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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 11:41:00 +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/t151748167365ij414jru4k74l.htm/, Retrieved Mon, 29 Apr 2024 06:52:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=314846, Retrieved Mon, 29 Apr 2024 06:52:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2018-02-01 10:41:00] [735c2f340331127bedaa54429b3079f9] [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=314846&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=314846&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314846&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
alpha0.122554251846108
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.122554251846108 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314846&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]0.122554251846108[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=314846&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314846&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
alpha0.122554251846108
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
215105
31410.61277125923053.38722874076946
41411.02789054338722.97210945661283
5811.3921351942471-3.3921351942471
61910.97641460335538.0235853966447
71711.95973910876445.04026089123556
81812.5774445113995.42255548860099
91013.2420017423985-3.24200174239851
101512.84468064437512.15531935562492
111613.10882419549312.89117580450687
121213.46315008317-1.46315008317004
131313.2838348193886-0.283834819388563
141013.2490496554505-3.24904965545052
151412.85086480571591.14913519428407
161512.99169620972142.00830379027856
172013.23782237821876.76217762178126
18914.0665559975066-5.06655599750663
191213.4456280177958-1.44562801779579
201313.2684601576271-0.268460157627059
211613.23555922385862.76444077614141
221213.5743531949515-1.57435319495147
231413.38140951700270.618590482997336
241513.45722041084551.54277958915447
251913.64629460915785.3537053908422
261614.30241396793691.69758603206306
271614.51046035404081.48953964595917
281414.6930097709465-0.693009770946469
291414.6080784769461-0.608078476946082
301414.5335558741402-0.533555874140234
311314.4681663331669-1.46816633316688
321814.288236306623.71176369338003
331514.74312872909170.256871270908295
341514.77460939551860.225390604481371
351514.8022319724240.197768027576014
361314.8264692850826-1.82646928508264
371414.6026277083294-0.602627708329447
381514.52877312039340.471226879606602
391414.5865239780734-0.586523978073361
401914.51464297075084.48535702924922
411615.06434254573310.935657454266904
421615.1790113450250.82098865497499
431215.2796269954096-3.27962699540961
441014.8776947626529-4.87769476265289
451114.2799125302823-3.27991253028229
461313.8779453040129-0.877945304012869
471413.77034937411780.229650625882233
481113.7984940347588-2.79849403475875
491113.4555266920331-2.4555266920331
501613.15459145540282.84540854459716
51913.5033083707825-4.50330837078246
521612.95140878256893.0485912174311
531913.32502659840585.67497340159421
541314.0205187178847-1.02051871788473
551513.89544980991941.10455019008059
561414.0308171320912-0.0308171320912169
571514.02704036152370.972959638476265
581114.1462807020937-3.14628070209365
591413.76069062455070.239309375449281
601513.79001900601871.20998099398133
611713.93830732148413.06169267851594
621614.31353077708231.68646922291772
631314.5202147509585-1.52021475095845
641514.33390596950930.66609403049068
651414.4155386250753-0.415538625075264
661514.3646125997660.635387400233995
671414.4424820272341-0.442482027234126
681214.3882539734311-2.3882539734311
691214.0955632944988-2.09556329449876
701513.83874310274531.1612568972547
711713.98106007298953.01893992701052
721314.3510439971126-1.3510439971126
73514.1854678108353-9.18546781083529
74713.0597496754219-6.05974967542187
751012.3171015875758-2.31710158757585
761512.03313093605912.96686906394094
77912.3967333545157-3.39673335451571
78911.9804492395323-2.98044923953231
791511.61518251281613.38481748718387
801412.03000628759361.96999371240643
811112.2714373931591-1.27143739315908
821812.11561733467135.8843826653287
832012.83677344979697.16322655020314
842013.71465732046126.28534267953882
851614.48495279014851.51504720985153
861514.67062826746340.329371732536641
871414.7109941737236-0.710994173723643
881314.623858814696-1.623858814696
891814.42484801255723.57515198744277
901414.8629980896144-0.862998089614399
911214.7572340043971-2.75723400439709
92914.4193232538236-5.41932325382355
931913.7551621469395.24483785306101
941314.397939326075-1.39793932607503
951214.2266159178417-2.22661591784165
961413.95373466988190.0462653301180644
97613.959404682801-7.95940468280097
981412.98394579675991.01605420324011
991113.1084675594731-2.10846755947308
1001112.8500658951801-1.85006589518006
1011412.62333245353031.37666754646973
1021212.7920489147287-0.792048914728687
1031912.69497995255866.30502004744141
1041313.4676869673475-0.467686967347483
1051413.4103699409660.589630059033963
1061713.48263161171693.51736838828308
1071213.9137000630101-1.9137000630101
1081613.679167983532.32083201646995
1091513.9635958149691.03640418503098
1101514.09061155447570.909388445524336
1111514.20206097505440.797939024945606
1121614.29985179527541.70014820472458
1131514.50821218653290.491787813467059
1141214.5684828740794-2.56848287407943
1151314.2537043770671-1.25370437706708
