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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Apr 2016 18:41:20 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/26/t1461692496ejcjzm8riwu07cp.htm/, Retrieved Fri, 03 May 2024 21:47:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294935, Retrieved Fri, 03 May 2024 21:47:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 17:41:20] [98ac3b2d1325a88ddcc6e107efd9e1d0] [Current]
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Dataseries X:
84.51
84.54
84.27
84.47
84.25
84.33
84.29
84.53
84.01
84.18
84.08
83.44
83.61
83.89
83.4
82.96
82.76
83.35
87.78
88.99
88.92
88.91
89.79
90.54
93.15
92.79
93.21
95.35
100.91
103.69
104.04
104.16
104.71
105.18
104.92
104.83
104.9
105.05
104.6
103.21
102.52
101.09
101.19
102.34
102.62
102.47
101.82
101.86
101.54
101.98
101.23
100.4
99.94
99.94
100
98.8
99.07
99.46
99.18
98.47
97.12
96.91
96.09
97.17
96.8
97.13
99.9
100.56
100.84
99.81
100.44
100.07
101.32
103.98
104.81
106.23
106.48
107.59
107.16
107.54
107.1
106.38
106.64
106.13




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294935&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]1 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=294935&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294935&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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999923117653715
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999923117653715 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294935&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]0.999923117653715[/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=294935&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294935&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
alpha0.999923117653715
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
284.5484.510.0300000000000011
384.2784.5399976935296-0.269997693529632
484.4784.27002075805620.199979241943836
584.2584.4699846251267-0.219984625126671
684.3384.25001691293410.0799830870658695
784.2984.3299938507126-0.0399938507126052
884.5384.29000307482110.239996925178914
984.0184.5299815484733-0.519981548473282
1084.1884.01003997740150.169960022598531
1184.0884.1799869330747-0.099986933074689
1283.4484.08000768723-0.64000768723001
1383.6183.44004920529260.169950794707361
1483.8983.60998693378410.280013066215858
1583.483.8899784719385-0.489978471938471
1682.9683.4000376706946-0.440037670694565
1782.7682.9600338311286-0.200033831128565
1883.3582.76001537907030.589984620929712
1987.7883.34995464059814.43004535940193
2088.9987.77965940771861.21034059228138
2188.9288.9899069461755-0.0699069461754647
2288.9188.92000537461-0.0100053746100457
2389.7988.91000076923670.879999230763346
2490.5489.78993234359440.750067656405591
2593.1590.53994233303872.6100576669613
2692.7993.1497993326426-0.359799332642623
2793.2192.79002766221690.419972337783108
2895.3593.20996771154132.14003228845871
29100.9195.34983546929655.56016453070346
30103.69100.9095725215052.78042747849486
31104.04103.6897862342120.350213765788226
