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

Mon, 23 Nov 2015 18:58:59 +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/2015/Nov/23/t14483051570zila276vghxeda.htm/, Retrieved Tue, 14 May 2024 17:14:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283958, Retrieved Tue, 14 May 2024 17:14:47 +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

153

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

-       [Exponential Smoothing] [] [2015-11-23 18:58:59] [2c14a834423fb5dcfbeb4b507321e1ef] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283958&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283958&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283958&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.857481828020786
beta	0.0829327915601131
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.857481828020786 \tabularnewline
beta & 0.0829327915601131 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283958&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]0.857481828020786[/C][/ROW]
[ROW][C]beta[/C][C]0.0829327915601131[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283958&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283958&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	0.857481828020786
beta	0.0829327915601131
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	98.92	96.3550091287498	2.56499087125017
14	97.98	97.8287258339956	0.151274166004384
15	98.76	99.0442848609837	-0.284284860983647
16	99.76	100.017975171317	-0.25797517131717
17	99.87	100.056022915493	-0.186022915492643
18	100.09	100.263653372726	-0.17365337272642
19	100.07	99.1053521360637	0.964647863936278
20	99.46	102.402257581402	-2.94225758140205
21	100.4	100.011913473841	0.388086526159256
22	101.25	100.341397675024	0.908602324976101
23	102.29	101.919001882125	0.370998117874862
24	102.1	102.674411893948	-0.574411893947584
25	105.91	103.665538482984	2.24446151701592
26	108.95	104.45373589344	4.49626410656026
27	110.07	109.73399537813	0.336004621869733
28	109.92	111.719362692934	-1.79936269293442
29	109.87	110.707975529516	-0.837975529515646
30	110.54	110.585943073867	-0.0459430738669937
31	110.79	109.805901966913	0.984098033087008
32	110.32	112.945381571851	-2.62538157185111
33	110.76	111.603443026423	-0.843443026422761
34	110.24	111.103336382824	-0.863336382824187
35	110.27	111.169590100477	-0.899590100476786
36	110.11	110.656897402157	-0.546897402157157
37	110.39	112.153323375082	-1.76332337508192
38	111.05	109.430397421377	1.61960257862253
39	110.85	111.135369829392	-0.285369829391882
40	110.24	111.722992961275	-1.4829929612749
41	108.7	110.581126713589	-1.88112671358866
42	109.93	109.066892059466	0.863107940534505
43	109.53	108.681284686605	0.848715313395459
44	109.83	110.616827106356	-0.786827106356299
45	107.86	110.676865810058	-2.81686581005843
46	104.61	107.924822566894	-3.31482256689378
47	103.61	105.129605591682	-1.51960559168171
48	103.11	103.36067579464	-0.25067579464006
49	102.59	104.076466091686	-1.48646609168649
50	102.91	101.395800032983	1.51419996701669
51	101.94	102.016143544844	-0.0761435448437027
52	101.8	101.851529642922	-0.0515296429216647
53	102.25	101.258797188175	0.991202811824692
54	102.6	102.145737348094	0.454262651905893
55	102.49	101.041726341044	1.448273658956
56	102.13	102.796100621596	-0.666100621595632
57	100.76	102.238882973784	-1.47888297378401
58	100.86	100.266694337773	0.593305662227451
59	101.12	101.021538454227	0.098461545772679
60	100.74	100.899392527767	-0.159392527767039
