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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 21 Dec 2012 04:35:09 -0500

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/2012/Dec/21/t1356082628hezhlsurv4f5qob.htm/, Retrieved Sat, 20 Apr 2024 02:27:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203379, Retrieved Sat, 20 Apr 2024 02:27:36 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [Exponential Smoothing] [] [2012-12-21 09:35:09] [4ee04462bf0eba90e570cdb92b0b1b71] [Current]

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Dataseries X:

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Histogram

Boxplots

0.43
0.45
0.44
0.44
0.44
0.48
0.47
0.47
0.47
0.49
0.49
0.46
0.45
0.44
0.42
0.43
0.43
0.47
0.47
0.47
0.47
0.48
0.48
0.48
0.49
0.49
0.47
0.5
0.51
0.5
0.49
0.5
0.51
0.51
0.5
0.53
0.5
0.49
0.46
0.46
0.47
0.49
0.5
0.5
0.51
0.5
0.52
0.5
0.48
0.47
0.43
0.42
0.45
0.5
0.52
0.52
0.51
0.52
0.52
0.51
0.51
0.51
0.48
0.49
0.47
0.51
0.5
0.51
0.51
0.52
0.51
0.52

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	'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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203379&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203379&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203379&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	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.743525256436444
beta	0
gamma	0.731293039629427

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.743525256436444 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.731293039629427 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203379&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]0.743525256436444[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.731293039629427[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203379&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203379&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	0.743525256436444
beta	0
gamma	0.731293039629427

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	0.45	0.455074786324786	-0.00507478632478625
14	0.44	0.440782906502641	-0.000782906502641345
15	0.42	0.419682147725851	0.000317852274148767
16	0.43	0.429816497567515	0.000183502432484717
17	0.43	0.430267621575371	-0.000267621575370525
18	0.47	0.4691333234896	0.000866676510399511
19	0.47	0.464259071345595	0.00574092865440534
20	0.47	0.46759228211023	0.00240771788976996
21	0.47	0.470113833153	-0.000113833152999787
22	0.48	0.490760547310077	-0.0107605473100766
23	0.48	0.483074493926641	-0.00307449392664072
24	0.48	0.451103215356108	0.0288967846438918
25	0.49	0.461534905454548	0.0284650945454519
26	0.49	0.472985751389072	0.0170142486109275
27	0.47	0.465324083261032	0.0046759167389675
28	0.5	0.478673565687692	0.0213264343123079
29	0.51	0.494760381538763	0.0152396184612371
30	0.5	0.545368854979175	-0.0453688549791751
31	0.49	0.50703152336108	-0.0170315233610805
32	0.5	0.492807669907283	0.00719233009271703
33	0.51	0.498413763403498	0.0115862365965022
34	0.51	0.525762896433451	-0.0157628964334511
35	0.5	0.515799052433075	-0.0157990524330747
36	0.53	0.480363218530423	0.0496367814695773
37	0.5	0.506134653071591	-0.00613465307159133
38	0.49	0.489712012794005	0.000287987205995321
39	0.46	0.467299791612783	-0.0072997916127831
40	0.46	0.474867973434887	-0.0148679734348867
41	0.47	0.462901700790999	0.00709829920900079
42	0.49	0.496089281878062	-0.0060892818780624
43	0.5	0.492272203686674	0.00772779631332604
44	0.5	0.501000911968088	-0.00100091196808794
45	0.51	0.501339236232005	0.00866076376799463
46	0.5	0.521383652306262	-0.0213836523062618
47	0.52	0.507233853000166	0.0127661469998338
48	0.5	0.505309993213614	-0.0053099932136137
49	0.48	0.47976672343367	0.000233276566329987
50	0.47	0.469283418489458	0.000716581510541714
51	0.43	0.445766717900573	-0.0157667179005734
52	0.42	0.445620051662781	-0.025620051662781
53	0.45	0.429779291741038	0.0202207082589616
54	0.5	0.470250276479454	0.0297497235205462
55	0.52	0.495671910210601	0.0243280897893986
56	0.52	0.515106215187458	0.00489378481254177
57	0.51	0.521639521846696	-0.0116395218466958
58	0.52	0.520955086410585	-0.000955086410585282
59	0.52	0.528399516511634	-0.0083995165116344
60	0.51	0.507348123107526	0.00265187689247448
61	0.51	0.488764390513189	0.0212356094868111
62	0.51	0.49398749834232	0.01601250165768
63	0.48	0.478752122821226	0.00124787717877356
64	0.49	0.48940816425968	0.000591835740320235
65	0.47	0.501654414820596	-0.0316544148205956
66	0.51	0.505342180269379	0.00465781973062096
67	0.5	0.511090477965116	-0.0110904779651155
68	0.51	0.500545120110863	0.00945487988913685
69	0.51	0.507368759005331	0.00263124099466938
70	0.52	0.519298949593338	0.000701050406662462
71	0.51	0.526578495374992	-0.0165784953749918
72	0.52	0.501518604011113	0.0184813959888869