32104.16104.0399730747440.120026925255999
33104.71104.1599907720480.55000922795162
34105.18104.7099577140.470042285999938
35104.92105.179963862046-0.259963862046206
36104.83104.920019986632-0.090019986631674
37104.9104.8300069209480.0699930790522245
38105.05104.8999946187680.150005381232134
39104.6105.049988467234-0.449988467234334
40103.21104.600034596169-1.39003459616916
41102.52103.210106869121-0.690106869121166
42101.09102.520053057035-1.43005305703528
43101.19101.0901099458340.0998900541656553
44102.34101.1899923202181.15000767978175
45102.62102.3399115847110.280088415288674
46102.47102.619978466145-0.14997846614547
47101.82102.470011530696-0.650011530696375
48101.86101.8200499744120.0399500255884107
49101.54101.859996928548-0.319996928548292
50101.98101.5400246021150.439975397885334
51101.23101.979966173659-0.749966173659104
52100.4101.230057659159-0.830057659159067
5399.94100.40006381678-0.460063816780405
5499.9499.9400353707857-3.53707856675101e-05
5510099.94000000271940.0599999972806131
5698.899.9999953870594-1.19999538705943
5799.0798.80009225846090.2699077415391
5899.4699.06997924885950.390020751140455
5999.1899.4599700142896-0.279970014289546
6098.4799.1800215247516-0.710021524751596
6197.1298.4700545881207-1.35005458812073
6296.9197.1201037953643-0.210103795364347
6396.0996.9100161532727-0.820016153272732
6497.1796.09006304476591.07993695523413
6596.897.169916971913-0.369916971913042
6697.1396.80002844008470.329971559915265
6799.997.12997463101232.77002536898775
68100.5699.89978703395040.660212966049627
69100.84100.5599492412780.28005075872187
7099.81100.839978469041-1.02997846904059
71100.4499.81007918716130.629920812838662
72100.07100.43995157021-0.369951570209935
73101.32100.0700284427451.24997155725526
74103.98101.3199038992542.66009610074612
75104.81103.979795485570.830204514429568
76106.23104.8099361719291.42006382807097
77106.48106.2298908221610.250109177838965
78107.59106.479980771021.11001922898042
79107.16107.589914659117-0.429914659117259
80107.54107.1600330528480.379966947152312
81107.1107.53997078725-0.439970787249607
82106.38107.100033825986-0.72003382598642
83106.64106.380055357890.259944642110057
84106.13106.639980014846-0.509980014846022

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 84.54 & 84.51 & 0.0300000000000011 \tabularnewline
3 & 84.27 & 84.5399976935296 & -0.269997693529632 \tabularnewline
4 & 84.47 & 84.2700207580562 & 0.199979241943836 \tabularnewline
5 & 84.25 & 84.4699846251267 & -0.219984625126671 \tabularnewline
6 & 84.33 & 84.2500169129341 & 0.0799830870658695 \tabularnewline
7 & 84.29 & 84.3299938507126 & -0.0399938507126052 \tabularnewline
8 & 84.53 & 84.2900030748211 & 0.239996925178914 \tabularnewline
9 & 84.01 & 84.5299815484733 & -0.519981548473282 \tabularnewline
10 & 84.18 & 84.0100399774015 & 0.169960022598531 \tabularnewline
11 & 84.08 & 84.1799869330747 & -0.099986933074689 \tabularnewline
12 & 83.44 & 84.08000768723 & -0.64000768723001 \tabularnewline
13 & 83.61 & 83.4400492052926 & 0.169950794707361 \tabularnewline
14 & 83.89 & 83.6099869337841 & 0.280013066215858 \tabularnewline
