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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 16 Dec 2014 08:57:33 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/16/t1418720269yds7mwczojre8bt.htm/, Retrieved Thu, 16 May 2024 19:00:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=269175, Retrieved Thu, 16 May 2024 19:00:46 +0000

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No (this computation is public)

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Estimated Impact

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

-     [Exponential Smoothing] [] [2014-11-30 20:59:40] [deebc1e457a5ecb4dd1aad0be1fbee4a]
- R PD    [Exponential Smoothing] [] [2014-12-16 08:57:33] [f2e79deb6e51141b138dd10990a8e48d] [Current]

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Dataseries X:

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5,06
5,05
5,05
5,04
5,06
5,07
5,09
5,08
5,09
5,09
5,09
5,1
5,12
5,14
5,14
5,14
5,13
5,15
5,16
5,17
5,17
5,18
5,21
5,19
5,22
5,24
5,21
5,24
5,28
5,3
5,32
5,32
5,29
5,3
5,32
5,31
5,35
5,36
5,33
5,35
5,35
5,35
5,37
5,39
5,4
5,39
5,4
5,4
5,4
5,38
5,32
5,36
5,35
5,39
5,4
5,41
5,36
5,38
5,41
5,35
5,4
5,41
5,42
5,41
5,41
5,42
5,4
5,42
5,41
5,34
5,46
5,45
5,47
5,48
5,43
5,5
5,51
5,51
5,52
5,55
5,55
5,48
5,61
5,59
5,68
5,71
5,68
5,7
5,76
5,78
5,77
5,85
5,82
5,84
5,89
5,84

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	'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269175&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269175&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269175&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.60367134940219
beta	0.0847382686242051
gamma	0.61082872252953

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.60367134940219 \tabularnewline
beta & 0.0847382686242051 \tabularnewline
gamma & 0.61082872252953 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269175&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]0.60367134940219[/C][/ROW]
[ROW][C]beta[/C][C]0.0847382686242051[/C][/ROW]
[ROW][C]gamma[/C][C]0.61082872252953[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269175&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269175&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	0.60367134940219
beta	0.0847382686242051
gamma	0.61082872252953

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	5.12	5.07843906267978	0.0415609373202228
14	5.14	5.12603374662358	0.0139662533764247
15	5.14	5.13731322369345	0.00268677630654501
16	5.14	5.14191076197677	-0.00191076197677287
17	5.13	5.13195891199302	-0.00195891199301901
18	5.15	5.1518846742924	-0.0018846742924028
19	5.16	5.18035831827516	-0.0203583182751617
20	5.17	5.16029150958433	0.00970849041566968
21	5.17	5.17791453307311	-0.00791453307311407
22	5.18	5.17390451424713	0.00609548575286833
23	5.21	5.17950074323159	0.0304992567684073
24	5.19	5.21242467051043	-0.0224246705104276
25	5.22	5.23274432850183	-0.0127443285018325
26	5.24	5.24069789017493	-0.000697890174931715
27	5.21	5.23913381813841	-0.0291338181384093
28	5.24	5.22059027205898	0.0194097279410181
29	5.28	5.22157022589402	0.0584297741059823
30	5.3	5.27974776210362	0.0202522378963819
31	5.32	5.3201640587146	-0.000164058714595683
32	5.32	5.32295022357645	-0.00295022357644736
