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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 24 Jan 2018 11:23:13 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Jan/24/t1516789422yni3y8zy3tenq2q.htm/, Retrieved Mon, 06 May 2024 08:52:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=312612, Retrieved Mon, 06 May 2024 08:52:31 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact46
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2018-01-24 10:23:13] [665745206c32fd7279b5ac29093ac087] [Current]
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Dataseries X:
10
15
14
14
8
19
17
18
10
15
16
12
13
10
14
15
20
9
12
13
16
12
14
15
19
16
16
14
14
14
13
18
15
15
15
13
14
15
14
19
16
16
12
10
11
13
14
11
11
16
9
16
19
13
15
14
15
11
14
15
17
16
13
15
14
15
14
12
12
15
17
13
5
7
10
15
9
9
15
14
11
18
20
20
16
15
14
13
18
14
12
9
19
13
12
14
6
14
11
11
14
12
19
13
14
17
12
16
15
15
15
16
15
12
13
14
17
14
14
14
15
11
11
16
12
12
19
18
16
16
13
11
10
14
14
14
16
10
16
7
16
15
17
11
11
10
13
14
13
13
12
10
15
6
15
15
11
14
14
16
12
15
20
12
9
13
15
19
11
11
17
15
14
15
11
12
15
16
16




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312612&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=312612&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312612&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0168700570885182
beta0.0858454568212193
gamma0.248293884948183

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0168700570885182 \tabularnewline
beta & 0.0858454568212193 \tabularnewline
gamma & 0.248293884948183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312612&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]0.0168700570885182[/C][/ROW]
[ROW][C]beta[/C][C]0.0858454568212193[/C][/ROW]
[ROW][C]gamma[/C][C]0.248293884948183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=312612&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312612&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
alpha0.0168700570885182
beta0.0858454568212193
gamma0.248293884948183







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131313.1097756410256-0.109775641025644
141010.455229775627-0.455229775626988
151414.3358634740781-0.335863474078065
161515.1346911520702-0.134691152070177
172020.2700508898343-0.270050889834337
1899.15273600860088-0.152736008600877
191216.4121790411113-4.41217904111132
201317.343375230462-4.34337523046201
21169.394441990890616.60555800910939
221214.3897841665352-2.38978416653524
231414.7299134782797-0.72991347827975
241510.55532116296744.44467883703256
251912.15599791193416.84400208806588
26169.541199318423956.45880068157605
271613.58438783535422.41561216464581
281414.4995018014177-0.499501801417686
291419.6158983644909-5.61589836449086
30148.449527158235535.55047284176447
311314.7861824051413-1.78618240514133
321815.80302843570332.19697156429672
331510.67114785254674.32885214745332
341513.46300093668611.53699906331386
351514.31097357494060.689026425059364
361311.46193372031011.53806627968986
371413.63352372571840.366476274281629
381510.84029919287394.15970080712611
391413.87928895431640.120711045683624
401914.06232029234574.93767970765428
411618.0476047005494-2.04760470054944
42169.698468277559766.30153172244024
431214.2892349908159-2.28923499081585
441016.3015307859515-6.30153078595152
451111.5660032182957-0.566003218295704
461313.6060054719675-0.606005471967462
471414.2199588566701-0.219958856670118
481111.5706508092246-0.570650809224594
491113.4254330351977-2.42543303519772
501611.51176875066684.48823124933316
51913.5715526726737-4.57155267267366
521614.84566675283751.15433324716248
531917.05089748901321.9491025109868
541310.80195658810762.1980434118924
551513.21520767215681.7847923278432
561414.3114714159728-0.311471415972793
571511.08040419018533.91959580981473
581113.1961459877233-2.19614598772329
591413.88503869791780.114961302082182
601511.16378921598513.83621078401494
611712.65454980092554.34545019907453
621612.5669737451813.43302625481903
631312.42009015681780.579909843182175
641515.2089621993132-0.208962199313234
651417.6133612249509-3.61336122495092
661511.35145322997653.64854677002346
671413.71050254415490.289497455845149
681214.2898711584974-2.28987115849743
691212.0754277368542-0.0754277368541612
701512.64227771677142.35772228322858
711713.99013118046763.0098688195324
721312.24827112135840.751728878641551
73513.8290132781365-8.82901327813649
74713.2950853853924-6.29508538539238
751012.2721686566952-2.27216865669523
761514.80076888717090.1992311128291
77916.3620246109609-7.36202461096085
78911.7851185299616-2.78511852996164
791513.1819258659511.818074134049
801413.12591376719150.874086232808471
811111.4784549178983-0.478454917898311
821812.60491797333575.39508202666425
832014.14007066690615.85992933309389
842011.87606167161748.12393832838263
851611.23413543378134.76586456621867
861511.55945764617473.4405423538253
871411.70825440951142.29174559048858
881314.9491972872216-1.94919728722157
891814.65742375889673.34257624110331
901411.42281019976592.57718980023406
911214.0859677583067-2.08596775830665
92913.7802327618126-4.78023276181264
931911.74560510153237.25439489846766
941314.4858633970582-1.48586339705824
951216.0580216520957-4.05802165209575
961414.2046050475533-0.204605047553272
