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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 01 Dec 2014 20:49:18 +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/Dec/01/t1417466975l1n0ljql3h3pdud.htm/, Retrieved Thu, 16 May 2024 17:14:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=262276, Retrieved Thu, 16 May 2024 17:14:18 +0000

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No (this computation is public)

User-defined keywords

Simon Dewilde

Estimated Impact

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

-       [Exponential Smoothing] [] [2014-12-01 20:49:18] [1a08c6aa6bf9a3504070a6066c5cb670] [Current]

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Dataseries X:

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Histogram

Boxplots

1,64
1,65
1,65
1,66
1,67
1,67
1,68
1,68
1,69
1,7
1,71
1,72
1,72
1,73
1,73
1,73
1,73
1,74
1,75
1,75
1,75
1,76
1,76
1,76
1,77
1,78
1,78
1,79
1,79
1,79
1,79
1,79
1,83
1,83
1,83
1,83
1,84
1,84
1,84
1,85
1,85
1,85
1,86
1,86
1,86
1,87
1,87
1,88
1,88
1,88
1,89
1,89
1,9
1,91
1,91
1,91
1,91
1,91
1,92
1,92
1,92
1,93
1,94
1,94
1,94
1,95
1,95
1,95
1,95
1,96
1,96
1,97

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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262276&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262276&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262276&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.942382858386597
beta	0
gamma	0.949735586222639

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.942382858386597 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.949735586222639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262276&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]0.942382858386597[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.949735586222639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262276&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262276&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	0.942382858386597
beta	0
gamma	0.949735586222639

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.72	1.68497596153846	0.0350240384615383
14	1.73	1.72772123413031	0.00227876586969278
15	1.73	1.73002458980507	-2.45898050676985e-05
16	1.73	1.73057396924183	-0.00057396924183295
17	1.73	1.73102228958131	-0.00102228958130768
18	1.74	1.74188145385113	-0.0018814538511287
19	1.75	1.74651428977386	0.0034857102261352
20	1.75	1.74870504912116	0.00129495087883735
21	1.75	1.75883127441272	-0.00883127441271725
22	1.76	1.75983138523602	0.000168614763982999
23	1.76	1.77014617068015	-0.0101461706801509
24	1.76	1.7707404791338	-0.0107404791337977
25	1.77	1.76227460697315	0.00772539302684927
26	1.78	1.77750224835905	0.00249775164095012
27	1.78	1.77988593043036	0.000114069569635111
28	1.79	1.7805359174655	0.0094640825344956
29	1.79	1.79041939317098	-0.000419393170980387
30	1.79	1.80179970231251	-0.0117997023125103
31	1.79	1.7973794477526	-0.00737944775259924
32	1.79	1.78921118781581	0.000788812184194798
33	1.83	1.79830631899943	0.0316936810005652
34	1.83	1.83798893652463	-0.00798893652462596
35	1.83	1.84005174958034	-0.010051749580344
36	1.83	1.84070251767745	-0.01070251767745
37	1.84	1.83328289165203	0.00671710834796779
38	1.84	1.84727428081574	-0.00727428081573955
39	1.84	1.84031852942302	-0.000318529423020575
40	1.85	1.8410724851077	0.0089275148923047
41	1.85	1.84990947449886	9.05255011414141e-05
42	1.85	1.86114757979327	-0.0111475797932734
43	1.86	1.85758375528681	0.0024162447131868
44	1.86	1.85909376377431	0.000906236225688861
45	1.86	1.86999070022634	-0.00999070022634041
46	1.87	1.86821919693238	0.00178080306762429
47	1.87	1.87937596581485	-0.00937596581485001
48	1.88	1.88062797023511	-0.000627970235105524
49	1.88	1.88365564524801	-0.00365564524800988
50	1.88	1.88710630572587	-0.00710630572586735
51	1.89	1.88068947719661	0.00931052280339473
52	1.89	1.89102363989309	-0.00102363989308674
53	1.9	1.88999926225708	0.0100007377429159
54	1.91	1.90996162077202	3.83792279785578e-05
55	1.91	1.91768147901765	-0.00768147901764848
56	1.91	1.90959293650289	0.000407063497108728
57	1.91	1.91942316933024	-0.0094231693302369
58	1.91	1.91883064644194	-0.00883064644194276
59	1.92	1.91937685709871	0.000623142901287066
60	1.92	1.93053054967368	-0.0105305496736776
61	1.92	1.9240605260148	-0.00406052601480167
62	1.93	1.92694081003461	0.00305918996539267
63	1.94	1.93100211648275	0.00899788351724751
64	1.94	1.9404761570439	-0.000476157043899361
65	1.94	1.9405709833775	-0.000570983377498058
66	1.95	1.95002558240882	-2.55824088244427e-05
67	1.95	1.95726272555708	-0.00726272555708318
68	1.95	1.95001142266294	-1.14226629426284e-05
69	1.95	1.95890936064682	-0.00890936064682046
70	1.96	1.95883346572873	0.00116653427127345
71	1.96	1.96931816939896	-0.00931816939895924
72	1.97	1.97049299790583	-0.00049299790582702

