Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 26 Jan 2009 13:41:29 -0700

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/Jan/26/t123300255651sz4zgemz02vtg.htm/, Retrieved Sun, 05 May 2024 20:33:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36975, Retrieved Sun, 05 May 2024 20:33:58 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

135

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] [0ebe94bd950a0b1969e8ed777006e521] [Current]
-           [Exponential Smoothing] [Maxime Jonckheere...] [2009-05-27 22:07:59] [74be16979710d4c4e7c6647856088456] 

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36975&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36975&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36975&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	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0985808158219716
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0985808158219716 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36975&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]0.0985808158219716[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36975&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36975&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	0.0985808158219716
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	66.0681703021014	0.241829697898638
6	66.39	66.3220100710102	0.0679899289898032
7	66.37	66.4087125736777	-0.0387125736776852
8	66.23	66.384896256582	-0.154896256581978
9	66.27	66.2296264572404	0.0403735427596388
10	66.27	66.2736065140232	-0.00360651402321821
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	66.2606852977832	-0.130685297783160
17	65.86	66.1178022345117	-0.257802234511743
18	65.9	65.8223878799129	0.0776121200871529
19	65.94	65.8700389460287	0.0699610539712694
20	65.94	65.916935763805	0.0230642361950260
21	65.91	65.9192094550254	-0.00920945502538473
22	65.95	65.8883015794357	0.0616984205642979
23	65.91	65.9343838600699	-0.0243838600698751
24	66.08	65.8919800792513	0.188019920748715
25	66.47	66.0805152364295	0.389484763570522
26	66.47	66.5089109621725	-0.0389109621724941
27	66.56	66.5050750877771	0.0549249122229014
28	66.78	66.600489630433	0.179510369567012
29	67.08	66.8381859091134	0.241814090886592
30	67.28	67.1620241394703	0.117975860529739
31	67.27	67.3736542960486	-0.103654296048589
32	67.27	67.3534359709807	-0.0834359709806591
33	67.26	67.3452107848925	-0.0852107848924817
34	67.37	67.326810636201	0.0431893637990441
35	67.5	67.4410682789191	0.0589317210808957
36	67.63	67.576877816061	0.0531221839389531
37	67.64	67.712114644292	-0.072114644291986
38	67.64	67.715005523825	-0.07500552382497
39	67.71	67.7076114180952	0.00238858190483882
40	67.87	67.777846886448	0.0921531135520155
41	67.93	67.9469314155625	-0.0169314155624818
42	68.33	68.0052623028033	0.324737697196682
43	68.39	68.4372752099211	-0.0472752099211107
44	68.39	68.4926147811589	-0.102614781158934
45	68.58	68.4824989323169	0.0975010676831118
46	68.44	68.6821106671126	-0.242110667112613
47	68.49	68.5182432000294	-0.0282432000294506
48	68.52	68.5654589623291	-0.0454589623291213
49	68.54	68.5909775807363	-0.0509775807362871
50	68.54	68.6059521692387	-0.0659521692386846
51	68.54	68.5994505505899	-0.0594505505899008
52	68.62	68.5935898668117	0.0264101331883211
53	68.75	68.6761933992874	0.0738066007126434
