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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 14 Dec 2013 12:13:57 -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/14/t1387041261e9h058yx0wq7nv2.htm/, Retrieved Fri, 29 Mar 2024 11:12:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232328, Retrieved Fri, 29 Mar 2024 11:12:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-14 17:13:57] [cbeaf4c3f774367e9472b81246022ded] [Current]
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Dataseries X:
86,5
86,6
98,8
84,4
91,4
95,7
78,5
81,7
94,3
98,5
95,4
91,7
92,8
90,6
102,2
91,8
95
102
88,9
89,6
97,9
108,6
100,8
95,1
101
100,9
102,5
105,4
98,4
105,3
96,5
88,1
107,9
107,1
92,5
95,7
85,2
85,5
94,7
86,2
88,8
93,4
83,4
82,9
96,7
96,2
92,8
92,8
90,2
95,9
107,5
98
95
108,5
91,8
91,7
108,3
105,1
104,8
103,2
98,6
102,4
121,2
102,6
108,9
105,5
90,8
99,6
111,6
104,7
103,1
101,7
98,8
101,4
114,2
96,9
98,3
104,8
94,4
94,5
102,4
105,5
101,2
99,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232328&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232328&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232328&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.238639444547544
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.238639444547544 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232328&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]0.238639444547544[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232328&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232328&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
alpha0.238639444547544
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
286.686.50.0999999999999943
398.886.523863944454812.2761360555452
484.489.4534342339402-5.05343423394015
591.488.24748549529513.15251450470487
695.788.9997998056266.70020019437402
778.590.5987318583688-12.0987318583688
881.787.711497207958-6.01149720795796
994.386.27691685335188.02308314664823
1098.588.191540959026710.3084590409733
1195.490.65154589870564.74845410129436
1291.791.784714347898-0.0847143478980428
1392.891.76449816297051.03550183702954
1490.692.0116097461871-1.41160974618715
15102.291.674743980439110.5252560195609
1691.894.1864852306678-2.38648523066784
179593.61697572080041.38302427919965
1810293.94701986658438.05298013341567
1988.995.8687785725751-6.96877857257505
2089.694.2057531248409-4.60575312484092
2197.993.10663875740584.79336124259424
22108.694.250523821854214.3494761781458
23100.897.67487484655513.12512515344488
2495.198.4206529773148-3.32065297731477
2510197.62821419527323.37178580472678
26100.998.43285528684652.4671447131535
27102.599.02161333081193.47838666918814
28105.499.85169359346855.54830640653151
2998.4101.175738352503-2.77573835250276
30105.3100.5133376938524.7866623061478
3196.5101.655624127828-5.15562412782798
3288.1100.425288849667-12.3252888496672
33107.997.483988764694610.4160112353054
34107.199.96965990028887.13034009971115
3592.5101.671240301119-9.171240301119
