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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 computationFri, 23 Nov 2012 11:59:10 -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/2012/Nov/23/t1353690006jkboy8p7iatz9nh.htm/, Retrieved Tue, 30 Apr 2024 14:27:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=192215, Retrieved Tue, 30 Apr 2024 14:27:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Workshop 8] [2012-11-23 16:59:10] [88970af05b38e2e8b1d3faaed6004b57] [Current]
- R P     [Exponential Smoothing] [Workshop 8] [2012-11-23 17:06:05] [498ff5d3288f0a3191251bab12f09e42]
- R P     [Exponential Smoothing] [Workshop 8] [2012-11-23 17:11:28] [498ff5d3288f0a3191251bab12f09e42]
-  M        [Exponential Smoothing] [Paper - triple ex...] [2012-12-09 11:48:06] [498ff5d3288f0a3191251bab12f09e42]
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Dataseries X:
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195
19650
20830
23595
22937
21814
21928
21777
21383
21467
22052
22680
24320
24977
25204
25739
26434
27525
30695
32436
30160
30236
31293
31077
32226
33865
32810
32242
32700
32819
33947
34148
35261
39506
41591
39148
41216
40225
41126
42362
40740
40256
39804
41002
41702
42254
43605
43271




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=192215&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=192215&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192215&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
alpha0.999957692084665
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999957692084665 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192215&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]0.999957692084665[/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=192215&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192215&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
alpha0.999957692084665
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21634815579769
31592816347.9674652131-419.967465213107
41617115928.017767948242.982232052038
51593716170.9897199283-233.989719928299
61571315937.0098996173-224.00989961726
71559415713.0094773919-119.009477391868
81568315594.005035042988.9949649571063
91643815682.9962348086755.003765191443
101703216437.9680573646594.031942635374
111769617031.9748677469664.025132253137
121774517695.971906480949.0280935190749
131939417744.99792572361649.00207427643
142014819393.9302341599754.069765840148
152010820147.9680968802-39.9680968801913
161858420108.0016909669-1524.00169096686
171844118584.0644773345-143.064477334512
181839118441.0060527598-50.0060527597961
191917818391.0021156518786.997884348155
201807919177.9667037601-1098.96670376014
211848318079.0464949903403.95350500974
221964418482.98290956931161.01709043069
231919519643.9508797872-448.950879787237
241965019195.0189941758454.981005824189
252083019649.98075070211180.01924929787
262359520829.95007584552765.04992415449
272293723594.8830165019-657.88301650191
282181422937.027833659-1123.02783365896
292192821814.0475129665113.952487033494
302177721927.9951789078-150.995178907826
312138321777.0063882912-394.006388291244
322146721383.016669588983.9833304110834
332205221466.9964468404585.003553159633
342268022051.9752497192628.024750280798
352432022679.9734295821640.02657041796
362497724319.9306138947657.06938610529
372520424976.972200764227.027799235955
382573925203.9903949271535.009605072908
392643425738.9773648589695.022635141075
402752526433.97059504121091.0294049588
413069527524.95384082033170.04615917969
423243630694.86588195551741.13411804451
