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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 17 Dec 2013 13:34:52 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/17/t1387305334q0r88cehu4geaqs.htm/, Retrieved Thu, 28 Mar 2024 11:18:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232417, Retrieved Thu, 28 Mar 2024 11:18:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-17 18:34:52] [c5b0870324cee902d4892ab6fd83304c] [Current]
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Dataseries X:
86,86
86,79
82,52
86,87
81,62
82,66
89,87
92,04
79,74
77,75
79,12
76,37
75,01
77,6
77,81
81,7
76,47
74,72
84,43
86,72
70,99
75,43
74,14
73,3
71,97
69,27
74,13
76,4
72,26
72,1
87,82
91,62
82,69
85,76
86,87
93,09
83,73
84,49
87,37
89,13
83,2
83,77
93,68
93,09
88,59
87,88
87,89
89,38
89,13
89,58
90,22
91,44
91,04
92,1
97,54
99,12
100
99,68
100,08
99,9
99,63
99,45
99,63
99,46
96,91
97,65
102,1
103,57
104,59
104,79
101,31
104,8
104,56
104,15
102,73
101,86
101,9
102,33
105,71
106,1
102,81
103,23
102,35
104,11




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232417&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]5 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=232417&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232417&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 time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.656149236821017
beta0.0249533508009569
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.656149236821017 \tabularnewline
beta & 0.0249533508009569 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232417&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]0.656149236821017[/C][/ROW]
[ROW][C]beta[/C][C]0.0249533508009569[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232417&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232417&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
alpha0.656149236821017
beta0.0249533508009569
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1375.0178.2042601495726-3.19426014957263
1477.678.5980898627413-0.998089862741281
1577.8178.1745098530363-0.364509853036324
1681.781.7156847188397-0.015684718839708
1776.4776.20840078908040.26159921091957
1874.7274.39858969403290.321410305967063
1984.4383.6620360935330.767963906467017
2086.7286.66356226399760.056437736002394
2170.9974.4316451426754-3.4416451426754
2275.4369.99061313408065.43938686591937
2374.1474.8442565786605-0.704256578660463
2473.371.65063885350451.64936114649552
2571.9770.3320853370011.63791466299898
2669.2774.7271759485818-5.45717594858183
2774.1371.59809606949772.53190393050232
2876.477.2095868468738-0.809586846873785
2972.2671.31362270547060.946377294529384
3072.170.02180004612892.07819995387111
3187.8280.66838028814467.15161971185539
3291.6287.79526876200793.82473123799214
3382.6977.07618504349535.61381495650467
3485.7682.02199102060353.73800897939655
3586.8784.01027842702192.85972157297807
3693.0984.3863071972628.703692802738
3783.7388.2298652647535-4.49986526475348
3884.4986.5948624528203-2.10486245282029
3987.3788.9041980806885-1.53419808068854
4089.1391.1239165395959-1.99391653959587
4183.285.460425376625-2.26042537662499