33	5.29	5.33163022497518	-0.0416302249751777
34	5.3	5.31182776784122	-0.0118277678412229
35	5.32	5.31282870468693	0.00717129531306604
36	5.31	5.3178314996179	-0.00783149961789587
37	5.35	5.34983865375346	0.000161346246538407
38	5.36	5.36932179679459	-0.00932179679458578
39	5.33	5.3553897815304	-0.0253897815303974
40	5.35	5.3512642149801	-0.00126421498010476
41	5.35	5.34818152436346	0.00181847563653648
42	5.35	5.3593366478077	-0.00933664780770194
43	5.37	5.37191134859364	-0.00191134859363729
44	5.39	5.36763835018155	0.0223616498184498
45	5.4	5.37812982783497	0.0218701721650314
46	5.39	5.4032300123874	-0.0132300123874041
47	5.4	5.40728159889009	-0.00728159889009294
48	5.4	5.39822988718871	0.00177011281128703
49	5.4	5.43744381324298	-0.0374438132429802
50	5.38	5.42908330522644	-0.0490833052264446
51	5.32	5.38213975484945	-0.0621397548494462
52	5.36	5.35484440654172	0.00515559345828187
53	5.35	5.34986551742873	0.000134482571272798
54	5.39	5.35071095597826	0.0392890440217446
55	5.4	5.39037906086635	0.00962093913364548
56	5.41	5.39538917207866	0.0146108279213406
57	5.36	5.39712302462058	-0.0371230246205778
58	5.38	5.37121259706434	0.00878740293565894
59	5.41	5.38418081033858	0.0258191896614193
60	5.35	5.39320677225084	-0.0432067722508434
61	5.4	5.3891937783034	0.0108062216965976
62	5.41	5.40310705688094	0.00689294311905986
63	5.42	5.38549984932473	0.03450015067527
64	5.41	5.43705766196941	-0.027057661969411
65	5.41	5.41349950057367	-0.00349950057366755
66	5.42	5.42371196709417	-0.00371196709417188
67	5.4	5.43009228433069	-0.0300922843306868
68	5.42	5.41010887103114	0.00989112896886191
69	5.41	5.39394992133233	0.0160500786676714
70	5.34	5.41155926545433	-0.0715592654543276
71	5.46	5.37626836875354	0.0837316312464607
72	5.45	5.40250816909383	0.0474918309061705
73	5.47	5.47056006533537	-0.000560065335365678
74	5.48	5.47991448417495	8.55158250541166e-05
75	5.43	5.4674541694692	-0.0374541694692017
76	5.5	5.45987185130865	0.0401281486913483
77	5.51	5.48510186586384	0.0248981341361585
78	5.51	5.51660559748527	-0.00660559748527412
79	5.52	5.51871611294075	0.00128388705924731
80	5.55	5.53299725964417	0.0170027403558324
81	5.55	5.52794477752029	0.0220552224797057
82	5.48	5.53356810736331	-0.0535681073633087
83	5.61	5.55494765303985	0.0550523469601485
84	5.59	5.55968115846383	0.030318841536169
85	5.68	5.61099993534582	0.0690000646541753
86	5.71	5.67092314478944	0.0390768552105563
87	5.68	5.68203112138912	-0.00203112138912065
88	5.7	5.72802271616398	-0.0280227161639806
89	5.76	5.71666796863025	0.0433320313697489
90	5.78	5.76128739497724	0.0187126050227553
91	5.77	5.79148806569486	-0.0214880656948653
92	5.85	5.80600115206701	0.0439988479329854
93	5.82	5.8283624272533	-0.00836242725329672
94	5.84	5.80491223723711	0.0350877627628883
95	5.89	5.92469685953212	-0.034696859532116
96	5.84	5.87635347102977	-0.0363534710297708

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5.12 & 5.07843906267978 & 0.0415609373202228 \tabularnewline
14 & 5.14 & 5.12603374662358 & 0.0139662533764247 \tabularnewline
15 & 5.14 & 5.13731322369345 & 0.00268677630654501 \tabularnewline
16 & 5.14 & 5.14191076197677 & -0.00191076197677287 \tabularnewline
17 & 5.13 & 5.13195891199302 & -0.00195891199301901 \tabularnewline
18 & 5.15 & 5.1518846742924 & -0.0018846742924028 \tabularnewline