15 & 83.4 & 83.8899784719385 & -0.489978471938471 \tabularnewline
16 & 82.96 & 83.4000376706946 & -0.440037670694565 \tabularnewline
17 & 82.76 & 82.9600338311286 & -0.200033831128565 \tabularnewline
18 & 83.35 & 82.7600153790703 & 0.589984620929712 \tabularnewline
19 & 87.78 & 83.3499546405981 & 4.43004535940193 \tabularnewline
20 & 88.99 & 87.7796594077186 & 1.21034059228138 \tabularnewline
21 & 88.92 & 88.9899069461755 & -0.0699069461754647 \tabularnewline
22 & 88.91 & 88.92000537461 & -0.0100053746100457 \tabularnewline
23 & 89.79 & 88.9100007692367 & 0.879999230763346 \tabularnewline
24 & 90.54 & 89.7899323435944 & 0.750067656405591 \tabularnewline
25 & 93.15 & 90.5399423330387 & 2.6100576669613 \tabularnewline
26 & 92.79 & 93.1497993326426 & -0.359799332642623 \tabularnewline
27 & 93.21 & 92.7900276622169 & 0.419972337783108 \tabularnewline
28 & 95.35 & 93.2099677115413 & 2.14003228845871 \tabularnewline
29 & 100.91 & 95.3498354692965 & 5.56016453070346 \tabularnewline
30 & 103.69 & 100.909572521505 & 2.78042747849486 \tabularnewline
31 & 104.04 & 103.689786234212 & 0.350213765788226 \tabularnewline
32 & 104.16 & 104.039973074744 & 0.120026925255999 \tabularnewline
33 & 104.71 & 104.159990772048 & 0.55000922795162 \tabularnewline
34 & 105.18 & 104.709957714 & 0.470042285999938 \tabularnewline
35 & 104.92 & 105.179963862046 & -0.259963862046206 \tabularnewline
36 & 104.83 & 104.920019986632 & -0.090019986631674 \tabularnewline
37 & 104.9 & 104.830006920948 & 0.0699930790522245 \tabularnewline
38 & 105.05 & 104.899994618768 & 0.150005381232134 \tabularnewline
39 & 104.6 & 105.049988467234 & -0.449988467234334 \tabularnewline
40 & 103.21 & 104.600034596169 & -1.39003459616916 \tabularnewline
41 & 102.52 & 103.210106869121 & -0.690106869121166 \tabularnewline
42 & 101.09 & 102.520053057035 & -1.43005305703528 \tabularnewline
43 & 101.19 & 101.090109945834 & 0.0998900541656553 \tabularnewline
44 & 102.34 & 101.189992320218 & 1.15000767978175 \tabularnewline
45 & 102.62 & 102.339911584711 & 0.280088415288674 \tabularnewline
46 & 102.47 & 102.619978466145 & -0.14997846614547 \tabularnewline
47 & 101.82 & 102.470011530696 & -0.650011530696375 \tabularnewline
48 & 101.86 & 101.820049974412 & 0.0399500255884107 \tabularnewline
49 & 101.54 & 101.859996928548 & -0.319996928548292 \tabularnewline
50 & 101.98 & 101.540024602115 & 0.439975397885334 \tabularnewline
51 & 101.23 & 101.979966173659 & -0.749966173659104 \tabularnewline
52 & 100.4 & 101.230057659159 & -0.830057659159067 \tabularnewline
53 & 99.94 & 100.40006381678 & -0.460063816780405 \tabularnewline
54 & 99.94 & 99.9400353707857 & -3.53707856675101e-05 \tabularnewline
55 & 100 & 99.9400000027194 & 0.0599999972806131 \tabularnewline
56 & 98.8 & 99.9999953870594 & -1.19999538705943 \tabularnewline
57 & 99.07 & 98.8000922584609 & 0.2699077415391 \tabularnewline
58 & 99.46 & 99.0699792488595 & 0.390020751140455 \tabularnewline
59 & 99.18 & 99.4599700142896 & -0.279970014289546 \tabularnewline
60 & 98.47 & 99.1800215247516 & -0.710021524751596 \tabularnewline
