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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, 01 Jun 2008 16:16:05 -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/Jun/02/t1212358721hv74rhptbcfun7z.htm/, Retrieved Sat, 18 May 2024 16:44:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13755, Retrieved Sat, 18 May 2024 16:44:19 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

303

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

-       [Exponential Smoothing] [Exponentional smo...] [2008-06-01 22:16:05] [d41d8cd98f00b204e9800998ecf8427e] [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	7 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 7 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13755&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13755&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13755&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	7 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.884706953444154
beta	0.000885825202857165
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.884706953444154 \tabularnewline
beta & 0.000885825202857165 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13755&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]0.884706953444154[/C][/ROW]
[ROW][C]beta[/C][C]0.000885825202857165[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13755&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13755&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	0.884706953444154
beta	0.000885825202857165
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	38	37.9245779519882	0.0754220480117596
14	38.01	38.0110634371662	-0.00106343716615243
15	38.06	38.068224964845	-0.00822496484497037
16	38.02	38.0332000276638	-0.0132000276637854
17	38.05	38.0654425985015	-0.0154425985015507
18	38.05	38.0636022037336	-0.0136022037335835
19	38.05	38.06296146455	-0.0129614645499672
20	38.05	38.0616255952028	-0.0116255952028155
21	38.03	38.0397886581437	-0.00978865814371943
22	37.98	37.9779112823335	0.00208871766650987
23	38.03	38.0115692622348	0.0184307377652289
24	38.04	38.0134805088262	0.0265194911737865
25	38.04	38.1424384294402	-0.102438429440205
26	38.08	38.0626354318814	0.0173645681186230
27	38.14	38.1352542280963	0.00474577190367143
28	38.37	38.1109545832191	0.259045416780936
29	38.49	38.3841662392335	0.105833760766473
30	38.55	38.4900235972082	0.0599764027917615
31	38.55	38.554789615662	-0.00478961566201974
32	38.55	38.5610652628292	-0.0110652628291561
33	38.48	38.5398792752465	-0.0598792752464945
34	38.51	38.4345036780709	0.0754963219291014
35	38.48	38.5355548555002	-0.0555548555001764
36	38.48	38.4728500446642	0.00714995533583362
37	38.48	38.5708833039678	-0.0908833039678143
38	38.43	38.5154740248018	-0.0854740248018473
39	38.43	38.4962049699704	-0.0662049699704284
40	38.45	38.4382704796058	0.0117295203941552
41	38.48	38.4749204226006	0.00507957739936415
42	38.47	38.4861773923873	-0.0161773923872914
43	38.47	38.475896572199	-0.0058965721990063
44	38.42	38.4802511697104	-0.0602511697103694
45	38.55	38.4097479357453	0.140252064254703
46	38.56	38.4968404145661	0.0631595854338656
47	38.57	38.571744730148	-0.00174473014796206
48	38.57	38.5637481837680	0.00625181623195914
49	38.57	38.6497359684850	-0.0797359684849539