433016032435.9263362451-2275.92633624515
443023630160.096289698775.9037103012561
453129330235.99678867231057.00321132775
463107731292.9552803976-215.955280397626
473222631077.00913661771148.99086338228
483386532225.95138859181639.04861140817
493281033864.9306552701-1054.93065527012
503224232810.0446319168-568.044631916848
513270032242.0240327842457.975967215807
523281932699.9806239916119.019376008448
533394732818.99496453831128.00503546168
543414833946.9522764585201.047723541538
553526134147.99149408991113.00850591007
563950635260.95291093044245.04708906964
574159139505.82040090722085.17959909284
583914841590.9117803981-2442.91178039806
594121639148.10335450482067.89664549522
604022541215.9125116038-990.912511603798
614112640225.0419234426900.958076557356
624236241125.9618823421236.03811765803
634074042361.947705804-1621.94770580397
644025640740.0686212262-484.068621226215
653980440256.0204799342-452.020479934246
664100239804.01912404421197.98087595581
674170241001.9493159265700.050684073474
684225441701.9703823149552.029617685075
694360542253.97664477771351.02335522233
704327143604.9428410183-333.942841018274

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 16348 & 15579 & 769 \tabularnewline
3 & 15928 & 16347.9674652131 & -419.967465213107 \tabularnewline
4 & 16171 & 15928.017767948 & 242.982232052038 \tabularnewline
5 & 15937 & 16170.9897199283 & -233.989719928299 \tabularnewline
6 & 15713 & 15937.0098996173 & -224.00989961726 \tabularnewline
7 & 15594 & 15713.0094773919 & -119.009477391868 \tabularnewline
8 & 15683 & 15594.0050350429 & 88.9949649571063 \tabularnewline
9 & 16438 & 15682.9962348086 & 755.003765191443 \tabularnewline
10 & 17032 & 16437.9680573646 & 594.031942635374 \tabularnewline
11 & 17696 & 17031.9748677469 & 664.025132253137 \tabularnewline
12 & 17745 & 17695.9719064809 & 49.0280935190749 \tabularnewline
13 & 19394 & 17744.9979257236 & 1649.00207427643 \tabularnewline
14 & 20148 & 19393.9302341599 & 754.069765840148 \tabularnewline
15 & 20108 & 20147.9680968802 & -39.9680968801913 \tabularnewline
16 & 18584 & 20108.0016909669 & -1524.00169096686 \tabularnewline
17 & 18441 & 18584.0644773345 & -143.064477334512 \tabularnewline
18 & 18391 & 18441.0060527598 & -50.0060527597961 \tabularnewline
19 & 19178 & 18391.0021156518 & 786.997884348155 \tabularnewline
20 & 18079 & 19177.9667037601 & -1098.96670376014 \tabularnewline
21 & 18483 & 18079.0464949903 & 403.95350500974 \tabularnewline
22 & 19644 & 18482.9829095693 & 1161.01709043069 \tabularnewline
23 & 19195 & 19643.9508797872 & -448.950879787237 \tabularnewline
24 & 19650 & 19195.0189941758 & 454.981005824189 \tabularnewline
25 & 20830 & 19649.9807507021 & 1180.01924929787 \tabularnewline
26 & 23595 & 20829.9500758455 & 2765.04992415449 \tabularnewline
27 & 22937 & 23594.8830165019 & -657.88301650191 \tabularnewline
28 & 21814 & 22937.027833659 & -1123.02783365896 \tabularnewline
29 & 21928 & 21814.0475129665 & 113.952487033494 \tabularnewline
30 & 21777 & 21927.9951789078 & -150.995178907826 \tabularnewline
31 & 21383 & 21777.0063882912 & -394.006388291244 \tabularnewline
32 & 21467 & 21383.0166695889 & 83.9833304110834 \tabularnewline
33 & 22052 & 21466.9964468404 & 585.003553159633 \tabularnewline
34 & 22680 & 22051.9752497192 & 628.024750280798 \tabularnewline
35 & 24320 & 22679.973429582 & 1640.02657041796 \tabularnewline
36 & 24977 & 24319.9306138947 & 657.06938610529 \tabularnewline
37 & 25204 & 24976.972200764 & 227.027799235955 \tabularnewline
38 & 25739 & 25203.9903949271 & 535.009605072908 \tabularnewline
