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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 02 Apr 2015 15:35:52 +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/Apr/02/t1427985472g2n4y6gshe1ubv1.htm/, Retrieved Thu, 09 May 2024 09:52:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278564, Retrieved Thu, 09 May 2024 09:52:34 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

117

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

-       [Exponential Smoothing] [Exonential smooth...] [2015-04-02 14:35:52] [fe7f0d9da4a60fe1aade911e6a24ddc7] [Current]

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Dataseries X:

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2,08
2,09
2,36
2,99
2,75
1,58
1,69
1,3
1,97
1,84
1,96
1,86
2,75
2,62
2,41
3,61
2,03
1,45
1,4
1,3
1,58
2,1
2,27
2,54
2,55
2,05
2,32
2,6
2,1
1,61
1,55
1,12
1,39
2,18
1,94
2,27
2,41
2,2
2,58
2,9
2,12
1,34
1,07
0,86
1
1,54
1,29
1,44
2,6
2,77
3,31
3,2
2,07
1,42
1,43
1,28
1,59
1,68
2,01
2,52
2,74
3,06
2,69
2,32
1,67
1,04
0,98
0,86
0,97
1,3
1,82
1,99
2,7
2,86
2,91
2,56
2,05
1,62
1,26
1,44
1,27
1,64
1,84
2,1
2,79
2,84
2,76
2,67
2,1
1,55
1,42
1,12
1,12
1,41
1,56
1,8

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	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278564&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278564&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278564&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	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999933893038648
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278564&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]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278564&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278564&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	0.999933893038648
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	2.09	2.08	0.00999999999999979
3	2.36	2.08999933893039	0.270000661069614
4	2.99	2.35998215107673	0.630017848923267
5	2.75	2.98995835143441	-0.239958351434411
6	1.58	2.75001586291746	-1.17001586291746
7	1.69	1.58007734619343	0.109922653806569
8	1.3	1.68999273334737	-0.389992733347373
9	1.97	1.30002578123455	0.669974218765449
10	1.84	1.96995571004021	-0.129955710040213
11	1.96	1.8400085909771	0.119991409022899
12	1.86	1.95999206773256	-0.099992067732561
13	2.75	1.86000661017176	0.889993389828243
14	2.62	2.74994116524137	-0.129941165241375
15	2.41	2.62000859001559	-0.210008590015589
16	3.61	2.41001388302974	1.19998611697026
17	2.03	3.60992067256414	-1.57992067256414
18	1.45	2.03010444375484	-0.58010444375484
19	1.4	1.45003834894204	-0.0500383489420435
20	1.3	1.4000033078832	-0.1000033078832
21	1.58	1.30000661091481	0.279993389085191
22	2.1	1.57998149048785	0.520018509512151
23	2.27	2.09996562315649	0.170034376843511
24	2.54	2.26998875954402	0.270011240455978
25	2.55	2.53998215037736	0.0100178496226371
26	2.05	2.5499993377504	-0.499999337750402
27	2.32	2.0500330534369	0.269966946563104
28	2.6	2.3199821533055	0.280017846694503
29	2.1	2.59998148887103	-0.499981488871031
30	1.61	2.10003305225696	-0.490033052256961
31	1.55	1.61003239459605	-0.0600323945960466
32	1.12	1.55000396855919	-0.430003968559189
33	1.39	1.12002842625573	0.269971573744269
34	2.18	1.38998215299961	0.790017847000392
35	1.94	2.17994777432072	-0.239947774320721
36	2.27	1.94001586221824	0.329984137781757
37	2.41	2.26997818575136	0.140021814248643
38	2.2	2.40999074358334	-0.209990743583337
39	2.58	2.20001388184997	0.379986118150029
