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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 18 Dec 2014 20:04:43 +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/2014/Dec/18/t1418933135l2aos878aq3lsyj.htm/, Retrieved Fri, 17 May 2024 12:36:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271268, Retrieved Fri, 17 May 2024 12:36:09 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-     [Exponential Smoothing] [] [2014-11-28 12:58:33] [24d0a9e7d3e0bd5045c9a6a8ddd5f7fc]
- R P   [Exponential Smoothing] [] [2014-12-04 09:59:04] [24d0a9e7d3e0bd5045c9a6a8ddd5f7fc]
-   PD      [Exponential Smoothing] [] [2014-12-18 20:04:43] [f149622c9d515219c1fb7480e3dc01f1] [Current]

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Dataseries X:

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Histogram

Boxplots

0,52
0,54
0,54
0,54
0,54
0,54
0,54
0,54
0,54
0,54
0,54
0,54
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,59
0,61
0,61
0,61
0,61
0,61
0,61
0,61
0,61
0,61
0,61
0,61
0,61
0,65
0,65
0,65
0,65
0,65
0,65
0,65
0,65
0,65
0,65
0,65
0,65
0,67
0,67
0,67
0,67
0,67
0,67
0,67
0,67
0,67
0,67
0,67
0,67

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271268&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271268&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271268&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.204855186477773
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.204855186477773 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271268&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]0.204855186477773[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271268&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271268&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	0.204855186477773
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	0.54	0.56	-0.02
4	0.54	0.555902896270445	-0.0159028962704446
5	0.54	0.552645105489426	-0.012645105489426
6	0.54	0.550054690046359	-0.0100546900463585
7	0.54	0.547994934641936	-0.00799493464193557
8	0.54	0.546357130814984	-0.00635713081498424
9	0.54	0.545054839596417	-0.00505483959641706
10	0.54	0.544019329488278	-0.00401932948827777
11	0.54	0.543195948996441	-0.00319594899644104
12	0.54	0.542541242268802	-0.0025412422688017
13	0.59	0.542020655609941	0.0479793443900588
14	0.59	0.601849473152048	-0.0118494731520479
15	0.59	0.599422047119822	-0.00942204711982175
16	0.59	0.597491891900088	-0.00749189190008825
17	0.59	0.595957138987824	-0.00595713898782435
18	0.59	0.5947367881696	-0.00473678816959966
19	0.59	0.593766432545811	-0.00376643254581055
20	0.59	0.592994859304283	-0.00299485930428256
21	0.59	0.592381346843029	-0.00238134684302904
22	0.59	0.591893515591432	-0.00189351559143214
23	0.59	0.591505619101851	-0.00150561910185076
24	0.59	0.591197185219977	-0.00119718521997658
25	0.59	0.59095193561849	-0.00095193561848983
26	0.59	0.590756926669849	-0.000756926669849278
27	0.59	0.590601866315747	-0.000601866315747324
28	0.59	0.5904785708794	-0.000478570879400175
29	0.59	0.590380533152658	-0.000380533152657847
30	0.59	0.590302578962709	-0.000302578962709132
31	0.59	0.590240594092879	-0.000240594092879132
32	0.59	0.590191307145117	-0.000191307145116948
33	0.59	0.590152116884229	-0.000152116884229447
34	0.59	0.590120954951544	-0.000120954951544183