50	38.57	38.6047511460951	-0.0347511460951324
51	38.62	38.6327009240801	-0.0127009240801428
52	38.73	38.6310731336794	0.0989268663205962
53	38.74	38.7442556557951	-0.00425565579510589
54	38.68	38.7448043212823	-0.0648043212823097
55	38.69	38.6926690465156	-0.0026690465155923
56	38.69	38.6935744879177	-0.00357448791773862
57	38.61	38.69629763108	-0.0862976310800008
58	38.77	38.5738555448935	0.196144455106456
59	38.78	38.7589220319659	0.0210779680341133
60	38.81	38.7719555882744	0.0380444117255863
61	38.81	38.8765313869043	-0.0665313869042876
62	38.81	38.8485761276802	-0.0385761276802228
63	38.76	38.8760369313363	-0.116036931336268
64	38.93	38.7958395307552	0.134160469244833
65	38.95	38.9282974367932	0.0217025632068300
66	38.97	38.9447515077507	0.0252484922492684
67	38.97	38.979528552073	-0.00952855207298597
68	38.96	38.9742673335675	-0.0142673335675028
69	38.92	38.9579263006439	-0.0379263006438535
70	38.95	38.9106305649485	0.0393694350514977
71	38.95	38.9367030277598	0.0132969722402194
72	38.97	38.9447158318443	0.0252841681556717
73	38.97	39.0260932016555	-0.0560932016554787
74	39.05	39.0106638810604	0.0393361189396302
75	39.08	39.09836780082	-0.018367800820009
76	38.83	39.1338081875414	-0.303808187541421
77	38.86	38.865632876974	-0.0056328769739693
78	38.87	38.8581124992192	0.0118875007808086
79	38.87	38.8768283415147	-0.00682834151466949
80	38.75	38.8731948752486	-0.123194875248643
81	38.86	38.7575298948335	0.102470105166503
82	38.93	38.8431671784028	0.0868328215972411
83	38.96	38.9080616628186	0.0519383371814257
84	38.95	38.9514864471542	-0.00148644715422108

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 38 & 37.9245779519882 & 0.0754220480117596 \tabularnewline
14 & 38.01 & 38.0110634371662 & -0.00106343716615243 \tabularnewline
15 & 38.06 & 38.068224964845 & -0.00822496484497037 \tabularnewline
16 & 38.02 & 38.0332000276638 & -0.0132000276637854 \tabularnewline
17 & 38.05 & 38.0654425985015 & -0.0154425985015507 \tabularnewline
18 & 38.05 & 38.0636022037336 & -0.0136022037335835 \tabularnewline
19 & 38.05 & 38.06296146455 & -0.0129614645499672 \tabularnewline
20 & 38.05 & 38.0616255952028 & -0.0116255952028155 \tabularnewline
21 & 38.03 & 38.0397886581437 & -0.00978865814371943 \tabularnewline
22 & 37.98 & 37.9779112823335 & 0.00208871766650987 \tabularnewline
23 & 38.03 & 38.0115692622348 & 0.0184307377652289 \tabularnewline
24 & 38.04 & 38.0134805088262 & 0.0265194911737865 \tabularnewline
25 & 38.04 & 38.1424384294402 & -0.102438429440205 \tabularnewline
26 & 38.08 & 38.0626354318814 & 0.0173645681186230 \tabularnewline
27 & 38.14 & 38.1352542280963 & 0.00474577190367143 \tabularnewline
28 & 38.37 & 38.1109545832191 & 0.259045416780936 \tabularnewline
29 & 38.49 & 38.3841662392335 & 0.105833760766473 \tabularnewline
30 & 38.55 & 38.4900235972082 & 0.0599764027917615 \tabularnewline
31 & 38.55 & 38.554789615662 & -0.00478961566201974 \tabularnewline
32 & 38.55 & 38.5610652628292 & -0.0110652628291561 \tabularnewline
33 & 38.48 & 38.5398792752465 & -0.0598792752464945 \tabularnewline
34 & 38.51 & 38.4345036780709 & 0.0754963219291014 \tabularnewline
35 & 38.48 & 38.5355548555002 & -0.0555548555001764 \tabularnewline
36 & 38.48 & 38.4728500446642 & 0.00714995533583362 \tabularnewline
