
NA
NA
NA
NA
NA
9
NA
NA
NA
NA
NA
8
9
NA
7
5.5
NA
2
NA
NA
8.5
NA
NA
NA
9
7.5
6
10.5
NA
8
NA
10.5
NA
9.5
NA
7.5
5
NA
10
NA
NA
NA
NA
NA
10
NA
3
6
7
NA
7
NA
8
10
5.5
6
NA
NA
NA
NA
9.5
8
NA
5.5
7
9
8
NA
NA
6
8
NA
9
NA
NA
9.5
NA
NA
NA
5
7
8
NA
NA
NA
NA
8
8.5
3.5
NA
NA
10.5
8.5
8
NA
NA
9.5
9
10
NA
NA
NA
NA
6.5
NA
NA
NA
6
4
NA
10.5
NA
NA
8.5
NA
7
NA
NA
5
NA
8.5
NA
9.5
NA
1.5
6
NA
NA
7.5
NA
NA
9
NA
8.5
7
NA
NA
9.5
NA
8
9.5
NA
8
9




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=267906&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=267906&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267906&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
alpha0.315371889263587
beta0.113287468655334
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.315371889263587 \tabularnewline
beta & 0.113287468655334 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267906&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]0.315371889263587[/C][/ROW]
[ROW][C]beta[/C][C]0.113287468655334[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267906&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267906&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
alpha0.315371889263587
beta0.113287468655334
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
38.55.53
455.55329871684993-0.553298716849929
52.54.46621882307818-1.96621882307818
652.863295203168372.13670479683163
73.52.630657868461640.869342131538362
842.029389555730521.97061044426948
94.51.845835656679752.65416434332024
1071.972682584526515.02731741547348
115.53.027569683309492.47243031669051
122.53.36505141753719-0.865051417537189
135.52.619078949017252.88092105098275
144.53.157409529138191.34259047086181
1553.258561534662691.74143846533731
164.53.547716547221840.952283452778163
177.53.622017133894173.87798286610583
1804.75755241456115-4.75755241456115
193.52.999706294344680.500293705655324
2062.917911373450513.08208862654949
211.53.76045787993792-2.26045787993792
223.52.837354478581960.66264552141804
2342.859790508568111.14020949143189
2463.073573833307712.92642616669229
2553.95523411202251.0447658879775
265.54.280798698162241.21920130183776
273.54.70493454797486-1.20493454797486
286.54.321516575410922.17848342458908
296.55.082965686280291.41703431371971
3075.654902505265351.34509749473465
313.56.25220969066199-2.75220969066199
3245.45901129267503-1.45901129267503
337.55.021524223666982.47847577633302
344.55.91436008747183-1.41436008747183
353.55.52897314143455-2.02897314143455
364.54.87726400615028-0.377264006150285
372.54.73297873254806-2.23297873254806
387.53.923674043401243.57632595659876
3935.07423458953104-2.07423458953104
403.54.36865958490629-0.868659584906291
414.54.012253852837430.487746147162571
422.54.101046398839-1.601046398839
4373.473890815090773.52610918490923
4404.58967568558893-4.58967568558893
4512.98199167056321-1.98199167056321
463.52.125885919804991.37411408019501
475.52.377295492521933.12270450747807
488.53.291728328646785.20827167135322
49105.049969900783754.95003009921625
508.56.903622446752361.59637755324764
5197.756662124567451.24333787543255
527.58.54278459370485-1.04278459370485
5398.570672023240720.429327976759284
5489.07816126919769-1.07816126919769
5599.07171057954263-0.0717105795426303
5679.38010409247967-2.38010409247967
575.58.87545957750789-3.37545957750789
5827.9363105729028-5.9363105729028
598.55.977450529302182.52254947069782
6096.776402006558822.22359799344118
617.57.56051659590785-0.0605165959078464
