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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 23 Nov 2016 16:00:47 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/23/t1479917076vpcdnil8ki392kb.htm/, Retrieved Tue, 07 May 2024 00:14:27 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 07 May 2024 00:14:27 +0200

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Estimated Impact

Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.79967097593047
beta	0.0583923958902654
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.79967097593047 \tabularnewline
beta & 0.0583923958902654 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.79967097593047[/C][/ROW]
[ROW][C]beta[/C][C]0.0583923958902654[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
Parameter	Value
alpha	0.79967097593047
beta	0.0583923958902654
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	96.44	95.8309722222222	0.609027777777754
14	96.83	96.7187051588574	0.111294841142637
15	96.7	96.6931957253212	0.00680427467884215
16	97.06	97.0881959421188	-0.0281959421187992
17	97.64	97.6730575668817	-0.0330575668816522
18	97.61	97.6399878781184	-0.0299878781183764
19	97.61	97.4504726552657	0.159527344734343
20	97.61	97.5207896711341	0.0892103288658888
21	97.55	97.7711251935506	-0.221125193550634
22	97.58	97.8650523637179	-0.285052363717867
23	97.79	97.6653817288546	0.124618271145408
24	97.79	97.9116318236926	-0.121631823692596
25	97.79	97.9431225765256	-0.153122576525618
26	97.79	98.1038981144259	-0.313898114425896
27	98	97.6798099349956	0.320190065004439
28	98.37	98.295405783143	0.0745942168570366
29	98.68	98.9432932160055	-0.263293216005508
30	98.89	98.697776349133	0.192223650866993
31	98.89	98.7053493781506	0.184650621849386
32	98.89	98.7642700763606	0.125729923639383
33	98.88	98.965945184083	-0.0859451840830019
34	98.97	99.1457827449459	-0.175782744945906
35	99.05	99.1112804119747	-0.0612804119747494
36	99.05	99.146580840998	-0.0965808409979871
37	99	99.1800045307713	-0.180004530771271
38	99.03	99.2740290035243	-0.244029003524261
39	99.2	99.0230555678632	0.176944432136764
40	100.3	99.4584294294547	0.841570570545315
41	100.79	100.671298030938	0.11870196906159
42	100.75	100.859683127095	-0.109683127095209
43	100.75	100.64739377433	0.102606225669902
44	100.17	100.648152188899	-0.478152188898832
45	99.98	100.31556729866	-0.335567298660337
46	99.93	100.257187865918	-0.327187865918177
47	100.04	100.096875212642	-0.0568752126418701
48	100.04	100.101158170625	-0.0611581706249922
49	100.49	100.12038172595	0.369618274050069
50	100.71	100.640947688103	0.069052311896769
51	100.7	100.739138775251	-0.0391387752508621
52	101.27	101.139240415969	0.13075958403131
53	101.07	101.610070774717	-0.540070774717265
54	101.17	101.166329300122	0.00367069987814261
55	100.71	101.032933490686	-0.322933490686154
56	100.59	100.502906986413	0.0870930135872783
57	100.52	100.603139736174	-0.0831397361744024
58	100.65	100.712328538004	-0.0623285380044933
59	100.62	100.794365795707	-0.174365795707374
60	100.62	100.674748879369	-0.0547488793691286
61	100.59	100.756605999295	-0.166605999295086
62	100.42	100.734329269418	-0.314329269418408
