Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 May 2008 10:27:48 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/27/t1211905700aar27iwki509kau.htm/, Retrieved Mon, 20 May 2024 02:07:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13360, Retrieved Mon, 20 May 2024 02:07:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [smoothing champag...] [2008-05-27 16:27:48] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
2815
2672
2755
2721
2946
3036
2282
2212
2922
4301
5764
7312
2541
2475
3031
3266
3776
3230
3028
1759
3595
4474
6838
8357
3113
3006
4047
3523
3937
3986
3260
1573
3528
5211
7614
9254
5375
3088
3718
4514
4520
4539
3663
1643
4739
5428
8314
10651
3633
4292
4154
4121
4647
4753
3965
1723
5048
6922
9858
11331
4016
4276
4968
4677
3523
1821
5222
6872
10803
13916
2639
2899
3370
3740
2927
3986
4217
1738
5221
6424
9842
13076




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13360&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13360&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13360&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 time5 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0
beta0
gamma0.89588635004732

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.89588635004732 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13360&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[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.89588635004732[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13360&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13360&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
beta0
gamma0.89588635004732







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1325412368.49607099695172.503929003050
1424752299.23063554187175.769364458128
1530312808.66370689647222.336293103529
1632662997.43890828896268.561091711039
1737763417.25819820299358.741801797015
1832302855.58006291701374.419937082992
1930282630.60624337706397.393756622937
2017591510.29684667595248.70315332405
2135953036.94605462600558.053945374004
2244743730.0172037031743.982796296901
2368385676.504419523171161.49558047683
2483576872.948968091051484.05103190895
2531132523.03998632031589.960013679685
2630062456.7000099164549.299990083599
2740473007.851757008041039.14824299196
2835233238.03912450669284.960875493313
2939373738.65008162431198.349918375688
3039863191.01777373524794.982226264764
3132602986.62588552958273.374114470421
3215731733.10660695269-160.106606952692
3335283536.89896687662-8.89896687661849
3452114396.54123557553814.458764424472
3576146717.07245571265896.927544287351
3692548202.490030351921051.50996964808
3753753051.577109649672323.42289035033
3830882948.81037311343139.189626886575
3937183938.81048358019-220.810483580192
4045143493.331683158681020.66831684132
4145203916.34906603009603.650933969909
4245393903.23149877607635.768501223933
4336633231.5380231399431.461976860098
4416431589.6692832313853.330716768616
4547393528.926503922331210.07349607767
4654285126.20372529982301.796274700182
4783147520.61759962115793.382400378851
48106519144.523459098311506.47654090169
4936335133.09996250202-1500.09996250202
5042923073.508459909291218.49154009071
5141543740.98938539335413.01061460665
5241214407.73449614259-286.734496142591
5346474457.15169796705189.848302032951
5447534472.80782081263280.192179187369
5539653618.07891877330346.921081226703
5617231637.4475444226385.5524555773732
5750484613.01483161235434.985168387647
5869225396.578888298841525.42111170116
