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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 29 Nov 2011 11:23:28 -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/2011/Nov/29/t132258393469vtbg6z9aasrvl.htm/, Retrieved Thu, 28 Mar 2024 23:53:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148596, Retrieved Thu, 28 Mar 2024 23:53:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:56:43] [74be16979710d4c4e7c6647856088456]
- RM D    [Exponential Smoothing] [] [2011-11-29 16:23:28] [fdaf10f0fcbe7b8f79ecbd42ec74e6ad] [Current]
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Dataseries X:
19.785
18.479
10.698
31.956
29.506
34.506
27.165
26.736
23.691
18.157
17.328
18.205
20.995
17.382
9.367
31.124
26.551
30.651
25.859
25.100
25.778
20.418
18.688
20.424
24.776
19.814
12.738
31.566
30.111
30.019
31.934
25.826
26.835
20.205
17.789
20.520
22.518
15.572
11.509
25.447
24.090
27.786
26.195
20.516
22.759
19.028
16.971
20.036
22.485
18.730
14.538
27.561
25.985
34.670
32.066
27.186
29.586
21.359
21.553
19.573
24.256
22.380
16.167
27.297
28.287
33.474
28.229
28.785
25.597
18.130
20.198
22.849
23.118




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148596&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148596&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148596&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.344861705580417
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.344861705580417 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148596&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]0.344861705580417[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148596&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148596&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
alpha0.344861705580417
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1320.99522.0603571047009-1.06535710470085
1417.38218.1281804498082-0.746180449808215
159.3679.76270060050331-0.395700600503309
1631.12431.1277128298013-0.00371282980125542
1726.55126.32819829693680.222801703063158
1830.65130.28154995221480.36945004778519
1925.85926.3828083391075-0.523808339107482
2025.125.6940994485057-0.594099448505677
2125.77822.47102484602973.30697515397033
2220.41818.09323981789332.32476018210667
2318.68818.14939312598010.538606874019877
2420.42419.42152889114531.00247110885467
2524.77621.99996909763862.77603090236141
2619.81419.60164491196250.212355088037484
2712.73811.79634003380060.941659966199431
2831.56633.8793629086387-2.31336290863869
2930.11128.43173685501451.67926314498551
3030.01932.9834412337066-2.96444123370656
3131.93427.34976041097954.58423958902054
3225.82628.3765712435344-2.55057124353441
3326.83527.0345278023745-0.19952780237449
3420.20520.8039975426702-0.598997542670165
3517.78918.6816813432546-0.892681343254619
3620.5219.76411583628530.755884163714697
3722.51823.4194445864729-0.901444586472877
3815.57218.0733377310463-2.50133773104632
3911.5099.80997967286471.6990203271353
4025.44730.021696998996-4.574696998996
4124.0926.4099456371106-2.31994563711059
4227.78626.54020748779171.24579251220826
4326.19527.3039049348923-1.1089049348923
4420.51621.6930804369684-1.17708043696844
4522.75922.36495996810770.39404003189226
4619.02816.07742059977682.95057940022322
4716.97114.98681405476281.98418594523719
