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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 28 May 2012 16:48:07 -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/28/t1338238163lmlduuzt8onchoh.htm/, Retrieved Thu, 02 May 2024 02:37:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167882, Retrieved Thu, 02 May 2024 02:37:27 +0000

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No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

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

-     [Classical Decomposition] [Opdracht9 oef2] [2012-05-24 17:03:56] [777bf889e818535ecd2adad718525067]
- RMPD    [Exponential Smoothing] [Opgave 10] [2012-05-28 20:48:07] [8d848c7c14a32373b3013fbc562b466f] [Current]

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Dataseries X:

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Histogram

Boxplots

1.26
1.26
1.28
1.34
1.39
1.47
1.57
1.63
1.72
1.43
1.35
1.41
1.44
1.43
1.43
1.42
1.45
1.51
1.48
1.48
1.45
1.38
1.46
1.45
1.41
1.45
1.47
1.47
1.53
1.56
1.66
1.79
1.78
1.46
1.41
1.43
1.43
1.45
1.35
1.35
1.29
1.29
1.26
1.3
1.3
1.16
1.24
1.15
1.21
1.22
1.17
1.13
1.15
1.2
1.23
1.25
1.38
1.28
1.26
1.25

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	'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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167882&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167882&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167882&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	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.801771995597131
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.801771995597131 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167882&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]0.801771995597131[/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=167882&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167882&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	0.801771995597131
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.44	1.39851228632479	0.0414877136752143
14	1.43	1.43104899195894	-0.00104899195894315
15	1.43	1.44698095823067	-0.0169809582306748
16	1.42	1.43597245344427	-0.0159724534442673
17	1.45	1.44993920621969	6.0793780306323e-05
18	1.51	1.50301096761827	0.00698903238173165
19	1.48	1.58122093003961	-0.101220930039615
20	1.48	1.54475450828024	-0.0647545082802403
21	1.45	1.56877584226717	-0.118775842267167
22	1.38	1.17323438349858	0.206765616501424
23	1.46	1.25245294977648	0.207547050223521
24	1.45	1.47396471439584	-0.0239647143958412
25	1.41	1.4943308561812	-0.0843308561812
26	1.45	1.41755778970667	0.0324422102933282
27	1.47	1.45718390216289	0.012816097837105
28	1.47	1.47026575637411	-0.000265756374111303
29	1.53	1.50000393760514	0.0299960623948585
30	1.56	1.57845032997153	-0.0184503299715293
31	1.66	1.61481347916489	0.0451865208351099
32	1.79	1.70296111747671	0.0870388825232935
33	1.78	1.83797760009523	-0.0579776000952279
34	1.46	1.55571390300373	-0.0957139030037266
35	1.41	1.39256776334803	0.0174322366519715
36	1.43	1.41575867940127	0.01424132059873
37	1.43	1.45479109028847	-0.0247910902884674
38	1.45	1.44890303266639	0.0010969673336092
39	1.35	1.45950696201594	-0.109506962015939
40	1.35	1.37192042256705	-0.0219204225670544
41	1.29	1.39029523881475	-0.100295238814753
42	1.29	1.35467428292206	-0.0646742829220563
43	1.26	1.36659096705577	-0.106590967055769
44	1.3	1.34134397615159	-0.0413439761515919
45	1.3	1.34468035001489	-0.0446803500148933
46	1.16	1.06559762363716	0.0944023763628379
47	1.24	1.07731012615453	0.162689873845467
48	1.15	1.21633201893468	-0.0663320189346766
49	1.21	1.18302566567505	0.0269743343249527
50	1.22	1.2237734138485	-0.00377341384849617
51	1.17	1.20854761176427	-0.0385476117642727
52	1.13	1.19521639710045	-0.065216397100448
53	1.15	1.16334163002496	-0.0133416300249622
54	1.2	1.20449871357756	-0.00449871357756004
55	1.23	1.25635342338379	-0.0263534233837912
56	1.25	1.30837242879153	-0.0583724287915348
57	1.38	1.29739450346691	0.082605496533086
58	1.28	1.14793609558399	0.132063904416006
59	1.26	1.20338105095744	0.0566189490425615
60	1.25	1.21195969391315	0.0380403060868526

