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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 28 Nov 2014 11:18:41 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/28/t1417173570zi0f3186wdymrao.htm/, Retrieved Sun, 19 May 2024 14:00:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260836, Retrieved Sun, 19 May 2024 14:00:58 +0000

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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] [] [2014-11-28 11:18:41] [d4b037465b17855a5e62fa4428b30753] [Current]

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260836&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260836&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260836&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.933517091788725
beta	0.0285483242911797
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.933517091788725 \tabularnewline
beta & 0.0285483242911797 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260836&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]0.933517091788725[/C][/ROW]
[ROW][C]beta[/C][C]0.0285483242911797[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260836&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260836&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	0.933517091788725
beta	0.0285483242911797
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.231	1.33306223290598	-0.102062232905983
14	1.276	1.28263489297637	-0.00663489297636621
15	1.281	1.27811378368379	0.002886216316214
16	1.312	1.30397437798644	0.00802562201355772
17	1.363	1.34205491430748	0.0209450856925246
18	1.419	1.38804585129282	0.0309541487071838
19	1.374	1.47483035853089	-0.100830358530891
20	1.422	1.32669627828479	0.0953037217152068
21	1.378	1.4047382583104	-0.0267382583103994
22	1.38	1.24243104682629	0.13756895317371
23	1.409	1.23975701946801	0.169242980531989
24	1.398	1.33028662245521	0.0677133775447851
25	1.445	1.44018079679025	0.00481920320974716
26	1.452	1.50662029899895	-0.0546202989989466
27	1.506	1.46740506390953	0.038594936090466
28	1.531	1.53736177076355	-0.00636177076354838
29	1.524	1.57290665418382	-0.0489066541838157
30	1.52	1.56252995714338	-0.042529957143377
31	1.499	1.57817072867659	-0.0791707286765895
32	1.491	1.47008943422286	0.0209105657771396
33	1.496	1.47538140943543	0.0206185905645742
34	1.493	1.37427930710645	0.118720692893555
35	1.507	1.36168663542899	0.145313364571009
36	1.569	1.428060564381	0.140939435619001
37	1.593	1.60901564259298	-0.0160156425929787
38	1.597	1.65838300798519	-0.0613830079851867
39	1.633	1.62520091865085	0.0077990813491482
40	1.686	1.66874862612815	0.0172513738718465
41	1.683	1.72946588461063	-0.0464658846106343
42	1.646	1.72781428494153	-0.0818142849415342
43	1.658	1.70932219484573	-0.0513221948457294
44	1.636	1.6396095662143	-0.00360956621430164
45	1.67	1.62705658568884	0.0429434143111629
46	1.634	1.55897658322988	0.0750234167701158
47	1.618	1.51185455019924	0.106145449800762
48	1.622	1.54482476578367	0.0771752342163325
49	1.688	1.65757169992125	0.0304283000787546
50	1.723	1.75026853032143	-0.0272685303214293
51	1.776	1.75743088328611	0.0185691167138922
52	1.809	1.81584661177675	-0.00684661177674584
53	1.754	1.8533752534367	-0.0993752534367023
54	1.714	1.80211510937638	-0.0881151093763755
