Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Jan 2010 14:46:18 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/25/t1264456060j2x45u3ttf7wyza.htm/, Retrieved Sun, 05 May 2024 21:14:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72502, Retrieved Sun, 05 May 2024 21:14:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact127
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Exponentional Smo...] [2010-01-25 21:20:41] [74be16979710d4c4e7c6647856088456]
-    D    [Exponential Smoothing] [Exponentional Smo...] [2010-01-25 21:46:18] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
68897
38683
44720
39525
45315
50380
40600
36279
42438
38064
31879
11379
70249
39253
47060
41697
38708
49267
39018
32228
40870
39383
34571
12066
70938
34077
45409
40809
37013
44953
37848
32745
43412
34931
33008
8620
68906
39556
50669
36432
40891
48428
36222
33425
39401
37967
34801
12657
69116
41519
51321
38529
41547
52073
38401
40898
40439
41888
37898
8771
68184
50530
47221
41756
45633
48138
39486
39341
41117
41629
29722
7054
56231
34418
34568
29789
30630
35502
33091
27630
33520




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72502&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72502&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72502&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.391420833329359
beta0
gamma0.570171376485047

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.391420833329359 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.570171376485047 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72502&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]0.391420833329359[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.570171376485047[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72502&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72502&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
alpha0.391420833329359
beta0
gamma0.570171376485047







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137024970721.3266559829-472.326655982892
143925339691.492306051-438.492306051041
154706047477.3180922313-417.31809223134
164169741877.6819068300-180.681906830039
173870838567.1700543144140.829945685604
184926748956.837972369310.162027630977
193901839926.8693283814-908.869328381443
203222835086.3714151689-2858.37141516886
214087039921.6311039019948.36889609805
223938335647.17825753963735.82174246039
233457131025.58419383343545.41580616663
241206612151.3362798722-85.3362798721682
257093870852.666644189885.3333558102022
263407740052.8523714584-5975.85237145841
274540945678.5874004602-269.58740046015
284080940218.8875217193590.112478280738
293701337321.6434689092-308.643468909242
304495347594.1354162223-2641.13541622234
313784836985.9703876026862.029612397411
323274532162.1728653753582.82713462468
334341239665.30700893763746.69299106237
343493137453.4070986882-2522.40709868816
353300830316.14208916392691.85791083609
3686209847.94311404445-1227.94311404445
376890668161.2547706059744.745229394146
383955635516.35040995884039.64959004124
395066947042.40367354383626.59632645623
403643243406.0623377924-6974.06233779241
414089137236.17937536623654.82062463385
424842848250.6920479249177.307952075083
433622239961.3031925521-3739.30319255215
443342533239.5664472244185.433552775576
453940141684.9962653044-2283.99626530438
463796734937.21618393583029.78381606419
473480131782.51523782613018.4847621739
481265710082.01572935142574.98427064861
496911670568.3842417824-1452.38424178238
504151938206.79106399763312.20893600245
515132149304.78172247482016.21827752518
