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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 computationThu, 01 Feb 2018 11:33:32 +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/Feb/01/t1517481226nfsr7gys071tl9c.htm/, Retrieved Sun, 28 Apr 2024 21:57:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=314764, Retrieved Sun, 28 Apr 2024 21:57:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact50
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2018-02-01 10:33:32] [473d63f6f39e594d120533dcf5adfbd0] [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=314764&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=314764&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314764&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
alpha0.419164436062564
beta0.260271577054952
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.419164436062564 \tabularnewline
beta & 0.260271577054952 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314764&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]0.419164436062564[/C][/ROW]
[ROW][C]beta[/C][C]0.260271577054952[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=314764&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314764&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
alpha0.419164436062564
beta0.260271577054952
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31420-6
41421.8304338507085-7.83043385070849
5822.039341306547-14.039341306547
61918.11405132427950.885948675720542
71720.5415660788894-3.54156607888944
81820.7268513299395-2.72685132993947
91020.9561458509711-10.9561458509711
101516.5407346359534-1.54073463595344
111615.90384006011750.0961599398825239
121215.9635641974779-3.96356419747792
131313.8891850227207-0.889185022720735
141013.006469208185-3.00646920818505
151410.90826762706163.09173237293839
161511.70351272811563.29648727188443
172012.94421931736637.05578068263371
18916.5304496130603-7.53044961306027
191213.1811045475201-1.1811045475201
201312.36432464857020.635675351429764
211612.3784242838513.62157571614898
221214.0392087184312-2.0392087184312
231413.10472292274730.895277077252691
241513.49794088592131.50205911407871
251914.30936982492534.69063017507465
261616.969066106071-0.969066106070958
271617.150697180732-1.15069718073197
281417.1306578312294-3.13065783122936
291415.9391453020872-1.93914530208723
301415.0355183126016-1.03551831260165
311314.3976881050099-1.39768810500989
321813.45556619613454.54443380386553
331515.4999526923249-0.499952692324909
341515.3753686342544-0.37536863425437
351515.2620543450804-0.262054345080422
361315.1676481408923-2.16764814089234
371414.0380017699865-0.0380017699864634
381513.79688155567941.20311844432058
391414.2072509143093-0.207250914309254
401914.00383322830834.99616677169174
411616.526567934222-0.526567934222022
421616.676921896203-0.676921896203012
431216.6904029547276-4.69040295472759
441014.5098685261589-4.50986852615893
451111.9129964373034-0.912996437303434
461310.72420041224822.2757995877518
471411.1203162466142.879683753386
481112.0837225210879-1.0837225210879
491111.2675794093577-0.267579409357715
501610.7643424640035.23565753599697
51913.1390591067702-4.13905910677023
521611.13267070525534.86732929474474
531913.43244904173895.5675509582611
541316.6331362145534-3.63313621455337
551515.5808597694632-0.580859769463158
561415.7446192397554-1.74461923975541
571515.2302401201242-0.230240120124211
581115.3255164584432-4.32551645844324
591413.23229950939230.767700490607723
601513.35773147529481.64226852470519
611714.02891715197892.97108284802112
621615.58122953894630.418770461053683
631316.1093897723743-3.10938977237432
641514.81944689374330.180553106256719
651414.928228794505-0.928228794505019
661514.47098215999320.52901784000681
671414.6822755310099-0.682275531009903
681214.31140386619-2.31140386618998
691213.0054932642956-1.00549326429557
701512.13727805817692.86272194182314
711713.20279429609083.79720570390924
721315.074275082491-2.07427508249099
73514.2583436004348-9.25834360043484
7479.421052384495-2.421052384495
75107.185581928778752.81441807122125
76157.451677905236797.54832209476321
77910.5255542839455-1.52555428394553
7899.62955161903418-0.629551619034183
79159.040439471748635.95956052825137
801411.86341652632772.1365834736723
811113.3170315284495-2.31703152844946
821812.65106927382645.34893072617365
832015.78195586059584.21804413940419
842018.89898923606981.1010107639302
851620.8295895931232-4.82958959312321
861519.7474014459927-4.7474014459927
871418.1817383436913-4.1817383436913
881316.3969677080357-3.39696770803566
891814.57054742403693.42945257596311
901415.9796613262618-1.97966132626183
911214.9054927523497-2.90549275234972
92913.1262692227118-4.12626922271177
931910.38517771556798.61482228443208
941313.924546369354-0.924546369354042
951213.3644860858812-1.36448608588116
961412.47115794176761.52884205823245
97612.957401510922-6.95740151092199
98149.127484808234044.87251519176596
991110.78782325528750.21217674471246
1001110.51786132439610.482138675603904
1011410.41365751887143.58634248112861
1021212.0018832819418-0.00188328194178311
1031912.0858469569346.91415304306603
1041315.8230776094597-2.82307760945973
1051415.1708193295441-1.17081932954406
1061715.08339656478191.91660343521808
1071216.4992065189998-4.49920651899978
1081614.73488902825661.26511097174335
1091515.5247877193016-0.524787719301571
1101515.5071719848754-0.507171984875441
1111515.4416094063412-0.441609406341216
