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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 27 May 2009 16:07:59 -0600

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/May/28/t1243462120n5nev5knzrzdva7.htm/, Retrieved Mon, 06 May 2024 09:37:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40526, Retrieved Mon, 06 May 2024 09:37:02 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

183

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

-     [Exponential Smoothing] [Nieuwe personenwa...] [2009-01-16 12:08:15] [74be16979710d4c4e7c6647856088456]
-   PD  [Exponential Smoothing] [double exponentia...] [2009-01-26 20:41:29] [a18c43c8b63fa6800a53bb187b9ddd45]
-           [Exponential Smoothing] [Maxime Jonckheere...] [2009-05-27 22:07:59] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40526&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40526&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40526&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0985808158232413
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0985808158232413 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40526&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]0.0985808158232413[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40526&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40526&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	0.0985808158232413
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	66.2	66.2	0
4	66.08	66.2	-0.120000000000005
5	66.31	66.0681703021012	0.241829697898794
6	66.39	66.3220100710104	0.0679899289896326
7	66.37	66.4087125736779	-0.0387125736779268
8	66.23	66.3848962565821	-0.154896256582134
9	66.27	66.2296264572403	0.0403735427596814
10	66.27	66.2736065140232	-0.00360651402323242
11	66.27	66.2732509809285	-0.00325098092854148
12	66.28	66.2729304965764	0.00706950342362234
13	66.28	66.2836274139913	-0.00362741399133881
14	66.28	66.2832698205607	-0.00326982056074598
15	66.26	66.2829474789823	-0.0229474789822746
16	66.13	66.2606852977831	-0.130685297783131
17	65.86	66.1178022345115	-0.257802234511544
18	65.9	65.8223878799124	0.0776121200876503
19	65.94	65.8700389460284	0.0699610539716247
20	65.94	65.9169357638047	0.0230642361952675
21	65.91	65.9192094550252	-0.0092094550252142
22	65.95	65.8883015794355	0.0616984205644684
23	65.91	65.9343838600698	-0.0243838600697899
24	66.08	65.8919800792512	0.188019920748815
25	66.47	66.0805152364296	0.38948476357038
26	66.47	66.5089109621731	-0.0389109621731194
27	66.56	66.5050750877776	0.0549249122223756
28	66.78	66.6004896304335	0.179510369566472
29	67.08	66.8381859091141	0.241814090885882
30	67.28	67.1620241394712	0.117975860528801
31	67.27	67.3736542960496	-0.103654296049584
32	67.27	67.3534359709814	-0.0834359709814265
33	67.26	67.3452107848931	-0.0852107848930643
34	67.37	67.3268106362014	0.0431893637986178
35	67.5	67.4410682789195	0.0589317210804552
36	67.63	67.5768778160615	0.0531221839384841
37	67.64	67.7121146442925	-0.0721146442924834
38	67.64	67.7150055238253	-0.0750055238253253
39	67.71	67.7076114180954	0.00238858190461144
40	67.87	67.7778468864482	0.0921531135518165
