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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Dec 2013 02:51:10 -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/16/t1387180918jvu2z57edoq7puh.htm/, Retrieved Fri, 29 Mar 2024 08:57:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232366, Retrieved Fri, 29 Mar 2024 08:57:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-16 07:51:10] [41a3153726230bb9de171cb3fce0abfe] [Current]
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Dataseries X:
155,28
173,24
180,16
181,52
182,25
182,19
182
181,65
180,07
182,62
180,38
181,15
180,5
181,14
180,93
211,91
223,81
226,88
226,8
231,81
232,06
232,32
228,37
226,31
225,72
219,98
219,31
215,19
213,81
213,7
213,6
213,52
218,39
219,97
221,09
219,17
219,17
218,45
216,88
216,19
214,59
269,87
272,71
280,35
274,5
268,86
261,7
263,98
263,01
262,79
263,59
267
267,89
267,86
266,84
268,24
267,67
269,07
270,87
271,68
271,63
275,21
276,66
276,08
278,3
279,06
279,28
279,12
262,72
262,55
260,7
259,14
260,61
260,53
259,07
257,01
257,08
256,83
256,75
257,61
258,58
259,57
259,29
258,51




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232366&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232366&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232366&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.799850524962499
beta0.020735492314969
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.799850524962499 \tabularnewline
beta & 0.020735492314969 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232366&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]0.799850524962499[/C][/ROW]
[ROW][C]beta[/C][C]0.020735492314969[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232366&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232366&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
alpha0.799850524962499
beta0.020735492314969
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13180.5165.08271634615415.4172836538462
14181.14177.5931193199393.54688068006092
15180.93179.5182169706211.41178302937928
16211.91210.9681371484150.941862851584659
17223.81223.1444791646680.665520835332188
18226.88226.469993399810.410006600189547
19226.8219.2908511866817.50914881331886
20231.81227.3028363767044.50716362329629
21232.06232.777184772219-0.717184772219127
22232.32237.253857307065-4.93385730706513
23228.37231.786409291954-3.41640929195447
24226.31229.890197381056-3.58019738105602
25225.72229.334362083305-3.61436208330539
26219.98224.291722051082-4.311722051082
27219.31219.418720019314-0.108720019313949
28215.19249.448139279254-34.2581392792544
29213.81232.72035752504-18.9103575250404
30213.7219.318208553049-5.61820855304936
31213.6207.6195595651265.98044043487414
32213.52212.6638814106890.856118589310995
33218.39212.9676558879365.42234411206383
34219.97220.408261881352-0.438261881351764
35221.09217.8120882765453.27791172345462
36219.17220.320331354385-1.15033135438458
37219.17220.82426858022-1.65426858021954
38218.45216.3654238155632.08457618443714
39216.88216.7114071065340.168592893465501
40216.19239.393920394934-23.203920394934
41214.59234.029322841504-19.4393228415039
42269.87222.30533523882247.5646647611775
