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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

Sun, 11 May 2014 16:34:43 -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/2014/May/11/t13998405199okavfwsw67wjdk.htm/, Retrieved Mon, 13 May 2024 21:50:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234802, Retrieved Mon, 13 May 2024 21:50:25 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

140

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

-       [Exponential Smoothing] [] [2014-05-11 20:34:43] [de6881b70973343210d9b2d7428035f3] [Current]

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Dataseries X:

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6
6,7
-0,6
5,8
16,4
1,5
5,1
14,7
4,3
1,5
9,1
4,3
5,7
13
14,5
9,7
-4,7
7,3
5,2
-2,5
11,5
4,9
-2,4
-0,3
4,4
7,9
-9,7
-4,1
16,4
-4,9
3,5
3,8
-0,2
3,1
0,7
-2,8
5,9
-5,3
-2,9
6,6
-8,1
1,3
6,9
-7,2
-1,9
4
-5,7
3,9
-7,6
-0,9
7,3
-3,7
-2,5
9,3
1,3
9,5
11,3
-1,7
8
-4,8
1,6
1,9
-0,9
5,5
1,7
-5,4
1,9
0,2
-13,3
-8,2
0,2
5,7
-1,2
-2,8
5,5
-17,3
1,4
-2,2
-8,6
-5
4,1
0,7
-4,2
-2,3

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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234802&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234802&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234802&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.0968005646355211
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0968005646355211 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234802&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]0.0968005646355211[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234802&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234802&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	0.0968005646355211
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	6.7	6	0.7
3	-0.6	6.06776039524487	-6.66776039524486
4	5.8	5.4223174241308	0.377682575869203
5	16.4	5.45887731072793	10.9411226892721
6	1.5	6.51798416479598	-5.01798416479598
7	5.1	6.03224046431163	-0.932240464311627
8	14.7	5.94199906099018	8.75800093900982
9	4.3	6.78977849696475	-2.48977849696475
10	1.5	6.54876653264119	-5.04876653264119
11	9.1	6.0600430815686	3.0399569184314
12	4.3	6.35431262774042	-2.05431262774042
13	5.7	6.15545400543726	-0.455454005437264
14	13	6.11136580054543	6.88863419945457
15	14.5	6.77818948062019	7.72181051937981
16	9.7	7.52566509890466	2.17433490109534
17	-4.7	7.73614194503741	-12.4361419450374
18	7.3	6.5323163828703	0.767683617129697
19	5.2	6.6066285904699	-1.4066285904699
20	-2.5	6.47046614867994	-8.97046614867994
21	11.5	5.6021199604439	5.8978800395561
22	4.9	6.1730380784255	-1.2730380784255
23	-2.4	6.04980727363139	-8.44980727363139
24	-0.3	5.23186115848254	-5.53186115848254
25	4.4	4.69637387485612	-0.296373874856121
26	7.9	4.66768471642683	3.23231528357317
27	-9.7	4.98057466095674	-14.6805746609567
28	-4.1	3.5594867446022	-7.6594867446022
29	16.4	2.81804410290642	13.5819558970936
30	-4.9	4.13278510259982	-9.03278510259982
31	3.5	3.25840640443684	0.241593595563162
32	3.8	3.28179280089968	0.518207199100322
