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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 04 Dec 2009 11:03:43 -0700

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/2009/Dec/04/t1259949877393hfhhx3wnudvj.htm/, Retrieved Sun, 28 Apr 2024 15:09:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63992, Retrieved Sun, 28 Apr 2024 15:09:22 +0000

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User-defined keywords

Estimated Impact

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [] [2009-12-04 18:03:43] [0545e25c765ce26b196961216dc11e13] [Current]

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Dataseries X:

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Histogram

Boxplots

1,4
1,2
1
1,7
2,4
2
2,1
2
1,8
2,7
2,3
1,9
2
2,3
2,8
2,4
2,3
2,7
2,7
2,9
3
2,2
2,3
2,8
2,8
2,8
2,2
2,6
2,8
2,5
2,4
2,3
1,9
1,7
2
2,1
1,7
1,8
1,8
1,8
1,3
1,3
1,3
1,2
1,4
2,2
2,9
3,1
3,5
3,6
4,4
4,1
5,1
5,8
5,9
5,4
5,5
4,8
3,2
2,7

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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63992&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63992&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63992&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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.83662597434103
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.83662597434103 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63992&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]0.83662597434103[/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=63992&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63992&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	0.83662597434103
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	2	1.70232491037523	0.297675089624768
14	2.3	2.23686640268501	0.0631335973149865
15	2.8	2.7491238604665	0.0508761395334987
16	2.4	2.41659124317405	-0.0165912431740511
17	2.3	2.37223843724851	-0.0722384372485143
18	2.7	2.73103950620319	-0.0310395062031872
19	2.7	2.82295149719121	-0.122951497191213
20	2.9	2.55182330868504	0.348176691314956
21	3	2.45709285416430	0.542907145835697
22	2.2	4.2256732282077	-2.02567322820770
23	2.3	2.18720589040239	0.112794109597607
24	2.8	1.90912398194133	0.890876018058667
25	2.8	2.84410496376943	-0.0441049637694317
26	2.8	3.13266827637733	-0.332668276377328
27	2.2	3.4070774219412	-1.20707742194120
28	2.6	2.07407062628186	0.525929373718139
29	2.8	2.46993914146424	0.330060858535761
30	2.5	3.24338176325385	-0.743381763253854
31	2.4	2.72229363595367	-0.322293635953673
32	2.3	2.36951056594137	-0.0695105659413673
33	1.9	2.02765849303223	-0.127658493032229
34	1.7	2.37245071415674	-0.672450714156736
35	2	1.82378794550119	0.176212054498808
36	2.1	1.73276166901427	0.367238330985731
37	1.7	2.07974523935379	-0.379745239353789
38	1.8	1.95290492841483	-0.152904928414835
39	1.8	2.05760562817595	-0.257605628175954
40	1.8	1.80471362847849	-0.00471362847849477
41	1.3	1.75991270057602	-0.45991270057602
42	1.3	1.54717044569962	-0.247170445699625
43	1.3	1.45490996364744	-0.154909963647439
44	1.2	1.32675459201488	-0.126754592014876
45	1.4	1.08653358163036	0.313466418369639
46	2.2	1.59754817254623	0.602451827453774
47	2.9	2.27412525993367	0.62587474006633
48	3.1	2.47557148397502	0.62442851602498
49	3.5	2.84488006942854	0.655119930571456
50	3.6	3.79389676589506	-0.193896765895060
51	4.4	4.00053141843505	0.399468581564948
52	4.1	4.26881251901869	-0.168812519018687
53	5.1	3.75298431879364	1.34701568120636
54	5.8	5.48543602683377	0.314563973166227
55	5.9	6.11769357806188	-0.217693578061883
56	5.4	5.76151131186642	-0.361511311866418
57	5.5	4.95742305463946	0.542576945360539
58	4.8	6.30278933425556	-1.50278933425556
59	3.2	5.33004462506922	-2.13004462506922
60	2.7	3.12041799431657	-0.420417994316566

