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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 22 Dec 2014 15:50:12 +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/2014/Dec/22/t1419263438a7gl424d1329d9q.htm/, Retrieved Thu, 16 May 2024 19:32:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271404, Retrieved Thu, 16 May 2024 19:32:08 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

144

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

-       [Exponential Smoothing] [] [2014-12-22 15:50:12] [d4b037465b17855a5e62fa4428b30753] [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	7 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 7 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271404&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271404&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271404&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	7 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0076841920358362
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0076841920358362 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271404&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0076841920358362[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271404&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271404&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	1
beta	0.0076841920358362
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.479	1.484	-0.00499999999999989
4	1.517	1.48896157903982	0.0280384209601789
5	1.575	1.52717703165086	0.0478229683491396
6	1.627	1.58554451252338	0.0414554874766211
7	1.613	1.63786306445009	-0.0248630644500885
8	1.558	1.62367201188825	-0.0656720118882546
9	1.545	1.56816737553753	-0.0231673755375257
10	1.406	1.55498935297493	-0.148989352974929
11	1.269	1.41484449017537	-0.145844490175375
12	1.191	1.2767237931055	-0.0857237931054982
13	1.231	1.19806507501724	0.0329349249827646
14	1.276	1.23831815330549	0.037681846694511
15	1.281	1.28360770785175	-0.00260770785175457
16	1.312	1.28858766972385	0.023412330276152
17	1.363	1.3197675745657	0.0432324254343033
18	1.419	1.37109978082491	0.0479002191750912
19	1.374	1.42746785530761	-0.0534678553076087
20	1.422	1.38205699803968	0.0399430019603191
21	1.378	1.43036392773723	-0.0523639277372316
22	1.38	1.38596155326075	-0.00596155326074821
23	1.409	1.38791574354066	0.0210842564593394
24	1.398	1.41707775901623	-0.0190777590162272
25	1.445	1.40593116185233	0.0390688381476672
26	1.452	1.45323137430728	-0.00123137430727671
27	1.506	1.46022191219063	0.0457780878093685
28	1.531	1.51457367980839	0.0164263201916077
29	1.524	1.53969990280719	-0.0156999028071865
30	1.52	1.53257926173907	-0.0125792617390721
31	1.499	1.5284826002762	-0.0294826002761999
32	1.491	1.50725605031396	-0.0162560503139619
33	1.496	1.49913113570161	-0.00313113570160528
34	1.493	1.50410707545358	-0.0111070754535838
35	1.507	1.50102172655284	0.00597827344715784
36	1.569	1.51506766475405	0.0539323352459473
37	1.593	1.57748209117502	0.0155179088249764
38	1.597	1.60160133376643	-0.00460133376642946
39	1.633	1.60556597623415	0.0274340237658528
40	1.686	1.64177678454108	0.0442232154589204
41	1.683	1.69511660422111	-0.0121166042211081
