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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 27 May 2012 08:00:29 -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/2012/May/27/t1338120055u534yqs1trxmp50.htm/, Retrieved Thu, 09 May 2024 00:01:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167682, Retrieved Thu, 09 May 2024 00:01:55 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

133

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

-       [Exponential Smoothing] [] [2012-05-27 12:00:29] [8c816eab22d9cf7f95700ac71a0ea328] [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	2 seconds
R Server	'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167682&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167682&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167682&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'AstonUniversity' @ aston.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.627213828350914
beta	0.0867300268830716
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.627213828350914 \tabularnewline
beta & 0.0867300268830716 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167682&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]0.627213828350914[/C][/ROW]
[ROW][C]beta[/C][C]0.0867300268830716[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167682&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167682&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	0.627213828350914
beta	0.0867300268830716
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	4.07	3.86178952991453	0.208210470085469
14	4.07	3.99723394681064	0.0727660531893628
15	4.3	4.28376743335781	0.0162325666421861
16	4.44	4.44864202562299	-0.00864202562298999
17	4.52	4.53786148504937	-0.0178614850493748
18	4.52	4.5403267381081	-0.0203267381081007
19	4.52	4.43805667759225	0.081943322407752
20	4.53	4.5389727217484	-0.00897272174839969
21	4.53	4.63279353189752	-0.102793531897524
22	4.53	4.59676017533939	-0.0667601753393905
23	4.53	4.5605291334399	-0.0305291334398978
24	4.53	4.54202863659128	-0.0120286365912756
25	4.53	4.61209555419047	-0.0820955541904702
26	4.53	4.5052232195057	0.024776780494296
27	4.53	4.72823074201218	-0.198230742012176
28	4.61	4.72530011737975	-0.115300117379749
29	4.63	4.7143652838456	-0.0843652838455968
30	4.63	4.64076175474174	-0.0107617547417442
31	4.63	4.54969849929413	0.0803015007058736
32	4.63	4.58268586476777	0.0473141352322264
33	4.63	4.64689071573509	-0.0168907157350944
34	4.63	4.6528977415892	-0.0228977415892029
35	4.63	4.63479850787568	-0.00479850787567759
36	4.63	4.61784729794818	0.0121527020518153
37	4.63	4.65679048396416	-0.0267904839641622
38	4.63	4.60728465927234	0.0227153407276584
39	4.66	4.72859083559195	-0.0685908355919453
40	4.7	4.8276654678635	-0.127665467863503
41	4.72	4.80961226479785	-0.0896122647978466
42	4.73	4.74897597894061	-0.0189759789406114
43	4.73	4.67508077568115	0.0549192243188505
44	4.74	4.66684304556095	0.0731569544390513
45	4.74	4.71172024705726	0.0282797529427361
46	4.74	4.73467473233064	0.00532526766936137
