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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 18:43:26 +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/t14616926301nrtpvvu4j7mcgl.htm/, Retrieved Fri, 03 May 2024 20:06:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294936, Retrieved Fri, 03 May 2024 20:06:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 17:43:26] [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'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294936&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294936&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294936&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.901730058109269
beta0.162185551012511
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.901730058109269 \tabularnewline
beta & 0.162185551012511 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294936&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]0.901730058109269[/C][/ROW]
[ROW][C]beta[/C][C]0.162185551012511[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294936&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294936&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
alpha0.901730058109269
beta0.162185551012511
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1383.6184.0740300143006-0.464030014300647
1483.8983.68174448449370.208255515506252
1583.483.10036210231180.299637897688172
1682.9682.68665102939920.273348970600765
1782.7682.4983501061410.26164989385903
1883.3583.03160224958920.31839775041081
1987.7886.2814186995541.49858130044602
2088.9988.45095175850580.539048241494186
2188.9289.0334436408375-0.11344364083746
2288.9189.7784854759993-0.868485475999321
2389.7989.45740214124130.332597858758675
2490.5489.66437656215070.875623437849356
2593.1591.08487333730212.06512666269789
2692.7993.8759317888083-1.08593178880831
2793.2192.68244745022860.527552549771428
2895.3593.03952379982862.31047620017141
29100.9195.55192251981675.35807748018331
30103.69102.4059854450611.28401455493939
31104.04109.224483595716-5.18448359571582
32104.16106.246392724344-2.08639272434387
33104.71104.846715408304-0.136715408303672
34105.18106.074651911256-0.894651911256304
35104.92106.412782625267-1.49278262526691
36104.83105.207366155298-0.377366155297551
37104.9105.718440164857-0.818440164856767
38105.05105.226605229431-0.176605229431345
39104.6104.705122081091-0.105122081090741
40103.21104.278057632951-1.06805763295068
41102.52103.199164312035-0.679164312035468
42101.09102.538748916374-1.44874891637384
43101.19104.047888535705-2.8578885357051
44102.34101.6615861128940.678413887106004
45102.62101.5715033310681.04849666893212
46102.47102.57751273027-0.107512730269505
47101.82102.463875738019-0.643875738019318
48101.86101.1783915335250.681608466475481
49101.54101.781702117017-0.241702117016558
50101.98101.1520026821450.827997317854724
51101.23100.9928847967620.237115203237607
52100.4100.2870420671990.112957932800867
5399.9499.9744804881052-0.034480488105217
5499.9499.57437351171930.365626488280711
55100102.555260819188-2.55526081918792
5698.8100.836127729591-2.03612772959137
