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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 06 Jun 2010 16:15:27 +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/2010/Jun/06/t127584095689amr8h3lymcl7r.htm/, Retrieved Sun, 28 Apr 2024 17:18:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77740, Retrieved Sun, 28 Apr 2024 17:18:17 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W62

Estimated Impact

110

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

-       [Exponential Smoothing] [Verbruik zonne-en...] [2010-06-06 16:15:27] [dd2ef098fd65ce7e9f689caa343b799f] [Current]

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Dataseries X:

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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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77740&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77740&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.553998137465133
beta	1
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.553998137465133 \tabularnewline
beta & 1 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77740&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]0.553998137465133[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77740&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	0.553998137465133
beta	1
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	5.451	4.212	1.239
4	5.397	5.1538073846386	0.243192615361401
5	5.635	5.67866758886888	-0.0436675888688809
6	5.708	6.02041601134176	-0.312416011341765
7	5.578	6.04020041992036	-0.462200419920356
8	5.574	5.72094637335361	-0.146946373353612
9	5.352	5.49493446426803	-0.142934464268032
10	5.302	5.19195971835948	0.110040281640522
11	4.923	5.09009462158497	-0.167094621584965
12	4.982	4.74212719545844	0.239872804541559
13	5.101	4.75250805235955	0.348491947640448
14	4.763	5.01612760214491	-0.253127602144911
15	5.505	4.80621882175727	0.698781178242728
16	5.385	5.51078920398326	-0.125789203983255
17	5.794	5.68886214552718	0.105137854472815
18	5.695	6.0531144229011	-0.358114422901099
19	5.798	5.96233107814677	-0.164331078146774
20	5.705	5.88786423423716	-0.182864234237159
21	5.422	5.70182361119575	-0.279823611195746
22	5.311	5.30704591448828	0.00395408551171528
23	4.968	5.07167108921977	-0.103671089219771
24	5.053	4.71923852726892	0.333761472731081
25	5.236	4.79404602415608	0.44195397584392
26	4.782	5.17363364571829	-0.391633645718287
27	5.531	4.87445096722443	0.65654903277557
28	5.566	5.51968648165158	0.0463135183484154
29	5.961	5.8525102605755	0.108489739424503
30	5.868	6.27988266374544	-0.411882663745436
31	5.872	6.19078749620182	-0.318787496201823
32	5.908	5.97665919894139	-0.0686591989413925
33	5.594	5.86306444415719	-0.269064444157188
34	5.526	5.48938435586401	0.0366156441359848
35	5.111	5.30533546579886	-0.194335465798859
36	5.177	4.88567860488831	0.291321395111693
37	5.835	4.89646625066499	0.938533749335014
38	5.348	5.78575428430557	-0.437754284305575