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.44 & 1.39851228632479 & 0.0414877136752143 \tabularnewline
14 & 1.43 & 1.43104899195894 & -0.00104899195894315 \tabularnewline
15 & 1.43 & 1.44698095823067 & -0.0169809582306748 \tabularnewline
16 & 1.42 & 1.43597245344427 & -0.0159724534442673 \tabularnewline
17 & 1.45 & 1.44993920621969 & 6.0793780306323e-05 \tabularnewline
18 & 1.51 & 1.50301096761827 & 0.00698903238173165 \tabularnewline
19 & 1.48 & 1.58122093003961 & -0.101220930039615 \tabularnewline
20 & 1.48 & 1.54475450828024 & -0.0647545082802403 \tabularnewline
21 & 1.45 & 1.56877584226717 & -0.118775842267167 \tabularnewline
22 & 1.38 & 1.17323438349858 & 0.206765616501424 \tabularnewline
23 & 1.46 & 1.25245294977648 & 0.207547050223521 \tabularnewline
24 & 1.45 & 1.47396471439584 & -0.0239647143958412 \tabularnewline
25 & 1.41 & 1.4943308561812 & -0.0843308561812 \tabularnewline
26 & 1.45 & 1.41755778970667 & 0.0324422102933282 \tabularnewline
27 & 1.47 & 1.45718390216289 & 0.012816097837105 \tabularnewline
28 & 1.47 & 1.47026575637411 & -0.000265756374111303 \tabularnewline
29 & 1.53 & 1.50000393760514 & 0.0299960623948585 \tabularnewline
30 & 1.56 & 1.57845032997153 & -0.0184503299715293 \tabularnewline
31 & 1.66 & 1.61481347916489 & 0.0451865208351099 \tabularnewline
32 & 1.79 & 1.70296111747671 & 0.0870388825232935 \tabularnewline
33 & 1.78 & 1.83797760009523 & -0.0579776000952279 \tabularnewline
34 & 1.46 & 1.55571390300373 & -0.0957139030037266 \tabularnewline
35 & 1.41 & 1.39256776334803 & 0.0174322366519715 \tabularnewline
36 & 1.43 & 1.41575867940127 & 0.01424132059873 \tabularnewline
37 & 1.43 & 1.45479109028847 & -0.0247910902884674 \tabularnewline
38 & 1.45 & 1.44890303266639 & 0.0010969673336092 \tabularnewline
39 & 1.35 & 1.45950696201594 & -0.109506962015939 \tabularnewline
40 & 1.35 & 1.37192042256705 & -0.0219204225670544 \tabularnewline
41 & 1.29 & 1.39029523881475 & -0.100295238814753 \tabularnewline
42 & 1.29 & 1.35467428292206 & -0.0646742829220563 \tabularnewline
43 & 1.26 & 1.36659096705577 & -0.106590967055769 \tabularnewline
44 & 1.3 & 1.34134397615159 & -0.0413439761515919 \tabularnewline
45 & 1.3 & 1.34468035001489 & -0.0446803500148933 \tabularnewline
46 & 1.16 & 1.06559762363716 & 0.0944023763628379 \tabularnewline
47 & 1.24 & 1.07731012615453 & 0.162689873845467 \tabularnewline
48 & 1.15 & 1.21633201893468 & -0.0663320189346766 \tabularnewline
49 & 1.21 & 1.18302566567505 & 0.0269743343249527 \tabularnewline
50 & 1.22 & 1.2237734138485 & -0.00377341384849617 \tabularnewline
51 & 1.17 & 1.20854761176427 & -0.0385476117642727 \tabularnewline
52 & 1.13 & 1.19521639710045 & -0.065216397100448 \tabularnewline
53 & 1.15 & 1.16334163002496 & -0.0133416300249622 \tabularnewline
54 & 1.2 & 1.20449871357756 & -0.00449871357756004 \tabularnewline
55 & 1.23 & 1.25635342338379 & -0.0263534233837912 \tabularnewline
56 & 1.25 & 1.30837242879153 & -0.0583724287915348 \tabularnewline
57 & 1.38 & 1.29739450346691 & 0.082605496533086 \tabularnewline
58 & 1.28 & 1.14793609558399 & 0.132063904416006 \tabularnewline
59 & 1.26 & 1.20338105095744 & 0.0566189490425615 \tabularnewline
