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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 24 Nov 2016 19:58:46 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/24/t148001757460acrithv60b5i6.htm/, Retrieved Tue, 07 May 2024 19:04:47 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 07 May 2024 19:04:47 +0200

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No (this computation is public)

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Estimated Impact

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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	1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 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=&T=0

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

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.954168984957743
beta	0.11027588575101
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.954168984957743 \tabularnewline
beta & 0.11027588575101 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.954168984957743[/C][/ROW]
[ROW][C]beta[/C][C]0.11027588575101[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.954168984957743
beta	0.11027588575101
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	85.91	81.3115197649573	4.5984802350427
14	86.84	87.0542831878999	-0.214283187899866
15	87.44	87.9068930849018	-0.466893084901756
16	87.79	88.3151764414296	-0.525176441429565
17	88.08	88.6438376005937	-0.563837600593743
18	88.38	88.9771147899526	-0.597114789952599
19	88.53	87.6887270730829	0.841272926917071
20	88.79	89.3234079142042	-0.533407914204233
21	88.85	90.1969514423243	-1.34695144232433
22	89.26	90.6462582723539	-1.38625827235388
23	89.31	90.2709451120408	-0.960945112040804
24	89.39	90.4715901750009	-1.08159017500093
25	89.76	90.7073989133596	-0.947398913359564
26	89.94	90.1189848945958	-0.178984894595814
27	89.99	90.1785143801721	-0.188514380172094
28	90.08	90.0638548140439	0.0161451859560486
29	89.95	90.1783231896243	-0.228323189624263
30	90.2	90.13658292572	0.0634170742800393
31	89.7	88.9202495970249	0.779750402975068
32	89.5	89.8026236237221	-0.302623623722099
33	89.25	90.2527714718397	-1.00277147183968
34	89.13	90.458580562844	-1.32858056284404
35	89.07	89.5937610518729	-0.523761051872881
36	89.06	89.6879924408697	-0.627992440869662
37	89.15	89.8924567149728	-0.742456714972747
38	89.38	89.0860702976827	0.293929702317314
39	89.4	89.1974253350896	0.202574664910415
40	89.51	89.1074835237145	0.40251647628547
41	89.62	89.2622388235488	0.357761176451206
42	89.65	89.5375893624045	0.112410637595531
43	89.68	88.150486173898	1.529513826102
44	89.92	89.5271981021751	0.392801897824853
45	90.26	90.5105280712041	-0.250528071204087
46	90.89	91.4000418935449	-0.510041893544923
47	91.08	91.4201299962696	-0.340129996269567
48	91.13	91.7711191158998	-0.641119115899798
49	91.83	92.0427508002359	-0.212750800235867
50	92.66	91.9299670954032	0.730032904596811
51	93.45	92.6398140815594	0.810185918440609
52	93.95	93.3892962803741	0.560703719625891
53	94.12	93.9600791730177	0.159920826982329
54	94.31	94.2817362108044	0.0282637891956199
55	94.25	93.116760190151	1.13323980984903
56	94.51	94.25903660716	0.250963392840049
57	94.58	95.2583932273855	-0.678393227385541
58	94.85	95.8635858703574	-1.01358587035737
59	95.31	95.4938396081522	-0.183839608152212
60	95.75	96.0794511381335	-0.329451138133535
61	96.06	96.8001831763737	-0.740183176373677
62	96.4	96.3039350721178	0.0960649278821819