3695.799.4826206098479-3.78262060984791
3785.298.5799381285797-13.3799381285797
3885.595.3869571254949-9.88695712549494
3994.793.02753916880151.67246083119855
4086.293.4266542925862-7.22665429258619
4188.891.7020895262663-2.90208952626629
4293.491.00953649369092.39046350630915
4383.491.5799953770477-8.17999537704765
4482.989.6279258238675-6.72792582386752
4596.788.02237734230278.6776226576973
4696.290.09320039332886.10679960667123
4792.891.5505236594281.24947634057204
4892.891.84869799931740.951302000682631
4990.292.0757161803572-1.87571618035723
5095.991.62809631294794.27190368705206
51107.592.647541035986614.8524589640134
529896.1919235933241.80807640667601
539596.6234019427127-1.62340194271268
54108.596.235994204826312.2640057951737
5591.899.1626697357144-7.36266973571443
5691.797.4056463195965-5.70564631959653
57108.396.044054051103312.2559459488967
58105.198.96880618475276.13119381524729
59104.8100.4319508712374.36804912876333
60103.2101.4743396890811.72566031091887
6198.6101.886150307157-3.28615030715656
62102.4101.1019452231571.29805477684303
63121.2101.41171229409519.7882877059049
64102.6106.133978280779-3.53397828077924
65108.9105.2906316668113.60936833318901
66105.5106.151969321011-0.651969321010711
6790.8105.996383724383-15.1963837243827
6899.6102.369927153265-2.76992715326466
69111.6101.7089132759729.89108672402757
70104.7104.0693167177660.63068328223406
71103.1104.219822625924-1.1198226259237
72101.7103.952588776481-2.25258877648149
7398.8103.415032242068-4.61503224206793
74101.4102.313703511252-0.913703511251825
75114.2102.09565781284612.1043421871544
7696.9104.984231309002-8.0842313090015
7798.3103.055014839828-4.75501483982752
78104.8101.9202807396362.87971926036424
7994.4102.607495344382-8.20749534438194
8094.5100.648863214272-6.14886321427208
81102.499.18150191221943.21849808778065
82105.599.94956250816475.55043749183534
83101.2101.274115828212-0.0741158282121148
8499.5101.256428868135-1.7564288681354

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 86.6 & 86.5 & 0.0999999999999943 \tabularnewline
3 & 98.8 & 86.5238639444548 & 12.2761360555452 \tabularnewline
4 & 84.4 & 89.4534342339402 & -5.05343423394015 \tabularnewline
5 & 91.4 & 88.2474854952951 & 3.15251450470487 \tabularnewline
6 & 95.7 & 88.999799805626 & 6.70020019437402 \tabularnewline
7 & 78.5 & 90.5987318583688 & -12.0987318583688 \tabularnewline
8 & 81.7 & 87.711497207958 & -6.01149720795796 \tabularnewline
9 & 94.3 & 86.2769168533518 & 8.02308314664823 \tabularnewline
10 & 98.5 & 88.1915409590267 & 10.3084590409733 \tabularnewline
11 & 95.4 & 90.6515458987056 & 4.74845410129436 \tabularnewline
12 & 91.7 & 91.784714347898 & -0.0847143478980428 \tabularnewline
13 & 92.8 & 91.7644981629705 & 1.03550183702954 \tabularnewline
14 & 90.6 & 92.0116097461871 & -1.41160974618715 \tabularnewline
15 & 102.2 & 91.6747439804391 & 10.5252560195609 \tabularnewline
16 & 91.8 & 94.1864852306678 & -2.38648523066784 \tabularnewline
17 & 95 & 93.6169757208004 & 1.38302427919965 \tabularnewline