42	1.646	1.69202349790745	-0.046023497907451
43	1.658	1.65466984451137	0.00333015548863091
44	1.636	1.66669543406565	-0.0306954340656531
45	1.67	1.64445956445567	0.0255404355443309
46	1.634	1.67865582206707	-0.0446558220670707
47	1.618	1.64231267815479	-0.0243126781547891
48	1.622	1.62612585486694	-0.00412585486694228
49	1.688	1.63009415100583	0.0579058489941671
50	1.723	1.6965391106695	0.0264608893304981
51	1.776	1.73174244122456	0.0442575587754432
52	1.809	1.78508252480522	0.0239174751947755
53	1.754	1.81826631127763	-0.0642663112776334
54	1.714	1.76277247660034	-0.0487724766003412
55	1.733	1.72239769952408	0.0106023004759193
56	1.783	1.74147916963696	0.0415208303630403
57	1.818	1.79179822367096	0.0262017763290436
58	1.81	1.82699956315195	-0.0169995631519488
59	1.764	1.81886893524416	-0.054868935244164
60	1.73	1.77244731180895	-0.0424473118089461
61	1.742	1.7381211385136	0.00387886148639893
62	1.785	1.75015094443014	0.0348490555698571
63	1.769	1.79341873126541	-0.0244187312654092
64	1.743	1.77723109304509	-0.0342310930450942
65	1.721	1.75096805475254	-0.0299680547525394
66	1.73	1.72873777446488	0.00126222553511957
67	1.753	1.73774747364828	0.0152525263517151
68	1.764	1.7608646769898	0.00313532301019714
69	1.758	1.77188876941391	-0.0138887694139076
70	1.7	1.76578204544259	-0.0657820454425897
71	1.678	1.7072765635729	-0.0292765635728989
72	1.688	1.68505159683626	0.00294840316374478

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.479 & 1.484 & -0.00499999999999989 \tabularnewline
4 & 1.517 & 1.48896157903982 & 0.0280384209601789 \tabularnewline
5 & 1.575 & 1.52717703165086 & 0.0478229683491396 \tabularnewline
6 & 1.627 & 1.58554451252338 & 0.0414554874766211 \tabularnewline
7 & 1.613 & 1.63786306445009 & -0.0248630644500885 \tabularnewline
8 & 1.558 & 1.62367201188825 & -0.0656720118882546 \tabularnewline
9 & 1.545 & 1.56816737553753 & -0.0231673755375257 \tabularnewline
10 & 1.406 & 1.55498935297493 & -0.148989352974929 \tabularnewline
11 & 1.269 & 1.41484449017537 & -0.145844490175375 \tabularnewline
12 & 1.191 & 1.2767237931055 & -0.0857237931054982 \tabularnewline
13 & 1.231 & 1.19806507501724 & 0.0329349249827646 \tabularnewline
14 & 1.276 & 1.23831815330549 & 0.037681846694511 \tabularnewline
15 & 1.281 & 1.28360770785175 & -0.00260770785175457 \tabularnewline
16 & 1.312 & 1.28858766972385 & 0.023412330276152 \tabularnewline
17 & 1.363 & 1.3197675745657 & 0.0432324254343033 \tabularnewline
18 & 1.419 & 1.37109978082491 & 0.0479002191750912 \tabularnewline
19 & 1.374 & 1.42746785530761 & -0.0534678553076087 \tabularnewline
20 & 1.422 & 1.38205699803968 & 0.0399430019603191 \tabularnewline
21 & 1.378 & 1.43036392773723 & -0.0523639277372316 \tabularnewline
22 & 1.38 & 1.38596155326075 & -0.00596155326074821 \tabularnewline
23 & 1.409 & 1.38791574354066 & 0.0210842564593394 \tabularnewline
24 & 1.398 & 1.41707775901623 & -0.0190777590162272 \tabularnewline
25 & 1.445 & 1.40593116185233 & 0.0390688381476672 \tabularnewline
26 & 1.452 & 1.45323137430728 & -0.00123137430727671 \tabularnewline
27 & 1.506 & 1.46022191219063 & 0.0457780878093685 \tabularnewline
28 & 1.531 & 1.51457367980839 & 0.0164263201916077 \tabularnewline