4820.03618.14140830210611.89459169789388
4922.48521.10365414399761.38134585600243
5018.7315.49664302805633.2333569719437
5114.53811.96277698031952.57522301968054
5227.56128.3665105927238-0.805510592723817
5325.98527.5317812451218-1.54678124512179
5434.6730.26472949620984.40527050379016
5532.06630.57535744286351.49064255713649
5627.18625.81635294462661.36964705537336
5729.58628.39580244672061.19019755327943
5821.35924.0577141605107-2.69871416051073
5921.55320.38576124297981.16723875702021
6019.57323.1999250672312-3.62692506723116
6124.25623.9217642146360.334235785363987
6222.3819.16696833754783.21303166245219
6316.16715.1949241139280.97207588607203
6427.29728.8309456188222-1.53394561882219
6528.28727.25937213480011.02762786519993
6633.47434.7795525336147-1.30555253361471
6728.22931.2112519254827-2.98225192548266
6828.78524.8304486204313.95455137956903
6925.59728.1837683957929-2.58676839579295
7018.1319.995374203146-1.86537420314603
7120.19819.14354212533781.05445787466218
7222.84918.77797183115424.07102816884577
7323.11824.7496484259217-1.63164842592167

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 20.995 & 22.0603571047009 & -1.06535710470085 \tabularnewline
14 & 17.382 & 18.1281804498082 & -0.746180449808215 \tabularnewline
15 & 9.367 & 9.76270060050331 & -0.395700600503309 \tabularnewline
16 & 31.124 & 31.1277128298013 & -0.00371282980125542 \tabularnewline
17 & 26.551 & 26.3281982969368 & 0.222801703063158 \tabularnewline
18 & 30.651 & 30.2815499522148 & 0.36945004778519 \tabularnewline
19 & 25.859 & 26.3828083391075 & -0.523808339107482 \tabularnewline
20 & 25.1 & 25.6940994485057 & -0.594099448505677 \tabularnewline
21 & 25.778 & 22.4710248460297 & 3.30697515397033 \tabularnewline
22 & 20.418 & 18.0932398178933 & 2.32476018210667 \tabularnewline
23 & 18.688 & 18.1493931259801 & 0.538606874019877 \tabularnewline
24 & 20.424 & 19.4215288911453 & 1.00247110885467 \tabularnewline
25 & 24.776 & 21.9999690976386 & 2.77603090236141 \tabularnewline
26 & 19.814 & 19.6016449119625 & 0.212355088037484 \tabularnewline
27 & 12.738 & 11.7963400338006 & 0.941659966199431 \tabularnewline
28 & 31.566 & 33.8793629086387 & -2.31336290863869 \tabularnewline
29 & 30.111 & 28.4317368550145 & 1.67926314498551 \tabularnewline
30 & 30.019 & 32.9834412337066 & -2.96444123370656 \tabularnewline
31 & 31.934 & 27.3497604109795 & 4.58423958902054 \tabularnewline
32 & 25.826 & 28.3765712435344 & -2.55057124353441 \tabularnewline
33 & 26.835 & 27.0345278023745 & -0.19952780237449 \tabularnewline
34 & 20.205 & 20.8039975426702 & -0.598997542670165 \tabularnewline
35 & 17.789 & 18.6816813432546 & -0.892681343254619 \tabularnewline
36 & 20.52 & 19.7641158362853 & 0.755884163714697 \tabularnewline
37 & 22.518 & 23.4194445864729 & -0.901444586472877 \tabularnewline
38 & 15.572 & 18.0733377310463 & -2.50133773104632 \tabularnewline
39 & 11.509 & 9.8099796728647 & 1.6990203271353 \tabularnewline
40 & 25.447 & 30.021696998996 & -4.574696998996 \tabularnewline
41 & 24.09 & 26.4099456371106 & -2.31994563711059 \tabularnewline
42 & 27.786 & 26.5402074877917 & 1.24579251220826 \tabularnewline
43 & 26.195 & 27.3039049348923 & -1.1089049348923 \tabularnewline
44 & 20.516 & 21.6930804369684 & -1.17708043696844 \tabularnewline
45 & 22.759 & 22.3649599681077 & 0.39404003189226 \tabularnewline
