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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 19 Dec 2011 15:27:42 -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/Dec/19/t1324326619snvgr1kq54lwlmn.htm/, Retrieved Thu, 16 May 2024 04:52:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157679, Retrieved Thu, 16 May 2024 04:52:23 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-12-19 20:27:42] [e0466c781e396ede6f5f4647349698a6] [Current]
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Dataseries X:
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971
20036
22485
18730
14538
27561
25985
34670
32066
27186
29586
21359
21553
19573
24256
22380
16167




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157679&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]2 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=157679&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157679&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.654670958181316
beta0.0646903047976537
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.654670958181316 \tabularnewline
beta & 0.0646903047976537 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157679&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]0.654670958181316[/C][/ROW]
[ROW][C]beta[/C][C]0.0646903047976537[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157679&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157679&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
alpha0.654670958181316
beta0.0646903047976537
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
334506270567450
42716529798.8125739614-2633.81257396137
52673625828.5016703412907.498329658825
62369124215.0175073945-524.017507394496
71815721642.1689056538-3485.1689056538
81732816983.1405669576344.859433042417
91820514846.12564550543358.87435449458
102099514824.54999105216170.45000894794
111738216904.9551523787477.044847621273
12936715278.2565628062-5911.25656280616
13311249218.9757459806121905.0242540194
142655122297.90284385424253.09715614581
153065124000.74825331876650.25174668127
162585927554.5850616163-1695.58506161631
172510025572.8353977493-472.835397749339
182577824371.55944039941406.44055960059
192041824460.1548473552-4042.15484735517
201868820810.5243289892-2122.52432898922
212042418327.72942260962096.27057739035
222477618695.63588972756080.36411027251
231981421929.3213599535-2115.32135995353
241273819707.9438835684-6969.94388356843
253156614013.202883745517552.7971162545
263011125116.16435196094994.83564803907
273001928209.32875734371809.67124265632
283193429293.89966985872640.10033014128
292582631033.9389183504-5207.9389183504
302683527415.5340802375-580.53408023747
312020526801.9706816058-6596.97068160577
321778921970.2335613123-4181.23356131226
332052018542.93052309181977.06947690821
342251819231.02023586693286.97976413307
351557220915.8766039038-5343.87660390377
361150916724.0441731928-5215.04417319283
372544712395.6929677113051.30703229
382409020578.52553528493511.47446471513
392778622664.6207518435121.37924815695
402619526021.5687107025173.431289297514
412051626146.5838032205-5630.5838032205
422275922233.4186859047525.581314095343
431902822372.7749073276-3344.7749073276
441697119836.6672061366-2865.66720613663
452003617492.8539211362543.14607886396
462248518797.73804532853687.26195467145
471873021007.8003351429-2277.80033514288
481453819216.2427682547-4678.24276825468
492756115655.057631194511905.9423688055
502598523455.28381246222529.71618753776
513467025224.30268129399445.69731870612
523206631921.0469849262144.953015073752
532718632535.0029889029-5349.00298890289
542958629325.6906543573260.309345642676
552135929799.6565262572-8440.65652625716