54	68.71	68.8134693141987	-0.103469314198662
55	68.72	68.7632692247924	-0.0432692247924109
56	68.72	68.7690037093124	-0.0490037093123874
57	68.72	68.76417288367	-0.0441728836700719
58	68.92	68.7598182847607	0.160181715239332
59	68.9	68.9756091289287	-0.0756091289287184
60	69.12	68.9481555193153	0.171844480684655
61	69.09	69.1850960884157	-0.0950960884157439
62	69.09	69.1457214384382	-0.0557214384382405
63	69.1	69.1402283735782	-0.0402283735782305
64	69.16	69.1462626276917	0.0137373723083130
65	68.83	69.2076168690611	-0.377616869061086
66	68.52	68.8403910900409	-0.320391090040914
67	68.53	68.4988066750026	0.0311933249974174
68	68.53	68.511881738429	0.0181182615709616
69	68.51	68.513667851436	-0.0036678514359636
70	68.38	68.4933062716491	-0.113306271649108
71	68.44	68.3521364469522	0.0878635530478107
72	68.41	68.4207981076927	-0.0107981076926649
73	68.42	68.389733621427	0.0302663785730175
74	68.42	68.4027173057187	0.0172826942813060
75	68.45	68.4044210478205	0.0455789521794543
76	68.63	68.4389142581107	0.191085741889296
77	68.84	68.6377516464381	0.202248353561913
78	68.72	68.8676894541309	-0.147689454130884
79	68.37	68.7331301072544	-0.363130107254349
80	68.37	68.3473324450317	0.0226675549682938
81	68.47	68.3495670310932	0.120432968906826
82	68.69	68.4614394114199	0.228560588580137
83	68.46	68.7039711007068	-0.243971100706844
84	68.17	68.4499202305622	-0.279920230562169
85	68.17	68.1323254658683	0.0376745341317104

\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 & 66.0681703021014 & 0.241829697898638 \tabularnewline
6 & 66.39 & 66.3220100710102 & 0.0679899289898032 \tabularnewline
7 & 66.37 & 66.4087125736777 & -0.0387125736776852 \tabularnewline
8 & 66.23 & 66.384896256582 & -0.154896256581978 \tabularnewline
9 & 66.27 & 66.2296264572404 & 0.0403735427596388 \tabularnewline
10 & 66.27 & 66.2736065140232 & -0.00360651402321821 \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 & 66.2606852977832 & -0.130685297783160 \tabularnewline
17 & 65.86 & 66.1178022345117 & -0.257802234511743 \tabularnewline
18 & 65.9 & 65.8223878799129 & 0.0776121200871529 \tabularnewline
19 & 65.94 & 65.8700389460287 & 0.0699610539712694 \tabularnewline
20 & 65.94 & 65.916935763805 & 0.0230642361950260 \tabularnewline
21 & 65.91 & 65.9192094550254 & -0.00920945502538473 \tabularnewline
22 & 65.95 & 65.8883015794357 & 0.0616984205642979 \tabularnewline
23 & 65.91 & 65.9343838600699 & -0.0243838600698751 \tabularnewline
24 & 66.08 & 65.8919800792513 & 0.188019920748715 \tabularnewline
25 & 66.47 & 66.0805152364295 & 0.389484763570522 \tabularnewline
26 & 66.47 & 66.5089109621725 & -0.0389109621724941 \tabularnewline
27 & 66.56 & 66.5050750877771 & 0.0549249122229014 \tabularnewline
28 & 66.78 & 66.600489630433 & 0.179510369567012 \tabularnewline
29 & 67.08 & 66.8381859091134 & 0.241814090886592 \tabularnewline
30 & 67.28 & 67.1620241394703 & 0.117975860529739 \tabularnewline
31 & 67.27 & 67.3736542960486 & -0.103654296048589 \tabularnewline
32 & 67.27 & 67.3534359709807 & -0.0834359709806591 \tabularnewline
33 & 67.26 & 67.3452107848925 & -0.0852107848924817 \tabularnewline
34 & 67.37 & 67.326810636201 & 0.0431893637990441 \tabularnewline
35 & 67.5 & 67.4410682789191 & 0.0589317210808957 \tabularnewline
36 & 67.63 & 67.576877816061 & 0.0531221839389531 \tabularnewline
37 & 67.64 & 67.712114644292 & -0.072114644291986 \tabularnewline
