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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 29 Nov 2015 14:33:48 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/29/t1448807691hx9siq9q7y4r4kt.htm/, Retrieved Wed, 15 May 2024 12:01:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284463, Retrieved Wed, 15 May 2024 12:01:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2015-11-29 14:33:48] [3f1a7081c5450f075552d8bc3f139f2c] [Current]
- R P     [Exponential Smoothing] [Double exponentia...] [2016-01-11 13:57:09] [b78554c675fd79077ee7678381a14583]
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Dataseries X:
26.133
25.979
25.541
25.308
25.663
25.78
25.328
24.806
24.651
24.531
24.633
25.174
24.449
24.277
24.393
24.301
24.381
24.286
24.335
24.273
24.556
24.841
25.464
25.514
25.531
25.042
24.676
24.809
25.313
25.64
25.447
25.021
24.752
24.939
25.365
25.214
25.563
25.475
25.659
25.841
25.888
25.759
25.944
25.818
25.789
25.662
26.927
27.521
27.485
27.444
27.395
27.45
27.437
27.45
27.458
27.816
27.599
27.588
27.667
27.64




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284463&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284463&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284463&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999955865518566
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999955865518566 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284463&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]0.999955865518566[/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=284463&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284463&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
alpha0.999955865518566
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
225.97926.133-0.154
325.54125.9790067967101-0.438006796710138
425.30825.5410193312028-0.23301933120284
525.66325.30801028418730.354989715812653
625.7825.6629843327130.117015667287021
725.32825.7799948355742-0.451994835574208
824.80625.3280199485577-0.522019948557677
924.65124.8060230390797-0.15502303907973
1024.53124.6510068418614-0.120006841861443
1124.63324.53100529643970.101994703560266
1225.17424.63299549851660.541004501483354
1324.44925.1739761230469-0.724976123046872
1424.27724.4490319964452-0.172031996445245
1524.39324.2770075925430.115992407457046
1624.30124.3929948807352-0.0919948807352462
1724.38124.30100406014640.0799959398536458
1824.28624.3809964694207-0.0949964694206749
1924.33524.28600419261990.0489958073800842
2024.27324.3349978375954-0.0619978375954489
2124.55624.27300273624240.28299726375759
2224.84124.55598751006250.285012489937483
2325.46424.84098742112160.623012578878441
2425.51425.46397250366290.0500274963370977
2525.53125.51399779206240.0170022079376047
2625.04225.5309992496164-0.488999249616366
2724.67625.0420215817283-0.366021581728308
2824.80924.67601615417270.132983845827297
2925.31324.80899413082690.504005869173071
3025.6425.31297775596230.327022244037678
3125.44725.6399855670428-0.192985567042843
3225.02125.4470085173179-0.426008517317921
3324.75225.021018801665-0.269018801664998
3424.93924.75201187300530.186988126994695
3525.36524.9389917473760.426008252624019
3625.21425.3649811983467-0.150981198346681