1161414.1000575750994-0.100057575099438
1171714.08779509384162.91220490615841
1181414.4446981873384-0.444698187338398
1191414.3901985336918-0.390198533691821
1201414.3423780443238-0.342378044323771
1211514.30041815925310.699581840746863
1221114.386154888351-3.38615488835099
1231113.9711672093741-2.9711672093741
1241613.60703803491962.39296196508043
1251213.9003056982462-1.90030569824619
1261213.6674151551187-1.66741515511873
1271913.46306633826635.5369336617337
1281814.14164110070163.8583588992984
1291614.61449938895891.38550061104111
1301614.78429837977741.21570162022264
1311314.9332877823118-1.93328778231184
1321114.6963551445474-3.69635514454739
1331014.2433511052499-4.24335110524988
1341413.72331038522560.276689614774375
1351413.75721987395790.242780126042113
1361413.78697361066810.213026389331919
1371613.81308090043612.18691909956387
1381014.0810971345311-4.08109713453115
1391613.58094132849742.41905867150261
140713.8774072541552-6.87740725415523
1411613.03455175348122.96544824651876
1421513.39798004472171.6020199552783
1431713.59431440178343.40568559821663
1441114.0116956522959-3.01169565229587
1451113.6425995448406-2.64259954484057
1461013.3187377346938-3.31873773469377
1471312.91201231454490.0879876854550687
1481412.92279557950751.07720442049245
1491313.0548115613463-0.0548115613463214
1501313.048094171453-0.0480941714530054
1511213.0422000262524-1.04220002625242
1521012.9144739817611-2.91447398176106
1531512.55729280340142.44270719659861
154612.8566569563596-6.85665695635964
1551512.01634449290762.98365550709243
1561512.38200416134582.6179958386542
1571112.7028506826883-1.70285068268829
1581412.49415909126581.5058409087342
1591412.6787062972351.32129370276502
1601612.84063645844633.15936354155368
1611213.2278298935913-1.2278298935913
1621513.07735411958791.92264588041207
1632013.31298254702686.68701745297317
1641214.1325049680578-2.13250496805782
165913.8711574171394-4.87115741713939
1661313.2741763642573-0.274176364257254
1671513.24057488506181.75942511493818
1681913.45619991370235.54380008629768
1691114.1356161856629-3.13561618566292
1701113.7513330899525-2.75133308995245
1711713.41414552153393.58585447846611
1721513.85360723437131.14639276562868
1731413.99410254208470.00589745791526752
1741513.99482530062731.00517469937267
1751114.1180137338836-3.11801373388358
1761213.7358878934816-1.73588789348159
1771513.52314745140721.47685254859276
1781613.7041420105872.29585798941296
1791613.98550916882452.01449083117554

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 15 & 10 & 5 \tabularnewline
3 & 14 & 10.6127712592305 & 3.38722874076946 \tabularnewline
4 & 14 & 11.0278905433872 & 2.97210945661283 \tabularnewline
5 & 8 & 11.3921351942471 & -3.3921351942471 \tabularnewline
6 & 19 & 10.9764146033553 & 8.0235853966447 \tabularnewline
7 & 17 & 11.9597391087644 & 5.04026089123556 \tabularnewline
8 & 18 & 12.577444511399 & 5.42255548860099 \tabularnewline
9 & 10 & 13.2420017423985 & -3.24200174239851 \tabularnewline
10 & 15 & 12.8446806443751 & 2.15531935562492 \tabularnewline
11 & 16 & 13.1088241954931 & 2.89117580450687 \tabularnewline
12 & 12 & 13.46315008317 & -1.46315008317004 \tabularnewline
13 & 13 & 13.2838348193886 & -0.283834819388563 \tabularnewline
14 & 10 & 13.2490496554505 & -3.24904965545052 \tabularnewline
15 & 14 & 12.8508648057159 & 1.14913519428407 \tabularnewline
16 & 15 & 12.9916962097214 & 2.00830379027856 \tabularnewline
17 & 20 & 13.2378223782187 & 6.76217762178126 \tabularnewline
18 & 9 & 14.0665559975066 & -5.06655599750663 \tabularnewline
19 & 12 & 13.4456280177958 & -1.44562801779579 \tabularnewline
20 & 13 & 13.2684601576271 & -0.268460157627059 \tabularnewline
21 & 16 & 13.2355592238586 & 2.76444077614141 \tabularnewline
22 & 12 & 13.5743531949515 & -1.57435319495147 \tabularnewline
23 & 14 & 13.3814095170027 & 0.618590482997336 \tabularnewline
24 & 15 & 13.4572204108455 & 1.54277958915447 \tabularnewline
25 & 19 & 13.6462946091578 & 5.3537053908422 \tabularnewline
26 & 16 & 14.3024139679369 & 1.69758603206306 \tabularnewline
27 & 16 & 14.5104603540408 & 1.48953964595917 \tabularnewline
28 & 14 & 14.6930097709465 & -0.693009770946469 \tabularnewline
29 & 14 & 14.6080784769461 & -0.608078476946082 \tabularnewline
30 & 14 & 14.5335558741402 & -0.533555874140234 \tabularnewline
31 & 13 & 14.4681663331669 & -1.46816633316688 \tabularnewline
32 & 18 & 14.28823630662 & 3.71176369338003 \tabularnewline
33 & 15 & 14.7431287290917 & 0.256871270908295 \tabularnewline
34 & 15 & 14.7746093955186 & 0.225390604481371 \tabularnewline
35 & 15 & 14.802231972424 & 0.197768027576014 \tabularnewline
36 & 13 & 14.8264692850826 & -1.82646928508264 \tabularnewline
37 & 14 & 14.6026277083294 & -0.602627708329447 \tabularnewline
38 & 15 & 14.5287731203934 & 0.471226879606602 \tabularnewline
39 & 14 & 14.5865239780734 & -0.586523978073361 \tabularnewline
40 & 19 & 14.5146429707508 & 4.48535702924922 \tabularnewline
41 & 16 & 15.0643425457331 & 0.935657454266904 \tabularnewline
42 & 16 & 15.179011345025 & 0.82098865497499 \tabularnewline
43 & 12 & 15.2796269954096 & -3.27962699540961 \tabularnewline
44 & 10 & 14.8776947626529 & -4.87769476265289 \tabularnewline
45 & 11 & 14.2799125302823 & -3.27991253028229 \tabularnewline
46 & 13 & 13.8779453040129 & -0.877945304012869 \tabularnewline
47 & 14 & 13.7703493741178 & 0.229650625882233 \tabularnewline
48 & 11 & 13.7984940347588 & -2.79849403475875 \tabularnewline