97612.6156436818408-6.61564368184081
981412.42214930025971.5778506997403
991112.2531056375863-1.25310563758627
1001114.3878874446008-3.38788744460079
1011415.3503855626225-1.3503855626225
1021211.8297635101360.170236489863989
1031913.29052586180115.70947413819887
1041312.44641696365030.553583036349741
1051413.43501075190440.564989248095555
1061713.91471363425483.08528636574523
1071214.9285677127414-2.92856771274142
1081614.02893695566531.97106304433467
1091510.90895555520144.09104444479855
1101512.90890731511982.09109268488019
1111512.07096383301022.92903616698975
1121613.77473681221062.22526318778937
1131515.3569723154454-0.356972315445368
1141212.2534180636276-0.253418063627588
1151315.0876934318275-2.08769343182751
1161412.8706779289311.12932207106899
1171713.88981422134463.11018577865537
1181415.0494036653355-1.04940366533549
1191414.5412360234008-0.541236023400812
1201414.8971056856367-0.897105685636728
1211512.26128364819672.7387163518033
1221113.7633117094692-2.76331170946922
1231113.0540789190033-2.05407891900328
1241614.50083366480731.49916633519268
1251215.4382731472036-3.43827314720357
1261212.3013431732901-0.301343173290089
1271914.6803124392474.31968756075303
1281813.35921763011284.64078236988721
1291614.92875460497591.07124539502412
1301615.04324006971720.956759930282779
1311314.7005385026557-1.70053850265568
1321114.9558777656577-3.95587776565768
1331013.1574439131552-3.15744391315517
1341413.20985803886940.790141961130592
1351412.73177379423721.26822620576283
1361415.1048271153939-1.10482711539392
1371614.79219713215451.20780286784554
1381012.5052304991545-2.50523049915448
1391615.97768876767030.0223112323296935
140714.6589056288409-7.65890562884091
1411615.12821892607680.871781073923174
1421515.189719186919-0.189719186919048
1431714.15568212238322.84431787761676
1441113.9204012890286-2.92040128902857
1451112.3190852496575-1.31908524965753
1461013.3535484363829-3.35354843638295
1471312.9036715516690.0963284483310289
1481414.6573920095614-0.657392009561409
1491314.8971948239935-1.89719482399345
1501311.62733905812991.37266094187005
1511215.7636825021564-3.76368250215643
1521012.4820008375213-2.48200083752129
1531515.104526703039-0.104526703039017
154614.8725183128728-8.87251831287285
1551514.4021308296010.597869170398987
1561512.68800609416252.31199390583747
1571111.5396794744113-0.53967947441132
1581412.0656262002951.93437379970498
1591412.5297055195831.47029448041705
1601614.1072235466881.89277645331197
1611214.0757045237581-2.07570452375814
1621511.58906634066063.41093365933938
1632014.49697993240145.50302006759859
1641211.68890564364920.311094356350772
165914.9473623575443-5.94736235754426
1661312.47646885094140.523531149058574
1671514.48996695659010.51003304340988
1681913.20626320866825.79373679133182
1691111.4390840527321-0.43908405273211
1701112.5893210952181-1.58932109521815
1711712.89423236298924.1057676370108
1721514.63671877406270.363281225937309
1731413.62583315611330.374166843886682
1741512.53855177545382.46144822454622
1751115.9584721845036-4.9584721845036
1761211.70872120376990.291278796230076
1771513.44127849682061.55872150317945
1781612.68961834851063.31038165148935
1791614.76389863647351.23610136352649

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 13 & 13.1097756410256 & -0.109775641025644 \tabularnewline
14 & 10 & 10.455229775627 & -0.455229775626988 \tabularnewline
15 & 14 & 14.3358634740781 & -0.335863474078065 \tabularnewline
16 & 15 & 15.1346911520702 & -0.134691152070177 \tabularnewline
17 & 20 & 20.2700508898343 & -0.270050889834337 \tabularnewline
18 & 9 & 9.15273600860088 & -0.152736008600877 \tabularnewline
19 & 12 & 16.4121790411113 & -4.41217904111132 \tabularnewline
20 & 13 & 17.343375230462 & -4.34337523046201 \tabularnewline
21 & 16 & 9.39444199089061 & 6.60555800910939 \tabularnewline
22 & 12 & 14.3897841665352 & -2.38978416653524 \tabularnewline
23 & 14 & 14.7299134782797 & -0.72991347827975 \tabularnewline
24 & 15 & 10.5553211629674 & 4.44467883703256 \tabularnewline
25 & 19 & 12.1559979119341 & 6.84400208806588 \tabularnewline
26 & 16 & 9.54119931842395 & 6.45880068157605 \tabularnewline
27 & 16 & 13.5843878353542 & 2.41561216464581 \tabularnewline
28 & 14 & 14.4995018014177 & -0.499501801417686 \tabularnewline
29 & 14 & 19.6158983644909 & -5.61589836449086 \tabularnewline
30 & 14 & 8.44952715823553 & 5.55047284176447 \tabularnewline
31 & 13 & 14.7861824051413 & -1.78618240514133 \tabularnewline
32 & 18 & 15.8030284357033 & 2.19697156429672 \tabularnewline
33 & 15 & 10.6711478525467 & 4.32885214745332 \tabularnewline
34 & 15 & 13.4630009366861 & 1.53699906331386 \tabularnewline
35 & 15 & 14.3109735749406 & 0.689026425059364 \tabularnewline
36 & 13 & 11.4619337203101 & 1.53806627968986 \tabularnewline
37 & 14 & 13.6335237257184 & 0.366476274281629 \tabularnewline
38 & 15 & 10.8402991928739 & 4.15970080712611 \tabularnewline
39 & 14 & 13.8792889543164 & 0.120711045683624 \tabularnewline
40 & 19 & 14.0623202923457 & 4.93767970765428 \tabularnewline
41 & 16 & 18.0476047005494 & -2.04760470054944 \tabularnewline
42 & 16 & 9.69846827755976 & 6.30153172244024 \tabularnewline
43 & 12 & 14.2892349908159 & -2.28923499081585 \tabularnewline
44 & 10 & 16.3015307859515 & -6.30153078595152 \tabularnewline
45 & 11 & 11.5660032182957 & -0.566003218295704 \tabularnewline
