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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 03 Jan 2015 10:50:46 +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/2015/Jan/03/t14202822987lpmtecdzayxybc.htm/, Retrieved Thu, 12 Feb 2026 16:02:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271889, Retrieved Thu, 12 Feb 2026 16:02:14 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

329

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

-       [Exponential Smoothing] [Voorspellen van t...] [2015-01-03 10:50:46] [5cb566f42d00ad61092156d0d2251413] [Current]

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Dataseries X:

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Boxplots

1,8
1,8
1,81
1,81
1,81
1,81
1,81
1,81
1,82
1,82
1,81
1,8
1,8
1,81
1,81
1,81
1,81
1,81
1,81
1,82
1,82
1,82
1,83
1,83
1,83
1,84
1,85
1,86
1,86
1,87
1,87
1,86
1,88
1,89
1,91
1,91
1,91
1,91
1,92
1,93
1,93
1,94
1,94
1,95
1,95
1,96
1,97
1,97
1,97
1,97
1,98
1,98
1,99
1,99
1,99
2
2
2,01
2,01
2,02
2,01
2,01
2,03
2,03
2,04
2,05
2,05
2,06
2,06
2,06
2,04
2,04
2,04
2,03
2,03
2,03
2,03
2,03
2,03
2,03
2,03
2,03
2,02
2,03
2,03
2,02
2,03
2,04
2,05
2,05
2,05
2,05
2,07
2,07
2,08
2,08

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	'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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271889&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271889&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271889&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.897683552095963
beta	0.105010829289059
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.897683552095963 \tabularnewline
beta & 0.105010829289059 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271889&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]0.897683552095963[/C][/ROW]
[ROW][C]beta[/C][C]0.105010829289059[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271889&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271889&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	0.897683552095963
beta	0.105010829289059
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.81	1.8	0.01
4	1.81	1.80991950046341	8.04995365928374e-05
5	1.81	1.81094201692491	-0.000942016924908362
6	1.81	1.81095783654414	-0.000957836544142276
7	1.81	1.81086916325831	-0.000869163258313765
8	1.81	1.8107781575494	-0.000778157549396141
9	1.82	1.81069549198437	0.00930450801563087
10	1.82	1.82054097280966	-0.000540972809656814
11	1.81	1.82149733182536	-0.0114973318253595
12	1.8	1.81153453439746	-0.0115345343974624
13	1.8	1.8004510207121	-0.000451020712098682
14	1.81	1.79927447882016	0.0107255211798449
15	1.81	1.80914199203449	0.00085800796550739
16	1.81	1.81023248233917	-0.000232482339172169
17	1.81	1.81032214213853	-0.000322142138533321
18	1.81	1.81030094860068	-0.000300948600675532
19	1.81	1.81027041078363	-0.000270410783629993
20	1.82	1.81024179558608	0.00975820441391551
21	1.82	1.8201355750219	-0.000135575021898537
22	1.82	1.8211350912081	-0.00113509120809541
23	1.83	1.82113035708505	0.00886964291494552
24	1.83	1.83094281837016	-0.000942818370155196
25	1.83	1.83185791837158	-0.00185791837157856
26	1.84	1.83177640870172	0.00822359129828043
27	1.85	1.84152011356458	0.00847988643542008
28	1.86	1.85229325952239	0.00770674047760656
29	1.86	1.86309885247739	-0.00309885247738628
30	1.87	1.86391232440681	0.0060876755931869
31	1.87	1.87354625532233	-0.00354625532233022
32	1.86	1.87419767185603	-0.0141976718560262
33	1.88	1.8639491222086	0.0160508777914043
34	1.89	1.88236725803337	0.00763274196663222