38 & 67.64 & 67.715005523825 & -0.07500552382497 \tabularnewline
39 & 67.71 & 67.7076114180952 & 0.00238858190483882 \tabularnewline
40 & 67.87 & 67.777846886448 & 0.0921531135520155 \tabularnewline
41 & 67.93 & 67.9469314155625 & -0.0169314155624818 \tabularnewline
42 & 68.33 & 68.0052623028033 & 0.324737697196682 \tabularnewline
43 & 68.39 & 68.4372752099211 & -0.0472752099211107 \tabularnewline
44 & 68.39 & 68.4926147811589 & -0.102614781158934 \tabularnewline
45 & 68.58 & 68.4824989323169 & 0.0975010676831118 \tabularnewline
46 & 68.44 & 68.6821106671126 & -0.242110667112613 \tabularnewline
47 & 68.49 & 68.5182432000294 & -0.0282432000294506 \tabularnewline
48 & 68.52 & 68.5654589623291 & -0.0454589623291213 \tabularnewline
49 & 68.54 & 68.5909775807363 & -0.0509775807362871 \tabularnewline
50 & 68.54 & 68.6059521692387 & -0.0659521692386846 \tabularnewline
51 & 68.54 & 68.5994505505899 & -0.0594505505899008 \tabularnewline
52 & 68.62 & 68.5935898668117 & 0.0264101331883211 \tabularnewline
53 & 68.75 & 68.6761933992874 & 0.0738066007126434 \tabularnewline
54 & 68.71 & 68.8134693141987 & -0.103469314198662 \tabularnewline
55 & 68.72 & 68.7632692247924 & -0.0432692247924109 \tabularnewline
56 & 68.72 & 68.7690037093124 & -0.0490037093123874 \tabularnewline
57 & 68.72 & 68.76417288367 & -0.0441728836700719 \tabularnewline
58 & 68.92 & 68.7598182847607 & 0.160181715239332 \tabularnewline
59 & 68.9 & 68.9756091289287 & -0.0756091289287184 \tabularnewline
60 & 69.12 & 68.9481555193153 & 0.171844480684655 \tabularnewline
61 & 69.09 & 69.1850960884157 & -0.0950960884157439 \tabularnewline
62 & 69.09 & 69.1457214384382 & -0.0557214384382405 \tabularnewline
63 & 69.1 & 69.1402283735782 & -0.0402283735782305 \tabularnewline
64 & 69.16 & 69.1462626276917 & 0.0137373723083130 \tabularnewline
65 & 68.83 & 69.2076168690611 & -0.377616869061086 \tabularnewline
66 & 68.52 & 68.8403910900409 & -0.320391090040914 \tabularnewline
67 & 68.53 & 68.4988066750026 & 0.0311933249974174 \tabularnewline
68 & 68.53 & 68.511881738429 & 0.0181182615709616 \tabularnewline
69 & 68.51 & 68.513667851436 & -0.0036678514359636 \tabularnewline
70 & 68.38 & 68.4933062716491 & -0.113306271649108 \tabularnewline
71 & 68.44 & 68.3521364469522 & 0.0878635530478107 \tabularnewline
72 & 68.41 & 68.4207981076927 & -0.0107981076926649 \tabularnewline
73 & 68.42 & 68.389733621427 & 0.0302663785730175 \tabularnewline
74 & 68.42 & 68.4027173057187 & 0.0172826942813060 \tabularnewline
75 & 68.45 & 68.4044210478205 & 0.0455789521794543 \tabularnewline
76 & 68.63 & 68.4389142581107 & 0.191085741889296 \tabularnewline
77 & 68.84 & 68.6377516464381 & 0.202248353561913 \tabularnewline
78 & 68.72 & 68.8676894541309 & -0.147689454130884 \tabularnewline
79 & 68.37 & 68.7331301072544 & -0.363130107254349 \tabularnewline
80 & 68.37 & 68.3473324450317 & 0.0226675549682938 \tabularnewline
81 & 68.47 & 68.3495670310932 & 0.120432968906826 \tabularnewline
82 & 68.69 & 68.4614394114199 & 0.228560588580137 \tabularnewline
83 & 68.46 & 68.7039711007068 & -0.243971100706844 \tabularnewline
84 & 68.17 & 68.4499202305622 & -0.279920230562169 \tabularnewline
85 & 68.17 & 68.1323254658683 & 0.0376745341317104 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36975&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]66.0681703021014[/C][C]0.241829697898638[/C][/ROW]
