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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 27 Dec 2011 05:28:36 -0500

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/2011/Dec/27/t1324981758ze14pk4u6o31qpg.htm/, Retrieved Wed, 15 May 2024 20:05:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160833, Retrieved Wed, 15 May 2024 20:05:29 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

174

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

-       [Exponential Smoothing] [Double exponentia...] [2011-12-27 10:28:36] [76c30f62b7052b57088120e90a652e05] [Current]

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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' @ 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160833&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160833&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160833&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' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.385872352490905
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.385872352490905 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160833&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]0.385872352490905[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160833&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160833&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	0.385872352490905
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	240.23	241.69	-1.45999999999998
4	240.33	242.126626365363	-1.79662636536324
5	240.33	241.533357923213	-1.20335792321336
6	240.34	241.069015370494	-0.729015370494466
7	240.34	240.79770849448	-0.457708494479732
8	240.27	240.62109144096	-0.351091440959749
9	240.29	240.415614960697	-0.12561496069722
10	240.29	240.387143620305	-0.0971436203049052
11	240.29	240.349658583008	-0.0596585830083711
12	240.29	240.326637985237	-0.0366379852366663
13	240.31	240.312500399683	-0.00250039968284455
14	239.95	240.331535564575	-0.381535564575074
15	242.33	239.824311538714	2.5056884612865
16	242.11	243.171187439879	-1.06118743987946
17	241.53	242.541704546019	-1.01170454601939
18	241.53	241.571315732821	-0.0413157328211469
19	241.53	241.555373133803	-0.0253731338025602
20	241.41	241.545582342972	-0.1355823429721
21	241.41	241.373264865333	0.0367351346667704
22	241.66	241.387439938166	0.272560061833843
23	241.8	241.742613330421	0.0573866695789604
24	241.99	241.904757259613	0.0852427403868887
25	246.24	242.127650076379	4.11234992362103
26	247.57	247.964492215672	-0.394492215672415
27	247.84	249.142268576372	-1.30226857637152
28	248.27	248.909759137232	-0.639759137232062
29	248.3	249.092893773921	-0.792893773920781
30	248.31	248.816937988103	-0.506937988102578
31	248.31	248.631324634066	-0.321324634066428
32	248.38	248.507334341606	-0.127334341605945
33	248.37	248.528199539658	-0.158199539657573
34	248.41	248.457154711127	-0.0471547111269501
35	248.68	248.478959011813	0.201040988186662
36	248.75	248.826535170872	-0.0765351708720345
37	248.75	248.867002364439	-0.117002364439344
38	247.95	248.821854386826	-0.871854386826158
39	248.13	247.685429883552	0.444570116447977