61	99.99	101.576598905912	-1.58659890591177
62	99.39	99.326435351677	0.0635646483230232
63	99.52	98.4715779724632	1.0484220275368
64	99.21	99.3244700632645	-0.114470063264534
65	99.38	98.8780126831679	0.501987316832071
66	99.37	99.2784772885991	0.0915227114009269
67	99.38	98.0286533647385	1.35134663526154
68	99.26	99.3705309815035	-0.110530981503459
69	99.36	99.1921422557254	0.167857744274613
70	99.2	99.0684287880598	0.131571211940212
71	98.53	99.457172618845	-0.927172618844963
72	98.65	98.4533407798482	0.196659220151801
73	99.15	99.271577938905	-0.121577938905034
74	100.17	98.6789162182056	1.49108378179436
75	99.98	99.4488902847246	0.531109715275377
76	100.07	99.9200929541843	0.149907045815695
77	99.94	100.034380022464	-0.0943800224642359
78	100.05	100.070078069292	-0.0200780692919977
79	99.13	99.0900718613738	0.0399281386262373
80	98.74	99.1998625654721	-0.459862565472065
81	98.64	98.8374013201657	-0.197401320165653
82	98.44	98.4464873746394	-0.00648737463939142
83	98.81	98.6034954719088	0.206504528091216
84	98.88	98.8536072123389	0.0263927876611234
85	99.63	99.592387079251	0.0376129207490408
86	100.08	99.4843842128496	0.595615787150393
87	100.07	99.4074305889416	0.662569411058442
88	100.55	100.003445241592	0.54655475840849
89	99.98	100.517649808911	-0.537649808911098
90	99.89	100.247282915212	-0.357282915212437
91	99.86	99.0265632425706	0.833436757429368
92	99.61	99.8409918167231	-0.230991816723105
93	100.12	99.8253298228339	0.294670177166125
94	100.24	100.028780834569	0.211219165431316
95	100.1	100.570586165812	-0.470586165812435
96	99.86	100.33081731078	-0.470817310780276
97	97.99	100.733188598639	-2.74318859863892
98	97.57	98.2016871441255	-0.631687144125507
99	98.28	96.8903882511489	1.38961174885108
100	97.97	97.9405092267461	0.02949077325394
101	97.99	97.6716391798297	0.31836082017027
102	97.84	98.0283316318571	-0.188331631857125
103	97.33	97.0206710034142	0.309328996585833
104	96.7	97.0837635272779	-0.383763527277907
105	96.79	96.8414632385999	-0.051463238599851
106	96.76	96.551532043975	0.208467956025032
107	96.23	96.7977111603139	-0.567711160313891
108	96.29	96.2732949230032	0.0167050769968284

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 98.92 & 96.3550091287498 & 2.56499087125017 \tabularnewline
14 & 97.98 & 97.8287258339956 & 0.151274166004384 \tabularnewline
15 & 98.76 & 99.0442848609837 & -0.284284860983647 \tabularnewline
16 & 99.76 & 100.017975171317 & -0.25797517131717 \tabularnewline
17 & 99.87 & 100.056022915493 & -0.186022915492643 \tabularnewline
18 & 100.09 & 100.263653372726 & -0.17365337272642 \tabularnewline
19 & 100.07 & 99.1053521360637 & 0.964647863936278 \tabularnewline
20 & 99.46 & 102.402257581402 & -2.94225758140205 \tabularnewline
21 & 100.4 & 100.011913473841 & 0.388086526159256 \tabularnewline
22 & 101.25 & 100.341397675024 & 0.908602324976101 \tabularnewline
23 & 102.29 & 101.919001882125 & 0.370998117874862 \tabularnewline
24 & 102.1 & 102.674411893948 & -0.574411893947584 \tabularnewline
25 & 105.91 & 103.665538482984 & 2.24446151701592 \tabularnewline
26 & 108.95 & 104.45373589344 & 4.49626410656026 \tabularnewline
27 & 110.07 & 109.73399537813 & 0.336004621869733 \tabularnewline
28 & 109.92 & 111.719362692934 & -1.79936269293442 \tabularnewline
29 & 109.87 & 110.707975529516 & -0.837975529515646 \tabularnewline
30 & 110.54 & 110.585943073867 & -0.0459430738669937 \tabularnewline
31 & 110.79 & 109.805901966913 & 0.984098033087008 \tabularnewline
32 & 110.32 & 112.945381571851 & -2.62538157185111 \tabularnewline
