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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 10 May 2013 07:59:07 -0400

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/2013/May/10/t13681871897eyw1nokinv4icu.htm/, Retrieved Mon, 29 Apr 2024 19:48:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208871, Retrieved Mon, 29 Apr 2024 19:48:03 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

162

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

-       [Exponential Smoothing] [gemiddelde consum...] [2013-05-10 11:59:07] [a5e81fc5b84eaf53b9dc73271fe36a59] [Current]

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Dataseries X:

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Histogram

Boxplots

1,26
1,26
1,28
1,34
1,39
1,47
1,57
1,63
1,72
1,43
1,35
1,41
1,44
1,43
1,43
1,42
1,45
1,51
1,48
1,48
1,45
1,38
1,46
1,45
1,41
1,45
1,47
1,47
1,53
1,56
1,66
1,79
1,78
1,46
1,41
1,43
1,43
1,45
1,35
1,35
1,29
1,29
1,26
1,3
1,3
1,16
1,24
1,15
1,21
1,22
1,17
1,13
1,15
1,2
1,23
1,25
1,38
1,28
1,26
1,25
1,26
1,28
1,31
1,22
1,23
1,36
1,54
1,58
1,44
1,29
1,28
1,23

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' @ 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208871&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208871&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208871&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' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.793820470471754
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.793820470471754 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208871&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]0.793820470471754[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208871&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208871&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	0.793820470471754
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.44	1.39851228632479	0.0414877136752143
14	1.43	1.43071910136126	-0.000719101361260188
15	1.43	1.44692128262837	-0.0169212826283665
16	1.42	1.43609517407268	-0.0160951740726831
17	1.45	1.450091514066	-9.15140659998315e-05
18	1.51	1.50304188697509	0.00695811302490834
19	1.48	1.58117173151147	-0.101171731511472
20	1.48	1.54554922531928	-0.0655492253192784
21	1.45	1.56945459375196	-0.119454593751955
22	1.38	1.17431877725445	0.205681222745549
23	1.46	1.25103242757621	0.208967572423786
24	1.45	1.47202151621236	-0.0220215162123558
25	1.41	1.49445065512027	-0.0844506551202728
26	1.45	1.41798283372196	0.0320171662780375
27	1.47	1.456831176257	0.0131688237429979
28	1.47	1.47006153677093	-6.15367709304593e-05
29	1.53	1.50008533336141	0.0299146666385941
30	1.56	1.57830871555143	-0.0183087155514321
31	1.66	1.61408707386554	0.0459129261344602
32	1.79	1.70256801137234	0.0874319886276596
33	1.78	1.83679881553122	-0.0567988155312196
34	1.46	1.55843678805691	-0.0984367880569113
35	1.41	1.39441291399506	0.0155870860049443
36	1.43	1.41426739230098	0.0157326076990221
37	1.43	1.45379491712559	-0.023794917125586
38	1.45	1.44949014282011	0.000509857179887163
39	1.35	1.4594411960273	-0.109441196027298
40	1.35	1.37261338345637	-0.0226133834563682
41	1.29	1.39091554201702	-0.100915542017022
42	1.29	1.35534055216793	-0.0653405521679289
43	1.26	1.36702526368031	-0.107025263680307
44	1.3	1.34266111616655	-0.0426611161665527
45	1.3	1.3438839113276	-0.0438839113276008
46	1.16	1.06718910159845	0.0928108984015503
47	1.24	1.07849094468675	0.161509055313254
48	1.15	1.21421127291558	-0.0642112729155766
49	1.21	1.18212794234761	0.0278720576523876
50	1.22	1.22384861719984	-0.00384861719983509
51	1.17	1.20767016780298	-0.0376701678029776
52	1.13	1.19571778416916	-0.0657177841691603
53	1.15	1.1636584848635	-0.0136584848635002
54	1.2	1.20468476784605	-0.00468476784605465
55	1.23	1.25592474839751	-0.0259247483975136
56	1.25	1.30921041973392	-0.0592104197339205
57	1.38	1.29704392362013	0.0829560763798733
58	1.28	1.14922096416646	0.130779035833537
59	1.26	1.20482684564547	0.0551731543545322
60	1.25	1.20959664786803	0.0404033521319735
61	1.26	1.27954424594743	-0.0195442459474315
62	1.28	1.27708473455066	0.00291526544933562
63	1.31	1.25930228226932	0.0506977177306844
64	1.22	1.31171529075766	-0.0917152907576557
65	1.23	1.26975220037923	-0.0397522003792348
66	1.36	1.29191495458751	0.0680850454124908
67	1.54	1.39654185333872	0.143458146661281
68	1.58	1.57742431006439	0.00257568993560642
69	1.44	1.6436167138805	-0.203616713880504
70	1.29	1.27816652251875	0.0118334774812503
71	1.28	1.22376259983311	0.0562374001668928
72	1.23	1.22633199129366	0.00366800870634076

