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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 13 Jan 2013 08:14:46 -0500

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/2013/Jan/13/t1358082958x6umvwn3u7pk5pz.htm/, Retrieved Sat, 04 May 2024 04:24:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205265, Retrieved Sat, 04 May 2024 04:24:37 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

110

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [] [2013-01-13 13:14:46] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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1,38
1,96
1,36
1,24
1,35
1,23
1,09
1,08
1,33
1,35
1,38
1,5
1,47
2,09
1,52
1,29
1,52
1,27
1,35
1,29
1,41
1,39
1,45
1,53
1,45
2,11
1,53
1,38
1,54
1,35
1,29
1,33
1,47
1,47
1,54
1,59
1,5
2
1,51
1,4
1,62
1,44
1,29
1,28
1,4
1,39
1,46
1,49
1,45
2,05
1,59
1,42
1,73
1,39
1,23
1,37
1,51
1,47
1,5
1,54
1,54
2,15
1,62
1,4
1,65
1,49
1,45
1,45
1,51
1,48
1,56
1,57

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205265&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205265&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205265&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	3 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.750937450216112
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.750937450216112 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205265&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]0.750937450216112[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205265&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205265&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	0.750937450216112
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.47	1.41690065482582	0.0530993451741839
14	2.09	2.05820122795301	0.0317987720469928
15	1.52	1.51259273651818	0.00740726348182008
16	1.29	1.29328586507888	-0.00328586507887674
17	1.52	1.52708750346153	-0.0070875034615312
18	1.27	1.27693627086853	-0.00693627086853121
19	1.35	1.18495182199274	0.165048178007262
20	1.29	1.29645674593536	-0.0064567459353575
21	1.41	1.5867487525063	-0.176748752506297
22	1.39	1.47676201907664	-0.0867620190766381
23	1.45	1.44384854921149	0.00615145078851342
24	1.53	1.57578943701536	-0.0457894370153578
25	1.45	1.52180180891329	-0.0718018089132888
26	2.11	2.06307710393435	0.0469228960656496
27	1.53	1.52041101403863	0.0095889859613747
28	1.38	1.29889179105731	0.0811082089426924
29	1.54	1.60725845107376	-0.0672584510737604
30	1.35	1.30581503364576	0.0441849663542362
31	1.29	1.28809243319506	0.00190756680493864
32	1.33	1.2372082497181	0.0927917502819013
33	1.47	1.55872592755614	-0.0887259275561429
34	1.47	1.53824109697472	-0.0682410969747242
35	1.54	1.54551409483967	-0.00551409483967391
36	1.59	1.66199751712029	-0.0719975171202885
37	1.5	1.5792809886293	-0.0792809886292976
38	2	2.17361701680457	-0.173617016804566
39	1.51	1.47495645783963	0.0350435421603703
40	1.4	1.29361373793837	0.106386262061631
41	1.62	1.58252879710042	0.0374712028995781
42	1.44	1.3765411577315	0.0634588422684976
43	1.29	1.35890909259016	-0.068909092590161
44	1.28	1.2757265538195	0.00427344618050141
45	1.4	1.47705128361418	-0.0770512836141755
46	1.39	1.46844118911944	-0.0784411891194403
47	1.46	1.48104973971395	-0.0210497397139453
48	1.49	1.56421500576614	-0.0742150057661413