39	6.038	5.67006625252106	0.367933747478943
40	6.039	6.20456250053701	-0.165562500537012
41	6.408	6.35178150387592	0.0562184961240844
42	6.214	6.65301170843406	-0.439011708434061
43	6.138	6.43667363325266	-0.298673633252663
44	6.529	6.13261795380528	0.39638204619472
45	6.058	6.4332167415228	-0.375216741522804
46	6.026	6.0984818620251	-0.0724818620250947
47	5.678	5.89130672535294	-0.213306725352941
48	5.733	5.48794334813406	0.245056651865938
49	6.488	5.47427335688384	1.01372664311616
50	5.936	6.44804778129672	-0.512047781296717
51	6.84	6.29287249926139	0.547127500738611
52	6.694	7.02758596708788	-0.333585967087883
53	7.193	7.08957980964685	0.103420190353151
54	6.991	7.45096884232088	-0.459968842320878
55	7.209	7.24541951828745	-0.0364195182874516
56	7.104	7.25433938559453	-0.150339385594534
57	6.83	7.1168601189862	-0.286860118986194
58	6.848	6.74482864872212	0.103171351277878
59	6.396	6.64603062298484	-0.250030622984839
60	6.414	6.21304286191415	0.200957138085845
61	7.151	6.14123136070608	1.00976863929392
62	6.882	7.0769098701672	-0.194909870167192
63	7.698	7.23721902409638	0.460780975903622
64	7.626	8.0160514879317	-0.390051487931706
65	7.936	8.10743655367772	-0.171436553677724
66	8.054	8.22495835439161	-0.170958354391608
67	8.128	8.24803446670228	-0.120034466702284
68	8.062	8.23282344696064	-0.170823446960643
69	7.708	8.09483955530055	-0.386839555300545
70	7.574	7.62287474882334	-0.0488747488233354
71	7.039	7.31106529584606	-0.272065295846058
72	7.146	6.72488502835075	0.421114971649247
73	7.07	6.7560222479278	0.313977752072207
74	6.607	6.90174873725945	-0.294748737259454
75	7.699	6.54695163381375	1.15204836618625
76	7.663	7.63191008010385	0.0310899198961545
77	7.988	8.11308339268983	-0.12508339268983
78	7.723	8.43844101440343	-0.715441014403434
79	8.087	8.04038862380369	0.0466113761963136
80	8.028	8.0903344538445	-0.0623344538444961
81	7.362	8.04539132562835	-0.683391325628348

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 5.451 & 4.212 & 1.239 \tabularnewline
4 & 5.397 & 5.1538073846386 & 0.243192615361401 \tabularnewline
5 & 5.635 & 5.67866758886888 & -0.0436675888688809 \tabularnewline
6 & 5.708 & 6.02041601134176 & -0.312416011341765 \tabularnewline
7 & 5.578 & 6.04020041992036 & -0.462200419920356 \tabularnewline
8 & 5.574 & 5.72094637335361 & -0.146946373353612 \tabularnewline
9 & 5.352 & 5.49493446426803 & -0.142934464268032 \tabularnewline
10 & 5.302 & 5.19195971835948 & 0.110040281640522 \tabularnewline
11 & 4.923 & 5.09009462158497 & -0.167094621584965 \tabularnewline
12 & 4.982 & 4.74212719545844 & 0.239872804541559 \tabularnewline
13 & 5.101 & 4.75250805235955 & 0.348491947640448 \tabularnewline
14 & 4.763 & 5.01612760214491 & -0.253127602144911 \tabularnewline
15 & 5.505 & 4.80621882175727 & 0.698781178242728 \tabularnewline
16 & 5.385 & 5.51078920398326 & -0.125789203983255 \tabularnewline
17 & 5.794 & 5.68886214552718 & 0.105137854472815 \tabularnewline
18 & 5.695 & 6.0531144229011 & -0.358114422901099 \tabularnewline