35	1.91	1.8939480836156	0.0160519163843986
36	1.91	1.91459982147836	-0.0045998214783578
37	1.91	1.9162792248946	-0.00627922489460397
38	1.91	1.91585913496936	-0.00585913496936374
39	1.92	1.91526383274754	0.00473616725245596
40	1.93	1.92462622094278	0.00537377905721659
41	1.93	1.93506755008035	-0.00506755008034854
42	1.94	1.93565816960862	0.00434183039138292
43	1.94	1.94510472435137	-0.00510472435137266
44	1.95	1.94559005780889	0.00440994219110724
45	1.95	1.95503226071545	-0.00503226071545271
46	1.96	1.95552397980147	0.00447602019853033
47	1.97	1.96497306500496	0.0050269349950387
48	1.97	1.97539056889866	-0.00539056889866329
49	1.97	1.97594830086103	-0.00594830086103171
50	1.97	1.97544464054542	-0.00544464054542138
51	1.98	1.97487986063434	0.00512013936566191
52	1.98	1.98428156746899	-0.00428156746899355
53	1.99	1.98483990836138	0.00516009163862385
54	1.99	1.99436029508792	-0.00436029508791869
55	1.99	1.99492335750864	-0.00492335750864048
56	2	1.99451686040322	0.00548313959677582
57	2	2.00396898093152	-0.00396898093151687
58	2.01	2.00456194641099	0.00543805358900551
59	2.01	2.01411207830089	-0.00411207830089433
60	2.02	2.0147015826674	0.00529841733260161
61	2.01	2.02423819740815	-0.0142381974081531
62	2.01	2.01489492947846	-0.00489492947846504
63	2.03	2.01347753165057	0.0165224683494265
64	2.03	2.03284369474905	-0.00284369474904622
65	2.04	2.03455710663212	0.00544289336788273
66	2.05	2.04422233484709	0.005777665152912
67	2.05	2.05473272242607	-0.00473272242607026
68	2.06	2.05536197079791	0.00463802920209266
69	2.06	2.06484039953021	-0.00484039953020865
70	2.06	2.06535391119535	-0.00535391119535289
71	2.04	2.064901757446	-0.0249017574460035
72	2.04	2.04455442226358	-0.00455442226357716
73	2.04	2.0420432257833	-0.00204322578330052
74	2.03	2.04159368134791	-0.0115936813479078
75	2.03	2.03147795434109	-0.00147795434108522
76	2.03	2.03030362751139	-0.000303627511392346
77	2.03	2.03015485266044	-0.000154852660444682
78	2.03	2.03012503312873	-0.000125033128733687
79	2.03	2.03011019566546	-0.000110195665460555
80	2.03	2.03009828978986	-9.82897898587076e-05
81	2.03	2.03008780618905	-8.780618904769e-05
82	2.03	2.03007845636264	-7.84563626372581e-05
83	2.02	2.03007010391535	-0.010070103915353
84	2.03	2.02014314040888	0.00985685959112459
85	2.03	2.0290334558833	0.000966544116702384
86	2.02	2.0300341941088	-0.0100341941088007
87	2.03	2.02021386226715	0.00978613773285142
88	2.04	2.0291084212131	0.0108915787868962
89	2.05	2.04002202736012	0.00997797263988254
90	2.05	2.05105609279629	-0.00105609279629482
91	2.05	2.05208550501216	-0.00208550501216154
92	2.05	2.05199423756729	-0.00199423756729189
93	2.07	2.05179690962236	0.0182030903776362
94	2.07	2.07144633228421	-0.00144633228420599
95	2.08	2.07332045074039	0.00667954925961478
96	2.08	2.08311869709657	-0.00311869709657175

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.81 & 1.8 & 0.01 \tabularnewline
4 & 1.81 & 1.80991950046341 & 8.04995365928374e-05 \tabularnewline
5 & 1.81 & 1.81094201692491 & -0.000942016924908362 \tabularnewline
6 & 1.81 & 1.81095783654414 & -0.000957836544142276 \tabularnewline
7 & 1.81 & 1.81086916325831 & -0.000869163258313765 \tabularnewline
8 & 1.81 & 1.8107781575494 & -0.000778157549396141 \tabularnewline
9 & 1.82 & 1.81069549198437 & 0.00930450801563087 \tabularnewline
10 & 1.82 & 1.82054097280966 & -0.000540972809656814 \tabularnewline
11 & 1.81 & 1.82149733182536 & -0.0114973318253595 \tabularnewline
12 & 1.8 & 1.81153453439746 & -0.0115345343974624 \tabularnewline
13 & 1.8 & 1.8004510207121 & -0.000451020712098682 \tabularnewline