523852941359.7354517122-2830.73545171221
534154740499.80004292361047.19995707643
545207349286.95816388652786.04183611346
553840140659.6398822971-2258.63988229705
564089835879.32735890285018.6726410972
574043945359.7092782919-4920.70927829195
584188839423.71683563932464.28316436071
593789836043.74644452721854.25355547282
60877113733.6503905962-4962.65039059618
616818469872.1572568186-1688.15725681855
625053039071.564860803511458.4351391965
634722152908.4566398564-5687.45663985639
644175640266.16560956431489.83439043573
654563342443.01320131823189.98679868184
664813852672.271164776-4534.27116477599
673948639429.153455326756.8465446733244
683934138080.35740540081260.64259459915
694111742640.8579964992-1523.85799649917
704162940597.01509117631031.98490882370
712972236444.7364522787-6722.73645227875
7270548412.0001831816-1358.00018318159
735623167097.673087001-10866.6730870010
743441837266.2125947004-2848.21259470037
753456839553.6556024449-4985.65560244493
762978929676.5440656061112.455934393929
773063031904.2004350705-1274.20043507054
783550237705.8080904286-2203.80809042857
793309126967.97441165476123.02558834527
802763028411.3177316676-781.317731667645
813352031206.34633940332313.65366059672

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 70249 & 70721.3266559829 & -472.326655982892 \tabularnewline
14 & 39253 & 39691.492306051 & -438.492306051041 \tabularnewline
15 & 47060 & 47477.3180922313 & -417.31809223134 \tabularnewline
16 & 41697 & 41877.6819068300 & -180.681906830039 \tabularnewline
17 & 38708 & 38567.1700543144 & 140.829945685604 \tabularnewline
18 & 49267 & 48956.837972369 & 310.162027630977 \tabularnewline
19 & 39018 & 39926.8693283814 & -908.869328381443 \tabularnewline
20 & 32228 & 35086.3714151689 & -2858.37141516886 \tabularnewline
21 & 40870 & 39921.6311039019 & 948.36889609805 \tabularnewline
22 & 39383 & 35647.1782575396 & 3735.82174246039 \tabularnewline
23 & 34571 & 31025.5841938334 & 3545.41580616663 \tabularnewline
24 & 12066 & 12151.3362798722 & -85.3362798721682 \tabularnewline
25 & 70938 & 70852.6666441898 & 85.3333558102022 \tabularnewline
26 & 34077 & 40052.8523714584 & -5975.85237145841 \tabularnewline
27 & 45409 & 45678.5874004602 & -269.58740046015 \tabularnewline
28 & 40809 & 40218.8875217193 & 590.112478280738 \tabularnewline
29 & 37013 & 37321.6434689092 & -308.643468909242 \tabularnewline
30 & 44953 & 47594.1354162223 & -2641.13541622234 \tabularnewline
31 & 37848 & 36985.9703876026 & 862.029612397411 \tabularnewline
32 & 32745 & 32162.1728653753 & 582.82713462468 \tabularnewline
33 & 43412 & 39665.3070089376 & 3746.69299106237 \tabularnewline
34 & 34931 & 37453.4070986882 & -2522.40709868816 \tabularnewline
35 & 33008 & 30316.1420891639 & 2691.85791083609 \tabularnewline
36 & 8620 & 9847.94311404445 & -1227.94311404445 \tabularnewline
37 & 68906 & 68161.2547706059 & 744.745229394146 \tabularnewline
38 & 39556 & 35516.3504099588 & 4039.64959004124 \tabularnewline
39 & 50669 & 47042.4036735438 & 3626.59632645623 \tabularnewline
40 & 36432 & 43406.0623377924 & -6974.06233779241 \tabularnewline
41 & 40891 & 37236.1793753662 & 3654.82062463385 \tabularnewline
42 & 48428 & 48250.6920479249 & 177.307952075083 \tabularnewline
43 & 36222 & 39961.3031925521 & -3739.30319255215 \tabularnewline
44 & 33425 & 33239.5664472244 & 185.433552775576 \tabularnewline
45 & 39401 & 41684.9962653044 & -2283.99626530438 \tabularnewline
46 & 37967 & 34937.2161839358 & 3029.78381606419 \tabularnewline
47 & 34801 & 31782.5152378261 & 3018.4847621739 \tabularnewline
48 & 12657 & 10082.0157293514 & 2574.98427064861 \tabularnewline