63	96.57	96.4224221821582	0.147577817841793
64	96.47	96.4683886336321	0.00161136636788228
65	96.34	96.3686643095941	-0.0286643095940633
66	96.22	96.3658316634858	-0.145831663485808
67	96.2	94.928549072094	1.27145092790603
68	96.71	96.0199771923629	0.690022807637121
69	97.05	97.2995865313648	-0.249586531364827
70	97.82	98.2476000302839	-0.427600030283941
71	98.22	98.4856989232803	-0.265698923280254
72	98.5	98.9886034500322	-0.488603450032173
73	98.94	99.5239808652657	-0.583980865265659
74	99.5	99.2168659972279	0.283134002772059
75	99.89	99.5376569911337	0.352343008866328
76	100	99.8153075010893	0.184692498910664
77	100.1	99.951143336934	0.14885666306597
78	100.16	100.1932622664	-0.0332622664004987
79	100.05	99.0211266281299	1.02887337187008
80	100.03	99.921704098702	0.108295901298007
81	100	100.609230818226	-0.609230818226465
82	100.32	101.174128325672	-0.854128325671979
83	100.53	100.935991124311	-0.405991124310546
84	100.49	101.203379325404	-0.713379325404077
85	100.38	101.404822081213	-1.02482208121314
86	100.22	100.555335585893	-0.335335585892906
87	100.5	100.062622130958	0.437377869042024
88	100.57	100.196122329493	0.373877670507326
89	100.6	100.313132461119	0.28686753888104
90	100.23	100.49541421475	-0.265414214750308
91	100.29	98.9428415114155	1.34715848858453
92	100.01	99.9308126806966	0.0791873193034149
93	100.13	100.380503969812	-0.250503969812414
94	100.22	101.137033557791	-0.91703355779147
95	100.2	100.713363663181	-0.513363663180982
96	100.34	100.706865414966	-0.366865414965631
97	100.73	101.103781097498	-0.373781097498011
98	100.29	100.85471514456	-0.564715144559898
99	101.11	100.102030895863	1.00796910413676
100	101.09	100.760581754308	0.329418245692196
101	101.01	100.810024695844	0.199975304155544
102	101.27	100.85378435757	0.416215642429947
103	101.57	100.066929324799	1.5030706752014
104	101.69	101.203381784582	0.486618215417664
105	101	102.127418659718	-1.12741865971789
106	101.43	102.025102900026	-0.595102900025779
107	101.13	101.969411167772	-0.839411167771942
108	101.23	101.666516663777	-0.43651666377724

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 85.91 & 81.3115197649573 & 4.5984802350427 \tabularnewline
14 & 86.84 & 87.0542831878999 & -0.214283187899866 \tabularnewline
15 & 87.44 & 87.9068930849018 & -0.466893084901756 \tabularnewline
16 & 87.79 & 88.3151764414296 & -0.525176441429565 \tabularnewline
17 & 88.08 & 88.6438376005937 & -0.563837600593743 \tabularnewline
18 & 88.38 & 88.9771147899526 & -0.597114789952599 \tabularnewline
19 & 88.53 & 87.6887270730829 & 0.841272926917071 \tabularnewline
20 & 88.79 & 89.3234079142042 & -0.533407914204233 \tabularnewline
21 & 88.85 & 90.1969514423243 & -1.34695144232433 \tabularnewline
22 & 89.26 & 90.6462582723539 & -1.38625827235388 \tabularnewline
23 & 89.31 & 90.2709451120408 & -0.960945112040804 \tabularnewline
24 & 89.39 & 90.4715901750009 & -1.08159017500093 \tabularnewline
25 & 89.76 & 90.7073989133596 & -0.947398913359564 \tabularnewline
26 & 89.94 & 90.1189848945958 & -0.178984894595814 \tabularnewline
27 & 89.99 & 90.1785143801721 & -0.188514380172094 \tabularnewline
28 & 90.08 & 90.0638548140439 & 0.0161451859560486 \tabularnewline
29 & 89.95 & 90.1783231896243 & -0.228323189624263 \tabularnewline
30 & 90.2 & 90.13658292572 & 0.0634170742800393 \tabularnewline
31 & 89.7 & 88.9202495970249 & 0.779750402975068 \tabularnewline
32 & 89.5 & 89.8026236237221 & -0.302623623722099 \tabularnewline