5998588231.398062488341626.60193751166
601133110494.1552287586836.844771241364
6140163789.18088238996226.819117610035
6242764165.13839832469110.861601675308
6349684110.9999574441857.0000425559
6446774150.85297496075526.147025039253
6535234627.23420033803-1104.23420033803
6618214723.82816953661-2902.82816953661
6752223928.880779987961293.11922001204
6868721714.092821587425157.90717841258
69108035002.712106443885800.28789355612
70139166763.182840345927152.81715965408
7126399688.64853526556-7049.64853526556
72289911243.8730364222-8344.87303642225
7333703992.38503378657-622.385033786572
7437404264.45779400998-524.457794009983
7529274878.7745975599-1951.77459755990
7639864622.22091281142-636.220912811418
7742173637.96585299977579.034147000228
7817382123.22403591592-385.224035915915
7952215087.36863818058133.631361819417
8064246334.9914575383389.0085424616655
81984210199.1108566255-357.110856625526
821307613171.2940980642-95.294098064247

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2541 & 2368.49607099695 & 172.503929003050 \tabularnewline
14 & 2475 & 2299.23063554187 & 175.769364458128 \tabularnewline
15 & 3031 & 2808.66370689647 & 222.336293103529 \tabularnewline
16 & 3266 & 2997.43890828896 & 268.561091711039 \tabularnewline
17 & 3776 & 3417.25819820299 & 358.741801797015 \tabularnewline
18 & 3230 & 2855.58006291701 & 374.419937082992 \tabularnewline
19 & 3028 & 2630.60624337706 & 397.393756622937 \tabularnewline
20 & 1759 & 1510.29684667595 & 248.70315332405 \tabularnewline
21 & 3595 & 3036.94605462600 & 558.053945374004 \tabularnewline
22 & 4474 & 3730.0172037031 & 743.982796296901 \tabularnewline
23 & 6838 & 5676.50441952317 & 1161.49558047683 \tabularnewline
24 & 8357 & 6872.94896809105 & 1484.05103190895 \tabularnewline
25 & 3113 & 2523.03998632031 & 589.960013679685 \tabularnewline
26 & 3006 & 2456.7000099164 & 549.299990083599 \tabularnewline
27 & 4047 & 3007.85175700804 & 1039.14824299196 \tabularnewline
28 & 3523 & 3238.03912450669 & 284.960875493313 \tabularnewline
29 & 3937 & 3738.65008162431 & 198.349918375688 \tabularnewline
30 & 3986 & 3191.01777373524 & 794.982226264764 \tabularnewline
31 & 3260 & 2986.62588552958 & 273.374114470421 \tabularnewline
32 & 1573 & 1733.10660695269 & -160.106606952692 \tabularnewline
33 & 3528 & 3536.89896687662 & -8.89896687661849 \tabularnewline
34 & 5211 & 4396.54123557553 & 814.458764424472 \tabularnewline
35 & 7614 & 6717.07245571265 & 896.927544287351 \tabularnewline
36 & 9254 & 8202.49003035192 & 1051.50996964808 \tabularnewline
37 & 5375 & 3051.57710964967 & 2323.42289035033 \tabularnewline
38 & 3088 & 2948.81037311343 & 139.189626886575 \tabularnewline
39 & 3718 & 3938.81048358019 & -220.810483580192 \tabularnewline
40 & 4514 & 3493.33168315868 & 1020.66831684132 \tabularnewline
41 & 4520 & 3916.34906603009 & 603.650933969909 \tabularnewline
42 & 4539 & 3903.23149877607 & 635.768501223933 \tabularnewline
43 & 3663 & 3231.5380231399 & 431.461976860098 \tabularnewline
44 & 1643 & 1589.66928323138 & 53.330716768616 \tabularnewline
45 & 4739 & 3528.92650392233 & 1210.07349607767 \tabularnewline
46 & 5428 & 5126.20372529982 & 301.796274700182 \tabularnewline
47 & 8314 & 7520.61759962115 & 793.382400378851 \tabularnewline
48 & 10651 & 9144.52345909831 & 1506.47654090169 \tabularnewline
49 & 3633 & 5133.09996250202 & -1500.09996250202 \tabularnewline
50 & 4292 & 3073.50845990929 & 1218.49154009071 \tabularnewline
51 & 4154 & 3740.98938539335 & 413.01061460665 \tabularnewline