41	67.93	67.9469314155628	-0.0169314155627802
42	68.33	68.0052623028036	0.324737697196426
43	68.39	68.4372752099218	-0.0472752099217502
44	68.39	68.4926147811594	-0.102614781159446
45	68.58	68.4824989323172	0.0975010676827708
46	68.44	68.682110667113	-0.242110667113025
47	68.49	68.5182432000295	-0.0282432000295216
48	68.52	68.5654589623291	-0.0454589623291497
49	68.54	68.5909775807363	-0.0509775807362587
50	68.54	68.6059521692386	-0.0659521692385852
51	68.54	68.5994505505897	-0.0594505505897303
52	68.62	68.5935898668115	0.0264101331885342
53	68.75	68.6761933992872	0.073806600712814
54	68.71	68.8134693141986	-0.103469314198605
55	68.72	68.7632692247922	-0.0432692247922262
56	68.72	68.7690037093122	-0.0490037093121742
57	68.72	68.7641728836698	-0.0441728836698161
58	68.92	68.7598182847604	0.160181715239631
59	68.9	68.9756091289287	-0.0756091289286616
60	69.12	68.9481555193152	0.171844480684811
61	69.09	69.1850960884158	-0.0950960884158292
62	69.09	69.1457214384382	-0.0557214384381837
63	69.1	69.1402283735781	-0.0402283735781168
64	69.16	69.1462626276915	0.0137373723084693
65	68.83	69.207616869061	-0.377616869060972
66	68.52	68.8403910900403	-0.320391090040332
67	68.53	68.4988066750016	0.0311933249983554
68	68.53	68.5118817384282	0.0181182615717717
69	68.51	68.5136678514353	-0.00366785143526727
70	68.38	68.4933062716485	-0.113306271648469
71	68.44	68.3521364469515	0.0878635530485354
72	68.41	68.4207981076921	-0.0107981076921249
73	68.42	68.3897336214265	0.0302663785735149
74	68.42	68.4027173057183	0.0172826942817181
75	68.45	68.4044210478202	0.0455789521798096
76	68.63	68.4389142581104	0.191085741889552
77	68.84	68.6377516464381	0.202248353561899
78	68.72	68.8676894541312	-0.147689454131154
79	68.37	68.7331301072544	-0.363130107254406
80	68.37	68.3473324450313	0.0226675549687059
81	68.47	68.3495670310928	0.120432968907167
82	68.69	68.4614394114197	0.228560588580294
83	68.46	68.703971100707	-0.243971100707
84	68.17	68.449920230562	-0.279920230561999
85	68.17	68.1323254658678	0.037674534132222

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 66.2 & 66.2 & 0 \tabularnewline
4 & 66.08 & 66.2 & -0.120000000000005 \tabularnewline
5 & 66.31 & 66.0681703021012 & 0.241829697898794 \tabularnewline
6 & 66.39 & 66.3220100710104 & 0.0679899289896326 \tabularnewline
7 & 66.37 & 66.4087125736779 & -0.0387125736779268 \tabularnewline
8 & 66.23 & 66.3848962565821 & -0.154896256582134 \tabularnewline
9 & 66.27 & 66.2296264572403 & 0.0403735427596814 \tabularnewline
10 & 66.27 & 66.2736065140232 & -0.00360651402323242 \tabularnewline
11 & 66.27 & 66.2732509809285 & -0.00325098092854148 \tabularnewline
12 & 66.28 & 66.2729304965764 & 0.00706950342362234 \tabularnewline
13 & 66.28 & 66.2836274139913 & -0.00362741399133881 \tabularnewline
14 & 66.28 & 66.2832698205607 & -0.00326982056074598 \tabularnewline
15 & 66.26 & 66.2829474789823 & -0.0229474789822746 \tabularnewline
16 & 66.13 & 66.2606852977831 & -0.130685297783131 \tabularnewline
17 & 65.86 & 66.1178022345115 & -0.257802234511544 \tabularnewline
18 & 65.9 & 65.8223878799124 & 0.0776121200876503 \tabularnewline
