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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 23 May 2015 12:53:52 +0100

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/2015/May/23/t1432382231tjg4p8xi4ohzrys.htm/, Retrieved Fri, 03 May 2024 01:48:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279258, Retrieved Fri, 03 May 2024 01:48:28 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

158

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

-       [Exponential Smoothing] [] [2015-05-23 11:53:52] [3b0947f879d0db9a6034293524e1b6d0] [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
-3,4
-4,2
-14,2
1,6
-4,9
-1,8
-0,5
-2,3
-5,3
-0,2
5,1
-1,5

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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279258&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279258&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279258&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.116747649819145
beta	0.275386978288426
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.116747649819145 \tabularnewline
beta & 0.275386978288426 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279258&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]0.116747649819145[/C][/ROW]
[ROW][C]beta[/C][C]0.275386978288426[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279258&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279258&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	0.116747649819145
beta	0.275386978288426
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	-0.6	7.4	-8
4	5.8	6.90881254139908	-1.10881254139908
5	16.4	7.18650583219457	9.21349416780543
6	1.5	8.96552521911122	-7.46552521911122
7	5.1	8.55728581370491	-3.45728581370491
8	14.7	8.50584449453487	6.19415550546513
9	4.3	9.78033321320969	-5.48033321320969
10	1.5	9.51565580994096	-8.01565580994096
11	9.1	8.69727584538235	0.402724154617649
12	4.3	8.87466985367555	-4.57466985367555
13	5.7	8.32388559377448	-2.62388559377448
14	13	7.91649083647506	5.08350916352494
15	14.5	8.57235510080234	5.92764489919766
16	9.7	9.51734865032449	0.182651349675512
17	-4.7	9.79750008853162	-14.4975000885316
18	7.3	7.89767237511226	-0.597672375112258
19	5.2	7.60140124558357	-2.40140124558357
20	-2.5	7.0173420803601	-9.5173420803601
21	11.5	5.29652355116381	6.20347644883619
22	4.9	5.61052026057189	-0.710520260571894
23	-2.4	5.09448032093555	-7.49448032093555
24	-0.3	3.54547558099113	-3.84547558099113
25	4.4	2.29884851957768	2.10115148042232
26	7.9	1.81402985619434	6.08597014380566
27	-9.7	1.99009810914779	-11.6900981091478
28	-4.1	-0.284993631236452	-3.81500636876355
29	16.4	-1.76334235884168	18.1633423588417
30	-4.9	-0.0918048558328071	-4.80819514416719
31	3.5	-1.25672760535896	4.75672760535896
32	3.8	-1.15203558849621	4.95203558849621
33	-0.2	-0.865330004443715	0.665330004443715
34	3.1	-1.05769634252839	4.15769634252839
35	0.7	-0.708663927499681	1.40866392749968
36	-2.8	-0.635284938645179	-2.16471506135482
37	5.9	-1.04868683177757	6.94868683177757
38	-5.3	-0.174714752998828	-5.12528524700117
39	-2.9	-0.875132469656874	-2.02486753034313
40	6.6	-1.27868478000892	7.87868478000892
41	-8.1	-0.272714752471228	-7.82728524752877
42	1.3	-1.35203315938399	2.65203315938399
43	6.9	-1.12265082927719	8.02265082927719
44	-7.2	-0.00832700619976764	-7.19167299380023
45	-1.9	-0.901457647331792	-0.998542352668208
46	4	-1.10365875909235	5.10365875909235