19 & 5.16 & 5.18035831827516 & -0.0203583182751617 \tabularnewline
20 & 5.17 & 5.16029150958433 & 0.00970849041566968 \tabularnewline
21 & 5.17 & 5.17791453307311 & -0.00791453307311407 \tabularnewline
22 & 5.18 & 5.17390451424713 & 0.00609548575286833 \tabularnewline
23 & 5.21 & 5.17950074323159 & 0.0304992567684073 \tabularnewline
24 & 5.19 & 5.21242467051043 & -0.0224246705104276 \tabularnewline
25 & 5.22 & 5.23274432850183 & -0.0127443285018325 \tabularnewline
26 & 5.24 & 5.24069789017493 & -0.000697890174931715 \tabularnewline
27 & 5.21 & 5.23913381813841 & -0.0291338181384093 \tabularnewline
28 & 5.24 & 5.22059027205898 & 0.0194097279410181 \tabularnewline
29 & 5.28 & 5.22157022589402 & 0.0584297741059823 \tabularnewline
30 & 5.3 & 5.27974776210362 & 0.0202522378963819 \tabularnewline
31 & 5.32 & 5.3201640587146 & -0.000164058714595683 \tabularnewline
32 & 5.32 & 5.32295022357645 & -0.00295022357644736 \tabularnewline
33 & 5.29 & 5.33163022497518 & -0.0416302249751777 \tabularnewline
34 & 5.3 & 5.31182776784122 & -0.0118277678412229 \tabularnewline
35 & 5.32 & 5.31282870468693 & 0.00717129531306604 \tabularnewline
36 & 5.31 & 5.3178314996179 & -0.00783149961789587 \tabularnewline
37 & 5.35 & 5.34983865375346 & 0.000161346246538407 \tabularnewline
38 & 5.36 & 5.36932179679459 & -0.00932179679458578 \tabularnewline
39 & 5.33 & 5.3553897815304 & -0.0253897815303974 \tabularnewline
40 & 5.35 & 5.3512642149801 & -0.00126421498010476 \tabularnewline
41 & 5.35 & 5.34818152436346 & 0.00181847563653648 \tabularnewline
42 & 5.35 & 5.3593366478077 & -0.00933664780770194 \tabularnewline
43 & 5.37 & 5.37191134859364 & -0.00191134859363729 \tabularnewline
44 & 5.39 & 5.36763835018155 & 0.0223616498184498 \tabularnewline
45 & 5.4 & 5.37812982783497 & 0.0218701721650314 \tabularnewline
46 & 5.39 & 5.4032300123874 & -0.0132300123874041 \tabularnewline
47 & 5.4 & 5.40728159889009 & -0.00728159889009294 \tabularnewline
48 & 5.4 & 5.39822988718871 & 0.00177011281128703 \tabularnewline
49 & 5.4 & 5.43744381324298 & -0.0374438132429802 \tabularnewline
50 & 5.38 & 5.42908330522644 & -0.0490833052264446 \tabularnewline
51 & 5.32 & 5.38213975484945 & -0.0621397548494462 \tabularnewline
52 & 5.36 & 5.35484440654172 & 0.00515559345828187 \tabularnewline
53 & 5.35 & 5.34986551742873 & 0.000134482571272798 \tabularnewline
54 & 5.39 & 5.35071095597826 & 0.0392890440217446 \tabularnewline
55 & 5.4 & 5.39037906086635 & 0.00962093913364548 \tabularnewline
56 & 5.41 & 5.39538917207866 & 0.0146108279213406 \tabularnewline
57 & 5.36 & 5.39712302462058 & -0.0371230246205778 \tabularnewline
58 & 5.38 & 5.37121259706434 & 0.00878740293565894 \tabularnewline
59 & 5.41 & 5.38418081033858 & 0.0258191896614193 \tabularnewline
60 & 5.35 & 5.39320677225084 & -0.0432067722508434 \tabularnewline
61 & 5.4 & 5.3891937783034 & 0.0108062216965976 \tabularnewline
62 & 5.41 & 5.40310705688094 & 0.00689294311905986 \tabularnewline
63 & 5.42 & 5.38549984932473 & 0.03450015067527 \tabularnewline
64 & 5.41 & 5.43705766196941 & -0.027057661969411 \tabularnewline
65 & 5.41 & 5.41349950057367 & -0.00349950057366755 \tabularnewline
66 & 5.42 & 5.42371196709417 & -0.00371196709417188 \tabularnewline
67 & 5.4 & 5.43009228433069 & -0.0300922843306868 \tabularnewline
