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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

Tue, 27 May 2008 05:53:50 -0600

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/2008/May/27/t1211889334bmvt3eogty6w8b6.htm/, Retrieved Fri, 01 May 2026 17:37:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13335, Retrieved Fri, 01 May 2026 17:37:20 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

477

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

-       [Exponential Smoothing] [inschrijvingsgeld...] [2008-05-27 11:53:50] [359689940591b99e4b3f32f3fb2e21b2] [Current]

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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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13335&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13335&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13335&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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.826917432391495
beta	0.00124120623207274
gamma	0.000613968311953702

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.826917432391495 \tabularnewline
beta & 0.00124120623207274 \tabularnewline
gamma & 0.000613968311953702 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13335&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]0.826917432391495[/C][/ROW]
[ROW][C]beta[/C][C]0.00124120623207274[/C][/ROW]
[ROW][C]gamma[/C][C]0.000613968311953702[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13335&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13335&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	0.826917432391495
beta	0.00124120623207274
gamma	0.000613968311953702

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	527.96	521.992083333334	5.9679166666665
14	527.96	526.580365951964	1.37963404803634
15	527.96	527.375933710503	0.584066289496946
16	527.96	527.771732091937	0.188267908063494
17	527.96	528.097931125538	-0.137931125537875
18	527.96	528.154248922756	-0.194248922756174
19	527.96	528.163797179449	-0.203797179448998
20	527.96	528.165240643889	-0.205240643889169
21	527.96	528.16527982854	-0.205279828540256
22	536.61	536.815075916622	-0.205075916622036
23	536.61	536.814830138215	-0.204830138215243
24	536.61	536.81457736571	-0.204577365709952
25	536.61	538.102457835952	-1.49245783595245
26	536.61	536.520213895132	0.0897861048678124
27	536.61	536.246850246725	0.36314975327457
28	536.61	536.457450974799	0.152549025200983
29	536.61	536.751566258199	-0.141566258199418
30	536.61	536.802355866071	-0.192355866071466
31	536.61	536.810954202613	-0.20095420261282
32	536.61	536.812237031668	-0.20223703166846
33	536.61	536.812251645196	-0.202251645196384
34	545.06	545.46204661433	-0.402046614329947
35	545.06	545.29621499441	-0.236214994409806
36	545.06	545.267269987405	-0.207269987405084
37	545.06	546.550044682062	-1.49004468206192
38	545.06	544.967224497414	0.0927755025863917
39	545.06	544.693625088429	0.366374911570574
40	545.06	544.904136891134	0.155863108865901
41	545.06	545.198231309737	-0.138231309737193
42	545.06	545.249046586726	-0.189046586725681
43	545.06	545.257657246254	-0.197657246254039
44	545.06	545.258946369516	-0.198946369516420
45	545.06	545.258965584685	-0.198965584685197