46 & 13 & 13.6060054719675 & -0.606005471967462 \tabularnewline
47 & 14 & 14.2199588566701 & -0.219958856670118 \tabularnewline
48 & 11 & 11.5706508092246 & -0.570650809224594 \tabularnewline
49 & 11 & 13.4254330351977 & -2.42543303519772 \tabularnewline
50 & 16 & 11.5117687506668 & 4.48823124933316 \tabularnewline
51 & 9 & 13.5715526726737 & -4.57155267267366 \tabularnewline
52 & 16 & 14.8456667528375 & 1.15433324716248 \tabularnewline
53 & 19 & 17.0508974890132 & 1.9491025109868 \tabularnewline
54 & 13 & 10.8019565881076 & 2.1980434118924 \tabularnewline
55 & 15 & 13.2152076721568 & 1.7847923278432 \tabularnewline
56 & 14 & 14.3114714159728 & -0.311471415972793 \tabularnewline
57 & 15 & 11.0804041901853 & 3.91959580981473 \tabularnewline
58 & 11 & 13.1961459877233 & -2.19614598772329 \tabularnewline
59 & 14 & 13.8850386979178 & 0.114961302082182 \tabularnewline
60 & 15 & 11.1637892159851 & 3.83621078401494 \tabularnewline
61 & 17 & 12.6545498009255 & 4.34545019907453 \tabularnewline
62 & 16 & 12.566973745181 & 3.43302625481903 \tabularnewline
63 & 13 & 12.4200901568178 & 0.579909843182175 \tabularnewline
64 & 15 & 15.2089621993132 & -0.208962199313234 \tabularnewline
65 & 14 & 17.6133612249509 & -3.61336122495092 \tabularnewline
66 & 15 & 11.3514532299765 & 3.64854677002346 \tabularnewline
67 & 14 & 13.7105025441549 & 0.289497455845149 \tabularnewline
68 & 12 & 14.2898711584974 & -2.28987115849743 \tabularnewline
69 & 12 & 12.0754277368542 & -0.0754277368541612 \tabularnewline
70 & 15 & 12.6422777167714 & 2.35772228322858 \tabularnewline
71 & 17 & 13.9901311804676 & 3.0098688195324 \tabularnewline
72 & 13 & 12.2482711213584 & 0.751728878641551 \tabularnewline
73 & 5 & 13.8290132781365 & -8.82901327813649 \tabularnewline
74 & 7 & 13.2950853853924 & -6.29508538539238 \tabularnewline
75 & 10 & 12.2721686566952 & -2.27216865669523 \tabularnewline
76 & 15 & 14.8007688871709 & 0.1992311128291 \tabularnewline
77 & 9 & 16.3620246109609 & -7.36202461096085 \tabularnewline
78 & 9 & 11.7851185299616 & -2.78511852996164 \tabularnewline
79 & 15 & 13.181925865951 & 1.818074134049 \tabularnewline
80 & 14 & 13.1259137671915 & 0.874086232808471 \tabularnewline
81 & 11 & 11.4784549178983 & -0.478454917898311 \tabularnewline
82 & 18 & 12.6049179733357 & 5.39508202666425 \tabularnewline
83 & 20 & 14.1400706669061 & 5.85992933309389 \tabularnewline
84 & 20 & 11.8760616716174 & 8.12393832838263 \tabularnewline
85 & 16 & 11.2341354337813 & 4.76586456621867 \tabularnewline
86 & 15 & 11.5594576461747 & 3.4405423538253 \tabularnewline
87 & 14 & 11.7082544095114 & 2.29174559048858 \tabularnewline
88 & 13 & 14.9491972872216 & -1.94919728722157 \tabularnewline
89 & 18 & 14.6574237588967 & 3.34257624110331 \tabularnewline
90 & 14 & 11.4228101997659 & 2.57718980023406 \tabularnewline
91 & 12 & 14.0859677583067 & -2.08596775830665 \tabularnewline
92 & 9 & 13.7802327618126 & -4.78023276181264 \tabularnewline
93 & 19 & 11.7456051015323 & 7.25439489846766 \tabularnewline
94 & 13 & 14.4858633970582 & -1.48586339705824 \tabularnewline
95 & 12 & 16.0580216520957 & -4.05802165209575 \tabularnewline
96 & 14 & 14.2046050475533 & -0.204605047553272 \tabularnewline
97 & 6 & 12.6156436818408 & -6.61564368184081 \tabularnewline
98 & 14 & 12.4221493002597 & 1.5778506997403 \tabularnewline
99 & 11 & 12.2531056375863 & -1.25310563758627 \tabularnewline
100 & 11 & 14.3878874446008 & -3.38788744460079 \tabularnewline
101 & 14 & 15.3503855626225 & -1.3503855626225 \tabularnewline
102 & 12 & 11.829763510136 & 0.170236489863989 \tabularnewline
103 & 19 & 13.2905258618011 & 5.70947413819887 \tabularnewline
104 & 13 & 12.4464169636503 & 0.553583036349741 \tabularnewline
105 & 14 & 13.4350107519044 & 0.564989248095555 \tabularnewline
106 & 17 & 13.9147136342548 & 3.08528636574523 \tabularnewline
107 & 12 & 14.9285677127414 & -2.92856771274142 \tabularnewline
108 & 16 & 14.0289369556653 & 1.97106304433467 \tabularnewline
109 & 15 & 10.9089555552014 & 4.09104444479855 \tabularnewline
110 & 15 & 12.9089073151198 & 2.09109268488019 \tabularnewline
111 & 15 & 12.0709638330102 & 2.92903616698975 \tabularnewline
112 & 16 & 13.7747368122106 & 2.22526318778937 \tabularnewline
113 & 15 & 15.3569723154454 & -0.356972315445368 \tabularnewline
114 & 12 & 12.2534180636276 & -0.253418063627588 \tabularnewline
115 & 13 & 15.0876934318275 & -2.08769343182751 \tabularnewline
116 & 14 & 12.870677928931 & 1.12932207106899 \tabularnewline
117 & 17 & 13.8898142213446 & 3.11018577865537 \tabularnewline
118 & 14 & 15.0494036653355 & -1.04940366533549 \tabularnewline
119 & 14 & 14.5412360234008 & -0.541236023400812 \tabularnewline
120 & 14 & 14.8971056856367 & -0.897105685636728 \tabularnewline
121 & 15 & 12.2612836481967 & 2.7387163518033 \tabularnewline
122 & 11 & 13.7633117094692 & -2.76331170946922 \tabularnewline
123 & 11 & 13.0540789190033 & -2.05407891900328 \tabularnewline
124 & 16 & 14.5008336648073 & 1.49916633519268 \tabularnewline
125 & 12 & 15.4382731472036 & -3.43827314720357 \tabularnewline
126 & 12 & 12.3013431732901 & -0.301343173290089 \tabularnewline
127 & 19 & 14.680312439247 & 4.31968756075303 \tabularnewline
128 & 18 & 13.3592176301128 & 4.64078236988721 \tabularnewline