47	4.76	4.73341504028999	0.0265849597100116
48	4.88	4.73656489422204	0.14343510577796
49	4.88	4.84457201633421	0.0354279836657856
50	4.88	4.85716941720427	0.0228305827957325
51	4.88	4.94914031941823	-0.0691403194182332
52	4.89	5.03044833525241	-0.140448335252407
53	4.97	5.02246811640765	-0.0524681164076499
54	4.97	5.01738682966521	-0.0473868296652151
55	4.97	4.95759900170933	0.0124009982906736
56	4.97	4.93155905165261	0.0384409483473851
57	4.97	4.93811082896834	0.0318891710316551
58	4.97	4.95514695764518	0.0148530423548241
59	4.97	4.9686817124807	0.00131828751929941
60	4.97	4.99906279115013	-0.0290627911501282

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4.07 & 3.86178952991453 & 0.208210470085469 \tabularnewline
14 & 4.07 & 3.99723394681064 & 0.0727660531893628 \tabularnewline
15 & 4.3 & 4.28376743335781 & 0.0162325666421861 \tabularnewline
16 & 4.44 & 4.44864202562299 & -0.00864202562298999 \tabularnewline
17 & 4.52 & 4.53786148504937 & -0.0178614850493748 \tabularnewline
18 & 4.52 & 4.5403267381081 & -0.0203267381081007 \tabularnewline
19 & 4.52 & 4.43805667759225 & 0.081943322407752 \tabularnewline
20 & 4.53 & 4.5389727217484 & -0.00897272174839969 \tabularnewline
21 & 4.53 & 4.63279353189752 & -0.102793531897524 \tabularnewline
22 & 4.53 & 4.59676017533939 & -0.0667601753393905 \tabularnewline
23 & 4.53 & 4.5605291334399 & -0.0305291334398978 \tabularnewline
24 & 4.53 & 4.54202863659128 & -0.0120286365912756 \tabularnewline
25 & 4.53 & 4.61209555419047 & -0.0820955541904702 \tabularnewline
26 & 4.53 & 4.5052232195057 & 0.024776780494296 \tabularnewline
27 & 4.53 & 4.72823074201218 & -0.198230742012176 \tabularnewline
28 & 4.61 & 4.72530011737975 & -0.115300117379749 \tabularnewline
29 & 4.63 & 4.7143652838456 & -0.0843652838455968 \tabularnewline
30 & 4.63 & 4.64076175474174 & -0.0107617547417442 \tabularnewline
31 & 4.63 & 4.54969849929413 & 0.0803015007058736 \tabularnewline
32 & 4.63 & 4.58268586476777 & 0.0473141352322264 \tabularnewline
33 & 4.63 & 4.64689071573509 & -0.0168907157350944 \tabularnewline
34 & 4.63 & 4.6528977415892 & -0.0228977415892029 \tabularnewline
35 & 4.63 & 4.63479850787568 & -0.00479850787567759 \tabularnewline
36 & 4.63 & 4.61784729794818 & 0.0121527020518153 \tabularnewline
37 & 4.63 & 4.65679048396416 & -0.0267904839641622 \tabularnewline
38 & 4.63 & 4.60728465927234 & 0.0227153407276584 \tabularnewline
39 & 4.66 & 4.72859083559195 & -0.0685908355919453 \tabularnewline
40 & 4.7 & 4.8276654678635 & -0.127665467863503 \tabularnewline
41 & 4.72 & 4.80961226479785 & -0.0896122647978466 \tabularnewline
42 & 4.73 & 4.74897597894061 & -0.0189759789406114 \tabularnewline
43 & 4.73 & 4.67508077568115 & 0.0549192243188505 \tabularnewline
44 & 4.74 & 4.66684304556095 & 0.0731569544390513 \tabularnewline
45 & 4.74 & 4.71172024705726 & 0.0282797529427361 \tabularnewline
46 & 4.74 & 4.73467473233064 & 0.00532526766936137 \tabularnewline
47 & 4.76 & 4.73341504028999 & 0.0265849597100116 \tabularnewline
48 & 4.88 & 4.73656489422204 & 0.14343510577796 \tabularnewline