6267.62212353416332-1.62212353416332
6310.57.133288826566623.36671117343338
6488.33807713555183-0.338077135551835
6510.58.362400643475522.13759935652448
669.59.243854396143830.25614560385617
677.59.54110201321254-2.04110201321254
6859.04093846344104-4.04093846344104
69107.765709345618772.23429065438123
70108.549337118519641.45066288148036
7139.13765954379936-6.13765954379936
7267.11355403481352-1.11355403481352
7376.6341254664750.365874533524998
7476.634338930122690.36566106987731
7586.647549296133751.35245070386625
76107.020285303369162.97971469663084
775.58.01267293250378-2.51267293250378
7867.18314391640553-1.18314391640553
799.56.730639987132892.76936001286711
8087.623587506063930.376412493936071
815.57.77531499130908-2.27531499130908
8277.00947043694078-0.0094704369407772
8396.957871203692142.04212879630786
8487.626249226964780.373750773035217
8567.78182097017946-1.78182097017946
8687.193925645472860.80607435452714
8797.450978927564261.54902107243574
889.57.997679653571521.50232034642848
8958.58332670851917-3.58332670851917
9077.43707968282211-0.437079682822108
9187.267454681346840.732545318653161
9287.492868673259170.507131326740828
938.57.665312055966830.834687944033165
943.57.97087905419557-4.47087905419557
9510.56.443485214910564.05651478508944
968.57.750321555622020.749678444377976
9788.04105894590528-0.0410589459052844
989.58.080953050499131.41904694950087
9998.632022769453980.367977230546019
100108.864761619245721.13523838075428
1016.59.3800325045566-2.8800325045566
10268.52610293645262-2.52610293645262
10347.69354099991907-3.69354099991907
10410.56.360840253646424.13915974635358
1058.57.64623572714780.853764272852197
10677.92601284250704-0.926012842507044
10757.61141399321806-2.61141399321806
1088.56.671987227479361.82801277252064
1099.57.197941528991632.30205847100837
1101.57.9556437333783-6.4556437333783
11165.720767654965270.279232345034726
1127.55.619858494069761.88014150593024
11396.091004179541342.90899582045866
1148.56.990553274541791.50944672545821
11577.50265296147713-0.502652961477128
1169.57.362234343080422.13776565691958
11788.1309069465751-0.130906946575104
1189.58.179426983092811.32057301690719
11988.73288401207463-0.732884012074635
12098.612554170631240.387445829368758

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8.5 & 5.5 & 3 \tabularnewline
4 & 5 & 5.55329871684993 & -0.553298716849929 \tabularnewline
5 & 2.5 & 4.46621882307818 & -1.96621882307818 \tabularnewline
6 & 5 & 2.86329520316837 & 2.13670479683163 \tabularnewline
7 & 3.5 & 2.63065786846164 & 0.869342131538362 \tabularnewline
8 & 4 & 2.02938955573052 & 1.97061044426948 \tabularnewline
9 & 4.5 & 1.84583565667975 & 2.65416434332024 \tabularnewline
10 & 7 & 1.97268258452651 & 5.02731741547348 \tabularnewline
11 & 5.5 & 3.02756968330949 & 2.47243031669051 \tabularnewline
12 & 2.5 & 3.36505141753719 & -0.865051417537189 \tabularnewline
13 & 5.5 & 2.61907894901725 & 2.88092105098275 \tabularnewline
14 & 4.5 & 3.15740952913819 & 1.34259047086181 \tabularnewline
15 & 5 & 3.25856153466269 & 1.74143846533731 \tabularnewline
16 & 4.5 & 3.54771654722184 & 0.952283452778163 \tabularnewline
17 & 7.5 & 3.62201713389417 & 3.87798286610583 \tabularnewline
18 & 0 & 4.75755241456115 & -4.75755241456115 \tabularnewline
19 & 3.5 & 2.99970629434468 & 0.500293705655324 \tabularnewline
20 & 6 & 2.91791137345051 & 3.08208862654949 \tabularnewline
21 & 1.5 & 3.76045787993792 & -2.26045787993792 \tabularnewline
