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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 23 Nov 2012 16:53:38 -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/2012/Nov/23/t1353707657kdjxifxht6v6w08.htm/, Retrieved Tue, 30 Apr 2024 06:23:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=192298, Retrieved Tue, 30 Apr 2024 06:23:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
- RM D  [Exponential Smoothing] [ws8] [2012-11-23 21:24:16] [74be16979710d4c4e7c6647856088456]
- R P       [Exponential Smoothing] [ws8] [2012-11-23 21:53:38] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-             [Exponential Smoothing] [ws8] [2012-11-23 22:00:51] [74be16979710d4c4e7c6647856088456]
-   PD          [Exponential Smoothing] [Deel 4: tijdreeks...] [2012-12-18 19:07:23] [5e6119a0aa181aac6bb71d6b937f8665]
-    D        [Exponential Smoothing] [Deel 4: tijdreeks...] [2012-12-18 19:07:09] [5e6119a0aa181aac6bb71d6b937f8665]
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Dataseries X:
88.1
101.7
114.8
103.4
96.4
110
71.1
79.4
119.2
99.1
113.2
103.6
97.5
102.4
120.8
89.5
101.7
112.5
72.4
84.7
117.2
112.8
111.3
102.3
95.2
103
116.4
95.1
100.7
112.4
75.3
93.3
118.6
118.7
110.7
113.3
89.5
106.3
115.1
105.7
95.8
114.7
79.6
80.6
125
127.5
99.5
104.3
90
96
108.9
95.8
87.2
108.4
74.9
80.8
119.1
107.9
106.9
96.8
93.7
95.2
112.7
98.5
91.5
112
76.7
84.7
114.9
108.4
104.6
111.3
90.8
109.1
121
95.2
110.5
102.4
86.7
99.1
126
110.3
104.6
103.1
102




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192298&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192298&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192298&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.355246105637169
beta0.225624128865559
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.355246105637169 \tabularnewline
beta & 0.225624128865559 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192298&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]0.355246105637169[/C][/ROW]
[ROW][C]beta[/C][C]0.225624128865559[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192298&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192298&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
alpha0.355246105637169
beta0.225624128865559
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3114.8115.3-0.500000000000014
4103.4128.682300900623-25.2823009006228
596.4131.234356581565-34.8343565815653
6110127.601035088618-17.6010350886178
771.1128.67902413985-57.57902413985
879.4110.939908964968-31.5399089649679
9119.299.923098329930119.2769016700699
1099.1108.503845791563-9.40384579156283
11113.2106.1421314871427.05786851285839
12103.6110.19408001573-6.5940800157298
1397.5108.867697679734-11.3676976797344
14102.4104.934361495846-2.53436149584559
15120.8103.93589921245916.8641007875407
1689.5111.180358087258-21.6803580872575
17101.7102.994321972666-1.294321972666
18112.5101.94660318188510.553396818115
1972.4105.953617196682-33.5536171966823
2084.791.6023936014691-6.9023936014691
21117.286.165672104243931.0343278957561
22112.896.693289518882316.1067104811177