37 & 38.48 & 38.5708833039678 & -0.0908833039678143 \tabularnewline
38 & 38.43 & 38.5154740248018 & -0.0854740248018473 \tabularnewline
39 & 38.43 & 38.4962049699704 & -0.0662049699704284 \tabularnewline
40 & 38.45 & 38.4382704796058 & 0.0117295203941552 \tabularnewline
41 & 38.48 & 38.4749204226006 & 0.00507957739936415 \tabularnewline
42 & 38.47 & 38.4861773923873 & -0.0161773923872914 \tabularnewline
43 & 38.47 & 38.475896572199 & -0.0058965721990063 \tabularnewline
44 & 38.42 & 38.4802511697104 & -0.0602511697103694 \tabularnewline
45 & 38.55 & 38.4097479357453 & 0.140252064254703 \tabularnewline
46 & 38.56 & 38.4968404145661 & 0.0631595854338656 \tabularnewline
47 & 38.57 & 38.571744730148 & -0.00174473014796206 \tabularnewline
48 & 38.57 & 38.5637481837680 & 0.00625181623195914 \tabularnewline
49 & 38.57 & 38.6497359684850 & -0.0797359684849539 \tabularnewline
50 & 38.57 & 38.6047511460951 & -0.0347511460951324 \tabularnewline
51 & 38.62 & 38.6327009240801 & -0.0127009240801428 \tabularnewline
52 & 38.73 & 38.6310731336794 & 0.0989268663205962 \tabularnewline
53 & 38.74 & 38.7442556557951 & -0.00425565579510589 \tabularnewline
54 & 38.68 & 38.7448043212823 & -0.0648043212823097 \tabularnewline
55 & 38.69 & 38.6926690465156 & -0.0026690465155923 \tabularnewline
56 & 38.69 & 38.6935744879177 & -0.00357448791773862 \tabularnewline
57 & 38.61 & 38.69629763108 & -0.0862976310800008 \tabularnewline
58 & 38.77 & 38.5738555448935 & 0.196144455106456 \tabularnewline
59 & 38.78 & 38.7589220319659 & 0.0210779680341133 \tabularnewline
60 & 38.81 & 38.7719555882744 & 0.0380444117255863 \tabularnewline
61 & 38.81 & 38.8765313869043 & -0.0665313869042876 \tabularnewline
62 & 38.81 & 38.8485761276802 & -0.0385761276802228 \tabularnewline
63 & 38.76 & 38.8760369313363 & -0.116036931336268 \tabularnewline
64 & 38.93 & 38.7958395307552 & 0.134160469244833 \tabularnewline
65 & 38.95 & 38.9282974367932 & 0.0217025632068300 \tabularnewline
66 & 38.97 & 38.9447515077507 & 0.0252484922492684 \tabularnewline
67 & 38.97 & 38.979528552073 & -0.00952855207298597 \tabularnewline
68 & 38.96 & 38.9742673335675 & -0.0142673335675028 \tabularnewline
69 & 38.92 & 38.9579263006439 & -0.0379263006438535 \tabularnewline
70 & 38.95 & 38.9106305649485 & 0.0393694350514977 \tabularnewline
71 & 38.95 & 38.9367030277598 & 0.0132969722402194 \tabularnewline
72 & 38.97 & 38.9447158318443 & 0.0252841681556717 \tabularnewline
73 & 38.97 & 39.0260932016555 & -0.0560932016554787 \tabularnewline
74 & 39.05 & 39.0106638810604 & 0.0393361189396302 \tabularnewline
75 & 39.08 & 39.09836780082 & -0.018367800820009 \tabularnewline
76 & 38.83 & 39.1338081875414 & -0.303808187541421 \tabularnewline
77 & 38.86 & 38.865632876974 & -0.0056328769739693 \tabularnewline
78 & 38.87 & 38.8581124992192 & 0.0118875007808086 \tabularnewline
79 & 38.87 & 38.8768283415147 & -0.00682834151466949 \tabularnewline
80 & 38.75 & 38.8731948752486 & -0.123194875248643 \tabularnewline
81 & 38.86 & 38.7575298948335 & 0.102470105166503 \tabularnewline
82 & 38.93 & 38.8431671784028 & 0.0868328215972411 \tabularnewline
83 & 38.96 & 38.9080616628186 & 0.0519383371814257 \tabularnewline
84 & 38.95 & 38.9514864471542 & -0.00148644715422108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13755&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]38[/C][C]37.9245779519882[/C][C]0.0754220480117596[/C][/ROW]