52 & 4121 & 4407.73449614259 & -286.734496142591 \tabularnewline
53 & 4647 & 4457.15169796705 & 189.848302032951 \tabularnewline
54 & 4753 & 4472.80782081263 & 280.192179187369 \tabularnewline
55 & 3965 & 3618.07891877330 & 346.921081226703 \tabularnewline
56 & 1723 & 1637.44754442263 & 85.5524555773732 \tabularnewline
57 & 5048 & 4613.01483161235 & 434.985168387647 \tabularnewline
58 & 6922 & 5396.57888829884 & 1525.42111170116 \tabularnewline
59 & 9858 & 8231.39806248834 & 1626.60193751166 \tabularnewline
60 & 11331 & 10494.1552287586 & 836.844771241364 \tabularnewline
61 & 4016 & 3789.18088238996 & 226.819117610035 \tabularnewline
62 & 4276 & 4165.13839832469 & 110.861601675308 \tabularnewline
63 & 4968 & 4110.9999574441 & 857.0000425559 \tabularnewline
64 & 4677 & 4150.85297496075 & 526.147025039253 \tabularnewline
65 & 3523 & 4627.23420033803 & -1104.23420033803 \tabularnewline
66 & 1821 & 4723.82816953661 & -2902.82816953661 \tabularnewline
67 & 5222 & 3928.88077998796 & 1293.11922001204 \tabularnewline
68 & 6872 & 1714.09282158742 & 5157.90717841258 \tabularnewline
69 & 10803 & 5002.71210644388 & 5800.28789355612 \tabularnewline
70 & 13916 & 6763.18284034592 & 7152.81715965408 \tabularnewline
71 & 2639 & 9688.64853526556 & -7049.64853526556 \tabularnewline
72 & 2899 & 11243.8730364222 & -8344.87303642225 \tabularnewline
73 & 3370 & 3992.38503378657 & -622.385033786572 \tabularnewline
74 & 3740 & 4264.45779400998 & -524.457794009983 \tabularnewline
75 & 2927 & 4878.7745975599 & -1951.77459755990 \tabularnewline
76 & 3986 & 4622.22091281142 & -636.220912811418 \tabularnewline
77 & 4217 & 3637.96585299977 & 579.034147000228 \tabularnewline
78 & 1738 & 2123.22403591592 & -385.224035915915 \tabularnewline
79 & 5221 & 5087.36863818058 & 133.631361819417 \tabularnewline
80 & 6424 & 6334.99145753833 & 89.0085424616655 \tabularnewline
81 & 9842 & 10199.1108566255 & -357.110856625526 \tabularnewline
82 & 13076 & 13171.2940980642 & -95.294098064247 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13360&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]2541[/C][C]2368.49607099695[/C][C]172.503929003050[/C][/ROW]
[ROW][C]14[/C][C]2475[/C][C]2299.23063554187[/C][C]175.769364458128[/C][/ROW]
[ROW][C]15[/C][C]3031[/C][C]2808.66370689647[/C][C]222.336293103529[/C][/ROW]
[ROW][C]16[/C][C]3266[/C][C]2997.43890828896[/C][C]268.561091711039[/C][/ROW]
[ROW][C]17[/C][C]3776[/C][C]3417.25819820299[/C][C]358.741801797015[/C][/ROW]
[ROW][C]18[/C][C]3230[/C][C]2855.58006291701[/C][C]374.419937082992[/C][/ROW]
[ROW][C]19[/C][C]3028[/C][C]2630.60624337706[/C][C]397.393756622937[/C][/ROW]
[ROW][C]20[/C][C]1759[/C][C]1510.29684667595[/C][C]248.70315332405[/C][/ROW]
[ROW][C]21[/C][C]3595[/C][C]3036.94605462600[/C][C]558.053945374004[/C][/ROW]
[ROW][C]22[/C][C]4474[/C][C]3730.0172037031[/C][C]743.982796296901[/C][/ROW]
[ROW][C]23[/C][C]6838[/C][C]5676.50441952317[/C][C]1161.49558047683[/C][/ROW]
[ROW][C]24[/C][C]8357[/C][C]6872.94896809105[/C][C]1484.05103190895[/C][/ROW]
[ROW][C]25[/C][C]3113[/C][C]2523.03998632031[/C][C]589.960013679685[/C][/ROW]
[ROW][C]26[/C][C]3006[/C][C]2456.7000099164[/C][C]549.299990083599[/C][/ROW]
[ROW][C]27[/C][C]4047[/C][C]3007.85175700804[/C][C]1039.14824299196[/C][/ROW]
[ROW][C]28[/C][C]3523[/C][C]3238.03912450669[/C][C]284.960875493313[/C][/ROW]
[ROW][C]29[/C][C]3937[/C][C]3738.65008162431[/C][C]198.349918375688[/C][/ROW]
[ROW][C]30[/C][C]3986[/C][C]3191.01777373524[/C][C]794.982226264764[/C][/ROW]
