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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 20 May 2014 16:23:56 -0400

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/2014/May/20/t1400617577mptv3s6l6owgfzn.htm/, Retrieved Wed, 15 May 2024 12:18:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235001, Retrieved Wed, 15 May 2024 12:18:13 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

125

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

-       [Exponential Smoothing] [] [2014-05-20 20:23:56] [29e8d6dad3f42e00cf84041db36f48fc] [Current]

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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=235001&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=235001&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235001&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	0.999945028647976
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999945028647976 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235001&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]0.999945028647976[/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=235001&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235001&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	0.999945028647976
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	1.026	1.005	0.0210000000000001
3	1.043	1.02599884560161	0.0170011543983923
4	1.068	1.04299906542356	0.0250009345764435
5	1.07	1.06799862566482	0.00200137433517544
6	1.091	1.06999988998175	0.0210001100182531
7	1.102	1.09099884559556	0.0110011544044404
8	1.091	1.10199939525167	-0.0109993952516687
9	1.121	1.09100060465163	0.0299993953483715
10	1.134	1.12099835089268	0.0130016491073222
11	1.225	1.13399928528177	0.0910007147182301
12	1.191	1.22499499756768	-0.0339949975676768
13	1.184	1.19100186875098	-0.00700186875097852
14	1.207	1.18400038490219	0.0229996150978082
15	1.271	1.20699873568006	0.0640012643199377
16	1.299	1.27099648176397	0.028003518236031
17	1.411	1.29899846060874	0.112001539391259
18	1.437	1.41099384312395	0.0260061568760492
19	1.462	1.4369985704064	0.0250014295936043
20	1.36	1.46199862563761	-0.101998625637613
21	1.33	1.36000560700236	-0.030005607002356
22	1.234	1.33000164944879	-0.0960016494487854
23	1.142	1.23400527734047	-0.0920052773404669
24	1.017	1.14200505765449	-0.125005057654489
25	1.016	1.01700687169703	-0.00100687169702907
26	1.013	1.0160000553491	-0.00300005534909853
27	1	1.0130001649171	-0.0130001649170985
28	1.018	1.00000071463664	0.0179992853633579
29	1.024	1.01799901055495	0.0060009894450519
30	1.075	1.0239996701175	0.0510003298825032
31	1.055	1.07499719644291	-0.0199971964429126
32	1.091	1.05500109927293	0.0359989007270749
33	1.062	1.09099802109176	-0.0289980210917555
34	1.083	1.06200159406043	0.0209984059395745
35	1.099	1.08299884568924	0.0160011543107648
36	1.097	1.09899912039491	-0.00199912039491368
37	1.138	1.09700010989435	0.040999890105649
38	1.138	1.13799774618061	2.25381939200631e-06
39	1.181	1.1379999998761	0.0430000001238957
40	1.223	1.18099763623186	0.0420023637681439
41	1.23	1.22299769107328	0.00700230892672438
42	1.232	1.22999961507361	0.00200038492638899