46 & 19.028 & 16.0774205997768 & 2.95057940022322 \tabularnewline
47 & 16.971 & 14.9868140547628 & 1.98418594523719 \tabularnewline
48 & 20.036 & 18.1414083021061 & 1.89459169789388 \tabularnewline
49 & 22.485 & 21.1036541439976 & 1.38134585600243 \tabularnewline
50 & 18.73 & 15.4966430280563 & 3.2333569719437 \tabularnewline
51 & 14.538 & 11.9627769803195 & 2.57522301968054 \tabularnewline
52 & 27.561 & 28.3665105927238 & -0.805510592723817 \tabularnewline
53 & 25.985 & 27.5317812451218 & -1.54678124512179 \tabularnewline
54 & 34.67 & 30.2647294962098 & 4.40527050379016 \tabularnewline
55 & 32.066 & 30.5753574428635 & 1.49064255713649 \tabularnewline
56 & 27.186 & 25.8163529446266 & 1.36964705537336 \tabularnewline
57 & 29.586 & 28.3958024467206 & 1.19019755327943 \tabularnewline
58 & 21.359 & 24.0577141605107 & -2.69871416051073 \tabularnewline
59 & 21.553 & 20.3857612429798 & 1.16723875702021 \tabularnewline
60 & 19.573 & 23.1999250672312 & -3.62692506723116 \tabularnewline
61 & 24.256 & 23.921764214636 & 0.334235785363987 \tabularnewline
62 & 22.38 & 19.1669683375478 & 3.21303166245219 \tabularnewline
63 & 16.167 & 15.194924113928 & 0.97207588607203 \tabularnewline
64 & 27.297 & 28.8309456188222 & -1.53394561882219 \tabularnewline
65 & 28.287 & 27.2593721348001 & 1.02762786519993 \tabularnewline
66 & 33.474 & 34.7795525336147 & -1.30555253361471 \tabularnewline
67 & 28.229 & 31.2112519254827 & -2.98225192548266 \tabularnewline
68 & 28.785 & 24.830448620431 & 3.95455137956903 \tabularnewline
69 & 25.597 & 28.1837683957929 & -2.58676839579295 \tabularnewline
70 & 18.13 & 19.995374203146 & -1.86537420314603 \tabularnewline
71 & 20.198 & 19.1435421253378 & 1.05445787466218 \tabularnewline
72 & 22.849 & 18.7779718311542 & 4.07102816884577 \tabularnewline
73 & 23.118 & 24.7496484259217 & -1.63164842592167 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148596&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]20.995[/C][C]22.0603571047009[/C][C]-1.06535710470085[/C][/ROW]
[ROW][C]14[/C][C]17.382[/C][C]18.1281804498082[/C][C]-0.746180449808215[/C][/ROW]
[ROW][C]15[/C][C]9.367[/C][C]9.76270060050331[/C][C]-0.395700600503309[/C][/ROW]
[ROW][C]16[/C][C]31.124[/C][C]31.1277128298013[/C][C]-0.00371282980125542[/C][/ROW]
[ROW][C]17[/C][C]26.551[/C][C]26.3281982969368[/C][C]0.222801703063158[/C][/ROW]
[ROW][C]18[/C][C]30.651[/C][C]30.2815499522148[/C][C]0.36945004778519[/C][/ROW]
[ROW][C]19[/C][C]25.859[/C][C]26.3828083391075[/C][C]-0.523808339107482[/C][/ROW]
[ROW][C]20[/C][C]25.1[/C][C]25.6940994485057[/C][C]-0.594099448505677[/C][/ROW]
[ROW][C]21[/C][C]25.778[/C][C]22.4710248460297[/C][C]3.30697515397033[/C][/ROW]
[ROW][C]22[/C][C]20.418[/C][C]18.0932398178933[/C][C]2.32476018210667[/C][/ROW]
[ROW][C]23[/C][C]18.688[/C][C]18.1493931259801[/C][C]0.538606874019877[/C][/ROW]
[ROW][C]24[/C][C]20.424[/C][C]19.4215288911453[/C][C]1.00247110885467[/C][/ROW]
[ROW][C]25[/C][C]24.776[/C][C]21.9999690976386[/C][C]2.77603090236141[/C][/ROW]
[ROW][C]26[/C][C]19.814[/C][C]19.6016449119625[/C][C]0.212355088037484[/C][/ROW]
[ROW][C]27[/C][C]12.738[/C][C]11.7963400338006[/C][C]0.941659966199431[/C][/ROW]
[ROW][C]28[/C][C]31.566[/C][C]33.8793629086387[/C][C]-2.31336290863869[/C][/ROW]