46	564.24	553.908743492912	10.3312565070883
47	564.24	562.626788218473	1.61321178152718
48	564.24	564.137370998639	0.102629001360697
49	564.24	565.686789795405	-1.44678979540538
50	564.24	564.150469971103	0.0895300288967746
51	564.24	563.884776505568	0.35522349443238
52	564.24	564.096593798579	0.143406201421499
53	564.24	564.390892507245	-0.150892507245089
54	564.24	564.441756000741	-0.201756000740943
55	564.24	564.450366446048	-0.210366446047601
56	564.24	564.451643265865	-0.211643265865177
57	564.24	564.451647454694	-0.211647454693662
58	573.68	573.102528765152	0.577471234848417
59	573.68	573.754532177217	-0.0745321772166108
60	573.68	573.868057474968	-0.188057474967650
61	573.68	575.175367495233	-1.49536749523281
62	573.68	573.597420916153	0.0825790838468947
63	573.68	573.324380424822	0.355619575177798
64	573.68	573.534875738535	0.145124261465298
65	573.68	573.828938633934	-0.148938633933767
66	573.68	573.879789186852	-0.199789186852172
67	573.68	573.888403901173	-0.208403901172915
68	573.68	573.889684253513	-0.209684253513387
69	573.68	573.88969119968	-0.209691199680606
70	576.3	582.540658853125	-6.24065885312518
71	576.29	577.545949217969	-1.25594921796858
72	576.29	576.672702394204	-0.382702394203648
73	576.29	577.808892723166	-1.51889272316566
74	576.29	576.201610771014	0.0883892289864434
75	576.29	575.923360132646	0.366639867354024
76	576.29	576.132913587683	0.157086412317085
77	576.29	576.426816860924	-0.136816860923773
78	576.3	576.477678073012	-0.177678073012316
79	576.29	576.494590989154	-0.204590989154212
80	576.3	576.489043134129	-0.189043134128838
81	576.29	576.496158731808	-0.206158731808500
82	589.85	585.139450326843	4.71054967315717
83	589.85	589.202299462886	0.647700537114133
84	589.85	589.906544286791	-0.0565442867909951
85	589.85	591.31589214378	-1.46589214377946
86	589.85	589.756234937563	0.0937650624367734
87	589.85	589.486091597673	0.363908402326615
88	589.85	589.696993643659	0.153006356341280
89	589.85	589.991117183196	-0.141117183195547
90	589.85	590.042038995871	-0.192038995871144
91	589.85	590.050679969148	-0.200679969147586
92	589.85	590.051978085697	-0.201978085696965
93	589.85	590.051992680225	-0.201992680224748
94	599.12	598.702852969377	0.417147030622914
95	599.12	599.214175455488	-0.0941754554883119
96	599.12	599.303308394385	-0.183308394384994

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 527.96 & 521.992083333334 & 5.9679166666665 \tabularnewline
14 & 527.96 & 526.580365951964 & 1.37963404803634 \tabularnewline
15 & 527.96 & 527.375933710503 & 0.584066289496946 \tabularnewline
16 & 527.96 & 527.771732091937 & 0.188267908063494 \tabularnewline
17 & 527.96 & 528.097931125538 & -0.137931125537875 \tabularnewline
18 & 527.96 & 528.154248922756 & -0.194248922756174 \tabularnewline
19 & 527.96 & 528.163797179449 & -0.203797179448998 \tabularnewline
20 & 527.96 & 528.165240643889 & -0.205240643889169 \tabularnewline
21 & 527.96 & 528.16527982854 & -0.205279828540256 \tabularnewline
22 & 536.61 & 536.815075916622 & -0.205075916622036 \tabularnewline
23 & 536.61 & 536.814830138215 & -0.204830138215243 \tabularnewline
24 & 536.61 & 536.81457736571 & -0.204577365709952 \tabularnewline
25 & 536.61 & 538.102457835952 & -1.49245783595245 \tabularnewline