3725.56325.21400666347690.348993336523105
3825.47525.5629845973601-0.0879845973600659
3925.65925.47500388315460.183996116845417
4025.84125.65899187942680.182008120573204
4125.88825.8409919671660.0470080328340181
4225.75925.8879979253248-0.128997925324846
4325.94425.75900569325650.184994306743459
4425.81825.9439918353722-0.125991835372201
4525.78925.8180055605843-0.02900556058432
4625.66225.7890012801454-0.127001280145379
4726.92725.66200560513561.26499439486436
4827.52126.92694417012840.594055829871632
4927.48527.520973781654-0.0359737816540076
5027.44427.4850015876842-0.0410015876841996
5127.39527.4440018095838-0.0490018095838103
5227.4527.39500216266950.0549978373305429
5327.43727.449997572699-0.0129975726989677
5427.4527.43700057364110.0129994263588671
5527.45827.44999942627710.0080005737229385
5627.81627.45799964689880.358000353101176
5727.59927.8159841998401-0.216984199840063
5827.58827.5990095764851-0.0110095764851401
5927.66727.5880004859020.0789995140980508
6027.6427.6669965133974-0.0269965133974139

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 25.979 & 26.133 & -0.154 \tabularnewline
3 & 25.541 & 25.9790067967101 & -0.438006796710138 \tabularnewline
4 & 25.308 & 25.5410193312028 & -0.23301933120284 \tabularnewline
5 & 25.663 & 25.3080102841873 & 0.354989715812653 \tabularnewline
6 & 25.78 & 25.662984332713 & 0.117015667287021 \tabularnewline
7 & 25.328 & 25.7799948355742 & -0.451994835574208 \tabularnewline
8 & 24.806 & 25.3280199485577 & -0.522019948557677 \tabularnewline
9 & 24.651 & 24.8060230390797 & -0.15502303907973 \tabularnewline
10 & 24.531 & 24.6510068418614 & -0.120006841861443 \tabularnewline
11 & 24.633 & 24.5310052964397 & 0.101994703560266 \tabularnewline
12 & 25.174 & 24.6329954985166 & 0.541004501483354 \tabularnewline
13 & 24.449 & 25.1739761230469 & -0.724976123046872 \tabularnewline
14 & 24.277 & 24.4490319964452 & -0.172031996445245 \tabularnewline
15 & 24.393 & 24.277007592543 & 0.115992407457046 \tabularnewline
16 & 24.301 & 24.3929948807352 & -0.0919948807352462 \tabularnewline
17 & 24.381 & 24.3010040601464 & 0.0799959398536458 \tabularnewline
18 & 24.286 & 24.3809964694207 & -0.0949964694206749 \tabularnewline
19 & 24.335 & 24.2860041926199 & 0.0489958073800842 \tabularnewline
20 & 24.273 & 24.3349978375954 & -0.0619978375954489 \tabularnewline
21 & 24.556 & 24.2730027362424 & 0.28299726375759 \tabularnewline
22 & 24.841 & 24.5559875100625 & 0.285012489937483 \tabularnewline
23 & 25.464 & 24.8409874211216 & 0.623012578878441 \tabularnewline
24 & 25.514 & 25.4639725036629 & 0.0500274963370977 \tabularnewline
25 & 25.531 & 25.5139977920624 & 0.0170022079376047 \tabularnewline
26 & 25.042 & 25.5309992496164 & -0.488999249616366 \tabularnewline
27 & 24.676 & 25.0420215817283 & -0.366021581728308 \tabularnewline
28 & 24.809 & 24.6760161541727 & 0.132983845827297 \tabularnewline
29 & 25.313 & 24.8089941308269 & 0.504005869173071 \tabularnewline
30 & 25.64 & 25.3129777559623 & 0.327022244037678 \tabularnewline
31 & 25.447 & 25.6399855670428 & -0.192985567042843 \tabularnewline
32 & 25.021 & 25.4470085173179 & -0.426008517317921 \tabularnewline
33 & 24.752 & 25.021018801665 & -0.269018801664998 \tabularnewline
