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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 27 Nov 2010 13:15:31 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/27/t1290863616hdvabccwiis6nr4.htm/, Retrieved Mon, 29 Apr 2024 15:58:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102374, Retrieved Mon, 29 Apr 2024 15:58:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact184

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Workshop 8 Regres...] [2010-11-27 09:22:21] [87d60b8864dc39f7ed759c345edfb471]
- RMP   [Spectral Analysis] [Workshop 8 Regres...] [2010-11-27 12:28:23] [87d60b8864dc39f7ed759c345edfb471]
- RMP     [Exponential Smoothing] [Workshop 8 Regres...] [2010-11-27 13:02:33] [87d60b8864dc39f7ed759c345edfb471]
-   P         [Exponential Smoothing] [Workshop 8 Regres...] [2010-11-27 13:15:31] [c52f616cc59ab01e55ce1a10b5754887] [Current]
-   P           [Exponential Smoothing] [Workshop 8 Regres...] [2010-11-27 13:17:03] [87d60b8864dc39f7ed759c345edfb471]
- R  D          [Exponential Smoothing] [ws 8 - exponentia...] [2010-11-28 09:11:22] [033eb2749a430605d9b2be7c4aac4a0c]
-   P             [Exponential Smoothing] [ws 8 - exponentia...] [2010-11-28 09:21:35] [033eb2749a430605d9b2be7c4aac4a0c]
-   P               [Exponential Smoothing] [ws 8 - exponentia...] [2010-11-28 09:23:28] [033eb2749a430605d9b2be7c4aac4a0c]
- RMP             [Multiple Regression] [ws 8 - werklooshe...] [2010-11-29 10:16:03] [033eb2749a430605d9b2be7c4aac4a0c]
- R  D              [Multiple Regression] [ws 8 multiple regr] [2010-11-30 16:05:15] [4eaa304e6a28c475ba490fccf4c01ad3]
- R  D            [Exponential Smoothing] [W8-exponentieel s...] [2010-11-29 11:56:04] [48146708a479232c43a8f6e52fbf83b4]
- R PD            [Exponential Smoothing] [W8-exponentieel s...] [2010-11-29 11:57:52] [48146708a479232c43a8f6e52fbf83b4]
- R PD            [Exponential Smoothing] [W8-exponentieel s...] [2010-11-29 11:59:42] [48146708a479232c43a8f6e52fbf83b4]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
24
25
17
18
18
16
20
16
18
17
23
30
23
18
15
12
21
15
20
31
27
34
21
31
19
16
20
21
22
17
24
25
26
25
17
32
33
13
32
25
29
22
18
17
20
15
20
33
29
23
26
18
20
11
28
26
22
17
12
14
17
21
19
18
10
29
31
19
9
20
28
19
30
29
26
23
13
21
19
28
23
18
21
20
23
21
21
15
28
19
26
10
16
22
19
31
31
29
19
22
23
15
20
18
23
25
21
24
25
17
13
28
21
25
9
16
19
17
25
20
29
14
22
15
19
20
15
20
18
33
22
16
17
16
21
26
18
18
17
22
30
30
24
21
21
29
31
20
16
22
20
28
38
22
20
17
28
22
31

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102374&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102374&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102374&T=0

As an alternative you can also use a QR Code:  
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'George Udny Yule' @ 72.249.76.132






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0387398850173385
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0387398850173385 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102374&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]0.0387398850173385[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102374&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102374&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0387398850173385
betaFALSE
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
225241
31724.0387398850173-7.03873988501734
41823.7660599112048-5.76605991120481
51823.5426834132417-5.54268341324165
61623.3279604951252-7.32796049512516
72023.0440761481324-3.04407614813242
81622.9261489881697-6.92614898816974
91822.6578307727551-4.65783077275509
101722.4773869441883-5.47738694418834
112322.2651936037750.73480639622499
123022.29365991907487.70634008092523
132322.59220264771430.407797352285677
141822.6080006702522-4.60800067025225
151522.4294872541269-7.42948725412686
161222.1416697721642-10.1416697721642
172121.7487826513067-0.748782651306744
181521.7197748974921-6.71977489749214
192021.4594515906209-1.4594515906209
203121.40291260381199.59708739618812
212721.77470266604165.22529733395845
223421.977130083940512.0228699160595
232122.4428946820671-1.44289468206707
243122.38699710799178.61300289200833
251922.7206638496821-3.72066384968208
261622.5765257599572-6.57652575995722
272022.3217519082029-2.32175190820292
282122.2318075062404-1.23180750624035
292222.1840874250851-0.18408742508511
301722.1769558994042-5.17695589940418
312421.97640122312142.02359877687858
322522.05479520705892.94520479294107
332622.16889210209003.83110789791002
342522.31730878154402.68269121845597
351722.4212359308840-5.42123593088404
363222.21121787426979.78878212573028
373322.590434168280310.4095658317197
381322.9936995516815-9.99369955168153
393222.60654478015169.39345521984844
402522.9704461552842.02955384471599
412923.04907083786485.9509291621352
422223.2796091493522-1.27960914935225
431823.2300372380392-5.23003723803921
441723.0274261968012-6.02742619680117
452022.7939243989866-2.7939243989866
461522.6856880890227-7.68568808902272
472022.3879454161749-2.38794541617485
483322.295436685324610.7045633146754
492922.71013023729596.2898697627041
502322.95379906867710.0462009313229039
