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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 12 Jan 2013 06:12:54 -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/2013/Jan/12/t1357989227t8i5tluhl75tt5f.htm/, Retrieved Sun, 28 Apr 2024 04:02:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205205, Retrieved Sun, 28 Apr 2024 04:02:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-01-12 11:12:54] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
2048
2037
2149
2124
2205
2489
2573
2702
2718
2646
2712
2634
2614
2637
2649
2579
2505
2462
2467
2447
2656
2626
2483
2540
2503
2467
2513
2443
2293
2071
2030
2052
1864
1670
1811
1905
1863
2014
2198
2962
3047
3033
3504
3801
3858
3674
3721
3844
4117
4105
4435
4296
4203
4563
4621
4697
4591
4357
4503
4444
4291
4200
4139
3970
3862
3702
3570
3801
3896
3918
3813
3667




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205205&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205205&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205205&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.193961188765786
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.193961188765786 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205205&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.193961188765786[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205205&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205205&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
alpha1
beta0.193961188765786
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
321492026123
421242161.85722621819-37.8572262181915
522052129.5143936175475.4856063824641
624892225.15567156618263.844328433815
725732560.3312311583212.6687688416819
827022646.7884806230555.21151937695
927182786.49737255497-68.4973725549685
1026462789.21154074687-143.211540746874
1127122689.4340600586322.5659399413698
1226342759.81097659528-125.810976595276
1326142657.40853001507-43.4085300150714
1426372628.988959930778.01104006922696
1526492653.54279078585-4.54279078585068
1625792664.66166568471-85.6616656847127
1725052578.04662717685-73.0466271768482
1824622489.8784165343-27.8784165342959
1924672441.471085722425.5289142776041
2024472451.42270428358-4.42270428358006
2126562430.56487130318225.435128696823
2226262683.29053685478-57.2905368547808
2324832642.1783962214-159.178396221398
2425402468.3039652644671.6960347355362
2525032539.21021339156-36.2102133915614
2624672495.18683735667-28.1868373566717
2725132453.7196848754259.2803151245762
2824432511.2177652674-68.2177652673968
2922932427.98616642119-134.986166421187
3020712251.8040891152-180.804089115198
3120301994.735113056735.2648869433015
3220521960.5751324499191.4248675500876
3318642000.30800844268-136.308008442682
3416701785.86954508684-115.869545086842
3518111569.39535038005241.604649619952
3619051757.25727543167147.742724568325
3718631879.91362992044-16.9136299204433
3820141834.63304215473179.36695784527
3921982020.4232705237177.576729476299
4029622238.86626407006723.133735929935
4130473143.12614312768-96.1261431276789
4230333209.48140213516-176.481402135164
4335043161.25085958197342.749140418025
4438013698.73089030591102.269109694093
4538584015.56712839619-157.567128396191
4636744042.00522086206-368.005220862055
4737213786.62649075164-65.6264907516352
4838443820.8974985909223.1025014090792
4941173948.37848722769168.621512772311
5041054254.08451629649-149.084516296492
5144354213.16790628905221.832093710948
5242964586.19472289163-290.194722891631
