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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 16 May 2012 04:22:57 -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/2012/May/16/t1337156626lsbz0n9uyywxpj7.htm/, Retrieved Wed, 01 May 2024 17:13:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166492, Retrieved Wed, 01 May 2024 17:13:18 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

143

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

-       [Exponential Smoothing] [opgave 10: expone...] [2012-05-16 08:22:57] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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Histogram

Boxplots

1,78
1,79
1,8
1,82
1,82
1,83
1,84
1,84
1,83
1,83
1,83
1,84
1,86
1,85
1,85
1,85
1,84
1,85
1,85
1,83
1,82
1,84
1,85
1,88
1,91
1,93
1,91
1,9
1,9
1,89
1,88
1,88
1,92
1,98
2
2
2,02
2,01
2,05
2,07
2,07
2,04
2,05
2,05
2,04
2,03
2,04
2,04
2,1
2,09
2,1
2,09
2,08
2,1
2,11
2,08
2,09
2,1
2,09
2,09

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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166492&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166492&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166492&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	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.013128910350907
gamma	0.132264992157619

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.013128910350907 \tabularnewline
gamma & 0.132264992157619 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166492&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]0.013128910350907[/C][/ROW]
[ROW][C]gamma[/C][C]0.132264992157619[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166492&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166492&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	0.013128910350907
gamma	0.132264992157619

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.86	1.84387452579659	0.01612547420341
14	1.85	1.85175781056145	-0.00175781056145463
15	1.85	1.8525724319186	-0.00257243191860335
16	1.85	1.85170174396538	-0.00170174396538458
17	1.84	1.84042145179196	-0.000421451791956295
18	1.85	1.84916479096343	0.00083520903656642
19	1.85	1.86354690221918	-0.0135469022191803
20	1.83	1.84561240529691	-0.0156124052969073
21	1.82	1.81680149812101	0.00319850187898796
22	1.84	1.81803291658777	0.0219670834122301
23	1.85	1.83953698925133	0.0104630107486674
24	1.88	1.86019162881295	0.0198083711870449
25	1.91	1.90119215815204	0.00880784184795891
26	1.93	1.90188158487584	0.0281184151241551
27	1.91	1.93339381168107	-0.0233938116810712
28	1.9	1.91221357079253	-0.0122135707925344
29	1.9	1.89048900406405	0.00951099593594629
30	1.89	1.90991316405091	-0.019913164050908
31	1.88	1.90403629303756	-0.0240362930375622
32	1.88	1.87561183101623	0.00438816898377259
33	1.92	1.86676033059646	0.0532396694035375
34	1.98	1.91886151033484	0.0611384896651574
35	2	1.98090098534542	0.0190990146545804
36	2	2.01251815522596	-0.0125181552259583
37	2.02	2.02364557265227	-0.0036455726522715
38	2.01	2.01235229026277	-0.00235229026276551
39	2.05	2.01409235817026	0.0359076418297408
40	2.07	2.05365448984151	0.0163455101584908
41	2.07	2.06126025642911	0.00873974357088558
42	2.04	2.08240759003134	-0.0424075900313361
43	2.05	2.05651382728705	-0.0065138272870473
44	2.05	2.04681076079705	0.003189239202948
45	2.04	2.03712543702834	0.00287456297166333
46	2.03	2.03969215067357	-0.00969215067356544
47	2.04	2.03096258796192	0.00903741203808472
48	2.04	2.05268639138257	-0.0126863913825694
49	2.1	2.06403661000116	0.035963389998841
50	2.09	2.09242317772259	-0.00242317772258893
51	2.1	2.09462883961116	0.00537116038884422
52	2.09	2.1037538696481	-0.0137538696481028
53	2.08	2.08084466536698	-0.000844665366980912
54	2.1	2.09202678354501	0.00797321645499238
55	2.11	2.11713975068791	-0.00713975068791273
56	2.08	2.10685198856327	-0.0268519885632679
57	2.09	2.06672721035049	0.0232727896495071
58	2.1	2.08970843878662	0.0102915612133834
59	2.09	2.10125224739732	-0.0112522473973233
60	2.09	2.10301712186213	-0.0130171218621267

