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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 26 May 2013 05:55:38 -0400

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/2013/May/26/t13695622146fiej6ekhrktcax.htm/, Retrieved Mon, 29 Apr 2024 13:11:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210569, Retrieved Mon, 29 Apr 2024 13:11:08 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

112

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

-       [Exponential Smoothing] [] [2013-05-26 09:55:38] [3ee9032f7b5fbe5092f0a094fc771125] [Current]

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Dataseries X:

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Histogram

Boxplots

0.66
0.67
0.67
0.67
0.67
0.67
0.67
0.67
0.67
0.67
0.67
0.67
0.67
0.69
0.7
0.7
0.7
0.7
0.7
0.7
0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.72
0.72
0.72
0.72
0.73
0.73
0.73
0.73
0.73
0.73
0.73
0.73
0.73
0.73
0.73
0.73
0.74
0.75
0.75
0.75
0.75
0.76
0.76
0.76
0.77
0.77
0.78
0.78
0.78
0.78
0.79
0.79
0.79
0.8
0.8
0.8
0.8
0.81
0.8
0.81
0.82
0.82
0.82
0.82

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210569&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210569&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210569&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	4 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.159375563626571
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.159375563626571 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210569&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.159375563626571[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210569&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210569&T=1

As an alternative you can also use a QR Code:

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.159375563626571
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	0.67	0.68	-0.01
4	0.67	0.678406244363734	-0.00840624436373427
5	0.67	0.677066494430282	-0.00706649443028151
6	0.67	0.675940267897591	-0.00594026789759128
7	0.67	0.67499353435332	-0.00499353435331984
8	0.67	0.674197687001271	-0.00419768700127088
9	0.67	0.673528678269515	-0.00352867826951542
10	0.67	0.672966293181455	-0.00296629318145458
11	0.67	0.672493538533779	-0.00249353853377854
12	0.67	0.672096129424533	-0.00209612942453308
13	0.67	0.671762057616064	-0.00176205761606385
14	0.69	0.671481228690361	0.0185187713096387
15	0.7	0.694432668305506	0.00556733169449353
16	0.7	0.705319964932212	-0.00531996493221243
17	0.7	0.704472092522667	-0.00447209252266745
18	0.7	0.703759350256277	-0.00375935025627716
19	0.7	0.703160201690313	-0.00316020169031328
20	0.7	0.702656542764746	-0.00265654276474603
21	0.71	0.702233154764316	0.00776684523568349
22	0.71	0.713471000101354	-0.00347100010135393
23	0.71	0.712917807503853	-0.00291780750385273
24	0.71	0.712452780288372	-0.00245278028837237
25	0.71	0.712061867047461	-0.00206186704746092
26	0.71	0.711733255824649	-0.00173325582464878
27	0.71	0.711457017200686	-0.00145701720068636
28	0.71	0.711224804263113	-0.00122480426311333
29	0.72	0.711029600393347	0.00897039960665258
30	0.72	0.722459262886613	-0.00245926288661324
31	0.72	0.722067316477953	-0.00206731647795333
32	0.72	0.721737836749085	-0.00173783674908501
33	0.73	0.721460868037709	0.00853913196229139
34	0.73	0.73282179700708	-0.00282179700708052
35	0.73	0.732372071518637	-0.00237207151863728
36	0.73	0.731994021283392	-0.00199402128339188
37	0.73	0.731676223017468	-0.00167622301746795
38	0.73	0.731409074029295	-0.00140907402929513
39	0.73	0.731184502061685	-0.00118450206168463
40	0.73	0.730995721377987	-0.000995721377986869
41	0.73	0.730837027722155	-0.000837027722155215
42	0.73	0.730703625957166	-0.000703625957165666
43	0.73	0.73059148517366	-0.000591485173660034
44	0.73	0.730497216890731	-0.000497216890731234
45	0.74	0.730417972668526	0.00958202733147373
46	0.75	0.741945113675165	0.00805488632483486
47	0.75	0.753228865723134	-0.00322886572313363
48	0.75	0.752714263428635	-0.00271426342863468
49	0.75	0.752281676164865	-0.00228167616486508
50	0.76	0.751918032740076	0.00808196725992361
51	0.76	0.763206100827338	-0.00320610082733819
52	0.76	0.762695126700938	-0.00269512670093752
53	0.77	0.762265589363931	0.00773441063606939
54	0.77	0.773498265418374	-0.0034982654183735
55	0.78	0.772940727395605	0.00705927260439509
56	0.78	0.784065802945724	-0.00406580294572401
57	0.78	0.783417813309655	-0.00341781330965463
58	0.78	0.782873097387058	-0.00287309738705799
59	0.79	0.782415195871642	0.00758480412835838
60	0.79	0.793624028304596	-0.00362402830459585
61	0.79	0.793046446750952	-0.00304644675095223
62	0.8	0.792560917582961	0.00743908241703906
63	0.8	0.803746525536041	-0.00374652553604105
64	0.8	0.803149420917093	-0.00314942091709314
65	0.8	0.802647480183334	-0.00264748018333416
66	0.81	0.802225536536925	0.00777446346307498
67	0.8	0.813464596033247	-0.0134645960332468
68	0.81	0.801318668451444	0.00868133154855599
69	0.82	0.812702260560024	0.00729773943997569
70	0.82	0.82386534189647	-0.00386534189647025
71	0.82	0.823249300853111	-0.00324930085311093
72	0.82	0.822731441698254	-0.00273144169825401