129 & 16 & 14.9287546049759 & 1.07124539502412 \tabularnewline
130 & 16 & 15.0432400697172 & 0.956759930282779 \tabularnewline
131 & 13 & 14.7005385026557 & -1.70053850265568 \tabularnewline
132 & 11 & 14.9558777656577 & -3.95587776565768 \tabularnewline
133 & 10 & 13.1574439131552 & -3.15744391315517 \tabularnewline
134 & 14 & 13.2098580388694 & 0.790141961130592 \tabularnewline
135 & 14 & 12.7317737942372 & 1.26822620576283 \tabularnewline
136 & 14 & 15.1048271153939 & -1.10482711539392 \tabularnewline
137 & 16 & 14.7921971321545 & 1.20780286784554 \tabularnewline
138 & 10 & 12.5052304991545 & -2.50523049915448 \tabularnewline
139 & 16 & 15.9776887676703 & 0.0223112323296935 \tabularnewline
140 & 7 & 14.6589056288409 & -7.65890562884091 \tabularnewline
141 & 16 & 15.1282189260768 & 0.871781073923174 \tabularnewline
142 & 15 & 15.189719186919 & -0.189719186919048 \tabularnewline
143 & 17 & 14.1556821223832 & 2.84431787761676 \tabularnewline
144 & 11 & 13.9204012890286 & -2.92040128902857 \tabularnewline
145 & 11 & 12.3190852496575 & -1.31908524965753 \tabularnewline
146 & 10 & 13.3535484363829 & -3.35354843638295 \tabularnewline
147 & 13 & 12.903671551669 & 0.0963284483310289 \tabularnewline
148 & 14 & 14.6573920095614 & -0.657392009561409 \tabularnewline
149 & 13 & 14.8971948239935 & -1.89719482399345 \tabularnewline
150 & 13 & 11.6273390581299 & 1.37266094187005 \tabularnewline
151 & 12 & 15.7636825021564 & -3.76368250215643 \tabularnewline
152 & 10 & 12.4820008375213 & -2.48200083752129 \tabularnewline
153 & 15 & 15.104526703039 & -0.104526703039017 \tabularnewline
154 & 6 & 14.8725183128728 & -8.87251831287285 \tabularnewline
155 & 15 & 14.402130829601 & 0.597869170398987 \tabularnewline
156 & 15 & 12.6880060941625 & 2.31199390583747 \tabularnewline
157 & 11 & 11.5396794744113 & -0.53967947441132 \tabularnewline
158 & 14 & 12.065626200295 & 1.93437379970498 \tabularnewline
159 & 14 & 12.529705519583 & 1.47029448041705 \tabularnewline
160 & 16 & 14.107223546688 & 1.89277645331197 \tabularnewline
161 & 12 & 14.0757045237581 & -2.07570452375814 \tabularnewline
162 & 15 & 11.5890663406606 & 3.41093365933938 \tabularnewline
163 & 20 & 14.4969799324014 & 5.50302006759859 \tabularnewline
164 & 12 & 11.6889056436492 & 0.311094356350772 \tabularnewline
165 & 9 & 14.9473623575443 & -5.94736235754426 \tabularnewline
166 & 13 & 12.4764688509414 & 0.523531149058574 \tabularnewline
167 & 15 & 14.4899669565901 & 0.51003304340988 \tabularnewline
168 & 19 & 13.2062632086682 & 5.79373679133182 \tabularnewline
169 & 11 & 11.4390840527321 & -0.43908405273211 \tabularnewline
170 & 11 & 12.5893210952181 & -1.58932109521815 \tabularnewline
171 & 17 & 12.8942323629892 & 4.1057676370108 \tabularnewline
172 & 15 & 14.6367187740627 & 0.363281225937309 \tabularnewline
173 & 14 & 13.6258331561133 & 0.374166843886682 \tabularnewline
174 & 15 & 12.5385517754538 & 2.46144822454622 \tabularnewline
175 & 11 & 15.9584721845036 & -4.9584721845036 \tabularnewline
176 & 12 & 11.7087212037699 & 0.291278796230076 \tabularnewline
177 & 15 & 13.4412784968206 & 1.55872150317945 \tabularnewline
178 & 16 & 12.6896183485106 & 3.31038165148935 \tabularnewline
179 & 16 & 14.7638986364735 & 1.23610136352649 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312612&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]13[/C][C]13.1097756410256[/C][C]-0.109775641025644[/C][/ROW]
[ROW][C]14[/C][C]10[/C][C]10.455229775627[/C][C]-0.455229775626988[/C][/ROW]
[ROW][C]15[/C][C]14[/C][C]14.3358634740781[/C][C]-0.335863474078065[/C][/ROW]
[ROW][C]16[/C][C]15[/C][C]15.1346911520702[/C][C]-0.134691152070177[/C][/ROW]
[ROW][C]17[/C][C]20[/C][C]20.2700508898343[/C][C]-0.270050889834337[/C][/ROW]
[ROW][C]18[/C][C]9[/C][C]9.15273600860088[/C][C]-0.152736008600877[/C][/ROW]
[ROW][C]19[/C][C]12[/C][C]16.4121790411113[/C][C]-4.41217904111132[/C][/ROW]
[ROW][C]20[/C][C]13[/C][C]17.343375230462[/C][C]-4.34337523046201[/C][/ROW]
[ROW][C]21[/C][C]16[/C][C]9.39444199089061[/C][C]6.60555800910939[/C][/ROW]
[ROW][C]22[/C][C]12[/C][C]14.3897841665352[/C][C]-2.38978416653524[/C][/ROW]
[ROW][C]23[/C][C]14[/C][C]14.7299134782797[/C][C]-0.72991347827975[/C][/ROW]
[ROW][C]24[/C][C]15[/C][C]10.5553211629674[/C][C]4.44467883703256[/C][/ROW]
[ROW][C]25[/C][C]19[/C][C]12.1559979119341[/C][C]6.84400208806588[/C][/ROW]
[ROW][C]26[/C][C]16[/C][C]9.54119931842395[/C][C]6.45880068157605[/C][/ROW]
[ROW][C]27[/C][C]16[/C][C]13.5843878353542[/C][C]2.41561216464581[/C][/ROW]
[ROW][C]28[/C][C]14[/C][C]14.4995018014177[/C][C]-0.499501801417686[/C][/ROW]
[ROW][C]29[/C][C]14[/C][C]19.6158983644909[/C][C]-5.61589836449086[/C][/ROW]
[ROW][C]30[/C][C]14[/C][C]8.44952715823553[/C][C]5.55047284176447[/C][/ROW]
[ROW][C]31[/C][C]13[/C][C]14.7861824051413[/C][C]-1.78618240514133[/C][/ROW]
[ROW][C]32[/C][C]18[/C][C]15.8030284357033[/C][C]2.19697156429672[/C][/ROW]
[ROW][C]33[/C][C]15[/C][C]10.6711478525467[/C][C]4.32885214745332[/C][/ROW]
[ROW][C]34[/C][C]15[/C][C]13.4630009366861[/C][C]1.53699906331386[/C][/ROW]
[ROW][C]35[/C][C]15[/C][C]14.3109735749406[/C][C]0.689026425059364[/C][/ROW]
[ROW][C]36[/C][C]13[/C][C]11.4619337203101[/C][C]1.53806627968986[/C][/ROW]
[ROW][C]37[/C][C]14[/C][C]13.6335237257184[/C][C]0.366476274281629[/C][/ROW]
[ROW][C]38[/C][C]15[/C][C]10.8402991928739[/C][C]4.15970080712611[/C][/ROW]