43	1.209	1.23199989003614	-0.0229998900361359
44	1.209	1.20900126433505	-1.26433505176493e-06
45	1.218	1.2090000000695	0.00899999993049772
46	1.225	1.21799950525784	0.00700049474216446
47	1.242	1.22499961517334	0.0170003848266607
48	1.294	1.24199906546586	0.052000934534139
49	1.33	1.29399714143832	0.0360028585616778
50	1.357	1.32999802087419	0.0270019791258118
51	1.407	1.3569985156647	0.0500014843352998
52	1.42	1.4069972513508	0.013002748649197
53	1.386	1.41999928522133	-0.0339992852213267
54	1.377	1.38600186898668	-0.00900186898667643
55	1.393	1.37700049484491	0.015999505155091
56	1.371	1.39299912048557	-0.0219991204855698
57	1.393	1.3710012093214	0.0219987906786037
58	1.405	1.39299879069673	0.0120012093032664
59	1.438	1.4049993402773	0.0330006597227013
60	1.424	1.43799818590912	-0.0139981859091174
61	1.47	1.42400076949921	0.0459992305007948
62	1.481	1.46999747136011	0.0110025286398929
63	1.506	1.48099939517613	0.0250006048238749
64	1.503	1.50599862568295	-0.00299862568295151
65	1.478	1.50300016483851	-0.0250001648385079
66	1.433	1.47800137429286	-0.0450013742928619
67	1.459	1.43300247378639	0.0259975262136123
68	1.51	1.45899857088083	0.0510014291191652
69	1.526	1.50999719638249	0.0160028036175139
70	1.543	1.52599912030425	0.017000879695751
71	1.529	1.54299906543866	-0.0139990654386575
72	1.499	1.52900076954755	-0.0300007695475542

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1.026 & 1.005 & 0.0210000000000001 \tabularnewline
3 & 1.043 & 1.02599884560161 & 0.0170011543983923 \tabularnewline
4 & 1.068 & 1.04299906542356 & 0.0250009345764435 \tabularnewline
5 & 1.07 & 1.06799862566482 & 0.00200137433517544 \tabularnewline
6 & 1.091 & 1.06999988998175 & 0.0210001100182531 \tabularnewline
7 & 1.102 & 1.09099884559556 & 0.0110011544044404 \tabularnewline
8 & 1.091 & 1.10199939525167 & -0.0109993952516687 \tabularnewline
9 & 1.121 & 1.09100060465163 & 0.0299993953483715 \tabularnewline
10 & 1.134 & 1.12099835089268 & 0.0130016491073222 \tabularnewline
11 & 1.225 & 1.13399928528177 & 0.0910007147182301 \tabularnewline
12 & 1.191 & 1.22499499756768 & -0.0339949975676768 \tabularnewline
13 & 1.184 & 1.19100186875098 & -0.00700186875097852 \tabularnewline
14 & 1.207 & 1.18400038490219 & 0.0229996150978082 \tabularnewline
15 & 1.271 & 1.20699873568006 & 0.0640012643199377 \tabularnewline
16 & 1.299 & 1.27099648176397 & 0.028003518236031 \tabularnewline
17 & 1.411 & 1.29899846060874 & 0.112001539391259 \tabularnewline
18 & 1.437 & 1.41099384312395 & 0.0260061568760492 \tabularnewline
19 & 1.462 & 1.4369985704064 & 0.0250014295936043 \tabularnewline
20 & 1.36 & 1.46199862563761 & -0.101998625637613 \tabularnewline
21 & 1.33 & 1.36000560700236 & -0.030005607002356 \tabularnewline
22 & 1.234 & 1.33000164944879 & -0.0960016494487854 \tabularnewline
23 & 1.142 & 1.23400527734047 & -0.0920052773404669 \tabularnewline
24 & 1.017 & 1.14200505765449 & -0.125005057654489 \tabularnewline
25 & 1.016 & 1.01700687169703 & -0.00100687169702907 \tabularnewline
26 & 1.013 & 1.0160000553491 & -0.00300005534909853 \tabularnewline
27 & 1 & 1.0130001649171 & -0.0130001649170985 \tabularnewline
28 & 1.018 & 1.00000071463664 & 0.0179992853633579 \tabularnewline