23111.3103.2089155388248.09108446117578
24102.3107.52553898609-5.22553898608969
2595.2106.692645926076-11.4926459260765
26103102.7122279055910.287772094409362
27116.4102.93982304536813.460176954632
2895.1108.925725070258-13.8257250702581
29100.7104.110255858764-3.41025585876355
30112.4102.7215023778919.67849762210903
3175.3106.758229441386-31.4582294413859
3293.393.6598514814247-0.359851481424698
33118.691.58020833392527.019791666075
34118.7101.39276964593817.3072303540616
35110.7109.1421921150381.55780788496247
36113.3111.4215551486091.87844485139097
3789.5113.965384502472-24.4653845024719
38106.3105.1897192940131.11028070598707
39115.1105.5887008724729.51129912752836
40105.7109.734462061905-4.03446206190485
4195.8108.744773762037-12.9447737620369
42114.7103.55218121872711.147818781273
4379.6107.811909360142-28.2119093601421
4480.695.8280037743317-15.2280037743317
4512587.236023707330837.7639762926692
46127.5100.49609993342327.0039000665772
4799.5112.098120096502-12.5981200965022
48104.3108.621911126206-4.32191112620568
4990107.739382939014-17.7393829390142
5096100.668501469655-4.66850146965523
51108.997.866809575017211.0331904249828
5295.8101.527415884188-5.72741588418776
5387.298.774817702637-11.574817702637
54108.493.017206930669315.3827930693307
5574.998.0691454652223-23.1691454652223
5680.887.5686024658359-6.7686024658359
57119.182.35177084220136.748229157799
58107.995.539571667881412.3604283321186
59106.9101.0544154278295.84558457217081
6096.8104.723422152174-7.92342215217444
6193.7102.865963989056-9.16596398905551
6295.299.832426478133-4.63242647813303
63112.798.038111834291614.6618881657084
6498.5104.273208354146-5.77320835414582
6591.5102.786081683415-11.2860816834153
6611298.435925161572613.5640748384274
6776.7104.000878958088-27.3008789580878
6884.792.8604944689162-8.16049446891623
69114.987.865576317365427.0344236826346
70108.497.540381421754110.8596185782459
71104.6102.339571162872.26042883712984
72111.3104.2651103394587.03488966054179
7390.8108.450619261222-17.650619261222
74109.1102.4519631942556.64803680574525
75121105.61816413239615.3818358676043
7695.2113.119899515454-17.9198995154544
77110.5107.3550056381073.14499436189284
78102.4109.325411157295-6.92541115729549
7986.7107.16325813365-20.4632581336502
8099.198.55166472153190.548335278468045
8112697.448308262599628.5516917374004
82110.3108.5815129852641.71848701473597
83104.6110.320066559663-5.720066559663
84103.1108.957627637656-5.85762763765619
85102107.076819562545-5.07681956254534

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 114.8 & 115.3 & -0.500000000000014 \tabularnewline
4 & 103.4 & 128.682300900623 & -25.2823009006228 \tabularnewline
5 & 96.4 & 131.234356581565 & -34.8343565815653 \tabularnewline
6 & 110 & 127.601035088618 & -17.6010350886178 \tabularnewline
7 & 71.1 & 128.67902413985 & -57.57902413985 \tabularnewline
8 & 79.4 & 110.939908964968 & -31.5399089649679 \tabularnewline
9 & 119.2 & 99.9230983299301 & 19.2769016700699 \tabularnewline
10 & 99.1 & 108.503845791563 & -9.40384579156283 \tabularnewline