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.86 & 1.84387452579659 & 0.01612547420341 \tabularnewline
14 & 1.85 & 1.85175781056145 & -0.00175781056145463 \tabularnewline
15 & 1.85 & 1.8525724319186 & -0.00257243191860335 \tabularnewline
16 & 1.85 & 1.85170174396538 & -0.00170174396538458 \tabularnewline
17 & 1.84 & 1.84042145179196 & -0.000421451791956295 \tabularnewline
18 & 1.85 & 1.84916479096343 & 0.00083520903656642 \tabularnewline
19 & 1.85 & 1.86354690221918 & -0.0135469022191803 \tabularnewline
20 & 1.83 & 1.84561240529691 & -0.0156124052969073 \tabularnewline
21 & 1.82 & 1.81680149812101 & 0.00319850187898796 \tabularnewline
22 & 1.84 & 1.81803291658777 & 0.0219670834122301 \tabularnewline
23 & 1.85 & 1.83953698925133 & 0.0104630107486674 \tabularnewline
24 & 1.88 & 1.86019162881295 & 0.0198083711870449 \tabularnewline
25 & 1.91 & 1.90119215815204 & 0.00880784184795891 \tabularnewline
26 & 1.93 & 1.90188158487584 & 0.0281184151241551 \tabularnewline
27 & 1.91 & 1.93339381168107 & -0.0233938116810712 \tabularnewline
28 & 1.9 & 1.91221357079253 & -0.0122135707925344 \tabularnewline
29 & 1.9 & 1.89048900406405 & 0.00951099593594629 \tabularnewline
30 & 1.89 & 1.90991316405091 & -0.019913164050908 \tabularnewline
31 & 1.88 & 1.90403629303756 & -0.0240362930375622 \tabularnewline
32 & 1.88 & 1.87561183101623 & 0.00438816898377259 \tabularnewline
33 & 1.92 & 1.86676033059646 & 0.0532396694035375 \tabularnewline
34 & 1.98 & 1.91886151033484 & 0.0611384896651574 \tabularnewline
35 & 2 & 1.98090098534542 & 0.0190990146545804 \tabularnewline
36 & 2 & 2.01251815522596 & -0.0125181552259583 \tabularnewline
37 & 2.02 & 2.02364557265227 & -0.0036455726522715 \tabularnewline
38 & 2.01 & 2.01235229026277 & -0.00235229026276551 \tabularnewline
39 & 2.05 & 2.01409235817026 & 0.0359076418297408 \tabularnewline
40 & 2.07 & 2.05365448984151 & 0.0163455101584908 \tabularnewline
41 & 2.07 & 2.06126025642911 & 0.00873974357088558 \tabularnewline
42 & 2.04 & 2.08240759003134 & -0.0424075900313361 \tabularnewline
43 & 2.05 & 2.05651382728705 & -0.0065138272870473 \tabularnewline
44 & 2.05 & 2.04681076079705 & 0.003189239202948 \tabularnewline
45 & 2.04 & 2.03712543702834 & 0.00287456297166333 \tabularnewline
46 & 2.03 & 2.03969215067357 & -0.00969215067356544 \tabularnewline
47 & 2.04 & 2.03096258796192 & 0.00903741203808472 \tabularnewline
48 & 2.04 & 2.05268639138257 & -0.0126863913825694 \tabularnewline
49 & 2.1 & 2.06403661000116 & 0.035963389998841 \tabularnewline
50 & 2.09 & 2.09242317772259 & -0.00242317772258893 \tabularnewline
51 & 2.1 & 2.09462883961116 & 0.00537116038884422 \tabularnewline
52 & 2.09 & 2.1037538696481 & -0.0137538696481028 \tabularnewline
53 & 2.08 & 2.08084466536698 & -0.000844665366980912 \tabularnewline
54 & 2.1 & 2.09202678354501 & 0.00797321645499238 \tabularnewline
55 & 2.11 & 2.11713975068791 & -0.00713975068791273 \tabularnewline
56 & 2.08 & 2.10685198856327 & -0.0268519885632679 \tabularnewline
57 & 2.09 & 2.06672721035049 & 0.0232727896495071 \tabularnewline
58 & 2.1 & 2.08970843878662 & 0.0102915612133834 \tabularnewline
59 & 2.09 & 2.10125224739732 & -0.0112522473973233 \tabularnewline