[ROW][C]29[/C][C]30.111[/C][C]28.4317368550145[/C][C]1.67926314498551[/C][/ROW]
[ROW][C]30[/C][C]30.019[/C][C]32.9834412337066[/C][C]-2.96444123370656[/C][/ROW]
[ROW][C]31[/C][C]31.934[/C][C]27.3497604109795[/C][C]4.58423958902054[/C][/ROW]
[ROW][C]32[/C][C]25.826[/C][C]28.3765712435344[/C][C]-2.55057124353441[/C][/ROW]
[ROW][C]33[/C][C]26.835[/C][C]27.0345278023745[/C][C]-0.19952780237449[/C][/ROW]
[ROW][C]34[/C][C]20.205[/C][C]20.8039975426702[/C][C]-0.598997542670165[/C][/ROW]
[ROW][C]35[/C][C]17.789[/C][C]18.6816813432546[/C][C]-0.892681343254619[/C][/ROW]
[ROW][C]36[/C][C]20.52[/C][C]19.7641158362853[/C][C]0.755884163714697[/C][/ROW]
[ROW][C]37[/C][C]22.518[/C][C]23.4194445864729[/C][C]-0.901444586472877[/C][/ROW]
[ROW][C]38[/C][C]15.572[/C][C]18.0733377310463[/C][C]-2.50133773104632[/C][/ROW]
[ROW][C]39[/C][C]11.509[/C][C]9.8099796728647[/C][C]1.6990203271353[/C][/ROW]
[ROW][C]40[/C][C]25.447[/C][C]30.021696998996[/C][C]-4.574696998996[/C][/ROW]
[ROW][C]41[/C][C]24.09[/C][C]26.4099456371106[/C][C]-2.31994563711059[/C][/ROW]
[ROW][C]42[/C][C]27.786[/C][C]26.5402074877917[/C][C]1.24579251220826[/C][/ROW]
[ROW][C]43[/C][C]26.195[/C][C]27.3039049348923[/C][C]-1.1089049348923[/C][/ROW]
[ROW][C]44[/C][C]20.516[/C][C]21.6930804369684[/C][C]-1.17708043696844[/C][/ROW]
[ROW][C]45[/C][C]22.759[/C][C]22.3649599681077[/C][C]0.39404003189226[/C][/ROW]
[ROW][C]46[/C][C]19.028[/C][C]16.0774205997768[/C][C]2.95057940022322[/C][/ROW]
[ROW][C]47[/C][C]16.971[/C][C]14.9868140547628[/C][C]1.98418594523719[/C][/ROW]
[ROW][C]48[/C][C]20.036[/C][C]18.1414083021061[/C][C]1.89459169789388[/C][/ROW]
[ROW][C]49[/C][C]22.485[/C][C]21.1036541439976[/C][C]1.38134585600243[/C][/ROW]
[ROW][C]50[/C][C]18.73[/C][C]15.4966430280563[/C][C]3.2333569719437[/C][/ROW]
[ROW][C]51[/C][C]14.538[/C][C]11.9627769803195[/C][C]2.57522301968054[/C][/ROW]
[ROW][C]52[/C][C]27.561[/C][C]28.3665105927238[/C][C]-0.805510592723817[/C][/ROW]
[ROW][C]53[/C][C]25.985[/C][C]27.5317812451218[/C][C]-1.54678124512179[/C][/ROW]
[ROW][C]54[/C][C]34.67[/C][C]30.2647294962098[/C][C]4.40527050379016[/C][/ROW]
[ROW][C]55[/C][C]32.066[/C][C]30.5753574428635[/C][C]1.49064255713649[/C][/ROW]
[ROW][C]56[/C][C]27.186[/C][C]25.8163529446266[/C][C]1.36964705537336[/C][/ROW]
[ROW][C]57[/C][C]29.586[/C][C]28.3958024467206[/C][C]1.19019755327943[/C][/ROW]
[ROW][C]58[/C][C]21.359[/C][C]24.0577141605107[/C][C]-2.69871416051073[/C][/ROW]
[ROW][C]59[/C][C]21.553[/C][C]20.3857612429798[/C][C]1.16723875702021[/C][/ROW]
[ROW][C]60[/C][C]19.573[/C][C]23.1999250672312[/C][C]-3.62692506723116[/C][/ROW]
[ROW][C]61[/C][C]24.256[/C][C]23.921764214636[/C][C]0.334235785363987[/C][/ROW]
[ROW][C]62[/C][C]22.38[/C][C]19.1669683375478[/C][C]3.21303166245219[/C][/ROW]
[ROW][C]63[/C][C]16.167[/C][C]15.194924113928[/C][C]0.97207588607203[/C][/ROW]
[ROW][C]64[/C][C]27.297[/C][C]28.8309456188222[/C][C]-1.53394561882219[/C][/ROW]
[ROW][C]65[/C][C]28.287[/C][C]27.2593721348001[/C][C]1.02762786519993[/C][/ROW]
[ROW][C]66[/C][C]33.474[/C][C]34.7795525336147[/C][C]-1.30555253361471[/C][/ROW]
[ROW][C]67[/C][C]28.229[/C][C]31.2112519254827[/C][C]-2.98225192548266[/C][/ROW]
[ROW][C]68[/C][C]28.785[/C][C]24.830448620431[/C][C]3.95455137956903[/C][/ROW]
[ROW][C]69[/C][C]25.597[/C][C]28.1837683957929[/C][C]-2.58676839579295[/C][/ROW]
