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

Sun, 12 Jan 2014 16:37:27 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Jan/12/t1389562725kyt6ul62a8ujkeb.htm/, Retrieved Tue, 25 Aug 2026 10:23:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233071, Retrieved Tue, 25 Aug 2026 10:23:03 +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

402

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

-       [Exponential Smoothing] [] [2014-01-12 21:37:27] [d2a4f136ae3d3de0026ab3b17b8e3059] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

1,31
1,32
1,32
1,33
1,33
1,33
1,34
1,33
1,32
1,31
1,31
1,33
1,34
1,33
1,33
1,34
1,34
1,34
1,35
1,35
1,35
1,34
1,35
1,36
1,35
1,36
1,36
1,36
1,37
1,39
1,39
1,38
1,37
1,39
1,38
1,4
1,41
1,4
1,42
1,43
1,44
1,44
1,44
1,46
1,46
1,49
1,49
1,48
1,49
1,5
1,5
1,5
1,47
1,49
1,49
1,5
1,52
1,52
1,52
1,52
1,53
1,54
1,51
1,49
1,49
1,49
1,48
1,49
1,49
1,47
1,49
1,49

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 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 & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233071&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]5 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=233071&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233071&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	5 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.741143083658237
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.741143083658237 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233071&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]0.741143083658237[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233071&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233071&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	0.741143083658237
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.34	1.33458333333333	0.0054166666666664
14	1.33	1.32878725230921	0.00121274769079038
15	1.33	1.32904213247852	0.000957867521477862
16	1.34	1.33869144330652	0.00130855669347985
17	1.34	1.3381839983222	0.00181600167780505
18	1.34	1.33805264267834	0.00194735732166085
19	1.35	1.35843530702809	-0.00843530702809292
20	1.35	1.34195626483842	0.0080437351615843
21	1.35	1.33852388412626	0.0114761158737369
22	1.34	1.3376353886394	0.00236461136059551
23	1.35	1.33999396460091	0.0100060353990898
24	1.36	1.36801592913785	-0.00801592913784566
25	1.35	1.37408318093448	-0.0240831809344817
26	1.36	1.34533527838915	0.0146647216108511
27	1.36	1.3554940184962	0.00450598150379955
28	1.36	1.36786376777989	-0.00786376777988607
29	1.37	1.36068967359491	0.009310326405088
30	1.39	1.36614668720628	0.0238533127937164
31	1.39	1.40007717446809	-0.0100771744680876
32	1.38	1.38664698762646	-0.00664698762646032
33	1.37	1.37321517481287	-0.00321517481286659
34	1.39	1.35907975488211	0.0309202451178865
35	1.38	1.38458017676538	-0.00458017676537747
36	1.4	1.39712656087339	0.00287343912660543
37	1.41	1.40710527339047	0.00289472660952783
38	1.4	1.40838202300055	-0.00838202300054935
39	1.42	1.3988301676	0.0211698324000049
40	1.43	1.42034821956702	0.00965178043298009
41	1.44	1.43060128585818	0.00939871414182059
42	1.44	1.43988836004027	0.00011163995972896
43	1.44	1.44743972938412	-0.00743972938412463
44	1.46	1.4368521943133	0.0231478056866954
45	1.46	1.44639093497517	0.0136090650248277
46	1.49	1.45356087357924	0.0364391264207606
47	1.49	1.47396204643213	0.0160379535678741
48	1.48	1.50371883525999	-0.0237188352599911
49	1.49	1.49399437794889	-0.00399437794888668
50	1.5	1.48724625073247	0.0127537492675263
51	1.5	1.50100872892734	-0.00100872892734438
52	1.5	1.50310776614667	-0.00310776614666608
53	1.47	1.50383867477995	-0.0338386747799462
54	1.49	1.47867663382262	0.0113233661773844
55	1.49	1.49258277232605	-0.00258277232604653
56	1.5	1.49351273239337	0.00648726760662588
57	1.52	1.48823446149366	0.0317655385063413
58	1.52	1.51477066413502	0.00522933586498198
59	1.52	1.50675993188061	0.0132400681193863
60	1.52	1.52415176749983	-0.00415176749983215
61	1.53	1.53403511932271	-0.00403511932270884
62	1.54	1.53159216548461	0.00840783451539084
63	1.51	1.53857118635202	-0.0285711863520213
64	1.49	1.51969914858054	-0.0296991485805389
65	1.49	1.49276712979285	-0.00276712979285176
66	1.49	1.5023240561592	-0.0123240561591971
67	1.48	1.49510437102031	-0.0151043710203058
68	1.49	1.48910187738711	0.000898122612892571
69	1.49	1.48622470558728	0.00377529441272428
70	1.47	1.48514705282158	-0.0151470528215825
71	1.49	1.46410813447121	0.0258918655287863
72	1.49	1.48637476529834	0.00362523470165965

