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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 30 Nov 2014 12:37:37 +0000

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/Nov/30/t1417351131m1l7d2vma88amy0.htm/, Retrieved Sun, 19 May 2024 20:35:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261380, Retrieved Sun, 19 May 2024 20:35:00 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [] [2014-11-30 12:37:37] [deb17a426e61079f456ada9a85a82a78] [Current]

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Dataseries X:

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1,5
1,6
1,8
1,5
1,3
1,6
1,6
1,8
1,8
1,6
1,8
2
1,3
1,1
1
1,2
1,2
1,3
1,3
1,4
1,1
0,9
1
1,1
1,4
1,5
1,8
1,8
1,8
1,7
1,5
1,1
1,3
1,6
1,9
1,9
2
2,2
2,2
2
2,3
2,6
3,2
3,2
3,1
2,8
2,3
1,9
1,9
2
2
1,8
1,6
1,4
0,2
0,3
0,4
0,7
1
1,1
0,8
0,8
1
1,1
1
0,8
1,6
1,5
1,6
1,6
1,6
1,9
2
1,9
2
2,1
2,3
2,3
2,6
2,6
2,7
2,6
2,6
2,4
2,5
2,5
2,5
2,4
2,1
2,1
2,3
2,3
2,3
2,9
2,8
2,9
3
3
2,9
2,6
2,8
2,9
3,1
2,8
2,4
1,6
1,5
1,7

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

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261380&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261380&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261380&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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.740702132693206
beta	0
gamma	0.34571069877143

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.740702132693206 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.34571069877143 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261380&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]0.740702132693206[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.34571069877143[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261380&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261380&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	0.740702132693206
beta	0
gamma	0.34571069877143

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.3	1.45788268960083	-0.157882689600832
14	1.1	1.12920796819142	-0.0292079681914168
15	1	1.01336082323361	-0.0133608232336124
16	1.2	1.22345210161089	-0.0234521016108873
17	1.2	1.23038387334623	-0.0303838733462325
18	1.3	1.3456430187265	-0.0456430187264991
19	1.3	1.13411526605523	0.165884733944766
20	1.4	1.39828460033324	0.00171539966675782
21	1.1	1.4052452726138	-0.305245272613796
22	0.9	1.04062208102201	-0.140622081022007
23	1	1.02072124990678	-0.0207212499067768
24	1.1	1.07962929910268	0.0203707008973237
25	1.4	0.683405771806494	0.716594228193506
26	1.5	1.0285206723416	0.4714793276584
27	1.8	1.26863571651706	0.531364283482939
28	1.8	2.04756272949414	-0.247562729494143
29	1.8	1.92004426952746	-0.120044269527463
30	1.7	2.05912918241197	-0.359129182411969
31	1.5	1.58697995983373	-0.0869799598337304
32	1.1	1.68222191703689	-0.582221917036886
33	1.3	1.22234054918566	0.0776594508143422
34	1.6	1.14506100599964	0.454938994000364
35	1.9	1.6612174869706	0.238782513029396
36	1.9	2.02242136255949	-0.12242136255949
37	2	1.29383940966898	0.706160590331016
38	2.2	1.51892291893539	0.681077081064614
39	2.2	1.87119618185272	0.328803818147277
40	2	2.51011341352375	-0.510113413523748
41	2.3	2.21505512601802	0.0849448739819811
42	2.6	2.54043817408046	0.059561825919543
43	3.2	2.33428713198869	0.865712868011311
44	3.2	3.20476238480219	-0.00476238480219449
45	3.1	3.35196180170507	-0.251961801705069
46	2.8	2.95198569187385	-0.15198569187385
47	2.3	3.17236505156024	-0.872365051560236