29 & 1.524 & 1.53969990280719 & -0.0156999028071865 \tabularnewline
30 & 1.52 & 1.53257926173907 & -0.0125792617390721 \tabularnewline
31 & 1.499 & 1.5284826002762 & -0.0294826002761999 \tabularnewline
32 & 1.491 & 1.50725605031396 & -0.0162560503139619 \tabularnewline
33 & 1.496 & 1.49913113570161 & -0.00313113570160528 \tabularnewline
34 & 1.493 & 1.50410707545358 & -0.0111070754535838 \tabularnewline
35 & 1.507 & 1.50102172655284 & 0.00597827344715784 \tabularnewline
36 & 1.569 & 1.51506766475405 & 0.0539323352459473 \tabularnewline
37 & 1.593 & 1.57748209117502 & 0.0155179088249764 \tabularnewline
38 & 1.597 & 1.60160133376643 & -0.00460133376642946 \tabularnewline
39 & 1.633 & 1.60556597623415 & 0.0274340237658528 \tabularnewline
40 & 1.686 & 1.64177678454108 & 0.0442232154589204 \tabularnewline
41 & 1.683 & 1.69511660422111 & -0.0121166042211081 \tabularnewline
42 & 1.646 & 1.69202349790745 & -0.046023497907451 \tabularnewline
43 & 1.658 & 1.65466984451137 & 0.00333015548863091 \tabularnewline
44 & 1.636 & 1.66669543406565 & -0.0306954340656531 \tabularnewline
45 & 1.67 & 1.64445956445567 & 0.0255404355443309 \tabularnewline
46 & 1.634 & 1.67865582206707 & -0.0446558220670707 \tabularnewline
47 & 1.618 & 1.64231267815479 & -0.0243126781547891 \tabularnewline
48 & 1.622 & 1.62612585486694 & -0.00412585486694228 \tabularnewline
49 & 1.688 & 1.63009415100583 & 0.0579058489941671 \tabularnewline
50 & 1.723 & 1.6965391106695 & 0.0264608893304981 \tabularnewline
51 & 1.776 & 1.73174244122456 & 0.0442575587754432 \tabularnewline
52 & 1.809 & 1.78508252480522 & 0.0239174751947755 \tabularnewline
53 & 1.754 & 1.81826631127763 & -0.0642663112776334 \tabularnewline
54 & 1.714 & 1.76277247660034 & -0.0487724766003412 \tabularnewline
55 & 1.733 & 1.72239769952408 & 0.0106023004759193 \tabularnewline
56 & 1.783 & 1.74147916963696 & 0.0415208303630403 \tabularnewline
57 & 1.818 & 1.79179822367096 & 0.0262017763290436 \tabularnewline
58 & 1.81 & 1.82699956315195 & -0.0169995631519488 \tabularnewline
59 & 1.764 & 1.81886893524416 & -0.054868935244164 \tabularnewline
60 & 1.73 & 1.77244731180895 & -0.0424473118089461 \tabularnewline
61 & 1.742 & 1.7381211385136 & 0.00387886148639893 \tabularnewline
62 & 1.785 & 1.75015094443014 & 0.0348490555698571 \tabularnewline
63 & 1.769 & 1.79341873126541 & -0.0244187312654092 \tabularnewline
64 & 1.743 & 1.77723109304509 & -0.0342310930450942 \tabularnewline
65 & 1.721 & 1.75096805475254 & -0.0299680547525394 \tabularnewline
66 & 1.73 & 1.72873777446488 & 0.00126222553511957 \tabularnewline
67 & 1.753 & 1.73774747364828 & 0.0152525263517151 \tabularnewline
68 & 1.764 & 1.7608646769898 & 0.00313532301019714 \tabularnewline
69 & 1.758 & 1.77188876941391 & -0.0138887694139076 \tabularnewline
70 & 1.7 & 1.76578204544259 & -0.0657820454425897 \tabularnewline
71 & 1.678 & 1.7072765635729 & -0.0292765635728989 \tabularnewline
72 & 1.688 & 1.68505159683626 & 0.00294840316374478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271404&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]1.479[/C][C]1.484[/C][C]-0.00499999999999989[/C][/ROW]
[ROW][C]4[/C][C]1.517[/C][C]1.48896157903982[/C][C]0.0280384209601789[/C][/ROW]