29 & 1.024 & 1.01799901055495 & 0.0060009894450519 \tabularnewline
30 & 1.075 & 1.0239996701175 & 0.0510003298825032 \tabularnewline
31 & 1.055 & 1.07499719644291 & -0.0199971964429126 \tabularnewline
32 & 1.091 & 1.05500109927293 & 0.0359989007270749 \tabularnewline
33 & 1.062 & 1.09099802109176 & -0.0289980210917555 \tabularnewline
34 & 1.083 & 1.06200159406043 & 0.0209984059395745 \tabularnewline
35 & 1.099 & 1.08299884568924 & 0.0160011543107648 \tabularnewline
36 & 1.097 & 1.09899912039491 & -0.00199912039491368 \tabularnewline
37 & 1.138 & 1.09700010989435 & 0.040999890105649 \tabularnewline
38 & 1.138 & 1.13799774618061 & 2.25381939200631e-06 \tabularnewline
39 & 1.181 & 1.1379999998761 & 0.0430000001238957 \tabularnewline
40 & 1.223 & 1.18099763623186 & 0.0420023637681439 \tabularnewline
41 & 1.23 & 1.22299769107328 & 0.00700230892672438 \tabularnewline
42 & 1.232 & 1.22999961507361 & 0.00200038492638899 \tabularnewline
43 & 1.209 & 1.23199989003614 & -0.0229998900361359 \tabularnewline
44 & 1.209 & 1.20900126433505 & -1.26433505176493e-06 \tabularnewline
45 & 1.218 & 1.2090000000695 & 0.00899999993049772 \tabularnewline
46 & 1.225 & 1.21799950525784 & 0.00700049474216446 \tabularnewline
47 & 1.242 & 1.22499961517334 & 0.0170003848266607 \tabularnewline
48 & 1.294 & 1.24199906546586 & 0.052000934534139 \tabularnewline
49 & 1.33 & 1.29399714143832 & 0.0360028585616778 \tabularnewline
50 & 1.357 & 1.32999802087419 & 0.0270019791258118 \tabularnewline
51 & 1.407 & 1.3569985156647 & 0.0500014843352998 \tabularnewline
52 & 1.42 & 1.4069972513508 & 0.013002748649197 \tabularnewline
53 & 1.386 & 1.41999928522133 & -0.0339992852213267 \tabularnewline
54 & 1.377 & 1.38600186898668 & -0.00900186898667643 \tabularnewline
55 & 1.393 & 1.37700049484491 & 0.015999505155091 \tabularnewline
56 & 1.371 & 1.39299912048557 & -0.0219991204855698 \tabularnewline
57 & 1.393 & 1.3710012093214 & 0.0219987906786037 \tabularnewline
58 & 1.405 & 1.39299879069673 & 0.0120012093032664 \tabularnewline
59 & 1.438 & 1.4049993402773 & 0.0330006597227013 \tabularnewline
60 & 1.424 & 1.43799818590912 & -0.0139981859091174 \tabularnewline
61 & 1.47 & 1.42400076949921 & 0.0459992305007948 \tabularnewline
62 & 1.481 & 1.46999747136011 & 0.0110025286398929 \tabularnewline
63 & 1.506 & 1.48099939517613 & 0.0250006048238749 \tabularnewline
64 & 1.503 & 1.50599862568295 & -0.00299862568295151 \tabularnewline
65 & 1.478 & 1.50300016483851 & -0.0250001648385079 \tabularnewline
66 & 1.433 & 1.47800137429286 & -0.0450013742928619 \tabularnewline
67 & 1.459 & 1.43300247378639 & 0.0259975262136123 \tabularnewline
68 & 1.51 & 1.45899857088083 & 0.0510014291191652 \tabularnewline
69 & 1.526 & 1.50999719638249 & 0.0160028036175139 \tabularnewline
70 & 1.543 & 1.52599912030425 & 0.017000879695751 \tabularnewline
71 & 1.529 & 1.54299906543866 & -0.0139990654386575 \tabularnewline
72 & 1.499 & 1.52900076954755 & -0.0300007695475542 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235001&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]1.026[/C][C]1.005[/C][C]0.0210000000000001[/C][/ROW]
[ROW][C]3[/C][C]1.043[/C][C]1.02599884560161[/C][C]0.0170011543983923[/C][/ROW]