49	1.45	1.4793943639434	-0.0293943639433998
50	2.05	2.06750770087042	-0.0175077008704223
51	1.59	1.52355349526021	0.0664465047397893
52	1.42	1.3735729968745	0.0464270031255005
53	1.73	1.60122514967582	0.128774850324184
54	1.39	1.45832357793569	-0.0683235779356912
55	1.23	1.31054584115567	-0.0805458411556716
56	1.37	1.23751864119065	0.132481358809347
57	1.51	1.52154458439405	-0.0115445843940483
58	1.47	1.56405251610183	-0.0940525161018286
59	1.5	1.5847892326607	-0.0847892326606958
60	1.54	1.6092727727374	-0.0692727727374027
61	1.54	1.53792226941176	0.00207773058824001
62	2.15	2.18951308235034	-0.0395130823503438
63	1.62	1.62147113088434	-0.00147113088433493
64	1.4	1.41111366000234	-0.0111136600023383
65	1.65	1.61180716756084	0.0381928324391572
66	1.49	1.36661580626519	0.123384193734811
67	1.45	1.35335675474686	0.0966432452531392
68	1.45	1.46867909880899	-0.0186790988089922
69	1.51	1.61190366823984	-0.10190366823984
70	1.48	1.56523461718958	-0.0852346171895766
71	1.56	1.59577155165242	-0.0357715516524182
72	1.57	1.66406153736462	-0.094061537364623

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.47 & 1.41690065482582 & 0.0530993451741839 \tabularnewline
14 & 2.09 & 2.05820122795301 & 0.0317987720469928 \tabularnewline
15 & 1.52 & 1.51259273651818 & 0.00740726348182008 \tabularnewline
16 & 1.29 & 1.29328586507888 & -0.00328586507887674 \tabularnewline
17 & 1.52 & 1.52708750346153 & -0.0070875034615312 \tabularnewline
18 & 1.27 & 1.27693627086853 & -0.00693627086853121 \tabularnewline
19 & 1.35 & 1.18495182199274 & 0.165048178007262 \tabularnewline
20 & 1.29 & 1.29645674593536 & -0.0064567459353575 \tabularnewline
21 & 1.41 & 1.5867487525063 & -0.176748752506297 \tabularnewline
22 & 1.39 & 1.47676201907664 & -0.0867620190766381 \tabularnewline
23 & 1.45 & 1.44384854921149 & 0.00615145078851342 \tabularnewline
24 & 1.53 & 1.57578943701536 & -0.0457894370153578 \tabularnewline
25 & 1.45 & 1.52180180891329 & -0.0718018089132888 \tabularnewline
26 & 2.11 & 2.06307710393435 & 0.0469228960656496 \tabularnewline
27 & 1.53 & 1.52041101403863 & 0.0095889859613747 \tabularnewline
28 & 1.38 & 1.29889179105731 & 0.0811082089426924 \tabularnewline
29 & 1.54 & 1.60725845107376 & -0.0672584510737604 \tabularnewline
30 & 1.35 & 1.30581503364576 & 0.0441849663542362 \tabularnewline
31 & 1.29 & 1.28809243319506 & 0.00190756680493864 \tabularnewline
32 & 1.33 & 1.2372082497181 & 0.0927917502819013 \tabularnewline
33 & 1.47 & 1.55872592755614 & -0.0887259275561429 \tabularnewline
34 & 1.47 & 1.53824109697472 & -0.0682410969747242 \tabularnewline
35 & 1.54 & 1.54551409483967 & -0.00551409483967391 \tabularnewline
36 & 1.59 & 1.66199751712029 & -0.0719975171202885 \tabularnewline
37 & 1.5 & 1.5792809886293 & -0.0792809886292976 \tabularnewline
38 & 2 & 2.17361701680457 & -0.173617016804566 \tabularnewline
39 & 1.51 & 1.47495645783963 & 0.0350435421603703 \tabularnewline
40 & 1.4 & 1.29361373793837 & 0.106386262061631 \tabularnewline
41 & 1.62 & 1.58252879710042 & 0.0374712028995781 \tabularnewline
42 & 1.44 & 1.3765411577315 & 0.0634588422684976 \tabularnewline
43 & 1.29 & 1.35890909259016 & -0.068909092590161 \tabularnewline
44 & 1.28 & 1.2757265538195 & 0.00427344618050141 \tabularnewline
45 & 1.4 & 1.47705128361418 & -0.0770512836141755 \tabularnewline