60 & 2.09 & 2.10301712186213 & -0.0130171218621267 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166492&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]1.86[/C][C]1.84387452579659[/C][C]0.01612547420341[/C][/ROW]
[ROW][C]14[/C][C]1.85[/C][C]1.85175781056145[/C][C]-0.00175781056145463[/C][/ROW]
[ROW][C]15[/C][C]1.85[/C][C]1.8525724319186[/C][C]-0.00257243191860335[/C][/ROW]
[ROW][C]16[/C][C]1.85[/C][C]1.85170174396538[/C][C]-0.00170174396538458[/C][/ROW]
[ROW][C]17[/C][C]1.84[/C][C]1.84042145179196[/C][C]-0.000421451791956295[/C][/ROW]
[ROW][C]18[/C][C]1.85[/C][C]1.84916479096343[/C][C]0.00083520903656642[/C][/ROW]
[ROW][C]19[/C][C]1.85[/C][C]1.86354690221918[/C][C]-0.0135469022191803[/C][/ROW]
[ROW][C]20[/C][C]1.83[/C][C]1.84561240529691[/C][C]-0.0156124052969073[/C][/ROW]
[ROW][C]21[/C][C]1.82[/C][C]1.81680149812101[/C][C]0.00319850187898796[/C][/ROW]
[ROW][C]22[/C][C]1.84[/C][C]1.81803291658777[/C][C]0.0219670834122301[/C][/ROW]
[ROW][C]23[/C][C]1.85[/C][C]1.83953698925133[/C][C]0.0104630107486674[/C][/ROW]
[ROW][C]24[/C][C]1.88[/C][C]1.86019162881295[/C][C]0.0198083711870449[/C][/ROW]
[ROW][C]25[/C][C]1.91[/C][C]1.90119215815204[/C][C]0.00880784184795891[/C][/ROW]
[ROW][C]26[/C][C]1.93[/C][C]1.90188158487584[/C][C]0.0281184151241551[/C][/ROW]
[ROW][C]27[/C][C]1.91[/C][C]1.93339381168107[/C][C]-0.0233938116810712[/C][/ROW]
[ROW][C]28[/C][C]1.9[/C][C]1.91221357079253[/C][C]-0.0122135707925344[/C][/ROW]
[ROW][C]29[/C][C]1.9[/C][C]1.89048900406405[/C][C]0.00951099593594629[/C][/ROW]
[ROW][C]30[/C][C]1.89[/C][C]1.90991316405091[/C][C]-0.019913164050908[/C][/ROW]
[ROW][C]31[/C][C]1.88[/C][C]1.90403629303756[/C][C]-0.0240362930375622[/C][/ROW]
[ROW][C]32[/C][C]1.88[/C][C]1.87561183101623[/C][C]0.00438816898377259[/C][/ROW]
[ROW][C]33[/C][C]1.92[/C][C]1.86676033059646[/C][C]0.0532396694035375[/C][/ROW]
[ROW][C]34[/C][C]1.98[/C][C]1.91886151033484[/C][C]0.0611384896651574[/C][/ROW]
[ROW][C]35[/C][C]2[/C][C]1.98090098534542[/C][C]0.0190990146545804[/C][/ROW]
[ROW][C]36[/C][C]2[/C][C]2.01251815522596[/C][C]-0.0125181552259583[/C][/ROW]
[ROW][C]37[/C][C]2.02[/C][C]2.02364557265227[/C][C]-0.0036455726522715[/C][/ROW]
[ROW][C]38[/C][C]2.01[/C][C]2.01235229026277[/C][C]-0.00235229026276551[/C][/ROW]
[ROW][C]39[/C][C]2.05[/C][C]2.01409235817026[/C][C]0.0359076418297408[/C][/ROW]
[ROW][C]40[/C][C]2.07[/C][C]2.05365448984151[/C][C]0.0163455101584908[/C][/ROW]
[ROW][C]41[/C][C]2.07[/C][C]2.06126025642911[/C][C]0.00873974357088558[/C][/ROW]
[ROW][C]42[/C][C]2.04[/C][C]2.08240759003134[/C][C]-0.0424075900313361[/C][/ROW]
[ROW][C]43[/C][C]2.05[/C][C]2.05651382728705[/C][C]-0.0065138272870473[/C][/ROW]
[ROW][C]44[/C][C]2.05[/C][C]2.04681076079705[/C][C]0.003189239202948[/C][/ROW]
[ROW][C]45[/C][C]2.04[/C][C]2.03712543702834[/C][C]0.00287456297166333[/C][/ROW]
[ROW][C]46[/C][C]2.03[/C][C]2.03969215067357[/C][C]-0.00969215067356544[/C][/ROW]
[ROW][C]47[/C][C]2.04[/C][C]2.03096258796192[/C][C]0.00903741203808472[/C][/ROW]
[ROW][C]48[/C][C]2.04[/C][C]2.05268639138257[/C][C]-0.0126863913825694[/C][/ROW]
[ROW][C]49[/C][C]2.1[/C][C]2.06403661000116[/C][C]0.035963389998841[/C][/ROW]