18 & 102 & 93.9470198665843 & 8.05298013341567 \tabularnewline
19 & 88.9 & 95.8687785725751 & -6.96877857257505 \tabularnewline
20 & 89.6 & 94.2057531248409 & -4.60575312484092 \tabularnewline
21 & 97.9 & 93.1066387574058 & 4.79336124259424 \tabularnewline
22 & 108.6 & 94.2505238218542 & 14.3494761781458 \tabularnewline
23 & 100.8 & 97.6748748465551 & 3.12512515344488 \tabularnewline
24 & 95.1 & 98.4206529773148 & -3.32065297731477 \tabularnewline
25 & 101 & 97.6282141952732 & 3.37178580472678 \tabularnewline
26 & 100.9 & 98.4328552868465 & 2.4671447131535 \tabularnewline
27 & 102.5 & 99.0216133308119 & 3.47838666918814 \tabularnewline
28 & 105.4 & 99.8516935934685 & 5.54830640653151 \tabularnewline
29 & 98.4 & 101.175738352503 & -2.77573835250276 \tabularnewline
30 & 105.3 & 100.513337693852 & 4.7866623061478 \tabularnewline
31 & 96.5 & 101.655624127828 & -5.15562412782798 \tabularnewline
32 & 88.1 & 100.425288849667 & -12.3252888496672 \tabularnewline
33 & 107.9 & 97.4839887646946 & 10.4160112353054 \tabularnewline
34 & 107.1 & 99.9696599002888 & 7.13034009971115 \tabularnewline
35 & 92.5 & 101.671240301119 & -9.171240301119 \tabularnewline
36 & 95.7 & 99.4826206098479 & -3.78262060984791 \tabularnewline
37 & 85.2 & 98.5799381285797 & -13.3799381285797 \tabularnewline
38 & 85.5 & 95.3869571254949 & -9.88695712549494 \tabularnewline
39 & 94.7 & 93.0275391688015 & 1.67246083119855 \tabularnewline
40 & 86.2 & 93.4266542925862 & -7.22665429258619 \tabularnewline
41 & 88.8 & 91.7020895262663 & -2.90208952626629 \tabularnewline
42 & 93.4 & 91.0095364936909 & 2.39046350630915 \tabularnewline
43 & 83.4 & 91.5799953770477 & -8.17999537704765 \tabularnewline
44 & 82.9 & 89.6279258238675 & -6.72792582386752 \tabularnewline
45 & 96.7 & 88.0223773423027 & 8.6776226576973 \tabularnewline
46 & 96.2 & 90.0932003933288 & 6.10679960667123 \tabularnewline
47 & 92.8 & 91.550523659428 & 1.24947634057204 \tabularnewline
48 & 92.8 & 91.8486979993174 & 0.951302000682631 \tabularnewline
49 & 90.2 & 92.0757161803572 & -1.87571618035723 \tabularnewline
50 & 95.9 & 91.6280963129479 & 4.27190368705206 \tabularnewline
51 & 107.5 & 92.6475410359866 & 14.8524589640134 \tabularnewline
52 & 98 & 96.191923593324 & 1.80807640667601 \tabularnewline
53 & 95 & 96.6234019427127 & -1.62340194271268 \tabularnewline
54 & 108.5 & 96.2359942048263 & 12.2640057951737 \tabularnewline
55 & 91.8 & 99.1626697357144 & -7.36266973571443 \tabularnewline
56 & 91.7 & 97.4056463195965 & -5.70564631959653 \tabularnewline
57 & 108.3 & 96.0440540511033 & 12.2559459488967 \tabularnewline
58 & 105.1 & 98.9688061847527 & 6.13119381524729 \tabularnewline
59 & 104.8 & 100.431950871237 & 4.36804912876333 \tabularnewline
60 & 103.2 & 101.474339689081 & 1.72566031091887 \tabularnewline
61 & 98.6 & 101.886150307157 & -3.28615030715656 \tabularnewline
62 & 102.4 & 101.101945223157 & 1.29805477684303 \tabularnewline
63 & 121.2 & 101.411712294095 & 19.7882877059049 \tabularnewline