5342034390.90820946601-187.908209466013
5445634261.46130977913301.538690220866
5546214679.94811259325-58.9481125932516
5646974726.51446659916-29.5144665991647
5745914796.7898055718-205.789805571802
5843574650.87457024722-293.874570247216
5945034359.87430925403143.125690745968
6044444533.63513837404-89.6351383740439
6142914457.24940037983-166.249400379828
6242004272.00346905056-72.0034690505581
6341394167.03759059825-28.037590598251
6439704100.59938619569-130.599386195686
6538623906.26817399709-44.2681739970885
6637023789.68186634412-87.6818663441227
6735703612.67498731481-42.6749873148137
6838013472.39769604467328.602303955332
6938963767.13378955102128.86621044898
7039183887.1288329214530.8711670785538
7138133915.11664118659-102.11664118659
7236673790.30997606927-123.309976069269

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2149 & 2026 & 123 \tabularnewline
4 & 2124 & 2161.85722621819 & -37.8572262181915 \tabularnewline
5 & 2205 & 2129.51439361754 & 75.4856063824641 \tabularnewline
6 & 2489 & 2225.15567156618 & 263.844328433815 \tabularnewline
7 & 2573 & 2560.33123115832 & 12.6687688416819 \tabularnewline
8 & 2702 & 2646.78848062305 & 55.21151937695 \tabularnewline
9 & 2718 & 2786.49737255497 & -68.4973725549685 \tabularnewline
10 & 2646 & 2789.21154074687 & -143.211540746874 \tabularnewline
11 & 2712 & 2689.43406005863 & 22.5659399413698 \tabularnewline
12 & 2634 & 2759.81097659528 & -125.810976595276 \tabularnewline
13 & 2614 & 2657.40853001507 & -43.4085300150714 \tabularnewline
14 & 2637 & 2628.98895993077 & 8.01104006922696 \tabularnewline
15 & 2649 & 2653.54279078585 & -4.54279078585068 \tabularnewline
16 & 2579 & 2664.66166568471 & -85.6616656847127 \tabularnewline
17 & 2505 & 2578.04662717685 & -73.0466271768482 \tabularnewline
18 & 2462 & 2489.8784165343 & -27.8784165342959 \tabularnewline
19 & 2467 & 2441.4710857224 & 25.5289142776041 \tabularnewline
20 & 2447 & 2451.42270428358 & -4.42270428358006 \tabularnewline
21 & 2656 & 2430.56487130318 & 225.435128696823 \tabularnewline
22 & 2626 & 2683.29053685478 & -57.2905368547808 \tabularnewline
23 & 2483 & 2642.1783962214 & -159.178396221398 \tabularnewline
24 & 2540 & 2468.30396526446 & 71.6960347355362 \tabularnewline
25 & 2503 & 2539.21021339156 & -36.2102133915614 \tabularnewline
26 & 2467 & 2495.18683735667 & -28.1868373566717 \tabularnewline
27 & 2513 & 2453.71968487542 & 59.2803151245762 \tabularnewline
28 & 2443 & 2511.2177652674 & -68.2177652673968 \tabularnewline
29 & 2293 & 2427.98616642119 & -134.986166421187 \tabularnewline
30 & 2071 & 2251.8040891152 & -180.804089115198 \tabularnewline
31 & 2030 & 1994.7351130567 & 35.2648869433015 \tabularnewline
32 & 2052 & 1960.57513244991 & 91.4248675500876 \tabularnewline
33 & 1864 & 2000.30800844268 & -136.308008442682 \tabularnewline
34 & 1670 & 1785.86954508684 & -115.869545086842 \tabularnewline
35 & 1811 & 1569.39535038005 & 241.604649619952 \tabularnewline
36 & 1905 & 1757.25727543167 & 147.742724568325 \tabularnewline
37 & 1863 & 1879.91362992044 & -16.9136299204433 \tabularnewline
38 & 2014 & 1834.63304215473 & 179.36695784527 \tabularnewline
39 & 2198 & 2020.4232705237 & 177.576729476299 \tabularnewline
40 & 2962 & 2238.86626407006 & 723.133735929935 \tabularnewline
41 & 3047 & 3143.12614312768 & -96.1261431276789 \tabularnewline
42 & 3033 & 3209.48140213516 & -176.481402135164 \tabularnewline
43 & 3504 & 3161.25085958197 & 342.749140418025 \tabularnewline