1121615.35535024924270.644649750757267
1131515.7947413879381-0.794741387938092
1141215.5440873772912-3.54408737729116
1151313.754357462136-0.754357462135976
1161413.05168528776420.948314712235778
1171713.16617063539463.83382936460545
1181414.9084188108296-0.908418810829607
1191414.5637798106589-0.563779810658856
1201414.3020947684517-0.302094768451743
1211514.11714128064910.882858719350873
1221114.5251950280123-3.52519502801227
1231112.7009626597494-1.70096265974938
1241611.45581439948874.54418560051127
1251213.3241653358451-1.32416533584514
1261212.588250340173-0.588250340172957
1271912.0966286331676.903371366833
1281815.49836258164692.50163741835307
1291617.32796631072-1.32796631072
1301617.4074597577865-1.40745975778649
1311317.3000833204677-4.30008332046767
1321115.5110975368543-4.51109753685428
1331013.1415167451258-3.14151674512583
1341411.00328675299222.99671324700775
1351411.7649156668522.23508433314803
1361412.45113690301481.54886309698523
1371613.01869428213652.9813057178635
1381014.5119309486772-4.51193094867719
1391612.37203301811493.62796698188513
140714.0398896352965-7.03988963529646
1411610.46813220466535.53186779533474
1421512.76951629403062.2304837059694
1431713.93041574708963.06958425291039
1441115.777917478793-4.77791747879305
1451113.8147710740303-2.81477107403033
1461012.3674239024441-2.36742390244414
1471310.8493108837142.150689116286
1481411.45966300674452.54033699325548
1491312.51048376280370.489516237196289
1501312.75507794483370.244922055166251
1511212.9238671052342-0.923867105234244
1521012.501950666636-2.50195066663596
1531511.14560343883883.85439656116116
154612.8741124289789-6.87411242897887
155159.355669781312395.64433021868761
1561511.70029025946543.29970974053461
1571113.422116293899-2.42211629389897
1581412.4813117199731.51868828002705
1591413.35803598374030.641964016259713
1601613.93730470022192.06269529977807
1611215.3371264649355-3.33712646493548
1621514.10946587102130.890534128978727
1632014.75104448151785.24895551848217
1641217.7921614777995-5.79216147779954
165915.5733298357152-6.57332983571524
1661312.30993233715430.690067662845726
1671512.16637678304692.83362321695313
1681913.23046211091465.76953788908542
1691116.1546153594177-5.15461535941766
1701113.9374011196626-2.9374011196626
1711712.3291037941954.67089620580497
1721514.4195129693360.580487030664036
1731414.8586972442131-0.858697244213134
1741514.60094571394910.39905428605093
1751114.9139343559369-3.91393435593687
1761212.992074658966-0.992074658966024
1771512.18672267298262.81327732701742
1781613.28335786600392.71664213399612
1791614.63586341270051.36413658729949

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 14 & 20 & -6 \tabularnewline
4 & 14 & 21.8304338507085 & -7.83043385070849 \tabularnewline
5 & 8 & 22.039341306547 & -14.039341306547 \tabularnewline
6 & 19 & 18.1140513242795 & 0.885948675720542 \tabularnewline
7 & 17 & 20.5415660788894 & -3.54156607888944 \tabularnewline
8 & 18 & 20.7268513299395 & -2.72685132993947 \tabularnewline
9 & 10 & 20.9561458509711 & -10.9561458509711 \tabularnewline
10 & 15 & 16.5407346359534 & -1.54073463595344 \tabularnewline
11 & 16 & 15.9038400601175 & 0.0961599398825239 \tabularnewline
12 & 12 & 15.9635641974779 & -3.96356419747792 \tabularnewline
13 & 13 & 13.8891850227207 & -0.889185022720735 \tabularnewline
14 & 10 & 13.006469208185 & -3.00646920818505 \tabularnewline
15 & 14 & 10.9082676270616 & 3.09173237293839 \tabularnewline
16 & 15 & 11.7035127281156 & 3.29648727188443 \tabularnewline
17 & 20 & 12.9442193173663 & 7.05578068263371 \tabularnewline
18 & 9 & 16.5304496130603 & -7.53044961306027 \tabularnewline
19 & 12 & 13.1811045475201 & -1.1811045475201 \tabularnewline
20 & 13 & 12.3643246485702 & 0.635675351429764 \tabularnewline
21 & 16 & 12.378424283851 & 3.62157571614898 \tabularnewline
22 & 12 & 14.0392087184312 & -2.0392087184312 \tabularnewline
23 & 14 & 13.1047229227473 & 0.895277077252691 \tabularnewline
24 & 15 & 13.4979408859213 & 1.50205911407871 \tabularnewline
25 & 19 & 14.3093698249253 & 4.69063017507465 \tabularnewline
26 & 16 & 16.969066106071 & -0.969066106070958 \tabularnewline
27 & 16 & 17.150697180732 & -1.15069718073197 \tabularnewline
28 & 14 & 17.1306578312294 & -3.13065783122936 \tabularnewline
29 & 14 & 15.9391453020872 & -1.93914530208723 \tabularnewline
30 & 14 & 15.0355183126016 & -1.03551831260165 \tabularnewline
31 & 13 & 14.3976881050099 & -1.39768810500989 \tabularnewline
32 & 18 & 13.4555661961345 & 4.54443380386553 \tabularnewline
33 & 15 & 15.4999526923249 & -0.499952692324909 \tabularnewline
34 & 15 & 15.3753686342544 & -0.37536863425437 \tabularnewline
35 & 15 & 15.2620543450804 & -0.262054345080422 \tabularnewline
36 & 13 & 15.1676481408923 & -2.16764814089234 \tabularnewline
37 & 14 & 14.0380017699865 & -0.0380017699864634 \tabularnewline
38 & 15 & 13.7968815556794 & 1.20311844432058 \tabularnewline
39 & 14 & 14.2072509143093 & -0.207250914309254 \tabularnewline
40 & 19 & 14.0038332283083 & 4.99616677169174 \tabularnewline
41 & 16 & 16.526567934222 & -0.526567934222022 \tabularnewline
42 & 16 & 16.676921896203 & -0.676921896203012 \tabularnewline
43 & 12 & 16.6904029547276 & -4.69040295472759 \tabularnewline
44 & 10 & 14.5098685261589 & -4.50986852615893 \tabularnewline
45 & 11 & 11.9129964373034 & -0.912996437303434 \tabularnewline
46 & 13 & 10.7242004122482 & 2.2757995877518 \tabularnewline
47 & 14 & 11.120316246614 & 2.879683753386 \tabularnewline
