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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 19 May 2017 08:16:37 +0100

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/2017/May/19/t1495178601bf60lan3biucrp3.htm/, Retrieved Wed, 15 May 2024 22:04:49 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 22:04:49 +0200

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Estimated Impact

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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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.315777930136277
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.315777930136277 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.315777930136277[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	1
beta	0.315777930136277
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	98.36	98.76	-0.400000000000006
4	98.51	98.6336888279455	-0.123688827945486
5	98.77	98.7446306258759	0.0253693741241108
6	98.78	99.0126417143256	-0.232641714325638
7	98.89	98.9491785953125	-0.0591785953125452
8	98.87	99.0404913009764	-0.170491300976366
9	99.05	98.9666539108478	0.0833460891521725
10	99.09	99.1729727663652	-0.0829727663652307
11	99.1	99.1867717979448	-0.0867717979447633
12	99.12	99.1693711791955	-0.049371179195532
13	99.37	99.1737808504208	0.196219149579207
14	99.46	99.485742527328	-0.0257425273280205
15	99.6	99.5676136053319	0.0323863946681087
16	99.87	99.7178405140048	0.152159485995242
17	99.88	100.035889121543	-0.155889121542955
18	100.01	99.9966627774113	0.0133372225886603
19	100.02	100.130874377954	-0.110874377954175
20	100.19	100.105862696379	0.0841373036213611
21	100.2	100.302431399963	-0.102431399963436
22	100.35	100.280085824502	0.0699141754979564
23	100.47	100.452163178128	0.0178368218720379
24	100.57	100.577795652819	-0.00779565281892758
25	101.41	100.675333957708	0.734666042292304
26	101.67	101.747325279884	-0.0773252798841639
27	101.82	101.982907663055	-0.162907663055151
28	101.86	102.081465018412	-0.221465018412246
29	101.98	102.0515312533	-0.0715312533004351
30	102.06	102.148943262193	-0.0889432621931689
31	102.17	102.200856942958	-0.0308569429582519
32	102.2	102.301113001381	-0.101113001380554
33	102.35	102.299183747095	0.0508162529052498
34	102.47	102.465230398254	0.00476960174556496
35	102.55	102.586736533221	-0.0367365332212302
36	102.62	102.6551359468	-0.0351359468002386
37	102.81	102.714040790246	0.0959592097537154
38	102.88	102.93434259088	-0.0543425908798412
39	102.94	102.987182400014	-0.0471824000135541
40	102.95	103.032283239398	-0.0822832393984072
41	102.94	103.016300008376	-0.076300008376279
42	103.05	102.982206149662	0.0677938503381625
43	103.09	103.113613951398	-0.0236139513975786
44	103.1	103.146157186703	-0.0461571867029278
45	103.14	103.141581765825	-0.00158176582495173
46	103.19	103.181082279087	0.0089177209132032
47	103.36	103.233898298538	0.126101701461707
48	103.43	103.443718432813	-0.0137184328125244
49	103.62	103.509386454494	0.110613545505714
50	103.79	103.734315770939	0.055684229060887
51	103.9	103.921899621533	-0.0218996215331941