47	-5.7	-0.429355609582823	-5.27064439041718
48	3.9	-1.1356833127525	5.0356833127525
49	-7.6	-0.476870319353925	-7.12312968064608
50	-0.9	-1.46658436064939	0.566584360649388
51	7.3	-1.5403262292918	8.8403262292918
52	-3.7	-0.363904773680169	-3.33609522631983
53	-2.5	-0.716309978259224	-1.78369002174078
54	9.3	-0.94482255358372	10.2448225535837
55	1.3	0.560344506813476	0.739655493186524
56	9.5	0.979586154661732	8.52041384533827
57	11.3	2.58115102633671	8.71884897366329
58	-1.7	4.48620054993985	-6.18620054993985
59	8	4.45222938280492	3.54777061719508
60	-4.8	5.66874007433482	-10.4687400743348
61	1.6	4.91227789872222	-3.31227789872222
62	1.9	4.88482353681085	-2.98482353681085
63	-0.9	4.79963428972495	-5.69963428972495
64	5.5	4.21424956512007	1.28575043487993
65	1.7	4.48572997278415	-2.78572997278415
66	-5.4	4.19231121309341	-9.59231121309341
67	1.9	2.79583977875174	-0.895839778751741
68	0.2	2.38585899620195	-2.18585899620195
69	-13.3	1.7549944246177	-15.0549944246177
70	-8.2	-0.86234131481285	-7.33765868518715
71	0.2	-2.81460771229008	3.01460771229008
72	5.7	-3.46134934066148	9.16134934066148
73	-1.2	-3.0959287797622	1.8959287797622
74	-2.8	-3.51777340045066	0.717773400450657
75	5.5	-4.05408791630906	9.55408791630906
76	-17.3	-3.25161207673804	-14.048387923262
77	1.4	-5.65633648603037	7.05633648603037
78	-2.2	-5.37026718080578	3.17026718080578
79	-8.6	-5.43596076338457	-3.16403923661543
80	-5	-6.3428960707684	1.3428960707684
81	4.1	-6.68048211362884	10.7804821136288
82	0.7	-5.56965123027458	6.26965123027458
83	-4.2	-4.7838750581907	0.583875058190703
84	-2.3	-4.64312785158877	2.34312785158877
85	-3.4	-4.22165862197973	0.821658621979731
86	-4.2	-3.95140038155027	-0.248599618449732
87	-14.2	-3.81408494765436	-10.3859150523456
88	1.6	-5.1941925621146	6.7941925621146
89	-4.9	-4.35012438157837	-0.549875618421627
90	-1.8	-4.38113783264453	2.58113783264453
91	-0.5	-3.96362722067129	3.46362722067129
92	-2.3	-3.33172972120204	1.03172972120204
93	-5.3	-2.95057962152556	-2.34942037847444
94	-0.2	-3.03970655327551	2.83970655327551
95	5.1	-2.43171632335528	7.53171632335528
96	-1.5	-1.03379440644091	-0.466205593559086

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & -0.6 & 7.4 & -8 \tabularnewline
4 & 5.8 & 6.90881254139908 & -1.10881254139908 \tabularnewline
5 & 16.4 & 7.18650583219457 & 9.21349416780543 \tabularnewline
6 & 1.5 & 8.96552521911122 & -7.46552521911122 \tabularnewline
7 & 5.1 & 8.55728581370491 & -3.45728581370491 \tabularnewline
8 & 14.7 & 8.50584449453487 & 6.19415550546513 \tabularnewline
9 & 4.3 & 9.78033321320969 & -5.48033321320969 \tabularnewline
10 & 1.5 & 9.51565580994096 & -8.01565580994096 \tabularnewline
11 & 9.1 & 8.69727584538235 & 0.402724154617649 \tabularnewline
12 & 4.3 & 8.87466985367555 & -4.57466985367555 \tabularnewline
13 & 5.7 & 8.32388559377448 & -2.62388559377448 \tabularnewline
14 & 13 & 7.91649083647506 & 5.08350916352494 \tabularnewline
15 & 14.5 & 8.57235510080234 & 5.92764489919766 \tabularnewline
16 & 9.7 & 9.51734865032449 & 0.182651349675512 \tabularnewline
17 & -4.7 & 9.79750008853162 & -14.4975000885316 \tabularnewline
18 & 7.3 & 7.89767237511226 & -0.597672375112258 \tabularnewline
19 & 5.2 & 7.60140124558357 & -2.40140124558357 \tabularnewline
20 & -2.5 & 7.0173420803601 & -9.5173420803601 \tabularnewline
21 & 11.5 & 5.29652355116381 & 6.20347644883619 \tabularnewline
