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of Irreproducible Research!

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 12:09:36 +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/t1418818217l4yy4yu57vq4dm0.htm/, Retrieved Thu, 16 May 2024 21:05:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270103, Retrieved Thu, 16 May 2024 21:05:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
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] [eeaae55b7499419163eef5a1870a44a7] [Current]
- R P     [Exponential Smoothing] [ES] [2014-12-17 12:29:23] [40df8d8b5657a9599acc6ccced535535]
- RMP     [Multiple Regression] [MR] [2014-12-17 12:43:41] [40df8d8b5657a9599acc6ccced535535]
- RMP     [ARIMA Forecasting] [ARIMA] [2014-12-17 14:03:06] [40df8d8b5657a9599acc6ccced535535]
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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 time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270103&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]1 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=270103&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270103&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0804776934489517
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0804776934489517 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270103&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]0.0804776934489517[/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=270103&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270103&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
alpha0.0804776934489517
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
212.212.9-0.700000000000001
312.812.8436656145857-0.0436656145857341
47.412.8401515066408-5.44015150664084
56.712.4023406613736-5.70234066137355
612.611.9434294376860.656570562313961
714.811.99626872212752.80373127787245
813.312.22190654842141.0780934515786
911.112.3086690227269-1.20866902272687
108.212.2113981276346-4.01139812763461
1111.411.8885700588171-0.488570058817135
126.411.8492510673953-5.44925106739531
1310.611.4107079104671-0.810707910467102
141211.34546400777190.654535992228109
156.311.3981395547057-5.09813955470573
1611.310.98785304246210.312146957537852
1711.911.01297390962190.887026090378097
189.311.0843597234046-1.78435972340457
199.610.9407585685818-1.34075856858177
201010.8328574115104-0.832857411510387
216.410.7658309680602-4.36583096806017
2213.810.41447896176273.38552103823732
2310.810.68693788604290.113062113957078
2413.810.69603686419073.10396313580935
2511.710.94583665791120.754163342088837
2610.911.0065299841662-0.106529984166224
2716.110.99795669675745.10204330324263
2813.411.4085573736791.99144262632099
299.911.5688240828812-1.66882408288125
3011.511.43452096991890.0654790300810966
318.311.4397905712291-3.1397905712291
3211.711.18710746814380.512892531856179
33911.2283838760948-2.2283838760948
349.711.0490486816279-1.34904868162786
3510.810.9404803553801-0.140480355380097
3610.310.9291748204042-0.629174820404218
3710.410.8785402820819-0.478540282081928
3812.710.84002846395761.85997153604244
399.310.989714683059-1.68971468305896
4011.810.85373034277960.94626965722045
415.910.9298839421734-5.02988394217338
4211.410.52509048419140.87490951580865
431310.59550118400022.40449881599983
4410.810.78900970261260.0109902973874298
4512.310.78989417639661.51010582360337
4611.310.91142400994410.388575990055942
4711.810.94269570935340.857304290646598
487.911.0116895812485-3.11168958124853
4912.710.76126798102051.93873201897948
5012.310.91729266212361.38270733787639
5111.611.02856975939080.571430240609153
526.711.0745571471221-4.37455714712205
5310.910.7225028780610.177497121938957
5412.110.73678743702851.36321256297148
5513.310.84649563977712.4535043602229