48	1.9	2.74978852845879	-0.849788528458791
49	1.9	1.48173919453659	0.418260805463406
50	2	1.4895527603609	0.510447239639103
51	2	1.69703346884597	0.302966531154031
52	1.8	2.19772062637939	-0.39772062637939
53	1.6	2.02401625650717	-0.424016256507169
54	1.4	1.89455467066205	-0.49455467066205
55	0.2	1.39807403825302	-1.19807403825302
56	0.3	0.503014581866726	-0.203014581866726
57	0.4	0.329610650444858	0.0703893495551417
58	0.7	0.322203866199465	0.377796133800535
59	1	0.620709232506032	0.379290767493968
60	1.1	0.946111125604867	0.153888874395133
61	0.8	0.767000431699766	0.0329995683002345
62	0.8	0.642776935174876	0.157223064825124
63	1	0.665827652718528	0.334172347281472
64	1.1	0.99393677175485	0.10606322824515
65	1	1.12197710215759	-0.121977102157587
66	0.8	1.12033963164264	-0.320339631642645
67	1.6	0.645107072862889	0.954892927137111
68	1.5	1.68816441773763	-0.188164417737627
69	1.6	1.70531983100286	-0.105319831002859
70	1.6	1.56020452010412	0.0397954798958797
71	1.6	1.67793955242712	-0.0779395524271203
72	1.9	1.69520200745915	0.204797992540851
73	2	1.35029982970785	0.649700170292148
74	1.9	1.55062475377181	0.349375246228185
75	2	1.64813623375513	0.351863766244872
76	2.1	2.061856165357	0.0381438346429981
77	2.3	2.17593197410509	0.124068025894906
78	2.3	2.45377338346897	-0.153773383468975
79	2.6	1.93298329411509	0.667016705884911
80	2.6	2.84376178471115	-0.243761784711155
81	2.7	2.97852601355474	-0.278526013554745
82	2.6	2.70920647628808	-0.109206476288084
83	2.6	2.78530336204663	-0.185303362046628
84	2.4	2.84176167864538	-0.441761678645381
85	2.5	1.89132999914719	0.608670000852811
86	2.5	1.96277570145764	0.537224298542362
87	2.5	2.15702584807693	0.342974151923069
88	2.4	2.57409354233959	-0.174093542339589
89	2.1	2.55956944257073	-0.459569442570728
90	2.1	2.37435401631158	-0.274354016311579
91	2.3	1.84653582772605	0.453464172273949
92	2.3	2.47067009697871	-0.170670096978714
93	2.3	2.61500099146023	-0.31500099146023
94	2.9	2.33441121109461	0.565588788905386
95	2.8	2.91263539824319	-0.112635398243194
96	2.9	3.01085110523509	-0.110851105235092
97	3	2.29731997504398	0.702680024956016
98	3	2.36042214051454	0.639577859485459
99	2.9	2.57553912489363	0.324460875106369
100	2.6	2.95435493395072	-0.354354933950722
101	2.8	2.78692127089788	0.0130787291021233
102	2.9	3.02463546365676	-0.12463546365676
103	3.1	2.58141027886317	0.518589721136829
104	2.8	3.28652782248589	-0.486527822485887
105	2.4	3.25716274655298	-0.857162746552985
106	1.6	2.65379168198688	-1.05379168198688
107	1.5	1.92406691899665	-0.424066918996652
108	1.7	1.69297521611097	0.00702478388903338

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.3 & 1.45788268960083 & -0.157882689600832 \tabularnewline
14 & 1.1 & 1.12920796819142 & -0.0292079681914168 \tabularnewline
15 & 1 & 1.01336082323361 & -0.0133608232336124 \tabularnewline
16 & 1.2 & 1.22345210161089 & -0.0234521016108873 \tabularnewline
17 & 1.2 & 1.23038387334623 & -0.0303838733462325 \tabularnewline
18 & 1.3 & 1.3456430187265 & -0.0456430187264991 \tabularnewline
19 & 1.3 & 1.13411526605523 & 0.165884733944766 \tabularnewline
20 & 1.4 & 1.39828460033324 & 0.00171539966675782 \tabularnewline
21 & 1.1 & 1.4052452726138 & -0.305245272613796 \tabularnewline
22 & 0.9 & 1.04062208102201 & -0.140622081022007 \tabularnewline
23 & 1 & 1.02072124990678 & -0.0207212499067768 \tabularnewline
24 & 1.1 & 1.07962929910268 & 0.0203707008973237 \tabularnewline
25 & 1.4 & 0.683405771806494 & 0.716594228193506 \tabularnewline