63	100.55	100.432537910662	0.117462089337565
64	100.41	100.927487213436	-0.517487213435786
65	100.4	100.650859862796	-0.250859862796418
66	99.93	100.466137008195	-0.536137008195041
67	100.26	99.7292560308757	0.530743969124345
68	100.34	99.8975047275366	0.442495272463447
69	100.24	100.197909095305	0.0420909046954847
70	99.98	100.367327208115	-0.387327208115096
71	100.08	100.107769346011	-0.0277693460110982
72	100.24	100.07693057203	0.163069427970129

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 96.44 & 95.8309722222222 & 0.609027777777754 \tabularnewline
14 & 96.83 & 96.7187051588574 & 0.111294841142637 \tabularnewline
15 & 96.7 & 96.6931957253212 & 0.00680427467884215 \tabularnewline
16 & 97.06 & 97.0881959421188 & -0.0281959421187992 \tabularnewline
17 & 97.64 & 97.6730575668817 & -0.0330575668816522 \tabularnewline
18 & 97.61 & 97.6399878781184 & -0.0299878781183764 \tabularnewline
19 & 97.61 & 97.4504726552657 & 0.159527344734343 \tabularnewline
20 & 97.61 & 97.5207896711341 & 0.0892103288658888 \tabularnewline
21 & 97.55 & 97.7711251935506 & -0.221125193550634 \tabularnewline
22 & 97.58 & 97.8650523637179 & -0.285052363717867 \tabularnewline
23 & 97.79 & 97.6653817288546 & 0.124618271145408 \tabularnewline
24 & 97.79 & 97.9116318236926 & -0.121631823692596 \tabularnewline
25 & 97.79 & 97.9431225765256 & -0.153122576525618 \tabularnewline
26 & 97.79 & 98.1038981144259 & -0.313898114425896 \tabularnewline
27 & 98 & 97.6798099349956 & 0.320190065004439 \tabularnewline
28 & 98.37 & 98.295405783143 & 0.0745942168570366 \tabularnewline
29 & 98.68 & 98.9432932160055 & -0.263293216005508 \tabularnewline
30 & 98.89 & 98.697776349133 & 0.192223650866993 \tabularnewline
31 & 98.89 & 98.7053493781506 & 0.184650621849386 \tabularnewline
32 & 98.89 & 98.7642700763606 & 0.125729923639383 \tabularnewline
33 & 98.88 & 98.965945184083 & -0.0859451840830019 \tabularnewline
34 & 98.97 & 99.1457827449459 & -0.175782744945906 \tabularnewline
35 & 99.05 & 99.1112804119747 & -0.0612804119747494 \tabularnewline
36 & 99.05 & 99.146580840998 & -0.0965808409979871 \tabularnewline
37 & 99 & 99.1800045307713 & -0.180004530771271 \tabularnewline
38 & 99.03 & 99.2740290035243 & -0.244029003524261 \tabularnewline
39 & 99.2 & 99.0230555678632 & 0.176944432136764 \tabularnewline
40 & 100.3 & 99.4584294294547 & 0.841570570545315 \tabularnewline
41 & 100.79 & 100.671298030938 & 0.11870196906159 \tabularnewline
42 & 100.75 & 100.859683127095 & -0.109683127095209 \tabularnewline
43 & 100.75 & 100.64739377433 & 0.102606225669902 \tabularnewline
44 & 100.17 & 100.648152188899 & -0.478152188898832 \tabularnewline
45 & 99.98 & 100.31556729866 & -0.335567298660337 \tabularnewline
46 & 99.93 & 100.257187865918 & -0.327187865918177 \tabularnewline
47 & 100.04 & 100.096875212642 & -0.0568752126418701 \tabularnewline
48 & 100.04 & 100.101158170625 & -0.0611581706249922 \tabularnewline
49 & 100.49 & 100.12038172595 & 0.369618274050069 \tabularnewline
50 & 100.71 & 100.640947688103 & 0.069052311896769 \tabularnewline
51 & 100.7 & 100.739138775251 & -0.0391387752508621 \tabularnewline
52 & 101.27 & 101.139240415969 & 0.13075958403131 \tabularnewline