5610.111.0439480115548-0.943948011554784
575.710.9679812528491-5.26798125284913
5814.310.54402627248753.75597372751248
59810.8462983747326-2.84629837473258
6013.310.61723484666662.6827651533334
619.310.8331375982721-1.5331375982721
6212.510.70975422062331.7902457793767
637.610.8538290716543-3.25382907165426
6415.910.59196841309045.30803158690962
659.211.019146551959-1.81914655195905
669.110.8727458334118-1.77274583341177
6711.110.73007933766760.369920662332449
681310.75984969933122.24015030066882
6914.510.9401318285083.55986817149202
7012.211.2266218079320.973378192068004
7112.311.30495703968310.995042960316862
7211.411.38503580201210.0149641979879434
738.811.3862400861504-2.58624008615044
7414.611.17810544931183.42189455068817
7512.611.45349162997681.14650837002324
761311.54575997911611.45424002088386
7712.611.6627938617180.937206138281967
7813.211.73821805001321.46178194998683
799.911.8558588896734-1.95585888967342
807.711.6984558775209-3.99845587752087
8110.511.3766693711406-0.87666937114059
8213.411.30611704223392.09388295776615
8310.911.4746279130269-0.574627913026942
844.311.4283831839951-7.12838318399515
8510.310.8547073473269-0.554707347326925
8611.810.81006577947490.989934220525132
8711.210.88973340220890.310266597791083
8811.410.91470294235340.485297057646603
898.610.9537585301904-2.35375853019036
9013.210.76433347274482.43566652725515
9112.610.96035029686921.63964970313084
925.611.0923055230414-5.49230552304139
939.910.6502974428301-0.750297442830078
948.810.5899152352305-1.78991523523047
957.710.44586698563-2.74586698562998
96910.2248859441089-1.22488594410886
977.310.1263099485889-2.82630994858893
9811.49.898855042954671.50114495704533
9913.610.01966372663023.58033627336979
1007.910.3078009316826-2.40780093168262
10110.710.11402666641660.585973333583429
10210.310.1611844487260.138815551274043
1038.310.1723560041073-1.87235600410734
1049.610.0216731115815-0.421673111581484
10514.29.987737832171964.21226216782803
1068.510.326730975641-1.82673097564105
10713.510.17971988016973.3202801198303
1084.910.4469283658181-5.54692836581805
1096.410.0005243652105-3.60052436521045
1109.69.71076246909157-0.110762469091569
11111.69.701848561058371.89815143894163
11211.19.85460741068121.2453925893188

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 12.2 & 12.9 & -0.700000000000001 \tabularnewline
3 & 12.8 & 12.8436656145857 & -0.0436656145857341 \tabularnewline
4 & 7.4 & 12.8401515066408 & -5.44015150664084 \tabularnewline
5 & 6.7 & 12.4023406613736 & -5.70234066137355 \tabularnewline
6 & 12.6 & 11.943429437686 & 0.656570562313961 \tabularnewline
7 & 14.8 & 11.9962687221275 & 2.80373127787245 \tabularnewline
8 & 13.3 & 12.2219065484214 & 1.0780934515786 \tabularnewline
9 & 11.1 & 12.3086690227269 & -1.20866902272687 \tabularnewline
10 & 8.2 & 12.2113981276346 & -4.01139812763461 \tabularnewline
11 & 11.4 & 11.8885700588171 & -0.488570058817135 \tabularnewline
12 & 6.4 & 11.8492510673953 & -5.44925106739531 \tabularnewline
13 & 10.6 & 11.4107079104671 & -0.810707910467102 \tabularnewline
14 & 12 & 11.3454640077719 & 0.654535992228109 \tabularnewline
15 & 6.3 & 11.3981395547057 & -5.09813955470573 \tabularnewline
16 & 11.3 & 10.9878530424621 & 0.312146957537852 \tabularnewline
17 & 11.9 & 11.0129739096219 & 0.887026090378097 \tabularnewline
18 & 9.3 & 11.0843597234046 & -1.78435972340457 \tabularnewline
19 & 9.6 & 10.9407585685818 & -1.34075856858177 \tabularnewline
20 & 10 & 10.8328574115104 & -0.832857411510387 \tabularnewline
21 & 6.4 & 10.7658309680602 & -4.36583096806017 \tabularnewline
22 & 13.8 & 10.4144789617627 & 3.38552103823732 \tabularnewline
23 & 10.8 & 10.6869378860429 & 0.113062113957078 \tabularnewline
24 & 13.8 & 10.6960368641907 & 3.10396313580935 \tabularnewline
