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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 Tue, 19 Nov 2019 08:23:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232284, Retrieved Tue, 19 Nov 2019 08:23:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact45
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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.106401285899114
gammaFALSE

\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
ParameterValue
alpha1
beta0.106401285899114
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3123.07124.79-1.72
4119.52121.876989788254-2.35698978825351
5118.03118.076203043932-0.0462030439322518
6117.27116.5812869806450.68871301935458
7117.27115.894566931521.37543306847979
8116.69116.0409147786750.649085221325379
9115.38115.529978280882-0.149978280881754
10114.31114.2040203989390.105979601061009
11113.33113.1452967647710.184703235229037
12111.79112.184949426509-0.394949426509044
13111.79110.6029262996631.18707370033663
14110.92110.7292324678360.190767532163775
15109.37109.879530378566-0.50953037856624
16107.04108.275315691082-1.23531569108214
17104.72105.81387651306-1.09387651305964
18104.14103.3774866454550.762513354544751
19104.14102.8786190468941.26138095310594
20102.95103.012831602313-0.0628316023131816
21102.13101.8161462390320.31385376096803
22101.01101.029540682783-0.0195406827832159
23100.0799.90746152900780.162538470992232
2499.498.98475583132940.415244168670611
2599.498.35893834483811.04106165516194
2699.3498.46970864364760.870291356352439
2797.7298.5023087630703-0.782308763070347
2896.2696.7990701047095-0.539070104709495
2995.7795.28171235237860.488287647621348
3095.0494.84366678597420.196333214025799
3195.0494.13455689241130.905443107588738
3294.5594.23089720336720.319102796632791
339493.77485015126290.225149848737075
3493.1493.2488063846885-0.108806384688549
3591.2192.3772292454436-1.16722924544365
3690.390.3230345527894-0.0230345527893832
3790.389.41058364675250.889416353247512
3889.7489.50521869043770.23478130956228
3989.0788.97019972368020.099800276319769
4089.0688.31081860141370.749181398586273
4188.9788.3805324655950.589467534404974
4288.7888.35325256925150.42674743074852
4388.7888.20865904463730.571340955362729
4488.2388.2694504569747-0.0394504569746914
4587.9187.71525287762330.194747122376711
4687.7987.41597422186930.374025778130701
4787.8987.33577104562180.554228954378161
488887.49474171905020.505258280949803
498887.65850184985440.341498150145569
5087.0887.6948376921621-0.614837692162084
5185.7586.7094181710968-0.9594181710968
5284.2985.2773348439771-0.987334843977109
5384.3983.7122811469650.677718853035046
5483.7283.884391304406-0.164391304405953
5583.7283.19689985822650.523100141773469
5681.7683.2525583859652-1.49255838596522
5781.5381.1337482544190.396251745580969
5880.5580.9459099496886-0.395909949688615
5979.8379.9237846219415-0.0937846219414951
6078.9879.1938058175694-0.213805817569352
6178.9878.32105660364730.65894339635274
6278.2778.3911690283539-0.121169028353933
6377.4177.6682764879259-0.258276487925926
6476.7576.7807955374931-0.0307955374930913
6576.3876.11751885270390.262481147296114
6674.9675.7754471843004-0.815447184300453
6774.9674.26868255530810.691317444691919
6874.4674.34223962038780.117760379612207
6974.0473.85476947620650.185230523793521
7073.2273.4544782421259-0.234478242125903
7172.9772.60952945564830.360470544351671
7272.9172.39788398509610.512116014903896
7372.9172.39237378761140.517626212388592
7473.2772.44744988222460.822550117775364
7572.9372.89497027247240.0350297275276006
7672.6772.5586974805260.111302519473952
7771.9472.3105402117219-0.370540211721888
7871.971.54111425671730.35888574328267
7971.8971.53930016129350.350699838706518
8071.7271.56661507509650.153384924903534
8170.8571.4129354283437-0.562935428343735
8269.8270.4830383748898-0.663038374889794
8369.6169.38249023920110.227509760798938
8469.4869.19669757030470.28330242969534