4283.7782.80691469785290.963085302147064
4393.6894.801329680237-1.12132968023697
4493.0995.5555386854325-2.46553868543252
4588.5981.42084870383157.16915129616849
4687.8886.86422757274021.01577242725982
4787.8986.84178769296471.0482123070353
4889.3888.08645589076761.29354410923239
4989.1382.45427564343596.67572435656407
5089.5889.08510888382240.494891116177598
5190.2293.4485182009301-3.22851820093011
5291.4494.5227179420315-3.08271794203149
5391.0488.15962690347282.88037309652725
5492.190.17828034820891.92171965179107
5597.54102.291297203956-4.75129720395601
5699.12100.34838695397-1.22838695397041
5710090.50549313380319.49450686619691
5899.6895.56402608959364.11597391040645
59100.0897.84291332623732.23708667376275
6099.9100.227461446854-0.327461446854088
6199.6395.63122889174863.99877110825136
6299.4598.58536945723520.864630542764829
6399.63102.122212053151-2.49221205315126
6499.46103.952853843473-4.492853843473
6596.9198.9150100886088-2.00501008860876
6697.6597.51859386564990.131406134350115
67102.1106.25316741232-4.15316741231977
68103.57106.014659676422-2.44465967642232
69104.5999.14145520914885.44854479085117
70104.7999.71024609230015.07975390769988
71101.31102.00566563288-0.695665632879624
72104.8101.5662560301613.23374396983908
73104.56100.8347794011353.72522059886509
74104.15102.5677698514071.5822301485929
75102.73105.468977806611-2.73897780661088
76101.86106.493507717927-4.63350771792703
77101.9102.260243549656-0.360243549656332
78102.33102.746000493247-0.416000493246813
79105.71109.707529468061-3.99752946806055
80106.1110.220553171448-4.12055317144824
81102.81104.996295269679-2.18629526967933
82103.23100.3381749020932.89182509790683
83102.3599.08577323654213.26422676345786
84104.11102.5342793292981.57572067070234

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 75.01 & 78.2042601495726 & -3.19426014957263 \tabularnewline
14 & 77.6 & 78.5980898627413 & -0.998089862741281 \tabularnewline
15 & 77.81 & 78.1745098530363 & -0.364509853036324 \tabularnewline
16 & 81.7 & 81.7156847188397 & -0.015684718839708 \tabularnewline
17 & 76.47 & 76.2084007890804 & 0.26159921091957 \tabularnewline
18 & 74.72 & 74.3985896940329 & 0.321410305967063 \tabularnewline
19 & 84.43 & 83.662036093533 & 0.767963906467017 \tabularnewline
20 & 86.72 & 86.6635622639976 & 0.056437736002394 \tabularnewline
21 & 70.99 & 74.4316451426754 & -3.4416451426754 \tabularnewline
22 & 75.43 & 69.9906131340806 & 5.43938686591937 \tabularnewline
23 & 74.14 & 74.8442565786605 & -0.704256578660463 \tabularnewline
24 & 73.3 & 71.6506388535045 & 1.64936114649552 \tabularnewline
25 & 71.97 & 70.332085337001 & 1.63791466299898 \tabularnewline
26 & 69.27 & 74.7271759485818 & -5.45717594858183 \tabularnewline
27 & 74.13 & 71.5980960694977 & 2.53190393050232 \tabularnewline
28 & 76.4 & 77.2095868468738 & -0.809586846873785 \tabularnewline
29 & 72.26 & 71.3136227054706 & 0.946377294529384 \tabularnewline
30 & 72.1 & 70.0218000461289 & 2.07819995387111 \tabularnewline
31 & 87.82 & 80.6683802881446 & 7.15161971185539 \tabularnewline
32 & 91.62 & 87.7952687620079 & 3.82473123799214 \tabularnewline
33 & 82.69 & 77.0761850434953 & 5.61381495650467 \tabularnewline