52	103.92	104.024984204375	-0.104984204374674
53	103.94	104.01183250962	-0.0718325096202364
54	103.98	104.009149388416	-0.0291493884158598
55	104.04	104.039944654877	5.53451228313406e-05
56	104.09	104.099962131645	-0.00996213164549431
57	104.16	104.146816310335	0.0131836896652544
58	104.22	104.220979428569	-0.000979428568783192
59	104.28	104.280670146643	-0.000670146642619329
60	104.32	104.340458529123	-0.0204585291229336

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 98.36 & 98.76 & -0.400000000000006 \tabularnewline
4 & 98.51 & 98.6336888279455 & -0.123688827945486 \tabularnewline
5 & 98.77 & 98.7446306258759 & 0.0253693741241108 \tabularnewline
6 & 98.78 & 99.0126417143256 & -0.232641714325638 \tabularnewline
7 & 98.89 & 98.9491785953125 & -0.0591785953125452 \tabularnewline
8 & 98.87 & 99.0404913009764 & -0.170491300976366 \tabularnewline
9 & 99.05 & 98.9666539108478 & 0.0833460891521725 \tabularnewline
10 & 99.09 & 99.1729727663652 & -0.0829727663652307 \tabularnewline
11 & 99.1 & 99.1867717979448 & -0.0867717979447633 \tabularnewline
12 & 99.12 & 99.1693711791955 & -0.049371179195532 \tabularnewline
13 & 99.37 & 99.1737808504208 & 0.196219149579207 \tabularnewline
14 & 99.46 & 99.485742527328 & -0.0257425273280205 \tabularnewline
15 & 99.6 & 99.5676136053319 & 0.0323863946681087 \tabularnewline
16 & 99.87 & 99.7178405140048 & 0.152159485995242 \tabularnewline
17 & 99.88 & 100.035889121543 & -0.155889121542955 \tabularnewline
18 & 100.01 & 99.9966627774113 & 0.0133372225886603 \tabularnewline
19 & 100.02 & 100.130874377954 & -0.110874377954175 \tabularnewline
20 & 100.19 & 100.105862696379 & 0.0841373036213611 \tabularnewline
21 & 100.2 & 100.302431399963 & -0.102431399963436 \tabularnewline
22 & 100.35 & 100.280085824502 & 0.0699141754979564 \tabularnewline
23 & 100.47 & 100.452163178128 & 0.0178368218720379 \tabularnewline
24 & 100.57 & 100.577795652819 & -0.00779565281892758 \tabularnewline
25 & 101.41 & 100.675333957708 & 0.734666042292304 \tabularnewline
26 & 101.67 & 101.747325279884 & -0.0773252798841639 \tabularnewline
27 & 101.82 & 101.982907663055 & -0.162907663055151 \tabularnewline
28 & 101.86 & 102.081465018412 & -0.221465018412246 \tabularnewline
29 & 101.98 & 102.0515312533 & -0.0715312533004351 \tabularnewline
30 & 102.06 & 102.148943262193 & -0.0889432621931689 \tabularnewline
31 & 102.17 & 102.200856942958 & -0.0308569429582519 \tabularnewline
32 & 102.2 & 102.301113001381 & -0.101113001380554 \tabularnewline
33 & 102.35 & 102.299183747095 & 0.0508162529052498 \tabularnewline
34 & 102.47 & 102.465230398254 & 0.00476960174556496 \tabularnewline
35 & 102.55 & 102.586736533221 & -0.0367365332212302 \tabularnewline
36 & 102.62 & 102.6551359468 & -0.0351359468002386 \tabularnewline
37 & 102.81 & 102.714040790246 & 0.0959592097537154 \tabularnewline
38 & 102.88 & 102.93434259088 & -0.0543425908798412 \tabularnewline
39 & 102.94 & 102.987182400014 & -0.0471824000135541 \tabularnewline
40 & 102.95 & 103.032283239398 & -0.0822832393984072 \tabularnewline
41 & 102.94 & 103.016300008376 & -0.076300008376279 \tabularnewline