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.34 & 1.33458333333333 & 0.0054166666666664 \tabularnewline
14 & 1.33 & 1.32878725230921 & 0.00121274769079038 \tabularnewline
15 & 1.33 & 1.32904213247852 & 0.000957867521477862 \tabularnewline
16 & 1.34 & 1.33869144330652 & 0.00130855669347985 \tabularnewline
17 & 1.34 & 1.3381839983222 & 0.00181600167780505 \tabularnewline
18 & 1.34 & 1.33805264267834 & 0.00194735732166085 \tabularnewline
19 & 1.35 & 1.35843530702809 & -0.00843530702809292 \tabularnewline
20 & 1.35 & 1.34195626483842 & 0.0080437351615843 \tabularnewline
21 & 1.35 & 1.33852388412626 & 0.0114761158737369 \tabularnewline
22 & 1.34 & 1.3376353886394 & 0.00236461136059551 \tabularnewline
23 & 1.35 & 1.33999396460091 & 0.0100060353990898 \tabularnewline
24 & 1.36 & 1.36801592913785 & -0.00801592913784566 \tabularnewline
25 & 1.35 & 1.37408318093448 & -0.0240831809344817 \tabularnewline
26 & 1.36 & 1.34533527838915 & 0.0146647216108511 \tabularnewline
27 & 1.36 & 1.3554940184962 & 0.00450598150379955 \tabularnewline
28 & 1.36 & 1.36786376777989 & -0.00786376777988607 \tabularnewline
29 & 1.37 & 1.36068967359491 & 0.009310326405088 \tabularnewline
30 & 1.39 & 1.36614668720628 & 0.0238533127937164 \tabularnewline
31 & 1.39 & 1.40007717446809 & -0.0100771744680876 \tabularnewline
32 & 1.38 & 1.38664698762646 & -0.00664698762646032 \tabularnewline
33 & 1.37 & 1.37321517481287 & -0.00321517481286659 \tabularnewline
34 & 1.39 & 1.35907975488211 & 0.0309202451178865 \tabularnewline
35 & 1.38 & 1.38458017676538 & -0.00458017676537747 \tabularnewline
36 & 1.4 & 1.39712656087339 & 0.00287343912660543 \tabularnewline
37 & 1.41 & 1.40710527339047 & 0.00289472660952783 \tabularnewline
38 & 1.4 & 1.40838202300055 & -0.00838202300054935 \tabularnewline
39 & 1.42 & 1.3988301676 & 0.0211698324000049 \tabularnewline
40 & 1.43 & 1.42034821956702 & 0.00965178043298009 \tabularnewline
41 & 1.44 & 1.43060128585818 & 0.00939871414182059 \tabularnewline
42 & 1.44 & 1.43988836004027 & 0.00011163995972896 \tabularnewline
43 & 1.44 & 1.44743972938412 & -0.00743972938412463 \tabularnewline
44 & 1.46 & 1.4368521943133 & 0.0231478056866954 \tabularnewline
45 & 1.46 & 1.44639093497517 & 0.0136090650248277 \tabularnewline
46 & 1.49 & 1.45356087357924 & 0.0364391264207606 \tabularnewline
47 & 1.49 & 1.47396204643213 & 0.0160379535678741 \tabularnewline
48 & 1.48 & 1.50371883525999 & -0.0237188352599911 \tabularnewline
49 & 1.49 & 1.49399437794889 & -0.00399437794888668 \tabularnewline
50 & 1.5 & 1.48724625073247 & 0.0127537492675263 \tabularnewline
51 & 1.5 & 1.50100872892734 & -0.00100872892734438 \tabularnewline
52 & 1.5 & 1.50310776614667 & -0.00310776614666608 \tabularnewline
53 & 1.47 & 1.50383867477995 & -0.0338386747799462 \tabularnewline
54 & 1.49 & 1.47867663382262 & 0.0113233661773844 \tabularnewline
55 & 1.49 & 1.49258277232605 & -0.00258277232604653 \tabularnewline
56 & 1.5 & 1.49351273239337 & 0.00648726760662588 \tabularnewline