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2 & 1.70232491037523 & 0.297675089624768 \tabularnewline
14 & 2.3 & 2.23686640268501 & 0.0631335973149865 \tabularnewline
15 & 2.8 & 2.7491238604665 & 0.0508761395334987 \tabularnewline
16 & 2.4 & 2.41659124317405 & -0.0165912431740511 \tabularnewline
17 & 2.3 & 2.37223843724851 & -0.0722384372485143 \tabularnewline
18 & 2.7 & 2.73103950620319 & -0.0310395062031872 \tabularnewline
19 & 2.7 & 2.82295149719121 & -0.122951497191213 \tabularnewline
20 & 2.9 & 2.55182330868504 & 0.348176691314956 \tabularnewline
21 & 3 & 2.45709285416430 & 0.542907145835697 \tabularnewline
22 & 2.2 & 4.2256732282077 & -2.02567322820770 \tabularnewline
23 & 2.3 & 2.18720589040239 & 0.112794109597607 \tabularnewline
24 & 2.8 & 1.90912398194133 & 0.890876018058667 \tabularnewline
25 & 2.8 & 2.84410496376943 & -0.0441049637694317 \tabularnewline
26 & 2.8 & 3.13266827637733 & -0.332668276377328 \tabularnewline
27 & 2.2 & 3.4070774219412 & -1.20707742194120 \tabularnewline
28 & 2.6 & 2.07407062628186 & 0.525929373718139 \tabularnewline
29 & 2.8 & 2.46993914146424 & 0.330060858535761 \tabularnewline
30 & 2.5 & 3.24338176325385 & -0.743381763253854 \tabularnewline
31 & 2.4 & 2.72229363595367 & -0.322293635953673 \tabularnewline
32 & 2.3 & 2.36951056594137 & -0.0695105659413673 \tabularnewline
33 & 1.9 & 2.02765849303223 & -0.127658493032229 \tabularnewline
34 & 1.7 & 2.37245071415674 & -0.672450714156736 \tabularnewline
35 & 2 & 1.82378794550119 & 0.176212054498808 \tabularnewline
36 & 2.1 & 1.73276166901427 & 0.367238330985731 \tabularnewline
37 & 1.7 & 2.07974523935379 & -0.379745239353789 \tabularnewline
38 & 1.8 & 1.95290492841483 & -0.152904928414835 \tabularnewline
39 & 1.8 & 2.05760562817595 & -0.257605628175954 \tabularnewline
40 & 1.8 & 1.80471362847849 & -0.00471362847849477 \tabularnewline
41 & 1.3 & 1.75991270057602 & -0.45991270057602 \tabularnewline
42 & 1.3 & 1.54717044569962 & -0.247170445699625 \tabularnewline
43 & 1.3 & 1.45490996364744 & -0.154909963647439 \tabularnewline
44 & 1.2 & 1.32675459201488 & -0.126754592014876 \tabularnewline
45 & 1.4 & 1.08653358163036 & 0.313466418369639 \tabularnewline
46 & 2.2 & 1.59754817254623 & 0.602451827453774 \tabularnewline
47 & 2.9 & 2.27412525993367 & 0.62587474006633 \tabularnewline
48 & 3.1 & 2.47557148397502 & 0.62442851602498 \tabularnewline
49 & 3.5 & 2.84488006942854 & 0.655119930571456 \tabularnewline
50 & 3.6 & 3.79389676589506 & -0.193896765895060 \tabularnewline
51 & 4.4 & 4.00053141843505 & 0.399468581564948 \tabularnewline
52 & 4.1 & 4.26881251901869 & -0.168812519018687 \tabularnewline
53 & 5.1 & 3.75298431879364 & 1.34701568120636 \tabularnewline
54 & 5.8 & 5.48543602683377 & 0.314563973166227 \tabularnewline
55 & 5.9 & 6.11769357806188 & -0.217693578061883 \tabularnewline
56 & 5.4 & 5.76151131186642 & -0.361511311866418 \tabularnewline
57 & 5.5 & 4.95742305463946 & 0.542576945360539 \tabularnewline
58 & 4.8 & 6.30278933425556 & -1.50278933425556 \tabularnewline
59 & 3.2 & 5.33004462506922 & -2.13004462506922 \tabularnewline