26 & 1.5 & 1.0285206723416 & 0.4714793276584 \tabularnewline
27 & 1.8 & 1.26863571651706 & 0.531364283482939 \tabularnewline
28 & 1.8 & 2.04756272949414 & -0.247562729494143 \tabularnewline
29 & 1.8 & 1.92004426952746 & -0.120044269527463 \tabularnewline
30 & 1.7 & 2.05912918241197 & -0.359129182411969 \tabularnewline
31 & 1.5 & 1.58697995983373 & -0.0869799598337304 \tabularnewline
32 & 1.1 & 1.68222191703689 & -0.582221917036886 \tabularnewline
33 & 1.3 & 1.22234054918566 & 0.0776594508143422 \tabularnewline
34 & 1.6 & 1.14506100599964 & 0.454938994000364 \tabularnewline
35 & 1.9 & 1.6612174869706 & 0.238782513029396 \tabularnewline
36 & 1.9 & 2.02242136255949 & -0.12242136255949 \tabularnewline
37 & 2 & 1.29383940966898 & 0.706160590331016 \tabularnewline
38 & 2.2 & 1.51892291893539 & 0.681077081064614 \tabularnewline
39 & 2.2 & 1.87119618185272 & 0.328803818147277 \tabularnewline
40 & 2 & 2.51011341352375 & -0.510113413523748 \tabularnewline
41 & 2.3 & 2.21505512601802 & 0.0849448739819811 \tabularnewline
42 & 2.6 & 2.54043817408046 & 0.059561825919543 \tabularnewline
43 & 3.2 & 2.33428713198869 & 0.865712868011311 \tabularnewline
44 & 3.2 & 3.20476238480219 & -0.00476238480219449 \tabularnewline
45 & 3.1 & 3.35196180170507 & -0.251961801705069 \tabularnewline
46 & 2.8 & 2.95198569187385 & -0.15198569187385 \tabularnewline
47 & 2.3 & 3.17236505156024 & -0.872365051560236 \tabularnewline
48 & 1.9 & 2.74978852845879 & -0.849788528458791 \tabularnewline
49 & 1.9 & 1.48173919453659 & 0.418260805463406 \tabularnewline
50 & 2 & 1.4895527603609 & 0.510447239639103 \tabularnewline
51 & 2 & 1.69703346884597 & 0.302966531154031 \tabularnewline
52 & 1.8 & 2.19772062637939 & -0.39772062637939 \tabularnewline
53 & 1.6 & 2.02401625650717 & -0.424016256507169 \tabularnewline
54 & 1.4 & 1.89455467066205 & -0.49455467066205 \tabularnewline
55 & 0.2 & 1.39807403825302 & -1.19807403825302 \tabularnewline
56 & 0.3 & 0.503014581866726 & -0.203014581866726 \tabularnewline
57 & 0.4 & 0.329610650444858 & 0.0703893495551417 \tabularnewline
58 & 0.7 & 0.322203866199465 & 0.377796133800535 \tabularnewline
59 & 1 & 0.620709232506032 & 0.379290767493968 \tabularnewline
60 & 1.1 & 0.946111125604867 & 0.153888874395133 \tabularnewline
61 & 0.8 & 0.767000431699766 & 0.0329995683002345 \tabularnewline
62 & 0.8 & 0.642776935174876 & 0.157223064825124 \tabularnewline
63 & 1 & 0.665827652718528 & 0.334172347281472 \tabularnewline
64 & 1.1 & 0.99393677175485 & 0.10606322824515 \tabularnewline
65 & 1 & 1.12197710215759 & -0.121977102157587 \tabularnewline
66 & 0.8 & 1.12033963164264 & -0.320339631642645 \tabularnewline
67 & 1.6 & 0.645107072862889 & 0.954892927137111 \tabularnewline
68 & 1.5 & 1.68816441773763 & -0.188164417737627 \tabularnewline
69 & 1.6 & 1.70531983100286 & -0.105319831002859 \tabularnewline
70 & 1.6 & 1.56020452010412 & 0.0397954798958797 \tabularnewline
71 & 1.6 & 1.67793955242712 & -0.0779395524271203 \tabularnewline
72 & 1.9 & 1.69520200745915 & 0.204797992540851 \tabularnewline
73 & 2 & 1.35029982970785 & 0.649700170292148 \tabularnewline
74 & 1.9 & 1.55062475377181 & 0.349375246228185 \tabularnewline
75 & 2 & 1.64813623375513 & 0.351863766244872 \tabularnewline
76 & 2.1 & 2.061856165357 & 0.0381438346429981 \tabularnewline
77 & 2.3 & 2.17593197410509 & 0.124068025894906 \tabularnewline
78 & 2.3 & 2.45377338346897 & -0.153773383468975 \tabularnewline
79 & 2.6 & 1.93298329411509 & 0.667016705884911 \tabularnewline
80 & 2.6 & 2.84376178471115 & -0.243761784711155 \tabularnewline