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.67 & 0.68 & -0.01 \tabularnewline
4 & 0.67 & 0.678406244363734 & -0.00840624436373427 \tabularnewline
5 & 0.67 & 0.677066494430282 & -0.00706649443028151 \tabularnewline
6 & 0.67 & 0.675940267897591 & -0.00594026789759128 \tabularnewline
7 & 0.67 & 0.67499353435332 & -0.00499353435331984 \tabularnewline
8 & 0.67 & 0.674197687001271 & -0.00419768700127088 \tabularnewline
9 & 0.67 & 0.673528678269515 & -0.00352867826951542 \tabularnewline
10 & 0.67 & 0.672966293181455 & -0.00296629318145458 \tabularnewline
11 & 0.67 & 0.672493538533779 & -0.00249353853377854 \tabularnewline
12 & 0.67 & 0.672096129424533 & -0.00209612942453308 \tabularnewline
13 & 0.67 & 0.671762057616064 & -0.00176205761606385 \tabularnewline
14 & 0.69 & 0.671481228690361 & 0.0185187713096387 \tabularnewline
15 & 0.7 & 0.694432668305506 & 0.00556733169449353 \tabularnewline
16 & 0.7 & 0.705319964932212 & -0.00531996493221243 \tabularnewline
17 & 0.7 & 0.704472092522667 & -0.00447209252266745 \tabularnewline
18 & 0.7 & 0.703759350256277 & -0.00375935025627716 \tabularnewline
19 & 0.7 & 0.703160201690313 & -0.00316020169031328 \tabularnewline
20 & 0.7 & 0.702656542764746 & -0.00265654276474603 \tabularnewline
21 & 0.71 & 0.702233154764316 & 0.00776684523568349 \tabularnewline
22 & 0.71 & 0.713471000101354 & -0.00347100010135393 \tabularnewline
23 & 0.71 & 0.712917807503853 & -0.00291780750385273 \tabularnewline
24 & 0.71 & 0.712452780288372 & -0.00245278028837237 \tabularnewline
25 & 0.71 & 0.712061867047461 & -0.00206186704746092 \tabularnewline
26 & 0.71 & 0.711733255824649 & -0.00173325582464878 \tabularnewline
27 & 0.71 & 0.711457017200686 & -0.00145701720068636 \tabularnewline
28 & 0.71 & 0.711224804263113 & -0.00122480426311333 \tabularnewline
29 & 0.72 & 0.711029600393347 & 0.00897039960665258 \tabularnewline
30 & 0.72 & 0.722459262886613 & -0.00245926288661324 \tabularnewline
31 & 0.72 & 0.722067316477953 & -0.00206731647795333 \tabularnewline
32 & 0.72 & 0.721737836749085 & -0.00173783674908501 \tabularnewline
33 & 0.73 & 0.721460868037709 & 0.00853913196229139 \tabularnewline
34 & 0.73 & 0.73282179700708 & -0.00282179700708052 \tabularnewline
35 & 0.73 & 0.732372071518637 & -0.00237207151863728 \tabularnewline
36 & 0.73 & 0.731994021283392 & -0.00199402128339188 \tabularnewline
37 & 0.73 & 0.731676223017468 & -0.00167622301746795 \tabularnewline
38 & 0.73 & 0.731409074029295 & -0.00140907402929513 \tabularnewline
39 & 0.73 & 0.731184502061685 & -0.00118450206168463 \tabularnewline
40 & 0.73 & 0.730995721377987 & -0.000995721377986869 \tabularnewline
41 & 0.73 & 0.730837027722155 & -0.000837027722155215 \tabularnewline
42 & 0.73 & 0.730703625957166 & -0.000703625957165666 \tabularnewline
43 & 0.73 & 0.73059148517366 & -0.000591485173660034 \tabularnewline