[ROW][C]5[/C][C]1.575[/C][C]1.52717703165086[/C][C]0.0478229683491396[/C][/ROW]
[ROW][C]6[/C][C]1.627[/C][C]1.58554451252338[/C][C]0.0414554874766211[/C][/ROW]
[ROW][C]7[/C][C]1.613[/C][C]1.63786306445009[/C][C]-0.0248630644500885[/C][/ROW]
[ROW][C]8[/C][C]1.558[/C][C]1.62367201188825[/C][C]-0.0656720118882546[/C][/ROW]
[ROW][C]9[/C][C]1.545[/C][C]1.56816737553753[/C][C]-0.0231673755375257[/C][/ROW]
[ROW][C]10[/C][C]1.406[/C][C]1.55498935297493[/C][C]-0.148989352974929[/C][/ROW]
[ROW][C]11[/C][C]1.269[/C][C]1.41484449017537[/C][C]-0.145844490175375[/C][/ROW]
[ROW][C]12[/C][C]1.191[/C][C]1.2767237931055[/C][C]-0.0857237931054982[/C][/ROW]
[ROW][C]13[/C][C]1.231[/C][C]1.19806507501724[/C][C]0.0329349249827646[/C][/ROW]
[ROW][C]14[/C][C]1.276[/C][C]1.23831815330549[/C][C]0.037681846694511[/C][/ROW]
[ROW][C]15[/C][C]1.281[/C][C]1.28360770785175[/C][C]-0.00260770785175457[/C][/ROW]
[ROW][C]16[/C][C]1.312[/C][C]1.28858766972385[/C][C]0.023412330276152[/C][/ROW]
[ROW][C]17[/C][C]1.363[/C][C]1.3197675745657[/C][C]0.0432324254343033[/C][/ROW]
[ROW][C]18[/C][C]1.419[/C][C]1.37109978082491[/C][C]0.0479002191750912[/C][/ROW]
[ROW][C]19[/C][C]1.374[/C][C]1.42746785530761[/C][C]-0.0534678553076087[/C][/ROW]
[ROW][C]20[/C][C]1.422[/C][C]1.38205699803968[/C][C]0.0399430019603191[/C][/ROW]
[ROW][C]21[/C][C]1.378[/C][C]1.43036392773723[/C][C]-0.0523639277372316[/C][/ROW]
[ROW][C]22[/C][C]1.38[/C][C]1.38596155326075[/C][C]-0.00596155326074821[/C][/ROW]
[ROW][C]23[/C][C]1.409[/C][C]1.38791574354066[/C][C]0.0210842564593394[/C][/ROW]
[ROW][C]24[/C][C]1.398[/C][C]1.41707775901623[/C][C]-0.0190777590162272[/C][/ROW]
[ROW][C]25[/C][C]1.445[/C][C]1.40593116185233[/C][C]0.0390688381476672[/C][/ROW]
[ROW][C]26[/C][C]1.452[/C][C]1.45323137430728[/C][C]-0.00123137430727671[/C][/ROW]
[ROW][C]27[/C][C]1.506[/C][C]1.46022191219063[/C][C]0.0457780878093685[/C][/ROW]
[ROW][C]28[/C][C]1.531[/C][C]1.51457367980839[/C][C]0.0164263201916077[/C][/ROW]
[ROW][C]29[/C][C]1.524[/C][C]1.53969990280719[/C][C]-0.0156999028071865[/C][/ROW]
[ROW][C]30[/C][C]1.52[/C][C]1.53257926173907[/C][C]-0.0125792617390721[/C][/ROW]
[ROW][C]31[/C][C]1.499[/C][C]1.5284826002762[/C][C]-0.0294826002761999[/C][/ROW]
[ROW][C]32[/C][C]1.491[/C][C]1.50725605031396[/C][C]-0.0162560503139619[/C][/ROW]
[ROW][C]33[/C][C]1.496[/C][C]1.49913113570161[/C][C]-0.00313113570160528[/C][/ROW]
[ROW][C]34[/C][C]1.493[/C][C]1.50410707545358[/C][C]-0.0111070754535838[/C][/ROW]
[ROW][C]35[/C][C]1.507[/C][C]1.50102172655284[/C][C]0.00597827344715784[/C][/ROW]
[ROW][C]36[/C][C]1.569[/C][C]1.51506766475405[/C][C]0.0539323352459473[/C][/ROW]
[ROW][C]37[/C][C]1.593[/C][C]1.57748209117502[/C][C]0.0155179088249764[/C][/ROW]
[ROW][C]38[/C][C]1.597[/C][C]1.60160133376643[/C][C]-0.00460133376642946[/C][/ROW]
[ROW][C]39[/C][C]1.633[/C][C]1.60556597623415[/C][C]0.0274340237658528[/C][/ROW]
[ROW][C]40[/C][C]1.686[/C][C]1.64177678454108[/C][C]0.0442232154589204[/C][/ROW]
[ROW][C]41[/C][C]1.683[/C][C]1.69511660422111[/C][C]-0.0121166042211081[/C][/ROW]
[ROW][C]42[/C][C]1.646[/C][C]1.69202349790745[/C][C]-0.046023497907451[/C][/ROW]
[ROW][C]43[/C][C]1.658[/C][C]1.65466984451137[/C][C]0.00333015548863091[/C][/ROW]