49 & 11 & 13.4555266920331 & -2.4555266920331 \tabularnewline
50 & 16 & 13.1545914554028 & 2.84540854459716 \tabularnewline
51 & 9 & 13.5033083707825 & -4.50330837078246 \tabularnewline
52 & 16 & 12.9514087825689 & 3.0485912174311 \tabularnewline
53 & 19 & 13.3250265984058 & 5.67497340159421 \tabularnewline
54 & 13 & 14.0205187178847 & -1.02051871788473 \tabularnewline
55 & 15 & 13.8954498099194 & 1.10455019008059 \tabularnewline
56 & 14 & 14.0308171320912 & -0.0308171320912169 \tabularnewline
57 & 15 & 14.0270403615237 & 0.972959638476265 \tabularnewline
58 & 11 & 14.1462807020937 & -3.14628070209365 \tabularnewline
59 & 14 & 13.7606906245507 & 0.239309375449281 \tabularnewline
60 & 15 & 13.7900190060187 & 1.20998099398133 \tabularnewline
61 & 17 & 13.9383073214841 & 3.06169267851594 \tabularnewline
62 & 16 & 14.3135307770823 & 1.68646922291772 \tabularnewline
63 & 13 & 14.5202147509585 & -1.52021475095845 \tabularnewline
64 & 15 & 14.3339059695093 & 0.66609403049068 \tabularnewline
65 & 14 & 14.4155386250753 & -0.415538625075264 \tabularnewline
66 & 15 & 14.364612599766 & 0.635387400233995 \tabularnewline
67 & 14 & 14.4424820272341 & -0.442482027234126 \tabularnewline
68 & 12 & 14.3882539734311 & -2.3882539734311 \tabularnewline
69 & 12 & 14.0955632944988 & -2.09556329449876 \tabularnewline
70 & 15 & 13.8387431027453 & 1.1612568972547 \tabularnewline
71 & 17 & 13.9810600729895 & 3.01893992701052 \tabularnewline
72 & 13 & 14.3510439971126 & -1.3510439971126 \tabularnewline
73 & 5 & 14.1854678108353 & -9.18546781083529 \tabularnewline
74 & 7 & 13.0597496754219 & -6.05974967542187 \tabularnewline
75 & 10 & 12.3171015875758 & -2.31710158757585 \tabularnewline
76 & 15 & 12.0331309360591 & 2.96686906394094 \tabularnewline
77 & 9 & 12.3967333545157 & -3.39673335451571 \tabularnewline
78 & 9 & 11.9804492395323 & -2.98044923953231 \tabularnewline
79 & 15 & 11.6151825128161 & 3.38481748718387 \tabularnewline
80 & 14 & 12.0300062875936 & 1.96999371240643 \tabularnewline
81 & 11 & 12.2714373931591 & -1.27143739315908 \tabularnewline
82 & 18 & 12.1156173346713 & 5.8843826653287 \tabularnewline
83 & 20 & 12.8367734497969 & 7.16322655020314 \tabularnewline
84 & 20 & 13.7146573204612 & 6.28534267953882 \tabularnewline
85 & 16 & 14.4849527901485 & 1.51504720985153 \tabularnewline
86 & 15 & 14.6706282674634 & 0.329371732536641 \tabularnewline
87 & 14 & 14.7109941737236 & -0.710994173723643 \tabularnewline
88 & 13 & 14.623858814696 & -1.623858814696 \tabularnewline
89 & 18 & 14.4248480125572 & 3.57515198744277 \tabularnewline
90 & 14 & 14.8629980896144 & -0.862998089614399 \tabularnewline
91 & 12 & 14.7572340043971 & -2.75723400439709 \tabularnewline
92 & 9 & 14.4193232538236 & -5.41932325382355 \tabularnewline
93 & 19 & 13.755162146939 & 5.24483785306101 \tabularnewline
94 & 13 & 14.397939326075 & -1.39793932607503 \tabularnewline
95 & 12 & 14.2266159178417 & -2.22661591784165 \tabularnewline
96 & 14 & 13.9537346698819 & 0.0462653301180644 \tabularnewline
97 & 6 & 13.959404682801 & -7.95940468280097 \tabularnewline
98 & 14 & 12.9839457967599 & 1.01605420324011 \tabularnewline
99 & 11 & 13.1084675594731 & -2.10846755947308 \tabularnewline
100 & 11 & 12.8500658951801 & -1.85006589518006 \tabularnewline
101 & 14 & 12.6233324535303 & 1.37666754646973 \tabularnewline
102 & 12 & 12.7920489147287 & -0.792048914728687 \tabularnewline
103 & 19 & 12.6949799525586 & 6.30502004744141 \tabularnewline
104 & 13 & 13.4676869673475 & -0.467686967347483 \tabularnewline
105 & 14 & 13.410369940966 & 0.589630059033963 \tabularnewline
106 & 17 & 13.4826316117169 & 3.51736838828308 \tabularnewline
107 & 12 & 13.9137000630101 & -1.9137000630101 \tabularnewline
108 & 16 & 13.67916798353 & 2.32083201646995 \tabularnewline
109 & 15 & 13.963595814969 & 1.03640418503098 \tabularnewline
110 & 15 & 14.0906115544757 & 0.909388445524336 \tabularnewline
111 & 15 & 14.2020609750544 & 0.797939024945606 \tabularnewline
112 & 16 & 14.2998517952754 & 1.70014820472458 \tabularnewline
113 & 15 & 14.5082121865329 & 0.491787813467059 \tabularnewline
114 & 12 & 14.5684828740794 & -2.56848287407943 \tabularnewline
115 & 13 & 14.2537043770671 & -1.25370437706708 \tabularnewline
116 & 14 & 14.1000575750994 & -0.100057575099438 \tabularnewline
117 & 17 & 14.0877950938416 & 2.91220490615841 \tabularnewline
118 & 14 & 14.4446981873384 & -0.444698187338398 \tabularnewline
119 & 14 & 14.3901985336918 & -0.390198533691821 \tabularnewline
120 & 14 & 14.3423780443238 & -0.342378044323771 \tabularnewline
121 & 15 & 14.3004181592531 & 0.699581840746863 \tabularnewline
122 & 11 & 14.386154888351 & -3.38615488835099 \tabularnewline
123 & 11 & 13.9711672093741 & -2.9711672093741 \tabularnewline
124 & 16 & 13.6070380349196 & 2.39296196508043 \tabularnewline
125 & 12 & 13.9003056982462 & -1.90030569824619 \tabularnewline
126 & 12 & 13.6674151551187 & -1.66741515511873 \tabularnewline
127 & 19 & 13.4630663382663 & 5.5369336617337 \tabularnewline
128 & 18 & 14.1416411007016 & 3.8583588992984 \tabularnewline
129 & 16 & 14.6144993889589 & 1.38550061104111 \tabularnewline
130 & 16 & 14.7842983797774 & 1.21570162022264 \tabularnewline
131 & 13 & 14.9332877823118 & -1.93328778231184 \tabularnewline
132 & 11 & 14.6963551445474 & -3.69635514454739 \tabularnewline
133 & 10 & 14.2433511052499 & -4.24335110524988 \tabularnewline
134 & 14 & 13.7233103852256 & 0.276689614774375 \tabularnewline