68 & 5.42 & 5.41010887103114 & 0.00989112896886191 \tabularnewline
69 & 5.41 & 5.39394992133233 & 0.0160500786676714 \tabularnewline
70 & 5.34 & 5.41155926545433 & -0.0715592654543276 \tabularnewline
71 & 5.46 & 5.37626836875354 & 0.0837316312464607 \tabularnewline
72 & 5.45 & 5.40250816909383 & 0.0474918309061705 \tabularnewline
73 & 5.47 & 5.47056006533537 & -0.000560065335365678 \tabularnewline
74 & 5.48 & 5.47991448417495 & 8.55158250541166e-05 \tabularnewline
75 & 5.43 & 5.4674541694692 & -0.0374541694692017 \tabularnewline
76 & 5.5 & 5.45987185130865 & 0.0401281486913483 \tabularnewline
77 & 5.51 & 5.48510186586384 & 0.0248981341361585 \tabularnewline
78 & 5.51 & 5.51660559748527 & -0.00660559748527412 \tabularnewline
79 & 5.52 & 5.51871611294075 & 0.00128388705924731 \tabularnewline
80 & 5.55 & 5.53299725964417 & 0.0170027403558324 \tabularnewline
81 & 5.55 & 5.52794477752029 & 0.0220552224797057 \tabularnewline
82 & 5.48 & 5.53356810736331 & -0.0535681073633087 \tabularnewline
83 & 5.61 & 5.55494765303985 & 0.0550523469601485 \tabularnewline
84 & 5.59 & 5.55968115846383 & 0.030318841536169 \tabularnewline
85 & 5.68 & 5.61099993534582 & 0.0690000646541753 \tabularnewline
86 & 5.71 & 5.67092314478944 & 0.0390768552105563 \tabularnewline
87 & 5.68 & 5.68203112138912 & -0.00203112138912065 \tabularnewline
88 & 5.7 & 5.72802271616398 & -0.0280227161639806 \tabularnewline
89 & 5.76 & 5.71666796863025 & 0.0433320313697489 \tabularnewline
90 & 5.78 & 5.76128739497724 & 0.0187126050227553 \tabularnewline
91 & 5.77 & 5.79148806569486 & -0.0214880656948653 \tabularnewline
92 & 5.85 & 5.80600115206701 & 0.0439988479329854 \tabularnewline
93 & 5.82 & 5.8283624272533 & -0.00836242725329672 \tabularnewline
94 & 5.84 & 5.80491223723711 & 0.0350877627628883 \tabularnewline
95 & 5.89 & 5.92469685953212 & -0.034696859532116 \tabularnewline
96 & 5.84 & 5.87635347102977 & -0.0363534710297708 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269175&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]5.12[/C][C]5.07843906267978[/C][C]0.0415609373202228[/C][/ROW]
[ROW][C]14[/C][C]5.14[/C][C]5.12603374662358[/C][C]0.0139662533764247[/C][/ROW]
[ROW][C]15[/C][C]5.14[/C][C]5.13731322369345[/C][C]0.00268677630654501[/C][/ROW]
[ROW][C]16[/C][C]5.14[/C][C]5.14191076197677[/C][C]-0.00191076197677287[/C][/ROW]
[ROW][C]17[/C][C]5.13[/C][C]5.13195891199302[/C][C]-0.00195891199301901[/C][/ROW]
[ROW][C]18[/C][C]5.15[/C][C]5.1518846742924[/C][C]-0.0018846742924028[/C][/ROW]
[ROW][C]19[/C][C]5.16[/C][C]5.18035831827516[/C][C]-0.0203583182751617[/C][/ROW]
[ROW][C]20[/C][C]5.17[/C][C]5.16029150958433[/C][C]0.00970849041566968[/C][/ROW]
[ROW][C]21[/C][C]5.17[/C][C]5.17791453307311[/C][C]-0.00791453307311407[/C][/ROW]
[ROW][C]22[/C][C]5.18[/C][C]5.17390451424713[/C][C]0.00609548575286833[/C][/ROW]
[ROW][C]23[/C][C]5.21[/C][C]5.17950074323159[/C][C]0.0304992567684073[/C][/ROW]
[ROW][C]24[/C][C]5.19[/C][C]5.21242467051043[/C][C]-0.0224246705104276[/C][/ROW]
[ROW][C]25[/C][C]5.22[/C][C]5.23274432850183[/C][C]-0.0127443285018325[/C][/ROW]
[ROW][C]26[/C][C]5.24[/C][C]5.24069789017493[/C][C]-0.000697890174931715[/C][/ROW]
[ROW][C]27[/C][C]5.21[/C][C]5.23913381813841[/C][C]-0.0291338181384093[/C][/ROW]
[ROW][C]28[/C][C]5.24[/C][C]5.22059027205898[/C][C]0.0194097279410181[/C][/ROW]