[ROW][C]31[/C][C]3260[/C][C]2986.62588552958[/C][C]273.374114470421[/C][/ROW]
[ROW][C]32[/C][C]1573[/C][C]1733.10660695269[/C][C]-160.106606952692[/C][/ROW]
[ROW][C]33[/C][C]3528[/C][C]3536.89896687662[/C][C]-8.89896687661849[/C][/ROW]
[ROW][C]34[/C][C]5211[/C][C]4396.54123557553[/C][C]814.458764424472[/C][/ROW]
[ROW][C]35[/C][C]7614[/C][C]6717.07245571265[/C][C]896.927544287351[/C][/ROW]
[ROW][C]36[/C][C]9254[/C][C]8202.49003035192[/C][C]1051.50996964808[/C][/ROW]
[ROW][C]37[/C][C]5375[/C][C]3051.57710964967[/C][C]2323.42289035033[/C][/ROW]
[ROW][C]38[/C][C]3088[/C][C]2948.81037311343[/C][C]139.189626886575[/C][/ROW]
[ROW][C]39[/C][C]3718[/C][C]3938.81048358019[/C][C]-220.810483580192[/C][/ROW]
[ROW][C]40[/C][C]4514[/C][C]3493.33168315868[/C][C]1020.66831684132[/C][/ROW]
[ROW][C]41[/C][C]4520[/C][C]3916.34906603009[/C][C]603.650933969909[/C][/ROW]
[ROW][C]42[/C][C]4539[/C][C]3903.23149877607[/C][C]635.768501223933[/C][/ROW]
[ROW][C]43[/C][C]3663[/C][C]3231.5380231399[/C][C]431.461976860098[/C][/ROW]
[ROW][C]44[/C][C]1643[/C][C]1589.66928323138[/C][C]53.330716768616[/C][/ROW]
[ROW][C]45[/C][C]4739[/C][C]3528.92650392233[/C][C]1210.07349607767[/C][/ROW]
[ROW][C]46[/C][C]5428[/C][C]5126.20372529982[/C][C]301.796274700182[/C][/ROW]
[ROW][C]47[/C][C]8314[/C][C]7520.61759962115[/C][C]793.382400378851[/C][/ROW]
[ROW][C]48[/C][C]10651[/C][C]9144.52345909831[/C][C]1506.47654090169[/C][/ROW]
[ROW][C]49[/C][C]3633[/C][C]5133.09996250202[/C][C]-1500.09996250202[/C][/ROW]
[ROW][C]50[/C][C]4292[/C][C]3073.50845990929[/C][C]1218.49154009071[/C][/ROW]
[ROW][C]51[/C][C]4154[/C][C]3740.98938539335[/C][C]413.01061460665[/C][/ROW]
[ROW][C]52[/C][C]4121[/C][C]4407.73449614259[/C][C]-286.734496142591[/C][/ROW]
[ROW][C]53[/C][C]4647[/C][C]4457.15169796705[/C][C]189.848302032951[/C][/ROW]
[ROW][C]54[/C][C]4753[/C][C]4472.80782081263[/C][C]280.192179187369[/C][/ROW]
[ROW][C]55[/C][C]3965[/C][C]3618.07891877330[/C][C]346.921081226703[/C][/ROW]
[ROW][C]56[/C][C]1723[/C][C]1637.44754442263[/C][C]85.5524555773732[/C][/ROW]
[ROW][C]57[/C][C]5048[/C][C]4613.01483161235[/C][C]434.985168387647[/C][/ROW]
[ROW][C]58[/C][C]6922[/C][C]5396.57888829884[/C][C]1525.42111170116[/C][/ROW]
[ROW][C]59[/C][C]9858[/C][C]8231.39806248834[/C][C]1626.60193751166[/C][/ROW]
[ROW][C]60[/C][C]11331[/C][C]10494.1552287586[/C][C]836.844771241364[/C][/ROW]
[ROW][C]61[/C][C]4016[/C][C]3789.18088238996[/C][C]226.819117610035[/C][/ROW]
[ROW][C]62[/C][C]4276[/C][C]4165.13839832469[/C][C]110.861601675308[/C][/ROW]
[ROW][C]63[/C][C]4968[/C][C]4110.9999574441[/C][C]857.0000425559[/C][/ROW]
[ROW][C]64[/C][C]4677[/C][C]4150.85297496075[/C][C]526.147025039253[/C][/ROW]
[ROW][C]65[/C][C]3523[/C][C]4627.23420033803[/C][C]-1104.23420033803[/C][/ROW]
[ROW][C]66[/C][C]1821[/C][C]4723.82816953661[/C][C]-2902.82816953661[/C][/ROW]
[ROW][C]67[/C][C]5222[/C][C]3928.88077998796[/C][C]1293.11922001204[/C][/ROW]
[ROW][C]68[/C][C]6872[/C][C]1714.09282158742[/C][C]5157.90717841258[/C][/ROW]
[ROW][C]69[/C][C]10803[/C][C]5002.71210644388[/C][C]5800.28789355612[/C][/ROW]
[ROW][C]70[/C][C]13916[/C][C]6763.18284034592[/C][C]7152.81715965408[/C][/ROW]
[ROW][C]71[/C][C]2639[/C][C]9688.64853526556[/C][C]-7049.64853526556[/C][/ROW]
[ROW][C]72[/C][C]2899[/C][C]11243.8730364222[/C][C]-8344.87303642225[/C][/ROW]
[ROW][C]73[/C][C]3370[/C][C]3992.38503378657[/C][C]-622.385033786572[/C][/ROW]
[ROW][C]74[/C][C]3740[/C][C]4264.45779400998[/C][C]-524.457794009983[/C][/ROW]
[ROW][C]75[/C][C]2927[/C][C]4878.7745975599[/C][C]-1951.77459755990[/C][/ROW]