14 & 1.81 & 1.79927447882016 & 0.0107255211798449 \tabularnewline
15 & 1.81 & 1.80914199203449 & 0.00085800796550739 \tabularnewline
16 & 1.81 & 1.81023248233917 & -0.000232482339172169 \tabularnewline
17 & 1.81 & 1.81032214213853 & -0.000322142138533321 \tabularnewline
18 & 1.81 & 1.81030094860068 & -0.000300948600675532 \tabularnewline
19 & 1.81 & 1.81027041078363 & -0.000270410783629993 \tabularnewline
20 & 1.82 & 1.81024179558608 & 0.00975820441391551 \tabularnewline
21 & 1.82 & 1.8201355750219 & -0.000135575021898537 \tabularnewline
22 & 1.82 & 1.8211350912081 & -0.00113509120809541 \tabularnewline
23 & 1.83 & 1.82113035708505 & 0.00886964291494552 \tabularnewline
24 & 1.83 & 1.83094281837016 & -0.000942818370155196 \tabularnewline
25 & 1.83 & 1.83185791837158 & -0.00185791837157856 \tabularnewline
26 & 1.84 & 1.83177640870172 & 0.00822359129828043 \tabularnewline
27 & 1.85 & 1.84152011356458 & 0.00847988643542008 \tabularnewline
28 & 1.86 & 1.85229325952239 & 0.00770674047760656 \tabularnewline
29 & 1.86 & 1.86309885247739 & -0.00309885247738628 \tabularnewline
30 & 1.87 & 1.86391232440681 & 0.0060876755931869 \tabularnewline
31 & 1.87 & 1.87354625532233 & -0.00354625532233022 \tabularnewline
32 & 1.86 & 1.87419767185603 & -0.0141976718560262 \tabularnewline
33 & 1.88 & 1.8639491222086 & 0.0160508777914043 \tabularnewline
34 & 1.89 & 1.88236725803337 & 0.00763274196663222 \tabularnewline
35 & 1.91 & 1.8939480836156 & 0.0160519163843986 \tabularnewline
36 & 1.91 & 1.91459982147836 & -0.0045998214783578 \tabularnewline
37 & 1.91 & 1.9162792248946 & -0.00627922489460397 \tabularnewline
38 & 1.91 & 1.91585913496936 & -0.00585913496936374 \tabularnewline
39 & 1.92 & 1.91526383274754 & 0.00473616725245596 \tabularnewline
40 & 1.93 & 1.92462622094278 & 0.00537377905721659 \tabularnewline
41 & 1.93 & 1.93506755008035 & -0.00506755008034854 \tabularnewline
42 & 1.94 & 1.93565816960862 & 0.00434183039138292 \tabularnewline
43 & 1.94 & 1.94510472435137 & -0.00510472435137266 \tabularnewline
44 & 1.95 & 1.94559005780889 & 0.00440994219110724 \tabularnewline
45 & 1.95 & 1.95503226071545 & -0.00503226071545271 \tabularnewline
46 & 1.96 & 1.95552397980147 & 0.00447602019853033 \tabularnewline
47 & 1.97 & 1.96497306500496 & 0.0050269349950387 \tabularnewline
48 & 1.97 & 1.97539056889866 & -0.00539056889866329 \tabularnewline
49 & 1.97 & 1.97594830086103 & -0.00594830086103171 \tabularnewline
50 & 1.97 & 1.97544464054542 & -0.00544464054542138 \tabularnewline
51 & 1.98 & 1.97487986063434 & 0.00512013936566191 \tabularnewline
52 & 1.98 & 1.98428156746899 & -0.00428156746899355 \tabularnewline
53 & 1.99 & 1.98483990836138 & 0.00516009163862385 \tabularnewline
54 & 1.99 & 1.99436029508792 & -0.00436029508791869 \tabularnewline
55 & 1.99 & 1.99492335750864 & -0.00492335750864048 \tabularnewline
56 & 2 & 1.99451686040322 & 0.00548313959677582 \tabularnewline
57 & 2 & 2.00396898093152 & -0.00396898093151687 \tabularnewline
58 & 2.01 & 2.00456194641099 & 0.00543805358900551 \tabularnewline
59 & 2.01 & 2.01411207830089 & -0.00411207830089433 \tabularnewline
60 & 2.02 & 2.0147015826674 & 0.00529841733260161 \tabularnewline
61 & 2.01 & 2.02423819740815 & -0.0142381974081531 \tabularnewline
62 & 2.01 & 2.01489492947846 & -0.00489492947846504 \tabularnewline
63 & 2.03 & 2.01347753165057 & 0.0165224683494265 \tabularnewline
64 & 2.03 & 2.03284369474905 & -0.00284369474904622 \tabularnewline
65 & 2.04 & 2.03455710663212 & 0.00544289336788273 \tabularnewline
66 & 2.05 & 2.04422233484709 & 0.005777665152912 \tabularnewline