33 & 89.25 & 90.2527714718397 & -1.00277147183968 \tabularnewline
34 & 89.13 & 90.458580562844 & -1.32858056284404 \tabularnewline
35 & 89.07 & 89.5937610518729 & -0.523761051872881 \tabularnewline
36 & 89.06 & 89.6879924408697 & -0.627992440869662 \tabularnewline
37 & 89.15 & 89.8924567149728 & -0.742456714972747 \tabularnewline
38 & 89.38 & 89.0860702976827 & 0.293929702317314 \tabularnewline
39 & 89.4 & 89.1974253350896 & 0.202574664910415 \tabularnewline
40 & 89.51 & 89.1074835237145 & 0.40251647628547 \tabularnewline
41 & 89.62 & 89.2622388235488 & 0.357761176451206 \tabularnewline
42 & 89.65 & 89.5375893624045 & 0.112410637595531 \tabularnewline
43 & 89.68 & 88.150486173898 & 1.529513826102 \tabularnewline
44 & 89.92 & 89.5271981021751 & 0.392801897824853 \tabularnewline
45 & 90.26 & 90.5105280712041 & -0.250528071204087 \tabularnewline
46 & 90.89 & 91.4000418935449 & -0.510041893544923 \tabularnewline
47 & 91.08 & 91.4201299962696 & -0.340129996269567 \tabularnewline
48 & 91.13 & 91.7711191158998 & -0.641119115899798 \tabularnewline
49 & 91.83 & 92.0427508002359 & -0.212750800235867 \tabularnewline
50 & 92.66 & 91.9299670954032 & 0.730032904596811 \tabularnewline
51 & 93.45 & 92.6398140815594 & 0.810185918440609 \tabularnewline
52 & 93.95 & 93.3892962803741 & 0.560703719625891 \tabularnewline
53 & 94.12 & 93.9600791730177 & 0.159920826982329 \tabularnewline
54 & 94.31 & 94.2817362108044 & 0.0282637891956199 \tabularnewline
55 & 94.25 & 93.116760190151 & 1.13323980984903 \tabularnewline
56 & 94.51 & 94.25903660716 & 0.250963392840049 \tabularnewline
57 & 94.58 & 95.2583932273855 & -0.678393227385541 \tabularnewline
58 & 94.85 & 95.8635858703574 & -1.01358587035737 \tabularnewline
59 & 95.31 & 95.4938396081522 & -0.183839608152212 \tabularnewline
60 & 95.75 & 96.0794511381335 & -0.329451138133535 \tabularnewline
61 & 96.06 & 96.8001831763737 & -0.740183176373677 \tabularnewline
62 & 96.4 & 96.3039350721178 & 0.0960649278821819 \tabularnewline
63 & 96.57 & 96.4224221821582 & 0.147577817841793 \tabularnewline
64 & 96.47 & 96.4683886336321 & 0.00161136636788228 \tabularnewline
65 & 96.34 & 96.3686643095941 & -0.0286643095940633 \tabularnewline
66 & 96.22 & 96.3658316634858 & -0.145831663485808 \tabularnewline
67 & 96.2 & 94.928549072094 & 1.27145092790603 \tabularnewline
68 & 96.71 & 96.0199771923629 & 0.690022807637121 \tabularnewline
69 & 97.05 & 97.2995865313648 & -0.249586531364827 \tabularnewline
70 & 97.82 & 98.2476000302839 & -0.427600030283941 \tabularnewline
71 & 98.22 & 98.4856989232803 & -0.265698923280254 \tabularnewline
72 & 98.5 & 98.9886034500322 & -0.488603450032173 \tabularnewline
73 & 98.94 & 99.5239808652657 & -0.583980865265659 \tabularnewline
74 & 99.5 & 99.2168659972279 & 0.283134002772059 \tabularnewline
75 & 99.89 & 99.5376569911337 & 0.352343008866328 \tabularnewline
76 & 100 & 99.8153075010893 & 0.184692498910664 \tabularnewline
77 & 100.1 & 99.951143336934 & 0.14885666306597 \tabularnewline
78 & 100.16 & 100.1932622664 & -0.0332622664004987 \tabularnewline
79 & 100.05 & 99.0211266281299 & 1.02887337187008 \tabularnewline
80 & 100.03 & 99.921704098702 & 0.108295901298007 \tabularnewline
81 & 100 & 100.609230818226 & -0.609230818226465 \tabularnewline
82 & 100.32 & 101.174128325672 & -0.854128325671979 \tabularnewline
83 & 100.53 & 100.935991124311 & -0.405991124310546 \tabularnewline
84 & 100.49 & 101.203379325404 & -0.713379325404077 \tabularnewline
