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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 May 2008 11:06:25 -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/t12101800587ad4h8gohcmfbs3.htm/, Retrieved Tue, 14 May 2024 02:40:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=11895, Retrieved Tue, 14 May 2024 02:40:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2008-05-07 17:06:25] [fe38921ec83f32fc5847db455ee6e655] [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 time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11895&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11895&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11895&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.633488893561455
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.633488893561455 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11895&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]0.633488893561455[/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=11895&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11895&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
alpha0.633488893561455
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
35353653152384
45240853395.2597351276-987.259735127598
54145452769.8416578638-11315.8416578638
63827145601.3816463071-7330.38164630705
73530640957.6662878048-5651.66628780481
82641437377.3984643648-10963.3984643648
93191730432.2073015011484.79269849903
103803031372.80698524136657.19301475875
112753435590.0648223858-8056.06482238582
121838730486.6372315933-12099.6372315933
135055622821.651429256327734.3485707437
144390140391.05321898443509.94678101556
154857242614.56552174965957.43447825042
164389946388.5340978413-2489.5340978413
173753244811.4418967163-7279.4418967163
184035740199.9963038206157.003696179410
193548940299.4564015983-4810.45640159834
202902737252.0856982242-8225.08569822419
213448532041.5852598082443.414740192
224259833589.4613600849008.53863991602
233030639296.27053569-8990.27053569
242645133601.0340012176-7150.03400121759
254746029071.566872859518388.4331271405
265010440720.43502890059383.56497109947
276146546664.819220104414800.1807798956
285372656040.56936687-2314.56936686996
293947754574.3153795803-15097.3153795803
304389545010.3337640216-1115.33376402163
313148144303.7822118998-12822.7822118998
322989636180.6920961039-6284.6920961039
333384232199.40945376861642.59054623138
343912033239.97232147525880.02767852476
353370236964.9045496546-3262.90454965462
362509434897.8907566973-9803.89075669728
375144228687.234848639722754.7651513603
384559443102.12584762572491.87415237429
395251844680.70044730777837.29955269231
404856449645.5426694524-1081.54266945243
414174548960.3974004415-7215.3974004415
424958544389.52328462965195.47671537039
433274747680.8000805739-14933.8000805739
443337938220.4035908632-4841.40359086318
453564535153.4281868028491.571813197195
463703435464.83347085111569.16652914890
473568136458.8830392153-777.883039215303
482097235966.1027733826-14994.1027733826
495855226467.505197525732084.4948024743
505495546792.67631042348162.3236895766
516554051963.417713423713576.5822865763
525157060564.031804493-8994.03180449299
535114554866.4125480082-3721.41254800819
544664152508.9390304848-5867.93903048476
553570448791.6648265769-13087.6648265769
563325340500.7745162855-7247.77451628553
573519335909.3898571809-716.389857180897
584166835455.56483919676212.43516080327
593486539391.0735155363-4526.07351553627

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 53536 & 53152 & 384 \tabularnewline