11 & 113.2 & 106.142131487142 & 7.05786851285839 \tabularnewline
12 & 103.6 & 110.19408001573 & -6.5940800157298 \tabularnewline
13 & 97.5 & 108.867697679734 & -11.3676976797344 \tabularnewline
14 & 102.4 & 104.934361495846 & -2.53436149584559 \tabularnewline
15 & 120.8 & 103.935899212459 & 16.8641007875407 \tabularnewline
16 & 89.5 & 111.180358087258 & -21.6803580872575 \tabularnewline
17 & 101.7 & 102.994321972666 & -1.294321972666 \tabularnewline
18 & 112.5 & 101.946603181885 & 10.553396818115 \tabularnewline
19 & 72.4 & 105.953617196682 & -33.5536171966823 \tabularnewline
20 & 84.7 & 91.6023936014691 & -6.9023936014691 \tabularnewline
21 & 117.2 & 86.1656721042439 & 31.0343278957561 \tabularnewline
22 & 112.8 & 96.6932895188823 & 16.1067104811177 \tabularnewline
23 & 111.3 & 103.208915538824 & 8.09108446117578 \tabularnewline
24 & 102.3 & 107.52553898609 & -5.22553898608969 \tabularnewline
25 & 95.2 & 106.692645926076 & -11.4926459260765 \tabularnewline
26 & 103 & 102.712227905591 & 0.287772094409362 \tabularnewline
27 & 116.4 & 102.939823045368 & 13.460176954632 \tabularnewline
28 & 95.1 & 108.925725070258 & -13.8257250702581 \tabularnewline
29 & 100.7 & 104.110255858764 & -3.41025585876355 \tabularnewline
30 & 112.4 & 102.721502377891 & 9.67849762210903 \tabularnewline
31 & 75.3 & 106.758229441386 & -31.4582294413859 \tabularnewline
32 & 93.3 & 93.6598514814247 & -0.359851481424698 \tabularnewline
33 & 118.6 & 91.580208333925 & 27.019791666075 \tabularnewline
34 & 118.7 & 101.392769645938 & 17.3072303540616 \tabularnewline
35 & 110.7 & 109.142192115038 & 1.55780788496247 \tabularnewline
36 & 113.3 & 111.421555148609 & 1.87844485139097 \tabularnewline
37 & 89.5 & 113.965384502472 & -24.4653845024719 \tabularnewline
38 & 106.3 & 105.189719294013 & 1.11028070598707 \tabularnewline
39 & 115.1 & 105.588700872472 & 9.51129912752836 \tabularnewline
40 & 105.7 & 109.734462061905 & -4.03446206190485 \tabularnewline
41 & 95.8 & 108.744773762037 & -12.9447737620369 \tabularnewline
42 & 114.7 & 103.552181218727 & 11.147818781273 \tabularnewline
43 & 79.6 & 107.811909360142 & -28.2119093601421 \tabularnewline
44 & 80.6 & 95.8280037743317 & -15.2280037743317 \tabularnewline
45 & 125 & 87.2360237073308 & 37.7639762926692 \tabularnewline
46 & 127.5 & 100.496099933423 & 27.0039000665772 \tabularnewline
47 & 99.5 & 112.098120096502 & -12.5981200965022 \tabularnewline
48 & 104.3 & 108.621911126206 & -4.32191112620568 \tabularnewline
49 & 90 & 107.739382939014 & -17.7393829390142 \tabularnewline
50 & 96 & 100.668501469655 & -4.66850146965523 \tabularnewline
51 & 108.9 & 97.8668095750172 & 11.0331904249828 \tabularnewline
52 & 95.8 & 101.527415884188 & -5.72741588418776 \tabularnewline
53 & 87.2 & 98.774817702637 & -11.574817702637 \tabularnewline
54 & 108.4 & 93.0172069306693 & 15.3827930693307 \tabularnewline
55 & 74.9 & 98.0691454652223 & -23.1691454652223 \tabularnewline
56 & 80.8 & 87.5686024658359 & -6.7686024658359 \tabularnewline
57 & 119.1 & 82.351770842201 & 36.748229157799 \tabularnewline
58 & 107.9 & 95.5395716678814 & 12.3604283321186 \tabularnewline