34 & 24.939 & 24.7520118730053 & 0.186988126994695 \tabularnewline
35 & 25.365 & 24.938991747376 & 0.426008252624019 \tabularnewline
36 & 25.214 & 25.3649811983467 & -0.150981198346681 \tabularnewline
37 & 25.563 & 25.2140066634769 & 0.348993336523105 \tabularnewline
38 & 25.475 & 25.5629845973601 & -0.0879845973600659 \tabularnewline
39 & 25.659 & 25.4750038831546 & 0.183996116845417 \tabularnewline
40 & 25.841 & 25.6589918794268 & 0.182008120573204 \tabularnewline
41 & 25.888 & 25.840991967166 & 0.0470080328340181 \tabularnewline
42 & 25.759 & 25.8879979253248 & -0.128997925324846 \tabularnewline
43 & 25.944 & 25.7590056932565 & 0.184994306743459 \tabularnewline
44 & 25.818 & 25.9439918353722 & -0.125991835372201 \tabularnewline
45 & 25.789 & 25.8180055605843 & -0.02900556058432 \tabularnewline
46 & 25.662 & 25.7890012801454 & -0.127001280145379 \tabularnewline
47 & 26.927 & 25.6620056051356 & 1.26499439486436 \tabularnewline
48 & 27.521 & 26.9269441701284 & 0.594055829871632 \tabularnewline
49 & 27.485 & 27.520973781654 & -0.0359737816540076 \tabularnewline
50 & 27.444 & 27.4850015876842 & -0.0410015876841996 \tabularnewline
51 & 27.395 & 27.4440018095838 & -0.0490018095838103 \tabularnewline
52 & 27.45 & 27.3950021626695 & 0.0549978373305429 \tabularnewline
53 & 27.437 & 27.449997572699 & -0.0129975726989677 \tabularnewline
54 & 27.45 & 27.4370005736411 & 0.0129994263588671 \tabularnewline
55 & 27.458 & 27.4499994262771 & 0.0080005737229385 \tabularnewline
56 & 27.816 & 27.4579996468988 & 0.358000353101176 \tabularnewline
57 & 27.599 & 27.8159841998401 & -0.216984199840063 \tabularnewline
58 & 27.588 & 27.5990095764851 & -0.0110095764851401 \tabularnewline
59 & 27.667 & 27.588000485902 & 0.0789995140980508 \tabularnewline
60 & 27.64 & 27.6669965133974 & -0.0269965133974139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284463&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]25.979[/C][C]26.133[/C][C]-0.154[/C][/ROW]
[ROW][C]3[/C][C]25.541[/C][C]25.9790067967101[/C][C]-0.438006796710138[/C][/ROW]
[ROW][C]4[/C][C]25.308[/C][C]25.5410193312028[/C][C]-0.23301933120284[/C][/ROW]
[ROW][C]5[/C][C]25.663[/C][C]25.3080102841873[/C][C]0.354989715812653[/C][/ROW]
[ROW][C]6[/C][C]25.78[/C][C]25.662984332713[/C][C]0.117015667287021[/C][/ROW]
[ROW][C]7[/C][C]25.328[/C][C]25.7799948355742[/C][C]-0.451994835574208[/C][/ROW]
[ROW][C]8[/C][C]24.806[/C][C]25.3280199485577[/C][C]-0.522019948557677[/C][/ROW]
[ROW][C]9[/C][C]24.651[/C][C]24.8060230390797[/C][C]-0.15502303907973[/C][/ROW]
[ROW][C]10[/C][C]24.531[/C][C]24.6510068418614[/C][C]-0.120006841861443[/C][/ROW]
[ROW][C]11[/C][C]24.633[/C][C]24.5310052964397[/C][C]0.101994703560266[/C][/ROW]
[ROW][C]12[/C][C]25.174[/C][C]24.6329954985166[/C][C]0.541004501483354[/C][/ROW]
[ROW][C]13[/C][C]24.449[/C][C]25.1739761230469[/C][C]-0.724976123046872[/C][/ROW]
[ROW][C]14[/C][C]24.277[/C][C]24.4490319964452[/C][C]-0.172031996445245[/C][/ROW]
[ROW][C]15[/C][C]24.393[/C][C]24.277007592543[/C][C]0.115992407457046[/C][/ROW]
[ROW][C]16[/C][C]24.301[/C][C]24.3929948807352[/C][C]-0.0919948807352462[/C][/ROW]
[ROW][C]17[/C][C]24.381[/C][C]24.3010040601464[/C][C]0.0799959398536458[/C][/ROW]
[ROW][C]18[/C][C]24.286[/C][C]24.3809964694207[/C][C]-0.0949964694206749[/C][/ROW]