67 & 2.05 & 2.05473272242607 & -0.00473272242607026 \tabularnewline
68 & 2.06 & 2.05536197079791 & 0.00463802920209266 \tabularnewline
69 & 2.06 & 2.06484039953021 & -0.00484039953020865 \tabularnewline
70 & 2.06 & 2.06535391119535 & -0.00535391119535289 \tabularnewline
71 & 2.04 & 2.064901757446 & -0.0249017574460035 \tabularnewline
72 & 2.04 & 2.04455442226358 & -0.00455442226357716 \tabularnewline
73 & 2.04 & 2.0420432257833 & -0.00204322578330052 \tabularnewline
74 & 2.03 & 2.04159368134791 & -0.0115936813479078 \tabularnewline
75 & 2.03 & 2.03147795434109 & -0.00147795434108522 \tabularnewline
76 & 2.03 & 2.03030362751139 & -0.000303627511392346 \tabularnewline
77 & 2.03 & 2.03015485266044 & -0.000154852660444682 \tabularnewline
78 & 2.03 & 2.03012503312873 & -0.000125033128733687 \tabularnewline
79 & 2.03 & 2.03011019566546 & -0.000110195665460555 \tabularnewline
80 & 2.03 & 2.03009828978986 & -9.82897898587076e-05 \tabularnewline
81 & 2.03 & 2.03008780618905 & -8.780618904769e-05 \tabularnewline
82 & 2.03 & 2.03007845636264 & -7.84563626372581e-05 \tabularnewline
83 & 2.02 & 2.03007010391535 & -0.010070103915353 \tabularnewline
84 & 2.03 & 2.02014314040888 & 0.00985685959112459 \tabularnewline
85 & 2.03 & 2.0290334558833 & 0.000966544116702384 \tabularnewline
86 & 2.02 & 2.0300341941088 & -0.0100341941088007 \tabularnewline
87 & 2.03 & 2.02021386226715 & 0.00978613773285142 \tabularnewline
88 & 2.04 & 2.0291084212131 & 0.0108915787868962 \tabularnewline
89 & 2.05 & 2.04002202736012 & 0.00997797263988254 \tabularnewline
90 & 2.05 & 2.05105609279629 & -0.00105609279629482 \tabularnewline
91 & 2.05 & 2.05208550501216 & -0.00208550501216154 \tabularnewline
92 & 2.05 & 2.05199423756729 & -0.00199423756729189 \tabularnewline
93 & 2.07 & 2.05179690962236 & 0.0182030903776362 \tabularnewline
94 & 2.07 & 2.07144633228421 & -0.00144633228420599 \tabularnewline
95 & 2.08 & 2.07332045074039 & 0.00667954925961478 \tabularnewline
96 & 2.08 & 2.08311869709657 & -0.00311869709657175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271889&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]1.81[/C][C]1.8[/C][C]0.01[/C][/ROW]
[ROW][C]4[/C][C]1.81[/C][C]1.80991950046341[/C][C]8.04995365928374e-05[/C][/ROW]
[ROW][C]5[/C][C]1.81[/C][C]1.81094201692491[/C][C]-0.000942016924908362[/C][/ROW]
[ROW][C]6[/C][C]1.81[/C][C]1.81095783654414[/C][C]-0.000957836544142276[/C][/ROW]
[ROW][C]7[/C][C]1.81[/C][C]1.81086916325831[/C][C]-0.000869163258313765[/C][/ROW]
[ROW][C]8[/C][C]1.81[/C][C]1.8107781575494[/C][C]-0.000778157549396141[/C][/ROW]
[ROW][C]9[/C][C]1.82[/C][C]1.81069549198437[/C][C]0.00930450801563087[/C][/ROW]
[ROW][C]10[/C][C]1.82[/C][C]1.82054097280966[/C][C]-0.000540972809656814[/C][/ROW]
[ROW][C]11[/C][C]1.81[/C][C]1.82149733182536[/C][C]-0.0114973318253595[/C][/ROW]
[ROW][C]12[/C][C]1.8[/C][C]1.81153453439746[/C][C]-0.0115345343974624[/C][/ROW]
[ROW][C]13[/C][C]1.8[/C][C]1.8004510207121[/C][C]-0.000451020712098682[/C][/ROW]
[ROW][C]14[/C][C]1.81[/C][C]1.79927447882016[/C][C]0.0107255211798449[/C][/ROW]
[ROW][C]15[/C][C]1.81[/C][C]1.80914199203449[/C][C]0.00085800796550739[/C][/ROW]
[ROW][C]16[/C][C]1.81[/C][C]1.81023248233917[/C][C]-0.000232482339172169[/C][/ROW]
[ROW][C]17[/C][C]1.81[/C][C]1.81032214213853[/C][C]-0.000322142138533321[/C][/ROW]
[ROW][C]18[/C][C]1.81[/C][C]1.81030094860068[/C][C]-0.000300948600675532[/C][/ROW]
[ROW][C]19[/C][C]1.81[/C][C]1.81027041078363[/C][C]-0.000270410783629993[/C][/ROW]
[ROW][C]20[/C][C]1.82[/C][C]1.81024179558608[/C][C]0.00975820441391551[/C][/ROW]