22 & 3.5 & 2.83735447858196 & 0.66264552141804 \tabularnewline
23 & 4 & 2.85979050856811 & 1.14020949143189 \tabularnewline
24 & 6 & 3.07357383330771 & 2.92642616669229 \tabularnewline
25 & 5 & 3.9552341120225 & 1.0447658879775 \tabularnewline
26 & 5.5 & 4.28079869816224 & 1.21920130183776 \tabularnewline
27 & 3.5 & 4.70493454797486 & -1.20493454797486 \tabularnewline
28 & 6.5 & 4.32151657541092 & 2.17848342458908 \tabularnewline
29 & 6.5 & 5.08296568628029 & 1.41703431371971 \tabularnewline
30 & 7 & 5.65490250526535 & 1.34509749473465 \tabularnewline
31 & 3.5 & 6.25220969066199 & -2.75220969066199 \tabularnewline
32 & 4 & 5.45901129267503 & -1.45901129267503 \tabularnewline
33 & 7.5 & 5.02152422366698 & 2.47847577633302 \tabularnewline
34 & 4.5 & 5.91436008747183 & -1.41436008747183 \tabularnewline
35 & 3.5 & 5.52897314143455 & -2.02897314143455 \tabularnewline
36 & 4.5 & 4.87726400615028 & -0.377264006150285 \tabularnewline
37 & 2.5 & 4.73297873254806 & -2.23297873254806 \tabularnewline
38 & 7.5 & 3.92367404340124 & 3.57632595659876 \tabularnewline
39 & 3 & 5.07423458953104 & -2.07423458953104 \tabularnewline
40 & 3.5 & 4.36865958490629 & -0.868659584906291 \tabularnewline
41 & 4.5 & 4.01225385283743 & 0.487746147162571 \tabularnewline
42 & 2.5 & 4.101046398839 & -1.601046398839 \tabularnewline
43 & 7 & 3.47389081509077 & 3.52610918490923 \tabularnewline
44 & 0 & 4.58967568558893 & -4.58967568558893 \tabularnewline
45 & 1 & 2.98199167056321 & -1.98199167056321 \tabularnewline
46 & 3.5 & 2.12588591980499 & 1.37411408019501 \tabularnewline
47 & 5.5 & 2.37729549252193 & 3.12270450747807 \tabularnewline
48 & 8.5 & 3.29172832864678 & 5.20827167135322 \tabularnewline
49 & 10 & 5.04996990078375 & 4.95003009921625 \tabularnewline
50 & 8.5 & 6.90362244675236 & 1.59637755324764 \tabularnewline
51 & 9 & 7.75666212456745 & 1.24333787543255 \tabularnewline
52 & 7.5 & 8.54278459370485 & -1.04278459370485 \tabularnewline
53 & 9 & 8.57067202324072 & 0.429327976759284 \tabularnewline
54 & 8 & 9.07816126919769 & -1.07816126919769 \tabularnewline
55 & 9 & 9.07171057954263 & -0.0717105795426303 \tabularnewline
56 & 7 & 9.38010409247967 & -2.38010409247967 \tabularnewline
57 & 5.5 & 8.87545957750789 & -3.37545957750789 \tabularnewline
58 & 2 & 7.9363105729028 & -5.9363105729028 \tabularnewline
59 & 8.5 & 5.97745052930218 & 2.52254947069782 \tabularnewline
60 & 9 & 6.77640200655882 & 2.22359799344118 \tabularnewline
61 & 7.5 & 7.56051659590785 & -0.0605165959078464 \tabularnewline
62 & 6 & 7.62212353416332 & -1.62212353416332 \tabularnewline
63 & 10.5 & 7.13328882656662 & 3.36671117343338 \tabularnewline
64 & 8 & 8.33807713555183 & -0.338077135551835 \tabularnewline
65 & 10.5 & 8.36240064347552 & 2.13759935652448 \tabularnewline
66 & 9.5 & 9.24385439614383 & 0.25614560385617 \tabularnewline
67 & 7.5 & 9.54110201321254 & -2.04110201321254 \tabularnewline
68 & 5 & 9.04093846344104 & -4.04093846344104 \tabularnewline
69 & 10 & 7.76570934561877 & 2.23429065438123 \tabularnewline
70 & 10 & 8.54933711851964 & 1.45066288148036 \tabularnewline
71 & 3 & 9.13765954379936 & -6.13765954379936 \tabularnewline
72 & 6 & 7.11355403481352 & -1.11355403481352 \tabularnewline
73 & 7 & 6.634125466475 & 0.365874533524998 \tabularnewline
74 & 7 & 6.63433893012269 & 0.36566106987731 \tabularnewline
75 & 8 & 6.64754929613375 & 1.35245070386625 \tabularnewline
76 & 10 & 7.02028530336916 & 2.97971469663084 \tabularnewline
77 & 5.5 & 8.01267293250378 & -2.51267293250378 \tabularnewline