40	2.9	2.57997488027237	0.320025119727627
41	2.12	2.89997884411178	-0.779978844111778
42	1.34	2.1200515620313	-0.780051562031303
43	1.07	1.34005156683846	-0.270051566838464
44	0.86	1.07001785228849	-0.210017852288492
45	1	0.860013883642044	0.139986116357956
46	1.54	0.999990745943216	0.540009254056784
47	1.29	1.53996430162911	-0.249964301629112
48	1.44	1.29001652438043	0.149983475619573
49	2.6	1.43999008504817	1.16000991495183
50	2.77	2.59992331526938	0.170076684730615
51	3.31	2.76998875674718	0.540011243252824
52	3.2	3.30996430149761	-0.109964301497612
53	2.07	3.20000726940583	-1.13000726940583
54	1.42	2.07007470134689	-0.650074701346886
55	1.43	1.42004297446316	0.00995702553684241
56	1.28	1.4299993417713	-0.149999341771297
57	1.59	1.28000991600069	0.309990083999311
58	1.68	1.5899795074975	0.0900204925025021
59	2.01	1.67999404901878	0.330005950981219
60	2.52	2.00997818430935	0.510021815690648
61	2.74	2.51996628400754	0.220033715992459
62	3.06	2.73998545423964	0.320014545760359
63	2.69	3.05997884481079	-0.369978844810791
64	2.32	2.6900244581772	-0.370024458177195
65	1.67	2.32002446119256	-0.650024461192556
66	1.04	1.67004297114193	-0.630042971141934
67	0.98	1.04004165022634	-0.0600416502263434
68	0.86	0.980003969171051	-0.120003969171051
69	0.97	0.860007933097752	0.109992066902248
70	1.3	0.969992728758684	0.330007271241316
71	1.82	1.29997818422207	0.520021815777926
72	1.99	1.81996562293792	0.170034377062078
73	2.7	1.98998875954401	0.710011240455993
74	2.86	2.69995306331437	0.160046936685632
75	2.91	2.85998941978334	0.0500105802166582
76	2.56	2.90999669395251	-0.349996693952506
77	2.05	2.56002313721792	-0.51002313721792
78	1.62	2.05003371607982	-0.43003371607982
79	1.26	1.62002842822225	-0.360028428222249
80	1.44	1.26002380038539	0.17997619961461
81	1.27	1.43998810232033	-0.169988102320328
82	1.64	1.27001123739691	0.36998876260309
83	1.84	1.63997554116717	0.20002445883283
84	2.1	1.83998677699083	0.260013223009169
85	2.79	2.09998281131592	0.690017188684084
86	2.84	2.78995438506038	0.0500456149396244
87	2.76	2.83999669163647	-0.0799966916364672
88	2.67	2.7600052883382	-0.0900052883382023
89	2.1	2.67000594997612	-0.570005949976117
90	1.55	2.10003768136131	-0.550037681361305
91	1.42	1.55003636131974	-0.130036361319744
92	1.12	1.42000859630871	-0.300008596308712
93	1.12	1.12001983265668	-1.98326566815954e-05
94	1.41	1.12000000131108	0.289999998688923
95	1.56	1.40998082898129	0.150019171018706
96	1.8	1.55999008268846	0.240009917311541

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2.09 & 2.08 & 0.00999999999999979 \tabularnewline
3 & 2.36 & 2.08999933893039 & 0.270000661069614 \tabularnewline
4 & 2.99 & 2.35998215107673 & 0.630017848923267 \tabularnewline
5 & 2.75 & 2.98995835143441 & -0.239958351434411 \tabularnewline
6 & 1.58 & 2.75001586291746 & -1.17001586291746 \tabularnewline
7 & 1.69 & 1.58007734619343 & 0.109922653806569 \tabularnewline
8 & 1.3 & 1.68999273334737 & -0.389992733347373 \tabularnewline
9 & 1.97 & 1.30002578123455 & 0.669974218765449 \tabularnewline
10 & 1.84 & 1.96995571004021 & -0.129955710040213 \tabularnewline
11 & 1.96 & 1.8400085909771 & 0.119991409022899 \tabularnewline
12 & 1.86 & 1.95999206773256 & -0.099992067732561 \tabularnewline
13 & 2.75 & 1.86000661017176 & 0.889993389828243 \tabularnewline
14 & 2.62 & 2.74994116524137 & -0.129941165241375 \tabularnewline
15 & 2.41 & 2.62000859001559 & -0.210008590015589 \tabularnewline
16 & 3.61 & 2.41001388302974 & 1.19998611697026 \tabularnewline
