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Author's title
Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 13 Dec 2013 03:41:18 -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/13/t1386924158jxxbjwkbyqvirr0.htm/, Retrieved Sat, 04 Dec 2021 20:38:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232284, Retrieved Sat, 04 Dec 2021 20:38:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-13 08:41:18] [2ad58ca14453c04e73fc838d0bf536d8] [Current]
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Dataseries X:
126,81
125,8
123,07
119,52
118,03
117,27
117,27
116,69
115,38
114,31
113,33
111,79
111,79
110,92
109,37
107,04
104,72
104,14
104,14
102,95
102,13
101,01
100,07
99,4
99,4
99,34
97,72
96,26
95,77
95,04
95,04
94,55
94
93,14
91,21
90,3
90,3
89,74
89,07
89,06
88,97
88,78
88,78
88,23
87,91
87,79
87,89
88
88
87,08
85,75
84,29
84,39
83,72
83,72
81,76
81,53
80,55
79,83
78,98
78,98
78,27
77,41
76,75
76,38
74,96
74,96
74,46
74,04
73,22
72,97
72,91
72,91
73,27
72,93
72,67
71,94
71,9
71,89
71,72
70,85
69,82
69,61
69,48

 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 seconds R Server 'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232284&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232284&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232284&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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 seconds R Server 'Gertrude Mary Cox' @ cox.wessa.net

 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.106401285899114 gamma FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.106401285899114 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232284&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.106401285899114[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232284&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232284&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 Parameter Value alpha 1 beta 0.106401285899114 gamma FALSE

 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 123.07 124.79 -1.72 4 119.52 121.876989788254 -2.35698978825351 5 118.03 118.076203043932 -0.0462030439322518 6 117.27 116.581286980645 0.68871301935458 7 117.27 115.89456693152 1.37543306847979 8 116.69 116.040914778675 0.649085221325379 9 115.38 115.529978280882 -0.149978280881754 10 114.31 114.204020398939 0.105979601061009 11 113.33 113.145296764771 0.184703235229037 12 111.79 112.184949426509 -0.394949426509044 13 111.79 110.602926299663 1.18707370033663 14 110.92 110.729232467836 0.190767532163775 15 109.37 109.879530378566 -0.50953037856624 16 107.04 108.275315691082 -1.23531569108214 17 104.72 105.81387651306 -1.09387651305964 18 104.14 103.377486645455 0.762513354544751 19 104.14 102.878619046894 1.26138095310594 20 102.95 103.012831602313 -0.0628316023131816 21 102.13 101.816146239032 0.31385376096803 22 101.01 101.029540682783 -0.0195406827832159 23 100.07 99.9074615290078 0.162538470992232 24 99.4 98.9847558313294 0.415244168670611 25 99.4 98.3589383448381 1.04106165516194 26 99.34 98.4697086436476 0.870291356352439 27 97.72 98.5023087630703 -0.782308763070347 28 96.26 96.7990701047095 -0.539070104709495 29 