49 & 69116 & 70568.3842417824 & -1452.38424178238 \tabularnewline
50 & 41519 & 38206.7910639976 & 3312.20893600245 \tabularnewline
51 & 51321 & 49304.7817224748 & 2016.21827752518 \tabularnewline
52 & 38529 & 41359.7354517122 & -2830.73545171221 \tabularnewline
53 & 41547 & 40499.8000429236 & 1047.19995707643 \tabularnewline
54 & 52073 & 49286.9581638865 & 2786.04183611346 \tabularnewline
55 & 38401 & 40659.6398822971 & -2258.63988229705 \tabularnewline
56 & 40898 & 35879.3273589028 & 5018.6726410972 \tabularnewline
57 & 40439 & 45359.7092782919 & -4920.70927829195 \tabularnewline
58 & 41888 & 39423.7168356393 & 2464.28316436071 \tabularnewline
59 & 37898 & 36043.7464445272 & 1854.25355547282 \tabularnewline
60 & 8771 & 13733.6503905962 & -4962.65039059618 \tabularnewline
61 & 68184 & 69872.1572568186 & -1688.15725681855 \tabularnewline
62 & 50530 & 39071.5648608035 & 11458.4351391965 \tabularnewline
63 & 47221 & 52908.4566398564 & -5687.45663985639 \tabularnewline
64 & 41756 & 40266.1656095643 & 1489.83439043573 \tabularnewline
65 & 45633 & 42443.0132013182 & 3189.98679868184 \tabularnewline
66 & 48138 & 52672.271164776 & -4534.27116477599 \tabularnewline
67 & 39486 & 39429.1534553267 & 56.8465446733244 \tabularnewline
68 & 39341 & 38080.3574054008 & 1260.64259459915 \tabularnewline
69 & 41117 & 42640.8579964992 & -1523.85799649917 \tabularnewline
70 & 41629 & 40597.0150911763 & 1031.98490882370 \tabularnewline
71 & 29722 & 36444.7364522787 & -6722.73645227875 \tabularnewline
72 & 7054 & 8412.0001831816 & -1358.00018318159 \tabularnewline
73 & 56231 & 67097.673087001 & -10866.6730870010 \tabularnewline
74 & 34418 & 37266.2125947004 & -2848.21259470037 \tabularnewline
75 & 34568 & 39553.6556024449 & -4985.65560244493 \tabularnewline
76 & 29789 & 29676.5440656061 & 112.455934393929 \tabularnewline
77 & 30630 & 31904.2004350705 & -1274.20043507054 \tabularnewline
78 & 35502 & 37705.8080904286 & -2203.80809042857 \tabularnewline
79 & 33091 & 26967.9744116547 & 6123.02558834527 \tabularnewline
80 & 27630 & 28411.3177316676 & -781.317731667645 \tabularnewline
81 & 33520 & 31206.3463394033 & 2313.65366059672 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72502&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]70249[/C][C]70721.3266559829[/C][C]-472.326655982892[/C][/ROW]
[ROW][C]14[/C][C]39253[/C][C]39691.492306051[/C][C]-438.492306051041[/C][/ROW]
[ROW][C]15[/C][C]47060[/C][C]47477.3180922313[/C][C]-417.31809223134[/C][/ROW]
[ROW][C]16[/C][C]41697[/C][C]41877.6819068300[/C][C]-180.681906830039[/C][/ROW]
[ROW][C]17[/C][C]38708[/C][C]38567.1700543144[/C][C]140.829945685604[/C][/ROW]
[ROW][C]18[/C][C]49267[/C][C]48956.837972369[/C][C]310.162027630977[/C][/ROW]
[ROW][C]19[/C][C]39018[/C][C]39926.8693283814[/C][C]-908.869328381443[/C][/ROW]
[ROW][C]20[/C][C]32228[/C][C]35086.3714151689[/C][C]-2858.37141516886[/C][/ROW]
[ROW][C]21[/C][C]40870[/C][C]39921.6311039019[/C][C]948.36889609805[/C][/ROW]
[ROW][C]22[/C][C]39383[/C][C]35647.1782575396[/C][C]3735.82174246039[/C][/ROW]
[ROW][C]23[/C][C]34571[/C][C]31025.5841938334[/C][C]3545.41580616663[/C][/ROW]
[ROW][C]24[/C][C]12066[/C][C]12151.3362798722[/C][C]-85.3362798721682[/C][/ROW]
[ROW][C]25[/C][C]70938[/C][C]70852.6666441898[/C][C]85.3333558102022[/C][/ROW]
[ROW][C]26[/C][C]34077[/C][C]40052.8523714584[/C][C]-5975.85237145841[/C][/ROW]
[ROW][C]27[/C][C]45409[/C][C]45678.5874004602[/C][C]-269.58740046015[/C][/ROW]
[ROW][C]28[/C][C]40809[/C][C]40218.8875217193[/C][C]590.112478280738[/C][/ROW]
[ROW][C]29[/C][C]37013[/C][C]37321.6434689092[/C][C]-308.643468909242[/C][/ROW]
