Free Statistics

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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 17 Dec 2014 12:29:23 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/17/t1418819386gdw0yz62osdashz.htm/, Retrieved Thu, 16 May 2024 15:23:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270125, Retrieved Thu, 16 May 2024 15:23:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [ES] [2014-12-17 12:09:36] [40df8d8b5657a9599acc6ccced535535]
- R P     [Exponential Smoothing] [ES] [2014-12-17 12:29:23] [eeaae55b7499419163eef5a1870a44a7] [Current]
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Dataseries X:
12.9
12.2
12.8
7.4
6.7
12.6
14.8
13.3
11.1
8.2
11.4
6.4
10.6
12
6.3
11.3
11.9
9.3
9.6
10
6.4
13.8
10.8
13.8
11.7
10.9
16.1
13.4
9.9
11.5
8.3
11.7
9
9.7
10.8
10.3
10.4
12.7
9.3
11.8
5.9
11.4
13
10.8
12.3
11.3
11.8
7.9
12.7
12.3
11.6
6.7
10.9
12.1
13.3
10.1
5.7
14.3
8
13.3
9.3
12.5
7.6
15.9
9.2
9.1
11.1
13
14.5
12.2
12.3
11.4
8.8
14.6
12.6
13
12.6
13.2
9.9
7.7
10.5
13.4
10.9
4.3
10.3
11.8
11.2
11.4
8.6
13.2
12.6
5.6
9.9
8.8
7.7
9
7.3
11.4
13.6
7.9
10.7
10.3
8.3
9.6
14.2
8.5
13.5
4.9
6.4
9.6
11.6
11.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270125&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270125&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270125&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.171818375249304
beta0.181913978203242
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.171818375249304 \tabularnewline
beta & 0.181913978203242 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270125&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]0.171818375249304[/C][/ROW]
[ROW][C]beta[/C][C]0.181913978203242[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270125&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270125&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
alpha0.171818375249304
beta0.181913978203242
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
312.811.51.3
47.411.0639969012451-3.66399690124512
56.79.66056543151196-2.96056543151196
612.68.285460494844174.31453950515583
714.88.295208223254016.50479177674599
813.38.884596378020324.41540362197968
911.19.252997835255041.84700216474496
108.29.23783093000338-1.03783093000338
1111.48.694558075617742.70544192438226
126.48.87901001812841-2.47901001812841
1310.68.095193507213052.50480649278695
14128.245978894696513.75402110530349
156.38.72873860720532-2.42873860720532
1611.38.073273538721143.22672646127886
1711.98.490376381588583.40962361841142
189.39.04547607240730.254523927592704
199.69.066427102265990.533572897734006
20109.152001314877610.847998685122393
216.49.31810484153292-2.91810484153292
2213.88.745913815225375.05408618477463
2310.89.70146304575581.0985369542442
2413.810.01171228566653.78828771433346
2511.710.90251747372390.797482526276125
2610.911.304373618446-0.40437361844601
2716.111.48708962489444.61291037510557
2813.412.67604909926510.723950900734904
299.913.2194418035434-3.31944180354341
3011.512.9643523249134-1.46435232491336
318.312.9822312697734-4.68223126977337
3211.712.3008708933286-0.600870893328555
33912.3019823062845-3.30198230628451
349.711.7357858438473-2.0357858438473
3510.811.3235143437822-0.523514343782177
3610.311.1547158255195-0.854715825519456
3710.410.9022956686233-0.502295668623324
3812.710.69472793460982.00527206539019
399.310.9806835273635-1.68068352736346
4011.810.580792498681.21920750132002
415.910.7172637847635-4.8172637847635
4211.49.665989194526231.73401080547377
43139.794542486604053.20545751339595
4410.810.27610766758170.52389233241829
4512.310.31330554078821.98669445921183
4611.310.66393614690430.636063853095694
4711.810.80238451293060.997615487069439
487.911.0341357267173-3.13413572671731