[ROW][C]4[/C][C]1.068[/C][C]1.04299906542356[/C][C]0.0250009345764435[/C][/ROW]
[ROW][C]5[/C][C]1.07[/C][C]1.06799862566482[/C][C]0.00200137433517544[/C][/ROW]
[ROW][C]6[/C][C]1.091[/C][C]1.06999988998175[/C][C]0.0210001100182531[/C][/ROW]
[ROW][C]7[/C][C]1.102[/C][C]1.09099884559556[/C][C]0.0110011544044404[/C][/ROW]
[ROW][C]8[/C][C]1.091[/C][C]1.10199939525167[/C][C]-0.0109993952516687[/C][/ROW]
[ROW][C]9[/C][C]1.121[/C][C]1.09100060465163[/C][C]0.0299993953483715[/C][/ROW]
[ROW][C]10[/C][C]1.134[/C][C]1.12099835089268[/C][C]0.0130016491073222[/C][/ROW]
[ROW][C]11[/C][C]1.225[/C][C]1.13399928528177[/C][C]0.0910007147182301[/C][/ROW]
[ROW][C]12[/C][C]1.191[/C][C]1.22499499756768[/C][C]-0.0339949975676768[/C][/ROW]
[ROW][C]13[/C][C]1.184[/C][C]1.19100186875098[/C][C]-0.00700186875097852[/C][/ROW]
[ROW][C]14[/C][C]1.207[/C][C]1.18400038490219[/C][C]0.0229996150978082[/C][/ROW]
[ROW][C]15[/C][C]1.271[/C][C]1.20699873568006[/C][C]0.0640012643199377[/C][/ROW]
[ROW][C]16[/C][C]1.299[/C][C]1.27099648176397[/C][C]0.028003518236031[/C][/ROW]
[ROW][C]17[/C][C]1.411[/C][C]1.29899846060874[/C][C]0.112001539391259[/C][/ROW]
[ROW][C]18[/C][C]1.437[/C][C]1.41099384312395[/C][C]0.0260061568760492[/C][/ROW]
[ROW][C]19[/C][C]1.462[/C][C]1.4369985704064[/C][C]0.0250014295936043[/C][/ROW]
[ROW][C]20[/C][C]1.36[/C][C]1.46199862563761[/C][C]-0.101998625637613[/C][/ROW]
[ROW][C]21[/C][C]1.33[/C][C]1.36000560700236[/C][C]-0.030005607002356[/C][/ROW]
[ROW][C]22[/C][C]1.234[/C][C]1.33000164944879[/C][C]-0.0960016494487854[/C][/ROW]
[ROW][C]23[/C][C]1.142[/C][C]1.23400527734047[/C][C]-0.0920052773404669[/C][/ROW]
[ROW][C]24[/C][C]1.017[/C][C]1.14200505765449[/C][C]-0.125005057654489[/C][/ROW]
[ROW][C]25[/C][C]1.016[/C][C]1.01700687169703[/C][C]-0.00100687169702907[/C][/ROW]
[ROW][C]26[/C][C]1.013[/C][C]1.0160000553491[/C][C]-0.00300005534909853[/C][/ROW]
[ROW][C]27[/C][C]1[/C][C]1.0130001649171[/C][C]-0.0130001649170985[/C][/ROW]
[ROW][C]28[/C][C]1.018[/C][C]1.00000071463664[/C][C]0.0179992853633579[/C][/ROW]
[ROW][C]29[/C][C]1.024[/C][C]1.01799901055495[/C][C]0.0060009894450519[/C][/ROW]
[ROW][C]30[/C][C]1.075[/C][C]1.0239996701175[/C][C]0.0510003298825032[/C][/ROW]
[ROW][C]31[/C][C]1.055[/C][C]1.07499719644291[/C][C]-0.0199971964429126[/C][/ROW]
[ROW][C]32[/C][C]1.091[/C][C]1.05500109927293[/C][C]0.0359989007270749[/C][/ROW]
[ROW][C]33[/C][C]1.062[/C][C]1.09099802109176[/C][C]-0.0289980210917555[/C][/ROW]
[ROW][C]34[/C][C]1.083[/C][C]1.06200159406043[/C][C]0.0209984059395745[/C][/ROW]
[ROW][C]35[/C][C]1.099[/C][C]1.08299884568924[/C][C]0.0160011543107648[/C][/ROW]
[ROW][C]36[/C][C]1.097[/C][C]1.09899912039491[/C][C]-0.00199912039491368[/C][/ROW]
[ROW][C]37[/C][C]1.138[/C][C]1.09700010989435[/C][C]0.040999890105649[/C][/ROW]
[ROW][C]38[/C][C]1.138[/C][C]1.13799774618061[/C][C]2.25381939200631e-06[/C][/ROW]
[ROW][C]39[/C][C]1.181[/C][C]1.1379999998761[/C][C]0.0430000001238957[/C][/ROW]
[ROW][C]40[/C][C]1.223[/C][C]1.18099763623186[/C][C]0.0420023637681439[/C][/ROW]
[ROW][C]41[/C][C]1.23[/C][C]1.22299769107328[/C][C]0.00700230892672438[/C][/ROW]
[ROW][C]42[/C][C]1.232[/C][C]1.22999961507361[/C][C]0.00200038492638899[/C][/ROW]