[ROW][C]50[/C][C]2.09[/C][C]2.09242317772259[/C][C]-0.00242317772258893[/C][/ROW]
[ROW][C]51[/C][C]2.1[/C][C]2.09462883961116[/C][C]0.00537116038884422[/C][/ROW]
[ROW][C]52[/C][C]2.09[/C][C]2.1037538696481[/C][C]-0.0137538696481028[/C][/ROW]
[ROW][C]53[/C][C]2.08[/C][C]2.08084466536698[/C][C]-0.000844665366980912[/C][/ROW]
[ROW][C]54[/C][C]2.1[/C][C]2.09202678354501[/C][C]0.00797321645499238[/C][/ROW]
[ROW][C]55[/C][C]2.11[/C][C]2.11713975068791[/C][C]-0.00713975068791273[/C][/ROW]
[ROW][C]56[/C][C]2.08[/C][C]2.10685198856327[/C][C]-0.0268519885632679[/C][/ROW]
[ROW][C]57[/C][C]2.09[/C][C]2.06672721035049[/C][C]0.0232727896495071[/C][/ROW]
[ROW][C]58[/C][C]2.1[/C][C]2.08970843878662[/C][C]0.0102915612133834[/C][/ROW]
[ROW][C]59[/C][C]2.09[/C][C]2.10125224739732[/C][C]-0.0112522473973233[/C][/ROW]
[ROW][C]60[/C][C]2.09[/C][C]2.10301712186213[/C][C]-0.0130171218621267[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166492&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166492&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	1.86	1.84387452579659	0.01612547420341
14	1.85	1.85175781056145	-0.00175781056145463
15	1.85	1.8525724319186	-0.00257243191860335
16	1.85	1.85170174396538	-0.00170174396538458
17	1.84	1.84042145179196	-0.000421451791956295
18	1.85	1.84916479096343	0.00083520903656642
19	1.85	1.86354690221918	-0.0135469022191803
20	1.83	1.84561240529691	-0.0156124052969073
21	1.82	1.81680149812101	0.00319850187898796
22	1.84	1.81803291658777	0.0219670834122301
23	1.85	1.83953698925133	0.0104630107486674
24	1.88	1.86019162881295	0.0198083711870449
25	1.91	1.90119215815204	0.00880784184795891
26	1.93	1.90188158487584	0.0281184151241551
27	1.91	1.93339381168107	-0.0233938116810712
28	1.9	1.91221357079253	-0.0122135707925344
29	1.9	1.89048900406405	0.00951099593594629
30	1.89	1.90991316405091	-0.019913164050908
31	1.88	1.90403629303756	-0.0240362930375622
32	1.88	1.87561183101623	0.00438816898377259
33	1.92	1.86676033059646	0.0532396694035375
34	1.98	1.91886151033484	0.0611384896651574
35	2	1.98090098534542	0.0190990146545804
36	2	2.01251815522596	-0.0125181552259583
37	2.02	2.02364557265227	-0.0036455726522715
38	2.01	2.01235229026277	-0.00235229026276551
39	2.05	2.01409235817026	0.0359076418297408
40	2.07	2.05365448984151	0.0163455101584908
41	2.07	2.06126025642911	0.00873974357088558
42	2.04	2.08240759003134	-0.0424075900313361
43	2.05	2.05651382728705	-0.0065138272870473
44	2.05	2.04681076079705	0.003189239202948
45	2.04	2.03712543702834	0.00287456297166333
46	2.03	2.03969215067357	-0.00969215067356544
47	2.04	2.03096258796192	0.00903741203808472
48	2.04	2.05268639138257	-0.0126863913825694
49	2.1	2.06403661000116	0.035963389998841
50	2.09	2.09242317772259	-0.00242317772258893
51	2.1	2.09462883961116	0.00537116038884422
52	2.09	2.1037538696481	-0.0137538696481028
53	2.08	2.08084466536698	-0.000844665366980912
54	2.1	2.09202678354501	0.00797321645499238
55	2.11	2.11713975068791	-0.00713975068791273
56	2.08	2.10685198856327	-0.0268519885632679
57	2.09	2.06672721035049	0.0232727896495071
58	2.1	2.08970843878662	0.0102915612133834
59	2.09	2.10125224739732	-0.0112522473973233
60	2.09	2.10301712186213	-0.0130171218621267