5799.0798.00665361611641.06334638388358
5899.4698.57206939613990.887930603860113
5999.1899.10841904560580.0715809543941646
6098.4798.5191982700767-0.0491982700767011
6197.1298.1771946606577-1.0571946606577
6296.9196.60939454001540.300605459984638
6396.0995.57572720109940.514272798900578
6497.1794.81176878728262.35823121271743
6596.896.50949823863630.2905017613637
6697.1396.48466083133190.645339168668073
6799.999.43383116494410.466168835055882
68100.56101.005642437112-0.445642437111715
69100.84100.664208320870.175791679129716
7099.81101.03411768565-1.22411768565036
71100.4499.89865334471910.541346655280918
72100.07100.097152809586-0.0271528095864397
73101.32100.0568401285321.26315987146771
74103.98101.4365155002662.54348449973378
75104.81103.4262821255291.38371787447134
76106.23104.7185982218151.51140177818513
77106.48106.4192443663380.0607556336615431
78107.59107.1833493393160.406650660683979
79107.16111.114322036295-3.95432203629498
80107.54109.00967005032-1.46967005031992
81107.1107.988602972188-0.88860297218821
82106.38107.282360710263-0.902360710263437
83106.64106.695921847481-0.0559218474811587
84106.13106.262595450573-0.132595450573191

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 83.61 & 84.0740300143006 & -0.464030014300647 \tabularnewline
14 & 83.89 & 83.6817444844937 & 0.208255515506252 \tabularnewline
15 & 83.4 & 83.1003621023118 & 0.299637897688172 \tabularnewline
16 & 82.96 & 82.6866510293992 & 0.273348970600765 \tabularnewline
17 & 82.76 & 82.498350106141 & 0.26164989385903 \tabularnewline
18 & 83.35 & 83.0316022495892 & 0.31839775041081 \tabularnewline
19 & 87.78 & 86.281418699554 & 1.49858130044602 \tabularnewline
20 & 88.99 & 88.4509517585058 & 0.539048241494186 \tabularnewline
21 & 88.92 & 89.0334436408375 & -0.11344364083746 \tabularnewline
22 & 88.91 & 89.7784854759993 & -0.868485475999321 \tabularnewline
23 & 89.79 & 89.4574021412413 & 0.332597858758675 \tabularnewline
24 & 90.54 & 89.6643765621507 & 0.875623437849356 \tabularnewline
25 & 93.15 & 91.0848733373021 & 2.06512666269789 \tabularnewline
26 & 92.79 & 93.8759317888083 & -1.08593178880831 \tabularnewline
27 & 93.21 & 92.6824474502286 & 0.527552549771428 \tabularnewline
28 & 95.35 & 93.0395237998286 & 2.31047620017141 \tabularnewline
29 & 100.91 & 95.5519225198167 & 5.35807748018331 \tabularnewline
30 & 103.69 & 102.405985445061 & 1.28401455493939 \tabularnewline
31 & 104.04 & 109.224483595716 & -5.18448359571582 \tabularnewline
32 & 104.16 & 106.246392724344 & -2.08639272434387 \tabularnewline
33 & 104.71 & 104.846715408304 & -0.136715408303672 \tabularnewline
34 & 105.18 & 106.074651911256 & -0.894651911256304 \tabularnewline
35 & 104.92 & 106.412782625267 & -1.49278262526691 \tabularnewline
36 & 104.83 & 105.207366155298 & -0.377366155297551 \tabularnewline
37 & 104.9 & 105.718440164857 & -0.818440164856767 \tabularnewline
38 & 105.05 & 105.226605229431 & -0.176605229431345 \tabularnewline
39 & 104.6 & 104.705122081091 & -0.105122081090741 \tabularnewline
40 & 103.21 & 104.278057632951 & -1.06805763295068 \tabularnewline
41 & 102.52 & 103.199164312035 & -0.679164312035468 \tabularnewline