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.45 & 0.455074786324786 & -0.00507478632478625 \tabularnewline
14 & 0.44 & 0.440782906502641 & -0.000782906502641345 \tabularnewline
15 & 0.42 & 0.419682147725851 & 0.000317852274148767 \tabularnewline
16 & 0.43 & 0.429816497567515 & 0.000183502432484717 \tabularnewline
17 & 0.43 & 0.430267621575371 & -0.000267621575370525 \tabularnewline
18 & 0.47 & 0.4691333234896 & 0.000866676510399511 \tabularnewline
19 & 0.47 & 0.464259071345595 & 0.00574092865440534 \tabularnewline
20 & 0.47 & 0.46759228211023 & 0.00240771788976996 \tabularnewline
21 & 0.47 & 0.470113833153 & -0.000113833152999787 \tabularnewline
22 & 0.48 & 0.490760547310077 & -0.0107605473100766 \tabularnewline
23 & 0.48 & 0.483074493926641 & -0.00307449392664072 \tabularnewline
24 & 0.48 & 0.451103215356108 & 0.0288967846438918 \tabularnewline
25 & 0.49 & 0.461534905454548 & 0.0284650945454519 \tabularnewline
26 & 0.49 & 0.472985751389072 & 0.0170142486109275 \tabularnewline
27 & 0.47 & 0.465324083261032 & 0.0046759167389675 \tabularnewline
28 & 0.5 & 0.478673565687692 & 0.0213264343123079 \tabularnewline
29 & 0.51 & 0.494760381538763 & 0.0152396184612371 \tabularnewline
30 & 0.5 & 0.545368854979175 & -0.0453688549791751 \tabularnewline
31 & 0.49 & 0.50703152336108 & -0.0170315233610805 \tabularnewline
32 & 0.5 & 0.492807669907283 & 0.00719233009271703 \tabularnewline
33 & 0.51 & 0.498413763403498 & 0.0115862365965022 \tabularnewline
34 & 0.51 & 0.525762896433451 & -0.0157628964334511 \tabularnewline
35 & 0.5 & 0.515799052433075 & -0.0157990524330747 \tabularnewline
36 & 0.53 & 0.480363218530423 & 0.0496367814695773 \tabularnewline
37 & 0.5 & 0.506134653071591 & -0.00613465307159133 \tabularnewline
38 & 0.49 & 0.489712012794005 & 0.000287987205995321 \tabularnewline
39 & 0.46 & 0.467299791612783 & -0.0072997916127831 \tabularnewline
40 & 0.46 & 0.474867973434887 & -0.0148679734348867 \tabularnewline
41 & 0.47 & 0.462901700790999 & 0.00709829920900079 \tabularnewline
42 & 0.49 & 0.496089281878062 & -0.0060892818780624 \tabularnewline
43 & 0.5 & 0.492272203686674 & 0.00772779631332604 \tabularnewline
44 & 0.5 & 0.501000911968088 & -0.00100091196808794 \tabularnewline
45 & 0.51 & 0.501339236232005 & 0.00866076376799463 \tabularnewline
46 & 0.5 & 0.521383652306262 & -0.0213836523062618 \tabularnewline
47 & 0.52 & 0.507233853000166 & 0.0127661469998338 \tabularnewline
48 & 0.5 & 0.505309993213614 & -0.0053099932136137 \tabularnewline
49 & 0.48 & 0.47976672343367 & 0.000233276566329987 \tabularnewline
50 & 0.47 & 0.469283418489458 & 0.000716581510541714 \tabularnewline
51 & 0.43 & 0.445766717900573 & -0.0157667179005734 \tabularnewline
52 & 0.42 & 0.445620051662781 & -0.025620051662781 \tabularnewline
53 & 0.45 & 0.429779291741038 & 0.0202207082589616 \tabularnewline
54 & 0.5 & 0.470250276479454 & 0.0297497235205462 \tabularnewline
55 & 0.52 & 0.495671910210601 & 0.0243280897893986 \tabularnewline
56 & 0.52 & 0.515106215187458 & 0.00489378481254177 \tabularnewline