55	1.733	1.78173369581549	-0.0487336958154887
56	1.783	1.71964393499257	0.0633560650074334
57	1.818	1.77651853613894	0.0414814638610619
58	1.81	1.71298663114982	0.0970133688501764
59	1.764	1.69282779873243	0.0711722012675657
60	1.73	1.69465793683832	0.0353420631616832
61	1.742	1.76756422203287	-0.0255642220328745
62	1.785	1.8049822060845	-0.0199822060844996
63	1.769	1.82301505355714	-0.0540150535571391
64	1.743	1.81106927973262	-0.0680692797326212
65	1.721	1.7827491085836	-0.0617491085835964
66	1.73	1.76582013816826	-0.0358201381682564
67	1.753	1.7967267613665	-0.0437267613664982
68	1.764	1.74674814567696	0.0172518543230382
69	1.758	1.75788573072363	0.00011426927636693
70	1.7	1.65708265461124	0.0429173453887606
71	1.678	1.58091847535426	0.0970815246457426
72	1.688	1.60145602202114	0.0865439779788584

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.231 & 1.33306223290598 & -0.102062232905983 \tabularnewline
14 & 1.276 & 1.28263489297637 & -0.00663489297636621 \tabularnewline
15 & 1.281 & 1.27811378368379 & 0.002886216316214 \tabularnewline
16 & 1.312 & 1.30397437798644 & 0.00802562201355772 \tabularnewline
17 & 1.363 & 1.34205491430748 & 0.0209450856925246 \tabularnewline
18 & 1.419 & 1.38804585129282 & 0.0309541487071838 \tabularnewline
19 & 1.374 & 1.47483035853089 & -0.100830358530891 \tabularnewline
20 & 1.422 & 1.32669627828479 & 0.0953037217152068 \tabularnewline
21 & 1.378 & 1.4047382583104 & -0.0267382583103994 \tabularnewline
22 & 1.38 & 1.24243104682629 & 0.13756895317371 \tabularnewline
23 & 1.409 & 1.23975701946801 & 0.169242980531989 \tabularnewline
24 & 1.398 & 1.33028662245521 & 0.0677133775447851 \tabularnewline
25 & 1.445 & 1.44018079679025 & 0.00481920320974716 \tabularnewline
26 & 1.452 & 1.50662029899895 & -0.0546202989989466 \tabularnewline
27 & 1.506 & 1.46740506390953 & 0.038594936090466 \tabularnewline
28 & 1.531 & 1.53736177076355 & -0.00636177076354838 \tabularnewline
29 & 1.524 & 1.57290665418382 & -0.0489066541838157 \tabularnewline
30 & 1.52 & 1.56252995714338 & -0.042529957143377 \tabularnewline
31 & 1.499 & 1.57817072867659 & -0.0791707286765895 \tabularnewline
32 & 1.491 & 1.47008943422286 & 0.0209105657771396 \tabularnewline
33 & 1.496 & 1.47538140943543 & 0.0206185905645742 \tabularnewline
34 & 1.493 & 1.37427930710645 & 0.118720692893555 \tabularnewline
35 & 1.507 & 1.36168663542899 & 0.145313364571009 \tabularnewline
36 & 1.569 & 1.428060564381 & 0.140939435619001 \tabularnewline
37 & 1.593 & 1.60901564259298 & -0.0160156425929787 \tabularnewline
38 & 1.597 & 1.65838300798519 & -0.0613830079851867 \tabularnewline
39 & 1.633 & 1.62520091865085 & 0.0077990813491482 \tabularnewline
40 & 1.686 & 1.66874862612815 & 0.0172513738718465 \tabularnewline
41 & 1.683 & 1.72946588461063 & -0.0464658846106343 \tabularnewline
42 & 1.646 & 1.72781428494153 & -0.0818142849415342 \tabularnewline
43 & 1.658 & 1.70932219484573 & -0.0513221948457294 \tabularnewline
44 & 1.636 & 1.6396095662143 & -0.00360956621430164 \tabularnewline
45 & 1.67 & 1.62705658568884 & 0.0429434143111629 \tabularnewline
46 & 1.634 & 1.55897658322988 & 0.0750234167701158 \tabularnewline
47 & 1.618 & 1.51185455019924 & 0.106145449800762 \tabularnewline
48 & 1.622 & 1.54482476578367 & 0.0771752342163325 \tabularnewline