[ROW][C]29[/C][C]5.28[/C][C]5.22157022589402[/C][C]0.0584297741059823[/C][/ROW]
[ROW][C]30[/C][C]5.3[/C][C]5.27974776210362[/C][C]0.0202522378963819[/C][/ROW]
[ROW][C]31[/C][C]5.32[/C][C]5.3201640587146[/C][C]-0.000164058714595683[/C][/ROW]
[ROW][C]32[/C][C]5.32[/C][C]5.32295022357645[/C][C]-0.00295022357644736[/C][/ROW]
[ROW][C]33[/C][C]5.29[/C][C]5.33163022497518[/C][C]-0.0416302249751777[/C][/ROW]
[ROW][C]34[/C][C]5.3[/C][C]5.31182776784122[/C][C]-0.0118277678412229[/C][/ROW]
[ROW][C]35[/C][C]5.32[/C][C]5.31282870468693[/C][C]0.00717129531306604[/C][/ROW]
[ROW][C]36[/C][C]5.31[/C][C]5.3178314996179[/C][C]-0.00783149961789587[/C][/ROW]
[ROW][C]37[/C][C]5.35[/C][C]5.34983865375346[/C][C]0.000161346246538407[/C][/ROW]
[ROW][C]38[/C][C]5.36[/C][C]5.36932179679459[/C][C]-0.00932179679458578[/C][/ROW]
[ROW][C]39[/C][C]5.33[/C][C]5.3553897815304[/C][C]-0.0253897815303974[/C][/ROW]
[ROW][C]40[/C][C]5.35[/C][C]5.3512642149801[/C][C]-0.00126421498010476[/C][/ROW]
[ROW][C]41[/C][C]5.35[/C][C]5.34818152436346[/C][C]0.00181847563653648[/C][/ROW]
[ROW][C]42[/C][C]5.35[/C][C]5.3593366478077[/C][C]-0.00933664780770194[/C][/ROW]
[ROW][C]43[/C][C]5.37[/C][C]5.37191134859364[/C][C]-0.00191134859363729[/C][/ROW]
[ROW][C]44[/C][C]5.39[/C][C]5.36763835018155[/C][C]0.0223616498184498[/C][/ROW]
[ROW][C]45[/C][C]5.4[/C][C]5.37812982783497[/C][C]0.0218701721650314[/C][/ROW]
[ROW][C]46[/C][C]5.39[/C][C]5.4032300123874[/C][C]-0.0132300123874041[/C][/ROW]
[ROW][C]47[/C][C]5.4[/C][C]5.40728159889009[/C][C]-0.00728159889009294[/C][/ROW]
[ROW][C]48[/C][C]5.4[/C][C]5.39822988718871[/C][C]0.00177011281128703[/C][/ROW]
[ROW][C]49[/C][C]5.4[/C][C]5.43744381324298[/C][C]-0.0374438132429802[/C][/ROW]
[ROW][C]50[/C][C]5.38[/C][C]5.42908330522644[/C][C]-0.0490833052264446[/C][/ROW]
[ROW][C]51[/C][C]5.32[/C][C]5.38213975484945[/C][C]-0.0621397548494462[/C][/ROW]
[ROW][C]52[/C][C]5.36[/C][C]5.35484440654172[/C][C]0.00515559345828187[/C][/ROW]
[ROW][C]53[/C][C]5.35[/C][C]5.34986551742873[/C][C]0.000134482571272798[/C][/ROW]
[ROW][C]54[/C][C]5.39[/C][C]5.35071095597826[/C][C]0.0392890440217446[/C][/ROW]
[ROW][C]55[/C][C]5.4[/C][C]5.39037906086635[/C][C]0.00962093913364548[/C][/ROW]
[ROW][C]56[/C][C]5.41[/C][C]5.39538917207866[/C][C]0.0146108279213406[/C][/ROW]
[ROW][C]57[/C][C]5.36[/C][C]5.39712302462058[/C][C]-0.0371230246205778[/C][/ROW]
[ROW][C]58[/C][C]5.38[/C][C]5.37121259706434[/C][C]0.00878740293565894[/C][/ROW]
[ROW][C]59[/C][C]5.41[/C][C]5.38418081033858[/C][C]0.0258191896614193[/C][/ROW]
[ROW][C]60[/C][C]5.35[/C][C]5.39320677225084[/C][C]-0.0432067722508434[/C][/ROW]
[ROW][C]61[/C][C]5.4[/C][C]5.3891937783034[/C][C]0.0108062216965976[/C][/ROW]
[ROW][C]62[/C][C]5.41[/C][C]5.40310705688094[/C][C]0.00689294311905986[/C][/ROW]
[ROW][C]63[/C][C]5.42[/C][C]5.38549984932473[/C][C]0.03450015067527[/C][/ROW]
[ROW][C]64[/C][C]5.41[/C][C]5.43705766196941[/C][C]-0.027057661969411[/C][/ROW]
[ROW][C]65[/C][C]5.41[/C][C]5.41349950057367[/C][C]-0.00349950057366755[/C][/ROW]
[ROW][C]66[/C][C]5.42[/C][C]5.42371196709417[/C][C]-0.00371196709417188[/C][/ROW]
[ROW][C]67[/C][C]5.4[/C][C]5.43009228433069[/C][C]-0.0300922843306868[/C][/ROW]
[ROW][C]68[/C][C]5.42[/C][C]5.41010887103114[/C][C]0.00989112896886191[/C][/ROW]