26 & 536.61 & 536.520213895132 & 0.0897861048678124 \tabularnewline
27 & 536.61 & 536.246850246725 & 0.36314975327457 \tabularnewline
28 & 536.61 & 536.457450974799 & 0.152549025200983 \tabularnewline
29 & 536.61 & 536.751566258199 & -0.141566258199418 \tabularnewline
30 & 536.61 & 536.802355866071 & -0.192355866071466 \tabularnewline
31 & 536.61 & 536.810954202613 & -0.20095420261282 \tabularnewline
32 & 536.61 & 536.812237031668 & -0.20223703166846 \tabularnewline
33 & 536.61 & 536.812251645196 & -0.202251645196384 \tabularnewline
34 & 545.06 & 545.46204661433 & -0.402046614329947 \tabularnewline
35 & 545.06 & 545.29621499441 & -0.236214994409806 \tabularnewline
36 & 545.06 & 545.267269987405 & -0.207269987405084 \tabularnewline
37 & 545.06 & 546.550044682062 & -1.49004468206192 \tabularnewline
38 & 545.06 & 544.967224497414 & 0.0927755025863917 \tabularnewline
39 & 545.06 & 544.693625088429 & 0.366374911570574 \tabularnewline
40 & 545.06 & 544.904136891134 & 0.155863108865901 \tabularnewline
41 & 545.06 & 545.198231309737 & -0.138231309737193 \tabularnewline
42 & 545.06 & 545.249046586726 & -0.189046586725681 \tabularnewline
43 & 545.06 & 545.257657246254 & -0.197657246254039 \tabularnewline
44 & 545.06 & 545.258946369516 & -0.198946369516420 \tabularnewline
45 & 545.06 & 545.258965584685 & -0.198965584685197 \tabularnewline
46 & 564.24 & 553.908743492912 & 10.3312565070883 \tabularnewline
47 & 564.24 & 562.626788218473 & 1.61321178152718 \tabularnewline
48 & 564.24 & 564.137370998639 & 0.102629001360697 \tabularnewline
49 & 564.24 & 565.686789795405 & -1.44678979540538 \tabularnewline
50 & 564.24 & 564.150469971103 & 0.0895300288967746 \tabularnewline
51 & 564.24 & 563.884776505568 & 0.35522349443238 \tabularnewline
52 & 564.24 & 564.096593798579 & 0.143406201421499 \tabularnewline
53 & 564.24 & 564.390892507245 & -0.150892507245089 \tabularnewline
54 & 564.24 & 564.441756000741 & -0.201756000740943 \tabularnewline
55 & 564.24 & 564.450366446048 & -0.210366446047601 \tabularnewline
56 & 564.24 & 564.451643265865 & -0.211643265865177 \tabularnewline
57 & 564.24 & 564.451647454694 & -0.211647454693662 \tabularnewline
58 & 573.68 & 573.102528765152 & 0.577471234848417 \tabularnewline
59 & 573.68 & 573.754532177217 & -0.0745321772166108 \tabularnewline
60 & 573.68 & 573.868057474968 & -0.188057474967650 \tabularnewline
61 & 573.68 & 575.175367495233 & -1.49536749523281 \tabularnewline
62 & 573.68 & 573.597420916153 & 0.0825790838468947 \tabularnewline
63 & 573.68 & 573.324380424822 & 0.355619575177798 \tabularnewline
64 & 573.68 & 573.534875738535 & 0.145124261465298 \tabularnewline
65 & 573.68 & 573.828938633934 & -0.148938633933767 \tabularnewline
66 & 573.68 & 573.879789186852 & -0.199789186852172 \tabularnewline
67 & 573.68 & 573.888403901173 & -0.208403901172915 \tabularnewline
68 & 573.68 & 573.889684253513 & -0.209684253513387 \tabularnewline
69 & 573.68 & 573.88969119968 & -0.209691199680606 \tabularnewline
70 & 576.3 & 582.540658853125 & -6.24065885312518 \tabularnewline
71 & 576.29 & 577.545949217969 & -1.25594921796858 \tabularnewline
72 & 576.29 & 576.672702394204 & -0.382702394203648 \tabularnewline
73 & 576.29 & 577.808892723166 & -1.51889272316566 \tabularnewline