59 & 106.9 & 101.054415427829 & 5.84558457217081 \tabularnewline
60 & 96.8 & 104.723422152174 & -7.92342215217444 \tabularnewline
61 & 93.7 & 102.865963989056 & -9.16596398905551 \tabularnewline
62 & 95.2 & 99.832426478133 & -4.63242647813303 \tabularnewline
63 & 112.7 & 98.0381118342916 & 14.6618881657084 \tabularnewline
64 & 98.5 & 104.273208354146 & -5.77320835414582 \tabularnewline
65 & 91.5 & 102.786081683415 & -11.2860816834153 \tabularnewline
66 & 112 & 98.4359251615726 & 13.5640748384274 \tabularnewline
67 & 76.7 & 104.000878958088 & -27.3008789580878 \tabularnewline
68 & 84.7 & 92.8604944689162 & -8.16049446891623 \tabularnewline
69 & 114.9 & 87.8655763173654 & 27.0344236826346 \tabularnewline
70 & 108.4 & 97.5403814217541 & 10.8596185782459 \tabularnewline
71 & 104.6 & 102.33957116287 & 2.26042883712984 \tabularnewline
72 & 111.3 & 104.265110339458 & 7.03488966054179 \tabularnewline
73 & 90.8 & 108.450619261222 & -17.650619261222 \tabularnewline
74 & 109.1 & 102.451963194255 & 6.64803680574525 \tabularnewline
75 & 121 & 105.618164132396 & 15.3818358676043 \tabularnewline
76 & 95.2 & 113.119899515454 & -17.9198995154544 \tabularnewline
77 & 110.5 & 107.355005638107 & 3.14499436189284 \tabularnewline
78 & 102.4 & 109.325411157295 & -6.92541115729549 \tabularnewline
79 & 86.7 & 107.16325813365 & -20.4632581336502 \tabularnewline
80 & 99.1 & 98.5516647215319 & 0.548335278468045 \tabularnewline
81 & 126 & 97.4483082625996 & 28.5516917374004 \tabularnewline
82 & 110.3 & 108.581512985264 & 1.71848701473597 \tabularnewline
83 & 104.6 & 110.320066559663 & -5.720066559663 \tabularnewline
84 & 103.1 & 108.957627637656 & -5.85762763765619 \tabularnewline
85 & 102 & 107.076819562545 & -5.07681956254534 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192298&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]114.8[/C][C]115.3[/C][C]-0.500000000000014[/C][/ROW]
[ROW][C]4[/C][C]103.4[/C][C]128.682300900623[/C][C]-25.2823009006228[/C][/ROW]
[ROW][C]5[/C][C]96.4[/C][C]131.234356581565[/C][C]-34.8343565815653[/C][/ROW]
[ROW][C]6[/C][C]110[/C][C]127.601035088618[/C][C]-17.6010350886178[/C][/ROW]
[ROW][C]7[/C][C]71.1[/C][C]128.67902413985[/C][C]-57.57902413985[/C][/ROW]
[ROW][C]8[/C][C]79.4[/C][C]110.939908964968[/C][C]-31.5399089649679[/C][/ROW]
[ROW][C]9[/C][C]119.2[/C][C]99.9230983299301[/C][C]19.2769016700699[/C][/ROW]
[ROW][C]10[/C][C]99.1[/C][C]108.503845791563[/C][C]-9.40384579156283[/C][/ROW]
[ROW][C]11[/C][C]113.2[/C][C]106.142131487142[/C][C]7.05786851285839[/C][/ROW]
[ROW][C]12[/C][C]103.6[/C][C]110.19408001573[/C][C]-6.5940800157298[/C][/ROW]
[ROW][C]13[/C][C]97.5[/C][C]108.867697679734[/C][C]-11.3676976797344[/C][/ROW]
[ROW][C]14[/C][C]102.4[/C][C]104.934361495846[/C][C]-2.53436149584559[/C][/ROW]
[ROW][C]15[/C][C]120.8[/C][C]103.935899212459[/C][C]16.8641007875407[/C][/ROW]
[ROW][C]16[/C][C]89.5[/C][C]111.180358087258[/C][C]-21.6803580872575[/C][/ROW]
[ROW][C]17[/C][C]101.7[/C][C]102.994321972666[/C][C]-1.294321972666[/C][/ROW]
[ROW][C]18[/C][C]112.5[/C][C]101.946603181885[/C][C]10.553396818115[/C][/ROW]