33 & 110.76 & 111.603443026423 & -0.843443026422761 \tabularnewline
34 & 110.24 & 111.103336382824 & -0.863336382824187 \tabularnewline
35 & 110.27 & 111.169590100477 & -0.899590100476786 \tabularnewline
36 & 110.11 & 110.656897402157 & -0.546897402157157 \tabularnewline
37 & 110.39 & 112.153323375082 & -1.76332337508192 \tabularnewline
38 & 111.05 & 109.430397421377 & 1.61960257862253 \tabularnewline
39 & 110.85 & 111.135369829392 & -0.285369829391882 \tabularnewline
40 & 110.24 & 111.722992961275 & -1.4829929612749 \tabularnewline
41 & 108.7 & 110.581126713589 & -1.88112671358866 \tabularnewline
42 & 109.93 & 109.066892059466 & 0.863107940534505 \tabularnewline
43 & 109.53 & 108.681284686605 & 0.848715313395459 \tabularnewline
44 & 109.83 & 110.616827106356 & -0.786827106356299 \tabularnewline
45 & 107.86 & 110.676865810058 & -2.81686581005843 \tabularnewline
46 & 104.61 & 107.924822566894 & -3.31482256689378 \tabularnewline
47 & 103.61 & 105.129605591682 & -1.51960559168171 \tabularnewline
48 & 103.11 & 103.36067579464 & -0.25067579464006 \tabularnewline
49 & 102.59 & 104.076466091686 & -1.48646609168649 \tabularnewline
50 & 102.91 & 101.395800032983 & 1.51419996701669 \tabularnewline
51 & 101.94 & 102.016143544844 & -0.0761435448437027 \tabularnewline
52 & 101.8 & 101.851529642922 & -0.0515296429216647 \tabularnewline
53 & 102.25 & 101.258797188175 & 0.991202811824692 \tabularnewline
54 & 102.6 & 102.145737348094 & 0.454262651905893 \tabularnewline
55 & 102.49 & 101.041726341044 & 1.448273658956 \tabularnewline
56 & 102.13 & 102.796100621596 & -0.666100621595632 \tabularnewline
57 & 100.76 & 102.238882973784 & -1.47888297378401 \tabularnewline
58 & 100.86 & 100.266694337773 & 0.593305662227451 \tabularnewline
59 & 101.12 & 101.021538454227 & 0.098461545772679 \tabularnewline
60 & 100.74 & 100.899392527767 & -0.159392527767039 \tabularnewline
61 & 99.99 & 101.576598905912 & -1.58659890591177 \tabularnewline
62 & 99.39 & 99.326435351677 & 0.0635646483230232 \tabularnewline
63 & 99.52 & 98.4715779724632 & 1.0484220275368 \tabularnewline
64 & 99.21 & 99.3244700632645 & -0.114470063264534 \tabularnewline
65 & 99.38 & 98.8780126831679 & 0.501987316832071 \tabularnewline
66 & 99.37 & 99.2784772885991 & 0.0915227114009269 \tabularnewline
67 & 99.38 & 98.0286533647385 & 1.35134663526154 \tabularnewline
68 & 99.26 & 99.3705309815035 & -0.110530981503459 \tabularnewline
69 & 99.36 & 99.1921422557254 & 0.167857744274613 \tabularnewline
70 & 99.2 & 99.0684287880598 & 0.131571211940212 \tabularnewline
71 & 98.53 & 99.457172618845 & -0.927172618844963 \tabularnewline
72 & 98.65 & 98.4533407798482 & 0.196659220151801 \tabularnewline
73 & 99.15 & 99.271577938905 & -0.121577938905034 \tabularnewline
74 & 100.17 & 98.6789162182056 & 1.49108378179436 \tabularnewline
75 & 99.98 & 99.4488902847246 & 0.531109715275377 \tabularnewline
76 & 100.07 & 99.9200929541843 & 0.149907045815695 \tabularnewline
77 & 99.94 & 100.034380022464 & -0.0943800224642359 \tabularnewline
78 & 100.05 & 100.070078069292 & -0.0200780692919977 \tabularnewline
79 & 99.13 & 99.0900718613738 & 0.0399281386262373 \tabularnewline
80 & 98.74 & 99.1998625654721 & -0.459862565472065 \tabularnewline
81 & 98.64 & 98.8374013201657 & -0.197401320165653 \tabularnewline
82 & 98.44 & 98.4464873746394 & -0.00648737463939142 \tabularnewline
83 & 98.81 & 98.6034954719088 & 0.206504528091216 \tabularnewline
84 & 98.88 & 98.8536072123389 & 0.0263927876611234 \tabularnewline
85 & 99.63 & 99.592387079251 & 0.0376129207490408 \tabularnewline