57 & 0.51 & 0.521639521846696 & -0.0116395218466958 \tabularnewline
58 & 0.52 & 0.520955086410585 & -0.000955086410585282 \tabularnewline
59 & 0.52 & 0.528399516511634 & -0.0083995165116344 \tabularnewline
60 & 0.51 & 0.507348123107526 & 0.00265187689247448 \tabularnewline
61 & 0.51 & 0.488764390513189 & 0.0212356094868111 \tabularnewline
62 & 0.51 & 0.49398749834232 & 0.01601250165768 \tabularnewline
63 & 0.48 & 0.478752122821226 & 0.00124787717877356 \tabularnewline
64 & 0.49 & 0.48940816425968 & 0.000591835740320235 \tabularnewline
65 & 0.47 & 0.501654414820596 & -0.0316544148205956 \tabularnewline
66 & 0.51 & 0.505342180269379 & 0.00465781973062096 \tabularnewline
67 & 0.5 & 0.511090477965116 & -0.0110904779651155 \tabularnewline
68 & 0.51 & 0.500545120110863 & 0.00945487988913685 \tabularnewline
69 & 0.51 & 0.507368759005331 & 0.00263124099466938 \tabularnewline
70 & 0.52 & 0.519298949593338 & 0.000701050406662462 \tabularnewline
71 & 0.51 & 0.526578495374992 & -0.0165784953749918 \tabularnewline
72 & 0.52 & 0.501518604011113 & 0.0184813959888869 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203379&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]0.45[/C][C]0.455074786324786[/C][C]-0.00507478632478625[/C][/ROW]
[ROW][C]14[/C][C]0.44[/C][C]0.440782906502641[/C][C]-0.000782906502641345[/C][/ROW]
[ROW][C]15[/C][C]0.42[/C][C]0.419682147725851[/C][C]0.000317852274148767[/C][/ROW]
[ROW][C]16[/C][C]0.43[/C][C]0.429816497567515[/C][C]0.000183502432484717[/C][/ROW]
[ROW][C]17[/C][C]0.43[/C][C]0.430267621575371[/C][C]-0.000267621575370525[/C][/ROW]
[ROW][C]18[/C][C]0.47[/C][C]0.4691333234896[/C][C]0.000866676510399511[/C][/ROW]
[ROW][C]19[/C][C]0.47[/C][C]0.464259071345595[/C][C]0.00574092865440534[/C][/ROW]
[ROW][C]20[/C][C]0.47[/C][C]0.46759228211023[/C][C]0.00240771788976996[/C][/ROW]
[ROW][C]21[/C][C]0.47[/C][C]0.470113833153[/C][C]-0.000113833152999787[/C][/ROW]
[ROW][C]22[/C][C]0.48[/C][C]0.490760547310077[/C][C]-0.0107605473100766[/C][/ROW]
[ROW][C]23[/C][C]0.48[/C][C]0.483074493926641[/C][C]-0.00307449392664072[/C][/ROW]
[ROW][C]24[/C][C]0.48[/C][C]0.451103215356108[/C][C]0.0288967846438918[/C][/ROW]
[ROW][C]25[/C][C]0.49[/C][C]0.461534905454548[/C][C]0.0284650945454519[/C][/ROW]
[ROW][C]26[/C][C]0.49[/C][C]0.472985751389072[/C][C]0.0170142486109275[/C][/ROW]
[ROW][C]27[/C][C]0.47[/C][C]0.465324083261032[/C][C]0.0046759167389675[/C][/ROW]
[ROW][C]28[/C][C]0.5[/C][C]0.478673565687692[/C][C]0.0213264343123079[/C][/ROW]
[ROW][C]29[/C][C]0.51[/C][C]0.494760381538763[/C][C]0.0152396184612371[/C][/ROW]
[ROW][C]30[/C][C]0.5[/C][C]0.545368854979175[/C][C]-0.0453688549791751[/C][/ROW]
[ROW][C]31[/C][C]0.49[/C][C]0.50703152336108[/C][C]-0.0170315233610805[/C][/ROW]
[ROW][C]32[/C][C]0.5[/C][C]0.492807669907283[/C][C]0.00719233009271703[/C][/ROW]
[ROW][C]33[/C][C]0.51[/C][C]0.498413763403498[/C][C]0.0115862365965022[/C][/ROW]
[ROW][C]34[/C][C]0.51[/C][C]0.525762896433451[/C][C]-0.0157628964334511[/C][/ROW]