[ROW][C]69[/C][C]5.41[/C][C]5.39394992133233[/C][C]0.0160500786676714[/C][/ROW]
[ROW][C]70[/C][C]5.34[/C][C]5.41155926545433[/C][C]-0.0715592654543276[/C][/ROW]
[ROW][C]71[/C][C]5.46[/C][C]5.37626836875354[/C][C]0.0837316312464607[/C][/ROW]
[ROW][C]72[/C][C]5.45[/C][C]5.40250816909383[/C][C]0.0474918309061705[/C][/ROW]
[ROW][C]73[/C][C]5.47[/C][C]5.47056006533537[/C][C]-0.000560065335365678[/C][/ROW]
[ROW][C]74[/C][C]5.48[/C][C]5.47991448417495[/C][C]8.55158250541166e-05[/C][/ROW]
[ROW][C]75[/C][C]5.43[/C][C]5.4674541694692[/C][C]-0.0374541694692017[/C][/ROW]
[ROW][C]76[/C][C]5.5[/C][C]5.45987185130865[/C][C]0.0401281486913483[/C][/ROW]
[ROW][C]77[/C][C]5.51[/C][C]5.48510186586384[/C][C]0.0248981341361585[/C][/ROW]
[ROW][C]78[/C][C]5.51[/C][C]5.51660559748527[/C][C]-0.00660559748527412[/C][/ROW]
[ROW][C]79[/C][C]5.52[/C][C]5.51871611294075[/C][C]0.00128388705924731[/C][/ROW]
[ROW][C]80[/C][C]5.55[/C][C]5.53299725964417[/C][C]0.0170027403558324[/C][/ROW]
[ROW][C]81[/C][C]5.55[/C][C]5.52794477752029[/C][C]0.0220552224797057[/C][/ROW]
[ROW][C]82[/C][C]5.48[/C][C]5.53356810736331[/C][C]-0.0535681073633087[/C][/ROW]
[ROW][C]83[/C][C]5.61[/C][C]5.55494765303985[/C][C]0.0550523469601485[/C][/ROW]
[ROW][C]84[/C][C]5.59[/C][C]5.55968115846383[/C][C]0.030318841536169[/C][/ROW]
[ROW][C]85[/C][C]5.68[/C][C]5.61099993534582[/C][C]0.0690000646541753[/C][/ROW]
[ROW][C]86[/C][C]5.71[/C][C]5.67092314478944[/C][C]0.0390768552105563[/C][/ROW]
[ROW][C]87[/C][C]5.68[/C][C]5.68203112138912[/C][C]-0.00203112138912065[/C][/ROW]
[ROW][C]88[/C][C]5.7[/C][C]5.72802271616398[/C][C]-0.0280227161639806[/C][/ROW]
[ROW][C]89[/C][C]5.76[/C][C]5.71666796863025[/C][C]0.0433320313697489[/C][/ROW]
[ROW][C]90[/C][C]5.78[/C][C]5.76128739497724[/C][C]0.0187126050227553[/C][/ROW]
[ROW][C]91[/C][C]5.77[/C][C]5.79148806569486[/C][C]-0.0214880656948653[/C][/ROW]
[ROW][C]92[/C][C]5.85[/C][C]5.80600115206701[/C][C]0.0439988479329854[/C][/ROW]
[ROW][C]93[/C][C]5.82[/C][C]5.8283624272533[/C][C]-0.00836242725329672[/C][/ROW]
[ROW][C]94[/C][C]5.84[/C][C]5.80491223723711[/C][C]0.0350877627628883[/C][/ROW]
[ROW][C]95[/C][C]5.89[/C][C]5.92469685953212[/C][C]-0.034696859532116[/C][/ROW]
[ROW][C]96[/C][C]5.84[/C][C]5.87635347102977[/C][C]-0.0363534710297708[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269175&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269175&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	5.12	5.07843906267978	0.0415609373202228
14	5.14	5.12603374662358	0.0139662533764247
15	5.14	5.13731322369345	0.00268677630654501
16	5.14	5.14191076197677	-0.00191076197677287
17	5.13	5.13195891199302	-0.00195891199301901
18	5.15	5.1518846742924	-0.0018846742924028
19	5.16	5.18035831827516	-0.0203583182751617
20	5.17	5.16029150958433	0.00970849041566968
21	5.17	5.17791453307311	-0.00791453307311407
22	5.18	5.17390451424713	0.00609548575286833
23	5.21	5.17950074323159	0.0304992567684073
24	5.19	5.21242467051043	-0.0224246705104276
25	5.22	5.23274432850183	-0.0127443285018325
26	5.24	5.24069789017493	-0.000697890174931715
27	5.21	5.23913381813841	-0.0291338181384093
28	5.24	5.22059027205898	0.0194097279410181
29	5.28	5.22157022589402	0.0584297741059823
30	5.3	5.27974776210362	0.0202522378963819
31	5.32	5.3201640587146	-0.000164058714595683
32	5.32	5.32295022357645	-0.00295022357644736