4912.710.45801509921152.24198490078851
5012.310.87568663119371.42431336880627
5111.611.19738574154810.402614258451864
526.711.3561223481271-4.65612234812715
5310.910.50014252564080.399857474359177
5412.110.52537095241051.57462904758946
5513.310.80166358620012.49833641379991
5610.111.3147545319594-1.2147545319594
575.711.1518996571882-5.45189965718825
5814.310.09061992058124.20938007941878
59810.8208946459634-2.82089464596336
6013.310.25506864431353.04493135568647
619.310.7922722101021-1.49227221010207
6212.510.50325812585621.99674187414383
637.610.8761312646107-3.27613126461073
6415.910.24062861111965.65937138888043
659.211.3172997468171-2.11729974681707
669.110.9916172146472-1.89161721464721
6711.110.64558639026910.454413609730928
681310.71684999680722.28315000319278
6914.511.17368663055383.32631336944618
7012.211.9137256957660.286274304233991
7112.312.14037802474980.159621975250177
7211.412.3502583270097-0.950258327009662
738.812.3397393687411-3.53973936874107
7414.611.77366131031492.82633868968513
7512.612.38973294668260.210267053317436
761312.56288754649180.437112453508188
7712.612.7886808130022-0.188680813002224
7813.212.90105385875190.298946141248067
799.913.1065540851775-3.20655408517754
807.712.6095203773563-4.90952037735628
8110.511.6664329931978-1.16643299319784
8213.411.33001858067292.06998141932705
8310.911.6143793132129-0.714379313212888
844.311.3980069514864-7.09800695148641
8510.39.862953590199630.437046409800368
8611.89.636221249200592.16377875079941
8711.29.773804677385021.42619532261498
8811.49.829235114470151.57076488552985
898.69.95860134410044-1.35860134410044
9013.29.542183960992663.65781603900734
9112.610.10200856084182.49799143915824
925.610.5406316128882-4.94063161288824
939.99.546737345244070.35326265475593
948.89.47347302494031-0.673473024940307
957.79.20274646490904-1.50274646490904
9698.742565399571830.257434600428175
977.38.59286220315947-1.29286220315947
9811.48.136379615529333.26362038447067
9913.68.564792717483185.03520728251682
1007.99.45497826732469-1.55497826732469
10110.79.164246187396681.53575381260332
10210.39.452560445064260.847439554935743
1038.39.6490973751717-1.3490973751717
1049.69.426061289733290.173938710266709
10514.29.470147446824584.72985255317542
1068.510.4448603660823-1.94486036608229
10713.510.21194608140763.28805391859243
1084.910.9809145800239-6.08091458002393
1096.49.95005606902903-3.55005606902903
1109.69.243084420072810.35691557992719
11111.69.218558103946382.38144189605362
11211.19.616317348970661.48368265102934

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 12.8 & 11.5 & 1.3 \tabularnewline
4 & 7.4 & 11.0639969012451 & -3.66399690124512 \tabularnewline
5 & 6.7 & 9.66056543151196 & -2.96056543151196 \tabularnewline
6 & 12.6 & 8.28546049484417 & 4.31453950515583 \tabularnewline
7 & 14.8 & 8.29520822325401 & 6.50479177674599 \tabularnewline
8 & 13.3 & 8.88459637802032 & 4.41540362197968 \tabularnewline
9 & 11.1 & 9.25299783525504 & 1.84700216474496 \tabularnewline
10 & 8.2 & 9.23783093000338 & -1.03783093000338 \tabularnewline
11 & 11.4 & 8.69455807561774 & 2.70544192438226 \tabularnewline
12 & 6.4 & 8.87901001812841 & -2.47901001812841 \tabularnewline
13 & 10.6 & 8.09519350721305 & 2.50480649278695 \tabularnewline
14 & 12 & 8.24597889469651 & 3.75402110530349 \tabularnewline
15 & 6.3 & 8.72873860720532 & -2.42873860720532 \tabularnewline
16 & 11.3 & 8.07327353872114 & 3.22672646127886 \tabularnewline
17 & 11.9 & 8.49037638158858 & 3.40962361841142 \tabularnewline
18 & 9.3 & 9.0454760724073 & 0.254523927592704 \tabularnewline
19 & 9.6 & 9.06642710226599 & 0.533572897734006 \tabularnewline
20 & 10 & 9.15200131487761 & 0.847998685122393 \tabularnewline
21 & 6.4 & 9.31810484153292 & -2.91810484153292 \tabularnewline
22 & 13.8 & 8.74591381522537 & 5.05408618477463 \tabularnewline