34 & 85.76 & 82.0219910206035 & 3.73800897939655 \tabularnewline
35 & 86.87 & 84.0102784270219 & 2.85972157297807 \tabularnewline
36 & 93.09 & 84.386307197262 & 8.703692802738 \tabularnewline
37 & 83.73 & 88.2298652647535 & -4.49986526475348 \tabularnewline
38 & 84.49 & 86.5948624528203 & -2.10486245282029 \tabularnewline
39 & 87.37 & 88.9041980806885 & -1.53419808068854 \tabularnewline
40 & 89.13 & 91.1239165395959 & -1.99391653959587 \tabularnewline
41 & 83.2 & 85.460425376625 & -2.26042537662499 \tabularnewline
42 & 83.77 & 82.8069146978529 & 0.963085302147064 \tabularnewline
43 & 93.68 & 94.801329680237 & -1.12132968023697 \tabularnewline
44 & 93.09 & 95.5555386854325 & -2.46553868543252 \tabularnewline
45 & 88.59 & 81.4208487038315 & 7.16915129616849 \tabularnewline
46 & 87.88 & 86.8642275727402 & 1.01577242725982 \tabularnewline
47 & 87.89 & 86.8417876929647 & 1.0482123070353 \tabularnewline
48 & 89.38 & 88.0864558907676 & 1.29354410923239 \tabularnewline
49 & 89.13 & 82.4542756434359 & 6.67572435656407 \tabularnewline
50 & 89.58 & 89.0851088838224 & 0.494891116177598 \tabularnewline
51 & 90.22 & 93.4485182009301 & -3.22851820093011 \tabularnewline
52 & 91.44 & 94.5227179420315 & -3.08271794203149 \tabularnewline
53 & 91.04 & 88.1596269034728 & 2.88037309652725 \tabularnewline
54 & 92.1 & 90.1782803482089 & 1.92171965179107 \tabularnewline
55 & 97.54 & 102.291297203956 & -4.75129720395601 \tabularnewline
56 & 99.12 & 100.34838695397 & -1.22838695397041 \tabularnewline
57 & 100 & 90.5054931338031 & 9.49450686619691 \tabularnewline
58 & 99.68 & 95.5640260895936 & 4.11597391040645 \tabularnewline
59 & 100.08 & 97.8429133262373 & 2.23708667376275 \tabularnewline
60 & 99.9 & 100.227461446854 & -0.327461446854088 \tabularnewline
61 & 99.63 & 95.6312288917486 & 3.99877110825136 \tabularnewline
62 & 99.45 & 98.5853694572352 & 0.864630542764829 \tabularnewline
63 & 99.63 & 102.122212053151 & -2.49221205315126 \tabularnewline
64 & 99.46 & 103.952853843473 & -4.492853843473 \tabularnewline
65 & 96.91 & 98.9150100886088 & -2.00501008860876 \tabularnewline
66 & 97.65 & 97.5185938656499 & 0.131406134350115 \tabularnewline
67 & 102.1 & 106.25316741232 & -4.15316741231977 \tabularnewline
68 & 103.57 & 106.014659676422 & -2.44465967642232 \tabularnewline
69 & 104.59 & 99.1414552091488 & 5.44854479085117 \tabularnewline
70 & 104.79 & 99.7102460923001 & 5.07975390769988 \tabularnewline
71 & 101.31 & 102.00566563288 & -0.695665632879624 \tabularnewline
72 & 104.8 & 101.566256030161 & 3.23374396983908 \tabularnewline
73 & 104.56 & 100.834779401135 & 3.72522059886509 \tabularnewline
74 & 104.15 & 102.567769851407 & 1.5822301485929 \tabularnewline
75 & 102.73 & 105.468977806611 & -2.73897780661088 \tabularnewline
76 & 101.86 & 106.493507717927 & -4.63350771792703 \tabularnewline
77 & 101.9 & 102.260243549656 & -0.360243549656332 \tabularnewline
78 & 102.33 & 102.746000493247 & -0.416000493246813 \tabularnewline
79 & 105.71 & 109.707529468061 & -3.99752946806055 \tabularnewline
80 & 106.1 & 110.220553171448 & -4.12055317144824 \tabularnewline
81 & 102.81 & 104.996295269679 & -2.18629526967933 \tabularnewline