512622.95558888744423.04441111255576
521823.0735290238902-5.07352902389016
532022.8769810928725-2.87698109287253
541122.7655271761376-11.7655271761376
552822.30973200616565.69026799383435
562622.53017233396463.46982766603537
572222.6645930587768-0.664593058776823
581722.6388468000965-5.63884680009649
591222.4203985234304-10.4203985234304
601422.0167134827978-8.01671348279783
611721.7061469242573-4.70614692425729
622121.5238313335369-0.523831333536862
631921.5035381679072-2.50353816790717
641821.4065513871459-3.40655138714592
651021.2745819781022-11.2745819781022
662920.8378059686528.162194031348
673121.15400842691569.84599157308437
681921.5354410083386-2.53544100833860
69921.4372183152073-12.4372183152073
702020.9554019077406-0.955401907740647
712820.91838974768947.08161025231057
721921.1927305146015-2.19273051460155
733021.10778438659198.89221561340813
742921.45226779700477.54773220299531
752621.74466607469044.25533392530961
762321.90951722166731.09048277833273
771321.9517623991133-8.95176239911326
782121.6049721530691-0.604972153069081
791921.5815356014205-2.58153560142049
802821.48152720905336.5184727909467
812321.73405209546321.26594790453678
821821.7830947717229-3.78309477172292
832121.6365381152567-0.63653811525668
842021.6118787018625-1.61187870186248
852321.54943470629041.45056529370957
862121.6056294389789-0.605629438978887
872121.5821674241497-0.58216742414973
881521.5596143250773-6.55961432507733
892821.30549562036586.69450437963425
901921.5648399502809-2.56483995028085
912621.46547834551914.53452165448090
921021.6411451930223-11.6411451930223
931621.1901685667745-5.19016856677449
942220.98910203327701.01089796672296
951921.0282641042722-2.02826410427215
963120.949689386087910.0503106139121
973121.33903726365939.66096273634065
982921.71330184922207.28669815077803
991921.9955876977392-2.99558769773917
1002221.87953897476940.120461025230600
1012321.88420562103591.11579437896409
1021521.9274313669800-6.92743136697997
1032021.6590634723577-1.65906347235766
1041821.5947915442021-3.59479154420206
1052321.45552973311841.54447026688163
1062521.51536233367013.48463766632993
1072121.6503567961908-0.650356796190774
1082421.62516204868612.3748379513139
1092521.71716299785483.28283700214519
1101721.8443397258486-4.84433972584858
1111321.6566705618843-8.65667056188428
1122821.32131213968396.6786878603161
1132121.5800437394592-0.580043739459242
1142521.55757291168763.44242708831244
115921.6909321412694-12.6909321412694
1161621.1992868893537-5.19928688935374
1171920.9978671130880-1.99786711308803
1181720.9204699708471-3.92046997084708
1192520.76859141496254.23140858503747
1202020.9325156970083-0.932515697008263
1212920.89639014612938.1036098538707
1221421.2103230600936-7.21032306009362
1232220.93099597380771.06900402619227
1241520.9724090668655-5.9724090668655
1251920.7410386263386-1.74103862633862
1262020.6735909901435-0.673590990143516
1271520.6474961526366-5.64749615263664
1282020.4287128010476-0.428712801047638
1291820.4121045164296-2.41210451642959
1303320.318659864813312.6813401351867
1312220.80993352351621.1900664764838
1321620.8560365619782-4.85603656197817
1331720.6679142639271-3.66791426392715
1341620.5258196870892-4.52581968708915
1352120.35048995280210.649510047197886
1362620.37565189734825.62434810265183
1371820.5935384961424-2.59353849614239
1381820.4930651130138-2.49306511301379
1391720.3964840571949-3.3964840571949
1402220.26490465535591.73509534464406
1413020.33212204950169.66787795049843
1423020.70665452966559.29334547033445
1432421.06667766461272.93332233538729
1442121.1803142346044-0.180314234604406
1452121.1733288818888-0.173328881888843
1462921.16661414093437.83338585906571
1473121.47007860841099.52992139158906
1482021.8392666673454-1.83926666734537
1491621.7680136881362-5.76801368813619
1502221.54456150107940.455438498920639
1512021.56220513616-1.56220513616002
1522821.50168548881176.49831451118832
1533821.753429445781616.2465705542184
1542222.3828197209781-0.382819720978119
1552022.3679893290051-2.36798932900506
1561722.2762536946771-5.27625369467712
1572822.0718522332235.92814776677698
1582222.3015079960738-0.301507996073752
1593122.28982761097408.71017238902595

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 25 & 24 & 1 \tabularnewline
3 & 17 & 24.0387398850173 & -7.03873988501734 \tabularnewline
4 & 18 & 23.7660599112048 & -5.76605991120481 \tabularnewline
5 & 18 & 23.5426834132417 & -5.54268341324165 \tabularnewline
6 & 16 & 23.3279604951252 & -7.32796049512516 \tabularnewline
7 & 20 & 23.0440761481324 & -3.04407614813242 \tabularnewline
8 & 16 & 22.9261489881697 & -6.92614898816974 \tabularnewline
9 & 18 & 22.6578307727551 & -4.65783077275509 \tabularnewline
10 & 17 & 22.4773869441883 & -5.47738694418834 \tabularnewline
11 & 23 & 22.265193603775 & 0.73480639622499 \tabularnewline
12 & 30 & 22.2936599190748 & 7.70634008092523 \tabularnewline
13 & 23 & 22.5922026477143 & 0.407797352285677 \tabularnewline
14 & 18 & 22.6080006702522 & -4.60800067025225 \tabularnewline
15 & 15 & 22.4294872541269 & -7.42948725412686 \tabularnewline
16 & 12 & 22.1416697721642 & -10.1416697721642 \tabularnewline
17 & 21 & 21.7487826513067 & -0.748782651306744 \tabularnewline