23 & 10.8 & 9.7014630457558 & 1.0985369542442 \tabularnewline
24 & 13.8 & 10.0117122856665 & 3.78828771433346 \tabularnewline
25 & 11.7 & 10.9025174737239 & 0.797482526276125 \tabularnewline
26 & 10.9 & 11.304373618446 & -0.40437361844601 \tabularnewline
27 & 16.1 & 11.4870896248944 & 4.61291037510557 \tabularnewline
28 & 13.4 & 12.6760490992651 & 0.723950900734904 \tabularnewline
29 & 9.9 & 13.2194418035434 & -3.31944180354341 \tabularnewline
30 & 11.5 & 12.9643523249134 & -1.46435232491336 \tabularnewline
31 & 8.3 & 12.9822312697734 & -4.68223126977337 \tabularnewline
32 & 11.7 & 12.3008708933286 & -0.600870893328555 \tabularnewline
33 & 9 & 12.3019823062845 & -3.30198230628451 \tabularnewline
34 & 9.7 & 11.7357858438473 & -2.0357858438473 \tabularnewline
35 & 10.8 & 11.3235143437822 & -0.523514343782177 \tabularnewline
36 & 10.3 & 11.1547158255195 & -0.854715825519456 \tabularnewline
37 & 10.4 & 10.9022956686233 & -0.502295668623324 \tabularnewline
38 & 12.7 & 10.6947279346098 & 2.00527206539019 \tabularnewline
39 & 9.3 & 10.9806835273635 & -1.68068352736346 \tabularnewline
40 & 11.8 & 10.58079249868 & 1.21920750132002 \tabularnewline
41 & 5.9 & 10.7172637847635 & -4.8172637847635 \tabularnewline
42 & 11.4 & 9.66598919452623 & 1.73401080547377 \tabularnewline
43 & 13 & 9.79454248660405 & 3.20545751339595 \tabularnewline
44 & 10.8 & 10.2761076675817 & 0.52389233241829 \tabularnewline
45 & 12.3 & 10.3133055407882 & 1.98669445921183 \tabularnewline
46 & 11.3 & 10.6639361469043 & 0.636063853095694 \tabularnewline
47 & 11.8 & 10.8023845129306 & 0.997615487069439 \tabularnewline
48 & 7.9 & 11.0341357267173 & -3.13413572671731 \tabularnewline
49 & 12.7 & 10.4580150992115 & 2.24198490078851 \tabularnewline
50 & 12.3 & 10.8756866311937 & 1.42431336880627 \tabularnewline
51 & 11.6 & 11.1973857415481 & 0.402614258451864 \tabularnewline
52 & 6.7 & 11.3561223481271 & -4.65612234812715 \tabularnewline
53 & 10.9 & 10.5001425256408 & 0.399857474359177 \tabularnewline
54 & 12.1 & 10.5253709524105 & 1.57462904758946 \tabularnewline
55 & 13.3 & 10.8016635862001 & 2.49833641379991 \tabularnewline
56 & 10.1 & 11.3147545319594 & -1.2147545319594 \tabularnewline
57 & 5.7 & 11.1518996571882 & -5.45189965718825 \tabularnewline
58 & 14.3 & 10.0906199205812 & 4.20938007941878 \tabularnewline
59 & 8 & 10.8208946459634 & -2.82089464596336 \tabularnewline
60 & 13.3 & 10.2550686443135 & 3.04493135568647 \tabularnewline
61 & 9.3 & 10.7922722101021 & -1.49227221010207 \tabularnewline
62 & 12.5 & 10.5032581258562 & 1.99674187414383 \tabularnewline
63 & 7.6 & 10.8761312646107 & -3.27613126461073 \tabularnewline
64 & 15.9 & 10.2406286111196 & 5.65937138888043 \tabularnewline
65 & 9.2 & 11.3172997468171 & -2.11729974681707 \tabularnewline
66 & 9.1 & 10.9916172146472 & -1.89161721464721 \tabularnewline
67 & 11.1 & 10.6455863902691 & 0.454413609730928 \tabularnewline
68 & 13 & 10.7168499968072 & 2.28315000319278 \tabularnewline
69 & 14.5 & 11.1736866305538 & 3.32631336944618 \tabularnewline
70 & 12.2 & 11.913725695766 & 0.286274304233991 \tabularnewline
71 & 12.3 & 12.1403780247498 & 0.159621975250177 \tabularnewline
72 & 11.4 & 12.3502583270097 & -0.950258327009662 \tabularnewline
73 & 8.8 & 12.3397393687411 & -3.53973936874107 \tabularnewline
74 & 14.6 & 11.7736613103149 & 2.82633868968513 \tabularnewline
75 & 12.6 & 12.3897329466826 & 0.210267053317436 \tabularnewline
76 & 13 & 12.5628875464918 & 0.437112453508188 \tabularnewline
77 & 12.6 & 12.7886808130022 & -0.188680813002224 \tabularnewline
78 & 13.2 & 12.9010538587519 & 0.298946141248067 \tabularnewline
79 & 9.9 & 13.1065540851775 & -3.20655408517754 \tabularnewline
80 & 7.7 & 12.6095203773563 & -4.90952037735628 \tabularnewline