64 & 102.6 & 106.133978280779 & -3.53397828077924 \tabularnewline
65 & 108.9 & 105.290631666811 & 3.60936833318901 \tabularnewline
66 & 105.5 & 106.151969321011 & -0.651969321010711 \tabularnewline
67 & 90.8 & 105.996383724383 & -15.1963837243827 \tabularnewline
68 & 99.6 & 102.369927153265 & -2.76992715326466 \tabularnewline
69 & 111.6 & 101.708913275972 & 9.89108672402757 \tabularnewline
70 & 104.7 & 104.069316717766 & 0.63068328223406 \tabularnewline
71 & 103.1 & 104.219822625924 & -1.1198226259237 \tabularnewline
72 & 101.7 & 103.952588776481 & -2.25258877648149 \tabularnewline
73 & 98.8 & 103.415032242068 & -4.61503224206793 \tabularnewline
74 & 101.4 & 102.313703511252 & -0.913703511251825 \tabularnewline
75 & 114.2 & 102.095657812846 & 12.1043421871544 \tabularnewline
76 & 96.9 & 104.984231309002 & -8.0842313090015 \tabularnewline
77 & 98.3 & 103.055014839828 & -4.75501483982752 \tabularnewline
78 & 104.8 & 101.920280739636 & 2.87971926036424 \tabularnewline
79 & 94.4 & 102.607495344382 & -8.20749534438194 \tabularnewline
80 & 94.5 & 100.648863214272 & -6.14886321427208 \tabularnewline
81 & 102.4 & 99.1815019122194 & 3.21849808778065 \tabularnewline
82 & 105.5 & 99.9495625081647 & 5.55043749183534 \tabularnewline
83 & 101.2 & 101.274115828212 & -0.0741158282121148 \tabularnewline
84 & 99.5 & 101.256428868135 & -1.7564288681354 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232328&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]2[/C][C]86.6[/C][C]86.5[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]3[/C][C]98.8[/C][C]86.5238639444548[/C][C]12.2761360555452[/C][/ROW]
[ROW][C]4[/C][C]84.4[/C][C]89.4534342339402[/C][C]-5.05343423394015[/C][/ROW]
[ROW][C]5[/C][C]91.4[/C][C]88.2474854952951[/C][C]3.15251450470487[/C][/ROW]
[ROW][C]6[/C][C]95.7[/C][C]88.999799805626[/C][C]6.70020019437402[/C][/ROW]
[ROW][C]7[/C][C]78.5[/C][C]90.5987318583688[/C][C]-12.0987318583688[/C][/ROW]
[ROW][C]8[/C][C]81.7[/C][C]87.711497207958[/C][C]-6.01149720795796[/C][/ROW]
[ROW][C]9[/C][C]94.3[/C][C]86.2769168533518[/C][C]8.02308314664823[/C][/ROW]
[ROW][C]10[/C][C]98.5[/C][C]88.1915409590267[/C][C]10.3084590409733[/C][/ROW]
[ROW][C]11[/C][C]95.4[/C][C]90.6515458987056[/C][C]4.74845410129436[/C][/ROW]
[ROW][C]12[/C][C]91.7[/C][C]91.784714347898[/C][C]-0.0847143478980428[/C][/ROW]
[ROW][C]13[/C][C]92.8[/C][C]91.7644981629705[/C][C]1.03550183702954[/C][/ROW]
[ROW][C]14[/C][C]90.6[/C][C]92.0116097461871[/C][C]-1.41160974618715[/C][/ROW]
[ROW][C]15[/C][C]102.2[/C][C]91.6747439804391[/C][C]10.5252560195609[/C][/ROW]
[ROW][C]16[/C][C]91.8[/C][C]94.1864852306678[/C][C]-2.38648523066784[/C][/ROW]
[ROW][C]17[/C][C]95[/C][C]93.6169757208004[/C][C]1.38302427919965[/C][/ROW]
[ROW][C]18[/C][C]102[/C][C]93.9470198665843[/C][C]8.05298013341567[/C][/ROW]
[ROW][C]19[/C][C]88.9[/C][C]95.8687785725751[/C][C]-6.96877857257505[/C][/ROW]
[ROW][C]20[/C][C]89.6[/C][C]94.2057531248409[/C][C]-4.60575312484092[/C][/ROW]
[ROW][C]21[/C][C]97.9[/C][C]93.1066387574058[/C][C]4.79336124259424[/C][/ROW]