[ROW][C]19[/C][C]24.335[/C][C]24.2860041926199[/C][C]0.0489958073800842[/C][/ROW]
[ROW][C]20[/C][C]24.273[/C][C]24.3349978375954[/C][C]-0.0619978375954489[/C][/ROW]
[ROW][C]21[/C][C]24.556[/C][C]24.2730027362424[/C][C]0.28299726375759[/C][/ROW]
[ROW][C]22[/C][C]24.841[/C][C]24.5559875100625[/C][C]0.285012489937483[/C][/ROW]
[ROW][C]23[/C][C]25.464[/C][C]24.8409874211216[/C][C]0.623012578878441[/C][/ROW]
[ROW][C]24[/C][C]25.514[/C][C]25.4639725036629[/C][C]0.0500274963370977[/C][/ROW]
[ROW][C]25[/C][C]25.531[/C][C]25.5139977920624[/C][C]0.0170022079376047[/C][/ROW]
[ROW][C]26[/C][C]25.042[/C][C]25.5309992496164[/C][C]-0.488999249616366[/C][/ROW]
[ROW][C]27[/C][C]24.676[/C][C]25.0420215817283[/C][C]-0.366021581728308[/C][/ROW]
[ROW][C]28[/C][C]24.809[/C][C]24.6760161541727[/C][C]0.132983845827297[/C][/ROW]
[ROW][C]29[/C][C]25.313[/C][C]24.8089941308269[/C][C]0.504005869173071[/C][/ROW]
[ROW][C]30[/C][C]25.64[/C][C]25.3129777559623[/C][C]0.327022244037678[/C][/ROW]
[ROW][C]31[/C][C]25.447[/C][C]25.6399855670428[/C][C]-0.192985567042843[/C][/ROW]
[ROW][C]32[/C][C]25.021[/C][C]25.4470085173179[/C][C]-0.426008517317921[/C][/ROW]
[ROW][C]33[/C][C]24.752[/C][C]25.021018801665[/C][C]-0.269018801664998[/C][/ROW]
[ROW][C]34[/C][C]24.939[/C][C]24.7520118730053[/C][C]0.186988126994695[/C][/ROW]
[ROW][C]35[/C][C]25.365[/C][C]24.938991747376[/C][C]0.426008252624019[/C][/ROW]
[ROW][C]36[/C][C]25.214[/C][C]25.3649811983467[/C][C]-0.150981198346681[/C][/ROW]
[ROW][C]37[/C][C]25.563[/C][C]25.2140066634769[/C][C]0.348993336523105[/C][/ROW]
[ROW][C]38[/C][C]25.475[/C][C]25.5629845973601[/C][C]-0.0879845973600659[/C][/ROW]
[ROW][C]39[/C][C]25.659[/C][C]25.4750038831546[/C][C]0.183996116845417[/C][/ROW]
[ROW][C]40[/C][C]25.841[/C][C]25.6589918794268[/C][C]0.182008120573204[/C][/ROW]
[ROW][C]41[/C][C]25.888[/C][C]25.840991967166[/C][C]0.0470080328340181[/C][/ROW]
[ROW][C]42[/C][C]25.759[/C][C]25.8879979253248[/C][C]-0.128997925324846[/C][/ROW]
[ROW][C]43[/C][C]25.944[/C][C]25.7590056932565[/C][C]0.184994306743459[/C][/ROW]
[ROW][C]44[/C][C]25.818[/C][C]25.9439918353722[/C][C]-0.125991835372201[/C][/ROW]
[ROW][C]45[/C][C]25.789[/C][C]25.8180055605843[/C][C]-0.02900556058432[/C][/ROW]
[ROW][C]46[/C][C]25.662[/C][C]25.7890012801454[/C][C]-0.127001280145379[/C][/ROW]
[ROW][C]47[/C][C]26.927[/C][C]25.6620056051356[/C][C]1.26499439486436[/C][/ROW]
[ROW][C]48[/C][C]27.521[/C][C]26.9269441701284[/C][C]0.594055829871632[/C][/ROW]
[ROW][C]49[/C][C]27.485[/C][C]27.520973781654[/C][C]-0.0359737816540076[/C][/ROW]
[ROW][C]50[/C][C]27.444[/C][C]27.4850015876842[/C][C]-0.0410015876841996[/C][/ROW]
[ROW][C]51[/C][C]27.395[/C][C]27.4440018095838[/C][C]-0.0490018095838103[/C][/ROW]
[ROW][C]52[/C][C]27.45[/C][C]27.3950021626695[/C][C]0.0549978373305429[/C][/ROW]
[ROW][C]53[/C][C]27.437[/C][C]27.449997572699[/C][C]-0.0129975726989677[/C][/ROW]
[ROW][C]54[/C][C]27.45[/C][C]27.4370005736411[/C][C]0.0129994263588671[/C][/ROW]
[ROW][C]55[/C][C]27.458[/C][C]27.4499994262771[/C][C]0.0080005737229385[/C][/ROW]
[ROW][C]56[/C][C]27.816[/C][C]27.4579996468988[/C][C]0.358000353101176[/C][/ROW]
[ROW][C]57[/C][C]27.599[/C][C]27.8159841998401[/C][C]-0.216984199840063[/C][/ROW]
[ROW][C]58[/C][C]27.588[/C][C]27.5990095764851[/C][C]-0.0110095764851401[/C][/ROW]