60 & 1.25 & 1.21195969391315 & 0.0380403060868526 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167882&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]1.44[/C][C]1.39851228632479[/C][C]0.0414877136752143[/C][/ROW]
[ROW][C]14[/C][C]1.43[/C][C]1.43104899195894[/C][C]-0.00104899195894315[/C][/ROW]
[ROW][C]15[/C][C]1.43[/C][C]1.44698095823067[/C][C]-0.0169809582306748[/C][/ROW]
[ROW][C]16[/C][C]1.42[/C][C]1.43597245344427[/C][C]-0.0159724534442673[/C][/ROW]
[ROW][C]17[/C][C]1.45[/C][C]1.44993920621969[/C][C]6.0793780306323e-05[/C][/ROW]
[ROW][C]18[/C][C]1.51[/C][C]1.50301096761827[/C][C]0.00698903238173165[/C][/ROW]
[ROW][C]19[/C][C]1.48[/C][C]1.58122093003961[/C][C]-0.101220930039615[/C][/ROW]
[ROW][C]20[/C][C]1.48[/C][C]1.54475450828024[/C][C]-0.0647545082802403[/C][/ROW]
[ROW][C]21[/C][C]1.45[/C][C]1.56877584226717[/C][C]-0.118775842267167[/C][/ROW]
[ROW][C]22[/C][C]1.38[/C][C]1.17323438349858[/C][C]0.206765616501424[/C][/ROW]
[ROW][C]23[/C][C]1.46[/C][C]1.25245294977648[/C][C]0.207547050223521[/C][/ROW]
[ROW][C]24[/C][C]1.45[/C][C]1.47396471439584[/C][C]-0.0239647143958412[/C][/ROW]
[ROW][C]25[/C][C]1.41[/C][C]1.4943308561812[/C][C]-0.0843308561812[/C][/ROW]
[ROW][C]26[/C][C]1.45[/C][C]1.41755778970667[/C][C]0.0324422102933282[/C][/ROW]
[ROW][C]27[/C][C]1.47[/C][C]1.45718390216289[/C][C]0.012816097837105[/C][/ROW]
[ROW][C]28[/C][C]1.47[/C][C]1.47026575637411[/C][C]-0.000265756374111303[/C][/ROW]
[ROW][C]29[/C][C]1.53[/C][C]1.50000393760514[/C][C]0.0299960623948585[/C][/ROW]
[ROW][C]30[/C][C]1.56[/C][C]1.57845032997153[/C][C]-0.0184503299715293[/C][/ROW]
[ROW][C]31[/C][C]1.66[/C][C]1.61481347916489[/C][C]0.0451865208351099[/C][/ROW]
[ROW][C]32[/C][C]1.79[/C][C]1.70296111747671[/C][C]0.0870388825232935[/C][/ROW]
[ROW][C]33[/C][C]1.78[/C][C]1.83797760009523[/C][C]-0.0579776000952279[/C][/ROW]
[ROW][C]34[/C][C]1.46[/C][C]1.55571390300373[/C][C]-0.0957139030037266[/C][/ROW]
[ROW][C]35[/C][C]1.41[/C][C]1.39256776334803[/C][C]0.0174322366519715[/C][/ROW]
[ROW][C]36[/C][C]1.43[/C][C]1.41575867940127[/C][C]0.01424132059873[/C][/ROW]
[ROW][C]37[/C][C]1.43[/C][C]1.45479109028847[/C][C]-0.0247910902884674[/C][/ROW]
[ROW][C]38[/C][C]1.45[/C][C]1.44890303266639[/C][C]0.0010969673336092[/C][/ROW]
[ROW][C]39[/C][C]1.35[/C][C]1.45950696201594[/C][C]-0.109506962015939[/C][/ROW]
[ROW][C]40[/C][C]1.35[/C][C]1.37192042256705[/C][C]-0.0219204225670544[/C][/ROW]
[ROW][C]41[/C][C]1.29[/C][C]1.39029523881475[/C][C]-0.100295238814753[/C][/ROW]
[ROW][C]42[/C][C]1.29[/C][C]1.35467428292206[/C][C]-0.0646742829220563[/C][/ROW]
[ROW][C]43[/C][C]1.26[/C][C]1.36659096705577[/C][C]-0.106590967055769[/C][/ROW]
[ROW][C]44[/C][C]1.3[/C][C]1.34134397615159[/C][C]-0.0413439761515919[/C][/ROW]
[ROW][C]45[/C][C]1.3[/C][C]1.34468035001489[/C][C]-0.0446803500148933[/C][/ROW]
[ROW][C]46[/C][C]1.16[/C][C]1.06559762363716[/C][C]0.0944023763628379[/C][/ROW]
[ROW][C]47[/C][C]1.24[/C][C]1.07731012615453[/C][C]0.162689873845467[/C][/ROW]
[ROW][C]48[/C][C]1.15[/C][C]1.21633201893468[/C][C]-0.0663320189346766[/C][/ROW]
[ROW][C]49[/C][C]1.21[/C][C]1.18302566567505[/C][C]0.0269743343249527[/C][/ROW]