135 & 14 & 13.7572198739579 & 0.242780126042113 \tabularnewline
136 & 14 & 13.7869736106681 & 0.213026389331919 \tabularnewline
137 & 16 & 13.8130809004361 & 2.18691909956387 \tabularnewline
138 & 10 & 14.0810971345311 & -4.08109713453115 \tabularnewline
139 & 16 & 13.5809413284974 & 2.41905867150261 \tabularnewline
140 & 7 & 13.8774072541552 & -6.87740725415523 \tabularnewline
141 & 16 & 13.0345517534812 & 2.96544824651876 \tabularnewline
142 & 15 & 13.3979800447217 & 1.6020199552783 \tabularnewline
143 & 17 & 13.5943144017834 & 3.40568559821663 \tabularnewline
144 & 11 & 14.0116956522959 & -3.01169565229587 \tabularnewline
145 & 11 & 13.6425995448406 & -2.64259954484057 \tabularnewline
146 & 10 & 13.3187377346938 & -3.31873773469377 \tabularnewline
147 & 13 & 12.9120123145449 & 0.0879876854550687 \tabularnewline
148 & 14 & 12.9227955795075 & 1.07720442049245 \tabularnewline
149 & 13 & 13.0548115613463 & -0.0548115613463214 \tabularnewline
150 & 13 & 13.048094171453 & -0.0480941714530054 \tabularnewline
151 & 12 & 13.0422000262524 & -1.04220002625242 \tabularnewline
152 & 10 & 12.9144739817611 & -2.91447398176106 \tabularnewline
153 & 15 & 12.5572928034014 & 2.44270719659861 \tabularnewline
154 & 6 & 12.8566569563596 & -6.85665695635964 \tabularnewline
155 & 15 & 12.0163444929076 & 2.98365550709243 \tabularnewline
156 & 15 & 12.3820041613458 & 2.6179958386542 \tabularnewline
157 & 11 & 12.7028506826883 & -1.70285068268829 \tabularnewline
158 & 14 & 12.4941590912658 & 1.5058409087342 \tabularnewline
159 & 14 & 12.678706297235 & 1.32129370276502 \tabularnewline
160 & 16 & 12.8406364584463 & 3.15936354155368 \tabularnewline
161 & 12 & 13.2278298935913 & -1.2278298935913 \tabularnewline
162 & 15 & 13.0773541195879 & 1.92264588041207 \tabularnewline
163 & 20 & 13.3129825470268 & 6.68701745297317 \tabularnewline
164 & 12 & 14.1325049680578 & -2.13250496805782 \tabularnewline
165 & 9 & 13.8711574171394 & -4.87115741713939 \tabularnewline
166 & 13 & 13.2741763642573 & -0.274176364257254 \tabularnewline
167 & 15 & 13.2405748850618 & 1.75942511493818 \tabularnewline
168 & 19 & 13.4561999137023 & 5.54380008629768 \tabularnewline
169 & 11 & 14.1356161856629 & -3.13561618566292 \tabularnewline
170 & 11 & 13.7513330899525 & -2.75133308995245 \tabularnewline
171 & 17 & 13.4141455215339 & 3.58585447846611 \tabularnewline
172 & 15 & 13.8536072343713 & 1.14639276562868 \tabularnewline
173 & 14 & 13.9941025420847 & 0.00589745791526752 \tabularnewline
174 & 15 & 13.9948253006273 & 1.00517469937267 \tabularnewline
175 & 11 & 14.1180137338836 & -3.11801373388358 \tabularnewline
176 & 12 & 13.7358878934816 & -1.73588789348159 \tabularnewline
177 & 15 & 13.5231474514072 & 1.47685254859276 \tabularnewline
178 & 16 & 13.704142010587 & 2.29585798941296 \tabularnewline
179 & 16 & 13.9855091688245 & 2.01449083117554 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314846&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]15[/C][C]10[/C][C]5[/C][/ROW]
[ROW][C]3[/C][C]14[/C][C]10.6127712592305[/C][C]3.38722874076946[/C][/ROW]
[ROW][C]4[/C][C]14[/C][C]11.0278905433872[/C][C]2.97210945661283[/C][/ROW]
[ROW][C]5[/C][C]8[/C][C]11.3921351942471[/C][C]-3.3921351942471[/C][/ROW]
[ROW][C]6[/C][C]19[/C][C]10.9764146033553[/C][C]8.0235853966447[/C][/ROW]
[ROW][C]7[/C][C]17[/C][C]11.9597391087644[/C][C]5.04026089123556[/C][/ROW]
[ROW][C]8[/C][C]18[/C][C]12.577444511399[/C][C]5.42255548860099[/C][/ROW]
[ROW][C]9[/C][C]10[/C][C]13.2420017423985[/C][C]-3.24200174239851[/C][/ROW]
[ROW][C]10[/C][C]15[/C][C]12.8446806443751[/C][C]2.15531935562492[/C][/ROW]
[ROW][C]11[/C][C]16[/C][C]13.1088241954931[/C][C]2.89117580450687[/C][/ROW]
[ROW][C]12[/C][C]12[/C][C]13.46315008317[/C][C]-1.46315008317004[/C][/ROW]
[ROW][C]13[/C][C]13[/C][C]13.2838348193886[/C][C]-0.283834819388563[/C][/ROW]
[ROW][C]14[/C][C]10[/C][C]13.2490496554505[/C][C]-3.24904965545052[/C][/ROW]
[ROW][C]15[/C][C]14[/C][C]12.8508648057159[/C][C]1.14913519428407[/C][/ROW]
[ROW][C]16[/C][C]15[/C][C]12.9916962097214[/C][C]2.00830379027856[/C][/ROW]
[ROW][C]17[/C][C]20[/C][C]13.2378223782187[/C][C]6.76217762178126[/C][/ROW]
[ROW][C]18[/C][C]9[/C][C]14.0665559975066[/C][C]-5.06655599750663[/C][/ROW]
[ROW][C]19[/C][C]12[/C][C]13.4456280177958[/C][C]-1.44562801779579[/C][/ROW]
[ROW][C]20[/C][C]13[/C][C]13.2684601576271[/C][C]-0.268460157627059[/C][/ROW]
[ROW][C]21[/C][C]16[/C][C]13.2355592238586[/C][C]2.76444077614141[/C][/ROW]
[ROW][C]22[/C][C]12[/C][C]13.5743531949515[/C][C]-1.57435319495147[/C][/ROW]
[ROW][C]23[/C][C]14[/C][C]13.3814095170027[/C][C]0.618590482997336[/C][/ROW]
[ROW][C]24[/C][C]15[/C][C]13.4572204108455[/C][C]1.54277958915447[/C][/ROW]
[ROW][C]25[/C][C]19[/C][C]13.6462946091578[/C][C]5.3537053908422[/C][/ROW]
[ROW][C]26[/C][C]16[/C][C]14.3024139679369[/C][C]1.69758603206306[/C][/ROW]
[ROW][C]27[/C][C]16[/C][C]14.5104603540408[/C][C]1.48953964595917[/C][/ROW]
[ROW][C]28[/C][C]14[/C][C]14.6930097709465[/C][C]-0.693009770946469[/C][/ROW]
[ROW][C]29[/C][C]14[/C][C]14.6080784769461[/C][C]-0.608078476946082[/C][/ROW]
[ROW][C]30[/C][C]14[/C][C]14.5335558741402[/C][C]-0.533555874140234[/C][/ROW]
[ROW][C]31[/C][C]13[/C][C]14.4681663331669[/C][C]-1.46816633316688[/C][/ROW]
[ROW][C]32[/C][C]18[/C][C]14.28823630662[/C][C]3.71176369338003[/C][/ROW]
[ROW][C]33[/C][C]15[/C][C]14.7431287290917[/C][C]0.256871270908295[/C][/ROW]
[ROW][C]34[/C][C]15[/C][C]14.7746093955186[/C][C]0.225390604481371[/C][/ROW]