60 & 2.7 & 3.12041799431657 & -0.420417994316566 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63992&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]2[/C][C]1.70232491037523[/C][C]0.297675089624768[/C][/ROW]
[ROW][C]14[/C][C]2.3[/C][C]2.23686640268501[/C][C]0.0631335973149865[/C][/ROW]
[ROW][C]15[/C][C]2.8[/C][C]2.7491238604665[/C][C]0.0508761395334987[/C][/ROW]
[ROW][C]16[/C][C]2.4[/C][C]2.41659124317405[/C][C]-0.0165912431740511[/C][/ROW]
[ROW][C]17[/C][C]2.3[/C][C]2.37223843724851[/C][C]-0.0722384372485143[/C][/ROW]
[ROW][C]18[/C][C]2.7[/C][C]2.73103950620319[/C][C]-0.0310395062031872[/C][/ROW]
[ROW][C]19[/C][C]2.7[/C][C]2.82295149719121[/C][C]-0.122951497191213[/C][/ROW]
[ROW][C]20[/C][C]2.9[/C][C]2.55182330868504[/C][C]0.348176691314956[/C][/ROW]
[ROW][C]21[/C][C]3[/C][C]2.45709285416430[/C][C]0.542907145835697[/C][/ROW]
[ROW][C]22[/C][C]2.2[/C][C]4.2256732282077[/C][C]-2.02567322820770[/C][/ROW]
[ROW][C]23[/C][C]2.3[/C][C]2.18720589040239[/C][C]0.112794109597607[/C][/ROW]
[ROW][C]24[/C][C]2.8[/C][C]1.90912398194133[/C][C]0.890876018058667[/C][/ROW]
[ROW][C]25[/C][C]2.8[/C][C]2.84410496376943[/C][C]-0.0441049637694317[/C][/ROW]
[ROW][C]26[/C][C]2.8[/C][C]3.13266827637733[/C][C]-0.332668276377328[/C][/ROW]
[ROW][C]27[/C][C]2.2[/C][C]3.4070774219412[/C][C]-1.20707742194120[/C][/ROW]
[ROW][C]28[/C][C]2.6[/C][C]2.07407062628186[/C][C]0.525929373718139[/C][/ROW]
[ROW][C]29[/C][C]2.8[/C][C]2.46993914146424[/C][C]0.330060858535761[/C][/ROW]
[ROW][C]30[/C][C]2.5[/C][C]3.24338176325385[/C][C]-0.743381763253854[/C][/ROW]
[ROW][C]31[/C][C]2.4[/C][C]2.72229363595367[/C][C]-0.322293635953673[/C][/ROW]
[ROW][C]32[/C][C]2.3[/C][C]2.36951056594137[/C][C]-0.0695105659413673[/C][/ROW]
[ROW][C]33[/C][C]1.9[/C][C]2.02765849303223[/C][C]-0.127658493032229[/C][/ROW]
[ROW][C]34[/C][C]1.7[/C][C]2.37245071415674[/C][C]-0.672450714156736[/C][/ROW]
[ROW][C]35[/C][C]2[/C][C]1.82378794550119[/C][C]0.176212054498808[/C][/ROW]
[ROW][C]36[/C][C]2.1[/C][C]1.73276166901427[/C][C]0.367238330985731[/C][/ROW]
[ROW][C]37[/C][C]1.7[/C][C]2.07974523935379[/C][C]-0.379745239353789[/C][/ROW]
[ROW][C]38[/C][C]1.8[/C][C]1.95290492841483[/C][C]-0.152904928414835[/C][/ROW]
[ROW][C]39[/C][C]1.8[/C][C]2.05760562817595[/C][C]-0.257605628175954[/C][/ROW]
[ROW][C]40[/C][C]1.8[/C][C]1.80471362847849[/C][C]-0.00471362847849477[/C][/ROW]
[ROW][C]41[/C][C]1.3[/C][C]1.75991270057602[/C][C]-0.45991270057602[/C][/ROW]
[ROW][C]42[/C][C]1.3[/C][C]1.54717044569962[/C][C]-0.247170445699625[/C][/ROW]
[ROW][C]43[/C][C]1.3[/C][C]1.45490996364744[/C][C]-0.154909963647439[/C][/ROW]
[ROW][C]44[/C][C]1.2[/C][C]1.32675459201488[/C][C]-0.126754592014876[/C][/ROW]
[ROW][C]45[/C][C]1.4[/C][C]1.08653358163036[/C][C]0.313466418369639[/C][/ROW]
[ROW][C]46[/C][C]2.2[/C][C]1.59754817254623[/C][C]0.602451827453774[/C][/ROW]
[ROW][C]47[/C][C]2.9[/C][C]2.27412525993367[/C][C]0.62587474006633[/C][/ROW]
[ROW][C]48[/C][C]3.1[/C][C]2.47557148397502[/C][C]0.62442851602498[/C][/ROW]
[ROW][C]49[/C][C]3.5[/C][C]2.84488006942854[/C][C]0.655119930571456[/C][/ROW]