[ROW][C]21[/C][C]1.82[/C][C]1.8201355750219[/C][C]-0.000135575021898537[/C][/ROW]
[ROW][C]22[/C][C]1.82[/C][C]1.8211350912081[/C][C]-0.00113509120809541[/C][/ROW]
[ROW][C]23[/C][C]1.83[/C][C]1.82113035708505[/C][C]0.00886964291494552[/C][/ROW]
[ROW][C]24[/C][C]1.83[/C][C]1.83094281837016[/C][C]-0.000942818370155196[/C][/ROW]
[ROW][C]25[/C][C]1.83[/C][C]1.83185791837158[/C][C]-0.00185791837157856[/C][/ROW]
[ROW][C]26[/C][C]1.84[/C][C]1.83177640870172[/C][C]0.00822359129828043[/C][/ROW]
[ROW][C]27[/C][C]1.85[/C][C]1.84152011356458[/C][C]0.00847988643542008[/C][/ROW]
[ROW][C]28[/C][C]1.86[/C][C]1.85229325952239[/C][C]0.00770674047760656[/C][/ROW]
[ROW][C]29[/C][C]1.86[/C][C]1.86309885247739[/C][C]-0.00309885247738628[/C][/ROW]
[ROW][C]30[/C][C]1.87[/C][C]1.86391232440681[/C][C]0.0060876755931869[/C][/ROW]
[ROW][C]31[/C][C]1.87[/C][C]1.87354625532233[/C][C]-0.00354625532233022[/C][/ROW]
[ROW][C]32[/C][C]1.86[/C][C]1.87419767185603[/C][C]-0.0141976718560262[/C][/ROW]
[ROW][C]33[/C][C]1.88[/C][C]1.8639491222086[/C][C]0.0160508777914043[/C][/ROW]
[ROW][C]34[/C][C]1.89[/C][C]1.88236725803337[/C][C]0.00763274196663222[/C][/ROW]
[ROW][C]35[/C][C]1.91[/C][C]1.8939480836156[/C][C]0.0160519163843986[/C][/ROW]
[ROW][C]36[/C][C]1.91[/C][C]1.91459982147836[/C][C]-0.0045998214783578[/C][/ROW]
[ROW][C]37[/C][C]1.91[/C][C]1.9162792248946[/C][C]-0.00627922489460397[/C][/ROW]
[ROW][C]38[/C][C]1.91[/C][C]1.91585913496936[/C][C]-0.00585913496936374[/C][/ROW]
[ROW][C]39[/C][C]1.92[/C][C]1.91526383274754[/C][C]0.00473616725245596[/C][/ROW]
[ROW][C]40[/C][C]1.93[/C][C]1.92462622094278[/C][C]0.00537377905721659[/C][/ROW]
[ROW][C]41[/C][C]1.93[/C][C]1.93506755008035[/C][C]-0.00506755008034854[/C][/ROW]
[ROW][C]42[/C][C]1.94[/C][C]1.93565816960862[/C][C]0.00434183039138292[/C][/ROW]
[ROW][C]43[/C][C]1.94[/C][C]1.94510472435137[/C][C]-0.00510472435137266[/C][/ROW]
[ROW][C]44[/C][C]1.95[/C][C]1.94559005780889[/C][C]0.00440994219110724[/C][/ROW]
[ROW][C]45[/C][C]1.95[/C][C]1.95503226071545[/C][C]-0.00503226071545271[/C][/ROW]
[ROW][C]46[/C][C]1.96[/C][C]1.95552397980147[/C][C]0.00447602019853033[/C][/ROW]
[ROW][C]47[/C][C]1.97[/C][C]1.96497306500496[/C][C]0.0050269349950387[/C][/ROW]
[ROW][C]48[/C][C]1.97[/C][C]1.97539056889866[/C][C]-0.00539056889866329[/C][/ROW]
[ROW][C]49[/C][C]1.97[/C][C]1.97594830086103[/C][C]-0.00594830086103171[/C][/ROW]
[ROW][C]50[/C][C]1.97[/C][C]1.97544464054542[/C][C]-0.00544464054542138[/C][/ROW]
[ROW][C]51[/C][C]1.98[/C][C]1.97487986063434[/C][C]0.00512013936566191[/C][/ROW]
[ROW][C]52[/C][C]1.98[/C][C]1.98428156746899[/C][C]-0.00428156746899355[/C][/ROW]
[ROW][C]53[/C][C]1.99[/C][C]1.98483990836138[/C][C]0.00516009163862385[/C][/ROW]
[ROW][C]54[/C][C]1.99[/C][C]1.99436029508792[/C][C]-0.00436029508791869[/C][/ROW]
[ROW][C]55[/C][C]1.99[/C][C]1.99492335750864[/C][C]-0.00492335750864048[/C][/ROW]
[ROW][C]56[/C][C]2[/C][C]1.99451686040322[/C][C]0.00548313959677582[/C][/ROW]
[ROW][C]57[/C][C]2[/C][C]2.00396898093152[/C][C]-0.00396898093151687[/C][/ROW]
[ROW][C]58[/C][C]2.01[/C][C]2.00456194641099[/C][C]0.00543805358900551[/C][/ROW]
[ROW][C]59[/C][C]2.01[/C][C]2.01411207830089[/C][C]-0.00411207830089433[/C][/ROW]
[ROW][C]60[/C][C]2.02[/C][C]2.0147015826674[/C][C]0.00529841733260161[/C][/ROW]
[ROW][C]61[/C][C]2.01[/C][C]2.02423819740815[/C][C]-0.0142381974081531[/C][/ROW]
[ROW][C]62[/C][C]2.01[/C][C]2.01489492947846[/C][C]-0.00489492947846504[/C][/ROW]
[ROW][C]63[/C][C]2.03[/C][C]2.01347753165057[/C][C]0.0165224683494265[/C][/ROW]
[ROW][C]64[/C][C]2.03[/C][C]2.03284369474905[/C][C]-0.00284369474904622[/C][/ROW]