44 & 0.73 & 0.730497216890731 & -0.000497216890731234 \tabularnewline
45 & 0.74 & 0.730417972668526 & 0.00958202733147373 \tabularnewline
46 & 0.75 & 0.741945113675165 & 0.00805488632483486 \tabularnewline
47 & 0.75 & 0.753228865723134 & -0.00322886572313363 \tabularnewline
48 & 0.75 & 0.752714263428635 & -0.00271426342863468 \tabularnewline
49 & 0.75 & 0.752281676164865 & -0.00228167616486508 \tabularnewline
50 & 0.76 & 0.751918032740076 & 0.00808196725992361 \tabularnewline
51 & 0.76 & 0.763206100827338 & -0.00320610082733819 \tabularnewline
52 & 0.76 & 0.762695126700938 & -0.00269512670093752 \tabularnewline
53 & 0.77 & 0.762265589363931 & 0.00773441063606939 \tabularnewline
54 & 0.77 & 0.773498265418374 & -0.0034982654183735 \tabularnewline
55 & 0.78 & 0.772940727395605 & 0.00705927260439509 \tabularnewline
56 & 0.78 & 0.784065802945724 & -0.00406580294572401 \tabularnewline
57 & 0.78 & 0.783417813309655 & -0.00341781330965463 \tabularnewline
58 & 0.78 & 0.782873097387058 & -0.00287309738705799 \tabularnewline
59 & 0.79 & 0.782415195871642 & 0.00758480412835838 \tabularnewline
60 & 0.79 & 0.793624028304596 & -0.00362402830459585 \tabularnewline
61 & 0.79 & 0.793046446750952 & -0.00304644675095223 \tabularnewline
62 & 0.8 & 0.792560917582961 & 0.00743908241703906 \tabularnewline
63 & 0.8 & 0.803746525536041 & -0.00374652553604105 \tabularnewline
64 & 0.8 & 0.803149420917093 & -0.00314942091709314 \tabularnewline
65 & 0.8 & 0.802647480183334 & -0.00264748018333416 \tabularnewline
66 & 0.81 & 0.802225536536925 & 0.00777446346307498 \tabularnewline
67 & 0.8 & 0.813464596033247 & -0.0134645960332468 \tabularnewline
68 & 0.81 & 0.801318668451444 & 0.00868133154855599 \tabularnewline
69 & 0.82 & 0.812702260560024 & 0.00729773943997569 \tabularnewline
70 & 0.82 & 0.82386534189647 & -0.00386534189647025 \tabularnewline
71 & 0.82 & 0.823249300853111 & -0.00324930085311093 \tabularnewline
72 & 0.82 & 0.822731441698254 & -0.00273144169825401 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210569&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]0.67[/C][C]0.68[/C][C]-0.01[/C][/ROW]
[ROW][C]4[/C][C]0.67[/C][C]0.678406244363734[/C][C]-0.00840624436373427[/C][/ROW]
[ROW][C]5[/C][C]0.67[/C][C]0.677066494430282[/C][C]-0.00706649443028151[/C][/ROW]
[ROW][C]6[/C][C]0.67[/C][C]0.675940267897591[/C][C]-0.00594026789759128[/C][/ROW]
[ROW][C]7[/C][C]0.67[/C][C]0.67499353435332[/C][C]-0.00499353435331984[/C][/ROW]
[ROW][C]8[/C][C]0.67[/C][C]0.674197687001271[/C][C]-0.00419768700127088[/C][/ROW]
[ROW][C]9[/C][C]0.67[/C][C]0.673528678269515[/C][C]-0.00352867826951542[/C][/ROW]
[ROW][C]10[/C][C]0.67[/C][C]0.672966293181455[/C][C]-0.00296629318145458[/C][/ROW]
[ROW][C]11[/C][C]0.67[/C][C]0.672493538533779[/C][C]-0.00249353853377854[/C][/ROW]