22 & 4.9 & 5.61052026057189 & -0.710520260571894 \tabularnewline
23 & -2.4 & 5.09448032093555 & -7.49448032093555 \tabularnewline
24 & -0.3 & 3.54547558099113 & -3.84547558099113 \tabularnewline
25 & 4.4 & 2.29884851957768 & 2.10115148042232 \tabularnewline
26 & 7.9 & 1.81402985619434 & 6.08597014380566 \tabularnewline
27 & -9.7 & 1.99009810914779 & -11.6900981091478 \tabularnewline
28 & -4.1 & -0.284993631236452 & -3.81500636876355 \tabularnewline
29 & 16.4 & -1.76334235884168 & 18.1633423588417 \tabularnewline
30 & -4.9 & -0.0918048558328071 & -4.80819514416719 \tabularnewline
31 & 3.5 & -1.25672760535896 & 4.75672760535896 \tabularnewline
32 & 3.8 & -1.15203558849621 & 4.95203558849621 \tabularnewline
33 & -0.2 & -0.865330004443715 & 0.665330004443715 \tabularnewline
34 & 3.1 & -1.05769634252839 & 4.15769634252839 \tabularnewline
35 & 0.7 & -0.708663927499681 & 1.40866392749968 \tabularnewline
36 & -2.8 & -0.635284938645179 & -2.16471506135482 \tabularnewline
37 & 5.9 & -1.04868683177757 & 6.94868683177757 \tabularnewline
38 & -5.3 & -0.174714752998828 & -5.12528524700117 \tabularnewline
39 & -2.9 & -0.875132469656874 & -2.02486753034313 \tabularnewline
40 & 6.6 & -1.27868478000892 & 7.87868478000892 \tabularnewline
41 & -8.1 & -0.272714752471228 & -7.82728524752877 \tabularnewline
42 & 1.3 & -1.35203315938399 & 2.65203315938399 \tabularnewline
43 & 6.9 & -1.12265082927719 & 8.02265082927719 \tabularnewline
44 & -7.2 & -0.00832700619976764 & -7.19167299380023 \tabularnewline
45 & -1.9 & -0.901457647331792 & -0.998542352668208 \tabularnewline
46 & 4 & -1.10365875909235 & 5.10365875909235 \tabularnewline
47 & -5.7 & -0.429355609582823 & -5.27064439041718 \tabularnewline
48 & 3.9 & -1.1356833127525 & 5.0356833127525 \tabularnewline
49 & -7.6 & -0.476870319353925 & -7.12312968064608 \tabularnewline
50 & -0.9 & -1.46658436064939 & 0.566584360649388 \tabularnewline
51 & 7.3 & -1.5403262292918 & 8.8403262292918 \tabularnewline
52 & -3.7 & -0.363904773680169 & -3.33609522631983 \tabularnewline
53 & -2.5 & -0.716309978259224 & -1.78369002174078 \tabularnewline
54 & 9.3 & -0.94482255358372 & 10.2448225535837 \tabularnewline
55 & 1.3 & 0.560344506813476 & 0.739655493186524 \tabularnewline
56 & 9.5 & 0.979586154661732 & 8.52041384533827 \tabularnewline
57 & 11.3 & 2.58115102633671 & 8.71884897366329 \tabularnewline
58 & -1.7 & 4.48620054993985 & -6.18620054993985 \tabularnewline
59 & 8 & 4.45222938280492 & 3.54777061719508 \tabularnewline
60 & -4.8 & 5.66874007433482 & -10.4687400743348 \tabularnewline
61 & 1.6 & 4.91227789872222 & -3.31227789872222 \tabularnewline
62 & 1.9 & 4.88482353681085 & -2.98482353681085 \tabularnewline
63 & -0.9 & 4.79963428972495 & -5.69963428972495 \tabularnewline
64 & 5.5 & 4.21424956512007 & 1.28575043487993 \tabularnewline
65 & 1.7 & 4.48572997278415 & -2.78572997278415 \tabularnewline
66 & -5.4 & 4.19231121309341 & -9.59231121309341 \tabularnewline
67 & 1.9 & 2.79583977875174 & -0.895839778751741 \tabularnewline
68 & 0.2 & 2.38585899620195 & -2.18585899620195 \tabularnewline
69 & -13.3 & 1.7549944246177 & -15.0549944246177 \tabularnewline
70 & -8.2 & -0.86234131481285 & -7.33765868518715 \tabularnewline
71 & 0.2 & -2.81460771229008 & 3.01460771229008 \tabularnewline
72 & 5.7 & -3.46134934066148 & 9.16134934066148 \tabularnewline
73 & -1.2 & -3.0959287797622 & 1.8959287797622 \tabularnewline
