Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 05 Jun 2009 02:16:34 -0600

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/2009/Jun/05/t1244189877vry99gsnzl0opwi.htm/, Retrieved Fri, 10 May 2024 06:34:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41754, Retrieved Fri, 10 May 2024 06:34:21 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

164

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

-       [Exponential Smoothing] [opgave10oef2] [2009-06-05 08:16:34] [791ed687546d9528c8a01d986e6abead] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41754&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41754&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41754&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.983881209935916
beta	0
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.983881209935916 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41754&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]0.983881209935916[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41754&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41754&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	0.983881209935916
beta	0
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	0.8766	0.8707	0.00590000000000002
4	0.886	0.876504899138622	0.00949510086137806
5	0.917	0.885846950462578	0.0311530495374219
6	0.9561	0.91649785053465	0.0396021494653497
7	0.9935	0.955461661266682	0.0380383387333185
8	0.9781	0.992886868003571	-0.0147868680035712
9	0.9806	0.978338346421055	0.00226165357894514
10	0.9812	0.980563544880763	0.000636455119236601
11	1.0013	0.981189741113548	0.0201102588864523
12	1.0194	1.00097584695887	0.0184241530411251
13	1.0622	1.01910302494502	0.0430969750549783
14	1.0785	1.06150532890669	0.0169946710933082
15	1.0797	1.07822606646444	0.00147393353556136
16	1.0862	1.07967624197477	0.00652375802522798
17	1.1556	1.08609484491396	0.0695051550860375
18	1.1674	1.15447966099680	0.0129203390032036
19	1.1365	1.16719173976805	-0.0306917397680504
20	1.1155	1.13699471371002	-0.0214947137100228
21	1.1267	1.11584646877778	0.0108535312222207
22	1.1714	1.12652505420878	0.044874945791225
23	1.171	1.17067667016965	0.000323329830345997
24	1.2298	1.17099478831434	0.0588052116856568
25	1.2638	1.22885213113816	0.0349478688618352
26	1.264	1.26323668263863	0.00076331736137103
27	1.2261	1.2639876962477	-0.0378876962476999
28	1.1989	1.22671070382183	-0.0278107038218283
29	1.2	1.19934827489644	0.000651725103561374
30	1.2146	1.19998949497988	0.0146105050201237
31	1.2266	1.21436449633685	0.0122355036631496
32	1.2191	1.22640277848513	-0.00730277848512517
33	1.2224	1.21921771195329	0.00318228804671361
34	1.2507	1.22234870536705	0.0283512946329485
35	1.2997	1.25024301143377	0.0494569885662337
36	1.3406	1.2989028131841	0.0416971868159008
37	1.3123	1.33992789179945	-0.0276278917994517
38	1.3013	1.31274532818783	-0.0114453281878286
39	1.3185	1.30148448484227	0.0170155151577260
40	1.2943	1.31822573048334	-0.0239257304833405
41	1.2697	1.29468565382679	-0.0249856538267907
42	1.2155	1.27010273850865	-0.054602738508648
43	1.2041	1.21638013007894	-0.0122801300789450
44	1.2295	1.20429794083870	0.0252020591612980
45	1.2234	1.22909377329920	-0.0056937732991964
46	1.2022	1.22349177673648	-0.0212917767364824