53 & 101.07 & 101.610070774717 & -0.540070774717265 \tabularnewline
54 & 101.17 & 101.166329300122 & 0.00367069987814261 \tabularnewline
55 & 100.71 & 101.032933490686 & -0.322933490686154 \tabularnewline
56 & 100.59 & 100.502906986413 & 0.0870930135872783 \tabularnewline
57 & 100.52 & 100.603139736174 & -0.0831397361744024 \tabularnewline
58 & 100.65 & 100.712328538004 & -0.0623285380044933 \tabularnewline
59 & 100.62 & 100.794365795707 & -0.174365795707374 \tabularnewline
60 & 100.62 & 100.674748879369 & -0.0547488793691286 \tabularnewline
61 & 100.59 & 100.756605999295 & -0.166605999295086 \tabularnewline
62 & 100.42 & 100.734329269418 & -0.314329269418408 \tabularnewline
63 & 100.55 & 100.432537910662 & 0.117462089337565 \tabularnewline
64 & 100.41 & 100.927487213436 & -0.517487213435786 \tabularnewline
65 & 100.4 & 100.650859862796 & -0.250859862796418 \tabularnewline
66 & 99.93 & 100.466137008195 & -0.536137008195041 \tabularnewline
67 & 100.26 & 99.7292560308757 & 0.530743969124345 \tabularnewline
68 & 100.34 & 99.8975047275366 & 0.442495272463447 \tabularnewline
69 & 100.24 & 100.197909095305 & 0.0420909046954847 \tabularnewline
70 & 99.98 & 100.367327208115 & -0.387327208115096 \tabularnewline
71 & 100.08 & 100.107769346011 & -0.0277693460110982 \tabularnewline
72 & 100.24 & 100.07693057203 & 0.163069427970129 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]96.44[/C][C]95.8309722222222[/C][C]0.609027777777754[/C][/ROW]
[ROW][C]14[/C][C]96.83[/C][C]96.7187051588574[/C][C]0.111294841142637[/C][/ROW]
[ROW][C]15[/C][C]96.7[/C][C]96.6931957253212[/C][C]0.00680427467884215[/C][/ROW]
[ROW][C]16[/C][C]97.06[/C][C]97.0881959421188[/C][C]-0.0281959421187992[/C][/ROW]
[ROW][C]17[/C][C]97.64[/C][C]97.6730575668817[/C][C]-0.0330575668816522[/C][/ROW]
[ROW][C]18[/C][C]97.61[/C][C]97.6399878781184[/C][C]-0.0299878781183764[/C][/ROW]
[ROW][C]19[/C][C]97.61[/C][C]97.4504726552657[/C][C]0.159527344734343[/C][/ROW]
[ROW][C]20[/C][C]97.61[/C][C]97.5207896711341[/C][C]0.0892103288658888[/C][/ROW]
[ROW][C]21[/C][C]97.55[/C][C]97.7711251935506[/C][C]-0.221125193550634[/C][/ROW]
[ROW][C]22[/C][C]97.58[/C][C]97.8650523637179[/C][C]-0.285052363717867[/C][/ROW]
[ROW][C]23[/C][C]97.79[/C][C]97.6653817288546[/C][C]0.124618271145408[/C][/ROW]
[ROW][C]24[/C][C]97.79[/C][C]97.9116318236926[/C][C]-0.121631823692596[/C][/ROW]
[ROW][C]25[/C][C]97.79[/C][C]97.9431225765256[/C][C]-0.153122576525618[/C][/ROW]
[ROW][C]26[/C][C]97.79[/C][C]98.1038981144259[/C][C]-0.313898114425896[/C][/ROW]
[ROW][C]27[/C][C]98[/C][C]97.6798099349956[/C][C]0.320190065004439[/C][/ROW]
[ROW][C]28[/C][C]98.37[/C][C]98.295405783143[/C][C]0.0745942168570366[/C][/ROW]
[ROW][C]29[/C][C]98.68[/C][C]98.9432932160055[/C][C]-0.263293216005508[/C][/ROW]
[ROW][C]30[/C][C]98.89[/C][C]98.697776349133[/C][C]0.192223650866993[/C][/ROW]
[ROW][C]31[/C][C]98.89[/C][C]98.7053493781506[/C][C]0.184650621849386[/C][/ROW]
[ROW][C]32[/C][C]98.89[/C][C]98.7642700763606[/C][C]0.125729923639383[/C][/ROW]
[ROW][C]33[/C][C]98.88[/C][C]98.965945184083[/C][C]-0.0859451840830019[/C][/ROW]
[ROW][C]34[/C][C]98.97[/C][C]99.1457827449459[/C][C]-0.175782744945906[/C][/ROW]