[ROW][C]43[/C][C]1.209[/C][C]1.23199989003614[/C][C]-0.0229998900361359[/C][/ROW]
[ROW][C]44[/C][C]1.209[/C][C]1.20900126433505[/C][C]-1.26433505176493e-06[/C][/ROW]
[ROW][C]45[/C][C]1.218[/C][C]1.2090000000695[/C][C]0.00899999993049772[/C][/ROW]
[ROW][C]46[/C][C]1.225[/C][C]1.21799950525784[/C][C]0.00700049474216446[/C][/ROW]
[ROW][C]47[/C][C]1.242[/C][C]1.22499961517334[/C][C]0.0170003848266607[/C][/ROW]
[ROW][C]48[/C][C]1.294[/C][C]1.24199906546586[/C][C]0.052000934534139[/C][/ROW]
[ROW][C]49[/C][C]1.33[/C][C]1.29399714143832[/C][C]0.0360028585616778[/C][/ROW]
[ROW][C]50[/C][C]1.357[/C][C]1.32999802087419[/C][C]0.0270019791258118[/C][/ROW]
[ROW][C]51[/C][C]1.407[/C][C]1.3569985156647[/C][C]0.0500014843352998[/C][/ROW]
[ROW][C]52[/C][C]1.42[/C][C]1.4069972513508[/C][C]0.013002748649197[/C][/ROW]
[ROW][C]53[/C][C]1.386[/C][C]1.41999928522133[/C][C]-0.0339992852213267[/C][/ROW]
[ROW][C]54[/C][C]1.377[/C][C]1.38600186898668[/C][C]-0.00900186898667643[/C][/ROW]
[ROW][C]55[/C][C]1.393[/C][C]1.37700049484491[/C][C]0.015999505155091[/C][/ROW]
[ROW][C]56[/C][C]1.371[/C][C]1.39299912048557[/C][C]-0.0219991204855698[/C][/ROW]
[ROW][C]57[/C][C]1.393[/C][C]1.3710012093214[/C][C]0.0219987906786037[/C][/ROW]
[ROW][C]58[/C][C]1.405[/C][C]1.39299879069673[/C][C]0.0120012093032664[/C][/ROW]
[ROW][C]59[/C][C]1.438[/C][C]1.4049993402773[/C][C]0.0330006597227013[/C][/ROW]
[ROW][C]60[/C][C]1.424[/C][C]1.43799818590912[/C][C]-0.0139981859091174[/C][/ROW]
[ROW][C]61[/C][C]1.47[/C][C]1.42400076949921[/C][C]0.0459992305007948[/C][/ROW]
[ROW][C]62[/C][C]1.481[/C][C]1.46999747136011[/C][C]0.0110025286398929[/C][/ROW]
[ROW][C]63[/C][C]1.506[/C][C]1.48099939517613[/C][C]0.0250006048238749[/C][/ROW]
[ROW][C]64[/C][C]1.503[/C][C]1.50599862568295[/C][C]-0.00299862568295151[/C][/ROW]
[ROW][C]65[/C][C]1.478[/C][C]1.50300016483851[/C][C]-0.0250001648385079[/C][/ROW]
[ROW][C]66[/C][C]1.433[/C][C]1.47800137429286[/C][C]-0.0450013742928619[/C][/ROW]
[ROW][C]67[/C][C]1.459[/C][C]1.43300247378639[/C][C]0.0259975262136123[/C][/ROW]
[ROW][C]68[/C][C]1.51[/C][C]1.45899857088083[/C][C]0.0510014291191652[/C][/ROW]
[ROW][C]69[/C][C]1.526[/C][C]1.50999719638249[/C][C]0.0160028036175139[/C][/ROW]
[ROW][C]70[/C][C]1.543[/C][C]1.52599912030425[/C][C]0.017000879695751[/C][/ROW]
[ROW][C]71[/C][C]1.529[/C][C]1.54299906543866[/C][C]-0.0139990654386575[/C][/ROW]
[ROW][C]72[/C][C]1.499[/C][C]1.52900076954755[/C][C]-0.0300007695475542[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235001&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235001&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
2	1.026	1.005	0.0210000000000001
3	1.043	1.02599884560161	0.0170011543983923
4	1.068	1.04299906542356	0.0250009345764435
5	1.07	1.06799862566482	0.00200137433517544
6	1.091	1.06999988998175	0.0210001100182531
7	1.102	1.09099884559556	0.0110011544044404
8	1.091	1.10199939525167	-0.0109993952516687
9	1.121	1.09100060465163	0.0299993953483715
10	1.134	1.12099835089268	0.0130016491073222
11	1.225	1.13399928528177	0.0910007147182301
12	1.191	1.22499499756768	-0.0339949975676768
13	1.184	1.19100186875098	-0.00700186875097852
14	1.207	1.18400038490219	0.0229996150978082