48 & 11 & 12.0837225210879 & -1.0837225210879 \tabularnewline
49 & 11 & 11.2675794093577 & -0.267579409357715 \tabularnewline
50 & 16 & 10.764342464003 & 5.23565753599697 \tabularnewline
51 & 9 & 13.1390591067702 & -4.13905910677023 \tabularnewline
52 & 16 & 11.1326707052553 & 4.86732929474474 \tabularnewline
53 & 19 & 13.4324490417389 & 5.5675509582611 \tabularnewline
54 & 13 & 16.6331362145534 & -3.63313621455337 \tabularnewline
55 & 15 & 15.5808597694632 & -0.580859769463158 \tabularnewline
56 & 14 & 15.7446192397554 & -1.74461923975541 \tabularnewline
57 & 15 & 15.2302401201242 & -0.230240120124211 \tabularnewline
58 & 11 & 15.3255164584432 & -4.32551645844324 \tabularnewline
59 & 14 & 13.2322995093923 & 0.767700490607723 \tabularnewline
60 & 15 & 13.3577314752948 & 1.64226852470519 \tabularnewline
61 & 17 & 14.0289171519789 & 2.97108284802112 \tabularnewline
62 & 16 & 15.5812295389463 & 0.418770461053683 \tabularnewline
63 & 13 & 16.1093897723743 & -3.10938977237432 \tabularnewline
64 & 15 & 14.8194468937433 & 0.180553106256719 \tabularnewline
65 & 14 & 14.928228794505 & -0.928228794505019 \tabularnewline
66 & 15 & 14.4709821599932 & 0.52901784000681 \tabularnewline
67 & 14 & 14.6822755310099 & -0.682275531009903 \tabularnewline
68 & 12 & 14.31140386619 & -2.31140386618998 \tabularnewline
69 & 12 & 13.0054932642956 & -1.00549326429557 \tabularnewline
70 & 15 & 12.1372780581769 & 2.86272194182314 \tabularnewline
71 & 17 & 13.2027942960908 & 3.79720570390924 \tabularnewline
72 & 13 & 15.074275082491 & -2.07427508249099 \tabularnewline
73 & 5 & 14.2583436004348 & -9.25834360043484 \tabularnewline
74 & 7 & 9.421052384495 & -2.421052384495 \tabularnewline
75 & 10 & 7.18558192877875 & 2.81441807122125 \tabularnewline
76 & 15 & 7.45167790523679 & 7.54832209476321 \tabularnewline
77 & 9 & 10.5255542839455 & -1.52555428394553 \tabularnewline
78 & 9 & 9.62955161903418 & -0.629551619034183 \tabularnewline
79 & 15 & 9.04043947174863 & 5.95956052825137 \tabularnewline
80 & 14 & 11.8634165263277 & 2.1365834736723 \tabularnewline
81 & 11 & 13.3170315284495 & -2.31703152844946 \tabularnewline
82 & 18 & 12.6510692738264 & 5.34893072617365 \tabularnewline
83 & 20 & 15.7819558605958 & 4.21804413940419 \tabularnewline
84 & 20 & 18.8989892360698 & 1.1010107639302 \tabularnewline
85 & 16 & 20.8295895931232 & -4.82958959312321 \tabularnewline
86 & 15 & 19.7474014459927 & -4.7474014459927 \tabularnewline
87 & 14 & 18.1817383436913 & -4.1817383436913 \tabularnewline
88 & 13 & 16.3969677080357 & -3.39696770803566 \tabularnewline
89 & 18 & 14.5705474240369 & 3.42945257596311 \tabularnewline
90 & 14 & 15.9796613262618 & -1.97966132626183 \tabularnewline
91 & 12 & 14.9054927523497 & -2.90549275234972 \tabularnewline
92 & 9 & 13.1262692227118 & -4.12626922271177 \tabularnewline
93 & 19 & 10.3851777155679 & 8.61482228443208 \tabularnewline
94 & 13 & 13.924546369354 & -0.924546369354042 \tabularnewline
95 & 12 & 13.3644860858812 & -1.36448608588116 \tabularnewline
96 & 14 & 12.4711579417676 & 1.52884205823245 \tabularnewline
97 & 6 & 12.957401510922 & -6.95740151092199 \tabularnewline
98 & 14 & 9.12748480823404 & 4.87251519176596 \tabularnewline
99 & 11 & 10.7878232552875 & 0.21217674471246 \tabularnewline
100 & 11 & 10.5178613243961 & 0.482138675603904 \tabularnewline
101 & 14 & 10.4136575188714 & 3.58634248112861 \tabularnewline
102 & 12 & 12.0018832819418 & -0.00188328194178311 \tabularnewline
103 & 19 & 12.085846956934 & 6.91415304306603 \tabularnewline
104 & 13 & 15.8230776094597 & -2.82307760945973 \tabularnewline
105 & 14 & 15.1708193295441 & -1.17081932954406 \tabularnewline
106 & 17 & 15.0833965647819 & 1.91660343521808 \tabularnewline
107 & 12 & 16.4992065189998 & -4.49920651899978 \tabularnewline
108 & 16 & 14.7348890282566 & 1.26511097174335 \tabularnewline
109 & 15 & 15.5247877193016 & -0.524787719301571 \tabularnewline
110 & 15 & 15.5071719848754 & -0.507171984875441 \tabularnewline
111 & 15 & 15.4416094063412 & -0.441609406341216 \tabularnewline
112 & 16 & 15.3553502492427 & 0.644649750757267 \tabularnewline
113 & 15 & 15.7947413879381 & -0.794741387938092 \tabularnewline
114 & 12 & 15.5440873772912 & -3.54408737729116 \tabularnewline
115 & 13 & 13.754357462136 & -0.754357462135976 \tabularnewline
116 & 14 & 13.0516852877642 & 0.948314712235778 \tabularnewline
117 & 17 & 13.1661706353946 & 3.83382936460545 \tabularnewline
118 & 14 & 14.9084188108296 & -0.908418810829607 \tabularnewline
119 & 14 & 14.5637798106589 & -0.563779810658856 \tabularnewline
120 & 14 & 14.3020947684517 & -0.302094768451743 \tabularnewline
121 & 15 & 14.1171412806491 & 0.882858719350873 \tabularnewline
122 & 11 & 14.5251950280123 & -3.52519502801227 \tabularnewline
123 & 11 & 12.7009626597494 & -1.70096265974938 \tabularnewline
124 & 16 & 11.4558143994887 & 4.54418560051127 \tabularnewline
125 & 12 & 13.3241653358451 & -1.32416533584514 \tabularnewline
126 & 12 & 12.588250340173 & -0.588250340172957 \tabularnewline
127 & 19 & 12.096628633167 & 6.903371366833 \tabularnewline
128 & 18 & 15.4983625816469 & 2.50163741835307 \tabularnewline
129 & 16 & 17.32796631072 & -1.32796631072 \tabularnewline
130 & 16 & 17.4074597577865 & -1.40745975778649 \tabularnewline
131 & 13 & 17.3000833204677 & -4.30008332046767 \tabularnewline
132 & 11 & 15.5110975368543 & -4.51109753685428 \tabularnewline
133 & 10 & 13.1415167451258 & -3.14151674512583 \tabularnewline