49 & 1.688 & 1.65757169992125 & 0.0304283000787546 \tabularnewline
50 & 1.723 & 1.75026853032143 & -0.0272685303214293 \tabularnewline
51 & 1.776 & 1.75743088328611 & 0.0185691167138922 \tabularnewline
52 & 1.809 & 1.81584661177675 & -0.00684661177674584 \tabularnewline
53 & 1.754 & 1.8533752534367 & -0.0993752534367023 \tabularnewline
54 & 1.714 & 1.80211510937638 & -0.0881151093763755 \tabularnewline
55 & 1.733 & 1.78173369581549 & -0.0487336958154887 \tabularnewline
56 & 1.783 & 1.71964393499257 & 0.0633560650074334 \tabularnewline
57 & 1.818 & 1.77651853613894 & 0.0414814638610619 \tabularnewline
58 & 1.81 & 1.71298663114982 & 0.0970133688501764 \tabularnewline
59 & 1.764 & 1.69282779873243 & 0.0711722012675657 \tabularnewline
60 & 1.73 & 1.69465793683832 & 0.0353420631616832 \tabularnewline
61 & 1.742 & 1.76756422203287 & -0.0255642220328745 \tabularnewline
62 & 1.785 & 1.8049822060845 & -0.0199822060844996 \tabularnewline
63 & 1.769 & 1.82301505355714 & -0.0540150535571391 \tabularnewline
64 & 1.743 & 1.81106927973262 & -0.0680692797326212 \tabularnewline
65 & 1.721 & 1.7827491085836 & -0.0617491085835964 \tabularnewline
66 & 1.73 & 1.76582013816826 & -0.0358201381682564 \tabularnewline
67 & 1.753 & 1.7967267613665 & -0.0437267613664982 \tabularnewline
68 & 1.764 & 1.74674814567696 & 0.0172518543230382 \tabularnewline
69 & 1.758 & 1.75788573072363 & 0.00011426927636693 \tabularnewline
70 & 1.7 & 1.65708265461124 & 0.0429173453887606 \tabularnewline
71 & 1.678 & 1.58091847535426 & 0.0970815246457426 \tabularnewline
72 & 1.688 & 1.60145602202114 & 0.0865439779788584 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260836&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]1.231[/C][C]1.33306223290598[/C][C]-0.102062232905983[/C][/ROW]
[ROW][C]14[/C][C]1.276[/C][C]1.28263489297637[/C][C]-0.00663489297636621[/C][/ROW]
[ROW][C]15[/C][C]1.281[/C][C]1.27811378368379[/C][C]0.002886216316214[/C][/ROW]
[ROW][C]16[/C][C]1.312[/C][C]1.30397437798644[/C][C]0.00802562201355772[/C][/ROW]
[ROW][C]17[/C][C]1.363[/C][C]1.34205491430748[/C][C]0.0209450856925246[/C][/ROW]
[ROW][C]18[/C][C]1.419[/C][C]1.38804585129282[/C][C]0.0309541487071838[/C][/ROW]
[ROW][C]19[/C][C]1.374[/C][C]1.47483035853089[/C][C]-0.100830358530891[/C][/ROW]
[ROW][C]20[/C][C]1.422[/C][C]1.32669627828479[/C][C]0.0953037217152068[/C][/ROW]
[ROW][C]21[/C][C]1.378[/C][C]1.4047382583104[/C][C]-0.0267382583103994[/C][/ROW]
[ROW][C]22[/C][C]1.38[/C][C]1.24243104682629[/C][C]0.13756895317371[/C][/ROW]
[ROW][C]23[/C][C]1.409[/C][C]1.23975701946801[/C][C]0.169242980531989[/C][/ROW]
[ROW][C]24[/C][C]1.398[/C][C]1.33028662245521[/C][C]0.0677133775447851[/C][/ROW]
[ROW][C]25[/C][C]1.445[/C][C]1.44018079679025[/C][C]0.00481920320974716[/C][/ROW]
[ROW][C]26[/C][C]1.452[/C][C]1.50662029899895[/C][C]-0.0546202989989466[/C][/ROW]
[ROW][C]27[/C][C]1.506[/C][C]1.46740506390953[/C][C]0.038594936090466[/C][/ROW]
[ROW][C]28[/C][C]1.531[/C][C]1.53736177076355[/C][C]-0.00636177076354838[/C][/ROW]
[ROW][C]29[/C][C]1.524[/C][C]1.57290665418382[/C][C]-0.0489066541838157[/C][/ROW]
[ROW][C]30[/C][C]1.52[/C][C]1.56252995714338[/C][C]-0.042529957143377[/C][/ROW]
[ROW][C]31[/C][C]1.499[/C][C]1.57817072867659[/C][C]-0.0791707286765895[/C][/ROW]
[ROW][C]32[/C][C]1.491[/C][C]1.47008943422286[/C][C]0.0209105657771396[/C][/ROW]