25 & 11.7 & 10.9458366579112 & 0.754163342088837 \tabularnewline
26 & 10.9 & 11.0065299841662 & -0.106529984166224 \tabularnewline
27 & 16.1 & 10.9979566967574 & 5.10204330324263 \tabularnewline
28 & 13.4 & 11.408557373679 & 1.99144262632099 \tabularnewline
29 & 9.9 & 11.5688240828812 & -1.66882408288125 \tabularnewline
30 & 11.5 & 11.4345209699189 & 0.0654790300810966 \tabularnewline
31 & 8.3 & 11.4397905712291 & -3.1397905712291 \tabularnewline
32 & 11.7 & 11.1871074681438 & 0.512892531856179 \tabularnewline
33 & 9 & 11.2283838760948 & -2.2283838760948 \tabularnewline
34 & 9.7 & 11.0490486816279 & -1.34904868162786 \tabularnewline
35 & 10.8 & 10.9404803553801 & -0.140480355380097 \tabularnewline
36 & 10.3 & 10.9291748204042 & -0.629174820404218 \tabularnewline
37 & 10.4 & 10.8785402820819 & -0.478540282081928 \tabularnewline
38 & 12.7 & 10.8400284639576 & 1.85997153604244 \tabularnewline
39 & 9.3 & 10.989714683059 & -1.68971468305896 \tabularnewline
40 & 11.8 & 10.8537303427796 & 0.94626965722045 \tabularnewline
41 & 5.9 & 10.9298839421734 & -5.02988394217338 \tabularnewline
42 & 11.4 & 10.5250904841914 & 0.87490951580865 \tabularnewline
43 & 13 & 10.5955011840002 & 2.40449881599983 \tabularnewline
44 & 10.8 & 10.7890097026126 & 0.0109902973874298 \tabularnewline
45 & 12.3 & 10.7898941763966 & 1.51010582360337 \tabularnewline
46 & 11.3 & 10.9114240099441 & 0.388575990055942 \tabularnewline
47 & 11.8 & 10.9426957093534 & 0.857304290646598 \tabularnewline
48 & 7.9 & 11.0116895812485 & -3.11168958124853 \tabularnewline
49 & 12.7 & 10.7612679810205 & 1.93873201897948 \tabularnewline
50 & 12.3 & 10.9172926621236 & 1.38270733787639 \tabularnewline
51 & 11.6 & 11.0285697593908 & 0.571430240609153 \tabularnewline
52 & 6.7 & 11.0745571471221 & -4.37455714712205 \tabularnewline
53 & 10.9 & 10.722502878061 & 0.177497121938957 \tabularnewline
54 & 12.1 & 10.7367874370285 & 1.36321256297148 \tabularnewline
55 & 13.3 & 10.8464956397771 & 2.4535043602229 \tabularnewline
56 & 10.1 & 11.0439480115548 & -0.943948011554784 \tabularnewline
57 & 5.7 & 10.9679812528491 & -5.26798125284913 \tabularnewline
58 & 14.3 & 10.5440262724875 & 3.75597372751248 \tabularnewline
59 & 8 & 10.8462983747326 & -2.84629837473258 \tabularnewline
60 & 13.3 & 10.6172348466666 & 2.6827651533334 \tabularnewline
61 & 9.3 & 10.8331375982721 & -1.5331375982721 \tabularnewline
62 & 12.5 & 10.7097542206233 & 1.7902457793767 \tabularnewline
63 & 7.6 & 10.8538290716543 & -3.25382907165426 \tabularnewline
64 & 15.9 & 10.5919684130904 & 5.30803158690962 \tabularnewline
65 & 9.2 & 11.019146551959 & -1.81914655195905 \tabularnewline
66 & 9.1 & 10.8727458334118 & -1.77274583341177 \tabularnewline
67 & 11.1 & 10.7300793376676 & 0.369920662332449 \tabularnewline
68 & 13 & 10.7598496993312 & 2.24015030066882 \tabularnewline
69 & 14.5 & 10.940131828508 & 3.55986817149202 \tabularnewline
70 & 12.2 & 11.226621807932 & 0.973378192068004 \tabularnewline
71 & 12.3 & 11.3049570396831 & 0.995042960316862 \tabularnewline
72 & 11.4 & 11.3850358020121 & 0.0149641979879434 \tabularnewline
73 & 8.8 & 11.3862400861504 & -2.58624008615044 \tabularnewline
74 & 14.6 & 11.1781054493118 & 3.42189455068817 \tabularnewline
75 & 12.6 & 11.4534916299768 & 1.14650837002324 \tabularnewline
76 & 13 & 11.5457599791161 & 1.45424002088386 \tabularnewline
77 & 12.6 & 11.662793861718 & 0.937206138281967 \tabularnewline
78 & 13.2 & 11.7382180500132 & 1.46178194998683 \tabularnewline
79 & 9.9 & 11.8558588896734 & -1.95585888967342 \tabularnewline
80 & 7.7 & 11.6984558775209 & -3.99845587752087 \tabularnewline
81 & 10.5 & 11.3766693711406 & -0.87666937114059 \tabularnewline
82 & 13.4 & 11.3061170422339 & 2.09388295776615 \tabularnewline
83 & 10.9 & 11.4746279130269 & -0.574627913026942 \tabularnewline