[ROW][C]35[/C][C]15[/C][C]14.802231972424[/C][C]0.197768027576014[/C][/ROW]
[ROW][C]36[/C][C]13[/C][C]14.8264692850826[/C][C]-1.82646928508264[/C][/ROW]
[ROW][C]37[/C][C]14[/C][C]14.6026277083294[/C][C]-0.602627708329447[/C][/ROW]
[ROW][C]38[/C][C]15[/C][C]14.5287731203934[/C][C]0.471226879606602[/C][/ROW]
[ROW][C]39[/C][C]14[/C][C]14.5865239780734[/C][C]-0.586523978073361[/C][/ROW]
[ROW][C]40[/C][C]19[/C][C]14.5146429707508[/C][C]4.48535702924922[/C][/ROW]
[ROW][C]41[/C][C]16[/C][C]15.0643425457331[/C][C]0.935657454266904[/C][/ROW]
[ROW][C]42[/C][C]16[/C][C]15.179011345025[/C][C]0.82098865497499[/C][/ROW]
[ROW][C]43[/C][C]12[/C][C]15.2796269954096[/C][C]-3.27962699540961[/C][/ROW]
[ROW][C]44[/C][C]10[/C][C]14.8776947626529[/C][C]-4.87769476265289[/C][/ROW]
[ROW][C]45[/C][C]11[/C][C]14.2799125302823[/C][C]-3.27991253028229[/C][/ROW]
[ROW][C]46[/C][C]13[/C][C]13.8779453040129[/C][C]-0.877945304012869[/C][/ROW]
[ROW][C]47[/C][C]14[/C][C]13.7703493741178[/C][C]0.229650625882233[/C][/ROW]
[ROW][C]48[/C][C]11[/C][C]13.7984940347588[/C][C]-2.79849403475875[/C][/ROW]
[ROW][C]49[/C][C]11[/C][C]13.4555266920331[/C][C]-2.4555266920331[/C][/ROW]
[ROW][C]50[/C][C]16[/C][C]13.1545914554028[/C][C]2.84540854459716[/C][/ROW]
[ROW][C]51[/C][C]9[/C][C]13.5033083707825[/C][C]-4.50330837078246[/C][/ROW]
[ROW][C]52[/C][C]16[/C][C]12.9514087825689[/C][C]3.0485912174311[/C][/ROW]
[ROW][C]53[/C][C]19[/C][C]13.3250265984058[/C][C]5.67497340159421[/C][/ROW]
[ROW][C]54[/C][C]13[/C][C]14.0205187178847[/C][C]-1.02051871788473[/C][/ROW]
[ROW][C]55[/C][C]15[/C][C]13.8954498099194[/C][C]1.10455019008059[/C][/ROW]
[ROW][C]56[/C][C]14[/C][C]14.0308171320912[/C][C]-0.0308171320912169[/C][/ROW]
[ROW][C]57[/C][C]15[/C][C]14.0270403615237[/C][C]0.972959638476265[/C][/ROW]
[ROW][C]58[/C][C]11[/C][C]14.1462807020937[/C][C]-3.14628070209365[/C][/ROW]
[ROW][C]59[/C][C]14[/C][C]13.7606906245507[/C][C]0.239309375449281[/C][/ROW]
[ROW][C]60[/C][C]15[/C][C]13.7900190060187[/C][C]1.20998099398133[/C][/ROW]
[ROW][C]61[/C][C]17[/C][C]13.9383073214841[/C][C]3.06169267851594[/C][/ROW]
[ROW][C]62[/C][C]16[/C][C]14.3135307770823[/C][C]1.68646922291772[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]14.5202147509585[/C][C]-1.52021475095845[/C][/ROW]
[ROW][C]64[/C][C]15[/C][C]14.3339059695093[/C][C]0.66609403049068[/C][/ROW]
[ROW][C]65[/C][C]14[/C][C]14.4155386250753[/C][C]-0.415538625075264[/C][/ROW]
[ROW][C]66[/C][C]15[/C][C]14.364612599766[/C][C]0.635387400233995[/C][/ROW]
[ROW][C]67[/C][C]14[/C][C]14.4424820272341[/C][C]-0.442482027234126[/C][/ROW]
[ROW][C]68[/C][C]12[/C][C]14.3882539734311[/C][C]-2.3882539734311[/C][/ROW]
[ROW][C]69[/C][C]12[/C][C]14.0955632944988[/C][C]-2.09556329449876[/C][/ROW]
[ROW][C]70[/C][C]15[/C][C]13.8387431027453[/C][C]1.1612568972547[/C][/ROW]
[ROW][C]71[/C][C]17[/C][C]13.9810600729895[/C][C]3.01893992701052[/C][/ROW]
[ROW][C]72[/C][C]13[/C][C]14.3510439971126[/C][C]-1.3510439971126[/C][/ROW]
[ROW][C]73[/C][C]5[/C][C]14.1854678108353[/C][C]-9.18546781083529[/C][/ROW]
[ROW][C]74[/C][C]7[/C][C]13.0597496754219[/C][C]-6.05974967542187[/C][/ROW]
[ROW][C]75[/C][C]10[/C][C]12.3171015875758[/C][C]-2.31710158757585[/C][/ROW]
[ROW][C]76[/C][C]15[/C][C]12.0331309360591[/C][C]2.96686906394094[/C][/ROW]
[ROW][C]77[/C][C]9[/C][C]12.3967333545157[/C][C]-3.39673335451571[/C][/ROW]
[ROW][C]78[/C][C]9[/C][C]11.9804492395323[/C][C]-2.98044923953231[/C][/ROW]
[ROW][C]79[/C][C]15[/C][C]11.6151825128161[/C][C]3.38481748718387[/C][/ROW]
[ROW][C]80[/C][C]14[/C][C]12.0300062875936[/C][C]1.96999371240643[/C][/ROW]
[ROW][C]81[/C][C]11[/C][C]12.2714373931591[/C][C]-1.27143739315908[/C][/ROW]
[ROW][C]82[/C][C]18[/C][C]12.1156173346713[/C][C]5.8843826653287[/C][/ROW]
[ROW][C]83[/C][C]20[/C][C]12.8367734497969[/C][C]7.16322655020314[/C][/ROW]
[ROW][C]84[/C][C]20[/C][C]13.7146573204612[/C][C]6.28534267953882[/C][/ROW]
[ROW][C]85[/C][C]16[/C][C]14.4849527901485[/C][C]1.51504720985153[/C][/ROW]
[ROW][C]86[/C][C]15[/C][C]14.6706282674634[/C][C]0.329371732536641[/C][/ROW]
[ROW][C]87[/C][C]14[/C][C]14.7109941737236[/C][C]-0.710994173723643[/C][/ROW]
[ROW][C]88[/C][C]13[/C][C]14.623858814696[/C][C]-1.623858814696[/C][/ROW]
[ROW][C]89[/C][C]18[/C][C]14.4248480125572[/C][C]3.57515198744277[/C][/ROW]
[ROW][C]90[/C][C]14[/C][C]14.8629980896144[/C][C]-0.862998089614399[/C][/ROW]
[ROW][C]91[/C][C]12[/C][C]14.7572340043971[/C][C]-2.75723400439709[/C][/ROW]
[ROW][C]92[/C][C]9[/C][C]14.4193232538236[/C][C]-5.41932325382355[/C][/ROW]
[ROW][C]93[/C][C]19[/C][C]13.755162146939[/C][C]5.24483785306101[/C][/ROW]
[ROW][C]94[/C][C]13[/C][C]14.397939326075[/C][C]-1.39793932607503[/C][/ROW]
[ROW][C]95[/C][C]12[/C][C]14.2266159178417[/C][C]-2.22661591784165[/C][/ROW]
[ROW][C]96[/C][C]14[/C][C]13.9537346698819[/C][C]0.0462653301180644[/C][/ROW]
[ROW][C]97[/C][C]6[/C][C]13.959404682801[/C][C]-7.95940468280097[/C][/ROW]
[ROW][C]98[/C][C]14[/C][C]12.9839457967599[/C][C]1.01605420324011[/C][/ROW]
[ROW][C]99[/C][C]11[/C][C]13.1084675594731[/C][C]-2.10846755947308[/C][/ROW]
[ROW][C]100[/C][C]11[/C][C]12.8500658951801[/C][C]-1.85006589518006[/C][/ROW]
[ROW][C]101[/C][C]14[/C][C]12.6233324535303[/C][C]1.37666754646973[/C][/ROW]
[ROW][C]102[/C][C]12[/C][C]12.7920489147287[/C][C]-0.792048914728687[/C][/ROW]
[ROW][C]103[/C][C]19[/C][C]12.6949799525586[/C][C]6.30502004744141[/C][/ROW]
[ROW][C]104[/C][C]13[/C][C]13.4676869673475[/C][C]-0.467686967347483[/C][/ROW]
[ROW][C]105[/C][C]14[/C][C]13.410369940966[/C][C]0.589630059033963[/C][/ROW]