17 & 2.03 & 3.60992067256414 & -1.57992067256414 \tabularnewline
18 & 1.45 & 2.03010444375484 & -0.58010444375484 \tabularnewline
19 & 1.4 & 1.45003834894204 & -0.0500383489420435 \tabularnewline
20 & 1.3 & 1.4000033078832 & -0.1000033078832 \tabularnewline
21 & 1.58 & 1.30000661091481 & 0.279993389085191 \tabularnewline
22 & 2.1 & 1.57998149048785 & 0.520018509512151 \tabularnewline
23 & 2.27 & 2.09996562315649 & 0.170034376843511 \tabularnewline
24 & 2.54 & 2.26998875954402 & 0.270011240455978 \tabularnewline
25 & 2.55 & 2.53998215037736 & 0.0100178496226371 \tabularnewline
26 & 2.05 & 2.5499993377504 & -0.499999337750402 \tabularnewline
27 & 2.32 & 2.0500330534369 & 0.269966946563104 \tabularnewline
28 & 2.6 & 2.3199821533055 & 0.280017846694503 \tabularnewline
29 & 2.1 & 2.59998148887103 & -0.499981488871031 \tabularnewline
30 & 1.61 & 2.10003305225696 & -0.490033052256961 \tabularnewline
31 & 1.55 & 1.61003239459605 & -0.0600323945960466 \tabularnewline
32 & 1.12 & 1.55000396855919 & -0.430003968559189 \tabularnewline
33 & 1.39 & 1.12002842625573 & 0.269971573744269 \tabularnewline
34 & 2.18 & 1.38998215299961 & 0.790017847000392 \tabularnewline
35 & 1.94 & 2.17994777432072 & -0.239947774320721 \tabularnewline
36 & 2.27 & 1.94001586221824 & 0.329984137781757 \tabularnewline
37 & 2.41 & 2.26997818575136 & 0.140021814248643 \tabularnewline
38 & 2.2 & 2.40999074358334 & -0.209990743583337 \tabularnewline
39 & 2.58 & 2.20001388184997 & 0.379986118150029 \tabularnewline
40 & 2.9 & 2.57997488027237 & 0.320025119727627 \tabularnewline
41 & 2.12 & 2.89997884411178 & -0.779978844111778 \tabularnewline
42 & 1.34 & 2.1200515620313 & -0.780051562031303 \tabularnewline
43 & 1.07 & 1.34005156683846 & -0.270051566838464 \tabularnewline
44 & 0.86 & 1.07001785228849 & -0.210017852288492 \tabularnewline
45 & 1 & 0.860013883642044 & 0.139986116357956 \tabularnewline
46 & 1.54 & 0.999990745943216 & 0.540009254056784 \tabularnewline
47 & 1.29 & 1.53996430162911 & -0.249964301629112 \tabularnewline
48 & 1.44 & 1.29001652438043 & 0.149983475619573 \tabularnewline
49 & 2.6 & 1.43999008504817 & 1.16000991495183 \tabularnewline
50 & 2.77 & 2.59992331526938 & 0.170076684730615 \tabularnewline
51 & 3.31 & 2.76998875674718 & 0.540011243252824 \tabularnewline
52 & 3.2 & 3.30996430149761 & -0.109964301497612 \tabularnewline
53 & 2.07 & 3.20000726940583 & -1.13000726940583 \tabularnewline
54 & 1.42 & 2.07007470134689 & -0.650074701346886 \tabularnewline
55 & 1.43 & 1.42004297446316 & 0.00995702553684241 \tabularnewline
56 & 1.28 & 1.4299993417713 & -0.149999341771297 \tabularnewline
57 & 1.59 & 1.28000991600069 & 0.309990083999311 \tabularnewline
58 & 1.68 & 1.5899795074975 & 0.0900204925025021 \tabularnewline
59 & 2.01 & 1.67999404901878 & 0.330005950981219 \tabularnewline
60 & 2.52 & 2.00997818430935 & 0.510021815690648 \tabularnewline
61 & 2.74 & 2.51996628400754 & 0.220033715992459 \tabularnewline
62 & 3.06 & 2.73998545423964 & 0.320014545760359 \tabularnewline
63 & 2.69 & 3.05997884481079 & -0.369978844810791 \tabularnewline
64 & 2.32 & 2.6900244581772 & -0.370024458177195 \tabularnewline
65 & 1.67 & 2.32002446119256 & -0.650024461192556 \tabularnewline
66 & 1.04 & 1.67004297114193 & -0.630042971141934 \tabularnewline
67 & 0.98 & 1.04004165022634 & -0.0600416502263434 \tabularnewline
68 & 0.86 & 0.980003969171051 & -0.120003969171051 \tabularnewline
69 & 0.97 & 0.860007933097752 & 0.109992066902248 \tabularnewline