42 & 101.09 & 102.538748916374 & -1.44874891637384 \tabularnewline
43 & 101.19 & 104.047888535705 & -2.8578885357051 \tabularnewline
44 & 102.34 & 101.661586112894 & 0.678413887106004 \tabularnewline
45 & 102.62 & 101.571503331068 & 1.04849666893212 \tabularnewline
46 & 102.47 & 102.57751273027 & -0.107512730269505 \tabularnewline
47 & 101.82 & 102.463875738019 & -0.643875738019318 \tabularnewline
48 & 101.86 & 101.178391533525 & 0.681608466475481 \tabularnewline
49 & 101.54 & 101.781702117017 & -0.241702117016558 \tabularnewline
50 & 101.98 & 101.152002682145 & 0.827997317854724 \tabularnewline
51 & 101.23 & 100.992884796762 & 0.237115203237607 \tabularnewline
52 & 100.4 & 100.287042067199 & 0.112957932800867 \tabularnewline
53 & 99.94 & 99.9744804881052 & -0.034480488105217 \tabularnewline
54 & 99.94 & 99.5743735117193 & 0.365626488280711 \tabularnewline
55 & 100 & 102.555260819188 & -2.55526081918792 \tabularnewline
56 & 98.8 & 100.836127729591 & -2.03612772959137 \tabularnewline
57 & 99.07 & 98.0066536161164 & 1.06334638388358 \tabularnewline
58 & 99.46 & 98.5720693961399 & 0.887930603860113 \tabularnewline
59 & 99.18 & 99.1084190456058 & 0.0715809543941646 \tabularnewline
60 & 98.47 & 98.5191982700767 & -0.0491982700767011 \tabularnewline
61 & 97.12 & 98.1771946606577 & -1.0571946606577 \tabularnewline
62 & 96.91 & 96.6093945400154 & 0.300605459984638 \tabularnewline
63 & 96.09 & 95.5757272010994 & 0.514272798900578 \tabularnewline
64 & 97.17 & 94.8117687872826 & 2.35823121271743 \tabularnewline
65 & 96.8 & 96.5094982386363 & 0.2905017613637 \tabularnewline
66 & 97.13 & 96.4846608313319 & 0.645339168668073 \tabularnewline
67 & 99.9 & 99.4338311649441 & 0.466168835055882 \tabularnewline
68 & 100.56 & 101.005642437112 & -0.445642437111715 \tabularnewline
69 & 100.84 & 100.66420832087 & 0.175791679129716 \tabularnewline
70 & 99.81 & 101.03411768565 & -1.22411768565036 \tabularnewline
71 & 100.44 & 99.8986533447191 & 0.541346655280918 \tabularnewline
72 & 100.07 & 100.097152809586 & -0.0271528095864397 \tabularnewline
73 & 101.32 & 100.056840128532 & 1.26315987146771 \tabularnewline
74 & 103.98 & 101.436515500266 & 2.54348449973378 \tabularnewline
75 & 104.81 & 103.426282125529 & 1.38371787447134 \tabularnewline
76 & 106.23 & 104.718598221815 & 1.51140177818513 \tabularnewline
77 & 106.48 & 106.419244366338 & 0.0607556336615431 \tabularnewline
78 & 107.59 & 107.183349339316 & 0.406650660683979 \tabularnewline
79 & 107.16 & 111.114322036295 & -3.95432203629498 \tabularnewline
80 & 107.54 & 109.00967005032 & -1.46967005031992 \tabularnewline
81 & 107.1 & 107.988602972188 & -0.88860297218821 \tabularnewline
82 & 106.38 & 107.282360710263 & -0.902360710263437 \tabularnewline
83 & 106.64 & 106.695921847481 & -0.0559218474811587 \tabularnewline
84 & 106.13 & 106.262595450573 & -0.132595450573191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294936&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]13[/C][C]83.61[/C][C]84.0740300143006[/C][C]-0.464030014300647[/C][/ROW]
[ROW][C]14[/C][C]83.89[/C][C]83.6817444844937[/C][C]0.208255515506252[/C][/ROW]
