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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 May 2008 09:09:45 -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/07/t1210173093t0k9zrji6k4pn6n.htm/, Retrieved Mon, 13 May 2024 23:27:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=11864, Retrieved Mon, 13 May 2024 23:27:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [double exponentia...] [2008-05-07 15:09:45] [42e511cfef8a9d9c5f2111ede83bec8b] [Current]
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Dataseries X:
56421
53152
53536
52408
41454
38271
35306
26414
31917
38030
27534
18387
50556
43901
48572
43899
37532
40357
35489
29027
34485
42598
30306
26451
47460
50104
61465
53726
39477
43895
31481
29896
33842
39120
33702
25094
51442
45594
52518
48564
41745
49585
32747
33379
35645
37034
35681
20972
58552
54955
65540
51570
51145
46641
35704
33253
35193
41668
34865
21210
56126
49231
59723
48103
47472
50497
40059
34149
36860
46356
36577




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11864&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]1 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=11864&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11864&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.639263220109391
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.639263220109391 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11864&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]0.639263220109391[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11864&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11864&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
alpha0.639263220109391
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
25315256421-3269
35353654331.2485334624-795.2485334624
45240853822.875395174-1414.87539517396
54145452918.3975940015-11464.3975940015
63827145589.6298714458-7318.62987144575
73530640911.0989730366-5605.09897303657
82641437327.9653545014-10913.9653545014
93191730351.06871782051565.93128217950
103803031352.11099173666677.8890082634
112753435621.0398226922-8087.03982269217
121838730451.2927044851-12064.2927044851
135055622739.034101873727816.9658981263
144390140521.3972955833379.60270441696
154857242681.8530030995890.14699690097
164389946447.2073392556-2548.20733925560
173753244818.2321100567-7286.23211005668
184035740160.4119089174196.588091082594
193548940286.083445058-4797.08344505802
202902737219.4844348368-8192.48443483678
213448531982.33045432702502.66954567304
224259833582.19504696369015.80495303639
233030639345.6675531198-9039.66755311985
242645133566.9405643941-7115.94056439408
254746029017.981485092518442.0185149075
265010440807.28562624939296.71437375073
276146546750.333193250414714.6668067496
285372656156.8784789699-2430.87847896993
293947754602.907274809-15125.907274809
304389544933.4710832385-1038.47108323854
313148144269.614714577-12788.614714577
322989636094.3236913982-6198.32369139817
333384232131.96332915461710.03667084535
343912033225.12687786445894.87312213561
353370236993.5024520571-3291.5024520571
362509434889.3659955571-9795.36599555712
375144228627.548787087222814.4512129128
384559443211.98833448242382.01166551755
395251844734.72078211937783.27921788067
404856449710.2849179522-1146.28491795223
414174548977.5071301393-7232.50713013926
424958544354.03133266235230.96866733769
433274747697.9972072359-14950.9972072359
443337938140.3745886918-4761.37458869178
453564535096.6029369777548.397063022348
463703435447.17300938391586.82699061614
473568136461.5731411616-780.573141161629
482097235962.5814414117-14990.5814414117
495855226379.654077862832172.3459221372
505495546946.25153052148008.74846947855
516554052065.949866166513474.0501338335