35	0.59	0.59009617670239	-9.61767023902604e-05
36	0.59	0.590076474406087	-7.6474406087268e-05
37	0.61	0.590060808227367	0.0199391917726326
38	0.61	0.614145455076166	-0.00414545507616615
39	0.61	0.613296237103503	-0.00329623710350291
40	0.61	0.61262098583699	-0.00262098583698989
41	0.61	0.612084063294598	-0.00208406329459776
42	0.61	0.611657132119751	-0.00165713211975138
43	0.61	0.611317660010341	-0.00131766001034139
44	0.61	0.611047730523209	-0.00104773052320861
45	0.61	0.610833097491498	-0.000833097491498291
46	0.61	0.610662433149523	-0.000662433149523189
47	0.61	0.610526730283149	-0.000526730283148646
48	0.61	0.610418826852771	-0.000418826852770726
49	0.65	0.610333027999744	0.0396669720002556
50	0.65	0.658459012945865	-0.00845901294586537
51	0.65	0.656726140271422	-0.00672614027142227
52	0.65	0.655348255551844	-0.00534825555184437
53	0.65	0.654252637663441	-0.00425263766344053
54	0.65	0.653381462781874	-0.00338146278187401
55	0.65	0.652688752593126	-0.00268875259312551
56	0.65	0.652137947679268	-0.00213794767926823
57	0.65	0.651699978008752	-0.00169997800875199
58	0.65	0.651351728696761	-0.00135172869676103
59	0.65	0.651074820062519	-0.00107482006251869
60	0.65	0.650854637598181	-0.000854637598181385
61	0.67	0.650679560653635	0.0193204393463651
62	0.67	0.674637452858767	-0.00463745285876715
63	0.67	0.673687446588603	-0.00368744658860254
64	0.67	0.672932054030068	-0.00293205403006747
65	0.67	0.672331407554975	-0.00233140755497507
66	0.67	0.671853806625545	-0.00185380662554502
67	0.67	0.671474044723575	-0.00147404472357526
68	0.67	0.671172079016851	-0.00117207901685068
69	0.67	0.670931972551287	-0.000931972551287075
70	0.67	0.670741053140501	-0.000741053140500991
71	0.67	0.670589244561214	-0.000589244561213675
72	0.67	0.670468534756745	-0.000468534756745242

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.54 & 0.56 & -0.02 \tabularnewline
4 & 0.54 & 0.555902896270445 & -0.0159028962704446 \tabularnewline
5 & 0.54 & 0.552645105489426 & -0.012645105489426 \tabularnewline
6 & 0.54 & 0.550054690046359 & -0.0100546900463585 \tabularnewline
7 & 0.54 & 0.547994934641936 & -0.00799493464193557 \tabularnewline
8 & 0.54 & 0.546357130814984 & -0.00635713081498424 \tabularnewline
9 & 0.54 & 0.545054839596417 & -0.00505483959641706 \tabularnewline
10 & 0.54 & 0.544019329488278 & -0.00401932948827777 \tabularnewline
11 & 0.54 & 0.543195948996441 & -0.00319594899644104 \tabularnewline
12 & 0.54 & 0.542541242268802 & -0.0025412422688017 \tabularnewline
13 & 0.59 & 0.542020655609941 & 0.0479793443900588 \tabularnewline
14 & 0.59 & 0.601849473152048 & -0.0118494731520479 \tabularnewline
15 & 0.59 & 0.599422047119822 & -0.00942204711982175 \tabularnewline
16 & 0.59 & 0.597491891900088 & -0.00749189190008825 \tabularnewline
17 & 0.59 & 0.595957138987824 & -0.00595713898782435 \tabularnewline
18 & 0.59 & 0.5947367881696 & -0.00473678816959966 \tabularnewline
19 & 0.59 & 0.593766432545811 & -0.00376643254581055 \tabularnewline
20 & 0.59 & 0.592994859304283 & -0.00299485930428256 \tabularnewline
21 & 0.59 & 0.592381346843029 & -0.00238134684302904 \tabularnewline
22 & 0.59 & 0.591893515591432 & -0.00189351559143214 \tabularnewline
23 & 0.59 & 0.591505619101851 & -0.00150561910185076 \tabularnewline