39 & 26434 & 25738.9773648589 & 695.022635141075 \tabularnewline
40 & 27525 & 26433.9705950412 & 1091.0294049588 \tabularnewline
41 & 30695 & 27524.9538408203 & 3170.04615917969 \tabularnewline
42 & 32436 & 30694.8658819555 & 1741.13411804451 \tabularnewline
43 & 30160 & 32435.9263362451 & -2275.92633624515 \tabularnewline
44 & 30236 & 30160.0962896987 & 75.9037103012561 \tabularnewline
45 & 31293 & 30235.9967886723 & 1057.00321132775 \tabularnewline
46 & 31077 & 31292.9552803976 & -215.955280397626 \tabularnewline
47 & 32226 & 31077.0091366177 & 1148.99086338228 \tabularnewline
48 & 33865 & 32225.9513885918 & 1639.04861140817 \tabularnewline
49 & 32810 & 33864.9306552701 & -1054.93065527012 \tabularnewline
50 & 32242 & 32810.0446319168 & -568.044631916848 \tabularnewline
51 & 32700 & 32242.0240327842 & 457.975967215807 \tabularnewline
52 & 32819 & 32699.9806239916 & 119.019376008448 \tabularnewline
53 & 33947 & 32818.9949645383 & 1128.00503546168 \tabularnewline
54 & 34148 & 33946.9522764585 & 201.047723541538 \tabularnewline
55 & 35261 & 34147.9914940899 & 1113.00850591007 \tabularnewline
56 & 39506 & 35260.9529109304 & 4245.04708906964 \tabularnewline
57 & 41591 & 39505.8204009072 & 2085.17959909284 \tabularnewline
58 & 39148 & 41590.9117803981 & -2442.91178039806 \tabularnewline
59 & 41216 & 39148.1033545048 & 2067.89664549522 \tabularnewline
60 & 40225 & 41215.9125116038 & -990.912511603798 \tabularnewline
61 & 41126 & 40225.0419234426 & 900.958076557356 \tabularnewline
62 & 42362 & 41125.961882342 & 1236.03811765803 \tabularnewline
63 & 40740 & 42361.947705804 & -1621.94770580397 \tabularnewline
64 & 40256 & 40740.0686212262 & -484.068621226215 \tabularnewline
65 & 39804 & 40256.0204799342 & -452.020479934246 \tabularnewline
66 & 41002 & 39804.0191240442 & 1197.98087595581 \tabularnewline
67 & 41702 & 41001.9493159265 & 700.050684073474 \tabularnewline
68 & 42254 & 41701.9703823149 & 552.029617685075 \tabularnewline
69 & 43605 & 42253.9766447777 & 1351.02335522233 \tabularnewline
70 & 43271 & 43604.9428410183 & -333.942841018274 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192215&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]16348[/C][C]15579[/C][C]769[/C][/ROW]
[ROW][C]3[/C][C]15928[/C][C]16347.9674652131[/C][C]-419.967465213107[/C][/ROW]
[ROW][C]4[/C][C]16171[/C][C]15928.017767948[/C][C]242.982232052038[/C][/ROW]
[ROW][C]5[/C][C]15937[/C][C]16170.9897199283[/C][C]-233.989719928299[/C][/ROW]
[ROW][C]6[/C][C]15713[/C][C]15937.0098996173[/C][C]-224.00989961726[/C][/ROW]
[ROW][C]7[/C][C]15594[/C][C]15713.0094773919[/C][C]-119.009477391868[/C][/ROW]
[ROW][C]8[/C][C]15683[/C][C]15594.0050350429[/C][C]88.9949649571063[/C][/ROW]
[ROW][C]9[/C][C]16438[/C][C]15682.9962348086[/C][C]755.003765191443[/C][/ROW]
[ROW][C]10[/C][C]17032[/C][C]16437.9680573646[/C][C]594.031942635374[/C][/ROW]
[ROW][C]11[/C][C]17696[/C][C]17031.9748677469[/C][C]664.025132253137[/C][/ROW]
[ROW][C]12[/C][C]17745[/C][C]17695.9719064809[/C][C]49.0280935190749[/C][/ROW]
[ROW][C]13[/C][C]19394[/C][C]17744.9979257236[/C][C]1649.00207427643[/C][/ROW]
[ROW][C]14[/C][C]20148[/C][C]19393.9302341599[/C][C]754.069765840148[/C][/ROW]
[ROW][C]15[/C][C]20108[/C][C]20147.9680968802[/C][C]-39.9680968801913[/C][/ROW]
[ROW][C]16[/C][C]18584[/C][C]20108.0016909669[/C][C]-1524.00169096686[/C][/ROW]
[ROW][C]17[/C][C]18441[/C][C]18584.0644773345[/C][C]-143.064477334512[/C][/ROW]
[ROW][C]18[/C][C]18391[/C][C]18441.0060527598[/C][C]-50.0060527597961[/C][/ROW]