[ROW][C]39[/C][C]14[/C][C]13.8792889543164[/C][C]0.120711045683624[/C][/ROW]
[ROW][C]40[/C][C]19[/C][C]14.0623202923457[/C][C]4.93767970765428[/C][/ROW]
[ROW][C]41[/C][C]16[/C][C]18.0476047005494[/C][C]-2.04760470054944[/C][/ROW]
[ROW][C]42[/C][C]16[/C][C]9.69846827755976[/C][C]6.30153172244024[/C][/ROW]
[ROW][C]43[/C][C]12[/C][C]14.2892349908159[/C][C]-2.28923499081585[/C][/ROW]
[ROW][C]44[/C][C]10[/C][C]16.3015307859515[/C][C]-6.30153078595152[/C][/ROW]
[ROW][C]45[/C][C]11[/C][C]11.5660032182957[/C][C]-0.566003218295704[/C][/ROW]
[ROW][C]46[/C][C]13[/C][C]13.6060054719675[/C][C]-0.606005471967462[/C][/ROW]
[ROW][C]47[/C][C]14[/C][C]14.2199588566701[/C][C]-0.219958856670118[/C][/ROW]
[ROW][C]48[/C][C]11[/C][C]11.5706508092246[/C][C]-0.570650809224594[/C][/ROW]
[ROW][C]49[/C][C]11[/C][C]13.4254330351977[/C][C]-2.42543303519772[/C][/ROW]
[ROW][C]50[/C][C]16[/C][C]11.5117687506668[/C][C]4.48823124933316[/C][/ROW]
[ROW][C]51[/C][C]9[/C][C]13.5715526726737[/C][C]-4.57155267267366[/C][/ROW]
[ROW][C]52[/C][C]16[/C][C]14.8456667528375[/C][C]1.15433324716248[/C][/ROW]
[ROW][C]53[/C][C]19[/C][C]17.0508974890132[/C][C]1.9491025109868[/C][/ROW]
[ROW][C]54[/C][C]13[/C][C]10.8019565881076[/C][C]2.1980434118924[/C][/ROW]
[ROW][C]55[/C][C]15[/C][C]13.2152076721568[/C][C]1.7847923278432[/C][/ROW]
[ROW][C]56[/C][C]14[/C][C]14.3114714159728[/C][C]-0.311471415972793[/C][/ROW]
[ROW][C]57[/C][C]15[/C][C]11.0804041901853[/C][C]3.91959580981473[/C][/ROW]
[ROW][C]58[/C][C]11[/C][C]13.1961459877233[/C][C]-2.19614598772329[/C][/ROW]
[ROW][C]59[/C][C]14[/C][C]13.8850386979178[/C][C]0.114961302082182[/C][/ROW]
[ROW][C]60[/C][C]15[/C][C]11.1637892159851[/C][C]3.83621078401494[/C][/ROW]
[ROW][C]61[/C][C]17[/C][C]12.6545498009255[/C][C]4.34545019907453[/C][/ROW]
[ROW][C]62[/C][C]16[/C][C]12.566973745181[/C][C]3.43302625481903[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]12.4200901568178[/C][C]0.579909843182175[/C][/ROW]
[ROW][C]64[/C][C]15[/C][C]15.2089621993132[/C][C]-0.208962199313234[/C][/ROW]
[ROW][C]65[/C][C]14[/C][C]17.6133612249509[/C][C]-3.61336122495092[/C][/ROW]
[ROW][C]66[/C][C]15[/C][C]11.3514532299765[/C][C]3.64854677002346[/C][/ROW]
[ROW][C]67[/C][C]14[/C][C]13.7105025441549[/C][C]0.289497455845149[/C][/ROW]
[ROW][C]68[/C][C]12[/C][C]14.2898711584974[/C][C]-2.28987115849743[/C][/ROW]
[ROW][C]69[/C][C]12[/C][C]12.0754277368542[/C][C]-0.0754277368541612[/C][/ROW]
[ROW][C]70[/C][C]15[/C][C]12.6422777167714[/C][C]2.35772228322858[/C][/ROW]
[ROW][C]71[/C][C]17[/C][C]13.9901311804676[/C][C]3.0098688195324[/C][/ROW]
[ROW][C]72[/C][C]13[/C][C]12.2482711213584[/C][C]0.751728878641551[/C][/ROW]
[ROW][C]73[/C][C]5[/C][C]13.8290132781365[/C][C]-8.82901327813649[/C][/ROW]
[ROW][C]74[/C][C]7[/C][C]13.2950853853924[/C][C]-6.29508538539238[/C][/ROW]
[ROW][C]75[/C][C]10[/C][C]12.2721686566952[/C][C]-2.27216865669523[/C][/ROW]
[ROW][C]76[/C][C]15[/C][C]14.8007688871709[/C][C]0.1992311128291[/C][/ROW]
[ROW][C]77[/C][C]9[/C][C]16.3620246109609[/C][C]-7.36202461096085[/C][/ROW]
[ROW][C]78[/C][C]9[/C][C]11.7851185299616[/C][C]-2.78511852996164[/C][/ROW]
[ROW][C]79[/C][C]15[/C][C]13.181925865951[/C][C]1.818074134049[/C][/ROW]
[ROW][C]80[/C][C]14[/C][C]13.1259137671915[/C][C]0.874086232808471[/C][/ROW]
[ROW][C]81[/C][C]11[/C][C]11.4784549178983[/C][C]-0.478454917898311[/C][/ROW]
[ROW][C]82[/C][C]18[/C][C]12.6049179733357[/C][C]5.39508202666425[/C][/ROW]
[ROW][C]83[/C][C]20[/C][C]14.1400706669061[/C][C]5.85992933309389[/C][/ROW]
[ROW][C]84[/C][C]20[/C][C]11.8760616716174[/C][C]8.12393832838263[/C][/ROW]
[ROW][C]85[/C][C]16[/C][C]11.2341354337813[/C][C]4.76586456621867[/C][/ROW]
[ROW][C]86[/C][C]15[/C][C]11.5594576461747[/C][C]3.4405423538253[/C][/ROW]
[ROW][C]87[/C][C]14[/C][C]11.7082544095114[/C][C]2.29174559048858[/C][/ROW]
[ROW][C]88[/C][C]13[/C][C]14.9491972872216[/C][C]-1.94919728722157[/C][/ROW]
[ROW][C]89[/C][C]18[/C][C]14.6574237588967[/C][C]3.34257624110331[/C][/ROW]
[ROW][C]90[/C][C]14[/C][C]11.4228101997659[/C][C]2.57718980023406[/C][/ROW]
[ROW][C]91[/C][C]12[/C][C]14.0859677583067[/C][C]-2.08596775830665[/C][/ROW]
[ROW][C]92[/C][C]9[/C][C]13.7802327618126[/C][C]-4.78023276181264[/C][/ROW]
[ROW][C]93[/C][C]19[/C][C]11.7456051015323[/C][C]7.25439489846766[/C][/ROW]
[ROW][C]94[/C][C]13[/C][C]14.4858633970582[/C][C]-1.48586339705824[/C][/ROW]
[ROW][C]95[/C][C]12[/C][C]16.0580216520957[/C][C]-4.05802165209575[/C][/ROW]
[ROW][C]96[/C][C]14[/C][C]14.2046050475533[/C][C]-0.204605047553272[/C][/ROW]
[ROW][C]97[/C][C]6[/C][C]12.6156436818408[/C][C]-6.61564368184081[/C][/ROW]
[ROW][C]98[/C][C]14[/C][C]12.4221493002597[/C][C]1.5778506997403[/C][/ROW]
[ROW][C]99[/C][C]11[/C][C]12.2531056375863[/C][C]-1.25310563758627[/C][/ROW]
[ROW][C]100[/C][C]11[/C][C]14.3878874446008[/C][C]-3.38788744460079[/C][/ROW]
[ROW][C]101[/C][C]14[/C][C]15.3503855626225[/C][C]-1.3503855626225[/C][/ROW]
[ROW][C]102[/C][C]12[/C][C]11.829763510136[/C][C]0.170236489863989[/C][/ROW]
[ROW][C]103[/C][C]19[/C][C]13.2905258618011[/C][C]5.70947413819887[/C][/ROW]
[ROW][C]104[/C][C]13[/C][C]12.4464169636503[/C][C]0.553583036349741[/C][/ROW]
[ROW][C]105[/C][C]14[/C][C]13.4350107519044[/C][C]0.564989248095555[/C][/ROW]
[ROW][C]106[/C][C]17[/C][C]13.9147136342548[/C][C]3.08528636574523[/C][/ROW]
[ROW][C]107[/C][C]12[/C][C]14.9285677127414[/C][C]-2.92856771274142[/C][/ROW]