4 & 52408 & 53395.2597351276 & -987.259735127598 \tabularnewline
5 & 41454 & 52769.8416578638 & -11315.8416578638 \tabularnewline
6 & 38271 & 45601.3816463071 & -7330.38164630705 \tabularnewline
7 & 35306 & 40957.6662878048 & -5651.66628780481 \tabularnewline
8 & 26414 & 37377.3984643648 & -10963.3984643648 \tabularnewline
9 & 31917 & 30432.207301501 & 1484.79269849903 \tabularnewline
10 & 38030 & 31372.8069852413 & 6657.19301475875 \tabularnewline
11 & 27534 & 35590.0648223858 & -8056.06482238582 \tabularnewline
12 & 18387 & 30486.6372315933 & -12099.6372315933 \tabularnewline
13 & 50556 & 22821.6514292563 & 27734.3485707437 \tabularnewline
14 & 43901 & 40391.0532189844 & 3509.94678101556 \tabularnewline
15 & 48572 & 42614.5655217496 & 5957.43447825042 \tabularnewline
16 & 43899 & 46388.5340978413 & -2489.5340978413 \tabularnewline
17 & 37532 & 44811.4418967163 & -7279.4418967163 \tabularnewline
18 & 40357 & 40199.9963038206 & 157.003696179410 \tabularnewline
19 & 35489 & 40299.4564015983 & -4810.45640159834 \tabularnewline
20 & 29027 & 37252.0856982242 & -8225.08569822419 \tabularnewline
21 & 34485 & 32041.585259808 & 2443.414740192 \tabularnewline
22 & 42598 & 33589.461360084 & 9008.53863991602 \tabularnewline
23 & 30306 & 39296.27053569 & -8990.27053569 \tabularnewline
24 & 26451 & 33601.0340012176 & -7150.03400121759 \tabularnewline
25 & 47460 & 29071.5668728595 & 18388.4331271405 \tabularnewline
26 & 50104 & 40720.4350289005 & 9383.56497109947 \tabularnewline
27 & 61465 & 46664.8192201044 & 14800.1807798956 \tabularnewline
28 & 53726 & 56040.56936687 & -2314.56936686996 \tabularnewline
29 & 39477 & 54574.3153795803 & -15097.3153795803 \tabularnewline
30 & 43895 & 45010.3337640216 & -1115.33376402163 \tabularnewline
31 & 31481 & 44303.7822118998 & -12822.7822118998 \tabularnewline
32 & 29896 & 36180.6920961039 & -6284.6920961039 \tabularnewline
33 & 33842 & 32199.4094537686 & 1642.59054623138 \tabularnewline
34 & 39120 & 33239.9723214752 & 5880.02767852476 \tabularnewline
35 & 33702 & 36964.9045496546 & -3262.90454965462 \tabularnewline
36 & 25094 & 34897.8907566973 & -9803.89075669728 \tabularnewline
37 & 51442 & 28687.2348486397 & 22754.7651513603 \tabularnewline
38 & 45594 & 43102.1258476257 & 2491.87415237429 \tabularnewline
39 & 52518 & 44680.7004473077 & 7837.29955269231 \tabularnewline
40 & 48564 & 49645.5426694524 & -1081.54266945243 \tabularnewline
41 & 41745 & 48960.3974004415 & -7215.3974004415 \tabularnewline
42 & 49585 & 44389.5232846296 & 5195.47671537039 \tabularnewline
43 & 32747 & 47680.8000805739 & -14933.8000805739 \tabularnewline
44 & 33379 & 38220.4035908632 & -4841.40359086318 \tabularnewline
45 & 35645 & 35153.4281868028 & 491.571813197195 \tabularnewline
46 & 37034 & 35464.8334708511 & 1569.16652914890 \tabularnewline
47 & 35681 & 36458.8830392153 & -777.883039215303 \tabularnewline
48 & 20972 & 35966.1027733826 & -14994.1027733826 \tabularnewline
49 & 58552 & 26467.5051975257 & 32084.4948024743 \tabularnewline
50 & 54955 & 46792.6763104234 & 8162.3236895766 \tabularnewline
51 & 65540 & 51963.4177134237 & 13576.5822865763 \tabularnewline
52 & 51570 & 60564.031804493 & -8994.03180449299 \tabularnewline
53 & 51145 & 54866.4125480082 & -3721.41254800819 \tabularnewline
54 & 46641 & 52508.9390304848 & -5867.93903048476 \tabularnewline
55 & 35704 & 48791.6648265769 & -13087.6648265769 \tabularnewline
56 & 33253 & 40500.7745162855 & -7247.77451628553 \tabularnewline
57 & 35193 & 35909.3898571809 & -716.389857180897 \tabularnewline
58 & 41668 & 35455.5648391967 & 6212.43516080327 \tabularnewline