47	1	1.20254319767931	-0.202543197679307
48	1.1861	1.0032647512823	0.182835248717699
49	1.2126	1.18315291700960	0.0294470829903952
50	1.194	1.21212534865128	-0.018125348651278
51	1.2028	1.19429215868975	0.00850784131025195
52	1.2273	1.20266286389202	0.0246371361079785
53	1.2767	1.22690287917530	0.0497971208247046
54	1.2661	1.27589733066363	-0.00979733066363075
55	1.2681	1.26625792111616	0.00184207888384447
56	1.281	1.26807030791719	0.0129296920828101
57	1.2722	1.28079158900772	-0.00859158900772394
58	1.2617	1.27233848601953	-0.0106384860195323
59	1.2888	1.26187147952275	0.0269285204772514
60	1.3205	1.28836594483169	0.0321340551683094
61	1.2993	1.31998203791083	-0.0206820379108343
62	1.308	1.29963336942718	0.00836663057281806
63	1.3246	1.30786514003825	0.0167348599617470
64	1.3513	1.32433025430552	0.0269697456944753
65	1.3518	1.35086528033107	0.000934719668930883
66	1.3421	1.35178493344989	-0.00968493344988763
67	1.3726	1.34225610940906	0.0303438905909366
68	1.3626	1.37211089319784	-0.00951089319783716
69	1.391	1.36275330409078	0.028246695909222
70	1.4233	1.39054469743864	0.0327553025613647
71	1.4683	1.42277202415453	0.0455279758454721
72	1.4559	1.46756614411530	-0.0116661441153041
73	1.4728	1.45608804412785	0.0167119558721482
74	1.4759	1.47253062349174	0.00336937650826319
75	1.552	1.47584568972742	0.0761543102725837
76	1.5754	1.55077248466024	0.0246275153397588
77	1.5554	1.57500303425044	-0.0196030342504385
78	1.5562	1.55571597719370	0.000484022806298334
79	1.5759	1.556192198138	0.0197078018620009
80	1.4955	1.57558233407916	-0.0800823340791619
81	1.4342	1.49679083033086	-0.062590830330864
82	1.3266	1.43520888845404	-0.108608888454040
83	1.2744	1.32835064387208	-0.0539506438720843
84	1.3511	1.27526961910240	0.0758303808976037
85	1.3244	1.34987770600983	-0.0254777060098319
86	1.2797	1.32481066979449	-0.045110669794487
87	1.305	1.28042712941607	0.0245728705839323
88	1.3203	1.30460391505779	0.0156960849422143

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.8766 & 0.8707 & 0.00590000000000002 \tabularnewline
4 & 0.886 & 0.876504899138622 & 0.00949510086137806 \tabularnewline
5 & 0.917 & 0.885846950462578 & 0.0311530495374219 \tabularnewline
6 & 0.9561 & 0.91649785053465 & 0.0396021494653497 \tabularnewline
7 & 0.9935 & 0.955461661266682 & 0.0380383387333185 \tabularnewline
8 & 0.9781 & 0.992886868003571 & -0.0147868680035712 \tabularnewline
9 & 0.9806 & 0.978338346421055 & 0.00226165357894514 \tabularnewline
10 & 0.9812 & 0.980563544880763 & 0.000636455119236601 \tabularnewline
11 & 1.0013 & 0.981189741113548 & 0.0201102588864523 \tabularnewline
12 & 1.0194 & 1.00097584695887 & 0.0184241530411251 \tabularnewline
13 & 1.0622 & 1.01910302494502 & 0.0430969750549783 \tabularnewline
14 & 1.0785 & 1.06150532890669 & 0.0169946710933082 \tabularnewline
15 & 1.0797 & 1.07822606646444 & 0.00147393353556136 \tabularnewline
16 & 1.0862 & 1.07967624197477 & 0.00652375802522798 \tabularnewline
17 & 1.1556 & 1.08609484491396 & 0.0695051550860375 \tabularnewline
18 & 1.1674 & 1.15447966099680 & 0.0129203390032036 \tabularnewline
19 & 1.1365 & 1.16719173976805 & -0.0306917397680504 \tabularnewline
20 & 1.1155 & 1.13699471371002 & -0.0214947137100228 \tabularnewline
21 & 1.1267 & 1.11584646877778 & 0.0108535312222207 \tabularnewline