74 & -2.8 & -3.51777340045066 & 0.717773400450657 \tabularnewline
75 & 5.5 & -4.05408791630906 & 9.55408791630906 \tabularnewline
76 & -17.3 & -3.25161207673804 & -14.048387923262 \tabularnewline
77 & 1.4 & -5.65633648603037 & 7.05633648603037 \tabularnewline
78 & -2.2 & -5.37026718080578 & 3.17026718080578 \tabularnewline
79 & -8.6 & -5.43596076338457 & -3.16403923661543 \tabularnewline
80 & -5 & -6.3428960707684 & 1.3428960707684 \tabularnewline
81 & 4.1 & -6.68048211362884 & 10.7804821136288 \tabularnewline
82 & 0.7 & -5.56965123027458 & 6.26965123027458 \tabularnewline
83 & -4.2 & -4.7838750581907 & 0.583875058190703 \tabularnewline
84 & -2.3 & -4.64312785158877 & 2.34312785158877 \tabularnewline
85 & -3.4 & -4.22165862197973 & 0.821658621979731 \tabularnewline
86 & -4.2 & -3.95140038155027 & -0.248599618449732 \tabularnewline
87 & -14.2 & -3.81408494765436 & -10.3859150523456 \tabularnewline
88 & 1.6 & -5.1941925621146 & 6.7941925621146 \tabularnewline
89 & -4.9 & -4.35012438157837 & -0.549875618421627 \tabularnewline
90 & -1.8 & -4.38113783264453 & 2.58113783264453 \tabularnewline
91 & -0.5 & -3.96362722067129 & 3.46362722067129 \tabularnewline
92 & -2.3 & -3.33172972120204 & 1.03172972120204 \tabularnewline
93 & -5.3 & -2.95057962152556 & -2.34942037847444 \tabularnewline
94 & -0.2 & -3.03970655327551 & 2.83970655327551 \tabularnewline
95 & 5.1 & -2.43171632335528 & 7.53171632335528 \tabularnewline
96 & -1.5 & -1.03379440644091 & -0.466205593559086 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279258&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]-0.6[/C][C]7.4[/C][C]-8[/C][/ROW]
[ROW][C]4[/C][C]5.8[/C][C]6.90881254139908[/C][C]-1.10881254139908[/C][/ROW]
[ROW][C]5[/C][C]16.4[/C][C]7.18650583219457[/C][C]9.21349416780543[/C][/ROW]
[ROW][C]6[/C][C]1.5[/C][C]8.96552521911122[/C][C]-7.46552521911122[/C][/ROW]
[ROW][C]7[/C][C]5.1[/C][C]8.55728581370491[/C][C]-3.45728581370491[/C][/ROW]
[ROW][C]8[/C][C]14.7[/C][C]8.50584449453487[/C][C]6.19415550546513[/C][/ROW]
[ROW][C]9[/C][C]4.3[/C][C]9.78033321320969[/C][C]-5.48033321320969[/C][/ROW]
[ROW][C]10[/C][C]1.5[/C][C]9.51565580994096[/C][C]-8.01565580994096[/C][/ROW]
[ROW][C]11[/C][C]9.1[/C][C]8.69727584538235[/C][C]0.402724154617649[/C][/ROW]
[ROW][C]12[/C][C]4.3[/C][C]8.87466985367555[/C][C]-4.57466985367555[/C][/ROW]
[ROW][C]13[/C][C]5.7[/C][C]8.32388559377448[/C][C]-2.62388559377448[/C][/ROW]
[ROW][C]14[/C][C]13[/C][C]7.91649083647506[/C][C]5.08350916352494[/C][/ROW]
[ROW][C]15[/C][C]14.5[/C][C]8.57235510080234[/C][C]5.92764489919766[/C][/ROW]
[ROW][C]16[/C][C]9.7[/C][C]9.51734865032449[/C][C]0.182651349675512[/C][/ROW]
[ROW][C]17[/C][C]-4.7[/C][C]9.79750008853162[/C][C]-14.4975000885316[/C][/ROW]
[ROW][C]18[/C][C]7.3[/C][C]7.89767237511226[/C][C]-0.597672375112258[/C][/ROW]
[ROW][C]19[/C][C]5.2[/C][C]7.60140124558357[/C][C]-2.40140124558357[/C][/ROW]
[ROW][C]20[/C][C]-2.5[/C][C]7.0173420803601[/C][C]-9.5173420803601[/C][/ROW]
[ROW][C]21[/C][C]11.5[/C][C]5.29652355116381[/C][C]6.20347644883619[/C][/ROW]
[ROW][C]22[/C][C]4.9[/C][C]5.61052026057189[/C][C]-0.710520260571894[/C][/ROW]
[ROW][C]23[/C][C]-2.4[/C][C]5.09448032093555[/C][C]-7.49448032093555[/C][/ROW]
[ROW][C]24[/C][C]-0.3[/C][C]3.54547558099113[/C][C]-3.84547558099113[/C][/ROW]
[ROW][C]25[/C][C]4.4[/C][C]2.29884851957768[/C][C]2.10115148042232[/C][/ROW]
[ROW][C]26[/C][C]7.9[/C][C]1.81402985619434[/C][C]6.08597014380566[/C][/ROW]
