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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 20 Dec 2013 13:40:39 -0500

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/Dec/20/t1387564919us5u0r3h6hm5hla.htm/, Retrieved Thu, 31 Oct 2024 23:04:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232481, Retrieved Thu, 31 Oct 2024 23:04:52 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

191

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

-       [Exponential Smoothing] [] [2013-12-20 18:40:39] [a3c700dc1d9df9ef9f271ed7f250ff74] [Current]

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Dataseries X:

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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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232481&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232481&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232481&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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.899894829794702
beta	0.0367668330068828
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.899894829794702 \tabularnewline
beta & 0.0367668330068828 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232481&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]0.899894829794702[/C][/ROW]
[ROW][C]beta[/C][C]0.0367668330068828[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232481&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232481&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	0.899894829794702
beta	0.0367668330068828
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	101.02	100.748809589115	0.271190410884529
14	100.92	100.897429082051	0.0225709179485989
15	100.93	100.930523322077	-0.000523322077455646
16	100.98	100.984065600126	-0.00406560012635282
17	101.07	101.076369548473	-0.00636954847259119
18	101.1	101.105971457559	-0.00597145755864403
19	101.11	101.073969095001	0.0360309049988103
20	101.19	101.173163363777	0.0168366362230614
21	101.31	101.301780811795	0.00821918820517453
22	101.52	101.603797585223	-0.0837975852225412
23	101.61	101.622199803509	-0.012199803508679
24	101.65	101.657654661848	-0.00765466184797958
25	101.66	101.692822685321	-0.0328226853214488
26	101.56	101.539538940355	0.0204610596447452
27	101.75	101.56574961352	0.184250386480002
28	101.83	101.78891893194	0.0410810680596683
29	101.98	101.927170936442	0.0528290635583204
30	102.06	102.017076579367	0.0429234206327891
31	102.07	102.041324319674	0.0286756803261312
32	102.1	102.140595139757	-0.0405951397574711
33	102.42	102.223811519706	0.196188480294452
34	102.91	102.701101400211	0.208898599789322
35	103.14	103.013260485946	0.126739514054023
36	103.23	103.201249966746	0.0287500332541981
37	103.23	103.294790340069	-0.0647903400693224
38	102.91	103.142669476174	-0.232669476174379
39	103.11	102.975936222171	0.134063777828885
40	103.14	103.156603778684	-0.016603778684356
41	103.26	103.259965205152	3.47948476502324e-05
42	103.3	103.314663268191	-0.0146632681908869
43	103.32	103.296339436013	0.0236605639871499
44	103.44	103.3956625227	0.0443374772997629
45	103.54	103.594321978194	-0.0543219781939115
46	103.98	103.855988932136	0.124011067863805
47	104.24	104.087140859979	0.152859140020695
48	104.29	104.292729172898	-0.00272917289824193