22 & 1.1714 & 1.12652505420878 & 0.044874945791225 \tabularnewline
23 & 1.171 & 1.17067667016965 & 0.000323329830345997 \tabularnewline
24 & 1.2298 & 1.17099478831434 & 0.0588052116856568 \tabularnewline
25 & 1.2638 & 1.22885213113816 & 0.0349478688618352 \tabularnewline
26 & 1.264 & 1.26323668263863 & 0.00076331736137103 \tabularnewline
27 & 1.2261 & 1.2639876962477 & -0.0378876962476999 \tabularnewline
28 & 1.1989 & 1.22671070382183 & -0.0278107038218283 \tabularnewline
29 & 1.2 & 1.19934827489644 & 0.000651725103561374 \tabularnewline
30 & 1.2146 & 1.19998949497988 & 0.0146105050201237 \tabularnewline
31 & 1.2266 & 1.21436449633685 & 0.0122355036631496 \tabularnewline
32 & 1.2191 & 1.22640277848513 & -0.00730277848512517 \tabularnewline
33 & 1.2224 & 1.21921771195329 & 0.00318228804671361 \tabularnewline
34 & 1.2507 & 1.22234870536705 & 0.0283512946329485 \tabularnewline
35 & 1.2997 & 1.25024301143377 & 0.0494569885662337 \tabularnewline
36 & 1.3406 & 1.2989028131841 & 0.0416971868159008 \tabularnewline
37 & 1.3123 & 1.33992789179945 & -0.0276278917994517 \tabularnewline
38 & 1.3013 & 1.31274532818783 & -0.0114453281878286 \tabularnewline
39 & 1.3185 & 1.30148448484227 & 0.0170155151577260 \tabularnewline
40 & 1.2943 & 1.31822573048334 & -0.0239257304833405 \tabularnewline
41 & 1.2697 & 1.29468565382679 & -0.0249856538267907 \tabularnewline
42 & 1.2155 & 1.27010273850865 & -0.054602738508648 \tabularnewline
43 & 1.2041 & 1.21638013007894 & -0.0122801300789450 \tabularnewline
44 & 1.2295 & 1.20429794083870 & 0.0252020591612980 \tabularnewline
45 & 1.2234 & 1.22909377329920 & -0.0056937732991964 \tabularnewline
46 & 1.2022 & 1.22349177673648 & -0.0212917767364824 \tabularnewline
47 & 1 & 1.20254319767931 & -0.202543197679307 \tabularnewline
48 & 1.1861 & 1.0032647512823 & 0.182835248717699 \tabularnewline
49 & 1.2126 & 1.18315291700960 & 0.0294470829903952 \tabularnewline
50 & 1.194 & 1.21212534865128 & -0.018125348651278 \tabularnewline
51 & 1.2028 & 1.19429215868975 & 0.00850784131025195 \tabularnewline
52 & 1.2273 & 1.20266286389202 & 0.0246371361079785 \tabularnewline
53 & 1.2767 & 1.22690287917530 & 0.0497971208247046 \tabularnewline
54 & 1.2661 & 1.27589733066363 & -0.00979733066363075 \tabularnewline
55 & 1.2681 & 1.26625792111616 & 0.00184207888384447 \tabularnewline
56 & 1.281 & 1.26807030791719 & 0.0129296920828101 \tabularnewline
57 & 1.2722 & 1.28079158900772 & -0.00859158900772394 \tabularnewline
58 & 1.2617 & 1.27233848601953 & -0.0106384860195323 \tabularnewline
59 & 1.2888 & 1.26187147952275 & 0.0269285204772514 \tabularnewline
60 & 1.3205 & 1.28836594483169 & 0.0321340551683094 \tabularnewline
61 & 1.2993 & 1.31998203791083 & -0.0206820379108343 \tabularnewline
62 & 1.308 & 1.29963336942718 & 0.00836663057281806 \tabularnewline
63 & 1.3246 & 1.30786514003825 & 0.0167348599617470 \tabularnewline
64 & 1.3513 & 1.32433025430552 & 0.0269697456944753 \tabularnewline
65 & 1.3518 & 1.35086528033107 & 0.000934719668930883 \tabularnewline
66 & 1.3421 & 1.35178493344989 & -0.00968493344988763 \tabularnewline
67 & 1.3726 & 1.34225610940906 & 0.0303438905909366 \tabularnewline
68 & 1.3626 & 1.37211089319784 & -0.00951089319783716 \tabularnewline
69 & 1.391 & 1.36275330409078 & 0.028246695909222 \tabularnewline