40	247.86	248.036977200233	-0.176977200232926
41	246.23	247.698686591642	-1.46868659164184
42	245.98	245.501961041453	0.478038958546875
43	245.98	245.43642305897	0.543576941030096
44	246.27	245.646174371965	0.623825628035007
45	246.31	246.176891434599	0.133108565400988
46	246.3	246.268254349867	0.0317456501330469
47	246.67	246.270504118565	0.399495881434831
48	246.78	246.794658534145	-0.0146585341448144
49	246.78	246.89900221109	-0.119002211090304
50	247.91	246.853082547945	1.05691745205473
51	247.99	248.390917771558	-0.400917771558312
52	248.6	248.316214687892	0.283785312108279
53	248.68	249.035719593877	-0.355719593877268
54	248.75	248.978457237361	-0.228457237360772
55	248.75	248.960301905737	-0.210301905736799
56	249.03	248.879152214637	0.150847785363197
57	249.05	249.217360204443	-0.167360204442929
58	249.57	249.172780528641	0.397219471358795
59	249.35	249.84605654051	-0.496056540509613
60	249.46	249.434642036255	0.025357963745364
61	249.46	249.554426973379	-0.0944269733794556
62	250.82	249.517990215023	1.30200978497706
63	254.19	251.380399793718	2.8096002062818
64	255.18	255.834546834875	-0.654546834875077
65	256.68	256.571975307886	0.108024692113645
66	256.73	258.113659049959	-1.38365904995936
67	256.73	257.629743277306	-0.899743277306243
68	257.39	257.282557222254	0.107442777745803
69	257.78	257.984016419661	-0.204016419661116
70	258.67	258.29529212386	0.374707876140349
71	258.71	259.329881533523	-0.619881533522857
72	258.91	259.130686387917	-0.220686387916658
73	258.91	259.245529612249	-0.335529612248592
74	261.38	259.11605801144	2.26394198856013
75	262.42	262.459650632468	-0.0396506324684651
76	262.77	263.48435054964	-0.714350549640187
77	263.24	263.558702422547	-0.31870242254729
78	262.83	263.905723969014	-1.07572396901446
79	262.83	263.08063183046	-0.250631830459952
80	263.09	262.983919936431	0.106080063568697
81	263.6	263.284853300113	0.315146699887123
82	265.68	263.916459698578	1.76354030142187
83	266.08	266.6769611434	-0.596961143400335
84	266.28	266.846610342651	-0.56661034265079

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 240.23 & 241.69 & -1.45999999999998 \tabularnewline
4 & 240.33 & 242.126626365363 & -1.79662636536324 \tabularnewline
5 & 240.33 & 241.533357923213 & -1.20335792321336 \tabularnewline
6 & 240.34 & 241.069015370494 & -0.729015370494466 \tabularnewline
7 & 240.34 & 240.79770849448 & -0.457708494479732 \tabularnewline
8 & 240.27 & 240.62109144096 & -0.351091440959749 \tabularnewline
9 & 240.29 & 240.415614960697 & -0.12561496069722 \tabularnewline
10 & 240.29 & 240.387143620305 & -0.0971436203049052 \tabularnewline
11 & 240.29 & 240.349658583008 & -0.0596585830083711 \tabularnewline
12 & 240.29 & 240.326637985237 & -0.0366379852366663 \tabularnewline
13 & 240.31 & 240.312500399683 & -0.00250039968284455 \tabularnewline
14 & 239.95 & 240.331535564575 & -0.381535564575074 \tabularnewline
15 & 242.33 & 239.824311538714 & 2.5056884612865 \tabularnewline
16 & 242.11 & 243.171187439879 & -1.06118743987946 \tabularnewline
17 & 241.53 & 242.541704546019 & -1.01170454601939 \tabularnewline
18 & 241.53 & 241.571315732821 & -0.0413157328211469 \tabularnewline