[ROW][C]30[/C][C]44953[/C][C]47594.1354162223[/C][C]-2641.13541622234[/C][/ROW]
[ROW][C]31[/C][C]37848[/C][C]36985.9703876026[/C][C]862.029612397411[/C][/ROW]
[ROW][C]32[/C][C]32745[/C][C]32162.1728653753[/C][C]582.82713462468[/C][/ROW]
[ROW][C]33[/C][C]43412[/C][C]39665.3070089376[/C][C]3746.69299106237[/C][/ROW]
[ROW][C]34[/C][C]34931[/C][C]37453.4070986882[/C][C]-2522.40709868816[/C][/ROW]
[ROW][C]35[/C][C]33008[/C][C]30316.1420891639[/C][C]2691.85791083609[/C][/ROW]
[ROW][C]36[/C][C]8620[/C][C]9847.94311404445[/C][C]-1227.94311404445[/C][/ROW]
[ROW][C]37[/C][C]68906[/C][C]68161.2547706059[/C][C]744.745229394146[/C][/ROW]
[ROW][C]38[/C][C]39556[/C][C]35516.3504099588[/C][C]4039.64959004124[/C][/ROW]
[ROW][C]39[/C][C]50669[/C][C]47042.4036735438[/C][C]3626.59632645623[/C][/ROW]
[ROW][C]40[/C][C]36432[/C][C]43406.0623377924[/C][C]-6974.06233779241[/C][/ROW]
[ROW][C]41[/C][C]40891[/C][C]37236.1793753662[/C][C]3654.82062463385[/C][/ROW]
[ROW][C]42[/C][C]48428[/C][C]48250.6920479249[/C][C]177.307952075083[/C][/ROW]
[ROW][C]43[/C][C]36222[/C][C]39961.3031925521[/C][C]-3739.30319255215[/C][/ROW]
[ROW][C]44[/C][C]33425[/C][C]33239.5664472244[/C][C]185.433552775576[/C][/ROW]
[ROW][C]45[/C][C]39401[/C][C]41684.9962653044[/C][C]-2283.99626530438[/C][/ROW]
[ROW][C]46[/C][C]37967[/C][C]34937.2161839358[/C][C]3029.78381606419[/C][/ROW]
[ROW][C]47[/C][C]34801[/C][C]31782.5152378261[/C][C]3018.4847621739[/C][/ROW]
[ROW][C]48[/C][C]12657[/C][C]10082.0157293514[/C][C]2574.98427064861[/C][/ROW]
[ROW][C]49[/C][C]69116[/C][C]70568.3842417824[/C][C]-1452.38424178238[/C][/ROW]
[ROW][C]50[/C][C]41519[/C][C]38206.7910639976[/C][C]3312.20893600245[/C][/ROW]
[ROW][C]51[/C][C]51321[/C][C]49304.7817224748[/C][C]2016.21827752518[/C][/ROW]
[ROW][C]52[/C][C]38529[/C][C]41359.7354517122[/C][C]-2830.73545171221[/C][/ROW]
[ROW][C]53[/C][C]41547[/C][C]40499.8000429236[/C][C]1047.19995707643[/C][/ROW]
[ROW][C]54[/C][C]52073[/C][C]49286.9581638865[/C][C]2786.04183611346[/C][/ROW]
[ROW][C]55[/C][C]38401[/C][C]40659.6398822971[/C][C]-2258.63988229705[/C][/ROW]
[ROW][C]56[/C][C]40898[/C][C]35879.3273589028[/C][C]5018.6726410972[/C][/ROW]
[ROW][C]57[/C][C]40439[/C][C]45359.7092782919[/C][C]-4920.70927829195[/C][/ROW]
[ROW][C]58[/C][C]41888[/C][C]39423.7168356393[/C][C]2464.28316436071[/C][/ROW]
[ROW][C]59[/C][C]37898[/C][C]36043.7464445272[/C][C]1854.25355547282[/C][/ROW]
[ROW][C]60[/C][C]8771[/C][C]13733.6503905962[/C][C]-4962.65039059618[/C][/ROW]
[ROW][C]61[/C][C]68184[/C][C]69872.1572568186[/C][C]-1688.15725681855[/C][/ROW]
[ROW][C]62[/C][C]50530[/C][C]39071.5648608035[/C][C]11458.4351391965[/C][/ROW]
[ROW][C]63[/C][C]47221[/C][C]52908.4566398564[/C][C]-5687.45663985639[/C][/ROW]
[ROW][C]64[/C][C]41756[/C][C]40266.1656095643[/C][C]1489.83439043573[/C][/ROW]
[ROW][C]65[/C][C]45633[/C][C]42443.0132013182[/C][C]3189.98679868184[/C][/ROW]
[ROW][C]66[/C][C]48138[/C][C]52672.271164776[/C][C]-4534.27116477599[/C][/ROW]
[ROW][C]67[/C][C]39486[/C][C]39429.1534553267[/C][C]56.8465446733244[/C][/ROW]
[ROW][C]68[/C][C]39341[/C][C]38080.3574054008[/C][C]1260.64259459915[/C][/ROW]
[ROW][C]69[/C][C]41117[/C][C]42640.8579964992[/C][C]-1523.85799649917[/C][/ROW]
[ROW][C]70[/C][C]41629[/C][C]40597.0150911763[/C][C]1031.98490882370[/C][/ROW]
[ROW][C]71[/C][C]29722[/C][C]36444.7364522787[/C][C]-6722.73645227875[/C][/ROW]
[ROW][C]72[/C][C]7054[/C][C]8412.0001831816[/C][C]-1358.00018318159[/C][/ROW]
[ROW][C]73[/C][C]56231[/C][C]67097.673087001[/C][C]-10866.6730870010[/C][/ROW]
[ROW][C]74[/C][C]34418[/C][C]37266.2125947004[/C][C]-2848.21259470037[/C][/ROW]