82 & 103.23 & 100.338174902093 & 2.89182509790683 \tabularnewline
83 & 102.35 & 99.0857732365421 & 3.26422676345786 \tabularnewline
84 & 104.11 & 102.534279329298 & 1.57572067070234 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232417&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]75.01[/C][C]78.2042601495726[/C][C]-3.19426014957263[/C][/ROW]
[ROW][C]14[/C][C]77.6[/C][C]78.5980898627413[/C][C]-0.998089862741281[/C][/ROW]
[ROW][C]15[/C][C]77.81[/C][C]78.1745098530363[/C][C]-0.364509853036324[/C][/ROW]
[ROW][C]16[/C][C]81.7[/C][C]81.7156847188397[/C][C]-0.015684718839708[/C][/ROW]
[ROW][C]17[/C][C]76.47[/C][C]76.2084007890804[/C][C]0.26159921091957[/C][/ROW]
[ROW][C]18[/C][C]74.72[/C][C]74.3985896940329[/C][C]0.321410305967063[/C][/ROW]
[ROW][C]19[/C][C]84.43[/C][C]83.662036093533[/C][C]0.767963906467017[/C][/ROW]
[ROW][C]20[/C][C]86.72[/C][C]86.6635622639976[/C][C]0.056437736002394[/C][/ROW]
[ROW][C]21[/C][C]70.99[/C][C]74.4316451426754[/C][C]-3.4416451426754[/C][/ROW]
[ROW][C]22[/C][C]75.43[/C][C]69.9906131340806[/C][C]5.43938686591937[/C][/ROW]
[ROW][C]23[/C][C]74.14[/C][C]74.8442565786605[/C][C]-0.704256578660463[/C][/ROW]
[ROW][C]24[/C][C]73.3[/C][C]71.6506388535045[/C][C]1.64936114649552[/C][/ROW]
[ROW][C]25[/C][C]71.97[/C][C]70.332085337001[/C][C]1.63791466299898[/C][/ROW]
[ROW][C]26[/C][C]69.27[/C][C]74.7271759485818[/C][C]-5.45717594858183[/C][/ROW]
[ROW][C]27[/C][C]74.13[/C][C]71.5980960694977[/C][C]2.53190393050232[/C][/ROW]
[ROW][C]28[/C][C]76.4[/C][C]77.2095868468738[/C][C]-0.809586846873785[/C][/ROW]
[ROW][C]29[/C][C]72.26[/C][C]71.3136227054706[/C][C]0.946377294529384[/C][/ROW]
[ROW][C]30[/C][C]72.1[/C][C]70.0218000461289[/C][C]2.07819995387111[/C][/ROW]
[ROW][C]31[/C][C]87.82[/C][C]80.6683802881446[/C][C]7.15161971185539[/C][/ROW]
[ROW][C]32[/C][C]91.62[/C][C]87.7952687620079[/C][C]3.82473123799214[/C][/ROW]
[ROW][C]33[/C][C]82.69[/C][C]77.0761850434953[/C][C]5.61381495650467[/C][/ROW]
[ROW][C]34[/C][C]85.76[/C][C]82.0219910206035[/C][C]3.73800897939655[/C][/ROW]
[ROW][C]35[/C][C]86.87[/C][C]84.0102784270219[/C][C]2.85972157297807[/C][/ROW]
[ROW][C]36[/C][C]93.09[/C][C]84.386307197262[/C][C]8.703692802738[/C][/ROW]
[ROW][C]37[/C][C]83.73[/C][C]88.2298652647535[/C][C]-4.49986526475348[/C][/ROW]
[ROW][C]38[/C][C]84.49[/C][C]86.5948624528203[/C][C]-2.10486245282029[/C][/ROW]
[ROW][C]39[/C][C]87.37[/C][C]88.9041980806885[/C][C]-1.53419808068854[/C][/ROW]
[ROW][C]40[/C][C]89.13[/C][C]91.1239165395959[/C][C]-1.99391653959587[/C][/ROW]
[ROW][C]41[/C][C]83.2[/C][C]85.460425376625[/C][C]-2.26042537662499[/C][/ROW]
[ROW][C]42[/C][C]83.77[/C][C]82.8069146978529[/C][C]0.963085302147064[/C][/ROW]
[ROW][C]43[/C][C]93.68[/C][C]94.801329680237[/C][C]-1.12132968023697[/C][/ROW]
[ROW][C]44[/C][C]93.09[/C][C]95.5555386854325[/C][C]-2.46553868543252[/C][/ROW]
[ROW][C]45[/C][C]88.59[/C][C]81.4208487038315[/C][C]7.16915129616849[/C][/ROW]
[ROW][C]46[/C][C]87.88[/C][C]86.8642275727402[/C][C]1.01577242725982[/C][/ROW]
[ROW][C]47[/C][C]87.89[/C][C]86.8417876929647[/C][C]1.0482123070353[/C][/ROW]
[ROW][C]48[/C][C]89.38[/C][C]88.0864558907676[/C][C]1.29354410923239[/C][/ROW]
[ROW][C]49[/C][C]89.13[/C][C]82.4542756434359[/C][C]6.67572435656407[/C][/ROW]