19 & 241.53 & 241.555373133803 & -0.0253731338025602 \tabularnewline
20 & 241.41 & 241.545582342972 & -0.1355823429721 \tabularnewline
21 & 241.41 & 241.373264865333 & 0.0367351346667704 \tabularnewline
22 & 241.66 & 241.387439938166 & 0.272560061833843 \tabularnewline
23 & 241.8 & 241.742613330421 & 0.0573866695789604 \tabularnewline
24 & 241.99 & 241.904757259613 & 0.0852427403868887 \tabularnewline
25 & 246.24 & 242.127650076379 & 4.11234992362103 \tabularnewline
26 & 247.57 & 247.964492215672 & -0.394492215672415 \tabularnewline
27 & 247.84 & 249.142268576372 & -1.30226857637152 \tabularnewline
28 & 248.27 & 248.909759137232 & -0.639759137232062 \tabularnewline
29 & 248.3 & 249.092893773921 & -0.792893773920781 \tabularnewline
30 & 248.31 & 248.816937988103 & -0.506937988102578 \tabularnewline
31 & 248.31 & 248.631324634066 & -0.321324634066428 \tabularnewline
32 & 248.38 & 248.507334341606 & -0.127334341605945 \tabularnewline
33 & 248.37 & 248.528199539658 & -0.158199539657573 \tabularnewline
34 & 248.41 & 248.457154711127 & -0.0471547111269501 \tabularnewline
35 & 248.68 & 248.478959011813 & 0.201040988186662 \tabularnewline
36 & 248.75 & 248.826535170872 & -0.0765351708720345 \tabularnewline
37 & 248.75 & 248.867002364439 & -0.117002364439344 \tabularnewline
38 & 247.95 & 248.821854386826 & -0.871854386826158 \tabularnewline
39 & 248.13 & 247.685429883552 & 0.444570116447977 \tabularnewline
40 & 247.86 & 248.036977200233 & -0.176977200232926 \tabularnewline
41 & 246.23 & 247.698686591642 & -1.46868659164184 \tabularnewline
42 & 245.98 & 245.501961041453 & 0.478038958546875 \tabularnewline
43 & 245.98 & 245.43642305897 & 0.543576941030096 \tabularnewline
44 & 246.27 & 245.646174371965 & 0.623825628035007 \tabularnewline
45 & 246.31 & 246.176891434599 & 0.133108565400988 \tabularnewline
46 & 246.3 & 246.268254349867 & 0.0317456501330469 \tabularnewline
47 & 246.67 & 246.270504118565 & 0.399495881434831 \tabularnewline
48 & 246.78 & 246.794658534145 & -0.0146585341448144 \tabularnewline
49 & 246.78 & 246.89900221109 & -0.119002211090304 \tabularnewline
50 & 247.91 & 246.853082547945 & 1.05691745205473 \tabularnewline
51 & 247.99 & 248.390917771558 & -0.400917771558312 \tabularnewline
52 & 248.6 & 248.316214687892 & 0.283785312108279 \tabularnewline
53 & 248.68 & 249.035719593877 & -0.355719593877268 \tabularnewline
54 & 248.75 & 248.978457237361 & -0.228457237360772 \tabularnewline
55 & 248.75 & 248.960301905737 & -0.210301905736799 \tabularnewline
56 & 249.03 & 248.879152214637 & 0.150847785363197 \tabularnewline
57 & 249.05 & 249.217360204443 & -0.167360204442929 \tabularnewline
58 & 249.57 & 249.172780528641 & 0.397219471358795 \tabularnewline
59 & 249.35 & 249.84605654051 & -0.496056540509613 \tabularnewline
60 & 249.46 & 249.434642036255 & 0.025357963745364 \tabularnewline
61 & 249.46 & 249.554426973379 & -0.0944269733794556 \tabularnewline
62 & 250.82 & 249.517990215023 & 1.30200978497706 \tabularnewline
63 & 254.19 & 251.380399793718 & 2.8096002062818 \tabularnewline
64 & 255.18 & 255.834546834875 & -0.654546834875077 \tabularnewline