84 & 4.3 & 11.4283831839951 & -7.12838318399515 \tabularnewline
85 & 10.3 & 10.8547073473269 & -0.554707347326925 \tabularnewline
86 & 11.8 & 10.8100657794749 & 0.989934220525132 \tabularnewline
87 & 11.2 & 10.8897334022089 & 0.310266597791083 \tabularnewline
88 & 11.4 & 10.9147029423534 & 0.485297057646603 \tabularnewline
89 & 8.6 & 10.9537585301904 & -2.35375853019036 \tabularnewline
90 & 13.2 & 10.7643334727448 & 2.43566652725515 \tabularnewline
91 & 12.6 & 10.9603502968692 & 1.63964970313084 \tabularnewline
92 & 5.6 & 11.0923055230414 & -5.49230552304139 \tabularnewline
93 & 9.9 & 10.6502974428301 & -0.750297442830078 \tabularnewline
94 & 8.8 & 10.5899152352305 & -1.78991523523047 \tabularnewline
95 & 7.7 & 10.44586698563 & -2.74586698562998 \tabularnewline
96 & 9 & 10.2248859441089 & -1.22488594410886 \tabularnewline
97 & 7.3 & 10.1263099485889 & -2.82630994858893 \tabularnewline
98 & 11.4 & 9.89885504295467 & 1.50114495704533 \tabularnewline
99 & 13.6 & 10.0196637266302 & 3.58033627336979 \tabularnewline
100 & 7.9 & 10.3078009316826 & -2.40780093168262 \tabularnewline
101 & 10.7 & 10.1140266664166 & 0.585973333583429 \tabularnewline
102 & 10.3 & 10.161184448726 & 0.138815551274043 \tabularnewline
103 & 8.3 & 10.1723560041073 & -1.87235600410734 \tabularnewline
104 & 9.6 & 10.0216731115815 & -0.421673111581484 \tabularnewline
105 & 14.2 & 9.98773783217196 & 4.21226216782803 \tabularnewline
106 & 8.5 & 10.326730975641 & -1.82673097564105 \tabularnewline
107 & 13.5 & 10.1797198801697 & 3.3202801198303 \tabularnewline
108 & 4.9 & 10.4469283658181 & -5.54692836581805 \tabularnewline
109 & 6.4 & 10.0005243652105 & -3.60052436521045 \tabularnewline
110 & 9.6 & 9.71076246909157 & -0.110762469091569 \tabularnewline
111 & 11.6 & 9.70184856105837 & 1.89815143894163 \tabularnewline
112 & 11.1 & 9.8546074106812 & 1.2453925893188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270103&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]12.2[/C][C]12.9[/C][C]-0.700000000000001[/C][/ROW]
[ROW][C]3[/C][C]12.8[/C][C]12.8436656145857[/C][C]-0.0436656145857341[/C][/ROW]
[ROW][C]4[/C][C]7.4[/C][C]12.8401515066408[/C][C]-5.44015150664084[/C][/ROW]
[ROW][C]5[/C][C]6.7[/C][C]12.4023406613736[/C][C]-5.70234066137355[/C][/ROW]
[ROW][C]6[/C][C]12.6[/C][C]11.943429437686[/C][C]0.656570562313961[/C][/ROW]
[ROW][C]7[/C][C]14.8[/C][C]11.9962687221275[/C][C]2.80373127787245[/C][/ROW]
[ROW][C]8[/C][C]13.3[/C][C]12.2219065484214[/C][C]1.0780934515786[/C][/ROW]
[ROW][C]9[/C][C]11.1[/C][C]12.3086690227269[/C][C]-1.20866902272687[/C][/ROW]
[ROW][C]10[/C][C]8.2[/C][C]12.2113981276346[/C][C]-4.01139812763461[/C][/ROW]
[ROW][C]11[/C][C]11.4[/C][C]11.8885700588171[/C][C]-0.488570058817135[/C][/ROW]
[ROW][C]12[/C][C]6.4[/C][C]11.8492510673953[/C][C]-5.44925106739531[/C][/ROW]
[ROW][C]13[/C][C]10.6[/C][C]11.4107079104671[/C][C]-0.810707910467102[/C][/ROW]
[ROW][C]14[/C][C]12[/C][C]11.3454640077719[/C][C]0.654535992228109[/C][/ROW]
[ROW][C]15[/C][C]6.3[/C][C]11.3981395547057[/C][C]-5.09813955470573[/C][/ROW]
[ROW][C]16[/C][C]11.3[/C][C]10.9878530424621[/C][C]0.312146957537852[/C][/ROW]
[ROW][C]17[/C][C]11.9[/C][C]11.0129739096219[/C][C]0.887026090378097[/C][/ROW]
[ROW][C]18[/C][C]9.3[/C][C]11.0843597234046[/C][C]-1.78435972340457[/C][/ROW]
[ROW][C]19[/C][C]9.6[/C][C]10.9407585685818[/C][C]-1.34075856858177[/C][/ROW]
[ROW][C]20[/C][C]10[/C][C]10.8328574115104[/C][C]-0.832857411510387[/C][/ROW]
[ROW][C]21[/C][C]6.4[/C][C]10.7658309680602[/C][C]-4.36583096806017[/C][/ROW]
[ROW][C]22[/C][C]13.8[/C][C]10.4144789617627[/C][C]3.38552103823732[/C][/ROW]
[ROW][C]23[/C][C]10.8[/C][C]10.6869378860429[/C][C]0.113062113957078[/C][/ROW]
[ROW][C]24[/C][C]13.8[/C][C]10.6960368641907[/C][C]3.10396313580935[/C][/ROW]