[ROW][C]6[/C][C]66.39[/C][C]66.3220100710102[/C][C]0.0679899289898032[/C][/ROW]
[ROW][C]7[/C][C]66.37[/C][C]66.4087125736777[/C][C]-0.0387125736776852[/C][/ROW]
[ROW][C]8[/C][C]66.23[/C][C]66.384896256582[/C][C]-0.154896256581978[/C][/ROW]
[ROW][C]9[/C][C]66.27[/C][C]66.2296264572404[/C][C]0.0403735427596388[/C][/ROW]
[ROW][C]10[/C][C]66.27[/C][C]66.2736065140232[/C][C]-0.00360651402321821[/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]66.2606852977832[/C][C]-0.130685297783160[/C][/ROW]
[ROW][C]17[/C][C]65.86[/C][C]66.1178022345117[/C][C]-0.257802234511743[/C][/ROW]
[ROW][C]18[/C][C]65.9[/C][C]65.8223878799129[/C][C]0.0776121200871529[/C][/ROW]
[ROW][C]19[/C][C]65.94[/C][C]65.8700389460287[/C][C]0.0699610539712694[/C][/ROW]
[ROW][C]20[/C][C]65.94[/C][C]65.916935763805[/C][C]0.0230642361950260[/C][/ROW]
[ROW][C]21[/C][C]65.91[/C][C]65.9192094550254[/C][C]-0.00920945502538473[/C][/ROW]
[ROW][C]22[/C][C]65.95[/C][C]65.8883015794357[/C][C]0.0616984205642979[/C][/ROW]
[ROW][C]23[/C][C]65.91[/C][C]65.9343838600699[/C][C]-0.0243838600698751[/C][/ROW]
[ROW][C]24[/C][C]66.08[/C][C]65.8919800792513[/C][C]0.188019920748715[/C][/ROW]
[ROW][C]25[/C][C]66.47[/C][C]66.0805152364295[/C][C]0.389484763570522[/C][/ROW]
[ROW][C]26[/C][C]66.47[/C][C]66.5089109621725[/C][C]-0.0389109621724941[/C][/ROW]
[ROW][C]27[/C][C]66.56[/C][C]66.5050750877771[/C][C]0.0549249122229014[/C][/ROW]
[ROW][C]28[/C][C]66.78[/C][C]66.600489630433[/C][C]0.179510369567012[/C][/ROW]
[ROW][C]29[/C][C]67.08[/C][C]66.8381859091134[/C][C]0.241814090886592[/C][/ROW]
[ROW][C]30[/C][C]67.28[/C][C]67.1620241394703[/C][C]0.117975860529739[/C][/ROW]
[ROW][C]31[/C][C]67.27[/C][C]67.3736542960486[/C][C]-0.103654296048589[/C][/ROW]
[ROW][C]32[/C][C]67.27[/C][C]67.3534359709807[/C][C]-0.0834359709806591[/C][/ROW]
[ROW][C]33[/C][C]67.26[/C][C]67.3452107848925[/C][C]-0.0852107848924817[/C][/ROW]
[ROW][C]34[/C][C]67.37[/C][C]67.326810636201[/C][C]0.0431893637990441[/C][/ROW]
[ROW][C]35[/C][C]67.5[/C][C]67.4410682789191[/C][C]0.0589317210808957[/C][/ROW]
[ROW][C]36[/C][C]67.63[/C][C]67.576877816061[/C][C]0.0531221839389531[/C][/ROW]
[ROW][C]37[/C][C]67.64[/C][C]67.712114644292[/C][C]-0.072114644291986[/C][/ROW]
[ROW][C]38[/C][C]67.64[/C][C]67.715005523825[/C][C]-0.07500552382497[/C][/ROW]
[ROW][C]39[/C][C]67.71[/C][C]67.7076114180952[/C][C]0.00238858190483882[/C][/ROW]
[ROW][C]40[/C][C]67.87[/C][C]67.777846886448[/C][C]0.0921531135520155[/C][/ROW]
[ROW][C]41[/C][C]67.93[/C][C]67.9469314155625[/C][C]-0.0169314155624818[/C][/ROW]
[ROW][C]42[/C][C]68.33[/C][C]68.0052623028033[/C][C]0.324737697196682[/C][/ROW]
[ROW][C]43[/C][C]68.39[/C][C]68.4372752099211[/C][C]-0.0472752099211107[/C][/ROW]
[ROW][C]44[/C][C]68.39[/C][C]68.4926147811589[/C][C]-0.102614781158934[/C][/ROW]
[ROW][C]45[/C][C]68.58[/C][C]68.4824989323169[/C][C]0.0975010676831118[/C][/ROW]
[ROW][C]46[/C][C]68.44[/C][C]68.6821106671126[/C][C]-0.242110667112613[/C][/ROW]
[ROW][C]47[/C][C]68.49[/C][C]68.5182432000294[/C][C]-0.0282432000294506[/C][/ROW]
[ROW][C]48[/C][C]68.52[/C][C]68.5654589623291[/C][C]-0.0454589623291213[/C][/ROW]
[ROW][C]49[/C][C]68.54[/C][C]68.5909775807363[/C][C]-0.0509775807362871[/C][/ROW]
[ROW][C]50[/C][C]68.54[/C][C]68.6059521692387[/C][C]-0.0659521692386846[/C][/ROW]
[ROW][C]51[/C][C]68.54[/C][C]68.5994505505899[/C][C]-0.0594505505899008[/C][/ROW]