[ROW][C]22[/C][C]108.6[/C][C]94.2505238218542[/C][C]14.3494761781458[/C][/ROW]
[ROW][C]23[/C][C]100.8[/C][C]97.6748748465551[/C][C]3.12512515344488[/C][/ROW]
[ROW][C]24[/C][C]95.1[/C][C]98.4206529773148[/C][C]-3.32065297731477[/C][/ROW]
[ROW][C]25[/C][C]101[/C][C]97.6282141952732[/C][C]3.37178580472678[/C][/ROW]
[ROW][C]26[/C][C]100.9[/C][C]98.4328552868465[/C][C]2.4671447131535[/C][/ROW]
[ROW][C]27[/C][C]102.5[/C][C]99.0216133308119[/C][C]3.47838666918814[/C][/ROW]
[ROW][C]28[/C][C]105.4[/C][C]99.8516935934685[/C][C]5.54830640653151[/C][/ROW]
[ROW][C]29[/C][C]98.4[/C][C]101.175738352503[/C][C]-2.77573835250276[/C][/ROW]
[ROW][C]30[/C][C]105.3[/C][C]100.513337693852[/C][C]4.7866623061478[/C][/ROW]
[ROW][C]31[/C][C]96.5[/C][C]101.655624127828[/C][C]-5.15562412782798[/C][/ROW]
[ROW][C]32[/C][C]88.1[/C][C]100.425288849667[/C][C]-12.3252888496672[/C][/ROW]
[ROW][C]33[/C][C]107.9[/C][C]97.4839887646946[/C][C]10.4160112353054[/C][/ROW]
[ROW][C]34[/C][C]107.1[/C][C]99.9696599002888[/C][C]7.13034009971115[/C][/ROW]
[ROW][C]35[/C][C]92.5[/C][C]101.671240301119[/C][C]-9.171240301119[/C][/ROW]
[ROW][C]36[/C][C]95.7[/C][C]99.4826206098479[/C][C]-3.78262060984791[/C][/ROW]
[ROW][C]37[/C][C]85.2[/C][C]98.5799381285797[/C][C]-13.3799381285797[/C][/ROW]
[ROW][C]38[/C][C]85.5[/C][C]95.3869571254949[/C][C]-9.88695712549494[/C][/ROW]
[ROW][C]39[/C][C]94.7[/C][C]93.0275391688015[/C][C]1.67246083119855[/C][/ROW]
[ROW][C]40[/C][C]86.2[/C][C]93.4266542925862[/C][C]-7.22665429258619[/C][/ROW]
[ROW][C]41[/C][C]88.8[/C][C]91.7020895262663[/C][C]-2.90208952626629[/C][/ROW]
[ROW][C]42[/C][C]93.4[/C][C]91.0095364936909[/C][C]2.39046350630915[/C][/ROW]
[ROW][C]43[/C][C]83.4[/C][C]91.5799953770477[/C][C]-8.17999537704765[/C][/ROW]
[ROW][C]44[/C][C]82.9[/C][C]89.6279258238675[/C][C]-6.72792582386752[/C][/ROW]
[ROW][C]45[/C][C]96.7[/C][C]88.0223773423027[/C][C]8.6776226576973[/C][/ROW]
[ROW][C]46[/C][C]96.2[/C][C]90.0932003933288[/C][C]6.10679960667123[/C][/ROW]
[ROW][C]47[/C][C]92.8[/C][C]91.550523659428[/C][C]1.24947634057204[/C][/ROW]
[ROW][C]48[/C][C]92.8[/C][C]91.8486979993174[/C][C]0.951302000682631[/C][/ROW]
[ROW][C]49[/C][C]90.2[/C][C]92.0757161803572[/C][C]-1.87571618035723[/C][/ROW]
[ROW][C]50[/C][C]95.9[/C][C]91.6280963129479[/C][C]4.27190368705206[/C][/ROW]
[ROW][C]51[/C][C]107.5[/C][C]92.6475410359866[/C][C]14.8524589640134[/C][/ROW]
[ROW][C]52[/C][C]98[/C][C]96.191923593324[/C][C]1.80807640667601[/C][/ROW]
[ROW][C]53[/C][C]95[/C][C]96.6234019427127[/C][C]-1.62340194271268[/C][/ROW]
[ROW][C]54[/C][C]108.5[/C][C]96.2359942048263[/C][C]12.2640057951737[/C][/ROW]
[ROW][C]55[/C][C]91.8[/C][C]99.1626697357144[/C][C]-7.36266973571443[/C][/ROW]
[ROW][C]56[/C][C]91.7[/C][C]97.4056463195965[/C][C]-5.70564631959653[/C][/ROW]
[ROW][C]57[/C][C]108.3[/C][C]96.0440540511033[/C][C]12.2559459488967[/C][/ROW]
[ROW][C]58[/C][C]105.1[/C][C]98.9688061847527[/C][C]6.13119381524729[/C][/ROW]
[ROW][C]59[/C][C]104.8[/C][C]100.431950871237[/C][C]4.36804912876333[/C][/ROW]