81 & 10.5 & 11.6664329931978 & -1.16643299319784 \tabularnewline
82 & 13.4 & 11.3300185806729 & 2.06998141932705 \tabularnewline
83 & 10.9 & 11.6143793132129 & -0.714379313212888 \tabularnewline
84 & 4.3 & 11.3980069514864 & -7.09800695148641 \tabularnewline
85 & 10.3 & 9.86295359019963 & 0.437046409800368 \tabularnewline
86 & 11.8 & 9.63622124920059 & 2.16377875079941 \tabularnewline
87 & 11.2 & 9.77380467738502 & 1.42619532261498 \tabularnewline
88 & 11.4 & 9.82923511447015 & 1.57076488552985 \tabularnewline
89 & 8.6 & 9.95860134410044 & -1.35860134410044 \tabularnewline
90 & 13.2 & 9.54218396099266 & 3.65781603900734 \tabularnewline
91 & 12.6 & 10.1020085608418 & 2.49799143915824 \tabularnewline
92 & 5.6 & 10.5406316128882 & -4.94063161288824 \tabularnewline
93 & 9.9 & 9.54673734524407 & 0.35326265475593 \tabularnewline
94 & 8.8 & 9.47347302494031 & -0.673473024940307 \tabularnewline
95 & 7.7 & 9.20274646490904 & -1.50274646490904 \tabularnewline
96 & 9 & 8.74256539957183 & 0.257434600428175 \tabularnewline
97 & 7.3 & 8.59286220315947 & -1.29286220315947 \tabularnewline
98 & 11.4 & 8.13637961552933 & 3.26362038447067 \tabularnewline
99 & 13.6 & 8.56479271748318 & 5.03520728251682 \tabularnewline
100 & 7.9 & 9.45497826732469 & -1.55497826732469 \tabularnewline
101 & 10.7 & 9.16424618739668 & 1.53575381260332 \tabularnewline
102 & 10.3 & 9.45256044506426 & 0.847439554935743 \tabularnewline
103 & 8.3 & 9.6490973751717 & -1.3490973751717 \tabularnewline
104 & 9.6 & 9.42606128973329 & 0.173938710266709 \tabularnewline
105 & 14.2 & 9.47014744682458 & 4.72985255317542 \tabularnewline
106 & 8.5 & 10.4448603660823 & -1.94486036608229 \tabularnewline
107 & 13.5 & 10.2119460814076 & 3.28805391859243 \tabularnewline
108 & 4.9 & 10.9809145800239 & -6.08091458002393 \tabularnewline
109 & 6.4 & 9.95005606902903 & -3.55005606902903 \tabularnewline
110 & 9.6 & 9.24308442007281 & 0.35691557992719 \tabularnewline
111 & 11.6 & 9.21855810394638 & 2.38144189605362 \tabularnewline
112 & 11.1 & 9.61631734897066 & 1.48368265102934 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270125&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]12.8[/C][C]11.5[/C][C]1.3[/C][/ROW]
[ROW][C]4[/C][C]7.4[/C][C]11.0639969012451[/C][C]-3.66399690124512[/C][/ROW]
[ROW][C]5[/C][C]6.7[/C][C]9.66056543151196[/C][C]-2.96056543151196[/C][/ROW]
[ROW][C]6[/C][C]12.6[/C][C]8.28546049484417[/C][C]4.31453950515583[/C][/ROW]
[ROW][C]7[/C][C]14.8[/C][C]8.29520822325401[/C][C]6.50479177674599[/C][/ROW]
[ROW][C]8[/C][C]13.3[/C][C]8.88459637802032[/C][C]4.41540362197968[/C][/ROW]
[ROW][C]9[/C][C]11.1[/C][C]9.25299783525504[/C][C]1.84700216474496[/C][/ROW]
[ROW][C]10[/C][C]8.2[/C][C]9.23783093000338[/C][C]-1.03783093000338[/C][/ROW]
[ROW][C]11[/C][C]11.4[/C][C]8.69455807561774[/C][C]2.70544192438226[/C][/ROW]
[ROW][C]12[/C][C]6.4[/C][C]8.87901001812841[/C][C]-2.47901001812841[/C][/ROW]
[ROW][C]13[/C][C]10.6[/C][C]8.09519350721305[/C][C]2.50480649278695[/C][/ROW]
[ROW][C]14[/C][C]12[/C][C]8.24597889469651[/C][C]3.75402110530349[/C][/ROW]
[ROW][C]15[/C][C]6.3[/C][C]8.72873860720532[/C][C]-2.42873860720532[/C][/ROW]
[ROW][C]16[/C][C]11.3[/C][C]8.07327353872114[/C][C]3.22672646127886[/C][/ROW]
[ROW][C]17[/C][C]11.9[/C][C]8.49037638158858[/C][C]3.40962361841142[/C][/ROW]
[ROW][C]18[/C][C]9.3[/C][C]9.0454760724073[/C][C]0.254523927592704[/C][/ROW]
[ROW][C]19[/C][C]9.6[/C][C]9.06642710226599[/C][C]0.533572897734006[/C][/ROW]
[ROW][C]20[/C][C]10[/C][C]9.15200131487761[/C][C]0.847998685122393[/C][/ROW]
[ROW][C]21[/C][C]6.4[/C][C]9.31810484153292[/C][C]-2.91810484153292[/C][/ROW]
[ROW][C]22[/C][C]13.8[/C][C]8.74591381522537[/C][C]5.05408618477463[/C][/ROW]
[ROW][C]23[/C][C]10.8[/C][C]9.7014630457558[/C][C]1.0985369542442[/C][/ROW]
[ROW][C]24[/C][C]13.8[/C][C]10.0117122856665[/C][C]3.78828771433346[/C][/ROW]