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.72 & 1.68497596153846 & 0.0350240384615383 \tabularnewline
14 & 1.73 & 1.72772123413031 & 0.00227876586969278 \tabularnewline
15 & 1.73 & 1.73002458980507 & -2.45898050676985e-05 \tabularnewline
16 & 1.73 & 1.73057396924183 & -0.00057396924183295 \tabularnewline
17 & 1.73 & 1.73102228958131 & -0.00102228958130768 \tabularnewline
18 & 1.74 & 1.74188145385113 & -0.0018814538511287 \tabularnewline
19 & 1.75 & 1.74651428977386 & 0.0034857102261352 \tabularnewline
20 & 1.75 & 1.74870504912116 & 0.00129495087883735 \tabularnewline
21 & 1.75 & 1.75883127441272 & -0.00883127441271725 \tabularnewline
22 & 1.76 & 1.75983138523602 & 0.000168614763982999 \tabularnewline
23 & 1.76 & 1.77014617068015 & -0.0101461706801509 \tabularnewline
24 & 1.76 & 1.7707404791338 & -0.0107404791337977 \tabularnewline
25 & 1.77 & 1.76227460697315 & 0.00772539302684927 \tabularnewline
26 & 1.78 & 1.77750224835905 & 0.00249775164095012 \tabularnewline
27 & 1.78 & 1.77988593043036 & 0.000114069569635111 \tabularnewline
28 & 1.79 & 1.7805359174655 & 0.0094640825344956 \tabularnewline
29 & 1.79 & 1.79041939317098 & -0.000419393170980387 \tabularnewline
30 & 1.79 & 1.80179970231251 & -0.0117997023125103 \tabularnewline
31 & 1.79 & 1.7973794477526 & -0.00737944775259924 \tabularnewline
32 & 1.79 & 1.78921118781581 & 0.000788812184194798 \tabularnewline
33 & 1.83 & 1.79830631899943 & 0.0316936810005652 \tabularnewline
34 & 1.83 & 1.83798893652463 & -0.00798893652462596 \tabularnewline
35 & 1.83 & 1.84005174958034 & -0.010051749580344 \tabularnewline
36 & 1.83 & 1.84070251767745 & -0.01070251767745 \tabularnewline
37 & 1.84 & 1.83328289165203 & 0.00671710834796779 \tabularnewline
38 & 1.84 & 1.84727428081574 & -0.00727428081573955 \tabularnewline
39 & 1.84 & 1.84031852942302 & -0.000318529423020575 \tabularnewline
40 & 1.85 & 1.8410724851077 & 0.0089275148923047 \tabularnewline
41 & 1.85 & 1.84990947449886 & 9.05255011414141e-05 \tabularnewline
42 & 1.85 & 1.86114757979327 & -0.0111475797932734 \tabularnewline
43 & 1.86 & 1.85758375528681 & 0.0024162447131868 \tabularnewline
44 & 1.86 & 1.85909376377431 & 0.000906236225688861 \tabularnewline
45 & 1.86 & 1.86999070022634 & -0.00999070022634041 \tabularnewline
46 & 1.87 & 1.86821919693238 & 0.00178080306762429 \tabularnewline
47 & 1.87 & 1.87937596581485 & -0.00937596581485001 \tabularnewline
48 & 1.88 & 1.88062797023511 & -0.000627970235105524 \tabularnewline
49 & 1.88 & 1.88365564524801 & -0.00365564524800988 \tabularnewline
50 & 1.88 & 1.88710630572587 & -0.00710630572586735 \tabularnewline
51 & 1.89 & 1.88068947719661 & 0.00931052280339473 \tabularnewline
52 & 1.89 & 1.89102363989309 & -0.00102363989308674 \tabularnewline
53 & 1.9 & 1.88999926225708 & 0.0100007377429159 \tabularnewline
54 & 1.91 & 1.90996162077202 & 3.83792279785578e-05 \tabularnewline
55 & 1.91 & 1.91768147901765 & -0.00768147901764848 \tabularnewline
56 & 1.91 & 1.90959293650289 & 0.000407063497108728 \tabularnewline