[ROW][C]33[/C][C]1.496[/C][C]1.47538140943543[/C][C]0.0206185905645742[/C][/ROW]
[ROW][C]34[/C][C]1.493[/C][C]1.37427930710645[/C][C]0.118720692893555[/C][/ROW]
[ROW][C]35[/C][C]1.507[/C][C]1.36168663542899[/C][C]0.145313364571009[/C][/ROW]
[ROW][C]36[/C][C]1.569[/C][C]1.428060564381[/C][C]0.140939435619001[/C][/ROW]
[ROW][C]37[/C][C]1.593[/C][C]1.60901564259298[/C][C]-0.0160156425929787[/C][/ROW]
[ROW][C]38[/C][C]1.597[/C][C]1.65838300798519[/C][C]-0.0613830079851867[/C][/ROW]
[ROW][C]39[/C][C]1.633[/C][C]1.62520091865085[/C][C]0.0077990813491482[/C][/ROW]
[ROW][C]40[/C][C]1.686[/C][C]1.66874862612815[/C][C]0.0172513738718465[/C][/ROW]
[ROW][C]41[/C][C]1.683[/C][C]1.72946588461063[/C][C]-0.0464658846106343[/C][/ROW]
[ROW][C]42[/C][C]1.646[/C][C]1.72781428494153[/C][C]-0.0818142849415342[/C][/ROW]
[ROW][C]43[/C][C]1.658[/C][C]1.70932219484573[/C][C]-0.0513221948457294[/C][/ROW]
[ROW][C]44[/C][C]1.636[/C][C]1.6396095662143[/C][C]-0.00360956621430164[/C][/ROW]
[ROW][C]45[/C][C]1.67[/C][C]1.62705658568884[/C][C]0.0429434143111629[/C][/ROW]
[ROW][C]46[/C][C]1.634[/C][C]1.55897658322988[/C][C]0.0750234167701158[/C][/ROW]
[ROW][C]47[/C][C]1.618[/C][C]1.51185455019924[/C][C]0.106145449800762[/C][/ROW]
[ROW][C]48[/C][C]1.622[/C][C]1.54482476578367[/C][C]0.0771752342163325[/C][/ROW]
[ROW][C]49[/C][C]1.688[/C][C]1.65757169992125[/C][C]0.0304283000787546[/C][/ROW]
[ROW][C]50[/C][C]1.723[/C][C]1.75026853032143[/C][C]-0.0272685303214293[/C][/ROW]
[ROW][C]51[/C][C]1.776[/C][C]1.75743088328611[/C][C]0.0185691167138922[/C][/ROW]
[ROW][C]52[/C][C]1.809[/C][C]1.81584661177675[/C][C]-0.00684661177674584[/C][/ROW]
[ROW][C]53[/C][C]1.754[/C][C]1.8533752534367[/C][C]-0.0993752534367023[/C][/ROW]
[ROW][C]54[/C][C]1.714[/C][C]1.80211510937638[/C][C]-0.0881151093763755[/C][/ROW]
[ROW][C]55[/C][C]1.733[/C][C]1.78173369581549[/C][C]-0.0487336958154887[/C][/ROW]
[ROW][C]56[/C][C]1.783[/C][C]1.71964393499257[/C][C]0.0633560650074334[/C][/ROW]
[ROW][C]57[/C][C]1.818[/C][C]1.77651853613894[/C][C]0.0414814638610619[/C][/ROW]
[ROW][C]58[/C][C]1.81[/C][C]1.71298663114982[/C][C]0.0970133688501764[/C][/ROW]
[ROW][C]59[/C][C]1.764[/C][C]1.69282779873243[/C][C]0.0711722012675657[/C][/ROW]
[ROW][C]60[/C][C]1.73[/C][C]1.69465793683832[/C][C]0.0353420631616832[/C][/ROW]
[ROW][C]61[/C][C]1.742[/C][C]1.76756422203287[/C][C]-0.0255642220328745[/C][/ROW]
[ROW][C]62[/C][C]1.785[/C][C]1.8049822060845[/C][C]-0.0199822060844996[/C][/ROW]
[ROW][C]63[/C][C]1.769[/C][C]1.82301505355714[/C][C]-0.0540150535571391[/C][/ROW]
[ROW][C]64[/C][C]1.743[/C][C]1.81106927973262[/C][C]-0.0680692797326212[/C][/ROW]
[ROW][C]65[/C][C]1.721[/C][C]1.7827491085836[/C][C]-0.0617491085835964[/C][/ROW]
[ROW][C]66[/C][C]1.73[/C][C]1.76582013816826[/C][C]-0.0358201381682564[/C][/ROW]
[ROW][C]67[/C][C]1.753[/C][C]1.7967267613665[/C][C]-0.0437267613664982[/C][/ROW]
[ROW][C]68[/C][C]1.764[/C][C]1.74674814567696[/C][C]0.0172518543230382[/C][/ROW]
[ROW][C]69[/C][C]1.758[/C][C]1.75788573072363[/C][C]0.00011426927636693[/C][/ROW]
[ROW][C]70[/C][C]1.7[/C][C]1.65708265461124[/C][C]0.0429173453887606[/C][/ROW]
[ROW][C]71[/C][C]1.678[/C][C]1.58091847535426[/C][C]0.0970815246457426[/C][/ROW]