95.77 95.2817123523786 0.488287647621348 30 95.04 94.8436667859742 0.196333214025799 31 95.04 94.1345568924113 0.905443107588738 32 94.55 94.2308972033672 0.319102796632791 33 94 93.7748501512629 0.225149848737075 34 93.14 93.2488063846885 -0.108806384688549 35 91.21 92.3772292454436 -1.16722924544365 36 90.3 90.3230345527894 -0.0230345527893832 37 90.3 89.4105836467525 0.889416353247512 38 89.74 89.5052186904377 0.23478130956228 39 89.07 88.9701997236802 0.099800276319769 40 89.06 88.3108186014137 0.749181398586273 41 88.97 88.380532465595 0.589467534404974 42 88.78 88.3532525692515 0.42674743074852 43 88.78 88.2086590446373 0.571340955362729 44 88.23 88.2694504569747 -0.0394504569746914 45 87.91 87.7152528776233 0.194747122376711 46 87.79 87.4159742218693 0.374025778130701 47 87.89 87.3357710456218 0.554228954378161 48 88 87.4947417190502 0.505258280949803 49 88 87.6585018498544 0.341498150145569 50 87.08 87.6948376921621 -0.614837692162084 51 85.75 86.7094181710968 -0.9594181710968 52 84.29 85.2773348439771 -0.987334843977109 53 84.39 83.712281146965 0.677718853035046 54 83.72 83.884391304406 -0.164391304405953 55 83.72 83.1968998582265 0.523100141773469 56 81.76 83.2525583859652 -1.49255838596522 57 81.53 81.133748254419 0.396251745580969 58 80.55 80.9459099496886 -0.395909949688615 59 79.83 79.9237846219415 -0.0937846219414951 60 78.98 79.1938058175694 -0.213805817569352 61 78.98 78.3210566036473 0.65894339635274 62 78.27 78.3911690283539 -0.121169028353933 63 77.41 77.6682764879259 -0.258276487925926 64 76.75 76.7807955374931 -0.0307955374930913 65 76.38 76.1175188527039 0.262481147296114 66 74.96 75.7754471843004 -0.815447184300453 67 74.96 74.2686825553081 0.691317444691919 68 74.46 74.3422396203878 0.117760379612207 69 74.04 73.8547694762065 0.185230523793521 70 73.22 73.4544782421259 -0.234478242125903 71 72.97 72.6095294556483 0.360470544351671 72 72.91 72.3978839850961 0.512116014903896 73 72.91 72.3923737876114 0.517626212388592 74 73.27 72.4474498822246 0.822550117775364 75 72.93 72.8949702724724 0.0350297275276006 76 72.67 72.558697480526 0.111302519473952 77 71.94 72.3105402117219 -0.370540211721888 78 71.9 71.5411142567173 0.35888574328267 79 71.89 71.5393001612935 0.350699838706518 80 71.72 71.5666150750965 0.153384924903534 81 70.85 71.4129354283437 -0.562935428343735 82 69.82 70.4830383748898 -0.663038374889794 83 69.61 69.3824902392011 0.227509760798938 84 69.48 69.1966975703047 0.28330242969534

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 123.07 & 124.79 & -1.72 \tabularnewline
4 & 119.52 & 121.876989788254 & -2.35698978825351 \tabularnewline
5 & 118.03 & 118.076203043932 & -0.0462030439322518 \tabularnewline
6 & 117.27 & 116.581286980645 & 0.68871301935458 \tabularnewline
7 & 117.27 & 115.89456693152 & 1.37543306847979 \tabularnewline
8 & 116.69 & 116.040914778675 & 0.649085221325379 \tabularnewline
9 & 115.38 & 115.529978280882 & -0.149978280881754 \tabularnewline
10 & 114.31 & 114.204020398939 & 0.105979601061009 \tabularnewline
11 & 113.33 & 113.145296764771 & 0.184703235229037 \tabularnewline
12 & 111.79 & 112.184949426509 & -0.394949426509044 \tabularnewline