562155324219.8836385441-2666.88363854408
571957322307.0873537332-2734.0873537332
582425620234.50378709724021.49621290275
592238022754.9184255979-374.918425597931
601616722381.2499609603-6214.24996096031

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 34506 & 27056 & 7450 \tabularnewline
4 & 27165 & 29798.8125739614 & -2633.81257396137 \tabularnewline
5 & 26736 & 25828.5016703412 & 907.498329658825 \tabularnewline
6 & 23691 & 24215.0175073945 & -524.017507394496 \tabularnewline
7 & 18157 & 21642.1689056538 & -3485.1689056538 \tabularnewline
8 & 17328 & 16983.1405669576 & 344.859433042417 \tabularnewline
9 & 18205 & 14846.1256455054 & 3358.87435449458 \tabularnewline
10 & 20995 & 14824.5499910521 & 6170.45000894794 \tabularnewline
11 & 17382 & 16904.9551523787 & 477.044847621273 \tabularnewline
12 & 9367 & 15278.2565628062 & -5911.25656280616 \tabularnewline
13 & 31124 & 9218.97574598061 & 21905.0242540194 \tabularnewline
14 & 26551 & 22297.9028438542 & 4253.09715614581 \tabularnewline
15 & 30651 & 24000.7482533187 & 6650.25174668127 \tabularnewline
16 & 25859 & 27554.5850616163 & -1695.58506161631 \tabularnewline
17 & 25100 & 25572.8353977493 & -472.835397749339 \tabularnewline
18 & 25778 & 24371.5594403994 & 1406.44055960059 \tabularnewline
19 & 20418 & 24460.1548473552 & -4042.15484735517 \tabularnewline
20 & 18688 & 20810.5243289892 & -2122.52432898922 \tabularnewline
21 & 20424 & 18327.7294226096 & 2096.27057739035 \tabularnewline
22 & 24776 & 18695.6358897275 & 6080.36411027251 \tabularnewline
23 & 19814 & 21929.3213599535 & -2115.32135995353 \tabularnewline
24 & 12738 & 19707.9438835684 & -6969.94388356843 \tabularnewline
25 & 31566 & 14013.2028837455 & 17552.7971162545 \tabularnewline
26 & 30111 & 25116.1643519609 & 4994.83564803907 \tabularnewline
27 & 30019 & 28209.3287573437 & 1809.67124265632 \tabularnewline
28 & 31934 & 29293.8996698587 & 2640.10033014128 \tabularnewline
29 & 25826 & 31033.9389183504 & -5207.9389183504 \tabularnewline
30 & 26835 & 27415.5340802375 & -580.53408023747 \tabularnewline
31 & 20205 & 26801.9706816058 & -6596.97068160577 \tabularnewline
32 & 17789 & 21970.2335613123 & -4181.23356131226 \tabularnewline
33 & 20520 & 18542.9305230918 & 1977.06947690821 \tabularnewline
34 & 22518 & 19231.0202358669 & 3286.97976413307 \tabularnewline
35 & 15572 & 20915.8766039038 & -5343.87660390377 \tabularnewline
36 & 11509 & 16724.0441731928 & -5215.04417319283 \tabularnewline
37 & 25447 & 12395.69296771 & 13051.30703229 \tabularnewline
38 & 24090 & 20578.5255352849 & 3511.47446471513 \tabularnewline
39 & 27786 & 22664.620751843 & 5121.37924815695 \tabularnewline
40 & 26195 & 26021.5687107025 & 173.431289297514 \tabularnewline
41 & 20516 & 26146.5838032205 & -5630.5838032205 \tabularnewline
42 & 22759 & 22233.4186859047 & 525.581314095343 \tabularnewline
43 & 19028 & 22372.7749073276 & -3344.7749073276 \tabularnewline
44 & 16971 & 19836.6672061366 & -2865.66720613663 \tabularnewline
45 & 20036 & 17492.853921136 & 2543.14607886396 \tabularnewline
46 & 22485 & 18797.7380453285 & 3687.26195467145 \tabularnewline
47 & 18730 & 21007.8003351429 & -2277.80033514288 \tabularnewline
48 & 14538 & 19216.2427682547 & -4678.24276825468 \tabularnewline
49 & 27561 & 15655.0576311945 & 11905.9423688055 \tabularnewline
50 & 25985 & 23455.2838124622 & 2529.71618753776 \tabularnewline
51 & 34670 & 25224.3026812939 & 9445.69731870612 \tabularnewline
52 & 32066 & 31921.0469849262 & 144.953015073752 \tabularnewline
53 & 27186 & 32535.0029889029 & -5349.00298890289 \tabularnewline
54 & 29586 & 29325.6906543573 & 260.309345642676 \tabularnewline
55 & 21359 & 29799.6565262572 & -8440.65652625716 \tabularnewline