[ROW][C]19[/C][C]72.4[/C][C]105.953617196682[/C][C]-33.5536171966823[/C][/ROW]
[ROW][C]20[/C][C]84.7[/C][C]91.6023936014691[/C][C]-6.9023936014691[/C][/ROW]
[ROW][C]21[/C][C]117.2[/C][C]86.1656721042439[/C][C]31.0343278957561[/C][/ROW]
[ROW][C]22[/C][C]112.8[/C][C]96.6932895188823[/C][C]16.1067104811177[/C][/ROW]
[ROW][C]23[/C][C]111.3[/C][C]103.208915538824[/C][C]8.09108446117578[/C][/ROW]
[ROW][C]24[/C][C]102.3[/C][C]107.52553898609[/C][C]-5.22553898608969[/C][/ROW]
[ROW][C]25[/C][C]95.2[/C][C]106.692645926076[/C][C]-11.4926459260765[/C][/ROW]
[ROW][C]26[/C][C]103[/C][C]102.712227905591[/C][C]0.287772094409362[/C][/ROW]
[ROW][C]27[/C][C]116.4[/C][C]102.939823045368[/C][C]13.460176954632[/C][/ROW]
[ROW][C]28[/C][C]95.1[/C][C]108.925725070258[/C][C]-13.8257250702581[/C][/ROW]
[ROW][C]29[/C][C]100.7[/C][C]104.110255858764[/C][C]-3.41025585876355[/C][/ROW]
[ROW][C]30[/C][C]112.4[/C][C]102.721502377891[/C][C]9.67849762210903[/C][/ROW]
[ROW][C]31[/C][C]75.3[/C][C]106.758229441386[/C][C]-31.4582294413859[/C][/ROW]
[ROW][C]32[/C][C]93.3[/C][C]93.6598514814247[/C][C]-0.359851481424698[/C][/ROW]
[ROW][C]33[/C][C]118.6[/C][C]91.580208333925[/C][C]27.019791666075[/C][/ROW]
[ROW][C]34[/C][C]118.7[/C][C]101.392769645938[/C][C]17.3072303540616[/C][/ROW]
[ROW][C]35[/C][C]110.7[/C][C]109.142192115038[/C][C]1.55780788496247[/C][/ROW]
[ROW][C]36[/C][C]113.3[/C][C]111.421555148609[/C][C]1.87844485139097[/C][/ROW]
[ROW][C]37[/C][C]89.5[/C][C]113.965384502472[/C][C]-24.4653845024719[/C][/ROW]
[ROW][C]38[/C][C]106.3[/C][C]105.189719294013[/C][C]1.11028070598707[/C][/ROW]
[ROW][C]39[/C][C]115.1[/C][C]105.588700872472[/C][C]9.51129912752836[/C][/ROW]
[ROW][C]40[/C][C]105.7[/C][C]109.734462061905[/C][C]-4.03446206190485[/C][/ROW]
[ROW][C]41[/C][C]95.8[/C][C]108.744773762037[/C][C]-12.9447737620369[/C][/ROW]
[ROW][C]42[/C][C]114.7[/C][C]103.552181218727[/C][C]11.147818781273[/C][/ROW]
[ROW][C]43[/C][C]79.6[/C][C]107.811909360142[/C][C]-28.2119093601421[/C][/ROW]
[ROW][C]44[/C][C]80.6[/C][C]95.8280037743317[/C][C]-15.2280037743317[/C][/ROW]
[ROW][C]45[/C][C]125[/C][C]87.2360237073308[/C][C]37.7639762926692[/C][/ROW]
[ROW][C]46[/C][C]127.5[/C][C]100.496099933423[/C][C]27.0039000665772[/C][/ROW]
[ROW][C]47[/C][C]99.5[/C][C]112.098120096502[/C][C]-12.5981200965022[/C][/ROW]
[ROW][C]48[/C][C]104.3[/C][C]108.621911126206[/C][C]-4.32191112620568[/C][/ROW]
[ROW][C]49[/C][C]90[/C][C]107.739382939014[/C][C]-17.7393829390142[/C][/ROW]
[ROW][C]50[/C][C]96[/C][C]100.668501469655[/C][C]-4.66850146965523[/C][/ROW]
[ROW][C]51[/C][C]108.9[/C][C]97.8668095750172[/C][C]11.0331904249828[/C][/ROW]
[ROW][C]52[/C][C]95.8[/C][C]101.527415884188[/C][C]-5.72741588418776[/C][/ROW]
[ROW][C]53[/C][C]87.2[/C][C]98.774817702637[/C][C]-11.574817702637[/C][/ROW]
[ROW][C]54[/C][C]108.4[/C][C]93.0172069306693[/C][C]15.3827930693307[/C][/ROW]
[ROW][C]55[/C][C]74.9[/C][C]98.0691454652223[/C][C]-23.1691454652223[/C][/ROW]
[ROW][C]56[/C][C]80.8[/C][C]87.5686024658359[/C][C]-6.7686024658359[/C][/ROW]
[ROW][C]57[/C][C]119.1[/C][C]82.351770842201[/C][C]36.748229157799[/C][/ROW]