49	104.29	104.351371211177	-0.0613712111765068
50	103.98	104.186655542399	-0.206655542399147
51	103.98	104.084111559321	-0.104111559321225
52	103.89	104.03122802091	-0.141228020909637
53	103.86	104.016443630516	-0.156443630515682
54	103.88	103.915562747973	-0.0355627479728184
55	103.88	103.867996957045	0.0120030429547455
56	104.31	103.944696590862	0.365303409137681
57	104.41	104.419271921475	-0.00927192147514688
58	104.8	104.739309950255	0.0606900497453182
59	104.89	104.912452312856	-0.0224523128559184
60	104.9	104.934480894305	-0.0344808943053465
61	104.9	104.947437019134	-0.0474370191338807
62	104.54	104.768878862816	-0.228878862815691
63	104.67	104.645372465128	0.0246275348724083
64	104.87	104.697312810235	0.17268718976463
65	105.04	104.96718894469	0.072811055309856
66	105.09	105.095484612094	-0.00548461209437789
67	105.1	105.090782821092	0.00921717890848583
68	105.46	105.212477291118	0.247522708882187
69	105.83	105.551829577676	0.278170422324422
70	106.27	106.158460603016	0.111539396984128
71	106.46	106.388639759534	0.0713602404661486
72	106.52	106.515592489413	0.00440751058694389
73	106.53	106.585255121212	-0.0552551212124541
74	105.96	106.401107177441	-0.441107177440699
75	106	106.128769662583	-0.128769662582741
76	106.15	106.068293477018	0.0817065229819463
77	106.32	106.254788048266	0.0652119517344261
78	106.41	106.376018657416	0.0339813425838855
79	106.41	106.416541153731	-0.00654115373079378
80	106.81	106.5572687487	0.252731251299963
81	106.99	106.913575435641	0.0764245643592147
82	107.35	107.326793922501	0.0232060774986707
83	107.53	107.472972305883	0.0570276941169823
84	107.56	107.57864312296	-0.0186431229599293

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 101.02 & 100.748809589115 & 0.271190410884529 \tabularnewline
14 & 100.92 & 100.897429082051 & 0.0225709179485989 \tabularnewline
15 & 100.93 & 100.930523322077 & -0.000523322077455646 \tabularnewline
16 & 100.98 & 100.984065600126 & -0.00406560012635282 \tabularnewline
17 & 101.07 & 101.076369548473 & -0.00636954847259119 \tabularnewline
18 & 101.1 & 101.105971457559 & -0.00597145755864403 \tabularnewline
19 & 101.11 & 101.073969095001 & 0.0360309049988103 \tabularnewline
20 & 101.19 & 101.173163363777 & 0.0168366362230614 \tabularnewline
21 & 101.31 & 101.301780811795 & 0.00821918820517453 \tabularnewline
22 & 101.52 & 101.603797585223 & -0.0837975852225412 \tabularnewline
23 & 101.61 & 101.622199803509 & -0.012199803508679 \tabularnewline
24 & 101.65 & 101.657654661848 & -0.00765466184797958 \tabularnewline
25 & 101.66 & 101.692822685321 & -0.0328226853214488 \tabularnewline
26 & 101.56 & 101.539538940355 & 0.0204610596447452 \tabularnewline
27 & 101.75 & 101.56574961352 & 0.184250386480002 \tabularnewline
28 & 101.83 & 101.78891893194 & 0.0410810680596683 \tabularnewline
29 & 101.98 & 101.927170936442 & 0.0528290635583204 \tabularnewline
30 & 102.06 & 102.017076579367 & 0.0429234206327891 \tabularnewline
31 & 102.07 & 102.041324319674 & 0.0286756803261312 \tabularnewline
32 & 102.1 & 102.140595139757 & -0.0405951397574711 \tabularnewline
33 & 102.42 & 102.223811519706 & 0.196188480294452 \tabularnewline
34 & 102.91 & 102.701101400211 & 0.208898599789322 \tabularnewline
35 & 103.14 & 103.013260485946 & 0.126739514054023 \tabularnewline