[ROW][C]75[/C][C]34568[/C][C]39553.6556024449[/C][C]-4985.65560244493[/C][/ROW]
[ROW][C]76[/C][C]29789[/C][C]29676.5440656061[/C][C]112.455934393929[/C][/ROW]
[ROW][C]77[/C][C]30630[/C][C]31904.2004350705[/C][C]-1274.20043507054[/C][/ROW]
[ROW][C]78[/C][C]35502[/C][C]37705.8080904286[/C][C]-2203.80809042857[/C][/ROW]
[ROW][C]79[/C][C]33091[/C][C]26967.9744116547[/C][C]6123.02558834527[/C][/ROW]
[ROW][C]80[/C][C]27630[/C][C]28411.3177316676[/C][C]-781.317731667645[/C][/ROW]
[ROW][C]81[/C][C]33520[/C][C]31206.3463394033[/C][C]2313.65366059672[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72502&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72502&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
137024970721.3266559829-472.326655982892
143925339691.492306051-438.492306051041
154706047477.3180922313-417.31809223134
164169741877.6819068300-180.681906830039
173870838567.1700543144140.829945685604
184926748956.837972369310.162027630977
193901839926.8693283814-908.869328381443
203222835086.3714151689-2858.37141516886
214087039921.6311039019948.36889609805
223938335647.17825753963735.82174246039
233457131025.58419383343545.41580616663
241206612151.3362798722-85.3362798721682
257093870852.666644189885.3333558102022
263407740052.8523714584-5975.85237145841
274540945678.5874004602-269.58740046015
284080940218.8875217193590.112478280738
293701337321.6434689092-308.643468909242
304495347594.1354162223-2641.13541622234
313784836985.9703876026862.029612397411
323274532162.1728653753582.82713462468
334341239665.30700893763746.69299106237
343493137453.4070986882-2522.40709868816
353300830316.14208916392691.85791083609
3686209847.94311404445-1227.94311404445
376890668161.2547706059744.745229394146
383955635516.35040995884039.64959004124
395066947042.40367354383626.59632645623
403643243406.0623377924-6974.06233779241
414089137236.17937536623654.82062463385
424842848250.6920479249177.307952075083
433622239961.3031925521-3739.30319255215
443342533239.5664472244185.433552775576
453940141684.9962653044-2283.99626530438
463796734937.21618393583029.78381606419
473480131782.51523782613018.4847621739
481265710082.01572935142574.98427064861
496911670568.3842417824-1452.38424178238
504151938206.79106399763312.20893600245
515132149304.78172247482016.21827752518
523852941359.7354517122-2830.73545171221
534154740499.80004292361047.19995707643
545207349286.95816388652786.04183611346
553840140659.6398822971-2258.63988229705
564089835879.32735890285018.6726410972
574043945359.7092782919-4920.70927829195
584188839423.71683563932464.28316436071
593789836043.74644452721854.25355547282
60877113733.6503905962-4962.65039059618
616818469872.1572568186-1688.15725681855
625053039071.564860803511458.4351391965
634722152908.4566398564-5687.45663985639
644175640266.16560956431489.83439043573
654563342443.01320131823189.98679868184
664813852672.271164776-4534.27116477599
673948639429.153455326756.8465446733244
683934138080.35740540081260.64259459915
694111742640.8579964992-1523.85799649917
704162940597.01509117631031.98490882370
712972236444.7364522787-6722.73645227875
7270548412.0001831816-1358.00018318159
735623167097.673087001-10866.6730870010
743441837266.2125947004-2848.21259470037
753456839553.6556024449-4985.65560244493
762978929676.5440656061112.455934393929
773063031904.2004350705-1274.20043507054
783550237705.8080904286-2203.80809042857
793309126967.97441165476123.02558834527
802763028411.3177316676-781.317731667645
813352031206.34633940332313.65366059672







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8231551.448674322324741.451857518138361.4454911265