70 & 1.4233 & 1.39054469743864 & 0.0327553025613647 \tabularnewline
71 & 1.4683 & 1.42277202415453 & 0.0455279758454721 \tabularnewline
72 & 1.4559 & 1.46756614411530 & -0.0116661441153041 \tabularnewline
73 & 1.4728 & 1.45608804412785 & 0.0167119558721482 \tabularnewline
74 & 1.4759 & 1.47253062349174 & 0.00336937650826319 \tabularnewline
75 & 1.552 & 1.47584568972742 & 0.0761543102725837 \tabularnewline
76 & 1.5754 & 1.55077248466024 & 0.0246275153397588 \tabularnewline
77 & 1.5554 & 1.57500303425044 & -0.0196030342504385 \tabularnewline
78 & 1.5562 & 1.55571597719370 & 0.000484022806298334 \tabularnewline
79 & 1.5759 & 1.556192198138 & 0.0197078018620009 \tabularnewline
80 & 1.4955 & 1.57558233407916 & -0.0800823340791619 \tabularnewline
81 & 1.4342 & 1.49679083033086 & -0.062590830330864 \tabularnewline
82 & 1.3266 & 1.43520888845404 & -0.108608888454040 \tabularnewline
83 & 1.2744 & 1.32835064387208 & -0.0539506438720843 \tabularnewline
84 & 1.3511 & 1.27526961910240 & 0.0758303808976037 \tabularnewline
85 & 1.3244 & 1.34987770600983 & -0.0254777060098319 \tabularnewline
86 & 1.2797 & 1.32481066979449 & -0.045110669794487 \tabularnewline
87 & 1.305 & 1.28042712941607 & 0.0245728705839323 \tabularnewline
88 & 1.3203 & 1.30460391505779 & 0.0156960849422143 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41754&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]0.8766[/C][C]0.8707[/C][C]0.00590000000000002[/C][/ROW]
[ROW][C]4[/C][C]0.886[/C][C]0.876504899138622[/C][C]0.00949510086137806[/C][/ROW]
[ROW][C]5[/C][C]0.917[/C][C]0.885846950462578[/C][C]0.0311530495374219[/C][/ROW]
[ROW][C]6[/C][C]0.9561[/C][C]0.91649785053465[/C][C]0.0396021494653497[/C][/ROW]
[ROW][C]7[/C][C]0.9935[/C][C]0.955461661266682[/C][C]0.0380383387333185[/C][/ROW]
[ROW][C]8[/C][C]0.9781[/C][C]0.992886868003571[/C][C]-0.0147868680035712[/C][/ROW]
[ROW][C]9[/C][C]0.9806[/C][C]0.978338346421055[/C][C]0.00226165357894514[/C][/ROW]
[ROW][C]10[/C][C]0.9812[/C][C]0.980563544880763[/C][C]0.000636455119236601[/C][/ROW]
[ROW][C]11[/C][C]1.0013[/C][C]0.981189741113548[/C][C]0.0201102588864523[/C][/ROW]
[ROW][C]12[/C][C]1.0194[/C][C]1.00097584695887[/C][C]0.0184241530411251[/C][/ROW]
[ROW][C]13[/C][C]1.0622[/C][C]1.01910302494502[/C][C]0.0430969750549783[/C][/ROW]
[ROW][C]14[/C][C]1.0785[/C][C]1.06150532890669[/C][C]0.0169946710933082[/C][/ROW]
[ROW][C]15[/C][C]1.0797[/C][C]1.07822606646444[/C][C]0.00147393353556136[/C][/ROW]
[ROW][C]16[/C][C]1.0862[/C][C]1.07967624197477[/C][C]0.00652375802522798[/C][/ROW]
[ROW][C]17[/C][C]1.1556[/C][C]1.08609484491396[/C][C]0.0695051550860375[/C][/ROW]
[ROW][C]18[/C][C]1.1674[/C][C]1.15447966099680[/C][C]0.0129203390032036[/C][/ROW]
[ROW][C]19[/C][C]1.1365[/C][C]1.16719173976805[/C][C]-0.0306917397680504[/C][/ROW]
[ROW][C]20[/C][C]1.1155[/C][C]1.13699471371002[/C][C]-0.0214947137100228[/C][/ROW]
[ROW][C]21[/C][C]1.1267[/C][C]1.11584646877778[/C][C]0.0108535312222207[/C][/ROW]
[ROW][C]22[/C][C]1.1714[/C][C]1.12652505420878[/C][C]0.044874945791225[/C][/ROW]
[ROW][C]23[/C][C]1.171[/C][C]1.17067667016965[/C][C]0.000323329830345997[/C][/ROW]
[ROW][C]24[/C][C]1.2298[/C][C]1.17099478831434[/C][C]0.0588052116856568[/C][/ROW]
[ROW][C]25[/C][C]1.2638[/C][C]1.22885213113816[/C][C]0.0349478688618352[/C][/ROW]