18 & 15 & 21.7197748974921 & -6.71977489749214 \tabularnewline
19 & 20 & 21.4594515906209 & -1.4594515906209 \tabularnewline
20 & 31 & 21.4029126038119 & 9.59708739618812 \tabularnewline
21 & 27 & 21.7747026660416 & 5.22529733395845 \tabularnewline
22 & 34 & 21.9771300839405 & 12.0228699160595 \tabularnewline
23 & 21 & 22.4428946820671 & -1.44289468206707 \tabularnewline
24 & 31 & 22.3869971079917 & 8.61300289200833 \tabularnewline
25 & 19 & 22.7206638496821 & -3.72066384968208 \tabularnewline
26 & 16 & 22.5765257599572 & -6.57652575995722 \tabularnewline
27 & 20 & 22.3217519082029 & -2.32175190820292 \tabularnewline
28 & 21 & 22.2318075062404 & -1.23180750624035 \tabularnewline
29 & 22 & 22.1840874250851 & -0.18408742508511 \tabularnewline
30 & 17 & 22.1769558994042 & -5.17695589940418 \tabularnewline
31 & 24 & 21.9764012231214 & 2.02359877687858 \tabularnewline
32 & 25 & 22.0547952070589 & 2.94520479294107 \tabularnewline
33 & 26 & 22.1688921020900 & 3.83110789791002 \tabularnewline
34 & 25 & 22.3173087815440 & 2.68269121845597 \tabularnewline
35 & 17 & 22.4212359308840 & -5.42123593088404 \tabularnewline
36 & 32 & 22.2112178742697 & 9.78878212573028 \tabularnewline
37 & 33 & 22.5904341682803 & 10.4095658317197 \tabularnewline
38 & 13 & 22.9936995516815 & -9.99369955168153 \tabularnewline
39 & 32 & 22.6065447801516 & 9.39345521984844 \tabularnewline
40 & 25 & 22.970446155284 & 2.02955384471599 \tabularnewline
41 & 29 & 23.0490708378648 & 5.9509291621352 \tabularnewline
42 & 22 & 23.2796091493522 & -1.27960914935225 \tabularnewline
43 & 18 & 23.2300372380392 & -5.23003723803921 \tabularnewline
44 & 17 & 23.0274261968012 & -6.02742619680117 \tabularnewline
45 & 20 & 22.7939243989866 & -2.7939243989866 \tabularnewline
46 & 15 & 22.6856880890227 & -7.68568808902272 \tabularnewline
47 & 20 & 22.3879454161749 & -2.38794541617485 \tabularnewline
48 & 33 & 22.2954366853246 & 10.7045633146754 \tabularnewline
49 & 29 & 22.7101302372959 & 6.2898697627041 \tabularnewline
50 & 23 & 22.9537990686771 & 0.0462009313229039 \tabularnewline
51 & 26 & 22.9555888874442 & 3.04441111255576 \tabularnewline
52 & 18 & 23.0735290238902 & -5.07352902389016 \tabularnewline
53 & 20 & 22.8769810928725 & -2.87698109287253 \tabularnewline
54 & 11 & 22.7655271761376 & -11.7655271761376 \tabularnewline
55 & 28 & 22.3097320061656 & 5.69026799383435 \tabularnewline
56 & 26 & 22.5301723339646 & 3.46982766603537 \tabularnewline
57 & 22 & 22.6645930587768 & -0.664593058776823 \tabularnewline
58 & 17 & 22.6388468000965 & -5.63884680009649 \tabularnewline
59 & 12 & 22.4203985234304 & -10.4203985234304 \tabularnewline
60 & 14 & 22.0167134827978 & -8.01671348279783 \tabularnewline
61 & 17 & 21.7061469242573 & -4.70614692425729 \tabularnewline
62 & 21 & 21.5238313335369 & -0.523831333536862 \tabularnewline
63 & 19 & 21.5035381679072 & -2.50353816790717 \tabularnewline
64 & 18 & 21.4065513871459 & -3.40655138714592 \tabularnewline
65 & 10 & 21.2745819781022 & -11.2745819781022 \tabularnewline
66 & 29 & 20.837805968652 & 8.162194031348 \tabularnewline
67 & 31 & 21.1540084269156 & 9.84599157308437 \tabularnewline
68 & 19 & 21.5354410083386 & -2.53544100833860 \tabularnewline
69 & 9 & 21.4372183152073 & -12.4372183152073 \tabularnewline
70 & 20 & 20.9554019077406 & -0.955401907740647 \tabularnewline
71 & 28 & 20.9183897476894 & 7.08161025231057 \tabularnewline
72 & 19 & 21.1927305146015 & -2.19273051460155 \tabularnewline
73 & 30 & 21.1077843865919 & 8.89221561340813 \tabularnewline
74 & 29 & 21.4522677970047 & 7.54773220299531 \tabularnewline
75 & 26 & 21.7446660746904 & 4.25533392530961 \tabularnewline
76 & 23 & 21.9095172216673 & 1.09048277833273 \tabularnewline
77 & 13 & 21.9517623991133 & -8.95176239911326 \tabularnewline
78 & 21 & 21.6049721530691 & -0.604972153069081 \tabularnewline
79 & 19 & 21.5815356014205 & -2.58153560142049 \tabularnewline
80 & 28 & 21.4815272090533 & 6.5184727909467 \tabularnewline
81 & 23 & 21.7340520954632 & 1.26594790453678 \tabularnewline
82 & 18 & 21.7830947717229 & -3.78309477172292 \tabularnewline
83 & 21 & 21.6365381152567 & -0.63653811525668 \tabularnewline
84 & 20 & 21.6118787018625 & -1.61187870186248 \tabularnewline
85 & 23 & 21.5494347062904 & 1.45056529370957 \tabularnewline
86 & 21 & 21.6056294389789 & -0.605629438978887 \tabularnewline
87 & 21 & 21.5821674241497 & -0.58216742414973 \tabularnewline
88 & 15 & 21.5596143250773 & -6.55961432507733 \tabularnewline
89 & 28 & 21.3054956203658 & 6.69450437963425 \tabularnewline
90 & 19 & 21.5648399502809 & -2.56483995028085 \tabularnewline
91 & 26 & 21.4654783455191 & 4.53452165448090 \tabularnewline
92 & 10 & 21.6411451930223 & -11.6411451930223 \tabularnewline
93 & 16 & 21.1901685667745 & -5.19016856677449 \tabularnewline
94 & 22 & 20.9891020332770 & 1.01089796672296 \tabularnewline
95 & 19 & 21.0282641042722 & -2.02826410427215 \tabularnewline
96 & 31 & 20.9496893860879 & 10.0503106139121 \tabularnewline
97 & 31 & 21.3390372636593 & 9.66096273634065 \tabularnewline
98 & 29 & 21.7133018492220 & 7.28669815077803 \tabularnewline
99 & 19 & 21.9955876977392 & -2.99558769773917 \tabularnewline
100 & 22 & 21.8795389747694 & 0.120461025230600 \tabularnewline