24 & 0.59 & 0.591197185219977 & -0.00119718521997658 \tabularnewline
25 & 0.59 & 0.59095193561849 & -0.00095193561848983 \tabularnewline
26 & 0.59 & 0.590756926669849 & -0.000756926669849278 \tabularnewline
27 & 0.59 & 0.590601866315747 & -0.000601866315747324 \tabularnewline
28 & 0.59 & 0.5904785708794 & -0.000478570879400175 \tabularnewline
29 & 0.59 & 0.590380533152658 & -0.000380533152657847 \tabularnewline
30 & 0.59 & 0.590302578962709 & -0.000302578962709132 \tabularnewline
31 & 0.59 & 0.590240594092879 & -0.000240594092879132 \tabularnewline
32 & 0.59 & 0.590191307145117 & -0.000191307145116948 \tabularnewline
33 & 0.59 & 0.590152116884229 & -0.000152116884229447 \tabularnewline
34 & 0.59 & 0.590120954951544 & -0.000120954951544183 \tabularnewline
35 & 0.59 & 0.59009617670239 & -9.61767023902604e-05 \tabularnewline
36 & 0.59 & 0.590076474406087 & -7.6474406087268e-05 \tabularnewline
37 & 0.61 & 0.590060808227367 & 0.0199391917726326 \tabularnewline
38 & 0.61 & 0.614145455076166 & -0.00414545507616615 \tabularnewline
39 & 0.61 & 0.613296237103503 & -0.00329623710350291 \tabularnewline
40 & 0.61 & 0.61262098583699 & -0.00262098583698989 \tabularnewline
41 & 0.61 & 0.612084063294598 & -0.00208406329459776 \tabularnewline
42 & 0.61 & 0.611657132119751 & -0.00165713211975138 \tabularnewline
43 & 0.61 & 0.611317660010341 & -0.00131766001034139 \tabularnewline
44 & 0.61 & 0.611047730523209 & -0.00104773052320861 \tabularnewline
45 & 0.61 & 0.610833097491498 & -0.000833097491498291 \tabularnewline
46 & 0.61 & 0.610662433149523 & -0.000662433149523189 \tabularnewline
47 & 0.61 & 0.610526730283149 & -0.000526730283148646 \tabularnewline
48 & 0.61 & 0.610418826852771 & -0.000418826852770726 \tabularnewline
49 & 0.65 & 0.610333027999744 & 0.0396669720002556 \tabularnewline
50 & 0.65 & 0.658459012945865 & -0.00845901294586537 \tabularnewline
51 & 0.65 & 0.656726140271422 & -0.00672614027142227 \tabularnewline
52 & 0.65 & 0.655348255551844 & -0.00534825555184437 \tabularnewline
53 & 0.65 & 0.654252637663441 & -0.00425263766344053 \tabularnewline
54 & 0.65 & 0.653381462781874 & -0.00338146278187401 \tabularnewline
55 & 0.65 & 0.652688752593126 & -0.00268875259312551 \tabularnewline
56 & 0.65 & 0.652137947679268 & -0.00213794767926823 \tabularnewline
57 & 0.65 & 0.651699978008752 & -0.00169997800875199 \tabularnewline
58 & 0.65 & 0.651351728696761 & -0.00135172869676103 \tabularnewline
59 & 0.65 & 0.651074820062519 & -0.00107482006251869 \tabularnewline
60 & 0.65 & 0.650854637598181 & -0.000854637598181385 \tabularnewline
61 & 0.67 & 0.650679560653635 & 0.0193204393463651 \tabularnewline
62 & 0.67 & 0.674637452858767 & -0.00463745285876715 \tabularnewline
63 & 0.67 & 0.673687446588603 & -0.00368744658860254 \tabularnewline
64 & 0.67 & 0.672932054030068 & -0.00293205403006747 \tabularnewline
65 & 0.67 & 0.672331407554975 & -0.00233140755497507 \tabularnewline
66 & 0.67 & 0.671853806625545 & -0.00185380662554502 \tabularnewline
67 & 0.67 & 0.671474044723575 & -0.00147404472357526 \tabularnewline
68 & 0.67 & 0.671172079016851 & -0.00117207901685068 \tabularnewline
69 & 0.67 & 0.670931972551287 & -0.000931972551287075 \tabularnewline
70 & 0.67 & 0.670741053140501 & -0.000741053140500991 \tabularnewline
71 & 0.67 & 0.670589244561214 & -0.000589244561213675 \tabularnewline