13 & 111.79 & 110.602926299663 & 1.18707370033663 \tabularnewline
14 & 110.92 & 110.729232467836 & 0.190767532163775 \tabularnewline
15 & 109.37 & 109.879530378566 & -0.50953037856624 \tabularnewline
16 & 107.04 & 108.275315691082 & -1.23531569108214 \tabularnewline
17 & 104.72 & 105.81387651306 & -1.09387651305964 \tabularnewline
18 & 104.14 & 103.377486645455 & 0.762513354544751 \tabularnewline
19 & 104.14 & 102.878619046894 & 1.26138095310594 \tabularnewline
20 & 102.95 & 103.012831602313 & -0.0628316023131816 \tabularnewline
21 & 102.13 & 101.816146239032 & 0.31385376096803 \tabularnewline
22 & 101.01 & 101.029540682783 & -0.0195406827832159 \tabularnewline
23 & 100.07 & 99.9074615290078 & 0.162538470992232 \tabularnewline
24 & 99.4 & 98.9847558313294 & 0.415244168670611 \tabularnewline
25 & 99.4 & 98.3589383448381 & 1.04106165516194 \tabularnewline
26 & 99.34 & 98.4697086436476 & 0.870291356352439 \tabularnewline
27 & 97.72 & 98.5023087630703 & -0.782308763070347 \tabularnewline
28 & 96.26 & 96.7990701047095 & -0.539070104709495 \tabularnewline
29 & 95.77 & 95.2817123523786 & 0.488287647621348 \tabularnewline
30 & 95.04 & 94.8436667859742 & 0.196333214025799 \tabularnewline
31 & 95.04 & 94.1345568924113 & 0.905443107588738 \tabularnewline
32 & 94.55 & 94.2308972033672 & 0.319102796632791 \tabularnewline
33 & 94 & 93.7748501512629 & 0.225149848737075 \tabularnewline
34 & 93.14 & 93.2488063846885 & -0.108806384688549 \tabularnewline
35 & 91.21 & 92.3772292454436 & -1.16722924544365 \tabularnewline
36 & 90.3 & 90.3230345527894 & -0.0230345527893832 \tabularnewline
37 & 90.3 & 89.4105836467525 & 0.889416353247512 \tabularnewline
38 & 89.74 & 89.5052186904377 & 0.23478130956228 \tabularnewline
39 & 89.07 & 88.9701997236802 & 0.099800276319769 \tabularnewline
40 & 89.06 & 88.3108186014137 & 0.749181398586273 \tabularnewline
41 & 88.97 & 88.380532465595 & 0.589467534404974 \tabularnewline
42 & 88.78 & 88.3532525692515 & 0.42674743074852 \tabularnewline
43 & 88.78 & 88.2086590446373 & 0.571340955362729 \tabularnewline
44 & 88.23 & 88.2694504569747 & -0.0394504569746914 \tabularnewline
45 & 87.91 & 87.7152528776233 & 0.194747122376711 \tabularnewline
46 & 87.79 & 87.4159742218693 & 0.374025778130701 \tabularnewline
47 & 87.89 & 87.3357710456218 & 0.554228954378161 \tabularnewline
48 & 88 & 87.4947417190502 & 0.505258280949803 \tabularnewline
49 & 88 & 87.6585018498544 & 0.341498150145569 \tabularnewline
50 & 87.08 & 87.6948376921621 & -0.614837692162084 \tabularnewline
51 & 85.75 & 86.7094181710968 & -0.9594181710968 \tabularnewline
52 & 84.29 & 85.2773348439771 & -0.987334843977109 \tabularnewline
53 & 84.39 & 83.712281146965 & 0.677718853035046 \tabularnewline
54 & 83.72 & 83.884391304406 & -0.164391304405953 \tabularnewline
55 & 83.72 & 83.1968998582265 & 0.523100141773469 \tabularnewline
56 & 81.76 & 83.2525583859652 & -1.49255838596522 \tabularnewline
57 & 81.53 & 81.133748254419 & 0.396251745580969 \tabularnewline
58 & 80.55 & 80.9459099496886 & -0.395909949688615 \tabularnewline
59 & 79.83 & 79.9237846219415 & -0.0937846219414951 \tabularnewline
60 & 78.98 & 79.1938058175694 & -0.213805817569352 \tabularnewline