[ROW][C]50[/C][C]89.58[/C][C]89.0851088838224[/C][C]0.494891116177598[/C][/ROW]
[ROW][C]51[/C][C]90.22[/C][C]93.4485182009301[/C][C]-3.22851820093011[/C][/ROW]
[ROW][C]52[/C][C]91.44[/C][C]94.5227179420315[/C][C]-3.08271794203149[/C][/ROW]
[ROW][C]53[/C][C]91.04[/C][C]88.1596269034728[/C][C]2.88037309652725[/C][/ROW]
[ROW][C]54[/C][C]92.1[/C][C]90.1782803482089[/C][C]1.92171965179107[/C][/ROW]
[ROW][C]55[/C][C]97.54[/C][C]102.291297203956[/C][C]-4.75129720395601[/C][/ROW]
[ROW][C]56[/C][C]99.12[/C][C]100.34838695397[/C][C]-1.22838695397041[/C][/ROW]
[ROW][C]57[/C][C]100[/C][C]90.5054931338031[/C][C]9.49450686619691[/C][/ROW]
[ROW][C]58[/C][C]99.68[/C][C]95.5640260895936[/C][C]4.11597391040645[/C][/ROW]
[ROW][C]59[/C][C]100.08[/C][C]97.8429133262373[/C][C]2.23708667376275[/C][/ROW]
[ROW][C]60[/C][C]99.9[/C][C]100.227461446854[/C][C]-0.327461446854088[/C][/ROW]
[ROW][C]61[/C][C]99.63[/C][C]95.6312288917486[/C][C]3.99877110825136[/C][/ROW]
[ROW][C]62[/C][C]99.45[/C][C]98.5853694572352[/C][C]0.864630542764829[/C][/ROW]
[ROW][C]63[/C][C]99.63[/C][C]102.122212053151[/C][C]-2.49221205315126[/C][/ROW]
[ROW][C]64[/C][C]99.46[/C][C]103.952853843473[/C][C]-4.492853843473[/C][/ROW]
[ROW][C]65[/C][C]96.91[/C][C]98.9150100886088[/C][C]-2.00501008860876[/C][/ROW]
[ROW][C]66[/C][C]97.65[/C][C]97.5185938656499[/C][C]0.131406134350115[/C][/ROW]
[ROW][C]67[/C][C]102.1[/C][C]106.25316741232[/C][C]-4.15316741231977[/C][/ROW]
[ROW][C]68[/C][C]103.57[/C][C]106.014659676422[/C][C]-2.44465967642232[/C][/ROW]
[ROW][C]69[/C][C]104.59[/C][C]99.1414552091488[/C][C]5.44854479085117[/C][/ROW]
[ROW][C]70[/C][C]104.79[/C][C]99.7102460923001[/C][C]5.07975390769988[/C][/ROW]
[ROW][C]71[/C][C]101.31[/C][C]102.00566563288[/C][C]-0.695665632879624[/C][/ROW]
[ROW][C]72[/C][C]104.8[/C][C]101.566256030161[/C][C]3.23374396983908[/C][/ROW]
[ROW][C]73[/C][C]104.56[/C][C]100.834779401135[/C][C]3.72522059886509[/C][/ROW]
[ROW][C]74[/C][C]104.15[/C][C]102.567769851407[/C][C]1.5822301485929[/C][/ROW]
[ROW][C]75[/C][C]102.73[/C][C]105.468977806611[/C][C]-2.73897780661088[/C][/ROW]
[ROW][C]76[/C][C]101.86[/C][C]106.493507717927[/C][C]-4.63350771792703[/C][/ROW]
[ROW][C]77[/C][C]101.9[/C][C]102.260243549656[/C][C]-0.360243549656332[/C][/ROW]
[ROW][C]78[/C][C]102.33[/C][C]102.746000493247[/C][C]-0.416000493246813[/C][/ROW]
[ROW][C]79[/C][C]105.71[/C][C]109.707529468061[/C][C]-3.99752946806055[/C][/ROW]
[ROW][C]80[/C][C]106.1[/C][C]110.220553171448[/C][C]-4.12055317144824[/C][/ROW]
[ROW][C]81[/C][C]102.81[/C][C]104.996295269679[/C][C]-2.18629526967933[/C][/ROW]
[ROW][C]82[/C][C]103.23[/C][C]100.338174902093[/C][C]2.89182509790683[/C][/ROW]
[ROW][C]83[/C][C]102.35[/C][C]99.0857732365421[/C][C]3.26422676345786[/C][/ROW]
[ROW][C]84[/C][C]104.11[/C][C]102.534279329298[/C][C]1.57572067070234[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232417&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232417&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
1375.0178.2042601495726-3.19426014957263
1477.678.5980898627413-0.998089862741281
1577.8178.1745098530363-0.364509853036324
1681.781.7156847188397-0.015684718839708
1776.4776.20840078908040.26159921091957