70 & 1.3 & 0.969992728758684 & 0.330007271241316 \tabularnewline
71 & 1.82 & 1.29997818422207 & 0.520021815777926 \tabularnewline
72 & 1.99 & 1.81996562293792 & 0.170034377062078 \tabularnewline
73 & 2.7 & 1.98998875954401 & 0.710011240455993 \tabularnewline
74 & 2.86 & 2.69995306331437 & 0.160046936685632 \tabularnewline
75 & 2.91 & 2.85998941978334 & 0.0500105802166582 \tabularnewline
76 & 2.56 & 2.90999669395251 & -0.349996693952506 \tabularnewline
77 & 2.05 & 2.56002313721792 & -0.51002313721792 \tabularnewline
78 & 1.62 & 2.05003371607982 & -0.43003371607982 \tabularnewline
79 & 1.26 & 1.62002842822225 & -0.360028428222249 \tabularnewline
80 & 1.44 & 1.26002380038539 & 0.17997619961461 \tabularnewline
81 & 1.27 & 1.43998810232033 & -0.169988102320328 \tabularnewline
82 & 1.64 & 1.27001123739691 & 0.36998876260309 \tabularnewline
83 & 1.84 & 1.63997554116717 & 0.20002445883283 \tabularnewline
84 & 2.1 & 1.83998677699083 & 0.260013223009169 \tabularnewline
85 & 2.79 & 2.09998281131592 & 0.690017188684084 \tabularnewline
86 & 2.84 & 2.78995438506038 & 0.0500456149396244 \tabularnewline
87 & 2.76 & 2.83999669163647 & -0.0799966916364672 \tabularnewline
88 & 2.67 & 2.7600052883382 & -0.0900052883382023 \tabularnewline
89 & 2.1 & 2.67000594997612 & -0.570005949976117 \tabularnewline
90 & 1.55 & 2.10003768136131 & -0.550037681361305 \tabularnewline
91 & 1.42 & 1.55003636131974 & -0.130036361319744 \tabularnewline
92 & 1.12 & 1.42000859630871 & -0.300008596308712 \tabularnewline
93 & 1.12 & 1.12001983265668 & -1.98326566815954e-05 \tabularnewline
94 & 1.41 & 1.12000000131108 & 0.289999998688923 \tabularnewline
95 & 1.56 & 1.40998082898129 & 0.150019171018706 \tabularnewline
96 & 1.8 & 1.55999008268846 & 0.240009917311541 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278564&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]2.09[/C][C]2.08[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]3[/C][C]2.36[/C][C]2.08999933893039[/C][C]0.270000661069614[/C][/ROW]
[ROW][C]4[/C][C]2.99[/C][C]2.35998215107673[/C][C]0.630017848923267[/C][/ROW]
[ROW][C]5[/C][C]2.75[/C][C]2.98995835143441[/C][C]-0.239958351434411[/C][/ROW]
[ROW][C]6[/C][C]1.58[/C][C]2.75001586291746[/C][C]-1.17001586291746[/C][/ROW]
[ROW][C]7[/C][C]1.69[/C][C]1.58007734619343[/C][C]0.109922653806569[/C][/ROW]
[ROW][C]8[/C][C]1.3[/C][C]1.68999273334737[/C][C]-0.389992733347373[/C][/ROW]
[ROW][C]9[/C][C]1.97[/C][C]1.30002578123455[/C][C]0.669974218765449[/C][/ROW]
[ROW][C]10[/C][C]1.84[/C][C]1.96995571004021[/C][C]-0.129955710040213[/C][/ROW]
[ROW][C]11[/C][C]1.96[/C][C]1.8400085909771[/C][C]0.119991409022899[/C][/ROW]
[ROW][C]12[/C][C]1.86[/C][C]1.95999206773256[/C][C]-0.099992067732561[/C][/ROW]
[ROW][C]13[/C][C]2.75[/C][C]1.86000661017176[/C][C]0.889993389828243[/C][/ROW]
[ROW][C]14[/C][C]2.62[/C][C]2.74994116524137[/C][C]-0.129941165241375[/C][/ROW]
[ROW][C]15[/C][C]2.41[/C][C]2.62000859001559[/C][C]-0.210008590015589[/C][/ROW]
[ROW][C]16[/C][C]3.61[/C][C]2.41001388302974[/C][C]1.19998611697026[/C][/ROW]
[ROW][C]17[/C][C]2.03[/C][C]3.60992067256414[/C][C]-1.57992067256414[/C][/ROW]
[ROW][C]18[/C][C]1.45[/C][C]2.03010444375484[/C][C]-0.58010444375484[/C][/ROW]
[ROW][C]19[/C][C]1.4[/C][C]1.45003834894204[/C][C]-0.0500383489420435[/C][/ROW]
[ROW][C]20[/C][C]1.3[/C][C]1.4000033078832[/C][C]-0.1000033078832[/C][/ROW]
[ROW][C]21[/C][C]1.58[/C][C]1.30000661091481[/C][C]0.279993389085191[/C][/ROW]
[ROW][C]22[/C][C]2.1[/C][C]1.57998149048785[/C][C]0.520018509512151[/C][/ROW]