65 & 256.68 & 256.571975307886 & 0.108024692113645 \tabularnewline
66 & 256.73 & 258.113659049959 & -1.38365904995936 \tabularnewline
67 & 256.73 & 257.629743277306 & -0.899743277306243 \tabularnewline
68 & 257.39 & 257.282557222254 & 0.107442777745803 \tabularnewline
69 & 257.78 & 257.984016419661 & -0.204016419661116 \tabularnewline
70 & 258.67 & 258.29529212386 & 0.374707876140349 \tabularnewline
71 & 258.71 & 259.329881533523 & -0.619881533522857 \tabularnewline
72 & 258.91 & 259.130686387917 & -0.220686387916658 \tabularnewline
73 & 258.91 & 259.245529612249 & -0.335529612248592 \tabularnewline
74 & 261.38 & 259.11605801144 & 2.26394198856013 \tabularnewline
75 & 262.42 & 262.459650632468 & -0.0396506324684651 \tabularnewline
76 & 262.77 & 263.48435054964 & -0.714350549640187 \tabularnewline
77 & 263.24 & 263.558702422547 & -0.31870242254729 \tabularnewline
78 & 262.83 & 263.905723969014 & -1.07572396901446 \tabularnewline
79 & 262.83 & 263.08063183046 & -0.250631830459952 \tabularnewline
80 & 263.09 & 262.983919936431 & 0.106080063568697 \tabularnewline
81 & 263.6 & 263.284853300113 & 0.315146699887123 \tabularnewline
82 & 265.68 & 263.916459698578 & 1.76354030142187 \tabularnewline
83 & 266.08 & 266.6769611434 & -0.596961143400335 \tabularnewline
84 & 266.28 & 266.846610342651 & -0.56661034265079 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160833&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]240.23[/C][C]241.69[/C][C]-1.45999999999998[/C][/ROW]
[ROW][C]4[/C][C]240.33[/C][C]242.126626365363[/C][C]-1.79662636536324[/C][/ROW]
[ROW][C]5[/C][C]240.33[/C][C]241.533357923213[/C][C]-1.20335792321336[/C][/ROW]
[ROW][C]6[/C][C]240.34[/C][C]241.069015370494[/C][C]-0.729015370494466[/C][/ROW]
[ROW][C]7[/C][C]240.34[/C][C]240.79770849448[/C][C]-0.457708494479732[/C][/ROW]
[ROW][C]8[/C][C]240.27[/C][C]240.62109144096[/C][C]-0.351091440959749[/C][/ROW]
[ROW][C]9[/C][C]240.29[/C][C]240.415614960697[/C][C]-0.12561496069722[/C][/ROW]
[ROW][C]10[/C][C]240.29[/C][C]240.387143620305[/C][C]-0.0971436203049052[/C][/ROW]
[ROW][C]11[/C][C]240.29[/C][C]240.349658583008[/C][C]-0.0596585830083711[/C][/ROW]
[ROW][C]12[/C][C]240.29[/C][C]240.326637985237[/C][C]-0.0366379852366663[/C][/ROW]
[ROW][C]13[/C][C]240.31[/C][C]240.312500399683[/C][C]-0.00250039968284455[/C][/ROW]
[ROW][C]14[/C][C]239.95[/C][C]240.331535564575[/C][C]-0.381535564575074[/C][/ROW]
[ROW][C]15[/C][C]242.33[/C][C]239.824311538714[/C][C]2.5056884612865[/C][/ROW]
[ROW][C]16[/C][C]242.11[/C][C]243.171187439879[/C][C]-1.06118743987946[/C][/ROW]
[ROW][C]17[/C][C]241.53[/C][C]242.541704546019[/C][C]-1.01170454601939[/C][/ROW]
[ROW][C]18[/C][C]241.53[/C][C]241.571315732821[/C][C]-0.0413157328211469[/C][/ROW]
[ROW][C]19[/C][C]241.53[/C][C]241.555373133803[/C][C]-0.0253731338025602[/C][/ROW]
[ROW][C]20[/C][C]241.41[/C][C]241.545582342972[/C][C]-0.1355823429721[/C][/ROW]
[ROW][C]21[/C][C]241.41[/C][C]241.373264865333[/C][C]0.0367351346667704[/C][/ROW]
[ROW][C]22[/C][C]241.66[/C][C]241.387439938166[/C][C]0.272560061833843[/C][/ROW]
[ROW][C]23[/C][C]241.8[/C][C]241.742613330421[/C][C]0.0573866695789604[/C][/ROW]