57 & 1.91 & 1.91942316933024 & -0.0094231693302369 \tabularnewline
58 & 1.91 & 1.91883064644194 & -0.00883064644194276 \tabularnewline
59 & 1.92 & 1.91937685709871 & 0.000623142901287066 \tabularnewline
60 & 1.92 & 1.93053054967368 & -0.0105305496736776 \tabularnewline
61 & 1.92 & 1.9240605260148 & -0.00406052601480167 \tabularnewline
62 & 1.93 & 1.92694081003461 & 0.00305918996539267 \tabularnewline
63 & 1.94 & 1.93100211648275 & 0.00899788351724751 \tabularnewline
64 & 1.94 & 1.9404761570439 & -0.000476157043899361 \tabularnewline
65 & 1.94 & 1.9405709833775 & -0.000570983377498058 \tabularnewline
66 & 1.95 & 1.95002558240882 & -2.55824088244427e-05 \tabularnewline
67 & 1.95 & 1.95726272555708 & -0.00726272555708318 \tabularnewline
68 & 1.95 & 1.95001142266294 & -1.14226629426284e-05 \tabularnewline
69 & 1.95 & 1.95890936064682 & -0.00890936064682046 \tabularnewline
70 & 1.96 & 1.95883346572873 & 0.00116653427127345 \tabularnewline
71 & 1.96 & 1.96931816939896 & -0.00931816939895924 \tabularnewline
72 & 1.97 & 1.97049299790583 & -0.00049299790582702 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262276&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]1.72[/C][C]1.68497596153846[/C][C]0.0350240384615383[/C][/ROW]
[ROW][C]14[/C][C]1.73[/C][C]1.72772123413031[/C][C]0.00227876586969278[/C][/ROW]
[ROW][C]15[/C][C]1.73[/C][C]1.73002458980507[/C][C]-2.45898050676985e-05[/C][/ROW]
[ROW][C]16[/C][C]1.73[/C][C]1.73057396924183[/C][C]-0.00057396924183295[/C][/ROW]
[ROW][C]17[/C][C]1.73[/C][C]1.73102228958131[/C][C]-0.00102228958130768[/C][/ROW]
[ROW][C]18[/C][C]1.74[/C][C]1.74188145385113[/C][C]-0.0018814538511287[/C][/ROW]
[ROW][C]19[/C][C]1.75[/C][C]1.74651428977386[/C][C]0.0034857102261352[/C][/ROW]
[ROW][C]20[/C][C]1.75[/C][C]1.74870504912116[/C][C]0.00129495087883735[/C][/ROW]
[ROW][C]21[/C][C]1.75[/C][C]1.75883127441272[/C][C]-0.00883127441271725[/C][/ROW]
[ROW][C]22[/C][C]1.76[/C][C]1.75983138523602[/C][C]0.000168614763982999[/C][/ROW]
[ROW][C]23[/C][C]1.76[/C][C]1.77014617068015[/C][C]-0.0101461706801509[/C][/ROW]
[ROW][C]24[/C][C]1.76[/C][C]1.7707404791338[/C][C]-0.0107404791337977[/C][/ROW]
[ROW][C]25[/C][C]1.77[/C][C]1.76227460697315[/C][C]0.00772539302684927[/C][/ROW]
[ROW][C]26[/C][C]1.78[/C][C]1.77750224835905[/C][C]0.00249775164095012[/C][/ROW]
[ROW][C]27[/C][C]1.78[/C][C]1.77988593043036[/C][C]0.000114069569635111[/C][/ROW]
[ROW][C]28[/C][C]1.79[/C][C]1.7805359174655[/C][C]0.0094640825344956[/C][/ROW]
[ROW][C]29[/C][C]1.79[/C][C]1.79041939317098[/C][C]-0.000419393170980387[/C][/ROW]
[ROW][C]30[/C][C]1.79[/C][C]1.80179970231251[/C][C]-0.0117997023125103[/C][/ROW]
[ROW][C]31[/C][C]1.79[/C][C]1.7973794477526[/C][C]-0.00737944775259924[/C][/ROW]
[ROW][C]32[/C][C]1.79[/C][C]1.78921118781581[/C][C]0.000788812184194798[/C][/ROW]
[ROW][C]33[/C][C]1.83[/C][C]1.79830631899943[/C][C]0.0316936810005652[/C][/ROW]
[ROW][C]34[/C][C]1.83[/C][C]1.83798893652463[/C][C]-0.00798893652462596[/C][/ROW]