134 & 14 & 11.0032867529922 & 2.99671324700775 \tabularnewline
135 & 14 & 11.764915666852 & 2.23508433314803 \tabularnewline
136 & 14 & 12.4511369030148 & 1.54886309698523 \tabularnewline
137 & 16 & 13.0186942821365 & 2.9813057178635 \tabularnewline
138 & 10 & 14.5119309486772 & -4.51193094867719 \tabularnewline
139 & 16 & 12.3720330181149 & 3.62796698188513 \tabularnewline
140 & 7 & 14.0398896352965 & -7.03988963529646 \tabularnewline
141 & 16 & 10.4681322046653 & 5.53186779533474 \tabularnewline
142 & 15 & 12.7695162940306 & 2.2304837059694 \tabularnewline
143 & 17 & 13.9304157470896 & 3.06958425291039 \tabularnewline
144 & 11 & 15.777917478793 & -4.77791747879305 \tabularnewline
145 & 11 & 13.8147710740303 & -2.81477107403033 \tabularnewline
146 & 10 & 12.3674239024441 & -2.36742390244414 \tabularnewline
147 & 13 & 10.849310883714 & 2.150689116286 \tabularnewline
148 & 14 & 11.4596630067445 & 2.54033699325548 \tabularnewline
149 & 13 & 12.5104837628037 & 0.489516237196289 \tabularnewline
150 & 13 & 12.7550779448337 & 0.244922055166251 \tabularnewline
151 & 12 & 12.9238671052342 & -0.923867105234244 \tabularnewline
152 & 10 & 12.501950666636 & -2.50195066663596 \tabularnewline
153 & 15 & 11.1456034388388 & 3.85439656116116 \tabularnewline
154 & 6 & 12.8741124289789 & -6.87411242897887 \tabularnewline
155 & 15 & 9.35566978131239 & 5.64433021868761 \tabularnewline
156 & 15 & 11.7002902594654 & 3.29970974053461 \tabularnewline
157 & 11 & 13.422116293899 & -2.42211629389897 \tabularnewline
158 & 14 & 12.481311719973 & 1.51868828002705 \tabularnewline
159 & 14 & 13.3580359837403 & 0.641964016259713 \tabularnewline
160 & 16 & 13.9373047002219 & 2.06269529977807 \tabularnewline
161 & 12 & 15.3371264649355 & -3.33712646493548 \tabularnewline
162 & 15 & 14.1094658710213 & 0.890534128978727 \tabularnewline
163 & 20 & 14.7510444815178 & 5.24895551848217 \tabularnewline
164 & 12 & 17.7921614777995 & -5.79216147779954 \tabularnewline
165 & 9 & 15.5733298357152 & -6.57332983571524 \tabularnewline
166 & 13 & 12.3099323371543 & 0.690067662845726 \tabularnewline
167 & 15 & 12.1663767830469 & 2.83362321695313 \tabularnewline
168 & 19 & 13.2304621109146 & 5.76953788908542 \tabularnewline
169 & 11 & 16.1546153594177 & -5.15461535941766 \tabularnewline
170 & 11 & 13.9374011196626 & -2.9374011196626 \tabularnewline
171 & 17 & 12.329103794195 & 4.67089620580497 \tabularnewline
172 & 15 & 14.419512969336 & 0.580487030664036 \tabularnewline
173 & 14 & 14.8586972442131 & -0.858697244213134 \tabularnewline
174 & 15 & 14.6009457139491 & 0.39905428605093 \tabularnewline
175 & 11 & 14.9139343559369 & -3.91393435593687 \tabularnewline
176 & 12 & 12.992074658966 & -0.992074658966024 \tabularnewline
177 & 15 & 12.1867226729826 & 2.81327732701742 \tabularnewline
178 & 16 & 13.2833578660039 & 2.71664213399612 \tabularnewline
179 & 16 & 14.6358634127005 & 1.36413658729949 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314764&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]14[/C][C]20[/C][C]-6[/C][/ROW]
[ROW][C]4[/C][C]14[/C][C]21.8304338507085[/C][C]-7.83043385070849[/C][/ROW]
[ROW][C]5[/C][C]8[/C][C]22.039341306547[/C][C]-14.039341306547[/C][/ROW]
[ROW][C]6[/C][C]19[/C][C]18.1140513242795[/C][C]0.885948675720542[/C][/ROW]
[ROW][C]7[/C][C]17[/C][C]20.5415660788894[/C][C]-3.54156607888944[/C][/ROW]
[ROW][C]8[/C][C]18[/C][C]20.7268513299395[/C][C]-2.72685132993947[/C][/ROW]
[ROW][C]9[/C][C]10[/C][C]20.9561458509711[/C][C]-10.9561458509711[/C][/ROW]
[ROW][C]10[/C][C]15[/C][C]16.5407346359534[/C][C]-1.54073463595344[/C][/ROW]
[ROW][C]11[/C][C]16[/C][C]15.9038400601175[/C][C]0.0961599398825239[/C][/ROW]
[ROW][C]12[/C][C]12[/C][C]15.9635641974779[/C][C]-3.96356419747792[/C][/ROW]
[ROW][C]13[/C][C]13[/C][C]13.8891850227207[/C][C]-0.889185022720735[/C][/ROW]
[ROW][C]14[/C][C]10[/C][C]13.006469208185[/C][C]-3.00646920818505[/C][/ROW]
[ROW][C]15[/C][C]14[/C][C]10.9082676270616[/C][C]3.09173237293839[/C][/ROW]
[ROW][C]16[/C][C]15[/C][C]11.7035127281156[/C][C]3.29648727188443[/C][/ROW]
[ROW][C]17[/C][C]20[/C][C]12.9442193173663[/C][C]7.05578068263371[/C][/ROW]
[ROW][C]18[/C][C]9[/C][C]16.5304496130603[/C][C]-7.53044961306027[/C][/ROW]
[ROW][C]19[/C][C]12[/C][C]13.1811045475201[/C][C]-1.1811045475201[/C][/ROW]
[ROW][C]20[/C][C]13[/C][C]12.3643246485702[/C][C]0.635675351429764[/C][/ROW]
[ROW][C]21[/C][C]16[/C][C]12.378424283851[/C][C]3.62157571614898[/C][/ROW]
[ROW][C]22[/C][C]12[/C][C]14.0392087184312[/C][C]-2.0392087184312[/C][/ROW]
[ROW][C]23[/C][C]14[/C][C]13.1047229227473[/C][C]0.895277077252691[/C][/ROW]
[ROW][C]24[/C][C]15[/C][C]13.4979408859213[/C][C]1.50205911407871[/C][/ROW]
[ROW][C]25[/C][C]19[/C][C]14.3093698249253[/C][C]4.69063017507465[/C][/ROW]
[ROW][C]26[/C][C]16[/C][C]16.969066106071[/C][C]-0.969066106070958[/C][/ROW]
[ROW][C]27[/C][C]16[/C][C]17.150697180732[/C][C]-1.15069718073197[/C][/ROW]
[ROW][C]28[/C][C]14[/C][C]17.1306578312294[/C][C]-3.13065783122936[/C][/ROW]
[ROW][C]29[/C][C]14[/C][C]15.9391453020872[/C][C]-1.93914530208723[/C][/ROW]
[ROW][C]30[/C][C]14[/C][C]15.0355183126016[/C][C]-1.03551831260165[/C][/ROW]
[ROW][C]31[/C][C]13[/C][C]14.3976881050099[/C][C]-1.39768810500989[/C][/ROW]
[ROW][C]32[/C][C]18[/C][C]13.4555661961345[/C][C]4.54443380386553[/C][/ROW]
[ROW][C]33[/C][C]15[/C][C]15.4999526923249[/C][C]-0.499952692324909[/C][/ROW]
[ROW][C]34[/C][C]15[/C][C]15.3753686342544[/C][C]-0.37536863425437[/C][/ROW]
[ROW][C]35[/C][C]15[/C][C]15.2620543450804[/C][C]-0.262054345080422[/C][/ROW]