[ROW][C]24[/C][C]241.99[/C][C]241.904757259613[/C][C]0.0852427403868887[/C][/ROW]
[ROW][C]25[/C][C]246.24[/C][C]242.127650076379[/C][C]4.11234992362103[/C][/ROW]
[ROW][C]26[/C][C]247.57[/C][C]247.964492215672[/C][C]-0.394492215672415[/C][/ROW]
[ROW][C]27[/C][C]247.84[/C][C]249.142268576372[/C][C]-1.30226857637152[/C][/ROW]
[ROW][C]28[/C][C]248.27[/C][C]248.909759137232[/C][C]-0.639759137232062[/C][/ROW]
[ROW][C]29[/C][C]248.3[/C][C]249.092893773921[/C][C]-0.792893773920781[/C][/ROW]
[ROW][C]30[/C][C]248.31[/C][C]248.816937988103[/C][C]-0.506937988102578[/C][/ROW]
[ROW][C]31[/C][C]248.31[/C][C]248.631324634066[/C][C]-0.321324634066428[/C][/ROW]
[ROW][C]32[/C][C]248.38[/C][C]248.507334341606[/C][C]-0.127334341605945[/C][/ROW]
[ROW][C]33[/C][C]248.37[/C][C]248.528199539658[/C][C]-0.158199539657573[/C][/ROW]
[ROW][C]34[/C][C]248.41[/C][C]248.457154711127[/C][C]-0.0471547111269501[/C][/ROW]
[ROW][C]35[/C][C]248.68[/C][C]248.478959011813[/C][C]0.201040988186662[/C][/ROW]
[ROW][C]36[/C][C]248.75[/C][C]248.826535170872[/C][C]-0.0765351708720345[/C][/ROW]
[ROW][C]37[/C][C]248.75[/C][C]248.867002364439[/C][C]-0.117002364439344[/C][/ROW]
[ROW][C]38[/C][C]247.95[/C][C]248.821854386826[/C][C]-0.871854386826158[/C][/ROW]
[ROW][C]39[/C][C]248.13[/C][C]247.685429883552[/C][C]0.444570116447977[/C][/ROW]
[ROW][C]40[/C][C]247.86[/C][C]248.036977200233[/C][C]-0.176977200232926[/C][/ROW]
[ROW][C]41[/C][C]246.23[/C][C]247.698686591642[/C][C]-1.46868659164184[/C][/ROW]
[ROW][C]42[/C][C]245.98[/C][C]245.501961041453[/C][C]0.478038958546875[/C][/ROW]
[ROW][C]43[/C][C]245.98[/C][C]245.43642305897[/C][C]0.543576941030096[/C][/ROW]
[ROW][C]44[/C][C]246.27[/C][C]245.646174371965[/C][C]0.623825628035007[/C][/ROW]
[ROW][C]45[/C][C]246.31[/C][C]246.176891434599[/C][C]0.133108565400988[/C][/ROW]
[ROW][C]46[/C][C]246.3[/C][C]246.268254349867[/C][C]0.0317456501330469[/C][/ROW]
[ROW][C]47[/C][C]246.67[/C][C]246.270504118565[/C][C]0.399495881434831[/C][/ROW]
[ROW][C]48[/C][C]246.78[/C][C]246.794658534145[/C][C]-0.0146585341448144[/C][/ROW]
[ROW][C]49[/C][C]246.78[/C][C]246.89900221109[/C][C]-0.119002211090304[/C][/ROW]
[ROW][C]50[/C][C]247.91[/C][C]246.853082547945[/C][C]1.05691745205473[/C][/ROW]
[ROW][C]51[/C][C]247.99[/C][C]248.390917771558[/C][C]-0.400917771558312[/C][/ROW]
[ROW][C]52[/C][C]248.6[/C][C]248.316214687892[/C][C]0.283785312108279[/C][/ROW]
[ROW][C]53[/C][C]248.68[/C][C]249.035719593877[/C][C]-0.355719593877268[/C][/ROW]
[ROW][C]54[/C][C]248.75[/C][C]248.978457237361[/C][C]-0.228457237360772[/C][/ROW]
[ROW][C]55[/C][C]248.75[/C][C]248.960301905737[/C][C]-0.210301905736799[/C][/ROW]
[ROW][C]56[/C][C]249.03[/C][C]248.879152214637[/C][C]0.150847785363197[/C][/ROW]
[ROW][C]57[/C][C]249.05[/C][C]249.217360204443[/C][C]-0.167360204442929[/C][/ROW]
[ROW][C]58[/C][C]249.57[/C][C]249.172780528641[/C][C]0.397219471358795[/C][/ROW]
[ROW][C]59[/C][C]249.35[/C][C]249.84605654051[/C][C]-0.496056540509613[/C][/ROW]
[ROW][C]60[/C][C]249.46[/C][C]249.434642036255[/C][C]0.025357963745364[/C][/ROW]
[ROW][C]61[/C][C]249.46[/C][C]249.554426973379[/C][C]-0.0944269733794556[/C][/ROW]
[ROW][C]62[/C][C]250.82[/C][C]249.517990215023[/C][C]1.30200978497706[/C][/ROW]