74 & 576.29 & 576.201610771014 & 0.0883892289864434 \tabularnewline
75 & 576.29 & 575.923360132646 & 0.366639867354024 \tabularnewline
76 & 576.29 & 576.132913587683 & 0.157086412317085 \tabularnewline
77 & 576.29 & 576.426816860924 & -0.136816860923773 \tabularnewline
78 & 576.3 & 576.477678073012 & -0.177678073012316 \tabularnewline
79 & 576.29 & 576.494590989154 & -0.204590989154212 \tabularnewline
80 & 576.3 & 576.489043134129 & -0.189043134128838 \tabularnewline
81 & 576.29 & 576.496158731808 & -0.206158731808500 \tabularnewline
82 & 589.85 & 585.139450326843 & 4.71054967315717 \tabularnewline
83 & 589.85 & 589.202299462886 & 0.647700537114133 \tabularnewline
84 & 589.85 & 589.906544286791 & -0.0565442867909951 \tabularnewline
85 & 589.85 & 591.31589214378 & -1.46589214377946 \tabularnewline
86 & 589.85 & 589.756234937563 & 0.0937650624367734 \tabularnewline
87 & 589.85 & 589.486091597673 & 0.363908402326615 \tabularnewline
88 & 589.85 & 589.696993643659 & 0.153006356341280 \tabularnewline
89 & 589.85 & 589.991117183196 & -0.141117183195547 \tabularnewline
90 & 589.85 & 590.042038995871 & -0.192038995871144 \tabularnewline
91 & 589.85 & 590.050679969148 & -0.200679969147586 \tabularnewline
92 & 589.85 & 590.051978085697 & -0.201978085696965 \tabularnewline
93 & 589.85 & 590.051992680225 & -0.201992680224748 \tabularnewline
94 & 599.12 & 598.702852969377 & 0.417147030622914 \tabularnewline
95 & 599.12 & 599.214175455488 & -0.0941754554883119 \tabularnewline
96 & 599.12 & 599.303308394385 & -0.183308394384994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13335&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]527.96[/C][C]521.992083333334[/C][C]5.9679166666665[/C][/ROW]
[ROW][C]14[/C][C]527.96[/C][C]526.580365951964[/C][C]1.37963404803634[/C][/ROW]
[ROW][C]15[/C][C]527.96[/C][C]527.375933710503[/C][C]0.584066289496946[/C][/ROW]
[ROW][C]16[/C][C]527.96[/C][C]527.771732091937[/C][C]0.188267908063494[/C][/ROW]
[ROW][C]17[/C][C]527.96[/C][C]528.097931125538[/C][C]-0.137931125537875[/C][/ROW]
[ROW][C]18[/C][C]527.96[/C][C]528.154248922756[/C][C]-0.194248922756174[/C][/ROW]
[ROW][C]19[/C][C]527.96[/C][C]528.163797179449[/C][C]-0.203797179448998[/C][/ROW]
[ROW][C]20[/C][C]527.96[/C][C]528.165240643889[/C][C]-0.205240643889169[/C][/ROW]
[ROW][C]21[/C][C]527.96[/C][C]528.16527982854[/C][C]-0.205279828540256[/C][/ROW]
[ROW][C]22[/C][C]536.61[/C][C]536.815075916622[/C][C]-0.205075916622036[/C][/ROW]
[ROW][C]23[/C][C]536.61[/C][C]536.814830138215[/C][C]-0.204830138215243[/C][/ROW]
[ROW][C]24[/C][C]536.61[/C][C]536.81457736571[/C][C]-0.204577365709952[/C][/ROW]
[ROW][C]25[/C][C]536.61[/C][C]538.102457835952[/C][C]-1.49245783595245[/C][/ROW]
[ROW][C]26[/C][C]536.61[/C][C]536.520213895132[/C][C]0.0897861048678124[/C][/ROW]
[ROW][C]27[/C][C]536.61[/C][C]536.246850246725[/C][C]0.36314975327457[/C][/ROW]
[ROW][C]28[/C][C]536.61[/C][C]536.457450974799[/C][C]0.152549025200983[/C][/ROW]
[ROW][C]29[/C][C]536.61[/C][C]536.751566258199[/C][C]-0.141566258199418[/C][/ROW]
[ROW][C]30[/C][C]536.61[/C][C]536.802355866071[/C][C]-0.192355866071466[/C][/ROW]
[ROW][C]31[/C][C]536.61[/C][C]536.810954202613[/C][C]-0.20095420261282[/C][/ROW]
[ROW][C]32[/C][C]536.61[/C][C]536.812237031668[/C][C]-0.20223703166846[/C][/ROW]