[ROW][C]14[/C][C]38.01[/C][C]38.0110634371662[/C][C]-0.00106343716615243[/C][/ROW]
[ROW][C]15[/C][C]38.06[/C][C]38.068224964845[/C][C]-0.00822496484497037[/C][/ROW]
[ROW][C]16[/C][C]38.02[/C][C]38.0332000276638[/C][C]-0.0132000276637854[/C][/ROW]
[ROW][C]17[/C][C]38.05[/C][C]38.0654425985015[/C][C]-0.0154425985015507[/C][/ROW]
[ROW][C]18[/C][C]38.05[/C][C]38.0636022037336[/C][C]-0.0136022037335835[/C][/ROW]
[ROW][C]19[/C][C]38.05[/C][C]38.06296146455[/C][C]-0.0129614645499672[/C][/ROW]
[ROW][C]20[/C][C]38.05[/C][C]38.0616255952028[/C][C]-0.0116255952028155[/C][/ROW]
[ROW][C]21[/C][C]38.03[/C][C]38.0397886581437[/C][C]-0.00978865814371943[/C][/ROW]
[ROW][C]22[/C][C]37.98[/C][C]37.9779112823335[/C][C]0.00208871766650987[/C][/ROW]
[ROW][C]23[/C][C]38.03[/C][C]38.0115692622348[/C][C]0.0184307377652289[/C][/ROW]
[ROW][C]24[/C][C]38.04[/C][C]38.0134805088262[/C][C]0.0265194911737865[/C][/ROW]
[ROW][C]25[/C][C]38.04[/C][C]38.1424384294402[/C][C]-0.102438429440205[/C][/ROW]
[ROW][C]26[/C][C]38.08[/C][C]38.0626354318814[/C][C]0.0173645681186230[/C][/ROW]
[ROW][C]27[/C][C]38.14[/C][C]38.1352542280963[/C][C]0.00474577190367143[/C][/ROW]
[ROW][C]28[/C][C]38.37[/C][C]38.1109545832191[/C][C]0.259045416780936[/C][/ROW]
[ROW][C]29[/C][C]38.49[/C][C]38.3841662392335[/C][C]0.105833760766473[/C][/ROW]
[ROW][C]30[/C][C]38.55[/C][C]38.4900235972082[/C][C]0.0599764027917615[/C][/ROW]
[ROW][C]31[/C][C]38.55[/C][C]38.554789615662[/C][C]-0.00478961566201974[/C][/ROW]
[ROW][C]32[/C][C]38.55[/C][C]38.5610652628292[/C][C]-0.0110652628291561[/C][/ROW]
[ROW][C]33[/C][C]38.48[/C][C]38.5398792752465[/C][C]-0.0598792752464945[/C][/ROW]
[ROW][C]34[/C][C]38.51[/C][C]38.4345036780709[/C][C]0.0754963219291014[/C][/ROW]
[ROW][C]35[/C][C]38.48[/C][C]38.5355548555002[/C][C]-0.0555548555001764[/C][/ROW]
[ROW][C]36[/C][C]38.48[/C][C]38.4728500446642[/C][C]0.00714995533583362[/C][/ROW]
[ROW][C]37[/C][C]38.48[/C][C]38.5708833039678[/C][C]-0.0908833039678143[/C][/ROW]
[ROW][C]38[/C][C]38.43[/C][C]38.5154740248018[/C][C]-0.0854740248018473[/C][/ROW]
[ROW][C]39[/C][C]38.43[/C][C]38.4962049699704[/C][C]-0.0662049699704284[/C][/ROW]
[ROW][C]40[/C][C]38.45[/C][C]38.4382704796058[/C][C]0.0117295203941552[/C][/ROW]
[ROW][C]41[/C][C]38.48[/C][C]38.4749204226006[/C][C]0.00507957739936415[/C][/ROW]
[ROW][C]42[/C][C]38.47[/C][C]38.4861773923873[/C][C]-0.0161773923872914[/C][/ROW]
[ROW][C]43[/C][C]38.47[/C][C]38.475896572199[/C][C]-0.0058965721990063[/C][/ROW]
[ROW][C]44[/C][C]38.42[/C][C]38.4802511697104[/C][C]-0.0602511697103694[/C][/ROW]
[ROW][C]45[/C][C]38.55[/C][C]38.4097479357453[/C][C]0.140252064254703[/C][/ROW]
[ROW][C]46[/C][C]38.56[/C][C]38.4968404145661[/C][C]0.0631595854338656[/C][/ROW]
[ROW][C]47[/C][C]38.57[/C][C]38.571744730148[/C][C]-0.00174473014796206[/C][/ROW]
[ROW][C]48[/C][C]38.57[/C][C]38.5637481837680[/C][C]0.00625181623195914[/C][/ROW]
[ROW][C]49[/C][C]38.57[/C][C]38.6497359684850[/C][C]-0.0797359684849539[/C][/ROW]
[ROW][C]50[/C][C]38.57[/C][C]38.6047511460951[/C][C]-0.0347511460951324[/C][/ROW]
[ROW][C]51[/C][C]38.62[/C][C]38.6327009240801[/C][C]-0.0127009240801428[/C][/ROW]
[ROW][C]52[/C][C]38.73[/C][C]38.6310731336794[/C][C]0.0989268663205962[/C][/ROW]