43272.71255.78939042455216.9206095754483
44280.35269.06291942737611.2870805726242
45274.5279.301169993938-4.80116999393772
46268.86277.89927368815-9.03927368815022
47261.7269.532494195976-7.83249419597558
48263.98262.4486211113751.53137888862511
49263.01265.221998237719-2.2119982377186
50262.79261.2814661460871.50853385391309
51263.59260.9897500105432.60024998945653
52267281.186090371393-14.1860903713933
53267.89284.184315618946-16.2943156189458
54267.86288.835262007637-20.9752620076374
55266.84260.6760597327596.16394026724134
56268.24263.351741247424.88825875257965
57267.67264.2791375505033.39086244949721
58269.07267.7445573690681.32544263093155
59270.87267.2446087228213.62539127717929
60271.68270.7246088101890.955391189810712
61271.63271.803597160101-0.173597160101338
62275.21269.7875015210335.42249847896665
63276.66272.459150448124.20084955187986
64276.08290.216772404363-14.1367724043628
65278.3292.474120836338-14.1741208363379
66279.06297.560817586391-18.500817586391
67279.28276.5305378721712.74946212782856
68279.12275.8810299469473.23897005305304
69262.72274.823394473129-12.1033944731295
70262.55264.859210992247-2.30921099224662
71260.7261.229013377607-0.529013377607498
72259.14260.099406706794-0.9594067067938
73260.61258.6368141431861.97318585681381
74260.53258.709422274811.82057772519022
75259.07257.4473643317361.62263566826448
76257.01268.621578442461-11.6115784424608
77257.08272.082153697488-15.0021536974876
78256.83274.817753052954-17.9877530529536
79256.75257.636781137944-0.886781137944126
80257.61253.3021892504384.30781074956201
81258.58249.1718197691859.40818023081459
82259.57257.8738764960151.69612350398523
83259.29257.3699782565871.92002174341258
84258.51257.7200334403050.789966559694619

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 180.5 & 165.082716346154 & 15.4172836538462 \tabularnewline
14 & 181.14 & 177.593119319939 & 3.54688068006092 \tabularnewline
15 & 180.93 & 179.518216970621 & 1.41178302937928 \tabularnewline
16 & 211.91 & 210.968137148415 & 0.941862851584659 \tabularnewline
17 & 223.81 & 223.144479164668 & 0.665520835332188 \tabularnewline
18 & 226.88 & 226.46999339981 & 0.410006600189547 \tabularnewline
19 & 226.8 & 219.290851186681 & 7.50914881331886 \tabularnewline
20 & 231.81 & 227.302836376704 & 4.50716362329629 \tabularnewline
21 & 232.06 & 232.777184772219 & -0.717184772219127 \tabularnewline
22 & 232.32 & 237.253857307065 & -4.93385730706513 \tabularnewline
23 & 228.37 & 231.786409291954 & -3.41640929195447 \tabularnewline
24 & 226.31 & 229.890197381056 & -3.58019738105602 \tabularnewline
25 & 225.72 & 229.334362083305 & -3.61436208330539 \tabularnewline
26 & 219.98 & 224.291722051082 & -4.311722051082 \tabularnewline
27 & 219.31 & 219.418720019314 & -0.108720019313949 \tabularnewline
28 & 215.19 & 249.448139279254 & -34.2581392792544 \tabularnewline
29 & 213.81 & 232.72035752504 & -18.9103575250404 \tabularnewline
30 & 213.7 & 219.318208553049 & -5.61820855304936 \tabularnewline
31 & 213.6 & 207.619559565126 & 5.98044043487414 \tabularnewline
32 & 213.52 & 212.663881410689 & 0.856118589310995 \tabularnewline
33 & 218.39 & 212.967655887936 & 5.42234411206383 \tabularnewline