56 & 21553 & 24219.8836385441 & -2666.88363854408 \tabularnewline
57 & 19573 & 22307.0873537332 & -2734.0873537332 \tabularnewline
58 & 24256 & 20234.5037870972 & 4021.49621290275 \tabularnewline
59 & 22380 & 22754.9184255979 & -374.918425597931 \tabularnewline
60 & 16167 & 22381.2499609603 & -6214.24996096031 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157679&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]3[/C][C]34506[/C][C]27056[/C][C]7450[/C][/ROW]
[ROW][C]4[/C][C]27165[/C][C]29798.8125739614[/C][C]-2633.81257396137[/C][/ROW]
[ROW][C]5[/C][C]26736[/C][C]25828.5016703412[/C][C]907.498329658825[/C][/ROW]
[ROW][C]6[/C][C]23691[/C][C]24215.0175073945[/C][C]-524.017507394496[/C][/ROW]
[ROW][C]7[/C][C]18157[/C][C]21642.1689056538[/C][C]-3485.1689056538[/C][/ROW]
[ROW][C]8[/C][C]17328[/C][C]16983.1405669576[/C][C]344.859433042417[/C][/ROW]
[ROW][C]9[/C][C]18205[/C][C]14846.1256455054[/C][C]3358.87435449458[/C][/ROW]
[ROW][C]10[/C][C]20995[/C][C]14824.5499910521[/C][C]6170.45000894794[/C][/ROW]
[ROW][C]11[/C][C]17382[/C][C]16904.9551523787[/C][C]477.044847621273[/C][/ROW]
[ROW][C]12[/C][C]9367[/C][C]15278.2565628062[/C][C]-5911.25656280616[/C][/ROW]
[ROW][C]13[/C][C]31124[/C][C]9218.97574598061[/C][C]21905.0242540194[/C][/ROW]
[ROW][C]14[/C][C]26551[/C][C]22297.9028438542[/C][C]4253.09715614581[/C][/ROW]
[ROW][C]15[/C][C]30651[/C][C]24000.7482533187[/C][C]6650.25174668127[/C][/ROW]
[ROW][C]16[/C][C]25859[/C][C]27554.5850616163[/C][C]-1695.58506161631[/C][/ROW]
[ROW][C]17[/C][C]25100[/C][C]25572.8353977493[/C][C]-472.835397749339[/C][/ROW]
[ROW][C]18[/C][C]25778[/C][C]24371.5594403994[/C][C]1406.44055960059[/C][/ROW]
[ROW][C]19[/C][C]20418[/C][C]24460.1548473552[/C][C]-4042.15484735517[/C][/ROW]
[ROW][C]20[/C][C]18688[/C][C]20810.5243289892[/C][C]-2122.52432898922[/C][/ROW]
[ROW][C]21[/C][C]20424[/C][C]18327.7294226096[/C][C]2096.27057739035[/C][/ROW]
[ROW][C]22[/C][C]24776[/C][C]18695.6358897275[/C][C]6080.36411027251[/C][/ROW]
[ROW][C]23[/C][C]19814[/C][C]21929.3213599535[/C][C]-2115.32135995353[/C][/ROW]
[ROW][C]24[/C][C]12738[/C][C]19707.9438835684[/C][C]-6969.94388356843[/C][/ROW]
[ROW][C]25[/C][C]31566[/C][C]14013.2028837455[/C][C]17552.7971162545[/C][/ROW]
[ROW][C]26[/C][C]30111[/C][C]25116.1643519609[/C][C]4994.83564803907[/C][/ROW]
[ROW][C]27[/C][C]30019[/C][C]28209.3287573437[/C][C]1809.67124265632[/C][/ROW]
[ROW][C]28[/C][C]31934[/C][C]29293.8996698587[/C][C]2640.10033014128[/C][/ROW]
[ROW][C]29[/C][C]25826[/C][C]31033.9389183504[/C][C]-5207.9389183504[/C][/ROW]
[ROW][C]30[/C][C]26835[/C][C]27415.5340802375[/C][C]-580.53408023747[/C][/ROW]
[ROW][C]31[/C][C]20205[/C][C]26801.9706816058[/C][C]-6596.97068160577[/C][/ROW]
[ROW][C]32[/C][C]17789[/C][C]21970.2335613123[/C][C]-4181.23356131226[/C][/ROW]
[ROW][C]33[/C][C]20520[/C][C]18542.9305230918[/C][C]1977.06947690821[/C][/ROW]
[ROW][C]34[/C][C]22518[/C][C]19231.0202358669[/C][C]3286.97976413307[/C][/ROW]
[ROW][C]35[/C][C]15572[/C][C]20915.8766039038[/C][C]-5343.87660390377[/C][/ROW]
[ROW][C]36[/C][C]11509[/C][C]16724.0441731928[/C][C]-5215.04417319283[/C][/ROW]
[ROW][C]37[/C][C]25447[/C][C]12395.69296771[/C][C]13051.30703229[/C][/ROW]
[ROW][C]38[/C][C]24090[/C][C]20578.5255352849[/C][C]3511.47446471513[/C][/ROW]
[ROW][C]39[/C][C]27786[/C][C]22664.620751843[/C][C]5121.37924815695[/C][/ROW]
[ROW][C]40[/C][C]26195[/C][C]26021.5687107025[/C][C]173.431289297514[/C][/ROW]
[ROW][C]41[/C][C]20516[/C][C]26146.5838032205[/C][C]-5630.5838032205[/C][/ROW]
[ROW][C]42[/C][C]22759[/C][C]22233.4186859047[/C][C]525.581314095343[/C][/ROW]
[ROW][C]43[/C][C]19028[/C][C]22372.7749073276[/C][C]-3344.7749073276[/C][/ROW]
[ROW][C]44[/C][C]16971[/C][C]19836.6672061366[/C][C]-2865.66720613663[/C][/ROW]