[ROW][C]50[/C][C]3.6[/C][C]3.79389676589506[/C][C]-0.193896765895060[/C][/ROW]
[ROW][C]51[/C][C]4.4[/C][C]4.00053141843505[/C][C]0.399468581564948[/C][/ROW]
[ROW][C]52[/C][C]4.1[/C][C]4.26881251901869[/C][C]-0.168812519018687[/C][/ROW]
[ROW][C]53[/C][C]5.1[/C][C]3.75298431879364[/C][C]1.34701568120636[/C][/ROW]
[ROW][C]54[/C][C]5.8[/C][C]5.48543602683377[/C][C]0.314563973166227[/C][/ROW]
[ROW][C]55[/C][C]5.9[/C][C]6.11769357806188[/C][C]-0.217693578061883[/C][/ROW]
[ROW][C]56[/C][C]5.4[/C][C]5.76151131186642[/C][C]-0.361511311866418[/C][/ROW]
[ROW][C]57[/C][C]5.5[/C][C]4.95742305463946[/C][C]0.542576945360539[/C][/ROW]
[ROW][C]58[/C][C]4.8[/C][C]6.30278933425556[/C][C]-1.50278933425556[/C][/ROW]
[ROW][C]59[/C][C]3.2[/C][C]5.33004462506922[/C][C]-2.13004462506922[/C][/ROW]
[ROW][C]60[/C][C]2.7[/C][C]3.12041799431657[/C][C]-0.420417994316566[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63992&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63992&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	2	1.70232491037523	0.297675089624768
14	2.3	2.23686640268501	0.0631335973149865
15	2.8	2.7491238604665	0.0508761395334987
16	2.4	2.41659124317405	-0.0165912431740511
17	2.3	2.37223843724851	-0.0722384372485143
18	2.7	2.73103950620319	-0.0310395062031872
19	2.7	2.82295149719121	-0.122951497191213
20	2.9	2.55182330868504	0.348176691314956
21	3	2.45709285416430	0.542907145835697
22	2.2	4.2256732282077	-2.02567322820770
23	2.3	2.18720589040239	0.112794109597607
24	2.8	1.90912398194133	0.890876018058667
25	2.8	2.84410496376943	-0.0441049637694317
26	2.8	3.13266827637733	-0.332668276377328
27	2.2	3.4070774219412	-1.20707742194120
28	2.6	2.07407062628186	0.525929373718139
29	2.8	2.46993914146424	0.330060858535761
30	2.5	3.24338176325385	-0.743381763253854
31	2.4	2.72229363595367	-0.322293635953673
32	2.3	2.36951056594137	-0.0695105659413673
33	1.9	2.02765849303223	-0.127658493032229
34	1.7	2.37245071415674	-0.672450714156736
35	2	1.82378794550119	0.176212054498808
36	2.1	1.73276166901427	0.367238330985731
37	1.7	2.07974523935379	-0.379745239353789
38	1.8	1.95290492841483	-0.152904928414835
39	1.8	2.05760562817595	-0.257605628175954
40	1.8	1.80471362847849	-0.00471362847849477
41	1.3	1.75991270057602	-0.45991270057602
42	1.3	1.54717044569962	-0.247170445699625
43	1.3	1.45490996364744	-0.154909963647439
44	1.2	1.32675459201488	-0.126754592014876
45	1.4	1.08653358163036	0.313466418369639
46	2.2	1.59754817254623	0.602451827453774
47	2.9	2.27412525993367	0.62587474006633
48	3.1	2.47557148397502	0.62442851602498
49	3.5	2.84488006942854	0.655119930571456
50	3.6	3.79389676589506	-0.193896765895060
51	4.4	4.00053141843505	0.399468581564948
52	4.1	4.26881251901869	-0.168812519018687
53	5.1	3.75298431879364	1.34701568120636
54	5.8	5.48543602683377	0.314563973166227
55	5.9	6.11769357806188	-0.217693578061883
56	5.4	5.76151131186642	-0.361511311866418
57	5.5	4.95742305463946	0.542576945360539
58	4.8	6.30278933425556	-1.50278933425556
59	3.2	5.33004462506922	-2.13004462506922
60	2.7	3.12041799431657	-0.420417994316566