34 & 219.97 & 220.408261881352 & -0.438261881351764 \tabularnewline
35 & 221.09 & 217.812088276545 & 3.27791172345462 \tabularnewline
36 & 219.17 & 220.320331354385 & -1.15033135438458 \tabularnewline
37 & 219.17 & 220.82426858022 & -1.65426858021954 \tabularnewline
38 & 218.45 & 216.365423815563 & 2.08457618443714 \tabularnewline
39 & 216.88 & 216.711407106534 & 0.168592893465501 \tabularnewline
40 & 216.19 & 239.393920394934 & -23.203920394934 \tabularnewline
41 & 214.59 & 234.029322841504 & -19.4393228415039 \tabularnewline
42 & 269.87 & 222.305335238822 & 47.5646647611775 \tabularnewline
43 & 272.71 & 255.789390424552 & 16.9206095754483 \tabularnewline
44 & 280.35 & 269.062919427376 & 11.2870805726242 \tabularnewline
45 & 274.5 & 279.301169993938 & -4.80116999393772 \tabularnewline
46 & 268.86 & 277.89927368815 & -9.03927368815022 \tabularnewline
47 & 261.7 & 269.532494195976 & -7.83249419597558 \tabularnewline
48 & 263.98 & 262.448621111375 & 1.53137888862511 \tabularnewline
49 & 263.01 & 265.221998237719 & -2.2119982377186 \tabularnewline
50 & 262.79 & 261.281466146087 & 1.50853385391309 \tabularnewline
51 & 263.59 & 260.989750010543 & 2.60024998945653 \tabularnewline
52 & 267 & 281.186090371393 & -14.1860903713933 \tabularnewline
53 & 267.89 & 284.184315618946 & -16.2943156189458 \tabularnewline
54 & 267.86 & 288.835262007637 & -20.9752620076374 \tabularnewline
55 & 266.84 & 260.676059732759 & 6.16394026724134 \tabularnewline
56 & 268.24 & 263.35174124742 & 4.88825875257965 \tabularnewline
57 & 267.67 & 264.279137550503 & 3.39086244949721 \tabularnewline
58 & 269.07 & 267.744557369068 & 1.32544263093155 \tabularnewline
59 & 270.87 & 267.244608722821 & 3.62539127717929 \tabularnewline
60 & 271.68 & 270.724608810189 & 0.955391189810712 \tabularnewline
61 & 271.63 & 271.803597160101 & -0.173597160101338 \tabularnewline
62 & 275.21 & 269.787501521033 & 5.42249847896665 \tabularnewline
63 & 276.66 & 272.45915044812 & 4.20084955187986 \tabularnewline
64 & 276.08 & 290.216772404363 & -14.1367724043628 \tabularnewline
65 & 278.3 & 292.474120836338 & -14.1741208363379 \tabularnewline
66 & 279.06 & 297.560817586391 & -18.500817586391 \tabularnewline
67 & 279.28 & 276.530537872171 & 2.74946212782856 \tabularnewline
68 & 279.12 & 275.881029946947 & 3.23897005305304 \tabularnewline
69 & 262.72 & 274.823394473129 & -12.1033944731295 \tabularnewline
70 & 262.55 & 264.859210992247 & -2.30921099224662 \tabularnewline
71 & 260.7 & 261.229013377607 & -0.529013377607498 \tabularnewline
72 & 259.14 & 260.099406706794 & -0.9594067067938 \tabularnewline
73 & 260.61 & 258.636814143186 & 1.97318585681381 \tabularnewline
74 & 260.53 & 258.70942227481 & 1.82057772519022 \tabularnewline
75 & 259.07 & 257.447364331736 & 1.62263566826448 \tabularnewline
76 & 257.01 & 268.621578442461 & -11.6115784424608 \tabularnewline
77 & 257.08 & 272.082153697488 & -15.0021536974876 \tabularnewline
78 & 256.83 & 274.817753052954 & -17.9877530529536 \tabularnewline
79 & 256.75 & 257.636781137944 & -0.886781137944126 \tabularnewline
80 & 257.61 & 253.302189250438 & 4.30781074956201 \tabularnewline
81 & 258.58 & 249.171819769185 & 9.40818023081459 \tabularnewline
82 & 259.57 & 257.873876496015 & 1.69612350398523 \tabularnewline