81 & 2.7 & 2.97852601355474 & -0.278526013554745 \tabularnewline
82 & 2.6 & 2.70920647628808 & -0.109206476288084 \tabularnewline
83 & 2.6 & 2.78530336204663 & -0.185303362046628 \tabularnewline
84 & 2.4 & 2.84176167864538 & -0.441761678645381 \tabularnewline
85 & 2.5 & 1.89132999914719 & 0.608670000852811 \tabularnewline
86 & 2.5 & 1.96277570145764 & 0.537224298542362 \tabularnewline
87 & 2.5 & 2.15702584807693 & 0.342974151923069 \tabularnewline
88 & 2.4 & 2.57409354233959 & -0.174093542339589 \tabularnewline
89 & 2.1 & 2.55956944257073 & -0.459569442570728 \tabularnewline
90 & 2.1 & 2.37435401631158 & -0.274354016311579 \tabularnewline
91 & 2.3 & 1.84653582772605 & 0.453464172273949 \tabularnewline
92 & 2.3 & 2.47067009697871 & -0.170670096978714 \tabularnewline
93 & 2.3 & 2.61500099146023 & -0.31500099146023 \tabularnewline
94 & 2.9 & 2.33441121109461 & 0.565588788905386 \tabularnewline
95 & 2.8 & 2.91263539824319 & -0.112635398243194 \tabularnewline
96 & 2.9 & 3.01085110523509 & -0.110851105235092 \tabularnewline
97 & 3 & 2.29731997504398 & 0.702680024956016 \tabularnewline
98 & 3 & 2.36042214051454 & 0.639577859485459 \tabularnewline
99 & 2.9 & 2.57553912489363 & 0.324460875106369 \tabularnewline
100 & 2.6 & 2.95435493395072 & -0.354354933950722 \tabularnewline
101 & 2.8 & 2.78692127089788 & 0.0130787291021233 \tabularnewline
102 & 2.9 & 3.02463546365676 & -0.12463546365676 \tabularnewline
103 & 3.1 & 2.58141027886317 & 0.518589721136829 \tabularnewline
104 & 2.8 & 3.28652782248589 & -0.486527822485887 \tabularnewline
105 & 2.4 & 3.25716274655298 & -0.857162746552985 \tabularnewline
106 & 1.6 & 2.65379168198688 & -1.05379168198688 \tabularnewline
107 & 1.5 & 1.92406691899665 & -0.424066918996652 \tabularnewline
108 & 1.7 & 1.69297521611097 & 0.00702478388903338 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261380&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]1.3[/C][C]1.45788268960083[/C][C]-0.157882689600832[/C][/ROW]
[ROW][C]14[/C][C]1.1[/C][C]1.12920796819142[/C][C]-0.0292079681914168[/C][/ROW]
[ROW][C]15[/C][C]1[/C][C]1.01336082323361[/C][C]-0.0133608232336124[/C][/ROW]
[ROW][C]16[/C][C]1.2[/C][C]1.22345210161089[/C][C]-0.0234521016108873[/C][/ROW]
[ROW][C]17[/C][C]1.2[/C][C]1.23038387334623[/C][C]-0.0303838733462325[/C][/ROW]
[ROW][C]18[/C][C]1.3[/C][C]1.3456430187265[/C][C]-0.0456430187264991[/C][/ROW]
[ROW][C]19[/C][C]1.3[/C][C]1.13411526605523[/C][C]0.165884733944766[/C][/ROW]
[ROW][C]20[/C][C]1.4[/C][C]1.39828460033324[/C][C]0.00171539966675782[/C][/ROW]
[ROW][C]21[/C][C]1.1[/C][C]1.4052452726138[/C][C]-0.305245272613796[/C][/ROW]
[ROW][C]22[/C][C]0.9[/C][C]1.04062208102201[/C][C]-0.140622081022007[/C][/ROW]
[ROW][C]23[/C][C]1[/C][C]1.02072124990678[/C][C]-0.0207212499067768[/C][/ROW]
[ROW][C]24[/C][C]1.1[/C][C]1.07962929910268[/C][C]0.0203707008973237[/C][/ROW]
[ROW][C]25[/C][C]1.4[/C][C]0.683405771806494[/C][C]0.716594228193506[/C][/ROW]
[ROW][C]26[/C][C]1.5[/C][C]1.0285206723416[/C][C]0.4714793276584[/C][/ROW]
[ROW][C]27[/C][C]1.8[/C][C]1.26863571651706[/C][C]0.531364283482939[/C][/ROW]
[ROW][C]28[/C][C]1.8[/C][C]2.04756272949414[/C][C]-0.247562729494143[/C][/ROW]
[ROW][C]29[/C][C]1.8[/C][C]1.92004426952746[/C][C]-0.120044269527463[/C][/ROW]
[ROW][C]30[/C][C]1.7[/C][C]2.05912918241197[/C][C]-0.359129182411969[/C][/ROW]
[ROW][C]31[/C][C]1.5[/C][C]1.58697995983373[/C][C]-0.0869799598337304[/C][/ROW]
[ROW][C]32[/C][C]1.1[/C][C]1.68222191703689[/C][C]-0.582221917036886[/C][/ROW]