[ROW][C]27[/C][C]-9.7[/C][C]1.99009810914779[/C][C]-11.6900981091478[/C][/ROW]
[ROW][C]28[/C][C]-4.1[/C][C]-0.284993631236452[/C][C]-3.81500636876355[/C][/ROW]
[ROW][C]29[/C][C]16.4[/C][C]-1.76334235884168[/C][C]18.1633423588417[/C][/ROW]
[ROW][C]30[/C][C]-4.9[/C][C]-0.0918048558328071[/C][C]-4.80819514416719[/C][/ROW]
[ROW][C]31[/C][C]3.5[/C][C]-1.25672760535896[/C][C]4.75672760535896[/C][/ROW]
[ROW][C]32[/C][C]3.8[/C][C]-1.15203558849621[/C][C]4.95203558849621[/C][/ROW]
[ROW][C]33[/C][C]-0.2[/C][C]-0.865330004443715[/C][C]0.665330004443715[/C][/ROW]
[ROW][C]34[/C][C]3.1[/C][C]-1.05769634252839[/C][C]4.15769634252839[/C][/ROW]
[ROW][C]35[/C][C]0.7[/C][C]-0.708663927499681[/C][C]1.40866392749968[/C][/ROW]
[ROW][C]36[/C][C]-2.8[/C][C]-0.635284938645179[/C][C]-2.16471506135482[/C][/ROW]
[ROW][C]37[/C][C]5.9[/C][C]-1.04868683177757[/C][C]6.94868683177757[/C][/ROW]
[ROW][C]38[/C][C]-5.3[/C][C]-0.174714752998828[/C][C]-5.12528524700117[/C][/ROW]
[ROW][C]39[/C][C]-2.9[/C][C]-0.875132469656874[/C][C]-2.02486753034313[/C][/ROW]
[ROW][C]40[/C][C]6.6[/C][C]-1.27868478000892[/C][C]7.87868478000892[/C][/ROW]
[ROW][C]41[/C][C]-8.1[/C][C]-0.272714752471228[/C][C]-7.82728524752877[/C][/ROW]
[ROW][C]42[/C][C]1.3[/C][C]-1.35203315938399[/C][C]2.65203315938399[/C][/ROW]
[ROW][C]43[/C][C]6.9[/C][C]-1.12265082927719[/C][C]8.02265082927719[/C][/ROW]
[ROW][C]44[/C][C]-7.2[/C][C]-0.00832700619976764[/C][C]-7.19167299380023[/C][/ROW]
[ROW][C]45[/C][C]-1.9[/C][C]-0.901457647331792[/C][C]-0.998542352668208[/C][/ROW]
[ROW][C]46[/C][C]4[/C][C]-1.10365875909235[/C][C]5.10365875909235[/C][/ROW]
[ROW][C]47[/C][C]-5.7[/C][C]-0.429355609582823[/C][C]-5.27064439041718[/C][/ROW]
[ROW][C]48[/C][C]3.9[/C][C]-1.1356833127525[/C][C]5.0356833127525[/C][/ROW]
[ROW][C]49[/C][C]-7.6[/C][C]-0.476870319353925[/C][C]-7.12312968064608[/C][/ROW]
[ROW][C]50[/C][C]-0.9[/C][C]-1.46658436064939[/C][C]0.566584360649388[/C][/ROW]
[ROW][C]51[/C][C]7.3[/C][C]-1.5403262292918[/C][C]8.8403262292918[/C][/ROW]
[ROW][C]52[/C][C]-3.7[/C][C]-0.363904773680169[/C][C]-3.33609522631983[/C][/ROW]
[ROW][C]53[/C][C]-2.5[/C][C]-0.716309978259224[/C][C]-1.78369002174078[/C][/ROW]
[ROW][C]54[/C][C]9.3[/C][C]-0.94482255358372[/C][C]10.2448225535837[/C][/ROW]
[ROW][C]55[/C][C]1.3[/C][C]0.560344506813476[/C][C]0.739655493186524[/C][/ROW]
[ROW][C]56[/C][C]9.5[/C][C]0.979586154661732[/C][C]8.52041384533827[/C][/ROW]
[ROW][C]57[/C][C]11.3[/C][C]2.58115102633671[/C][C]8.71884897366329[/C][/ROW]
[ROW][C]58[/C][C]-1.7[/C][C]4.48620054993985[/C][C]-6.18620054993985[/C][/ROW]
[ROW][C]59[/C][C]8[/C][C]4.45222938280492[/C][C]3.54777061719508[/C][/ROW]
[ROW][C]60[/C][C]-4.8[/C][C]5.66874007433482[/C][C]-10.4687400743348[/C][/ROW]
[ROW][C]61[/C][C]1.6[/C][C]4.91227789872222[/C][C]-3.31227789872222[/C][/ROW]
[ROW][C]62[/C][C]1.9[/C][C]4.88482353681085[/C][C]-2.98482353681085[/C][/ROW]
[ROW][C]63[/C][C]-0.9[/C][C]4.79963428972495[/C][C]-5.69963428972495[/C][/ROW]
[ROW][C]64[/C][C]5.5[/C][C]4.21424956512007[/C][C]1.28575043487993[/C][/ROW]
[ROW][C]65[/C][C]1.7[/C][C]4.48572997278415[/C][C]-2.78572997278415[/C][/ROW]
[ROW][C]66[/C][C]-5.4[/C][C]4.19231121309341[/C][C]-9.59231121309341[/C][/ROW]
[ROW][C]67[/C][C]1.9[/C][C]2.79583977875174[/C][C]-0.895839778751741[/C][/ROW]
[ROW][C]68[/C][C]0.2[/C][C]2.38585899620195[/C][C]-2.18585899620195[/C][/ROW]
[ROW][C]69[/C][C]-13.3[/C][C]1.7549944246177[/C][C]-15.0549944246177[/C][/ROW]