[ROW][C]19[/C][C]19178[/C][C]18391.0021156518[/C][C]786.997884348155[/C][/ROW]
[ROW][C]20[/C][C]18079[/C][C]19177.9667037601[/C][C]-1098.96670376014[/C][/ROW]
[ROW][C]21[/C][C]18483[/C][C]18079.0464949903[/C][C]403.95350500974[/C][/ROW]
[ROW][C]22[/C][C]19644[/C][C]18482.9829095693[/C][C]1161.01709043069[/C][/ROW]
[ROW][C]23[/C][C]19195[/C][C]19643.9508797872[/C][C]-448.950879787237[/C][/ROW]
[ROW][C]24[/C][C]19650[/C][C]19195.0189941758[/C][C]454.981005824189[/C][/ROW]
[ROW][C]25[/C][C]20830[/C][C]19649.9807507021[/C][C]1180.01924929787[/C][/ROW]
[ROW][C]26[/C][C]23595[/C][C]20829.9500758455[/C][C]2765.04992415449[/C][/ROW]
[ROW][C]27[/C][C]22937[/C][C]23594.8830165019[/C][C]-657.88301650191[/C][/ROW]
[ROW][C]28[/C][C]21814[/C][C]22937.027833659[/C][C]-1123.02783365896[/C][/ROW]
[ROW][C]29[/C][C]21928[/C][C]21814.0475129665[/C][C]113.952487033494[/C][/ROW]
[ROW][C]30[/C][C]21777[/C][C]21927.9951789078[/C][C]-150.995178907826[/C][/ROW]
[ROW][C]31[/C][C]21383[/C][C]21777.0063882912[/C][C]-394.006388291244[/C][/ROW]
[ROW][C]32[/C][C]21467[/C][C]21383.0166695889[/C][C]83.9833304110834[/C][/ROW]
[ROW][C]33[/C][C]22052[/C][C]21466.9964468404[/C][C]585.003553159633[/C][/ROW]
[ROW][C]34[/C][C]22680[/C][C]22051.9752497192[/C][C]628.024750280798[/C][/ROW]
[ROW][C]35[/C][C]24320[/C][C]22679.973429582[/C][C]1640.02657041796[/C][/ROW]
[ROW][C]36[/C][C]24977[/C][C]24319.9306138947[/C][C]657.06938610529[/C][/ROW]
[ROW][C]37[/C][C]25204[/C][C]24976.972200764[/C][C]227.027799235955[/C][/ROW]
[ROW][C]38[/C][C]25739[/C][C]25203.9903949271[/C][C]535.009605072908[/C][/ROW]
[ROW][C]39[/C][C]26434[/C][C]25738.9773648589[/C][C]695.022635141075[/C][/ROW]
[ROW][C]40[/C][C]27525[/C][C]26433.9705950412[/C][C]1091.0294049588[/C][/ROW]
[ROW][C]41[/C][C]30695[/C][C]27524.9538408203[/C][C]3170.04615917969[/C][/ROW]
[ROW][C]42[/C][C]32436[/C][C]30694.8658819555[/C][C]1741.13411804451[/C][/ROW]
[ROW][C]43[/C][C]30160[/C][C]32435.9263362451[/C][C]-2275.92633624515[/C][/ROW]
[ROW][C]44[/C][C]30236[/C][C]30160.0962896987[/C][C]75.9037103012561[/C][/ROW]
[ROW][C]45[/C][C]31293[/C][C]30235.9967886723[/C][C]1057.00321132775[/C][/ROW]
[ROW][C]46[/C][C]31077[/C][C]31292.9552803976[/C][C]-215.955280397626[/C][/ROW]
[ROW][C]47[/C][C]32226[/C][C]31077.0091366177[/C][C]1148.99086338228[/C][/ROW]
[ROW][C]48[/C][C]33865[/C][C]32225.9513885918[/C][C]1639.04861140817[/C][/ROW]
[ROW][C]49[/C][C]32810[/C][C]33864.9306552701[/C][C]-1054.93065527012[/C][/ROW]
[ROW][C]50[/C][C]32242[/C][C]32810.0446319168[/C][C]-568.044631916848[/C][/ROW]
[ROW][C]51[/C][C]32700[/C][C]32242.0240327842[/C][C]457.975967215807[/C][/ROW]
[ROW][C]52[/C][C]32819[/C][C]32699.9806239916[/C][C]119.019376008448[/C][/ROW]
[ROW][C]53[/C][C]33947[/C][C]32818.9949645383[/C][C]1128.00503546168[/C][/ROW]
[ROW][C]54[/C][C]34148[/C][C]33946.9522764585[/C][C]201.047723541538[/C][/ROW]
[ROW][C]55[/C][C]35261[/C][C]34147.9914940899[/C][C]1113.00850591007[/C][/ROW]
[ROW][C]56[/C][C]39506[/C][C]35260.9529109304[/C][C]4245.04708906964[/C][/ROW]
[ROW][C]57[/C][C]41591[/C][C]39505.8204009072[/C][C]2085.17959909284[/C][/ROW]
[ROW][C]58[/C][C]39148[/C][C]41590.9117803981[/C][C]-2442.91178039806[/C][/ROW]
[ROW][C]59[/C][C]41216[/C][C]39148.1033545048[/C][C]2067.89664549522[/C][/ROW]
[ROW][C]60[/C][C]40225[/C][C]41215.9125116038[/C][C]-990.912511603798[/C][/ROW]
[ROW][C]61[/C][C]41126[/C][C]40225.0419234426[/C][C]900.958076557356[/C][/ROW]
[ROW][C]62[/C][C]42362[/C][C]41125.961882342[/C][C]1236.03811765803[/C][/ROW]
[ROW][C]63[/C][C]40740[/C][C]42361.947705804[/C][C]-1621.94770580397[/C][/ROW]