19 & 5.798 & 5.96233107814677 & -0.164331078146774 \tabularnewline
20 & 5.705 & 5.88786423423716 & -0.182864234237159 \tabularnewline
21 & 5.422 & 5.70182361119575 & -0.279823611195746 \tabularnewline
22 & 5.311 & 5.30704591448828 & 0.00395408551171528 \tabularnewline
23 & 4.968 & 5.07167108921977 & -0.103671089219771 \tabularnewline
24 & 5.053 & 4.71923852726892 & 0.333761472731081 \tabularnewline
25 & 5.236 & 4.79404602415608 & 0.44195397584392 \tabularnewline
26 & 4.782 & 5.17363364571829 & -0.391633645718287 \tabularnewline
27 & 5.531 & 4.87445096722443 & 0.65654903277557 \tabularnewline
28 & 5.566 & 5.51968648165158 & 0.0463135183484154 \tabularnewline
29 & 5.961 & 5.8525102605755 & 0.108489739424503 \tabularnewline
30 & 5.868 & 6.27988266374544 & -0.411882663745436 \tabularnewline
31 & 5.872 & 6.19078749620182 & -0.318787496201823 \tabularnewline
32 & 5.908 & 5.97665919894139 & -0.0686591989413925 \tabularnewline
33 & 5.594 & 5.86306444415719 & -0.269064444157188 \tabularnewline
34 & 5.526 & 5.48938435586401 & 0.0366156441359848 \tabularnewline
35 & 5.111 & 5.30533546579886 & -0.194335465798859 \tabularnewline
36 & 5.177 & 4.88567860488831 & 0.291321395111693 \tabularnewline
37 & 5.835 & 4.89646625066499 & 0.938533749335014 \tabularnewline
38 & 5.348 & 5.78575428430557 & -0.437754284305575 \tabularnewline
39 & 6.038 & 5.67006625252106 & 0.367933747478943 \tabularnewline
40 & 6.039 & 6.20456250053701 & -0.165562500537012 \tabularnewline
41 & 6.408 & 6.35178150387592 & 0.0562184961240844 \tabularnewline
42 & 6.214 & 6.65301170843406 & -0.439011708434061 \tabularnewline
43 & 6.138 & 6.43667363325266 & -0.298673633252663 \tabularnewline
44 & 6.529 & 6.13261795380528 & 0.39638204619472 \tabularnewline
45 & 6.058 & 6.4332167415228 & -0.375216741522804 \tabularnewline
46 & 6.026 & 6.0984818620251 & -0.0724818620250947 \tabularnewline
47 & 5.678 & 5.89130672535294 & -0.213306725352941 \tabularnewline
48 & 5.733 & 5.48794334813406 & 0.245056651865938 \tabularnewline
49 & 6.488 & 5.47427335688384 & 1.01372664311616 \tabularnewline
50 & 5.936 & 6.44804778129672 & -0.512047781296717 \tabularnewline
51 & 6.84 & 6.29287249926139 & 0.547127500738611 \tabularnewline
52 & 6.694 & 7.02758596708788 & -0.333585967087883 \tabularnewline
53 & 7.193 & 7.08957980964685 & 0.103420190353151 \tabularnewline
54 & 6.991 & 7.45096884232088 & -0.459968842320878 \tabularnewline
55 & 7.209 & 7.24541951828745 & -0.0364195182874516 \tabularnewline
56 & 7.104 & 7.25433938559453 & -0.150339385594534 \tabularnewline
57 & 6.83 & 7.1168601189862 & -0.286860118986194 \tabularnewline
58 & 6.848 & 6.74482864872212 & 0.103171351277878 \tabularnewline
59 & 6.396 & 6.64603062298484 & -0.250030622984839 \tabularnewline
60 & 6.414 & 6.21304286191415 & 0.200957138085845 \tabularnewline
61 & 7.151 & 6.14123136070608 & 1.00976863929392 \tabularnewline
62 & 6.882 & 7.0769098701672 & -0.194909870167192 \tabularnewline
63 & 7.698 & 7.23721902409638 & 0.460780975903622 \tabularnewline