[ROW][C]44[/C][C]1.636[/C][C]1.66669543406565[/C][C]-0.0306954340656531[/C][/ROW]
[ROW][C]45[/C][C]1.67[/C][C]1.64445956445567[/C][C]0.0255404355443309[/C][/ROW]
[ROW][C]46[/C][C]1.634[/C][C]1.67865582206707[/C][C]-0.0446558220670707[/C][/ROW]
[ROW][C]47[/C][C]1.618[/C][C]1.64231267815479[/C][C]-0.0243126781547891[/C][/ROW]
[ROW][C]48[/C][C]1.622[/C][C]1.62612585486694[/C][C]-0.00412585486694228[/C][/ROW]
[ROW][C]49[/C][C]1.688[/C][C]1.63009415100583[/C][C]0.0579058489941671[/C][/ROW]
[ROW][C]50[/C][C]1.723[/C][C]1.6965391106695[/C][C]0.0264608893304981[/C][/ROW]
[ROW][C]51[/C][C]1.776[/C][C]1.73174244122456[/C][C]0.0442575587754432[/C][/ROW]
[ROW][C]52[/C][C]1.809[/C][C]1.78508252480522[/C][C]0.0239174751947755[/C][/ROW]
[ROW][C]53[/C][C]1.754[/C][C]1.81826631127763[/C][C]-0.0642663112776334[/C][/ROW]
[ROW][C]54[/C][C]1.714[/C][C]1.76277247660034[/C][C]-0.0487724766003412[/C][/ROW]
[ROW][C]55[/C][C]1.733[/C][C]1.72239769952408[/C][C]0.0106023004759193[/C][/ROW]
[ROW][C]56[/C][C]1.783[/C][C]1.74147916963696[/C][C]0.0415208303630403[/C][/ROW]
[ROW][C]57[/C][C]1.818[/C][C]1.79179822367096[/C][C]0.0262017763290436[/C][/ROW]
[ROW][C]58[/C][C]1.81[/C][C]1.82699956315195[/C][C]-0.0169995631519488[/C][/ROW]
[ROW][C]59[/C][C]1.764[/C][C]1.81886893524416[/C][C]-0.054868935244164[/C][/ROW]
[ROW][C]60[/C][C]1.73[/C][C]1.77244731180895[/C][C]-0.0424473118089461[/C][/ROW]
[ROW][C]61[/C][C]1.742[/C][C]1.7381211385136[/C][C]0.00387886148639893[/C][/ROW]
[ROW][C]62[/C][C]1.785[/C][C]1.75015094443014[/C][C]0.0348490555698571[/C][/ROW]
[ROW][C]63[/C][C]1.769[/C][C]1.79341873126541[/C][C]-0.0244187312654092[/C][/ROW]
[ROW][C]64[/C][C]1.743[/C][C]1.77723109304509[/C][C]-0.0342310930450942[/C][/ROW]
[ROW][C]65[/C][C]1.721[/C][C]1.75096805475254[/C][C]-0.0299680547525394[/C][/ROW]
[ROW][C]66[/C][C]1.73[/C][C]1.72873777446488[/C][C]0.00126222553511957[/C][/ROW]
[ROW][C]67[/C][C]1.753[/C][C]1.73774747364828[/C][C]0.0152525263517151[/C][/ROW]
[ROW][C]68[/C][C]1.764[/C][C]1.7608646769898[/C][C]0.00313532301019714[/C][/ROW]
[ROW][C]69[/C][C]1.758[/C][C]1.77188876941391[/C][C]-0.0138887694139076[/C][/ROW]
[ROW][C]70[/C][C]1.7[/C][C]1.76578204544259[/C][C]-0.0657820454425897[/C][/ROW]
[ROW][C]71[/C][C]1.678[/C][C]1.7072765635729[/C][C]-0.0292765635728989[/C][/ROW]
[ROW][C]72[/C][C]1.688[/C][C]1.68505159683626[/C][C]0.00294840316374478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271404&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271404&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
3	1.479	1.484	-0.00499999999999989
4	1.517	1.48896157903982	0.0280384209601789
5	1.575	1.52717703165086	0.0478229683491396
6	1.627	1.58554451252338	0.0414554874766211
7	1.613	1.63786306445009	-0.0248630644500885
8	1.558	1.62367201188825	-0.0656720118882546
9	1.545	1.56816737553753	-0.0231673755375257
10	1.406	1.55498935297493	-0.148989352974929
11	1.269	1.41484449017537	-0.145844490175375
12	1.191	1.2767237931055	-0.0857237931054982
13	1.231	1.19806507501724	0.0329349249827646
14	1.276	1.23831815330549	0.037681846694511
15	1.281	1.28360770785175	-0.00260770785175457
16	1.312	1.28858766972385	0.023412330276152
17	1.363	1.3197675745657	0.0432324254343033