[ROW][C]53[/C][C]38.74[/C][C]38.7442556557951[/C][C]-0.00425565579510589[/C][/ROW]
[ROW][C]54[/C][C]38.68[/C][C]38.7448043212823[/C][C]-0.0648043212823097[/C][/ROW]
[ROW][C]55[/C][C]38.69[/C][C]38.6926690465156[/C][C]-0.0026690465155923[/C][/ROW]
[ROW][C]56[/C][C]38.69[/C][C]38.6935744879177[/C][C]-0.00357448791773862[/C][/ROW]
[ROW][C]57[/C][C]38.61[/C][C]38.69629763108[/C][C]-0.0862976310800008[/C][/ROW]
[ROW][C]58[/C][C]38.77[/C][C]38.5738555448935[/C][C]0.196144455106456[/C][/ROW]
[ROW][C]59[/C][C]38.78[/C][C]38.7589220319659[/C][C]0.0210779680341133[/C][/ROW]
[ROW][C]60[/C][C]38.81[/C][C]38.7719555882744[/C][C]0.0380444117255863[/C][/ROW]
[ROW][C]61[/C][C]38.81[/C][C]38.8765313869043[/C][C]-0.0665313869042876[/C][/ROW]
[ROW][C]62[/C][C]38.81[/C][C]38.8485761276802[/C][C]-0.0385761276802228[/C][/ROW]
[ROW][C]63[/C][C]38.76[/C][C]38.8760369313363[/C][C]-0.116036931336268[/C][/ROW]
[ROW][C]64[/C][C]38.93[/C][C]38.7958395307552[/C][C]0.134160469244833[/C][/ROW]
[ROW][C]65[/C][C]38.95[/C][C]38.9282974367932[/C][C]0.0217025632068300[/C][/ROW]
[ROW][C]66[/C][C]38.97[/C][C]38.9447515077507[/C][C]0.0252484922492684[/C][/ROW]
[ROW][C]67[/C][C]38.97[/C][C]38.979528552073[/C][C]-0.00952855207298597[/C][/ROW]
[ROW][C]68[/C][C]38.96[/C][C]38.9742673335675[/C][C]-0.0142673335675028[/C][/ROW]
[ROW][C]69[/C][C]38.92[/C][C]38.9579263006439[/C][C]-0.0379263006438535[/C][/ROW]
[ROW][C]70[/C][C]38.95[/C][C]38.9106305649485[/C][C]0.0393694350514977[/C][/ROW]
[ROW][C]71[/C][C]38.95[/C][C]38.9367030277598[/C][C]0.0132969722402194[/C][/ROW]
[ROW][C]72[/C][C]38.97[/C][C]38.9447158318443[/C][C]0.0252841681556717[/C][/ROW]
[ROW][C]73[/C][C]38.97[/C][C]39.0260932016555[/C][C]-0.0560932016554787[/C][/ROW]
[ROW][C]74[/C][C]39.05[/C][C]39.0106638810604[/C][C]0.0393361189396302[/C][/ROW]
[ROW][C]75[/C][C]39.08[/C][C]39.09836780082[/C][C]-0.018367800820009[/C][/ROW]
[ROW][C]76[/C][C]38.83[/C][C]39.1338081875414[/C][C]-0.303808187541421[/C][/ROW]
[ROW][C]77[/C][C]38.86[/C][C]38.865632876974[/C][C]-0.0056328769739693[/C][/ROW]
[ROW][C]78[/C][C]38.87[/C][C]38.8581124992192[/C][C]0.0118875007808086[/C][/ROW]
[ROW][C]79[/C][C]38.87[/C][C]38.8768283415147[/C][C]-0.00682834151466949[/C][/ROW]
[ROW][C]80[/C][C]38.75[/C][C]38.8731948752486[/C][C]-0.123194875248643[/C][/ROW]
[ROW][C]81[/C][C]38.86[/C][C]38.7575298948335[/C][C]0.102470105166503[/C][/ROW]
[ROW][C]82[/C][C]38.93[/C][C]38.8431671784028[/C][C]0.0868328215972411[/C][/ROW]
[ROW][C]83[/C][C]38.96[/C][C]38.9080616628186[/C][C]0.0519383371814257[/C][/ROW]
[ROW][C]84[/C][C]38.95[/C][C]38.9514864471542[/C][C]-0.00148644715422108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13755&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13755&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	38	37.9245779519882	0.0754220480117596
14	38.01	38.0110634371662	-0.00106343716615243
15	38.06	38.068224964845	-0.00822496484497037
16	38.02	38.0332000276638	-0.0132000276637854
17	38.05	38.0654425985015	-0.0154425985015507
18	38.05	38.0636022037336	-0.0136022037335835
19	38.05	38.06296146455	-0.0129614645499672
20	38.05	38.0616255952028	-0.0116255952028155
21	38.03	38.0397886581437	-0.00978865814371943
22	37.98	37.9779112823335	0.00208871766650987
23	38.03	38.0115692622348	0.0184307377652289