72 & 0.67 & 0.670468534756745 & -0.000468534756745242 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271268&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]0.54[/C][C]0.56[/C][C]-0.02[/C][/ROW]
[ROW][C]4[/C][C]0.54[/C][C]0.555902896270445[/C][C]-0.0159028962704446[/C][/ROW]
[ROW][C]5[/C][C]0.54[/C][C]0.552645105489426[/C][C]-0.012645105489426[/C][/ROW]
[ROW][C]6[/C][C]0.54[/C][C]0.550054690046359[/C][C]-0.0100546900463585[/C][/ROW]
[ROW][C]7[/C][C]0.54[/C][C]0.547994934641936[/C][C]-0.00799493464193557[/C][/ROW]
[ROW][C]8[/C][C]0.54[/C][C]0.546357130814984[/C][C]-0.00635713081498424[/C][/ROW]
[ROW][C]9[/C][C]0.54[/C][C]0.545054839596417[/C][C]-0.00505483959641706[/C][/ROW]
[ROW][C]10[/C][C]0.54[/C][C]0.544019329488278[/C][C]-0.00401932948827777[/C][/ROW]
[ROW][C]11[/C][C]0.54[/C][C]0.543195948996441[/C][C]-0.00319594899644104[/C][/ROW]
[ROW][C]12[/C][C]0.54[/C][C]0.542541242268802[/C][C]-0.0025412422688017[/C][/ROW]
[ROW][C]13[/C][C]0.59[/C][C]0.542020655609941[/C][C]0.0479793443900588[/C][/ROW]
[ROW][C]14[/C][C]0.59[/C][C]0.601849473152048[/C][C]-0.0118494731520479[/C][/ROW]
[ROW][C]15[/C][C]0.59[/C][C]0.599422047119822[/C][C]-0.00942204711982175[/C][/ROW]
[ROW][C]16[/C][C]0.59[/C][C]0.597491891900088[/C][C]-0.00749189190008825[/C][/ROW]
[ROW][C]17[/C][C]0.59[/C][C]0.595957138987824[/C][C]-0.00595713898782435[/C][/ROW]
[ROW][C]18[/C][C]0.59[/C][C]0.5947367881696[/C][C]-0.00473678816959966[/C][/ROW]
[ROW][C]19[/C][C]0.59[/C][C]0.593766432545811[/C][C]-0.00376643254581055[/C][/ROW]
[ROW][C]20[/C][C]0.59[/C][C]0.592994859304283[/C][C]-0.00299485930428256[/C][/ROW]
[ROW][C]21[/C][C]0.59[/C][C]0.592381346843029[/C][C]-0.00238134684302904[/C][/ROW]
[ROW][C]22[/C][C]0.59[/C][C]0.591893515591432[/C][C]-0.00189351559143214[/C][/ROW]
[ROW][C]23[/C][C]0.59[/C][C]0.591505619101851[/C][C]-0.00150561910185076[/C][/ROW]
[ROW][C]24[/C][C]0.59[/C][C]0.591197185219977[/C][C]-0.00119718521997658[/C][/ROW]
[ROW][C]25[/C][C]0.59[/C][C]0.59095193561849[/C][C]-0.00095193561848983[/C][/ROW]
[ROW][C]26[/C][C]0.59[/C][C]0.590756926669849[/C][C]-0.000756926669849278[/C][/ROW]
[ROW][C]27[/C][C]0.59[/C][C]0.590601866315747[/C][C]-0.000601866315747324[/C][/ROW]
[ROW][C]28[/C][C]0.59[/C][C]0.5904785708794[/C][C]-0.000478570879400175[/C][/ROW]
[ROW][C]29[/C][C]0.59[/C][C]0.590380533152658[/C][C]-0.000380533152657847[/C][/ROW]
[ROW][C]30[/C][C]0.59[/C][C]0.590302578962709[/C][C]-0.000302578962709132[/C][/ROW]
[ROW][C]31[/C][C]0.59[/C][C]0.590240594092879[/C][C]-0.000240594092879132[/C][/ROW]
[ROW][C]32[/C][C]0.59[/C][C]0.590191307145117[/C][C]-0.000191307145116948[/C][/ROW]
[ROW][C]33[/C][C]0.59[/C][C]0.590152116884229[/C][C]-0.000152116884229447[/C][/ROW]
[ROW][C]34[/C][C]0.59[/C][C]0.590120954951544[/C][C]-0.000120954951544183[/C][/ROW]
[ROW][C]35[/C][C]0.59[/C][C]0.59009617670239[/C][C]-9.61767023902604e-05[/C][/ROW]
[ROW][C]36[/C][C]0.59[/C][C]0.590076474406087[/C][C]-7.6474406087268e-05[/C][/ROW]
[ROW][C]37[/C][C]0.61[/C][C]0.590060808227367[/C][C]0.0199391917726326[/C][/ROW]
[ROW][C]38[/C][C]0.61[/C][C]0.614145455076166[/C][C]-0.00414545507616615[/C][/ROW]
[ROW][C]39[/C][C]0.61[/C][C]0.613296237103503[/C][C]-0.00329623710350291[/C][/ROW]
[ROW][C]40[/C][C]0.61[/C][C]0.61262098583699[/C][C]-0.00262098583698989[/C][/ROW]