42 & 103.05 & 102.982206149662 & 0.0677938503381625 \tabularnewline
43 & 103.09 & 103.113613951398 & -0.0236139513975786 \tabularnewline
44 & 103.1 & 103.146157186703 & -0.0461571867029278 \tabularnewline
45 & 103.14 & 103.141581765825 & -0.00158176582495173 \tabularnewline
46 & 103.19 & 103.181082279087 & 0.0089177209132032 \tabularnewline
47 & 103.36 & 103.233898298538 & 0.126101701461707 \tabularnewline
48 & 103.43 & 103.443718432813 & -0.0137184328125244 \tabularnewline
49 & 103.62 & 103.509386454494 & 0.110613545505714 \tabularnewline
50 & 103.79 & 103.734315770939 & 0.055684229060887 \tabularnewline
51 & 103.9 & 103.921899621533 & -0.0218996215331941 \tabularnewline
52 & 103.92 & 104.024984204375 & -0.104984204374674 \tabularnewline
53 & 103.94 & 104.01183250962 & -0.0718325096202364 \tabularnewline
54 & 103.98 & 104.009149388416 & -0.0291493884158598 \tabularnewline
55 & 104.04 & 104.039944654877 & 5.53451228313406e-05 \tabularnewline
56 & 104.09 & 104.099962131645 & -0.00996213164549431 \tabularnewline
57 & 104.16 & 104.146816310335 & 0.0131836896652544 \tabularnewline
58 & 104.22 & 104.220979428569 & -0.000979428568783192 \tabularnewline
59 & 104.28 & 104.280670146643 & -0.000670146642619329 \tabularnewline
60 & 104.32 & 104.340458529123 & -0.0204585291229336 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]3[/C][C]98.36[/C][C]98.76[/C][C]-0.400000000000006[/C][/ROW]
[ROW][C]4[/C][C]98.51[/C][C]98.6336888279455[/C][C]-0.123688827945486[/C][/ROW]
[ROW][C]5[/C][C]98.77[/C][C]98.7446306258759[/C][C]0.0253693741241108[/C][/ROW]
[ROW][C]6[/C][C]98.78[/C][C]99.0126417143256[/C][C]-0.232641714325638[/C][/ROW]
[ROW][C]7[/C][C]98.89[/C][C]98.9491785953125[/C][C]-0.0591785953125452[/C][/ROW]
[ROW][C]8[/C][C]98.87[/C][C]99.0404913009764[/C][C]-0.170491300976366[/C][/ROW]
[ROW][C]9[/C][C]99.05[/C][C]98.9666539108478[/C][C]0.0833460891521725[/C][/ROW]
[ROW][C]10[/C][C]99.09[/C][C]99.1729727663652[/C][C]-0.0829727663652307[/C][/ROW]
[ROW][C]11[/C][C]99.1[/C][C]99.1867717979448[/C][C]-0.0867717979447633[/C][/ROW]
[ROW][C]12[/C][C]99.12[/C][C]99.1693711791955[/C][C]-0.049371179195532[/C][/ROW]
[ROW][C]13[/C][C]99.37[/C][C]99.1737808504208[/C][C]0.196219149579207[/C][/ROW]
[ROW][C]14[/C][C]99.46[/C][C]99.485742527328[/C][C]-0.0257425273280205[/C][/ROW]
[ROW][C]15[/C][C]99.6[/C][C]99.5676136053319[/C][C]0.0323863946681087[/C][/ROW]
[ROW][C]16[/C][C]99.87[/C][C]99.7178405140048[/C][C]0.152159485995242[/C][/ROW]
[ROW][C]17[/C][C]99.88[/C][C]100.035889121543[/C][C]-0.155889121542955[/C][/ROW]
[ROW][C]18[/C][C]100.01[/C][C]99.9966627774113[/C][C]0.0133372225886603[/C][/ROW]
[ROW][C]19[/C][C]100.02[/C][C]100.130874377954[/C][C]-0.110874377954175[/C][/ROW]
[ROW][C]20[/C][C]100.19[/C][C]100.105862696379[/C][C]0.0841373036213611[/C][/ROW]
[ROW][C]21[/C][C]100.2[/C][C]100.302431399963[/C][C]-0.102431399963436[/C][/ROW]
[ROW][C]22[/C][C]100.35[/C][C]100.280085824502[/C][C]0.0699141754979564[/C][/ROW]
[ROW][C]23[/C][C]100.47[/C][C]100.452163178128[/C][C]0.0178368218720379[/C][/ROW]
[ROW][C]24[/C][C]100.57[/C][C]100.577795652819[/C][C]-0.00779565281892758[/C][/ROW]