1874.7274.39858969403290.321410305967063
1984.4383.6620360935330.767963906467017
2086.7286.66356226399760.056437736002394
2170.9974.4316451426754-3.4416451426754
2275.4369.99061313408065.43938686591937
2374.1474.8442565786605-0.704256578660463
2473.371.65063885350451.64936114649552
2571.9770.3320853370011.63791466299898
2669.2774.7271759485818-5.45717594858183
2774.1371.59809606949772.53190393050232
2876.477.2095868468738-0.809586846873785
2972.2671.31362270547060.946377294529384
3072.170.02180004612892.07819995387111
3187.8280.66838028814467.15161971185539
3291.6287.79526876200793.82473123799214
3382.6977.07618504349535.61381495650467
3485.7682.02199102060353.73800897939655
3586.8784.01027842702192.85972157297807
3693.0984.3863071972628.703692802738
3783.7388.2298652647535-4.49986526475348
3884.4986.5948624528203-2.10486245282029
3987.3788.9041980806885-1.53419808068854
4089.1391.1239165395959-1.99391653959587
4183.285.460425376625-2.26042537662499
4283.7782.80691469785290.963085302147064
4393.6894.801329680237-1.12132968023697
4493.0995.5555386854325-2.46553868543252
4588.5981.42084870383157.16915129616849
4687.8886.86422757274021.01577242725982
4787.8986.84178769296471.0482123070353
4889.3888.08645589076761.29354410923239
4989.1382.45427564343596.67572435656407
5089.5889.08510888382240.494891116177598
5190.2293.4485182009301-3.22851820093011
5291.4494.5227179420315-3.08271794203149
5391.0488.15962690347282.88037309652725
5492.190.17828034820891.92171965179107
5597.54102.291297203956-4.75129720395601
5699.12100.34838695397-1.22838695397041
5710090.50549313380319.49450686619691
5899.6895.56402608959364.11597391040645
59100.0897.84291332623732.23708667376275
6099.9100.227461446854-0.327461446854088
6199.6395.63122889174863.99877110825136
6299.4598.58536945723520.864630542764829
6399.63102.122212053151-2.49221205315126
6499.46103.952853843473-4.492853843473
6596.9198.9150100886088-2.00501008860876
6697.6597.51859386564990.131406134350115
67102.1106.25316741232-4.15316741231977
68103.57106.014659676422-2.44465967642232
69104.5999.14145520914885.44854479085117
70104.7999.71024609230015.07975390769988
71101.31102.00566563288-0.695665632879624
72104.8101.5662560301613.23374396983908
73104.56100.8347794011353.72522059886509
74104.15102.5677698514071.5822301485929
75102.73105.468977806611-2.73897780661088
76101.86106.493507717927-4.63350771792703
77101.9102.260243549656-0.360243549656332
78102.33102.746000493247-0.416000493246813
79105.71109.707529468061-3.99752946806055
80106.1110.220553171448-4.12055317144824
81102.81104.996295269679-2.18629526967933
82103.23100.3381749020932.89182509790683
83102.3599.08577323654213.26422676345786
84104.11102.5342793292981.57572067070234







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85100.79524440497894.1005626854204107.489926124536
8699.197429621939291.1296122589483107.26524698493
8799.399066093463990.1060778487541108.692054338174
88101.43864253844791.0149841683128111.862300908581
89101.66018494822890.1713740064768113.148995889979
90102.31421054561289.8080508800594114.820370211165
91108.27506487333694.7876469609951121.762482785676
92111.39209314816396.9513160260468125.83287027028