[ROW][C]35[/C][C]99.05[/C][C]99.1112804119747[/C][C]-0.0612804119747494[/C][/ROW]
[ROW][C]36[/C][C]99.05[/C][C]99.146580840998[/C][C]-0.0965808409979871[/C][/ROW]
[ROW][C]37[/C][C]99[/C][C]99.1800045307713[/C][C]-0.180004530771271[/C][/ROW]
[ROW][C]38[/C][C]99.03[/C][C]99.2740290035243[/C][C]-0.244029003524261[/C][/ROW]
[ROW][C]39[/C][C]99.2[/C][C]99.0230555678632[/C][C]0.176944432136764[/C][/ROW]
[ROW][C]40[/C][C]100.3[/C][C]99.4584294294547[/C][C]0.841570570545315[/C][/ROW]
[ROW][C]41[/C][C]100.79[/C][C]100.671298030938[/C][C]0.11870196906159[/C][/ROW]
[ROW][C]42[/C][C]100.75[/C][C]100.859683127095[/C][C]-0.109683127095209[/C][/ROW]
[ROW][C]43[/C][C]100.75[/C][C]100.64739377433[/C][C]0.102606225669902[/C][/ROW]
[ROW][C]44[/C][C]100.17[/C][C]100.648152188899[/C][C]-0.478152188898832[/C][/ROW]
[ROW][C]45[/C][C]99.98[/C][C]100.31556729866[/C][C]-0.335567298660337[/C][/ROW]
[ROW][C]46[/C][C]99.93[/C][C]100.257187865918[/C][C]-0.327187865918177[/C][/ROW]
[ROW][C]47[/C][C]100.04[/C][C]100.096875212642[/C][C]-0.0568752126418701[/C][/ROW]
[ROW][C]48[/C][C]100.04[/C][C]100.101158170625[/C][C]-0.0611581706249922[/C][/ROW]
[ROW][C]49[/C][C]100.49[/C][C]100.12038172595[/C][C]0.369618274050069[/C][/ROW]
[ROW][C]50[/C][C]100.71[/C][C]100.640947688103[/C][C]0.069052311896769[/C][/ROW]
[ROW][C]51[/C][C]100.7[/C][C]100.739138775251[/C][C]-0.0391387752508621[/C][/ROW]
[ROW][C]52[/C][C]101.27[/C][C]101.139240415969[/C][C]0.13075958403131[/C][/ROW]
[ROW][C]53[/C][C]101.07[/C][C]101.610070774717[/C][C]-0.540070774717265[/C][/ROW]
[ROW][C]54[/C][C]101.17[/C][C]101.166329300122[/C][C]0.00367069987814261[/C][/ROW]
[ROW][C]55[/C][C]100.71[/C][C]101.032933490686[/C][C]-0.322933490686154[/C][/ROW]
[ROW][C]56[/C][C]100.59[/C][C]100.502906986413[/C][C]0.0870930135872783[/C][/ROW]
[ROW][C]57[/C][C]100.52[/C][C]100.603139736174[/C][C]-0.0831397361744024[/C][/ROW]
[ROW][C]58[/C][C]100.65[/C][C]100.712328538004[/C][C]-0.0623285380044933[/C][/ROW]
[ROW][C]59[/C][C]100.62[/C][C]100.794365795707[/C][C]-0.174365795707374[/C][/ROW]
[ROW][C]60[/C][C]100.62[/C][C]100.674748879369[/C][C]-0.0547488793691286[/C][/ROW]
[ROW][C]61[/C][C]100.59[/C][C]100.756605999295[/C][C]-0.166605999295086[/C][/ROW]
[ROW][C]62[/C][C]100.42[/C][C]100.734329269418[/C][C]-0.314329269418408[/C][/ROW]
[ROW][C]63[/C][C]100.55[/C][C]100.432537910662[/C][C]0.117462089337565[/C][/ROW]
[ROW][C]64[/C][C]100.41[/C][C]100.927487213436[/C][C]-0.517487213435786[/C][/ROW]
[ROW][C]65[/C][C]100.4[/C][C]100.650859862796[/C][C]-0.250859862796418[/C][/ROW]
[ROW][C]66[/C][C]99.93[/C][C]100.466137008195[/C][C]-0.536137008195041[/C][/ROW]
[ROW][C]67[/C][C]100.26[/C][C]99.7292560308757[/C][C]0.530743969124345[/C][/ROW]
[ROW][C]68[/C][C]100.34[/C][C]99.8975047275366[/C][C]0.442495272463447[/C][/ROW]
[ROW][C]69[/C][C]100.24[/C][C]100.197909095305[/C][C]0.0420909046954847[/C][/ROW]
[ROW][C]70[/C][C]99.98[/C][C]100.367327208115[/C][C]-0.387327208115096[/C][/ROW]
[ROW][C]71[/C][C]100.08[/C][C]100.107769346011[/C][C]-0.0277693460110982[/C][/ROW]
[ROW][C]72[/C][C]100.24[/C][C]100.07693057203[/C][C]0.163069427970129[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