85 & 100.38 & 101.404822081213 & -1.02482208121314 \tabularnewline
86 & 100.22 & 100.555335585893 & -0.335335585892906 \tabularnewline
87 & 100.5 & 100.062622130958 & 0.437377869042024 \tabularnewline
88 & 100.57 & 100.196122329493 & 0.373877670507326 \tabularnewline
89 & 100.6 & 100.313132461119 & 0.28686753888104 \tabularnewline
90 & 100.23 & 100.49541421475 & -0.265414214750308 \tabularnewline
91 & 100.29 & 98.9428415114155 & 1.34715848858453 \tabularnewline
92 & 100.01 & 99.9308126806966 & 0.0791873193034149 \tabularnewline
93 & 100.13 & 100.380503969812 & -0.250503969812414 \tabularnewline
94 & 100.22 & 101.137033557791 & -0.91703355779147 \tabularnewline
95 & 100.2 & 100.713363663181 & -0.513363663180982 \tabularnewline
96 & 100.34 & 100.706865414966 & -0.366865414965631 \tabularnewline
97 & 100.73 & 101.103781097498 & -0.373781097498011 \tabularnewline
98 & 100.29 & 100.85471514456 & -0.564715144559898 \tabularnewline
99 & 101.11 & 100.102030895863 & 1.00796910413676 \tabularnewline
100 & 101.09 & 100.760581754308 & 0.329418245692196 \tabularnewline
101 & 101.01 & 100.810024695844 & 0.199975304155544 \tabularnewline
102 & 101.27 & 100.85378435757 & 0.416215642429947 \tabularnewline
103 & 101.57 & 100.066929324799 & 1.5030706752014 \tabularnewline
104 & 101.69 & 101.203381784582 & 0.486618215417664 \tabularnewline
105 & 101 & 102.127418659718 & -1.12741865971789 \tabularnewline
106 & 101.43 & 102.025102900026 & -0.595102900025779 \tabularnewline
107 & 101.13 & 101.969411167772 & -0.839411167771942 \tabularnewline
108 & 101.23 & 101.666516663777 & -0.43651666377724 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]85.91[/C][C]81.3115197649573[/C][C]4.5984802350427[/C][/ROW]
[ROW][C]14[/C][C]86.84[/C][C]87.0542831878999[/C][C]-0.214283187899866[/C][/ROW]
[ROW][C]15[/C][C]87.44[/C][C]87.9068930849018[/C][C]-0.466893084901756[/C][/ROW]
[ROW][C]16[/C][C]87.79[/C][C]88.3151764414296[/C][C]-0.525176441429565[/C][/ROW]
[ROW][C]17[/C][C]88.08[/C][C]88.6438376005937[/C][C]-0.563837600593743[/C][/ROW]
[ROW][C]18[/C][C]88.38[/C][C]88.9771147899526[/C][C]-0.597114789952599[/C][/ROW]
[ROW][C]19[/C][C]88.53[/C][C]87.6887270730829[/C][C]0.841272926917071[/C][/ROW]
[ROW][C]20[/C][C]88.79[/C][C]89.3234079142042[/C][C]-0.533407914204233[/C][/ROW]
[ROW][C]21[/C][C]88.85[/C][C]90.1969514423243[/C][C]-1.34695144232433[/C][/ROW]
[ROW][C]22[/C][C]89.26[/C][C]90.6462582723539[/C][C]-1.38625827235388[/C][/ROW]
[ROW][C]23[/C][C]89.31[/C][C]90.2709451120408[/C][C]-0.960945112040804[/C][/ROW]
[ROW][C]24[/C][C]89.39[/C][C]90.4715901750009[/C][C]-1.08159017500093[/C][/ROW]
[ROW][C]25[/C][C]89.76[/C][C]90.7073989133596[/C][C]-0.947398913359564[/C][/ROW]
[ROW][C]26[/C][C]89.94[/C][C]90.1189848945958[/C][C]-0.178984894595814[/C][/ROW]
[ROW][C]27[/C][C]89.99[/C][C]90.1785143801721[/C][C]-0.188514380172094[/C][/ROW]
[ROW][C]28[/C][C]90.08[/C][C]90.0638548140439[/C][C]0.0161451859560486[/C][/ROW]
[ROW][C]29[/C][C]89.95[/C][C]90.1783231896243[/C][C]-0.228323189624263[/C][/ROW]
[ROW][C]30[/C][C]90.2[/C][C]90.13658292572[/C][C]0.0634170742800393[/C][/ROW]
[ROW][C]31[/C][C]89.7[/C][C]88.9202495970249[/C][C]0.779750402975068[/C][/ROW]
[ROW][C]32[/C][C]89.5[/C][C]89.8026236237221[/C][C]-0.302623623722099[/C][/ROW]
[ROW][C]33[/C][C]89.25[/C][C]90.2527714718397[/C][C]-1.00277147183968[/C][/ROW]
[ROW][C]34[/C][C]89.13[/C][C]90.458580562844[/C][C]-1.32858056284404[/C][/ROW]
[ROW][C]35[/C][C]89.07[/C][C]89.5937610518729[/C][C]-0.523761051872881[/C][/ROW]