33	-0.2	3.33195555037078	-3.53195555037078
34	3.1	2.99006025882733	0.109939741172674
35	0.7	3.00070248784872	-2.30070248784872
36	-2.8	2.77799318796662	-5.57799318796662
37	5.9	2.23804029783836	3.66195970216164
38	-5.3	2.59252006468013	-7.89252006468013
39	-2.9	1.82851966602192	-4.72851966602192
40	6.6	1.37079629246083	5.22920370753917
41	-8.1	1.87698616394478	-9.97698616394478
42	1.3	0.911208269914144	0.388791730085856
43	6.9	0.948843528912076	5.95115647108792
44	-7.2	1.52491883554772	-8.72491883554772
45	-1.9	0.68034176586761	-2.58034176586761
46	4	0.430563225979008	3.56943677402099
47	-5.7	0.776086721135033	-6.47608672113503
48	3.9	0.149197869900561	3.75080213009944
49	-7.6	0.512277633930302	-8.1122776339303
50	-0.9	-0.27299542151426	-0.62700457848574
51	7.3	-0.333689818740737	7.63368981874074
52	-3.7	0.405255665965795	-4.1052556659658
53	-2.5	0.00786459952713391	-2.50786459952713
54	9.3	-0.234898109736528	9.53489810973653
55	1.3	0.688085411028131	0.611914588971869
56	9.5	0.747319088749321	8.75268091125068
57	11.3	1.59458354303293	9.70541645696707
58	-1.7	2.53407333609022	-4.23407333609022
59	8	2.12421264644849	5.87578735355151
60	-4.8	2.69299217995053	-7.49299217995053
61	1.6	1.96766630612177	-0.367666306121772
62	1.9	1.93207600009173	-0.0320760000917286
63	-0.9	1.9289710251716	-2.8289710251716
64	5.5	1.65512503259746	3.84487496740254
65	1.7	2.02731110039501	-0.327311100395007
66	-5.4	1.9956272010653	-7.3956272010653
67	1.9	1.27972631216836	0.620273687831643
68	0.2	1.33976915537902	-1.13976915537902
69	-13.3	1.22943885758418	-14.5294388575842
70	-8.2	-0.177019027667252	-8.02298097233275
71	0.2	-0.953648115849104	1.1536481158491
72	5.7	-0.841974326844205	6.54197432684421
73	-1.2	-0.208707518174603	-0.991292481825397
74	-2.8	-0.304665190134249	-2.49533480986575
75	5.5	-0.546215008683924	6.04621500868392
76	-17.3	0.0390620180644418	-17.3390620180644
77	1.4	-1.63936897553451	3.03936897553451
78	-2.2	-1.34515634256709	-0.854843657432912
79	-8.6	-1.42790569128169	-7.17209430871831
80	-5	-2.12216846998483	-2.87783153001517
81	4.1	-2.4007441870162	6.5007441870162
82	0.7	-1.77146847916195	2.47146847916195
83	-4.2	-1.53222893490018	-2.66777106509982
84	-2.3	-1.79047068032015	-0.509529319679849

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 6.7 & 6 & 0.7 \tabularnewline
3 & -0.6 & 6.06776039524487 & -6.66776039524486 \tabularnewline
4 & 5.8 & 5.4223174241308 & 0.377682575869203 \tabularnewline
5 & 16.4 & 5.45887731072793 & 10.9411226892721 \tabularnewline
6 & 1.5 & 6.51798416479598 & -5.01798416479598 \tabularnewline
7 & 5.1 & 6.03224046431163 & -0.932240464311627 \tabularnewline
8 & 14.7 & 5.94199906099018 & 8.75800093900982 \tabularnewline
9 & 4.3 & 6.78977849696475 & -2.48977849696475 \tabularnewline
10 & 1.5 & 6.54876653264119 & -5.04876653264119 \tabularnewline
11 & 9.1 & 6.0600430815686 & 3.0399569184314 \tabularnewline
12 & 4.3 & 6.35431262774042 & -2.05431262774042 \tabularnewline
13 & 5.7 & 6.15545400543726 & -0.455454005437264 \tabularnewline
14 & 13 & 6.11136580054543 & 6.88863419945457 \tabularnewline