[ROW][C]36[/C][C]13[/C][C]15.1676481408923[/C][C]-2.16764814089234[/C][/ROW]
[ROW][C]37[/C][C]14[/C][C]14.0380017699865[/C][C]-0.0380017699864634[/C][/ROW]
[ROW][C]38[/C][C]15[/C][C]13.7968815556794[/C][C]1.20311844432058[/C][/ROW]
[ROW][C]39[/C][C]14[/C][C]14.2072509143093[/C][C]-0.207250914309254[/C][/ROW]
[ROW][C]40[/C][C]19[/C][C]14.0038332283083[/C][C]4.99616677169174[/C][/ROW]
[ROW][C]41[/C][C]16[/C][C]16.526567934222[/C][C]-0.526567934222022[/C][/ROW]
[ROW][C]42[/C][C]16[/C][C]16.676921896203[/C][C]-0.676921896203012[/C][/ROW]
[ROW][C]43[/C][C]12[/C][C]16.6904029547276[/C][C]-4.69040295472759[/C][/ROW]
[ROW][C]44[/C][C]10[/C][C]14.5098685261589[/C][C]-4.50986852615893[/C][/ROW]
[ROW][C]45[/C][C]11[/C][C]11.9129964373034[/C][C]-0.912996437303434[/C][/ROW]
[ROW][C]46[/C][C]13[/C][C]10.7242004122482[/C][C]2.2757995877518[/C][/ROW]
[ROW][C]47[/C][C]14[/C][C]11.120316246614[/C][C]2.879683753386[/C][/ROW]
[ROW][C]48[/C][C]11[/C][C]12.0837225210879[/C][C]-1.0837225210879[/C][/ROW]
[ROW][C]49[/C][C]11[/C][C]11.2675794093577[/C][C]-0.267579409357715[/C][/ROW]
[ROW][C]50[/C][C]16[/C][C]10.764342464003[/C][C]5.23565753599697[/C][/ROW]
[ROW][C]51[/C][C]9[/C][C]13.1390591067702[/C][C]-4.13905910677023[/C][/ROW]
[ROW][C]52[/C][C]16[/C][C]11.1326707052553[/C][C]4.86732929474474[/C][/ROW]
[ROW][C]53[/C][C]19[/C][C]13.4324490417389[/C][C]5.5675509582611[/C][/ROW]
[ROW][C]54[/C][C]13[/C][C]16.6331362145534[/C][C]-3.63313621455337[/C][/ROW]
[ROW][C]55[/C][C]15[/C][C]15.5808597694632[/C][C]-0.580859769463158[/C][/ROW]
[ROW][C]56[/C][C]14[/C][C]15.7446192397554[/C][C]-1.74461923975541[/C][/ROW]
[ROW][C]57[/C][C]15[/C][C]15.2302401201242[/C][C]-0.230240120124211[/C][/ROW]
[ROW][C]58[/C][C]11[/C][C]15.3255164584432[/C][C]-4.32551645844324[/C][/ROW]
[ROW][C]59[/C][C]14[/C][C]13.2322995093923[/C][C]0.767700490607723[/C][/ROW]
[ROW][C]60[/C][C]15[/C][C]13.3577314752948[/C][C]1.64226852470519[/C][/ROW]
[ROW][C]61[/C][C]17[/C][C]14.0289171519789[/C][C]2.97108284802112[/C][/ROW]
[ROW][C]62[/C][C]16[/C][C]15.5812295389463[/C][C]0.418770461053683[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]16.1093897723743[/C][C]-3.10938977237432[/C][/ROW]
[ROW][C]64[/C][C]15[/C][C]14.8194468937433[/C][C]0.180553106256719[/C][/ROW]
[ROW][C]65[/C][C]14[/C][C]14.928228794505[/C][C]-0.928228794505019[/C][/ROW]
[ROW][C]66[/C][C]15[/C][C]14.4709821599932[/C][C]0.52901784000681[/C][/ROW]
[ROW][C]67[/C][C]14[/C][C]14.6822755310099[/C][C]-0.682275531009903[/C][/ROW]
[ROW][C]68[/C][C]12[/C][C]14.31140386619[/C][C]-2.31140386618998[/C][/ROW]
[ROW][C]69[/C][C]12[/C][C]13.0054932642956[/C][C]-1.00549326429557[/C][/ROW]
[ROW][C]70[/C][C]15[/C][C]12.1372780581769[/C][C]2.86272194182314[/C][/ROW]
[ROW][C]71[/C][C]17[/C][C]13.2027942960908[/C][C]3.79720570390924[/C][/ROW]
[ROW][C]72[/C][C]13[/C][C]15.074275082491[/C][C]-2.07427508249099[/C][/ROW]
[ROW][C]73[/C][C]5[/C][C]14.2583436004348[/C][C]-9.25834360043484[/C][/ROW]
[ROW][C]74[/C][C]7[/C][C]9.421052384495[/C][C]-2.421052384495[/C][/ROW]
[ROW][C]75[/C][C]10[/C][C]7.18558192877875[/C][C]2.81441807122125[/C][/ROW]
[ROW][C]76[/C][C]15[/C][C]7.45167790523679[/C][C]7.54832209476321[/C][/ROW]
[ROW][C]77[/C][C]9[/C][C]10.5255542839455[/C][C]-1.52555428394553[/C][/ROW]
[ROW][C]78[/C][C]9[/C][C]9.62955161903418[/C][C]-0.629551619034183[/C][/ROW]
[ROW][C]79[/C][C]15[/C][C]9.04043947174863[/C][C]5.95956052825137[/C][/ROW]
[ROW][C]80[/C][C]14[/C][C]11.8634165263277[/C][C]2.1365834736723[/C][/ROW]
[ROW][C]81[/C][C]11[/C][C]13.3170315284495[/C][C]-2.31703152844946[/C][/ROW]
[ROW][C]82[/C][C]18[/C][C]12.6510692738264[/C][C]5.34893072617365[/C][/ROW]
[ROW][C]83[/C][C]20[/C][C]15.7819558605958[/C][C]4.21804413940419[/C][/ROW]
[ROW][C]84[/C][C]20[/C][C]18.8989892360698[/C][C]1.1010107639302[/C][/ROW]
[ROW][C]85[/C][C]16[/C][C]20.8295895931232[/C][C]-4.82958959312321[/C][/ROW]
[ROW][C]86[/C][C]15[/C][C]19.7474014459927[/C][C]-4.7474014459927[/C][/ROW]
[ROW][C]87[/C][C]14[/C][C]18.1817383436913[/C][C]-4.1817383436913[/C][/ROW]
[ROW][C]88[/C][C]13[/C][C]16.3969677080357[/C][C]-3.39696770803566[/C][/ROW]
[ROW][C]89[/C][C]18[/C][C]14.5705474240369[/C][C]3.42945257596311[/C][/ROW]
[ROW][C]90[/C][C]14[/C][C]15.9796613262618[/C][C]-1.97966132626183[/C][/ROW]
[ROW][C]91[/C][C]12[/C][C]14.9054927523497[/C][C]-2.90549275234972[/C][/ROW]
[ROW][C]92[/C][C]9[/C][C]13.1262692227118[/C][C]-4.12626922271177[/C][/ROW]
[ROW][C]93[/C][C]19[/C][C]10.3851777155679[/C][C]8.61482228443208[/C][/ROW]
[ROW][C]94[/C][C]13[/C][C]13.924546369354[/C][C]-0.924546369354042[/C][/ROW]
[ROW][C]95[/C][C]12[/C][C]13.3644860858812[/C][C]-1.36448608588116[/C][/ROW]
[ROW][C]96[/C][C]14[/C][C]12.4711579417676[/C][C]1.52884205823245[/C][/ROW]
[ROW][C]97[/C][C]6[/C][C]12.957401510922[/C][C]-6.95740151092199[/C][/ROW]
[ROW][C]98[/C][C]14[/C][C]9.12748480823404[/C][C]4.87251519176596[/C][/ROW]
[ROW][C]99[/C][C]11[/C][C]10.7878232552875[/C][C]0.21217674471246[/C][/ROW]
[ROW][C]100[/C][C]11[/C][C]10.5178613243961[/C][C]0.482138675603904[/C][/ROW]
[ROW][C]101[/C][C]14[/C][C]10.4136575188714[/C][C]3.58634248112861[/C][/ROW]
[ROW][C]102[/C][C]12[/C][C]12.0018832819418[/C][C]-0.00188328194178311[/C][/ROW]
[ROW][C]103[/C][C]19[/C][C]12.085846956934[/C][C]6.91415304306603[/C][/ROW]
[ROW][C]104[/C][C]13[/C][C]15.8230776094597[/C][C]-2.82307760945973[/C][/ROW]
[ROW][C]105[/C][C]14[/C][C]15.1708193295441[/C][C]-1.17081932954406[/C][/ROW]
[ROW][C]106[/C][C]17[/C][C]15.0833965647819[/C][C]1.91660343521808[/C][/ROW]