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.44 & 1.39851228632479 & 0.0414877136752143 \tabularnewline
14 & 1.43 & 1.43071910136126 & -0.000719101361260188 \tabularnewline
15 & 1.43 & 1.44692128262837 & -0.0169212826283665 \tabularnewline
16 & 1.42 & 1.43609517407268 & -0.0160951740726831 \tabularnewline
17 & 1.45 & 1.450091514066 & -9.15140659998315e-05 \tabularnewline
18 & 1.51 & 1.50304188697509 & 0.00695811302490834 \tabularnewline
19 & 1.48 & 1.58117173151147 & -0.101171731511472 \tabularnewline
20 & 1.48 & 1.54554922531928 & -0.0655492253192784 \tabularnewline
21 & 1.45 & 1.56945459375196 & -0.119454593751955 \tabularnewline
22 & 1.38 & 1.17431877725445 & 0.205681222745549 \tabularnewline
23 & 1.46 & 1.25103242757621 & 0.208967572423786 \tabularnewline
24 & 1.45 & 1.47202151621236 & -0.0220215162123558 \tabularnewline
25 & 1.41 & 1.49445065512027 & -0.0844506551202728 \tabularnewline
26 & 1.45 & 1.41798283372196 & 0.0320171662780375 \tabularnewline
27 & 1.47 & 1.456831176257 & 0.0131688237429979 \tabularnewline
28 & 1.47 & 1.47006153677093 & -6.15367709304593e-05 \tabularnewline
29 & 1.53 & 1.50008533336141 & 0.0299146666385941 \tabularnewline
30 & 1.56 & 1.57830871555143 & -0.0183087155514321 \tabularnewline
31 & 1.66 & 1.61408707386554 & 0.0459129261344602 \tabularnewline
32 & 1.79 & 1.70256801137234 & 0.0874319886276596 \tabularnewline
33 & 1.78 & 1.83679881553122 & -0.0567988155312196 \tabularnewline
34 & 1.46 & 1.55843678805691 & -0.0984367880569113 \tabularnewline
35 & 1.41 & 1.39441291399506 & 0.0155870860049443 \tabularnewline
36 & 1.43 & 1.41426739230098 & 0.0157326076990221 \tabularnewline
37 & 1.43 & 1.45379491712559 & -0.023794917125586 \tabularnewline
38 & 1.45 & 1.44949014282011 & 0.000509857179887163 \tabularnewline
39 & 1.35 & 1.4594411960273 & -0.109441196027298 \tabularnewline
40 & 1.35 & 1.37261338345637 & -0.0226133834563682 \tabularnewline
41 & 1.29 & 1.39091554201702 & -0.100915542017022 \tabularnewline
42 & 1.29 & 1.35534055216793 & -0.0653405521679289 \tabularnewline
43 & 1.26 & 1.36702526368031 & -0.107025263680307 \tabularnewline
44 & 1.3 & 1.34266111616655 & -0.0426611161665527 \tabularnewline
45 & 1.3 & 1.3438839113276 & -0.0438839113276008 \tabularnewline
46 & 1.16 & 1.06718910159845 & 0.0928108984015503 \tabularnewline
47 & 1.24 & 1.07849094468675 & 0.161509055313254 \tabularnewline
48 & 1.15 & 1.21421127291558 & -0.0642112729155766 \tabularnewline
49 & 1.21 & 1.18212794234761 & 0.0278720576523876 \tabularnewline
50 & 1.22 & 1.22384861719984 & -0.00384861719983509 \tabularnewline
51 & 1.17 & 1.20767016780298 & -0.0376701678029776 \tabularnewline
52 & 1.13 & 1.19571778416916 & -0.0657177841691603 \tabularnewline
53 & 1.15 & 1.1636584848635 & -0.0136584848635002 \tabularnewline
54 & 1.2 & 1.20468476784605 & -0.00468476784605465 \tabularnewline
55 & 1.23 & 1.25592474839751 & -0.0259247483975136 \tabularnewline
56 & 1.25 & 1.30921041973392 & -0.0592104197339205 \tabularnewline