[ROW][C]35[/C][C]1.83[/C][C]1.84005174958034[/C][C]-0.010051749580344[/C][/ROW]
[ROW][C]36[/C][C]1.83[/C][C]1.84070251767745[/C][C]-0.01070251767745[/C][/ROW]
[ROW][C]37[/C][C]1.84[/C][C]1.83328289165203[/C][C]0.00671710834796779[/C][/ROW]
[ROW][C]38[/C][C]1.84[/C][C]1.84727428081574[/C][C]-0.00727428081573955[/C][/ROW]
[ROW][C]39[/C][C]1.84[/C][C]1.84031852942302[/C][C]-0.000318529423020575[/C][/ROW]
[ROW][C]40[/C][C]1.85[/C][C]1.8410724851077[/C][C]0.0089275148923047[/C][/ROW]
[ROW][C]41[/C][C]1.85[/C][C]1.84990947449886[/C][C]9.05255011414141e-05[/C][/ROW]
[ROW][C]42[/C][C]1.85[/C][C]1.86114757979327[/C][C]-0.0111475797932734[/C][/ROW]
[ROW][C]43[/C][C]1.86[/C][C]1.85758375528681[/C][C]0.0024162447131868[/C][/ROW]
[ROW][C]44[/C][C]1.86[/C][C]1.85909376377431[/C][C]0.000906236225688861[/C][/ROW]
[ROW][C]45[/C][C]1.86[/C][C]1.86999070022634[/C][C]-0.00999070022634041[/C][/ROW]
[ROW][C]46[/C][C]1.87[/C][C]1.86821919693238[/C][C]0.00178080306762429[/C][/ROW]
[ROW][C]47[/C][C]1.87[/C][C]1.87937596581485[/C][C]-0.00937596581485001[/C][/ROW]
[ROW][C]48[/C][C]1.88[/C][C]1.88062797023511[/C][C]-0.000627970235105524[/C][/ROW]
[ROW][C]49[/C][C]1.88[/C][C]1.88365564524801[/C][C]-0.00365564524800988[/C][/ROW]
[ROW][C]50[/C][C]1.88[/C][C]1.88710630572587[/C][C]-0.00710630572586735[/C][/ROW]
[ROW][C]51[/C][C]1.89[/C][C]1.88068947719661[/C][C]0.00931052280339473[/C][/ROW]
[ROW][C]52[/C][C]1.89[/C][C]1.89102363989309[/C][C]-0.00102363989308674[/C][/ROW]
[ROW][C]53[/C][C]1.9[/C][C]1.88999926225708[/C][C]0.0100007377429159[/C][/ROW]
[ROW][C]54[/C][C]1.91[/C][C]1.90996162077202[/C][C]3.83792279785578e-05[/C][/ROW]
[ROW][C]55[/C][C]1.91[/C][C]1.91768147901765[/C][C]-0.00768147901764848[/C][/ROW]
[ROW][C]56[/C][C]1.91[/C][C]1.90959293650289[/C][C]0.000407063497108728[/C][/ROW]
[ROW][C]57[/C][C]1.91[/C][C]1.91942316933024[/C][C]-0.0094231693302369[/C][/ROW]
[ROW][C]58[/C][C]1.91[/C][C]1.91883064644194[/C][C]-0.00883064644194276[/C][/ROW]
[ROW][C]59[/C][C]1.92[/C][C]1.91937685709871[/C][C]0.000623142901287066[/C][/ROW]
[ROW][C]60[/C][C]1.92[/C][C]1.93053054967368[/C][C]-0.0105305496736776[/C][/ROW]
[ROW][C]61[/C][C]1.92[/C][C]1.9240605260148[/C][C]-0.00406052601480167[/C][/ROW]
[ROW][C]62[/C][C]1.93[/C][C]1.92694081003461[/C][C]0.00305918996539267[/C][/ROW]
[ROW][C]63[/C][C]1.94[/C][C]1.93100211648275[/C][C]0.00899788351724751[/C][/ROW]
[ROW][C]64[/C][C]1.94[/C][C]1.9404761570439[/C][C]-0.000476157043899361[/C][/ROW]
[ROW][C]65[/C][C]1.94[/C][C]1.9405709833775[/C][C]-0.000570983377498058[/C][/ROW]
[ROW][C]66[/C][C]1.95[/C][C]1.95002558240882[/C][C]-2.55824088244427e-05[/C][/ROW]
[ROW][C]67[/C][C]1.95[/C][C]1.95726272555708[/C][C]-0.00726272555708318[/C][/ROW]
[ROW][C]68[/C][C]1.95[/C][C]1.95001142266294[/C][C]-1.14226629426284e-05[/C][/ROW]
[ROW][C]69[/C][C]1.95[/C][C]1.95890936064682[/C][C]-0.00890936064682046[/C][/ROW]
[ROW][C]70[/C][C]1.96[/C][C]1.95883346572873[/C][C]0.00116653427127345[/C][/ROW]
[ROW][C]71[/C][C]1.96[/C][C]1.96931816939896[/C][C]-0.00931816939895924[/C][/ROW]