101 & 23 & 21.8842056210359 & 1.11579437896409 \tabularnewline
102 & 15 & 21.9274313669800 & -6.92743136697997 \tabularnewline
103 & 20 & 21.6590634723577 & -1.65906347235766 \tabularnewline
104 & 18 & 21.5947915442021 & -3.59479154420206 \tabularnewline
105 & 23 & 21.4555297331184 & 1.54447026688163 \tabularnewline
106 & 25 & 21.5153623336701 & 3.48463766632993 \tabularnewline
107 & 21 & 21.6503567961908 & -0.650356796190774 \tabularnewline
108 & 24 & 21.6251620486861 & 2.3748379513139 \tabularnewline
109 & 25 & 21.7171629978548 & 3.28283700214519 \tabularnewline
110 & 17 & 21.8443397258486 & -4.84433972584858 \tabularnewline
111 & 13 & 21.6566705618843 & -8.65667056188428 \tabularnewline
112 & 28 & 21.3213121396839 & 6.6786878603161 \tabularnewline
113 & 21 & 21.5800437394592 & -0.580043739459242 \tabularnewline
114 & 25 & 21.5575729116876 & 3.44242708831244 \tabularnewline
115 & 9 & 21.6909321412694 & -12.6909321412694 \tabularnewline
116 & 16 & 21.1992868893537 & -5.19928688935374 \tabularnewline
117 & 19 & 20.9978671130880 & -1.99786711308803 \tabularnewline
118 & 17 & 20.9204699708471 & -3.92046997084708 \tabularnewline
119 & 25 & 20.7685914149625 & 4.23140858503747 \tabularnewline
120 & 20 & 20.9325156970083 & -0.932515697008263 \tabularnewline
121 & 29 & 20.8963901461293 & 8.1036098538707 \tabularnewline
122 & 14 & 21.2103230600936 & -7.21032306009362 \tabularnewline
123 & 22 & 20.9309959738077 & 1.06900402619227 \tabularnewline
124 & 15 & 20.9724090668655 & -5.9724090668655 \tabularnewline
125 & 19 & 20.7410386263386 & -1.74103862633862 \tabularnewline
126 & 20 & 20.6735909901435 & -0.673590990143516 \tabularnewline
127 & 15 & 20.6474961526366 & -5.64749615263664 \tabularnewline
128 & 20 & 20.4287128010476 & -0.428712801047638 \tabularnewline
129 & 18 & 20.4121045164296 & -2.41210451642959 \tabularnewline
130 & 33 & 20.3186598648133 & 12.6813401351867 \tabularnewline
131 & 22 & 20.8099335235162 & 1.1900664764838 \tabularnewline
132 & 16 & 20.8560365619782 & -4.85603656197817 \tabularnewline
133 & 17 & 20.6679142639271 & -3.66791426392715 \tabularnewline
134 & 16 & 20.5258196870892 & -4.52581968708915 \tabularnewline
135 & 21 & 20.3504899528021 & 0.649510047197886 \tabularnewline
136 & 26 & 20.3756518973482 & 5.62434810265183 \tabularnewline
137 & 18 & 20.5935384961424 & -2.59353849614239 \tabularnewline
138 & 18 & 20.4930651130138 & -2.49306511301379 \tabularnewline
139 & 17 & 20.3964840571949 & -3.3964840571949 \tabularnewline
140 & 22 & 20.2649046553559 & 1.73509534464406 \tabularnewline
141 & 30 & 20.3321220495016 & 9.66787795049843 \tabularnewline
142 & 30 & 20.7066545296655 & 9.29334547033445 \tabularnewline
143 & 24 & 21.0666776646127 & 2.93332233538729 \tabularnewline
144 & 21 & 21.1803142346044 & -0.180314234604406 \tabularnewline
145 & 21 & 21.1733288818888 & -0.173328881888843 \tabularnewline
146 & 29 & 21.1666141409343 & 7.83338585906571 \tabularnewline
147 & 31 & 21.4700786084109 & 9.52992139158906 \tabularnewline
148 & 20 & 21.8392666673454 & -1.83926666734537 \tabularnewline
149 & 16 & 21.7680136881362 & -5.76801368813619 \tabularnewline
150 & 22 & 21.5445615010794 & 0.455438498920639 \tabularnewline
151 & 20 & 21.56220513616 & -1.56220513616002 \tabularnewline
152 & 28 & 21.5016854888117 & 6.49831451118832 \tabularnewline
153 & 38 & 21.7534294457816 & 16.2465705542184 \tabularnewline
154 & 22 & 22.3828197209781 & -0.382819720978119 \tabularnewline
155 & 20 & 22.3679893290051 & -2.36798932900506 \tabularnewline
156 & 17 & 22.2762536946771 & -5.27625369467712 \tabularnewline
157 & 28 & 22.071852233223 & 5.92814776677698 \tabularnewline
158 & 22 & 22.3015079960738 & -0.301507996073752 \tabularnewline
159 & 31 & 22.2898276109740 & 8.71017238902595 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102374&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]25[/C][C]24[/C][C]1[/C][/ROW]
[ROW][C]3[/C][C]17[/C][C]24.0387398850173[/C][C]-7.03873988501734[/C][/ROW]
[ROW][C]4[/C][C]18[/C][C]23.7660599112048[/C][C]-5.76605991120481[/C][/ROW]
[ROW][C]5[/C][C]18[/C][C]23.5426834132417[/C][C]-5.54268341324165[/C][/ROW]
[ROW][C]6[/C][C]16[/C][C]23.3279604951252[/C][C]-7.32796049512516[/C][/ROW]
[ROW][C]7[/C][C]20[/C][C]23.0440761481324[/C][C]-3.04407614813242[/C][/ROW]
[ROW][C]8[/C][C]16[/C][C]22.9261489881697[/C][C]-6.92614898816974[/C][/ROW]
[ROW][C]9[/C][C]18[/C][C]22.6578307727551[/C][C]-4.65783077275509[/C][/ROW]
[ROW][C]10[/C][C]17[/C][C]22.4773869441883[/C][C]-5.47738694418834[/C][/ROW]
[ROW][C]11[/C][C]23[/C][C]22.265193603775[/C][C]0.73480639622499[/C][/ROW]
[ROW][C]12[/C][C]30[/C][C]22.2936599190748[/C][C]7.70634008092523[/C][/ROW]
[ROW][C]13[/C][C]23[/C][C]22.5922026477143[/C][C]0.407797352285677[/C][/ROW]
[ROW][C]14[/C][C]18[/C][C]22.6080006702522[/C][C]-4.60800067025225[/C][/ROW]
[ROW][C]15[/C][C]15[/C][C]22.4294872541269[/C][C]-7.42948725412686[/C][/ROW]
[ROW][C]16[/C][C]12[/C][C]22.1416697721642[/C][C]-10.1416697721642[/C][/ROW]
[ROW][C]17[/C][C]21[/C][C]21.7487826513067[/C][C]-0.748782651306744[/C][/ROW]
[ROW][C]18[/C][C]15[/C][C]21.7197748974921[/C][C]-6.71977489749214[/C][/ROW]
[ROW][C]19[/C][C]20[/C][C]21.4594515906209[/C][C]-1.4594515906209[/C][/ROW]