36 & 103.23 & 103.201249966746 & 0.0287500332541981 \tabularnewline
37 & 103.23 & 103.294790340069 & -0.0647903400693224 \tabularnewline
38 & 102.91 & 103.142669476174 & -0.232669476174379 \tabularnewline
39 & 103.11 & 102.975936222171 & 0.134063777828885 \tabularnewline
40 & 103.14 & 103.156603778684 & -0.016603778684356 \tabularnewline
41 & 103.26 & 103.259965205152 & 3.47948476502324e-05 \tabularnewline
42 & 103.3 & 103.314663268191 & -0.0146632681908869 \tabularnewline
43 & 103.32 & 103.296339436013 & 0.0236605639871499 \tabularnewline
44 & 103.44 & 103.3956625227 & 0.0443374772997629 \tabularnewline
45 & 103.54 & 103.594321978194 & -0.0543219781939115 \tabularnewline
46 & 103.98 & 103.855988932136 & 0.124011067863805 \tabularnewline
47 & 104.24 & 104.087140859979 & 0.152859140020695 \tabularnewline
48 & 104.29 & 104.292729172898 & -0.00272917289824193 \tabularnewline
49 & 104.29 & 104.351371211177 & -0.0613712111765068 \tabularnewline
50 & 103.98 & 104.186655542399 & -0.206655542399147 \tabularnewline
51 & 103.98 & 104.084111559321 & -0.104111559321225 \tabularnewline
52 & 103.89 & 104.03122802091 & -0.141228020909637 \tabularnewline
53 & 103.86 & 104.016443630516 & -0.156443630515682 \tabularnewline
54 & 103.88 & 103.915562747973 & -0.0355627479728184 \tabularnewline
55 & 103.88 & 103.867996957045 & 0.0120030429547455 \tabularnewline
56 & 104.31 & 103.944696590862 & 0.365303409137681 \tabularnewline
57 & 104.41 & 104.419271921475 & -0.00927192147514688 \tabularnewline
58 & 104.8 & 104.739309950255 & 0.0606900497453182 \tabularnewline
59 & 104.89 & 104.912452312856 & -0.0224523128559184 \tabularnewline
60 & 104.9 & 104.934480894305 & -0.0344808943053465 \tabularnewline
61 & 104.9 & 104.947437019134 & -0.0474370191338807 \tabularnewline
62 & 104.54 & 104.768878862816 & -0.228878862815691 \tabularnewline
63 & 104.67 & 104.645372465128 & 0.0246275348724083 \tabularnewline
64 & 104.87 & 104.697312810235 & 0.17268718976463 \tabularnewline
65 & 105.04 & 104.96718894469 & 0.072811055309856 \tabularnewline
66 & 105.09 & 105.095484612094 & -0.00548461209437789 \tabularnewline
67 & 105.1 & 105.090782821092 & 0.00921717890848583 \tabularnewline
68 & 105.46 & 105.212477291118 & 0.247522708882187 \tabularnewline
69 & 105.83 & 105.551829577676 & 0.278170422324422 \tabularnewline
70 & 106.27 & 106.158460603016 & 0.111539396984128 \tabularnewline
71 & 106.46 & 106.388639759534 & 0.0713602404661486 \tabularnewline
72 & 106.52 & 106.515592489413 & 0.00440751058694389 \tabularnewline
73 & 106.53 & 106.585255121212 & -0.0552551212124541 \tabularnewline
74 & 105.96 & 106.401107177441 & -0.441107177440699 \tabularnewline
75 & 106 & 106.128769662583 & -0.128769662582741 \tabularnewline
76 & 106.15 & 106.068293477018 & 0.0817065229819463 \tabularnewline
77 & 106.32 & 106.254788048266 & 0.0652119517344261 \tabularnewline
78 & 106.41 & 106.376018657416 & 0.0339813425838855 \tabularnewline
79 & 106.41 & 106.416541153731 & -0.00654115373079378 \tabularnewline
80 & 106.81 & 106.5572687487 & 0.252731251299963 \tabularnewline
81 & 106.99 & 106.913575435641 & 0.0764245643592147 \tabularnewline
82 & 107.35 & 107.326793922501 & 0.0232060774986707 \tabularnewline
83 & 107.53 & 107.472972305883 & 0.0570276941169823 \tabularnewline