[ROW][C]35[/C][C]0.5[/C][C]0.515799052433075[/C][C]-0.0157990524330747[/C][/ROW]
[ROW][C]36[/C][C]0.53[/C][C]0.480363218530423[/C][C]0.0496367814695773[/C][/ROW]
[ROW][C]37[/C][C]0.5[/C][C]0.506134653071591[/C][C]-0.00613465307159133[/C][/ROW]
[ROW][C]38[/C][C]0.49[/C][C]0.489712012794005[/C][C]0.000287987205995321[/C][/ROW]
[ROW][C]39[/C][C]0.46[/C][C]0.467299791612783[/C][C]-0.0072997916127831[/C][/ROW]
[ROW][C]40[/C][C]0.46[/C][C]0.474867973434887[/C][C]-0.0148679734348867[/C][/ROW]
[ROW][C]41[/C][C]0.47[/C][C]0.462901700790999[/C][C]0.00709829920900079[/C][/ROW]
[ROW][C]42[/C][C]0.49[/C][C]0.496089281878062[/C][C]-0.0060892818780624[/C][/ROW]
[ROW][C]43[/C][C]0.5[/C][C]0.492272203686674[/C][C]0.00772779631332604[/C][/ROW]
[ROW][C]44[/C][C]0.5[/C][C]0.501000911968088[/C][C]-0.00100091196808794[/C][/ROW]
[ROW][C]45[/C][C]0.51[/C][C]0.501339236232005[/C][C]0.00866076376799463[/C][/ROW]
[ROW][C]46[/C][C]0.5[/C][C]0.521383652306262[/C][C]-0.0213836523062618[/C][/ROW]
[ROW][C]47[/C][C]0.52[/C][C]0.507233853000166[/C][C]0.0127661469998338[/C][/ROW]
[ROW][C]48[/C][C]0.5[/C][C]0.505309993213614[/C][C]-0.0053099932136137[/C][/ROW]
[ROW][C]49[/C][C]0.48[/C][C]0.47976672343367[/C][C]0.000233276566329987[/C][/ROW]
[ROW][C]50[/C][C]0.47[/C][C]0.469283418489458[/C][C]0.000716581510541714[/C][/ROW]
[ROW][C]51[/C][C]0.43[/C][C]0.445766717900573[/C][C]-0.0157667179005734[/C][/ROW]
[ROW][C]52[/C][C]0.42[/C][C]0.445620051662781[/C][C]-0.025620051662781[/C][/ROW]
[ROW][C]53[/C][C]0.45[/C][C]0.429779291741038[/C][C]0.0202207082589616[/C][/ROW]
[ROW][C]54[/C][C]0.5[/C][C]0.470250276479454[/C][C]0.0297497235205462[/C][/ROW]
[ROW][C]55[/C][C]0.52[/C][C]0.495671910210601[/C][C]0.0243280897893986[/C][/ROW]
[ROW][C]56[/C][C]0.52[/C][C]0.515106215187458[/C][C]0.00489378481254177[/C][/ROW]
[ROW][C]57[/C][C]0.51[/C][C]0.521639521846696[/C][C]-0.0116395218466958[/C][/ROW]
[ROW][C]58[/C][C]0.52[/C][C]0.520955086410585[/C][C]-0.000955086410585282[/C][/ROW]
[ROW][C]59[/C][C]0.52[/C][C]0.528399516511634[/C][C]-0.0083995165116344[/C][/ROW]
[ROW][C]60[/C][C]0.51[/C][C]0.507348123107526[/C][C]0.00265187689247448[/C][/ROW]
[ROW][C]61[/C][C]0.51[/C][C]0.488764390513189[/C][C]0.0212356094868111[/C][/ROW]
[ROW][C]62[/C][C]0.51[/C][C]0.49398749834232[/C][C]0.01601250165768[/C][/ROW]
[ROW][C]63[/C][C]0.48[/C][C]0.478752122821226[/C][C]0.00124787717877356[/C][/ROW]
[ROW][C]64[/C][C]0.49[/C][C]0.48940816425968[/C][C]0.000591835740320235[/C][/ROW]
[ROW][C]65[/C][C]0.47[/C][C]0.501654414820596[/C][C]-0.0316544148205956[/C][/ROW]
[ROW][C]66[/C][C]0.51[/C][C]0.505342180269379[/C][C]0.00465781973062096[/C][/ROW]
[ROW][C]67[/C][C]0.5[/C][C]0.511090477965116[/C][C]-0.0110904779651155[/C][/ROW]
[ROW][C]68[/C][C]0.51[/C][C]0.500545120110863[/C][C]0.00945487988913685[/C][/ROW]
[ROW][C]69[/C][C]0.51[/C][C]0.507368759005331[/C][C]0.00263124099466938[/C][/ROW]
[ROW][C]70[/C][C]0.52[/C][C]0.519298949593338[/C][C]0.000701050406662462[/C][/ROW]
[ROW][C]71[/C][C]0.51[/C][C]0.526578495374992[/C][C]-0.0165784953749918[/C][/ROW]