[ROW][C]76[/C][C]3986[/C][C]4622.22091281142[/C][C]-636.220912811418[/C][/ROW]
[ROW][C]77[/C][C]4217[/C][C]3637.96585299977[/C][C]579.034147000228[/C][/ROW]
[ROW][C]78[/C][C]1738[/C][C]2123.22403591592[/C][C]-385.224035915915[/C][/ROW]
[ROW][C]79[/C][C]5221[/C][C]5087.36863818058[/C][C]133.631361819417[/C][/ROW]
[ROW][C]80[/C][C]6424[/C][C]6334.99145753833[/C][C]89.0085424616655[/C][/ROW]
[ROW][C]81[/C][C]9842[/C][C]10199.1108566255[/C][C]-357.110856625526[/C][/ROW]
[ROW][C]82[/C][C]13076[/C][C]13171.2940980642[/C][C]-95.294098064247[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13360&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13360&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
1325412368.49607099695172.503929003050
1424752299.23063554187175.769364458128
1530312808.66370689647222.336293103529
1632662997.43890828896268.561091711039
1737763417.25819820299358.741801797015
1832302855.58006291701374.419937082992
1930282630.60624337706397.393756622937
2017591510.29684667595248.70315332405
2135953036.94605462600558.053945374004
2244743730.0172037031743.982796296901
2368385676.504419523171161.49558047683
2483576872.948968091051484.05103190895
2531132523.03998632031589.960013679685
2630062456.7000099164549.299990083599
2740473007.851757008041039.14824299196
2835233238.03912450669284.960875493313
2939373738.65008162431198.349918375688
3039863191.01777373524794.982226264764
3132602986.62588552958273.374114470421
3215731733.10660695269-160.106606952692
3335283536.89896687662-8.89896687661849
3452114396.54123557553814.458764424472
3576146717.07245571265896.927544287351
3692548202.490030351921051.50996964808
3753753051.577109649672323.42289035033
3830882948.81037311343139.189626886575
3937183938.81048358019-220.810483580192
4045143493.331683158681020.66831684132
4145203916.34906603009603.650933969909
4245393903.23149877607635.768501223933
4336633231.5380231399431.461976860098
4416431589.6692832313853.330716768616
4547393528.926503922331210.07349607767
4654285126.20372529982301.796274700182
4783147520.61759962115793.382400378851
48106519144.523459098311506.47654090169
4936335133.09996250202-1500.09996250202
5042923073.508459909291218.49154009071
5141543740.98938539335413.01061460665
5241214407.73449614259-286.734496142591
5346474457.15169796705189.848302032951
5447534472.80782081263280.192179187369
5539653618.07891877330346.921081226703
5617231637.4475444226385.5524555773732
5750484613.01483161235434.985168387647
5869225396.578888298841525.42111170116
5998588231.398062488341626.60193751166
601133110494.1552287586836.844771241364
6140163789.18088238996226.819117610035
6242764165.13839832469110.861601675308
6349684110.9999574441857.0000425559
6446774150.85297496075526.147025039253
6535234627.23420033803-1104.23420033803
6618214723.82816953661-2902.82816953661
6752223928.880779987961293.11922001204
6868721714.092821587425157.90717841258
69108035002.712106443885800.28789355612
70139166763.182840345927152.81715965408
7126399688.64853526556-7049.64853526556
72289911243.8730364222-8344.87303642225
7333703992.38503378657-622.385033786572
7437404264.45779400998-524.457794009983
7529274878.7745975599-1951.77459755990
7639864622.22091281142-636.220912811418
7742173637.96585299977579.034147000228
7817382123.22403591592-385.224035915915
7952215087.36863818058133.631361819417
8064246334.9914575383389.0085424616655
81984210199.1108566255-357.110856625526
821307613171.2940980642-95.294098064247