33	5.29	5.33163022497518	-0.0416302249751777
34	5.3	5.31182776784122	-0.0118277678412229
35	5.32	5.31282870468693	0.00717129531306604
36	5.31	5.3178314996179	-0.00783149961789587
37	5.35	5.34983865375346	0.000161346246538407
38	5.36	5.36932179679459	-0.00932179679458578
39	5.33	5.3553897815304	-0.0253897815303974
40	5.35	5.3512642149801	-0.00126421498010476
41	5.35	5.34818152436346	0.00181847563653648
42	5.35	5.3593366478077	-0.00933664780770194
43	5.37	5.37191134859364	-0.00191134859363729
44	5.39	5.36763835018155	0.0223616498184498
45	5.4	5.37812982783497	0.0218701721650314
46	5.39	5.4032300123874	-0.0132300123874041
47	5.4	5.40728159889009	-0.00728159889009294
48	5.4	5.39822988718871	0.00177011281128703
49	5.4	5.43744381324298	-0.0374438132429802
50	5.38	5.42908330522644	-0.0490833052264446
51	5.32	5.38213975484945	-0.0621397548494462
52	5.36	5.35484440654172	0.00515559345828187
53	5.35	5.34986551742873	0.000134482571272798
54	5.39	5.35071095597826	0.0392890440217446
55	5.4	5.39037906086635	0.00962093913364548
56	5.41	5.39538917207866	0.0146108279213406
57	5.36	5.39712302462058	-0.0371230246205778
58	5.38	5.37121259706434	0.00878740293565894
59	5.41	5.38418081033858	0.0258191896614193
60	5.35	5.39320677225084	-0.0432067722508434
61	5.4	5.3891937783034	0.0108062216965976
62	5.41	5.40310705688094	0.00689294311905986
63	5.42	5.38549984932473	0.03450015067527
64	5.41	5.43705766196941	-0.027057661969411
65	5.41	5.41349950057367	-0.00349950057366755
66	5.42	5.42371196709417	-0.00371196709417188
67	5.4	5.43009228433069	-0.0300922843306868
68	5.42	5.41010887103114	0.00989112896886191
69	5.41	5.39394992133233	0.0160500786676714
70	5.34	5.41155926545433	-0.0715592654543276
71	5.46	5.37626836875354	0.0837316312464607
72	5.45	5.40250816909383	0.0474918309061705
73	5.47	5.47056006533537	-0.000560065335365678
74	5.48	5.47991448417495	8.55158250541166e-05
75	5.43	5.4674541694692	-0.0374541694692017
76	5.5	5.45987185130865	0.0401281486913483
77	5.51	5.48510186586384	0.0248981341361585
78	5.51	5.51660559748527	-0.00660559748527412
79	5.52	5.51871611294075	0.00128388705924731
80	5.55	5.53299725964417	0.0170027403558324
81	5.55	5.52794477752029	0.0220552224797057
82	5.48	5.53356810736331	-0.0535681073633087
83	5.61	5.55494765303985	0.0550523469601485
84	5.59	5.55968115846383	0.030318841536169
85	5.68	5.61099993534582	0.0690000646541753
86	5.71	5.67092314478944	0.0390768552105563
87	5.68	5.68203112138912	-0.00203112138912065
88	5.7	5.72802271616398	-0.0280227161639806
89	5.76	5.71666796863025	0.0433320313697489
90	5.78	5.76128739497724	0.0187126050227553
91	5.77	5.79148806569486	-0.0214880656948653
92	5.85	5.80600115206701	0.0439988479329854
93	5.82	5.8283624272533	-0.00836242725329672
94	5.84	5.80491223723711	0.0350877627628883
95	5.89	5.92469685953212	-0.034696859532116
96	5.84	5.87635347102977	-0.0363534710297708

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	5.90427302728391	5.85581824575114	5.95272780881667
98	5.91767021254561	5.85640230602005	5.97893811907116
99	5.89433081458185	5.82119685112873	5.96746477803496
100	5.93681649752959	5.85157313287193	6.02205986218725
101	5.96201567748993	5.86490460510275	6.05912674987712
102	5.97420780825058	5.8653818210572	6.08303379544397
103	5.98197578917888	5.86143915246589	6.10251242589188