[ROW][C]52[/C][C]68.62[/C][C]68.5935898668117[/C][C]0.0264101331883211[/C][/ROW]
[ROW][C]53[/C][C]68.75[/C][C]68.6761933992874[/C][C]0.0738066007126434[/C][/ROW]
[ROW][C]54[/C][C]68.71[/C][C]68.8134693141987[/C][C]-0.103469314198662[/C][/ROW]
[ROW][C]55[/C][C]68.72[/C][C]68.7632692247924[/C][C]-0.0432692247924109[/C][/ROW]
[ROW][C]56[/C][C]68.72[/C][C]68.7690037093124[/C][C]-0.0490037093123874[/C][/ROW]
[ROW][C]57[/C][C]68.72[/C][C]68.76417288367[/C][C]-0.0441728836700719[/C][/ROW]
[ROW][C]58[/C][C]68.92[/C][C]68.7598182847607[/C][C]0.160181715239332[/C][/ROW]
[ROW][C]59[/C][C]68.9[/C][C]68.9756091289287[/C][C]-0.0756091289287184[/C][/ROW]
[ROW][C]60[/C][C]69.12[/C][C]68.9481555193153[/C][C]0.171844480684655[/C][/ROW]
[ROW][C]61[/C][C]69.09[/C][C]69.1850960884157[/C][C]-0.0950960884157439[/C][/ROW]
[ROW][C]62[/C][C]69.09[/C][C]69.1457214384382[/C][C]-0.0557214384382405[/C][/ROW]
[ROW][C]63[/C][C]69.1[/C][C]69.1402283735782[/C][C]-0.0402283735782305[/C][/ROW]
[ROW][C]64[/C][C]69.16[/C][C]69.1462626276917[/C][C]0.0137373723083130[/C][/ROW]
[ROW][C]65[/C][C]68.83[/C][C]69.2076168690611[/C][C]-0.377616869061086[/C][/ROW]
[ROW][C]66[/C][C]68.52[/C][C]68.8403910900409[/C][C]-0.320391090040914[/C][/ROW]
[ROW][C]67[/C][C]68.53[/C][C]68.4988066750026[/C][C]0.0311933249974174[/C][/ROW]
[ROW][C]68[/C][C]68.53[/C][C]68.511881738429[/C][C]0.0181182615709616[/C][/ROW]
[ROW][C]69[/C][C]68.51[/C][C]68.513667851436[/C][C]-0.0036678514359636[/C][/ROW]
[ROW][C]70[/C][C]68.38[/C][C]68.4933062716491[/C][C]-0.113306271649108[/C][/ROW]
[ROW][C]71[/C][C]68.44[/C][C]68.3521364469522[/C][C]0.0878635530478107[/C][/ROW]
[ROW][C]72[/C][C]68.41[/C][C]68.4207981076927[/C][C]-0.0107981076926649[/C][/ROW]
[ROW][C]73[/C][C]68.42[/C][C]68.389733621427[/C][C]0.0302663785730175[/C][/ROW]
[ROW][C]74[/C][C]68.42[/C][C]68.4027173057187[/C][C]0.0172826942813060[/C][/ROW]
[ROW][C]75[/C][C]68.45[/C][C]68.4044210478205[/C][C]0.0455789521794543[/C][/ROW]
[ROW][C]76[/C][C]68.63[/C][C]68.4389142581107[/C][C]0.191085741889296[/C][/ROW]
[ROW][C]77[/C][C]68.84[/C][C]68.6377516464381[/C][C]0.202248353561913[/C][/ROW]
[ROW][C]78[/C][C]68.72[/C][C]68.8676894541309[/C][C]-0.147689454130884[/C][/ROW]
[ROW][C]79[/C][C]68.37[/C][C]68.7331301072544[/C][C]-0.363130107254349[/C][/ROW]
[ROW][C]80[/C][C]68.37[/C][C]68.3473324450317[/C][C]0.0226675549682938[/C][/ROW]
[ROW][C]81[/C][C]68.47[/C][C]68.3495670310932[/C][C]0.120432968906826[/C][/ROW]
[ROW][C]82[/C][C]68.69[/C][C]68.4614394114199[/C][C]0.228560588580137[/C][/ROW]
[ROW][C]83[/C][C]68.46[/C][C]68.7039711007068[/C][C]-0.243971100706844[/C][/ROW]
[ROW][C]84[/C][C]68.17[/C][C]68.4499202305622[/C][C]-0.279920230562169[/C][/ROW]
[ROW][C]85[/C][C]68.17[/C][C]68.1323254658683[/C][C]0.0376745341317104[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36975&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36975&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	66.0681703021014	0.241829697898638
6	66.39	66.3220100710102	0.0679899289898032
7	66.37	66.4087125736777	-0.0387125736776852
8	66.23	66.384896256582	-0.154896256581978
9	66.27	66.2296264572404	0.0403735427596388
10	66.27	66.2736065140232	-0.00360651402321821
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	66.2606852977832	-0.130685297783160
17	65.86	66.1178022345117	-0.257802234511743
18	65.9	65.8223878799129	0.0776121200871529