[ROW][C]60[/C][C]103.2[/C][C]101.474339689081[/C][C]1.72566031091887[/C][/ROW]
[ROW][C]61[/C][C]98.6[/C][C]101.886150307157[/C][C]-3.28615030715656[/C][/ROW]
[ROW][C]62[/C][C]102.4[/C][C]101.101945223157[/C][C]1.29805477684303[/C][/ROW]
[ROW][C]63[/C][C]121.2[/C][C]101.411712294095[/C][C]19.7882877059049[/C][/ROW]
[ROW][C]64[/C][C]102.6[/C][C]106.133978280779[/C][C]-3.53397828077924[/C][/ROW]
[ROW][C]65[/C][C]108.9[/C][C]105.290631666811[/C][C]3.60936833318901[/C][/ROW]
[ROW][C]66[/C][C]105.5[/C][C]106.151969321011[/C][C]-0.651969321010711[/C][/ROW]
[ROW][C]67[/C][C]90.8[/C][C]105.996383724383[/C][C]-15.1963837243827[/C][/ROW]
[ROW][C]68[/C][C]99.6[/C][C]102.369927153265[/C][C]-2.76992715326466[/C][/ROW]
[ROW][C]69[/C][C]111.6[/C][C]101.708913275972[/C][C]9.89108672402757[/C][/ROW]
[ROW][C]70[/C][C]104.7[/C][C]104.069316717766[/C][C]0.63068328223406[/C][/ROW]
[ROW][C]71[/C][C]103.1[/C][C]104.219822625924[/C][C]-1.1198226259237[/C][/ROW]
[ROW][C]72[/C][C]101.7[/C][C]103.952588776481[/C][C]-2.25258877648149[/C][/ROW]
[ROW][C]73[/C][C]98.8[/C][C]103.415032242068[/C][C]-4.61503224206793[/C][/ROW]
[ROW][C]74[/C][C]101.4[/C][C]102.313703511252[/C][C]-0.913703511251825[/C][/ROW]
[ROW][C]75[/C][C]114.2[/C][C]102.095657812846[/C][C]12.1043421871544[/C][/ROW]
[ROW][C]76[/C][C]96.9[/C][C]104.984231309002[/C][C]-8.0842313090015[/C][/ROW]
[ROW][C]77[/C][C]98.3[/C][C]103.055014839828[/C][C]-4.75501483982752[/C][/ROW]
[ROW][C]78[/C][C]104.8[/C][C]101.920280739636[/C][C]2.87971926036424[/C][/ROW]
[ROW][C]79[/C][C]94.4[/C][C]102.607495344382[/C][C]-8.20749534438194[/C][/ROW]
[ROW][C]80[/C][C]94.5[/C][C]100.648863214272[/C][C]-6.14886321427208[/C][/ROW]
[ROW][C]81[/C][C]102.4[/C][C]99.1815019122194[/C][C]3.21849808778065[/C][/ROW]
[ROW][C]82[/C][C]105.5[/C][C]99.9495625081647[/C][C]5.55043749183534[/C][/ROW]
[ROW][C]83[/C][C]101.2[/C][C]101.274115828212[/C][C]-0.0741158282121148[/C][/ROW]
[ROW][C]84[/C][C]99.5[/C][C]101.256428868135[/C][C]-1.7564288681354[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232328&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232328&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
286.686.50.0999999999999943
398.886.523863944454812.2761360555452
484.489.4534342339402-5.05343423394015
591.488.24748549529513.15251450470487
695.788.9997998056266.70020019437402
778.590.5987318583688-12.0987318583688
881.787.711497207958-6.01149720795796
994.386.27691685335188.02308314664823
1098.588.191540959026710.3084590409733
1195.490.65154589870564.74845410129436
1291.791.784714347898-0.0847143478980428
1392.891.76449816297051.03550183702954
1490.692.0116097461871-1.41160974618715
15102.291.674743980439110.5252560195609
1691.894.1864852306678-2.38648523066784
179593.61697572080041.38302427919965
1810293.94701986658438.05298013341567
1988.995.8687785725751-6.96877857257505
2089.694.2057531248409-4.60575312484092
2197.993.10663875740584.79336124259424
22108.694.250523821854214.3494761781458
23100.897.67487484655513.12512515344488
2495.198.4206529773148-3.32065297731477