[ROW][C]59[/C][C]27.667[/C][C]27.588000485902[/C][C]0.0789995140980508[/C][/ROW]
[ROW][C]60[/C][C]27.64[/C][C]27.6669965133974[/C][C]-0.0269965133974139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284463&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284463&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
225.97926.133-0.154
325.54125.9790067967101-0.438006796710138
425.30825.5410193312028-0.23301933120284
525.66325.30801028418730.354989715812653
625.7825.6629843327130.117015667287021
725.32825.7799948355742-0.451994835574208
824.80625.3280199485577-0.522019948557677
924.65124.8060230390797-0.15502303907973
1024.53124.6510068418614-0.120006841861443
1124.63324.53100529643970.101994703560266
1225.17424.63299549851660.541004501483354
1324.44925.1739761230469-0.724976123046872
1424.27724.4490319964452-0.172031996445245
1524.39324.2770075925430.115992407457046
1624.30124.3929948807352-0.0919948807352462
1724.38124.30100406014640.0799959398536458
1824.28624.3809964694207-0.0949964694206749
1924.33524.28600419261990.0489958073800842
2024.27324.3349978375954-0.0619978375954489
2124.55624.27300273624240.28299726375759
2224.84124.55598751006250.285012489937483
2325.46424.84098742112160.623012578878441
2425.51425.46397250366290.0500274963370977
2525.53125.51399779206240.0170022079376047
2625.04225.5309992496164-0.488999249616366
2724.67625.0420215817283-0.366021581728308
2824.80924.67601615417270.132983845827297
2925.31324.80899413082690.504005869173071
3025.6425.31297775596230.327022244037678
3125.44725.6399855670428-0.192985567042843
3225.02125.4470085173179-0.426008517317921
3324.75225.021018801665-0.269018801664998
3424.93924.75201187300530.186988126994695
3525.36524.9389917473760.426008252624019
3625.21425.3649811983467-0.150981198346681
3725.56325.21400666347690.348993336523105
3825.47525.5629845973601-0.0879845973600659
3925.65925.47500388315460.183996116845417
4025.84125.65899187942680.182008120573204
4125.88825.8409919671660.0470080328340181
4225.75925.8879979253248-0.128997925324846
4325.94425.75900569325650.184994306743459
4425.81825.9439918353722-0.125991835372201
4525.78925.8180055605843-0.02900556058432
4625.66225.7890012801454-0.127001280145379
4726.92725.66200560513561.26499439486436
4827.52126.92694417012840.594055829871632
4927.48527.520973781654-0.0359737816540076
5027.44427.4850015876842-0.0410015876841996
5127.39527.4440018095838-0.0490018095838103
5227.4527.39500216266950.0549978373305429
5327.43727.449997572699-0.0129975726989677
5427.4527.43700057364110.0129994263588671
5527.45827.44999942627710.0080005737229385
5627.81627.45799964689880.358000353101176
5727.59927.8159841998401-0.216984199840063
5827.58827.5990095764851-0.0110095764851401
5927.66727.5880004859020.0789995140980508
6027.6427.6669965133974-0.0269965133974139







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6127.640001191477127.007030996713128.2729713862411
6227.640001191477126.744865910847628.5351364721066
6327.640001191477126.543696911728228.736305471226
6427.640001191477126.374102705434928.9058996775193
6527.640001191477126.224686781131529.0553156018227
6627.640001191477126.089604215441629.1903981675126
6727.640001191477125.96538282108129.3146195618732