78 & 6 & 7.18314391640553 & -1.18314391640553 \tabularnewline
79 & 9.5 & 6.73063998713289 & 2.76936001286711 \tabularnewline
80 & 8 & 7.62358750606393 & 0.376412493936071 \tabularnewline
81 & 5.5 & 7.77531499130908 & -2.27531499130908 \tabularnewline
82 & 7 & 7.00947043694078 & -0.0094704369407772 \tabularnewline
83 & 9 & 6.95787120369214 & 2.04212879630786 \tabularnewline
84 & 8 & 7.62624922696478 & 0.373750773035217 \tabularnewline
85 & 6 & 7.78182097017946 & -1.78182097017946 \tabularnewline
86 & 8 & 7.19392564547286 & 0.80607435452714 \tabularnewline
87 & 9 & 7.45097892756426 & 1.54902107243574 \tabularnewline
88 & 9.5 & 7.99767965357152 & 1.50232034642848 \tabularnewline
89 & 5 & 8.58332670851917 & -3.58332670851917 \tabularnewline
90 & 7 & 7.43707968282211 & -0.437079682822108 \tabularnewline
91 & 8 & 7.26745468134684 & 0.732545318653161 \tabularnewline
92 & 8 & 7.49286867325917 & 0.507131326740828 \tabularnewline
93 & 8.5 & 7.66531205596683 & 0.834687944033165 \tabularnewline
94 & 3.5 & 7.97087905419557 & -4.47087905419557 \tabularnewline
95 & 10.5 & 6.44348521491056 & 4.05651478508944 \tabularnewline
96 & 8.5 & 7.75032155562202 & 0.749678444377976 \tabularnewline
97 & 8 & 8.04105894590528 & -0.0410589459052844 \tabularnewline
98 & 9.5 & 8.08095305049913 & 1.41904694950087 \tabularnewline
99 & 9 & 8.63202276945398 & 0.367977230546019 \tabularnewline
100 & 10 & 8.86476161924572 & 1.13523838075428 \tabularnewline
101 & 6.5 & 9.3800325045566 & -2.8800325045566 \tabularnewline
102 & 6 & 8.52610293645262 & -2.52610293645262 \tabularnewline
103 & 4 & 7.69354099991907 & -3.69354099991907 \tabularnewline
104 & 10.5 & 6.36084025364642 & 4.13915974635358 \tabularnewline
105 & 8.5 & 7.6462357271478 & 0.853764272852197 \tabularnewline
106 & 7 & 7.92601284250704 & -0.926012842507044 \tabularnewline
107 & 5 & 7.61141399321806 & -2.61141399321806 \tabularnewline
108 & 8.5 & 6.67198722747936 & 1.82801277252064 \tabularnewline
109 & 9.5 & 7.19794152899163 & 2.30205847100837 \tabularnewline
110 & 1.5 & 7.9556437333783 & -6.4556437333783 \tabularnewline
111 & 6 & 5.72076765496527 & 0.279232345034726 \tabularnewline
112 & 7.5 & 5.61985849406976 & 1.88014150593024 \tabularnewline
113 & 9 & 6.09100417954134 & 2.90899582045866 \tabularnewline
114 & 8.5 & 6.99055327454179 & 1.50944672545821 \tabularnewline
115 & 7 & 7.50265296147713 & -0.502652961477128 \tabularnewline
116 & 9.5 & 7.36223434308042 & 2.13776565691958 \tabularnewline
117 & 8 & 8.1309069465751 & -0.130906946575104 \tabularnewline
118 & 9.5 & 8.17942698309281 & 1.32057301690719 \tabularnewline
119 & 8 & 8.73288401207463 & -0.732884012074635 \tabularnewline
120 & 9 & 8.61255417063124 & 0.387445829368758 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267906&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]8.5[/C][C]5.5[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]5[/C][C]5.55329871684993[/C][C]-0.553298716849929[/C][/ROW]
[ROW][C]5[/C][C]2.5[/C][C]4.46621882307818[/C][C]-1.96621882307818[/C][/ROW]
[ROW][C]6[/C][C]5[/C][C]2.86329520316837[/C][C]2.13670479683163[/C][/ROW]
[ROW][C]7[/C][C]3.5[/C][C]2.63065786846164[/C][C]0.869342131538362[/C][/ROW]
[ROW][C]8[/C][C]4[/C][C]2.02938955573052[/C][C]1.97061044426948[/C][/ROW]
[ROW][C]9[/C][C]4.5[/C][C]1.84583565667975[/C][C]2.65416434332024[/C][/ROW]
[ROW][C]10[/C][C]7[/C][C]1.97268258452651[/C][C]5.02731741547348[/C][/ROW]