[ROW][C]65[/C][C]2.04[/C][C]2.03455710663212[/C][C]0.00544289336788273[/C][/ROW]
[ROW][C]66[/C][C]2.05[/C][C]2.04422233484709[/C][C]0.005777665152912[/C][/ROW]
[ROW][C]67[/C][C]2.05[/C][C]2.05473272242607[/C][C]-0.00473272242607026[/C][/ROW]
[ROW][C]68[/C][C]2.06[/C][C]2.05536197079791[/C][C]0.00463802920209266[/C][/ROW]
[ROW][C]69[/C][C]2.06[/C][C]2.06484039953021[/C][C]-0.00484039953020865[/C][/ROW]
[ROW][C]70[/C][C]2.06[/C][C]2.06535391119535[/C][C]-0.00535391119535289[/C][/ROW]
[ROW][C]71[/C][C]2.04[/C][C]2.064901757446[/C][C]-0.0249017574460035[/C][/ROW]
[ROW][C]72[/C][C]2.04[/C][C]2.04455442226358[/C][C]-0.00455442226357716[/C][/ROW]
[ROW][C]73[/C][C]2.04[/C][C]2.0420432257833[/C][C]-0.00204322578330052[/C][/ROW]
[ROW][C]74[/C][C]2.03[/C][C]2.04159368134791[/C][C]-0.0115936813479078[/C][/ROW]
[ROW][C]75[/C][C]2.03[/C][C]2.03147795434109[/C][C]-0.00147795434108522[/C][/ROW]
[ROW][C]76[/C][C]2.03[/C][C]2.03030362751139[/C][C]-0.000303627511392346[/C][/ROW]
[ROW][C]77[/C][C]2.03[/C][C]2.03015485266044[/C][C]-0.000154852660444682[/C][/ROW]
[ROW][C]78[/C][C]2.03[/C][C]2.03012503312873[/C][C]-0.000125033128733687[/C][/ROW]
[ROW][C]79[/C][C]2.03[/C][C]2.03011019566546[/C][C]-0.000110195665460555[/C][/ROW]
[ROW][C]80[/C][C]2.03[/C][C]2.03009828978986[/C][C]-9.82897898587076e-05[/C][/ROW]
[ROW][C]81[/C][C]2.03[/C][C]2.03008780618905[/C][C]-8.780618904769e-05[/C][/ROW]
[ROW][C]82[/C][C]2.03[/C][C]2.03007845636264[/C][C]-7.84563626372581e-05[/C][/ROW]
[ROW][C]83[/C][C]2.02[/C][C]2.03007010391535[/C][C]-0.010070103915353[/C][/ROW]
[ROW][C]84[/C][C]2.03[/C][C]2.02014314040888[/C][C]0.00985685959112459[/C][/ROW]
[ROW][C]85[/C][C]2.03[/C][C]2.0290334558833[/C][C]0.000966544116702384[/C][/ROW]
[ROW][C]86[/C][C]2.02[/C][C]2.0300341941088[/C][C]-0.0100341941088007[/C][/ROW]
[ROW][C]87[/C][C]2.03[/C][C]2.02021386226715[/C][C]0.00978613773285142[/C][/ROW]
[ROW][C]88[/C][C]2.04[/C][C]2.0291084212131[/C][C]0.0108915787868962[/C][/ROW]
[ROW][C]89[/C][C]2.05[/C][C]2.04002202736012[/C][C]0.00997797263988254[/C][/ROW]
[ROW][C]90[/C][C]2.05[/C][C]2.05105609279629[/C][C]-0.00105609279629482[/C][/ROW]
[ROW][C]91[/C][C]2.05[/C][C]2.05208550501216[/C][C]-0.00208550501216154[/C][/ROW]
[ROW][C]92[/C][C]2.05[/C][C]2.05199423756729[/C][C]-0.00199423756729189[/C][/ROW]
[ROW][C]93[/C][C]2.07[/C][C]2.05179690962236[/C][C]0.0182030903776362[/C][/ROW]
[ROW][C]94[/C][C]2.07[/C][C]2.07144633228421[/C][C]-0.00144633228420599[/C][/ROW]
[ROW][C]95[/C][C]2.08[/C][C]2.07332045074039[/C][C]0.00667954925961478[/C][/ROW]
[ROW][C]96[/C][C]2.08[/C][C]2.08311869709657[/C][C]-0.00311869709657175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271889&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271889&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	1.81	1.8	0.01
4	1.81	1.80991950046341	8.04995365928374e-05
5	1.81	1.81094201692491	-0.000942016924908362
6	1.81	1.81095783654414	-0.000957836544142276
7	1.81	1.81086916325831	-0.000869163258313765
8	1.81	1.8107781575494	-0.000778157549396141
9	1.82	1.81069549198437	0.00930450801563087
10	1.82	1.82054097280966	-0.000540972809656814
11	1.81	1.82149733182536	-0.0114973318253595
12	1.8	1.81153453439746	-0.0115345343974624
13	1.8	1.8004510207121	-0.000451020712098682
14	1.81	1.79927447882016	0.0107255211798449
15	1.81	1.80914199203449	0.00085800796550739
16	1.81	1.81023248233917	-0.000232482339172169
17	1.81	1.81032214213853	-0.000322142138533321
18	1.81	1.81030094860068	-0.000300948600675532
19	1.81	1.81027041078363	-0.000270410783629993
20	1.82	1.81024179558608	0.00975820441391551
21	1.82	1.8201355750219	-0.000135575021898537