15 & 14.5 & 6.77818948062019 & 7.72181051937981 \tabularnewline
16 & 9.7 & 7.52566509890466 & 2.17433490109534 \tabularnewline
17 & -4.7 & 7.73614194503741 & -12.4361419450374 \tabularnewline
18 & 7.3 & 6.5323163828703 & 0.767683617129697 \tabularnewline
19 & 5.2 & 6.6066285904699 & -1.4066285904699 \tabularnewline
20 & -2.5 & 6.47046614867994 & -8.97046614867994 \tabularnewline
21 & 11.5 & 5.6021199604439 & 5.8978800395561 \tabularnewline
22 & 4.9 & 6.1730380784255 & -1.2730380784255 \tabularnewline
23 & -2.4 & 6.04980727363139 & -8.44980727363139 \tabularnewline
24 & -0.3 & 5.23186115848254 & -5.53186115848254 \tabularnewline
25 & 4.4 & 4.69637387485612 & -0.296373874856121 \tabularnewline
26 & 7.9 & 4.66768471642683 & 3.23231528357317 \tabularnewline
27 & -9.7 & 4.98057466095674 & -14.6805746609567 \tabularnewline
28 & -4.1 & 3.5594867446022 & -7.6594867446022 \tabularnewline
29 & 16.4 & 2.81804410290642 & 13.5819558970936 \tabularnewline
30 & -4.9 & 4.13278510259982 & -9.03278510259982 \tabularnewline
31 & 3.5 & 3.25840640443684 & 0.241593595563162 \tabularnewline
32 & 3.8 & 3.28179280089968 & 0.518207199100322 \tabularnewline
33 & -0.2 & 3.33195555037078 & -3.53195555037078 \tabularnewline
34 & 3.1 & 2.99006025882733 & 0.109939741172674 \tabularnewline
35 & 0.7 & 3.00070248784872 & -2.30070248784872 \tabularnewline
36 & -2.8 & 2.77799318796662 & -5.57799318796662 \tabularnewline
37 & 5.9 & 2.23804029783836 & 3.66195970216164 \tabularnewline
38 & -5.3 & 2.59252006468013 & -7.89252006468013 \tabularnewline
39 & -2.9 & 1.82851966602192 & -4.72851966602192 \tabularnewline
40 & 6.6 & 1.37079629246083 & 5.22920370753917 \tabularnewline
41 & -8.1 & 1.87698616394478 & -9.97698616394478 \tabularnewline
42 & 1.3 & 0.911208269914144 & 0.388791730085856 \tabularnewline
43 & 6.9 & 0.948843528912076 & 5.95115647108792 \tabularnewline
44 & -7.2 & 1.52491883554772 & -8.72491883554772 \tabularnewline
45 & -1.9 & 0.68034176586761 & -2.58034176586761 \tabularnewline
46 & 4 & 0.430563225979008 & 3.56943677402099 \tabularnewline
47 & -5.7 & 0.776086721135033 & -6.47608672113503 \tabularnewline
48 & 3.9 & 0.149197869900561 & 3.75080213009944 \tabularnewline
49 & -7.6 & 0.512277633930302 & -8.1122776339303 \tabularnewline
50 & -0.9 & -0.27299542151426 & -0.62700457848574 \tabularnewline
51 & 7.3 & -0.333689818740737 & 7.63368981874074 \tabularnewline
52 & -3.7 & 0.405255665965795 & -4.1052556659658 \tabularnewline
53 & -2.5 & 0.00786459952713391 & -2.50786459952713 \tabularnewline
54 & 9.3 & -0.234898109736528 & 9.53489810973653 \tabularnewline
55 & 1.3 & 0.688085411028131 & 0.611914588971869 \tabularnewline
56 & 9.5 & 0.747319088749321 & 8.75268091125068 \tabularnewline
57 & 11.3 & 1.59458354303293 & 9.70541645696707 \tabularnewline
58 & -1.7 & 2.53407333609022 & -4.23407333609022 \tabularnewline
59 & 8 & 2.12421264644849 & 5.87578735355151 \tabularnewline
60 & -4.8 & 2.69299217995053 & -7.49299217995053 \tabularnewline
61 & 1.6 & 1.96766630612177 & -0.367666306121772 \tabularnewline
62 & 1.9 & 1.93207600009173 & -0.0320760000917286 \tabularnewline