64 & 7.626 & 8.0160514879317 & -0.390051487931706 \tabularnewline
65 & 7.936 & 8.10743655367772 & -0.171436553677724 \tabularnewline
66 & 8.054 & 8.22495835439161 & -0.170958354391608 \tabularnewline
67 & 8.128 & 8.24803446670228 & -0.120034466702284 \tabularnewline
68 & 8.062 & 8.23282344696064 & -0.170823446960643 \tabularnewline
69 & 7.708 & 8.09483955530055 & -0.386839555300545 \tabularnewline
70 & 7.574 & 7.62287474882334 & -0.0488747488233354 \tabularnewline
71 & 7.039 & 7.31106529584606 & -0.272065295846058 \tabularnewline
72 & 7.146 & 6.72488502835075 & 0.421114971649247 \tabularnewline
73 & 7.07 & 6.7560222479278 & 0.313977752072207 \tabularnewline
74 & 6.607 & 6.90174873725945 & -0.294748737259454 \tabularnewline
75 & 7.699 & 6.54695163381375 & 1.15204836618625 \tabularnewline
76 & 7.663 & 7.63191008010385 & 0.0310899198961545 \tabularnewline
77 & 7.988 & 8.11308339268983 & -0.12508339268983 \tabularnewline
78 & 7.723 & 8.43844101440343 & -0.715441014403434 \tabularnewline
79 & 8.087 & 8.04038862380369 & 0.0466113761963136 \tabularnewline
80 & 8.028 & 8.0903344538445 & -0.0623344538444961 \tabularnewline
81 & 7.362 & 8.04539132562835 & -0.683391325628348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77740&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]5.451[/C][C]4.212[/C][C]1.239[/C][/ROW]
[ROW][C]4[/C][C]5.397[/C][C]5.1538073846386[/C][C]0.243192615361401[/C][/ROW]
[ROW][C]5[/C][C]5.635[/C][C]5.67866758886888[/C][C]-0.0436675888688809[/C][/ROW]
[ROW][C]6[/C][C]5.708[/C][C]6.02041601134176[/C][C]-0.312416011341765[/C][/ROW]
[ROW][C]7[/C][C]5.578[/C][C]6.04020041992036[/C][C]-0.462200419920356[/C][/ROW]
[ROW][C]8[/C][C]5.574[/C][C]5.72094637335361[/C][C]-0.146946373353612[/C][/ROW]
[ROW][C]9[/C][C]5.352[/C][C]5.49493446426803[/C][C]-0.142934464268032[/C][/ROW]
[ROW][C]10[/C][C]5.302[/C][C]5.19195971835948[/C][C]0.110040281640522[/C][/ROW]
[ROW][C]11[/C][C]4.923[/C][C]5.09009462158497[/C][C]-0.167094621584965[/C][/ROW]
[ROW][C]12[/C][C]4.982[/C][C]4.74212719545844[/C][C]0.239872804541559[/C][/ROW]
[ROW][C]13[/C][C]5.101[/C][C]4.75250805235955[/C][C]0.348491947640448[/C][/ROW]
[ROW][C]14[/C][C]4.763[/C][C]5.01612760214491[/C][C]-0.253127602144911[/C][/ROW]
[ROW][C]15[/C][C]5.505[/C][C]4.80621882175727[/C][C]0.698781178242728[/C][/ROW]
[ROW][C]16[/C][C]5.385[/C][C]5.51078920398326[/C][C]-0.125789203983255[/C][/ROW]
[ROW][C]17[/C][C]5.794[/C][C]5.68886214552718[/C][C]0.105137854472815[/C][/ROW]
[ROW][C]18[/C][C]5.695[/C][C]6.0531144229011[/C][C]-0.358114422901099[/C][/ROW]
[ROW][C]19[/C][C]5.798[/C][C]5.96233107814677[/C][C]-0.164331078146774[/C][/ROW]
[ROW][C]20[/C][C]5.705[/C][C]5.88786423423716[/C][C]-0.182864234237159[/C][/ROW]
[ROW][C]21[/C][C]5.422[/C][C]5.70182361119575[/C][C]-0.279823611195746[/C][/ROW]
[ROW][C]22[/C][C]5.311[/C][C]5.30704591448828[/C][C]0.00395408551171528[/C][/ROW]
[ROW][C]23[/C][C]4.968[/C][C]5.07167108921977[/C][C]-0.103671089219771[/C][/ROW]
[ROW][C]24[/C][C]5.053[/C][C]4.71923852726892[/C][C]0.333761472731081[/C][/ROW]