84 & 107.56 & 107.57864312296 & -0.0186431229599293 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232481&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]101.02[/C][C]100.748809589115[/C][C]0.271190410884529[/C][/ROW]
[ROW][C]14[/C][C]100.92[/C][C]100.897429082051[/C][C]0.0225709179485989[/C][/ROW]
[ROW][C]15[/C][C]100.93[/C][C]100.930523322077[/C][C]-0.000523322077455646[/C][/ROW]
[ROW][C]16[/C][C]100.98[/C][C]100.984065600126[/C][C]-0.00406560012635282[/C][/ROW]
[ROW][C]17[/C][C]101.07[/C][C]101.076369548473[/C][C]-0.00636954847259119[/C][/ROW]
[ROW][C]18[/C][C]101.1[/C][C]101.105971457559[/C][C]-0.00597145755864403[/C][/ROW]
[ROW][C]19[/C][C]101.11[/C][C]101.073969095001[/C][C]0.0360309049988103[/C][/ROW]
[ROW][C]20[/C][C]101.19[/C][C]101.173163363777[/C][C]0.0168366362230614[/C][/ROW]
[ROW][C]21[/C][C]101.31[/C][C]101.301780811795[/C][C]0.00821918820517453[/C][/ROW]
[ROW][C]22[/C][C]101.52[/C][C]101.603797585223[/C][C]-0.0837975852225412[/C][/ROW]
[ROW][C]23[/C][C]101.61[/C][C]101.622199803509[/C][C]-0.012199803508679[/C][/ROW]
[ROW][C]24[/C][C]101.65[/C][C]101.657654661848[/C][C]-0.00765466184797958[/C][/ROW]
[ROW][C]25[/C][C]101.66[/C][C]101.692822685321[/C][C]-0.0328226853214488[/C][/ROW]
[ROW][C]26[/C][C]101.56[/C][C]101.539538940355[/C][C]0.0204610596447452[/C][/ROW]
[ROW][C]27[/C][C]101.75[/C][C]101.56574961352[/C][C]0.184250386480002[/C][/ROW]
[ROW][C]28[/C][C]101.83[/C][C]101.78891893194[/C][C]0.0410810680596683[/C][/ROW]
[ROW][C]29[/C][C]101.98[/C][C]101.927170936442[/C][C]0.0528290635583204[/C][/ROW]
[ROW][C]30[/C][C]102.06[/C][C]102.017076579367[/C][C]0.0429234206327891[/C][/ROW]
[ROW][C]31[/C][C]102.07[/C][C]102.041324319674[/C][C]0.0286756803261312[/C][/ROW]
[ROW][C]32[/C][C]102.1[/C][C]102.140595139757[/C][C]-0.0405951397574711[/C][/ROW]
[ROW][C]33[/C][C]102.42[/C][C]102.223811519706[/C][C]0.196188480294452[/C][/ROW]
[ROW][C]34[/C][C]102.91[/C][C]102.701101400211[/C][C]0.208898599789322[/C][/ROW]
[ROW][C]35[/C][C]103.14[/C][C]103.013260485946[/C][C]0.126739514054023[/C][/ROW]
[ROW][C]36[/C][C]103.23[/C][C]103.201249966746[/C][C]0.0287500332541981[/C][/ROW]
[ROW][C]37[/C][C]103.23[/C][C]103.294790340069[/C][C]-0.0647903400693224[/C][/ROW]
[ROW][C]38[/C][C]102.91[/C][C]103.142669476174[/C][C]-0.232669476174379[/C][/ROW]
[ROW][C]39[/C][C]103.11[/C][C]102.975936222171[/C][C]0.134063777828885[/C][/ROW]
[ROW][C]40[/C][C]103.14[/C][C]103.156603778684[/C][C]-0.016603778684356[/C][/ROW]
[ROW][C]41[/C][C]103.26[/C][C]103.259965205152[/C][C]3.47948476502324e-05[/C][/ROW]
[ROW][C]42[/C][C]103.3[/C][C]103.314663268191[/C][C]-0.0146632681908869[/C][/ROW]
[ROW][C]43[/C][C]103.32[/C][C]103.296339436013[/C][C]0.0236605639871499[/C][/ROW]
[ROW][C]44[/C][C]103.44[/C][C]103.3956625227[/C][C]0.0443374772997629[/C][/ROW]
[ROW][C]45[/C][C]103.54[/C][C]103.594321978194[/C][C]-0.0543219781939115[/C][/ROW]
[ROW][C]46[/C][C]103.98[/C][C]103.855988932136[/C][C]0.124011067863805[/C][/ROW]
[ROW][C]47[/C][C]104.24[/C][C]104.087140859979[/C][C]0.152859140020695[/C][/ROW]
[ROW][C]48[/C][C]104.29[/C][C]104.292729172898[/C][C]-0.00272917289824193[/C][/ROW]
[ROW][C]49[/C][C]104.29[/C][C]104.351371211177[/C][C]-0.0613712111765068[/C][/ROW]
[ROW][C]50[/C][C]103.98[/C][C]104.186655542399[/C][C]-0.206655542399147[/C][/ROW]
[ROW][C]51[/C][C]103.98[/C][C]104.084111559321[/C][C]-0.104111559321225[/C][/ROW]