15	1.271	1.20699873568006	0.0640012643199377
16	1.299	1.27099648176397	0.028003518236031
17	1.411	1.29899846060874	0.112001539391259
18	1.437	1.41099384312395	0.0260061568760492
19	1.462	1.4369985704064	0.0250014295936043
20	1.36	1.46199862563761	-0.101998625637613
21	1.33	1.36000560700236	-0.030005607002356
22	1.234	1.33000164944879	-0.0960016494487854
23	1.142	1.23400527734047	-0.0920052773404669
24	1.017	1.14200505765449	-0.125005057654489
25	1.016	1.01700687169703	-0.00100687169702907
26	1.013	1.0160000553491	-0.00300005534909853
27	1	1.0130001649171	-0.0130001649170985
28	1.018	1.00000071463664	0.0179992853633579
29	1.024	1.01799901055495	0.0060009894450519
30	1.075	1.0239996701175	0.0510003298825032
31	1.055	1.07499719644291	-0.0199971964429126
32	1.091	1.05500109927293	0.0359989007270749
33	1.062	1.09099802109176	-0.0289980210917555
34	1.083	1.06200159406043	0.0209984059395745
35	1.099	1.08299884568924	0.0160011543107648
36	1.097	1.09899912039491	-0.00199912039491368
37	1.138	1.09700010989435	0.040999890105649
38	1.138	1.13799774618061	2.25381939200631e-06
39	1.181	1.1379999998761	0.0430000001238957
40	1.223	1.18099763623186	0.0420023637681439
41	1.23	1.22299769107328	0.00700230892672438
42	1.232	1.22999961507361	0.00200038492638899
43	1.209	1.23199989003614	-0.0229998900361359
44	1.209	1.20900126433505	-1.26433505176493e-06
45	1.218	1.2090000000695	0.00899999993049772
46	1.225	1.21799950525784	0.00700049474216446
47	1.242	1.22499961517334	0.0170003848266607
48	1.294	1.24199906546586	0.052000934534139
49	1.33	1.29399714143832	0.0360028585616778
50	1.357	1.32999802087419	0.0270019791258118
51	1.407	1.3569985156647	0.0500014843352998
52	1.42	1.4069972513508	0.013002748649197
53	1.386	1.41999928522133	-0.0339992852213267
54	1.377	1.38600186898668	-0.00900186898667643
55	1.393	1.37700049484491	0.015999505155091
56	1.371	1.39299912048557	-0.0219991204855698
57	1.393	1.3710012093214	0.0219987906786037
58	1.405	1.39299879069673	0.0120012093032664
59	1.438	1.4049993402773	0.0330006597227013
60	1.424	1.43799818590912	-0.0139981859091174
61	1.47	1.42400076949921	0.0459992305007948
62	1.481	1.46999747136011	0.0110025286398929
63	1.506	1.48099939517613	0.0250006048238749
64	1.503	1.50599862568295	-0.00299862568295151
65	1.478	1.50300016483851	-0.0250001648385079
66	1.433	1.47800137429286	-0.0450013742928619
67	1.459	1.43300247378639	0.0259975262136123
68	1.51	1.45899857088083	0.0510014291191652
69	1.526	1.50999719638249	0.0160028036175139
70	1.543	1.52599912030425	0.017000879695751
71	1.529	1.54299906543866	-0.0139990654386575
72	1.499	1.52900076954755	-0.0300007695475542

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.49900164918286	1.42222034351095	1.57578295485478
74	1.49900164918286	1.39041946986054	1.60758382850519
75	1.49900164918286	1.36601740037088	1.63198589799484
76	1.49900164918286	1.3454453689538	1.65255792941193
77	1.49900164918286	1.32732098060457	1.67068231776115
78	1.49900164918286	1.31093524407767	1.68706805428806
79	1.49900164918286	1.29586698081015	1.70213631755557
80	1.49900164918286	1.28184176738931	1.71616153097642
81	1.49900164918286	1.26866898752522	1.7293343108405