61 & 78.98 & 78.3210566036473 & 0.65894339635274 \tabularnewline
62 & 78.27 & 78.3911690283539 & -0.121169028353933 \tabularnewline
63 & 77.41 & 77.6682764879259 & -0.258276487925926 \tabularnewline
64 & 76.75 & 76.7807955374931 & -0.0307955374930913 \tabularnewline
65 & 76.38 & 76.1175188527039 & 0.262481147296114 \tabularnewline
66 & 74.96 & 75.7754471843004 & -0.815447184300453 \tabularnewline
67 & 74.96 & 74.2686825553081 & 0.691317444691919 \tabularnewline
68 & 74.46 & 74.3422396203878 & 0.117760379612207 \tabularnewline
69 & 74.04 & 73.8547694762065 & 0.185230523793521 \tabularnewline
70 & 73.22 & 73.4544782421259 & -0.234478242125903 \tabularnewline
71 & 72.97 & 72.6095294556483 & 0.360470544351671 \tabularnewline
72 & 72.91 & 72.3978839850961 & 0.512116014903896 \tabularnewline
73 & 72.91 & 72.3923737876114 & 0.517626212388592 \tabularnewline
74 & 73.27 & 72.4474498822246 & 0.822550117775364 \tabularnewline
75 & 72.93 & 72.8949702724724 & 0.0350297275276006 \tabularnewline
76 & 72.67 & 72.558697480526 & 0.111302519473952 \tabularnewline
77 & 71.94 & 72.3105402117219 & -0.370540211721888 \tabularnewline
78 & 71.9 & 71.5411142567173 & 0.35888574328267 \tabularnewline
79 & 71.89 & 71.5393001612935 & 0.350699838706518 \tabularnewline
80 & 71.72 & 71.5666150750965 & 0.153384924903534 \tabularnewline
81 & 70.85 & 71.4129354283437 & -0.562935428343735 \tabularnewline
82 & 69.82 & 70.4830383748898 & -0.663038374889794 \tabularnewline
83 & 69.61 & 69.3824902392011 & 0.227509760798938 \tabularnewline
84 & 69.48 & 69.1966975703047 & 0.28330242969534 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232284&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]123.07[/C][C]124.79[/C][C]-1.72[/C][/ROW]
[ROW][C]4[/C][C]119.52[/C][C]121.876989788254[/C][C]-2.35698978825351[/C][/ROW]
[ROW][C]5[/C][C]118.03[/C][C]118.076203043932[/C][C]-0.0462030439322518[/C][/ROW]
[ROW][C]6[/C][C]117.27[/C][C]116.581286980645[/C][C]0.68871301935458[/C][/ROW]
[ROW][C]7[/C][C]117.27[/C][C]115.89456693152[/C][C]1.37543306847979[/C][/ROW]
[ROW][C]8[/C][C]116.69[/C][C]116.040914778675[/C][C]0.649085221325379[/C][/ROW]
[ROW][C]9[/C][C]115.38[/C][C]115.529978280882[/C][C]-0.149978280881754[/C][/ROW]
[ROW][C]10[/C][C]114.31[/C][C]114.204020398939[/C][C]0.105979601061009[/C][/ROW]
[ROW][C]11[/C][C]113.33[/C][C]113.145296764771[/C][C]0.184703235229037[/C][/ROW]
[ROW][C]12[/C][C]111.79[/C][C]112.184949426509[/C][C]-0.394949426509044[/C][/ROW]
[ROW][C]13[/C][C]111.79[/C][C]110.602926299663[/C][C]1.18707370033663[/C][/ROW]
[ROW][C]14[/C][C]110.92[/C][C]110.729232467836[/C][C]0.190767532163775[/C][/ROW]
[ROW][C]15[/C][C]109.37[/C][C]109.879530378566[/C][C]-0.50953037856624[/C][/ROW]
[ROW][C]16[/C][C]107.04[/C][C]108.275315691082[/C][C]-1.23531569108214[/C][/ROW]
[ROW][C]17[/C][C]104.72[/C][C]105.81387651306[/C][C]-1.09387651305964[/C][/ROW]
[ROW][C]18[/C][C]104.14[/C][C]103.377486645455[/C][C]0.762513354544751[/C][/ROW]
[ROW][C]19[/C][C]104.14[/C][C]102.878619046894[/C][C]1.26138095310594[/C][/ROW]
[ROW][C]20[/C][C]102.95[/C][C]103.012831602313[/C][C]-0.0628316023131816[/C][/ROW]
[ROW][C]21[/C][C]102.13[/C][C]101.816146239032[/C][C]0.31385376096803[/C][/ROW]