[ROW][C]23[/C][C]2.27[/C][C]2.09996562315649[/C][C]0.170034376843511[/C][/ROW]
[ROW][C]24[/C][C]2.54[/C][C]2.26998875954402[/C][C]0.270011240455978[/C][/ROW]
[ROW][C]25[/C][C]2.55[/C][C]2.53998215037736[/C][C]0.0100178496226371[/C][/ROW]
[ROW][C]26[/C][C]2.05[/C][C]2.5499993377504[/C][C]-0.499999337750402[/C][/ROW]
[ROW][C]27[/C][C]2.32[/C][C]2.0500330534369[/C][C]0.269966946563104[/C][/ROW]
[ROW][C]28[/C][C]2.6[/C][C]2.3199821533055[/C][C]0.280017846694503[/C][/ROW]
[ROW][C]29[/C][C]2.1[/C][C]2.59998148887103[/C][C]-0.499981488871031[/C][/ROW]
[ROW][C]30[/C][C]1.61[/C][C]2.10003305225696[/C][C]-0.490033052256961[/C][/ROW]
[ROW][C]31[/C][C]1.55[/C][C]1.61003239459605[/C][C]-0.0600323945960466[/C][/ROW]
[ROW][C]32[/C][C]1.12[/C][C]1.55000396855919[/C][C]-0.430003968559189[/C][/ROW]
[ROW][C]33[/C][C]1.39[/C][C]1.12002842625573[/C][C]0.269971573744269[/C][/ROW]
[ROW][C]34[/C][C]2.18[/C][C]1.38998215299961[/C][C]0.790017847000392[/C][/ROW]
[ROW][C]35[/C][C]1.94[/C][C]2.17994777432072[/C][C]-0.239947774320721[/C][/ROW]
[ROW][C]36[/C][C]2.27[/C][C]1.94001586221824[/C][C]0.329984137781757[/C][/ROW]
[ROW][C]37[/C][C]2.41[/C][C]2.26997818575136[/C][C]0.140021814248643[/C][/ROW]
[ROW][C]38[/C][C]2.2[/C][C]2.40999074358334[/C][C]-0.209990743583337[/C][/ROW]
[ROW][C]39[/C][C]2.58[/C][C]2.20001388184997[/C][C]0.379986118150029[/C][/ROW]
[ROW][C]40[/C][C]2.9[/C][C]2.57997488027237[/C][C]0.320025119727627[/C][/ROW]
[ROW][C]41[/C][C]2.12[/C][C]2.89997884411178[/C][C]-0.779978844111778[/C][/ROW]
[ROW][C]42[/C][C]1.34[/C][C]2.1200515620313[/C][C]-0.780051562031303[/C][/ROW]
[ROW][C]43[/C][C]1.07[/C][C]1.34005156683846[/C][C]-0.270051566838464[/C][/ROW]
[ROW][C]44[/C][C]0.86[/C][C]1.07001785228849[/C][C]-0.210017852288492[/C][/ROW]
[ROW][C]45[/C][C]1[/C][C]0.860013883642044[/C][C]0.139986116357956[/C][/ROW]
[ROW][C]46[/C][C]1.54[/C][C]0.999990745943216[/C][C]0.540009254056784[/C][/ROW]
[ROW][C]47[/C][C]1.29[/C][C]1.53996430162911[/C][C]-0.249964301629112[/C][/ROW]
[ROW][C]48[/C][C]1.44[/C][C]1.29001652438043[/C][C]0.149983475619573[/C][/ROW]
[ROW][C]49[/C][C]2.6[/C][C]1.43999008504817[/C][C]1.16000991495183[/C][/ROW]
[ROW][C]50[/C][C]2.77[/C][C]2.59992331526938[/C][C]0.170076684730615[/C][/ROW]
[ROW][C]51[/C][C]3.31[/C][C]2.76998875674718[/C][C]0.540011243252824[/C][/ROW]
[ROW][C]52[/C][C]3.2[/C][C]3.30996430149761[/C][C]-0.109964301497612[/C][/ROW]
[ROW][C]53[/C][C]2.07[/C][C]3.20000726940583[/C][C]-1.13000726940583[/C][/ROW]
[ROW][C]54[/C][C]1.42[/C][C]2.07007470134689[/C][C]-0.650074701346886[/C][/ROW]
[ROW][C]55[/C][C]1.43[/C][C]1.42004297446316[/C][C]0.00995702553684241[/C][/ROW]
[ROW][C]56[/C][C]1.28[/C][C]1.4299993417713[/C][C]-0.149999341771297[/C][/ROW]
[ROW][C]57[/C][C]1.59[/C][C]1.28000991600069[/C][C]0.309990083999311[/C][/ROW]
[ROW][C]58[/C][C]1.68[/C][C]1.5899795074975[/C][C]0.0900204925025021[/C][/ROW]
[ROW][C]59[/C][C]2.01[/C][C]1.67999404901878[/C][C]0.330005950981219[/C][/ROW]
[ROW][C]60[/C][C]2.52[/C][C]2.00997818430935[/C][C]0.510021815690648[/C][/ROW]
[ROW][C]61[/C][C]2.74[/C][C]2.51996628400754[/C][C]0.220033715992459[/C][/ROW]
[ROW][C]62[/C][C]3.06[/C][C]2.73998545423964[/C][C]0.320014545760359[/C][/ROW]
[ROW][C]63[/C][C]2.69[/C][C]3.05997884481079[/C][C]-0.369978844810791[/C][/ROW]
[ROW][C]64[/C][C]2.32[/C][C]2.6900244581772[/C][C]-0.370024458177195[/C][/ROW]
[ROW][C]65[/C][C]1.67[/C][C]2.32002446119256[/C][C]-0.650024461192556[/C][/ROW]
[ROW][C]66[/C][C]1.04[/C][C]1.67004297114193[/C][C]-0.630042971141934[/C][/ROW]