19 & 65.94 & 65.8700389460284 & 0.0699610539716247 \tabularnewline
20 & 65.94 & 65.9169357638047 & 0.0230642361952675 \tabularnewline
21 & 65.91 & 65.9192094550252 & -0.0092094550252142 \tabularnewline
22 & 65.95 & 65.8883015794355 & 0.0616984205644684 \tabularnewline
23 & 65.91 & 65.9343838600698 & -0.0243838600697899 \tabularnewline
24 & 66.08 & 65.8919800792512 & 0.188019920748815 \tabularnewline
25 & 66.47 & 66.0805152364296 & 0.38948476357038 \tabularnewline
26 & 66.47 & 66.5089109621731 & -0.0389109621731194 \tabularnewline
27 & 66.56 & 66.5050750877776 & 0.0549249122223756 \tabularnewline
28 & 66.78 & 66.6004896304335 & 0.179510369566472 \tabularnewline
29 & 67.08 & 66.8381859091141 & 0.241814090885882 \tabularnewline
30 & 67.28 & 67.1620241394712 & 0.117975860528801 \tabularnewline
31 & 67.27 & 67.3736542960496 & -0.103654296049584 \tabularnewline
32 & 67.27 & 67.3534359709814 & -0.0834359709814265 \tabularnewline
33 & 67.26 & 67.3452107848931 & -0.0852107848930643 \tabularnewline
34 & 67.37 & 67.3268106362014 & 0.0431893637986178 \tabularnewline
35 & 67.5 & 67.4410682789195 & 0.0589317210804552 \tabularnewline
36 & 67.63 & 67.5768778160615 & 0.0531221839384841 \tabularnewline
37 & 67.64 & 67.7121146442925 & -0.0721146442924834 \tabularnewline
38 & 67.64 & 67.7150055238253 & -0.0750055238253253 \tabularnewline
39 & 67.71 & 67.7076114180954 & 0.00238858190461144 \tabularnewline
40 & 67.87 & 67.7778468864482 & 0.0921531135518165 \tabularnewline
41 & 67.93 & 67.9469314155628 & -0.0169314155627802 \tabularnewline
42 & 68.33 & 68.0052623028036 & 0.324737697196426 \tabularnewline
43 & 68.39 & 68.4372752099218 & -0.0472752099217502 \tabularnewline
44 & 68.39 & 68.4926147811594 & -0.102614781159446 \tabularnewline
45 & 68.58 & 68.4824989323172 & 0.0975010676827708 \tabularnewline
46 & 68.44 & 68.682110667113 & -0.242110667113025 \tabularnewline
47 & 68.49 & 68.5182432000295 & -0.0282432000295216 \tabularnewline
48 & 68.52 & 68.5654589623291 & -0.0454589623291497 \tabularnewline
49 & 68.54 & 68.5909775807363 & -0.0509775807362587 \tabularnewline
50 & 68.54 & 68.6059521692386 & -0.0659521692385852 \tabularnewline
51 & 68.54 & 68.5994505505897 & -0.0594505505897303 \tabularnewline
52 & 68.62 & 68.5935898668115 & 0.0264101331885342 \tabularnewline
53 & 68.75 & 68.6761933992872 & 0.073806600712814 \tabularnewline
54 & 68.71 & 68.8134693141986 & -0.103469314198605 \tabularnewline
55 & 68.72 & 68.7632692247922 & -0.0432692247922262 \tabularnewline
56 & 68.72 & 68.7690037093122 & -0.0490037093121742 \tabularnewline
57 & 68.72 & 68.7641728836698 & -0.0441728836698161 \tabularnewline
58 & 68.92 & 68.7598182847604 & 0.160181715239631 \tabularnewline
59 & 68.9 & 68.9756091289287 & -0.0756091289286616 \tabularnewline
60 & 69.12 & 68.9481555193152 & 0.171844480684811 \tabularnewline
61 & 69.09 & 69.1850960884158 & -0.0950960884158292 \tabularnewline
62 & 69.09 & 69.1457214384382 & -0.0557214384381837 \tabularnewline
63 & 69.1 & 69.1402283735781 & -0.0402283735781168 \tabularnewline
64 & 69.16 & 69.1462626276915 & 0.0137373723084693 \tabularnewline
65 & 68.83 & 69.207616869061 & -0.377616869060972 \tabularnewline