57 & 1.52 & 1.48823446149366 & 0.0317655385063413 \tabularnewline
58 & 1.52 & 1.51477066413502 & 0.00522933586498198 \tabularnewline
59 & 1.52 & 1.50675993188061 & 0.0132400681193863 \tabularnewline
60 & 1.52 & 1.52415176749983 & -0.00415176749983215 \tabularnewline
61 & 1.53 & 1.53403511932271 & -0.00403511932270884 \tabularnewline
62 & 1.54 & 1.53159216548461 & 0.00840783451539084 \tabularnewline
63 & 1.51 & 1.53857118635202 & -0.0285711863520213 \tabularnewline
64 & 1.49 & 1.51969914858054 & -0.0296991485805389 \tabularnewline
65 & 1.49 & 1.49276712979285 & -0.00276712979285176 \tabularnewline
66 & 1.49 & 1.5023240561592 & -0.0123240561591971 \tabularnewline
67 & 1.48 & 1.49510437102031 & -0.0151043710203058 \tabularnewline
68 & 1.49 & 1.48910187738711 & 0.000898122612892571 \tabularnewline
69 & 1.49 & 1.48622470558728 & 0.00377529441272428 \tabularnewline
70 & 1.47 & 1.48514705282158 & -0.0151470528215825 \tabularnewline
71 & 1.49 & 1.46410813447121 & 0.0258918655287863 \tabularnewline
72 & 1.49 & 1.48637476529834 & 0.00362523470165965 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233071&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]1.34[/C][C]1.33458333333333[/C][C]0.0054166666666664[/C][/ROW]
[ROW][C]14[/C][C]1.33[/C][C]1.32878725230921[/C][C]0.00121274769079038[/C][/ROW]
[ROW][C]15[/C][C]1.33[/C][C]1.32904213247852[/C][C]0.000957867521477862[/C][/ROW]
[ROW][C]16[/C][C]1.34[/C][C]1.33869144330652[/C][C]0.00130855669347985[/C][/ROW]
[ROW][C]17[/C][C]1.34[/C][C]1.3381839983222[/C][C]0.00181600167780505[/C][/ROW]
[ROW][C]18[/C][C]1.34[/C][C]1.33805264267834[/C][C]0.00194735732166085[/C][/ROW]
[ROW][C]19[/C][C]1.35[/C][C]1.35843530702809[/C][C]-0.00843530702809292[/C][/ROW]
[ROW][C]20[/C][C]1.35[/C][C]1.34195626483842[/C][C]0.0080437351615843[/C][/ROW]
[ROW][C]21[/C][C]1.35[/C][C]1.33852388412626[/C][C]0.0114761158737369[/C][/ROW]
[ROW][C]22[/C][C]1.34[/C][C]1.3376353886394[/C][C]0.00236461136059551[/C][/ROW]
[ROW][C]23[/C][C]1.35[/C][C]1.33999396460091[/C][C]0.0100060353990898[/C][/ROW]
[ROW][C]24[/C][C]1.36[/C][C]1.36801592913785[/C][C]-0.00801592913784566[/C][/ROW]
[ROW][C]25[/C][C]1.35[/C][C]1.37408318093448[/C][C]-0.0240831809344817[/C][/ROW]
[ROW][C]26[/C][C]1.36[/C][C]1.34533527838915[/C][C]0.0146647216108511[/C][/ROW]
[ROW][C]27[/C][C]1.36[/C][C]1.3554940184962[/C][C]0.00450598150379955[/C][/ROW]
[ROW][C]28[/C][C]1.36[/C][C]1.36786376777989[/C][C]-0.00786376777988607[/C][/ROW]
[ROW][C]29[/C][C]1.37[/C][C]1.36068967359491[/C][C]0.009310326405088[/C][/ROW]
[ROW][C]30[/C][C]1.39[/C][C]1.36614668720628[/C][C]0.0238533127937164[/C][/ROW]
[ROW][C]31[/C][C]1.39[/C][C]1.40007717446809[/C][C]-0.0100771744680876[/C][/ROW]
[ROW][C]32[/C][C]1.38[/C][C]1.38664698762646[/C][C]-0.00664698762646032[/C][/ROW]
[ROW][C]33[/C][C]1.37[/C][C]1.37321517481287[/C][C]-0.00321517481286659[/C][/ROW]
[ROW][C]34[/C][C]1.39[/C][C]1.35907975488211[/C][C]0.0309202451178865[/C][/ROW]