[ROW][C]45[/C][C]20036[/C][C]17492.853921136[/C][C]2543.14607886396[/C][/ROW]
[ROW][C]46[/C][C]22485[/C][C]18797.7380453285[/C][C]3687.26195467145[/C][/ROW]
[ROW][C]47[/C][C]18730[/C][C]21007.8003351429[/C][C]-2277.80033514288[/C][/ROW]
[ROW][C]48[/C][C]14538[/C][C]19216.2427682547[/C][C]-4678.24276825468[/C][/ROW]
[ROW][C]49[/C][C]27561[/C][C]15655.0576311945[/C][C]11905.9423688055[/C][/ROW]
[ROW][C]50[/C][C]25985[/C][C]23455.2838124622[/C][C]2529.71618753776[/C][/ROW]
[ROW][C]51[/C][C]34670[/C][C]25224.3026812939[/C][C]9445.69731870612[/C][/ROW]
[ROW][C]52[/C][C]32066[/C][C]31921.0469849262[/C][C]144.953015073752[/C][/ROW]
[ROW][C]53[/C][C]27186[/C][C]32535.0029889029[/C][C]-5349.00298890289[/C][/ROW]
[ROW][C]54[/C][C]29586[/C][C]29325.6906543573[/C][C]260.309345642676[/C][/ROW]
[ROW][C]55[/C][C]21359[/C][C]29799.6565262572[/C][C]-8440.65652625716[/C][/ROW]
[ROW][C]56[/C][C]21553[/C][C]24219.8836385441[/C][C]-2666.88363854408[/C][/ROW]
[ROW][C]57[/C][C]19573[/C][C]22307.0873537332[/C][C]-2734.0873537332[/C][/ROW]
[ROW][C]58[/C][C]24256[/C][C]20234.5037870972[/C][C]4021.49621290275[/C][/ROW]
[ROW][C]59[/C][C]22380[/C][C]22754.9184255979[/C][C]-374.918425597931[/C][/ROW]
[ROW][C]60[/C][C]16167[/C][C]22381.2499609603[/C][C]-6214.24996096031[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157679&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157679&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
334506270567450
42716529798.8125739614-2633.81257396137
52673625828.5016703412907.498329658825
62369124215.0175073945-524.017507394496
71815721642.1689056538-3485.1689056538
81732816983.1405669576344.859433042417
91820514846.12564550543358.87435449458
102099514824.54999105216170.45000894794
111738216904.9551523787477.044847621273
12936715278.2565628062-5911.25656280616
13311249218.9757459806121905.0242540194
142655122297.90284385424253.09715614581
153065124000.74825331876650.25174668127
162585927554.5850616163-1695.58506161631
172510025572.8353977493-472.835397749339
182577824371.55944039941406.44055960059
192041824460.1548473552-4042.15484735517
201868820810.5243289892-2122.52432898922
212042418327.72942260962096.27057739035
222477618695.63588972756080.36411027251
231981421929.3213599535-2115.32135995353
241273819707.9438835684-6969.94388356843
253156614013.202883745517552.7971162545
263011125116.16435196094994.83564803907
273001928209.32875734371809.67124265632
283193429293.89966985872640.10033014128
292582631033.9389183504-5207.9389183504
302683527415.5340802375-580.53408023747
312020526801.9706816058-6596.97068160577
321778921970.2335613123-4181.23356131226
332052018542.93052309181977.06947690821
342251819231.02023586693286.97976413307
351557220915.8766039038-5343.87660390377
361150916724.0441731928-5215.04417319283
372544712395.6929677113051.30703229
382409020578.52553528493511.47446471513
392778622664.6207518435121.37924815695
402619526021.5687107025173.431289297514
412051626146.5838032205-5630.5838032205
422275922233.4186859047525.581314095343
431902822372.7749073276-3344.7749073276
441697119836.6672061366-2865.66720613663
452003617492.8539211362543.14607886396
462248518797.73804532853687.26195467145
471873021007.8003351429-2277.80033514288
481453819216.2427682547-4678.24276825468
492756115655.057631194511905.9423688055
502598523455.28381246222529.71618753776
513467025224.30268129399445.69731870612
523206631921.0469849262144.953015073752
532718632535.0029889029-5349.00298890289
542958629325.6906543573260.309345642676
552135929799.6565262572-8440.65652625716
562155324219.8836385441-2666.88363854408
571957322307.0873537332-2734.0873537332
582425620234.50378709724021.49621290275
592238022754.9184255979-374.918425597931