83 & 259.29 & 257.369978256587 & 1.92002174341258 \tabularnewline
84 & 258.51 & 257.720033440305 & 0.789966559694619 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232366&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]180.5[/C][C]165.082716346154[/C][C]15.4172836538462[/C][/ROW]
[ROW][C]14[/C][C]181.14[/C][C]177.593119319939[/C][C]3.54688068006092[/C][/ROW]
[ROW][C]15[/C][C]180.93[/C][C]179.518216970621[/C][C]1.41178302937928[/C][/ROW]
[ROW][C]16[/C][C]211.91[/C][C]210.968137148415[/C][C]0.941862851584659[/C][/ROW]
[ROW][C]17[/C][C]223.81[/C][C]223.144479164668[/C][C]0.665520835332188[/C][/ROW]
[ROW][C]18[/C][C]226.88[/C][C]226.46999339981[/C][C]0.410006600189547[/C][/ROW]
[ROW][C]19[/C][C]226.8[/C][C]219.290851186681[/C][C]7.50914881331886[/C][/ROW]
[ROW][C]20[/C][C]231.81[/C][C]227.302836376704[/C][C]4.50716362329629[/C][/ROW]
[ROW][C]21[/C][C]232.06[/C][C]232.777184772219[/C][C]-0.717184772219127[/C][/ROW]
[ROW][C]22[/C][C]232.32[/C][C]237.253857307065[/C][C]-4.93385730706513[/C][/ROW]
[ROW][C]23[/C][C]228.37[/C][C]231.786409291954[/C][C]-3.41640929195447[/C][/ROW]
[ROW][C]24[/C][C]226.31[/C][C]229.890197381056[/C][C]-3.58019738105602[/C][/ROW]
[ROW][C]25[/C][C]225.72[/C][C]229.334362083305[/C][C]-3.61436208330539[/C][/ROW]
[ROW][C]26[/C][C]219.98[/C][C]224.291722051082[/C][C]-4.311722051082[/C][/ROW]
[ROW][C]27[/C][C]219.31[/C][C]219.418720019314[/C][C]-0.108720019313949[/C][/ROW]
[ROW][C]28[/C][C]215.19[/C][C]249.448139279254[/C][C]-34.2581392792544[/C][/ROW]
[ROW][C]29[/C][C]213.81[/C][C]232.72035752504[/C][C]-18.9103575250404[/C][/ROW]
[ROW][C]30[/C][C]213.7[/C][C]219.318208553049[/C][C]-5.61820855304936[/C][/ROW]
[ROW][C]31[/C][C]213.6[/C][C]207.619559565126[/C][C]5.98044043487414[/C][/ROW]
[ROW][C]32[/C][C]213.52[/C][C]212.663881410689[/C][C]0.856118589310995[/C][/ROW]
[ROW][C]33[/C][C]218.39[/C][C]212.967655887936[/C][C]5.42234411206383[/C][/ROW]
[ROW][C]34[/C][C]219.97[/C][C]220.408261881352[/C][C]-0.438261881351764[/C][/ROW]
[ROW][C]35[/C][C]221.09[/C][C]217.812088276545[/C][C]3.27791172345462[/C][/ROW]
[ROW][C]36[/C][C]219.17[/C][C]220.320331354385[/C][C]-1.15033135438458[/C][/ROW]
[ROW][C]37[/C][C]219.17[/C][C]220.82426858022[/C][C]-1.65426858021954[/C][/ROW]
[ROW][C]38[/C][C]218.45[/C][C]216.365423815563[/C][C]2.08457618443714[/C][/ROW]
[ROW][C]39[/C][C]216.88[/C][C]216.711407106534[/C][C]0.168592893465501[/C][/ROW]
[ROW][C]40[/C][C]216.19[/C][C]239.393920394934[/C][C]-23.203920394934[/C][/ROW]
[ROW][C]41[/C][C]214.59[/C][C]234.029322841504[/C][C]-19.4393228415039[/C][/ROW]
[ROW][C]42[/C][C]269.87[/C][C]222.305335238822[/C][C]47.5646647611775[/C][/ROW]
[ROW][C]43[/C][C]272.71[/C][C]255.789390424552[/C][C]16.9206095754483[/C][/ROW]
[ROW][C]44[/C][C]280.35[/C][C]269.062919427376[/C][C]11.2870805726242[/C][/ROW]
[ROW][C]45[/C][C]274.5[/C][C]279.301169993938[/C][C]-4.80116999393772[/C][/ROW]
[ROW][C]46[/C][C]268.86[/C][C]277.89927368815[/C][C]-9.03927368815022[/C][/ROW]
[ROW][C]47[/C][C]261.7[/C][C]269.532494195976[/C][C]-7.83249419597558[/C][/ROW]
[ROW][C]48[/C][C]263.98[/C][C]262.448621111375[/C][C]1.53137888862511[/C][/ROW]
[ROW][C]49[/C][C]263.01[/C][C]265.221998237719[/C][C]-2.2119982377186[/C][/ROW]