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
833372.96463989007-115.8826753137256861.81195509386
843767.81519021363278.9678750098387256.66250541742
853434.79877754344-54.04853766034926923.64609274723
863794.60321518051305.7558999767187283.4505303843
873130.20637723689-358.6409379669066619.05369244068
884052.23928140902563.391966205237541.08659661281
894156.71464150857667.8673263047777645.56195671236
901778.10708042871-1710.740234775085266.9543956325
915207.087151172831718.239835969048695.93446637663
926414.732995767352925.885680563569903.58031097114
939879.1801147216390.3327995172213368.0274299248
9413085.9214163684NANA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
83 & 3372.96463989007 & -115.882675313725 & 6861.81195509386 \tabularnewline
84 & 3767.81519021363 & 278.967875009838 & 7256.66250541742 \tabularnewline
85 & 3434.79877754344 & -54.0485376603492 & 6923.64609274723 \tabularnewline
86 & 3794.60321518051 & 305.755899976718 & 7283.4505303843 \tabularnewline
87 & 3130.20637723689 & -358.640937966906 & 6619.05369244068 \tabularnewline
88 & 4052.23928140902 & 563.39196620523 & 7541.08659661281 \tabularnewline
89 & 4156.71464150857 & 667.867326304777 & 7645.56195671236 \tabularnewline
90 & 1778.10708042871 & -1710.74023477508 & 5266.9543956325 \tabularnewline
91 & 5207.08715117283 & 1718.23983596904 & 8695.93446637663 \tabularnewline
92 & 6414.73299576735 & 2925.88568056356 & 9903.58031097114 \tabularnewline
93 & 9879.180114721 & 6390.33279951722 & 13368.0274299248 \tabularnewline
94 & 13085.9214163684 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13360&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]83[/C][C]3372.96463989007[/C][C]-115.882675313725[/C][C]6861.81195509386[/C][/ROW]
[ROW][C]84[/C][C]3767.81519021363[/C][C]278.967875009838[/C][C]7256.66250541742[/C][/ROW]
[ROW][C]85[/C][C]3434.79877754344[/C][C]-54.0485376603492[/C][C]6923.64609274723[/C][/ROW]
[ROW][C]86[/C][C]3794.60321518051[/C][C]305.755899976718[/C][C]7283.4505303843[/C][/ROW]
[ROW][C]87[/C][C]3130.20637723689[/C][C]-358.640937966906[/C][C]6619.05369244068[/C][/ROW]
[ROW][C]88[/C][C]4052.23928140902[/C][C]563.39196620523[/C][C]7541.08659661281[/C][/ROW]
[ROW][C]89[/C][C]4156.71464150857[/C][C]667.867326304777[/C][C]7645.56195671236[/C][/ROW]
[ROW][C]90[/C][C]1778.10708042871[/C][C]-1710.74023477508[/C][C]5266.9543956325[/C][/ROW]
[ROW][C]91[/C][C]5207.08715117283[/C][C]1718.23983596904[/C][C]8695.93446637663[/C][/ROW]
[ROW][C]92[/C][C]6414.73299576735[/C][C]2925.88568056356[/C][C]9903.58031097114[/C][/ROW]
[ROW][C]93[/C][C]9879.180114721[/C][C]6390.33279951722[/C][C]13368.0274299248[/C][/ROW]
[ROW][C]94[/C][C]13085.9214163684[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13360&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13360&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
833372.96463989007-115.8826753137256861.81195509386
843767.81519021363278.9678750098387256.66250541742
853434.79877754344-54.04853766034926923.64609274723
863794.60321518051305.7558999767187283.4505303843
873130.20637723689-358.6409379669066619.05369244068
884052.23928140902563.391966205237541.08659661281
894156.71464150857667.8673263047777645.56195671236
901778.10708042871-1710.740234775085266.9543956325
915207.087151172831718.239835969048695.93446637663
926414.732995767352925.885680563569903.58031097114
939879.1801147216390.3327995172213368.0274299248
9413085.9214163684NANA



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')