[ROW][C]52[/C][C]103.89[/C][C]104.03122802091[/C][C]-0.141228020909637[/C][/ROW]
[ROW][C]53[/C][C]103.86[/C][C]104.016443630516[/C][C]-0.156443630515682[/C][/ROW]
[ROW][C]54[/C][C]103.88[/C][C]103.915562747973[/C][C]-0.0355627479728184[/C][/ROW]
[ROW][C]55[/C][C]103.88[/C][C]103.867996957045[/C][C]0.0120030429547455[/C][/ROW]
[ROW][C]56[/C][C]104.31[/C][C]103.944696590862[/C][C]0.365303409137681[/C][/ROW]
[ROW][C]57[/C][C]104.41[/C][C]104.419271921475[/C][C]-0.00927192147514688[/C][/ROW]
[ROW][C]58[/C][C]104.8[/C][C]104.739309950255[/C][C]0.0606900497453182[/C][/ROW]
[ROW][C]59[/C][C]104.89[/C][C]104.912452312856[/C][C]-0.0224523128559184[/C][/ROW]
[ROW][C]60[/C][C]104.9[/C][C]104.934480894305[/C][C]-0.0344808943053465[/C][/ROW]
[ROW][C]61[/C][C]104.9[/C][C]104.947437019134[/C][C]-0.0474370191338807[/C][/ROW]
[ROW][C]62[/C][C]104.54[/C][C]104.768878862816[/C][C]-0.228878862815691[/C][/ROW]
[ROW][C]63[/C][C]104.67[/C][C]104.645372465128[/C][C]0.0246275348724083[/C][/ROW]
[ROW][C]64[/C][C]104.87[/C][C]104.697312810235[/C][C]0.17268718976463[/C][/ROW]
[ROW][C]65[/C][C]105.04[/C][C]104.96718894469[/C][C]0.072811055309856[/C][/ROW]
[ROW][C]66[/C][C]105.09[/C][C]105.095484612094[/C][C]-0.00548461209437789[/C][/ROW]
[ROW][C]67[/C][C]105.1[/C][C]105.090782821092[/C][C]0.00921717890848583[/C][/ROW]
[ROW][C]68[/C][C]105.46[/C][C]105.212477291118[/C][C]0.247522708882187[/C][/ROW]
[ROW][C]69[/C][C]105.83[/C][C]105.551829577676[/C][C]0.278170422324422[/C][/ROW]
[ROW][C]70[/C][C]106.27[/C][C]106.158460603016[/C][C]0.111539396984128[/C][/ROW]
[ROW][C]71[/C][C]106.46[/C][C]106.388639759534[/C][C]0.0713602404661486[/C][/ROW]
[ROW][C]72[/C][C]106.52[/C][C]106.515592489413[/C][C]0.00440751058694389[/C][/ROW]
[ROW][C]73[/C][C]106.53[/C][C]106.585255121212[/C][C]-0.0552551212124541[/C][/ROW]
[ROW][C]74[/C][C]105.96[/C][C]106.401107177441[/C][C]-0.441107177440699[/C][/ROW]
[ROW][C]75[/C][C]106[/C][C]106.128769662583[/C][C]-0.128769662582741[/C][/ROW]
[ROW][C]76[/C][C]106.15[/C][C]106.068293477018[/C][C]0.0817065229819463[/C][/ROW]
[ROW][C]77[/C][C]106.32[/C][C]106.254788048266[/C][C]0.0652119517344261[/C][/ROW]
[ROW][C]78[/C][C]106.41[/C][C]106.376018657416[/C][C]0.0339813425838855[/C][/ROW]
[ROW][C]79[/C][C]106.41[/C][C]106.416541153731[/C][C]-0.00654115373079378[/C][/ROW]
[ROW][C]80[/C][C]106.81[/C][C]106.5572687487[/C][C]0.252731251299963[/C][/ROW]
[ROW][C]81[/C][C]106.99[/C][C]106.913575435641[/C][C]0.0764245643592147[/C][/ROW]
[ROW][C]82[/C][C]107.35[/C][C]107.326793922501[/C][C]0.0232060774986707[/C][/ROW]
[ROW][C]83[/C][C]107.53[/C][C]107.472972305883[/C][C]0.0570276941169823[/C][/ROW]
[ROW][C]84[/C][C]107.56[/C][C]107.57864312296[/C][C]-0.0186431229599293[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232481&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232481&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	101.02	100.748809589115	0.271190410884529
14	100.92	100.897429082051	0.0225709179485989
15	100.93	100.930523322077	-0.000523322077455646
16	100.98	100.984065600126	-0.00406560012635282
17	101.07	101.076369548473	-0.00636954847259119
18	101.1	101.105971457559	-0.00597145755864403
19	101.11	101.073969095001	0.0360309049988103
20	101.19	101.173163363777	0.0168366362230614
21	101.31	101.301780811795	0.00821918820517453