61 & 97.12 & 98.4700545881207 & -1.35005458812073 \tabularnewline
62 & 96.91 & 97.1201037953643 & -0.210103795364347 \tabularnewline
63 & 96.09 & 96.9100161532727 & -0.820016153272732 \tabularnewline
64 & 97.17 & 96.0900630447659 & 1.07993695523413 \tabularnewline
65 & 96.8 & 97.169916971913 & -0.369916971913042 \tabularnewline
66 & 97.13 & 96.8000284400847 & 0.329971559915265 \tabularnewline
67 & 99.9 & 97.1299746310123 & 2.77002536898775 \tabularnewline
68 & 100.56 & 99.8997870339504 & 0.660212966049627 \tabularnewline
69 & 100.84 & 100.559949241278 & 0.28005075872187 \tabularnewline
70 & 99.81 & 100.839978469041 & -1.02997846904059 \tabularnewline
71 & 100.44 & 99.8100791871613 & 0.629920812838662 \tabularnewline
72 & 100.07 & 100.43995157021 & -0.369951570209935 \tabularnewline
73 & 101.32 & 100.070028442745 & 1.24997155725526 \tabularnewline
74 & 103.98 & 101.319903899254 & 2.66009610074612 \tabularnewline
75 & 104.81 & 103.97979548557 & 0.830204514429568 \tabularnewline
76 & 106.23 & 104.809936171929 & 1.42006382807097 \tabularnewline
77 & 106.48 & 106.229890822161 & 0.250109177838965 \tabularnewline
78 & 107.59 & 106.47998077102 & 1.11001922898042 \tabularnewline
79 & 107.16 & 107.589914659117 & -0.429914659117259 \tabularnewline
80 & 107.54 & 107.160033052848 & 0.379966947152312 \tabularnewline
81 & 107.1 & 107.53997078725 & -0.439970787249607 \tabularnewline
82 & 106.38 & 107.100033825986 & -0.72003382598642 \tabularnewline
83 & 106.64 & 106.38005535789 & 0.259944642110057 \tabularnewline
84 & 106.13 & 106.639980014846 & -0.509980014846022 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294935&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]84.54[/C][C]84.51[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]3[/C][C]84.27[/C][C]84.5399976935296[/C][C]-0.269997693529632[/C][/ROW]
[ROW][C]4[/C][C]84.47[/C][C]84.2700207580562[/C][C]0.199979241943836[/C][/ROW]
[ROW][C]5[/C][C]84.25[/C][C]84.4699846251267[/C][C]-0.219984625126671[/C][/ROW]
[ROW][C]6[/C][C]84.33[/C][C]84.2500169129341[/C][C]0.0799830870658695[/C][/ROW]
[ROW][C]7[/C][C]84.29[/C][C]84.3299938507126[/C][C]-0.0399938507126052[/C][/ROW]
[ROW][C]8[/C][C]84.53[/C][C]84.2900030748211[/C][C]0.239996925178914[/C][/ROW]
[ROW][C]9[/C][C]84.01[/C][C]84.5299815484733[/C][C]-0.519981548473282[/C][/ROW]
[ROW][C]10[/C][C]84.18[/C][C]84.0100399774015[/C][C]0.169960022598531[/C][/ROW]
[ROW][C]11[/C][C]84.08[/C][C]84.1799869330747[/C][C]-0.099986933074689[/C][/ROW]
[ROW][C]12[/C][C]83.44[/C][C]84.08000768723[/C][C]-0.64000768723001[/C][/ROW]
[ROW][C]13[/C][C]83.61[/C][C]83.4400492052926[/C][C]0.169950794707361[/C][/ROW]
[ROW][C]14[/C][C]83.89[/C][C]83.6099869337841[/C][C]0.280013066215858[/C][/ROW]
[ROW][C]15[/C][C]83.4[/C][C]83.8899784719385[/C][C]-0.489978471938471[/C][/ROW]
[ROW][C]16[/C][C]82.96[/C][C]83.4000376706946[/C][C]-0.440037670694565[/C][/ROW]
[ROW][C]17[/C][C]82.76[/C][C]82.9600338311286[/C][C]-0.200033831128565[/C][/ROW]
[ROW][C]18[/C][C]83.35[/C][C]82.7600153790703[/C][C]0.589984620929712[/C][/ROW]
[ROW][C]19[/C][C]87.78[/C][C]83.3499546405981[/C][C]4.43004535940193[/C][/ROW]