[ROW][C]50[/C][C]262.79[/C][C]261.281466146087[/C][C]1.50853385391309[/C][/ROW]
[ROW][C]51[/C][C]263.59[/C][C]260.989750010543[/C][C]2.60024998945653[/C][/ROW]
[ROW][C]52[/C][C]267[/C][C]281.186090371393[/C][C]-14.1860903713933[/C][/ROW]
[ROW][C]53[/C][C]267.89[/C][C]284.184315618946[/C][C]-16.2943156189458[/C][/ROW]
[ROW][C]54[/C][C]267.86[/C][C]288.835262007637[/C][C]-20.9752620076374[/C][/ROW]
[ROW][C]55[/C][C]266.84[/C][C]260.676059732759[/C][C]6.16394026724134[/C][/ROW]
[ROW][C]56[/C][C]268.24[/C][C]263.35174124742[/C][C]4.88825875257965[/C][/ROW]
[ROW][C]57[/C][C]267.67[/C][C]264.279137550503[/C][C]3.39086244949721[/C][/ROW]
[ROW][C]58[/C][C]269.07[/C][C]267.744557369068[/C][C]1.32544263093155[/C][/ROW]
[ROW][C]59[/C][C]270.87[/C][C]267.244608722821[/C][C]3.62539127717929[/C][/ROW]
[ROW][C]60[/C][C]271.68[/C][C]270.724608810189[/C][C]0.955391189810712[/C][/ROW]
[ROW][C]61[/C][C]271.63[/C][C]271.803597160101[/C][C]-0.173597160101338[/C][/ROW]
[ROW][C]62[/C][C]275.21[/C][C]269.787501521033[/C][C]5.42249847896665[/C][/ROW]
[ROW][C]63[/C][C]276.66[/C][C]272.45915044812[/C][C]4.20084955187986[/C][/ROW]
[ROW][C]64[/C][C]276.08[/C][C]290.216772404363[/C][C]-14.1367724043628[/C][/ROW]
[ROW][C]65[/C][C]278.3[/C][C]292.474120836338[/C][C]-14.1741208363379[/C][/ROW]
[ROW][C]66[/C][C]279.06[/C][C]297.560817586391[/C][C]-18.500817586391[/C][/ROW]
[ROW][C]67[/C][C]279.28[/C][C]276.530537872171[/C][C]2.74946212782856[/C][/ROW]
[ROW][C]68[/C][C]279.12[/C][C]275.881029946947[/C][C]3.23897005305304[/C][/ROW]
[ROW][C]69[/C][C]262.72[/C][C]274.823394473129[/C][C]-12.1033944731295[/C][/ROW]
[ROW][C]70[/C][C]262.55[/C][C]264.859210992247[/C][C]-2.30921099224662[/C][/ROW]
[ROW][C]71[/C][C]260.7[/C][C]261.229013377607[/C][C]-0.529013377607498[/C][/ROW]
[ROW][C]72[/C][C]259.14[/C][C]260.099406706794[/C][C]-0.9594067067938[/C][/ROW]
[ROW][C]73[/C][C]260.61[/C][C]258.636814143186[/C][C]1.97318585681381[/C][/ROW]
[ROW][C]74[/C][C]260.53[/C][C]258.70942227481[/C][C]1.82057772519022[/C][/ROW]
[ROW][C]75[/C][C]259.07[/C][C]257.447364331736[/C][C]1.62263566826448[/C][/ROW]
[ROW][C]76[/C][C]257.01[/C][C]268.621578442461[/C][C]-11.6115784424608[/C][/ROW]
[ROW][C]77[/C][C]257.08[/C][C]272.082153697488[/C][C]-15.0021536974876[/C][/ROW]
[ROW][C]78[/C][C]256.83[/C][C]274.817753052954[/C][C]-17.9877530529536[/C][/ROW]
[ROW][C]79[/C][C]256.75[/C][C]257.636781137944[/C][C]-0.886781137944126[/C][/ROW]
[ROW][C]80[/C][C]257.61[/C][C]253.302189250438[/C][C]4.30781074956201[/C][/ROW]
[ROW][C]81[/C][C]258.58[/C][C]249.171819769185[/C][C]9.40818023081459[/C][/ROW]
[ROW][C]82[/C][C]259.57[/C][C]257.873876496015[/C][C]1.69612350398523[/C][/ROW]
[ROW][C]83[/C][C]259.29[/C][C]257.369978256587[/C][C]1.92002174341258[/C][/ROW]
[ROW][C]84[/C][C]258.51[/C][C]257.720033440305[/C][C]0.789966559694619[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232366&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232366&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
13180.5165.08271634615415.4172836538462
14181.14177.5931193199393.54688068006092
15180.93179.5182169706211.41178302937928
16211.91210.9681371484150.941862851584659
17223.81223.1444791646680.665520835332188