[ROW][C]35[/C][C]1.38[/C][C]1.38458017676538[/C][C]-0.00458017676537747[/C][/ROW]
[ROW][C]36[/C][C]1.4[/C][C]1.39712656087339[/C][C]0.00287343912660543[/C][/ROW]
[ROW][C]37[/C][C]1.41[/C][C]1.40710527339047[/C][C]0.00289472660952783[/C][/ROW]
[ROW][C]38[/C][C]1.4[/C][C]1.40838202300055[/C][C]-0.00838202300054935[/C][/ROW]
[ROW][C]39[/C][C]1.42[/C][C]1.3988301676[/C][C]0.0211698324000049[/C][/ROW]
[ROW][C]40[/C][C]1.43[/C][C]1.42034821956702[/C][C]0.00965178043298009[/C][/ROW]
[ROW][C]41[/C][C]1.44[/C][C]1.43060128585818[/C][C]0.00939871414182059[/C][/ROW]
[ROW][C]42[/C][C]1.44[/C][C]1.43988836004027[/C][C]0.00011163995972896[/C][/ROW]
[ROW][C]43[/C][C]1.44[/C][C]1.44743972938412[/C][C]-0.00743972938412463[/C][/ROW]
[ROW][C]44[/C][C]1.46[/C][C]1.4368521943133[/C][C]0.0231478056866954[/C][/ROW]
[ROW][C]45[/C][C]1.46[/C][C]1.44639093497517[/C][C]0.0136090650248277[/C][/ROW]
[ROW][C]46[/C][C]1.49[/C][C]1.45356087357924[/C][C]0.0364391264207606[/C][/ROW]
[ROW][C]47[/C][C]1.49[/C][C]1.47396204643213[/C][C]0.0160379535678741[/C][/ROW]
[ROW][C]48[/C][C]1.48[/C][C]1.50371883525999[/C][C]-0.0237188352599911[/C][/ROW]
[ROW][C]49[/C][C]1.49[/C][C]1.49399437794889[/C][C]-0.00399437794888668[/C][/ROW]
[ROW][C]50[/C][C]1.5[/C][C]1.48724625073247[/C][C]0.0127537492675263[/C][/ROW]
[ROW][C]51[/C][C]1.5[/C][C]1.50100872892734[/C][C]-0.00100872892734438[/C][/ROW]
[ROW][C]52[/C][C]1.5[/C][C]1.50310776614667[/C][C]-0.00310776614666608[/C][/ROW]
[ROW][C]53[/C][C]1.47[/C][C]1.50383867477995[/C][C]-0.0338386747799462[/C][/ROW]
[ROW][C]54[/C][C]1.49[/C][C]1.47867663382262[/C][C]0.0113233661773844[/C][/ROW]
[ROW][C]55[/C][C]1.49[/C][C]1.49258277232605[/C][C]-0.00258277232604653[/C][/ROW]
[ROW][C]56[/C][C]1.5[/C][C]1.49351273239337[/C][C]0.00648726760662588[/C][/ROW]
[ROW][C]57[/C][C]1.52[/C][C]1.48823446149366[/C][C]0.0317655385063413[/C][/ROW]
[ROW][C]58[/C][C]1.52[/C][C]1.51477066413502[/C][C]0.00522933586498198[/C][/ROW]
[ROW][C]59[/C][C]1.52[/C][C]1.50675993188061[/C][C]0.0132400681193863[/C][/ROW]
[ROW][C]60[/C][C]1.52[/C][C]1.52415176749983[/C][C]-0.00415176749983215[/C][/ROW]
[ROW][C]61[/C][C]1.53[/C][C]1.53403511932271[/C][C]-0.00403511932270884[/C][/ROW]
[ROW][C]62[/C][C]1.54[/C][C]1.53159216548461[/C][C]0.00840783451539084[/C][/ROW]
[ROW][C]63[/C][C]1.51[/C][C]1.53857118635202[/C][C]-0.0285711863520213[/C][/ROW]
[ROW][C]64[/C][C]1.49[/C][C]1.51969914858054[/C][C]-0.0296991485805389[/C][/ROW]
[ROW][C]65[/C][C]1.49[/C][C]1.49276712979285[/C][C]-0.00276712979285176[/C][/ROW]
[ROW][C]66[/C][C]1.49[/C][C]1.5023240561592[/C][C]-0.0123240561591971[/C][/ROW]
[ROW][C]67[/C][C]1.48[/C][C]1.49510437102031[/C][C]-0.0151043710203058[/C][/ROW]
[ROW][C]68[/C][C]1.49[/C][C]1.48910187738711[/C][C]0.000898122612892571[/C][/ROW]
[ROW][C]69[/C][C]1.49[/C][C]1.48622470558728[/C][C]0.00377529441272428[/C][/ROW]
[ROW][C]70[/C][C]1.47[/C][C]1.48514705282158[/C][C]-0.0151470528215825[/C][/ROW]
[ROW][C]71[/C][C]1.49[/C][C]1.46410813447121[/C][C]0.0258918655287863[/C][/ROW]