[ROW][C]67[/C][C]0.98[/C][C]1.04004165022634[/C][C]-0.0600416502263434[/C][/ROW]
[ROW][C]68[/C][C]0.86[/C][C]0.980003969171051[/C][C]-0.120003969171051[/C][/ROW]
[ROW][C]69[/C][C]0.97[/C][C]0.860007933097752[/C][C]0.109992066902248[/C][/ROW]
[ROW][C]70[/C][C]1.3[/C][C]0.969992728758684[/C][C]0.330007271241316[/C][/ROW]
[ROW][C]71[/C][C]1.82[/C][C]1.29997818422207[/C][C]0.520021815777926[/C][/ROW]
[ROW][C]72[/C][C]1.99[/C][C]1.81996562293792[/C][C]0.170034377062078[/C][/ROW]
[ROW][C]73[/C][C]2.7[/C][C]1.98998875954401[/C][C]0.710011240455993[/C][/ROW]
[ROW][C]74[/C][C]2.86[/C][C]2.69995306331437[/C][C]0.160046936685632[/C][/ROW]
[ROW][C]75[/C][C]2.91[/C][C]2.85998941978334[/C][C]0.0500105802166582[/C][/ROW]
[ROW][C]76[/C][C]2.56[/C][C]2.90999669395251[/C][C]-0.349996693952506[/C][/ROW]
[ROW][C]77[/C][C]2.05[/C][C]2.56002313721792[/C][C]-0.51002313721792[/C][/ROW]
[ROW][C]78[/C][C]1.62[/C][C]2.05003371607982[/C][C]-0.43003371607982[/C][/ROW]
[ROW][C]79[/C][C]1.26[/C][C]1.62002842822225[/C][C]-0.360028428222249[/C][/ROW]
[ROW][C]80[/C][C]1.44[/C][C]1.26002380038539[/C][C]0.17997619961461[/C][/ROW]
[ROW][C]81[/C][C]1.27[/C][C]1.43998810232033[/C][C]-0.169988102320328[/C][/ROW]
[ROW][C]82[/C][C]1.64[/C][C]1.27001123739691[/C][C]0.36998876260309[/C][/ROW]
[ROW][C]83[/C][C]1.84[/C][C]1.63997554116717[/C][C]0.20002445883283[/C][/ROW]
[ROW][C]84[/C][C]2.1[/C][C]1.83998677699083[/C][C]0.260013223009169[/C][/ROW]
[ROW][C]85[/C][C]2.79[/C][C]2.09998281131592[/C][C]0.690017188684084[/C][/ROW]
[ROW][C]86[/C][C]2.84[/C][C]2.78995438506038[/C][C]0.0500456149396244[/C][/ROW]
[ROW][C]87[/C][C]2.76[/C][C]2.83999669163647[/C][C]-0.0799966916364672[/C][/ROW]
[ROW][C]88[/C][C]2.67[/C][C]2.7600052883382[/C][C]-0.0900052883382023[/C][/ROW]
[ROW][C]89[/C][C]2.1[/C][C]2.67000594997612[/C][C]-0.570005949976117[/C][/ROW]
[ROW][C]90[/C][C]1.55[/C][C]2.10003768136131[/C][C]-0.550037681361305[/C][/ROW]
[ROW][C]91[/C][C]1.42[/C][C]1.55003636131974[/C][C]-0.130036361319744[/C][/ROW]
[ROW][C]92[/C][C]1.12[/C][C]1.42000859630871[/C][C]-0.300008596308712[/C][/ROW]
[ROW][C]93[/C][C]1.12[/C][C]1.12001983265668[/C][C]-1.98326566815954e-05[/C][/ROW]
[ROW][C]94[/C][C]1.41[/C][C]1.12000000131108[/C][C]0.289999998688923[/C][/ROW]
[ROW][C]95[/C][C]1.56[/C][C]1.40998082898129[/C][C]0.150019171018706[/C][/ROW]
[ROW][C]96[/C][C]1.8[/C][C]1.55999008268846[/C][C]0.240009917311541[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278564&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278564&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	2.09	2.08	0.00999999999999979
3	2.36	2.08999933893039	0.270000661069614
4	2.99	2.35998215107673	0.630017848923267
5	2.75	2.98995835143441	-0.239958351434411
6	1.58	2.75001586291746	-1.17001586291746
7	1.69	1.58007734619343	0.109922653806569
8	1.3	1.68999273334737	-0.389992733347373
9	1.97	1.30002578123455	0.669974218765449
10	1.84	1.96995571004021	-0.129955710040213
11	1.96	1.8400085909771	0.119991409022899
12	1.86	1.95999206773256	-0.099992067732561
13	2.75	1.86000661017176	0.889993389828243
14	2.62	2.74994116524137	-0.129941165241375
15	2.41	2.62000859001559	-0.210008590015589
16	3.61	2.41001388302974	1.19998611697026
17	2.03	3.60992067256414	-1.57992067256414
18	1.45	2.03010444375484	-0.58010444375484
19	1.4	1.45003834894204	-0.0500383489420435
20	1.3	1.4000033078832	-0.1000033078832
21	1.58	1.30000661091481	0.279993389085191
22	2.1	1.57998149048785	0.520018509512151
23	2.27	2.09996562315649	0.170034376843511
24	2.54	2.26998875954402	0.270011240455978