66 & 68.52 & 68.8403910900403 & -0.320391090040332 \tabularnewline
67 & 68.53 & 68.4988066750016 & 0.0311933249983554 \tabularnewline
68 & 68.53 & 68.5118817384282 & 0.0181182615717717 \tabularnewline
69 & 68.51 & 68.5136678514353 & -0.00366785143526727 \tabularnewline
70 & 68.38 & 68.4933062716485 & -0.113306271648469 \tabularnewline
71 & 68.44 & 68.3521364469515 & 0.0878635530485354 \tabularnewline
72 & 68.41 & 68.4207981076921 & -0.0107981076921249 \tabularnewline
73 & 68.42 & 68.3897336214265 & 0.0302663785735149 \tabularnewline
74 & 68.42 & 68.4027173057183 & 0.0172826942817181 \tabularnewline
75 & 68.45 & 68.4044210478202 & 0.0455789521798096 \tabularnewline
76 & 68.63 & 68.4389142581104 & 0.191085741889552 \tabularnewline
77 & 68.84 & 68.6377516464381 & 0.202248353561899 \tabularnewline
78 & 68.72 & 68.8676894541312 & -0.147689454131154 \tabularnewline
79 & 68.37 & 68.7331301072544 & -0.363130107254406 \tabularnewline
80 & 68.37 & 68.3473324450313 & 0.0226675549687059 \tabularnewline
81 & 68.47 & 68.3495670310928 & 0.120432968907167 \tabularnewline
82 & 68.69 & 68.4614394114197 & 0.228560588580294 \tabularnewline
83 & 68.46 & 68.703971100707 & -0.243971100707 \tabularnewline
84 & 68.17 & 68.449920230562 & -0.279920230561999 \tabularnewline
85 & 68.17 & 68.1323254658678 & 0.037674534132222 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40526&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]66.2[/C][C]66.2[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]66.08[/C][C]66.2[/C][C]-0.120000000000005[/C][/ROW]
[ROW][C]5[/C][C]66.31[/C][C]66.0681703021012[/C][C]0.241829697898794[/C][/ROW]
[ROW][C]6[/C][C]66.39[/C][C]66.3220100710104[/C][C]0.0679899289896326[/C][/ROW]
[ROW][C]7[/C][C]66.37[/C][C]66.4087125736779[/C][C]-0.0387125736779268[/C][/ROW]
[ROW][C]8[/C][C]66.23[/C][C]66.3848962565821[/C][C]-0.154896256582134[/C][/ROW]
[ROW][C]9[/C][C]66.27[/C][C]66.2296264572403[/C][C]0.0403735427596814[/C][/ROW]
[ROW][C]10[/C][C]66.27[/C][C]66.2736065140232[/C][C]-0.00360651402323242[/C][/ROW]
[ROW][C]11[/C][C]66.27[/C][C]66.2732509809285[/C][C]-0.00325098092854148[/C][/ROW]
[ROW][C]12[/C][C]66.28[/C][C]66.2729304965764[/C][C]0.00706950342362234[/C][/ROW]
[ROW][C]13[/C][C]66.28[/C][C]66.2836274139913[/C][C]-0.00362741399133881[/C][/ROW]
[ROW][C]14[/C][C]66.28[/C][C]66.2832698205607[/C][C]-0.00326982056074598[/C][/ROW]
[ROW][C]15[/C][C]66.26[/C][C]66.2829474789823[/C][C]-0.0229474789822746[/C][/ROW]
[ROW][C]16[/C][C]66.13[/C][C]66.2606852977831[/C][C]-0.130685297783131[/C][/ROW]
[ROW][C]17[/C][C]65.86[/C][C]66.1178022345115[/C][C]-0.257802234511544[/C][/ROW]
[ROW][C]18[/C][C]65.9[/C][C]65.8223878799124[/C][C]0.0776121200876503[/C][/ROW]
[ROW][C]19[/C][C]65.94[/C][C]65.8700389460284[/C][C]0.0699610539716247[/C][/ROW]
[ROW][C]20[/C][C]65.94[/C][C]65.9169357638047[/C][C]0.0230642361952675[/C][/ROW]
[ROW][C]21[/C][C]65.91[/C][C]65.9192094550252[/C][C]-0.0092094550252142[/C][/ROW]
[ROW][C]22[/C][C]65.95[/C][C]65.8883015794355[/C][C]0.0616984205644684[/C][/ROW]
[ROW][C]23[/C][C]65.91[/C][C]65.9343838600698[/C][C]-0.0243838600697899[/C][/ROW]