[ROW][C]70[/C][C]-8.2[/C][C]-0.86234131481285[/C][C]-7.33765868518715[/C][/ROW]
[ROW][C]71[/C][C]0.2[/C][C]-2.81460771229008[/C][C]3.01460771229008[/C][/ROW]
[ROW][C]72[/C][C]5.7[/C][C]-3.46134934066148[/C][C]9.16134934066148[/C][/ROW]
[ROW][C]73[/C][C]-1.2[/C][C]-3.0959287797622[/C][C]1.8959287797622[/C][/ROW]
[ROW][C]74[/C][C]-2.8[/C][C]-3.51777340045066[/C][C]0.717773400450657[/C][/ROW]
[ROW][C]75[/C][C]5.5[/C][C]-4.05408791630906[/C][C]9.55408791630906[/C][/ROW]
[ROW][C]76[/C][C]-17.3[/C][C]-3.25161207673804[/C][C]-14.048387923262[/C][/ROW]
[ROW][C]77[/C][C]1.4[/C][C]-5.65633648603037[/C][C]7.05633648603037[/C][/ROW]
[ROW][C]78[/C][C]-2.2[/C][C]-5.37026718080578[/C][C]3.17026718080578[/C][/ROW]
[ROW][C]79[/C][C]-8.6[/C][C]-5.43596076338457[/C][C]-3.16403923661543[/C][/ROW]
[ROW][C]80[/C][C]-5[/C][C]-6.3428960707684[/C][C]1.3428960707684[/C][/ROW]
[ROW][C]81[/C][C]4.1[/C][C]-6.68048211362884[/C][C]10.7804821136288[/C][/ROW]
[ROW][C]82[/C][C]0.7[/C][C]-5.56965123027458[/C][C]6.26965123027458[/C][/ROW]
[ROW][C]83[/C][C]-4.2[/C][C]-4.7838750581907[/C][C]0.583875058190703[/C][/ROW]
[ROW][C]84[/C][C]-2.3[/C][C]-4.64312785158877[/C][C]2.34312785158877[/C][/ROW]
[ROW][C]85[/C][C]-3.4[/C][C]-4.22165862197973[/C][C]0.821658621979731[/C][/ROW]
[ROW][C]86[/C][C]-4.2[/C][C]-3.95140038155027[/C][C]-0.248599618449732[/C][/ROW]
[ROW][C]87[/C][C]-14.2[/C][C]-3.81408494765436[/C][C]-10.3859150523456[/C][/ROW]
[ROW][C]88[/C][C]1.6[/C][C]-5.1941925621146[/C][C]6.7941925621146[/C][/ROW]
[ROW][C]89[/C][C]-4.9[/C][C]-4.35012438157837[/C][C]-0.549875618421627[/C][/ROW]
[ROW][C]90[/C][C]-1.8[/C][C]-4.38113783264453[/C][C]2.58113783264453[/C][/ROW]
[ROW][C]91[/C][C]-0.5[/C][C]-3.96362722067129[/C][C]3.46362722067129[/C][/ROW]
[ROW][C]92[/C][C]-2.3[/C][C]-3.33172972120204[/C][C]1.03172972120204[/C][/ROW]
[ROW][C]93[/C][C]-5.3[/C][C]-2.95057962152556[/C][C]-2.34942037847444[/C][/ROW]
[ROW][C]94[/C][C]-0.2[/C][C]-3.03970655327551[/C][C]2.83970655327551[/C][/ROW]
[ROW][C]95[/C][C]5.1[/C][C]-2.43171632335528[/C][C]7.53171632335528[/C][/ROW]
[ROW][C]96[/C][C]-1.5[/C][C]-1.03379440644091[/C][C]-0.466205593559086[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279258&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279258&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	-0.6	7.4	-8
4	5.8	6.90881254139908	-1.10881254139908
5	16.4	7.18650583219457	9.21349416780543
6	1.5	8.96552521911122	-7.46552521911122
7	5.1	8.55728581370491	-3.45728581370491
8	14.7	8.50584449453487	6.19415550546513
9	4.3	9.78033321320969	-5.48033321320969
10	1.5	9.51565580994096	-8.01565580994096
11	9.1	8.69727584538235	0.402724154617649
12	4.3	8.87466985367555	-4.57466985367555
13	5.7	8.32388559377448	-2.62388559377448
14	13	7.91649083647506	5.08350916352494
15	14.5	8.57235510080234	5.92764489919766
16	9.7	9.51734865032449	0.182651349675512
17	-4.7	9.79750008853162	-14.4975000885316
18	7.3	7.89767237511226	-0.597672375112258
19	5.2	7.60140124558357	-2.40140124558357
20	-2.5	7.0173420803601	-9.5173420803601
21	11.5	5.29652355116381	6.20347644883619
22	4.9	5.61052026057189	-0.710520260571894
23	-2.4	5.09448032093555	-7.49448032093555
24	-0.3	3.54547558099113	-3.84547558099113
25	4.4	2.29884851957768	2.10115148042232
26	7.9	1.81402985619434	6.08597014380566
27	-9.7	1.99009810914779	-11.6900981091478
28	-4.1	-0.284993631236452	-3.81500636876355
29	16.4	-1.76334235884168	18.1633423588417