[ROW][C]58[/C][C]107.9[/C][C]95.5395716678814[/C][C]12.3604283321186[/C][/ROW]
[ROW][C]59[/C][C]106.9[/C][C]101.054415427829[/C][C]5.84558457217081[/C][/ROW]
[ROW][C]60[/C][C]96.8[/C][C]104.723422152174[/C][C]-7.92342215217444[/C][/ROW]
[ROW][C]61[/C][C]93.7[/C][C]102.865963989056[/C][C]-9.16596398905551[/C][/ROW]
[ROW][C]62[/C][C]95.2[/C][C]99.832426478133[/C][C]-4.63242647813303[/C][/ROW]
[ROW][C]63[/C][C]112.7[/C][C]98.0381118342916[/C][C]14.6618881657084[/C][/ROW]
[ROW][C]64[/C][C]98.5[/C][C]104.273208354146[/C][C]-5.77320835414582[/C][/ROW]
[ROW][C]65[/C][C]91.5[/C][C]102.786081683415[/C][C]-11.2860816834153[/C][/ROW]
[ROW][C]66[/C][C]112[/C][C]98.4359251615726[/C][C]13.5640748384274[/C][/ROW]
[ROW][C]67[/C][C]76.7[/C][C]104.000878958088[/C][C]-27.3008789580878[/C][/ROW]
[ROW][C]68[/C][C]84.7[/C][C]92.8604944689162[/C][C]-8.16049446891623[/C][/ROW]
[ROW][C]69[/C][C]114.9[/C][C]87.8655763173654[/C][C]27.0344236826346[/C][/ROW]
[ROW][C]70[/C][C]108.4[/C][C]97.5403814217541[/C][C]10.8596185782459[/C][/ROW]
[ROW][C]71[/C][C]104.6[/C][C]102.33957116287[/C][C]2.26042883712984[/C][/ROW]
[ROW][C]72[/C][C]111.3[/C][C]104.265110339458[/C][C]7.03488966054179[/C][/ROW]
[ROW][C]73[/C][C]90.8[/C][C]108.450619261222[/C][C]-17.650619261222[/C][/ROW]
[ROW][C]74[/C][C]109.1[/C][C]102.451963194255[/C][C]6.64803680574525[/C][/ROW]
[ROW][C]75[/C][C]121[/C][C]105.618164132396[/C][C]15.3818358676043[/C][/ROW]
[ROW][C]76[/C][C]95.2[/C][C]113.119899515454[/C][C]-17.9198995154544[/C][/ROW]
[ROW][C]77[/C][C]110.5[/C][C]107.355005638107[/C][C]3.14499436189284[/C][/ROW]
[ROW][C]78[/C][C]102.4[/C][C]109.325411157295[/C][C]-6.92541115729549[/C][/ROW]
[ROW][C]79[/C][C]86.7[/C][C]107.16325813365[/C][C]-20.4632581336502[/C][/ROW]
[ROW][C]80[/C][C]99.1[/C][C]98.5516647215319[/C][C]0.548335278468045[/C][/ROW]
[ROW][C]81[/C][C]126[/C][C]97.4483082625996[/C][C]28.5516917374004[/C][/ROW]
[ROW][C]82[/C][C]110.3[/C][C]108.581512985264[/C][C]1.71848701473597[/C][/ROW]
[ROW][C]83[/C][C]104.6[/C][C]110.320066559663[/C][C]-5.720066559663[/C][/ROW]
[ROW][C]84[/C][C]103.1[/C][C]108.957627637656[/C][C]-5.85762763765619[/C][/ROW]
[ROW][C]85[/C][C]102[/C][C]107.076819562545[/C][C]-5.07681956254534[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192298&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192298&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
3114.8115.3-0.500000000000014
4103.4128.682300900623-25.2823009006228
596.4131.234356581565-34.8343565815653
6110127.601035088618-17.6010350886178
771.1128.67902413985-57.57902413985
879.4110.939908964968-31.5399089649679
9119.299.923098329930119.2769016700699
1099.1108.503845791563-9.40384579156283
11113.2106.1421314871427.05786851285839
12103.6110.19408001573-6.5940800157298
1397.5108.867697679734-11.3676976797344
14102.4104.934361495846-2.53436149584559
15120.8103.93589921245916.8641007875407
1689.5111.180358087258-21.6803580872575
17101.7102.994321972666-1.294321972666
18112.5101.94660318188510.553396818115
1972.4105.953617196682-33.5536171966823
2084.791.6023936014691-6.9023936014691
21117.286.165672104243931.0343278957561