[ROW][C]20[/C][C]88.99[/C][C]87.7796594077186[/C][C]1.21034059228138[/C][/ROW]
[ROW][C]21[/C][C]88.92[/C][C]88.9899069461755[/C][C]-0.0699069461754647[/C][/ROW]
[ROW][C]22[/C][C]88.91[/C][C]88.92000537461[/C][C]-0.0100053746100457[/C][/ROW]
[ROW][C]23[/C][C]89.79[/C][C]88.9100007692367[/C][C]0.879999230763346[/C][/ROW]
[ROW][C]24[/C][C]90.54[/C][C]89.7899323435944[/C][C]0.750067656405591[/C][/ROW]
[ROW][C]25[/C][C]93.15[/C][C]90.5399423330387[/C][C]2.6100576669613[/C][/ROW]
[ROW][C]26[/C][C]92.79[/C][C]93.1497993326426[/C][C]-0.359799332642623[/C][/ROW]
[ROW][C]27[/C][C]93.21[/C][C]92.7900276622169[/C][C]0.419972337783108[/C][/ROW]
[ROW][C]28[/C][C]95.35[/C][C]93.2099677115413[/C][C]2.14003228845871[/C][/ROW]
[ROW][C]29[/C][C]100.91[/C][C]95.3498354692965[/C][C]5.56016453070346[/C][/ROW]
[ROW][C]30[/C][C]103.69[/C][C]100.909572521505[/C][C]2.78042747849486[/C][/ROW]
[ROW][C]31[/C][C]104.04[/C][C]103.689786234212[/C][C]0.350213765788226[/C][/ROW]
[ROW][C]32[/C][C]104.16[/C][C]104.039973074744[/C][C]0.120026925255999[/C][/ROW]
[ROW][C]33[/C][C]104.71[/C][C]104.159990772048[/C][C]0.55000922795162[/C][/ROW]
[ROW][C]34[/C][C]105.18[/C][C]104.709957714[/C][C]0.470042285999938[/C][/ROW]
[ROW][C]35[/C][C]104.92[/C][C]105.179963862046[/C][C]-0.259963862046206[/C][/ROW]
[ROW][C]36[/C][C]104.83[/C][C]104.920019986632[/C][C]-0.090019986631674[/C][/ROW]
[ROW][C]37[/C][C]104.9[/C][C]104.830006920948[/C][C]0.0699930790522245[/C][/ROW]
[ROW][C]38[/C][C]105.05[/C][C]104.899994618768[/C][C]0.150005381232134[/C][/ROW]
[ROW][C]39[/C][C]104.6[/C][C]105.049988467234[/C][C]-0.449988467234334[/C][/ROW]
[ROW][C]40[/C][C]103.21[/C][C]104.600034596169[/C][C]-1.39003459616916[/C][/ROW]
[ROW][C]41[/C][C]102.52[/C][C]103.210106869121[/C][C]-0.690106869121166[/C][/ROW]
[ROW][C]42[/C][C]101.09[/C][C]102.520053057035[/C][C]-1.43005305703528[/C][/ROW]
[ROW][C]43[/C][C]101.19[/C][C]101.090109945834[/C][C]0.0998900541656553[/C][/ROW]
[ROW][C]44[/C][C]102.34[/C][C]101.189992320218[/C][C]1.15000767978175[/C][/ROW]
[ROW][C]45[/C][C]102.62[/C][C]102.339911584711[/C][C]0.280088415288674[/C][/ROW]
[ROW][C]46[/C][C]102.47[/C][C]102.619978466145[/C][C]-0.14997846614547[/C][/ROW]
[ROW][C]47[/C][C]101.82[/C][C]102.470011530696[/C][C]-0.650011530696375[/C][/ROW]
[ROW][C]48[/C][C]101.86[/C][C]101.820049974412[/C][C]0.0399500255884107[/C][/ROW]
[ROW][C]49[/C][C]101.54[/C][C]101.859996928548[/C][C]-0.319996928548292[/C][/ROW]
[ROW][C]50[/C][C]101.98[/C][C]101.540024602115[/C][C]0.439975397885334[/C][/ROW]
[ROW][C]51[/C][C]101.23[/C][C]101.979966173659[/C][C]-0.749966173659104[/C][/ROW]
[ROW][C]52[/C][C]100.4[/C][C]101.230057659159[/C][C]-0.830057659159067[/C][/ROW]
[ROW][C]53[/C][C]99.94[/C][C]100.40006381678[/C][C]-0.460063816780405[/C][/ROW]
[ROW][C]54[/C][C]99.94[/C][C]99.9400353707857[/C][C]-3.53707856675101e-05[/C][/ROW]
[ROW][C]55[/C][C]100[/C][C]99.9400000027194[/C][C]0.0599999972806131[/C][/ROW]
[ROW][C]56[/C][C]98.8[/C][C]99.9999953870594[/C][C]-1.19999538705943[/C][/ROW]
[ROW][C]57[/C][C]99.07[/C][C]98.8000922584609[/C][C]0.2699077415391[/C][/ROW]
[ROW][C]58[/C][C]99.46[/C][C]99.0699792488595[/C][C]0.390020751140455[/C][/ROW]