[ROW][C]25[/C][C]5.236[/C][C]4.79404602415608[/C][C]0.44195397584392[/C][/ROW]
[ROW][C]26[/C][C]4.782[/C][C]5.17363364571829[/C][C]-0.391633645718287[/C][/ROW]
[ROW][C]27[/C][C]5.531[/C][C]4.87445096722443[/C][C]0.65654903277557[/C][/ROW]
[ROW][C]28[/C][C]5.566[/C][C]5.51968648165158[/C][C]0.0463135183484154[/C][/ROW]
[ROW][C]29[/C][C]5.961[/C][C]5.8525102605755[/C][C]0.108489739424503[/C][/ROW]
[ROW][C]30[/C][C]5.868[/C][C]6.27988266374544[/C][C]-0.411882663745436[/C][/ROW]
[ROW][C]31[/C][C]5.872[/C][C]6.19078749620182[/C][C]-0.318787496201823[/C][/ROW]
[ROW][C]32[/C][C]5.908[/C][C]5.97665919894139[/C][C]-0.0686591989413925[/C][/ROW]
[ROW][C]33[/C][C]5.594[/C][C]5.86306444415719[/C][C]-0.269064444157188[/C][/ROW]
[ROW][C]34[/C][C]5.526[/C][C]5.48938435586401[/C][C]0.0366156441359848[/C][/ROW]
[ROW][C]35[/C][C]5.111[/C][C]5.30533546579886[/C][C]-0.194335465798859[/C][/ROW]
[ROW][C]36[/C][C]5.177[/C][C]4.88567860488831[/C][C]0.291321395111693[/C][/ROW]
[ROW][C]37[/C][C]5.835[/C][C]4.89646625066499[/C][C]0.938533749335014[/C][/ROW]
[ROW][C]38[/C][C]5.348[/C][C]5.78575428430557[/C][C]-0.437754284305575[/C][/ROW]
[ROW][C]39[/C][C]6.038[/C][C]5.67006625252106[/C][C]0.367933747478943[/C][/ROW]
[ROW][C]40[/C][C]6.039[/C][C]6.20456250053701[/C][C]-0.165562500537012[/C][/ROW]
[ROW][C]41[/C][C]6.408[/C][C]6.35178150387592[/C][C]0.0562184961240844[/C][/ROW]
[ROW][C]42[/C][C]6.214[/C][C]6.65301170843406[/C][C]-0.439011708434061[/C][/ROW]
[ROW][C]43[/C][C]6.138[/C][C]6.43667363325266[/C][C]-0.298673633252663[/C][/ROW]
[ROW][C]44[/C][C]6.529[/C][C]6.13261795380528[/C][C]0.39638204619472[/C][/ROW]
[ROW][C]45[/C][C]6.058[/C][C]6.4332167415228[/C][C]-0.375216741522804[/C][/ROW]
[ROW][C]46[/C][C]6.026[/C][C]6.0984818620251[/C][C]-0.0724818620250947[/C][/ROW]
[ROW][C]47[/C][C]5.678[/C][C]5.89130672535294[/C][C]-0.213306725352941[/C][/ROW]
[ROW][C]48[/C][C]5.733[/C][C]5.48794334813406[/C][C]0.245056651865938[/C][/ROW]
[ROW][C]49[/C][C]6.488[/C][C]5.47427335688384[/C][C]1.01372664311616[/C][/ROW]
[ROW][C]50[/C][C]5.936[/C][C]6.44804778129672[/C][C]-0.512047781296717[/C][/ROW]
[ROW][C]51[/C][C]6.84[/C][C]6.29287249926139[/C][C]0.547127500738611[/C][/ROW]
[ROW][C]52[/C][C]6.694[/C][C]7.02758596708788[/C][C]-0.333585967087883[/C][/ROW]
[ROW][C]53[/C][C]7.193[/C][C]7.08957980964685[/C][C]0.103420190353151[/C][/ROW]
[ROW][C]54[/C][C]6.991[/C][C]7.45096884232088[/C][C]-0.459968842320878[/C][/ROW]
[ROW][C]55[/C][C]7.209[/C][C]7.24541951828745[/C][C]-0.0364195182874516[/C][/ROW]
[ROW][C]56[/C][C]7.104[/C][C]7.25433938559453[/C][C]-0.150339385594534[/C][/ROW]
[ROW][C]57[/C][C]6.83[/C][C]7.1168601189862[/C][C]-0.286860118986194[/C][/ROW]
[ROW][C]58[/C][C]6.848[/C][C]6.74482864872212[/C][C]0.103171351277878[/C][/ROW]
[ROW][C]59[/C][C]6.396[/C][C]6.64603062298484[/C][C]-0.250030622984839[/C][/ROW]
[ROW][C]60[/C][C]6.414[/C][C]6.21304286191415[/C][C]0.200957138085845[/C][/ROW]
[ROW][C]61[/C][C]7.151[/C][C]6.14123136070608[/C][C]1.00976863929392[/C][/ROW]