\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
tObservedFittedResiduals
3123.07124.79-1.72
4119.52121.876989788254-2.35698978825351
5118.03118.076203043932-0.0462030439322518
6117.27116.5812869806450.68871301935458
7117.27115.894566931521.37543306847979
8116.69116.0409147786750.649085221325379
9115.38115.529978280882-0.149978280881754
10114.31114.2040203989390.105979601061009
11113.33113.1452967647710.184703235229037
12111.79112.184949426509-0.394949426509044
13111.79110.6029262996631.18707370033663
14110.92110.7292324678360.190767532163775
15109.37109.879530378566-0.50953037856624
16107.04108.275315691082-1.23531569108214
17104.72105.81387651306-1.09387651305964
18104.14103.3774866454550.762513354544751
19104.14102.8786190468941.26138095310594
20102.95103.012831602313-0.0628316023131816
21102.13101.8161462390320.31385376096803
22101.01101.029540682783-0.0195406827832159
23100.0799.90746152900780.162538470992232
2499.498.98475583132940.415244168670611
2599.498.35893834483811.04106165516194
2699.3498.46970864364760.870291356352439
2797.7298.5023087630703-0.782308763070347
2896.2696.7990701047095-0.539070104709495
2995.7795.28171235237860.488287647621348
3095.0494.84366678597420.196333214025799
3195.0494.13455689241130.905443107588738
3294.5594.23089720336720.319102796632791
339493.77485015126290.225149848737075
3493.1493.2488063846885-0.108806384688549
3591.2192.3772292454436-1.16722924544365
3690.390.3230345527894-0.0230345527893832
3790.389.41058364675250.889416353247512
3889.7489.50521869043770.23478130956228
3989.0788.97019972368020.099800276319769
4089.0688.31081860141370.749181398586273
4188.9788.3805324655950.589467534404974
4288.7888.35325256925150.42674743074852
4388.7888.20865904463730.571340955362729
4488.2388.2694504569747-0.0394504569746914
4587.9187.71525287762330.194747122376711
4687.7987.41597422186930.374025778130701
4787.8987.33577104562180.554228954378161
488887.49474171905020.505258280949803
498887.65850184985440.341498150145569
5087.0887.6948376921621-0.614837692162084
5185.7586.7094181710968-0.9594181710968
5284.2985.2773348439771-0.987334843977109
5384.3983.7122811469650.677718853035046
5483.7283.884391304406-0.164391304405953
5583.7283.19689985822650.523100141773469
5681.7683.2525583859652-1.49255838596522
5781.5381.1337482544190.396251745580969
5880.5580.9459099496886-0.395909949688615
5979.8379.9237846219415-0.0937846219414951
6078.9879.1938058175694-0.213805817569352
6178.9878.32105660364730.65894339635274
6278.2778.3911690283539-0.121169028353933
6377.4177.6682764879259-0.258276487925926
6476.7576.7807955374931-0.0307955374930913
6576.3876.11751885270390.262481147296114
6674.9675.7754471843004-0.815447184300453
6774.9674.26868255530810.691317444691919
6874.4674.34223962038780.117760379612207
6974.0473.85476947620650.185230523793521
7073.2273.4544782421259-0.234478242125903
7172.9772.60952945564830.360470544351671
7272.9172.39788398509610.512116014903896
7372.9172.39237378761140.517626212388592
7473.2772.44744988222460.822550117775364
7572.9372.89497027247240.0350297275276006
7672.6772.5586974805260.111302519473952
7771.9472.3105402117219-0.370540211721888
7871.971.54111425671730.35888574328267
7971.8971.53930016129350.350699838706518
8071.7271.56661507509650.153384924903534
8170.8571.4129354283437-0.562935428343735
8269.8270.4830383748898-0.663038374889794
8369.6169.38249023920110.227509760798938
8469.4869.19669757030470.28330242969534







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8569.096841313122667.779031817517370.4146508087279
8668.713682626245266.748367884329770.6789973681607
8768.330523939367865.797375323970.8636725548356
8867.947365252490464.875056203863571.0196743011172
8967.56420656561363.963025317012571.1653878142135
9067.181047878735663.05255738015971.3095383773122
9166.797889191858262.138899330443171.4568790532732
9266.414730504980861.21924342628871.6102175836735
9366.031571818103460.291845904009671.7712977321972
9465.64841313122659.355590975409371.9412352870426
9565.265254444348658.409754554762772.1207543339344
9664.882095757471257.453867225254172.3103242896882

\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
tForecast95% Lower Bound95% Upper Bound
8569.096841313122667.779031817517370.4146508087279
8668.713682626245266.748367884329770.6789973681607
8768.330523939367865.797375323970.8636725548356
8867.947365252490464.875056203863571.0196743011172
8967.56420656561363.963025317012571.1653878142135
9067.181047878735663.05255738015971.3095383773122
9166.797889191858262.138899330443171.4568790532732
9266.414730504980861.21924342628871.6102175836735
9366.031571818103460.291845904009671.7712977321972
9465.64841313122659.355590975409371.9412352870426
9565.265254444348658.409754554762772.1207543339344
9664.882095757471257.453867225254172.3103242896882



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,'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')