[ROW][C]24[/C][C]66.08[/C][C]65.8919800792512[/C][C]0.188019920748815[/C][/ROW]
[ROW][C]25[/C][C]66.47[/C][C]66.0805152364296[/C][C]0.38948476357038[/C][/ROW]
[ROW][C]26[/C][C]66.47[/C][C]66.5089109621731[/C][C]-0.0389109621731194[/C][/ROW]
[ROW][C]27[/C][C]66.56[/C][C]66.5050750877776[/C][C]0.0549249122223756[/C][/ROW]
[ROW][C]28[/C][C]66.78[/C][C]66.6004896304335[/C][C]0.179510369566472[/C][/ROW]
[ROW][C]29[/C][C]67.08[/C][C]66.8381859091141[/C][C]0.241814090885882[/C][/ROW]
[ROW][C]30[/C][C]67.28[/C][C]67.1620241394712[/C][C]0.117975860528801[/C][/ROW]
[ROW][C]31[/C][C]67.27[/C][C]67.3736542960496[/C][C]-0.103654296049584[/C][/ROW]
[ROW][C]32[/C][C]67.27[/C][C]67.3534359709814[/C][C]-0.0834359709814265[/C][/ROW]
[ROW][C]33[/C][C]67.26[/C][C]67.3452107848931[/C][C]-0.0852107848930643[/C][/ROW]
[ROW][C]34[/C][C]67.37[/C][C]67.3268106362014[/C][C]0.0431893637986178[/C][/ROW]
[ROW][C]35[/C][C]67.5[/C][C]67.4410682789195[/C][C]0.0589317210804552[/C][/ROW]
[ROW][C]36[/C][C]67.63[/C][C]67.5768778160615[/C][C]0.0531221839384841[/C][/ROW]
[ROW][C]37[/C][C]67.64[/C][C]67.7121146442925[/C][C]-0.0721146442924834[/C][/ROW]
[ROW][C]38[/C][C]67.64[/C][C]67.7150055238253[/C][C]-0.0750055238253253[/C][/ROW]
[ROW][C]39[/C][C]67.71[/C][C]67.7076114180954[/C][C]0.00238858190461144[/C][/ROW]
[ROW][C]40[/C][C]67.87[/C][C]67.7778468864482[/C][C]0.0921531135518165[/C][/ROW]
[ROW][C]41[/C][C]67.93[/C][C]67.9469314155628[/C][C]-0.0169314155627802[/C][/ROW]
[ROW][C]42[/C][C]68.33[/C][C]68.0052623028036[/C][C]0.324737697196426[/C][/ROW]
[ROW][C]43[/C][C]68.39[/C][C]68.4372752099218[/C][C]-0.0472752099217502[/C][/ROW]
[ROW][C]44[/C][C]68.39[/C][C]68.4926147811594[/C][C]-0.102614781159446[/C][/ROW]
[ROW][C]45[/C][C]68.58[/C][C]68.4824989323172[/C][C]0.0975010676827708[/C][/ROW]
[ROW][C]46[/C][C]68.44[/C][C]68.682110667113[/C][C]-0.242110667113025[/C][/ROW]
[ROW][C]47[/C][C]68.49[/C][C]68.5182432000295[/C][C]-0.0282432000295216[/C][/ROW]
[ROW][C]48[/C][C]68.52[/C][C]68.5654589623291[/C][C]-0.0454589623291497[/C][/ROW]
[ROW][C]49[/C][C]68.54[/C][C]68.5909775807363[/C][C]-0.0509775807362587[/C][/ROW]
[ROW][C]50[/C][C]68.54[/C][C]68.6059521692386[/C][C]-0.0659521692385852[/C][/ROW]
[ROW][C]51[/C][C]68.54[/C][C]68.5994505505897[/C][C]-0.0594505505897303[/C][/ROW]
[ROW][C]52[/C][C]68.62[/C][C]68.5935898668115[/C][C]0.0264101331885342[/C][/ROW]
[ROW][C]53[/C][C]68.75[/C][C]68.6761933992872[/C][C]0.073806600712814[/C][/ROW]
[ROW][C]54[/C][C]68.71[/C][C]68.8134693141986[/C][C]-0.103469314198605[/C][/ROW]
[ROW][C]55[/C][C]68.72[/C][C]68.7632692247922[/C][C]-0.0432692247922262[/C][/ROW]
[ROW][C]56[/C][C]68.72[/C][C]68.7690037093122[/C][C]-0.0490037093121742[/C][/ROW]
[ROW][C]57[/C][C]68.72[/C][C]68.7641728836698[/C][C]-0.0441728836698161[/C][/ROW]
[ROW][C]58[/C][C]68.92[/C][C]68.7598182847604[/C][C]0.160181715239631[/C][/ROW]
[ROW][C]59[/C][C]68.9[/C][C]68.9756091289287[/C][C]-0.0756091289286616[/C][/ROW]
[ROW][C]60[/C][C]69.12[/C][C]68.9481555193152[/C][C]0.171844480684811[/C][/ROW]
[ROW][C]61[/C][C]69.09[/C][C]69.1850960884158[/C][C]-0.0950960884158292[/C][/ROW]
[ROW][C]62[/C][C]69.09[/C][C]69.1457214384382[/C][C]-0.0557214384381837[/C][/ROW]