[ROW][C]15[/C][C]83.4[/C][C]83.1003621023118[/C][C]0.299637897688172[/C][/ROW]
[ROW][C]16[/C][C]82.96[/C][C]82.6866510293992[/C][C]0.273348970600765[/C][/ROW]
[ROW][C]17[/C][C]82.76[/C][C]82.498350106141[/C][C]0.26164989385903[/C][/ROW]
[ROW][C]18[/C][C]83.35[/C][C]83.0316022495892[/C][C]0.31839775041081[/C][/ROW]
[ROW][C]19[/C][C]87.78[/C][C]86.281418699554[/C][C]1.49858130044602[/C][/ROW]
[ROW][C]20[/C][C]88.99[/C][C]88.4509517585058[/C][C]0.539048241494186[/C][/ROW]
[ROW][C]21[/C][C]88.92[/C][C]89.0334436408375[/C][C]-0.11344364083746[/C][/ROW]
[ROW][C]22[/C][C]88.91[/C][C]89.7784854759993[/C][C]-0.868485475999321[/C][/ROW]
[ROW][C]23[/C][C]89.79[/C][C]89.4574021412413[/C][C]0.332597858758675[/C][/ROW]
[ROW][C]24[/C][C]90.54[/C][C]89.6643765621507[/C][C]0.875623437849356[/C][/ROW]
[ROW][C]25[/C][C]93.15[/C][C]91.0848733373021[/C][C]2.06512666269789[/C][/ROW]
[ROW][C]26[/C][C]92.79[/C][C]93.8759317888083[/C][C]-1.08593178880831[/C][/ROW]
[ROW][C]27[/C][C]93.21[/C][C]92.6824474502286[/C][C]0.527552549771428[/C][/ROW]
[ROW][C]28[/C][C]95.35[/C][C]93.0395237998286[/C][C]2.31047620017141[/C][/ROW]
[ROW][C]29[/C][C]100.91[/C][C]95.5519225198167[/C][C]5.35807748018331[/C][/ROW]
[ROW][C]30[/C][C]103.69[/C][C]102.405985445061[/C][C]1.28401455493939[/C][/ROW]
[ROW][C]31[/C][C]104.04[/C][C]109.224483595716[/C][C]-5.18448359571582[/C][/ROW]
[ROW][C]32[/C][C]104.16[/C][C]106.246392724344[/C][C]-2.08639272434387[/C][/ROW]
[ROW][C]33[/C][C]104.71[/C][C]104.846715408304[/C][C]-0.136715408303672[/C][/ROW]
[ROW][C]34[/C][C]105.18[/C][C]106.074651911256[/C][C]-0.894651911256304[/C][/ROW]
[ROW][C]35[/C][C]104.92[/C][C]106.412782625267[/C][C]-1.49278262526691[/C][/ROW]
[ROW][C]36[/C][C]104.83[/C][C]105.207366155298[/C][C]-0.377366155297551[/C][/ROW]
[ROW][C]37[/C][C]104.9[/C][C]105.718440164857[/C][C]-0.818440164856767[/C][/ROW]
[ROW][C]38[/C][C]105.05[/C][C]105.226605229431[/C][C]-0.176605229431345[/C][/ROW]
[ROW][C]39[/C][C]104.6[/C][C]104.705122081091[/C][C]-0.105122081090741[/C][/ROW]
[ROW][C]40[/C][C]103.21[/C][C]104.278057632951[/C][C]-1.06805763295068[/C][/ROW]
[ROW][C]41[/C][C]102.52[/C][C]103.199164312035[/C][C]-0.679164312035468[/C][/ROW]
[ROW][C]42[/C][C]101.09[/C][C]102.538748916374[/C][C]-1.44874891637384[/C][/ROW]
[ROW][C]43[/C][C]101.19[/C][C]104.047888535705[/C][C]-2.8578885357051[/C][/ROW]
[ROW][C]44[/C][C]102.34[/C][C]101.661586112894[/C][C]0.678413887106004[/C][/ROW]
[ROW][C]45[/C][C]102.62[/C][C]101.571503331068[/C][C]1.04849666893212[/C][/ROW]
[ROW][C]46[/C][C]102.47[/C][C]102.57751273027[/C][C]-0.107512730269505[/C][/ROW]
[ROW][C]47[/C][C]101.82[/C][C]102.463875738019[/C][C]-0.643875738019318[/C][/ROW]
[ROW][C]48[/C][C]101.86[/C][C]101.178391533525[/C][C]0.681608466475481[/C][/ROW]
[ROW][C]49[/C][C]101.54[/C][C]101.781702117017[/C][C]-0.241702117016558[/C][/ROW]
[ROW][C]50[/C][C]101.98[/C][C]101.152002682145[/C][C]0.827997317854724[/C][/ROW]
[ROW][C]51[/C][C]101.23[/C][C]100.992884796762[/C][C]0.237115203237607[/C][/ROW]
[ROW][C]52[/C][C]100.4[/C][C]100.287042067199[/C][C]0.112957932800867[/C][/ROW]