[ROW][C]25[/C][C]11.7[/C][C]10.9458366579112[/C][C]0.754163342088837[/C][/ROW]
[ROW][C]26[/C][C]10.9[/C][C]11.0065299841662[/C][C]-0.106529984166224[/C][/ROW]
[ROW][C]27[/C][C]16.1[/C][C]10.9979566967574[/C][C]5.10204330324263[/C][/ROW]
[ROW][C]28[/C][C]13.4[/C][C]11.408557373679[/C][C]1.99144262632099[/C][/ROW]
[ROW][C]29[/C][C]9.9[/C][C]11.5688240828812[/C][C]-1.66882408288125[/C][/ROW]
[ROW][C]30[/C][C]11.5[/C][C]11.4345209699189[/C][C]0.0654790300810966[/C][/ROW]
[ROW][C]31[/C][C]8.3[/C][C]11.4397905712291[/C][C]-3.1397905712291[/C][/ROW]
[ROW][C]32[/C][C]11.7[/C][C]11.1871074681438[/C][C]0.512892531856179[/C][/ROW]
[ROW][C]33[/C][C]9[/C][C]11.2283838760948[/C][C]-2.2283838760948[/C][/ROW]
[ROW][C]34[/C][C]9.7[/C][C]11.0490486816279[/C][C]-1.34904868162786[/C][/ROW]
[ROW][C]35[/C][C]10.8[/C][C]10.9404803553801[/C][C]-0.140480355380097[/C][/ROW]
[ROW][C]36[/C][C]10.3[/C][C]10.9291748204042[/C][C]-0.629174820404218[/C][/ROW]
[ROW][C]37[/C][C]10.4[/C][C]10.8785402820819[/C][C]-0.478540282081928[/C][/ROW]
[ROW][C]38[/C][C]12.7[/C][C]10.8400284639576[/C][C]1.85997153604244[/C][/ROW]
[ROW][C]39[/C][C]9.3[/C][C]10.989714683059[/C][C]-1.68971468305896[/C][/ROW]
[ROW][C]40[/C][C]11.8[/C][C]10.8537303427796[/C][C]0.94626965722045[/C][/ROW]
[ROW][C]41[/C][C]5.9[/C][C]10.9298839421734[/C][C]-5.02988394217338[/C][/ROW]
[ROW][C]42[/C][C]11.4[/C][C]10.5250904841914[/C][C]0.87490951580865[/C][/ROW]
[ROW][C]43[/C][C]13[/C][C]10.5955011840002[/C][C]2.40449881599983[/C][/ROW]
[ROW][C]44[/C][C]10.8[/C][C]10.7890097026126[/C][C]0.0109902973874298[/C][/ROW]
[ROW][C]45[/C][C]12.3[/C][C]10.7898941763966[/C][C]1.51010582360337[/C][/ROW]
[ROW][C]46[/C][C]11.3[/C][C]10.9114240099441[/C][C]0.388575990055942[/C][/ROW]
[ROW][C]47[/C][C]11.8[/C][C]10.9426957093534[/C][C]0.857304290646598[/C][/ROW]
[ROW][C]48[/C][C]7.9[/C][C]11.0116895812485[/C][C]-3.11168958124853[/C][/ROW]
[ROW][C]49[/C][C]12.7[/C][C]10.7612679810205[/C][C]1.93873201897948[/C][/ROW]
[ROW][C]50[/C][C]12.3[/C][C]10.9172926621236[/C][C]1.38270733787639[/C][/ROW]
[ROW][C]51[/C][C]11.6[/C][C]11.0285697593908[/C][C]0.571430240609153[/C][/ROW]
[ROW][C]52[/C][C]6.7[/C][C]11.0745571471221[/C][C]-4.37455714712205[/C][/ROW]
[ROW][C]53[/C][C]10.9[/C][C]10.722502878061[/C][C]0.177497121938957[/C][/ROW]
[ROW][C]54[/C][C]12.1[/C][C]10.7367874370285[/C][C]1.36321256297148[/C][/ROW]
[ROW][C]55[/C][C]13.3[/C][C]10.8464956397771[/C][C]2.4535043602229[/C][/ROW]
[ROW][C]56[/C][C]10.1[/C][C]11.0439480115548[/C][C]-0.943948011554784[/C][/ROW]
[ROW][C]57[/C][C]5.7[/C][C]10.9679812528491[/C][C]-5.26798125284913[/C][/ROW]
[ROW][C]58[/C][C]14.3[/C][C]10.5440262724875[/C][C]3.75597372751248[/C][/ROW]
[ROW][C]59[/C][C]8[/C][C]10.8462983747326[/C][C]-2.84629837473258[/C][/ROW]
[ROW][C]60[/C][C]13.3[/C][C]10.6172348466666[/C][C]2.6827651533334[/C][/ROW]
[ROW][C]61[/C][C]9.3[/C][C]10.8331375982721[/C][C]-1.5331375982721[/C][/ROW]
[ROW][C]62[/C][C]12.5[/C][C]10.7097542206233[/C][C]1.7902457793767[/C][/ROW]
[ROW][C]63[/C][C]7.6[/C][C]10.8538290716543[/C][C]-3.25382907165426[/C][/ROW]
[ROW][C]64[/C][C]15.9[/C][C]10.5919684130904[/C][C]5.30803158690962[/C][/ROW]
[ROW][C]65[/C][C]9.2[/C][C]11.019146551959[/C][C]-1.81914655195905[/C][/ROW]
[ROW][C]66[/C][C]9.1[/C][C]10.8727458334118[/C][C]-1.77274583341177[/C][/ROW]
[ROW][C]67[/C][C]11.1[/C][C]10.7300793376676[/C][C]0.369920662332449[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]10.7598496993312[/C][C]2.24015030066882[/C][/ROW]
[ROW][C]69[/C][C]14.5[/C][C]10.940131828508[/C][C]3.55986817149202[/C][/ROW]
[ROW][C]70[/C][C]12.2[/C][C]11.226621807932[/C][C]0.973378192068004[/C][/ROW]
[ROW][C]71[/C][C]12.3[/C][C]11.3049570396831[/C][C]0.995042960316862[/C][/ROW]
[ROW][C]72[/C][C]11.4[/C][C]11.3850358020121[/C][C]0.0149641979879434[/C][/ROW]