22112.896.693289518882316.1067104811177
23111.3103.2089155388248.09108446117578
24102.3107.52553898609-5.22553898608969
2595.2106.692645926076-11.4926459260765
26103102.7122279055910.287772094409362
27116.4102.93982304536813.460176954632
2895.1108.925725070258-13.8257250702581
29100.7104.110255858764-3.41025585876355
30112.4102.7215023778919.67849762210903
3175.3106.758229441386-31.4582294413859
3293.393.6598514814247-0.359851481424698
33118.691.58020833392527.019791666075
34118.7101.39276964593817.3072303540616
35110.7109.1421921150381.55780788496247
36113.3111.4215551486091.87844485139097
3789.5113.965384502472-24.4653845024719
38106.3105.1897192940131.11028070598707
39115.1105.5887008724729.51129912752836
40105.7109.734462061905-4.03446206190485
4195.8108.744773762037-12.9447737620369
42114.7103.55218121872711.147818781273
4379.6107.811909360142-28.2119093601421
4480.695.8280037743317-15.2280037743317
4512587.236023707330837.7639762926692
46127.5100.49609993342327.0039000665772
4799.5112.098120096502-12.5981200965022
48104.3108.621911126206-4.32191112620568
4990107.739382939014-17.7393829390142
5096100.668501469655-4.66850146965523
51108.997.866809575017211.0331904249828
5295.8101.527415884188-5.72741588418776
5387.298.774817702637-11.574817702637
54108.493.017206930669315.3827930693307
5574.998.0691454652223-23.1691454652223
5680.887.5686024658359-6.7686024658359
57119.182.35177084220136.748229157799
58107.995.539571667881412.3604283321186
59106.9101.0544154278295.84558457217081
6096.8104.723422152174-7.92342215217444
6193.7102.865963989056-9.16596398905551
6295.299.832426478133-4.63242647813303
63112.798.038111834291614.6618881657084
6498.5104.273208354146-5.77320835414582
6591.5102.786081683415-11.2860816834153
6611298.435925161572613.5640748384274
6776.7104.000878958088-27.3008789580878
6884.792.8604944689162-8.16049446891623
69114.987.865576317365427.0344236826346
70108.497.540381421754110.8596185782459
71104.6102.339571162872.26042883712984
72111.3104.2651103394587.03488966054179
7390.8108.450619261222-17.650619261222
74109.1102.4519631942556.64803680574525
75121105.61816413239615.3818358676043
7695.2113.119899515454-17.9198995154544
77110.5107.3550056381073.14499436189284
78102.4109.325411157295-6.92541115729549
7986.7107.16325813365-20.4632581336502
8099.198.55166472153190.548335278468045
8112697.448308262599628.5516917374004
82110.3108.5815129852641.71848701473597
83104.6110.320066559663-5.720066559663
84103.1108.957627637656-5.85762763765619
85102107.076819562545-5.07681956254534







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
86105.06647280105170.9257391018018139.2072065003
87104.85964641817367.6232073900714142.096085446275
88104.65282003529663.4659661987051145.839673871887
89104.44599365241858.5114789496276150.380508355209
90104.23916726954152.8349178475851155.643416691497
91104.03234088666346.5120408788718161.552640894455
92103.82551450378639.6108733765126168.040155631059
93103.61868812090832.1891504207559175.048225821061
94103.41186173803124.2946233704422182.529100105619
95103.20503535515315.9664422971382190.443628413168