25	2.55	2.53998215037736	0.0100178496226371
26	2.05	2.5499993377504	-0.499999337750402
27	2.32	2.0500330534369	0.269966946563104
28	2.6	2.3199821533055	0.280017846694503
29	2.1	2.59998148887103	-0.499981488871031
30	1.61	2.10003305225696	-0.490033052256961
31	1.55	1.61003239459605	-0.0600323945960466
32	1.12	1.55000396855919	-0.430003968559189
33	1.39	1.12002842625573	0.269971573744269
34	2.18	1.38998215299961	0.790017847000392
35	1.94	2.17994777432072	-0.239947774320721
36	2.27	1.94001586221824	0.329984137781757
37	2.41	2.26997818575136	0.140021814248643
38	2.2	2.40999074358334	-0.209990743583337
39	2.58	2.20001388184997	0.379986118150029
40	2.9	2.57997488027237	0.320025119727627
41	2.12	2.89997884411178	-0.779978844111778
42	1.34	2.1200515620313	-0.780051562031303
43	1.07	1.34005156683846	-0.270051566838464
44	0.86	1.07001785228849	-0.210017852288492
45	1	0.860013883642044	0.139986116357956
46	1.54	0.999990745943216	0.540009254056784
47	1.29	1.53996430162911	-0.249964301629112
48	1.44	1.29001652438043	0.149983475619573
49	2.6	1.43999008504817	1.16000991495183
50	2.77	2.59992331526938	0.170076684730615
51	3.31	2.76998875674718	0.540011243252824
52	3.2	3.30996430149761	-0.109964301497612
53	2.07	3.20000726940583	-1.13000726940583
54	1.42	2.07007470134689	-0.650074701346886
55	1.43	1.42004297446316	0.00995702553684241
56	1.28	1.4299993417713	-0.149999341771297
57	1.59	1.28000991600069	0.309990083999311
58	1.68	1.5899795074975	0.0900204925025021
59	2.01	1.67999404901878	0.330005950981219
60	2.52	2.00997818430935	0.510021815690648
61	2.74	2.51996628400754	0.220033715992459
62	3.06	2.73998545423964	0.320014545760359
63	2.69	3.05997884481079	-0.369978844810791
64	2.32	2.6900244581772	-0.370024458177195
65	1.67	2.32002446119256	-0.650024461192556
66	1.04	1.67004297114193	-0.630042971141934
67	0.98	1.04004165022634	-0.0600416502263434
68	0.86	0.980003969171051	-0.120003969171051
69	0.97	0.860007933097752	0.109992066902248
70	1.3	0.969992728758684	0.330007271241316
71	1.82	1.29997818422207	0.520021815777926
72	1.99	1.81996562293792	0.170034377062078
73	2.7	1.98998875954401	0.710011240455993
74	2.86	2.69995306331437	0.160046936685632
75	2.91	2.85998941978334	0.0500105802166582
76	2.56	2.90999669395251	-0.349996693952506
77	2.05	2.56002313721792	-0.51002313721792
78	1.62	2.05003371607982	-0.43003371607982
79	1.26	1.62002842822225	-0.360028428222249
80	1.44	1.26002380038539	0.17997619961461
81	1.27	1.43998810232033	-0.169988102320328
82	1.64	1.27001123739691	0.36998876260309
83	1.84	1.63997554116717	0.20002445883283
84	2.1	1.83998677699083	0.260013223009169
85	2.79	2.09998281131592	0.690017188684084
86	2.84	2.78995438506038	0.0500456149396244
87	2.76	2.83999669163647	-0.0799966916364672
88	2.67	2.7600052883382	-0.0900052883382023
89	2.1	2.67000594997612	-0.570005949976117
90	1.55	2.10003768136131	-0.550037681361305
91	1.42	1.55003636131974	-0.130036361319744
92	1.12	1.42000859630871	-0.300008596308712
93	1.12	1.12001983265668	-1.98326566815954e-05
94	1.41	1.12000000131108	0.289999998688923
95	1.56	1.40998082898129	0.150019171018706
96	1.8	1.55999008268846	0.240009917311541

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	1.79998413367367	0.882330168066881	2.71763809928046
98	1.79998413367367	0.502268344679723	3.09769992266762
99	1.79998413367367	0.210630888666602	3.38933737868074
100	1.79998413367367	-0.035232803319015	3.63520107066636
101	1.79998413367367	-0.251843996125493	3.85181226347284
102	1.79998413367367	-0.447676014712968	4.04764428206031