[ROW][C]11[/C][C]5.5[/C][C]3.02756968330949[/C][C]2.47243031669051[/C][/ROW]
[ROW][C]12[/C][C]2.5[/C][C]3.36505141753719[/C][C]-0.865051417537189[/C][/ROW]
[ROW][C]13[/C][C]5.5[/C][C]2.61907894901725[/C][C]2.88092105098275[/C][/ROW]
[ROW][C]14[/C][C]4.5[/C][C]3.15740952913819[/C][C]1.34259047086181[/C][/ROW]
[ROW][C]15[/C][C]5[/C][C]3.25856153466269[/C][C]1.74143846533731[/C][/ROW]
[ROW][C]16[/C][C]4.5[/C][C]3.54771654722184[/C][C]0.952283452778163[/C][/ROW]
[ROW][C]17[/C][C]7.5[/C][C]3.62201713389417[/C][C]3.87798286610583[/C][/ROW]
[ROW][C]18[/C][C]0[/C][C]4.75755241456115[/C][C]-4.75755241456115[/C][/ROW]
[ROW][C]19[/C][C]3.5[/C][C]2.99970629434468[/C][C]0.500293705655324[/C][/ROW]
[ROW][C]20[/C][C]6[/C][C]2.91791137345051[/C][C]3.08208862654949[/C][/ROW]
[ROW][C]21[/C][C]1.5[/C][C]3.76045787993792[/C][C]-2.26045787993792[/C][/ROW]
[ROW][C]22[/C][C]3.5[/C][C]2.83735447858196[/C][C]0.66264552141804[/C][/ROW]
[ROW][C]23[/C][C]4[/C][C]2.85979050856811[/C][C]1.14020949143189[/C][/ROW]
[ROW][C]24[/C][C]6[/C][C]3.07357383330771[/C][C]2.92642616669229[/C][/ROW]
[ROW][C]25[/C][C]5[/C][C]3.9552341120225[/C][C]1.0447658879775[/C][/ROW]
[ROW][C]26[/C][C]5.5[/C][C]4.28079869816224[/C][C]1.21920130183776[/C][/ROW]
[ROW][C]27[/C][C]3.5[/C][C]4.70493454797486[/C][C]-1.20493454797486[/C][/ROW]
[ROW][C]28[/C][C]6.5[/C][C]4.32151657541092[/C][C]2.17848342458908[/C][/ROW]
[ROW][C]29[/C][C]6.5[/C][C]5.08296568628029[/C][C]1.41703431371971[/C][/ROW]
[ROW][C]30[/C][C]7[/C][C]5.65490250526535[/C][C]1.34509749473465[/C][/ROW]
[ROW][C]31[/C][C]3.5[/C][C]6.25220969066199[/C][C]-2.75220969066199[/C][/ROW]
[ROW][C]32[/C][C]4[/C][C]5.45901129267503[/C][C]-1.45901129267503[/C][/ROW]
[ROW][C]33[/C][C]7.5[/C][C]5.02152422366698[/C][C]2.47847577633302[/C][/ROW]
[ROW][C]34[/C][C]4.5[/C][C]5.91436008747183[/C][C]-1.41436008747183[/C][/ROW]
[ROW][C]35[/C][C]3.5[/C][C]5.52897314143455[/C][C]-2.02897314143455[/C][/ROW]
[ROW][C]36[/C][C]4.5[/C][C]4.87726400615028[/C][C]-0.377264006150285[/C][/ROW]
[ROW][C]37[/C][C]2.5[/C][C]4.73297873254806[/C][C]-2.23297873254806[/C][/ROW]
[ROW][C]38[/C][C]7.5[/C][C]3.92367404340124[/C][C]3.57632595659876[/C][/ROW]
[ROW][C]39[/C][C]3[/C][C]5.07423458953104[/C][C]-2.07423458953104[/C][/ROW]
[ROW][C]40[/C][C]3.5[/C][C]4.36865958490629[/C][C]-0.868659584906291[/C][/ROW]
[ROW][C]41[/C][C]4.5[/C][C]4.01225385283743[/C][C]0.487746147162571[/C][/ROW]
[ROW][C]42[/C][C]2.5[/C][C]4.101046398839[/C][C]-1.601046398839[/C][/ROW]
[ROW][C]43[/C][C]7[/C][C]3.47389081509077[/C][C]3.52610918490923[/C][/ROW]
[ROW][C]44[/C][C]0[/C][C]4.58967568558893[/C][C]-4.58967568558893[/C][/ROW]
[ROW][C]45[/C][C]1[/C][C]2.98199167056321[/C][C]-1.98199167056321[/C][/ROW]
[ROW][C]46[/C][C]3.5[/C][C]2.12588591980499[/C][C]1.37411408019501[/C][/ROW]
[ROW][C]47[/C][C]5.5[/C][C]2.37729549252193[/C][C]3.12270450747807[/C][/ROW]
[ROW][C]48[/C][C]8.5[/C][C]3.29172832864678[/C][C]5.20827167135322[/C][/ROW]
[ROW][C]49[/C][C]10[/C][C]5.04996990078375[/C][C]4.95003009921625[/C][/ROW]
[ROW][C]50[/C][C]8.5[/C][C]6.90362244675236[/C][C]1.59637755324764[/C][/ROW]
[ROW][C]51[/C][C]9[/C][C]7.75666212456745[/C][C]1.24333787543255[/C][/ROW]
[ROW][C]52[/C][C]7.5[/C][C]8.54278459370485[/C][C]-1.04278459370485[/C][/ROW]
[ROW][C]53[/C][C]9[/C][C]8.57067202324072[/C][C]0.429327976759284[/C][/ROW]
[ROW][C]54[/C][C]8[/C][C]9.07816126919769[/C][C]-1.07816126919769[/C][/ROW]
[ROW][C]55[/C][C]9[/C][C]9.07171057954263[/C][C]-0.0717105795426303[/C][/ROW]
[ROW][C]56[/C][C]7[/C][C]9.38010409247967[/C][C]-2.38010409247967[/C][/ROW]