63 & -0.9 & 1.9289710251716 & -2.8289710251716 \tabularnewline
64 & 5.5 & 1.65512503259746 & 3.84487496740254 \tabularnewline
65 & 1.7 & 2.02731110039501 & -0.327311100395007 \tabularnewline
66 & -5.4 & 1.9956272010653 & -7.3956272010653 \tabularnewline
67 & 1.9 & 1.27972631216836 & 0.620273687831643 \tabularnewline
68 & 0.2 & 1.33976915537902 & -1.13976915537902 \tabularnewline
69 & -13.3 & 1.22943885758418 & -14.5294388575842 \tabularnewline
70 & -8.2 & -0.177019027667252 & -8.02298097233275 \tabularnewline
71 & 0.2 & -0.953648115849104 & 1.1536481158491 \tabularnewline
72 & 5.7 & -0.841974326844205 & 6.54197432684421 \tabularnewline
73 & -1.2 & -0.208707518174603 & -0.991292481825397 \tabularnewline
74 & -2.8 & -0.304665190134249 & -2.49533480986575 \tabularnewline
75 & 5.5 & -0.546215008683924 & 6.04621500868392 \tabularnewline
76 & -17.3 & 0.0390620180644418 & -17.3390620180644 \tabularnewline
77 & 1.4 & -1.63936897553451 & 3.03936897553451 \tabularnewline
78 & -2.2 & -1.34515634256709 & -0.854843657432912 \tabularnewline
79 & -8.6 & -1.42790569128169 & -7.17209430871831 \tabularnewline
80 & -5 & -2.12216846998483 & -2.87783153001517 \tabularnewline
81 & 4.1 & -2.4007441870162 & 6.5007441870162 \tabularnewline
82 & 0.7 & -1.77146847916195 & 2.47146847916195 \tabularnewline
83 & -4.2 & -1.53222893490018 & -2.66777106509982 \tabularnewline
84 & -2.3 & -1.79047068032015 & -0.509529319679849 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234802&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]2[/C][C]6.7[/C][C]6[/C][C]0.7[/C][/ROW]
[ROW][C]3[/C][C]-0.6[/C][C]6.06776039524487[/C][C]-6.66776039524486[/C][/ROW]
[ROW][C]4[/C][C]5.8[/C][C]5.4223174241308[/C][C]0.377682575869203[/C][/ROW]
[ROW][C]5[/C][C]16.4[/C][C]5.45887731072793[/C][C]10.9411226892721[/C][/ROW]
[ROW][C]6[/C][C]1.5[/C][C]6.51798416479598[/C][C]-5.01798416479598[/C][/ROW]
[ROW][C]7[/C][C]5.1[/C][C]6.03224046431163[/C][C]-0.932240464311627[/C][/ROW]
[ROW][C]8[/C][C]14.7[/C][C]5.94199906099018[/C][C]8.75800093900982[/C][/ROW]
[ROW][C]9[/C][C]4.3[/C][C]6.78977849696475[/C][C]-2.48977849696475[/C][/ROW]
[ROW][C]10[/C][C]1.5[/C][C]6.54876653264119[/C][C]-5.04876653264119[/C][/ROW]
[ROW][C]11[/C][C]9.1[/C][C]6.0600430815686[/C][C]3.0399569184314[/C][/ROW]
[ROW][C]12[/C][C]4.3[/C][C]6.35431262774042[/C][C]-2.05431262774042[/C][/ROW]
[ROW][C]13[/C][C]5.7[/C][C]6.15545400543726[/C][C]-0.455454005437264[/C][/ROW]
[ROW][C]14[/C][C]13[/C][C]6.11136580054543[/C][C]6.88863419945457[/C][/ROW]
[ROW][C]15[/C][C]14.5[/C][C]6.77818948062019[/C][C]7.72181051937981[/C][/ROW]
[ROW][C]16[/C][C]9.7[/C][C]7.52566509890466[/C][C]2.17433490109534[/C][/ROW]
[ROW][C]17[/C][C]-4.7[/C][C]7.73614194503741[/C][C]-12.4361419450374[/C][/ROW]
[ROW][C]18[/C][C]7.3[/C][C]6.5323163828703[/C][C]0.767683617129697[/C][/ROW]
[ROW][C]19[/C][C]5.2[/C][C]6.6066285904699[/C][C]-1.4066285904699[/C][/ROW]
[ROW][C]20[/C][C]-2.5[/C][C]6.47046614867994[/C][C]-8.97046614867994[/C][/ROW]
[ROW][C]21[/C][C]11.5[/C][C]5.6021199604439[/C][C]5.8978800395561[/C][/ROW]
[ROW][C]22[/C][C]4.9[/C][C]6.1730380784255[/C][C]-1.2730380784255[/C][/ROW]