44 & 3801 & 3698.73089030591 & 102.269109694093 \tabularnewline
45 & 3858 & 4015.56712839619 & -157.567128396191 \tabularnewline
46 & 3674 & 4042.00522086206 & -368.005220862055 \tabularnewline
47 & 3721 & 3786.62649075164 & -65.6264907516352 \tabularnewline
48 & 3844 & 3820.89749859092 & 23.1025014090792 \tabularnewline
49 & 4117 & 3948.37848722769 & 168.621512772311 \tabularnewline
50 & 4105 & 4254.08451629649 & -149.084516296492 \tabularnewline
51 & 4435 & 4213.16790628905 & 221.832093710948 \tabularnewline
52 & 4296 & 4586.19472289163 & -290.194722891631 \tabularnewline
53 & 4203 & 4390.90820946601 & -187.908209466013 \tabularnewline
54 & 4563 & 4261.46130977913 & 301.538690220866 \tabularnewline
55 & 4621 & 4679.94811259325 & -58.9481125932516 \tabularnewline
56 & 4697 & 4726.51446659916 & -29.5144665991647 \tabularnewline
57 & 4591 & 4796.7898055718 & -205.789805571802 \tabularnewline
58 & 4357 & 4650.87457024722 & -293.874570247216 \tabularnewline
59 & 4503 & 4359.87430925403 & 143.125690745968 \tabularnewline
60 & 4444 & 4533.63513837404 & -89.6351383740439 \tabularnewline
61 & 4291 & 4457.24940037983 & -166.249400379828 \tabularnewline
62 & 4200 & 4272.00346905056 & -72.0034690505581 \tabularnewline
63 & 4139 & 4167.03759059825 & -28.037590598251 \tabularnewline
64 & 3970 & 4100.59938619569 & -130.599386195686 \tabularnewline
65 & 3862 & 3906.26817399709 & -44.2681739970885 \tabularnewline
66 & 3702 & 3789.68186634412 & -87.6818663441227 \tabularnewline
67 & 3570 & 3612.67498731481 & -42.6749873148137 \tabularnewline
68 & 3801 & 3472.39769604467 & 328.602303955332 \tabularnewline
69 & 3896 & 3767.13378955102 & 128.86621044898 \tabularnewline
70 & 3918 & 3887.12883292145 & 30.8711670785538 \tabularnewline
71 & 3813 & 3915.11664118659 & -102.11664118659 \tabularnewline
72 & 3667 & 3790.30997606927 & -123.309976069269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205205&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]2149[/C][C]2026[/C][C]123[/C][/ROW]
[ROW][C]4[/C][C]2124[/C][C]2161.85722621819[/C][C]-37.8572262181915[/C][/ROW]
[ROW][C]5[/C][C]2205[/C][C]2129.51439361754[/C][C]75.4856063824641[/C][/ROW]
[ROW][C]6[/C][C]2489[/C][C]2225.15567156618[/C][C]263.844328433815[/C][/ROW]
[ROW][C]7[/C][C]2573[/C][C]2560.33123115832[/C][C]12.6687688416819[/C][/ROW]
[ROW][C]8[/C][C]2702[/C][C]2646.78848062305[/C][C]55.21151937695[/C][/ROW]
[ROW][C]9[/C][C]2718[/C][C]2786.49737255497[/C][C]-68.4973725549685[/C][/ROW]
[ROW][C]10[/C][C]2646[/C][C]2789.21154074687[/C][C]-143.211540746874[/C][/ROW]
[ROW][C]11[/C][C]2712[/C][C]2689.43406005863[/C][C]22.5659399413698[/C][/ROW]
[ROW][C]12[/C][C]2634[/C][C]2759.81097659528[/C][C]-125.810976595276[/C][/ROW]
[ROW][C]13[/C][C]2614[/C][C]2657.40853001507[/C][C]-43.4085300150714[/C][/ROW]
[ROW][C]14[/C][C]2637[/C][C]2628.98895993077[/C][C]8.01104006922696[/C][/ROW]
[ROW][C]15[/C][C]2649[/C][C]2653.54279078585[/C][C]-4.54279078585068[/C][/ROW]
[ROW][C]16[/C][C]2579[/C][C]2664.66166568471[/C][C]-85.6616656847127[/C][/ROW]
[ROW][C]17[/C][C]2505[/C][C]2578.04662717685[/C][C]-73.0466271768482[/C][/ROW]
[ROW][C]18[/C][C]2462[/C][C]2489.8784165343[/C][C]-27.8784165342959[/C][/ROW]
[ROW][C]19[/C][C]2467[/C][C]2441.4710857224[/C][C]25.5289142776041[/C][/ROW]
[ROW][C]20[/C][C]2447[/C][C]2451.42270428358[/C][C]-4.42270428358006[/C][/ROW]
[ROW][C]21[/C][C]2656[/C][C]2430.56487130318[/C][C]225.435128696823[/C][/ROW]
[ROW][C]22[/C][C]2626[/C][C]2683.29053685478[/C][C]-57.2905368547808[/C][/ROW]