[ROW][C]73[/C][C]8.8[/C][C]11.3862400861504[/C][C]-2.58624008615044[/C][/ROW]
[ROW][C]74[/C][C]14.6[/C][C]11.1781054493118[/C][C]3.42189455068817[/C][/ROW]
[ROW][C]75[/C][C]12.6[/C][C]11.4534916299768[/C][C]1.14650837002324[/C][/ROW]
[ROW][C]76[/C][C]13[/C][C]11.5457599791161[/C][C]1.45424002088386[/C][/ROW]
[ROW][C]77[/C][C]12.6[/C][C]11.662793861718[/C][C]0.937206138281967[/C][/ROW]
[ROW][C]78[/C][C]13.2[/C][C]11.7382180500132[/C][C]1.46178194998683[/C][/ROW]
[ROW][C]79[/C][C]9.9[/C][C]11.8558588896734[/C][C]-1.95585888967342[/C][/ROW]
[ROW][C]80[/C][C]7.7[/C][C]11.6984558775209[/C][C]-3.99845587752087[/C][/ROW]
[ROW][C]81[/C][C]10.5[/C][C]11.3766693711406[/C][C]-0.87666937114059[/C][/ROW]
[ROW][C]82[/C][C]13.4[/C][C]11.3061170422339[/C][C]2.09388295776615[/C][/ROW]
[ROW][C]83[/C][C]10.9[/C][C]11.4746279130269[/C][C]-0.574627913026942[/C][/ROW]
[ROW][C]84[/C][C]4.3[/C][C]11.4283831839951[/C][C]-7.12838318399515[/C][/ROW]
[ROW][C]85[/C][C]10.3[/C][C]10.8547073473269[/C][C]-0.554707347326925[/C][/ROW]
[ROW][C]86[/C][C]11.8[/C][C]10.8100657794749[/C][C]0.989934220525132[/C][/ROW]
[ROW][C]87[/C][C]11.2[/C][C]10.8897334022089[/C][C]0.310266597791083[/C][/ROW]
[ROW][C]88[/C][C]11.4[/C][C]10.9147029423534[/C][C]0.485297057646603[/C][/ROW]
[ROW][C]89[/C][C]8.6[/C][C]10.9537585301904[/C][C]-2.35375853019036[/C][/ROW]
[ROW][C]90[/C][C]13.2[/C][C]10.7643334727448[/C][C]2.43566652725515[/C][/ROW]
[ROW][C]91[/C][C]12.6[/C][C]10.9603502968692[/C][C]1.63964970313084[/C][/ROW]
[ROW][C]92[/C][C]5.6[/C][C]11.0923055230414[/C][C]-5.49230552304139[/C][/ROW]
[ROW][C]93[/C][C]9.9[/C][C]10.6502974428301[/C][C]-0.750297442830078[/C][/ROW]
[ROW][C]94[/C][C]8.8[/C][C]10.5899152352305[/C][C]-1.78991523523047[/C][/ROW]
[ROW][C]95[/C][C]7.7[/C][C]10.44586698563[/C][C]-2.74586698562998[/C][/ROW]
[ROW][C]96[/C][C]9[/C][C]10.2248859441089[/C][C]-1.22488594410886[/C][/ROW]
[ROW][C]97[/C][C]7.3[/C][C]10.1263099485889[/C][C]-2.82630994858893[/C][/ROW]
[ROW][C]98[/C][C]11.4[/C][C]9.89885504295467[/C][C]1.50114495704533[/C][/ROW]
[ROW][C]99[/C][C]13.6[/C][C]10.0196637266302[/C][C]3.58033627336979[/C][/ROW]
[ROW][C]100[/C][C]7.9[/C][C]10.3078009316826[/C][C]-2.40780093168262[/C][/ROW]
[ROW][C]101[/C][C]10.7[/C][C]10.1140266664166[/C][C]0.585973333583429[/C][/ROW]
[ROW][C]102[/C][C]10.3[/C][C]10.161184448726[/C][C]0.138815551274043[/C][/ROW]
[ROW][C]103[/C][C]8.3[/C][C]10.1723560041073[/C][C]-1.87235600410734[/C][/ROW]
[ROW][C]104[/C][C]9.6[/C][C]10.0216731115815[/C][C]-0.421673111581484[/C][/ROW]
[ROW][C]105[/C][C]14.2[/C][C]9.98773783217196[/C][C]4.21226216782803[/C][/ROW]
[ROW][C]106[/C][C]8.5[/C][C]10.326730975641[/C][C]-1.82673097564105[/C][/ROW]
[ROW][C]107[/C][C]13.5[/C][C]10.1797198801697[/C][C]3.3202801198303[/C][/ROW]
[ROW][C]108[/C][C]4.9[/C][C]10.4469283658181[/C][C]-5.54692836581805[/C][/ROW]
[ROW][C]109[/C][C]6.4[/C][C]10.0005243652105[/C][C]-3.60052436521045[/C][/ROW]
[ROW][C]110[/C][C]9.6[/C][C]9.71076246909157[/C][C]-0.110762469091569[/C][/ROW]
[ROW][C]111[/C][C]11.6[/C][C]9.70184856105837[/C][C]1.89815143894163[/C][/ROW]
[ROW][C]112[/C][C]11.1[/C][C]9.8546074106812[/C][C]1.2453925893188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270103&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270103&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
212.212.9-0.700000000000001
312.812.8436656145857-0.0436656145857341
47.412.8401515066408-5.44015150664084
56.712.4023406613736-5.70234066137355
612.611.9434294376860.656570562313961
714.811.99626872212752.80373127787245
813.312.22190654842141.0780934515786
911.112.3086690227269-1.20866902272687
108.212.2113981276346-4.01139812763461
1111.411.8885700588171-0.488570058817135
126.411.8492510673953-5.44925106739531
1310.611.4107079104671-0.810707910467102
141211.34546400777190.654535992228109