[ROW][C]64[/C][C]40256[/C][C]40740.0686212262[/C][C]-484.068621226215[/C][/ROW]
[ROW][C]65[/C][C]39804[/C][C]40256.0204799342[/C][C]-452.020479934246[/C][/ROW]
[ROW][C]66[/C][C]41002[/C][C]39804.0191240442[/C][C]1197.98087595581[/C][/ROW]
[ROW][C]67[/C][C]41702[/C][C]41001.9493159265[/C][C]700.050684073474[/C][/ROW]
[ROW][C]68[/C][C]42254[/C][C]41701.9703823149[/C][C]552.029617685075[/C][/ROW]
[ROW][C]69[/C][C]43605[/C][C]42253.9766447777[/C][C]1351.02335522233[/C][/ROW]
[ROW][C]70[/C][C]43271[/C][C]43604.9428410183[/C][C]-333.942841018274[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192215&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192215&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
21634815579769
31592816347.9674652131-419.967465213107
41617115928.017767948242.982232052038
51593716170.9897199283-233.989719928299
61571315937.0098996173-224.00989961726
71559415713.0094773919-119.009477391868
81568315594.005035042988.9949649571063
91643815682.9962348086755.003765191443
101703216437.9680573646594.031942635374
111769617031.9748677469664.025132253137
121774517695.971906480949.0280935190749
131939417744.99792572361649.00207427643
142014819393.9302341599754.069765840148
152010820147.9680968802-39.9680968801913
161858420108.0016909669-1524.00169096686
171844118584.0644773345-143.064477334512
181839118441.0060527598-50.0060527597961
191917818391.0021156518786.997884348155
201807919177.9667037601-1098.96670376014
211848318079.0464949903403.95350500974
221964418482.98290956931161.01709043069
231919519643.9508797872-448.950879787237
241965019195.0189941758454.981005824189
252083019649.98075070211180.01924929787
262359520829.95007584552765.04992415449
272293723594.8830165019-657.88301650191
282181422937.027833659-1123.02783365896
292192821814.0475129665113.952487033494
302177721927.9951789078-150.995178907826
312138321777.0063882912-394.006388291244
322146721383.016669588983.9833304110834
332205221466.9964468404585.003553159633
342268022051.9752497192628.024750280798
352432022679.9734295821640.02657041796
362497724319.9306138947657.06938610529
372520424976.972200764227.027799235955
382573925203.9903949271535.009605072908
392643425738.9773648589695.022635141075
402752526433.97059504121091.0294049588
413069527524.95384082033170.04615917969
423243630694.86588195551741.13411804451
433016032435.9263362451-2275.92633624515
443023630160.096289698775.9037103012561
453129330235.99678867231057.00321132775
463107731292.9552803976-215.955280397626
473222631077.00913661771148.99086338228
483386532225.95138859181639.04861140817
493281033864.9306552701-1054.93065527012
503224232810.0446319168-568.044631916848
513270032242.0240327842457.975967215807
523281932699.9806239916119.019376008448
533394732818.99496453831128.00503546168
543414833946.9522764585201.047723541538
553526134147.99149408991113.00850591007
563950635260.95291093044245.04708906964
574159139505.82040090722085.17959909284
583914841590.9117803981-2442.91178039806
594121639148.10335450482067.89664549522
604022541215.9125116038-990.912511603798
614112640225.0419234426900.958076557356
624236241125.9618823421236.03811765803
634074042361.947705804-1621.94770580397
644025640740.0686212262-484.068621226215
653980440256.0204799342-452.020479934246
664100239804.01912404421197.98087595581
674170241001.9493159265700.050684073474
684225441701.9703823149552.029617685075
694360542253.97664477771351.02335522233
704327143604.9428410183-333.942841018274







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7143271.014128425441038.786247101545503.2420097494