[ROW][C]57[/C][C]5.5[/C][C]8.87545957750789[/C][C]-3.37545957750789[/C][/ROW]
[ROW][C]58[/C][C]2[/C][C]7.9363105729028[/C][C]-5.9363105729028[/C][/ROW]
[ROW][C]59[/C][C]8.5[/C][C]5.97745052930218[/C][C]2.52254947069782[/C][/ROW]
[ROW][C]60[/C][C]9[/C][C]6.77640200655882[/C][C]2.22359799344118[/C][/ROW]
[ROW][C]61[/C][C]7.5[/C][C]7.56051659590785[/C][C]-0.0605165959078464[/C][/ROW]
[ROW][C]62[/C][C]6[/C][C]7.62212353416332[/C][C]-1.62212353416332[/C][/ROW]
[ROW][C]63[/C][C]10.5[/C][C]7.13328882656662[/C][C]3.36671117343338[/C][/ROW]
[ROW][C]64[/C][C]8[/C][C]8.33807713555183[/C][C]-0.338077135551835[/C][/ROW]
[ROW][C]65[/C][C]10.5[/C][C]8.36240064347552[/C][C]2.13759935652448[/C][/ROW]
[ROW][C]66[/C][C]9.5[/C][C]9.24385439614383[/C][C]0.25614560385617[/C][/ROW]
[ROW][C]67[/C][C]7.5[/C][C]9.54110201321254[/C][C]-2.04110201321254[/C][/ROW]
[ROW][C]68[/C][C]5[/C][C]9.04093846344104[/C][C]-4.04093846344104[/C][/ROW]
[ROW][C]69[/C][C]10[/C][C]7.76570934561877[/C][C]2.23429065438123[/C][/ROW]
[ROW][C]70[/C][C]10[/C][C]8.54933711851964[/C][C]1.45066288148036[/C][/ROW]
[ROW][C]71[/C][C]3[/C][C]9.13765954379936[/C][C]-6.13765954379936[/C][/ROW]
[ROW][C]72[/C][C]6[/C][C]7.11355403481352[/C][C]-1.11355403481352[/C][/ROW]
[ROW][C]73[/C][C]7[/C][C]6.634125466475[/C][C]0.365874533524998[/C][/ROW]
[ROW][C]74[/C][C]7[/C][C]6.63433893012269[/C][C]0.36566106987731[/C][/ROW]
[ROW][C]75[/C][C]8[/C][C]6.64754929613375[/C][C]1.35245070386625[/C][/ROW]
[ROW][C]76[/C][C]10[/C][C]7.02028530336916[/C][C]2.97971469663084[/C][/ROW]
[ROW][C]77[/C][C]5.5[/C][C]8.01267293250378[/C][C]-2.51267293250378[/C][/ROW]
[ROW][C]78[/C][C]6[/C][C]7.18314391640553[/C][C]-1.18314391640553[/C][/ROW]
[ROW][C]79[/C][C]9.5[/C][C]6.73063998713289[/C][C]2.76936001286711[/C][/ROW]
[ROW][C]80[/C][C]8[/C][C]7.62358750606393[/C][C]0.376412493936071[/C][/ROW]
[ROW][C]81[/C][C]5.5[/C][C]7.77531499130908[/C][C]-2.27531499130908[/C][/ROW]
[ROW][C]82[/C][C]7[/C][C]7.00947043694078[/C][C]-0.0094704369407772[/C][/ROW]
[ROW][C]83[/C][C]9[/C][C]6.95787120369214[/C][C]2.04212879630786[/C][/ROW]
[ROW][C]84[/C][C]8[/C][C]7.62624922696478[/C][C]0.373750773035217[/C][/ROW]
[ROW][C]85[/C][C]6[/C][C]7.78182097017946[/C][C]-1.78182097017946[/C][/ROW]
[ROW][C]86[/C][C]8[/C][C]7.19392564547286[/C][C]0.80607435452714[/C][/ROW]
[ROW][C]87[/C][C]9[/C][C]7.45097892756426[/C][C]1.54902107243574[/C][/ROW]
[ROW][C]88[/C][C]9.5[/C][C]7.99767965357152[/C][C]1.50232034642848[/C][/ROW]
[ROW][C]89[/C][C]5[/C][C]8.58332670851917[/C][C]-3.58332670851917[/C][/ROW]
[ROW][C]90[/C][C]7[/C][C]7.43707968282211[/C][C]-0.437079682822108[/C][/ROW]
[ROW][C]91[/C][C]8[/C][C]7.26745468134684[/C][C]0.732545318653161[/C][/ROW]
[ROW][C]92[/C][C]8[/C][C]7.49286867325917[/C][C]0.507131326740828[/C][/ROW]
[ROW][C]93[/C][C]8.5[/C][C]7.66531205596683[/C][C]0.834687944033165[/C][/ROW]
[ROW][C]94[/C][C]3.5[/C][C]7.97087905419557[/C][C]-4.47087905419557[/C][/ROW]
[ROW][C]95[/C][C]10.5[/C][C]6.44348521491056[/C][C]4.05651478508944[/C][/ROW]
[ROW][C]96[/C][C]8.5[/C][C]7.75032155562202[/C][C]0.749678444377976[/C][/ROW]
[ROW][C]97[/C][C]8[/C][C]8.04105894590528[/C][C]-0.0410589459052844[/C][/ROW]
[ROW][C]98[/C][C]9.5[/C][C]8.08095305049913[/C][C]1.41904694950087[/C][/ROW]
[ROW][C]99[/C][C]9[/C][C]8.63202276945398[/C][C]0.367977230546019[/C][/ROW]
[ROW][C]100[/C][C]10[/C][C]8.86476161924572[/C][C]1.13523838075428[/C][/ROW]
[ROW][C]101[/C][C]6.5[/C][C]9.3800325045566[/C][C]-2.8800325045566[/C][/ROW]