22	1.82	1.8211350912081	-0.00113509120809541
23	1.83	1.82113035708505	0.00886964291494552
24	1.83	1.83094281837016	-0.000942818370155196
25	1.83	1.83185791837158	-0.00185791837157856
26	1.84	1.83177640870172	0.00822359129828043
27	1.85	1.84152011356458	0.00847988643542008
28	1.86	1.85229325952239	0.00770674047760656
29	1.86	1.86309885247739	-0.00309885247738628
30	1.87	1.86391232440681	0.0060876755931869
31	1.87	1.87354625532233	-0.00354625532233022
32	1.86	1.87419767185603	-0.0141976718560262
33	1.88	1.8639491222086	0.0160508777914043
34	1.89	1.88236725803337	0.00763274196663222
35	1.91	1.8939480836156	0.0160519163843986
36	1.91	1.91459982147836	-0.0045998214783578
37	1.91	1.9162792248946	-0.00627922489460397
38	1.91	1.91585913496936	-0.00585913496936374
39	1.92	1.91526383274754	0.00473616725245596
40	1.93	1.92462622094278	0.00537377905721659
41	1.93	1.93506755008035	-0.00506755008034854
42	1.94	1.93565816960862	0.00434183039138292
43	1.94	1.94510472435137	-0.00510472435137266
44	1.95	1.94559005780889	0.00440994219110724
45	1.95	1.95503226071545	-0.00503226071545271
46	1.96	1.95552397980147	0.00447602019853033
47	1.97	1.96497306500496	0.0050269349950387
48	1.97	1.97539056889866	-0.00539056889866329
49	1.97	1.97594830086103	-0.00594830086103171
50	1.97	1.97544464054542	-0.00544464054542138
51	1.98	1.97487986063434	0.00512013936566191
52	1.98	1.98428156746899	-0.00428156746899355
53	1.99	1.98483990836138	0.00516009163862385
54	1.99	1.99436029508792	-0.00436029508791869
55	1.99	1.99492335750864	-0.00492335750864048
56	2	1.99451686040322	0.00548313959677582
57	2	2.00396898093152	-0.00396898093151687
58	2.01	2.00456194641099	0.00543805358900551
59	2.01	2.01411207830089	-0.00411207830089433
60	2.02	2.0147015826674	0.00529841733260161
61	2.01	2.02423819740815	-0.0142381974081531
62	2.01	2.01489492947846	-0.00489492947846504
63	2.03	2.01347753165057	0.0165224683494265
64	2.03	2.03284369474905	-0.00284369474904622
65	2.04	2.03455710663212	0.00544289336788273
66	2.05	2.04422233484709	0.005777665152912
67	2.05	2.05473272242607	-0.00473272242607026
68	2.06	2.05536197079791	0.00463802920209266
69	2.06	2.06484039953021	-0.00484039953020865
70	2.06	2.06535391119535	-0.00535391119535289
71	2.04	2.064901757446	-0.0249017574460035
72	2.04	2.04455442226358	-0.00455442226357716
73	2.04	2.0420432257833	-0.00204322578330052
74	2.03	2.04159368134791	-0.0115936813479078
75	2.03	2.03147795434109	-0.00147795434108522
76	2.03	2.03030362751139	-0.000303627511392346
77	2.03	2.03015485266044	-0.000154852660444682
78	2.03	2.03012503312873	-0.000125033128733687
79	2.03	2.03011019566546	-0.000110195665460555
80	2.03	2.03009828978986	-9.82897898587076e-05
81	2.03	2.03008780618905	-8.780618904769e-05
82	2.03	2.03007845636264	-7.84563626372581e-05
83	2.02	2.03007010391535	-0.010070103915353
84	2.03	2.02014314040888	0.00985685959112459
85	2.03	2.0290334558833	0.000966544116702384
86	2.02	2.0300341941088	-0.0100341941088007
87	2.03	2.02021386226715	0.00978613773285142
88	2.04	2.0291084212131	0.0108915787868962
89	2.05	2.04002202736012	0.00997797263988254
90	2.05	2.05105609279629	-0.00105609279629482
91	2.05	2.05208550501216	-0.00208550501216154
92	2.05	2.05199423756729	-0.00199423756729189
93	2.07	2.05179690962236	0.0182030903776362
94	2.07	2.07144633228421	-0.00144633228420599
95	2.08	2.07332045074039	0.00667954925961478
96	2.08	2.08311869709657	-0.00311869709657175

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	2.08382723021752	2.06965087468867	2.09800358574637
98	2.08733536642603	2.06736750344245	2.10730322940961