[ROW][C]59[/C][C]99.18[/C][C]99.4599700142896[/C][C]-0.279970014289546[/C][/ROW]
[ROW][C]60[/C][C]98.47[/C][C]99.1800215247516[/C][C]-0.710021524751596[/C][/ROW]
[ROW][C]61[/C][C]97.12[/C][C]98.4700545881207[/C][C]-1.35005458812073[/C][/ROW]
[ROW][C]62[/C][C]96.91[/C][C]97.1201037953643[/C][C]-0.210103795364347[/C][/ROW]
[ROW][C]63[/C][C]96.09[/C][C]96.9100161532727[/C][C]-0.820016153272732[/C][/ROW]
[ROW][C]64[/C][C]97.17[/C][C]96.0900630447659[/C][C]1.07993695523413[/C][/ROW]
[ROW][C]65[/C][C]96.8[/C][C]97.169916971913[/C][C]-0.369916971913042[/C][/ROW]
[ROW][C]66[/C][C]97.13[/C][C]96.8000284400847[/C][C]0.329971559915265[/C][/ROW]
[ROW][C]67[/C][C]99.9[/C][C]97.1299746310123[/C][C]2.77002536898775[/C][/ROW]
[ROW][C]68[/C][C]100.56[/C][C]99.8997870339504[/C][C]0.660212966049627[/C][/ROW]
[ROW][C]69[/C][C]100.84[/C][C]100.559949241278[/C][C]0.28005075872187[/C][/ROW]
[ROW][C]70[/C][C]99.81[/C][C]100.839978469041[/C][C]-1.02997846904059[/C][/ROW]
[ROW][C]71[/C][C]100.44[/C][C]99.8100791871613[/C][C]0.629920812838662[/C][/ROW]
[ROW][C]72[/C][C]100.07[/C][C]100.43995157021[/C][C]-0.369951570209935[/C][/ROW]
[ROW][C]73[/C][C]101.32[/C][C]100.070028442745[/C][C]1.24997155725526[/C][/ROW]
[ROW][C]74[/C][C]103.98[/C][C]101.319903899254[/C][C]2.66009610074612[/C][/ROW]
[ROW][C]75[/C][C]104.81[/C][C]103.97979548557[/C][C]0.830204514429568[/C][/ROW]
[ROW][C]76[/C][C]106.23[/C][C]104.809936171929[/C][C]1.42006382807097[/C][/ROW]
[ROW][C]77[/C][C]106.48[/C][C]106.229890822161[/C][C]0.250109177838965[/C][/ROW]
[ROW][C]78[/C][C]107.59[/C][C]106.47998077102[/C][C]1.11001922898042[/C][/ROW]
[ROW][C]79[/C][C]107.16[/C][C]107.589914659117[/C][C]-0.429914659117259[/C][/ROW]
[ROW][C]80[/C][C]107.54[/C][C]107.160033052848[/C][C]0.379966947152312[/C][/ROW]
[ROW][C]81[/C][C]107.1[/C][C]107.53997078725[/C][C]-0.439970787249607[/C][/ROW]
[ROW][C]82[/C][C]106.38[/C][C]107.100033825986[/C][C]-0.72003382598642[/C][/ROW]
[ROW][C]83[/C][C]106.64[/C][C]106.38005535789[/C][C]0.259944642110057[/C][/ROW]
[ROW][C]84[/C][C]106.13[/C][C]106.639980014846[/C][C]-0.509980014846022[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294935&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294935&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
284.5484.510.0300000000000011
384.2784.5399976935296-0.269997693529632
484.4784.27002075805620.199979241943836
584.2584.4699846251267-0.219984625126671
684.3384.25001691293410.0799830870658695
784.2984.3299938507126-0.0399938507126052
884.5384.29000307482110.239996925178914
984.0184.5299815484733-0.519981548473282
1084.1884.01003997740150.169960022598531
1184.0884.1799869330747-0.099986933074689
1283.4484.08000768723-0.64000768723001
1383.6183.44004920529260.169950794707361
1483.8983.60998693378410.280013066215858
1583.483.8899784719385-0.489978471938471
1682.9683.4000376706946-0.440037670694565
1782.7682.9600338311286-0.200033831128565
1883.3582.76001537907030.589984620929712
1987.7883.34995464059814.43004535940193
2088.9987.77965940771861.21034059228138
2188.9288.9899069461755-0.0699069461754647