59 & 34865 & 39391.0735155363 & -4526.07351553627 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11895&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]53536[/C][C]53152[/C][C]384[/C][/ROW]
[ROW][C]4[/C][C]52408[/C][C]53395.2597351276[/C][C]-987.259735127598[/C][/ROW]
[ROW][C]5[/C][C]41454[/C][C]52769.8416578638[/C][C]-11315.8416578638[/C][/ROW]
[ROW][C]6[/C][C]38271[/C][C]45601.3816463071[/C][C]-7330.38164630705[/C][/ROW]
[ROW][C]7[/C][C]35306[/C][C]40957.6662878048[/C][C]-5651.66628780481[/C][/ROW]
[ROW][C]8[/C][C]26414[/C][C]37377.3984643648[/C][C]-10963.3984643648[/C][/ROW]
[ROW][C]9[/C][C]31917[/C][C]30432.207301501[/C][C]1484.79269849903[/C][/ROW]
[ROW][C]10[/C][C]38030[/C][C]31372.8069852413[/C][C]6657.19301475875[/C][/ROW]
[ROW][C]11[/C][C]27534[/C][C]35590.0648223858[/C][C]-8056.06482238582[/C][/ROW]
[ROW][C]12[/C][C]18387[/C][C]30486.6372315933[/C][C]-12099.6372315933[/C][/ROW]
[ROW][C]13[/C][C]50556[/C][C]22821.6514292563[/C][C]27734.3485707437[/C][/ROW]
[ROW][C]14[/C][C]43901[/C][C]40391.0532189844[/C][C]3509.94678101556[/C][/ROW]
[ROW][C]15[/C][C]48572[/C][C]42614.5655217496[/C][C]5957.43447825042[/C][/ROW]
[ROW][C]16[/C][C]43899[/C][C]46388.5340978413[/C][C]-2489.5340978413[/C][/ROW]
[ROW][C]17[/C][C]37532[/C][C]44811.4418967163[/C][C]-7279.4418967163[/C][/ROW]
[ROW][C]18[/C][C]40357[/C][C]40199.9963038206[/C][C]157.003696179410[/C][/ROW]
[ROW][C]19[/C][C]35489[/C][C]40299.4564015983[/C][C]-4810.45640159834[/C][/ROW]
[ROW][C]20[/C][C]29027[/C][C]37252.0856982242[/C][C]-8225.08569822419[/C][/ROW]
[ROW][C]21[/C][C]34485[/C][C]32041.585259808[/C][C]2443.414740192[/C][/ROW]
[ROW][C]22[/C][C]42598[/C][C]33589.461360084[/C][C]9008.53863991602[/C][/ROW]
[ROW][C]23[/C][C]30306[/C][C]39296.27053569[/C][C]-8990.27053569[/C][/ROW]
[ROW][C]24[/C][C]26451[/C][C]33601.0340012176[/C][C]-7150.03400121759[/C][/ROW]
[ROW][C]25[/C][C]47460[/C][C]29071.5668728595[/C][C]18388.4331271405[/C][/ROW]
[ROW][C]26[/C][C]50104[/C][C]40720.4350289005[/C][C]9383.56497109947[/C][/ROW]
[ROW][C]27[/C][C]61465[/C][C]46664.8192201044[/C][C]14800.1807798956[/C][/ROW]
[ROW][C]28[/C][C]53726[/C][C]56040.56936687[/C][C]-2314.56936686996[/C][/ROW]
[ROW][C]29[/C][C]39477[/C][C]54574.3153795803[/C][C]-15097.3153795803[/C][/ROW]
[ROW][C]30[/C][C]43895[/C][C]45010.3337640216[/C][C]-1115.33376402163[/C][/ROW]
[ROW][C]31[/C][C]31481[/C][C]44303.7822118998[/C][C]-12822.7822118998[/C][/ROW]
[ROW][C]32[/C][C]29896[/C][C]36180.6920961039[/C][C]-6284.6920961039[/C][/ROW]
[ROW][C]33[/C][C]33842[/C][C]32199.4094537686[/C][C]1642.59054623138[/C][/ROW]
[ROW][C]34[/C][C]39120[/C][C]33239.9723214752[/C][C]5880.02767852476[/C][/ROW]
[ROW][C]35[/C][C]33702[/C][C]36964.9045496546[/C][C]-3262.90454965462[/C][/ROW]
[ROW][C]36[/C][C]25094[/C][C]34897.8907566973[/C][C]-9803.89075669728[/C][/ROW]
[ROW][C]37[/C][C]51442[/C][C]28687.2348486397[/C][C]22754.7651513603[/C][/ROW]
[ROW][C]38[/C][C]45594[/C][C]43102.1258476257[/C][C]2491.87415237429[/C][/ROW]
[ROW][C]39[/C][C]52518[/C][C]44680.7004473077[/C][C]7837.29955269231[/C][/ROW]
[ROW][C]40[/C][C]48564[/C][C]49645.5426694524[/C][C]-1081.54266945243[/C][/ROW]
[ROW][C]41[/C][C]41745[/C][C]48960.3974004415[/C][C]-7215.3974004415[/C][/ROW]
[ROW][C]42[/C][C]49585[/C][C]44389.5232846296[/C][C]5195.47671537039[/C][/ROW]
[ROW][C]43[/C][C]32747[/C][C]47680.8000805739[/C][C]-14933.8000805739[/C][/ROW]
[ROW][C]44[/C][C]33379[/C][C]38220.4035908632[/C][C]-4841.40359086318[/C][/ROW]
[ROW][C]45[/C][C]35645[/C][C]35153.4281868028[/C][C]491.571813197195[/C][/ROW]
[ROW][C]46[/C][C]37034[/C][C]35464.8334708511[/C][C]1569.16652914890[/C][/ROW]