86 & 100.08 & 99.4843842128496 & 0.595615787150393 \tabularnewline
87 & 100.07 & 99.4074305889416 & 0.662569411058442 \tabularnewline
88 & 100.55 & 100.003445241592 & 0.54655475840849 \tabularnewline
89 & 99.98 & 100.517649808911 & -0.537649808911098 \tabularnewline
90 & 99.89 & 100.247282915212 & -0.357282915212437 \tabularnewline
91 & 99.86 & 99.0265632425706 & 0.833436757429368 \tabularnewline
92 & 99.61 & 99.8409918167231 & -0.230991816723105 \tabularnewline
93 & 100.12 & 99.8253298228339 & 0.294670177166125 \tabularnewline
94 & 100.24 & 100.028780834569 & 0.211219165431316 \tabularnewline
95 & 100.1 & 100.570586165812 & -0.470586165812435 \tabularnewline
96 & 99.86 & 100.33081731078 & -0.470817310780276 \tabularnewline
97 & 97.99 & 100.733188598639 & -2.74318859863892 \tabularnewline
98 & 97.57 & 98.2016871441255 & -0.631687144125507 \tabularnewline
99 & 98.28 & 96.8903882511489 & 1.38961174885108 \tabularnewline
100 & 97.97 & 97.9405092267461 & 0.02949077325394 \tabularnewline
101 & 97.99 & 97.6716391798297 & 0.31836082017027 \tabularnewline
102 & 97.84 & 98.0283316318571 & -0.188331631857125 \tabularnewline
103 & 97.33 & 97.0206710034142 & 0.309328996585833 \tabularnewline
104 & 96.7 & 97.0837635272779 & -0.383763527277907 \tabularnewline
105 & 96.79 & 96.8414632385999 & -0.051463238599851 \tabularnewline
106 & 96.76 & 96.551532043975 & 0.208467956025032 \tabularnewline
107 & 96.23 & 96.7977111603139 & -0.567711160313891 \tabularnewline
108 & 96.29 & 96.2732949230032 & 0.0167050769968284 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283958&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]98.92[/C][C]96.3550091287498[/C][C]2.56499087125017[/C][/ROW]
[ROW][C]14[/C][C]97.98[/C][C]97.8287258339956[/C][C]0.151274166004384[/C][/ROW]
[ROW][C]15[/C][C]98.76[/C][C]99.0442848609837[/C][C]-0.284284860983647[/C][/ROW]
[ROW][C]16[/C][C]99.76[/C][C]100.017975171317[/C][C]-0.25797517131717[/C][/ROW]
[ROW][C]17[/C][C]99.87[/C][C]100.056022915493[/C][C]-0.186022915492643[/C][/ROW]
[ROW][C]18[/C][C]100.09[/C][C]100.263653372726[/C][C]-0.17365337272642[/C][/ROW]
[ROW][C]19[/C][C]100.07[/C][C]99.1053521360637[/C][C]0.964647863936278[/C][/ROW]
[ROW][C]20[/C][C]99.46[/C][C]102.402257581402[/C][C]-2.94225758140205[/C][/ROW]
[ROW][C]21[/C][C]100.4[/C][C]100.011913473841[/C][C]0.388086526159256[/C][/ROW]
[ROW][C]22[/C][C]101.25[/C][C]100.341397675024[/C][C]0.908602324976101[/C][/ROW]
[ROW][C]23[/C][C]102.29[/C][C]101.919001882125[/C][C]0.370998117874862[/C][/ROW]
[ROW][C]24[/C][C]102.1[/C][C]102.674411893948[/C][C]-0.574411893947584[/C][/ROW]
[ROW][C]25[/C][C]105.91[/C][C]103.665538482984[/C][C]2.24446151701592[/C][/ROW]
[ROW][C]26[/C][C]108.95[/C][C]104.45373589344[/C][C]4.49626410656026[/C][/ROW]
[ROW][C]27[/C][C]110.07[/C][C]109.73399537813[/C][C]0.336004621869733[/C][/ROW]
[ROW][C]28[/C][C]109.92[/C][C]111.719362692934[/C][C]-1.79936269293442[/C][/ROW]
[ROW][C]29[/C][C]109.87[/C][C]110.707975529516[/C][C]-0.837975529515646[/C][/ROW]
[ROW][C]30[/C][C]110.54[/C][C]110.585943073867[/C][C]-0.0459430738669937[/C][/ROW]
[ROW][C]31[/C][C]110.79[/C][C]109.805901966913[/C][C]0.984098033087008[/C][/ROW]
[ROW][C]32[/C][C]110.32[/C][C]112.945381571851[/C][C]-2.62538157185111[/C][/ROW]
[ROW][C]33[/C][C]110.76[/C][C]111.603443026423[/C][C]-0.843443026422761[/C][/ROW]
[ROW][C]34[/C][C]110.24[/C][C]111.103336382824[/C][C]-0.863336382824187[/C][/ROW]
[ROW][C]35[/C][C]110.27[/C][C]111.169590100477[/C][C]-0.899590100476786[/C][/ROW]