[ROW][C]22[/C][C]101.01[/C][C]101.029540682783[/C][C]-0.0195406827832159[/C][/ROW]
[ROW][C]23[/C][C]100.07[/C][C]99.9074615290078[/C][C]0.162538470992232[/C][/ROW]
[ROW][C]24[/C][C]99.4[/C][C]98.9847558313294[/C][C]0.415244168670611[/C][/ROW]
[ROW][C]25[/C][C]99.4[/C][C]98.3589383448381[/C][C]1.04106165516194[/C][/ROW]
[ROW][C]26[/C][C]99.34[/C][C]98.4697086436476[/C][C]0.870291356352439[/C][/ROW]
[ROW][C]27[/C][C]97.72[/C][C]98.5023087630703[/C][C]-0.782308763070347[/C][/ROW]
[ROW][C]28[/C][C]96.26[/C][C]96.7990701047095[/C][C]-0.539070104709495[/C][/ROW]
[ROW][C]29[/C][C]95.77[/C][C]95.2817123523786[/C][C]0.488287647621348[/C][/ROW]
[ROW][C]30[/C][C]95.04[/C][C]94.8436667859742[/C][C]0.196333214025799[/C][/ROW]
[ROW][C]31[/C][C]95.04[/C][C]94.1345568924113[/C][C]0.905443107588738[/C][/ROW]
[ROW][C]32[/C][C]94.55[/C][C]94.2308972033672[/C][C]0.319102796632791[/C][/ROW]
[ROW][C]33[/C][C]94[/C][C]93.7748501512629[/C][C]0.225149848737075[/C][/ROW]
[ROW][C]34[/C][C]93.14[/C][C]93.2488063846885[/C][C]-0.108806384688549[/C][/ROW]
[ROW][C]35[/C][C]91.21[/C][C]92.3772292454436[/C][C]-1.16722924544365[/C][/ROW]
[ROW][C]36[/C][C]90.3[/C][C]90.3230345527894[/C][C]-0.0230345527893832[/C][/ROW]
[ROW][C]37[/C][C]90.3[/C][C]89.4105836467525[/C][C]0.889416353247512[/C][/ROW]
[ROW][C]38[/C][C]89.74[/C][C]89.5052186904377[/C][C]0.23478130956228[/C][/ROW]
[ROW][C]39[/C][C]89.07[/C][C]88.9701997236802[/C][C]0.099800276319769[/C][/ROW]
[ROW][C]40[/C][C]89.06[/C][C]88.3108186014137[/C][C]0.749181398586273[/C][/ROW]
[ROW][C]41[/C][C]88.97[/C][C]88.380532465595[/C][C]0.589467534404974[/C][/ROW]
[ROW][C]42[/C][C]88.78[/C][C]88.3532525692515[/C][C]0.42674743074852[/C][/ROW]
[ROW][C]43[/C][C]88.78[/C][C]88.2086590446373[/C][C]0.571340955362729[/C][/ROW]
[ROW][C]44[/C][C]88.23[/C][C]88.2694504569747[/C][C]-0.0394504569746914[/C][/ROW]
[ROW][C]45[/C][C]87.91[/C][C]87.7152528776233[/C][C]0.194747122376711[/C][/ROW]
[ROW][C]46[/C][C]87.79[/C][C]87.4159742218693[/C][C]0.374025778130701[/C][/ROW]
[ROW][C]47[/C][C]87.89[/C][C]87.3357710456218[/C][C]0.554228954378161[/C][/ROW]
[ROW][C]48[/C][C]88[/C][C]87.4947417190502[/C][C]0.505258280949803[/C][/ROW]
[ROW][C]49[/C][C]88[/C][C]87.6585018498544[/C][C]0.341498150145569[/C][/ROW]
[ROW][C]50[/C][C]87.08[/C][C]87.6948376921621[/C][C]-0.614837692162084[/C][/ROW]
[ROW][C]51[/C][C]85.75[/C][C]86.7094181710968[/C][C]-0.9594181710968[/C][/ROW]
[ROW][C]52[/C][C]84.29[/C][C]85.2773348439771[/C][C]-0.987334843977109[/C][/ROW]
[ROW][C]53[/C][C]84.39[/C][C]83.712281146965[/C][C]0.677718853035046[/C][/ROW]
[ROW][C]54[/C][C]83.72[/C][C]83.884391304406[/C][C]-0.164391304405953[/C][/ROW]
[ROW][C]55[/C][C]83.72[/C][C]83.1968998582265[/C][C]0.523100141773469[/C][/ROW]
[ROW][C]56[/C][C]81.76[/C][C]83.2525583859652[/C][C]-1.49255838596522[/C][/ROW]
[ROW][C]57[/C][C]81.53[/C][C]81.133748254419[/C][C]0.396251745580969[/C][/ROW]
[ROW][C]58[/C][C]80.55[/C][C]80.9459099496886[/C][C]-0.395909949688615[/C][/ROW]
[ROW][C]59[/C][C]79.83[/C][C]79.9237846219415[/C][C]-0.0937846219414951[/C][/ROW]
[ROW][C]60[/C][C]78.98[/C][C]79.1938058175694[/C][C]-0.213805817569352[/C][/ROW]
[ROW][C]61[/C][C]78.98[/C][C]78.3210566036473[/C][C]0.65894339635274[/C][/ROW]