[ROW][C]107[/C][C]12[/C][C]16.4992065189998[/C][C]-4.49920651899978[/C][/ROW]
[ROW][C]108[/C][C]16[/C][C]14.7348890282566[/C][C]1.26511097174335[/C][/ROW]
[ROW][C]109[/C][C]15[/C][C]15.5247877193016[/C][C]-0.524787719301571[/C][/ROW]
[ROW][C]110[/C][C]15[/C][C]15.5071719848754[/C][C]-0.507171984875441[/C][/ROW]
[ROW][C]111[/C][C]15[/C][C]15.4416094063412[/C][C]-0.441609406341216[/C][/ROW]
[ROW][C]112[/C][C]16[/C][C]15.3553502492427[/C][C]0.644649750757267[/C][/ROW]
[ROW][C]113[/C][C]15[/C][C]15.7947413879381[/C][C]-0.794741387938092[/C][/ROW]
[ROW][C]114[/C][C]12[/C][C]15.5440873772912[/C][C]-3.54408737729116[/C][/ROW]
[ROW][C]115[/C][C]13[/C][C]13.754357462136[/C][C]-0.754357462135976[/C][/ROW]
[ROW][C]116[/C][C]14[/C][C]13.0516852877642[/C][C]0.948314712235778[/C][/ROW]
[ROW][C]117[/C][C]17[/C][C]13.1661706353946[/C][C]3.83382936460545[/C][/ROW]
[ROW][C]118[/C][C]14[/C][C]14.9084188108296[/C][C]-0.908418810829607[/C][/ROW]
[ROW][C]119[/C][C]14[/C][C]14.5637798106589[/C][C]-0.563779810658856[/C][/ROW]
[ROW][C]120[/C][C]14[/C][C]14.3020947684517[/C][C]-0.302094768451743[/C][/ROW]
[ROW][C]121[/C][C]15[/C][C]14.1171412806491[/C][C]0.882858719350873[/C][/ROW]
[ROW][C]122[/C][C]11[/C][C]14.5251950280123[/C][C]-3.52519502801227[/C][/ROW]
[ROW][C]123[/C][C]11[/C][C]12.7009626597494[/C][C]-1.70096265974938[/C][/ROW]
[ROW][C]124[/C][C]16[/C][C]11.4558143994887[/C][C]4.54418560051127[/C][/ROW]
[ROW][C]125[/C][C]12[/C][C]13.3241653358451[/C][C]-1.32416533584514[/C][/ROW]
[ROW][C]126[/C][C]12[/C][C]12.588250340173[/C][C]-0.588250340172957[/C][/ROW]
[ROW][C]127[/C][C]19[/C][C]12.096628633167[/C][C]6.903371366833[/C][/ROW]
[ROW][C]128[/C][C]18[/C][C]15.4983625816469[/C][C]2.50163741835307[/C][/ROW]
[ROW][C]129[/C][C]16[/C][C]17.32796631072[/C][C]-1.32796631072[/C][/ROW]
[ROW][C]130[/C][C]16[/C][C]17.4074597577865[/C][C]-1.40745975778649[/C][/ROW]
[ROW][C]131[/C][C]13[/C][C]17.3000833204677[/C][C]-4.30008332046767[/C][/ROW]
[ROW][C]132[/C][C]11[/C][C]15.5110975368543[/C][C]-4.51109753685428[/C][/ROW]
[ROW][C]133[/C][C]10[/C][C]13.1415167451258[/C][C]-3.14151674512583[/C][/ROW]
[ROW][C]134[/C][C]14[/C][C]11.0032867529922[/C][C]2.99671324700775[/C][/ROW]
[ROW][C]135[/C][C]14[/C][C]11.764915666852[/C][C]2.23508433314803[/C][/ROW]
[ROW][C]136[/C][C]14[/C][C]12.4511369030148[/C][C]1.54886309698523[/C][/ROW]
[ROW][C]137[/C][C]16[/C][C]13.0186942821365[/C][C]2.9813057178635[/C][/ROW]
[ROW][C]138[/C][C]10[/C][C]14.5119309486772[/C][C]-4.51193094867719[/C][/ROW]
[ROW][C]139[/C][C]16[/C][C]12.3720330181149[/C][C]3.62796698188513[/C][/ROW]
[ROW][C]140[/C][C]7[/C][C]14.0398896352965[/C][C]-7.03988963529646[/C][/ROW]
[ROW][C]141[/C][C]16[/C][C]10.4681322046653[/C][C]5.53186779533474[/C][/ROW]
[ROW][C]142[/C][C]15[/C][C]12.7695162940306[/C][C]2.2304837059694[/C][/ROW]
[ROW][C]143[/C][C]17[/C][C]13.9304157470896[/C][C]3.06958425291039[/C][/ROW]
[ROW][C]144[/C][C]11[/C][C]15.777917478793[/C][C]-4.77791747879305[/C][/ROW]
[ROW][C]145[/C][C]11[/C][C]13.8147710740303[/C][C]-2.81477107403033[/C][/ROW]
[ROW][C]146[/C][C]10[/C][C]12.3674239024441[/C][C]-2.36742390244414[/C][/ROW]
[ROW][C]147[/C][C]13[/C][C]10.849310883714[/C][C]2.150689116286[/C][/ROW]
[ROW][C]148[/C][C]14[/C][C]11.4596630067445[/C][C]2.54033699325548[/C][/ROW]
[ROW][C]149[/C][C]13[/C][C]12.5104837628037[/C][C]0.489516237196289[/C][/ROW]
[ROW][C]150[/C][C]13[/C][C]12.7550779448337[/C][C]0.244922055166251[/C][/ROW]
[ROW][C]151[/C][C]12[/C][C]12.9238671052342[/C][C]-0.923867105234244[/C][/ROW]
[ROW][C]152[/C][C]10[/C][C]12.501950666636[/C][C]-2.50195066663596[/C][/ROW]
[ROW][C]153[/C][C]15[/C][C]11.1456034388388[/C][C]3.85439656116116[/C][/ROW]
[ROW][C]154[/C][C]6[/C][C]12.8741124289789[/C][C]-6.87411242897887[/C][/ROW]
[ROW][C]155[/C][C]15[/C][C]9.35566978131239[/C][C]5.64433021868761[/C][/ROW]
[ROW][C]156[/C][C]15[/C][C]11.7002902594654[/C][C]3.29970974053461[/C][/ROW]
[ROW][C]157[/C][C]11[/C][C]13.422116293899[/C][C]-2.42211629389897[/C][/ROW]
[ROW][C]158[/C][C]14[/C][C]12.481311719973[/C][C]1.51868828002705[/C][/ROW]
[ROW][C]159[/C][C]14[/C][C]13.3580359837403[/C][C]0.641964016259713[/C][/ROW]
[ROW][C]160[/C][C]16[/C][C]13.9373047002219[/C][C]2.06269529977807[/C][/ROW]
[ROW][C]161[/C][C]12[/C][C]15.3371264649355[/C][C]-3.33712646493548[/C][/ROW]
[ROW][C]162[/C][C]15[/C][C]14.1094658710213[/C][C]0.890534128978727[/C][/ROW]
[ROW][C]163[/C][C]20[/C][C]14.7510444815178[/C][C]5.24895551848217[/C][/ROW]
[ROW][C]164[/C][C]12[/C][C]17.7921614777995[/C][C]-5.79216147779954[/C][/ROW]
[ROW][C]165[/C][C]9[/C][C]15.5733298357152[/C][C]-6.57332983571524[/C][/ROW]
[ROW][C]166[/C][C]13[/C][C]12.3099323371543[/C][C]0.690067662845726[/C][/ROW]
[ROW][C]167[/C][C]15[/C][C]12.1663767830469[/C][C]2.83362321695313[/C][/ROW]
[ROW][C]168[/C][C]19[/C][C]13.2304621109146[/C][C]5.76953788908542[/C][/ROW]
[ROW][C]169[/C][C]11[/C][C]16.1546153594177[/C][C]-5.15461535941766[/C][/ROW]
[ROW][C]170[/C][C]11[/C][C]13.9374011196626[/C][C]-2.9374011196626[/C][/ROW]
[ROW][C]171[/C][C]17[/C][C]12.329103794195[/C][C]4.67089620580497[/C][/ROW]
[ROW][C]172[/C][C]15[/C][C]14.419512969336[/C][C]0.580487030664036[/C][/ROW]
[ROW][C]173[/C][C]14[/C][C]14.8586972442131[/C][C]-0.858697244213134[/C][/ROW]
[ROW][C]174[/C][C]15[/C][C]14.6009457139491[/C][C]0.39905428605093[/C][/ROW]
[ROW][C]175[/C][C]11[/C][C]14.9139343559369[/C][C]-3.91393435593687[/C][/ROW]
[ROW][C]176[/C][C]12[/C][C]12.992074658966[/C][C]-0.992074658966024[/C][/ROW]