[ROW][C]72[/C][C]0.52[/C][C]0.501518604011113[/C][C]0.0184813959888869[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203379&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203379&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	0.45	0.455074786324786	-0.00507478632478625
14	0.44	0.440782906502641	-0.000782906502641345
15	0.42	0.419682147725851	0.000317852274148767
16	0.43	0.429816497567515	0.000183502432484717
17	0.43	0.430267621575371	-0.000267621575370525
18	0.47	0.4691333234896	0.000866676510399511
19	0.47	0.464259071345595	0.00574092865440534
20	0.47	0.46759228211023	0.00240771788976996
21	0.47	0.470113833153	-0.000113833152999787
22	0.48	0.490760547310077	-0.0107605473100766
23	0.48	0.483074493926641	-0.00307449392664072
24	0.48	0.451103215356108	0.0288967846438918
25	0.49	0.461534905454548	0.0284650945454519
26	0.49	0.472985751389072	0.0170142486109275
27	0.47	0.465324083261032	0.0046759167389675
28	0.5	0.478673565687692	0.0213264343123079
29	0.51	0.494760381538763	0.0152396184612371
30	0.5	0.545368854979175	-0.0453688549791751
31	0.49	0.50703152336108	-0.0170315233610805
32	0.5	0.492807669907283	0.00719233009271703
33	0.51	0.498413763403498	0.0115862365965022
34	0.51	0.525762896433451	-0.0157628964334511
35	0.5	0.515799052433075	-0.0157990524330747
36	0.53	0.480363218530423	0.0496367814695773
37	0.5	0.506134653071591	-0.00613465307159133
38	0.49	0.489712012794005	0.000287987205995321
39	0.46	0.467299791612783	-0.0072997916127831
40	0.46	0.474867973434887	-0.0148679734348867
41	0.47	0.462901700790999	0.00709829920900079
42	0.49	0.496089281878062	-0.0060892818780624
43	0.5	0.492272203686674	0.00772779631332604
44	0.5	0.501000911968088	-0.00100091196808794
45	0.51	0.501339236232005	0.00866076376799463
46	0.5	0.521383652306262	-0.0213836523062618
47	0.52	0.507233853000166	0.0127661469998338
48	0.5	0.505309993213614	-0.0053099932136137
49	0.48	0.47976672343367	0.000233276566329987
50	0.47	0.469283418489458	0.000716581510541714
51	0.43	0.445766717900573	-0.0157667179005734
52	0.42	0.445620051662781	-0.025620051662781
53	0.45	0.429779291741038	0.0202207082589616
54	0.5	0.470250276479454	0.0297497235205462
55	0.52	0.495671910210601	0.0243280897893986
56	0.52	0.515106215187458	0.00489378481254177
57	0.51	0.521639521846696	-0.0116395218466958
58	0.52	0.520955086410585	-0.000955086410585282
59	0.52	0.528399516511634	-0.0083995165116344
60	0.51	0.507348123107526	0.00265187689247448
61	0.51	0.488764390513189	0.0212356094868111
62	0.51	0.49398749834232	0.01601250165768
63	0.48	0.478752122821226	0.00124787717877356
64	0.49	0.48940816425968	0.000591835740320235
65	0.47	0.501654414820596	-0.0316544148205956
66	0.51	0.505342180269379	0.00465781973062096
67	0.5	0.511090477965116	-0.0110904779651155
68	0.51	0.500545120110863	0.00945487988913685
69	0.51	0.507368759005331	0.00263124099466938
70	0.52	0.519298949593338	0.000701050406662462
71	0.51	0.526578495374992	-0.0165784953749918
72	0.52	0.501518604011113	0.0184813959888869