[ROW][C]41[/C][C]0.61[/C][C]0.612084063294598[/C][C]-0.00208406329459776[/C][/ROW]
[ROW][C]42[/C][C]0.61[/C][C]0.611657132119751[/C][C]-0.00165713211975138[/C][/ROW]
[ROW][C]43[/C][C]0.61[/C][C]0.611317660010341[/C][C]-0.00131766001034139[/C][/ROW]
[ROW][C]44[/C][C]0.61[/C][C]0.611047730523209[/C][C]-0.00104773052320861[/C][/ROW]
[ROW][C]45[/C][C]0.61[/C][C]0.610833097491498[/C][C]-0.000833097491498291[/C][/ROW]
[ROW][C]46[/C][C]0.61[/C][C]0.610662433149523[/C][C]-0.000662433149523189[/C][/ROW]
[ROW][C]47[/C][C]0.61[/C][C]0.610526730283149[/C][C]-0.000526730283148646[/C][/ROW]
[ROW][C]48[/C][C]0.61[/C][C]0.610418826852771[/C][C]-0.000418826852770726[/C][/ROW]
[ROW][C]49[/C][C]0.65[/C][C]0.610333027999744[/C][C]0.0396669720002556[/C][/ROW]
[ROW][C]50[/C][C]0.65[/C][C]0.658459012945865[/C][C]-0.00845901294586537[/C][/ROW]
[ROW][C]51[/C][C]0.65[/C][C]0.656726140271422[/C][C]-0.00672614027142227[/C][/ROW]
[ROW][C]52[/C][C]0.65[/C][C]0.655348255551844[/C][C]-0.00534825555184437[/C][/ROW]
[ROW][C]53[/C][C]0.65[/C][C]0.654252637663441[/C][C]-0.00425263766344053[/C][/ROW]
[ROW][C]54[/C][C]0.65[/C][C]0.653381462781874[/C][C]-0.00338146278187401[/C][/ROW]
[ROW][C]55[/C][C]0.65[/C][C]0.652688752593126[/C][C]-0.00268875259312551[/C][/ROW]
[ROW][C]56[/C][C]0.65[/C][C]0.652137947679268[/C][C]-0.00213794767926823[/C][/ROW]
[ROW][C]57[/C][C]0.65[/C][C]0.651699978008752[/C][C]-0.00169997800875199[/C][/ROW]
[ROW][C]58[/C][C]0.65[/C][C]0.651351728696761[/C][C]-0.00135172869676103[/C][/ROW]
[ROW][C]59[/C][C]0.65[/C][C]0.651074820062519[/C][C]-0.00107482006251869[/C][/ROW]
[ROW][C]60[/C][C]0.65[/C][C]0.650854637598181[/C][C]-0.000854637598181385[/C][/ROW]
[ROW][C]61[/C][C]0.67[/C][C]0.650679560653635[/C][C]0.0193204393463651[/C][/ROW]
[ROW][C]62[/C][C]0.67[/C][C]0.674637452858767[/C][C]-0.00463745285876715[/C][/ROW]
[ROW][C]63[/C][C]0.67[/C][C]0.673687446588603[/C][C]-0.00368744658860254[/C][/ROW]
[ROW][C]64[/C][C]0.67[/C][C]0.672932054030068[/C][C]-0.00293205403006747[/C][/ROW]
[ROW][C]65[/C][C]0.67[/C][C]0.672331407554975[/C][C]-0.00233140755497507[/C][/ROW]
[ROW][C]66[/C][C]0.67[/C][C]0.671853806625545[/C][C]-0.00185380662554502[/C][/ROW]
[ROW][C]67[/C][C]0.67[/C][C]0.671474044723575[/C][C]-0.00147404472357526[/C][/ROW]
[ROW][C]68[/C][C]0.67[/C][C]0.671172079016851[/C][C]-0.00117207901685068[/C][/ROW]
[ROW][C]69[/C][C]0.67[/C][C]0.670931972551287[/C][C]-0.000931972551287075[/C][/ROW]
[ROW][C]70[/C][C]0.67[/C][C]0.670741053140501[/C][C]-0.000741053140500991[/C][/ROW]
[ROW][C]71[/C][C]0.67[/C][C]0.670589244561214[/C][C]-0.000589244561213675[/C][/ROW]
[ROW][C]72[/C][C]0.67[/C][C]0.670468534756745[/C][C]-0.000468534756745242[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271268&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271268&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	0.54	0.56	-0.02
4	0.54	0.555902896270445	-0.0159028962704446
5	0.54	0.552645105489426	-0.012645105489426
6	0.54	0.550054690046359	-0.0100546900463585
7	0.54	0.547994934641936	-0.00799493464193557
8	0.54	0.546357130814984	-0.00635713081498424
9	0.54	0.545054839596417	-0.00505483959641706
10	0.54	0.544019329488278	-0.00401932948827777
11	0.54	0.543195948996441	-0.00319594899644104
12	0.54	0.542541242268802	-0.0025412422688017
13	0.59	0.542020655609941	0.0479793443900588