[ROW][C]106[/C][C]17[/C][C]13.4826316117169[/C][C]3.51736838828308[/C][/ROW]
[ROW][C]107[/C][C]12[/C][C]13.9137000630101[/C][C]-1.9137000630101[/C][/ROW]
[ROW][C]108[/C][C]16[/C][C]13.67916798353[/C][C]2.32083201646995[/C][/ROW]
[ROW][C]109[/C][C]15[/C][C]13.963595814969[/C][C]1.03640418503098[/C][/ROW]
[ROW][C]110[/C][C]15[/C][C]14.0906115544757[/C][C]0.909388445524336[/C][/ROW]
[ROW][C]111[/C][C]15[/C][C]14.2020609750544[/C][C]0.797939024945606[/C][/ROW]
[ROW][C]112[/C][C]16[/C][C]14.2998517952754[/C][C]1.70014820472458[/C][/ROW]
[ROW][C]113[/C][C]15[/C][C]14.5082121865329[/C][C]0.491787813467059[/C][/ROW]
[ROW][C]114[/C][C]12[/C][C]14.5684828740794[/C][C]-2.56848287407943[/C][/ROW]
[ROW][C]115[/C][C]13[/C][C]14.2537043770671[/C][C]-1.25370437706708[/C][/ROW]
[ROW][C]116[/C][C]14[/C][C]14.1000575750994[/C][C]-0.100057575099438[/C][/ROW]
[ROW][C]117[/C][C]17[/C][C]14.0877950938416[/C][C]2.91220490615841[/C][/ROW]
[ROW][C]118[/C][C]14[/C][C]14.4446981873384[/C][C]-0.444698187338398[/C][/ROW]
[ROW][C]119[/C][C]14[/C][C]14.3901985336918[/C][C]-0.390198533691821[/C][/ROW]
[ROW][C]120[/C][C]14[/C][C]14.3423780443238[/C][C]-0.342378044323771[/C][/ROW]
[ROW][C]121[/C][C]15[/C][C]14.3004181592531[/C][C]0.699581840746863[/C][/ROW]
[ROW][C]122[/C][C]11[/C][C]14.386154888351[/C][C]-3.38615488835099[/C][/ROW]
[ROW][C]123[/C][C]11[/C][C]13.9711672093741[/C][C]-2.9711672093741[/C][/ROW]
[ROW][C]124[/C][C]16[/C][C]13.6070380349196[/C][C]2.39296196508043[/C][/ROW]
[ROW][C]125[/C][C]12[/C][C]13.9003056982462[/C][C]-1.90030569824619[/C][/ROW]
[ROW][C]126[/C][C]12[/C][C]13.6674151551187[/C][C]-1.66741515511873[/C][/ROW]
[ROW][C]127[/C][C]19[/C][C]13.4630663382663[/C][C]5.5369336617337[/C][/ROW]
[ROW][C]128[/C][C]18[/C][C]14.1416411007016[/C][C]3.8583588992984[/C][/ROW]
[ROW][C]129[/C][C]16[/C][C]14.6144993889589[/C][C]1.38550061104111[/C][/ROW]
[ROW][C]130[/C][C]16[/C][C]14.7842983797774[/C][C]1.21570162022264[/C][/ROW]
[ROW][C]131[/C][C]13[/C][C]14.9332877823118[/C][C]-1.93328778231184[/C][/ROW]
[ROW][C]132[/C][C]11[/C][C]14.6963551445474[/C][C]-3.69635514454739[/C][/ROW]
[ROW][C]133[/C][C]10[/C][C]14.2433511052499[/C][C]-4.24335110524988[/C][/ROW]
[ROW][C]134[/C][C]14[/C][C]13.7233103852256[/C][C]0.276689614774375[/C][/ROW]
[ROW][C]135[/C][C]14[/C][C]13.7572198739579[/C][C]0.242780126042113[/C][/ROW]
[ROW][C]136[/C][C]14[/C][C]13.7869736106681[/C][C]0.213026389331919[/C][/ROW]
[ROW][C]137[/C][C]16[/C][C]13.8130809004361[/C][C]2.18691909956387[/C][/ROW]
[ROW][C]138[/C][C]10[/C][C]14.0810971345311[/C][C]-4.08109713453115[/C][/ROW]
[ROW][C]139[/C][C]16[/C][C]13.5809413284974[/C][C]2.41905867150261[/C][/ROW]
[ROW][C]140[/C][C]7[/C][C]13.8774072541552[/C][C]-6.87740725415523[/C][/ROW]
[ROW][C]141[/C][C]16[/C][C]13.0345517534812[/C][C]2.96544824651876[/C][/ROW]
[ROW][C]142[/C][C]15[/C][C]13.3979800447217[/C][C]1.6020199552783[/C][/ROW]
[ROW][C]143[/C][C]17[/C][C]13.5943144017834[/C][C]3.40568559821663[/C][/ROW]
[ROW][C]144[/C][C]11[/C][C]14.0116956522959[/C][C]-3.01169565229587[/C][/ROW]
[ROW][C]145[/C][C]11[/C][C]13.6425995448406[/C][C]-2.64259954484057[/C][/ROW]
[ROW][C]146[/C][C]10[/C][C]13.3187377346938[/C][C]-3.31873773469377[/C][/ROW]
[ROW][C]147[/C][C]13[/C][C]12.9120123145449[/C][C]0.0879876854550687[/C][/ROW]
[ROW][C]148[/C][C]14[/C][C]12.9227955795075[/C][C]1.07720442049245[/C][/ROW]
[ROW][C]149[/C][C]13[/C][C]13.0548115613463[/C][C]-0.0548115613463214[/C][/ROW]
[ROW][C]150[/C][C]13[/C][C]13.048094171453[/C][C]-0.0480941714530054[/C][/ROW]
[ROW][C]151[/C][C]12[/C][C]13.0422000262524[/C][C]-1.04220002625242[/C][/ROW]
[ROW][C]152[/C][C]10[/C][C]12.9144739817611[/C][C]-2.91447398176106[/C][/ROW]
[ROW][C]153[/C][C]15[/C][C]12.5572928034014[/C][C]2.44270719659861[/C][/ROW]
[ROW][C]154[/C][C]6[/C][C]12.8566569563596[/C][C]-6.85665695635964[/C][/ROW]
[ROW][C]155[/C][C]15[/C][C]12.0163444929076[/C][C]2.98365550709243[/C][/ROW]
[ROW][C]156[/C][C]15[/C][C]12.3820041613458[/C][C]2.6179958386542[/C][/ROW]
[ROW][C]157[/C][C]11[/C][C]12.7028506826883[/C][C]-1.70285068268829[/C][/ROW]
[ROW][C]158[/C][C]14[/C][C]12.4941590912658[/C][C]1.5058409087342[/C][/ROW]
[ROW][C]159[/C][C]14[/C][C]12.678706297235[/C][C]1.32129370276502[/C][/ROW]
[ROW][C]160[/C][C]16[/C][C]12.8406364584463[/C][C]3.15936354155368[/C][/ROW]
[ROW][C]161[/C][C]12[/C][C]13.2278298935913[/C][C]-1.2278298935913[/C][/ROW]
[ROW][C]162[/C][C]15[/C][C]13.0773541195879[/C][C]1.92264588041207[/C][/ROW]
[ROW][C]163[/C][C]20[/C][C]13.3129825470268[/C][C]6.68701745297317[/C][/ROW]
[ROW][C]164[/C][C]12[/C][C]14.1325049680578[/C][C]-2.13250496805782[/C][/ROW]
[ROW][C]165[/C][C]9[/C][C]13.8711574171394[/C][C]-4.87115741713939[/C][/ROW]
[ROW][C]166[/C][C]13[/C][C]13.2741763642573[/C][C]-0.274176364257254[/C][/ROW]
[ROW][C]167[/C][C]15[/C][C]13.2405748850618[/C][C]1.75942511493818[/C][/ROW]
[ROW][C]168[/C][C]19[/C][C]13.4561999137023[/C][C]5.54380008629768[/C][/ROW]
[ROW][C]169[/C][C]11[/C][C]14.1356161856629[/C][C]-3.13561618566292[/C][/ROW]
[ROW][C]170[/C][C]11[/C][C]13.7513330899525[/C][C]-2.75133308995245[/C][/ROW]
[ROW][C]171[/C][C]17[/C][C]13.4141455215339[/C][C]3.58585447846611[/C][/ROW]
[ROW][C]172[/C][C]15[/C][C]13.8536072343713[/C][C]1.14639276562868[/C][/ROW]
[ROW][C]173[/C][C]14[/C][C]13.9941025420847[/C][C]0.00589745791526752[/C][/ROW]
[ROW][C]174[/C][C]15[/C][C]13.9948253006273[/C][C]1.00517469937267[/C][/ROW]