22	101.52	101.603797585223	-0.0837975852225412
23	101.61	101.622199803509	-0.012199803508679
24	101.65	101.657654661848	-0.00765466184797958
25	101.66	101.692822685321	-0.0328226853214488
26	101.56	101.539538940355	0.0204610596447452
27	101.75	101.56574961352	0.184250386480002
28	101.83	101.78891893194	0.0410810680596683
29	101.98	101.927170936442	0.0528290635583204
30	102.06	102.017076579367	0.0429234206327891
31	102.07	102.041324319674	0.0286756803261312
32	102.1	102.140595139757	-0.0405951397574711
33	102.42	102.223811519706	0.196188480294452
34	102.91	102.701101400211	0.208898599789322
35	103.14	103.013260485946	0.126739514054023
36	103.23	103.201249966746	0.0287500332541981
37	103.23	103.294790340069	-0.0647903400693224
38	102.91	103.142669476174	-0.232669476174379
39	103.11	102.975936222171	0.134063777828885
40	103.14	103.156603778684	-0.016603778684356
41	103.26	103.259965205152	3.47948476502324e-05
42	103.3	103.314663268191	-0.0146632681908869
43	103.32	103.296339436013	0.0236605639871499
44	103.44	103.3956625227	0.0443374772997629
45	103.54	103.594321978194	-0.0543219781939115
46	103.98	103.855988932136	0.124011067863805
47	104.24	104.087140859979	0.152859140020695
48	104.29	104.292729172898	-0.00272917289824193
49	104.29	104.351371211177	-0.0613712111765068
50	103.98	104.186655542399	-0.206655542399147
51	103.98	104.084111559321	-0.104111559321225
52	103.89	104.03122802091	-0.141228020909637
53	103.86	104.016443630516	-0.156443630515682
54	103.88	103.915562747973	-0.0355627479728184
55	103.88	103.867996957045	0.0120030429547455
56	104.31	103.944696590862	0.365303409137681
57	104.41	104.419271921475	-0.00927192147514688
58	104.8	104.739309950255	0.0606900497453182
59	104.89	104.912452312856	-0.0224523128559184
60	104.9	104.934480894305	-0.0344808943053465
61	104.9	104.947437019134	-0.0474370191338807
62	104.54	104.768878862816	-0.228878862815691
63	104.67	104.645372465128	0.0246275348724083
64	104.87	104.697312810235	0.17268718976463
65	105.04	104.96718894469	0.072811055309856
66	105.09	105.095484612094	-0.00548461209437789
67	105.1	105.090782821092	0.00921717890848583
68	105.46	105.212477291118	0.247522708882187
69	105.83	105.551829577676	0.278170422324422
70	106.27	106.158460603016	0.111539396984128
71	106.46	106.388639759534	0.0713602404661486
72	106.52	106.515592489413	0.00440751058694389
73	106.53	106.585255121212	-0.0552551212124541
74	105.96	106.401107177441	-0.441107177440699
75	106	106.128769662583	-0.128769662582741
76	106.15	106.068293477018	0.0817065229819463
77	106.32	106.254788048266	0.0652119517344261
78	106.41	106.376018657416	0.0339813425838855
79	106.41	106.416541153731	-0.00654115373079378
80	106.81	106.5572687487	0.252731251299963
81	106.99	106.913575435641	0.0764245643592147
82	107.35	107.326793922501	0.0232060774986707
83	107.53	107.472972305883	0.0570276941169823
84	107.56	107.57864312296	-0.0186431229599293

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	107.619188555343	107.374687986786	107.8636891239
86	107.443024185069	107.109031552746	107.777016817393
87	107.614320710663	107.20509077369	108.023550647637
88	107.709422296521	107.232843843701	108.186000749341
89	107.837143917784	107.297758160272	108.376529675297
90	107.910028405839	107.311166139047	108.508890672631
91	107.927480751377	107.271592132784	108.58336936997