[ROW][C]53[/C][C]99.94[/C][C]99.9744804881052[/C][C]-0.034480488105217[/C][/ROW]
[ROW][C]54[/C][C]99.94[/C][C]99.5743735117193[/C][C]0.365626488280711[/C][/ROW]
[ROW][C]55[/C][C]100[/C][C]102.555260819188[/C][C]-2.55526081918792[/C][/ROW]
[ROW][C]56[/C][C]98.8[/C][C]100.836127729591[/C][C]-2.03612772959137[/C][/ROW]
[ROW][C]57[/C][C]99.07[/C][C]98.0066536161164[/C][C]1.06334638388358[/C][/ROW]
[ROW][C]58[/C][C]99.46[/C][C]98.5720693961399[/C][C]0.887930603860113[/C][/ROW]
[ROW][C]59[/C][C]99.18[/C][C]99.1084190456058[/C][C]0.0715809543941646[/C][/ROW]
[ROW][C]60[/C][C]98.47[/C][C]98.5191982700767[/C][C]-0.0491982700767011[/C][/ROW]
[ROW][C]61[/C][C]97.12[/C][C]98.1771946606577[/C][C]-1.0571946606577[/C][/ROW]
[ROW][C]62[/C][C]96.91[/C][C]96.6093945400154[/C][C]0.300605459984638[/C][/ROW]
[ROW][C]63[/C][C]96.09[/C][C]95.5757272010994[/C][C]0.514272798900578[/C][/ROW]
[ROW][C]64[/C][C]97.17[/C][C]94.8117687872826[/C][C]2.35823121271743[/C][/ROW]
[ROW][C]65[/C][C]96.8[/C][C]96.5094982386363[/C][C]0.2905017613637[/C][/ROW]
[ROW][C]66[/C][C]97.13[/C][C]96.4846608313319[/C][C]0.645339168668073[/C][/ROW]
[ROW][C]67[/C][C]99.9[/C][C]99.4338311649441[/C][C]0.466168835055882[/C][/ROW]
[ROW][C]68[/C][C]100.56[/C][C]101.005642437112[/C][C]-0.445642437111715[/C][/ROW]
[ROW][C]69[/C][C]100.84[/C][C]100.66420832087[/C][C]0.175791679129716[/C][/ROW]
[ROW][C]70[/C][C]99.81[/C][C]101.03411768565[/C][C]-1.22411768565036[/C][/ROW]
[ROW][C]71[/C][C]100.44[/C][C]99.8986533447191[/C][C]0.541346655280918[/C][/ROW]
[ROW][C]72[/C][C]100.07[/C][C]100.097152809586[/C][C]-0.0271528095864397[/C][/ROW]
[ROW][C]73[/C][C]101.32[/C][C]100.056840128532[/C][C]1.26315987146771[/C][/ROW]
[ROW][C]74[/C][C]103.98[/C][C]101.436515500266[/C][C]2.54348449973378[/C][/ROW]
[ROW][C]75[/C][C]104.81[/C][C]103.426282125529[/C][C]1.38371787447134[/C][/ROW]
[ROW][C]76[/C][C]106.23[/C][C]104.718598221815[/C][C]1.51140177818513[/C][/ROW]
[ROW][C]77[/C][C]106.48[/C][C]106.419244366338[/C][C]0.0607556336615431[/C][/ROW]
[ROW][C]78[/C][C]107.59[/C][C]107.183349339316[/C][C]0.406650660683979[/C][/ROW]
[ROW][C]79[/C][C]107.16[/C][C]111.114322036295[/C][C]-3.95432203629498[/C][/ROW]
[ROW][C]80[/C][C]107.54[/C][C]109.00967005032[/C][C]-1.46967005031992[/C][/ROW]
[ROW][C]81[/C][C]107.1[/C][C]107.988602972188[/C][C]-0.88860297218821[/C][/ROW]
[ROW][C]82[/C][C]106.38[/C][C]107.282360710263[/C][C]-0.902360710263437[/C][/ROW]
[ROW][C]83[/C][C]106.64[/C][C]106.695921847481[/C][C]-0.0559218474811587[/C][/ROW]
[ROW][C]84[/C][C]106.13[/C][C]106.262595450573[/C][C]-0.132595450573191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294936&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294936&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
1383.6184.0740300143006-0.464030014300647
1483.8983.68174448449370.208255515506252
1583.483.10036210231180.299637897688172
1682.9682.68665102939920.273348970600765
1782.7682.4983501061410.26164989385903
1883.3583.03160224958920.31839775041081
1987.7886.2814186995541.49858130044602
2088.9988.45095175850580.539048241494186
2188.9289.0334436408375-0.11344364083746
2288.9189.7784854759993-0.868485475999321