156.311.3981395547057-5.09813955470573
1611.310.98785304246210.312146957537852
1711.911.01297390962190.887026090378097
189.311.0843597234046-1.78435972340457
199.610.9407585685818-1.34075856858177
201010.8328574115104-0.832857411510387
216.410.7658309680602-4.36583096806017
2213.810.41447896176273.38552103823732
2310.810.68693788604290.113062113957078
2413.810.69603686419073.10396313580935
2511.710.94583665791120.754163342088837
2610.911.0065299841662-0.106529984166224
2716.110.99795669675745.10204330324263
2813.411.4085573736791.99144262632099
299.911.5688240828812-1.66882408288125
3011.511.43452096991890.0654790300810966
318.311.4397905712291-3.1397905712291
3211.711.18710746814380.512892531856179
33911.2283838760948-2.2283838760948
349.711.0490486816279-1.34904868162786
3510.810.9404803553801-0.140480355380097
3610.310.9291748204042-0.629174820404218
3710.410.8785402820819-0.478540282081928
3812.710.84002846395761.85997153604244
399.310.989714683059-1.68971468305896
4011.810.85373034277960.94626965722045
415.910.9298839421734-5.02988394217338
4211.410.52509048419140.87490951580865
431310.59550118400022.40449881599983
4410.810.78900970261260.0109902973874298
4512.310.78989417639661.51010582360337
4611.310.91142400994410.388575990055942
4711.810.94269570935340.857304290646598
487.911.0116895812485-3.11168958124853
4912.710.76126798102051.93873201897948
5012.310.91729266212361.38270733787639
5111.611.02856975939080.571430240609153
526.711.0745571471221-4.37455714712205
5310.910.7225028780610.177497121938957
5412.110.73678743702851.36321256297148
5513.310.84649563977712.4535043602229
5610.111.0439480115548-0.943948011554784
575.710.9679812528491-5.26798125284913
5814.310.54402627248753.75597372751248
59810.8462983747326-2.84629837473258
6013.310.61723484666662.6827651533334
619.310.8331375982721-1.5331375982721
6212.510.70975422062331.7902457793767
637.610.8538290716543-3.25382907165426
6415.910.59196841309045.30803158690962
659.211.019146551959-1.81914655195905
669.110.8727458334118-1.77274583341177
6711.110.73007933766760.369920662332449
681310.75984969933122.24015030066882
6914.510.9401318285083.55986817149202
7012.211.2266218079320.973378192068004
7112.311.30495703968310.995042960316862
7211.411.38503580201210.0149641979879434
738.811.3862400861504-2.58624008615044
7414.611.17810544931183.42189455068817
7512.611.45349162997681.14650837002324
761311.54575997911611.45424002088386
7712.611.6627938617180.937206138281967
7813.211.73821805001321.46178194998683
799.911.8558588896734-1.95585888967342
807.711.6984558775209-3.99845587752087
8110.511.3766693711406-0.87666937114059
8213.411.30611704223392.09388295776615
8310.911.4746279130269-0.574627913026942
844.311.4283831839951-7.12838318399515
8510.310.8547073473269-0.554707347326925
8611.810.81006577947490.989934220525132
8711.210.88973340220890.310266597791083
8811.410.91470294235340.485297057646603
898.610.9537585301904-2.35375853019036
9013.210.76433347274482.43566652725515
9112.610.96035029686921.63964970313084
925.611.0923055230414-5.49230552304139
939.910.6502974428301-0.750297442830078
948.810.5899152352305-1.78991523523047
957.710.44586698563-2.74586698562998
96910.2248859441089-1.22488594410886
977.310.1263099485889-2.82630994858893
9811.49.898855042954671.50114495704533
9913.610.01966372663023.58033627336979
1007.910.3078009316826-2.40780093168262
10110.710.11402666641660.585973333583429
10210.310.1611844487260.138815551274043
1038.310.1723560041073-1.87235600410734
1049.610.0216731115815-0.421673111581484
10514.29.987737832171964.21226216782803
1068.510.326730975641-1.82673097564105
10713.510.17971988016973.3202801198303
1084.910.4469283658181-5.54692836581805
1096.410.0005243652105-3.60052436521045
1109.69.71076246909157-0.110762469091569