525157060679.4145426363-9109.41454263626
535114554856.1008687993-3711.10086879929
544664152483.7305772599-5842.7305772599
553570448748.6878142091-13044.6878142091
563325340409.6986767761-7156.69867677608
573519335834.6844353076-641.684435307587
584166835424.47917689886243.52082310121
593486539415.7324030945-4550.7324030945

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 53152 & 56421 & -3269 \tabularnewline
3 & 53536 & 54331.2485334624 & -795.2485334624 \tabularnewline
4 & 52408 & 53822.875395174 & -1414.87539517396 \tabularnewline
5 & 41454 & 52918.3975940015 & -11464.3975940015 \tabularnewline
6 & 38271 & 45589.6298714458 & -7318.62987144575 \tabularnewline
7 & 35306 & 40911.0989730366 & -5605.09897303657 \tabularnewline
8 & 26414 & 37327.9653545014 & -10913.9653545014 \tabularnewline
9 & 31917 & 30351.0687178205 & 1565.93128217950 \tabularnewline
10 & 38030 & 31352.1109917366 & 6677.8890082634 \tabularnewline
11 & 27534 & 35621.0398226922 & -8087.03982269217 \tabularnewline
12 & 18387 & 30451.2927044851 & -12064.2927044851 \tabularnewline
13 & 50556 & 22739.0341018737 & 27816.9658981263 \tabularnewline
14 & 43901 & 40521.397295583 & 3379.60270441696 \tabularnewline
15 & 48572 & 42681.853003099 & 5890.14699690097 \tabularnewline
16 & 43899 & 46447.2073392556 & -2548.20733925560 \tabularnewline
17 & 37532 & 44818.2321100567 & -7286.23211005668 \tabularnewline
18 & 40357 & 40160.4119089174 & 196.588091082594 \tabularnewline
19 & 35489 & 40286.083445058 & -4797.08344505802 \tabularnewline
20 & 29027 & 37219.4844348368 & -8192.48443483678 \tabularnewline
21 & 34485 & 31982.3304543270 & 2502.66954567304 \tabularnewline
22 & 42598 & 33582.1950469636 & 9015.80495303639 \tabularnewline
23 & 30306 & 39345.6675531198 & -9039.66755311985 \tabularnewline
24 & 26451 & 33566.9405643941 & -7115.94056439408 \tabularnewline
25 & 47460 & 29017.9814850925 & 18442.0185149075 \tabularnewline
26 & 50104 & 40807.2856262493 & 9296.71437375073 \tabularnewline
27 & 61465 & 46750.3331932504 & 14714.6668067496 \tabularnewline
28 & 53726 & 56156.8784789699 & -2430.87847896993 \tabularnewline
29 & 39477 & 54602.907274809 & -15125.907274809 \tabularnewline
30 & 43895 & 44933.4710832385 & -1038.47108323854 \tabularnewline
31 & 31481 & 44269.614714577 & -12788.614714577 \tabularnewline
32 & 29896 & 36094.3236913982 & -6198.32369139817 \tabularnewline
33 & 33842 & 32131.9633291546 & 1710.03667084535 \tabularnewline
34 & 39120 & 33225.1268778644 & 5894.87312213561 \tabularnewline
35 & 33702 & 36993.5024520571 & -3291.5024520571 \tabularnewline
36 & 25094 & 34889.3659955571 & -9795.36599555712 \tabularnewline
37 & 51442 & 28627.5487870872 & 22814.4512129128 \tabularnewline
38 & 45594 & 43211.9883344824 & 2382.01166551755 \tabularnewline
39 & 52518 & 44734.7207821193 & 7783.27921788067 \tabularnewline
40 & 48564 & 49710.2849179522 & -1146.28491795223 \tabularnewline
41 & 41745 & 48977.5071301393 & -7232.50713013926 \tabularnewline
42 & 49585 & 44354.0313326623 & 5230.96866733769 \tabularnewline
43 & 32747 & 47697.9972072359 & -14950.9972072359 \tabularnewline
44 & 33379 & 38140.3745886918 & -4761.37458869178 \tabularnewline
45 & 35645 & 35096.6029369777 & 548.397063022348 \tabularnewline
46 & 37034 & 35447.1730093839 & 1586.82699061614 \tabularnewline
47 & 35681 & 36461.5731411616 & -780.573141161629 \tabularnewline
48 & 20972 & 35962.5814414117 & -14990.5814414117 \tabularnewline
49 & 58552 & 26379.6540778628 & 32172.3459221372 \tabularnewline
50 & 54955 & 46946.2515305214 & 8008.74846947855 \tabularnewline
51 & 65540 & 52065.9498661665 & 13474.0501338335 \tabularnewline
52 & 51570 & 60679.4145426363 & -9109.41454263626 \tabularnewline
53 & 51145 & 54856.1008687993 & -3711.10086879929 \tabularnewline