[ROW][C]26[/C][C]1.264[/C][C]1.26323668263863[/C][C]0.00076331736137103[/C][/ROW]
[ROW][C]27[/C][C]1.2261[/C][C]1.2639876962477[/C][C]-0.0378876962476999[/C][/ROW]
[ROW][C]28[/C][C]1.1989[/C][C]1.22671070382183[/C][C]-0.0278107038218283[/C][/ROW]
[ROW][C]29[/C][C]1.2[/C][C]1.19934827489644[/C][C]0.000651725103561374[/C][/ROW]
[ROW][C]30[/C][C]1.2146[/C][C]1.19998949497988[/C][C]0.0146105050201237[/C][/ROW]
[ROW][C]31[/C][C]1.2266[/C][C]1.21436449633685[/C][C]0.0122355036631496[/C][/ROW]
[ROW][C]32[/C][C]1.2191[/C][C]1.22640277848513[/C][C]-0.00730277848512517[/C][/ROW]
[ROW][C]33[/C][C]1.2224[/C][C]1.21921771195329[/C][C]0.00318228804671361[/C][/ROW]
[ROW][C]34[/C][C]1.2507[/C][C]1.22234870536705[/C][C]0.0283512946329485[/C][/ROW]
[ROW][C]35[/C][C]1.2997[/C][C]1.25024301143377[/C][C]0.0494569885662337[/C][/ROW]
[ROW][C]36[/C][C]1.3406[/C][C]1.2989028131841[/C][C]0.0416971868159008[/C][/ROW]
[ROW][C]37[/C][C]1.3123[/C][C]1.33992789179945[/C][C]-0.0276278917994517[/C][/ROW]
[ROW][C]38[/C][C]1.3013[/C][C]1.31274532818783[/C][C]-0.0114453281878286[/C][/ROW]
[ROW][C]39[/C][C]1.3185[/C][C]1.30148448484227[/C][C]0.0170155151577260[/C][/ROW]
[ROW][C]40[/C][C]1.2943[/C][C]1.31822573048334[/C][C]-0.0239257304833405[/C][/ROW]
[ROW][C]41[/C][C]1.2697[/C][C]1.29468565382679[/C][C]-0.0249856538267907[/C][/ROW]
[ROW][C]42[/C][C]1.2155[/C][C]1.27010273850865[/C][C]-0.054602738508648[/C][/ROW]
[ROW][C]43[/C][C]1.2041[/C][C]1.21638013007894[/C][C]-0.0122801300789450[/C][/ROW]
[ROW][C]44[/C][C]1.2295[/C][C]1.20429794083870[/C][C]0.0252020591612980[/C][/ROW]
[ROW][C]45[/C][C]1.2234[/C][C]1.22909377329920[/C][C]-0.0056937732991964[/C][/ROW]
[ROW][C]46[/C][C]1.2022[/C][C]1.22349177673648[/C][C]-0.0212917767364824[/C][/ROW]
[ROW][C]47[/C][C]1[/C][C]1.20254319767931[/C][C]-0.202543197679307[/C][/ROW]
[ROW][C]48[/C][C]1.1861[/C][C]1.0032647512823[/C][C]0.182835248717699[/C][/ROW]
[ROW][C]49[/C][C]1.2126[/C][C]1.18315291700960[/C][C]0.0294470829903952[/C][/ROW]
[ROW][C]50[/C][C]1.194[/C][C]1.21212534865128[/C][C]-0.018125348651278[/C][/ROW]
[ROW][C]51[/C][C]1.2028[/C][C]1.19429215868975[/C][C]0.00850784131025195[/C][/ROW]
[ROW][C]52[/C][C]1.2273[/C][C]1.20266286389202[/C][C]0.0246371361079785[/C][/ROW]
[ROW][C]53[/C][C]1.2767[/C][C]1.22690287917530[/C][C]0.0497971208247046[/C][/ROW]
[ROW][C]54[/C][C]1.2661[/C][C]1.27589733066363[/C][C]-0.00979733066363075[/C][/ROW]
[ROW][C]55[/C][C]1.2681[/C][C]1.26625792111616[/C][C]0.00184207888384447[/C][/ROW]
[ROW][C]56[/C][C]1.281[/C][C]1.26807030791719[/C][C]0.0129296920828101[/C][/ROW]
[ROW][C]57[/C][C]1.2722[/C][C]1.28079158900772[/C][C]-0.00859158900772394[/C][/ROW]
[ROW][C]58[/C][C]1.2617[/C][C]1.27233848601953[/C][C]-0.0106384860195323[/C][/ROW]
[ROW][C]59[/C][C]1.2888[/C][C]1.26187147952275[/C][C]0.0269285204772514[/C][/ROW]
[ROW][C]60[/C][C]1.3205[/C][C]1.28836594483169[/C][C]0.0321340551683094[/C][/ROW]
[ROW][C]61[/C][C]1.2993[/C][C]1.31998203791083[/C][C]-0.0206820379108343[/C][/ROW]
[ROW][C]62[/C][C]1.308[/C][C]1.29963336942718[/C][C]0.00836663057281806[/C][/ROW]
[ROW][C]63[/C][C]1.3246[/C][C]1.30786514003825[/C][C]0.0167348599617470[/C][/ROW]
[ROW][C]64[/C][C]1.3513[/C][C]1.32433025430552[/C][C]0.0269697456944753[/C][/ROW]
[ROW][C]65[/C][C]1.3518[/C][C]1.35086528033107[/C][C]0.000934719668930883[/C][/ROW]