[ROW][C]70[/C][C]18.13[/C][C]19.995374203146[/C][C]-1.86537420314603[/C][/ROW]
[ROW][C]71[/C][C]20.198[/C][C]19.1435421253378[/C][C]1.05445787466218[/C][/ROW]
[ROW][C]72[/C][C]22.849[/C][C]18.7779718311542[/C][C]4.07102816884577[/C][/ROW]
[ROW][C]73[/C][C]23.118[/C][C]24.7496484259217[/C][C]-1.63164842592167[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148596&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148596&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
1320.99522.0603571047009-1.06535710470085
1417.38218.1281804498082-0.746180449808215
159.3679.76270060050331-0.395700600503309
1631.12431.1277128298013-0.00371282980125542
1726.55126.32819829693680.222801703063158
1830.65130.28154995221480.36945004778519
1925.85926.3828083391075-0.523808339107482
2025.125.6940994485057-0.594099448505677
2125.77822.47102484602973.30697515397033
2220.41818.09323981789332.32476018210667
2318.68818.14939312598010.538606874019877
2420.42419.42152889114531.00247110885467
2524.77621.99996909763862.77603090236141
2619.81419.60164491196250.212355088037484
2712.73811.79634003380060.941659966199431
2831.56633.8793629086387-2.31336290863869
2930.11128.43173685501451.67926314498551
3030.01932.9834412337066-2.96444123370656
3131.93427.34976041097954.58423958902054
3225.82628.3765712435344-2.55057124353441
3326.83527.0345278023745-0.19952780237449
3420.20520.8039975426702-0.598997542670165
3517.78918.6816813432546-0.892681343254619
3620.5219.76411583628530.755884163714697
3722.51823.4194445864729-0.901444586472877
3815.57218.0733377310463-2.50133773104632
3911.5099.80997967286471.6990203271353
4025.44730.021696998996-4.574696998996
4124.0926.4099456371106-2.31994563711059
4227.78626.54020748779171.24579251220826
4326.19527.3039049348923-1.1089049348923
4420.51621.6930804369684-1.17708043696844
4522.75922.36495996810770.39404003189226
4619.02816.07742059977682.95057940022322
4716.97114.98681405476281.98418594523719
4820.03618.14140830210611.89459169789388
4922.48521.10365414399761.38134585600243
5018.7315.49664302805633.2333569719437
5114.53811.96277698031952.57522301968054
5227.56128.3665105927238-0.805510592723817
5325.98527.5317812451218-1.54678124512179
5434.6730.26472949620984.40527050379016
5532.06630.57535744286351.49064255713649
5627.18625.81635294462661.36964705537336
5729.58628.39580244672061.19019755327943
5821.35924.0577141605107-2.69871416051073
5921.55320.38576124297981.16723875702021
6019.57323.1999250672312-3.62692506723116
6124.25623.9217642146360.334235785363987
6222.3819.16696833754783.21303166245219
6316.16715.1949241139280.97207588607203
6427.29728.8309456188222-1.53394561882219
6528.28727.25937213480011.02762786519993
6633.47434.7795525336147-1.30555253361471
6728.22931.2112519254827-2.98225192548266
6828.78524.8304486204313.95455137956903
6925.59728.1837683957929-2.58676839579295
7018.1319.995374203146-1.86537420314603
7120.19819.14354212533781.05445787466218
7222.84918.77797183115424.07102816884577
7323.11824.7496484259217-1.63164842592167







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7421.202903787653617.053292214793125.352515360514
7514.654672039629210.265234972333719.0441091069247
7626.313671142003821.696849797195530.9304924868122
7726.94928164370922.11576109528831.78280219213
7832.586516717176227.545603857967237.6274295763852