[ROW][C]33[/C][C]536.61[/C][C]536.812251645196[/C][C]-0.202251645196384[/C][/ROW]
[ROW][C]34[/C][C]545.06[/C][C]545.46204661433[/C][C]-0.402046614329947[/C][/ROW]
[ROW][C]35[/C][C]545.06[/C][C]545.29621499441[/C][C]-0.236214994409806[/C][/ROW]
[ROW][C]36[/C][C]545.06[/C][C]545.267269987405[/C][C]-0.207269987405084[/C][/ROW]
[ROW][C]37[/C][C]545.06[/C][C]546.550044682062[/C][C]-1.49004468206192[/C][/ROW]
[ROW][C]38[/C][C]545.06[/C][C]544.967224497414[/C][C]0.0927755025863917[/C][/ROW]
[ROW][C]39[/C][C]545.06[/C][C]544.693625088429[/C][C]0.366374911570574[/C][/ROW]
[ROW][C]40[/C][C]545.06[/C][C]544.904136891134[/C][C]0.155863108865901[/C][/ROW]
[ROW][C]41[/C][C]545.06[/C][C]545.198231309737[/C][C]-0.138231309737193[/C][/ROW]
[ROW][C]42[/C][C]545.06[/C][C]545.249046586726[/C][C]-0.189046586725681[/C][/ROW]
[ROW][C]43[/C][C]545.06[/C][C]545.257657246254[/C][C]-0.197657246254039[/C][/ROW]
[ROW][C]44[/C][C]545.06[/C][C]545.258946369516[/C][C]-0.198946369516420[/C][/ROW]
[ROW][C]45[/C][C]545.06[/C][C]545.258965584685[/C][C]-0.198965584685197[/C][/ROW]
[ROW][C]46[/C][C]564.24[/C][C]553.908743492912[/C][C]10.3312565070883[/C][/ROW]
[ROW][C]47[/C][C]564.24[/C][C]562.626788218473[/C][C]1.61321178152718[/C][/ROW]
[ROW][C]48[/C][C]564.24[/C][C]564.137370998639[/C][C]0.102629001360697[/C][/ROW]
[ROW][C]49[/C][C]564.24[/C][C]565.686789795405[/C][C]-1.44678979540538[/C][/ROW]
[ROW][C]50[/C][C]564.24[/C][C]564.150469971103[/C][C]0.0895300288967746[/C][/ROW]
[ROW][C]51[/C][C]564.24[/C][C]563.884776505568[/C][C]0.35522349443238[/C][/ROW]
[ROW][C]52[/C][C]564.24[/C][C]564.096593798579[/C][C]0.143406201421499[/C][/ROW]
[ROW][C]53[/C][C]564.24[/C][C]564.390892507245[/C][C]-0.150892507245089[/C][/ROW]
[ROW][C]54[/C][C]564.24[/C][C]564.441756000741[/C][C]-0.201756000740943[/C][/ROW]
[ROW][C]55[/C][C]564.24[/C][C]564.450366446048[/C][C]-0.210366446047601[/C][/ROW]
[ROW][C]56[/C][C]564.24[/C][C]564.451643265865[/C][C]-0.211643265865177[/C][/ROW]
[ROW][C]57[/C][C]564.24[/C][C]564.451647454694[/C][C]-0.211647454693662[/C][/ROW]
[ROW][C]58[/C][C]573.68[/C][C]573.102528765152[/C][C]0.577471234848417[/C][/ROW]
[ROW][C]59[/C][C]573.68[/C][C]573.754532177217[/C][C]-0.0745321772166108[/C][/ROW]
[ROW][C]60[/C][C]573.68[/C][C]573.868057474968[/C][C]-0.188057474967650[/C][/ROW]
[ROW][C]61[/C][C]573.68[/C][C]575.175367495233[/C][C]-1.49536749523281[/C][/ROW]
[ROW][C]62[/C][C]573.68[/C][C]573.597420916153[/C][C]0.0825790838468947[/C][/ROW]
[ROW][C]63[/C][C]573.68[/C][C]573.324380424822[/C][C]0.355619575177798[/C][/ROW]
[ROW][C]64[/C][C]573.68[/C][C]573.534875738535[/C][C]0.145124261465298[/C][/ROW]
[ROW][C]65[/C][C]573.68[/C][C]573.828938633934[/C][C]-0.148938633933767[/C][/ROW]
[ROW][C]66[/C][C]573.68[/C][C]573.879789186852[/C][C]-0.199789186852172[/C][/ROW]
[ROW][C]67[/C][C]573.68[/C][C]573.888403901173[/C][C]-0.208403901172915[/C][/ROW]
[ROW][C]68[/C][C]573.68[/C][C]573.889684253513[/C][C]-0.209684253513387[/C][/ROW]
[ROW][C]69[/C][C]573.68[/C][C]573.88969119968[/C][C]-0.209691199680606[/C][/ROW]
[ROW][C]70[/C][C]576.3[/C][C]582.540658853125[/C][C]-6.24065885312518[/C][/ROW]
[ROW][C]71[/C][C]576.29[/C][C]577.545949217969[/C][C]-1.25594921796858[/C][/ROW]
[ROW][C]72[/C][C]576.29[/C][C]576.672702394204[/C][C]-0.382702394203648[/C][/ROW]