57 & 1.38 & 1.29704392362013 & 0.0829560763798733 \tabularnewline
58 & 1.28 & 1.14922096416646 & 0.130779035833537 \tabularnewline
59 & 1.26 & 1.20482684564547 & 0.0551731543545322 \tabularnewline
60 & 1.25 & 1.20959664786803 & 0.0404033521319735 \tabularnewline
61 & 1.26 & 1.27954424594743 & -0.0195442459474315 \tabularnewline
62 & 1.28 & 1.27708473455066 & 0.00291526544933562 \tabularnewline
63 & 1.31 & 1.25930228226932 & 0.0506977177306844 \tabularnewline
64 & 1.22 & 1.31171529075766 & -0.0917152907576557 \tabularnewline
65 & 1.23 & 1.26975220037923 & -0.0397522003792348 \tabularnewline
66 & 1.36 & 1.29191495458751 & 0.0680850454124908 \tabularnewline
67 & 1.54 & 1.39654185333872 & 0.143458146661281 \tabularnewline
68 & 1.58 & 1.57742431006439 & 0.00257568993560642 \tabularnewline
69 & 1.44 & 1.6436167138805 & -0.203616713880504 \tabularnewline
70 & 1.29 & 1.27816652251875 & 0.0118334774812503 \tabularnewline
71 & 1.28 & 1.22376259983311 & 0.0562374001668928 \tabularnewline
72 & 1.23 & 1.22633199129366 & 0.00366800870634076 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208871&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]1.44[/C][C]1.39851228632479[/C][C]0.0414877136752143[/C][/ROW]
[ROW][C]14[/C][C]1.43[/C][C]1.43071910136126[/C][C]-0.000719101361260188[/C][/ROW]
[ROW][C]15[/C][C]1.43[/C][C]1.44692128262837[/C][C]-0.0169212826283665[/C][/ROW]
[ROW][C]16[/C][C]1.42[/C][C]1.43609517407268[/C][C]-0.0160951740726831[/C][/ROW]
[ROW][C]17[/C][C]1.45[/C][C]1.450091514066[/C][C]-9.15140659998315e-05[/C][/ROW]
[ROW][C]18[/C][C]1.51[/C][C]1.50304188697509[/C][C]0.00695811302490834[/C][/ROW]
[ROW][C]19[/C][C]1.48[/C][C]1.58117173151147[/C][C]-0.101171731511472[/C][/ROW]
[ROW][C]20[/C][C]1.48[/C][C]1.54554922531928[/C][C]-0.0655492253192784[/C][/ROW]
[ROW][C]21[/C][C]1.45[/C][C]1.56945459375196[/C][C]-0.119454593751955[/C][/ROW]
[ROW][C]22[/C][C]1.38[/C][C]1.17431877725445[/C][C]0.205681222745549[/C][/ROW]
[ROW][C]23[/C][C]1.46[/C][C]1.25103242757621[/C][C]0.208967572423786[/C][/ROW]
[ROW][C]24[/C][C]1.45[/C][C]1.47202151621236[/C][C]-0.0220215162123558[/C][/ROW]
[ROW][C]25[/C][C]1.41[/C][C]1.49445065512027[/C][C]-0.0844506551202728[/C][/ROW]
[ROW][C]26[/C][C]1.45[/C][C]1.41798283372196[/C][C]0.0320171662780375[/C][/ROW]
[ROW][C]27[/C][C]1.47[/C][C]1.456831176257[/C][C]0.0131688237429979[/C][/ROW]
[ROW][C]28[/C][C]1.47[/C][C]1.47006153677093[/C][C]-6.15367709304593e-05[/C][/ROW]
[ROW][C]29[/C][C]1.53[/C][C]1.50008533336141[/C][C]0.0299146666385941[/C][/ROW]
[ROW][C]30[/C][C]1.56[/C][C]1.57830871555143[/C][C]-0.0183087155514321[/C][/ROW]
[ROW][C]31[/C][C]1.66[/C][C]1.61408707386554[/C][C]0.0459129261344602[/C][/ROW]
[ROW][C]32[/C][C]1.79[/C][C]1.70256801137234[/C][C]0.0874319886276596[/C][/ROW]
[ROW][C]33[/C][C]1.78[/C][C]1.83679881553122[/C][C]-0.0567988155312196[/C][/ROW]
[ROW][C]34[/C][C]1.46[/C][C]1.55843678805691[/C][C]-0.0984367880569113[/C][/ROW]