18	1.419	1.37109978082491	0.0479002191750912
19	1.374	1.42746785530761	-0.0534678553076087
20	1.422	1.38205699803968	0.0399430019603191
21	1.378	1.43036392773723	-0.0523639277372316
22	1.38	1.38596155326075	-0.00596155326074821
23	1.409	1.38791574354066	0.0210842564593394
24	1.398	1.41707775901623	-0.0190777590162272
25	1.445	1.40593116185233	0.0390688381476672
26	1.452	1.45323137430728	-0.00123137430727671
27	1.506	1.46022191219063	0.0457780878093685
28	1.531	1.51457367980839	0.0164263201916077
29	1.524	1.53969990280719	-0.0156999028071865
30	1.52	1.53257926173907	-0.0125792617390721
31	1.499	1.5284826002762	-0.0294826002761999
32	1.491	1.50725605031396	-0.0162560503139619
33	1.496	1.49913113570161	-0.00313113570160528
34	1.493	1.50410707545358	-0.0111070754535838
35	1.507	1.50102172655284	0.00597827344715784
36	1.569	1.51506766475405	0.0539323352459473
37	1.593	1.57748209117502	0.0155179088249764
38	1.597	1.60160133376643	-0.00460133376642946
39	1.633	1.60556597623415	0.0274340237658528
40	1.686	1.64177678454108	0.0442232154589204
41	1.683	1.69511660422111	-0.0121166042211081
42	1.646	1.69202349790745	-0.046023497907451
43	1.658	1.65466984451137	0.00333015548863091
44	1.636	1.66669543406565	-0.0306954340656531
45	1.67	1.64445956445567	0.0255404355443309
46	1.634	1.67865582206707	-0.0446558220670707
47	1.618	1.64231267815479	-0.0243126781547891
48	1.622	1.62612585486694	-0.00412585486694228
49	1.688	1.63009415100583	0.0579058489941671
50	1.723	1.6965391106695	0.0264608893304981
51	1.776	1.73174244122456	0.0442575587754432
52	1.809	1.78508252480522	0.0239174751947755
53	1.754	1.81826631127763	-0.0642663112776334
54	1.714	1.76277247660034	-0.0487724766003412
55	1.733	1.72239769952408	0.0106023004759193
56	1.783	1.74147916963696	0.0415208303630403
57	1.818	1.79179822367096	0.0262017763290436
58	1.81	1.82699956315195	-0.0169995631519488
59	1.764	1.81886893524416	-0.054868935244164
60	1.73	1.77244731180895	-0.0424473118089461
61	1.742	1.7381211385136	0.00387886148639893
62	1.785	1.75015094443014	0.0348490555698571
63	1.769	1.79341873126541	-0.0244187312654092
64	1.743	1.77723109304509	-0.0342310930450942
65	1.721	1.75096805475254	-0.0299680547525394
66	1.73	1.72873777446488	0.00126222553511957
67	1.753	1.73774747364828	0.0152525263517151
68	1.764	1.7608646769898	0.00313532301019714
69	1.758	1.77188876941391	-0.0138887694139076
70	1.7	1.76578204544259	-0.0657820454425897
71	1.678	1.7072765635729	-0.0292765635728989
72	1.688	1.68505159683626	0.00294840316374478

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.69507425293236	1.61249477201225	1.77765373385248
74	1.70214850586473	1.58491392603562	1.81938308569383
75	1.70922275879709	1.5650890242304	1.85335649336379
76	1.71629701172946	1.54922835461367	1.88336566884525
77	1.72337126466182	1.53586937058384	1.91087315873981
78	1.73044551759419	1.52426498737528	1.93662604781309
79	1.73751977052655	1.51397314498693	1.96106639606618
80	1.74459402345892	1.50470693782616	1.98448110909167
81	1.75166827639128	1.49626785243871	2.00706870034385
82	1.75874252932365	1.48851191074091	2.02897314790638
83	1.76581678225601	1.48133084029952	2.0503027242125