t	Observed	Fitted	Residuals
13	96.44	95.8309722222222	0.609027777777754
14	96.83	96.7187051588574	0.111294841142637
15	96.7	96.6931957253212	0.00680427467884215
16	97.06	97.0881959421188	-0.0281959421187992
17	97.64	97.6730575668817	-0.0330575668816522
18	97.61	97.6399878781184	-0.0299878781183764
19	97.61	97.4504726552657	0.159527344734343
20	97.61	97.5207896711341	0.0892103288658888
21	97.55	97.7711251935506	-0.221125193550634
22	97.58	97.8650523637179	-0.285052363717867
23	97.79	97.6653817288546	0.124618271145408
24	97.79	97.9116318236926	-0.121631823692596
25	97.79	97.9431225765256	-0.153122576525618
26	97.79	98.1038981144259	-0.313898114425896
27	98	97.6798099349956	0.320190065004439
28	98.37	98.295405783143	0.0745942168570366
29	98.68	98.9432932160055	-0.263293216005508
30	98.89	98.697776349133	0.192223650866993
31	98.89	98.7053493781506	0.184650621849386
32	98.89	98.7642700763606	0.125729923639383
33	98.88	98.965945184083	-0.0859451840830019
34	98.97	99.1457827449459	-0.175782744945906
35	99.05	99.1112804119747	-0.0612804119747494
36	99.05	99.146580840998	-0.0965808409979871
37	99	99.1800045307713	-0.180004530771271
38	99.03	99.2740290035243	-0.244029003524261
39	99.2	99.0230555678632	0.176944432136764
40	100.3	99.4584294294547	0.841570570545315
41	100.79	100.671298030938	0.11870196906159
42	100.75	100.859683127095	-0.109683127095209
43	100.75	100.64739377433	0.102606225669902
44	100.17	100.648152188899	-0.478152188898832
45	99.98	100.31556729866	-0.335567298660337
46	99.93	100.257187865918	-0.327187865918177
47	100.04	100.096875212642	-0.0568752126418701
48	100.04	100.101158170625	-0.0611581706249922
49	100.49	100.12038172595	0.369618274050069
50	100.71	100.640947688103	0.069052311896769
51	100.7	100.739138775251	-0.0391387752508621
52	101.27	101.139240415969	0.13075958403131
53	101.07	101.610070774717	-0.540070774717265
54	101.17	101.166329300122	0.00367069987814261
55	100.71	101.032933490686	-0.322933490686154
56	100.59	100.502906986413	0.0870930135872783
57	100.52	100.603139736174	-0.0831397361744024
58	100.65	100.712328538004	-0.0623285380044933
59	100.62	100.794365795707	-0.174365795707374
60	100.62	100.674748879369	-0.0547488793691286
61	100.59	100.756605999295	-0.166605999295086
62	100.42	100.734329269418	-0.314329269418408
63	100.55	100.432537910662	0.117462089337565
64	100.41	100.927487213436	-0.517487213435786
65	100.4	100.650859862796	-0.250859862796418
66	99.93	100.466137008195	-0.536137008195041
67	100.26	99.7292560308757	0.530743969124345
68	100.34	99.8975047275366	0.442495272463447
69	100.24	100.197909095305	0.0420909046954847
70	99.98	100.367327208115	-0.387327208115096
71	100.08	100.107769346011	-0.0277693460110982
72	100.24	100.07693057203	0.163069427970129

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	100.268319880372	99.7391399889835	100.79749977176
74	100.315216929548	99.6219438362083	101.008490022888
75	100.33150047373	99.4924721611419	101.170528786317
76	100.580049689009	99.6047162600004	101.555383118017
77	100.769548662955	99.6633076831641	101.875789642746
78	100.738889317264	99.5049237219677	101.972854912561
79	100.680110978252	99.3202571585604	102.039964797943