104	6.02622449180051	5.89317813878462	6.15927084481641
105	6.00598498090746	5.86157519658333	6.15039476523158
106	5.99543062006969	5.83936366914473	6.15149757099464
107	6.07515772299822	5.90500700842265	6.24530843757379
108	6.04405907575341	3.12796690467869	8.96015124682814

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 5.90427302728391 & 5.85581824575114 & 5.95272780881667 \tabularnewline
98 & 5.91767021254561 & 5.85640230602005 & 5.97893811907116 \tabularnewline
99 & 5.89433081458185 & 5.82119685112873 & 5.96746477803496 \tabularnewline
100 & 5.93681649752959 & 5.85157313287193 & 6.02205986218725 \tabularnewline
101 & 5.96201567748993 & 5.86490460510275 & 6.05912674987712 \tabularnewline
102 & 5.97420780825058 & 5.8653818210572 & 6.08303379544397 \tabularnewline
103 & 5.98197578917888 & 5.86143915246589 & 6.10251242589188 \tabularnewline
104 & 6.02622449180051 & 5.89317813878462 & 6.15927084481641 \tabularnewline
105 & 6.00598498090746 & 5.86157519658333 & 6.15039476523158 \tabularnewline
106 & 5.99543062006969 & 5.83936366914473 & 6.15149757099464 \tabularnewline
107 & 6.07515772299822 & 5.90500700842265 & 6.24530843757379 \tabularnewline
108 & 6.04405907575341 & 3.12796690467869 & 8.96015124682814 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269175&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]5.90427302728391[/C][C]5.85581824575114[/C][C]5.95272780881667[/C][/ROW]
[ROW][C]98[/C][C]5.91767021254561[/C][C]5.85640230602005[/C][C]5.97893811907116[/C][/ROW]
[ROW][C]99[/C][C]5.89433081458185[/C][C]5.82119685112873[/C][C]5.96746477803496[/C][/ROW]
[ROW][C]100[/C][C]5.93681649752959[/C][C]5.85157313287193[/C][C]6.02205986218725[/C][/ROW]
[ROW][C]101[/C][C]5.96201567748993[/C][C]5.86490460510275[/C][C]6.05912674987712[/C][/ROW]
[ROW][C]102[/C][C]5.97420780825058[/C][C]5.8653818210572[/C][C]6.08303379544397[/C][/ROW]
[ROW][C]103[/C][C]5.98197578917888[/C][C]5.86143915246589[/C][C]6.10251242589188[/C][/ROW]
[ROW][C]104[/C][C]6.02622449180051[/C][C]5.89317813878462[/C][C]6.15927084481641[/C][/ROW]
[ROW][C]105[/C][C]6.00598498090746[/C][C]5.86157519658333[/C][C]6.15039476523158[/C][/ROW]
[ROW][C]106[/C][C]5.99543062006969[/C][C]5.83936366914473[/C][C]6.15149757099464[/C][/ROW]
[ROW][C]107[/C][C]6.07515772299822[/C][C]5.90500700842265[/C][C]6.24530843757379[/C][/ROW]
[ROW][C]108[/C][C]6.04405907575341[/C][C]3.12796690467869[/C][C]8.96015124682814[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269175&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269175&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	5.90427302728391	5.85581824575114	5.95272780881667
98	5.91767021254561	5.85640230602005	5.97893811907116
99	5.89433081458185	5.82119685112873	5.96746477803496
100	5.93681649752959	5.85157313287193	6.02205986218725
101	5.96201567748993	5.86490460510275	6.05912674987712
102	5.97420780825058	5.8653818210572	6.08303379544397
103	5.98197578917888	5.86143915246589	6.10251242589188
104	6.02622449180051	5.89317813878462	6.15927084481641
105	6.00598498090746	5.86157519658333	6.15039476523158
106	5.99543062006969	5.83936366914473	6.15149757099464
107	6.07515772299822	5.90500700842265	6.24530843757379
108	6.04405907575341	3.12796690467869	8.96015124682814

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code