[ROW][C]25[/C][C]11.7[/C][C]10.9025174737239[/C][C]0.797482526276125[/C][/ROW]
[ROW][C]26[/C][C]10.9[/C][C]11.304373618446[/C][C]-0.40437361844601[/C][/ROW]
[ROW][C]27[/C][C]16.1[/C][C]11.4870896248944[/C][C]4.61291037510557[/C][/ROW]
[ROW][C]28[/C][C]13.4[/C][C]12.6760490992651[/C][C]0.723950900734904[/C][/ROW]
[ROW][C]29[/C][C]9.9[/C][C]13.2194418035434[/C][C]-3.31944180354341[/C][/ROW]
[ROW][C]30[/C][C]11.5[/C][C]12.9643523249134[/C][C]-1.46435232491336[/C][/ROW]
[ROW][C]31[/C][C]8.3[/C][C]12.9822312697734[/C][C]-4.68223126977337[/C][/ROW]
[ROW][C]32[/C][C]11.7[/C][C]12.3008708933286[/C][C]-0.600870893328555[/C][/ROW]
[ROW][C]33[/C][C]9[/C][C]12.3019823062845[/C][C]-3.30198230628451[/C][/ROW]
[ROW][C]34[/C][C]9.7[/C][C]11.7357858438473[/C][C]-2.0357858438473[/C][/ROW]
[ROW][C]35[/C][C]10.8[/C][C]11.3235143437822[/C][C]-0.523514343782177[/C][/ROW]
[ROW][C]36[/C][C]10.3[/C][C]11.1547158255195[/C][C]-0.854715825519456[/C][/ROW]
[ROW][C]37[/C][C]10.4[/C][C]10.9022956686233[/C][C]-0.502295668623324[/C][/ROW]
[ROW][C]38[/C][C]12.7[/C][C]10.6947279346098[/C][C]2.00527206539019[/C][/ROW]
[ROW][C]39[/C][C]9.3[/C][C]10.9806835273635[/C][C]-1.68068352736346[/C][/ROW]
[ROW][C]40[/C][C]11.8[/C][C]10.58079249868[/C][C]1.21920750132002[/C][/ROW]
[ROW][C]41[/C][C]5.9[/C][C]10.7172637847635[/C][C]-4.8172637847635[/C][/ROW]
[ROW][C]42[/C][C]11.4[/C][C]9.66598919452623[/C][C]1.73401080547377[/C][/ROW]
[ROW][C]43[/C][C]13[/C][C]9.79454248660405[/C][C]3.20545751339595[/C][/ROW]
[ROW][C]44[/C][C]10.8[/C][C]10.2761076675817[/C][C]0.52389233241829[/C][/ROW]
[ROW][C]45[/C][C]12.3[/C][C]10.3133055407882[/C][C]1.98669445921183[/C][/ROW]
[ROW][C]46[/C][C]11.3[/C][C]10.6639361469043[/C][C]0.636063853095694[/C][/ROW]
[ROW][C]47[/C][C]11.8[/C][C]10.8023845129306[/C][C]0.997615487069439[/C][/ROW]
[ROW][C]48[/C][C]7.9[/C][C]11.0341357267173[/C][C]-3.13413572671731[/C][/ROW]
[ROW][C]49[/C][C]12.7[/C][C]10.4580150992115[/C][C]2.24198490078851[/C][/ROW]
[ROW][C]50[/C][C]12.3[/C][C]10.8756866311937[/C][C]1.42431336880627[/C][/ROW]
[ROW][C]51[/C][C]11.6[/C][C]11.1973857415481[/C][C]0.402614258451864[/C][/ROW]
[ROW][C]52[/C][C]6.7[/C][C]11.3561223481271[/C][C]-4.65612234812715[/C][/ROW]
[ROW][C]53[/C][C]10.9[/C][C]10.5001425256408[/C][C]0.399857474359177[/C][/ROW]
[ROW][C]54[/C][C]12.1[/C][C]10.5253709524105[/C][C]1.57462904758946[/C][/ROW]
[ROW][C]55[/C][C]13.3[/C][C]10.8016635862001[/C][C]2.49833641379991[/C][/ROW]
[ROW][C]56[/C][C]10.1[/C][C]11.3147545319594[/C][C]-1.2147545319594[/C][/ROW]
[ROW][C]57[/C][C]5.7[/C][C]11.1518996571882[/C][C]-5.45189965718825[/C][/ROW]
[ROW][C]58[/C][C]14.3[/C][C]10.0906199205812[/C][C]4.20938007941878[/C][/ROW]
[ROW][C]59[/C][C]8[/C][C]10.8208946459634[/C][C]-2.82089464596336[/C][/ROW]
[ROW][C]60[/C][C]13.3[/C][C]10.2550686443135[/C][C]3.04493135568647[/C][/ROW]
[ROW][C]61[/C][C]9.3[/C][C]10.7922722101021[/C][C]-1.49227221010207[/C][/ROW]
[ROW][C]62[/C][C]12.5[/C][C]10.5032581258562[/C][C]1.99674187414383[/C][/ROW]
[ROW][C]63[/C][C]7.6[/C][C]10.8761312646107[/C][C]-3.27613126461073[/C][/ROW]
[ROW][C]64[/C][C]15.9[/C][C]10.2406286111196[/C][C]5.65937138888043[/C][/ROW]
[ROW][C]65[/C][C]9.2[/C][C]11.3172997468171[/C][C]-2.11729974681707[/C][/ROW]
[ROW][C]66[/C][C]9.1[/C][C]10.9916172146472[/C][C]-1.89161721464721[/C][/ROW]
[ROW][C]67[/C][C]11.1[/C][C]10.6455863902691[/C][C]0.454413609730928[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]10.7168499968072[/C][C]2.28315000319278[/C][/ROW]
[ROW][C]69[/C][C]14.5[/C][C]11.1736866305538[/C][C]3.32631336944618[/C][/ROW]
[ROW][C]70[/C][C]12.2[/C][C]11.913725695766[/C][C]0.286274304233991[/C][/ROW]
[ROW][C]71[/C][C]12.3[/C][C]12.1403780247498[/C][C]0.159621975250177[/C][/ROW]
[ROW][C]72[/C][C]11.4[/C][C]12.3502583270097[/C][C]-0.950258327009662[/C][/ROW]