[ROW][C]36[/C][C]110.11[/C][C]110.656897402157[/C][C]-0.546897402157157[/C][/ROW]
[ROW][C]37[/C][C]110.39[/C][C]112.153323375082[/C][C]-1.76332337508192[/C][/ROW]
[ROW][C]38[/C][C]111.05[/C][C]109.430397421377[/C][C]1.61960257862253[/C][/ROW]
[ROW][C]39[/C][C]110.85[/C][C]111.135369829392[/C][C]-0.285369829391882[/C][/ROW]
[ROW][C]40[/C][C]110.24[/C][C]111.722992961275[/C][C]-1.4829929612749[/C][/ROW]
[ROW][C]41[/C][C]108.7[/C][C]110.581126713589[/C][C]-1.88112671358866[/C][/ROW]
[ROW][C]42[/C][C]109.93[/C][C]109.066892059466[/C][C]0.863107940534505[/C][/ROW]
[ROW][C]43[/C][C]109.53[/C][C]108.681284686605[/C][C]0.848715313395459[/C][/ROW]
[ROW][C]44[/C][C]109.83[/C][C]110.616827106356[/C][C]-0.786827106356299[/C][/ROW]
[ROW][C]45[/C][C]107.86[/C][C]110.676865810058[/C][C]-2.81686581005843[/C][/ROW]
[ROW][C]46[/C][C]104.61[/C][C]107.924822566894[/C][C]-3.31482256689378[/C][/ROW]
[ROW][C]47[/C][C]103.61[/C][C]105.129605591682[/C][C]-1.51960559168171[/C][/ROW]
[ROW][C]48[/C][C]103.11[/C][C]103.36067579464[/C][C]-0.25067579464006[/C][/ROW]
[ROW][C]49[/C][C]102.59[/C][C]104.076466091686[/C][C]-1.48646609168649[/C][/ROW]
[ROW][C]50[/C][C]102.91[/C][C]101.395800032983[/C][C]1.51419996701669[/C][/ROW]
[ROW][C]51[/C][C]101.94[/C][C]102.016143544844[/C][C]-0.0761435448437027[/C][/ROW]
[ROW][C]52[/C][C]101.8[/C][C]101.851529642922[/C][C]-0.0515296429216647[/C][/ROW]
[ROW][C]53[/C][C]102.25[/C][C]101.258797188175[/C][C]0.991202811824692[/C][/ROW]
[ROW][C]54[/C][C]102.6[/C][C]102.145737348094[/C][C]0.454262651905893[/C][/ROW]
[ROW][C]55[/C][C]102.49[/C][C]101.041726341044[/C][C]1.448273658956[/C][/ROW]
[ROW][C]56[/C][C]102.13[/C][C]102.796100621596[/C][C]-0.666100621595632[/C][/ROW]
[ROW][C]57[/C][C]100.76[/C][C]102.238882973784[/C][C]-1.47888297378401[/C][/ROW]
[ROW][C]58[/C][C]100.86[/C][C]100.266694337773[/C][C]0.593305662227451[/C][/ROW]
[ROW][C]59[/C][C]101.12[/C][C]101.021538454227[/C][C]0.098461545772679[/C][/ROW]
[ROW][C]60[/C][C]100.74[/C][C]100.899392527767[/C][C]-0.159392527767039[/C][/ROW]
[ROW][C]61[/C][C]99.99[/C][C]101.576598905912[/C][C]-1.58659890591177[/C][/ROW]
[ROW][C]62[/C][C]99.39[/C][C]99.326435351677[/C][C]0.0635646483230232[/C][/ROW]
[ROW][C]63[/C][C]99.52[/C][C]98.4715779724632[/C][C]1.0484220275368[/C][/ROW]
[ROW][C]64[/C][C]99.21[/C][C]99.3244700632645[/C][C]-0.114470063264534[/C][/ROW]
[ROW][C]65[/C][C]99.38[/C][C]98.8780126831679[/C][C]0.501987316832071[/C][/ROW]
[ROW][C]66[/C][C]99.37[/C][C]99.2784772885991[/C][C]0.0915227114009269[/C][/ROW]
[ROW][C]67[/C][C]99.38[/C][C]98.0286533647385[/C][C]1.35134663526154[/C][/ROW]
[ROW][C]68[/C][C]99.26[/C][C]99.3705309815035[/C][C]-0.110530981503459[/C][/ROW]
[ROW][C]69[/C][C]99.36[/C][C]99.1921422557254[/C][C]0.167857744274613[/C][/ROW]
[ROW][C]70[/C][C]99.2[/C][C]99.0684287880598[/C][C]0.131571211940212[/C][/ROW]
[ROW][C]71[/C][C]98.53[/C][C]99.457172618845[/C][C]-0.927172618844963[/C][/ROW]
[ROW][C]72[/C][C]98.65[/C][C]98.4533407798482[/C][C]0.196659220151801[/C][/ROW]
[ROW][C]73[/C][C]99.15[/C][C]99.271577938905[/C][C]-0.121577938905034[/C][/ROW]
[ROW][C]74[/C][C]100.17[/C][C]98.6789162182056[/C][C]1.49108378179436[/C][/ROW]
[ROW][C]75[/C][C]99.98[/C][C]99.4488902847246[/C][C]0.531109715275377[/C][/ROW]
[ROW][C]76[/C][C]100.07[/C][C]99.9200929541843[/C][C]0.149907045815695[/C][/ROW]
[ROW][C]77[/C][C]99.94[/C][C]100.034380022464[/C][C]-0.0943800224642359[/C][/ROW]
[ROW][C]78[/C][C]100.05[/C][C]100.070078069292[/C][C]-0.0200780692919977[/C][/ROW]
[ROW][C]79[/C][C]99.13[/C][C]99.0900718613738[/C][C]0.0399281386262373[/C][/ROW]