[ROW][C]35[/C][C]1.41[/C][C]1.39441291399506[/C][C]0.0155870860049443[/C][/ROW]
[ROW][C]36[/C][C]1.43[/C][C]1.41426739230098[/C][C]0.0157326076990221[/C][/ROW]
[ROW][C]37[/C][C]1.43[/C][C]1.45379491712559[/C][C]-0.023794917125586[/C][/ROW]
[ROW][C]38[/C][C]1.45[/C][C]1.44949014282011[/C][C]0.000509857179887163[/C][/ROW]
[ROW][C]39[/C][C]1.35[/C][C]1.4594411960273[/C][C]-0.109441196027298[/C][/ROW]
[ROW][C]40[/C][C]1.35[/C][C]1.37261338345637[/C][C]-0.0226133834563682[/C][/ROW]
[ROW][C]41[/C][C]1.29[/C][C]1.39091554201702[/C][C]-0.100915542017022[/C][/ROW]
[ROW][C]42[/C][C]1.29[/C][C]1.35534055216793[/C][C]-0.0653405521679289[/C][/ROW]
[ROW][C]43[/C][C]1.26[/C][C]1.36702526368031[/C][C]-0.107025263680307[/C][/ROW]
[ROW][C]44[/C][C]1.3[/C][C]1.34266111616655[/C][C]-0.0426611161665527[/C][/ROW]
[ROW][C]45[/C][C]1.3[/C][C]1.3438839113276[/C][C]-0.0438839113276008[/C][/ROW]
[ROW][C]46[/C][C]1.16[/C][C]1.06718910159845[/C][C]0.0928108984015503[/C][/ROW]
[ROW][C]47[/C][C]1.24[/C][C]1.07849094468675[/C][C]0.161509055313254[/C][/ROW]
[ROW][C]48[/C][C]1.15[/C][C]1.21421127291558[/C][C]-0.0642112729155766[/C][/ROW]
[ROW][C]49[/C][C]1.21[/C][C]1.18212794234761[/C][C]0.0278720576523876[/C][/ROW]
[ROW][C]50[/C][C]1.22[/C][C]1.22384861719984[/C][C]-0.00384861719983509[/C][/ROW]
[ROW][C]51[/C][C]1.17[/C][C]1.20767016780298[/C][C]-0.0376701678029776[/C][/ROW]
[ROW][C]52[/C][C]1.13[/C][C]1.19571778416916[/C][C]-0.0657177841691603[/C][/ROW]
[ROW][C]53[/C][C]1.15[/C][C]1.1636584848635[/C][C]-0.0136584848635002[/C][/ROW]
[ROW][C]54[/C][C]1.2[/C][C]1.20468476784605[/C][C]-0.00468476784605465[/C][/ROW]
[ROW][C]55[/C][C]1.23[/C][C]1.25592474839751[/C][C]-0.0259247483975136[/C][/ROW]
[ROW][C]56[/C][C]1.25[/C][C]1.30921041973392[/C][C]-0.0592104197339205[/C][/ROW]
[ROW][C]57[/C][C]1.38[/C][C]1.29704392362013[/C][C]0.0829560763798733[/C][/ROW]
[ROW][C]58[/C][C]1.28[/C][C]1.14922096416646[/C][C]0.130779035833537[/C][/ROW]
[ROW][C]59[/C][C]1.26[/C][C]1.20482684564547[/C][C]0.0551731543545322[/C][/ROW]
[ROW][C]60[/C][C]1.25[/C][C]1.20959664786803[/C][C]0.0404033521319735[/C][/ROW]
[ROW][C]61[/C][C]1.26[/C][C]1.27954424594743[/C][C]-0.0195442459474315[/C][/ROW]
[ROW][C]62[/C][C]1.28[/C][C]1.27708473455066[/C][C]0.00291526544933562[/C][/ROW]
[ROW][C]63[/C][C]1.31[/C][C]1.25930228226932[/C][C]0.0506977177306844[/C][/ROW]
[ROW][C]64[/C][C]1.22[/C][C]1.31171529075766[/C][C]-0.0917152907576557[/C][/ROW]
[ROW][C]65[/C][C]1.23[/C][C]1.26975220037923[/C][C]-0.0397522003792348[/C][/ROW]
[ROW][C]66[/C][C]1.36[/C][C]1.29191495458751[/C][C]0.0680850454124908[/C][/ROW]
[ROW][C]67[/C][C]1.54[/C][C]1.39654185333872[/C][C]0.143458146661281[/C][/ROW]
[ROW][C]68[/C][C]1.58[/C][C]1.57742431006439[/C][C]0.00257568993560642[/C][/ROW]
[ROW][C]69[/C][C]1.44[/C][C]1.6436167138805[/C][C]-0.203616713880504[/C][/ROW]
[ROW][C]70[/C][C]1.29[/C][C]1.27816652251875[/C][C]0.0118334774812503[/C][/ROW]
[ROW][C]71[/C][C]1.28[/C][C]1.22376259983311[/C][C]0.0562374001668928[/C][/ROW]