2288.9188.92000537461-0.0100053746100457
2389.7988.91000076923670.879999230763346
2490.5489.78993234359440.750067656405591
2593.1590.53994233303872.6100576669613
2692.7993.1497993326426-0.359799332642623
2793.2192.79002766221690.419972337783108
2895.3593.20996771154132.14003228845871
29100.9195.34983546929655.56016453070346
30103.69100.9095725215052.78042747849486
31104.04103.6897862342120.350213765788226
32104.16104.0399730747440.120026925255999
33104.71104.1599907720480.55000922795162
34105.18104.7099577140.470042285999938
35104.92105.179963862046-0.259963862046206
36104.83104.920019986632-0.090019986631674
37104.9104.8300069209480.0699930790522245
38105.05104.8999946187680.150005381232134
39104.6105.049988467234-0.449988467234334
40103.21104.600034596169-1.39003459616916
41102.52103.210106869121-0.690106869121166
42101.09102.520053057035-1.43005305703528
43101.19101.0901099458340.0998900541656553
44102.34101.1899923202181.15000767978175
45102.62102.3399115847110.280088415288674
46102.47102.619978466145-0.14997846614547
47101.82102.470011530696-0.650011530696375
48101.86101.8200499744120.0399500255884107
49101.54101.859996928548-0.319996928548292
50101.98101.5400246021150.439975397885334
51101.23101.979966173659-0.749966173659104
52100.4101.230057659159-0.830057659159067
5399.94100.40006381678-0.460063816780405
5499.9499.9400353707857-3.53707856675101e-05
5510099.94000000271940.0599999972806131
5698.899.9999953870594-1.19999538705943
5799.0798.80009225846090.2699077415391
5899.4699.06997924885950.390020751140455
5999.1899.4599700142896-0.279970014289546
6098.4799.1800215247516-0.710021524751596
6197.1298.4700545881207-1.35005458812073
6296.9197.1201037953643-0.210103795364347
6396.0996.9100161532727-0.820016153272732
6497.1796.09006304476591.07993695523413
6596.897.169916971913-0.369916971913042
6697.1396.80002844008470.329971559915265
6799.997.12997463101232.77002536898775
68100.5699.89978703395040.660212966049627
69100.84100.5599492412780.28005075872187
7099.81100.839978469041-1.02997846904059
71100.4499.81007918716130.629920812838662
72100.07100.43995157021-0.369951570209935
73101.32100.0700284427451.24997155725526
74103.98101.3199038992542.66009610074612
75104.81103.979795485570.830204514429568
76106.23104.8099361719291.42006382807097
77106.48106.2298908221610.250109177838965
78107.59106.479980771021.11001922898042
79107.16107.589914659117-0.429914659117259
80107.54107.1600330528480.379966947152312
81107.1107.53997078725-0.439970787249607
82106.38107.100033825986-0.72003382598642
83106.64106.380055357890.259944642110057
84106.13106.639980014846-0.509980014846022







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85106.13003920846103.880210959629108.379867457291
86106.13003920846102.948423893329109.311654523591
87106.13003920846102.233422101569110.026656315351
88106.13003920846101.630642166416110.629436250504
89106.13003920846101.099579725849111.160498691071
90106.13003920846100.619461065431111.640617351489
91106.13003920846100.177945431085112.082132985835
92106.1300392084699.7669920454332112.493086371487