2389.7989.45740214124130.332597858758675
2490.5489.66437656215070.875623437849356
2593.1591.08487333730212.06512666269789
2692.7993.8759317888083-1.08593178880831
2793.2192.68244745022860.527552549771428
2895.3593.03952379982862.31047620017141
29100.9195.55192251981675.35807748018331
30103.69102.4059854450611.28401455493939
31104.04109.224483595716-5.18448359571582
32104.16106.246392724344-2.08639272434387
33104.71104.846715408304-0.136715408303672
34105.18106.074651911256-0.894651911256304
35104.92106.412782625267-1.49278262526691
36104.83105.207366155298-0.377366155297551
37104.9105.718440164857-0.818440164856767
38105.05105.226605229431-0.176605229431345
39104.6104.705122081091-0.105122081090741
40103.21104.278057632951-1.06805763295068
41102.52103.199164312035-0.679164312035468
42101.09102.538748916374-1.44874891637384
43101.19104.047888535705-2.8578885357051
44102.34101.6615861128940.678413887106004
45102.62101.5715033310681.04849666893212
46102.47102.57751273027-0.107512730269505
47101.82102.463875738019-0.643875738019318
48101.86101.1783915335250.681608466475481
49101.54101.781702117017-0.241702117016558
50101.98101.1520026821450.827997317854724
51101.23100.9928847967620.237115203237607
52100.4100.2870420671990.112957932800867
5399.9499.9744804881052-0.034480488105217
5499.9499.57437351171930.365626488280711
55100102.555260819188-2.55526081918792
5698.8100.836127729591-2.03612772959137
5799.0798.00665361611641.06334638388358
5899.4698.57206939613990.887930603860113
5999.1899.10841904560580.0715809543941646
6098.4798.5191982700767-0.0491982700767011
6197.1298.1771946606577-1.0571946606577
6296.9196.60939454001540.300605459984638
6396.0995.57572720109940.514272798900578
6497.1794.81176878728262.35823121271743
6596.896.50949823863630.2905017613637
6697.1396.48466083133190.645339168668073
6799.999.43383116494410.466168835055882
68100.56101.005642437112-0.445642437111715
69100.84100.664208320870.175791679129716
7099.81101.03411768565-1.22411768565036
71100.4499.89865334471910.541346655280918
72100.07100.097152809586-0.0271528095864397
73101.32100.0568401285321.26315987146771
74103.98101.4365155002662.54348449973378
75104.81103.4262821255291.38371787447134
76106.23104.7185982218151.51140177818513
77106.48106.4192443663380.0607556336615431
78107.59107.1833493393160.406650660683979
79107.16111.114322036295-3.95432203629498
80107.54109.00967005032-1.46967005031992
81107.1107.988602972188-0.88860297218821
82106.38107.282360710263-0.902360710263437
83106.64106.695921847481-0.0559218474811587
84106.13106.262595450573-0.132595450573191







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85106.228104879234103.371648298187109.08456146028
86106.382073298898102.242121766471110.522024831325
87105.35953782529100.033119941583110.685955708997
88104.63468150586998.1215780619505111.147784949787
89103.85287438255196.1464341420206111.559314623082
90103.60760022828594.6481232738412112.567077182729
91105.58133783896895.1338618181277116.028813859809
92106.76373534710794.8325540814319118.694916612782
93106.8346982873793.4873715754727120.182024999267