93109.62742589706194.2552150809245124.999636713197
94108.27655032164491.9903311057769124.562769537511
95105.33397547221188.1476935370412122.520257407381
96106.08586702359988.0107198167515124.161014230446

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 100.795244404978 & 94.1005626854204 & 107.489926124536 \tabularnewline
86 & 99.1974296219392 & 91.1296122589483 & 107.26524698493 \tabularnewline
87 & 99.3990660934639 & 90.1060778487541 & 108.692054338174 \tabularnewline
88 & 101.438642538447 & 91.0149841683128 & 111.862300908581 \tabularnewline
89 & 101.660184948228 & 90.1713740064768 & 113.148995889979 \tabularnewline
90 & 102.314210545612 & 89.8080508800594 & 114.820370211165 \tabularnewline
91 & 108.275064873336 & 94.7876469609951 & 121.762482785676 \tabularnewline
92 & 111.392093148163 & 96.9513160260468 & 125.83287027028 \tabularnewline
93 & 109.627425897061 & 94.2552150809245 & 124.999636713197 \tabularnewline
94 & 108.276550321644 & 91.9903311057769 & 124.562769537511 \tabularnewline
95 & 105.333975472211 & 88.1476935370412 & 122.520257407381 \tabularnewline
96 & 106.085867023599 & 88.0107198167515 & 124.161014230446 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232417&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]100.795244404978[/C][C]94.1005626854204[/C][C]107.489926124536[/C][/ROW]
[ROW][C]86[/C][C]99.1974296219392[/C][C]91.1296122589483[/C][C]107.26524698493[/C][/ROW]
[ROW][C]87[/C][C]99.3990660934639[/C][C]90.1060778487541[/C][C]108.692054338174[/C][/ROW]
[ROW][C]88[/C][C]101.438642538447[/C][C]91.0149841683128[/C][C]111.862300908581[/C][/ROW]
[ROW][C]89[/C][C]101.660184948228[/C][C]90.1713740064768[/C][C]113.148995889979[/C][/ROW]
[ROW][C]90[/C][C]102.314210545612[/C][C]89.8080508800594[/C][C]114.820370211165[/C][/ROW]
[ROW][C]91[/C][C]108.275064873336[/C][C]94.7876469609951[/C][C]121.762482785676[/C][/ROW]
[ROW][C]92[/C][C]111.392093148163[/C][C]96.9513160260468[/C][C]125.83287027028[/C][/ROW]
[ROW][C]93[/C][C]109.627425897061[/C][C]94.2552150809245[/C][C]124.999636713197[/C][/ROW]
[ROW][C]94[/C][C]108.276550321644[/C][C]91.9903311057769[/C][C]124.562769537511[/C][/ROW]
[ROW][C]95[/C][C]105.333975472211[/C][C]88.1476935370412[/C][C]122.520257407381[/C][/ROW]
[ROW][C]96[/C][C]106.085867023599[/C][C]88.0107198167515[/C][C]124.161014230446[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232417&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232417&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
85100.79524440497894.1005626854204107.489926124536
8699.197429621939291.1296122589483107.26524698493
8799.399066093463990.1060778487541108.692054338174
88101.43864253844791.0149841683128111.862300908581
89101.66018494822890.1713740064768113.148995889979
90102.31421054561289.8080508800594114.820370211165
91108.27506487333694.7876469609951121.762482785676
92111.39209314816396.9513160260468125.83287027028
93109.62742589706194.2552150809245124.999636713197
94108.27655032164491.9903311057769124.562769537511
95105.33397547221188.1476935370412122.520257407381
96106.08586702359988.0107198167515124.161014230446



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')