601616722381.2499609603-6214.24996096031







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6117921.56187104556315.8624370282529527.2613050628
6217530.16275745093383.3939191936231676.9315957081
6317138.7636438562592.96202733950533684.5652603729
6416747.3645302615-2122.5287913326935617.2578518557
6516355.9654166668-4799.2278931145737511.1587264482
6615964.5663030722-7458.8132151832539387.9458213276
6715573.1671894775-10115.226164717441261.5605436723
6815181.7680758828-12777.879741472543141.4158932381
6914790.3689622881-15453.356565725245034.0944903014
7014398.9698486934-18146.380099572746944.3197969596
7114007.5707350988-20860.40427492948875.5457451265
7213616.1716215041-23597.988786245650830.3320292538

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 17921.5618710455 & 6315.86243702825 & 29527.2613050628 \tabularnewline
62 & 17530.1627574509 & 3383.39391919362 & 31676.9315957081 \tabularnewline
63 & 17138.7636438562 & 592.962027339505 & 33684.5652603729 \tabularnewline
64 & 16747.3645302615 & -2122.52879133269 & 35617.2578518557 \tabularnewline
65 & 16355.9654166668 & -4799.22789311457 & 37511.1587264482 \tabularnewline
66 & 15964.5663030722 & -7458.81321518325 & 39387.9458213276 \tabularnewline
67 & 15573.1671894775 & -10115.2261647174 & 41261.5605436723 \tabularnewline
68 & 15181.7680758828 & -12777.8797414725 & 43141.4158932381 \tabularnewline
69 & 14790.3689622881 & -15453.3565657252 & 45034.0944903014 \tabularnewline
70 & 14398.9698486934 & -18146.3800995727 & 46944.3197969596 \tabularnewline
71 & 14007.5707350988 & -20860.404274929 & 48875.5457451265 \tabularnewline
72 & 13616.1716215041 & -23597.9887862456 & 50830.3320292538 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157679&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]17921.5618710455[/C][C]6315.86243702825[/C][C]29527.2613050628[/C][/ROW]
[ROW][C]62[/C][C]17530.1627574509[/C][C]3383.39391919362[/C][C]31676.9315957081[/C][/ROW]
[ROW][C]63[/C][C]17138.7636438562[/C][C]592.962027339505[/C][C]33684.5652603729[/C][/ROW]
[ROW][C]64[/C][C]16747.3645302615[/C][C]-2122.52879133269[/C][C]35617.2578518557[/C][/ROW]
[ROW][C]65[/C][C]16355.9654166668[/C][C]-4799.22789311457[/C][C]37511.1587264482[/C][/ROW]
[ROW][C]66[/C][C]15964.5663030722[/C][C]-7458.81321518325[/C][C]39387.9458213276[/C][/ROW]
[ROW][C]67[/C][C]15573.1671894775[/C][C]-10115.2261647174[/C][C]41261.5605436723[/C][/ROW]
[ROW][C]68[/C][C]15181.7680758828[/C][C]-12777.8797414725[/C][C]43141.4158932381[/C][/ROW]
[ROW][C]69[/C][C]14790.3689622881[/C][C]-15453.3565657252[/C][C]45034.0944903014[/C][/ROW]
[ROW][C]70[/C][C]14398.9698486934[/C][C]-18146.3800995727[/C][C]46944.3197969596[/C][/ROW]
[ROW][C]71[/C][C]14007.5707350988[/C][C]-20860.404274929[/C][C]48875.5457451265[/C][/ROW]
[ROW][C]72[/C][C]13616.1716215041[/C][C]-23597.9887862456[/C][C]50830.3320292538[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157679&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157679&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
6117921.56187104556315.8624370282529527.2613050628
6217530.16275745093383.3939191936231676.9315957081
6317138.7636438562592.96202733950533684.5652603729
6416747.3645302615-2122.5287913326935617.2578518557
6516355.9654166668-4799.2278931145737511.1587264482
6615964.5663030722-7458.8132151832539387.9458213276
6715573.1671894775-10115.226164717441261.5605436723
6815181.7680758828-12777.879741472543141.4158932381
6914790.3689622881-15453.356565725245034.0944903014
7014398.9698486934-18146.380099572746944.3197969596
7114007.5707350988-20860.40427492948875.5457451265
7213616.1716215041-23597.988786245650830.3320292538



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