[ROW][C]20[/C][C]31[/C][C]21.4029126038119[/C][C]9.59708739618812[/C][/ROW]
[ROW][C]21[/C][C]27[/C][C]21.7747026660416[/C][C]5.22529733395845[/C][/ROW]
[ROW][C]22[/C][C]34[/C][C]21.9771300839405[/C][C]12.0228699160595[/C][/ROW]
[ROW][C]23[/C][C]21[/C][C]22.4428946820671[/C][C]-1.44289468206707[/C][/ROW]
[ROW][C]24[/C][C]31[/C][C]22.3869971079917[/C][C]8.61300289200833[/C][/ROW]
[ROW][C]25[/C][C]19[/C][C]22.7206638496821[/C][C]-3.72066384968208[/C][/ROW]
[ROW][C]26[/C][C]16[/C][C]22.5765257599572[/C][C]-6.57652575995722[/C][/ROW]
[ROW][C]27[/C][C]20[/C][C]22.3217519082029[/C][C]-2.32175190820292[/C][/ROW]
[ROW][C]28[/C][C]21[/C][C]22.2318075062404[/C][C]-1.23180750624035[/C][/ROW]
[ROW][C]29[/C][C]22[/C][C]22.1840874250851[/C][C]-0.18408742508511[/C][/ROW]
[ROW][C]30[/C][C]17[/C][C]22.1769558994042[/C][C]-5.17695589940418[/C][/ROW]
[ROW][C]31[/C][C]24[/C][C]21.9764012231214[/C][C]2.02359877687858[/C][/ROW]
[ROW][C]32[/C][C]25[/C][C]22.0547952070589[/C][C]2.94520479294107[/C][/ROW]
[ROW][C]33[/C][C]26[/C][C]22.1688921020900[/C][C]3.83110789791002[/C][/ROW]
[ROW][C]34[/C][C]25[/C][C]22.3173087815440[/C][C]2.68269121845597[/C][/ROW]
[ROW][C]35[/C][C]17[/C][C]22.4212359308840[/C][C]-5.42123593088404[/C][/ROW]
[ROW][C]36[/C][C]32[/C][C]22.2112178742697[/C][C]9.78878212573028[/C][/ROW]
[ROW][C]37[/C][C]33[/C][C]22.5904341682803[/C][C]10.4095658317197[/C][/ROW]
[ROW][C]38[/C][C]13[/C][C]22.9936995516815[/C][C]-9.99369955168153[/C][/ROW]
[ROW][C]39[/C][C]32[/C][C]22.6065447801516[/C][C]9.39345521984844[/C][/ROW]
[ROW][C]40[/C][C]25[/C][C]22.970446155284[/C][C]2.02955384471599[/C][/ROW]
[ROW][C]41[/C][C]29[/C][C]23.0490708378648[/C][C]5.9509291621352[/C][/ROW]
[ROW][C]42[/C][C]22[/C][C]23.2796091493522[/C][C]-1.27960914935225[/C][/ROW]
[ROW][C]43[/C][C]18[/C][C]23.2300372380392[/C][C]-5.23003723803921[/C][/ROW]
[ROW][C]44[/C][C]17[/C][C]23.0274261968012[/C][C]-6.02742619680117[/C][/ROW]
[ROW][C]45[/C][C]20[/C][C]22.7939243989866[/C][C]-2.7939243989866[/C][/ROW]
[ROW][C]46[/C][C]15[/C][C]22.6856880890227[/C][C]-7.68568808902272[/C][/ROW]
[ROW][C]47[/C][C]20[/C][C]22.3879454161749[/C][C]-2.38794541617485[/C][/ROW]
[ROW][C]48[/C][C]33[/C][C]22.2954366853246[/C][C]10.7045633146754[/C][/ROW]
[ROW][C]49[/C][C]29[/C][C]22.7101302372959[/C][C]6.2898697627041[/C][/ROW]
[ROW][C]50[/C][C]23[/C][C]22.9537990686771[/C][C]0.0462009313229039[/C][/ROW]
[ROW][C]51[/C][C]26[/C][C]22.9555888874442[/C][C]3.04441111255576[/C][/ROW]
[ROW][C]52[/C][C]18[/C][C]23.0735290238902[/C][C]-5.07352902389016[/C][/ROW]
[ROW][C]53[/C][C]20[/C][C]22.8769810928725[/C][C]-2.87698109287253[/C][/ROW]
[ROW][C]54[/C][C]11[/C][C]22.7655271761376[/C][C]-11.7655271761376[/C][/ROW]
[ROW][C]55[/C][C]28[/C][C]22.3097320061656[/C][C]5.69026799383435[/C][/ROW]
[ROW][C]56[/C][C]26[/C][C]22.5301723339646[/C][C]3.46982766603537[/C][/ROW]
[ROW][C]57[/C][C]22[/C][C]22.6645930587768[/C][C]-0.664593058776823[/C][/ROW]
[ROW][C]58[/C][C]17[/C][C]22.6388468000965[/C][C]-5.63884680009649[/C][/ROW]
[ROW][C]59[/C][C]12[/C][C]22.4203985234304[/C][C]-10.4203985234304[/C][/ROW]
[ROW][C]60[/C][C]14[/C][C]22.0167134827978[/C][C]-8.01671348279783[/C][/ROW]
[ROW][C]61[/C][C]17[/C][C]21.7061469242573[/C][C]-4.70614692425729[/C][/ROW]
[ROW][C]62[/C][C]21[/C][C]21.5238313335369[/C][C]-0.523831333536862[/C][/ROW]
[ROW][C]63[/C][C]19[/C][C]21.5035381679072[/C][C]-2.50353816790717[/C][/ROW]
[ROW][C]64[/C][C]18[/C][C]21.4065513871459[/C][C]-3.40655138714592[/C][/ROW]
[ROW][C]65[/C][C]10[/C][C]21.2745819781022[/C][C]-11.2745819781022[/C][/ROW]
[ROW][C]66[/C][C]29[/C][C]20.837805968652[/C][C]8.162194031348[/C][/ROW]
[ROW][C]67[/C][C]31[/C][C]21.1540084269156[/C][C]9.84599157308437[/C][/ROW]
[ROW][C]68[/C][C]19[/C][C]21.5354410083386[/C][C]-2.53544100833860[/C][/ROW]
[ROW][C]69[/C][C]9[/C][C]21.4372183152073[/C][C]-12.4372183152073[/C][/ROW]
[ROW][C]70[/C][C]20[/C][C]20.9554019077406[/C][C]-0.955401907740647[/C][/ROW]
[ROW][C]71[/C][C]28[/C][C]20.9183897476894[/C][C]7.08161025231057[/C][/ROW]
[ROW][C]72[/C][C]19[/C][C]21.1927305146015[/C][C]-2.19273051460155[/C][/ROW]
[ROW][C]73[/C][C]30[/C][C]21.1077843865919[/C][C]8.89221561340813[/C][/ROW]
[ROW][C]74[/C][C]29[/C][C]21.4522677970047[/C][C]7.54773220299531[/C][/ROW]
[ROW][C]75[/C][C]26[/C][C]21.7446660746904[/C][C]4.25533392530961[/C][/ROW]
[ROW][C]76[/C][C]23[/C][C]21.9095172216673[/C][C]1.09048277833273[/C][/ROW]
[ROW][C]77[/C][C]13[/C][C]21.9517623991133[/C][C]-8.95176239911326[/C][/ROW]
[ROW][C]78[/C][C]21[/C][C]21.6049721530691[/C][C]-0.604972153069081[/C][/ROW]
[ROW][C]79[/C][C]19[/C][C]21.5815356014205[/C][C]-2.58153560142049[/C][/ROW]
[ROW][C]80[/C][C]28[/C][C]21.4815272090533[/C][C]6.5184727909467[/C][/ROW]
[ROW][C]81[/C][C]23[/C][C]21.7340520954632[/C][C]1.26594790453678[/C][/ROW]
[ROW][C]82[/C][C]18[/C][C]21.7830947717229[/C][C]-3.78309477172292[/C][/ROW]
[ROW][C]83[/C][C]21[/C][C]21.6365381152567[/C][C]-0.63653811525668[/C][/ROW]
[ROW][C]84[/C][C]20[/C][C]21.6118787018625[/C][C]-1.61187870186248[/C][/ROW]
[ROW][C]85[/C][C]23[/C][C]21.5494347062904[/C][C]1.45056529370957[/C][/ROW]
[ROW][C]86[/C][C]21[/C][C]21.6056294389789[/C][C]-0.605629438978887[/C][/ROW]
[ROW][C]87[/C][C]21[/C][C]21.5821674241497[/C][C]-0.58216742414973[/C][/ROW]