46 & 1.39 & 1.46844118911944 & -0.0784411891194403 \tabularnewline
47 & 1.46 & 1.48104973971395 & -0.0210497397139453 \tabularnewline
48 & 1.49 & 1.56421500576614 & -0.0742150057661413 \tabularnewline
49 & 1.45 & 1.4793943639434 & -0.0293943639433998 \tabularnewline
50 & 2.05 & 2.06750770087042 & -0.0175077008704223 \tabularnewline
51 & 1.59 & 1.52355349526021 & 0.0664465047397893 \tabularnewline
52 & 1.42 & 1.3735729968745 & 0.0464270031255005 \tabularnewline
53 & 1.73 & 1.60122514967582 & 0.128774850324184 \tabularnewline
54 & 1.39 & 1.45832357793569 & -0.0683235779356912 \tabularnewline
55 & 1.23 & 1.31054584115567 & -0.0805458411556716 \tabularnewline
56 & 1.37 & 1.23751864119065 & 0.132481358809347 \tabularnewline
57 & 1.51 & 1.52154458439405 & -0.0115445843940483 \tabularnewline
58 & 1.47 & 1.56405251610183 & -0.0940525161018286 \tabularnewline
59 & 1.5 & 1.5847892326607 & -0.0847892326606958 \tabularnewline
60 & 1.54 & 1.6092727727374 & -0.0692727727374027 \tabularnewline
61 & 1.54 & 1.53792226941176 & 0.00207773058824001 \tabularnewline
62 & 2.15 & 2.18951308235034 & -0.0395130823503438 \tabularnewline
63 & 1.62 & 1.62147113088434 & -0.00147113088433493 \tabularnewline
64 & 1.4 & 1.41111366000234 & -0.0111136600023383 \tabularnewline
65 & 1.65 & 1.61180716756084 & 0.0381928324391572 \tabularnewline
66 & 1.49 & 1.36661580626519 & 0.123384193734811 \tabularnewline
67 & 1.45 & 1.35335675474686 & 0.0966432452531392 \tabularnewline
68 & 1.45 & 1.46867909880899 & -0.0186790988089922 \tabularnewline
69 & 1.51 & 1.61190366823984 & -0.10190366823984 \tabularnewline
70 & 1.48 & 1.56523461718958 & -0.0852346171895766 \tabularnewline
71 & 1.56 & 1.59577155165242 & -0.0357715516524182 \tabularnewline
72 & 1.57 & 1.66406153736462 & -0.094061537364623 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205265&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]1.47[/C][C]1.41690065482582[/C][C]0.0530993451741839[/C][/ROW]
[ROW][C]14[/C][C]2.09[/C][C]2.05820122795301[/C][C]0.0317987720469928[/C][/ROW]
[ROW][C]15[/C][C]1.52[/C][C]1.51259273651818[/C][C]0.00740726348182008[/C][/ROW]
[ROW][C]16[/C][C]1.29[/C][C]1.29328586507888[/C][C]-0.00328586507887674[/C][/ROW]
[ROW][C]17[/C][C]1.52[/C][C]1.52708750346153[/C][C]-0.0070875034615312[/C][/ROW]
[ROW][C]18[/C][C]1.27[/C][C]1.27693627086853[/C][C]-0.00693627086853121[/C][/ROW]
[ROW][C]19[/C][C]1.35[/C][C]1.18495182199274[/C][C]0.165048178007262[/C][/ROW]
[ROW][C]20[/C][C]1.29[/C][C]1.29645674593536[/C][C]-0.0064567459353575[/C][/ROW]
[ROW][C]21[/C][C]1.41[/C][C]1.5867487525063[/C][C]-0.176748752506297[/C][/ROW]
[ROW][C]22[/C][C]1.39[/C][C]1.47676201907664[/C][C]-0.0867620190766381[/C][/ROW]
[ROW][C]23[/C][C]1.45[/C][C]1.44384854921149[/C][C]0.00615145078851342[/C][/ROW]
[ROW][C]24[/C][C]1.53[/C][C]1.57578943701536[/C][C]-0.0457894370153578[/C][/ROW]
[ROW][C]25[/C][C]1.45[/C][C]1.52180180891329[/C][C]-0.0718018089132888[/C][/ROW]
[ROW][C]26[/C][C]2.11[/C][C]2.06307710393435[/C][C]0.0469228960656496[/C][/ROW]
[ROW][C]27[/C][C]1.53[/C][C]1.52041101403863[/C][C]0.0095889859613747[/C][/ROW]
[ROW][C]28[/C][C]1.38[/C][C]1.29889179105731[/C][C]0.0811082089426924[/C][/ROW]
[ROW][C]29[/C][C]1.54[/C][C]1.60725845107376[/C][C]-0.0672584510737604[/C][/ROW]
[ROW][C]30[/C][C]1.35[/C][C]1.30581503364576[/C][C]0.0441849663542362[/C][/ROW]