99	2.09084350263454	2.06562778960829	2.11605921566079
100	2.09435163884305	2.06408795365559	2.12461532403052
101	2.09785977505156	2.06261119186847	2.13310835823466
102	2.10136791126007	2.06112962351738	2.14160619900277
103	2.10487604746858	2.05960537391005	2.15014672102712
104	2.10838418367709	2.05801577532893	2.15875259202525
105	2.1118923198856	2.05634666733847	2.16743797243274
106	2.11540045609412	2.05458898967784	2.17621192251039
107	2.11890859230263	2.05273689863283	2.18508028597242
108	2.12241672851114	2.05078665804937	2.1940467989729

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 2.08382723021752 & 2.06965087468867 & 2.09800358574637 \tabularnewline
98 & 2.08733536642603 & 2.06736750344245 & 2.10730322940961 \tabularnewline
99 & 2.09084350263454 & 2.06562778960829 & 2.11605921566079 \tabularnewline
100 & 2.09435163884305 & 2.06408795365559 & 2.12461532403052 \tabularnewline
101 & 2.09785977505156 & 2.06261119186847 & 2.13310835823466 \tabularnewline
102 & 2.10136791126007 & 2.06112962351738 & 2.14160619900277 \tabularnewline
103 & 2.10487604746858 & 2.05960537391005 & 2.15014672102712 \tabularnewline
104 & 2.10838418367709 & 2.05801577532893 & 2.15875259202525 \tabularnewline
105 & 2.1118923198856 & 2.05634666733847 & 2.16743797243274 \tabularnewline
106 & 2.11540045609412 & 2.05458898967784 & 2.17621192251039 \tabularnewline
107 & 2.11890859230263 & 2.05273689863283 & 2.18508028597242 \tabularnewline
108 & 2.12241672851114 & 2.05078665804937 & 2.1940467989729 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271889&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]2.08382723021752[/C][C]2.06965087468867[/C][C]2.09800358574637[/C][/ROW]
[ROW][C]98[/C][C]2.08733536642603[/C][C]2.06736750344245[/C][C]2.10730322940961[/C][/ROW]
[ROW][C]99[/C][C]2.09084350263454[/C][C]2.06562778960829[/C][C]2.11605921566079[/C][/ROW]
[ROW][C]100[/C][C]2.09435163884305[/C][C]2.06408795365559[/C][C]2.12461532403052[/C][/ROW]
[ROW][C]101[/C][C]2.09785977505156[/C][C]2.06261119186847[/C][C]2.13310835823466[/C][/ROW]
[ROW][C]102[/C][C]2.10136791126007[/C][C]2.06112962351738[/C][C]2.14160619900277[/C][/ROW]
[ROW][C]103[/C][C]2.10487604746858[/C][C]2.05960537391005[/C][C]2.15014672102712[/C][/ROW]
[ROW][C]104[/C][C]2.10838418367709[/C][C]2.05801577532893[/C][C]2.15875259202525[/C][/ROW]
[ROW][C]105[/C][C]2.1118923198856[/C][C]2.05634666733847[/C][C]2.16743797243274[/C][/ROW]
[ROW][C]106[/C][C]2.11540045609412[/C][C]2.05458898967784[/C][C]2.17621192251039[/C][/ROW]
[ROW][C]107[/C][C]2.11890859230263[/C][C]2.05273689863283[/C][C]2.18508028597242[/C][/ROW]
[ROW][C]108[/C][C]2.12241672851114[/C][C]2.05078665804937[/C][C]2.1940467989729[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271889&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271889&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	2.08382723021752	2.06965087468867	2.09800358574637
98	2.08733536642603	2.06736750344245	2.10730322940961
99	2.09084350263454	2.06562778960829	2.11605921566079
100	2.09435163884305	2.06408795365559	2.12461532403052
101	2.09785977505156	2.06261119186847	2.13310835823466
102	2.10136791126007	2.06112962351738	2.14160619900277
103	2.10487604746858	2.05960537391005	2.15014672102712
104	2.10838418367709	2.05801577532893	2.15875259202525
105	2.1118923198856	2.05634666733847	2.16743797243274
106	2.11540045609412	2.05458898967784	2.17621192251039
107	2.11890859230263	2.05273689863283	2.18508028597242
108	2.12241672851114	2.05078665804937	2.1940467989729

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