[ROW][C]62[/C][C]78.27[/C][C]78.3911690283539[/C][C]-0.121169028353933[/C][/ROW]
[ROW][C]63[/C][C]77.41[/C][C]77.6682764879259[/C][C]-0.258276487925926[/C][/ROW]
[ROW][C]64[/C][C]76.75[/C][C]76.7807955374931[/C][C]-0.0307955374930913[/C][/ROW]
[ROW][C]65[/C][C]76.38[/C][C]76.1175188527039[/C][C]0.262481147296114[/C][/ROW]
[ROW][C]66[/C][C]74.96[/C][C]75.7754471843004[/C][C]-0.815447184300453[/C][/ROW]
[ROW][C]67[/C][C]74.96[/C][C]74.2686825553081[/C][C]0.691317444691919[/C][/ROW]
[ROW][C]68[/C][C]74.46[/C][C]74.3422396203878[/C][C]0.117760379612207[/C][/ROW]
[ROW][C]69[/C][C]74.04[/C][C]73.8547694762065[/C][C]0.185230523793521[/C][/ROW]
[ROW][C]70[/C][C]73.22[/C][C]73.4544782421259[/C][C]-0.234478242125903[/C][/ROW]
[ROW][C]71[/C][C]72.97[/C][C]72.6095294556483[/C][C]0.360470544351671[/C][/ROW]
[ROW][C]72[/C][C]72.91[/C][C]72.3978839850961[/C][C]0.512116014903896[/C][/ROW]
[ROW][C]73[/C][C]72.91[/C][C]72.3923737876114[/C][C]0.517626212388592[/C][/ROW]
[ROW][C]74[/C][C]73.27[/C][C]72.4474498822246[/C][C]0.822550117775364[/C][/ROW]
[ROW][C]75[/C][C]72.93[/C][C]72.8949702724724[/C][C]0.0350297275276006[/C][/ROW]
[ROW][C]76[/C][C]72.67[/C][C]72.558697480526[/C][C]0.111302519473952[/C][/ROW]
[ROW][C]77[/C][C]71.94[/C][C]72.3105402117219[/C][C]-0.370540211721888[/C][/ROW]
[ROW][C]78[/C][C]71.9[/C][C]71.5411142567173[/C][C]0.35888574328267[/C][/ROW]
[ROW][C]79[/C][C]71.89[/C][C]71.5393001612935[/C][C]0.350699838706518[/C][/ROW]
[ROW][C]80[/C][C]71.72[/C][C]71.5666150750965[/C][C]0.153384924903534[/C][/ROW]
[ROW][C]81[/C][C]70.85[/C][C]71.4129354283437[/C][C]-0.562935428343735[/C][/ROW]
[ROW][C]82[/C][C]69.82[/C][C]70.4830383748898[/C][C]-0.663038374889794[/C][/ROW]
[ROW][C]83[/C][C]69.61[/C][C]69.3824902392011[/C][C]0.227509760798938[/C][/ROW]
[ROW][C]84[/C][C]69.48[/C][C]69.1966975703047[/C][C]0.28330242969534[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232284&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232284&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 t Observed Fitted Residuals 3 123.07 124.79 -1.72 4 119.52 121.876989788254 -2.35698978825351 5 118.03 118.076203043932 -0.0462030439322518 6 117.27 116.581286980645 0.68871301935458 7 117.27 115.89456693152 1.37543306847979 8 116.69 116.040914778675 0.649085221325379 9 115.38 115.529978280882 -0.149978280881754 10 114.31 114.204020398939 0.105979601061009 11 113.33 113.145296764771 0.184703235229037 12 111.79 112.184949426509 -0.394949426509044 13 111.79 110.602926299663 1.18707370033663 14 110.92 110.729232467836 0.190767532163775 15 109.37 109.879530378566 -0.50953037856624 16 107.04 108.275315691082 -1.23531569108214 17 104.72 105.81387651306 -1.09387651305964 18 104.14 103.377486645455 0.762513354544751 19 104.14 102.878619046894 1.26138095310594 20 102.95 103.012831602313 -0.0628316023131816 21 102.13 101.816146239032 0.31385376096803 22 101.01 101.029540682783 -0.0195406827832159 23 100.07 99.9074615290078 0.162538470992232 24 99.4 98.9847558313294 0.415244168670611 25 99.4 98.3589383448381 1.04106165516194 26 99.34 98.4697086436476 0.870291356352439 27 97.72 98.5023087630703 -0.782308763070347 28 96.26 96.7990701047095 -0.539070104709495 29 95.77 95.2817123523786 0.488287647621348 30 95.04 94.8436667859742 0.196333214025799 31 95.04 94.1345568924113 0.905443107588738 32 94.55 94.2308972033672 0.319102796632791 33 94 93.7748501512629 0.225149848737075 34 93.14 93.2488063846885 -0.108806384688549 35 91.21 92.3772292454436 -1.16722924544365 36 90.3 90.3230345527894 -0.0230345527893832 37 90.3 89.4105836467525 0.889416353247512 38 89.74 89.5052186904377 0.23478130956228 39 89.07 88.9701997236802 0.099800276319769 40 89.06 88.3108186014137 0.749181398586273 41 88.97 88.380532465595 0.589467534404974 42 88.78 88.3532525692515 0.42674743074852 43 88.78 88.2086590446373 0.571340955362729 44 88.23 88.2694504569747 -0.0394504569746914 45 87.91 87.7152528776233 0.194747122376711 46 87.79 87.4159742218693 0.374025778130701 47 87.89 87.3357710456218 0.554228954378161 48 88 87.4947417190502 0.505258280949803 49 88 87.6585018498544 0.341498150145569 50 87.08 87.6948376921621 -0.614837692162084 51 85.75 86.7094181710968 -0.9594181710968 52 84.29 85.2773348439771 -0.987334843977109 53 84.39 83.712281146965 0.677718853035046 54 83.72 83.884391304406 -0.164391304405953 55 83.72 83.1968998582265 0.523100141773469 56 81.76 83.2525583859652 -1.49255838596522 57 81.53 81.133748254419 0.396251745580969 58 80.55 80.9459099496886 -0.395909949688615 59 79.83 79.9237846219415 -0.0937846219414951 60 78.98 79.1938058175694 -0.213805817569352 61 78.98 78.3210566036473 0.65894339635274 62 78.27 78.3911690283539 -0.121169028353933 63 77.41 77.6682764879259 -0.258276487925926 64 76.75 76.7807955374931 -0.0307955374930913 65 76.38 76.1175188527039 0.262481147296114 66 74.96 75.7754471843004 -0.815447184300453 67 74.96 74.2686825553081 0.691317444691919 68 74.46 74.3422396203878 0.117760379612207 69 74.04 73.8547694762065 0.185230523793521 70 73.22 73.4544782421259 -0.234478242125903 71 72.97 72.6095294556483 0.360470544351671 72 72.91 72.3978839850961 0.512116014903896 73 72.91 72.3923737876114 0.517626212388592 74 73.27 72.4474498822246 0.822550117775364 75 72.93 72.8949702724724 0.0350297275276006 76 72.67 72.558697480526 0.111302519473952 77 71.94 72.3105402117219 -0.370540211721888 78 71.9 71.5411142567173 0.35888574328267 79 71.89 71.5393001612935 0.350699838706518 80 71.72 71.5666150750965 0.153384924903534 81 70.85 71.4129354283437 -0.562935428343735 82 69.82 70.4830383748898 -0.663038374889794 83 69.61 69.3824902392011 0.227509760798938 84 69.48 69.1966975703047 0.28330242969534

 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 69.0968413131226 67.7790318175173 70.4146508087279 86 68.7136826262452 66.7483678843297 70.6789973681607 87 68.3305239393678 65.7973753239 70.8636725548356 88 67.9473652524904 64.8750562038635 71.0196743011172 89 67.564206565613 63.9630253170125 71.1653878142135 90 67.1810478787356 63.052557380159 71.3095383773122 91 66.7978891918582 62.1388993304431 71.4568790532732 92 66.4147305049808 61.219243426288 71.6102175836735 93 66.0315718181034 60.2918459040096 71.7712977321972 94 65.648413131226 59.3555909754093 71.9412352870426 95 65.2652544443486 58.4097545547627 72.1207543339344 96 64.8820957574712 57.4538672252541 72.3103242896882