[ROW][C]31[/C][C]1.29[/C][C]1.28809243319506[/C][C]0.00190756680493864[/C][/ROW]
[ROW][C]32[/C][C]1.33[/C][C]1.2372082497181[/C][C]0.0927917502819013[/C][/ROW]
[ROW][C]33[/C][C]1.47[/C][C]1.55872592755614[/C][C]-0.0887259275561429[/C][/ROW]
[ROW][C]34[/C][C]1.47[/C][C]1.53824109697472[/C][C]-0.0682410969747242[/C][/ROW]
[ROW][C]35[/C][C]1.54[/C][C]1.54551409483967[/C][C]-0.00551409483967391[/C][/ROW]
[ROW][C]36[/C][C]1.59[/C][C]1.66199751712029[/C][C]-0.0719975171202885[/C][/ROW]
[ROW][C]37[/C][C]1.5[/C][C]1.5792809886293[/C][C]-0.0792809886292976[/C][/ROW]
[ROW][C]38[/C][C]2[/C][C]2.17361701680457[/C][C]-0.173617016804566[/C][/ROW]
[ROW][C]39[/C][C]1.51[/C][C]1.47495645783963[/C][C]0.0350435421603703[/C][/ROW]
[ROW][C]40[/C][C]1.4[/C][C]1.29361373793837[/C][C]0.106386262061631[/C][/ROW]
[ROW][C]41[/C][C]1.62[/C][C]1.58252879710042[/C][C]0.0374712028995781[/C][/ROW]
[ROW][C]42[/C][C]1.44[/C][C]1.3765411577315[/C][C]0.0634588422684976[/C][/ROW]
[ROW][C]43[/C][C]1.29[/C][C]1.35890909259016[/C][C]-0.068909092590161[/C][/ROW]
[ROW][C]44[/C][C]1.28[/C][C]1.2757265538195[/C][C]0.00427344618050141[/C][/ROW]
[ROW][C]45[/C][C]1.4[/C][C]1.47705128361418[/C][C]-0.0770512836141755[/C][/ROW]
[ROW][C]46[/C][C]1.39[/C][C]1.46844118911944[/C][C]-0.0784411891194403[/C][/ROW]
[ROW][C]47[/C][C]1.46[/C][C]1.48104973971395[/C][C]-0.0210497397139453[/C][/ROW]
[ROW][C]48[/C][C]1.49[/C][C]1.56421500576614[/C][C]-0.0742150057661413[/C][/ROW]
[ROW][C]49[/C][C]1.45[/C][C]1.4793943639434[/C][C]-0.0293943639433998[/C][/ROW]
[ROW][C]50[/C][C]2.05[/C][C]2.06750770087042[/C][C]-0.0175077008704223[/C][/ROW]
[ROW][C]51[/C][C]1.59[/C][C]1.52355349526021[/C][C]0.0664465047397893[/C][/ROW]
[ROW][C]52[/C][C]1.42[/C][C]1.3735729968745[/C][C]0.0464270031255005[/C][/ROW]
[ROW][C]53[/C][C]1.73[/C][C]1.60122514967582[/C][C]0.128774850324184[/C][/ROW]
[ROW][C]54[/C][C]1.39[/C][C]1.45832357793569[/C][C]-0.0683235779356912[/C][/ROW]
[ROW][C]55[/C][C]1.23[/C][C]1.31054584115567[/C][C]-0.0805458411556716[/C][/ROW]
[ROW][C]56[/C][C]1.37[/C][C]1.23751864119065[/C][C]0.132481358809347[/C][/ROW]
[ROW][C]57[/C][C]1.51[/C][C]1.52154458439405[/C][C]-0.0115445843940483[/C][/ROW]
[ROW][C]58[/C][C]1.47[/C][C]1.56405251610183[/C][C]-0.0940525161018286[/C][/ROW]
[ROW][C]59[/C][C]1.5[/C][C]1.5847892326607[/C][C]-0.0847892326606958[/C][/ROW]
[ROW][C]60[/C][C]1.54[/C][C]1.6092727727374[/C][C]-0.0692727727374027[/C][/ROW]
[ROW][C]61[/C][C]1.54[/C][C]1.53792226941176[/C][C]0.00207773058824001[/C][/ROW]
[ROW][C]62[/C][C]2.15[/C][C]2.18951308235034[/C][C]-0.0395130823503438[/C][/ROW]
[ROW][C]63[/C][C]1.62[/C][C]1.62147113088434[/C][C]-0.00147113088433493[/C][/ROW]
[ROW][C]64[/C][C]1.4[/C][C]1.41111366000234[/C][C]-0.0111136600023383[/C][/ROW]
[ROW][C]65[/C][C]1.65[/C][C]1.61180716756084[/C][C]0.0381928324391572[/C][/ROW]
[ROW][C]66[/C][C]1.49[/C][C]1.36661580626519[/C][C]0.123384193734811[/C][/ROW]
[ROW][C]67[/C][C]1.45[/C][C]1.35335675474686[/C][C]0.0966432452531392[/C][/ROW]
[ROW][C]68[/C][C]1.45[/C][C]1.46867909880899[/C][C]-0.0186790988089922[/C][/ROW]
[ROW][C]69[/C][C]1.51[/C][C]1.61190366823984[/C][C]-0.10190366823984[/C][/ROW]
[ROW][C]70[/C][C]1.48[/C][C]1.56523461718958[/C][C]-0.0852346171895766[/C][/ROW]
[ROW][C]71[/C][C]1.56[/C][C]1.59577155165242[/C][C]-0.0357715516524182[/C][/ROW]