[ROW][C]63[/C][C]69.1[/C][C]69.1402283735781[/C][C]-0.0402283735781168[/C][/ROW]
[ROW][C]64[/C][C]69.16[/C][C]69.1462626276915[/C][C]0.0137373723084693[/C][/ROW]
[ROW][C]65[/C][C]68.83[/C][C]69.207616869061[/C][C]-0.377616869060972[/C][/ROW]
[ROW][C]66[/C][C]68.52[/C][C]68.8403910900403[/C][C]-0.320391090040332[/C][/ROW]
[ROW][C]67[/C][C]68.53[/C][C]68.4988066750016[/C][C]0.0311933249983554[/C][/ROW]
[ROW][C]68[/C][C]68.53[/C][C]68.5118817384282[/C][C]0.0181182615717717[/C][/ROW]
[ROW][C]69[/C][C]68.51[/C][C]68.5136678514353[/C][C]-0.00366785143526727[/C][/ROW]
[ROW][C]70[/C][C]68.38[/C][C]68.4933062716485[/C][C]-0.113306271648469[/C][/ROW]
[ROW][C]71[/C][C]68.44[/C][C]68.3521364469515[/C][C]0.0878635530485354[/C][/ROW]
[ROW][C]72[/C][C]68.41[/C][C]68.4207981076921[/C][C]-0.0107981076921249[/C][/ROW]
[ROW][C]73[/C][C]68.42[/C][C]68.3897336214265[/C][C]0.0302663785735149[/C][/ROW]
[ROW][C]74[/C][C]68.42[/C][C]68.4027173057183[/C][C]0.0172826942817181[/C][/ROW]
[ROW][C]75[/C][C]68.45[/C][C]68.4044210478202[/C][C]0.0455789521798096[/C][/ROW]
[ROW][C]76[/C][C]68.63[/C][C]68.4389142581104[/C][C]0.191085741889552[/C][/ROW]
[ROW][C]77[/C][C]68.84[/C][C]68.6377516464381[/C][C]0.202248353561899[/C][/ROW]
[ROW][C]78[/C][C]68.72[/C][C]68.8676894541312[/C][C]-0.147689454131154[/C][/ROW]
[ROW][C]79[/C][C]68.37[/C][C]68.7331301072544[/C][C]-0.363130107254406[/C][/ROW]
[ROW][C]80[/C][C]68.37[/C][C]68.3473324450313[/C][C]0.0226675549687059[/C][/ROW]
[ROW][C]81[/C][C]68.47[/C][C]68.3495670310928[/C][C]0.120432968907167[/C][/ROW]
[ROW][C]82[/C][C]68.69[/C][C]68.4614394114197[/C][C]0.228560588580294[/C][/ROW]
[ROW][C]83[/C][C]68.46[/C][C]68.703971100707[/C][C]-0.243971100707[/C][/ROW]
[ROW][C]84[/C][C]68.17[/C][C]68.449920230562[/C][C]-0.279920230561999[/C][/ROW]
[ROW][C]85[/C][C]68.17[/C][C]68.1323254658678[/C][C]0.037674534132222[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40526&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40526&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	66.2	66.2	0
4	66.08	66.2	-0.120000000000005
5	66.31	66.0681703021012	0.241829697898794
6	66.39	66.3220100710104	0.0679899289896326
7	66.37	66.4087125736779	-0.0387125736779268
8	66.23	66.3848962565821	-0.154896256582134
9	66.27	66.2296264572403	0.0403735427596814
10	66.27	66.2736065140232	-0.00360651402323242
11	66.27	66.2732509809285	-0.00325098092854148
12	66.28	66.2729304965764	0.00706950342362234
13	66.28	66.2836274139913	-0.00362741399133881
14	66.28	66.2832698205607	-0.00326982056074598
15	66.26	66.2829474789823	-0.0229474789822746
16	66.13	66.2606852977831	-0.130685297783131
17	65.86	66.1178022345115	-0.257802234511544
18	65.9	65.8223878799124	0.0776121200876503
19	65.94	65.8700389460284	0.0699610539716247
20	65.94	65.9169357638047	0.0230642361952675
21	65.91	65.9192094550252	-0.0092094550252142
22	65.95	65.8883015794355	0.0616984205644684
23	65.91	65.9343838600698	-0.0243838600697899
24	66.08	65.8919800792512	0.188019920748815
25	66.47	66.0805152364296	0.38948476357038
26	66.47	66.5089109621731	-0.0389109621731194
27	66.56	66.5050750877776	0.0549249122223756
28	66.78	66.6004896304335	0.179510369566472