[ROW][C]50[/C][C]1.22[/C][C]1.2237734138485[/C][C]-0.00377341384849617[/C][/ROW]
[ROW][C]51[/C][C]1.17[/C][C]1.20854761176427[/C][C]-0.0385476117642727[/C][/ROW]
[ROW][C]52[/C][C]1.13[/C][C]1.19521639710045[/C][C]-0.065216397100448[/C][/ROW]
[ROW][C]53[/C][C]1.15[/C][C]1.16334163002496[/C][C]-0.0133416300249622[/C][/ROW]
[ROW][C]54[/C][C]1.2[/C][C]1.20449871357756[/C][C]-0.00449871357756004[/C][/ROW]
[ROW][C]55[/C][C]1.23[/C][C]1.25635342338379[/C][C]-0.0263534233837912[/C][/ROW]
[ROW][C]56[/C][C]1.25[/C][C]1.30837242879153[/C][C]-0.0583724287915348[/C][/ROW]
[ROW][C]57[/C][C]1.38[/C][C]1.29739450346691[/C][C]0.082605496533086[/C][/ROW]
[ROW][C]58[/C][C]1.28[/C][C]1.14793609558399[/C][C]0.132063904416006[/C][/ROW]
[ROW][C]59[/C][C]1.26[/C][C]1.20338105095744[/C][C]0.0566189490425615[/C][/ROW]
[ROW][C]60[/C][C]1.25[/C][C]1.21195969391315[/C][C]0.0380403060868526[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167882&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167882&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	1.44	1.39851228632479	0.0414877136752143
14	1.43	1.43104899195894	-0.00104899195894315
15	1.43	1.44698095823067	-0.0169809582306748
16	1.42	1.43597245344427	-0.0159724534442673
17	1.45	1.44993920621969	6.0793780306323e-05
18	1.51	1.50301096761827	0.00698903238173165
19	1.48	1.58122093003961	-0.101220930039615
20	1.48	1.54475450828024	-0.0647545082802403
21	1.45	1.56877584226717	-0.118775842267167
22	1.38	1.17323438349858	0.206765616501424
23	1.46	1.25245294977648	0.207547050223521
24	1.45	1.47396471439584	-0.0239647143958412
25	1.41	1.4943308561812	-0.0843308561812
26	1.45	1.41755778970667	0.0324422102933282
27	1.47	1.45718390216289	0.012816097837105
28	1.47	1.47026575637411	-0.000265756374111303
29	1.53	1.50000393760514	0.0299960623948585
30	1.56	1.57845032997153	-0.0184503299715293
31	1.66	1.61481347916489	0.0451865208351099
32	1.79	1.70296111747671	0.0870388825232935
33	1.78	1.83797760009523	-0.0579776000952279
34	1.46	1.55571390300373	-0.0957139030037266
35	1.41	1.39256776334803	0.0174322366519715
36	1.43	1.41575867940127	0.01424132059873
37	1.43	1.45479109028847	-0.0247910902884674
38	1.45	1.44890303266639	0.0010969673336092
39	1.35	1.45950696201594	-0.109506962015939
40	1.35	1.37192042256705	-0.0219204225670544
41	1.29	1.39029523881475	-0.100295238814753
42	1.29	1.35467428292206	-0.0646742829220563
43	1.26	1.36659096705577	-0.106590967055769
44	1.3	1.34134397615159	-0.0413439761515919
45	1.3	1.34468035001489	-0.0446803500148933
46	1.16	1.06559762363716	0.0944023763628379
47	1.24	1.07731012615453	0.162689873845467
48	1.15	1.21633201893468	-0.0663320189346766
49	1.21	1.18302566567505	0.0269743343249527
50	1.22	1.2237734138485	-0.00377341384849617
51	1.17	1.20854761176427	-0.0385476117642727
52	1.13	1.19521639710045	-0.065216397100448
53	1.15	1.16334163002496	-0.0133416300249622
54	1.2	1.20449871357756	-0.00449871357756004
55	1.23	1.25635342338379	-0.0263534233837912
56	1.25	1.30837242879153	-0.0583724287915348
57	1.38	1.29739450346691	0.082605496533086
58	1.28	1.14793609558399	0.132063904416006
59	1.26	1.20338105095744	0.0566189490425615
60	1.25	1.21195969391315	0.0380403060868526