[ROW][C]62[/C][C]6.882[/C][C]7.0769098701672[/C][C]-0.194909870167192[/C][/ROW]
[ROW][C]63[/C][C]7.698[/C][C]7.23721902409638[/C][C]0.460780975903622[/C][/ROW]
[ROW][C]64[/C][C]7.626[/C][C]8.0160514879317[/C][C]-0.390051487931706[/C][/ROW]
[ROW][C]65[/C][C]7.936[/C][C]8.10743655367772[/C][C]-0.171436553677724[/C][/ROW]
[ROW][C]66[/C][C]8.054[/C][C]8.22495835439161[/C][C]-0.170958354391608[/C][/ROW]
[ROW][C]67[/C][C]8.128[/C][C]8.24803446670228[/C][C]-0.120034466702284[/C][/ROW]
[ROW][C]68[/C][C]8.062[/C][C]8.23282344696064[/C][C]-0.170823446960643[/C][/ROW]
[ROW][C]69[/C][C]7.708[/C][C]8.09483955530055[/C][C]-0.386839555300545[/C][/ROW]
[ROW][C]70[/C][C]7.574[/C][C]7.62287474882334[/C][C]-0.0488747488233354[/C][/ROW]
[ROW][C]71[/C][C]7.039[/C][C]7.31106529584606[/C][C]-0.272065295846058[/C][/ROW]
[ROW][C]72[/C][C]7.146[/C][C]6.72488502835075[/C][C]0.421114971649247[/C][/ROW]
[ROW][C]73[/C][C]7.07[/C][C]6.7560222479278[/C][C]0.313977752072207[/C][/ROW]
[ROW][C]74[/C][C]6.607[/C][C]6.90174873725945[/C][C]-0.294748737259454[/C][/ROW]
[ROW][C]75[/C][C]7.699[/C][C]6.54695163381375[/C][C]1.15204836618625[/C][/ROW]
[ROW][C]76[/C][C]7.663[/C][C]7.63191008010385[/C][C]0.0310899198961545[/C][/ROW]
[ROW][C]77[/C][C]7.988[/C][C]8.11308339268983[/C][C]-0.12508339268983[/C][/ROW]
[ROW][C]78[/C][C]7.723[/C][C]8.43844101440343[/C][C]-0.715441014403434[/C][/ROW]
[ROW][C]79[/C][C]8.087[/C][C]8.04038862380369[/C][C]0.0466113761963136[/C][/ROW]
[ROW][C]80[/C][C]8.028[/C][C]8.0903344538445[/C][C]-0.0623344538444961[/C][/ROW]
[ROW][C]81[/C][C]7.362[/C][C]8.04539132562835[/C][C]-0.683391325628348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77740&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77740&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	5.451	4.212	1.239
4	5.397	5.1538073846386	0.243192615361401
5	5.635	5.67866758886888	-0.0436675888688809
6	5.708	6.02041601134176	-0.312416011341765
7	5.578	6.04020041992036	-0.462200419920356
8	5.574	5.72094637335361	-0.146946373353612
9	5.352	5.49493446426803	-0.142934464268032
10	5.302	5.19195971835948	0.110040281640522
11	4.923	5.09009462158497	-0.167094621584965
12	4.982	4.74212719545844	0.239872804541559
13	5.101	4.75250805235955	0.348491947640448
14	4.763	5.01612760214491	-0.253127602144911
15	5.505	4.80621882175727	0.698781178242728
16	5.385	5.51078920398326	-0.125789203983255
17	5.794	5.68886214552718	0.105137854472815
18	5.695	6.0531144229011	-0.358114422901099
19	5.798	5.96233107814677	-0.164331078146774
20	5.705	5.88786423423716	-0.182864234237159
21	5.422	5.70182361119575	-0.279823611195746
22	5.311	5.30704591448828	0.00395408551171528
23	4.968	5.07167108921977	-0.103671089219771
24	5.053	4.71923852726892	0.333761472731081
25	5.236	4.79404602415608	0.44195397584392
26	4.782	5.17363364571829	-0.391633645718287
27	5.531	4.87445096722443	0.65654903277557
28	5.566	5.51968648165158	0.0463135183484154
29	5.961	5.8525102605755	0.108489739424503
30	5.868	6.27988266374544	-0.411882663745436
31	5.872	6.19078749620182	-0.318787496201823