24	38.04	38.0134805088262	0.0265194911737865
25	38.04	38.1424384294402	-0.102438429440205
26	38.08	38.0626354318814	0.0173645681186230
27	38.14	38.1352542280963	0.00474577190367143
28	38.37	38.1109545832191	0.259045416780936
29	38.49	38.3841662392335	0.105833760766473
30	38.55	38.4900235972082	0.0599764027917615
31	38.55	38.554789615662	-0.00478961566201974
32	38.55	38.5610652628292	-0.0110652628291561
33	38.48	38.5398792752465	-0.0598792752464945
34	38.51	38.4345036780709	0.0754963219291014
35	38.48	38.5355548555002	-0.0555548555001764
36	38.48	38.4728500446642	0.00714995533583362
37	38.48	38.5708833039678	-0.0908833039678143
38	38.43	38.5154740248018	-0.0854740248018473
39	38.43	38.4962049699704	-0.0662049699704284
40	38.45	38.4382704796058	0.0117295203941552
41	38.48	38.4749204226006	0.00507957739936415
42	38.47	38.4861773923873	-0.0161773923872914
43	38.47	38.475896572199	-0.0058965721990063
44	38.42	38.4802511697104	-0.0602511697103694
45	38.55	38.4097479357453	0.140252064254703
46	38.56	38.4968404145661	0.0631595854338656
47	38.57	38.571744730148	-0.00174473014796206
48	38.57	38.5637481837680	0.00625181623195914
49	38.57	38.6497359684850	-0.0797359684849539
50	38.57	38.6047511460951	-0.0347511460951324
51	38.62	38.6327009240801	-0.0127009240801428
52	38.73	38.6310731336794	0.0989268663205962
53	38.74	38.7442556557951	-0.00425565579510589
54	38.68	38.7448043212823	-0.0648043212823097
55	38.69	38.6926690465156	-0.0026690465155923
56	38.69	38.6935744879177	-0.00357448791773862
57	38.61	38.69629763108	-0.0862976310800008
58	38.77	38.5738555448935	0.196144455106456
59	38.78	38.7589220319659	0.0210779680341133
60	38.81	38.7719555882744	0.0380444117255863
61	38.81	38.8765313869043	-0.0665313869042876
62	38.81	38.8485761276802	-0.0385761276802228
63	38.76	38.8760369313363	-0.116036931336268
64	38.93	38.7958395307552	0.134160469244833
65	38.95	38.9282974367932	0.0217025632068300
66	38.97	38.9447515077507	0.0252484922492684
67	38.97	38.979528552073	-0.00952855207298597
68	38.96	38.9742673335675	-0.0142673335675028
69	38.92	38.9579263006439	-0.0379263006438535
70	38.95	38.9106305649485	0.0393694350514977
71	38.95	38.9367030277598	0.0132969722402194
72	38.97	38.9447158318443	0.0252841681556717
73	38.97	39.0260932016555	-0.0560932016554787
74	39.05	39.0106638810604	0.0393361189396302
75	39.08	39.09836780082	-0.018367800820009
76	38.83	39.1338081875414	-0.303808187541421
77	38.86	38.865632876974	-0.0056328769739693
78	38.87	38.8581124992192	0.0118875007808086
79	38.87	38.8768283415147	-0.00682834151466949
80	38.75	38.8731948752486	-0.123194875248643
81	38.86	38.7575298948335	0.102470105166503
82	38.93	38.8431671784028	0.0868328215972411
83	38.96	38.9080616628186	0.0519383371814257
84	38.95	38.9514864471542	-0.00148644715422108

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	38.9995974910554	38.8513113128462	39.1478836692645
86	39.0446853645329	38.8465518012755	39.2428189277904
87	39.0907691990618	38.8528948146844	39.3286435834393
88	39.1091624201676	38.8373234865306	39.3810013538047
89	39.1443830134385	38.8422208152678	39.4465452116093
90	39.1438501879932	38.8143078219297	39.4733925540567
91	39.1499166137263	38.7950273158838	39.5048059115688
92	39.1387744937712	38.7603422794291	39.5172067081133