[ROW][C]63[/C][C]254.19[/C][C]251.380399793718[/C][C]2.8096002062818[/C][/ROW]
[ROW][C]64[/C][C]255.18[/C][C]255.834546834875[/C][C]-0.654546834875077[/C][/ROW]
[ROW][C]65[/C][C]256.68[/C][C]256.571975307886[/C][C]0.108024692113645[/C][/ROW]
[ROW][C]66[/C][C]256.73[/C][C]258.113659049959[/C][C]-1.38365904995936[/C][/ROW]
[ROW][C]67[/C][C]256.73[/C][C]257.629743277306[/C][C]-0.899743277306243[/C][/ROW]
[ROW][C]68[/C][C]257.39[/C][C]257.282557222254[/C][C]0.107442777745803[/C][/ROW]
[ROW][C]69[/C][C]257.78[/C][C]257.984016419661[/C][C]-0.204016419661116[/C][/ROW]
[ROW][C]70[/C][C]258.67[/C][C]258.29529212386[/C][C]0.374707876140349[/C][/ROW]
[ROW][C]71[/C][C]258.71[/C][C]259.329881533523[/C][C]-0.619881533522857[/C][/ROW]
[ROW][C]72[/C][C]258.91[/C][C]259.130686387917[/C][C]-0.220686387916658[/C][/ROW]
[ROW][C]73[/C][C]258.91[/C][C]259.245529612249[/C][C]-0.335529612248592[/C][/ROW]
[ROW][C]74[/C][C]261.38[/C][C]259.11605801144[/C][C]2.26394198856013[/C][/ROW]
[ROW][C]75[/C][C]262.42[/C][C]262.459650632468[/C][C]-0.0396506324684651[/C][/ROW]
[ROW][C]76[/C][C]262.77[/C][C]263.48435054964[/C][C]-0.714350549640187[/C][/ROW]
[ROW][C]77[/C][C]263.24[/C][C]263.558702422547[/C][C]-0.31870242254729[/C][/ROW]
[ROW][C]78[/C][C]262.83[/C][C]263.905723969014[/C][C]-1.07572396901446[/C][/ROW]
[ROW][C]79[/C][C]262.83[/C][C]263.08063183046[/C][C]-0.250631830459952[/C][/ROW]
[ROW][C]80[/C][C]263.09[/C][C]262.983919936431[/C][C]0.106080063568697[/C][/ROW]
[ROW][C]81[/C][C]263.6[/C][C]263.284853300113[/C][C]0.315146699887123[/C][/ROW]
[ROW][C]82[/C][C]265.68[/C][C]263.916459698578[/C][C]1.76354030142187[/C][/ROW]
[ROW][C]83[/C][C]266.08[/C][C]266.6769611434[/C][C]-0.596961143400335[/C][/ROW]
[ROW][C]84[/C][C]266.28[/C][C]266.846610342651[/C][C]-0.56661034265079[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160833&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160833&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	240.23	241.69	-1.45999999999998
4	240.33	242.126626365363	-1.79662636536324
5	240.33	241.533357923213	-1.20335792321336
6	240.34	241.069015370494	-0.729015370494466
7	240.34	240.79770849448	-0.457708494479732
8	240.27	240.62109144096	-0.351091440959749
9	240.29	240.415614960697	-0.12561496069722
10	240.29	240.387143620305	-0.0971436203049052
11	240.29	240.349658583008	-0.0596585830083711
12	240.29	240.326637985237	-0.0366379852366663
13	240.31	240.312500399683	-0.00250039968284455
14	239.95	240.331535564575	-0.381535564575074
15	242.33	239.824311538714	2.5056884612865
16	242.11	243.171187439879	-1.06118743987946
17	241.53	242.541704546019	-1.01170454601939
18	241.53	241.571315732821	-0.0413157328211469
19	241.53	241.555373133803	-0.0253731338025602
20	241.41	241.545582342972	-0.1355823429721
21	241.41	241.373264865333	0.0367351346667704
22	241.66	241.387439938166	0.272560061833843
23	241.8	241.742613330421	0.0573866695789604
24	241.99	241.904757259613	0.0852427403868887
25	246.24	242.127650076379	4.11234992362103
26	247.57	247.964492215672	-0.394492215672415
27	247.84	249.142268576372	-1.30226857637152
28	248.27	248.909759137232	-0.639759137232062