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	2.11464547118766	2.07607604652848	2.15321489584684
62	2.10661941754096	2.05186410490725	2.16137473017466
63	2.11091694374218	2.04333551066473	2.17849837681963
64	2.11426146409968	2.03568677780314	2.19283615039623
65	2.10473123813655	2.01672681237496	2.19273566389815
66	2.11664157602387	2.01919103997989	2.21409211206785
67	2.13356404671598	2.02701682375756	2.2401112696744
68	2.13011147450496	2.01585628671892	2.244366662291
69	2.11656394180574	1.99548457743993	2.23764330617156
70	2.11604110412075	1.98774057234028	2.24434163590121
71	2.11695733351054	1.98160355497043	2.25231111205065
72	2.12992633349291	-9.39757093143756	13.6574235984234

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 2.11464547118766 & 2.07607604652848 & 2.15321489584684 \tabularnewline
62 & 2.10661941754096 & 2.05186410490725 & 2.16137473017466 \tabularnewline
63 & 2.11091694374218 & 2.04333551066473 & 2.17849837681963 \tabularnewline
64 & 2.11426146409968 & 2.03568677780314 & 2.19283615039623 \tabularnewline
65 & 2.10473123813655 & 2.01672681237496 & 2.19273566389815 \tabularnewline
66 & 2.11664157602387 & 2.01919103997989 & 2.21409211206785 \tabularnewline
67 & 2.13356404671598 & 2.02701682375756 & 2.2401112696744 \tabularnewline
68 & 2.13011147450496 & 2.01585628671892 & 2.244366662291 \tabularnewline
69 & 2.11656394180574 & 1.99548457743993 & 2.23764330617156 \tabularnewline
70 & 2.11604110412075 & 1.98774057234028 & 2.24434163590121 \tabularnewline
71 & 2.11695733351054 & 1.98160355497043 & 2.25231111205065 \tabularnewline
72 & 2.12992633349291 & -9.39757093143756 & 13.6574235984234 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166492&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]2.11464547118766[/C][C]2.07607604652848[/C][C]2.15321489584684[/C][/ROW]
[ROW][C]62[/C][C]2.10661941754096[/C][C]2.05186410490725[/C][C]2.16137473017466[/C][/ROW]
[ROW][C]63[/C][C]2.11091694374218[/C][C]2.04333551066473[/C][C]2.17849837681963[/C][/ROW]
[ROW][C]64[/C][C]2.11426146409968[/C][C]2.03568677780314[/C][C]2.19283615039623[/C][/ROW]
[ROW][C]65[/C][C]2.10473123813655[/C][C]2.01672681237496[/C][C]2.19273566389815[/C][/ROW]
[ROW][C]66[/C][C]2.11664157602387[/C][C]2.01919103997989[/C][C]2.21409211206785[/C][/ROW]
[ROW][C]67[/C][C]2.13356404671598[/C][C]2.02701682375756[/C][C]2.2401112696744[/C][/ROW]
[ROW][C]68[/C][C]2.13011147450496[/C][C]2.01585628671892[/C][C]2.244366662291[/C][/ROW]
[ROW][C]69[/C][C]2.11656394180574[/C][C]1.99548457743993[/C][C]2.23764330617156[/C][/ROW]
[ROW][C]70[/C][C]2.11604110412075[/C][C]1.98774057234028[/C][C]2.24434163590121[/C][/ROW]
[ROW][C]71[/C][C]2.11695733351054[/C][C]1.98160355497043[/C][C]2.25231111205065[/C][/ROW]
[ROW][C]72[/C][C]2.12992633349291[/C][C]-9.39757093143756[/C][C]13.6574235984234[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166492&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166492&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	2.11464547118766	2.07607604652848	2.15321489584684
62	2.10661941754096	2.05186410490725	2.16137473017466
63	2.11091694374218	2.04333551066473	2.17849837681963
64	2.11426146409968	2.03568677780314	2.19283615039623
65	2.10473123813655	2.01672681237496	2.19273566389815
66	2.11664157602387	2.01919103997989	2.21409211206785
67	2.13356404671598	2.02701682375756	2.2401112696744
68	2.13011147450496	2.01585628671892	2.244366662291
69	2.11656394180574	1.99548457743993	2.23764330617156
70	2.11604110412075	1.98774057234028	2.24434163590121
71	2.11695733351054	1.98160355497043	2.25231111205065
72	2.12992633349291	-9.39757093143756	13.6574235984234

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code