80	100.417119627974	98.9323353927407	101.901903863207
81	100.273657843374	98.6642984393421	101.883017247407
82	100.311623837784	98.5776157733425	102.045631902225
83	100.440147975116	98.5811040778488	102.299191872383
84	100.477360565211	98.4926591814329	102.462061948989

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 100.268319880372 & 99.7391399889835 & 100.79749977176 \tabularnewline
74 & 100.315216929548 & 99.6219438362083 & 101.008490022888 \tabularnewline
75 & 100.33150047373 & 99.4924721611419 & 101.170528786317 \tabularnewline
76 & 100.580049689009 & 99.6047162600004 & 101.555383118017 \tabularnewline
77 & 100.769548662955 & 99.6633076831641 & 101.875789642746 \tabularnewline
78 & 100.738889317264 & 99.5049237219677 & 101.972854912561 \tabularnewline
79 & 100.680110978252 & 99.3202571585604 & 102.039964797943 \tabularnewline
80 & 100.417119627974 & 98.9323353927407 & 101.901903863207 \tabularnewline
81 & 100.273657843374 & 98.6642984393421 & 101.883017247407 \tabularnewline
82 & 100.311623837784 & 98.5776157733425 & 102.045631902225 \tabularnewline
83 & 100.440147975116 & 98.5811040778488 & 102.299191872383 \tabularnewline
84 & 100.477360565211 & 98.4926591814329 & 102.462061948989 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]73[/C][C]100.268319880372[/C][C]99.7391399889835[/C][C]100.79749977176[/C][/ROW]
[ROW][C]74[/C][C]100.315216929548[/C][C]99.6219438362083[/C][C]101.008490022888[/C][/ROW]
[ROW][C]75[/C][C]100.33150047373[/C][C]99.4924721611419[/C][C]101.170528786317[/C][/ROW]
[ROW][C]76[/C][C]100.580049689009[/C][C]99.6047162600004[/C][C]101.555383118017[/C][/ROW]
[ROW][C]77[/C][C]100.769548662955[/C][C]99.6633076831641[/C][C]101.875789642746[/C][/ROW]
[ROW][C]78[/C][C]100.738889317264[/C][C]99.5049237219677[/C][C]101.972854912561[/C][/ROW]
[ROW][C]79[/C][C]100.680110978252[/C][C]99.3202571585604[/C][C]102.039964797943[/C][/ROW]
[ROW][C]80[/C][C]100.417119627974[/C][C]98.9323353927407[/C][C]101.901903863207[/C][/ROW]
[ROW][C]81[/C][C]100.273657843374[/C][C]98.6642984393421[/C][C]101.883017247407[/C][/ROW]
[ROW][C]82[/C][C]100.311623837784[/C][C]98.5776157733425[/C][C]102.045631902225[/C][/ROW]
[ROW][C]83[/C][C]100.440147975116[/C][C]98.5811040778488[/C][C]102.299191872383[/C][/ROW]
[ROW][C]84[/C][C]100.477360565211[/C][C]98.4926591814329[/C][C]102.462061948989[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
t	Forecast	95% Lower Bound	95% Upper Bound
73	100.268319880372	99.7391399889835	100.79749977176
74	100.315216929548	99.6219438362083	101.008490022888
75	100.33150047373	99.4924721611419	101.170528786317
76	100.580049689009	99.6047162600004	101.555383118017
77	100.769548662955	99.6633076831641	101.875789642746
78	100.738889317264	99.5049237219677	101.972854912561
79	100.680110978252	99.3202571585604	102.039964797943
80	100.417119627974	98.9323353927407	101.901903863207
81	100.273657843374	98.6642984393421	101.883017247407
82	100.311623837784	98.5776157733425	102.045631902225
83	100.440147975116	98.5811040778488	102.299191872383
84	100.477360565211	98.4926591814329	102.462061948989

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code