7243271.014128425440114.233963450146427.7942934008
7343271.014128425439404.791074099247137.2371827517
7443271.014128425438806.700026390747735.3282304602
7543271.014128425438279.769784832548262.2584720184
7643271.014128425437803.387605584848738.6406512661
7743271.014128425437365.308456019149176.7198008318
7843271.014128425436957.553968979249584.4742878716
7943271.014128425436574.582326283649967.4459305673
8043271.014128425436212.35854987850329.6697069729
8143271.014128425435867.836549008650674.1917078423
8243271.014128425435538.649809007851003.3784478431

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
71 & 43271.0141284254 & 41038.7862471015 & 45503.2420097494 \tabularnewline
72 & 43271.0141284254 & 40114.2339634501 & 46427.7942934008 \tabularnewline
73 & 43271.0141284254 & 39404.7910740992 & 47137.2371827517 \tabularnewline
74 & 43271.0141284254 & 38806.7000263907 & 47735.3282304602 \tabularnewline
75 & 43271.0141284254 & 38279.7697848325 & 48262.2584720184 \tabularnewline
76 & 43271.0141284254 & 37803.3876055848 & 48738.6406512661 \tabularnewline
77 & 43271.0141284254 & 37365.3084560191 & 49176.7198008318 \tabularnewline
78 & 43271.0141284254 & 36957.5539689792 & 49584.4742878716 \tabularnewline
79 & 43271.0141284254 & 36574.5823262836 & 49967.4459305673 \tabularnewline
80 & 43271.0141284254 & 36212.358549878 & 50329.6697069729 \tabularnewline
81 & 43271.0141284254 & 35867.8365490086 & 50674.1917078423 \tabularnewline
82 & 43271.0141284254 & 35538.6498090078 & 51003.3784478431 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192215&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]71[/C][C]43271.0141284254[/C][C]41038.7862471015[/C][C]45503.2420097494[/C][/ROW]
[ROW][C]72[/C][C]43271.0141284254[/C][C]40114.2339634501[/C][C]46427.7942934008[/C][/ROW]
[ROW][C]73[/C][C]43271.0141284254[/C][C]39404.7910740992[/C][C]47137.2371827517[/C][/ROW]
[ROW][C]74[/C][C]43271.0141284254[/C][C]38806.7000263907[/C][C]47735.3282304602[/C][/ROW]
[ROW][C]75[/C][C]43271.0141284254[/C][C]38279.7697848325[/C][C]48262.2584720184[/C][/ROW]
[ROW][C]76[/C][C]43271.0141284254[/C][C]37803.3876055848[/C][C]48738.6406512661[/C][/ROW]
[ROW][C]77[/C][C]43271.0141284254[/C][C]37365.3084560191[/C][C]49176.7198008318[/C][/ROW]
[ROW][C]78[/C][C]43271.0141284254[/C][C]36957.5539689792[/C][C]49584.4742878716[/C][/ROW]
[ROW][C]79[/C][C]43271.0141284254[/C][C]36574.5823262836[/C][C]49967.4459305673[/C][/ROW]
[ROW][C]80[/C][C]43271.0141284254[/C][C]36212.358549878[/C][C]50329.6697069729[/C][/ROW]
[ROW][C]81[/C][C]43271.0141284254[/C][C]35867.8365490086[/C][C]50674.1917078423[/C][/ROW]
[ROW][C]82[/C][C]43271.0141284254[/C][C]35538.6498090078[/C][C]51003.3784478431[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192215&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192215&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
7143271.014128425441038.786247101545503.2420097494
7243271.014128425440114.233963450146427.7942934008
7343271.014128425439404.791074099247137.2371827517
7443271.014128425438806.700026390747735.3282304602
7543271.014128425438279.769784832548262.2584720184
7643271.014128425437803.387605584848738.6406512661
7743271.014128425437365.308456019149176.7198008318
7843271.014128425436957.553968979249584.4742878716
7943271.014128425436574.582326283649967.4459305673
8043271.014128425436212.35854987850329.6697069729
8143271.014128425435867.836549008650674.1917078423
8243271.014128425435538.649809007851003.3784478431



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')