[ROW][C]36[/C][C]89.06[/C][C]89.6879924408697[/C][C]-0.627992440869662[/C][/ROW]
[ROW][C]37[/C][C]89.15[/C][C]89.8924567149728[/C][C]-0.742456714972747[/C][/ROW]
[ROW][C]38[/C][C]89.38[/C][C]89.0860702976827[/C][C]0.293929702317314[/C][/ROW]
[ROW][C]39[/C][C]89.4[/C][C]89.1974253350896[/C][C]0.202574664910415[/C][/ROW]
[ROW][C]40[/C][C]89.51[/C][C]89.1074835237145[/C][C]0.40251647628547[/C][/ROW]
[ROW][C]41[/C][C]89.62[/C][C]89.2622388235488[/C][C]0.357761176451206[/C][/ROW]
[ROW][C]42[/C][C]89.65[/C][C]89.5375893624045[/C][C]0.112410637595531[/C][/ROW]
[ROW][C]43[/C][C]89.68[/C][C]88.150486173898[/C][C]1.529513826102[/C][/ROW]
[ROW][C]44[/C][C]89.92[/C][C]89.5271981021751[/C][C]0.392801897824853[/C][/ROW]
[ROW][C]45[/C][C]90.26[/C][C]90.5105280712041[/C][C]-0.250528071204087[/C][/ROW]
[ROW][C]46[/C][C]90.89[/C][C]91.4000418935449[/C][C]-0.510041893544923[/C][/ROW]
[ROW][C]47[/C][C]91.08[/C][C]91.4201299962696[/C][C]-0.340129996269567[/C][/ROW]
[ROW][C]48[/C][C]91.13[/C][C]91.7711191158998[/C][C]-0.641119115899798[/C][/ROW]
[ROW][C]49[/C][C]91.83[/C][C]92.0427508002359[/C][C]-0.212750800235867[/C][/ROW]
[ROW][C]50[/C][C]92.66[/C][C]91.9299670954032[/C][C]0.730032904596811[/C][/ROW]
[ROW][C]51[/C][C]93.45[/C][C]92.6398140815594[/C][C]0.810185918440609[/C][/ROW]
[ROW][C]52[/C][C]93.95[/C][C]93.3892962803741[/C][C]0.560703719625891[/C][/ROW]
[ROW][C]53[/C][C]94.12[/C][C]93.9600791730177[/C][C]0.159920826982329[/C][/ROW]
[ROW][C]54[/C][C]94.31[/C][C]94.2817362108044[/C][C]0.0282637891956199[/C][/ROW]
[ROW][C]55[/C][C]94.25[/C][C]93.116760190151[/C][C]1.13323980984903[/C][/ROW]
[ROW][C]56[/C][C]94.51[/C][C]94.25903660716[/C][C]0.250963392840049[/C][/ROW]
[ROW][C]57[/C][C]94.58[/C][C]95.2583932273855[/C][C]-0.678393227385541[/C][/ROW]
[ROW][C]58[/C][C]94.85[/C][C]95.8635858703574[/C][C]-1.01358587035737[/C][/ROW]
[ROW][C]59[/C][C]95.31[/C][C]95.4938396081522[/C][C]-0.183839608152212[/C][/ROW]
[ROW][C]60[/C][C]95.75[/C][C]96.0794511381335[/C][C]-0.329451138133535[/C][/ROW]
[ROW][C]61[/C][C]96.06[/C][C]96.8001831763737[/C][C]-0.740183176373677[/C][/ROW]
[ROW][C]62[/C][C]96.4[/C][C]96.3039350721178[/C][C]0.0960649278821819[/C][/ROW]
[ROW][C]63[/C][C]96.57[/C][C]96.4224221821582[/C][C]0.147577817841793[/C][/ROW]
[ROW][C]64[/C][C]96.47[/C][C]96.4683886336321[/C][C]0.00161136636788228[/C][/ROW]
[ROW][C]65[/C][C]96.34[/C][C]96.3686643095941[/C][C]-0.0286643095940633[/C][/ROW]
[ROW][C]66[/C][C]96.22[/C][C]96.3658316634858[/C][C]-0.145831663485808[/C][/ROW]
[ROW][C]67[/C][C]96.2[/C][C]94.928549072094[/C][C]1.27145092790603[/C][/ROW]
[ROW][C]68[/C][C]96.71[/C][C]96.0199771923629[/C][C]0.690022807637121[/C][/ROW]
[ROW][C]69[/C][C]97.05[/C][C]97.2995865313648[/C][C]-0.249586531364827[/C][/ROW]
[ROW][C]70[/C][C]97.82[/C][C]98.2476000302839[/C][C]-0.427600030283941[/C][/ROW]
[ROW][C]71[/C][C]98.22[/C][C]98.4856989232803[/C][C]-0.265698923280254[/C][/ROW]
[ROW][C]72[/C][C]98.5[/C][C]98.9886034500322[/C][C]-0.488603450032173[/C][/ROW]
[ROW][C]73[/C][C]98.94[/C][C]99.5239808652657[/C][C]-0.583980865265659[/C][/ROW]
[ROW][C]74[/C][C]99.5[/C][C]99.2168659972279[/C][C]0.283134002772059[/C][/ROW]
[ROW][C]75[/C][C]99.89[/C][C]99.5376569911337[/C][C]0.352343008866328[/C][/ROW]
[ROW][C]76[/C][C]100[/C][C]99.8153075010893[/C][C]0.184692498910664[/C][/ROW]
[ROW][C]77[/C][C]100.1[/C][C]99.951143336934[/C][C]0.14885666306597[/C][/ROW]
[ROW][C]78[/C][C]100.16[/C][C]100.1932622664[/C][C]-0.0332622664004987[/C][/ROW]