32	5.908	5.97665919894139	-0.0686591989413925
33	5.594	5.86306444415719	-0.269064444157188
34	5.526	5.48938435586401	0.0366156441359848
35	5.111	5.30533546579886	-0.194335465798859
36	5.177	4.88567860488831	0.291321395111693
37	5.835	4.89646625066499	0.938533749335014
38	5.348	5.78575428430557	-0.437754284305575
39	6.038	5.67006625252106	0.367933747478943
40	6.039	6.20456250053701	-0.165562500537012
41	6.408	6.35178150387592	0.0562184961240844
42	6.214	6.65301170843406	-0.439011708434061
43	6.138	6.43667363325266	-0.298673633252663
44	6.529	6.13261795380528	0.39638204619472
45	6.058	6.4332167415228	-0.375216741522804
46	6.026	6.0984818620251	-0.0724818620250947
47	5.678	5.89130672535294	-0.213306725352941
48	5.733	5.48794334813406	0.245056651865938
49	6.488	5.47427335688384	1.01372664311616
50	5.936	6.44804778129672	-0.512047781296717
51	6.84	6.29287249926139	0.547127500738611
52	6.694	7.02758596708788	-0.333585967087883
53	7.193	7.08957980964685	0.103420190353151
54	6.991	7.45096884232088	-0.459968842320878
55	7.209	7.24541951828745	-0.0364195182874516
56	7.104	7.25433938559453	-0.150339385594534
57	6.83	7.1168601189862	-0.286860118986194
58	6.848	6.74482864872212	0.103171351277878
59	6.396	6.64603062298484	-0.250030622984839
60	6.414	6.21304286191415	0.200957138085845
61	7.151	6.14123136070608	1.00976863929392
62	6.882	7.0769098701672	-0.194909870167192
63	7.698	7.23721902409638	0.460780975903622
64	7.626	8.0160514879317	-0.390051487931706
65	7.936	8.10743655367772	-0.171436553677724
66	8.054	8.22495835439161	-0.170958354391608
67	8.128	8.24803446670228	-0.120034466702284
68	8.062	8.23282344696064	-0.170823446960643
69	7.708	8.09483955530055	-0.386839555300545
70	7.574	7.62287474882334	-0.0488747488233354
71	7.039	7.31106529584606	-0.272065295846058
72	7.146	6.72488502835075	0.421114971649247
73	7.07	6.7560222479278	0.313977752072207
74	6.607	6.90174873725945	-0.294748737259454
75	7.699	6.54695163381375	1.15204836618625
76	7.663	7.63191008010385	0.0310899198961545
77	7.988	8.11308339268983	-0.12508339268983
78	7.723	8.43844101440343	-0.715441014403434
79	8.087	8.04038862380369	0.0466113761963136
80	8.028	8.0903344538445	-0.0623344538444961
81	7.362	8.04539132562835	-0.683391325628348

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
82	7.27778632562609	6.4802156409	8.07535701035218
83	6.88877884718177	5.6983780161021	8.07917967826143
84	6.49977136873744	4.71815462908445	8.28138810839043
85	6.11076389029312	3.60120242003291	8.62032536055333
86	5.72175641184879	2.37829362494746	9.06521919875012
87	5.33274893340447	1.0657640868295	9.59973377997944
88	4.94374145496014	-0.326326397001926	10.2138093069222
89	4.55473397651582	-1.79101873126404	10.9004866842957
90	4.16572649807149	-3.3230994475414	11.6545524436844
91	3.77671901962717	-4.91844587709575	12.4718839163501
92	3.38771154118285	-6.57367293144941	13.3490960138151
93	2.99870406273852	-8.2859246730961	14.2833327985731

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