[ROW][C]72[/C][C]1.57[/C][C]1.66406153736462[/C][C]-0.094061537364623[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205265&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205265&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	1.47	1.41690065482582	0.0530993451741839
14	2.09	2.05820122795301	0.0317987720469928
15	1.52	1.51259273651818	0.00740726348182008
16	1.29	1.29328586507888	-0.00328586507887674
17	1.52	1.52708750346153	-0.0070875034615312
18	1.27	1.27693627086853	-0.00693627086853121
19	1.35	1.18495182199274	0.165048178007262
20	1.29	1.29645674593536	-0.0064567459353575
21	1.41	1.5867487525063	-0.176748752506297
22	1.39	1.47676201907664	-0.0867620190766381
23	1.45	1.44384854921149	0.00615145078851342
24	1.53	1.57578943701536	-0.0457894370153578
25	1.45	1.52180180891329	-0.0718018089132888
26	2.11	2.06307710393435	0.0469228960656496
27	1.53	1.52041101403863	0.0095889859613747
28	1.38	1.29889179105731	0.0811082089426924
29	1.54	1.60725845107376	-0.0672584510737604
30	1.35	1.30581503364576	0.0441849663542362
31	1.29	1.28809243319506	0.00190756680493864
32	1.33	1.2372082497181	0.0927917502819013
33	1.47	1.55872592755614	-0.0887259275561429
34	1.47	1.53824109697472	-0.0682410969747242
35	1.54	1.54551409483967	-0.00551409483967391
36	1.59	1.66199751712029	-0.0719975171202885
37	1.5	1.5792809886293	-0.0792809886292976
38	2	2.17361701680457	-0.173617016804566
39	1.51	1.47495645783963	0.0350435421603703
40	1.4	1.29361373793837	0.106386262061631
41	1.62	1.58252879710042	0.0374712028995781
42	1.44	1.3765411577315	0.0634588422684976
43	1.29	1.35890909259016	-0.068909092590161
44	1.28	1.2757265538195	0.00427344618050141
45	1.4	1.47705128361418	-0.0770512836141755
46	1.39	1.46844118911944	-0.0784411891194403
47	1.46	1.48104973971395	-0.0210497397139453
48	1.49	1.56421500576614	-0.0742150057661413
49	1.45	1.4793943639434	-0.0293943639433998
50	2.05	2.06750770087042	-0.0175077008704223
51	1.59	1.52355349526021	0.0664465047397893
52	1.42	1.3735729968745	0.0464270031255005
53	1.73	1.60122514967582	0.128774850324184
54	1.39	1.45832357793569	-0.0683235779356912
55	1.23	1.31054584115567	-0.0805458411556716
56	1.37	1.23751864119065	0.132481358809347
57	1.51	1.52154458439405	-0.0115445843940483
58	1.47	1.56405251610183	-0.0940525161018286
59	1.5	1.5847892326607	-0.0847892326606958
60	1.54	1.6092727727374	-0.0692727727374027
61	1.54	1.53792226941176	0.00207773058824001
62	2.15	2.18951308235034	-0.0395130823503438
63	1.62	1.62147113088434	-0.00147113088433493
64	1.4	1.41111366000234	-0.0111136600023383
65	1.65	1.61180716756084	0.0381928324391572
66	1.49	1.36661580626519	0.123384193734811
67	1.45	1.35335675474686	0.0966432452531392
68	1.45	1.46867909880899	-0.0186790988089922
69	1.51	1.61190366823984	-0.10190366823984
70	1.48	1.56523461718958	-0.0852346171895766
71	1.56	1.59577155165242	-0.0357715516524182
72	1.57	1.66406153736462	-0.094061537364623

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.59144378249553	1.44757603390832	1.73531153108275
74	2.25184545467524	2.04266255572817	2.46102835362231
75	1.69736658277192	1.49693725386436	1.89779591167947
76	1.47512601799137	1.2655675468666	1.68468448911614
77	1.7075510199708	1.44901468378713	1.96608735615446
78	1.44374031812562	1.19575606167028	1.69172457458096
79	1.33374102320915	1.07897804618031	1.588504000238