[ROW][C]79[/C][C]100.05[/C][C]99.0211266281299[/C][C]1.02887337187008[/C][/ROW]
[ROW][C]80[/C][C]100.03[/C][C]99.921704098702[/C][C]0.108295901298007[/C][/ROW]
[ROW][C]81[/C][C]100[/C][C]100.609230818226[/C][C]-0.609230818226465[/C][/ROW]
[ROW][C]82[/C][C]100.32[/C][C]101.174128325672[/C][C]-0.854128325671979[/C][/ROW]
[ROW][C]83[/C][C]100.53[/C][C]100.935991124311[/C][C]-0.405991124310546[/C][/ROW]
[ROW][C]84[/C][C]100.49[/C][C]101.203379325404[/C][C]-0.713379325404077[/C][/ROW]
[ROW][C]85[/C][C]100.38[/C][C]101.404822081213[/C][C]-1.02482208121314[/C][/ROW]
[ROW][C]86[/C][C]100.22[/C][C]100.555335585893[/C][C]-0.335335585892906[/C][/ROW]
[ROW][C]87[/C][C]100.5[/C][C]100.062622130958[/C][C]0.437377869042024[/C][/ROW]
[ROW][C]88[/C][C]100.57[/C][C]100.196122329493[/C][C]0.373877670507326[/C][/ROW]
[ROW][C]89[/C][C]100.6[/C][C]100.313132461119[/C][C]0.28686753888104[/C][/ROW]
[ROW][C]90[/C][C]100.23[/C][C]100.49541421475[/C][C]-0.265414214750308[/C][/ROW]
[ROW][C]91[/C][C]100.29[/C][C]98.9428415114155[/C][C]1.34715848858453[/C][/ROW]
[ROW][C]92[/C][C]100.01[/C][C]99.9308126806966[/C][C]0.0791873193034149[/C][/ROW]
[ROW][C]93[/C][C]100.13[/C][C]100.380503969812[/C][C]-0.250503969812414[/C][/ROW]
[ROW][C]94[/C][C]100.22[/C][C]101.137033557791[/C][C]-0.91703355779147[/C][/ROW]
[ROW][C]95[/C][C]100.2[/C][C]100.713363663181[/C][C]-0.513363663180982[/C][/ROW]
[ROW][C]96[/C][C]100.34[/C][C]100.706865414966[/C][C]-0.366865414965631[/C][/ROW]
[ROW][C]97[/C][C]100.73[/C][C]101.103781097498[/C][C]-0.373781097498011[/C][/ROW]
[ROW][C]98[/C][C]100.29[/C][C]100.85471514456[/C][C]-0.564715144559898[/C][/ROW]
[ROW][C]99[/C][C]101.11[/C][C]100.102030895863[/C][C]1.00796910413676[/C][/ROW]
[ROW][C]100[/C][C]101.09[/C][C]100.760581754308[/C][C]0.329418245692196[/C][/ROW]
[ROW][C]101[/C][C]101.01[/C][C]100.810024695844[/C][C]0.199975304155544[/C][/ROW]
[ROW][C]102[/C][C]101.27[/C][C]100.85378435757[/C][C]0.416215642429947[/C][/ROW]
[ROW][C]103[/C][C]101.57[/C][C]100.066929324799[/C][C]1.5030706752014[/C][/ROW]
[ROW][C]104[/C][C]101.69[/C][C]101.203381784582[/C][C]0.486618215417664[/C][/ROW]
[ROW][C]105[/C][C]101[/C][C]102.127418659718[/C][C]-1.12741865971789[/C][/ROW]
[ROW][C]106[/C][C]101.43[/C][C]102.025102900026[/C][C]-0.595102900025779[/C][/ROW]
[ROW][C]107[/C][C]101.13[/C][C]101.969411167772[/C][C]-0.839411167771942[/C][/ROW]
[ROW][C]108[/C][C]101.23[/C][C]101.666516663777[/C][C]-0.43651666377724[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	85.91	81.3115197649573	4.5984802350427
14	86.84	87.0542831878999	-0.214283187899866
15	87.44	87.9068930849018	-0.466893084901756
16	87.79	88.3151764414296	-0.525176441429565
17	88.08	88.6438376005937	-0.563837600593743
18	88.38	88.9771147899526	-0.597114789952599
19	88.53	87.6887270730829	0.841272926917071
20	88.79	89.3234079142042	-0.533407914204233
21	88.85	90.1969514423243	-1.34695144232433
22	89.26	90.6462582723539	-1.38625827235388
23	89.31	90.2709451120408	-0.960945112040804
24	89.39	90.4715901750009	-1.08159017500093
25	89.76	90.7073989133596	-0.947398913359564
26	89.94	90.1189848945958	-0.178984894595814
27	89.99	90.1785143801721	-0.188514380172094
28	90.08	90.0638548140439	0.0161451859560486
29	89.95	90.1783231896243	-0.228323189624263
30	90.2	90.13658292572	0.0634170742800393
31	89.7	88.9202495970249	0.779750402975068
32	89.5	89.8026236237221	-0.302623623722099
33	89.25	90.2527714718397	-1.00277147183968