[ROW][C]66[/C][C]1.3421[/C][C]1.35178493344989[/C][C]-0.00968493344988763[/C][/ROW]
[ROW][C]67[/C][C]1.3726[/C][C]1.34225610940906[/C][C]0.0303438905909366[/C][/ROW]
[ROW][C]68[/C][C]1.3626[/C][C]1.37211089319784[/C][C]-0.00951089319783716[/C][/ROW]
[ROW][C]69[/C][C]1.391[/C][C]1.36275330409078[/C][C]0.028246695909222[/C][/ROW]
[ROW][C]70[/C][C]1.4233[/C][C]1.39054469743864[/C][C]0.0327553025613647[/C][/ROW]
[ROW][C]71[/C][C]1.4683[/C][C]1.42277202415453[/C][C]0.0455279758454721[/C][/ROW]
[ROW][C]72[/C][C]1.4559[/C][C]1.46756614411530[/C][C]-0.0116661441153041[/C][/ROW]
[ROW][C]73[/C][C]1.4728[/C][C]1.45608804412785[/C][C]0.0167119558721482[/C][/ROW]
[ROW][C]74[/C][C]1.4759[/C][C]1.47253062349174[/C][C]0.00336937650826319[/C][/ROW]
[ROW][C]75[/C][C]1.552[/C][C]1.47584568972742[/C][C]0.0761543102725837[/C][/ROW]
[ROW][C]76[/C][C]1.5754[/C][C]1.55077248466024[/C][C]0.0246275153397588[/C][/ROW]
[ROW][C]77[/C][C]1.5554[/C][C]1.57500303425044[/C][C]-0.0196030342504385[/C][/ROW]
[ROW][C]78[/C][C]1.5562[/C][C]1.55571597719370[/C][C]0.000484022806298334[/C][/ROW]
[ROW][C]79[/C][C]1.5759[/C][C]1.556192198138[/C][C]0.0197078018620009[/C][/ROW]
[ROW][C]80[/C][C]1.4955[/C][C]1.57558233407916[/C][C]-0.0800823340791619[/C][/ROW]
[ROW][C]81[/C][C]1.4342[/C][C]1.49679083033086[/C][C]-0.062590830330864[/C][/ROW]
[ROW][C]82[/C][C]1.3266[/C][C]1.43520888845404[/C][C]-0.108608888454040[/C][/ROW]
[ROW][C]83[/C][C]1.2744[/C][C]1.32835064387208[/C][C]-0.0539506438720843[/C][/ROW]
[ROW][C]84[/C][C]1.3511[/C][C]1.27526961910240[/C][C]0.0758303808976037[/C][/ROW]
[ROW][C]85[/C][C]1.3244[/C][C]1.34987770600983[/C][C]-0.0254777060098319[/C][/ROW]
[ROW][C]86[/C][C]1.2797[/C][C]1.32481066979449[/C][C]-0.045110669794487[/C][/ROW]
[ROW][C]87[/C][C]1.305[/C][C]1.28042712941607[/C][C]0.0245728705839323[/C][/ROW]
[ROW][C]88[/C][C]1.3203[/C][C]1.30460391505779[/C][C]0.0156960849422143[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41754&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41754&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	0.8766	0.8707	0.00590000000000002
4	0.886	0.876504899138622	0.00949510086137806
5	0.917	0.885846950462578	0.0311530495374219
6	0.9561	0.91649785053465	0.0396021494653497
7	0.9935	0.955461661266682	0.0380383387333185
8	0.9781	0.992886868003571	-0.0147868680035712
9	0.9806	0.978338346421055	0.00226165357894514
10	0.9812	0.980563544880763	0.000636455119236601
11	1.0013	0.981189741113548	0.0201102588864523
12	1.0194	1.00097584695887	0.0184241530411251
13	1.0622	1.01910302494502	0.0430969750549783
14	1.0785	1.06150532890669	0.0169946710933082
15	1.0797	1.07822606646444	0.00147393353556136
16	1.0862	1.07967624197477	0.00652375802522798
17	1.1556	1.08609484491396	0.0695051550860375
18	1.1674	1.15447966099680	0.0129203390032036
19	1.1365	1.16719173976805	-0.0306917397680504
20	1.1155	1.13699471371002	-0.0214947137100228
21	1.1267	1.11584646877778	0.0108535312222207
22	1.1714	1.12652505420878	0.044874945791225
23	1.171	1.17067667016965	0.000323329830345997
24	1.2298	1.17099478831434	0.0588052116856568
25	1.2638	1.22885213113816	0.0349478688618352
26	1.264	1.26323668263863	0.00076331736137103
27	1.2261	1.2639876962477	-0.0378876962476999
28	1.1989	1.22671070382183	-0.0278107038218283