93	39.1583267375353	38.7574521805277	39.5592012945428
94	39.1514282242753	38.7295111203404	39.5733453282101
95	39.1353362289596	38.6934566258026	39.5772158321166
96	39.1265448268803	29.0738705286303	49.1792191251302

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 38.9995974910554 & 38.8513113128462 & 39.1478836692645 \tabularnewline
86 & 39.0446853645329 & 38.8465518012755 & 39.2428189277904 \tabularnewline
87 & 39.0907691990618 & 38.8528948146844 & 39.3286435834393 \tabularnewline
88 & 39.1091624201676 & 38.8373234865306 & 39.3810013538047 \tabularnewline
89 & 39.1443830134385 & 38.8422208152678 & 39.4465452116093 \tabularnewline
90 & 39.1438501879932 & 38.8143078219297 & 39.4733925540567 \tabularnewline
91 & 39.1499166137263 & 38.7950273158838 & 39.5048059115688 \tabularnewline
92 & 39.1387744937712 & 38.7603422794291 & 39.5172067081133 \tabularnewline
93 & 39.1583267375353 & 38.7574521805277 & 39.5592012945428 \tabularnewline
94 & 39.1514282242753 & 38.7295111203404 & 39.5733453282101 \tabularnewline
95 & 39.1353362289596 & 38.6934566258026 & 39.5772158321166 \tabularnewline
96 & 39.1265448268803 & 29.0738705286303 & 49.1792191251302 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13755&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]85[/C][C]38.9995974910554[/C][C]38.8513113128462[/C][C]39.1478836692645[/C][/ROW]
[ROW][C]86[/C][C]39.0446853645329[/C][C]38.8465518012755[/C][C]39.2428189277904[/C][/ROW]
[ROW][C]87[/C][C]39.0907691990618[/C][C]38.8528948146844[/C][C]39.3286435834393[/C][/ROW]
[ROW][C]88[/C][C]39.1091624201676[/C][C]38.8373234865306[/C][C]39.3810013538047[/C][/ROW]
[ROW][C]89[/C][C]39.1443830134385[/C][C]38.8422208152678[/C][C]39.4465452116093[/C][/ROW]
[ROW][C]90[/C][C]39.1438501879932[/C][C]38.8143078219297[/C][C]39.4733925540567[/C][/ROW]
[ROW][C]91[/C][C]39.1499166137263[/C][C]38.7950273158838[/C][C]39.5048059115688[/C][/ROW]
[ROW][C]92[/C][C]39.1387744937712[/C][C]38.7603422794291[/C][C]39.5172067081133[/C][/ROW]
[ROW][C]93[/C][C]39.1583267375353[/C][C]38.7574521805277[/C][C]39.5592012945428[/C][/ROW]
[ROW][C]94[/C][C]39.1514282242753[/C][C]38.7295111203404[/C][C]39.5733453282101[/C][/ROW]
[ROW][C]95[/C][C]39.1353362289596[/C][C]38.6934566258026[/C][C]39.5772158321166[/C][/ROW]
[ROW][C]96[/C][C]39.1265448268803[/C][C]29.0738705286303[/C][C]49.1792191251302[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13755&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13755&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
85	38.9995974910554	38.8513113128462	39.1478836692645
86	39.0446853645329	38.8465518012755	39.2428189277904
87	39.0907691990618	38.8528948146844	39.3286435834393
88	39.1091624201676	38.8373234865306	39.3810013538047
89	39.1443830134385	38.8422208152678	39.4465452116093
90	39.1438501879932	38.8143078219297	39.4733925540567
91	39.1499166137263	38.7950273158838	39.5048059115688
92	39.1387744937712	38.7603422794291	39.5172067081133
93	39.1583267375353	38.7574521805277	39.5592012945428
94	39.1514282242753	38.7295111203404	39.5733453282101
95	39.1353362289596	38.6934566258026	39.5772158321166
96	39.1265448268803	29.0738705286303	49.1792191251302

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=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