34	89.13	90.458580562844	-1.32858056284404
35	89.07	89.5937610518729	-0.523761051872881
36	89.06	89.6879924408697	-0.627992440869662
37	89.15	89.8924567149728	-0.742456714972747
38	89.38	89.0860702976827	0.293929702317314
39	89.4	89.1974253350896	0.202574664910415
40	89.51	89.1074835237145	0.40251647628547
41	89.62	89.2622388235488	0.357761176451206
42	89.65	89.5375893624045	0.112410637595531
43	89.68	88.150486173898	1.529513826102
44	89.92	89.5271981021751	0.392801897824853
45	90.26	90.5105280712041	-0.250528071204087
46	90.89	91.4000418935449	-0.510041893544923
47	91.08	91.4201299962696	-0.340129996269567
48	91.13	91.7711191158998	-0.641119115899798
49	91.83	92.0427508002359	-0.212750800235867
50	92.66	91.9299670954032	0.730032904596811
51	93.45	92.6398140815594	0.810185918440609
52	93.95	93.3892962803741	0.560703719625891
53	94.12	93.9600791730177	0.159920826982329
54	94.31	94.2817362108044	0.0282637891956199
55	94.25	93.116760190151	1.13323980984903
56	94.51	94.25903660716	0.250963392840049
57	94.58	95.2583932273855	-0.678393227385541
58	94.85	95.8635858703574	-1.01358587035737
59	95.31	95.4938396081522	-0.183839608152212
60	95.75	96.0794511381335	-0.329451138133535
61	96.06	96.8001831763737	-0.740183176373677
62	96.4	96.3039350721178	0.0960649278821819
63	96.57	96.4224221821582	0.147577817841793
64	96.47	96.4683886336321	0.00161136636788228
65	96.34	96.3686643095941	-0.0286643095940633
66	96.22	96.3658316634858	-0.145831663485808
67	96.2	94.928549072094	1.27145092790603
68	96.71	96.0199771923629	0.690022807637121
69	97.05	97.2995865313648	-0.249586531364827
70	97.82	98.2476000302839	-0.427600030283941
71	98.22	98.4856989232803	-0.265698923280254
72	98.5	98.9886034500322	-0.488603450032173
73	98.94	99.5239808652657	-0.583980865265659
74	99.5	99.2168659972279	0.283134002772059
75	99.89	99.5376569911337	0.352343008866328
76	100	99.8153075010893	0.184692498910664
77	100.1	99.951143336934	0.14885666306597
78	100.16	100.1932622664	-0.0332622664004987
79	100.05	99.0211266281299	1.02887337187008
80	100.03	99.921704098702	0.108295901298007
81	100	100.609230818226	-0.609230818226465
82	100.32	101.174128325672	-0.854128325671979
83	100.53	100.935991124311	-0.405991124310546
84	100.49	101.203379325404	-0.713379325404077
85	100.38	101.404822081213	-1.02482208121314
86	100.22	100.555335585893	-0.335335585892906
87	100.5	100.062622130958	0.437377869042024
88	100.57	100.196122329493	0.373877670507326
89	100.6	100.313132461119	0.28686753888104
90	100.23	100.49541421475	-0.265414214750308
91	100.29	98.9428415114155	1.34715848858453
92	100.01	99.9308126806966	0.0791873193034149
93	100.13	100.380503969812	-0.250503969812414
94	100.22	101.137033557791	-0.91703355779147
95	100.2	100.713363663181	-0.513363663180982
96	100.34	100.706865414966	-0.366865414965631
97	100.73	101.103781097498	-0.373781097498011
98	100.29	100.85471514456	-0.564715144559898
99	101.11	100.102030895863	1.00796910413676
100	101.09	100.760581754308	0.329418245692196
101	101.01	100.810024695844	0.199975304155544
102	101.27	100.85378435757	0.416215642429947
103	101.57	100.066929324799	1.5030706752014
104	101.69	101.203381784582	0.486618215417664
105	101	102.127418659718	-1.12741865971789
106	101.43	102.025102900026	-0.595102900025779
107	101.13	101.969411167772	-0.839411167771942
108	101.23	101.666516663777	-0.43651666377724

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	101.997321497627	100.42698015738	103.567662837874