94106.76853063915491.9821676841698121.554893594138
95107.05218115643790.7372855067381123.367076806135
96106.64059384280436.5158909000208176.765296785586

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 106.228104879234 & 103.371648298187 & 109.08456146028 \tabularnewline
86 & 106.382073298898 & 102.242121766471 & 110.522024831325 \tabularnewline
87 & 105.35953782529 & 100.033119941583 & 110.685955708997 \tabularnewline
88 & 104.634681505869 & 98.1215780619505 & 111.147784949787 \tabularnewline
89 & 103.852874382551 & 96.1464341420206 & 111.559314623082 \tabularnewline
90 & 103.607600228285 & 94.6481232738412 & 112.567077182729 \tabularnewline
91 & 105.581337838968 & 95.1338618181277 & 116.028813859809 \tabularnewline
92 & 106.763735347107 & 94.8325540814319 & 118.694916612782 \tabularnewline
93 & 106.83469828737 & 93.4873715754727 & 120.182024999267 \tabularnewline
94 & 106.768530639154 & 91.9821676841698 & 121.554893594138 \tabularnewline
95 & 107.052181156437 & 90.7372855067381 & 123.367076806135 \tabularnewline
96 & 106.640593842804 & 36.5158909000208 & 176.765296785586 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294936&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]106.228104879234[/C][C]103.371648298187[/C][C]109.08456146028[/C][/ROW]
[ROW][C]86[/C][C]106.382073298898[/C][C]102.242121766471[/C][C]110.522024831325[/C][/ROW]
[ROW][C]87[/C][C]105.35953782529[/C][C]100.033119941583[/C][C]110.685955708997[/C][/ROW]
[ROW][C]88[/C][C]104.634681505869[/C][C]98.1215780619505[/C][C]111.147784949787[/C][/ROW]
[ROW][C]89[/C][C]103.852874382551[/C][C]96.1464341420206[/C][C]111.559314623082[/C][/ROW]
[ROW][C]90[/C][C]103.607600228285[/C][C]94.6481232738412[/C][C]112.567077182729[/C][/ROW]
[ROW][C]91[/C][C]105.581337838968[/C][C]95.1338618181277[/C][C]116.028813859809[/C][/ROW]
[ROW][C]92[/C][C]106.763735347107[/C][C]94.8325540814319[/C][C]118.694916612782[/C][/ROW]
[ROW][C]93[/C][C]106.83469828737[/C][C]93.4873715754727[/C][C]120.182024999267[/C][/ROW]
[ROW][C]94[/C][C]106.768530639154[/C][C]91.9821676841698[/C][C]121.554893594138[/C][/ROW]
[ROW][C]95[/C][C]107.052181156437[/C][C]90.7372855067381[/C][C]123.367076806135[/C][/ROW]
[ROW][C]96[/C][C]106.640593842804[/C][C]36.5158909000208[/C][C]176.765296785586[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294936&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294936&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
85106.228104879234103.371648298187109.08456146028
86106.382073298898102.242121766471110.522024831325
87105.35953782529100.033119941583110.685955708997
88104.63468150586998.1215780619505111.147784949787
89103.85287438255196.1464341420206111.559314623082
90103.60760022828594.6481232738412112.567077182729
91105.58133783896895.1338618181277116.028813859809
92106.76373534710794.8325540814319118.694916612782
93106.8346982873793.4873715754727120.182024999267
94106.76853063915491.9821676841698121.554893594138
95107.05218115643790.7372855067381123.367076806135
96106.64059384280436.5158909000208176.765296785586



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