[ROW][C]25[/C][C]101.41[/C][C]100.675333957708[/C][C]0.734666042292304[/C][/ROW]
[ROW][C]26[/C][C]101.67[/C][C]101.747325279884[/C][C]-0.0773252798841639[/C][/ROW]
[ROW][C]27[/C][C]101.82[/C][C]101.982907663055[/C][C]-0.162907663055151[/C][/ROW]
[ROW][C]28[/C][C]101.86[/C][C]102.081465018412[/C][C]-0.221465018412246[/C][/ROW]
[ROW][C]29[/C][C]101.98[/C][C]102.0515312533[/C][C]-0.0715312533004351[/C][/ROW]
[ROW][C]30[/C][C]102.06[/C][C]102.148943262193[/C][C]-0.0889432621931689[/C][/ROW]
[ROW][C]31[/C][C]102.17[/C][C]102.200856942958[/C][C]-0.0308569429582519[/C][/ROW]
[ROW][C]32[/C][C]102.2[/C][C]102.301113001381[/C][C]-0.101113001380554[/C][/ROW]
[ROW][C]33[/C][C]102.35[/C][C]102.299183747095[/C][C]0.0508162529052498[/C][/ROW]
[ROW][C]34[/C][C]102.47[/C][C]102.465230398254[/C][C]0.00476960174556496[/C][/ROW]
[ROW][C]35[/C][C]102.55[/C][C]102.586736533221[/C][C]-0.0367365332212302[/C][/ROW]
[ROW][C]36[/C][C]102.62[/C][C]102.6551359468[/C][C]-0.0351359468002386[/C][/ROW]
[ROW][C]37[/C][C]102.81[/C][C]102.714040790246[/C][C]0.0959592097537154[/C][/ROW]
[ROW][C]38[/C][C]102.88[/C][C]102.93434259088[/C][C]-0.0543425908798412[/C][/ROW]
[ROW][C]39[/C][C]102.94[/C][C]102.987182400014[/C][C]-0.0471824000135541[/C][/ROW]
[ROW][C]40[/C][C]102.95[/C][C]103.032283239398[/C][C]-0.0822832393984072[/C][/ROW]
[ROW][C]41[/C][C]102.94[/C][C]103.016300008376[/C][C]-0.076300008376279[/C][/ROW]
[ROW][C]42[/C][C]103.05[/C][C]102.982206149662[/C][C]0.0677938503381625[/C][/ROW]
[ROW][C]43[/C][C]103.09[/C][C]103.113613951398[/C][C]-0.0236139513975786[/C][/ROW]
[ROW][C]44[/C][C]103.1[/C][C]103.146157186703[/C][C]-0.0461571867029278[/C][/ROW]
[ROW][C]45[/C][C]103.14[/C][C]103.141581765825[/C][C]-0.00158176582495173[/C][/ROW]
[ROW][C]46[/C][C]103.19[/C][C]103.181082279087[/C][C]0.0089177209132032[/C][/ROW]
[ROW][C]47[/C][C]103.36[/C][C]103.233898298538[/C][C]0.126101701461707[/C][/ROW]
[ROW][C]48[/C][C]103.43[/C][C]103.443718432813[/C][C]-0.0137184328125244[/C][/ROW]
[ROW][C]49[/C][C]103.62[/C][C]103.509386454494[/C][C]0.110613545505714[/C][/ROW]
[ROW][C]50[/C][C]103.79[/C][C]103.734315770939[/C][C]0.055684229060887[/C][/ROW]
[ROW][C]51[/C][C]103.9[/C][C]103.921899621533[/C][C]-0.0218996215331941[/C][/ROW]
[ROW][C]52[/C][C]103.92[/C][C]104.024984204375[/C][C]-0.104984204374674[/C][/ROW]
[ROW][C]53[/C][C]103.94[/C][C]104.01183250962[/C][C]-0.0718325096202364[/C][/ROW]
[ROW][C]54[/C][C]103.98[/C][C]104.009149388416[/C][C]-0.0291493884158598[/C][/ROW]
[ROW][C]55[/C][C]104.04[/C][C]104.039944654877[/C][C]5.53451228313406e-05[/C][/ROW]
[ROW][C]56[/C][C]104.09[/C][C]104.099962131645[/C][C]-0.00996213164549431[/C][/ROW]
[ROW][C]57[/C][C]104.16[/C][C]104.146816310335[/C][C]0.0131836896652544[/C][/ROW]
[ROW][C]58[/C][C]104.22[/C][C]104.220979428569[/C][C]-0.000979428568783192[/C][/ROW]
[ROW][C]59[/C][C]104.28[/C][C]104.280670146643[/C][C]-0.000670146642619329[/C][/ROW]
[ROW][C]60[/C][C]104.32[/C][C]104.340458529123[/C][C]-0.0204585291229336[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
3	98.36	98.76	-0.400000000000006
4	98.51	98.6336888279455	-0.123688827945486