[ROW][C]47[/C][C]35681[/C][C]36458.8830392153[/C][C]-777.883039215303[/C][/ROW]
[ROW][C]48[/C][C]20972[/C][C]35966.1027733826[/C][C]-14994.1027733826[/C][/ROW]
[ROW][C]49[/C][C]58552[/C][C]26467.5051975257[/C][C]32084.4948024743[/C][/ROW]
[ROW][C]50[/C][C]54955[/C][C]46792.6763104234[/C][C]8162.3236895766[/C][/ROW]
[ROW][C]51[/C][C]65540[/C][C]51963.4177134237[/C][C]13576.5822865763[/C][/ROW]
[ROW][C]52[/C][C]51570[/C][C]60564.031804493[/C][C]-8994.03180449299[/C][/ROW]
[ROW][C]53[/C][C]51145[/C][C]54866.4125480082[/C][C]-3721.41254800819[/C][/ROW]
[ROW][C]54[/C][C]46641[/C][C]52508.9390304848[/C][C]-5867.93903048476[/C][/ROW]
[ROW][C]55[/C][C]35704[/C][C]48791.6648265769[/C][C]-13087.6648265769[/C][/ROW]
[ROW][C]56[/C][C]33253[/C][C]40500.7745162855[/C][C]-7247.77451628553[/C][/ROW]
[ROW][C]57[/C][C]35193[/C][C]35909.3898571809[/C][C]-716.389857180897[/C][/ROW]
[ROW][C]58[/C][C]41668[/C][C]35455.5648391967[/C][C]6212.43516080327[/C][/ROW]
[ROW][C]59[/C][C]34865[/C][C]39391.0735155363[/C][C]-4526.07351553627[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11895&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11895&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
35353653152384
45240853395.2597351276-987.259735127598
54145452769.8416578638-11315.8416578638
63827145601.3816463071-7330.38164630705
73530640957.6662878048-5651.66628780481
82641437377.3984643648-10963.3984643648
93191730432.2073015011484.79269849903
103803031372.80698524136657.19301475875
112753435590.0648223858-8056.06482238582
121838730486.6372315933-12099.6372315933
135055622821.651429256327734.3485707437
144390140391.05321898443509.94678101556
154857242614.56552174965957.43447825042
164389946388.5340978413-2489.5340978413
173753244811.4418967163-7279.4418967163
184035740199.9963038206157.003696179410
193548940299.4564015983-4810.45640159834
202902737252.0856982242-8225.08569822419
213448532041.5852598082443.414740192
224259833589.4613600849008.53863991602
233030639296.27053569-8990.27053569
242645133601.0340012176-7150.03400121759
254746029071.566872859518388.4331271405
265010440720.43502890059383.56497109947
276146546664.819220104414800.1807798956
285372656040.56936687-2314.56936686996
293947754574.3153795803-15097.3153795803
304389545010.3337640216-1115.33376402163
313148144303.7822118998-12822.7822118998
322989636180.6920961039-6284.6920961039
333384232199.40945376861642.59054623138
343912033239.97232147525880.02767852476
353370236964.9045496546-3262.90454965462
362509434897.8907566973-9803.89075669728
375144228687.234848639722754.7651513603
384559443102.12584762572491.87415237429
395251844680.70044730777837.29955269231
404856449645.5426694524-1081.54266945243
414174548960.3974004415-7215.3974004415
424958544389.52328462965195.47671537039
433274747680.8000805739-14933.8000805739
443337938220.4035908632-4841.40359086318
453564535153.4281868028491.571813197195
463703435464.83347085111569.16652914890
473568136458.8830392153-777.883039215303
482097235966.1027733826-14994.1027733826
495855226467.505197525732084.4948024743
505495546792.67631042348162.3236895766
516554051963.417713423713576.5822865763
525157060564.031804493-8994.03180449299
535114554866.4125480082-3721.41254800819
544664152508.9390304848-5867.93903048476
553570448791.6648265769-13087.6648265769
563325340500.7745162855-7247.77451628553
573519335909.3898571809-716.389857180897
584166835455.56483919676212.43516080327
593486539391.0735155363-4526.07351553627







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6036523.856212001416529.629876411656518.0825475912