[ROW][C]175[/C][C]11[/C][C]14.1180137338836[/C][C]-3.11801373388358[/C][/ROW]
[ROW][C]176[/C][C]12[/C][C]13.7358878934816[/C][C]-1.73588789348159[/C][/ROW]
[ROW][C]177[/C][C]15[/C][C]13.5231474514072[/C][C]1.47685254859276[/C][/ROW]
[ROW][C]178[/C][C]16[/C][C]13.704142010587[/C][C]2.29585798941296[/C][/ROW]
[ROW][C]179[/C][C]16[/C][C]13.9855091688245[/C][C]2.01449083117554[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=314846&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314846&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
215105
31410.61277125923053.38722874076946
41411.02789054338722.97210945661283
5811.3921351942471-3.3921351942471
61910.97641460335538.0235853966447
71711.95973910876445.04026089123556
81812.5774445113995.42255548860099
91013.2420017423985-3.24200174239851
101512.84468064437512.15531935562492
111613.10882419549312.89117580450687
121213.46315008317-1.46315008317004
131313.2838348193886-0.283834819388563
141013.2490496554505-3.24904965545052
151412.85086480571591.14913519428407
161512.99169620972142.00830379027856
172013.23782237821876.76217762178126
18914.0665559975066-5.06655599750663
191213.4456280177958-1.44562801779579
201313.2684601576271-0.268460157627059
211613.23555922385862.76444077614141
221213.5743531949515-1.57435319495147
231413.38140951700270.618590482997336
241513.45722041084551.54277958915447
251913.64629460915785.3537053908422
261614.30241396793691.69758603206306
271614.51046035404081.48953964595917
281414.6930097709465-0.693009770946469
291414.6080784769461-0.608078476946082
301414.5335558741402-0.533555874140234
311314.4681663331669-1.46816633316688
321814.288236306623.71176369338003
331514.74312872909170.256871270908295
341514.77460939551860.225390604481371
351514.8022319724240.197768027576014
361314.8264692850826-1.82646928508264
371414.6026277083294-0.602627708329447
381514.52877312039340.471226879606602
391414.5865239780734-0.586523978073361
401914.51464297075084.48535702924922
411615.06434254573310.935657454266904
421615.1790113450250.82098865497499
431215.2796269954096-3.27962699540961
441014.8776947626529-4.87769476265289
451114.2799125302823-3.27991253028229
461313.8779453040129-0.877945304012869
471413.77034937411780.229650625882233
481113.7984940347588-2.79849403475875
491113.4555266920331-2.4555266920331
501613.15459145540282.84540854459716
51913.5033083707825-4.50330837078246
521612.95140878256893.0485912174311
531913.32502659840585.67497340159421
541314.0205187178847-1.02051871788473
551513.89544980991941.10455019008059
561414.0308171320912-0.0308171320912169
571514.02704036152370.972959638476265
581114.1462807020937-3.14628070209365
591413.76069062455070.239309375449281
601513.79001900601871.20998099398133
611713.93830732148413.06169267851594
621614.31353077708231.68646922291772
631314.5202147509585-1.52021475095845
641514.33390596950930.66609403049068
651414.4155386250753-0.415538625075264
661514.3646125997660.635387400233995
671414.4424820272341-0.442482027234126
681214.3882539734311-2.3882539734311
691214.0955632944988-2.09556329449876
701513.83874310274531.1612568972547
711713.98106007298953.01893992701052
721314.3510439971126-1.3510439971126
73514.1854678108353-9.18546781083529
74713.0597496754219-6.05974967542187
751012.3171015875758-2.31710158757585
761512.03313093605912.96686906394094
77912.3967333545157-3.39673335451571
78911.9804492395323-2.98044923953231
791511.61518251281613.38481748718387
801412.03000628759361.96999371240643
811112.2714373931591-1.27143739315908
821812.11561733467135.8843826653287
832012.83677344979697.16322655020314
842013.71465732046126.28534267953882
851614.48495279014851.51504720985153
861514.67062826746340.329371732536641
871414.7109941737236-0.710994173723643
881314.623858814696-1.623858814696
891814.42484801255723.57515198744277
901414.8629980896144-0.862998089614399
911214.7572340043971-2.75723400439709
92914.4193232538236-5.41932325382355
931913.7551621469395.24483785306101
941314.397939326075-1.39793932607503
951214.2266159178417-2.22661591784165
961413.95373466988190.0462653301180644
97613.959404682801-7.95940468280097
981412.98394579675991.01605420324011
991113.1084675594731-2.10846755947308
1001112.8500658951801-1.85006589518006
1011412.62333245353031.37666754646973
1021212.7920489147287-0.792048914728687
1031912.69497995255866.30502004744141
1041313.4676869673475-0.467686967347483
1051413.4103699409660.589630059033963
1061713.48263161171693.51736838828308
1071213.9137000630101-1.9137000630101
1081613.679167983532.32083201646995
1091513.9635958149691.03640418503098
1101514.09061155447570.909388445524336
1111514.20206097505440.797939024945606
1121614.29985179527541.70014820472458
1131514.50821218653290.491787813467059
1141214.5684828740794-2.56848287407943
1151314.2537043770671-1.25370437706708
1161414.1000575750994-0.100057575099438
1171714.08779509384162.91220490615841
1181414.4446981873384-0.444698187338398
1191414.3901985336918-0.390198533691821
1201414.3423780443238-0.342378044323771
1211514.30041815925310.699581840746863
1221114.386154888351-3.38615488835099
1231113.9711672093741-2.9711672093741
1241613.60703803491962.39296196508043
1251213.9003056982462-1.90030569824619
1261213.6674151551187-1.66741515511873
1271913.46306633826635.5369336617337
1281814.14164110070163.8583588992984
1291614.61449938895891.38550061104111
1301614.78429837977741.21570162022264
1311314.9332877823118-1.93328778231184
1321114.6963551445474-3.69635514454739