[ROW][C]108[/C][C]16[/C][C]14.0289369556653[/C][C]1.97106304433467[/C][/ROW]
[ROW][C]109[/C][C]15[/C][C]10.9089555552014[/C][C]4.09104444479855[/C][/ROW]
[ROW][C]110[/C][C]15[/C][C]12.9089073151198[/C][C]2.09109268488019[/C][/ROW]
[ROW][C]111[/C][C]15[/C][C]12.0709638330102[/C][C]2.92903616698975[/C][/ROW]
[ROW][C]112[/C][C]16[/C][C]13.7747368122106[/C][C]2.22526318778937[/C][/ROW]
[ROW][C]113[/C][C]15[/C][C]15.3569723154454[/C][C]-0.356972315445368[/C][/ROW]
[ROW][C]114[/C][C]12[/C][C]12.2534180636276[/C][C]-0.253418063627588[/C][/ROW]
[ROW][C]115[/C][C]13[/C][C]15.0876934318275[/C][C]-2.08769343182751[/C][/ROW]
[ROW][C]116[/C][C]14[/C][C]12.870677928931[/C][C]1.12932207106899[/C][/ROW]
[ROW][C]117[/C][C]17[/C][C]13.8898142213446[/C][C]3.11018577865537[/C][/ROW]
[ROW][C]118[/C][C]14[/C][C]15.0494036653355[/C][C]-1.04940366533549[/C][/ROW]
[ROW][C]119[/C][C]14[/C][C]14.5412360234008[/C][C]-0.541236023400812[/C][/ROW]
[ROW][C]120[/C][C]14[/C][C]14.8971056856367[/C][C]-0.897105685636728[/C][/ROW]
[ROW][C]121[/C][C]15[/C][C]12.2612836481967[/C][C]2.7387163518033[/C][/ROW]
[ROW][C]122[/C][C]11[/C][C]13.7633117094692[/C][C]-2.76331170946922[/C][/ROW]
[ROW][C]123[/C][C]11[/C][C]13.0540789190033[/C][C]-2.05407891900328[/C][/ROW]
[ROW][C]124[/C][C]16[/C][C]14.5008336648073[/C][C]1.49916633519268[/C][/ROW]
[ROW][C]125[/C][C]12[/C][C]15.4382731472036[/C][C]-3.43827314720357[/C][/ROW]
[ROW][C]126[/C][C]12[/C][C]12.3013431732901[/C][C]-0.301343173290089[/C][/ROW]
[ROW][C]127[/C][C]19[/C][C]14.680312439247[/C][C]4.31968756075303[/C][/ROW]
[ROW][C]128[/C][C]18[/C][C]13.3592176301128[/C][C]4.64078236988721[/C][/ROW]
[ROW][C]129[/C][C]16[/C][C]14.9287546049759[/C][C]1.07124539502412[/C][/ROW]
[ROW][C]130[/C][C]16[/C][C]15.0432400697172[/C][C]0.956759930282779[/C][/ROW]
[ROW][C]131[/C][C]13[/C][C]14.7005385026557[/C][C]-1.70053850265568[/C][/ROW]
[ROW][C]132[/C][C]11[/C][C]14.9558777656577[/C][C]-3.95587776565768[/C][/ROW]
[ROW][C]133[/C][C]10[/C][C]13.1574439131552[/C][C]-3.15744391315517[/C][/ROW]
[ROW][C]134[/C][C]14[/C][C]13.2098580388694[/C][C]0.790141961130592[/C][/ROW]
[ROW][C]135[/C][C]14[/C][C]12.7317737942372[/C][C]1.26822620576283[/C][/ROW]
[ROW][C]136[/C][C]14[/C][C]15.1048271153939[/C][C]-1.10482711539392[/C][/ROW]
[ROW][C]137[/C][C]16[/C][C]14.7921971321545[/C][C]1.20780286784554[/C][/ROW]
[ROW][C]138[/C][C]10[/C][C]12.5052304991545[/C][C]-2.50523049915448[/C][/ROW]
[ROW][C]139[/C][C]16[/C][C]15.9776887676703[/C][C]0.0223112323296935[/C][/ROW]
[ROW][C]140[/C][C]7[/C][C]14.6589056288409[/C][C]-7.65890562884091[/C][/ROW]
[ROW][C]141[/C][C]16[/C][C]15.1282189260768[/C][C]0.871781073923174[/C][/ROW]
[ROW][C]142[/C][C]15[/C][C]15.189719186919[/C][C]-0.189719186919048[/C][/ROW]
[ROW][C]143[/C][C]17[/C][C]14.1556821223832[/C][C]2.84431787761676[/C][/ROW]
[ROW][C]144[/C][C]11[/C][C]13.9204012890286[/C][C]-2.92040128902857[/C][/ROW]
[ROW][C]145[/C][C]11[/C][C]12.3190852496575[/C][C]-1.31908524965753[/C][/ROW]
[ROW][C]146[/C][C]10[/C][C]13.3535484363829[/C][C]-3.35354843638295[/C][/ROW]
[ROW][C]147[/C][C]13[/C][C]12.903671551669[/C][C]0.0963284483310289[/C][/ROW]
[ROW][C]148[/C][C]14[/C][C]14.6573920095614[/C][C]-0.657392009561409[/C][/ROW]
[ROW][C]149[/C][C]13[/C][C]14.8971948239935[/C][C]-1.89719482399345[/C][/ROW]
[ROW][C]150[/C][C]13[/C][C]11.6273390581299[/C][C]1.37266094187005[/C][/ROW]
[ROW][C]151[/C][C]12[/C][C]15.7636825021564[/C][C]-3.76368250215643[/C][/ROW]
[ROW][C]152[/C][C]10[/C][C]12.4820008375213[/C][C]-2.48200083752129[/C][/ROW]
[ROW][C]153[/C][C]15[/C][C]15.104526703039[/C][C]-0.104526703039017[/C][/ROW]
[ROW][C]154[/C][C]6[/C][C]14.8725183128728[/C][C]-8.87251831287285[/C][/ROW]
[ROW][C]155[/C][C]15[/C][C]14.402130829601[/C][C]0.597869170398987[/C][/ROW]
[ROW][C]156[/C][C]15[/C][C]12.6880060941625[/C][C]2.31199390583747[/C][/ROW]
[ROW][C]157[/C][C]11[/C][C]11.5396794744113[/C][C]-0.53967947441132[/C][/ROW]
[ROW][C]158[/C][C]14[/C][C]12.065626200295[/C][C]1.93437379970498[/C][/ROW]
[ROW][C]159[/C][C]14[/C][C]12.529705519583[/C][C]1.47029448041705[/C][/ROW]
[ROW][C]160[/C][C]16[/C][C]14.107223546688[/C][C]1.89277645331197[/C][/ROW]
[ROW][C]161[/C][C]12[/C][C]14.0757045237581[/C][C]-2.07570452375814[/C][/ROW]
[ROW][C]162[/C][C]15[/C][C]11.5890663406606[/C][C]3.41093365933938[/C][/ROW]
[ROW][C]163[/C][C]20[/C][C]14.4969799324014[/C][C]5.50302006759859[/C][/ROW]
[ROW][C]164[/C][C]12[/C][C]11.6889056436492[/C][C]0.311094356350772[/C][/ROW]
[ROW][C]165[/C][C]9[/C][C]14.9473623575443[/C][C]-5.94736235754426[/C][/ROW]
[ROW][C]166[/C][C]13[/C][C]12.4764688509414[/C][C]0.523531149058574[/C][/ROW]
[ROW][C]167[/C][C]15[/C][C]14.4899669565901[/C][C]0.51003304340988[/C][/ROW]
[ROW][C]168[/C][C]19[/C][C]13.2062632086682[/C][C]5.79373679133182[/C][/ROW]
[ROW][C]169[/C][C]11[/C][C]11.4390840527321[/C][C]-0.43908405273211[/C][/ROW]
[ROW][C]170[/C][C]11[/C][C]12.5893210952181[/C][C]-1.58932109521815[/C][/ROW]
[ROW][C]171[/C][C]17[/C][C]12.8942323629892[/C][C]4.1057676370108[/C][/ROW]
[ROW][C]172[/C][C]15[/C][C]14.6367187740627[/C][C]0.363281225937309[/C][/ROW]
[ROW][C]173[/C][C]14[/C][C]13.6258331561133[/C][C]0.374166843886682[/C][/ROW]
[ROW][C]174[/C][C]15[/C][C]12.5385517754538[/C][C]2.46144822454622[/C][/ROW]
[ROW][C]175[/C][C]11[/C][C]15.9584721845036[/C][C]-4.9584721845036[/C][/ROW]