14	0.59	0.601849473152048	-0.0118494731520479
15	0.59	0.599422047119822	-0.00942204711982175
16	0.59	0.597491891900088	-0.00749189190008825
17	0.59	0.595957138987824	-0.00595713898782435
18	0.59	0.5947367881696	-0.00473678816959966
19	0.59	0.593766432545811	-0.00376643254581055
20	0.59	0.592994859304283	-0.00299485930428256
21	0.59	0.592381346843029	-0.00238134684302904
22	0.59	0.591893515591432	-0.00189351559143214
23	0.59	0.591505619101851	-0.00150561910185076
24	0.59	0.591197185219977	-0.00119718521997658
25	0.59	0.59095193561849	-0.00095193561848983
26	0.59	0.590756926669849	-0.000756926669849278
27	0.59	0.590601866315747	-0.000601866315747324
28	0.59	0.5904785708794	-0.000478570879400175
29	0.59	0.590380533152658	-0.000380533152657847
30	0.59	0.590302578962709	-0.000302578962709132
31	0.59	0.590240594092879	-0.000240594092879132
32	0.59	0.590191307145117	-0.000191307145116948
33	0.59	0.590152116884229	-0.000152116884229447
34	0.59	0.590120954951544	-0.000120954951544183
35	0.59	0.59009617670239	-9.61767023902604e-05
36	0.59	0.590076474406087	-7.6474406087268e-05
37	0.61	0.590060808227367	0.0199391917726326
38	0.61	0.614145455076166	-0.00414545507616615
39	0.61	0.613296237103503	-0.00329623710350291
40	0.61	0.61262098583699	-0.00262098583698989
41	0.61	0.612084063294598	-0.00208406329459776
42	0.61	0.611657132119751	-0.00165713211975138
43	0.61	0.611317660010341	-0.00131766001034139
44	0.61	0.611047730523209	-0.00104773052320861
45	0.61	0.610833097491498	-0.000833097491498291
46	0.61	0.610662433149523	-0.000662433149523189
47	0.61	0.610526730283149	-0.000526730283148646
48	0.61	0.610418826852771	-0.000418826852770726
49	0.65	0.610333027999744	0.0396669720002556
50	0.65	0.658459012945865	-0.00845901294586537
51	0.65	0.656726140271422	-0.00672614027142227
52	0.65	0.655348255551844	-0.00534825555184437
53	0.65	0.654252637663441	-0.00425263766344053
54	0.65	0.653381462781874	-0.00338146278187401
55	0.65	0.652688752593126	-0.00268875259312551
56	0.65	0.652137947679268	-0.00213794767926823
57	0.65	0.651699978008752	-0.00169997800875199
58	0.65	0.651351728696761	-0.00135172869676103
59	0.65	0.651074820062519	-0.00107482006251869
60	0.65	0.650854637598181	-0.000854637598181385
61	0.67	0.650679560653635	0.0193204393463651
62	0.67	0.674637452858767	-0.00463745285876715
63	0.67	0.673687446588603	-0.00368744658860254
64	0.67	0.672932054030068	-0.00293205403006747
65	0.67	0.672331407554975	-0.00233140755497507
66	0.67	0.671853806625545	-0.00185380662554502
67	0.67	0.671474044723575	-0.00147404472357526
68	0.67	0.671172079016851	-0.00117207901685068
69	0.67	0.670931972551287	-0.000931972551287075
70	0.67	0.670741053140501	-0.000741053140500991
71	0.67	0.670589244561214	-0.000589244561213675
72	0.67	0.670468534756745	-0.000468534756745242

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.670372552981781	0.651686913854262	0.6890581921093
74	0.670745105963562	0.641487452157118	0.700002759770006
75	0.671117658945343	0.631749188533694	0.710486129356991
76	0.671490211927124	0.621891255778022	0.721089168076225
77	0.671862764908905	0.611730783863609	0.7319947459542
78	0.672235317890685	0.601196051177141	0.74327458460423
79	0.672607870872466	0.590257836652858	0.754957905092075
80	0.672980423854247	0.57890592051067	0.767054927197824