[ROW][C]80[/C][C]98.74[/C][C]99.1998625654721[/C][C]-0.459862565472065[/C][/ROW]
[ROW][C]81[/C][C]98.64[/C][C]98.8374013201657[/C][C]-0.197401320165653[/C][/ROW]
[ROW][C]82[/C][C]98.44[/C][C]98.4464873746394[/C][C]-0.00648737463939142[/C][/ROW]
[ROW][C]83[/C][C]98.81[/C][C]98.6034954719088[/C][C]0.206504528091216[/C][/ROW]
[ROW][C]84[/C][C]98.88[/C][C]98.8536072123389[/C][C]0.0263927876611234[/C][/ROW]
[ROW][C]85[/C][C]99.63[/C][C]99.592387079251[/C][C]0.0376129207490408[/C][/ROW]
[ROW][C]86[/C][C]100.08[/C][C]99.4843842128496[/C][C]0.595615787150393[/C][/ROW]
[ROW][C]87[/C][C]100.07[/C][C]99.4074305889416[/C][C]0.662569411058442[/C][/ROW]
[ROW][C]88[/C][C]100.55[/C][C]100.003445241592[/C][C]0.54655475840849[/C][/ROW]
[ROW][C]89[/C][C]99.98[/C][C]100.517649808911[/C][C]-0.537649808911098[/C][/ROW]
[ROW][C]90[/C][C]99.89[/C][C]100.247282915212[/C][C]-0.357282915212437[/C][/ROW]
[ROW][C]91[/C][C]99.86[/C][C]99.0265632425706[/C][C]0.833436757429368[/C][/ROW]
[ROW][C]92[/C][C]99.61[/C][C]99.8409918167231[/C][C]-0.230991816723105[/C][/ROW]
[ROW][C]93[/C][C]100.12[/C][C]99.8253298228339[/C][C]0.294670177166125[/C][/ROW]
[ROW][C]94[/C][C]100.24[/C][C]100.028780834569[/C][C]0.211219165431316[/C][/ROW]
[ROW][C]95[/C][C]100.1[/C][C]100.570586165812[/C][C]-0.470586165812435[/C][/ROW]
[ROW][C]96[/C][C]99.86[/C][C]100.33081731078[/C][C]-0.470817310780276[/C][/ROW]
[ROW][C]97[/C][C]97.99[/C][C]100.733188598639[/C][C]-2.74318859863892[/C][/ROW]
[ROW][C]98[/C][C]97.57[/C][C]98.2016871441255[/C][C]-0.631687144125507[/C][/ROW]
[ROW][C]99[/C][C]98.28[/C][C]96.8903882511489[/C][C]1.38961174885108[/C][/ROW]
[ROW][C]100[/C][C]97.97[/C][C]97.9405092267461[/C][C]0.02949077325394[/C][/ROW]
[ROW][C]101[/C][C]97.99[/C][C]97.6716391798297[/C][C]0.31836082017027[/C][/ROW]
[ROW][C]102[/C][C]97.84[/C][C]98.0283316318571[/C][C]-0.188331631857125[/C][/ROW]
[ROW][C]103[/C][C]97.33[/C][C]97.0206710034142[/C][C]0.309328996585833[/C][/ROW]
[ROW][C]104[/C][C]96.7[/C][C]97.0837635272779[/C][C]-0.383763527277907[/C][/ROW]
[ROW][C]105[/C][C]96.79[/C][C]96.8414632385999[/C][C]-0.051463238599851[/C][/ROW]
[ROW][C]106[/C][C]96.76[/C][C]96.551532043975[/C][C]0.208467956025032[/C][/ROW]
[ROW][C]107[/C][C]96.23[/C][C]96.7977111603139[/C][C]-0.567711160313891[/C][/ROW]
[ROW][C]108[/C][C]96.29[/C][C]96.2732949230032[/C][C]0.0167050769968284[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283958&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283958&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	98.92	96.3550091287498	2.56499087125017
14	97.98	97.8287258339956	0.151274166004384
15	98.76	99.0442848609837	-0.284284860983647
16	99.76	100.017975171317	-0.25797517131717
17	99.87	100.056022915493	-0.186022915492643
18	100.09	100.263653372726	-0.17365337272642
19	100.07	99.1053521360637	0.964647863936278
20	99.46	102.402257581402	-2.94225758140205
21	100.4	100.011913473841	0.388086526159256
22	101.25	100.341397675024	0.908602324976101
23	102.29	101.919001882125	0.370998117874862
24	102.1	102.674411893948	-0.574411893947584
25	105.91	103.665538482984	2.24446151701592
26	108.95	104.45373589344	4.49626410656026
27	110.07	109.73399537813	0.336004621869733
28	109.92	111.719362692934	-1.79936269293442
29	109.87	110.707975529516	-0.837975529515646
30	110.54	110.585943073867	-0.0459430738669937
31	110.79	109.805901966913	0.984098033087008
32	110.32	112.945381571851	-2.62538157185111
33	110.76	111.603443026423	-0.843443026422761
34	110.24	111.103336382824	-0.863336382824187