[ROW][C]73[/C][C]576.29[/C][C]577.808892723166[/C][C]-1.51889272316566[/C][/ROW]
[ROW][C]74[/C][C]576.29[/C][C]576.201610771014[/C][C]0.0883892289864434[/C][/ROW]
[ROW][C]75[/C][C]576.29[/C][C]575.923360132646[/C][C]0.366639867354024[/C][/ROW]
[ROW][C]76[/C][C]576.29[/C][C]576.132913587683[/C][C]0.157086412317085[/C][/ROW]
[ROW][C]77[/C][C]576.29[/C][C]576.426816860924[/C][C]-0.136816860923773[/C][/ROW]
[ROW][C]78[/C][C]576.3[/C][C]576.477678073012[/C][C]-0.177678073012316[/C][/ROW]
[ROW][C]79[/C][C]576.29[/C][C]576.494590989154[/C][C]-0.204590989154212[/C][/ROW]
[ROW][C]80[/C][C]576.3[/C][C]576.489043134129[/C][C]-0.189043134128838[/C][/ROW]
[ROW][C]81[/C][C]576.29[/C][C]576.496158731808[/C][C]-0.206158731808500[/C][/ROW]
[ROW][C]82[/C][C]589.85[/C][C]585.139450326843[/C][C]4.71054967315717[/C][/ROW]
[ROW][C]83[/C][C]589.85[/C][C]589.202299462886[/C][C]0.647700537114133[/C][/ROW]
[ROW][C]84[/C][C]589.85[/C][C]589.906544286791[/C][C]-0.0565442867909951[/C][/ROW]
[ROW][C]85[/C][C]589.85[/C][C]591.31589214378[/C][C]-1.46589214377946[/C][/ROW]
[ROW][C]86[/C][C]589.85[/C][C]589.756234937563[/C][C]0.0937650624367734[/C][/ROW]
[ROW][C]87[/C][C]589.85[/C][C]589.486091597673[/C][C]0.363908402326615[/C][/ROW]
[ROW][C]88[/C][C]589.85[/C][C]589.696993643659[/C][C]0.153006356341280[/C][/ROW]
[ROW][C]89[/C][C]589.85[/C][C]589.991117183196[/C][C]-0.141117183195547[/C][/ROW]
[ROW][C]90[/C][C]589.85[/C][C]590.042038995871[/C][C]-0.192038995871144[/C][/ROW]
[ROW][C]91[/C][C]589.85[/C][C]590.050679969148[/C][C]-0.200679969147586[/C][/ROW]
[ROW][C]92[/C][C]589.85[/C][C]590.051978085697[/C][C]-0.201978085696965[/C][/ROW]
[ROW][C]93[/C][C]589.85[/C][C]590.051992680225[/C][C]-0.201992680224748[/C][/ROW]
[ROW][C]94[/C][C]599.12[/C][C]598.702852969377[/C][C]0.417147030622914[/C][/ROW]
[ROW][C]95[/C][C]599.12[/C][C]599.214175455488[/C][C]-0.0941754554883119[/C][/ROW]
[ROW][C]96[/C][C]599.12[/C][C]599.303308394385[/C][C]-0.183308394384994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13335&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13335&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	527.96	521.992083333334	5.9679166666665
14	527.96	526.580365951964	1.37963404803634
15	527.96	527.375933710503	0.584066289496946
16	527.96	527.771732091937	0.188267908063494
17	527.96	528.097931125538	-0.137931125537875
18	527.96	528.154248922756	-0.194248922756174
19	527.96	528.163797179449	-0.203797179448998
20	527.96	528.165240643889	-0.205240643889169
21	527.96	528.16527982854	-0.205279828540256
22	536.61	536.815075916622	-0.205075916622036
23	536.61	536.814830138215	-0.204830138215243
24	536.61	536.81457736571	-0.204577365709952
25	536.61	538.102457835952	-1.49245783595245
26	536.61	536.520213895132	0.0897861048678124
27	536.61	536.246850246725	0.36314975327457
28	536.61	536.457450974799	0.152549025200983
29	536.61	536.751566258199	-0.141566258199418
30	536.61	536.802355866071	-0.192355866071466
31	536.61	536.810954202613	-0.20095420261282
32	536.61	536.812237031668	-0.20223703166846
33	536.61	536.812251645196	-0.202251645196384
34	545.06	545.46204661433	-0.402046614329947
35	545.06	545.29621499441	-0.236214994409806
36	545.06	545.267269987405	-0.207269987405084
37	545.06	546.550044682062	-1.49004468206192