82	1.49900164918286	1.2562098540332	1.74179344433252
83	1.49900164918286	1.24435959343069	1.75364370493504
84	1.49900164918286	1.23303680691345	1.76496649145228

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.49900164918286 & 1.42222034351095 & 1.57578295485478 \tabularnewline
74 & 1.49900164918286 & 1.39041946986054 & 1.60758382850519 \tabularnewline
75 & 1.49900164918286 & 1.36601740037088 & 1.63198589799484 \tabularnewline
76 & 1.49900164918286 & 1.3454453689538 & 1.65255792941193 \tabularnewline
77 & 1.49900164918286 & 1.32732098060457 & 1.67068231776115 \tabularnewline
78 & 1.49900164918286 & 1.31093524407767 & 1.68706805428806 \tabularnewline
79 & 1.49900164918286 & 1.29586698081015 & 1.70213631755557 \tabularnewline
80 & 1.49900164918286 & 1.28184176738931 & 1.71616153097642 \tabularnewline
81 & 1.49900164918286 & 1.26866898752522 & 1.7293343108405 \tabularnewline
82 & 1.49900164918286 & 1.2562098540332 & 1.74179344433252 \tabularnewline
83 & 1.49900164918286 & 1.24435959343069 & 1.75364370493504 \tabularnewline
84 & 1.49900164918286 & 1.23303680691345 & 1.76496649145228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235001&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]1.49900164918286[/C][C]1.42222034351095[/C][C]1.57578295485478[/C][/ROW]
[ROW][C]74[/C][C]1.49900164918286[/C][C]1.39041946986054[/C][C]1.60758382850519[/C][/ROW]
[ROW][C]75[/C][C]1.49900164918286[/C][C]1.36601740037088[/C][C]1.63198589799484[/C][/ROW]
[ROW][C]76[/C][C]1.49900164918286[/C][C]1.3454453689538[/C][C]1.65255792941193[/C][/ROW]
[ROW][C]77[/C][C]1.49900164918286[/C][C]1.32732098060457[/C][C]1.67068231776115[/C][/ROW]
[ROW][C]78[/C][C]1.49900164918286[/C][C]1.31093524407767[/C][C]1.68706805428806[/C][/ROW]
[ROW][C]79[/C][C]1.49900164918286[/C][C]1.29586698081015[/C][C]1.70213631755557[/C][/ROW]
[ROW][C]80[/C][C]1.49900164918286[/C][C]1.28184176738931[/C][C]1.71616153097642[/C][/ROW]
[ROW][C]81[/C][C]1.49900164918286[/C][C]1.26866898752522[/C][C]1.7293343108405[/C][/ROW]
[ROW][C]82[/C][C]1.49900164918286[/C][C]1.2562098540332[/C][C]1.74179344433252[/C][/ROW]
[ROW][C]83[/C][C]1.49900164918286[/C][C]1.24435959343069[/C][C]1.75364370493504[/C][/ROW]
[ROW][C]84[/C][C]1.49900164918286[/C][C]1.23303680691345[/C][C]1.76496649145228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235001&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235001&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	1.49900164918286	1.42222034351095	1.57578295485478
74	1.49900164918286	1.39041946986054	1.60758382850519
75	1.49900164918286	1.36601740037088	1.63198589799484
76	1.49900164918286	1.3454453689538	1.65255792941193
77	1.49900164918286	1.32732098060457	1.67068231776115
78	1.49900164918286	1.31093524407767	1.68706805428806
79	1.49900164918286	1.29586698081015	1.70213631755557
80	1.49900164918286	1.28184176738931	1.71616153097642
81	1.49900164918286	1.26866898752522	1.7293343108405
82	1.49900164918286	1.2562098540332	1.74179344433252
83	1.49900164918286	1.24435959343069	1.75364370493504
84	1.49900164918286	1.23303680691345	1.76496649145228

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 = 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code