30	-4.9	-0.0918048558328071	-4.80819514416719
31	3.5	-1.25672760535896	4.75672760535896
32	3.8	-1.15203558849621	4.95203558849621
33	-0.2	-0.865330004443715	0.665330004443715
34	3.1	-1.05769634252839	4.15769634252839
35	0.7	-0.708663927499681	1.40866392749968
36	-2.8	-0.635284938645179	-2.16471506135482
37	5.9	-1.04868683177757	6.94868683177757
38	-5.3	-0.174714752998828	-5.12528524700117
39	-2.9	-0.875132469656874	-2.02486753034313
40	6.6	-1.27868478000892	7.87868478000892
41	-8.1	-0.272714752471228	-7.82728524752877
42	1.3	-1.35203315938399	2.65203315938399
43	6.9	-1.12265082927719	8.02265082927719
44	-7.2	-0.00832700619976764	-7.19167299380023
45	-1.9	-0.901457647331792	-0.998542352668208
46	4	-1.10365875909235	5.10365875909235
47	-5.7	-0.429355609582823	-5.27064439041718
48	3.9	-1.1356833127525	5.0356833127525
49	-7.6	-0.476870319353925	-7.12312968064608
50	-0.9	-1.46658436064939	0.566584360649388
51	7.3	-1.5403262292918	8.8403262292918
52	-3.7	-0.363904773680169	-3.33609522631983
53	-2.5	-0.716309978259224	-1.78369002174078
54	9.3	-0.94482255358372	10.2448225535837
55	1.3	0.560344506813476	0.739655493186524
56	9.5	0.979586154661732	8.52041384533827
57	11.3	2.58115102633671	8.71884897366329
58	-1.7	4.48620054993985	-6.18620054993985
59	8	4.45222938280492	3.54777061719508
60	-4.8	5.66874007433482	-10.4687400743348
61	1.6	4.91227789872222	-3.31227789872222
62	1.9	4.88482353681085	-2.98482353681085
63	-0.9	4.79963428972495	-5.69963428972495
64	5.5	4.21424956512007	1.28575043487993
65	1.7	4.48572997278415	-2.78572997278415
66	-5.4	4.19231121309341	-9.59231121309341
67	1.9	2.79583977875174	-0.895839778751741
68	0.2	2.38585899620195	-2.18585899620195
69	-13.3	1.7549944246177	-15.0549944246177
70	-8.2	-0.86234131481285	-7.33765868518715
71	0.2	-2.81460771229008	3.01460771229008
72	5.7	-3.46134934066148	9.16134934066148
73	-1.2	-3.0959287797622	1.8959287797622
74	-2.8	-3.51777340045066	0.717773400450657
75	5.5	-4.05408791630906	9.55408791630906
76	-17.3	-3.25161207673804	-14.048387923262
77	1.4	-5.65633648603037	7.05633648603037
78	-2.2	-5.37026718080578	3.17026718080578
79	-8.6	-5.43596076338457	-3.16403923661543
80	-5	-6.3428960707684	1.3428960707684
81	4.1	-6.68048211362884	10.7804821136288
82	0.7	-5.56965123027458	6.26965123027458
83	-4.2	-4.7838750581907	0.583875058190703
84	-2.3	-4.64312785158877	2.34312785158877
85	-3.4	-4.22165862197973	0.821658621979731
86	-4.2	-3.95140038155027	-0.248599618449732
87	-14.2	-3.81408494765436	-10.3859150523456
88	1.6	-5.1941925621146	6.7941925621146
89	-4.9	-4.35012438157837	-0.549875618421627
90	-1.8	-4.38113783264453	2.58113783264453
91	-0.5	-3.96362722067129	3.46362722067129
92	-2.3	-3.33172972120204	1.03172972120204
93	-5.3	-2.95057962152556	-2.34942037847444
94	-0.2	-3.03970655327551	2.83970655327551
95	5.1	-2.43171632335528	7.53171632335528
96	-1.5	-1.03379440644091	-0.466205593559086

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	-0.584599951404916	-13.0145466100862	11.8453467072764
98	-0.0809770889883548	-12.6479589458631	12.4860047678863
99	0.422645773428206	-12.3442441200021	13.1895356668585
100	0.926268635844767	-12.1127619993734	13.9652992710629
101	1.42989149826133	-11.961037235221	14.8208202317436
102	1.93351436067789	-11.8945313131234	15.7615600344792
103	2.43713722309445	-11.9165855215244	16.7908599677133
104	2.94076008551101	-12.0285389312029	17.9100591022249