38	545.06	544.967224497414	0.0927755025863917
39	545.06	544.693625088429	0.366374911570574
40	545.06	544.904136891134	0.155863108865901
41	545.06	545.198231309737	-0.138231309737193
42	545.06	545.249046586726	-0.189046586725681
43	545.06	545.257657246254	-0.197657246254039
44	545.06	545.258946369516	-0.198946369516420
45	545.06	545.258965584685	-0.198965584685197
46	564.24	553.908743492912	10.3312565070883
47	564.24	562.626788218473	1.61321178152718
48	564.24	564.137370998639	0.102629001360697
49	564.24	565.686789795405	-1.44678979540538
50	564.24	564.150469971103	0.0895300288967746
51	564.24	563.884776505568	0.35522349443238
52	564.24	564.096593798579	0.143406201421499
53	564.24	564.390892507245	-0.150892507245089
54	564.24	564.441756000741	-0.201756000740943
55	564.24	564.450366446048	-0.210366446047601
56	564.24	564.451643265865	-0.211643265865177
57	564.24	564.451647454694	-0.211647454693662
58	573.68	573.102528765152	0.577471234848417
59	573.68	573.754532177217	-0.0745321772166108
60	573.68	573.868057474968	-0.188057474967650
61	573.68	575.175367495233	-1.49536749523281
62	573.68	573.597420916153	0.0825790838468947
63	573.68	573.324380424822	0.355619575177798
64	573.68	573.534875738535	0.145124261465298
65	573.68	573.828938633934	-0.148938633933767
66	573.68	573.879789186852	-0.199789186852172
67	573.68	573.888403901173	-0.208403901172915
68	573.68	573.889684253513	-0.209684253513387
69	573.68	573.88969119968	-0.209691199680606
70	576.3	582.540658853125	-6.24065885312518
71	576.29	577.545949217969	-1.25594921796858
72	576.29	576.672702394204	-0.382702394203648
73	576.29	577.808892723166	-1.51889272316566
74	576.29	576.201610771014	0.0883892289864434
75	576.29	575.923360132646	0.366639867354024
76	576.29	576.132913587683	0.157086412317085
77	576.29	576.426816860924	-0.136816860923773
78	576.3	576.477678073012	-0.177678073012316
79	576.29	576.494590989154	-0.204590989154212
80	576.3	576.489043134129	-0.189043134128838
81	576.29	576.496158731808	-0.206158731808500
82	589.85	585.139450326843	4.71054967315717
83	589.85	589.202299462886	0.647700537114133
84	589.85	589.906544286791	-0.0565442867909951
85	589.85	591.31589214378	-1.46589214377946
86	589.85	589.756234937563	0.0937650624367734
87	589.85	589.486091597673	0.363908402326615
88	589.85	589.696993643659	0.153006356341280
89	589.85	589.991117183196	-0.141117183195547
90	589.85	590.042038995871	-0.192038995871144
91	589.85	590.050679969148	-0.200679969147586
92	589.85	590.051978085697	-0.201978085696965
93	589.85	590.051992680225	-0.201992680224748
94	599.12	598.702852969377	0.417147030622914
95	599.12	599.214175455488	-0.0941754554883119
96	599.12	599.303308394385	-0.183308394384994

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	600.605986070096	597.366650388677	603.845321751516
98	600.258473963714	596.052959150077	604.463988777351
99	599.910534720117	594.92081938788	604.900250052353
100	599.819829999531	594.151847067988	605.487812931074
101	599.986579465223	593.711813238305	606.261345692142
102	600.153513769703	593.324365706026	606.98266183338
103	600.320476966478	592.977468806333	607.663485126623
104	600.487449431184	592.663113676393	608.311785185974
105	600.65441925074	592.375610829532	608.933227671949