7928.369981202668623.129877767022633.6100846383146
8027.562207869105122.130213246648332.9942024915619
8125.266285230019719.648950707265230.8836197527743
8218.442581359262412.645829794578924.2393329239458
8320.146939218143714.176159514889626.1177189213977
8421.393997500369615.254120316995327.533874683744
8522.225690559440615.921249792088428.5301313267927

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 21.2029037876536 & 17.0532922147931 & 25.352515360514 \tabularnewline
75 & 14.6546720396292 & 10.2652349723337 & 19.0441091069247 \tabularnewline
76 & 26.3136711420038 & 21.6968497971955 & 30.9304924868122 \tabularnewline
77 & 26.949281643709 & 22.115761095288 & 31.78280219213 \tabularnewline
78 & 32.5865167171762 & 27.5456038579672 & 37.6274295763852 \tabularnewline
79 & 28.3699812026686 & 23.1298777670226 & 33.6100846383146 \tabularnewline
80 & 27.5622078691051 & 22.1302132466483 & 32.9942024915619 \tabularnewline
81 & 25.2662852300197 & 19.6489507072652 & 30.8836197527743 \tabularnewline
82 & 18.4425813592624 & 12.6458297945789 & 24.2393329239458 \tabularnewline
83 & 20.1469392181437 & 14.1761595148896 & 26.1177189213977 \tabularnewline
84 & 21.3939975003696 & 15.2541203169953 & 27.533874683744 \tabularnewline
85 & 22.2256905594406 & 15.9212497920884 & 28.5301313267927 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148596&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]74[/C][C]21.2029037876536[/C][C]17.0532922147931[/C][C]25.352515360514[/C][/ROW]
[ROW][C]75[/C][C]14.6546720396292[/C][C]10.2652349723337[/C][C]19.0441091069247[/C][/ROW]
[ROW][C]76[/C][C]26.3136711420038[/C][C]21.6968497971955[/C][C]30.9304924868122[/C][/ROW]
[ROW][C]77[/C][C]26.949281643709[/C][C]22.115761095288[/C][C]31.78280219213[/C][/ROW]
[ROW][C]78[/C][C]32.5865167171762[/C][C]27.5456038579672[/C][C]37.6274295763852[/C][/ROW]
[ROW][C]79[/C][C]28.3699812026686[/C][C]23.1298777670226[/C][C]33.6100846383146[/C][/ROW]
[ROW][C]80[/C][C]27.5622078691051[/C][C]22.1302132466483[/C][C]32.9942024915619[/C][/ROW]
[ROW][C]81[/C][C]25.2662852300197[/C][C]19.6489507072652[/C][C]30.8836197527743[/C][/ROW]
[ROW][C]82[/C][C]18.4425813592624[/C][C]12.6458297945789[/C][C]24.2393329239458[/C][/ROW]
[ROW][C]83[/C][C]20.1469392181437[/C][C]14.1761595148896[/C][C]26.1177189213977[/C][/ROW]
[ROW][C]84[/C][C]21.3939975003696[/C][C]15.2541203169953[/C][C]27.533874683744[/C][/ROW]
[ROW][C]85[/C][C]22.2256905594406[/C][C]15.9212497920884[/C][C]28.5301313267927[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148596&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148596&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
7421.202903787653617.053292214793125.352515360514
7514.654672039629210.265234972333719.0441091069247
7626.313671142003821.696849797195530.9304924868122
7726.94928164370922.11576109528831.78280219213
7832.586516717176227.545603857967237.6274295763852
7928.369981202668623.129877767022633.6100846383146
8027.562207869105122.130213246648332.9942024915619
8125.266285230019719.648950707265230.8836197527743
8218.442581359262412.645829794578924.2393329239458
8320.146939218143714.176159514889626.1177189213977
8421.393997500369615.254120316995327.533874683744
8522.225690559440615.921249792088428.5301313267927



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')