54 & 46641 & 52483.7305772599 & -5842.7305772599 \tabularnewline
55 & 35704 & 48748.6878142091 & -13044.6878142091 \tabularnewline
56 & 33253 & 40409.6986767761 & -7156.69867677608 \tabularnewline
57 & 35193 & 35834.6844353076 & -641.684435307587 \tabularnewline
58 & 41668 & 35424.4791768988 & 6243.52082310121 \tabularnewline
59 & 34865 & 39415.7324030945 & -4550.7324030945 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11864&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]53152[/C][C]56421[/C][C]-3269[/C][/ROW]
[ROW][C]3[/C][C]53536[/C][C]54331.2485334624[/C][C]-795.2485334624[/C][/ROW]
[ROW][C]4[/C][C]52408[/C][C]53822.875395174[/C][C]-1414.87539517396[/C][/ROW]
[ROW][C]5[/C][C]41454[/C][C]52918.3975940015[/C][C]-11464.3975940015[/C][/ROW]
[ROW][C]6[/C][C]38271[/C][C]45589.6298714458[/C][C]-7318.62987144575[/C][/ROW]
[ROW][C]7[/C][C]35306[/C][C]40911.0989730366[/C][C]-5605.09897303657[/C][/ROW]
[ROW][C]8[/C][C]26414[/C][C]37327.9653545014[/C][C]-10913.9653545014[/C][/ROW]
[ROW][C]9[/C][C]31917[/C][C]30351.0687178205[/C][C]1565.93128217950[/C][/ROW]
[ROW][C]10[/C][C]38030[/C][C]31352.1109917366[/C][C]6677.8890082634[/C][/ROW]
[ROW][C]11[/C][C]27534[/C][C]35621.0398226922[/C][C]-8087.03982269217[/C][/ROW]
[ROW][C]12[/C][C]18387[/C][C]30451.2927044851[/C][C]-12064.2927044851[/C][/ROW]
[ROW][C]13[/C][C]50556[/C][C]22739.0341018737[/C][C]27816.9658981263[/C][/ROW]
[ROW][C]14[/C][C]43901[/C][C]40521.397295583[/C][C]3379.60270441696[/C][/ROW]
[ROW][C]15[/C][C]48572[/C][C]42681.853003099[/C][C]5890.14699690097[/C][/ROW]
[ROW][C]16[/C][C]43899[/C][C]46447.2073392556[/C][C]-2548.20733925560[/C][/ROW]
[ROW][C]17[/C][C]37532[/C][C]44818.2321100567[/C][C]-7286.23211005668[/C][/ROW]
[ROW][C]18[/C][C]40357[/C][C]40160.4119089174[/C][C]196.588091082594[/C][/ROW]
[ROW][C]19[/C][C]35489[/C][C]40286.083445058[/C][C]-4797.08344505802[/C][/ROW]
[ROW][C]20[/C][C]29027[/C][C]37219.4844348368[/C][C]-8192.48443483678[/C][/ROW]
[ROW][C]21[/C][C]34485[/C][C]31982.3304543270[/C][C]2502.66954567304[/C][/ROW]
[ROW][C]22[/C][C]42598[/C][C]33582.1950469636[/C][C]9015.80495303639[/C][/ROW]
[ROW][C]23[/C][C]30306[/C][C]39345.6675531198[/C][C]-9039.66755311985[/C][/ROW]
[ROW][C]24[/C][C]26451[/C][C]33566.9405643941[/C][C]-7115.94056439408[/C][/ROW]
[ROW][C]25[/C][C]47460[/C][C]29017.9814850925[/C][C]18442.0185149075[/C][/ROW]
[ROW][C]26[/C][C]50104[/C][C]40807.2856262493[/C][C]9296.71437375073[/C][/ROW]
[ROW][C]27[/C][C]61465[/C][C]46750.3331932504[/C][C]14714.6668067496[/C][/ROW]
[ROW][C]28[/C][C]53726[/C][C]56156.8784789699[/C][C]-2430.87847896993[/C][/ROW]
[ROW][C]29[/C][C]39477[/C][C]54602.907274809[/C][C]-15125.907274809[/C][/ROW]
[ROW][C]30[/C][C]43895[/C][C]44933.4710832385[/C][C]-1038.47108323854[/C][/ROW]
[ROW][C]31[/C][C]31481[/C][C]44269.614714577[/C][C]-12788.614714577[/C][/ROW]
[ROW][C]32[/C][C]29896[/C][C]36094.3236913982[/C][C]-6198.32369139817[/C][/ROW]
[ROW][C]33[/C][C]33842[/C][C]32131.9633291546[/C][C]1710.03667084535[/C][/ROW]
[ROW][C]34[/C][C]39120[/C][C]33225.1268778644[/C][C]5894.87312213561[/C][/ROW]
[ROW][C]35[/C][C]33702[/C][C]36993.5024520571[/C][C]-3291.5024520571[/C][/ROW]
[ROW][C]36[/C][C]25094[/C][C]34889.3659955571[/C][C]-9795.36599555712[/C][/ROW]
[ROW][C]37[/C][C]51442[/C][C]28627.5487870872[/C][C]22814.4512129128[/C][/ROW]
[ROW][C]38[/C][C]45594[/C][C]43211.9883344824[/C][C]2382.01166551755[/C][/ROW]
[ROW][C]39[/C][C]52518[/C][C]44734.7207821193[/C][C]7783.27921788067[/C][/ROW]
[ROW][C]40[/C][C]48564[/C][C]49710.2849179522[/C][C]-1146.28491795223[/C][/ROW]
[ROW][C]41[/C][C]41745[/C][C]48977.5071301393[/C][C]-7232.50713013926[/C][/ROW]
[ROW][C]42[/C][C]49585[/C][C]44354.0313326623[/C][C]5230.96866733769[/C][/ROW]
[ROW][C]43[/C][C]32747[/C][C]47697.9972072359[/C][C]-14950.9972072359[/C][/ROW]