93106.1300392084699.3810157188623112.879062698058
94106.1300392084699.015949883228113.244128533692
95106.1300392084698.6687245929504113.59135382397
96106.1300392084698.3369547962484113.923123620672

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 106.13003920846 & 103.880210959629 & 108.379867457291 \tabularnewline
86 & 106.13003920846 & 102.948423893329 & 109.311654523591 \tabularnewline
87 & 106.13003920846 & 102.233422101569 & 110.026656315351 \tabularnewline
88 & 106.13003920846 & 101.630642166416 & 110.629436250504 \tabularnewline
89 & 106.13003920846 & 101.099579725849 & 111.160498691071 \tabularnewline
90 & 106.13003920846 & 100.619461065431 & 111.640617351489 \tabularnewline
91 & 106.13003920846 & 100.177945431085 & 112.082132985835 \tabularnewline
92 & 106.13003920846 & 99.7669920454332 & 112.493086371487 \tabularnewline
93 & 106.13003920846 & 99.3810157188623 & 112.879062698058 \tabularnewline
94 & 106.13003920846 & 99.015949883228 & 113.244128533692 \tabularnewline
95 & 106.13003920846 & 98.6687245929504 & 113.59135382397 \tabularnewline
96 & 106.13003920846 & 98.3369547962484 & 113.923123620672 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294935&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]106.13003920846[/C][C]103.880210959629[/C][C]108.379867457291[/C][/ROW]
[ROW][C]86[/C][C]106.13003920846[/C][C]102.948423893329[/C][C]109.311654523591[/C][/ROW]
[ROW][C]87[/C][C]106.13003920846[/C][C]102.233422101569[/C][C]110.026656315351[/C][/ROW]
[ROW][C]88[/C][C]106.13003920846[/C][C]101.630642166416[/C][C]110.629436250504[/C][/ROW]
[ROW][C]89[/C][C]106.13003920846[/C][C]101.099579725849[/C][C]111.160498691071[/C][/ROW]
[ROW][C]90[/C][C]106.13003920846[/C][C]100.619461065431[/C][C]111.640617351489[/C][/ROW]
[ROW][C]91[/C][C]106.13003920846[/C][C]100.177945431085[/C][C]112.082132985835[/C][/ROW]
[ROW][C]92[/C][C]106.13003920846[/C][C]99.7669920454332[/C][C]112.493086371487[/C][/ROW]
[ROW][C]93[/C][C]106.13003920846[/C][C]99.3810157188623[/C][C]112.879062698058[/C][/ROW]
[ROW][C]94[/C][C]106.13003920846[/C][C]99.015949883228[/C][C]113.244128533692[/C][/ROW]
[ROW][C]95[/C][C]106.13003920846[/C][C]98.6687245929504[/C][C]113.59135382397[/C][/ROW]
[ROW][C]96[/C][C]106.13003920846[/C][C]98.3369547962484[/C][C]113.923123620672[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294935&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294935&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
85106.13003920846103.880210959629108.379867457291
86106.13003920846102.948423893329109.311654523591
87106.13003920846102.233422101569110.026656315351
88106.13003920846101.630642166416110.629436250504
89106.13003920846101.099579725849111.160498691071
90106.13003920846100.619461065431111.640617351489
91106.13003920846100.177945431085112.082132985835
92106.1300392084699.7669920454332112.493086371487
93106.1300392084699.3810157188623112.879062698058
94106.1300392084699.015949883228113.244128533692
95106.1300392084698.6687245929504113.59135382397
96106.1300392084698.3369547962484113.923123620672



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