[ROW][C]12[/C][C]0.67[/C][C]0.672096129424533[/C][C]-0.00209612942453308[/C][/ROW]
[ROW][C]13[/C][C]0.67[/C][C]0.671762057616064[/C][C]-0.00176205761606385[/C][/ROW]
[ROW][C]14[/C][C]0.69[/C][C]0.671481228690361[/C][C]0.0185187713096387[/C][/ROW]
[ROW][C]15[/C][C]0.7[/C][C]0.694432668305506[/C][C]0.00556733169449353[/C][/ROW]
[ROW][C]16[/C][C]0.7[/C][C]0.705319964932212[/C][C]-0.00531996493221243[/C][/ROW]
[ROW][C]17[/C][C]0.7[/C][C]0.704472092522667[/C][C]-0.00447209252266745[/C][/ROW]
[ROW][C]18[/C][C]0.7[/C][C]0.703759350256277[/C][C]-0.00375935025627716[/C][/ROW]
[ROW][C]19[/C][C]0.7[/C][C]0.703160201690313[/C][C]-0.00316020169031328[/C][/ROW]
[ROW][C]20[/C][C]0.7[/C][C]0.702656542764746[/C][C]-0.00265654276474603[/C][/ROW]
[ROW][C]21[/C][C]0.71[/C][C]0.702233154764316[/C][C]0.00776684523568349[/C][/ROW]
[ROW][C]22[/C][C]0.71[/C][C]0.713471000101354[/C][C]-0.00347100010135393[/C][/ROW]
[ROW][C]23[/C][C]0.71[/C][C]0.712917807503853[/C][C]-0.00291780750385273[/C][/ROW]
[ROW][C]24[/C][C]0.71[/C][C]0.712452780288372[/C][C]-0.00245278028837237[/C][/ROW]
[ROW][C]25[/C][C]0.71[/C][C]0.712061867047461[/C][C]-0.00206186704746092[/C][/ROW]
[ROW][C]26[/C][C]0.71[/C][C]0.711733255824649[/C][C]-0.00173325582464878[/C][/ROW]
[ROW][C]27[/C][C]0.71[/C][C]0.711457017200686[/C][C]-0.00145701720068636[/C][/ROW]
[ROW][C]28[/C][C]0.71[/C][C]0.711224804263113[/C][C]-0.00122480426311333[/C][/ROW]
[ROW][C]29[/C][C]0.72[/C][C]0.711029600393347[/C][C]0.00897039960665258[/C][/ROW]
[ROW][C]30[/C][C]0.72[/C][C]0.722459262886613[/C][C]-0.00245926288661324[/C][/ROW]
[ROW][C]31[/C][C]0.72[/C][C]0.722067316477953[/C][C]-0.00206731647795333[/C][/ROW]
[ROW][C]32[/C][C]0.72[/C][C]0.721737836749085[/C][C]-0.00173783674908501[/C][/ROW]
[ROW][C]33[/C][C]0.73[/C][C]0.721460868037709[/C][C]0.00853913196229139[/C][/ROW]
[ROW][C]34[/C][C]0.73[/C][C]0.73282179700708[/C][C]-0.00282179700708052[/C][/ROW]
[ROW][C]35[/C][C]0.73[/C][C]0.732372071518637[/C][C]-0.00237207151863728[/C][/ROW]
[ROW][C]36[/C][C]0.73[/C][C]0.731994021283392[/C][C]-0.00199402128339188[/C][/ROW]
[ROW][C]37[/C][C]0.73[/C][C]0.731676223017468[/C][C]-0.00167622301746795[/C][/ROW]
[ROW][C]38[/C][C]0.73[/C][C]0.731409074029295[/C][C]-0.00140907402929513[/C][/ROW]
[ROW][C]39[/C][C]0.73[/C][C]0.731184502061685[/C][C]-0.00118450206168463[/C][/ROW]
[ROW][C]40[/C][C]0.73[/C][C]0.730995721377987[/C][C]-0.000995721377986869[/C][/ROW]
[ROW][C]41[/C][C]0.73[/C][C]0.730837027722155[/C][C]-0.000837027722155215[/C][/ROW]
[ROW][C]42[/C][C]0.73[/C][C]0.730703625957166[/C][C]-0.000703625957165666[/C][/ROW]
[ROW][C]43[/C][C]0.73[/C][C]0.73059148517366[/C][C]-0.000591485173660034[/C][/ROW]
[ROW][C]44[/C][C]0.73[/C][C]0.730497216890731[/C][C]-0.000497216890731234[/C][/ROW]
[ROW][C]45[/C][C]0.74[/C][C]0.730417972668526[/C][C]0.00958202733147373[/C][/ROW]