[ROW][C]88[/C][C]15[/C][C]21.5596143250773[/C][C]-6.55961432507733[/C][/ROW]
[ROW][C]89[/C][C]28[/C][C]21.3054956203658[/C][C]6.69450437963425[/C][/ROW]
[ROW][C]90[/C][C]19[/C][C]21.5648399502809[/C][C]-2.56483995028085[/C][/ROW]
[ROW][C]91[/C][C]26[/C][C]21.4654783455191[/C][C]4.53452165448090[/C][/ROW]
[ROW][C]92[/C][C]10[/C][C]21.6411451930223[/C][C]-11.6411451930223[/C][/ROW]
[ROW][C]93[/C][C]16[/C][C]21.1901685667745[/C][C]-5.19016856677449[/C][/ROW]
[ROW][C]94[/C][C]22[/C][C]20.9891020332770[/C][C]1.01089796672296[/C][/ROW]
[ROW][C]95[/C][C]19[/C][C]21.0282641042722[/C][C]-2.02826410427215[/C][/ROW]
[ROW][C]96[/C][C]31[/C][C]20.9496893860879[/C][C]10.0503106139121[/C][/ROW]
[ROW][C]97[/C][C]31[/C][C]21.3390372636593[/C][C]9.66096273634065[/C][/ROW]
[ROW][C]98[/C][C]29[/C][C]21.7133018492220[/C][C]7.28669815077803[/C][/ROW]
[ROW][C]99[/C][C]19[/C][C]21.9955876977392[/C][C]-2.99558769773917[/C][/ROW]
[ROW][C]100[/C][C]22[/C][C]21.8795389747694[/C][C]0.120461025230600[/C][/ROW]
[ROW][C]101[/C][C]23[/C][C]21.8842056210359[/C][C]1.11579437896409[/C][/ROW]
[ROW][C]102[/C][C]15[/C][C]21.9274313669800[/C][C]-6.92743136697997[/C][/ROW]
[ROW][C]103[/C][C]20[/C][C]21.6590634723577[/C][C]-1.65906347235766[/C][/ROW]
[ROW][C]104[/C][C]18[/C][C]21.5947915442021[/C][C]-3.59479154420206[/C][/ROW]
[ROW][C]105[/C][C]23[/C][C]21.4555297331184[/C][C]1.54447026688163[/C][/ROW]
[ROW][C]106[/C][C]25[/C][C]21.5153623336701[/C][C]3.48463766632993[/C][/ROW]
[ROW][C]107[/C][C]21[/C][C]21.6503567961908[/C][C]-0.650356796190774[/C][/ROW]
[ROW][C]108[/C][C]24[/C][C]21.6251620486861[/C][C]2.3748379513139[/C][/ROW]
[ROW][C]109[/C][C]25[/C][C]21.7171629978548[/C][C]3.28283700214519[/C][/ROW]
[ROW][C]110[/C][C]17[/C][C]21.8443397258486[/C][C]-4.84433972584858[/C][/ROW]
[ROW][C]111[/C][C]13[/C][C]21.6566705618843[/C][C]-8.65667056188428[/C][/ROW]
[ROW][C]112[/C][C]28[/C][C]21.3213121396839[/C][C]6.6786878603161[/C][/ROW]
[ROW][C]113[/C][C]21[/C][C]21.5800437394592[/C][C]-0.580043739459242[/C][/ROW]
[ROW][C]114[/C][C]25[/C][C]21.5575729116876[/C][C]3.44242708831244[/C][/ROW]
[ROW][C]115[/C][C]9[/C][C]21.6909321412694[/C][C]-12.6909321412694[/C][/ROW]
[ROW][C]116[/C][C]16[/C][C]21.1992868893537[/C][C]-5.19928688935374[/C][/ROW]
[ROW][C]117[/C][C]19[/C][C]20.9978671130880[/C][C]-1.99786711308803[/C][/ROW]
[ROW][C]118[/C][C]17[/C][C]20.9204699708471[/C][C]-3.92046997084708[/C][/ROW]
[ROW][C]119[/C][C]25[/C][C]20.7685914149625[/C][C]4.23140858503747[/C][/ROW]
[ROW][C]120[/C][C]20[/C][C]20.9325156970083[/C][C]-0.932515697008263[/C][/ROW]
[ROW][C]121[/C][C]29[/C][C]20.8963901461293[/C][C]8.1036098538707[/C][/ROW]
[ROW][C]122[/C][C]14[/C][C]21.2103230600936[/C][C]-7.21032306009362[/C][/ROW]
[ROW][C]123[/C][C]22[/C][C]20.9309959738077[/C][C]1.06900402619227[/C][/ROW]
[ROW][C]124[/C][C]15[/C][C]20.9724090668655[/C][C]-5.9724090668655[/C][/ROW]
[ROW][C]125[/C][C]19[/C][C]20.7410386263386[/C][C]-1.74103862633862[/C][/ROW]
[ROW][C]126[/C][C]20[/C][C]20.6735909901435[/C][C]-0.673590990143516[/C][/ROW]
[ROW][C]127[/C][C]15[/C][C]20.6474961526366[/C][C]-5.64749615263664[/C][/ROW]
[ROW][C]128[/C][C]20[/C][C]20.4287128010476[/C][C]-0.428712801047638[/C][/ROW]
[ROW][C]129[/C][C]18[/C][C]20.4121045164296[/C][C]-2.41210451642959[/C][/ROW]
[ROW][C]130[/C][C]33[/C][C]20.3186598648133[/C][C]12.6813401351867[/C][/ROW]
[ROW][C]131[/C][C]22[/C][C]20.8099335235162[/C][C]1.1900664764838[/C][/ROW]
[ROW][C]132[/C][C]16[/C][C]20.8560365619782[/C][C]-4.85603656197817[/C][/ROW]
[ROW][C]133[/C][C]17[/C][C]20.6679142639271[/C][C]-3.66791426392715[/C][/ROW]
[ROW][C]134[/C][C]16[/C][C]20.5258196870892[/C][C]-4.52581968708915[/C][/ROW]
[ROW][C]135[/C][C]21[/C][C]20.3504899528021[/C][C]0.649510047197886[/C][/ROW]
[ROW][C]136[/C][C]26[/C][C]20.3756518973482[/C][C]5.62434810265183[/C][/ROW]
[ROW][C]137[/C][C]18[/C][C]20.5935384961424[/C][C]-2.59353849614239[/C][/ROW]
[ROW][C]138[/C][C]18[/C][C]20.4930651130138[/C][C]-2.49306511301379[/C][/ROW]
[ROW][C]139[/C][C]17[/C][C]20.3964840571949[/C][C]-3.3964840571949[/C][/ROW]
[ROW][C]140[/C][C]22[/C][C]20.2649046553559[/C][C]1.73509534464406[/C][/ROW]
[ROW][C]141[/C][C]30[/C][C]20.3321220495016[/C][C]9.66787795049843[/C][/ROW]
[ROW][C]142[/C][C]30[/C][C]20.7066545296655[/C][C]9.29334547033445[/C][/ROW]
[ROW][C]143[/C][C]24[/C][C]21.0666776646127[/C][C]2.93332233538729[/C][/ROW]
[ROW][C]144[/C][C]21[/C][C]21.1803142346044[/C][C]-0.180314234604406[/C][/ROW]
[ROW][C]145[/C][C]21[/C][C]21.1733288818888[/C][C]-0.173328881888843[/C][/ROW]
[ROW][C]146[/C][C]29[/C][C]21.1666141409343[/C][C]7.83338585906571[/C][/ROW]
[ROW][C]147[/C][C]31[/C][C]21.4700786084109[/C][C]9.52992139158906[/C][/ROW]
[ROW][C]148[/C][C]20[/C][C]21.8392666673454[/C][C]-1.83926666734537[/C][/ROW]
[ROW][C]149[/C][C]16[/C][C]21.7680136881362[/C][C]-5.76801368813619[/C][/ROW]
[ROW][C]150[/C][C]22[/C][C]21.5445615010794[/C][C]0.455438498920639[/C][/ROW]
[ROW][C]151[/C][C]20[/C][C]21.56220513616[/C][C]-1.56220513616002[/C][/ROW]
[ROW][C]152[/C][C]28[/C][C]21.5016854888117[/C][C]6.49831451118832[/C][/ROW]
[ROW][C]153[/C][C]38[/C][C]21.7534294457816[/C][C]16.2465705542184[/C][/ROW]
[ROW][C]154[/C][C]22[/C][C]22.3828197209781[/C][C]-0.382819720978119[/C][/ROW]