[ROW][C]23[/C][C]-2.4[/C][C]6.04980727363139[/C][C]-8.44980727363139[/C][/ROW]
[ROW][C]24[/C][C]-0.3[/C][C]5.23186115848254[/C][C]-5.53186115848254[/C][/ROW]
[ROW][C]25[/C][C]4.4[/C][C]4.69637387485612[/C][C]-0.296373874856121[/C][/ROW]
[ROW][C]26[/C][C]7.9[/C][C]4.66768471642683[/C][C]3.23231528357317[/C][/ROW]
[ROW][C]27[/C][C]-9.7[/C][C]4.98057466095674[/C][C]-14.6805746609567[/C][/ROW]
[ROW][C]28[/C][C]-4.1[/C][C]3.5594867446022[/C][C]-7.6594867446022[/C][/ROW]
[ROW][C]29[/C][C]16.4[/C][C]2.81804410290642[/C][C]13.5819558970936[/C][/ROW]
[ROW][C]30[/C][C]-4.9[/C][C]4.13278510259982[/C][C]-9.03278510259982[/C][/ROW]
[ROW][C]31[/C][C]3.5[/C][C]3.25840640443684[/C][C]0.241593595563162[/C][/ROW]
[ROW][C]32[/C][C]3.8[/C][C]3.28179280089968[/C][C]0.518207199100322[/C][/ROW]
[ROW][C]33[/C][C]-0.2[/C][C]3.33195555037078[/C][C]-3.53195555037078[/C][/ROW]
[ROW][C]34[/C][C]3.1[/C][C]2.99006025882733[/C][C]0.109939741172674[/C][/ROW]
[ROW][C]35[/C][C]0.7[/C][C]3.00070248784872[/C][C]-2.30070248784872[/C][/ROW]
[ROW][C]36[/C][C]-2.8[/C][C]2.77799318796662[/C][C]-5.57799318796662[/C][/ROW]
[ROW][C]37[/C][C]5.9[/C][C]2.23804029783836[/C][C]3.66195970216164[/C][/ROW]
[ROW][C]38[/C][C]-5.3[/C][C]2.59252006468013[/C][C]-7.89252006468013[/C][/ROW]
[ROW][C]39[/C][C]-2.9[/C][C]1.82851966602192[/C][C]-4.72851966602192[/C][/ROW]
[ROW][C]40[/C][C]6.6[/C][C]1.37079629246083[/C][C]5.22920370753917[/C][/ROW]
[ROW][C]41[/C][C]-8.1[/C][C]1.87698616394478[/C][C]-9.97698616394478[/C][/ROW]
[ROW][C]42[/C][C]1.3[/C][C]0.911208269914144[/C][C]0.388791730085856[/C][/ROW]
[ROW][C]43[/C][C]6.9[/C][C]0.948843528912076[/C][C]5.95115647108792[/C][/ROW]
[ROW][C]44[/C][C]-7.2[/C][C]1.52491883554772[/C][C]-8.72491883554772[/C][/ROW]
[ROW][C]45[/C][C]-1.9[/C][C]0.68034176586761[/C][C]-2.58034176586761[/C][/ROW]
[ROW][C]46[/C][C]4[/C][C]0.430563225979008[/C][C]3.56943677402099[/C][/ROW]
[ROW][C]47[/C][C]-5.7[/C][C]0.776086721135033[/C][C]-6.47608672113503[/C][/ROW]
[ROW][C]48[/C][C]3.9[/C][C]0.149197869900561[/C][C]3.75080213009944[/C][/ROW]
[ROW][C]49[/C][C]-7.6[/C][C]0.512277633930302[/C][C]-8.1122776339303[/C][/ROW]
[ROW][C]50[/C][C]-0.9[/C][C]-0.27299542151426[/C][C]-0.62700457848574[/C][/ROW]
[ROW][C]51[/C][C]7.3[/C][C]-0.333689818740737[/C][C]7.63368981874074[/C][/ROW]
[ROW][C]52[/C][C]-3.7[/C][C]0.405255665965795[/C][C]-4.1052556659658[/C][/ROW]
[ROW][C]53[/C][C]-2.5[/C][C]0.00786459952713391[/C][C]-2.50786459952713[/C][/ROW]
[ROW][C]54[/C][C]9.3[/C][C]-0.234898109736528[/C][C]9.53489810973653[/C][/ROW]
[ROW][C]55[/C][C]1.3[/C][C]0.688085411028131[/C][C]0.611914588971869[/C][/ROW]
[ROW][C]56[/C][C]9.5[/C][C]0.747319088749321[/C][C]8.75268091125068[/C][/ROW]
[ROW][C]57[/C][C]11.3[/C][C]1.59458354303293[/C][C]9.70541645696707[/C][/ROW]
[ROW][C]58[/C][C]-1.7[/C][C]2.53407333609022[/C][C]-4.23407333609022[/C][/ROW]
[ROW][C]59[/C][C]8[/C][C]2.12421264644849[/C][C]5.87578735355151[/C][/ROW]
[ROW][C]60[/C][C]-4.8[/C][C]2.69299217995053[/C][C]-7.49299217995053[/C][/ROW]
[ROW][C]61[/C][C]1.6[/C][C]1.96766630612177[/C][C]-0.367666306121772[/C][/ROW]