[ROW][C]102[/C][C]6[/C][C]8.52610293645262[/C][C]-2.52610293645262[/C][/ROW]
[ROW][C]103[/C][C]4[/C][C]7.69354099991907[/C][C]-3.69354099991907[/C][/ROW]
[ROW][C]104[/C][C]10.5[/C][C]6.36084025364642[/C][C]4.13915974635358[/C][/ROW]
[ROW][C]105[/C][C]8.5[/C][C]7.6462357271478[/C][C]0.853764272852197[/C][/ROW]
[ROW][C]106[/C][C]7[/C][C]7.92601284250704[/C][C]-0.926012842507044[/C][/ROW]
[ROW][C]107[/C][C]5[/C][C]7.61141399321806[/C][C]-2.61141399321806[/C][/ROW]
[ROW][C]108[/C][C]8.5[/C][C]6.67198722747936[/C][C]1.82801277252064[/C][/ROW]
[ROW][C]109[/C][C]9.5[/C][C]7.19794152899163[/C][C]2.30205847100837[/C][/ROW]
[ROW][C]110[/C][C]1.5[/C][C]7.9556437333783[/C][C]-6.4556437333783[/C][/ROW]
[ROW][C]111[/C][C]6[/C][C]5.72076765496527[/C][C]0.279232345034726[/C][/ROW]
[ROW][C]112[/C][C]7.5[/C][C]5.61985849406976[/C][C]1.88014150593024[/C][/ROW]
[ROW][C]113[/C][C]9[/C][C]6.09100417954134[/C][C]2.90899582045866[/C][/ROW]
[ROW][C]114[/C][C]8.5[/C][C]6.99055327454179[/C][C]1.50944672545821[/C][/ROW]
[ROW][C]115[/C][C]7[/C][C]7.50265296147713[/C][C]-0.502652961477128[/C][/ROW]
[ROW][C]116[/C][C]9.5[/C][C]7.36223434308042[/C][C]2.13776565691958[/C][/ROW]
[ROW][C]117[/C][C]8[/C][C]8.1309069465751[/C][C]-0.130906946575104[/C][/ROW]
[ROW][C]118[/C][C]9.5[/C][C]8.17942698309281[/C][C]1.32057301690719[/C][/ROW]
[ROW][C]119[/C][C]8[/C][C]8.73288401207463[/C][C]-0.732884012074635[/C][/ROW]
[ROW][C]120[/C][C]9[/C][C]8.61255417063124[/C][C]0.387445829368758[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267906&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267906&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
38.55.53
455.55329871684993-0.553298716849929
52.54.46621882307818-1.96621882307818
652.863295203168372.13670479683163
73.52.630657868461640.869342131538362
842.029389555730521.97061044426948
94.51.845835656679752.65416434332024
1071.972682584526515.02731741547348
115.53.027569683309492.47243031669051
122.53.36505141753719-0.865051417537189
135.52.619078949017252.88092105098275
144.53.157409529138191.34259047086181
1553.258561534662691.74143846533731
164.53.547716547221840.952283452778163
177.53.622017133894173.87798286610583
1804.75755241456115-4.75755241456115
193.52.999706294344680.500293705655324
2062.917911373450513.08208862654949
211.53.76045787993792-2.26045787993792
223.52.837354478581960.66264552141804
2342.859790508568111.14020949143189
2463.073573833307712.92642616669229
2553.95523411202251.0447658879775
265.54.280798698162241.21920130183776
273.54.70493454797486-1.20493454797486
286.54.321516575410922.17848342458908
296.55.082965686280291.41703431371971
3075.654902505265351.34509749473465
313.56.25220969066199-2.75220969066199
3245.45901129267503-1.45901129267503
337.55.021524223666982.47847577633302
344.55.91436008747183-1.41436008747183
353.55.52897314143455-2.02897314143455
364.54.87726400615028-0.377264006150285
372.54.73297873254806-2.23297873254806
387.53.923674043401243.57632595659876
3935.07423458953104-2.07423458953104
403.54.36865958490629-0.868659584906291
414.54.012253852837430.487746147162571
422.54.101046398839-1.601046398839
4373.473890815090773.52610918490923
4404.58967568558893-4.58967568558893
4512.98199167056321-1.98199167056321
463.52.125885919804991.37411408019501
475.52.377295492521933.12270450747807
488.53.291728328646785.20827167135322
49105.049969900783754.95003009921625
508.56.903622446752361.59637755324764
5197.756662124567451.24333787543255