[ROW][C]72[/C][C]1.97[/C][C]1.97049299790583[/C][C]-0.00049299790582702[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262276&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262276&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	1.72	1.68497596153846	0.0350240384615383
14	1.73	1.72772123413031	0.00227876586969278
15	1.73	1.73002458980507	-2.45898050676985e-05
16	1.73	1.73057396924183	-0.00057396924183295
17	1.73	1.73102228958131	-0.00102228958130768
18	1.74	1.74188145385113	-0.0018814538511287
19	1.75	1.74651428977386	0.0034857102261352
20	1.75	1.74870504912116	0.00129495087883735
21	1.75	1.75883127441272	-0.00883127441271725
22	1.76	1.75983138523602	0.000168614763982999
23	1.76	1.77014617068015	-0.0101461706801509
24	1.76	1.7707404791338	-0.0107404791337977
25	1.77	1.76227460697315	0.00772539302684927
26	1.78	1.77750224835905	0.00249775164095012
27	1.78	1.77988593043036	0.000114069569635111
28	1.79	1.7805359174655	0.0094640825344956
29	1.79	1.79041939317098	-0.000419393170980387
30	1.79	1.80179970231251	-0.0117997023125103
31	1.79	1.7973794477526	-0.00737944775259924
32	1.79	1.78921118781581	0.000788812184194798
33	1.83	1.79830631899943	0.0316936810005652
34	1.83	1.83798893652463	-0.00798893652462596
35	1.83	1.84005174958034	-0.010051749580344
36	1.83	1.84070251767745	-0.01070251767745
37	1.84	1.83328289165203	0.00671710834796779
38	1.84	1.84727428081574	-0.00727428081573955
39	1.84	1.84031852942302	-0.000318529423020575
40	1.85	1.8410724851077	0.0089275148923047
41	1.85	1.84990947449886	9.05255011414141e-05
42	1.85	1.86114757979327	-0.0111475797932734
43	1.86	1.85758375528681	0.0024162447131868
44	1.86	1.85909376377431	0.000906236225688861
45	1.86	1.86999070022634	-0.00999070022634041
46	1.87	1.86821919693238	0.00178080306762429
47	1.87	1.87937596581485	-0.00937596581485001
48	1.88	1.88062797023511	-0.000627970235105524
49	1.88	1.88365564524801	-0.00365564524800988
50	1.88	1.88710630572587	-0.00710630572586735
51	1.89	1.88068947719661	0.00931052280339473
52	1.89	1.89102363989309	-0.00102363989308674
53	1.9	1.88999926225708	0.0100007377429159
54	1.91	1.90996162077202	3.83792279785578e-05
55	1.91	1.91768147901765	-0.00768147901764848
56	1.91	1.90959293650289	0.000407063497108728
57	1.91	1.91942316933024	-0.0094231693302369
58	1.91	1.91883064644194	-0.00883064644194276
59	1.92	1.91937685709871	0.000623142901287066
60	1.92	1.93053054967368	-0.0105305496736776
61	1.92	1.9240605260148	-0.00406052601480167
62	1.93	1.92694081003461	0.00305918996539267
63	1.94	1.93100211648275	0.00899788351724751
64	1.94	1.9404761570439	-0.000476157043899361
65	1.94	1.9405709833775	-0.000570983377498058
66	1.95	1.95002558240882	-2.55824088244427e-05
67	1.95	1.95726272555708	-0.00726272555708318
68	1.95	1.95001142266294	-1.14226629426284e-05
69	1.95	1.95890936064682	-0.00890936064682046
70	1.96	1.95883346572873	0.00116653427127345
71	1.96	1.96931816939896	-0.00931816939895924
72	1.97	1.97049299790583	-0.00049299790582702