[ROW][C]72[/C][C]1.49[/C][C]1.48637476529834[/C][C]0.00362523470165965[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233071&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233071&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	1.34	1.33458333333333	0.0054166666666664
14	1.33	1.32878725230921	0.00121274769079038
15	1.33	1.32904213247852	0.000957867521477862
16	1.34	1.33869144330652	0.00130855669347985
17	1.34	1.3381839983222	0.00181600167780505
18	1.34	1.33805264267834	0.00194735732166085
19	1.35	1.35843530702809	-0.00843530702809292
20	1.35	1.34195626483842	0.0080437351615843
21	1.35	1.33852388412626	0.0114761158737369
22	1.34	1.3376353886394	0.00236461136059551
23	1.35	1.33999396460091	0.0100060353990898
24	1.36	1.36801592913785	-0.00801592913784566
25	1.35	1.37408318093448	-0.0240831809344817
26	1.36	1.34533527838915	0.0146647216108511
27	1.36	1.3554940184962	0.00450598150379955
28	1.36	1.36786376777989	-0.00786376777988607
29	1.37	1.36068967359491	0.009310326405088
30	1.39	1.36614668720628	0.0238533127937164
31	1.39	1.40007717446809	-0.0100771744680876
32	1.38	1.38664698762646	-0.00664698762646032
33	1.37	1.37321517481287	-0.00321517481286659
34	1.39	1.35907975488211	0.0309202451178865
35	1.38	1.38458017676538	-0.00458017676537747
36	1.4	1.39712656087339	0.00287343912660543
37	1.41	1.40710527339047	0.00289472660952783
38	1.4	1.40838202300055	-0.00838202300054935
39	1.42	1.3988301676	0.0211698324000049
40	1.43	1.42034821956702	0.00965178043298009
41	1.44	1.43060128585818	0.00939871414182059
42	1.44	1.43988836004027	0.00011163995972896
43	1.44	1.44743972938412	-0.00743972938412463
44	1.46	1.4368521943133	0.0231478056866954
45	1.46	1.44639093497517	0.0136090650248277
46	1.49	1.45356087357924	0.0364391264207606
47	1.49	1.47396204643213	0.0160379535678741
48	1.48	1.50371883525999	-0.0237188352599911
49	1.49	1.49399437794889	-0.00399437794888668
50	1.5	1.48724625073247	0.0127537492675263
51	1.5	1.50100872892734	-0.00100872892734438
52	1.5	1.50310776614667	-0.00310776614666608
53	1.47	1.50383867477995	-0.0338386747799462
54	1.49	1.47867663382262	0.0113233661773844
55	1.49	1.49258277232605	-0.00258277232604653
56	1.5	1.49351273239337	0.00648726760662588
57	1.52	1.48823446149366	0.0317655385063413
58	1.52	1.51477066413502	0.00522933586498198
59	1.52	1.50675993188061	0.0132400681193863
60	1.52	1.52415176749983	-0.00415176749983215
61	1.53	1.53403511932271	-0.00403511932270884
62	1.54	1.53159216548461	0.00840783451539084
63	1.51	1.53857118635202	-0.0285711863520213
64	1.49	1.51969914858054	-0.0296991485805389
65	1.49	1.49276712979285	-0.00276712979285176
66	1.49	1.5023240561592	-0.0123240561591971
67	1.48	1.49510437102031	-0.0151043710203058
68	1.49	1.48910187738711	0.000898122612892571
69	1.49	1.48622470558728	0.00377529441272428
70	1.47	1.48514705282158	-0.0151470528215825
71	1.49	1.46410813447121	0.0258918655287863
72	1.49	1.48637476529834	0.00362523470165965