[ROW][C]72[/C][C]1.23[/C][C]1.22633199129366[/C][C]0.00366800870634076[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208871&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208871&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	1.44	1.39851228632479	0.0414877136752143
14	1.43	1.43071910136126	-0.000719101361260188
15	1.43	1.44692128262837	-0.0169212826283665
16	1.42	1.43609517407268	-0.0160951740726831
17	1.45	1.450091514066	-9.15140659998315e-05
18	1.51	1.50304188697509	0.00695811302490834
19	1.48	1.58117173151147	-0.101171731511472
20	1.48	1.54554922531928	-0.0655492253192784
21	1.45	1.56945459375196	-0.119454593751955
22	1.38	1.17431877725445	0.205681222745549
23	1.46	1.25103242757621	0.208967572423786
24	1.45	1.47202151621236	-0.0220215162123558
25	1.41	1.49445065512027	-0.0844506551202728
26	1.45	1.41798283372196	0.0320171662780375
27	1.47	1.456831176257	0.0131688237429979
28	1.47	1.47006153677093	-6.15367709304593e-05
29	1.53	1.50008533336141	0.0299146666385941
30	1.56	1.57830871555143	-0.0183087155514321
31	1.66	1.61408707386554	0.0459129261344602
32	1.79	1.70256801137234	0.0874319886276596
33	1.78	1.83679881553122	-0.0567988155312196
34	1.46	1.55843678805691	-0.0984367880569113
35	1.41	1.39441291399506	0.0155870860049443
36	1.43	1.41426739230098	0.0157326076990221
37	1.43	1.45379491712559	-0.023794917125586
38	1.45	1.44949014282011	0.000509857179887163
39	1.35	1.4594411960273	-0.109441196027298
40	1.35	1.37261338345637	-0.0226133834563682
41	1.29	1.39091554201702	-0.100915542017022
42	1.29	1.35534055216793	-0.0653405521679289
43	1.26	1.36702526368031	-0.107025263680307
44	1.3	1.34266111616655	-0.0426611161665527
45	1.3	1.3438839113276	-0.0438839113276008
46	1.16	1.06718910159845	0.0928108984015503
47	1.24	1.07849094468675	0.161509055313254
48	1.15	1.21421127291558	-0.0642112729155766
49	1.21	1.18212794234761	0.0278720576523876
50	1.22	1.22384861719984	-0.00384861719983509
51	1.17	1.20767016780298	-0.0376701678029776
52	1.13	1.19571778416916	-0.0657177841691603
53	1.15	1.1636584848635	-0.0136584848635002
54	1.2	1.20468476784605	-0.00468476784605465
55	1.23	1.25592474839751	-0.0259247483975136
56	1.25	1.30921041973392	-0.0592104197339205
57	1.38	1.29704392362013	0.0829560763798733
58	1.28	1.14922096416646	0.130779035833537
59	1.26	1.20482684564547	0.0551731543545322
60	1.25	1.20959664786803	0.0404033521319735
61	1.26	1.27954424594743	-0.0195442459474315
62	1.28	1.27708473455066	0.00291526544933562
63	1.31	1.25930228226932	0.0506977177306844
64	1.22	1.31171529075766	-0.0917152907576557
65	1.23	1.26975220037923	-0.0397522003792348
66	1.36	1.29191495458751	0.0680850454124908
67	1.54	1.39654185333872	0.143458146661281
68	1.58	1.57742431006439	0.00257568993560642
69	1.44	1.6436167138805	-0.203616713880504
70	1.29	1.27816652251875	0.0118334774812503
71	1.28	1.22376259983311	0.0562374001668928
72	1.23	1.22633199129366	0.00366800870634076