19	65.94	65.8700389460287	0.0699610539712694
20	65.94	65.916935763805	0.0230642361950260
21	65.91	65.9192094550254	-0.00920945502538473
22	65.95	65.8883015794357	0.0616984205642979
23	65.91	65.9343838600699	-0.0243838600698751
24	66.08	65.8919800792513	0.188019920748715
25	66.47	66.0805152364295	0.389484763570522
26	66.47	66.5089109621725	-0.0389109621724941
27	66.56	66.5050750877771	0.0549249122229014
28	66.78	66.600489630433	0.179510369567012
29	67.08	66.8381859091134	0.241814090886592
30	67.28	67.1620241394703	0.117975860529739
31	67.27	67.3736542960486	-0.103654296048589
32	67.27	67.3534359709807	-0.0834359709806591
33	67.26	67.3452107848925	-0.0852107848924817
34	67.37	67.326810636201	0.0431893637990441
35	67.5	67.4410682789191	0.0589317210808957
36	67.63	67.576877816061	0.0531221839389531
37	67.64	67.712114644292	-0.072114644291986
38	67.64	67.715005523825	-0.07500552382497
39	67.71	67.7076114180952	0.00238858190483882
40	67.87	67.777846886448	0.0921531135520155
41	67.93	67.9469314155625	-0.0169314155624818
42	68.33	68.0052623028033	0.324737697196682
43	68.39	68.4372752099211	-0.0472752099211107
44	68.39	68.4926147811589	-0.102614781158934
45	68.58	68.4824989323169	0.0975010676831118
46	68.44	68.6821106671126	-0.242110667112613
47	68.49	68.5182432000294	-0.0282432000294506
48	68.52	68.5654589623291	-0.0454589623291213
49	68.54	68.5909775807363	-0.0509775807362871
50	68.54	68.6059521692387	-0.0659521692386846
51	68.54	68.5994505505899	-0.0594505505899008
52	68.62	68.5935898668117	0.0264101331883211
53	68.75	68.6761933992874	0.0738066007126434
54	68.71	68.8134693141987	-0.103469314198662
55	68.72	68.7632692247924	-0.0432692247924109
56	68.72	68.7690037093124	-0.0490037093123874
57	68.72	68.76417288367	-0.0441728836700719
58	68.92	68.7598182847607	0.160181715239332
59	68.9	68.9756091289287	-0.0756091289287184
60	69.12	68.9481555193153	0.171844480684655
61	69.09	69.1850960884157	-0.0950960884157439
62	69.09	69.1457214384382	-0.0557214384382405
63	69.1	69.1402283735782	-0.0402283735782305
64	69.16	69.1462626276917	0.0137373723083130
65	68.83	69.2076168690611	-0.377616869061086
66	68.52	68.8403910900409	-0.320391090040914
67	68.53	68.4988066750026	0.0311933249974174
68	68.53	68.511881738429	0.0181182615709616
69	68.51	68.513667851436	-0.0036678514359636
70	68.38	68.4933062716491	-0.113306271649108
71	68.44	68.3521364469522	0.0878635530478107
72	68.41	68.4207981076927	-0.0107981076926649
73	68.42	68.389733621427	0.0302663785730175
74	68.42	68.4027173057187	0.0172826942813060
75	68.45	68.4044210478205	0.0455789521794543
76	68.63	68.4389142581107	0.191085741889296
77	68.84	68.6377516464381	0.202248353561913
78	68.72	68.8676894541309	-0.147689454130884
79	68.37	68.7331301072544	-0.363130107254349
80	68.37	68.3473324450317	0.0226675549682938
81	68.47	68.3495670310932	0.120432968906826
82	68.69	68.4614394114199	0.228560588580137
83	68.46	68.7039711007068	-0.243971100706844
84	68.17	68.4499202305622	-0.279920230562169
85	68.17	68.1323254658683	0.0376745341317104

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
86	68.1360394521787	67.86587417651	68.4062047278475
87	68.1020789043574	67.7007329689587	68.5034248397561
88	68.0681183565361	67.5526704964204	68.5835662166518
89	68.0341578087148	67.4110753651058	68.6572402523238
90	68.0001972608935	67.2720949944398	68.7282995273472