105	3.44438294792757	-12.2299887687497	19.1187546646049
106	3.94800581034413	-12.5191377154883	20.4151493361765
107	4.45162867276069	-12.8931684406043	21.7964257861257
108	4.95525153517726	-13.3485965305027	23.2590996008572

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & -0.584599951404916 & -13.0145466100862 & 11.8453467072764 \tabularnewline
98 & -0.0809770889883548 & -12.6479589458631 & 12.4860047678863 \tabularnewline
99 & 0.422645773428206 & -12.3442441200021 & 13.1895356668585 \tabularnewline
100 & 0.926268635844767 & -12.1127619993734 & 13.9652992710629 \tabularnewline
101 & 1.42989149826133 & -11.961037235221 & 14.8208202317436 \tabularnewline
102 & 1.93351436067789 & -11.8945313131234 & 15.7615600344792 \tabularnewline
103 & 2.43713722309445 & -11.9165855215244 & 16.7908599677133 \tabularnewline
104 & 2.94076008551101 & -12.0285389312029 & 17.9100591022249 \tabularnewline
105 & 3.44438294792757 & -12.2299887687497 & 19.1187546646049 \tabularnewline
106 & 3.94800581034413 & -12.5191377154883 & 20.4151493361765 \tabularnewline
107 & 4.45162867276069 & -12.8931684406043 & 21.7964257861257 \tabularnewline
108 & 4.95525153517726 & -13.3485965305027 & 23.2590996008572 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279258&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]97[/C][C]-0.584599951404916[/C][C]-13.0145466100862[/C][C]11.8453467072764[/C][/ROW]
[ROW][C]98[/C][C]-0.0809770889883548[/C][C]-12.6479589458631[/C][C]12.4860047678863[/C][/ROW]
[ROW][C]99[/C][C]0.422645773428206[/C][C]-12.3442441200021[/C][C]13.1895356668585[/C][/ROW]
[ROW][C]100[/C][C]0.926268635844767[/C][C]-12.1127619993734[/C][C]13.9652992710629[/C][/ROW]
[ROW][C]101[/C][C]1.42989149826133[/C][C]-11.961037235221[/C][C]14.8208202317436[/C][/ROW]
[ROW][C]102[/C][C]1.93351436067789[/C][C]-11.8945313131234[/C][C]15.7615600344792[/C][/ROW]
[ROW][C]103[/C][C]2.43713722309445[/C][C]-11.9165855215244[/C][C]16.7908599677133[/C][/ROW]
[ROW][C]104[/C][C]2.94076008551101[/C][C]-12.0285389312029[/C][C]17.9100591022249[/C][/ROW]
[ROW][C]105[/C][C]3.44438294792757[/C][C]-12.2299887687497[/C][C]19.1187546646049[/C][/ROW]
[ROW][C]106[/C][C]3.94800581034413[/C][C]-12.5191377154883[/C][C]20.4151493361765[/C][/ROW]
[ROW][C]107[/C][C]4.45162867276069[/C][C]-12.8931684406043[/C][C]21.7964257861257[/C][/ROW]
[ROW][C]108[/C][C]4.95525153517726[/C][C]-13.3485965305027[/C][C]23.2590996008572[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279258&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279258&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
97	-0.584599951404916	-13.0145466100862	11.8453467072764
98	-0.0809770889883548	-12.6479589458631	12.4860047678863
99	0.422645773428206	-12.3442441200021	13.1895356668585
100	0.926268635844767	-12.1127619993734	13.9652992710629
101	1.42989149826133	-11.961037235221	14.8208202317436
102	1.93351436067789	-11.8945313131234	15.7615600344792
103	2.43713722309445	-11.9165855215244	16.7908599677133
104	2.94076008551101	-12.0285389312029	17.9100591022249
105	3.44438294792757	-12.2299887687497	19.1187546646049
106	3.94800581034413	-12.5191377154883	20.4151493361765
107	4.45162867276069	-12.8931684406043	21.7964257861257
108	4.95525153517726	-13.3485965305027	23.2590996008572

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 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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