[ROW][C]177[/C][C]15[/C][C]12.1867226729826[/C][C]2.81327732701742[/C][/ROW]
[ROW][C]178[/C][C]16[/C][C]13.2833578660039[/C][C]2.71664213399612[/C][/ROW]
[ROW][C]179[/C][C]16[/C][C]14.6358634127005[/C][C]1.36413658729949[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=314764&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314764&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
31420-6
41421.8304338507085-7.83043385070849
5822.039341306547-14.039341306547
61918.11405132427950.885948675720542
71720.5415660788894-3.54156607888944
81820.7268513299395-2.72685132993947
91020.9561458509711-10.9561458509711
101516.5407346359534-1.54073463595344
111615.90384006011750.0961599398825239
121215.9635641974779-3.96356419747792
131313.8891850227207-0.889185022720735
141013.006469208185-3.00646920818505
151410.90826762706163.09173237293839
161511.70351272811563.29648727188443
172012.94421931736637.05578068263371
18916.5304496130603-7.53044961306027
191213.1811045475201-1.1811045475201
201312.36432464857020.635675351429764
211612.3784242838513.62157571614898
221214.0392087184312-2.0392087184312
231413.10472292274730.895277077252691
241513.49794088592131.50205911407871
251914.30936982492534.69063017507465
261616.969066106071-0.969066106070958
271617.150697180732-1.15069718073197
281417.1306578312294-3.13065783122936
291415.9391453020872-1.93914530208723
301415.0355183126016-1.03551831260165
311314.3976881050099-1.39768810500989
321813.45556619613454.54443380386553
331515.4999526923249-0.499952692324909
341515.3753686342544-0.37536863425437
351515.2620543450804-0.262054345080422
361315.1676481408923-2.16764814089234
371414.0380017699865-0.0380017699864634
381513.79688155567941.20311844432058
391414.2072509143093-0.207250914309254
401914.00383322830834.99616677169174
411616.526567934222-0.526567934222022
421616.676921896203-0.676921896203012
431216.6904029547276-4.69040295472759
441014.5098685261589-4.50986852615893
451111.9129964373034-0.912996437303434
461310.72420041224822.2757995877518
471411.1203162466142.879683753386
481112.0837225210879-1.0837225210879
491111.2675794093577-0.267579409357715
501610.7643424640035.23565753599697
51913.1390591067702-4.13905910677023
521611.13267070525534.86732929474474
531913.43244904173895.5675509582611
541316.6331362145534-3.63313621455337
551515.5808597694632-0.580859769463158
561415.7446192397554-1.74461923975541
571515.2302401201242-0.230240120124211
581115.3255164584432-4.32551645844324
591413.23229950939230.767700490607723
601513.35773147529481.64226852470519
611714.02891715197892.97108284802112
621615.58122953894630.418770461053683
631316.1093897723743-3.10938977237432
641514.81944689374330.180553106256719
651414.928228794505-0.928228794505019
661514.47098215999320.52901784000681
671414.6822755310099-0.682275531009903
681214.31140386619-2.31140386618998
691213.0054932642956-1.00549326429557
701512.13727805817692.86272194182314
711713.20279429609083.79720570390924
721315.074275082491-2.07427508249099
73514.2583436004348-9.25834360043484
7479.421052384495-2.421052384495
75107.185581928778752.81441807122125
76157.451677905236797.54832209476321
77910.5255542839455-1.52555428394553
7899.62955161903418-0.629551619034183
79159.040439471748635.95956052825137
801411.86341652632772.1365834736723
811113.3170315284495-2.31703152844946
821812.65106927382645.34893072617365
832015.78195586059584.21804413940419
842018.89898923606981.1010107639302
851620.8295895931232-4.82958959312321
861519.7474014459927-4.7474014459927
871418.1817383436913-4.1817383436913
881316.3969677080357-3.39696770803566
891814.57054742403693.42945257596311
901415.9796613262618-1.97966132626183
911214.9054927523497-2.90549275234972
92913.1262692227118-4.12626922271177
931910.38517771556798.61482228443208
941313.924546369354-0.924546369354042
951213.3644860858812-1.36448608588116
961412.47115794176761.52884205823245
97612.957401510922-6.95740151092199
98149.127484808234044.87251519176596
991110.78782325528750.21217674471246
1001110.51786132439610.482138675603904
1011410.41365751887143.58634248112861
1021212.0018832819418-0.00188328194178311
1031912.0858469569346.91415304306603
1041315.8230776094597-2.82307760945973
1051415.1708193295441-1.17081932954406
1061715.08339656478191.91660343521808
1071216.4992065189998-4.49920651899978
1081614.73488902825661.26511097174335
1091515.5247877193016-0.524787719301571
1101515.5071719848754-0.507171984875441
1111515.4416094063412-0.441609406341216
1121615.35535024924270.644649750757267
1131515.7947413879381-0.794741387938092
1141215.5440873772912-3.54408737729116
1151313.754357462136-0.754357462135976
1161413.05168528776420.948314712235778
1171713.16617063539463.83382936460545
1181414.9084188108296-0.908418810829607
1191414.5637798106589-0.563779810658856
1201414.3020947684517-0.302094768451743
1211514.11714128064910.882858719350873
1221114.5251950280123-3.52519502801227
1231112.7009626597494-1.70096265974938
1241611.45581439948874.54418560051127
1251213.3241653358451-1.32416533584514
1261212.588250340173-0.588250340172957
1271912.0966286331676.903371366833
1281815.49836258164692.50163741835307
1291617.32796631072-1.32796631072
1301617.4074597577865-1.40745975778649
1311317.3000833204677-4.30008332046767
1321115.5110975368543-4.51109753685428
1331013.1415167451258-3.14151674512583
1341411.00328675299222.99671324700775
1351411.7649156668522.23508433314803
1361412.45113690301481.54886309698523
1371613.01869428213652.9813057178635