18226.88226.469993399810.410006600189547
19226.8219.2908511866817.50914881331886
20231.81227.3028363767044.50716362329629
21232.06232.777184772219-0.717184772219127
22232.32237.253857307065-4.93385730706513
23228.37231.786409291954-3.41640929195447
24226.31229.890197381056-3.58019738105602
25225.72229.334362083305-3.61436208330539
26219.98224.291722051082-4.311722051082
27219.31219.418720019314-0.108720019313949
28215.19249.448139279254-34.2581392792544
29213.81232.72035752504-18.9103575250404
30213.7219.318208553049-5.61820855304936
31213.6207.6195595651265.98044043487414
32213.52212.6638814106890.856118589310995
33218.39212.9676558879365.42234411206383
34219.97220.408261881352-0.438261881351764
35221.09217.8120882765453.27791172345462
36219.17220.320331354385-1.15033135438458
37219.17220.82426858022-1.65426858021954
38218.45216.3654238155632.08457618443714
39216.88216.7114071065340.168592893465501
40216.19239.393920394934-23.203920394934
41214.59234.029322841504-19.4393228415039
42269.87222.30533523882247.5646647611775
43272.71255.78939042455216.9206095754483
44280.35269.06291942737611.2870805726242
45274.5279.301169993938-4.80116999393772
46268.86277.89927368815-9.03927368815022
47261.7269.532494195976-7.83249419597558
48263.98262.4486211113751.53137888862511
49263.01265.221998237719-2.2119982377186
50262.79261.2814661460871.50853385391309
51263.59260.9897500105432.60024998945653
52267281.186090371393-14.1860903713933
53267.89284.184315618946-16.2943156189458
54267.86288.835262007637-20.9752620076374
55266.84260.6760597327596.16394026724134
56268.24263.351741247424.88825875257965
57267.67264.2791375505033.39086244949721
58269.07267.7445573690681.32544263093155
59270.87267.2446087228213.62539127717929
60271.68270.7246088101890.955391189810712
61271.63271.803597160101-0.173597160101338
62275.21269.7875015210335.42249847896665
63276.66272.459150448124.20084955187986
64276.08290.216772404363-14.1367724043628
65278.3292.474120836338-14.1741208363379
66279.06297.560817586391-18.500817586391
67279.28276.5305378721712.74946212782856
68279.12275.8810299469473.23897005305304
69262.72274.823394473129-12.1033944731295
70262.55264.859210992247-2.30921099224662
71260.7261.229013377607-0.529013377607498
72259.14260.099406706794-0.9594067067938
73260.61258.6368141431861.97318585681381
74260.53258.709422274811.82057772519022
75259.07257.4473643317361.62263566826448
76257.01268.621578442461-11.6115784424608
77257.08272.082153697488-15.0021536974876
78256.83274.817753052954-17.9877530529536
79256.75257.636781137944-0.886781137944126
80257.61253.3021892504384.30781074956201
81258.58249.1718197691859.40818023081459
82259.57257.8738764960151.69612350398523
83259.29257.3699782565871.92002174341258
84258.51257.7200334403050.789966559694619







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85257.879591561251236.54448785447279.214695268032
86255.946632340547228.403951759849283.489312921246
87252.761802360412219.982780490765285.540824230059
88259.535453593923222.078383075042296.992524112805
89271.343639672166229.575790276448313.111489067884
90285.468674098115239.650795199286331.286552996944
91286.383819340695236.710316333703336.057322347686