2510197.62821419527323.37178580472678
26100.998.43285528684652.4671447131535
27102.599.02161333081193.47838666918814
28105.499.85169359346855.54830640653151
2998.4101.175738352503-2.77573835250276
30105.3100.5133376938524.7866623061478
3196.5101.655624127828-5.15562412782798
3288.1100.425288849667-12.3252888496672
33107.997.483988764694610.4160112353054
34107.199.96965990028887.13034009971115
3592.5101.671240301119-9.171240301119
3695.799.4826206098479-3.78262060984791
3785.298.5799381285797-13.3799381285797
3885.595.3869571254949-9.88695712549494
3994.793.02753916880151.67246083119855
4086.293.4266542925862-7.22665429258619
4188.891.7020895262663-2.90208952626629
4293.491.00953649369092.39046350630915
4383.491.5799953770477-8.17999537704765
4482.989.6279258238675-6.72792582386752
4596.788.02237734230278.6776226576973
4696.290.09320039332886.10679960667123
4792.891.5505236594281.24947634057204
4892.891.84869799931740.951302000682631
4990.292.0757161803572-1.87571618035723
5095.991.62809631294794.27190368705206
51107.592.647541035986614.8524589640134
529896.1919235933241.80807640667601
539596.6234019427127-1.62340194271268
54108.596.235994204826312.2640057951737
5591.899.1626697357144-7.36266973571443
5691.797.4056463195965-5.70564631959653
57108.396.044054051103312.2559459488967
58105.198.96880618475276.13119381524729
59104.8100.4319508712374.36804912876333
60103.2101.4743396890811.72566031091887
6198.6101.886150307157-3.28615030715656
62102.4101.1019452231571.29805477684303
63121.2101.41171229409519.7882877059049
64102.6106.133978280779-3.53397828077924
65108.9105.2906316668113.60936833318901
66105.5106.151969321011-0.651969321010711
6790.8105.996383724383-15.1963837243827
6899.6102.369927153265-2.76992715326466
69111.6101.7089132759729.89108672402757
70104.7104.0693167177660.63068328223406
71103.1104.219822625924-1.1198226259237
72101.7103.952588776481-2.25258877648149
7398.8103.415032242068-4.61503224206793
74101.4102.313703511252-0.913703511251825
75114.2102.09565781284612.1043421871544
7696.9104.984231309002-8.0842313090015
7798.3103.055014839828-4.75501483982752
78104.8101.9202807396362.87971926036424
7994.4102.607495344382-8.20749534438194
8094.5100.648863214272-6.14886321427208
81102.499.18150191221943.21849808778065
82105.599.94956250816475.55043749183534
83101.2101.274115828212-0.0741158282121148
8499.5101.256428868135-1.7564288681354







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85100.83727565865687.0592202442631114.615331073049
86100.83727565865686.672330450739115.002220866574
87100.83727565865686.295730538398115.378820778915
88100.83727565865685.9286407035131115.745910613799
89100.83727565865685.5703749264537116.104176390859
90100.83727565865685.2203259018012116.454225415511
91100.83727565865684.8779529459173116.796598371395
92100.83727565865684.542772193053117.13177912426
93100.83727565865684.2143485718955117.460202745417
94100.83727565865683.8922891826223117.78226213469
95100.83727565865683.5762377867847118.098313530528