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.498190050000405	0.466961508457288	0.529418591543522
74	0.486644309164547	0.447729614123131	0.525559004205963
75	0.456734007927945	0.411418611279315	0.502049404576575
76	0.466339175219133	0.415421429229362	0.517256921208905
77	0.472097332414903	0.416135304753862	0.528059360075944
78	0.506131611922414	0.445543822532213	0.566719401312615
79	0.505462980721382	0.440578376180339	0.570347585262426
80	0.507017123570989	0.438103093143914	0.575931153998064
81	0.505530991078237	0.432810462525702	0.578251519630772
82	0.515142764468613	0.43880530999038	0.591480218946846
83	0.518660141152956	0.438869548728331	0.59845073357758
84	0.512502549748499	0.429402186796652	0.595602912700346

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.498190050000405 & 0.466961508457288 & 0.529418591543522 \tabularnewline
74 & 0.486644309164547 & 0.447729614123131 & 0.525559004205963 \tabularnewline
75 & 0.456734007927945 & 0.411418611279315 & 0.502049404576575 \tabularnewline
76 & 0.466339175219133 & 0.415421429229362 & 0.517256921208905 \tabularnewline
77 & 0.472097332414903 & 0.416135304753862 & 0.528059360075944 \tabularnewline
78 & 0.506131611922414 & 0.445543822532213 & 0.566719401312615 \tabularnewline
79 & 0.505462980721382 & 0.440578376180339 & 0.570347585262426 \tabularnewline
80 & 0.507017123570989 & 0.438103093143914 & 0.575931153998064 \tabularnewline
81 & 0.505530991078237 & 0.432810462525702 & 0.578251519630772 \tabularnewline
82 & 0.515142764468613 & 0.43880530999038 & 0.591480218946846 \tabularnewline
83 & 0.518660141152956 & 0.438869548728331 & 0.59845073357758 \tabularnewline
84 & 0.512502549748499 & 0.429402186796652 & 0.595602912700346 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203379&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]0.498190050000405[/C][C]0.466961508457288[/C][C]0.529418591543522[/C][/ROW]
[ROW][C]74[/C][C]0.486644309164547[/C][C]0.447729614123131[/C][C]0.525559004205963[/C][/ROW]
[ROW][C]75[/C][C]0.456734007927945[/C][C]0.411418611279315[/C][C]0.502049404576575[/C][/ROW]
[ROW][C]76[/C][C]0.466339175219133[/C][C]0.415421429229362[/C][C]0.517256921208905[/C][/ROW]
[ROW][C]77[/C][C]0.472097332414903[/C][C]0.416135304753862[/C][C]0.528059360075944[/C][/ROW]
[ROW][C]78[/C][C]0.506131611922414[/C][C]0.445543822532213[/C][C]0.566719401312615[/C][/ROW]
[ROW][C]79[/C][C]0.505462980721382[/C][C]0.440578376180339[/C][C]0.570347585262426[/C][/ROW]
[ROW][C]80[/C][C]0.507017123570989[/C][C]0.438103093143914[/C][C]0.575931153998064[/C][/ROW]
[ROW][C]81[/C][C]0.505530991078237[/C][C]0.432810462525702[/C][C]0.578251519630772[/C][/ROW]
[ROW][C]82[/C][C]0.515142764468613[/C][C]0.43880530999038[/C][C]0.591480218946846[/C][/ROW]
[ROW][C]83[/C][C]0.518660141152956[/C][C]0.438869548728331[/C][C]0.59845073357758[/C][/ROW]
[ROW][C]84[/C][C]0.512502549748499[/C][C]0.429402186796652[/C][C]0.595602912700346[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203379&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203379&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	0.498190050000405	0.466961508457288	0.529418591543522
74	0.486644309164547	0.447729614123131	0.525559004205963
75	0.456734007927945	0.411418611279315	0.502049404576575
76	0.466339175219133	0.415421429229362	0.517256921208905
77	0.472097332414903	0.416135304753862	0.528059360075944
78	0.506131611922414	0.445543822532213	0.566719401312615
79	0.505462980721382	0.440578376180339	0.570347585262426
80	0.507017123570989	0.438103093143914	0.575931153998064
81	0.505530991078237	0.432810462525702	0.578251519630772
82	0.515142764468613	0.43880530999038	0.591480218946846
83	0.518660141152956	0.438869548728331	0.59845073357758
84	0.512502549748499	0.429402186796652	0.595602912700346

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