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.97383623745977	1.95661529091747	1.99105718400207
74	1.98093268992444	1.95726979683606	2.00459558301281
75	1.98243603973405	1.95374276493295	2.01112931453514
76	1.98291219966174	1.94994743774374	2.01587696157974
77	1.98345055923489	1.94670757299521	2.02019354547458
78	1.99347308812715	1.95330570649342	2.03364046976087
79	2.00033831562857	1.95701638057474	2.0436602506824
80	2.00032807971114	1.95406619943907	2.04658995998321
81	2.00874987770953	1.95972403681102	2.05777571860805
82	2.01762137509144	1.96597929355607	2.06926345662681
83	2.02643302286938	1.97230099820001	2.08056504753875
84	2.03687205713784	1.9803596903116	2.09338442396409

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.97383623745977 & 1.95661529091747 & 1.99105718400207 \tabularnewline
74 & 1.98093268992444 & 1.95726979683606 & 2.00459558301281 \tabularnewline
75 & 1.98243603973405 & 1.95374276493295 & 2.01112931453514 \tabularnewline
76 & 1.98291219966174 & 1.94994743774374 & 2.01587696157974 \tabularnewline
77 & 1.98345055923489 & 1.94670757299521 & 2.02019354547458 \tabularnewline
78 & 1.99347308812715 & 1.95330570649342 & 2.03364046976087 \tabularnewline
79 & 2.00033831562857 & 1.95701638057474 & 2.0436602506824 \tabularnewline
80 & 2.00032807971114 & 1.95406619943907 & 2.04658995998321 \tabularnewline
81 & 2.00874987770953 & 1.95972403681102 & 2.05777571860805 \tabularnewline
82 & 2.01762137509144 & 1.96597929355607 & 2.06926345662681 \tabularnewline
83 & 2.02643302286938 & 1.97230099820001 & 2.08056504753875 \tabularnewline
84 & 2.03687205713784 & 1.9803596903116 & 2.09338442396409 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262276&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]1.97383623745977[/C][C]1.95661529091747[/C][C]1.99105718400207[/C][/ROW]
[ROW][C]74[/C][C]1.98093268992444[/C][C]1.95726979683606[/C][C]2.00459558301281[/C][/ROW]
[ROW][C]75[/C][C]1.98243603973405[/C][C]1.95374276493295[/C][C]2.01112931453514[/C][/ROW]
[ROW][C]76[/C][C]1.98291219966174[/C][C]1.94994743774374[/C][C]2.01587696157974[/C][/ROW]
[ROW][C]77[/C][C]1.98345055923489[/C][C]1.94670757299521[/C][C]2.02019354547458[/C][/ROW]
[ROW][C]78[/C][C]1.99347308812715[/C][C]1.95330570649342[/C][C]2.03364046976087[/C][/ROW]
[ROW][C]79[/C][C]2.00033831562857[/C][C]1.95701638057474[/C][C]2.0436602506824[/C][/ROW]
[ROW][C]80[/C][C]2.00032807971114[/C][C]1.95406619943907[/C][C]2.04658995998321[/C][/ROW]
[ROW][C]81[/C][C]2.00874987770953[/C][C]1.95972403681102[/C][C]2.05777571860805[/C][/ROW]
[ROW][C]82[/C][C]2.01762137509144[/C][C]1.96597929355607[/C][C]2.06926345662681[/C][/ROW]
[ROW][C]83[/C][C]2.02643302286938[/C][C]1.97230099820001[/C][C]2.08056504753875[/C][/ROW]
[ROW][C]84[/C][C]2.03687205713784[/C][C]1.9803596903116[/C][C]2.09338442396409[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262276&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262276&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	1.97383623745977	1.95661529091747	1.99105718400207
74	1.98093268992444	1.95726979683606	2.00459558301281
75	1.98243603973405	1.95374276493295	2.01112931453514
76	1.98291219966174	1.94994743774374	2.01587696157974
77	1.98345055923489	1.94670757299521	2.02019354547458
78	1.99347308812715	1.95330570649342	2.03364046976087
79	2.00033831562857	1.95701638057474	2.0436602506824
80	2.00032807971114	1.95406619943907	2.04658995998321
81	2.00874987770953	1.95972403681102	2.05777571860805
82	2.01762137509144	1.96597929355607	2.06926345662681
83	2.02643302286938	1.97230099820001	2.08056504753875
84	2.03687205713784	1.9803596903116	2.09338442396409

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