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.25475835420363	1.10290851035206	1.40660819805519
74	1.27244415681309	1.07856627825899	1.46632203536718
75	1.26219927067227	1.0339036541845	1.49049488716004
76	1.24500474593096	0.986839788544361	1.50316970331757
77	1.2865608563383	1.00164086416976	1.57148084850684
78	1.36251355355686	1.05314377699132	1.67188333012241
79	1.4286335400812	1.09660957201999	1.76065750814241
80	1.46658890468473	1.11336068938758	1.81981711998187
81	1.48822402029326	1.11499429372141	1.86145374686511
82	1.32883036363178	0.936617812185763	1.72104291507779
83	1.27418796417319	0.863869865344135	1.68450606300224
84	1.22127622377622	0.793618417882796	1.64893402966965

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.25475835420363 & 1.10290851035206 & 1.40660819805519 \tabularnewline
74 & 1.27244415681309 & 1.07856627825899 & 1.46632203536718 \tabularnewline
75 & 1.26219927067227 & 1.0339036541845 & 1.49049488716004 \tabularnewline
76 & 1.24500474593096 & 0.986839788544361 & 1.50316970331757 \tabularnewline
77 & 1.2865608563383 & 1.00164086416976 & 1.57148084850684 \tabularnewline
78 & 1.36251355355686 & 1.05314377699132 & 1.67188333012241 \tabularnewline
79 & 1.4286335400812 & 1.09660957201999 & 1.76065750814241 \tabularnewline
80 & 1.46658890468473 & 1.11336068938758 & 1.81981711998187 \tabularnewline
81 & 1.48822402029326 & 1.11499429372141 & 1.86145374686511 \tabularnewline
82 & 1.32883036363178 & 0.936617812185763 & 1.72104291507779 \tabularnewline
83 & 1.27418796417319 & 0.863869865344135 & 1.68450606300224 \tabularnewline
84 & 1.22127622377622 & 0.793618417882796 & 1.64893402966965 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208871&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]1.25475835420363[/C][C]1.10290851035206[/C][C]1.40660819805519[/C][/ROW]
[ROW][C]74[/C][C]1.27244415681309[/C][C]1.07856627825899[/C][C]1.46632203536718[/C][/ROW]
[ROW][C]75[/C][C]1.26219927067227[/C][C]1.0339036541845[/C][C]1.49049488716004[/C][/ROW]
[ROW][C]76[/C][C]1.24500474593096[/C][C]0.986839788544361[/C][C]1.50316970331757[/C][/ROW]
[ROW][C]77[/C][C]1.2865608563383[/C][C]1.00164086416976[/C][C]1.57148084850684[/C][/ROW]
[ROW][C]78[/C][C]1.36251355355686[/C][C]1.05314377699132[/C][C]1.67188333012241[/C][/ROW]
[ROW][C]79[/C][C]1.4286335400812[/C][C]1.09660957201999[/C][C]1.76065750814241[/C][/ROW]
[ROW][C]80[/C][C]1.46658890468473[/C][C]1.11336068938758[/C][C]1.81981711998187[/C][/ROW]
[ROW][C]81[/C][C]1.48822402029326[/C][C]1.11499429372141[/C][C]1.86145374686511[/C][/ROW]
[ROW][C]82[/C][C]1.32883036363178[/C][C]0.936617812185763[/C][C]1.72104291507779[/C][/ROW]
[ROW][C]83[/C][C]1.27418796417319[/C][C]0.863869865344135[/C][C]1.68450606300224[/C][/ROW]
[ROW][C]84[/C][C]1.22127622377622[/C][C]0.793618417882796[/C][C]1.64893402966965[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208871&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208871&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	1.25475835420363	1.10290851035206	1.40660819805519
74	1.27244415681309	1.07856627825899	1.46632203536718
75	1.26219927067227	1.0339036541845	1.49049488716004
76	1.24500474593096	0.986839788544361	1.50316970331757
77	1.2865608563383	1.00164086416976	1.57148084850684
78	1.36251355355686	1.05314377699132	1.67188333012241
79	1.4286335400812	1.09660957201999	1.76065750814241
80	1.46658890468473	1.11336068938758	1.81981711998187
81	1.48822402029326	1.11499429372141	1.86145374686511
82	1.32883036363178	0.936617812185763	1.72104291507779
83	1.27418796417319	0.863869865344135	1.68450606300224
84	1.22127622377622	0.793618417882796	1.64893402966965

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