96102.9982089722767.23673800085476198.759679943697
97102.791382589398-1.86794737973227207.450712558529

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 105.066472801051 & 70.9257391018018 & 139.2072065003 \tabularnewline
87 & 104.859646418173 & 67.6232073900714 & 142.096085446275 \tabularnewline
88 & 104.652820035296 & 63.4659661987051 & 145.839673871887 \tabularnewline
89 & 104.445993652418 & 58.5114789496276 & 150.380508355209 \tabularnewline
90 & 104.239167269541 & 52.8349178475851 & 155.643416691497 \tabularnewline
91 & 104.032340886663 & 46.5120408788718 & 161.552640894455 \tabularnewline
92 & 103.825514503786 & 39.6108733765126 & 168.040155631059 \tabularnewline
93 & 103.618688120908 & 32.1891504207559 & 175.048225821061 \tabularnewline
94 & 103.411861738031 & 24.2946233704422 & 182.529100105619 \tabularnewline
95 & 103.205035355153 & 15.9664422971382 & 190.443628413168 \tabularnewline
96 & 102.998208972276 & 7.23673800085476 & 198.759679943697 \tabularnewline
97 & 102.791382589398 & -1.86794737973227 & 207.450712558529 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192298&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]86[/C][C]105.066472801051[/C][C]70.9257391018018[/C][C]139.2072065003[/C][/ROW]
[ROW][C]87[/C][C]104.859646418173[/C][C]67.6232073900714[/C][C]142.096085446275[/C][/ROW]
[ROW][C]88[/C][C]104.652820035296[/C][C]63.4659661987051[/C][C]145.839673871887[/C][/ROW]
[ROW][C]89[/C][C]104.445993652418[/C][C]58.5114789496276[/C][C]150.380508355209[/C][/ROW]
[ROW][C]90[/C][C]104.239167269541[/C][C]52.8349178475851[/C][C]155.643416691497[/C][/ROW]
[ROW][C]91[/C][C]104.032340886663[/C][C]46.5120408788718[/C][C]161.552640894455[/C][/ROW]
[ROW][C]92[/C][C]103.825514503786[/C][C]39.6108733765126[/C][C]168.040155631059[/C][/ROW]
[ROW][C]93[/C][C]103.618688120908[/C][C]32.1891504207559[/C][C]175.048225821061[/C][/ROW]
[ROW][C]94[/C][C]103.411861738031[/C][C]24.2946233704422[/C][C]182.529100105619[/C][/ROW]
[ROW][C]95[/C][C]103.205035355153[/C][C]15.9664422971382[/C][C]190.443628413168[/C][/ROW]
[ROW][C]96[/C][C]102.998208972276[/C][C]7.23673800085476[/C][C]198.759679943697[/C][/ROW]
[ROW][C]97[/C][C]102.791382589398[/C][C]-1.86794737973227[/C][C]207.450712558529[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192298&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192298&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
86105.06647280105170.9257391018018139.2072065003
87104.85964641817367.6232073900714142.096085446275
88104.65282003529663.4659661987051145.839673871887
89104.44599365241858.5114789496276150.380508355209
90104.23916726954152.8349178475851155.643416691497
91104.03234088666346.5120408788718161.552640894455
92103.82551450378639.6108733765126168.040155631059
93103.61868812090832.1891504207559175.048225821061
94103.41186173803124.2946233704422182.529100105619
95103.20503535515315.9664422971382190.443628413168
96102.9982089722767.23673800085476198.759679943697
97102.791382589398-1.86794737973227207.450712558529



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')