110	102.136150270436	99.848454014313	104.423846526559
111	102.093792870932	99.1649351338251	105.022650608038
112	101.752827301578	98.209589086127	105.296065517029
113	101.440710181723	97.2913551647692	105.590065198677
114	101.241221470337	96.4851051623789	105.997337778295
115	100.000894423975	94.6325028994583	105.369285948493
116	99.3922789424013	93.4032299854688	105.381327899334
117	99.4625245285354	92.842669050229	106.082380006842
118	100.263479981088	93.0015539507115	107.525406011464
119	100.630164621654	92.7141958600772	108.546133383232
120	101.100744201472	92.5183164261121	109.683171976832

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 101.997321497627 & 100.42698015738 & 103.567662837874 \tabularnewline
110 & 102.136150270436 & 99.848454014313 & 104.423846526559 \tabularnewline
111 & 102.093792870932 & 99.1649351338251 & 105.022650608038 \tabularnewline
112 & 101.752827301578 & 98.209589086127 & 105.296065517029 \tabularnewline
113 & 101.440710181723 & 97.2913551647692 & 105.590065198677 \tabularnewline
114 & 101.241221470337 & 96.4851051623789 & 105.997337778295 \tabularnewline
115 & 100.000894423975 & 94.6325028994583 & 105.369285948493 \tabularnewline
116 & 99.3922789424013 & 93.4032299854688 & 105.381327899334 \tabularnewline
117 & 99.4625245285354 & 92.842669050229 & 106.082380006842 \tabularnewline
118 & 100.263479981088 & 93.0015539507115 & 107.525406011464 \tabularnewline
119 & 100.630164621654 & 92.7141958600772 & 108.546133383232 \tabularnewline
120 & 101.100744201472 & 92.5183164261121 & 109.683171976832 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]101.997321497627[/C][C]100.42698015738[/C][C]103.567662837874[/C][/ROW]
[ROW][C]110[/C][C]102.136150270436[/C][C]99.848454014313[/C][C]104.423846526559[/C][/ROW]
[ROW][C]111[/C][C]102.093792870932[/C][C]99.1649351338251[/C][C]105.022650608038[/C][/ROW]
[ROW][C]112[/C][C]101.752827301578[/C][C]98.209589086127[/C][C]105.296065517029[/C][/ROW]
[ROW][C]113[/C][C]101.440710181723[/C][C]97.2913551647692[/C][C]105.590065198677[/C][/ROW]
[ROW][C]114[/C][C]101.241221470337[/C][C]96.4851051623789[/C][C]105.997337778295[/C][/ROW]
[ROW][C]115[/C][C]100.000894423975[/C][C]94.6325028994583[/C][C]105.369285948493[/C][/ROW]
[ROW][C]116[/C][C]99.3922789424013[/C][C]93.4032299854688[/C][C]105.381327899334[/C][/ROW]
[ROW][C]117[/C][C]99.4625245285354[/C][C]92.842669050229[/C][C]106.082380006842[/C][/ROW]
[ROW][C]118[/C][C]100.263479981088[/C][C]93.0015539507115[/C][C]107.525406011464[/C][/ROW]
[ROW][C]119[/C][C]100.630164621654[/C][C]92.7141958600772[/C][C]108.546133383232[/C][/ROW]
[ROW][C]120[/C][C]101.100744201472[/C][C]92.5183164261121[/C][C]109.683171976832[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	101.997321497627	100.42698015738	103.567662837874
110	102.136150270436	99.848454014313	104.423846526559
111	102.093792870932	99.1649351338251	105.022650608038
112	101.752827301578	98.209589086127	105.296065517029
113	101.440710181723	97.2913551647692	105.590065198677
114	101.241221470337	96.4851051623789	105.997337778295
115	100.000894423975	94.6325028994583	105.369285948493
116	99.3922789424013	93.4032299854688	105.381327899334
117	99.4625245285354	92.842669050229	106.082380006842
118	100.263479981088	93.0015539507115	107.525406011464
119	100.630164621654	92.7141958600772	108.546133383232
120	101.100744201472	92.5183164261121	109.683171976832

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code