29	1.2	1.19934827489644	0.000651725103561374
30	1.2146	1.19998949497988	0.0146105050201237
31	1.2266	1.21436449633685	0.0122355036631496
32	1.2191	1.22640277848513	-0.00730277848512517
33	1.2224	1.21921771195329	0.00318228804671361
34	1.2507	1.22234870536705	0.0283512946329485
35	1.2997	1.25024301143377	0.0494569885662337
36	1.3406	1.2989028131841	0.0416971868159008
37	1.3123	1.33992789179945	-0.0276278917994517
38	1.3013	1.31274532818783	-0.0114453281878286
39	1.3185	1.30148448484227	0.0170155151577260
40	1.2943	1.31822573048334	-0.0239257304833405
41	1.2697	1.29468565382679	-0.0249856538267907
42	1.2155	1.27010273850865	-0.054602738508648
43	1.2041	1.21638013007894	-0.0122801300789450
44	1.2295	1.20429794083870	0.0252020591612980
45	1.2234	1.22909377329920	-0.0056937732991964
46	1.2022	1.22349177673648	-0.0212917767364824
47	1	1.20254319767931	-0.202543197679307
48	1.1861	1.0032647512823	0.182835248717699
49	1.2126	1.18315291700960	0.0294470829903952
50	1.194	1.21212534865128	-0.018125348651278
51	1.2028	1.19429215868975	0.00850784131025195
52	1.2273	1.20266286389202	0.0246371361079785
53	1.2767	1.22690287917530	0.0497971208247046
54	1.2661	1.27589733066363	-0.00979733066363075
55	1.2681	1.26625792111616	0.00184207888384447
56	1.281	1.26807030791719	0.0129296920828101
57	1.2722	1.28079158900772	-0.00859158900772394
58	1.2617	1.27233848601953	-0.0106384860195323
59	1.2888	1.26187147952275	0.0269285204772514
60	1.3205	1.28836594483169	0.0321340551683094
61	1.2993	1.31998203791083	-0.0206820379108343
62	1.308	1.29963336942718	0.00836663057281806
63	1.3246	1.30786514003825	0.0167348599617470
64	1.3513	1.32433025430552	0.0269697456944753
65	1.3518	1.35086528033107	0.000934719668930883
66	1.3421	1.35178493344989	-0.00968493344988763
67	1.3726	1.34225610940906	0.0303438905909366
68	1.3626	1.37211089319784	-0.00951089319783716
69	1.391	1.36275330409078	0.028246695909222
70	1.4233	1.39054469743864	0.0327553025613647
71	1.4683	1.42277202415453	0.0455279758454721
72	1.4559	1.46756614411530	-0.0116661441153041
73	1.4728	1.45608804412785	0.0167119558721482
74	1.4759	1.47253062349174	0.00336937650826319
75	1.552	1.47584568972742	0.0761543102725837
76	1.5754	1.55077248466024	0.0246275153397588
77	1.5554	1.57500303425044	-0.0196030342504385
78	1.5562	1.55571597719370	0.000484022806298334
79	1.5759	1.556192198138	0.0197078018620009
80	1.4955	1.57558233407916	-0.0800823340791619
81	1.4342	1.49679083033086	-0.062590830330864
82	1.3266	1.43520888845404	-0.108608888454040
83	1.2744	1.32835064387208	-0.0539506438720843
84	1.3511	1.27526961910240	0.0758303808976037
85	1.3244	1.34987770600983	-0.0254777060098319
86	1.2797	1.32481066979449	-0.045110669794487
87	1.305	1.28042712941607	0.0245728705839323
88	1.3203	1.30460391505779	0.0156960849422143

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
89	1.32004699810199	1.23453042725961	1.40556356894436
90	1.32004699810199	1.20007903695736	1.44001495924662
91	1.32004699810199	1.17351529670683	1.46657869949715
92	1.32004699810199	1.15107727499658	1.4890167212074
93	1.32004699810199	1.13128790523788	1.50880609096609
94	1.32004699810199	1.11338489961405	1.52670909658993
95	1.32004699810199	1.09691374024023	1.54318025596374
96	1.32004699810199	1.08157754811612	1.55851644808785