[ROW][C]44[/C][C]33379[/C][C]38140.3745886918[/C][C]-4761.37458869178[/C][/ROW]
[ROW][C]45[/C][C]35645[/C][C]35096.6029369777[/C][C]548.397063022348[/C][/ROW]
[ROW][C]46[/C][C]37034[/C][C]35447.1730093839[/C][C]1586.82699061614[/C][/ROW]
[ROW][C]47[/C][C]35681[/C][C]36461.5731411616[/C][C]-780.573141161629[/C][/ROW]
[ROW][C]48[/C][C]20972[/C][C]35962.5814414117[/C][C]-14990.5814414117[/C][/ROW]
[ROW][C]49[/C][C]58552[/C][C]26379.6540778628[/C][C]32172.3459221372[/C][/ROW]
[ROW][C]50[/C][C]54955[/C][C]46946.2515305214[/C][C]8008.74846947855[/C][/ROW]
[ROW][C]51[/C][C]65540[/C][C]52065.9498661665[/C][C]13474.0501338335[/C][/ROW]
[ROW][C]52[/C][C]51570[/C][C]60679.4145426363[/C][C]-9109.41454263626[/C][/ROW]
[ROW][C]53[/C][C]51145[/C][C]54856.1008687993[/C][C]-3711.10086879929[/C][/ROW]
[ROW][C]54[/C][C]46641[/C][C]52483.7305772599[/C][C]-5842.7305772599[/C][/ROW]
[ROW][C]55[/C][C]35704[/C][C]48748.6878142091[/C][C]-13044.6878142091[/C][/ROW]
[ROW][C]56[/C][C]33253[/C][C]40409.6986767761[/C][C]-7156.69867677608[/C][/ROW]
[ROW][C]57[/C][C]35193[/C][C]35834.6844353076[/C][C]-641.684435307587[/C][/ROW]
[ROW][C]58[/C][C]41668[/C][C]35424.4791768988[/C][C]6243.52082310121[/C][/ROW]
[ROW][C]59[/C][C]34865[/C][C]39415.7324030945[/C][C]-4550.7324030945[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11864&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11864&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
25315256421-3269
35353654331.2485334624-795.2485334624
45240853822.875395174-1414.87539517396
54145452918.3975940015-11464.3975940015
63827145589.6298714458-7318.62987144575
73530640911.0989730366-5605.09897303657
82641437327.9653545014-10913.9653545014
93191730351.06871782051565.93128217950
103803031352.11099173666677.8890082634
112753435621.0398226922-8087.03982269217
121838730451.2927044851-12064.2927044851
135055622739.034101873727816.9658981263
144390140521.3972955833379.60270441696
154857242681.8530030995890.14699690097
164389946447.2073392556-2548.20733925560
173753244818.2321100567-7286.23211005668
184035740160.4119089174196.588091082594
193548940286.083445058-4797.08344505802
202902737219.4844348368-8192.48443483678
213448531982.33045432702502.66954567304
224259833582.19504696369015.80495303639
233030639345.6675531198-9039.66755311985
242645133566.9405643941-7115.94056439408
254746029017.981485092518442.0185149075
265010440807.28562624939296.71437375073
276146546750.333193250414714.6668067496
285372656156.8784789699-2430.87847896993
293947754602.907274809-15125.907274809
304389544933.4710832385-1038.47108323854
313148144269.614714577-12788.614714577
322989636094.3236913982-6198.32369139817
333384232131.96332915461710.03667084535
343912033225.12687786445894.87312213561
353370236993.5024520571-3291.5024520571
362509434889.3659955571-9795.36599555712
375144228627.548787087222814.4512129128
384559443211.98833448242382.01166551755
395251844734.72078211937783.27921788067
404856449710.2849179522-1146.28491795223
414174548977.5071301393-7232.50713013926
424958544354.03133266235230.96866733769
433274747697.9972072359-14950.9972072359
443337938140.3745886918-4761.37458869178
453564535096.6029369777548.397063022348
463703435447.17300938391586.82699061614
473568136461.5731411616-780.573141161629
482097235962.5814414117-14990.5814414117
495855226379.654077862832172.3459221372
505495546946.25153052148008.74846947855
516554052065.949866166513474.0501338335
525157060679.4145426363-9109.41454263626
535114554856.1008687993-3711.10086879929
544664152483.7305772599-5842.7305772599
553570448748.6878142091-13044.6878142091
563325340409.6986767761-7156.69867677608
573519335834.6844353076-641.684435307587
584166835424.47917689886243.52082310121