[ROW][C]33[/C][C]1.3[/C][C]1.22234054918566[/C][C]0.0776594508143422[/C][/ROW]
[ROW][C]34[/C][C]1.6[/C][C]1.14506100599964[/C][C]0.454938994000364[/C][/ROW]
[ROW][C]35[/C][C]1.9[/C][C]1.6612174869706[/C][C]0.238782513029396[/C][/ROW]
[ROW][C]36[/C][C]1.9[/C][C]2.02242136255949[/C][C]-0.12242136255949[/C][/ROW]
[ROW][C]37[/C][C]2[/C][C]1.29383940966898[/C][C]0.706160590331016[/C][/ROW]
[ROW][C]38[/C][C]2.2[/C][C]1.51892291893539[/C][C]0.681077081064614[/C][/ROW]
[ROW][C]39[/C][C]2.2[/C][C]1.87119618185272[/C][C]0.328803818147277[/C][/ROW]
[ROW][C]40[/C][C]2[/C][C]2.51011341352375[/C][C]-0.510113413523748[/C][/ROW]
[ROW][C]41[/C][C]2.3[/C][C]2.21505512601802[/C][C]0.0849448739819811[/C][/ROW]
[ROW][C]42[/C][C]2.6[/C][C]2.54043817408046[/C][C]0.059561825919543[/C][/ROW]
[ROW][C]43[/C][C]3.2[/C][C]2.33428713198869[/C][C]0.865712868011311[/C][/ROW]
[ROW][C]44[/C][C]3.2[/C][C]3.20476238480219[/C][C]-0.00476238480219449[/C][/ROW]
[ROW][C]45[/C][C]3.1[/C][C]3.35196180170507[/C][C]-0.251961801705069[/C][/ROW]
[ROW][C]46[/C][C]2.8[/C][C]2.95198569187385[/C][C]-0.15198569187385[/C][/ROW]
[ROW][C]47[/C][C]2.3[/C][C]3.17236505156024[/C][C]-0.872365051560236[/C][/ROW]
[ROW][C]48[/C][C]1.9[/C][C]2.74978852845879[/C][C]-0.849788528458791[/C][/ROW]
[ROW][C]49[/C][C]1.9[/C][C]1.48173919453659[/C][C]0.418260805463406[/C][/ROW]
[ROW][C]50[/C][C]2[/C][C]1.4895527603609[/C][C]0.510447239639103[/C][/ROW]
[ROW][C]51[/C][C]2[/C][C]1.69703346884597[/C][C]0.302966531154031[/C][/ROW]
[ROW][C]52[/C][C]1.8[/C][C]2.19772062637939[/C][C]-0.39772062637939[/C][/ROW]
[ROW][C]53[/C][C]1.6[/C][C]2.02401625650717[/C][C]-0.424016256507169[/C][/ROW]
[ROW][C]54[/C][C]1.4[/C][C]1.89455467066205[/C][C]-0.49455467066205[/C][/ROW]
[ROW][C]55[/C][C]0.2[/C][C]1.39807403825302[/C][C]-1.19807403825302[/C][/ROW]
[ROW][C]56[/C][C]0.3[/C][C]0.503014581866726[/C][C]-0.203014581866726[/C][/ROW]
[ROW][C]57[/C][C]0.4[/C][C]0.329610650444858[/C][C]0.0703893495551417[/C][/ROW]
[ROW][C]58[/C][C]0.7[/C][C]0.322203866199465[/C][C]0.377796133800535[/C][/ROW]
[ROW][C]59[/C][C]1[/C][C]0.620709232506032[/C][C]0.379290767493968[/C][/ROW]
[ROW][C]60[/C][C]1.1[/C][C]0.946111125604867[/C][C]0.153888874395133[/C][/ROW]
[ROW][C]61[/C][C]0.8[/C][C]0.767000431699766[/C][C]0.0329995683002345[/C][/ROW]
[ROW][C]62[/C][C]0.8[/C][C]0.642776935174876[/C][C]0.157223064825124[/C][/ROW]
[ROW][C]63[/C][C]1[/C][C]0.665827652718528[/C][C]0.334172347281472[/C][/ROW]
[ROW][C]64[/C][C]1.1[/C][C]0.99393677175485[/C][C]0.10606322824515[/C][/ROW]
[ROW][C]65[/C][C]1[/C][C]1.12197710215759[/C][C]-0.121977102157587[/C][/ROW]
[ROW][C]66[/C][C]0.8[/C][C]1.12033963164264[/C][C]-0.320339631642645[/C][/ROW]
[ROW][C]67[/C][C]1.6[/C][C]0.645107072862889[/C][C]0.954892927137111[/C][/ROW]
[ROW][C]68[/C][C]1.5[/C][C]1.68816441773763[/C][C]-0.188164417737627[/C][/ROW]
[ROW][C]69[/C][C]1.6[/C][C]1.70531983100286[/C][C]-0.105319831002859[/C][/ROW]
[ROW][C]70[/C][C]1.6[/C][C]1.56020452010412[/C][C]0.0397954798958797[/C][/ROW]
[ROW][C]71[/C][C]1.6[/C][C]1.67793955242712[/C][C]-0.0779395524271203[/C][/ROW]
[ROW][C]72[/C][C]1.9[/C][C]1.69520200745915[/C][C]0.204797992540851[/C][/ROW]
[ROW][C]73[/C][C]2[/C][C]1.35029982970785[/C][C]0.649700170292148[/C][/ROW]
[ROW][C]74[/C][C]1.9[/C][C]1.55062475377181[/C][C]0.349375246228185[/C][/ROW]
[ROW][C]75[/C][C]2[/C][C]1.64813623375513[/C][C]0.351863766244872[/C][/ROW]
[ROW][C]76[/C][C]2.1[/C][C]2.061856165357[/C][C]0.0381438346429981[/C][/ROW]
[ROW][C]77[/C][C]2.3[/C][C]2.17593197410509[/C][C]0.124068025894906[/C][/ROW]