5	98.77	98.7446306258759	0.0253693741241108
6	98.78	99.0126417143256	-0.232641714325638
7	98.89	98.9491785953125	-0.0591785953125452
8	98.87	99.0404913009764	-0.170491300976366
9	99.05	98.9666539108478	0.0833460891521725
10	99.09	99.1729727663652	-0.0829727663652307
11	99.1	99.1867717979448	-0.0867717979447633
12	99.12	99.1693711791955	-0.049371179195532
13	99.37	99.1737808504208	0.196219149579207
14	99.46	99.485742527328	-0.0257425273280205
15	99.6	99.5676136053319	0.0323863946681087
16	99.87	99.7178405140048	0.152159485995242
17	99.88	100.035889121543	-0.155889121542955
18	100.01	99.9966627774113	0.0133372225886603
19	100.02	100.130874377954	-0.110874377954175
20	100.19	100.105862696379	0.0841373036213611
21	100.2	100.302431399963	-0.102431399963436
22	100.35	100.280085824502	0.0699141754979564
23	100.47	100.452163178128	0.0178368218720379
24	100.57	100.577795652819	-0.00779565281892758
25	101.41	100.675333957708	0.734666042292304
26	101.67	101.747325279884	-0.0773252798841639
27	101.82	101.982907663055	-0.162907663055151
28	101.86	102.081465018412	-0.221465018412246
29	101.98	102.0515312533	-0.0715312533004351
30	102.06	102.148943262193	-0.0889432621931689
31	102.17	102.200856942958	-0.0308569429582519
32	102.2	102.301113001381	-0.101113001380554
33	102.35	102.299183747095	0.0508162529052498
34	102.47	102.465230398254	0.00476960174556496
35	102.55	102.586736533221	-0.0367365332212302
36	102.62	102.6551359468	-0.0351359468002386
37	102.81	102.714040790246	0.0959592097537154
38	102.88	102.93434259088	-0.0543425908798412
39	102.94	102.987182400014	-0.0471824000135541
40	102.95	103.032283239398	-0.0822832393984072
41	102.94	103.016300008376	-0.076300008376279
42	103.05	102.982206149662	0.0677938503381625
43	103.09	103.113613951398	-0.0236139513975786
44	103.1	103.146157186703	-0.0461571867029278
45	103.14	103.141581765825	-0.00158176582495173
46	103.19	103.181082279087	0.0089177209132032
47	103.36	103.233898298538	0.126101701461707
48	103.43	103.443718432813	-0.0137184328125244
49	103.62	103.509386454494	0.110613545505714
50	103.79	103.734315770939	0.055684229060887
51	103.9	103.921899621533	-0.0218996215331941
52	103.92	104.024984204375	-0.104984204374674
53	103.94	104.01183250962	-0.0718325096202364
54	103.98	104.009149388416	-0.0291493884158598
55	104.04	104.039944654877	5.53451228313406e-05
56	104.09	104.099962131645	-0.00996213164549431
57	104.16	104.146816310335	0.0131836896652544
58	104.22	104.220979428569	-0.000979428568783192
59	104.28	104.280670146643	-0.000670146642619329
60	104.32	104.340458529123	-0.0204585291229336

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	104.373998177143	104.098845780845	104.649150573441
62	104.427996354286	103.973264120013	104.882728588559
63	104.481994531429	103.842998121844	105.120990941013
64	104.535992708571	103.70207869545	105.369906721693
65	104.589990885714	103.549237007649	105.630744763779
66	104.643989062857	103.384352888357	105.903625237358
67	104.69798724	103.207666712779	106.188307767221
68	104.751985417143	103.019535331193	106.484435503093