593486539415.7324030945-4550.7324030945







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6036506.616553236216667.509481054556345.7236254179
6136506.616553236212960.200050024760053.0330564476
6236506.61655323629761.9480964403463251.285010032
6336506.61655323626907.2778514146466105.9552550577
6436506.61655323624304.6847430734568708.5483633989
6536506.61655323621897.2540478736971115.9790585986
6636506.6165532362-353.27402919516373366.5071356675
6736506.6165532362-2474.0850113846275487.318117857
6836506.6165532362-4485.3174727554677498.5505792278
6936506.6165532362-6402.3826883270279415.6157947993
7036506.6165532362-8237.3861357688781250.6192422412
7136506.6165532362-10000.042511406583013.2756178788

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
60 & 36506.6165532362 & 16667.5094810545 & 56345.7236254179 \tabularnewline
61 & 36506.6165532362 & 12960.2000500247 & 60053.0330564476 \tabularnewline
62 & 36506.6165532362 & 9761.94809644034 & 63251.285010032 \tabularnewline
63 & 36506.6165532362 & 6907.27785141464 & 66105.9552550577 \tabularnewline
64 & 36506.6165532362 & 4304.68474307345 & 68708.5483633989 \tabularnewline
65 & 36506.6165532362 & 1897.25404787369 & 71115.9790585986 \tabularnewline
66 & 36506.6165532362 & -353.274029195163 & 73366.5071356675 \tabularnewline
67 & 36506.6165532362 & -2474.08501138462 & 75487.318117857 \tabularnewline
68 & 36506.6165532362 & -4485.31747275546 & 77498.5505792278 \tabularnewline
69 & 36506.6165532362 & -6402.38268832702 & 79415.6157947993 \tabularnewline
70 & 36506.6165532362 & -8237.38613576887 & 81250.6192422412 \tabularnewline
71 & 36506.6165532362 & -10000.0425114065 & 83013.2756178788 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11864&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]60[/C][C]36506.6165532362[/C][C]16667.5094810545[/C][C]56345.7236254179[/C][/ROW]
[ROW][C]61[/C][C]36506.6165532362[/C][C]12960.2000500247[/C][C]60053.0330564476[/C][/ROW]
[ROW][C]62[/C][C]36506.6165532362[/C][C]9761.94809644034[/C][C]63251.285010032[/C][/ROW]
[ROW][C]63[/C][C]36506.6165532362[/C][C]6907.27785141464[/C][C]66105.9552550577[/C][/ROW]
[ROW][C]64[/C][C]36506.6165532362[/C][C]4304.68474307345[/C][C]68708.5483633989[/C][/ROW]
[ROW][C]65[/C][C]36506.6165532362[/C][C]1897.25404787369[/C][C]71115.9790585986[/C][/ROW]
[ROW][C]66[/C][C]36506.6165532362[/C][C]-353.274029195163[/C][C]73366.5071356675[/C][/ROW]
[ROW][C]67[/C][C]36506.6165532362[/C][C]-2474.08501138462[/C][C]75487.318117857[/C][/ROW]
[ROW][C]68[/C][C]36506.6165532362[/C][C]-4485.31747275546[/C][C]77498.5505792278[/C][/ROW]
[ROW][C]69[/C][C]36506.6165532362[/C][C]-6402.38268832702[/C][C]79415.6157947993[/C][/ROW]
[ROW][C]70[/C][C]36506.6165532362[/C][C]-8237.38613576887[/C][C]81250.6192422412[/C][/ROW]
[ROW][C]71[/C][C]36506.6165532362[/C][C]-10000.0425114065[/C][C]83013.2756178788[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11864&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11864&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
6036506.616553236216667.509481054556345.7236254179
6136506.616553236212960.200050024760053.0330564476
6236506.61655323629761.9480964403463251.285010032
6336506.61655323626907.2778514146466105.9552550577
6436506.61655323624304.6847430734568708.5483633989
6536506.61655323621897.2540478736971115.9790585986
6636506.6165532362-353.27402919516373366.5071356675
6736506.6165532362-2474.0850113846275487.318117857
6836506.6165532362-4485.3174727554677498.5505792278
6936506.6165532362-6402.3826883270279415.6157947993
7036506.6165532362-8237.3861357688781250.6192422412
7136506.6165532362-10000.042511406583013.2756178788



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=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')