527.58.54278459370485-1.04278459370485
5398.570672023240720.429327976759284
5489.07816126919769-1.07816126919769
5599.07171057954263-0.0717105795426303
5679.38010409247967-2.38010409247967
575.58.87545957750789-3.37545957750789
5827.9363105729028-5.9363105729028
598.55.977450529302182.52254947069782
6096.776402006558822.22359799344118
617.57.56051659590785-0.0605165959078464
6267.62212353416332-1.62212353416332
6310.57.133288826566623.36671117343338
6488.33807713555183-0.338077135551835
6510.58.362400643475522.13759935652448
669.59.243854396143830.25614560385617
677.59.54110201321254-2.04110201321254
6859.04093846344104-4.04093846344104
69107.765709345618772.23429065438123
70108.549337118519641.45066288148036
7139.13765954379936-6.13765954379936
7267.11355403481352-1.11355403481352
7376.6341254664750.365874533524998
7476.634338930122690.36566106987731
7586.647549296133751.35245070386625
76107.020285303369162.97971469663084
775.58.01267293250378-2.51267293250378
7867.18314391640553-1.18314391640553
799.56.730639987132892.76936001286711
8087.623587506063930.376412493936071
815.57.77531499130908-2.27531499130908
8277.00947043694078-0.0094704369407772
8396.957871203692142.04212879630786
8487.626249226964780.373750773035217
8567.78182097017946-1.78182097017946
8687.193925645472860.80607435452714
8797.450978927564261.54902107243574
889.57.997679653571521.50232034642848
8958.58332670851917-3.58332670851917
9077.43707968282211-0.437079682822108
9187.267454681346840.732545318653161
9287.492868673259170.507131326740828
938.57.665312055966830.834687944033165
943.57.97087905419557-4.47087905419557
9510.56.443485214910564.05651478508944
968.57.750321555622020.749678444377976
9788.04105894590528-0.0410589459052844
989.58.080953050499131.41904694950087
9998.632022769453980.367977230546019
100108.864761619245721.13523838075428
1016.59.3800325045566-2.8800325045566
10268.52610293645262-2.52610293645262
10347.69354099991907-3.69354099991907
10410.56.360840253646424.13915974635358
1058.57.64623572714780.853764272852197
10677.92601284250704-0.926012842507044
10757.61141399321806-2.61141399321806
1088.56.671987227479361.82801277252064
1099.57.197941528991632.30205847100837
1101.57.9556437333783-6.4556437333783
11165.720767654965270.279232345034726
1127.55.619858494069761.88014150593024
11396.091004179541342.90899582045866
1148.56.990553274541791.50944672545821
11577.50265296147713-0.502652961477128
1169.57.362234343080422.13776565691958
11788.1309069465751-0.130906946575104
1189.58.179426983092811.32057301690719
11988.73288401207463-0.732884012074635
12098.612554170631240.387445829368758







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1218.859387409661224.163371510235513.555403309087

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 8.85938740966122 & 4.1633715102355 & 13.555403309087 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267906&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]121[/C][C]8.85938740966122[/C][C]4.1633715102355[/C][C]13.555403309087[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267906&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267906&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
1218.859387409661224.163371510235513.555403309087



Parameters (Session):
par1 = additive ; par2 = 12 ;
Parameters (R input):
par1 = 1 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
x<-na.omit(x)
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')