[ROW][C]176[/C][C]12[/C][C]11.7087212037699[/C][C]0.291278796230076[/C][/ROW]
[ROW][C]177[/C][C]15[/C][C]13.4412784968206[/C][C]1.55872150317945[/C][/ROW]
[ROW][C]178[/C][C]16[/C][C]12.6896183485106[/C][C]3.31038165148935[/C][/ROW]
[ROW][C]179[/C][C]16[/C][C]14.7638986364735[/C][C]1.23610136352649[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=312612&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312612&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
131313.1097756410256-0.109775641025644
141010.455229775627-0.455229775626988
151414.3358634740781-0.335863474078065
161515.1346911520702-0.134691152070177
172020.2700508898343-0.270050889834337
1899.15273600860088-0.152736008600877
191216.4121790411113-4.41217904111132
201317.343375230462-4.34337523046201
21169.394441990890616.60555800910939
221214.3897841665352-2.38978416653524
231414.7299134782797-0.72991347827975
241510.55532116296744.44467883703256
251912.15599791193416.84400208806588
26169.541199318423956.45880068157605
271613.58438783535422.41561216464581
281414.4995018014177-0.499501801417686
291419.6158983644909-5.61589836449086
30148.449527158235535.55047284176447
311314.7861824051413-1.78618240514133
321815.80302843570332.19697156429672
331510.67114785254674.32885214745332
341513.46300093668611.53699906331386
351514.31097357494060.689026425059364
361311.46193372031011.53806627968986
371413.63352372571840.366476274281629
381510.84029919287394.15970080712611
391413.87928895431640.120711045683624
401914.06232029234574.93767970765428
411618.0476047005494-2.04760470054944
42169.698468277559766.30153172244024
431214.2892349908159-2.28923499081585
441016.3015307859515-6.30153078595152
451111.5660032182957-0.566003218295704
461313.6060054719675-0.606005471967462
471414.2199588566701-0.219958856670118
481111.5706508092246-0.570650809224594
491113.4254330351977-2.42543303519772
501611.51176875066684.48823124933316
51913.5715526726737-4.57155267267366
521614.84566675283751.15433324716248
531917.05089748901321.9491025109868
541310.80195658810762.1980434118924
551513.21520767215681.7847923278432
561414.3114714159728-0.311471415972793
571511.08040419018533.91959580981473
581113.1961459877233-2.19614598772329
591413.88503869791780.114961302082182
601511.16378921598513.83621078401494
611712.65454980092554.34545019907453
621612.5669737451813.43302625481903
631312.42009015681780.579909843182175
641515.2089621993132-0.208962199313234
651417.6133612249509-3.61336122495092
661511.35145322997653.64854677002346
671413.71050254415490.289497455845149
681214.2898711584974-2.28987115849743
691212.0754277368542-0.0754277368541612
701512.64227771677142.35772228322858
711713.99013118046763.0098688195324
721312.24827112135840.751728878641551
73513.8290132781365-8.82901327813649
74713.2950853853924-6.29508538539238
751012.2721686566952-2.27216865669523
761514.80076888717090.1992311128291
77916.3620246109609-7.36202461096085
78911.7851185299616-2.78511852996164
791513.1819258659511.818074134049
801413.12591376719150.874086232808471
811111.4784549178983-0.478454917898311
821812.60491797333575.39508202666425
832014.14007066690615.85992933309389
842011.87606167161748.12393832838263
851611.23413543378134.76586456621867
861511.55945764617473.4405423538253
871411.70825440951142.29174559048858
881314.9491972872216-1.94919728722157
891814.65742375889673.34257624110331
901411.42281019976592.57718980023406
911214.0859677583067-2.08596775830665
92913.7802327618126-4.78023276181264
931911.74560510153237.25439489846766
941314.4858633970582-1.48586339705824
951216.0580216520957-4.05802165209575
961414.2046050475533-0.204605047553272
97612.6156436818408-6.61564368184081
981412.42214930025971.5778506997403
991112.2531056375863-1.25310563758627
1001114.3878874446008-3.38788744460079
1011415.3503855626225-1.3503855626225
1021211.8297635101360.170236489863989
1031913.29052586180115.70947413819887
1041312.44641696365030.553583036349741
1051413.43501075190440.564989248095555
1061713.91471363425483.08528636574523
1071214.9285677127414-2.92856771274142
1081614.02893695566531.97106304433467
1091510.90895555520144.09104444479855
1101512.90890731511982.09109268488019
1111512.07096383301022.92903616698975
1121613.77473681221062.22526318778937
1131515.3569723154454-0.356972315445368
1141212.2534180636276-0.253418063627588
1151315.0876934318275-2.08769343182751
1161412.8706779289311.12932207106899
1171713.88981422134463.11018577865537
1181415.0494036653355-1.04940366533549
1191414.5412360234008-0.541236023400812
1201414.8971056856367-0.897105685636728
1211512.26128364819672.7387163518033
1221113.7633117094692-2.76331170946922
1231113.0540789190033-2.05407891900328
1241614.50083366480731.49916633519268
1251215.4382731472036-3.43827314720357
1261212.3013431732901-0.301343173290089
1271914.6803124392474.31968756075303
1281813.35921763011284.64078236988721
1291614.92875460497591.07124539502412
1301615.04324006971720.956759930282779
1311314.7005385026557-1.70053850265568
1321114.9558777656577-3.95587776565768
1331013.1574439131552-3.15744391315517
1341413.20985803886940.790141961130592
1351412.73177379423721.26822620576283
1361415.1048271153939-1.10482711539392
1371614.79219713215451.20780286784554
1381012.5052304991545-2.50523049915448