106	609.472519949444	600.76188808015	618.183151818737
107	609.638557144742	600.515533075183	618.7615812143
108	609.80536779441	600.286855682872	619.323879905947

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 600.605986070096 & 597.366650388677 & 603.845321751516 \tabularnewline
98 & 600.258473963714 & 596.052959150077 & 604.463988777351 \tabularnewline
99 & 599.910534720117 & 594.92081938788 & 604.900250052353 \tabularnewline
100 & 599.819829999531 & 594.151847067988 & 605.487812931074 \tabularnewline
101 & 599.986579465223 & 593.711813238305 & 606.261345692142 \tabularnewline
102 & 600.153513769703 & 593.324365706026 & 606.98266183338 \tabularnewline
103 & 600.320476966478 & 592.977468806333 & 607.663485126623 \tabularnewline
104 & 600.487449431184 & 592.663113676393 & 608.311785185974 \tabularnewline
105 & 600.65441925074 & 592.375610829532 & 608.933227671949 \tabularnewline
106 & 609.472519949444 & 600.76188808015 & 618.183151818737 \tabularnewline
107 & 609.638557144742 & 600.515533075183 & 618.7615812143 \tabularnewline
108 & 609.80536779441 & 600.286855682872 & 619.323879905947 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13335&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]600.605986070096[/C][C]597.366650388677[/C][C]603.845321751516[/C][/ROW]
[ROW][C]98[/C][C]600.258473963714[/C][C]596.052959150077[/C][C]604.463988777351[/C][/ROW]
[ROW][C]99[/C][C]599.910534720117[/C][C]594.92081938788[/C][C]604.900250052353[/C][/ROW]
[ROW][C]100[/C][C]599.819829999531[/C][C]594.151847067988[/C][C]605.487812931074[/C][/ROW]
[ROW][C]101[/C][C]599.986579465223[/C][C]593.711813238305[/C][C]606.261345692142[/C][/ROW]
[ROW][C]102[/C][C]600.153513769703[/C][C]593.324365706026[/C][C]606.98266183338[/C][/ROW]
[ROW][C]103[/C][C]600.320476966478[/C][C]592.977468806333[/C][C]607.663485126623[/C][/ROW]
[ROW][C]104[/C][C]600.487449431184[/C][C]592.663113676393[/C][C]608.311785185974[/C][/ROW]
[ROW][C]105[/C][C]600.65441925074[/C][C]592.375610829532[/C][C]608.933227671949[/C][/ROW]
[ROW][C]106[/C][C]609.472519949444[/C][C]600.76188808015[/C][C]618.183151818737[/C][/ROW]
[ROW][C]107[/C][C]609.638557144742[/C][C]600.515533075183[/C][C]618.7615812143[/C][/ROW]
[ROW][C]108[/C][C]609.80536779441[/C][C]600.286855682872[/C][C]619.323879905947[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13335&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13335&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	600.605986070096	597.366650388677	603.845321751516
98	600.258473963714	596.052959150077	604.463988777351
99	599.910534720117	594.92081938788	604.900250052353
100	599.819829999531	594.151847067988	605.487812931074
101	599.986579465223	593.711813238305	606.261345692142
102	600.153513769703	593.324365706026	606.98266183338
103	600.320476966478	592.977468806333	607.663485126623
104	600.487449431184	592.663113676393	608.311785185974
105	600.65441925074	592.375610829532	608.933227671949
106	609.472519949444	600.76188808015	618.183151818737
107	609.638557144742	600.515533075183	618.7615812143
108	609.80536779441	600.286855682872	619.323879905947

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 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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