35	110.27	111.169590100477	-0.899590100476786
36	110.11	110.656897402157	-0.546897402157157
37	110.39	112.153323375082	-1.76332337508192
38	111.05	109.430397421377	1.61960257862253
39	110.85	111.135369829392	-0.285369829391882
40	110.24	111.722992961275	-1.4829929612749
41	108.7	110.581126713589	-1.88112671358866
42	109.93	109.066892059466	0.863107940534505
43	109.53	108.681284686605	0.848715313395459
44	109.83	110.616827106356	-0.786827106356299
45	107.86	110.676865810058	-2.81686581005843
46	104.61	107.924822566894	-3.31482256689378
47	103.61	105.129605591682	-1.51960559168171
48	103.11	103.36067579464	-0.25067579464006
49	102.59	104.076466091686	-1.48646609168649
50	102.91	101.395800032983	1.51419996701669
51	101.94	102.016143544844	-0.0761435448437027
52	101.8	101.851529642922	-0.0515296429216647
53	102.25	101.258797188175	0.991202811824692
54	102.6	102.145737348094	0.454262651905893
55	102.49	101.041726341044	1.448273658956
56	102.13	102.796100621596	-0.666100621595632
57	100.76	102.238882973784	-1.47888297378401
58	100.86	100.266694337773	0.593305662227451
59	101.12	101.021538454227	0.098461545772679
60	100.74	100.899392527767	-0.159392527767039
61	99.99	101.576598905912	-1.58659890591177
62	99.39	99.326435351677	0.0635646483230232
63	99.52	98.4715779724632	1.0484220275368
64	99.21	99.3244700632645	-0.114470063264534
65	99.38	98.8780126831679	0.501987316832071
66	99.37	99.2784772885991	0.0915227114009269
67	99.38	98.0286533647385	1.35134663526154
68	99.26	99.3705309815035	-0.110530981503459
69	99.36	99.1921422557254	0.167857744274613
70	99.2	99.0684287880598	0.131571211940212
71	98.53	99.457172618845	-0.927172618844963
72	98.65	98.4533407798482	0.196659220151801
73	99.15	99.271577938905	-0.121577938905034
74	100.17	98.6789162182056	1.49108378179436
75	99.98	99.4488902847246	0.531109715275377
76	100.07	99.9200929541843	0.149907045815695
77	99.94	100.034380022464	-0.0943800224642359
78	100.05	100.070078069292	-0.0200780692919977
79	99.13	99.0900718613738	0.0399281386262373
80	98.74	99.1998625654721	-0.459862565472065
81	98.64	98.8374013201657	-0.197401320165653
82	98.44	98.4464873746394	-0.00648737463939142
83	98.81	98.6034954719088	0.206504528091216
84	98.88	98.8536072123389	0.0263927876611234
85	99.63	99.592387079251	0.0376129207490408
86	100.08	99.4843842128496	0.595615787150393
87	100.07	99.4074305889416	0.662569411058442
88	100.55	100.003445241592	0.54655475840849
89	99.98	100.517649808911	-0.537649808911098
90	99.89	100.247282915212	-0.357282915212437
91	99.86	99.0265632425706	0.833436757429368
92	99.61	99.8409918167231	-0.230991816723105
93	100.12	99.8253298228339	0.294670177166125
94	100.24	100.028780834569	0.211219165431316
95	100.1	100.570586165812	-0.470586165812435
96	99.86	100.33081731078	-0.470817310780276
97	97.99	100.733188598639	-2.74318859863892
98	97.57	98.2016871441255	-0.631687144125507
99	98.28	96.8903882511489	1.38961174885108
100	97.97	97.9405092267461	0.02949077325394
101	97.99	97.6716391798297	0.31836082017027
102	97.84	98.0283316318571	-0.188331631857125
103	97.33	97.0206710034142	0.309328996585833
104	96.7	97.0837635272779	-0.383763527277907
105	96.79	96.8414632385999	-0.051463238599851
106	96.76	96.551532043975	0.208467956025032
107	96.23	96.7977111603139	-0.567711160313891
108	96.29	96.2732949230032	0.0167050769968284

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	96.5813317188845	94.3273440306095	98.8353194071595
110	96.7301211445863	93.6495862775135	99.8106560116591
111	96.3251217879885	92.5140365540106	100.136207021966