29	248.3	249.092893773921	-0.792893773920781
30	248.31	248.816937988103	-0.506937988102578
31	248.31	248.631324634066	-0.321324634066428
32	248.38	248.507334341606	-0.127334341605945
33	248.37	248.528199539658	-0.158199539657573
34	248.41	248.457154711127	-0.0471547111269501
35	248.68	248.478959011813	0.201040988186662
36	248.75	248.826535170872	-0.0765351708720345
37	248.75	248.867002364439	-0.117002364439344
38	247.95	248.821854386826	-0.871854386826158
39	248.13	247.685429883552	0.444570116447977
40	247.86	248.036977200233	-0.176977200232926
41	246.23	247.698686591642	-1.46868659164184
42	245.98	245.501961041453	0.478038958546875
43	245.98	245.43642305897	0.543576941030096
44	246.27	245.646174371965	0.623825628035007
45	246.31	246.176891434599	0.133108565400988
46	246.3	246.268254349867	0.0317456501330469
47	246.67	246.270504118565	0.399495881434831
48	246.78	246.794658534145	-0.0146585341448144
49	246.78	246.89900221109	-0.119002211090304
50	247.91	246.853082547945	1.05691745205473
51	247.99	248.390917771558	-0.400917771558312
52	248.6	248.316214687892	0.283785312108279
53	248.68	249.035719593877	-0.355719593877268
54	248.75	248.978457237361	-0.228457237360772
55	248.75	248.960301905737	-0.210301905736799
56	249.03	248.879152214637	0.150847785363197
57	249.05	249.217360204443	-0.167360204442929
58	249.57	249.172780528641	0.397219471358795
59	249.35	249.84605654051	-0.496056540509613
60	249.46	249.434642036255	0.025357963745364
61	249.46	249.554426973379	-0.0944269733794556
62	250.82	249.517990215023	1.30200978497706
63	254.19	251.380399793718	2.8096002062818
64	255.18	255.834546834875	-0.654546834875077
65	256.68	256.571975307886	0.108024692113645
66	256.73	258.113659049959	-1.38365904995936
67	256.73	257.629743277306	-0.899743277306243
68	257.39	257.282557222254	0.107442777745803
69	257.78	257.984016419661	-0.204016419661116
70	258.67	258.29529212386	0.374707876140349
71	258.71	259.329881533523	-0.619881533522857
72	258.91	259.130686387917	-0.220686387916658
73	258.91	259.245529612249	-0.335529612248592
74	261.38	259.11605801144	2.26394198856013
75	262.42	262.459650632468	-0.0396506324684651
76	262.77	263.48435054964	-0.714350549640187
77	263.24	263.558702422547	-0.31870242254729
78	262.83	263.905723969014	-1.07572396901446
79	262.83	263.08063183046	-0.250631830459952
80	263.09	262.983919936431	0.106080063568697
81	263.6	263.284853300113	0.315146699887123
82	265.68	263.916459698578	1.76354030142187
83	266.08	266.6769611434	-0.596961143400335
84	266.28	266.846610342651	-0.56661034265079

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	266.827971076786	265.045490062943	268.610452090629
86	267.375942153573	264.329702346901	270.422181960245
87	267.923913230359	263.536068569455	272.311757891264
88	268.471884307146	262.637142190031	274.306626424261
89	269.019855383932	261.630752125899	276.408958641965
90	269.567826460718	260.519995753568	278.615657167869
91	270.115797537505	259.309153201798	280.922441873212
92	270.663768614291	258.002568970473	283.32496825811
93	271.211739691078	256.604322056368	285.819157325788
94	271.759710767864	255.118143894995	288.401277640734