29	67.08	66.8381859091141	0.241814090885882
30	67.28	67.1620241394712	0.117975860528801
31	67.27	67.3736542960496	-0.103654296049584
32	67.27	67.3534359709814	-0.0834359709814265
33	67.26	67.3452107848931	-0.0852107848930643
34	67.37	67.3268106362014	0.0431893637986178
35	67.5	67.4410682789195	0.0589317210804552
36	67.63	67.5768778160615	0.0531221839384841
37	67.64	67.7121146442925	-0.0721146442924834
38	67.64	67.7150055238253	-0.0750055238253253
39	67.71	67.7076114180954	0.00238858190461144
40	67.87	67.7778468864482	0.0921531135518165
41	67.93	67.9469314155628	-0.0169314155627802
42	68.33	68.0052623028036	0.324737697196426
43	68.39	68.4372752099218	-0.0472752099217502
44	68.39	68.4926147811594	-0.102614781159446
45	68.58	68.4824989323172	0.0975010676827708
46	68.44	68.682110667113	-0.242110667113025
47	68.49	68.5182432000295	-0.0282432000295216
48	68.52	68.5654589623291	-0.0454589623291497
49	68.54	68.5909775807363	-0.0509775807362587
50	68.54	68.6059521692386	-0.0659521692385852
51	68.54	68.5994505505897	-0.0594505505897303
52	68.62	68.5935898668115	0.0264101331885342
53	68.75	68.6761933992872	0.073806600712814
54	68.71	68.8134693141986	-0.103469314198605
55	68.72	68.7632692247922	-0.0432692247922262
56	68.72	68.7690037093122	-0.0490037093121742
57	68.72	68.7641728836698	-0.0441728836698161
58	68.92	68.7598182847604	0.160181715239631
59	68.9	68.9756091289287	-0.0756091289286616
60	69.12	68.9481555193152	0.171844480684811
61	69.09	69.1850960884158	-0.0950960884158292
62	69.09	69.1457214384382	-0.0557214384381837
63	69.1	69.1402283735781	-0.0402283735781168
64	69.16	69.1462626276915	0.0137373723084693
65	68.83	69.207616869061	-0.377616869060972
66	68.52	68.8403910900403	-0.320391090040332
67	68.53	68.4988066750016	0.0311933249983554
68	68.53	68.5118817384282	0.0181182615717717
69	68.51	68.5136678514353	-0.00366785143526727
70	68.38	68.4933062716485	-0.113306271648469
71	68.44	68.3521364469515	0.0878635530485354
72	68.41	68.4207981076921	-0.0107981076921249
73	68.42	68.3897336214265	0.0302663785735149
74	68.42	68.4027173057183	0.0172826942817181
75	68.45	68.4044210478202	0.0455789521798096
76	68.63	68.4389142581104	0.191085741889552
77	68.84	68.6377516464381	0.202248353561899
78	68.72	68.8676894541312	-0.147689454131154
79	68.37	68.7331301072544	-0.363130107254406
80	68.37	68.3473324450313	0.0226675549687059
81	68.47	68.3495670310928	0.120432968907167
82	68.69	68.4614394114197	0.228560588580294
83	68.46	68.703971100707	-0.243971100707
84	68.17	68.449920230562	-0.279920230561999
85	68.17	68.1323254658678	0.037674534132222

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
86	68.1360394521783	67.8658741765095	68.4062047278471
87	68.1020789043566	67.7007329689576	68.5034248397555
88	68.0681183565349	67.5526704964185	68.5835662166512
89	68.0341578087131	67.411075365103	68.6572402523233
90	68.0001972608914	67.2720949944361	68.7282995273468
91	67.9662367130697	67.1338854178875	68.798588008252
92	67.932276165248	66.9954316309181	68.8691206995779
93	67.8983156174263	66.8561263042013	68.9405049306513
94	67.8643550696046	66.7155861749493	69.0131239642599