11111.69.701848561058371.89815143894163
11211.19.85460741068121.2453925893188







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1139.954833733707994.9427199119292414.9669475554867
1149.954833733707994.9265152312264514.9831522361895
1159.954833733707994.9103626055984414.9993048618175
1169.954833733707994.8942615365880415.0154059308279
1179.954833733707994.8782115336426715.0314559337733
1189.954833733707994.8622121139399615.047455353476
1199.954833733707994.8462628022183115.0634046651977
1209.954833733707994.830363130612115.0793043368039
1219.954833733707994.814512638491615.0951548289244
1229.954833733707994.7987108723072615.1109565951087
1239.954833733707994.7829573854382615.1267100819777
1249.954833733707994.7672517380452215.1424157293708

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
113 & 9.95483373370799 & 4.94271991192924 & 14.9669475554867 \tabularnewline
114 & 9.95483373370799 & 4.92651523122645 & 14.9831522361895 \tabularnewline
115 & 9.95483373370799 & 4.91036260559844 & 14.9993048618175 \tabularnewline
116 & 9.95483373370799 & 4.89426153658804 & 15.0154059308279 \tabularnewline
117 & 9.95483373370799 & 4.87821153364267 & 15.0314559337733 \tabularnewline
118 & 9.95483373370799 & 4.86221211393996 & 15.047455353476 \tabularnewline
119 & 9.95483373370799 & 4.84626280221831 & 15.0634046651977 \tabularnewline
120 & 9.95483373370799 & 4.8303631306121 & 15.0793043368039 \tabularnewline
121 & 9.95483373370799 & 4.8145126384916 & 15.0951548289244 \tabularnewline
122 & 9.95483373370799 & 4.79871087230726 & 15.1109565951087 \tabularnewline
123 & 9.95483373370799 & 4.78295738543826 & 15.1267100819777 \tabularnewline
124 & 9.95483373370799 & 4.76725173804522 & 15.1424157293708 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270103&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]9.95483373370799[/C][C]4.94271991192924[/C][C]14.9669475554867[/C][/ROW]
[ROW][C]114[/C][C]9.95483373370799[/C][C]4.92651523122645[/C][C]14.9831522361895[/C][/ROW]
[ROW][C]115[/C][C]9.95483373370799[/C][C]4.91036260559844[/C][C]14.9993048618175[/C][/ROW]
[ROW][C]116[/C][C]9.95483373370799[/C][C]4.89426153658804[/C][C]15.0154059308279[/C][/ROW]
[ROW][C]117[/C][C]9.95483373370799[/C][C]4.87821153364267[/C][C]15.0314559337733[/C][/ROW]
[ROW][C]118[/C][C]9.95483373370799[/C][C]4.86221211393996[/C][C]15.047455353476[/C][/ROW]
[ROW][C]119[/C][C]9.95483373370799[/C][C]4.84626280221831[/C][C]15.0634046651977[/C][/ROW]
[ROW][C]120[/C][C]9.95483373370799[/C][C]4.8303631306121[/C][C]15.0793043368039[/C][/ROW]
[ROW][C]121[/C][C]9.95483373370799[/C][C]4.8145126384916[/C][C]15.0951548289244[/C][/ROW]
[ROW][C]122[/C][C]9.95483373370799[/C][C]4.79871087230726[/C][C]15.1109565951087[/C][/ROW]
[ROW][C]123[/C][C]9.95483373370799[/C][C]4.78295738543826[/C][C]15.1267100819777[/C][/ROW]
[ROW][C]124[/C][C]9.95483373370799[/C][C]4.76725173804522[/C][C]15.1424157293708[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270103&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270103&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
1139.954833733707994.9427199119292414.9669475554867
1149.954833733707994.9265152312264514.9831522361895
1159.954833733707994.9103626055984414.9993048618175
1169.954833733707994.8942615365880415.0154059308279
1179.954833733707994.8782115336426715.0314559337733
1189.954833733707994.8622121139399615.047455353476
1199.954833733707994.8462628022183115.0634046651977
1209.954833733707994.830363130612115.0793043368039
1219.954833733707994.814512638491615.0951548289244
1229.954833733707994.7987108723072615.1109565951087
1239.954833733707994.7829573854382615.1267100819777
1249.954833733707994.7672517380452215.1424157293708



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