6827.640001191477125.849760260865729.4302421220885
6927.640001191477125.741165102499329.5388372804549
7027.640001191477125.638453191559929.6415491913943
7127.640001191477125.540760781438129.7392416015161
7227.640001191477125.44741682541329.8325855575412

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 27.6400011914771 & 27.0070309967131 & 28.2729713862411 \tabularnewline
62 & 27.6400011914771 & 26.7448659108476 & 28.5351364721066 \tabularnewline
63 & 27.6400011914771 & 26.5436969117282 & 28.736305471226 \tabularnewline
64 & 27.6400011914771 & 26.3741027054349 & 28.9058996775193 \tabularnewline
65 & 27.6400011914771 & 26.2246867811315 & 29.0553156018227 \tabularnewline
66 & 27.6400011914771 & 26.0896042154416 & 29.1903981675126 \tabularnewline
67 & 27.6400011914771 & 25.965382821081 & 29.3146195618732 \tabularnewline
68 & 27.6400011914771 & 25.8497602608657 & 29.4302421220885 \tabularnewline
69 & 27.6400011914771 & 25.7411651024993 & 29.5388372804549 \tabularnewline
70 & 27.6400011914771 & 25.6384531915599 & 29.6415491913943 \tabularnewline
71 & 27.6400011914771 & 25.5407607814381 & 29.7392416015161 \tabularnewline
72 & 27.6400011914771 & 25.447416825413 & 29.8325855575412 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284463&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]61[/C][C]27.6400011914771[/C][C]27.0070309967131[/C][C]28.2729713862411[/C][/ROW]
[ROW][C]62[/C][C]27.6400011914771[/C][C]26.7448659108476[/C][C]28.5351364721066[/C][/ROW]
[ROW][C]63[/C][C]27.6400011914771[/C][C]26.5436969117282[/C][C]28.736305471226[/C][/ROW]
[ROW][C]64[/C][C]27.6400011914771[/C][C]26.3741027054349[/C][C]28.9058996775193[/C][/ROW]
[ROW][C]65[/C][C]27.6400011914771[/C][C]26.2246867811315[/C][C]29.0553156018227[/C][/ROW]
[ROW][C]66[/C][C]27.6400011914771[/C][C]26.0896042154416[/C][C]29.1903981675126[/C][/ROW]
[ROW][C]67[/C][C]27.6400011914771[/C][C]25.965382821081[/C][C]29.3146195618732[/C][/ROW]
[ROW][C]68[/C][C]27.6400011914771[/C][C]25.8497602608657[/C][C]29.4302421220885[/C][/ROW]
[ROW][C]69[/C][C]27.6400011914771[/C][C]25.7411651024993[/C][C]29.5388372804549[/C][/ROW]
[ROW][C]70[/C][C]27.6400011914771[/C][C]25.6384531915599[/C][C]29.6415491913943[/C][/ROW]
[ROW][C]71[/C][C]27.6400011914771[/C][C]25.5407607814381[/C][C]29.7392416015161[/C][/ROW]
[ROW][C]72[/C][C]27.6400011914771[/C][C]25.447416825413[/C][C]29.8325855575412[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284463&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284463&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
6127.640001191477127.007030996713128.2729713862411
6227.640001191477126.744865910847628.5351364721066
6327.640001191477126.543696911728228.736305471226
6427.640001191477126.374102705434928.9058996775193
6527.640001191477126.224686781131529.0553156018227
6627.640001191477126.089604215441629.1903981675126
6727.640001191477125.96538282108129.3146195618732
6827.640001191477125.849760260865729.4302421220885
6927.640001191477125.741165102499329.5388372804549
7027.640001191477125.638453191559929.6415491913943
7127.640001191477125.540760781438129.7392416015161
7227.640001191477125.44741682541329.8325855575412



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')