91	67.9662367130722	67.1338854178922	68.7985880082522
92	67.9322761652509	66.995431630924	68.8691206995778
93	67.8983156174296	66.8561263042083	68.9405049306509
94	67.8643550696083	66.7155861749575	69.0131239642591
95	67.830394521787	66.57356097946	69.087228064114
96	67.7964339739657	66.4298839567905	69.162983991141
97	67.7624734261444	66.28444304495	69.2405038073389

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 68.1360394521787 & 67.86587417651 & 68.4062047278475 \tabularnewline
87 & 68.1020789043574 & 67.7007329689587 & 68.5034248397561 \tabularnewline
88 & 68.0681183565361 & 67.5526704964204 & 68.5835662166518 \tabularnewline
89 & 68.0341578087148 & 67.4110753651058 & 68.6572402523238 \tabularnewline
90 & 68.0001972608935 & 67.2720949944398 & 68.7282995273472 \tabularnewline
91 & 67.9662367130722 & 67.1338854178922 & 68.7985880082522 \tabularnewline
92 & 67.9322761652509 & 66.995431630924 & 68.8691206995778 \tabularnewline
93 & 67.8983156174296 & 66.8561263042083 & 68.9405049306509 \tabularnewline
94 & 67.8643550696083 & 66.7155861749575 & 69.0131239642591 \tabularnewline
95 & 67.830394521787 & 66.57356097946 & 69.087228064114 \tabularnewline
96 & 67.7964339739657 & 66.4298839567905 & 69.162983991141 \tabularnewline
97 & 67.7624734261444 & 66.28444304495 & 69.2405038073389 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36975&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]68.1360394521787[/C][C]67.86587417651[/C][C]68.4062047278475[/C][/ROW]
[ROW][C]87[/C][C]68.1020789043574[/C][C]67.7007329689587[/C][C]68.5034248397561[/C][/ROW]
[ROW][C]88[/C][C]68.0681183565361[/C][C]67.5526704964204[/C][C]68.5835662166518[/C][/ROW]
[ROW][C]89[/C][C]68.0341578087148[/C][C]67.4110753651058[/C][C]68.6572402523238[/C][/ROW]
[ROW][C]90[/C][C]68.0001972608935[/C][C]67.2720949944398[/C][C]68.7282995273472[/C][/ROW]
[ROW][C]91[/C][C]67.9662367130722[/C][C]67.1338854178922[/C][C]68.7985880082522[/C][/ROW]
[ROW][C]92[/C][C]67.9322761652509[/C][C]66.995431630924[/C][C]68.8691206995778[/C][/ROW]
[ROW][C]93[/C][C]67.8983156174296[/C][C]66.8561263042083[/C][C]68.9405049306509[/C][/ROW]
[ROW][C]94[/C][C]67.8643550696083[/C][C]66.7155861749575[/C][C]69.0131239642591[/C][/ROW]
[ROW][C]95[/C][C]67.830394521787[/C][C]66.57356097946[/C][C]69.087228064114[/C][/ROW]
[ROW][C]96[/C][C]67.7964339739657[/C][C]66.4298839567905[/C][C]69.162983991141[/C][/ROW]
[ROW][C]97[/C][C]67.7624734261444[/C][C]66.28444304495[/C][C]69.2405038073389[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36975&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36975&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	68.1360394521787	67.86587417651	68.4062047278475
87	68.1020789043574	67.7007329689587	68.5034248397561
88	68.0681183565361	67.5526704964204	68.5835662166518
89	68.0341578087148	67.4110753651058	68.6572402523238
90	68.0001972608935	67.2720949944398	68.7282995273472
91	67.9662367130722	67.1338854178922	68.7985880082522
92	67.9322761652509	66.995431630924	68.8691206995778
93	67.8983156174296	66.8561263042083	68.9405049306509
94	67.8643550696083	66.7155861749575	69.0131239642591
95	67.830394521787	66.57356097946	69.087228064114
96	67.7964339739657	66.4298839567905	69.162983991141
97	67.7624734261444	66.28444304495	69.2405038073389

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 ;

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