[ROW][C]62[/C][C]1.9[/C][C]1.93207600009173[/C][C]-0.0320760000917286[/C][/ROW]
[ROW][C]63[/C][C]-0.9[/C][C]1.9289710251716[/C][C]-2.8289710251716[/C][/ROW]
[ROW][C]64[/C][C]5.5[/C][C]1.65512503259746[/C][C]3.84487496740254[/C][/ROW]
[ROW][C]65[/C][C]1.7[/C][C]2.02731110039501[/C][C]-0.327311100395007[/C][/ROW]
[ROW][C]66[/C][C]-5.4[/C][C]1.9956272010653[/C][C]-7.3956272010653[/C][/ROW]
[ROW][C]67[/C][C]1.9[/C][C]1.27972631216836[/C][C]0.620273687831643[/C][/ROW]
[ROW][C]68[/C][C]0.2[/C][C]1.33976915537902[/C][C]-1.13976915537902[/C][/ROW]
[ROW][C]69[/C][C]-13.3[/C][C]1.22943885758418[/C][C]-14.5294388575842[/C][/ROW]
[ROW][C]70[/C][C]-8.2[/C][C]-0.177019027667252[/C][C]-8.02298097233275[/C][/ROW]
[ROW][C]71[/C][C]0.2[/C][C]-0.953648115849104[/C][C]1.1536481158491[/C][/ROW]
[ROW][C]72[/C][C]5.7[/C][C]-0.841974326844205[/C][C]6.54197432684421[/C][/ROW]
[ROW][C]73[/C][C]-1.2[/C][C]-0.208707518174603[/C][C]-0.991292481825397[/C][/ROW]
[ROW][C]74[/C][C]-2.8[/C][C]-0.304665190134249[/C][C]-2.49533480986575[/C][/ROW]
[ROW][C]75[/C][C]5.5[/C][C]-0.546215008683924[/C][C]6.04621500868392[/C][/ROW]
[ROW][C]76[/C][C]-17.3[/C][C]0.0390620180644418[/C][C]-17.3390620180644[/C][/ROW]
[ROW][C]77[/C][C]1.4[/C][C]-1.63936897553451[/C][C]3.03936897553451[/C][/ROW]
[ROW][C]78[/C][C]-2.2[/C][C]-1.34515634256709[/C][C]-0.854843657432912[/C][/ROW]
[ROW][C]79[/C][C]-8.6[/C][C]-1.42790569128169[/C][C]-7.17209430871831[/C][/ROW]
[ROW][C]80[/C][C]-5[/C][C]-2.12216846998483[/C][C]-2.87783153001517[/C][/ROW]
[ROW][C]81[/C][C]4.1[/C][C]-2.4007441870162[/C][C]6.5007441870162[/C][/ROW]
[ROW][C]82[/C][C]0.7[/C][C]-1.77146847916195[/C][C]2.47146847916195[/C][/ROW]
[ROW][C]83[/C][C]-4.2[/C][C]-1.53222893490018[/C][C]-2.66777106509982[/C][/ROW]
[ROW][C]84[/C][C]-2.3[/C][C]-1.79047068032015[/C][C]-0.509529319679849[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234802&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234802&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
2	6.7	6	0.7
3	-0.6	6.06776039524487	-6.66776039524486
4	5.8	5.4223174241308	0.377682575869203
5	16.4	5.45887731072793	10.9411226892721
6	1.5	6.51798416479598	-5.01798416479598
7	5.1	6.03224046431163	-0.932240464311627
8	14.7	5.94199906099018	8.75800093900982
9	4.3	6.78977849696475	-2.48977849696475
10	1.5	6.54876653264119	-5.04876653264119
11	9.1	6.0600430815686	3.0399569184314
12	4.3	6.35431262774042	-2.05431262774042
13	5.7	6.15545400543726	-0.455454005437264
14	13	6.11136580054543	6.88863419945457
15	14.5	6.77818948062019	7.72181051937981
16	9.7	7.52566509890466	2.17433490109534
17	-4.7	7.73614194503741	-12.4361419450374
18	7.3	6.5323163828703	0.767683617129697
19	5.2	6.6066285904699	-1.4066285904699
20	-2.5	6.47046614867994	-8.97046614867994
21	11.5	5.6021199604439	5.8978800395561
22	4.9	6.1730380784255	-1.2730380784255
23	-2.4	6.04980727363139	-8.44980727363139
24	-0.3	5.23186115848254	-5.53186115848254
25	4.4	4.69637387485612	-0.296373874856121
26	7.9	4.66768471642683	3.23231528357317
27	-9.7	4.98057466095674	-14.6805746609567
28	-4.1	3.5594867446022	-7.6594867446022
29	16.4	2.81804410290642	13.5819558970936