[ROW][C]23[/C][C]2483[/C][C]2642.1783962214[/C][C]-159.178396221398[/C][/ROW]
[ROW][C]24[/C][C]2540[/C][C]2468.30396526446[/C][C]71.6960347355362[/C][/ROW]
[ROW][C]25[/C][C]2503[/C][C]2539.21021339156[/C][C]-36.2102133915614[/C][/ROW]
[ROW][C]26[/C][C]2467[/C][C]2495.18683735667[/C][C]-28.1868373566717[/C][/ROW]
[ROW][C]27[/C][C]2513[/C][C]2453.71968487542[/C][C]59.2803151245762[/C][/ROW]
[ROW][C]28[/C][C]2443[/C][C]2511.2177652674[/C][C]-68.2177652673968[/C][/ROW]
[ROW][C]29[/C][C]2293[/C][C]2427.98616642119[/C][C]-134.986166421187[/C][/ROW]
[ROW][C]30[/C][C]2071[/C][C]2251.8040891152[/C][C]-180.804089115198[/C][/ROW]
[ROW][C]31[/C][C]2030[/C][C]1994.7351130567[/C][C]35.2648869433015[/C][/ROW]
[ROW][C]32[/C][C]2052[/C][C]1960.57513244991[/C][C]91.4248675500876[/C][/ROW]
[ROW][C]33[/C][C]1864[/C][C]2000.30800844268[/C][C]-136.308008442682[/C][/ROW]
[ROW][C]34[/C][C]1670[/C][C]1785.86954508684[/C][C]-115.869545086842[/C][/ROW]
[ROW][C]35[/C][C]1811[/C][C]1569.39535038005[/C][C]241.604649619952[/C][/ROW]
[ROW][C]36[/C][C]1905[/C][C]1757.25727543167[/C][C]147.742724568325[/C][/ROW]
[ROW][C]37[/C][C]1863[/C][C]1879.91362992044[/C][C]-16.9136299204433[/C][/ROW]
[ROW][C]38[/C][C]2014[/C][C]1834.63304215473[/C][C]179.36695784527[/C][/ROW]
[ROW][C]39[/C][C]2198[/C][C]2020.4232705237[/C][C]177.576729476299[/C][/ROW]
[ROW][C]40[/C][C]2962[/C][C]2238.86626407006[/C][C]723.133735929935[/C][/ROW]
[ROW][C]41[/C][C]3047[/C][C]3143.12614312768[/C][C]-96.1261431276789[/C][/ROW]
[ROW][C]42[/C][C]3033[/C][C]3209.48140213516[/C][C]-176.481402135164[/C][/ROW]
[ROW][C]43[/C][C]3504[/C][C]3161.25085958197[/C][C]342.749140418025[/C][/ROW]
[ROW][C]44[/C][C]3801[/C][C]3698.73089030591[/C][C]102.269109694093[/C][/ROW]
[ROW][C]45[/C][C]3858[/C][C]4015.56712839619[/C][C]-157.567128396191[/C][/ROW]
[ROW][C]46[/C][C]3674[/C][C]4042.00522086206[/C][C]-368.005220862055[/C][/ROW]
[ROW][C]47[/C][C]3721[/C][C]3786.62649075164[/C][C]-65.6264907516352[/C][/ROW]
[ROW][C]48[/C][C]3844[/C][C]3820.89749859092[/C][C]23.1025014090792[/C][/ROW]
[ROW][C]49[/C][C]4117[/C][C]3948.37848722769[/C][C]168.621512772311[/C][/ROW]
[ROW][C]50[/C][C]4105[/C][C]4254.08451629649[/C][C]-149.084516296492[/C][/ROW]
[ROW][C]51[/C][C]4435[/C][C]4213.16790628905[/C][C]221.832093710948[/C][/ROW]
[ROW][C]52[/C][C]4296[/C][C]4586.19472289163[/C][C]-290.194722891631[/C][/ROW]
[ROW][C]53[/C][C]4203[/C][C]4390.90820946601[/C][C]-187.908209466013[/C][/ROW]
[ROW][C]54[/C][C]4563[/C][C]4261.46130977913[/C][C]301.538690220866[/C][/ROW]
[ROW][C]55[/C][C]4621[/C][C]4679.94811259325[/C][C]-58.9481125932516[/C][/ROW]
[ROW][C]56[/C][C]4697[/C][C]4726.51446659916[/C][C]-29.5144665991647[/C][/ROW]
[ROW][C]57[/C][C]4591[/C][C]4796.7898055718[/C][C]-205.789805571802[/C][/ROW]
[ROW][C]58[/C][C]4357[/C][C]4650.87457024722[/C][C]-293.874570247216[/C][/ROW]
[ROW][C]59[/C][C]4503[/C][C]4359.87430925403[/C][C]143.125690745968[/C][/ROW]
[ROW][C]60[/C][C]4444[/C][C]4533.63513837404[/C][C]-89.6351383740439[/C][/ROW]
[ROW][C]61[/C][C]4291[/C][C]4457.24940037983[/C][C]-166.249400379828[/C][/ROW]
[ROW][C]62[/C][C]4200[/C][C]4272.00346905056[/C][C]-72.0034690505581[/C][/ROW]
[ROW][C]63[/C][C]4139[/C][C]4167.03759059825[/C][C]-28.037590598251[/C][/ROW]
[ROW][C]64[/C][C]3970[/C][C]4100.59938619569[/C][C]-130.599386195686[/C][/ROW]
[ROW][C]65[/C][C]3862[/C][C]3906.26817399709[/C][C]-44.2681739970885[/C][/ROW]
[ROW][C]66[/C][C]3702[/C][C]3789.68186634412[/C][C]-87.6818663441227[/C][/ROW]