97	1.32004699810199	1.06716974252308	1.57292425368090
98	1.32004699810199	1.05353971076883	1.58655428543515
99	1.32004699810199	1.04057363261926	1.59952036358471
100	1.32004699810199	1.02818300610092	1.61191099010306

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
89 & 1.32004699810199 & 1.23453042725961 & 1.40556356894436 \tabularnewline
90 & 1.32004699810199 & 1.20007903695736 & 1.44001495924662 \tabularnewline
91 & 1.32004699810199 & 1.17351529670683 & 1.46657869949715 \tabularnewline
92 & 1.32004699810199 & 1.15107727499658 & 1.4890167212074 \tabularnewline
93 & 1.32004699810199 & 1.13128790523788 & 1.50880609096609 \tabularnewline
94 & 1.32004699810199 & 1.11338489961405 & 1.52670909658993 \tabularnewline
95 & 1.32004699810199 & 1.09691374024023 & 1.54318025596374 \tabularnewline
96 & 1.32004699810199 & 1.08157754811612 & 1.55851644808785 \tabularnewline
97 & 1.32004699810199 & 1.06716974252308 & 1.57292425368090 \tabularnewline
98 & 1.32004699810199 & 1.05353971076883 & 1.58655428543515 \tabularnewline
99 & 1.32004699810199 & 1.04057363261926 & 1.59952036358471 \tabularnewline
100 & 1.32004699810199 & 1.02818300610092 & 1.61191099010306 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41754&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]89[/C][C]1.32004699810199[/C][C]1.23453042725961[/C][C]1.40556356894436[/C][/ROW]
[ROW][C]90[/C][C]1.32004699810199[/C][C]1.20007903695736[/C][C]1.44001495924662[/C][/ROW]
[ROW][C]91[/C][C]1.32004699810199[/C][C]1.17351529670683[/C][C]1.46657869949715[/C][/ROW]
[ROW][C]92[/C][C]1.32004699810199[/C][C]1.15107727499658[/C][C]1.4890167212074[/C][/ROW]
[ROW][C]93[/C][C]1.32004699810199[/C][C]1.13128790523788[/C][C]1.50880609096609[/C][/ROW]
[ROW][C]94[/C][C]1.32004699810199[/C][C]1.11338489961405[/C][C]1.52670909658993[/C][/ROW]
[ROW][C]95[/C][C]1.32004699810199[/C][C]1.09691374024023[/C][C]1.54318025596374[/C][/ROW]
[ROW][C]96[/C][C]1.32004699810199[/C][C]1.08157754811612[/C][C]1.55851644808785[/C][/ROW]
[ROW][C]97[/C][C]1.32004699810199[/C][C]1.06716974252308[/C][C]1.57292425368090[/C][/ROW]
[ROW][C]98[/C][C]1.32004699810199[/C][C]1.05353971076883[/C][C]1.58655428543515[/C][/ROW]
[ROW][C]99[/C][C]1.32004699810199[/C][C]1.04057363261926[/C][C]1.59952036358471[/C][/ROW]
[ROW][C]100[/C][C]1.32004699810199[/C][C]1.02818300610092[/C][C]1.61191099010306[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41754&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41754&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
89	1.32004699810199	1.23453042725961	1.40556356894436
90	1.32004699810199	1.20007903695736	1.44001495924662
91	1.32004699810199	1.17351529670683	1.46657869949715
92	1.32004699810199	1.15107727499658	1.4890167212074
93	1.32004699810199	1.13128790523788	1.50880609096609
94	1.32004699810199	1.11338489961405	1.52670909658993
95	1.32004699810199	1.09691374024023	1.54318025596374
96	1.32004699810199	1.08157754811612	1.55851644808785
97	1.32004699810199	1.06716974252308	1.57292425368090
98	1.32004699810199	1.05353971076883	1.58655428543515
99	1.32004699810199	1.04057363261926	1.59952036358471
100	1.32004699810199	1.02818300610092	1.61191099010306

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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