8324304.384592471216991.290531290831617.4786536516
84764.600984153938-7019.140587253798548.34255556167
8556682.367001068248454.85699176164909.8770103754
8633886.709801125225238.171828956942535.2477732936
8736547.321756950227497.321913921145597.3215999793
8830390.715952451820956.322211377839825.1096935257
8932093.192702091822289.465178113741896.9202260698
9038070.980283296227911.336516549648230.6240500428
9131085.127836243620581.621299377941588.6343731094
9227736.022764146716899.559426287338572.4861020060
9331910.813216274420751.322825779043070.3036067698

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
82 & 31551.4486743223 & 24741.4518575181 & 38361.4454911265 \tabularnewline
83 & 24304.3845924712 & 16991.2905312908 & 31617.4786536516 \tabularnewline
84 & 764.600984153938 & -7019.14058725379 & 8548.34255556167 \tabularnewline
85 & 56682.3670010682 & 48454.856991761 & 64909.8770103754 \tabularnewline
86 & 33886.7098011252 & 25238.1718289569 & 42535.2477732936 \tabularnewline
87 & 36547.3217569502 & 27497.3219139211 & 45597.3215999793 \tabularnewline
88 & 30390.7159524518 & 20956.3222113778 & 39825.1096935257 \tabularnewline
89 & 32093.1927020918 & 22289.4651781137 & 41896.9202260698 \tabularnewline
90 & 38070.9802832962 & 27911.3365165496 & 48230.6240500428 \tabularnewline
91 & 31085.1278362436 & 20581.6212993779 & 41588.6343731094 \tabularnewline
92 & 27736.0227641467 & 16899.5594262873 & 38572.4861020060 \tabularnewline
93 & 31910.8132162744 & 20751.3228257790 & 43070.3036067698 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72502&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]82[/C][C]31551.4486743223[/C][C]24741.4518575181[/C][C]38361.4454911265[/C][/ROW]
[ROW][C]83[/C][C]24304.3845924712[/C][C]16991.2905312908[/C][C]31617.4786536516[/C][/ROW]
[ROW][C]84[/C][C]764.600984153938[/C][C]-7019.14058725379[/C][C]8548.34255556167[/C][/ROW]
[ROW][C]85[/C][C]56682.3670010682[/C][C]48454.856991761[/C][C]64909.8770103754[/C][/ROW]
[ROW][C]86[/C][C]33886.7098011252[/C][C]25238.1718289569[/C][C]42535.2477732936[/C][/ROW]
[ROW][C]87[/C][C]36547.3217569502[/C][C]27497.3219139211[/C][C]45597.3215999793[/C][/ROW]
[ROW][C]88[/C][C]30390.7159524518[/C][C]20956.3222113778[/C][C]39825.1096935257[/C][/ROW]
[ROW][C]89[/C][C]32093.1927020918[/C][C]22289.4651781137[/C][C]41896.9202260698[/C][/ROW]
[ROW][C]90[/C][C]38070.9802832962[/C][C]27911.3365165496[/C][C]48230.6240500428[/C][/ROW]
[ROW][C]91[/C][C]31085.1278362436[/C][C]20581.6212993779[/C][C]41588.6343731094[/C][/ROW]
[ROW][C]92[/C][C]27736.0227641467[/C][C]16899.5594262873[/C][C]38572.4861020060[/C][/ROW]
[ROW][C]93[/C][C]31910.8132162744[/C][C]20751.3228257790[/C][C]43070.3036067698[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72502&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72502&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
8231551.448674322324741.451857518138361.4454911265
8324304.384592471216991.290531290831617.4786536516
84764.600984153938-7019.140587253798548.34255556167
8556682.367001068248454.85699176164909.8770103754
8633886.709801125225238.171828956942535.2477732936
8736547.321756950227497.321913921145597.3215999793
8830390.715952451820956.322211377839825.1096935257
8932093.192702091822289.465178113741896.9202260698
9038070.980283296227911.336516549648230.6240500428
9131085.127836243620581.621299377941588.6343731094
9227736.022764146716899.559426287338572.4861020060
9331910.813216274420751.322825779043070.3036067698



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