[ROW][C]72[/C][C]1.688[/C][C]1.60145602202114[/C][C]0.0865439779788584[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260836&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260836&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	1.231	1.33306223290598	-0.102062232905983
14	1.276	1.28263489297637	-0.00663489297636621
15	1.281	1.27811378368379	0.002886216316214
16	1.312	1.30397437798644	0.00802562201355772
17	1.363	1.34205491430748	0.0209450856925246
18	1.419	1.38804585129282	0.0309541487071838
19	1.374	1.47483035853089	-0.100830358530891
20	1.422	1.32669627828479	0.0953037217152068
21	1.378	1.4047382583104	-0.0267382583103994
22	1.38	1.24243104682629	0.13756895317371
23	1.409	1.23975701946801	0.169242980531989
24	1.398	1.33028662245521	0.0677133775447851
25	1.445	1.44018079679025	0.00481920320974716
26	1.452	1.50662029899895	-0.0546202989989466
27	1.506	1.46740506390953	0.038594936090466
28	1.531	1.53736177076355	-0.00636177076354838
29	1.524	1.57290665418382	-0.0489066541838157
30	1.52	1.56252995714338	-0.042529957143377
31	1.499	1.57817072867659	-0.0791707286765895
32	1.491	1.47008943422286	0.0209105657771396
33	1.496	1.47538140943543	0.0206185905645742
34	1.493	1.37427930710645	0.118720692893555
35	1.507	1.36168663542899	0.145313364571009
36	1.569	1.428060564381	0.140939435619001
37	1.593	1.60901564259298	-0.0160156425929787
38	1.597	1.65838300798519	-0.0613830079851867
39	1.633	1.62520091865085	0.0077990813491482
40	1.686	1.66874862612815	0.0172513738718465
41	1.683	1.72946588461063	-0.0464658846106343
42	1.646	1.72781428494153	-0.0818142849415342
43	1.658	1.70932219484573	-0.0513221948457294
44	1.636	1.6396095662143	-0.00360956621430164
45	1.67	1.62705658568884	0.0429434143111629
46	1.634	1.55897658322988	0.0750234167701158
47	1.618	1.51185455019924	0.106145449800762
48	1.622	1.54482476578367	0.0771752342163325
49	1.688	1.65757169992125	0.0304283000787546
50	1.723	1.75026853032143	-0.0272685303214293
51	1.776	1.75743088328611	0.0185691167138922
52	1.809	1.81584661177675	-0.00684661177674584
53	1.754	1.8533752534367	-0.0993752534367023
54	1.714	1.80211510937638	-0.0881151093763755
55	1.733	1.78173369581549	-0.0487336958154887
56	1.783	1.71964393499257	0.0633560650074334
57	1.818	1.77651853613894	0.0414814638610619
58	1.81	1.71298663114982	0.0970133688501764
59	1.764	1.69282779873243	0.0711722012675657
60	1.73	1.69465793683832	0.0353420631616832
61	1.742	1.76756422203287	-0.0255642220328745
62	1.785	1.8049822060845	-0.0199822060844996
63	1.769	1.82301505355714	-0.0540150535571391
64	1.743	1.81106927973262	-0.0680692797326212
65	1.721	1.7827491085836	-0.0617491085835964
66	1.73	1.76582013816826	-0.0358201381682564
67	1.753	1.7967267613665	-0.0437267613664982
68	1.764	1.74674814567696	0.0172518543230382
69	1.758	1.75788573072363	0.00011426927636693
70	1.7	1.65708265461124	0.0429173453887606
71	1.678	1.58091847535426	0.0970815246457426
72	1.688	1.60145602202114	0.0865439779788584

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.71637819587778	1.58455544892868	1.84820094282688
74	1.77698047523592	1.594230140364	1.95973081010784
75	1.81088553215131	1.58656477883511	2.0352062854675
76	1.84934996942398	1.58825943515361	2.11044050369434
77	1.88772848894444	1.59282550641923	2.18263147146964
78	1.93454750668337	1.60783204871862	2.26126296464812
79	2.00370211148771	1.64660462444406	2.36079959853136
80	2.00509746974877	1.61867887871525	2.39151606078229