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 69.0968413131226 & 67.7790318175173 & 70.4146508087279 \tabularnewline
86 & 68.7136826262452 & 66.7483678843297 & 70.6789973681607 \tabularnewline
87 & 68.3305239393678 & 65.7973753239 & 70.8636725548356 \tabularnewline
88 & 67.9473652524904 & 64.8750562038635 & 71.0196743011172 \tabularnewline
89 & 67.564206565613 & 63.9630253170125 & 71.1653878142135 \tabularnewline
90 & 67.1810478787356 & 63.052557380159 & 71.3095383773122 \tabularnewline
91 & 66.7978891918582 & 62.1388993304431 & 71.4568790532732 \tabularnewline
92 & 66.4147305049808 & 61.219243426288 & 71.6102175836735 \tabularnewline
93 & 66.0315718181034 & 60.2918459040096 & 71.7712977321972 \tabularnewline
94 & 65.648413131226 & 59.3555909754093 & 71.9412352870426 \tabularnewline
95 & 65.2652544443486 & 58.4097545547627 & 72.1207543339344 \tabularnewline
96 & 64.8820957574712 & 57.4538672252541 & 72.3103242896882 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232284&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]69.0968413131226[/C][C]67.7790318175173[/C][C]70.4146508087279[/C][/ROW]
[ROW][C]86[/C][C]68.7136826262452[/C][C]66.7483678843297[/C][C]70.6789973681607[/C][/ROW]
[ROW][C]87[/C][C]68.3305239393678[/C][C]65.7973753239[/C][C]70.8636725548356[/C][/ROW]
[ROW][C]88[/C][C]67.9473652524904[/C][C]64.8750562038635[/C][C]71.0196743011172[/C][/ROW]
[ROW][C]89[/C][C]67.564206565613[/C][C]63.9630253170125[/C][C]71.1653878142135[/C][/ROW]
[ROW][C]90[/C][C]67.1810478787356[/C][C]63.052557380159[/C][C]71.3095383773122[/C][/ROW]
[ROW][C]91[/C][C]66.7978891918582[/C][C]62.1388993304431[/C][C]71.4568790532732[/C][/ROW]
[ROW][C]92[/C][C]66.4147305049808[/C][C]61.219243426288[/C][C]71.6102175836735[/C][/ROW]
[ROW][C]93[/C][C]66.0315718181034[/C][C]60.2918459040096[/C][C]71.7712977321972[/C][/ROW]
[ROW][C]94[/C][C]65.648413131226[/C][C]59.3555909754093[/C][C]71.9412352870426[/C][/ROW]
[ROW][C]95[/C][C]65.2652544443486[/C][C]58.4097545547627[/C][C]72.1207543339344[/C][/ROW]
[ROW][C]96[/C][C]64.8820957574712[/C][C]57.4538672252541[/C][C]72.3103242896882[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232284&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232284&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 t Forecast 95% Lower Bound 95% Upper Bound 85 69.0968413131226 67.7790318175173 70.4146508087279 86 68.7136826262452 66.7483678843297 70.6789973681607 87 68.3305239393678 65.7973753239 70.8636725548356 88 67.9473652524904 64.8750562038635 71.0196743011172 89 67.564206565613 63.9630253170125 71.1653878142135 90 67.1810478787356 63.052557380159 71.3095383773122 91 66.7978891918582 62.1388993304431 71.4568790532732 92 66.4147305049808 61.219243426288 71.6102175836735 93 66.0315718181034 60.2918459040096 71.7712977321972 94 65.648413131226 59.3555909754093 71.9412352870426 95 65.2652544443486 58.4097545547627 72.1207543339344 96 64.8820957574712 57.4538672252541 72.3103242896882

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,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.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
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)