[ROW][C]46[/C][C]0.75[/C][C]0.741945113675165[/C][C]0.00805488632483486[/C][/ROW]
[ROW][C]47[/C][C]0.75[/C][C]0.753228865723134[/C][C]-0.00322886572313363[/C][/ROW]
[ROW][C]48[/C][C]0.75[/C][C]0.752714263428635[/C][C]-0.00271426342863468[/C][/ROW]
[ROW][C]49[/C][C]0.75[/C][C]0.752281676164865[/C][C]-0.00228167616486508[/C][/ROW]
[ROW][C]50[/C][C]0.76[/C][C]0.751918032740076[/C][C]0.00808196725992361[/C][/ROW]
[ROW][C]51[/C][C]0.76[/C][C]0.763206100827338[/C][C]-0.00320610082733819[/C][/ROW]
[ROW][C]52[/C][C]0.76[/C][C]0.762695126700938[/C][C]-0.00269512670093752[/C][/ROW]
[ROW][C]53[/C][C]0.77[/C][C]0.762265589363931[/C][C]0.00773441063606939[/C][/ROW]
[ROW][C]54[/C][C]0.77[/C][C]0.773498265418374[/C][C]-0.0034982654183735[/C][/ROW]
[ROW][C]55[/C][C]0.78[/C][C]0.772940727395605[/C][C]0.00705927260439509[/C][/ROW]
[ROW][C]56[/C][C]0.78[/C][C]0.784065802945724[/C][C]-0.00406580294572401[/C][/ROW]
[ROW][C]57[/C][C]0.78[/C][C]0.783417813309655[/C][C]-0.00341781330965463[/C][/ROW]
[ROW][C]58[/C][C]0.78[/C][C]0.782873097387058[/C][C]-0.00287309738705799[/C][/ROW]
[ROW][C]59[/C][C]0.79[/C][C]0.782415195871642[/C][C]0.00758480412835838[/C][/ROW]
[ROW][C]60[/C][C]0.79[/C][C]0.793624028304596[/C][C]-0.00362402830459585[/C][/ROW]
[ROW][C]61[/C][C]0.79[/C][C]0.793046446750952[/C][C]-0.00304644675095223[/C][/ROW]
[ROW][C]62[/C][C]0.8[/C][C]0.792560917582961[/C][C]0.00743908241703906[/C][/ROW]
[ROW][C]63[/C][C]0.8[/C][C]0.803746525536041[/C][C]-0.00374652553604105[/C][/ROW]
[ROW][C]64[/C][C]0.8[/C][C]0.803149420917093[/C][C]-0.00314942091709314[/C][/ROW]
[ROW][C]65[/C][C]0.8[/C][C]0.802647480183334[/C][C]-0.00264748018333416[/C][/ROW]
[ROW][C]66[/C][C]0.81[/C][C]0.802225536536925[/C][C]0.00777446346307498[/C][/ROW]
[ROW][C]67[/C][C]0.8[/C][C]0.813464596033247[/C][C]-0.0134645960332468[/C][/ROW]
[ROW][C]68[/C][C]0.81[/C][C]0.801318668451444[/C][C]0.00868133154855599[/C][/ROW]
[ROW][C]69[/C][C]0.82[/C][C]0.812702260560024[/C][C]0.00729773943997569[/C][/ROW]
[ROW][C]70[/C][C]0.82[/C][C]0.82386534189647[/C][C]-0.00386534189647025[/C][/ROW]
[ROW][C]71[/C][C]0.82[/C][C]0.823249300853111[/C][C]-0.00324930085311093[/C][/ROW]
[ROW][C]72[/C][C]0.82[/C][C]0.822731441698254[/C][C]-0.00273144169825401[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210569&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210569&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	0.67	0.68	-0.01
4	0.67	0.678406244363734	-0.00840624436373427
5	0.67	0.677066494430282	-0.00706649443028151
6	0.67	0.675940267897591	-0.00594026789759128
7	0.67	0.67499353435332	-0.00499353435331984
8	0.67	0.674197687001271	-0.00419768700127088
9	0.67	0.673528678269515	-0.00352867826951542
10	0.67	0.672966293181455	-0.00296629318145458
11	0.67	0.672493538533779	-0.00249353853377854
12	0.67	0.672096129424533	-0.00209612942453308