92	108.114153428841	107.40183092546	108.826475932221
93	108.230141277231	107.462910151896	108.997372402567
94	108.574099762322	107.751188231105	109.39701129354
95	108.704398379924	107.827857762744	109.580938997104
96	108.749979216926	106.118703011101	111.381255422752

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 107.619188555343 & 107.374687986786 & 107.8636891239 \tabularnewline
86 & 107.443024185069 & 107.109031552746 & 107.777016817393 \tabularnewline
87 & 107.614320710663 & 107.20509077369 & 108.023550647637 \tabularnewline
88 & 107.709422296521 & 107.232843843701 & 108.186000749341 \tabularnewline
89 & 107.837143917784 & 107.297758160272 & 108.376529675297 \tabularnewline
90 & 107.910028405839 & 107.311166139047 & 108.508890672631 \tabularnewline
91 & 107.927480751377 & 107.271592132784 & 108.58336936997 \tabularnewline
92 & 108.114153428841 & 107.40183092546 & 108.826475932221 \tabularnewline
93 & 108.230141277231 & 107.462910151896 & 108.997372402567 \tabularnewline
94 & 108.574099762322 & 107.751188231105 & 109.39701129354 \tabularnewline
95 & 108.704398379924 & 107.827857762744 & 109.580938997104 \tabularnewline
96 & 108.749979216926 & 106.118703011101 & 111.381255422752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232481&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]85[/C][C]107.619188555343[/C][C]107.374687986786[/C][C]107.8636891239[/C][/ROW]
[ROW][C]86[/C][C]107.443024185069[/C][C]107.109031552746[/C][C]107.777016817393[/C][/ROW]
[ROW][C]87[/C][C]107.614320710663[/C][C]107.20509077369[/C][C]108.023550647637[/C][/ROW]
[ROW][C]88[/C][C]107.709422296521[/C][C]107.232843843701[/C][C]108.186000749341[/C][/ROW]
[ROW][C]89[/C][C]107.837143917784[/C][C]107.297758160272[/C][C]108.376529675297[/C][/ROW]
[ROW][C]90[/C][C]107.910028405839[/C][C]107.311166139047[/C][C]108.508890672631[/C][/ROW]
[ROW][C]91[/C][C]107.927480751377[/C][C]107.271592132784[/C][C]108.58336936997[/C][/ROW]
[ROW][C]92[/C][C]108.114153428841[/C][C]107.40183092546[/C][C]108.826475932221[/C][/ROW]
[ROW][C]93[/C][C]108.230141277231[/C][C]107.462910151896[/C][C]108.997372402567[/C][/ROW]
[ROW][C]94[/C][C]108.574099762322[/C][C]107.751188231105[/C][C]109.39701129354[/C][/ROW]
[ROW][C]95[/C][C]108.704398379924[/C][C]107.827857762744[/C][C]109.580938997104[/C][/ROW]
[ROW][C]96[/C][C]108.749979216926[/C][C]106.118703011101[/C][C]111.381255422752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232481&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232481&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
85	107.619188555343	107.374687986786	107.8636891239
86	107.443024185069	107.109031552746	107.777016817393
87	107.614320710663	107.20509077369	108.023550647637
88	107.709422296521	107.232843843701	108.186000749341
89	107.837143917784	107.297758160272	108.376529675297
90	107.910028405839	107.311166139047	108.508890672631
91	107.927480751377	107.271592132784	108.58336936997
92	108.114153428841	107.40183092546	108.826475932221
93	108.230141277231	107.462910151896	108.997372402567
94	108.574099762322	107.751188231105	109.39701129354
95	108.704398379924	107.827857762744	109.580938997104
96	108.749979216926	106.118703011101	111.381255422752

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=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