1381014.5119309486772-4.51193094867719
1391612.37203301811493.62796698188513
140714.0398896352965-7.03988963529646
1411610.46813220466535.53186779533474
1421512.76951629403062.2304837059694
1431713.93041574708963.06958425291039
1441115.777917478793-4.77791747879305
1451113.8147710740303-2.81477107403033
1461012.3674239024441-2.36742390244414
1471310.8493108837142.150689116286
1481411.45966300674452.54033699325548
1491312.51048376280370.489516237196289
1501312.75507794483370.244922055166251
1511212.9238671052342-0.923867105234244
1521012.501950666636-2.50195066663596
1531511.14560343883883.85439656116116
154612.8741124289789-6.87411242897887
155159.355669781312395.64433021868761
1561511.70029025946543.29970974053461
1571113.422116293899-2.42211629389897
1581412.4813117199731.51868828002705
1591413.35803598374030.641964016259713
1601613.93730470022192.06269529977807
1611215.3371264649355-3.33712646493548
1621514.10946587102130.890534128978727
1632014.75104448151785.24895551848217
1641217.7921614777995-5.79216147779954
165915.5733298357152-6.57332983571524
1661312.30993233715430.690067662845726
1671512.16637678304692.83362321695313
1681913.23046211091465.76953788908542
1691116.1546153594177-5.15461535941766
1701113.9374011196626-2.9374011196626
1711712.3291037941954.67089620580497
1721514.4195129693360.580487030664036
1731414.8586972442131-0.858697244213134
1741514.60094571394910.39905428605093
1751114.9139343559369-3.91393435593687
1761212.992074658966-0.992074658966024
1771512.18672267298262.81327732701742
1781613.28335786600392.71664213399612
1791614.63586341270051.36413658729949







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
18015.57026938300268.464605111743222.675933654262
18115.9328778099777.8966897084284723.9690659115255
18216.29548623695147.0710190710708525.5199534028319
18316.65809466392586.0174286948766627.2987606329749
18417.02070309090024.7658618364775329.2755443453228
18517.38331151787463.3417744983998631.4248485373493
18617.7459199448491.7654150399458533.7264248497521
18718.10852837182330.052550379303166736.1645063643435
18818.4711367987977-1.7845304644082438.7268040620037
18918.8337452257721-3.7361365573890241.4036270089333
19019.1963536527465-5.7944995781268244.1872068836199
19119.5589620797209-7.953280330476747.0712044899185

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
180 & 15.5702693830026 & 8.4646051117432 & 22.675933654262 \tabularnewline
181 & 15.932877809977 & 7.89668970842847 & 23.9690659115255 \tabularnewline
182 & 16.2954862369514 & 7.07101907107085 & 25.5199534028319 \tabularnewline
183 & 16.6580946639258 & 6.01742869487666 & 27.2987606329749 \tabularnewline
184 & 17.0207030909002 & 4.76586183647753 & 29.2755443453228 \tabularnewline
185 & 17.3833115178746 & 3.34177449839986 & 31.4248485373493 \tabularnewline
186 & 17.745919944849 & 1.76541503994585 & 33.7264248497521 \tabularnewline
187 & 18.1085283718233 & 0.0525503793031667 & 36.1645063643435 \tabularnewline
188 & 18.4711367987977 & -1.78453046440824 & 38.7268040620037 \tabularnewline
189 & 18.8337452257721 & -3.73613655738902 & 41.4036270089333 \tabularnewline
190 & 19.1963536527465 & -5.79449957812682 & 44.1872068836199 \tabularnewline
191 & 19.5589620797209 & -7.9532803304767 & 47.0712044899185 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314764&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]15.5702693830026[/C][C]8.4646051117432[/C][C]22.675933654262[/C][/ROW]
[ROW][C]181[/C][C]15.932877809977[/C][C]7.89668970842847[/C][C]23.9690659115255[/C][/ROW]
[ROW][C]182[/C][C]16.2954862369514[/C][C]7.07101907107085[/C][C]25.5199534028319[/C][/ROW]
[ROW][C]183[/C][C]16.6580946639258[/C][C]6.01742869487666[/C][C]27.2987606329749[/C][/ROW]
[ROW][C]184[/C][C]17.0207030909002[/C][C]4.76586183647753[/C][C]29.2755443453228[/C][/ROW]
[ROW][C]185[/C][C]17.3833115178746[/C][C]3.34177449839986[/C][C]31.4248485373493[/C][/ROW]
[ROW][C]186[/C][C]17.745919944849[/C][C]1.76541503994585[/C][C]33.7264248497521[/C][/ROW]
[ROW][C]187[/C][C]18.1085283718233[/C][C]0.0525503793031667[/C][C]36.1645063643435[/C][/ROW]
[ROW][C]188[/C][C]18.4711367987977[/C][C]-1.78453046440824[/C][C]38.7268040620037[/C][/ROW]
[ROW][C]189[/C][C]18.8337452257721[/C][C]-3.73613655738902[/C][C]41.4036270089333[/C][/ROW]
[ROW][C]190[/C][C]19.1963536527465[/C][C]-5.79449957812682[/C][C]44.1872068836199[/C][/ROW]
[ROW][C]191[/C][C]19.5589620797209[/C][C]-7.9532803304767[/C][C]47.0712044899185[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=314764&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314764&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
18015.57026938300268.464605111743222.675933654262
18115.9328778099777.8966897084284723.9690659115255
18216.29548623695147.0710190710708525.5199534028319
18316.65809466392586.0174286948766627.2987606329749
18417.02070309090024.7658618364775329.2755443453228
18517.38331151787463.3417744983998631.4248485373493
18617.7459199448491.7654150399458533.7264248497521
18718.10852837182330.052550379303166736.1645063643435
18818.4711367987977-1.7845304644082438.7268040620037
18918.8337452257721-3.7361365573890241.4036270089333
19019.1963536527465-5.7944995781268244.1872068836199
19119.5589620797209-7.953280330476747.0712044899185



Parameters (Session):
par1 = less ; par2 = 0.95 ; par3 = 20 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Single'
par1 <- '12'
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')