13	0.67	0.671762057616064	-0.00176205761606385
14	0.69	0.671481228690361	0.0185187713096387
15	0.7	0.694432668305506	0.00556733169449353
16	0.7	0.705319964932212	-0.00531996493221243
17	0.7	0.704472092522667	-0.00447209252266745
18	0.7	0.703759350256277	-0.00375935025627716
19	0.7	0.703160201690313	-0.00316020169031328
20	0.7	0.702656542764746	-0.00265654276474603
21	0.71	0.702233154764316	0.00776684523568349
22	0.71	0.713471000101354	-0.00347100010135393
23	0.71	0.712917807503853	-0.00291780750385273
24	0.71	0.712452780288372	-0.00245278028837237
25	0.71	0.712061867047461	-0.00206186704746092
26	0.71	0.711733255824649	-0.00173325582464878
27	0.71	0.711457017200686	-0.00145701720068636
28	0.71	0.711224804263113	-0.00122480426311333
29	0.72	0.711029600393347	0.00897039960665258
30	0.72	0.722459262886613	-0.00245926288661324
31	0.72	0.722067316477953	-0.00206731647795333
32	0.72	0.721737836749085	-0.00173783674908501
33	0.73	0.721460868037709	0.00853913196229139
34	0.73	0.73282179700708	-0.00282179700708052
35	0.73	0.732372071518637	-0.00237207151863728
36	0.73	0.731994021283392	-0.00199402128339188
37	0.73	0.731676223017468	-0.00167622301746795
38	0.73	0.731409074029295	-0.00140907402929513
39	0.73	0.731184502061685	-0.00118450206168463
40	0.73	0.730995721377987	-0.000995721377986869
41	0.73	0.730837027722155	-0.000837027722155215
42	0.73	0.730703625957166	-0.000703625957165666
43	0.73	0.73059148517366	-0.000591485173660034
44	0.73	0.730497216890731	-0.000497216890731234
45	0.74	0.730417972668526	0.00958202733147373
46	0.75	0.741945113675165	0.00805488632483486
47	0.75	0.753228865723134	-0.00322886572313363
48	0.75	0.752714263428635	-0.00271426342863468
49	0.75	0.752281676164865	-0.00228167616486508
50	0.76	0.751918032740076	0.00808196725992361
51	0.76	0.763206100827338	-0.00320610082733819
52	0.76	0.762695126700938	-0.00269512670093752
53	0.77	0.762265589363931	0.00773441063606939
54	0.77	0.773498265418374	-0.0034982654183735
55	0.78	0.772940727395605	0.00705927260439509
56	0.78	0.784065802945724	-0.00406580294572401
57	0.78	0.783417813309655	-0.00341781330965463
58	0.78	0.782873097387058	-0.00287309738705799
59	0.79	0.782415195871642	0.00758480412835838
60	0.79	0.793624028304596	-0.00362402830459585
61	0.79	0.793046446750952	-0.00304644675095223
62	0.8	0.792560917582961	0.00743908241703906
63	0.8	0.803746525536041	-0.00374652553604105
64	0.8	0.803149420917093	-0.00314942091709314
65	0.8	0.802647480183334	-0.00264748018333416
66	0.81	0.802225536536925	0.00777446346307498
67	0.8	0.813464596033247	-0.0134645960332468
68	0.81	0.801318668451444	0.00868133154855599
69	0.82	0.812702260560024	0.00729773943997569
70	0.82	0.82386534189647	-0.00386534189647025
71	0.82	0.823249300853111	-0.00324930085311093
72	0.82	0.822731441698254	-0.00273144169825401