96100.83727565865683.2658701896736118.408681127639

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 100.837275658656 & 87.0592202442631 & 114.615331073049 \tabularnewline
86 & 100.837275658656 & 86.672330450739 & 115.002220866574 \tabularnewline
87 & 100.837275658656 & 86.295730538398 & 115.378820778915 \tabularnewline
88 & 100.837275658656 & 85.9286407035131 & 115.745910613799 \tabularnewline
89 & 100.837275658656 & 85.5703749264537 & 116.104176390859 \tabularnewline
90 & 100.837275658656 & 85.2203259018012 & 116.454225415511 \tabularnewline
91 & 100.837275658656 & 84.8779529459173 & 116.796598371395 \tabularnewline
92 & 100.837275658656 & 84.542772193053 & 117.13177912426 \tabularnewline
93 & 100.837275658656 & 84.2143485718955 & 117.460202745417 \tabularnewline
94 & 100.837275658656 & 83.8922891826223 & 117.78226213469 \tabularnewline
95 & 100.837275658656 & 83.5762377867847 & 118.098313530528 \tabularnewline
96 & 100.837275658656 & 83.2658701896736 & 118.408681127639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232328&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]100.837275658656[/C][C]87.0592202442631[/C][C]114.615331073049[/C][/ROW]
[ROW][C]86[/C][C]100.837275658656[/C][C]86.672330450739[/C][C]115.002220866574[/C][/ROW]
[ROW][C]87[/C][C]100.837275658656[/C][C]86.295730538398[/C][C]115.378820778915[/C][/ROW]
[ROW][C]88[/C][C]100.837275658656[/C][C]85.9286407035131[/C][C]115.745910613799[/C][/ROW]
[ROW][C]89[/C][C]100.837275658656[/C][C]85.5703749264537[/C][C]116.104176390859[/C][/ROW]
[ROW][C]90[/C][C]100.837275658656[/C][C]85.2203259018012[/C][C]116.454225415511[/C][/ROW]
[ROW][C]91[/C][C]100.837275658656[/C][C]84.8779529459173[/C][C]116.796598371395[/C][/ROW]
[ROW][C]92[/C][C]100.837275658656[/C][C]84.542772193053[/C][C]117.13177912426[/C][/ROW]
[ROW][C]93[/C][C]100.837275658656[/C][C]84.2143485718955[/C][C]117.460202745417[/C][/ROW]
[ROW][C]94[/C][C]100.837275658656[/C][C]83.8922891826223[/C][C]117.78226213469[/C][/ROW]
[ROW][C]95[/C][C]100.837275658656[/C][C]83.5762377867847[/C][C]118.098313530528[/C][/ROW]
[ROW][C]96[/C][C]100.837275658656[/C][C]83.2658701896736[/C][C]118.408681127639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232328&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232328&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85100.83727565865687.0592202442631114.615331073049
86100.83727565865686.672330450739115.002220866574
87100.83727565865686.295730538398115.378820778915
88100.83727565865685.9286407035131115.745910613799
89100.83727565865685.5703749264537116.104176390859
90100.83727565865685.2203259018012116.454225415511
91100.83727565865684.8779529459173116.796598371395
92100.83727565865684.542772193053117.13177912426
93100.83727565865684.2143485718955117.460202745417
94100.83727565865683.8922891826223117.78226213469
95100.83727565865683.5762377867847118.098313530528
96100.83727565865683.2658701896736118.408681127639



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