84	1.77289103518837	1.47464084871219	2.07114122166456

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.69507425293236 & 1.61249477201225 & 1.77765373385248 \tabularnewline
74 & 1.70214850586473 & 1.58491392603562 & 1.81938308569383 \tabularnewline
75 & 1.70922275879709 & 1.5650890242304 & 1.85335649336379 \tabularnewline
76 & 1.71629701172946 & 1.54922835461367 & 1.88336566884525 \tabularnewline
77 & 1.72337126466182 & 1.53586937058384 & 1.91087315873981 \tabularnewline
78 & 1.73044551759419 & 1.52426498737528 & 1.93662604781309 \tabularnewline
79 & 1.73751977052655 & 1.51397314498693 & 1.96106639606618 \tabularnewline
80 & 1.74459402345892 & 1.50470693782616 & 1.98448110909167 \tabularnewline
81 & 1.75166827639128 & 1.49626785243871 & 2.00706870034385 \tabularnewline
82 & 1.75874252932365 & 1.48851191074091 & 2.02897314790638 \tabularnewline
83 & 1.76581678225601 & 1.48133084029952 & 2.0503027242125 \tabularnewline
84 & 1.77289103518837 & 1.47464084871219 & 2.07114122166456 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271404&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]1.69507425293236[/C][C]1.61249477201225[/C][C]1.77765373385248[/C][/ROW]
[ROW][C]74[/C][C]1.70214850586473[/C][C]1.58491392603562[/C][C]1.81938308569383[/C][/ROW]
[ROW][C]75[/C][C]1.70922275879709[/C][C]1.5650890242304[/C][C]1.85335649336379[/C][/ROW]
[ROW][C]76[/C][C]1.71629701172946[/C][C]1.54922835461367[/C][C]1.88336566884525[/C][/ROW]
[ROW][C]77[/C][C]1.72337126466182[/C][C]1.53586937058384[/C][C]1.91087315873981[/C][/ROW]
[ROW][C]78[/C][C]1.73044551759419[/C][C]1.52426498737528[/C][C]1.93662604781309[/C][/ROW]
[ROW][C]79[/C][C]1.73751977052655[/C][C]1.51397314498693[/C][C]1.96106639606618[/C][/ROW]
[ROW][C]80[/C][C]1.74459402345892[/C][C]1.50470693782616[/C][C]1.98448110909167[/C][/ROW]
[ROW][C]81[/C][C]1.75166827639128[/C][C]1.49626785243871[/C][C]2.00706870034385[/C][/ROW]
[ROW][C]82[/C][C]1.75874252932365[/C][C]1.48851191074091[/C][C]2.02897314790638[/C][/ROW]
[ROW][C]83[/C][C]1.76581678225601[/C][C]1.48133084029952[/C][C]2.0503027242125[/C][/ROW]
[ROW][C]84[/C][C]1.77289103518837[/C][C]1.47464084871219[/C][C]2.07114122166456[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271404&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271404&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	1.69507425293236	1.61249477201225	1.77765373385248
74	1.70214850586473	1.58491392603562	1.81938308569383
75	1.70922275879709	1.5650890242304	1.85335649336379
76	1.71629701172946	1.54922835461367	1.88336566884525
77	1.72337126466182	1.53586937058384	1.91087315873981
78	1.73044551759419	1.52426498737528	1.93662604781309
79	1.73751977052655	1.51397314498693	1.96106639606618
80	1.74459402345892	1.50470693782616	1.98448110909167
81	1.75166827639128	1.49626785243871	2.00706870034385
82	1.75874252932365	1.48851191074091	2.02897314790638
83	1.76581678225601	1.48133084029952	2.0503027242125
84	1.77289103518837	1.47464084871219	2.07114122166456

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 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

R code (references can be found in the software module):

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code