112	95.9715972945199	91.4674595176949	100.475735071345
113	95.6966459971348	90.5149529303913	100.878339063878
114	95.6582236829016	89.7945544151702	101.521892950633
115	94.8640080983076	88.3636887942227	101.364327402393
116	94.5126548457832	87.348548022	101.676761669566
117	94.6127417707405	86.7469375090024	102.478546032479
118	94.3812359817299	85.8318401908413	102.930631772618
119	94.2965231434521	85.0424618562016	103.550584430703
120	94.3391785178475	77.4464919787954	111.231865056899

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 96.5813317188845 & 94.3273440306095 & 98.8353194071595 \tabularnewline
110 & 96.7301211445863 & 93.6495862775135 & 99.8106560116591 \tabularnewline
111 & 96.3251217879885 & 92.5140365540106 & 100.136207021966 \tabularnewline
112 & 95.9715972945199 & 91.4674595176949 & 100.475735071345 \tabularnewline
113 & 95.6966459971348 & 90.5149529303913 & 100.878339063878 \tabularnewline
114 & 95.6582236829016 & 89.7945544151702 & 101.521892950633 \tabularnewline
115 & 94.8640080983076 & 88.3636887942227 & 101.364327402393 \tabularnewline
116 & 94.5126548457832 & 87.348548022 & 101.676761669566 \tabularnewline
117 & 94.6127417707405 & 86.7469375090024 & 102.478546032479 \tabularnewline
118 & 94.3812359817299 & 85.8318401908413 & 102.930631772618 \tabularnewline
119 & 94.2965231434521 & 85.0424618562016 & 103.550584430703 \tabularnewline
120 & 94.3391785178475 & 77.4464919787954 & 111.231865056899 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283958&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]96.5813317188845[/C][C]94.3273440306095[/C][C]98.8353194071595[/C][/ROW]
[ROW][C]110[/C][C]96.7301211445863[/C][C]93.6495862775135[/C][C]99.8106560116591[/C][/ROW]
[ROW][C]111[/C][C]96.3251217879885[/C][C]92.5140365540106[/C][C]100.136207021966[/C][/ROW]
[ROW][C]112[/C][C]95.9715972945199[/C][C]91.4674595176949[/C][C]100.475735071345[/C][/ROW]
[ROW][C]113[/C][C]95.6966459971348[/C][C]90.5149529303913[/C][C]100.878339063878[/C][/ROW]
[ROW][C]114[/C][C]95.6582236829016[/C][C]89.7945544151702[/C][C]101.521892950633[/C][/ROW]
[ROW][C]115[/C][C]94.8640080983076[/C][C]88.3636887942227[/C][C]101.364327402393[/C][/ROW]
[ROW][C]116[/C][C]94.5126548457832[/C][C]87.348548022[/C][C]101.676761669566[/C][/ROW]
[ROW][C]117[/C][C]94.6127417707405[/C][C]86.7469375090024[/C][C]102.478546032479[/C][/ROW]
[ROW][C]118[/C][C]94.3812359817299[/C][C]85.8318401908413[/C][C]102.930631772618[/C][/ROW]
[ROW][C]119[/C][C]94.2965231434521[/C][C]85.0424618562016[/C][C]103.550584430703[/C][/ROW]
[ROW][C]120[/C][C]94.3391785178475[/C][C]77.4464919787954[/C][C]111.231865056899[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283958&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283958&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	96.5813317188845	94.3273440306095	98.8353194071595
110	96.7301211445863	93.6495862775135	99.8106560116591
111	96.3251217879885	92.5140365540106	100.136207021966
112	95.9715972945199	91.4674595176949	100.475735071345
113	95.6966459971348	90.5149529303913	100.878339063878
114	95.6582236829016	89.7945544151702	101.521892950633
115	94.8640080983076	88.3636887942227	101.364327402393
116	94.5126548457832	87.348548022	101.676761669566
117	94.6127417707405	86.7469375090024	102.478546032479
118	94.3812359817299	85.8318401908413	102.930631772618
119	94.2965231434521	85.0424618562016	103.550584430703
120	94.3391785178475	77.4464919787954	111.231865056899

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code