[ROW][C]78[/C][C]2.3[/C][C]2.45377338346897[/C][C]-0.153773383468975[/C][/ROW]
[ROW][C]79[/C][C]2.6[/C][C]1.93298329411509[/C][C]0.667016705884911[/C][/ROW]
[ROW][C]80[/C][C]2.6[/C][C]2.84376178471115[/C][C]-0.243761784711155[/C][/ROW]
[ROW][C]81[/C][C]2.7[/C][C]2.97852601355474[/C][C]-0.278526013554745[/C][/ROW]
[ROW][C]82[/C][C]2.6[/C][C]2.70920647628808[/C][C]-0.109206476288084[/C][/ROW]
[ROW][C]83[/C][C]2.6[/C][C]2.78530336204663[/C][C]-0.185303362046628[/C][/ROW]
[ROW][C]84[/C][C]2.4[/C][C]2.84176167864538[/C][C]-0.441761678645381[/C][/ROW]
[ROW][C]85[/C][C]2.5[/C][C]1.89132999914719[/C][C]0.608670000852811[/C][/ROW]
[ROW][C]86[/C][C]2.5[/C][C]1.96277570145764[/C][C]0.537224298542362[/C][/ROW]
[ROW][C]87[/C][C]2.5[/C][C]2.15702584807693[/C][C]0.342974151923069[/C][/ROW]
[ROW][C]88[/C][C]2.4[/C][C]2.57409354233959[/C][C]-0.174093542339589[/C][/ROW]
[ROW][C]89[/C][C]2.1[/C][C]2.55956944257073[/C][C]-0.459569442570728[/C][/ROW]
[ROW][C]90[/C][C]2.1[/C][C]2.37435401631158[/C][C]-0.274354016311579[/C][/ROW]
[ROW][C]91[/C][C]2.3[/C][C]1.84653582772605[/C][C]0.453464172273949[/C][/ROW]
[ROW][C]92[/C][C]2.3[/C][C]2.47067009697871[/C][C]-0.170670096978714[/C][/ROW]
[ROW][C]93[/C][C]2.3[/C][C]2.61500099146023[/C][C]-0.31500099146023[/C][/ROW]
[ROW][C]94[/C][C]2.9[/C][C]2.33441121109461[/C][C]0.565588788905386[/C][/ROW]
[ROW][C]95[/C][C]2.8[/C][C]2.91263539824319[/C][C]-0.112635398243194[/C][/ROW]
[ROW][C]96[/C][C]2.9[/C][C]3.01085110523509[/C][C]-0.110851105235092[/C][/ROW]
[ROW][C]97[/C][C]3[/C][C]2.29731997504398[/C][C]0.702680024956016[/C][/ROW]
[ROW][C]98[/C][C]3[/C][C]2.36042214051454[/C][C]0.639577859485459[/C][/ROW]
[ROW][C]99[/C][C]2.9[/C][C]2.57553912489363[/C][C]0.324460875106369[/C][/ROW]
[ROW][C]100[/C][C]2.6[/C][C]2.95435493395072[/C][C]-0.354354933950722[/C][/ROW]
[ROW][C]101[/C][C]2.8[/C][C]2.78692127089788[/C][C]0.0130787291021233[/C][/ROW]
[ROW][C]102[/C][C]2.9[/C][C]3.02463546365676[/C][C]-0.12463546365676[/C][/ROW]
[ROW][C]103[/C][C]3.1[/C][C]2.58141027886317[/C][C]0.518589721136829[/C][/ROW]
[ROW][C]104[/C][C]2.8[/C][C]3.28652782248589[/C][C]-0.486527822485887[/C][/ROW]
[ROW][C]105[/C][C]2.4[/C][C]3.25716274655298[/C][C]-0.857162746552985[/C][/ROW]
[ROW][C]106[/C][C]1.6[/C][C]2.65379168198688[/C][C]-1.05379168198688[/C][/ROW]
[ROW][C]107[/C][C]1.5[/C][C]1.92406691899665[/C][C]-0.424066918996652[/C][/ROW]
[ROW][C]108[/C][C]1.7[/C][C]1.69297521611097[/C][C]0.00702478388903338[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261380&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261380&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.3	1.45788268960083	-0.157882689600832
14	1.1	1.12920796819142	-0.0292079681914168
15	1	1.01336082323361	-0.0133608232336124
16	1.2	1.22345210161089	-0.0234521016108873
17	1.2	1.23038387334623	-0.0303838733462325
18	1.3	1.3456430187265	-0.0456430187264991
19	1.3	1.13411526605523	0.165884733944766
20	1.4	1.39828460033324	0.00171539966675782
21	1.1	1.4052452726138	-0.305245272613796
22	0.9	1.04062208102201	-0.140622081022007
23	1	1.02072124990678	-0.0207212499067768
24	1.1	1.07962929910268	0.0203707008973237
25	1.4	0.683405771806494	0.716594228193506
26	1.5	1.0285206723416	0.4714793276584
27	1.8	1.26863571651706	0.531364283482939
28	1.8	2.04756272949414	-0.247562729494143
29	1.8	1.92004426952746	-0.120044269527463
30	1.7	2.05912918241197	-0.359129182411969
31	1.5	1.58697995983373	-0.0869799598337304
32	1.1	1.68222191703689	-0.582221917036886
33	1.3	1.22234054918566	0.0776594508143422