80	1.34729075376206	1.06981614834099	1.62476535918314
81	1.47362957256533	1.15585438683836	1.79140475829229
82	1.50616147216596	1.16623239321674	1.84609055111518
83	1.61457882819956	1.23830183608095	1.99085582031818
84	1.69659036027064	-12.3544498666263	15.7476305871675

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.59144378249553 & 1.44757603390832 & 1.73531153108275 \tabularnewline
74 & 2.25184545467524 & 2.04266255572817 & 2.46102835362231 \tabularnewline
75 & 1.69736658277192 & 1.49693725386436 & 1.89779591167947 \tabularnewline
76 & 1.47512601799137 & 1.2655675468666 & 1.68468448911614 \tabularnewline
77 & 1.7075510199708 & 1.44901468378713 & 1.96608735615446 \tabularnewline
78 & 1.44374031812562 & 1.19575606167028 & 1.69172457458096 \tabularnewline
79 & 1.33374102320915 & 1.07897804618031 & 1.588504000238 \tabularnewline
80 & 1.34729075376206 & 1.06981614834099 & 1.62476535918314 \tabularnewline
81 & 1.47362957256533 & 1.15585438683836 & 1.79140475829229 \tabularnewline
82 & 1.50616147216596 & 1.16623239321674 & 1.84609055111518 \tabularnewline
83 & 1.61457882819956 & 1.23830183608095 & 1.99085582031818 \tabularnewline
84 & 1.69659036027064 & -12.3544498666263 & 15.7476305871675 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205265&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]1.59144378249553[/C][C]1.44757603390832[/C][C]1.73531153108275[/C][/ROW]
[ROW][C]74[/C][C]2.25184545467524[/C][C]2.04266255572817[/C][C]2.46102835362231[/C][/ROW]
[ROW][C]75[/C][C]1.69736658277192[/C][C]1.49693725386436[/C][C]1.89779591167947[/C][/ROW]
[ROW][C]76[/C][C]1.47512601799137[/C][C]1.2655675468666[/C][C]1.68468448911614[/C][/ROW]
[ROW][C]77[/C][C]1.7075510199708[/C][C]1.44901468378713[/C][C]1.96608735615446[/C][/ROW]
[ROW][C]78[/C][C]1.44374031812562[/C][C]1.19575606167028[/C][C]1.69172457458096[/C][/ROW]
[ROW][C]79[/C][C]1.33374102320915[/C][C]1.07897804618031[/C][C]1.588504000238[/C][/ROW]
[ROW][C]80[/C][C]1.34729075376206[/C][C]1.06981614834099[/C][C]1.62476535918314[/C][/ROW]
[ROW][C]81[/C][C]1.47362957256533[/C][C]1.15585438683836[/C][C]1.79140475829229[/C][/ROW]
[ROW][C]82[/C][C]1.50616147216596[/C][C]1.16623239321674[/C][C]1.84609055111518[/C][/ROW]
[ROW][C]83[/C][C]1.61457882819956[/C][C]1.23830183608095[/C][C]1.99085582031818[/C][/ROW]
[ROW][C]84[/C][C]1.69659036027064[/C][C]-12.3544498666263[/C][C]15.7476305871675[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205265&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205265&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	1.59144378249553	1.44757603390832	1.73531153108275
74	2.25184545467524	2.04266255572817	2.46102835362231
75	1.69736658277192	1.49693725386436	1.89779591167947
76	1.47512601799137	1.2655675468666	1.68468448911614
77	1.7075510199708	1.44901468378713	1.96608735615446
78	1.44374031812562	1.19575606167028	1.69172457458096
79	1.33374102320915	1.07897804618031	1.588504000238
80	1.34729075376206	1.06981614834099	1.62476535918314
81	1.47362957256533	1.15585438683836	1.79140475829229
82	1.50616147216596	1.16623239321674	1.84609055111518
83	1.61457882819956	1.23830183608095	1.99085582031818
84	1.69659036027064	-12.3544498666263	15.7476305871675

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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