[ROW][C]73[/C][C]8.8[/C][C]12.3397393687411[/C][C]-3.53973936874107[/C][/ROW]
[ROW][C]74[/C][C]14.6[/C][C]11.7736613103149[/C][C]2.82633868968513[/C][/ROW]
[ROW][C]75[/C][C]12.6[/C][C]12.3897329466826[/C][C]0.210267053317436[/C][/ROW]
[ROW][C]76[/C][C]13[/C][C]12.5628875464918[/C][C]0.437112453508188[/C][/ROW]
[ROW][C]77[/C][C]12.6[/C][C]12.7886808130022[/C][C]-0.188680813002224[/C][/ROW]
[ROW][C]78[/C][C]13.2[/C][C]12.9010538587519[/C][C]0.298946141248067[/C][/ROW]
[ROW][C]79[/C][C]9.9[/C][C]13.1065540851775[/C][C]-3.20655408517754[/C][/ROW]
[ROW][C]80[/C][C]7.7[/C][C]12.6095203773563[/C][C]-4.90952037735628[/C][/ROW]
[ROW][C]81[/C][C]10.5[/C][C]11.6664329931978[/C][C]-1.16643299319784[/C][/ROW]
[ROW][C]82[/C][C]13.4[/C][C]11.3300185806729[/C][C]2.06998141932705[/C][/ROW]
[ROW][C]83[/C][C]10.9[/C][C]11.6143793132129[/C][C]-0.714379313212888[/C][/ROW]
[ROW][C]84[/C][C]4.3[/C][C]11.3980069514864[/C][C]-7.09800695148641[/C][/ROW]
[ROW][C]85[/C][C]10.3[/C][C]9.86295359019963[/C][C]0.437046409800368[/C][/ROW]
[ROW][C]86[/C][C]11.8[/C][C]9.63622124920059[/C][C]2.16377875079941[/C][/ROW]
[ROW][C]87[/C][C]11.2[/C][C]9.77380467738502[/C][C]1.42619532261498[/C][/ROW]
[ROW][C]88[/C][C]11.4[/C][C]9.82923511447015[/C][C]1.57076488552985[/C][/ROW]
[ROW][C]89[/C][C]8.6[/C][C]9.95860134410044[/C][C]-1.35860134410044[/C][/ROW]
[ROW][C]90[/C][C]13.2[/C][C]9.54218396099266[/C][C]3.65781603900734[/C][/ROW]
[ROW][C]91[/C][C]12.6[/C][C]10.1020085608418[/C][C]2.49799143915824[/C][/ROW]
[ROW][C]92[/C][C]5.6[/C][C]10.5406316128882[/C][C]-4.94063161288824[/C][/ROW]
[ROW][C]93[/C][C]9.9[/C][C]9.54673734524407[/C][C]0.35326265475593[/C][/ROW]
[ROW][C]94[/C][C]8.8[/C][C]9.47347302494031[/C][C]-0.673473024940307[/C][/ROW]
[ROW][C]95[/C][C]7.7[/C][C]9.20274646490904[/C][C]-1.50274646490904[/C][/ROW]
[ROW][C]96[/C][C]9[/C][C]8.74256539957183[/C][C]0.257434600428175[/C][/ROW]
[ROW][C]97[/C][C]7.3[/C][C]8.59286220315947[/C][C]-1.29286220315947[/C][/ROW]
[ROW][C]98[/C][C]11.4[/C][C]8.13637961552933[/C][C]3.26362038447067[/C][/ROW]
[ROW][C]99[/C][C]13.6[/C][C]8.56479271748318[/C][C]5.03520728251682[/C][/ROW]
[ROW][C]100[/C][C]7.9[/C][C]9.45497826732469[/C][C]-1.55497826732469[/C][/ROW]
[ROW][C]101[/C][C]10.7[/C][C]9.16424618739668[/C][C]1.53575381260332[/C][/ROW]
[ROW][C]102[/C][C]10.3[/C][C]9.45256044506426[/C][C]0.847439554935743[/C][/ROW]
[ROW][C]103[/C][C]8.3[/C][C]9.6490973751717[/C][C]-1.3490973751717[/C][/ROW]
[ROW][C]104[/C][C]9.6[/C][C]9.42606128973329[/C][C]0.173938710266709[/C][/ROW]
[ROW][C]105[/C][C]14.2[/C][C]9.47014744682458[/C][C]4.72985255317542[/C][/ROW]
[ROW][C]106[/C][C]8.5[/C][C]10.4448603660823[/C][C]-1.94486036608229[/C][/ROW]
[ROW][C]107[/C][C]13.5[/C][C]10.2119460814076[/C][C]3.28805391859243[/C][/ROW]
[ROW][C]108[/C][C]4.9[/C][C]10.9809145800239[/C][C]-6.08091458002393[/C][/ROW]
[ROW][C]109[/C][C]6.4[/C][C]9.95005606902903[/C][C]-3.55005606902903[/C][/ROW]
[ROW][C]110[/C][C]9.6[/C][C]9.24308442007281[/C][C]0.35691557992719[/C][/ROW]
[ROW][C]111[/C][C]11.6[/C][C]9.21855810394638[/C][C]2.38144189605362[/C][/ROW]
[ROW][C]112[/C][C]11.1[/C][C]9.61631734897066[/C][C]1.48368265102934[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270125&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270125&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
312.811.51.3
47.411.0639969012451-3.66399690124512
56.79.66056543151196-2.96056543151196
612.68.285460494844174.31453950515583
714.88.295208223254016.50479177674599
813.38.884596378020324.41540362197968
911.19.252997835255041.84700216474496
108.29.23783093000338-1.03783093000338
1111.48.694558075617742.70544192438226
126.48.87901001812841-2.47901001812841
1310.68.095193507213052.50480649278695
14128.245978894696513.75402110530349