34	1.6	1.14506100599964	0.454938994000364
35	1.9	1.6612174869706	0.238782513029396
36	1.9	2.02242136255949	-0.12242136255949
37	2	1.29383940966898	0.706160590331016
38	2.2	1.51892291893539	0.681077081064614
39	2.2	1.87119618185272	0.328803818147277
40	2	2.51011341352375	-0.510113413523748
41	2.3	2.21505512601802	0.0849448739819811
42	2.6	2.54043817408046	0.059561825919543
43	3.2	2.33428713198869	0.865712868011311
44	3.2	3.20476238480219	-0.00476238480219449
45	3.1	3.35196180170507	-0.251961801705069
46	2.8	2.95198569187385	-0.15198569187385
47	2.3	3.17236505156024	-0.872365051560236
48	1.9	2.74978852845879	-0.849788528458791
49	1.9	1.48173919453659	0.418260805463406
50	2	1.4895527603609	0.510447239639103
51	2	1.69703346884597	0.302966531154031
52	1.8	2.19772062637939	-0.39772062637939
53	1.6	2.02401625650717	-0.424016256507169
54	1.4	1.89455467066205	-0.49455467066205
55	0.2	1.39807403825302	-1.19807403825302
56	0.3	0.503014581866726	-0.203014581866726
57	0.4	0.329610650444858	0.0703893495551417
58	0.7	0.322203866199465	0.377796133800535
59	1	0.620709232506032	0.379290767493968
60	1.1	0.946111125604867	0.153888874395133
61	0.8	0.767000431699766	0.0329995683002345
62	0.8	0.642776935174876	0.157223064825124
63	1	0.665827652718528	0.334172347281472
64	1.1	0.99393677175485	0.10606322824515
65	1	1.12197710215759	-0.121977102157587
66	0.8	1.12033963164264	-0.320339631642645
67	1.6	0.645107072862889	0.954892927137111
68	1.5	1.68816441773763	-0.188164417737627
69	1.6	1.70531983100286	-0.105319831002859
70	1.6	1.56020452010412	0.0397954798958797
71	1.6	1.67793955242712	-0.0779395524271203
72	1.9	1.69520200745915	0.204797992540851
73	2	1.35029982970785	0.649700170292148
74	1.9	1.55062475377181	0.349375246228185
75	2	1.64813623375513	0.351863766244872
76	2.1	2.061856165357	0.0381438346429981
77	2.3	2.17593197410509	0.124068025894906
78	2.3	2.45377338346897	-0.153773383468975
79	2.6	1.93298329411509	0.667016705884911
80	2.6	2.84376178471115	-0.243761784711155
81	2.7	2.97852601355474	-0.278526013554745
82	2.6	2.70920647628808	-0.109206476288084
83	2.6	2.78530336204663	-0.185303362046628
84	2.4	2.84176167864538	-0.441761678645381
85	2.5	1.89132999914719	0.608670000852811
86	2.5	1.96277570145764	0.537224298542362
87	2.5	2.15702584807693	0.342974151923069
88	2.4	2.57409354233959	-0.174093542339589
89	2.1	2.55956944257073	-0.459569442570728
90	2.1	2.37435401631158	-0.274354016311579
91	2.3	1.84653582772605	0.453464172273949
92	2.3	2.47067009697871	-0.170670096978714
93	2.3	2.61500099146023	-0.31500099146023
94	2.9	2.33441121109461	0.565588788905386
95	2.8	2.91263539824319	-0.112635398243194
96	2.9	3.01085110523509	-0.110851105235092
97	3	2.29731997504398	0.702680024956016
98	3	2.36042214051454	0.639577859485459
99	2.9	2.57553912489363	0.324460875106369
100	2.6	2.95435493395072	-0.354354933950722
101	2.8	2.78692127089788	0.0130787291021233
102	2.9	3.02463546365676	-0.12463546365676
103	3.1	2.58141027886317	0.518589721136829
104	2.8	3.28652782248589	-0.486527822485887
105	2.4	3.25716274655298	-0.857162746552985
106	1.6	2.65379168198688	-1.05379168198688
107	1.5	1.92406691899665	-0.424066918996652
108	1.7	1.69297521611097	0.00702478388903338

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	1.34999802840115	0.66518891361329	2.03480714318901
110	1.11077911418766	0.252281733728522	1.9692764946468
111	0.980903692221545	-0.019336943733412	1.9811443281765
112	0.985944175851864	-0.215043849064168	2.1869322007679