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	2.62604682917858	1.33954459577247	3.9125490625847
62	2.83427593187052	1.11464541097857	4.55390645276247
63	3.20892447903329	1.04094454475208	5.3769044133145
64	3.10684805552705	0.769832198229048	5.44386391282505
65	2.98430971978455	0.517888224088255	5.45073121548084
66	3.26094305278603	0.413772819594682	6.10811328597738
67	3.44350181674455	0.302389567315443	6.58461406617367
68	3.34863588555818	0.149546384376985	6.54772538673937
69	3.14337834327917	-0.0136688797499414	6.30042556630829
70	3.44986001815668	-0.115342532700712	7.01506256901407
71	3.47000455992472	-0.222852876854585	7.16286199670402
72	3.29557716932162	-18.9742467079709	25.5654010466141

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 2.62604682917858 & 1.33954459577247 & 3.9125490625847 \tabularnewline
62 & 2.83427593187052 & 1.11464541097857 & 4.55390645276247 \tabularnewline
63 & 3.20892447903329 & 1.04094454475208 & 5.3769044133145 \tabularnewline
64 & 3.10684805552705 & 0.769832198229048 & 5.44386391282505 \tabularnewline
65 & 2.98430971978455 & 0.517888224088255 & 5.45073121548084 \tabularnewline
66 & 3.26094305278603 & 0.413772819594682 & 6.10811328597738 \tabularnewline
67 & 3.44350181674455 & 0.302389567315443 & 6.58461406617367 \tabularnewline
68 & 3.34863588555818 & 0.149546384376985 & 6.54772538673937 \tabularnewline
69 & 3.14337834327917 & -0.0136688797499414 & 6.30042556630829 \tabularnewline
70 & 3.44986001815668 & -0.115342532700712 & 7.01506256901407 \tabularnewline
71 & 3.47000455992472 & -0.222852876854585 & 7.16286199670402 \tabularnewline
72 & 3.29557716932162 & -18.9742467079709 & 25.5654010466141 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63992&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]61[/C][C]2.62604682917858[/C][C]1.33954459577247[/C][C]3.9125490625847[/C][/ROW]
[ROW][C]62[/C][C]2.83427593187052[/C][C]1.11464541097857[/C][C]4.55390645276247[/C][/ROW]
[ROW][C]63[/C][C]3.20892447903329[/C][C]1.04094454475208[/C][C]5.3769044133145[/C][/ROW]
[ROW][C]64[/C][C]3.10684805552705[/C][C]0.769832198229048[/C][C]5.44386391282505[/C][/ROW]
[ROW][C]65[/C][C]2.98430971978455[/C][C]0.517888224088255[/C][C]5.45073121548084[/C][/ROW]
[ROW][C]66[/C][C]3.26094305278603[/C][C]0.413772819594682[/C][C]6.10811328597738[/C][/ROW]
[ROW][C]67[/C][C]3.44350181674455[/C][C]0.302389567315443[/C][C]6.58461406617367[/C][/ROW]
[ROW][C]68[/C][C]3.34863588555818[/C][C]0.149546384376985[/C][C]6.54772538673937[/C][/ROW]
[ROW][C]69[/C][C]3.14337834327917[/C][C]-0.0136688797499414[/C][C]6.30042556630829[/C][/ROW]
[ROW][C]70[/C][C]3.44986001815668[/C][C]-0.115342532700712[/C][C]7.01506256901407[/C][/ROW]
[ROW][C]71[/C][C]3.47000455992472[/C][C]-0.222852876854585[/C][C]7.16286199670402[/C][/ROW]
[ROW][C]72[/C][C]3.29557716932162[/C][C]-18.9742467079709[/C][C]25.5654010466141[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63992&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63992&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
61	2.62604682917858	1.33954459577247	3.9125490625847
62	2.83427593187052	1.11464541097857	4.55390645276247
63	3.20892447903329	1.04094454475208	5.3769044133145
64	3.10684805552705	0.769832198229048	5.44386391282505
65	2.98430971978455	0.517888224088255	5.45073121548084
66	3.26094305278603	0.413772819594682	6.10811328597738
67	3.44350181674455	0.302389567315443	6.58461406617367
68	3.34863588555818	0.149546384376985	6.54772538673937
69	3.14337834327917	-0.0136688797499414	6.30042556630829
70	3.44986001815668	-0.115342532700712	7.01506256901407
71	3.47000455992472	-0.222852876854585	7.16286199670402
72	3.29557716932162	-18.9742467079709	25.5654010466141

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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