156.38.72873860720532-2.42873860720532
1611.38.073273538721143.22672646127886
1711.98.490376381588583.40962361841142
189.39.04547607240730.254523927592704
199.69.066427102265990.533572897734006
20109.152001314877610.847998685122393
216.49.31810484153292-2.91810484153292
2213.88.745913815225375.05408618477463
2310.89.70146304575581.0985369542442
2413.810.01171228566653.78828771433346
2511.710.90251747372390.797482526276125
2610.911.304373618446-0.40437361844601
2716.111.48708962489444.61291037510557
2813.412.67604909926510.723950900734904
299.913.2194418035434-3.31944180354341
3011.512.9643523249134-1.46435232491336
318.312.9822312697734-4.68223126977337
3211.712.3008708933286-0.600870893328555
33912.3019823062845-3.30198230628451
349.711.7357858438473-2.0357858438473
3510.811.3235143437822-0.523514343782177
3610.311.1547158255195-0.854715825519456
3710.410.9022956686233-0.502295668623324
3812.710.69472793460982.00527206539019
399.310.9806835273635-1.68068352736346
4011.810.580792498681.21920750132002
415.910.7172637847635-4.8172637847635
4211.49.665989194526231.73401080547377
43139.794542486604053.20545751339595
4410.810.27610766758170.52389233241829
4512.310.31330554078821.98669445921183
4611.310.66393614690430.636063853095694
4711.810.80238451293060.997615487069439
487.911.0341357267173-3.13413572671731
4912.710.45801509921152.24198490078851
5012.310.87568663119371.42431336880627
5111.611.19738574154810.402614258451864
526.711.3561223481271-4.65612234812715
5310.910.50014252564080.399857474359177
5412.110.52537095241051.57462904758946
5513.310.80166358620012.49833641379991
5610.111.3147545319594-1.2147545319594
575.711.1518996571882-5.45189965718825
5814.310.09061992058124.20938007941878
59810.8208946459634-2.82089464596336
6013.310.25506864431353.04493135568647
619.310.7922722101021-1.49227221010207
6212.510.50325812585621.99674187414383
637.610.8761312646107-3.27613126461073
6415.910.24062861111965.65937138888043
659.211.3172997468171-2.11729974681707
669.110.9916172146472-1.89161721464721
6711.110.64558639026910.454413609730928
681310.71684999680722.28315000319278
6914.511.17368663055383.32631336944618
7012.211.9137256957660.286274304233991
7112.312.14037802474980.159621975250177
7211.412.3502583270097-0.950258327009662
738.812.3397393687411-3.53973936874107
7414.611.77366131031492.82633868968513
7512.612.38973294668260.210267053317436
761312.56288754649180.437112453508188
7712.612.7886808130022-0.188680813002224
7813.212.90105385875190.298946141248067
799.913.1065540851775-3.20655408517754
807.712.6095203773563-4.90952037735628
8110.511.6664329931978-1.16643299319784
8213.411.33001858067292.06998141932705
8310.911.6143793132129-0.714379313212888
844.311.3980069514864-7.09800695148641
8510.39.862953590199630.437046409800368
8611.89.636221249200592.16377875079941
8711.29.773804677385021.42619532261498
8811.49.829235114470151.57076488552985
898.69.95860134410044-1.35860134410044
9013.29.542183960992663.65781603900734
9112.610.10200856084182.49799143915824
925.610.5406316128882-4.94063161288824
939.99.546737345244070.35326265475593
948.89.47347302494031-0.673473024940307
957.79.20274646490904-1.50274646490904
9698.742565399571830.257434600428175
977.38.59286220315947-1.29286220315947
9811.48.136379615529333.26362038447067
9913.68.564792717483185.03520728251682
1007.99.45497826732469-1.55497826732469
10110.79.164246187396681.53575381260332
10210.39.452560445064260.847439554935743
1038.39.6490973751717-1.3490973751717
1049.69.426061289733290.173938710266709
10514.29.470147446824584.72985255317542
1068.510.4448603660823-1.94486036608229
10713.510.21194608140763.28805391859243
1084.910.9809145800239-6.08091458002393
1096.49.95005606902903-3.55005606902903
1109.69.243084420072810.35691557992719