95	67.8303945217829	66.5735609794505	69.0872280641152
96	67.7964339739612	66.4298839567796	69.1629839911427
97	67.7624734261395	66.2844430449377	69.2405038073412

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 68.1360394521783 & 67.8658741765095 & 68.4062047278471 \tabularnewline
87 & 68.1020789043566 & 67.7007329689576 & 68.5034248397555 \tabularnewline
88 & 68.0681183565349 & 67.5526704964185 & 68.5835662166512 \tabularnewline
89 & 68.0341578087131 & 67.411075365103 & 68.6572402523233 \tabularnewline
90 & 68.0001972608914 & 67.2720949944361 & 68.7282995273468 \tabularnewline
91 & 67.9662367130697 & 67.1338854178875 & 68.798588008252 \tabularnewline
92 & 67.932276165248 & 66.9954316309181 & 68.8691206995779 \tabularnewline
93 & 67.8983156174263 & 66.8561263042013 & 68.9405049306513 \tabularnewline
94 & 67.8643550696046 & 66.7155861749493 & 69.0131239642599 \tabularnewline
95 & 67.8303945217829 & 66.5735609794505 & 69.0872280641152 \tabularnewline
96 & 67.7964339739612 & 66.4298839567796 & 69.1629839911427 \tabularnewline
97 & 67.7624734261395 & 66.2844430449377 & 69.2405038073412 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40526&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]86[/C][C]68.1360394521783[/C][C]67.8658741765095[/C][C]68.4062047278471[/C][/ROW]
[ROW][C]87[/C][C]68.1020789043566[/C][C]67.7007329689576[/C][C]68.5034248397555[/C][/ROW]
[ROW][C]88[/C][C]68.0681183565349[/C][C]67.5526704964185[/C][C]68.5835662166512[/C][/ROW]
[ROW][C]89[/C][C]68.0341578087131[/C][C]67.411075365103[/C][C]68.6572402523233[/C][/ROW]
[ROW][C]90[/C][C]68.0001972608914[/C][C]67.2720949944361[/C][C]68.7282995273468[/C][/ROW]
[ROW][C]91[/C][C]67.9662367130697[/C][C]67.1338854178875[/C][C]68.798588008252[/C][/ROW]
[ROW][C]92[/C][C]67.932276165248[/C][C]66.9954316309181[/C][C]68.8691206995779[/C][/ROW]
[ROW][C]93[/C][C]67.8983156174263[/C][C]66.8561263042013[/C][C]68.9405049306513[/C][/ROW]
[ROW][C]94[/C][C]67.8643550696046[/C][C]66.7155861749493[/C][C]69.0131239642599[/C][/ROW]
[ROW][C]95[/C][C]67.8303945217829[/C][C]66.5735609794505[/C][C]69.0872280641152[/C][/ROW]
[ROW][C]96[/C][C]67.7964339739612[/C][C]66.4298839567796[/C][C]69.1629839911427[/C][/ROW]
[ROW][C]97[/C][C]67.7624734261395[/C][C]66.2844430449377[/C][C]69.2405038073412[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40526&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40526&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
86	68.1360394521783	67.8658741765095	68.4062047278471
87	68.1020789043566	67.7007329689576	68.5034248397555
88	68.0681183565349	67.5526704964185	68.5835662166512
89	68.0341578087131	67.411075365103	68.6572402523233
90	68.0001972608914	67.2720949944361	68.7282995273468
91	67.9662367130697	67.1338854178875	68.798588008252
92	67.932276165248	66.9954316309181	68.8691206995779
93	67.8983156174263	66.8561263042013	68.9405049306513
94	67.8643550696046	66.7155861749493	69.0131239642599
95	67.8303945217829	66.5735609794505	69.0872280641152
96	67.7964339739612	66.4298839567796	69.1629839911427
97	67.7624734261395	66.2844430449377	69.2405038073412

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code