[ROW][C]67[/C][C]3570[/C][C]3612.67498731481[/C][C]-42.6749873148137[/C][/ROW]
[ROW][C]68[/C][C]3801[/C][C]3472.39769604467[/C][C]328.602303955332[/C][/ROW]
[ROW][C]69[/C][C]3896[/C][C]3767.13378955102[/C][C]128.86621044898[/C][/ROW]
[ROW][C]70[/C][C]3918[/C][C]3887.12883292145[/C][C]30.8711670785538[/C][/ROW]
[ROW][C]71[/C][C]3813[/C][C]3915.11664118659[/C][C]-102.11664118659[/C][/ROW]
[ROW][C]72[/C][C]3667[/C][C]3790.30997606927[/C][C]-123.309976069269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205205&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205205&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
321492026123
421242161.85722621819-37.8572262181915
522052129.5143936175475.4856063824641
624892225.15567156618263.844328433815
725732560.3312311583212.6687688416819
827022646.7884806230555.21151937695
927182786.49737255497-68.4973725549685
1026462789.21154074687-143.211540746874
1127122689.4340600586322.5659399413698
1226342759.81097659528-125.810976595276
1326142657.40853001507-43.4085300150714
1426372628.988959930778.01104006922696
1526492653.54279078585-4.54279078585068
1625792664.66166568471-85.6616656847127
1725052578.04662717685-73.0466271768482
1824622489.8784165343-27.8784165342959
1924672441.471085722425.5289142776041
2024472451.42270428358-4.42270428358006
2126562430.56487130318225.435128696823
2226262683.29053685478-57.2905368547808
2324832642.1783962214-159.178396221398
2425402468.3039652644671.6960347355362
2525032539.21021339156-36.2102133915614
2624672495.18683735667-28.1868373566717
2725132453.7196848754259.2803151245762
2824432511.2177652674-68.2177652673968
2922932427.98616642119-134.986166421187
3020712251.8040891152-180.804089115198
3120301994.735113056735.2648869433015
3220521960.5751324499191.4248675500876
3318642000.30800844268-136.308008442682
3416701785.86954508684-115.869545086842
3518111569.39535038005241.604649619952
3619051757.25727543167147.742724568325
3718631879.91362992044-16.9136299204433
3820141834.63304215473179.36695784527
3921982020.4232705237177.576729476299
4029622238.86626407006723.133735929935
4130473143.12614312768-96.1261431276789
4230333209.48140213516-176.481402135164
4335043161.25085958197342.749140418025
4438013698.73089030591102.269109694093
4538584015.56712839619-157.567128396191
4636744042.00522086206-368.005220862055
4737213786.62649075164-65.6264907516352
4838443820.8974985909223.1025014090792
4941173948.37848722769168.621512772311
5041054254.08451629649-149.084516296492
5144354213.16790628905221.832093710948
5242964586.19472289163-290.194722891631
5342034390.90820946601-187.908209466013
5445634261.46130977913301.538690220866
5546214679.94811259325-58.9481125932516
5646974726.51446659916-29.5144665991647
5745914796.7898055718-205.789805571802
5843574650.87457024722-293.874570247216
5945034359.87430925403143.125690745968
6044444533.63513837404-89.6351383740439
6142914457.24940037983-166.249400379828
6242004272.00346905056-72.0034690505581
6341394167.03759059825-28.037590598251
6439704100.59938619569-130.599386195686
6538623906.26817399709-44.2681739970885
6637023789.68186634412-87.6818663441227
6735703612.67498731481-42.6749873148137
6838013472.39769604467328.602303955332
6938963767.13378955102128.86621044898
7039183887.1288329214530.8711670785538
7138133915.11664118659-102.11664118659
7236673790.30997606927-123.309976069269







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
733620.392626524193284.59899659743956.18625645098