95	272.307681844651	253.547419690518	291.067943998783
96	272.855652921437	251.895216860593	293.816088982281

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 266.827971076786 & 265.045490062943 & 268.610452090629 \tabularnewline
86 & 267.375942153573 & 264.329702346901 & 270.422181960245 \tabularnewline
87 & 267.923913230359 & 263.536068569455 & 272.311757891264 \tabularnewline
88 & 268.471884307146 & 262.637142190031 & 274.306626424261 \tabularnewline
89 & 269.019855383932 & 261.630752125899 & 276.408958641965 \tabularnewline
90 & 269.567826460718 & 260.519995753568 & 278.615657167869 \tabularnewline
91 & 270.115797537505 & 259.309153201798 & 280.922441873212 \tabularnewline
92 & 270.663768614291 & 258.002568970473 & 283.32496825811 \tabularnewline
93 & 271.211739691078 & 256.604322056368 & 285.819157325788 \tabularnewline
94 & 271.759710767864 & 255.118143894995 & 288.401277640734 \tabularnewline
95 & 272.307681844651 & 253.547419690518 & 291.067943998783 \tabularnewline
96 & 272.855652921437 & 251.895216860593 & 293.816088982281 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160833&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]85[/C][C]266.827971076786[/C][C]265.045490062943[/C][C]268.610452090629[/C][/ROW]
[ROW][C]86[/C][C]267.375942153573[/C][C]264.329702346901[/C][C]270.422181960245[/C][/ROW]
[ROW][C]87[/C][C]267.923913230359[/C][C]263.536068569455[/C][C]272.311757891264[/C][/ROW]
[ROW][C]88[/C][C]268.471884307146[/C][C]262.637142190031[/C][C]274.306626424261[/C][/ROW]
[ROW][C]89[/C][C]269.019855383932[/C][C]261.630752125899[/C][C]276.408958641965[/C][/ROW]
[ROW][C]90[/C][C]269.567826460718[/C][C]260.519995753568[/C][C]278.615657167869[/C][/ROW]
[ROW][C]91[/C][C]270.115797537505[/C][C]259.309153201798[/C][C]280.922441873212[/C][/ROW]
[ROW][C]92[/C][C]270.663768614291[/C][C]258.002568970473[/C][C]283.32496825811[/C][/ROW]
[ROW][C]93[/C][C]271.211739691078[/C][C]256.604322056368[/C][C]285.819157325788[/C][/ROW]
[ROW][C]94[/C][C]271.759710767864[/C][C]255.118143894995[/C][C]288.401277640734[/C][/ROW]
[ROW][C]95[/C][C]272.307681844651[/C][C]253.547419690518[/C][C]291.067943998783[/C][/ROW]
[ROW][C]96[/C][C]272.855652921437[/C][C]251.895216860593[/C][C]293.816088982281[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160833&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160833&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
85	266.827971076786	265.045490062943	268.610452090629
86	267.375942153573	264.329702346901	270.422181960245
87	267.923913230359	263.536068569455	272.311757891264
88	268.471884307146	262.637142190031	274.306626424261
89	269.019855383932	261.630752125899	276.408958641965
90	269.567826460718	260.519995753568	278.615657167869
91	270.115797537505	259.309153201798	280.922441873212
92	270.663768614291	258.002568970473	283.32496825811
93	271.211739691078	256.604322056368	285.819157325788
94	271.759710767864	255.118143894995	288.401277640734
95	272.307681844651	253.547419690518	291.067943998783
96	272.855652921437	251.895216860593	293.816088982281

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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