92284.09877506134230.719562965872337.477987156809
93277.772751265344220.806282234641334.739220296047
94277.479182651819217.020748592866337.937616710773
95275.708398206276211.835699286992339.581097125559
96274.30964486677207.086678053783341.532611679758

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 257.879591561251 & 236.54448785447 & 279.214695268032 \tabularnewline
86 & 255.946632340547 & 228.403951759849 & 283.489312921246 \tabularnewline
87 & 252.761802360412 & 219.982780490765 & 285.540824230059 \tabularnewline
88 & 259.535453593923 & 222.078383075042 & 296.992524112805 \tabularnewline
89 & 271.343639672166 & 229.575790276448 & 313.111489067884 \tabularnewline
90 & 285.468674098115 & 239.650795199286 & 331.286552996944 \tabularnewline
91 & 286.383819340695 & 236.710316333703 & 336.057322347686 \tabularnewline
92 & 284.09877506134 & 230.719562965872 & 337.477987156809 \tabularnewline
93 & 277.772751265344 & 220.806282234641 & 334.739220296047 \tabularnewline
94 & 277.479182651819 & 217.020748592866 & 337.937616710773 \tabularnewline
95 & 275.708398206276 & 211.835699286992 & 339.581097125559 \tabularnewline
96 & 274.30964486677 & 207.086678053783 & 341.532611679758 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232366&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]257.879591561251[/C][C]236.54448785447[/C][C]279.214695268032[/C][/ROW]
[ROW][C]86[/C][C]255.946632340547[/C][C]228.403951759849[/C][C]283.489312921246[/C][/ROW]
[ROW][C]87[/C][C]252.761802360412[/C][C]219.982780490765[/C][C]285.540824230059[/C][/ROW]
[ROW][C]88[/C][C]259.535453593923[/C][C]222.078383075042[/C][C]296.992524112805[/C][/ROW]
[ROW][C]89[/C][C]271.343639672166[/C][C]229.575790276448[/C][C]313.111489067884[/C][/ROW]
[ROW][C]90[/C][C]285.468674098115[/C][C]239.650795199286[/C][C]331.286552996944[/C][/ROW]
[ROW][C]91[/C][C]286.383819340695[/C][C]236.710316333703[/C][C]336.057322347686[/C][/ROW]
[ROW][C]92[/C][C]284.09877506134[/C][C]230.719562965872[/C][C]337.477987156809[/C][/ROW]
[ROW][C]93[/C][C]277.772751265344[/C][C]220.806282234641[/C][C]334.739220296047[/C][/ROW]
[ROW][C]94[/C][C]277.479182651819[/C][C]217.020748592866[/C][C]337.937616710773[/C][/ROW]
[ROW][C]95[/C][C]275.708398206276[/C][C]211.835699286992[/C][C]339.581097125559[/C][/ROW]
[ROW][C]96[/C][C]274.30964486677[/C][C]207.086678053783[/C][C]341.532611679758[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232366&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232366&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
85257.879591561251236.54448785447279.214695268032
86255.946632340547228.403951759849283.489312921246
87252.761802360412219.982780490765285.540824230059
88259.535453593923222.078383075042296.992524112805
89271.343639672166229.575790276448313.111489067884
90285.468674098115239.650795199286331.286552996944
91286.383819340695236.710316333703336.057322347686
92284.09877506134230.719562965872337.477987156809
93277.772751265344220.806282234641334.739220296047
94277.479182651819217.020748592866337.937616710773
95275.708398206276211.835699286992339.581097125559
96274.30964486677207.086678053783341.532611679758



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