30	-4.9	4.13278510259982	-9.03278510259982
31	3.5	3.25840640443684	0.241593595563162
32	3.8	3.28179280089968	0.518207199100322
33	-0.2	3.33195555037078	-3.53195555037078
34	3.1	2.99006025882733	0.109939741172674
35	0.7	3.00070248784872	-2.30070248784872
36	-2.8	2.77799318796662	-5.57799318796662
37	5.9	2.23804029783836	3.66195970216164
38	-5.3	2.59252006468013	-7.89252006468013
39	-2.9	1.82851966602192	-4.72851966602192
40	6.6	1.37079629246083	5.22920370753917
41	-8.1	1.87698616394478	-9.97698616394478
42	1.3	0.911208269914144	0.388791730085856
43	6.9	0.948843528912076	5.95115647108792
44	-7.2	1.52491883554772	-8.72491883554772
45	-1.9	0.68034176586761	-2.58034176586761
46	4	0.430563225979008	3.56943677402099
47	-5.7	0.776086721135033	-6.47608672113503
48	3.9	0.149197869900561	3.75080213009944
49	-7.6	0.512277633930302	-8.1122776339303
50	-0.9	-0.27299542151426	-0.62700457848574
51	7.3	-0.333689818740737	7.63368981874074
52	-3.7	0.405255665965795	-4.1052556659658
53	-2.5	0.00786459952713391	-2.50786459952713
54	9.3	-0.234898109736528	9.53489810973653
55	1.3	0.688085411028131	0.611914588971869
56	9.5	0.747319088749321	8.75268091125068
57	11.3	1.59458354303293	9.70541645696707
58	-1.7	2.53407333609022	-4.23407333609022
59	8	2.12421264644849	5.87578735355151
60	-4.8	2.69299217995053	-7.49299217995053
61	1.6	1.96766630612177	-0.367666306121772
62	1.9	1.93207600009173	-0.0320760000917286
63	-0.9	1.9289710251716	-2.8289710251716
64	5.5	1.65512503259746	3.84487496740254
65	1.7	2.02731110039501	-0.327311100395007
66	-5.4	1.9956272010653	-7.3956272010653
67	1.9	1.27972631216836	0.620273687831643
68	0.2	1.33976915537902	-1.13976915537902
69	-13.3	1.22943885758418	-14.5294388575842
70	-8.2	-0.177019027667252	-8.02298097233275
71	0.2	-0.953648115849104	1.1536481158491
72	5.7	-0.841974326844205	6.54197432684421
73	-1.2	-0.208707518174603	-0.991292481825397
74	-2.8	-0.304665190134249	-2.49533480986575
75	5.5	-0.546215008683924	6.04621500868392
76	-17.3	0.0390620180644418	-17.3390620180644
77	1.4	-1.63936897553451	3.03936897553451
78	-2.2	-1.34515634256709	-0.854843657432912
79	-8.6	-1.42790569128169	-7.17209430871831
80	-5	-2.12216846998483	-2.87783153001517
81	4.1	-2.4007441870162	6.5007441870162
82	0.7	-1.77146847916195	2.47146847916195
83	-4.2	-1.53222893490018	-2.66777106509982
84	-2.3	-1.79047068032015	-0.509529319679849

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	-1.83979340616351	-13.9315146847069	10.2519278723799
86	-1.83979340616351	-13.9880344171097	10.3084476047827
87	-1.83979340616351	-14.0442924062082	10.3647055938812
88	-1.83979340616351	-14.1002922550745	10.4207054427475
89	-1.83979340616351	-14.1560374848672	10.4764506725402
90	-1.83979340616351	-14.2115315374149	10.5319447250879
91	-1.83979340616351	-14.2667777776962	10.5871909653691
92	-1.83979340616351	-14.3217794962204	10.6421926838934
93	-1.83979340616351	-14.3765399113151	10.696953098988
94	-1.83979340616351	-14.4310621713232	10.7514753589962
95	-1.83979340616351	-14.4853493567155	10.8057625443885
96	-1.83979340616351	-14.5394044821216	10.8598176697946