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.50205218370187	1.47364412244871	1.53046024495504
74	1.50582077530225	1.47046109050975	1.54118046009475
75	1.49699611245896	1.45584278120758	1.53814944371034
76	1.49900743101997	1.452780966332	1.54523389570793
77	1.50105827012752	1.45026284314823	1.55185369710682
78	1.51019215911253	1.45520611755224	1.56517820067282
79	1.51138665922723	1.45250751070306	1.57026580775141
80	1.52072102186441	1.45819068126569	1.58325136246314
81	1.51792298852165	1.45194319722269	1.58390277982061
82	1.50914912195817	1.43989147094173	1.57840677297461
83	1.5099595448985	1.43757231129494	1.58234677850206
84	1.50727272727273	1.43188571941834	1.58265973512712

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.50205218370187 & 1.47364412244871 & 1.53046024495504 \tabularnewline
74 & 1.50582077530225 & 1.47046109050975 & 1.54118046009475 \tabularnewline
75 & 1.49699611245896 & 1.45584278120758 & 1.53814944371034 \tabularnewline
76 & 1.49900743101997 & 1.452780966332 & 1.54523389570793 \tabularnewline
77 & 1.50105827012752 & 1.45026284314823 & 1.55185369710682 \tabularnewline
78 & 1.51019215911253 & 1.45520611755224 & 1.56517820067282 \tabularnewline
79 & 1.51138665922723 & 1.45250751070306 & 1.57026580775141 \tabularnewline
80 & 1.52072102186441 & 1.45819068126569 & 1.58325136246314 \tabularnewline
81 & 1.51792298852165 & 1.45194319722269 & 1.58390277982061 \tabularnewline
82 & 1.50914912195817 & 1.43989147094173 & 1.57840677297461 \tabularnewline
83 & 1.5099595448985 & 1.43757231129494 & 1.58234677850206 \tabularnewline
84 & 1.50727272727273 & 1.43188571941834 & 1.58265973512712 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233071&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]1.50205218370187[/C][C]1.47364412244871[/C][C]1.53046024495504[/C][/ROW]
[ROW][C]74[/C][C]1.50582077530225[/C][C]1.47046109050975[/C][C]1.54118046009475[/C][/ROW]
[ROW][C]75[/C][C]1.49699611245896[/C][C]1.45584278120758[/C][C]1.53814944371034[/C][/ROW]
[ROW][C]76[/C][C]1.49900743101997[/C][C]1.452780966332[/C][C]1.54523389570793[/C][/ROW]
[ROW][C]77[/C][C]1.50105827012752[/C][C]1.45026284314823[/C][C]1.55185369710682[/C][/ROW]
[ROW][C]78[/C][C]1.51019215911253[/C][C]1.45520611755224[/C][C]1.56517820067282[/C][/ROW]
[ROW][C]79[/C][C]1.51138665922723[/C][C]1.45250751070306[/C][C]1.57026580775141[/C][/ROW]
[ROW][C]80[/C][C]1.52072102186441[/C][C]1.45819068126569[/C][C]1.58325136246314[/C][/ROW]
[ROW][C]81[/C][C]1.51792298852165[/C][C]1.45194319722269[/C][C]1.58390277982061[/C][/ROW]
[ROW][C]82[/C][C]1.50914912195817[/C][C]1.43989147094173[/C][C]1.57840677297461[/C][/ROW]
[ROW][C]83[/C][C]1.5099595448985[/C][C]1.43757231129494[/C][C]1.58234677850206[/C][/ROW]
[ROW][C]84[/C][C]1.50727272727273[/C][C]1.43188571941834[/C][C]1.58265973512712[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233071&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233071&T=3

As an alternative you can also use a QR Code:

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

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.50205218370187	1.47364412244871	1.53046024495504
74	1.50582077530225	1.47046109050975	1.54118046009475
75	1.49699611245896	1.45584278120758	1.53814944371034
76	1.49900743101997	1.452780966332	1.54523389570793
77	1.50105827012752	1.45026284314823	1.55185369710682
78	1.51019215911253	1.45520611755224	1.56517820067282
79	1.51138665922723	1.45250751070306	1.57026580775141
80	1.52072102186441	1.45819068126569	1.58325136246314
81	1.51792298852165	1.45194319722269	1.58390277982061
82	1.50914912195817	1.43989147094173	1.57840677297461
83	1.5099595448985	1.43757231129494	1.58234677850206
84	1.50727272727273	1.43188571941834	1.58265973512712

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 = 50 ; par2 = 5 ; par3 = 0 ; par4 = P1 P5 Q1 Q3 P95 P99 ;

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