1331014.2433511052499-4.24335110524988
1341413.72331038522560.276689614774375
1351413.75721987395790.242780126042113
1361413.78697361066810.213026389331919
1371613.81308090043612.18691909956387
1381014.0810971345311-4.08109713453115
1391613.58094132849742.41905867150261
140713.8774072541552-6.87740725415523
1411613.03455175348122.96544824651876
1421513.39798004472171.6020199552783
1431713.59431440178343.40568559821663
1441114.0116956522959-3.01169565229587
1451113.6425995448406-2.64259954484057
1461013.3187377346938-3.31873773469377
1471312.91201231454490.0879876854550687
1481412.92279557950751.07720442049245
1491313.0548115613463-0.0548115613463214
1501313.048094171453-0.0480941714530054
1511213.0422000262524-1.04220002625242
1521012.9144739817611-2.91447398176106
1531512.55729280340142.44270719659861
154612.8566569563596-6.85665695635964
1551512.01634449290762.98365550709243
1561512.38200416134582.6179958386542
1571112.7028506826883-1.70285068268829
1581412.49415909126581.5058409087342
1591412.6787062972351.32129370276502
1601612.84063645844633.15936354155368
1611213.2278298935913-1.2278298935913
1621513.07735411958791.92264588041207
1632013.31298254702686.68701745297317
1641214.1325049680578-2.13250496805782
165913.8711574171394-4.87115741713939
1661313.2741763642573-0.274176364257254
1671513.24057488506181.75942511493818
1681913.45619991370235.54380008629768
1691114.1356161856629-3.13561618566292
1701113.7513330899525-2.75133308995245
1711713.41414552153393.58585447846611
1721513.85360723437131.14639276562868
1731413.99410254208470.00589745791526752
1741513.99482530062731.00517469937267
1751114.1180137338836-3.11801373388358
1761213.7358878934816-1.73588789348159
1771513.52314745140721.47685254859276
1781613.7041420105872.29585798941296
1791613.98550916882452.01449083117554







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
18014.232393585498.3172555587001920.1475316122799
18114.232393585498.2729997749636120.1917873960164
18214.232393585498.2290702307217820.2357169402583
18314.232393585498.1854598158121120.2793273551679
18414.232393585498.1421616746481620.3226254963319
18514.232393585498.0991691936385520.3656179773415
18614.232393585498.0564759893941120.4083111815859
18714.232393585498.014075897663820.4507112733162
18814.232393585497.9719629629451320.4928242080349
18914.232393585497.9301314287193920.5346557422606
19014.232393585497.8885757282664620.5762114427136
19114.232393585497.8472904760176420.6174966949624

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
180 & 14.23239358549 & 8.31725555870019 & 20.1475316122799 \tabularnewline
181 & 14.23239358549 & 8.27299977496361 & 20.1917873960164 \tabularnewline
182 & 14.23239358549 & 8.22907023072178 & 20.2357169402583 \tabularnewline
183 & 14.23239358549 & 8.18545981581211 & 20.2793273551679 \tabularnewline
184 & 14.23239358549 & 8.14216167464816 & 20.3226254963319 \tabularnewline
185 & 14.23239358549 & 8.09916919363855 & 20.3656179773415 \tabularnewline
186 & 14.23239358549 & 8.05647598939411 & 20.4083111815859 \tabularnewline
187 & 14.23239358549 & 8.0140758976638 & 20.4507112733162 \tabularnewline
188 & 14.23239358549 & 7.97196296294513 & 20.4928242080349 \tabularnewline
189 & 14.23239358549 & 7.93013142871939 & 20.5346557422606 \tabularnewline
190 & 14.23239358549 & 7.88857572826646 & 20.5762114427136 \tabularnewline
191 & 14.23239358549 & 7.84729047601764 & 20.6174966949624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314846&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]14.23239358549[/C][C]8.31725555870019[/C][C]20.1475316122799[/C][/ROW]
[ROW][C]181[/C][C]14.23239358549[/C][C]8.27299977496361[/C][C]20.1917873960164[/C][/ROW]
[ROW][C]182[/C][C]14.23239358549[/C][C]8.22907023072178[/C][C]20.2357169402583[/C][/ROW]
[ROW][C]183[/C][C]14.23239358549[/C][C]8.18545981581211[/C][C]20.2793273551679[/C][/ROW]
[ROW][C]184[/C][C]14.23239358549[/C][C]8.14216167464816[/C][C]20.3226254963319[/C][/ROW]
[ROW][C]185[/C][C]14.23239358549[/C][C]8.09916919363855[/C][C]20.3656179773415[/C][/ROW]
[ROW][C]186[/C][C]14.23239358549[/C][C]8.05647598939411[/C][C]20.4083111815859[/C][/ROW]
[ROW][C]187[/C][C]14.23239358549[/C][C]8.0140758976638[/C][C]20.4507112733162[/C][/ROW]
[ROW][C]188[/C][C]14.23239358549[/C][C]7.97196296294513[/C][C]20.4928242080349[/C][/ROW]
[ROW][C]189[/C][C]14.23239358549[/C][C]7.93013142871939[/C][C]20.5346557422606[/C][/ROW]
[ROW][C]190[/C][C]14.23239358549[/C][C]7.88857572826646[/C][C]20.5762114427136[/C][/ROW]
[ROW][C]191[/C][C]14.23239358549[/C][C]7.84729047601764[/C][C]20.6174966949624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=314846&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314846&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
18014.232393585498.3172555587001920.1475316122799
18114.232393585498.2729997749636120.1917873960164
18214.232393585498.2290702307217820.2357169402583
18314.232393585498.1854598158121120.2793273551679
18414.232393585498.1421616746481620.3226254963319
18514.232393585498.0991691936385520.3656179773415
18614.232393585498.0564759893941120.4083111815859
18714.232393585498.014075897663820.4507112733162
18814.232393585497.9719629629451320.4928242080349
18914.232393585497.9301314287193920.5346557422606
19014.232393585497.8885757282664620.5762114427136
19114.232393585497.8472904760176420.6174966949624



Parameters (Session):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')