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.822296116638082	0.811652129322537	0.832940103953626
74	0.824592233276163	0.808295625815315	0.840888840737011
75	0.826888349914245	0.805379971677628	0.848396728150862
76	0.829184466552327	0.802535963536706	0.855832969567948
77	0.831480583190408	0.799638283671743	0.863322882709074
78	0.83377669982849	0.796631931698257	0.870921467958724
79	0.836072816466572	0.793489915162156	0.878655717770988
80	0.838368933104653	0.790198438204915	0.886539428004392
81	0.840665049742735	0.786750593669321	0.894579505816149
82	0.842961166380817	0.783143318241558	0.902779014520076
83	0.845257283018898	0.779375789305301	0.911138776732496
84	0.84755339965698	0.775448525788753	0.919658273525208

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.822296116638082 & 0.811652129322537 & 0.832940103953626 \tabularnewline
74 & 0.824592233276163 & 0.808295625815315 & 0.840888840737011 \tabularnewline
75 & 0.826888349914245 & 0.805379971677628 & 0.848396728150862 \tabularnewline
76 & 0.829184466552327 & 0.802535963536706 & 0.855832969567948 \tabularnewline
77 & 0.831480583190408 & 0.799638283671743 & 0.863322882709074 \tabularnewline
78 & 0.83377669982849 & 0.796631931698257 & 0.870921467958724 \tabularnewline
79 & 0.836072816466572 & 0.793489915162156 & 0.878655717770988 \tabularnewline
80 & 0.838368933104653 & 0.790198438204915 & 0.886539428004392 \tabularnewline
81 & 0.840665049742735 & 0.786750593669321 & 0.894579505816149 \tabularnewline
82 & 0.842961166380817 & 0.783143318241558 & 0.902779014520076 \tabularnewline
83 & 0.845257283018898 & 0.779375789305301 & 0.911138776732496 \tabularnewline
84 & 0.84755339965698 & 0.775448525788753 & 0.919658273525208 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210569&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]0.822296116638082[/C][C]0.811652129322537[/C][C]0.832940103953626[/C][/ROW]
[ROW][C]74[/C][C]0.824592233276163[/C][C]0.808295625815315[/C][C]0.840888840737011[/C][/ROW]
[ROW][C]75[/C][C]0.826888349914245[/C][C]0.805379971677628[/C][C]0.848396728150862[/C][/ROW]
[ROW][C]76[/C][C]0.829184466552327[/C][C]0.802535963536706[/C][C]0.855832969567948[/C][/ROW]
[ROW][C]77[/C][C]0.831480583190408[/C][C]0.799638283671743[/C][C]0.863322882709074[/C][/ROW]
[ROW][C]78[/C][C]0.83377669982849[/C][C]0.796631931698257[/C][C]0.870921467958724[/C][/ROW]
[ROW][C]79[/C][C]0.836072816466572[/C][C]0.793489915162156[/C][C]0.878655717770988[/C][/ROW]
[ROW][C]80[/C][C]0.838368933104653[/C][C]0.790198438204915[/C][C]0.886539428004392[/C][/ROW]
[ROW][C]81[/C][C]0.840665049742735[/C][C]0.786750593669321[/C][C]0.894579505816149[/C][/ROW]
[ROW][C]82[/C][C]0.842961166380817[/C][C]0.783143318241558[/C][C]0.902779014520076[/C][/ROW]
[ROW][C]83[/C][C]0.845257283018898[/C][C]0.779375789305301[/C][C]0.911138776732496[/C][/ROW]
[ROW][C]84[/C][C]0.84755339965698[/C][C]0.775448525788753[/C][C]0.919658273525208[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210569&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210569&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	0.822296116638082	0.811652129322537	0.832940103953626
74	0.824592233276163	0.808295625815315	0.840888840737011
75	0.826888349914245	0.805379971677628	0.848396728150862
76	0.829184466552327	0.802535963536706	0.855832969567948
77	0.831480583190408	0.799638283671743	0.863322882709074
78	0.83377669982849	0.796631931698257	0.870921467958724
79	0.836072816466572	0.793489915162156	0.878655717770988
80	0.838368933104653	0.790198438204915	0.886539428004392
81	0.840665049742735	0.786750593669321	0.894579505816149
82	0.842961166380817	0.783143318241558	0.902779014520076
83	0.845257283018898	0.779375789305301	0.911138776732496
84	0.84755339965698	0.775448525788753	0.919658273525208

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code