[ROW][C]155[/C][C]20[/C][C]22.3679893290051[/C][C]-2.36798932900506[/C][/ROW]
[ROW][C]156[/C][C]17[/C][C]22.2762536946771[/C][C]-5.27625369467712[/C][/ROW]
[ROW][C]157[/C][C]28[/C][C]22.071852233223[/C][C]5.92814776677698[/C][/ROW]
[ROW][C]158[/C][C]22[/C][C]22.3015079960738[/C][C]-0.301507996073752[/C][/ROW]
[ROW][C]159[/C][C]31[/C][C]22.2898276109740[/C][C]8.71017238902595[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102374&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102374&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
225241
31724.0387398850173-7.03873988501734
41823.7660599112048-5.76605991120481
51823.5426834132417-5.54268341324165
61623.3279604951252-7.32796049512516
72023.0440761481324-3.04407614813242
81622.9261489881697-6.92614898816974
91822.6578307727551-4.65783077275509
101722.4773869441883-5.47738694418834
112322.2651936037750.73480639622499
123022.29365991907487.70634008092523
132322.59220264771430.407797352285677
141822.6080006702522-4.60800067025225
151522.4294872541269-7.42948725412686
161222.1416697721642-10.1416697721642
172121.7487826513067-0.748782651306744
181521.7197748974921-6.71977489749214
192021.4594515906209-1.4594515906209
203121.40291260381199.59708739618812
212721.77470266604165.22529733395845
223421.977130083940512.0228699160595
232122.4428946820671-1.44289468206707
243122.38699710799178.61300289200833
251922.7206638496821-3.72066384968208
261622.5765257599572-6.57652575995722
272022.3217519082029-2.32175190820292
282122.2318075062404-1.23180750624035
292222.1840874250851-0.18408742508511
301722.1769558994042-5.17695589940418
312421.97640122312142.02359877687858
322522.05479520705892.94520479294107
332622.16889210209003.83110789791002
342522.31730878154402.68269121845597
351722.4212359308840-5.42123593088404
363222.21121787426979.78878212573028
373322.590434168280310.4095658317197
381322.9936995516815-9.99369955168153
393222.60654478015169.39345521984844
402522.9704461552842.02955384471599
412923.04907083786485.9509291621352
422223.2796091493522-1.27960914935225
431823.2300372380392-5.23003723803921
441723.0274261968012-6.02742619680117
452022.7939243989866-2.7939243989866
461522.6856880890227-7.68568808902272
472022.3879454161749-2.38794541617485
483322.295436685324610.7045633146754
492922.71013023729596.2898697627041
502322.95379906867710.0462009313229039
512622.95558888744423.04441111255576
521823.0735290238902-5.07352902389016
532022.8769810928725-2.87698109287253
541122.7655271761376-11.7655271761376
552822.30973200616565.69026799383435
562622.53017233396463.46982766603537
572222.6645930587768-0.664593058776823
581722.6388468000965-5.63884680009649
591222.4203985234304-10.4203985234304
601422.0167134827978-8.01671348279783
611721.7061469242573-4.70614692425729
622121.5238313335369-0.523831333536862
631921.5035381679072-2.50353816790717
641821.4065513871459-3.40655138714592
651021.2745819781022-11.2745819781022
662920.8378059686528.162194031348
673121.15400842691569.84599157308437
681921.5354410083386-2.53544100833860
69921.4372183152073-12.4372183152073
702020.9554019077406-0.955401907740647
712820.91838974768947.08161025231057
721921.1927305146015-2.19273051460155
733021.10778438659198.89221561340813
742921.45226779700477.54773220299531
752621.74466607469044.25533392530961
762321.90951722166731.09048277833273
771321.9517623991133-8.95176239911326
782121.6049721530691-0.604972153069081
791921.5815356014205-2.58153560142049
802821.48152720905336.5184727909467
812321.73405209546321.26594790453678
821821.7830947717229-3.78309477172292
832121.6365381152567-0.63653811525668
842021.6118787018625-1.61187870186248
852321.54943470629041.45056529370957
862121.6056294389789-0.605629438978887
872121.5821674241497-0.58216742414973
881521.5596143250773-6.55961432507733
892821.30549562036586.69450437963425
901921.5648399502809-2.56483995028085
912621.46547834551914.53452165448090
921021.6411451930223-11.6411451930223
931621.1901685667745-5.19016856677449
942220.98910203327701.01089796672296
951921.0282641042722-2.02826410427215
963120.949689386087910.0503106139121
973121.33903726365939.66096273634065
982921.71330184922207.28669815077803
991921.9955876977392-2.99558769773917
1002221.87953897476940.120461025230600
1012321.88420562103591.11579437896409
1021521.9274313669800-6.92743136697997
1032021.6590634723577-1.65906347235766
1041821.5947915442021-3.59479154420206
1052321.45552973311841.54447026688163
1062521.51536233367013.48463766632993
1072121.6503567961908-0.650356796190774
1082421.62516204868612.3748379513139
1092521.71716299785483.28283700214519
1101721.8443397258486-4.84433972584858
1111321.6566705618843-8.65667056188428
1122821.32131213968396.6786878603161
1132121.5800437394592-0.580043739459242
1142521.55757291168763.44242708831244
115921.6909321412694-12.6909321412694
1161621.1992868893537-5.19928688935374
1171920.9978671130880-1.99786711308803
1181720.9204699708471-3.92046997084708
1192520.76859141496254.23140858503747
1202020.9325156970083-0.932515697008263
1212920.89639014612938.1036098538707
1221421.2103230600936-7.21032306009362
1232220.93099597380771.06900402619227