81	2.00503128863001	1.59009778641771	2.41996479084232
82	1.91300465906315	1.47017878968201	2.35583052844428
83	1.80527108017867	1.33503834040395	2.27550381995339
84	1.73678722473225	1.23952800440391	2.23404644506059

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.71637819587778 & 1.58455544892868 & 1.84820094282688 \tabularnewline
74 & 1.77698047523592 & 1.594230140364 & 1.95973081010784 \tabularnewline
75 & 1.81088553215131 & 1.58656477883511 & 2.0352062854675 \tabularnewline
76 & 1.84934996942398 & 1.58825943515361 & 2.11044050369434 \tabularnewline
77 & 1.88772848894444 & 1.59282550641923 & 2.18263147146964 \tabularnewline
78 & 1.93454750668337 & 1.60783204871862 & 2.26126296464812 \tabularnewline
79 & 2.00370211148771 & 1.64660462444406 & 2.36079959853136 \tabularnewline
80 & 2.00509746974877 & 1.61867887871525 & 2.39151606078229 \tabularnewline
81 & 2.00503128863001 & 1.59009778641771 & 2.41996479084232 \tabularnewline
82 & 1.91300465906315 & 1.47017878968201 & 2.35583052844428 \tabularnewline
83 & 1.80527108017867 & 1.33503834040395 & 2.27550381995339 \tabularnewline
84 & 1.73678722473225 & 1.23952800440391 & 2.23404644506059 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260836&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]73[/C][C]1.71637819587778[/C][C]1.58455544892868[/C][C]1.84820094282688[/C][/ROW]
[ROW][C]74[/C][C]1.77698047523592[/C][C]1.594230140364[/C][C]1.95973081010784[/C][/ROW]
[ROW][C]75[/C][C]1.81088553215131[/C][C]1.58656477883511[/C][C]2.0352062854675[/C][/ROW]
[ROW][C]76[/C][C]1.84934996942398[/C][C]1.58825943515361[/C][C]2.11044050369434[/C][/ROW]
[ROW][C]77[/C][C]1.88772848894444[/C][C]1.59282550641923[/C][C]2.18263147146964[/C][/ROW]
[ROW][C]78[/C][C]1.93454750668337[/C][C]1.60783204871862[/C][C]2.26126296464812[/C][/ROW]
[ROW][C]79[/C][C]2.00370211148771[/C][C]1.64660462444406[/C][C]2.36079959853136[/C][/ROW]
[ROW][C]80[/C][C]2.00509746974877[/C][C]1.61867887871525[/C][C]2.39151606078229[/C][/ROW]
[ROW][C]81[/C][C]2.00503128863001[/C][C]1.59009778641771[/C][C]2.41996479084232[/C][/ROW]
[ROW][C]82[/C][C]1.91300465906315[/C][C]1.47017878968201[/C][C]2.35583052844428[/C][/ROW]
[ROW][C]83[/C][C]1.80527108017867[/C][C]1.33503834040395[/C][C]2.27550381995339[/C][/ROW]
[ROW][C]84[/C][C]1.73678722473225[/C][C]1.23952800440391[/C][C]2.23404644506059[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260836&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260836&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
73	1.71637819587778	1.58455544892868	1.84820094282688
74	1.77698047523592	1.594230140364	1.95973081010784
75	1.81088553215131	1.58656477883511	2.0352062854675
76	1.84934996942398	1.58825943515361	2.11044050369434
77	1.88772848894444	1.59282550641923	2.18263147146964
78	1.93454750668337	1.60783204871862	2.26126296464812
79	2.00370211148771	1.64660462444406	2.36079959853136
80	2.00509746974877	1.61867887871525	2.39151606078229
81	2.00503128863001	1.59009778641771	2.41996479084232
82	1.91300465906315	1.47017878968201	2.35583052844428
83	1.80527108017867	1.33503834040395	2.27550381995339
84	1.73678722473225	1.23952800440391	2.23404644506059

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=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