103	1.79998413367367	-0.627762478115905	4.22773074546325
104	1.79998413367367	-0.795383100354316	4.39535136770166
105	1.79998413367367	-0.952815994900215	4.55278426224756
106	1.79998413367367	-1.1017198512784	4.70168811862574
107	1.79998413367367	-1.24334685139795	4.8433151187453
108	1.79998413367367	-1.3786698193554	4.97863808670275

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 1.79998413367367 & 0.882330168066881 & 2.71763809928046 \tabularnewline
98 & 1.79998413367367 & 0.502268344679723 & 3.09769992266762 \tabularnewline
99 & 1.79998413367367 & 0.210630888666602 & 3.38933737868074 \tabularnewline
100 & 1.79998413367367 & -0.035232803319015 & 3.63520107066636 \tabularnewline
101 & 1.79998413367367 & -0.251843996125493 & 3.85181226347284 \tabularnewline
102 & 1.79998413367367 & -0.447676014712968 & 4.04764428206031 \tabularnewline
103 & 1.79998413367367 & -0.627762478115905 & 4.22773074546325 \tabularnewline
104 & 1.79998413367367 & -0.795383100354316 & 4.39535136770166 \tabularnewline
105 & 1.79998413367367 & -0.952815994900215 & 4.55278426224756 \tabularnewline
106 & 1.79998413367367 & -1.1017198512784 & 4.70168811862574 \tabularnewline
107 & 1.79998413367367 & -1.24334685139795 & 4.8433151187453 \tabularnewline
108 & 1.79998413367367 & -1.3786698193554 & 4.97863808670275 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278564&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]1.79998413367367[/C][C]0.882330168066881[/C][C]2.71763809928046[/C][/ROW]
[ROW][C]98[/C][C]1.79998413367367[/C][C]0.502268344679723[/C][C]3.09769992266762[/C][/ROW]
[ROW][C]99[/C][C]1.79998413367367[/C][C]0.210630888666602[/C][C]3.38933737868074[/C][/ROW]
[ROW][C]100[/C][C]1.79998413367367[/C][C]-0.035232803319015[/C][C]3.63520107066636[/C][/ROW]
[ROW][C]101[/C][C]1.79998413367367[/C][C]-0.251843996125493[/C][C]3.85181226347284[/C][/ROW]
[ROW][C]102[/C][C]1.79998413367367[/C][C]-0.447676014712968[/C][C]4.04764428206031[/C][/ROW]
[ROW][C]103[/C][C]1.79998413367367[/C][C]-0.627762478115905[/C][C]4.22773074546325[/C][/ROW]
[ROW][C]104[/C][C]1.79998413367367[/C][C]-0.795383100354316[/C][C]4.39535136770166[/C][/ROW]
[ROW][C]105[/C][C]1.79998413367367[/C][C]-0.952815994900215[/C][C]4.55278426224756[/C][/ROW]
[ROW][C]106[/C][C]1.79998413367367[/C][C]-1.1017198512784[/C][C]4.70168811862574[/C][/ROW]
[ROW][C]107[/C][C]1.79998413367367[/C][C]-1.24334685139795[/C][C]4.8433151187453[/C][/ROW]
[ROW][C]108[/C][C]1.79998413367367[/C][C]-1.3786698193554[/C][C]4.97863808670275[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278564&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278564&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	1.79998413367367	0.882330168066881	2.71763809928046
98	1.79998413367367	0.502268344679723	3.09769992266762
99	1.79998413367367	0.210630888666602	3.38933737868074
100	1.79998413367367	-0.035232803319015	3.63520107066636
101	1.79998413367367	-0.251843996125493	3.85181226347284
102	1.79998413367367	-0.447676014712968	4.04764428206031
103	1.79998413367367	-0.627762478115905	4.22773074546325
104	1.79998413367367	-0.795383100354316	4.39535136770166
105	1.79998413367367	-0.952815994900215	4.55278426224756
106	1.79998413367367	-1.1017198512784	4.70168811862574
107	1.79998413367367	-1.24334685139795	4.8433151187453
108	1.79998413367367	-1.3786698193554	4.97863808670275

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = additive ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code