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.28083208017591	1.13195681405128	1.42970734630053
62	1.29385749772743	1.10303922306007	1.48467577239479
63	1.27476389333717	1.04968749957191	1.49984028710244
64	1.28705257418606	1.03228375326457	1.54182139510754
65	1.31774951951569	1.03640467560155	1.59909436342983
66	1.37135646207839	1.06573792487814	1.67697499927864
67	1.42248589893563	1.09438460457096	1.75058719330029
68	1.48928727765567	1.14014800967351	1.83842654563783
69	1.55305650385304	1.18407683296254	1.92203617474355
70	1.34717136366307	0.959365011711721	1.73497771561442
71	1.28177587590061	0.876015434633638	1.68753631716757
72	1.24127622377622	0.818323147442084	1.66422930011036

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.28083208017591 & 1.13195681405128 & 1.42970734630053 \tabularnewline
62 & 1.29385749772743 & 1.10303922306007 & 1.48467577239479 \tabularnewline
63 & 1.27476389333717 & 1.04968749957191 & 1.49984028710244 \tabularnewline
64 & 1.28705257418606 & 1.03228375326457 & 1.54182139510754 \tabularnewline
65 & 1.31774951951569 & 1.03640467560155 & 1.59909436342983 \tabularnewline
66 & 1.37135646207839 & 1.06573792487814 & 1.67697499927864 \tabularnewline
67 & 1.42248589893563 & 1.09438460457096 & 1.75058719330029 \tabularnewline
68 & 1.48928727765567 & 1.14014800967351 & 1.83842654563783 \tabularnewline
69 & 1.55305650385304 & 1.18407683296254 & 1.92203617474355 \tabularnewline
70 & 1.34717136366307 & 0.959365011711721 & 1.73497771561442 \tabularnewline
71 & 1.28177587590061 & 0.876015434633638 & 1.68753631716757 \tabularnewline
72 & 1.24127622377622 & 0.818323147442084 & 1.66422930011036 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167882&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]1.28083208017591[/C][C]1.13195681405128[/C][C]1.42970734630053[/C][/ROW]
[ROW][C]62[/C][C]1.29385749772743[/C][C]1.10303922306007[/C][C]1.48467577239479[/C][/ROW]
[ROW][C]63[/C][C]1.27476389333717[/C][C]1.04968749957191[/C][C]1.49984028710244[/C][/ROW]
[ROW][C]64[/C][C]1.28705257418606[/C][C]1.03228375326457[/C][C]1.54182139510754[/C][/ROW]
[ROW][C]65[/C][C]1.31774951951569[/C][C]1.03640467560155[/C][C]1.59909436342983[/C][/ROW]
[ROW][C]66[/C][C]1.37135646207839[/C][C]1.06573792487814[/C][C]1.67697499927864[/C][/ROW]
[ROW][C]67[/C][C]1.42248589893563[/C][C]1.09438460457096[/C][C]1.75058719330029[/C][/ROW]
[ROW][C]68[/C][C]1.48928727765567[/C][C]1.14014800967351[/C][C]1.83842654563783[/C][/ROW]
[ROW][C]69[/C][C]1.55305650385304[/C][C]1.18407683296254[/C][C]1.92203617474355[/C][/ROW]
[ROW][C]70[/C][C]1.34717136366307[/C][C]0.959365011711721[/C][C]1.73497771561442[/C][/ROW]
[ROW][C]71[/C][C]1.28177587590061[/C][C]0.876015434633638[/C][C]1.68753631716757[/C][/ROW]
[ROW][C]72[/C][C]1.24127622377622[/C][C]0.818323147442084[/C][C]1.66422930011036[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167882&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167882&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	1.28083208017591	1.13195681405128	1.42970734630053
62	1.29385749772743	1.10303922306007	1.48467577239479
63	1.27476389333717	1.04968749957191	1.49984028710244
64	1.28705257418606	1.03228375326457	1.54182139510754
65	1.31774951951569	1.03640467560155	1.59909436342983
66	1.37135646207839	1.06573792487814	1.67697499927864
67	1.42248589893563	1.09438460457096	1.75058719330029
68	1.48928727765567	1.14014800967351	1.83842654563783
69	1.55305650385304	1.18407683296254	1.92203617474355
70	1.34717136366307	0.959365011711721	1.73497771561442
71	1.28177587590061	0.876015434633638	1.68753631716757
72	1.24127622377622	0.818323147442084	1.66422930011036

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 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code