743573.785253048393050.815018744944096.75548735183
753527.177879572582826.674068935764227.6816902094
763480.570506096772601.443321521034359.69769067251
773433.963132620972371.67362579614496.25263944584
783387.355759145162135.967396493544638.74412179679
793340.748385669351893.720329002214787.7764423365
803294.141012193551644.688023888374943.59400049872
813247.533638717741388.805094192325106.26218324317
823200.926265241931126.099959714455275.75257076942
833154.31889176613856.6512863965451.98649713625
843107.71151829032580.564399754935634.85863682571

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 3620.39262652419 & 3284.5989965974 & 3956.18625645098 \tabularnewline
74 & 3573.78525304839 & 3050.81501874494 & 4096.75548735183 \tabularnewline
75 & 3527.17787957258 & 2826.67406893576 & 4227.6816902094 \tabularnewline
76 & 3480.57050609677 & 2601.44332152103 & 4359.69769067251 \tabularnewline
77 & 3433.96313262097 & 2371.6736257961 & 4496.25263944584 \tabularnewline
78 & 3387.35575914516 & 2135.96739649354 & 4638.74412179679 \tabularnewline
79 & 3340.74838566935 & 1893.72032900221 & 4787.7764423365 \tabularnewline
80 & 3294.14101219355 & 1644.68802388837 & 4943.59400049872 \tabularnewline
81 & 3247.53363871774 & 1388.80509419232 & 5106.26218324317 \tabularnewline
82 & 3200.92626524193 & 1126.09995971445 & 5275.75257076942 \tabularnewline
83 & 3154.31889176613 & 856.651286396 & 5451.98649713625 \tabularnewline
84 & 3107.71151829032 & 580.56439975493 & 5634.85863682571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205205&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]73[/C][C]3620.39262652419[/C][C]3284.5989965974[/C][C]3956.18625645098[/C][/ROW]
[ROW][C]74[/C][C]3573.78525304839[/C][C]3050.81501874494[/C][C]4096.75548735183[/C][/ROW]
[ROW][C]75[/C][C]3527.17787957258[/C][C]2826.67406893576[/C][C]4227.6816902094[/C][/ROW]
[ROW][C]76[/C][C]3480.57050609677[/C][C]2601.44332152103[/C][C]4359.69769067251[/C][/ROW]
[ROW][C]77[/C][C]3433.96313262097[/C][C]2371.6736257961[/C][C]4496.25263944584[/C][/ROW]
[ROW][C]78[/C][C]3387.35575914516[/C][C]2135.96739649354[/C][C]4638.74412179679[/C][/ROW]
[ROW][C]79[/C][C]3340.74838566935[/C][C]1893.72032900221[/C][C]4787.7764423365[/C][/ROW]
[ROW][C]80[/C][C]3294.14101219355[/C][C]1644.68802388837[/C][C]4943.59400049872[/C][/ROW]
[ROW][C]81[/C][C]3247.53363871774[/C][C]1388.80509419232[/C][C]5106.26218324317[/C][/ROW]
[ROW][C]82[/C][C]3200.92626524193[/C][C]1126.09995971445[/C][C]5275.75257076942[/C][/ROW]
[ROW][C]83[/C][C]3154.31889176613[/C][C]856.651286396[/C][C]5451.98649713625[/C][/ROW]
[ROW][C]84[/C][C]3107.71151829032[/C][C]580.56439975493[/C][C]5634.85863682571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205205&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205205&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
733620.392626524193284.59899659743956.18625645098
743573.785253048393050.815018744944096.75548735183
753527.177879572582826.674068935764227.6816902094
763480.570506096772601.443321521034359.69769067251
773433.963132620972371.67362579614496.25263944584
783387.355759145162135.967396493544638.74412179679
793340.748385669351893.720329002214787.7764423365
803294.141012193551644.688023888374943.59400049872
813247.533638717741388.805094192325106.26218324317
823200.926265241931126.099959714455275.75257076942
833154.31889176613856.6512863965451.98649713625
843107.71151829032580.564399754935634.85863682571



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')