1391615.97768876767030.0223112323296935
140714.6589056288409-7.65890562884091
1411615.12821892607680.871781073923174
1421515.189719186919-0.189719186919048
1431714.15568212238322.84431787761676
1441113.9204012890286-2.92040128902857
1451112.3190852496575-1.31908524965753
1461013.3535484363829-3.35354843638295
1471312.9036715516690.0963284483310289
1481414.6573920095614-0.657392009561409
1491314.8971948239935-1.89719482399345
1501311.62733905812991.37266094187005
1511215.7636825021564-3.76368250215643
1521012.4820008375213-2.48200083752129
1531515.104526703039-0.104526703039017
154614.8725183128728-8.87251831287285
1551514.4021308296010.597869170398987
1561512.68800609416252.31199390583747
1571111.5396794744113-0.53967947441132
1581412.0656262002951.93437379970498
1591412.5297055195831.47029448041705
1601614.1072235466881.89277645331197
1611214.0757045237581-2.07570452375814
1621511.58906634066063.41093365933938
1632014.49697993240145.50302006759859
1641211.68890564364920.311094356350772
165914.9473623575443-5.94736235754426
1661312.47646885094140.523531149058574
1671514.48996695659010.51003304340988
1681913.20626320866825.79373679133182
1691111.4390840527321-0.43908405273211
1701112.5893210952181-1.58932109521815
1711712.89423236298924.1057676370108
1721514.63671877406270.363281225937309
1731413.62583315611330.374166843886682
1741512.53855177545382.46144822454622
1751115.9584721845036-4.9584721845036
1761211.70872120376990.291278796230076
1771513.44127849682061.55872150317945
1781612.68961834851063.31038165148935
1791614.76389863647351.23610136352649







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
18014.80033733142758.4543715836602321.1463030791947
18111.42367754462925.0766471625928617.7707079266656
18212.31090278522315.9626330025862818.6591725678599
18314.04548779382877.6957906447920620.3951849428653
18414.81186470441488.4605390515109321.1631903573187
18513.80369688822787.450528454123320.1568653223323
18613.22526669847556.8700281020266219.5805052949244
18714.79450408249848.4369548793054921.1520532856913
18811.91915757732925.5590443050290918.2792708496292
18913.96503194186977.6020881703982220.3279757133413
19013.62124963864427.2551960256913919.9873032515971
19115.13513123618438.7656755880585121.5045868843101

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
180 & 14.8003373314275 & 8.45437158366023 & 21.1463030791947 \tabularnewline
181 & 11.4236775446292 & 5.07664716259286 & 17.7707079266656 \tabularnewline
182 & 12.3109027852231 & 5.96263300258628 & 18.6591725678599 \tabularnewline
183 & 14.0454877938287 & 7.69579064479206 & 20.3951849428653 \tabularnewline
184 & 14.8118647044148 & 8.46053905151093 & 21.1631903573187 \tabularnewline
185 & 13.8036968882278 & 7.4505284541233 & 20.1568653223323 \tabularnewline
186 & 13.2252666984755 & 6.87002810202662 & 19.5805052949244 \tabularnewline
187 & 14.7945040824984 & 8.43695487930549 & 21.1520532856913 \tabularnewline
188 & 11.9191575773292 & 5.55904430502909 & 18.2792708496292 \tabularnewline
189 & 13.9650319418697 & 7.60208817039822 & 20.3279757133413 \tabularnewline
190 & 13.6212496386442 & 7.25519602569139 & 19.9873032515971 \tabularnewline
191 & 15.1351312361843 & 8.76567558805851 & 21.5045868843101 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312612&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]180[/C][C]14.8003373314275[/C][C]8.45437158366023[/C][C]21.1463030791947[/C][/ROW]
[ROW][C]181[/C][C]11.4236775446292[/C][C]5.07664716259286[/C][C]17.7707079266656[/C][/ROW]
[ROW][C]182[/C][C]12.3109027852231[/C][C]5.96263300258628[/C][C]18.6591725678599[/C][/ROW]
[ROW][C]183[/C][C]14.0454877938287[/C][C]7.69579064479206[/C][C]20.3951849428653[/C][/ROW]
[ROW][C]184[/C][C]14.8118647044148[/C][C]8.46053905151093[/C][C]21.1631903573187[/C][/ROW]
[ROW][C]185[/C][C]13.8036968882278[/C][C]7.4505284541233[/C][C]20.1568653223323[/C][/ROW]
[ROW][C]186[/C][C]13.2252666984755[/C][C]6.87002810202662[/C][C]19.5805052949244[/C][/ROW]
[ROW][C]187[/C][C]14.7945040824984[/C][C]8.43695487930549[/C][C]21.1520532856913[/C][/ROW]
[ROW][C]188[/C][C]11.9191575773292[/C][C]5.55904430502909[/C][C]18.2792708496292[/C][/ROW]
[ROW][C]189[/C][C]13.9650319418697[/C][C]7.60208817039822[/C][C]20.3279757133413[/C][/ROW]
[ROW][C]190[/C][C]13.6212496386442[/C][C]7.25519602569139[/C][C]19.9873032515971[/C][/ROW]
[ROW][C]191[/C][C]15.1351312361843[/C][C]8.76567558805851[/C][C]21.5045868843101[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=312612&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312612&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
18014.80033733142758.4543715836602321.1463030791947
18111.42367754462925.0766471625928617.7707079266656
18212.31090278522315.9626330025862818.6591725678599
18314.04548779382877.6957906447920620.3951849428653
18414.81186470441488.4605390515109321.1631903573187
18513.80369688822787.450528454123320.1568653223323
18613.22526669847556.8700281020266219.5805052949244
18714.79450408249848.4369548793054921.1520532856913
18811.91915757732925.5590443050290918.2792708496292
18913.96503194186977.6020881703982220.3279757133413
19013.62124963864427.2551960256913919.9873032515971
19115.13513123618438.7656755880585121.5045868843101



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')