113	1.01232660800065	-0.396191833920582	2.42084504992189
114	1.06697583529625	-0.579909583634074	2.71386125422658
115	0.936634078547016	-0.685208007724171	2.5584761648182
116	0.981952356564007	-0.878910941870381	2.8428156549984
117	1.0506838159701	-1.09941127587952	3.20077890781972
118	1.01655220878296	-1.230397633658	3.26350205122392
119	1.05498972535807	-1.44546763032804	3.55544708104418
120	1.1207980067519	-22.3879382105567	24.6295342240605

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1.34999802840115 & 0.66518891361329 & 2.03480714318901 \tabularnewline
110 & 1.11077911418766 & 0.252281733728522 & 1.9692764946468 \tabularnewline
111 & 0.980903692221545 & -0.019336943733412 & 1.9811443281765 \tabularnewline
112 & 0.985944175851864 & -0.215043849064168 & 2.1869322007679 \tabularnewline
113 & 1.01232660800065 & -0.396191833920582 & 2.42084504992189 \tabularnewline
114 & 1.06697583529625 & -0.579909583634074 & 2.71386125422658 \tabularnewline
115 & 0.936634078547016 & -0.685208007724171 & 2.5584761648182 \tabularnewline
116 & 0.981952356564007 & -0.878910941870381 & 2.8428156549984 \tabularnewline
117 & 1.0506838159701 & -1.09941127587952 & 3.20077890781972 \tabularnewline
118 & 1.01655220878296 & -1.230397633658 & 3.26350205122392 \tabularnewline
119 & 1.05498972535807 & -1.44546763032804 & 3.55544708104418 \tabularnewline
120 & 1.1207980067519 & -22.3879382105567 & 24.6295342240605 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261380&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]109[/C][C]1.34999802840115[/C][C]0.66518891361329[/C][C]2.03480714318901[/C][/ROW]
[ROW][C]110[/C][C]1.11077911418766[/C][C]0.252281733728522[/C][C]1.9692764946468[/C][/ROW]
[ROW][C]111[/C][C]0.980903692221545[/C][C]-0.019336943733412[/C][C]1.9811443281765[/C][/ROW]
[ROW][C]112[/C][C]0.985944175851864[/C][C]-0.215043849064168[/C][C]2.1869322007679[/C][/ROW]
[ROW][C]113[/C][C]1.01232660800065[/C][C]-0.396191833920582[/C][C]2.42084504992189[/C][/ROW]
[ROW][C]114[/C][C]1.06697583529625[/C][C]-0.579909583634074[/C][C]2.71386125422658[/C][/ROW]
[ROW][C]115[/C][C]0.936634078547016[/C][C]-0.685208007724171[/C][C]2.5584761648182[/C][/ROW]
[ROW][C]116[/C][C]0.981952356564007[/C][C]-0.878910941870381[/C][C]2.8428156549984[/C][/ROW]
[ROW][C]117[/C][C]1.0506838159701[/C][C]-1.09941127587952[/C][C]3.20077890781972[/C][/ROW]
[ROW][C]118[/C][C]1.01655220878296[/C][C]-1.230397633658[/C][C]3.26350205122392[/C][/ROW]
[ROW][C]119[/C][C]1.05498972535807[/C][C]-1.44546763032804[/C][C]3.55544708104418[/C][/ROW]
[ROW][C]120[/C][C]1.1207980067519[/C][C]-22.3879382105567[/C][C]24.6295342240605[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261380&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261380&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
109	1.34999802840115	0.66518891361329	2.03480714318901
110	1.11077911418766	0.252281733728522	1.9692764946468
111	0.980903692221545	-0.019336943733412	1.9811443281765
112	0.985944175851864	-0.215043849064168	2.1869322007679
113	1.01232660800065	-0.396191833920582	2.42084504992189
114	1.06697583529625	-0.579909583634074	2.71386125422658
115	0.936634078547016	-0.685208007724171	2.5584761648182
116	0.981952356564007	-0.878910941870381	2.8428156549984
117	1.0506838159701	-1.09941127587952	3.20077890781972
118	1.01655220878296	-1.230397633658	3.26350205122392
119	1.05498972535807	-1.44546763032804	3.55544708104418
120	1.1207980067519	-22.3879382105567	24.6295342240605

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code