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & -1.83979340616351 & -13.9315146847069 & 10.2519278723799 \tabularnewline
86 & -1.83979340616351 & -13.9880344171097 & 10.3084476047827 \tabularnewline
87 & -1.83979340616351 & -14.0442924062082 & 10.3647055938812 \tabularnewline
88 & -1.83979340616351 & -14.1002922550745 & 10.4207054427475 \tabularnewline
89 & -1.83979340616351 & -14.1560374848672 & 10.4764506725402 \tabularnewline
90 & -1.83979340616351 & -14.2115315374149 & 10.5319447250879 \tabularnewline
91 & -1.83979340616351 & -14.2667777776962 & 10.5871909653691 \tabularnewline
92 & -1.83979340616351 & -14.3217794962204 & 10.6421926838934 \tabularnewline
93 & -1.83979340616351 & -14.3765399113151 & 10.696953098988 \tabularnewline
94 & -1.83979340616351 & -14.4310621713232 & 10.7514753589962 \tabularnewline
95 & -1.83979340616351 & -14.4853493567155 & 10.8057625443885 \tabularnewline
96 & -1.83979340616351 & -14.5394044821216 & 10.8598176697946 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234802&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]-1.83979340616351[/C][C]-13.9315146847069[/C][C]10.2519278723799[/C][/ROW]
[ROW][C]86[/C][C]-1.83979340616351[/C][C]-13.9880344171097[/C][C]10.3084476047827[/C][/ROW]
[ROW][C]87[/C][C]-1.83979340616351[/C][C]-14.0442924062082[/C][C]10.3647055938812[/C][/ROW]
[ROW][C]88[/C][C]-1.83979340616351[/C][C]-14.1002922550745[/C][C]10.4207054427475[/C][/ROW]
[ROW][C]89[/C][C]-1.83979340616351[/C][C]-14.1560374848672[/C][C]10.4764506725402[/C][/ROW]
[ROW][C]90[/C][C]-1.83979340616351[/C][C]-14.2115315374149[/C][C]10.5319447250879[/C][/ROW]
[ROW][C]91[/C][C]-1.83979340616351[/C][C]-14.2667777776962[/C][C]10.5871909653691[/C][/ROW]
[ROW][C]92[/C][C]-1.83979340616351[/C][C]-14.3217794962204[/C][C]10.6421926838934[/C][/ROW]
[ROW][C]93[/C][C]-1.83979340616351[/C][C]-14.3765399113151[/C][C]10.696953098988[/C][/ROW]
[ROW][C]94[/C][C]-1.83979340616351[/C][C]-14.4310621713232[/C][C]10.7514753589962[/C][/ROW]
[ROW][C]95[/C][C]-1.83979340616351[/C][C]-14.4853493567155[/C][C]10.8057625443885[/C][/ROW]
[ROW][C]96[/C][C]-1.83979340616351[/C][C]-14.5394044821216[/C][C]10.8598176697946[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234802&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234802&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	-1.83979340616351	-13.9315146847069	10.2519278723799
86	-1.83979340616351	-13.9880344171097	10.3084476047827
87	-1.83979340616351	-14.0442924062082	10.3647055938812
88	-1.83979340616351	-14.1002922550745	10.4207054427475
89	-1.83979340616351	-14.1560374848672	10.4764506725402
90	-1.83979340616351	-14.2115315374149	10.5319447250879
91	-1.83979340616351	-14.2667777776962	10.5871909653691
92	-1.83979340616351	-14.3217794962204	10.6421926838934
93	-1.83979340616351	-14.3765399113151	10.696953098988
94	-1.83979340616351	-14.4310621713232	10.7514753589962
95	-1.83979340616351	-14.4853493567155	10.8057625443885
96	-1.83979340616351	-14.5394044821216	10.8598176697946

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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