82 & 7.27778632562609 & 6.4802156409 & 8.07535701035218 \tabularnewline
83 & 6.88877884718177 & 5.6983780161021 & 8.07917967826143 \tabularnewline
84 & 6.49977136873744 & 4.71815462908445 & 8.28138810839043 \tabularnewline
85 & 6.11076389029312 & 3.60120242003291 & 8.62032536055333 \tabularnewline
86 & 5.72175641184879 & 2.37829362494746 & 9.06521919875012 \tabularnewline
87 & 5.33274893340447 & 1.0657640868295 & 9.59973377997944 \tabularnewline
88 & 4.94374145496014 & -0.326326397001926 & 10.2138093069222 \tabularnewline
89 & 4.55473397651582 & -1.79101873126404 & 10.9004866842957 \tabularnewline
90 & 4.16572649807149 & -3.3230994475414 & 11.6545524436844 \tabularnewline
91 & 3.77671901962717 & -4.91844587709575 & 12.4718839163501 \tabularnewline
92 & 3.38771154118285 & -6.57367293144941 & 13.3490960138151 \tabularnewline
93 & 2.99870406273852 & -8.2859246730961 & 14.2833327985731 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77740&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]82[/C][C]7.27778632562609[/C][C]6.4802156409[/C][C]8.07535701035218[/C][/ROW]
[ROW][C]83[/C][C]6.88877884718177[/C][C]5.6983780161021[/C][C]8.07917967826143[/C][/ROW]
[ROW][C]84[/C][C]6.49977136873744[/C][C]4.71815462908445[/C][C]8.28138810839043[/C][/ROW]
[ROW][C]85[/C][C]6.11076389029312[/C][C]3.60120242003291[/C][C]8.62032536055333[/C][/ROW]
[ROW][C]86[/C][C]5.72175641184879[/C][C]2.37829362494746[/C][C]9.06521919875012[/C][/ROW]
[ROW][C]87[/C][C]5.33274893340447[/C][C]1.0657640868295[/C][C]9.59973377997944[/C][/ROW]
[ROW][C]88[/C][C]4.94374145496014[/C][C]-0.326326397001926[/C][C]10.2138093069222[/C][/ROW]
[ROW][C]89[/C][C]4.55473397651582[/C][C]-1.79101873126404[/C][C]10.9004866842957[/C][/ROW]
[ROW][C]90[/C][C]4.16572649807149[/C][C]-3.3230994475414[/C][C]11.6545524436844[/C][/ROW]
[ROW][C]91[/C][C]3.77671901962717[/C][C]-4.91844587709575[/C][C]12.4718839163501[/C][/ROW]
[ROW][C]92[/C][C]3.38771154118285[/C][C]-6.57367293144941[/C][C]13.3490960138151[/C][/ROW]
[ROW][C]93[/C][C]2.99870406273852[/C][C]-8.2859246730961[/C][C]14.2833327985731[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77740&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77740&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
82	7.27778632562609	6.4802156409	8.07535701035218
83	6.88877884718177	5.6983780161021	8.07917967826143
84	6.49977136873744	4.71815462908445	8.28138810839043
85	6.11076389029312	3.60120242003291	8.62032536055333
86	5.72175641184879	2.37829362494746	9.06521919875012
87	5.33274893340447	1.0657640868295	9.59973377997944
88	4.94374145496014	-0.326326397001926	10.2138093069222
89	4.55473397651582	-1.79101873126404	10.9004866842957
90	4.16572649807149	-3.3230994475414	11.6545524436844
91	3.77671901962717	-4.91844587709575	12.4718839163501
92	3.38771154118285	-6.57367293144941	13.3490960138151
93	2.99870406273852	-8.2859246730961	14.2833327985731

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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