1241520.9724090668655-5.9724090668655
1251920.7410386263386-1.74103862633862
1262020.6735909901435-0.673590990143516
1271520.6474961526366-5.64749615263664
1282020.4287128010476-0.428712801047638
1291820.4121045164296-2.41210451642959
1303320.318659864813312.6813401351867
1312220.80993352351621.1900664764838
1321620.8560365619782-4.85603656197817
1331720.6679142639271-3.66791426392715
1341620.5258196870892-4.52581968708915
1352120.35048995280210.649510047197886
1362620.37565189734825.62434810265183
1371820.5935384961424-2.59353849614239
1381820.4930651130138-2.49306511301379
1391720.3964840571949-3.3964840571949
1402220.26490465535591.73509534464406
1413020.33212204950169.66787795049843
1423020.70665452966559.29334547033445
1432421.06667766461272.93332233538729
1442121.1803142346044-0.180314234604406
1452121.1733288818888-0.173328881888843
1462921.16661414093437.83338585906571
1473121.47007860841099.52992139158906
1482021.8392666673454-1.83926666734537
1491621.7680136881362-5.76801368813619
1502221.54456150107940.455438498920639
1512021.56220513616-1.56220513616002
1522821.50168548881176.49831451118832
1533821.753429445781616.2465705542184
1542222.3828197209781-0.382819720978119
1552022.3679893290051-2.36798932900506
1561722.2762536946771-5.27625369467712
1572822.0718522332235.92814776677698
1582222.3015079960738-0.301507996073752
1593122.28982761097408.71017238902595






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
16022.627258687806111.149668781840734.1048485937715
16122.627258687806111.141059349664434.1134580259478
16222.627258687806111.132456365820134.1220610097922
16322.627258687806111.123859815840334.1306575597719
16422.627258687806111.115269685311734.1392476903005
16522.627258687806111.106685959874534.1478314157377
16622.627258687806111.098108625222634.1564087503896
16722.627258687806111.089537667102934.1649797085094
16822.627258687806111.080973071315234.1735443042971
16922.627258687806111.072414823712034.1821025519003
17022.627258687806111.063862910198134.1906544654141
17122.627258687806111.055317316730534.1992000588817

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
160 & 22.6272586878061 & 11.1496687818407 & 34.1048485937715 \tabularnewline
161 & 22.6272586878061 & 11.1410593496644 & 34.1134580259478 \tabularnewline
162 & 22.6272586878061 & 11.1324563658201 & 34.1220610097922 \tabularnewline
163 & 22.6272586878061 & 11.1238598158403 & 34.1306575597719 \tabularnewline
164 & 22.6272586878061 & 11.1152696853117 & 34.1392476903005 \tabularnewline
165 & 22.6272586878061 & 11.1066859598745 & 34.1478314157377 \tabularnewline
166 & 22.6272586878061 & 11.0981086252226 & 34.1564087503896 \tabularnewline
167 & 22.6272586878061 & 11.0895376671029 & 34.1649797085094 \tabularnewline
168 & 22.6272586878061 & 11.0809730713152 & 34.1735443042971 \tabularnewline
169 & 22.6272586878061 & 11.0724148237120 & 34.1821025519003 \tabularnewline
170 & 22.6272586878061 & 11.0638629101981 & 34.1906544654141 \tabularnewline
171 & 22.6272586878061 & 11.0553173167305 & 34.1992000588817 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102374&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]160[/C][C]22.6272586878061[/C][C]11.1496687818407[/C][C]34.1048485937715[/C][/ROW]
[ROW][C]161[/C][C]22.6272586878061[/C][C]11.1410593496644[/C][C]34.1134580259478[/C][/ROW]
[ROW][C]162[/C][C]22.6272586878061[/C][C]11.1324563658201[/C][C]34.1220610097922[/C][/ROW]
[ROW][C]163[/C][C]22.6272586878061[/C][C]11.1238598158403[/C][C]34.1306575597719[/C][/ROW]
[ROW][C]164[/C][C]22.6272586878061[/C][C]11.1152696853117[/C][C]34.1392476903005[/C][/ROW]
[ROW][C]165[/C][C]22.6272586878061[/C][C]11.1066859598745[/C][C]34.1478314157377[/C][/ROW]
[ROW][C]166[/C][C]22.6272586878061[/C][C]11.0981086252226[/C][C]34.1564087503896[/C][/ROW]
[ROW][C]167[/C][C]22.6272586878061[/C][C]11.0895376671029[/C][C]34.1649797085094[/C][/ROW]
[ROW][C]168[/C][C]22.6272586878061[/C][C]11.0809730713152[/C][C]34.1735443042971[/C][/ROW]
[ROW][C]169[/C][C]22.6272586878061[/C][C]11.0724148237120[/C][C]34.1821025519003[/C][/ROW]
[ROW][C]170[/C][C]22.6272586878061[/C][C]11.0638629101981[/C][C]34.1906544654141[/C][/ROW]
[ROW][C]171[/C][C]22.6272586878061[/C][C]11.0553173167305[/C][C]34.1992000588817[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102374&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102374&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
16022.627258687806111.149668781840734.1048485937715
16122.627258687806111.141059349664434.1134580259478
16222.627258687806111.132456365820134.1220610097922
16322.627258687806111.123859815840334.1306575597719
16422.627258687806111.115269685311734.1392476903005
16522.627258687806111.106685959874534.1478314157377
16622.627258687806111.098108625222634.1564087503896
16722.627258687806111.089537667102934.1649797085094
16822.627258687806111.080973071315234.1735443042971
16922.627258687806111.072414823712034.1821025519003
17022.627258687806111.063862910198134.1906544654141
17122.627258687806111.055317316730534.1992000588817


Figures (Output of Computation)

Input Parameters & R Code

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=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')