69	104.805983594286	102.820343623939	106.791623564632
70	104.859981771429	102.610470186927	107.10949335593
71	104.913979948571	102.390274171032	107.43768572611
72	104.967978125714	102.160090973328	107.7758652781

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 104.373998177143 & 104.098845780845 & 104.649150573441 \tabularnewline
62 & 104.427996354286 & 103.973264120013 & 104.882728588559 \tabularnewline
63 & 104.481994531429 & 103.842998121844 & 105.120990941013 \tabularnewline
64 & 104.535992708571 & 103.70207869545 & 105.369906721693 \tabularnewline
65 & 104.589990885714 & 103.549237007649 & 105.630744763779 \tabularnewline
66 & 104.643989062857 & 103.384352888357 & 105.903625237358 \tabularnewline
67 & 104.69798724 & 103.207666712779 & 106.188307767221 \tabularnewline
68 & 104.751985417143 & 103.019535331193 & 106.484435503093 \tabularnewline
69 & 104.805983594286 & 102.820343623939 & 106.791623564632 \tabularnewline
70 & 104.859981771429 & 102.610470186927 & 107.10949335593 \tabularnewline
71 & 104.913979948571 & 102.390274171032 & 107.43768572611 \tabularnewline
72 & 104.967978125714 & 102.160090973328 & 107.7758652781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]61[/C][C]104.373998177143[/C][C]104.098845780845[/C][C]104.649150573441[/C][/ROW]
[ROW][C]62[/C][C]104.427996354286[/C][C]103.973264120013[/C][C]104.882728588559[/C][/ROW]
[ROW][C]63[/C][C]104.481994531429[/C][C]103.842998121844[/C][C]105.120990941013[/C][/ROW]
[ROW][C]64[/C][C]104.535992708571[/C][C]103.70207869545[/C][C]105.369906721693[/C][/ROW]
[ROW][C]65[/C][C]104.589990885714[/C][C]103.549237007649[/C][C]105.630744763779[/C][/ROW]
[ROW][C]66[/C][C]104.643989062857[/C][C]103.384352888357[/C][C]105.903625237358[/C][/ROW]
[ROW][C]67[/C][C]104.69798724[/C][C]103.207666712779[/C][C]106.188307767221[/C][/ROW]
[ROW][C]68[/C][C]104.751985417143[/C][C]103.019535331193[/C][C]106.484435503093[/C][/ROW]
[ROW][C]69[/C][C]104.805983594286[/C][C]102.820343623939[/C][C]106.791623564632[/C][/ROW]
[ROW][C]70[/C][C]104.859981771429[/C][C]102.610470186927[/C][C]107.10949335593[/C][/ROW]
[ROW][C]71[/C][C]104.913979948571[/C][C]102.390274171032[/C][C]107.43768572611[/C][/ROW]
[ROW][C]72[/C][C]104.967978125714[/C][C]102.160090973328[/C][C]107.7758652781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
61	104.373998177143	104.098845780845	104.649150573441
62	104.427996354286	103.973264120013	104.882728588559
63	104.481994531429	103.842998121844	105.120990941013
64	104.535992708571	103.70207869545	105.369906721693
65	104.589990885714	103.549237007649	105.630744763779
66	104.643989062857	103.384352888357	105.903625237358
67	104.69798724	103.207666712779	106.188307767221
68	104.751985417143	103.019535331193	106.484435503093
69	104.805983594286	102.820343623939	106.791623564632
70	104.859981771429	102.610470186927	107.10949335593
71	104.913979948571	102.390274171032	107.43768572611
72	104.967978125714	102.160090973328	107.7758652781

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 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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