11111.69.218558103946382.38144189605362
11211.19.616317348970661.48368265102934







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1139.906199287666614.4691007611559415.3432978141773
1149.941157283877124.3930803819501215.4892341858041
1159.976115280087634.2836259369377915.6686046232375
11610.01107327629814.138285661878715.8838608907176
11710.04603127250873.9555044663230816.1365580786942
11810.08098926871923.7345853026300116.4273932348083
11910.11594726492973.4755877056574716.7563068242019
12010.15090526114023.1791857283205117.1226247939599
12110.18586325735072.8465104967188217.5252160179826
12210.22082125356122.4789989022629217.9626436048595
12310.25577924977172.0782626642148218.4332958353286
12410.29073724598221.6459843490197418.9354901429447

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
113 & 9.90619928766661 & 4.46910076115594 & 15.3432978141773 \tabularnewline
114 & 9.94115728387712 & 4.39308038195012 & 15.4892341858041 \tabularnewline
115 & 9.97611528008763 & 4.28362593693779 & 15.6686046232375 \tabularnewline
116 & 10.0110732762981 & 4.1382856618787 & 15.8838608907176 \tabularnewline
117 & 10.0460312725087 & 3.95550446632308 & 16.1365580786942 \tabularnewline
118 & 10.0809892687192 & 3.73458530263001 & 16.4273932348083 \tabularnewline
119 & 10.1159472649297 & 3.47558770565747 & 16.7563068242019 \tabularnewline
120 & 10.1509052611402 & 3.17918572832051 & 17.1226247939599 \tabularnewline
121 & 10.1858632573507 & 2.84651049671882 & 17.5252160179826 \tabularnewline
122 & 10.2208212535612 & 2.47899890226292 & 17.9626436048595 \tabularnewline
123 & 10.2557792497717 & 2.07826266421482 & 18.4332958353286 \tabularnewline
124 & 10.2907372459822 & 1.64598434901974 & 18.9354901429447 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270125&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]113[/C][C]9.90619928766661[/C][C]4.46910076115594[/C][C]15.3432978141773[/C][/ROW]
[ROW][C]114[/C][C]9.94115728387712[/C][C]4.39308038195012[/C][C]15.4892341858041[/C][/ROW]
[ROW][C]115[/C][C]9.97611528008763[/C][C]4.28362593693779[/C][C]15.6686046232375[/C][/ROW]
[ROW][C]116[/C][C]10.0110732762981[/C][C]4.1382856618787[/C][C]15.8838608907176[/C][/ROW]
[ROW][C]117[/C][C]10.0460312725087[/C][C]3.95550446632308[/C][C]16.1365580786942[/C][/ROW]
[ROW][C]118[/C][C]10.0809892687192[/C][C]3.73458530263001[/C][C]16.4273932348083[/C][/ROW]
[ROW][C]119[/C][C]10.1159472649297[/C][C]3.47558770565747[/C][C]16.7563068242019[/C][/ROW]
[ROW][C]120[/C][C]10.1509052611402[/C][C]3.17918572832051[/C][C]17.1226247939599[/C][/ROW]
[ROW][C]121[/C][C]10.1858632573507[/C][C]2.84651049671882[/C][C]17.5252160179826[/C][/ROW]
[ROW][C]122[/C][C]10.2208212535612[/C][C]2.47899890226292[/C][C]17.9626436048595[/C][/ROW]
[ROW][C]123[/C][C]10.2557792497717[/C][C]2.07826266421482[/C][C]18.4332958353286[/C][/ROW]
[ROW][C]124[/C][C]10.2907372459822[/C][C]1.64598434901974[/C][C]18.9354901429447[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270125&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270125&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
1139.906199287666614.4691007611559415.3432978141773
1149.941157283877124.3930803819501215.4892341858041
1159.976115280087634.2836259369377915.6686046232375
11610.01107327629814.138285661878715.8838608907176
11710.04603127250873.9555044663230816.1365580786942
11810.08098926871923.7345853026300116.4273932348083
11910.11594726492973.4755877056574716.7563068242019
12010.15090526114023.1791857283205117.1226247939599
12110.18586325735072.8465104967188217.5252160179826
12210.22082125356122.4789989022629217.9626436048595
12310.25577924977172.0782626642148218.4332958353286
12410.29073724598221.6459843490197418.9354901429447



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')