81	0.673352976836028	0.567139350507296	0.77956660316476
82	0.673725529817809	0.554961900182141	0.792489159453477
83	0.67409808279959	0.542379773628283	0.805816391970897
84	0.674470635781371	0.529400380282111	0.81954089128063

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.670372552981781 & 0.651686913854262 & 0.6890581921093 \tabularnewline
74 & 0.670745105963562 & 0.641487452157118 & 0.700002759770006 \tabularnewline
75 & 0.671117658945343 & 0.631749188533694 & 0.710486129356991 \tabularnewline
76 & 0.671490211927124 & 0.621891255778022 & 0.721089168076225 \tabularnewline
77 & 0.671862764908905 & 0.611730783863609 & 0.7319947459542 \tabularnewline
78 & 0.672235317890685 & 0.601196051177141 & 0.74327458460423 \tabularnewline
79 & 0.672607870872466 & 0.590257836652858 & 0.754957905092075 \tabularnewline
80 & 0.672980423854247 & 0.57890592051067 & 0.767054927197824 \tabularnewline
81 & 0.673352976836028 & 0.567139350507296 & 0.77956660316476 \tabularnewline
82 & 0.673725529817809 & 0.554961900182141 & 0.792489159453477 \tabularnewline
83 & 0.67409808279959 & 0.542379773628283 & 0.805816391970897 \tabularnewline
84 & 0.674470635781371 & 0.529400380282111 & 0.81954089128063 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271268&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]0.670372552981781[/C][C]0.651686913854262[/C][C]0.6890581921093[/C][/ROW]
[ROW][C]74[/C][C]0.670745105963562[/C][C]0.641487452157118[/C][C]0.700002759770006[/C][/ROW]
[ROW][C]75[/C][C]0.671117658945343[/C][C]0.631749188533694[/C][C]0.710486129356991[/C][/ROW]
[ROW][C]76[/C][C]0.671490211927124[/C][C]0.621891255778022[/C][C]0.721089168076225[/C][/ROW]
[ROW][C]77[/C][C]0.671862764908905[/C][C]0.611730783863609[/C][C]0.7319947459542[/C][/ROW]
[ROW][C]78[/C][C]0.672235317890685[/C][C]0.601196051177141[/C][C]0.74327458460423[/C][/ROW]
[ROW][C]79[/C][C]0.672607870872466[/C][C]0.590257836652858[/C][C]0.754957905092075[/C][/ROW]
[ROW][C]80[/C][C]0.672980423854247[/C][C]0.57890592051067[/C][C]0.767054927197824[/C][/ROW]
[ROW][C]81[/C][C]0.673352976836028[/C][C]0.567139350507296[/C][C]0.77956660316476[/C][/ROW]
[ROW][C]82[/C][C]0.673725529817809[/C][C]0.554961900182141[/C][C]0.792489159453477[/C][/ROW]
[ROW][C]83[/C][C]0.67409808279959[/C][C]0.542379773628283[/C][C]0.805816391970897[/C][/ROW]
[ROW][C]84[/C][C]0.674470635781371[/C][C]0.529400380282111[/C][C]0.81954089128063[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271268&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271268&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	0.670372552981781	0.651686913854262	0.6890581921093
74	0.670745105963562	0.641487452157118	0.700002759770006
75	0.671117658945343	0.631749188533694	0.710486129356991
76	0.671490211927124	0.621891255778022	0.721089168076225
77	0.671862764908905	0.611730783863609	0.7319947459542
78	0.672235317890685	0.601196051177141	0.74327458460423
79	0.672607870872466	0.590257836652858	0.754957905092075
80	0.672980423854247	0.57890592051067	0.767054927197824
81	0.673352976836028	0.567139350507296	0.77956660316476
82	0.673725529817809	0.554961900182141	0.792489159453477
83	0.67409808279959	0.542379773628283	0.805816391970897
84	0.674470635781371	0.529400380282111	0.81954089128063

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