6136523.856212001412855.318219702260192.3942043006
6236523.85621200149679.2982043337963368.414219669
6336523.85621200146841.1862080891766206.5262159136
6436523.85621200144251.7087393699768796.0036846328
6536523.85621200141855.1079445863971192.6044794164
6636523.8562120014-386.20624207080373433.9186660736
6736523.8562120014-2499.0000942408575546.7125182436
6836523.8562120014-4503.1339070866777550.8463310895
6936523.8562120014-6413.8256323398279461.5380563426
7036523.8562120014-8243.0414479882881290.753871991
7136523.8562120014-10000.392627008583048.1050510113

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
60 & 36523.8562120014 & 16529.6298764116 & 56518.0825475912 \tabularnewline
61 & 36523.8562120014 & 12855.3182197022 & 60192.3942043006 \tabularnewline
62 & 36523.8562120014 & 9679.29820433379 & 63368.414219669 \tabularnewline
63 & 36523.8562120014 & 6841.18620808917 & 66206.5262159136 \tabularnewline
64 & 36523.8562120014 & 4251.70873936997 & 68796.0036846328 \tabularnewline
65 & 36523.8562120014 & 1855.10794458639 & 71192.6044794164 \tabularnewline
66 & 36523.8562120014 & -386.206242070803 & 73433.9186660736 \tabularnewline
67 & 36523.8562120014 & -2499.00009424085 & 75546.7125182436 \tabularnewline
68 & 36523.8562120014 & -4503.13390708667 & 77550.8463310895 \tabularnewline
69 & 36523.8562120014 & -6413.82563233982 & 79461.5380563426 \tabularnewline
70 & 36523.8562120014 & -8243.04144798828 & 81290.753871991 \tabularnewline
71 & 36523.8562120014 & -10000.3926270085 & 83048.1050510113 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11895&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]36523.8562120014[/C][C]16529.6298764116[/C][C]56518.0825475912[/C][/ROW]
[ROW][C]61[/C][C]36523.8562120014[/C][C]12855.3182197022[/C][C]60192.3942043006[/C][/ROW]
[ROW][C]62[/C][C]36523.8562120014[/C][C]9679.29820433379[/C][C]63368.414219669[/C][/ROW]
[ROW][C]63[/C][C]36523.8562120014[/C][C]6841.18620808917[/C][C]66206.5262159136[/C][/ROW]
[ROW][C]64[/C][C]36523.8562120014[/C][C]4251.70873936997[/C][C]68796.0036846328[/C][/ROW]
[ROW][C]65[/C][C]36523.8562120014[/C][C]1855.10794458639[/C][C]71192.6044794164[/C][/ROW]
[ROW][C]66[/C][C]36523.8562120014[/C][C]-386.206242070803[/C][C]73433.9186660736[/C][/ROW]
[ROW][C]67[/C][C]36523.8562120014[/C][C]-2499.00009424085[/C][C]75546.7125182436[/C][/ROW]
[ROW][C]68[/C][C]36523.8562120014[/C][C]-4503.13390708667[/C][C]77550.8463310895[/C][/ROW]
[ROW][C]69[/C][C]36523.8562120014[/C][C]-6413.82563233982[/C][C]79461.5380563426[/C][/ROW]
[ROW][C]70[/C][C]36523.8562120014[/C][C]-8243.04144798828[/C][C]81290.753871991[/C][/ROW]
[ROW][C]71[/C][C]36523.8562120014[/C][C]-10000.3926270085[/C][C]83048.1050510113[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11895&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11895&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
6036523.856212001416529.629876411656518.0825475912
6136523.856212001412855.318219702260192.3942043006
6236523.85621200149679.2982043337963368.414219669
6336523.85621200146841.1862080891766206.5262159136
6436523.85621200144251.7087393699768796.0036846328
6536523.85621200141855.1079445863971192.6044794164
6636523.8562120014-386.20624207080373433.9186660736
6736523.8562120014-2499.0000942408575546.7125182436
6836523.8562120014-4503.1339070866777550.8463310895
6936523.8562120014-6413.8256323398279461.5380563426
7036523.8562120014-8243.0414479882881290.753871991
7136523.8562120014-10000.392627008583048.1050510113



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=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')