49 & 4.88 & 4.84457201633421 & 0.0354279836657856 \tabularnewline
50 & 4.88 & 4.85716941720427 & 0.0228305827957325 \tabularnewline
51 & 4.88 & 4.94914031941823 & -0.0691403194182332 \tabularnewline
52 & 4.89 & 5.03044833525241 & -0.140448335252407 \tabularnewline
53 & 4.97 & 5.02246811640765 & -0.0524681164076499 \tabularnewline
54 & 4.97 & 5.01738682966521 & -0.0473868296652151 \tabularnewline
55 & 4.97 & 4.95759900170933 & 0.0124009982906736 \tabularnewline
56 & 4.97 & 4.93155905165261 & 0.0384409483473851 \tabularnewline
57 & 4.97 & 4.93811082896834 & 0.0318891710316551 \tabularnewline
58 & 4.97 & 4.95514695764518 & 0.0148530423548241 \tabularnewline
59 & 4.97 & 4.9686817124807 & 0.00131828751929941 \tabularnewline
60 & 4.97 & 4.99906279115013 & -0.0290627911501282 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167682&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]4.07[/C][C]3.86178952991453[/C][C]0.208210470085469[/C][/ROW]
[ROW][C]14[/C][C]4.07[/C][C]3.99723394681064[/C][C]0.0727660531893628[/C][/ROW]
[ROW][C]15[/C][C]4.3[/C][C]4.28376743335781[/C][C]0.0162325666421861[/C][/ROW]
[ROW][C]16[/C][C]4.44[/C][C]4.44864202562299[/C][C]-0.00864202562298999[/C][/ROW]
[ROW][C]17[/C][C]4.52[/C][C]4.53786148504937[/C][C]-0.0178614850493748[/C][/ROW]
[ROW][C]18[/C][C]4.52[/C][C]4.5403267381081[/C][C]-0.0203267381081007[/C][/ROW]
[ROW][C]19[/C][C]4.52[/C][C]4.43805667759225[/C][C]0.081943322407752[/C][/ROW]
[ROW][C]20[/C][C]4.53[/C][C]4.5389727217484[/C][C]-0.00897272174839969[/C][/ROW]
[ROW][C]21[/C][C]4.53[/C][C]4.63279353189752[/C][C]-0.102793531897524[/C][/ROW]
[ROW][C]22[/C][C]4.53[/C][C]4.59676017533939[/C][C]-0.0667601753393905[/C][/ROW]
[ROW][C]23[/C][C]4.53[/C][C]4.5605291334399[/C][C]-0.0305291334398978[/C][/ROW]
[ROW][C]24[/C][C]4.53[/C][C]4.54202863659128[/C][C]-0.0120286365912756[/C][/ROW]
[ROW][C]25[/C][C]4.53[/C][C]4.61209555419047[/C][C]-0.0820955541904702[/C][/ROW]
[ROW][C]26[/C][C]4.53[/C][C]4.5052232195057[/C][C]0.024776780494296[/C][/ROW]
[ROW][C]27[/C][C]4.53[/C][C]4.72823074201218[/C][C]-0.198230742012176[/C][/ROW]
[ROW][C]28[/C][C]4.61[/C][C]4.72530011737975[/C][C]-0.115300117379749[/C][/ROW]
[ROW][C]29[/C][C]4.63[/C][C]4.7143652838456[/C][C]-0.0843652838455968[/C][/ROW]
[ROW][C]30[/C][C]4.63[/C][C]4.64076175474174[/C][C]-0.0107617547417442[/C][/ROW]
[ROW][C]31[/C][C]4.63[/C][C]4.54969849929413[/C][C]0.0803015007058736[/C][/ROW]
[ROW][C]32[/C][C]4.63[/C][C]4.58268586476777[/C][C]0.0473141352322264[/C][/ROW]
[ROW][C]33[/C][C]4.63[/C][C]4.64689071573509[/C][C]-0.0168907157350944[/C][/ROW]
[ROW][C]34[/C][C]4.63[/C][C]4.6528977415892[/C][C]-0.0228977415892029[/C][/ROW]
[ROW][C]35[/C][C]4.63[/C][C]4.63479850787568[/C][C]-0.00479850787567759[/C][/ROW]
[ROW][C]36[/C][C]4.63[/C][C]4.61784729794818[/C][C]0.0121527020518153[/C][/ROW]
[ROW][C]37[/C][C]4.63[/C][C]4.65679048396416[/C][C]-0.0267904839641622[/C][/ROW]
[ROW][C]38[/C][C]4.63[/C][C]4.60728465927234[/C][C]0.0227153407276584[/C][/ROW]
[ROW][C]39[/C][C]4.66[/C][C]4.72859083559195[/C][C]-0.0685908355919453[/C][/ROW]
[ROW][C]40[/C][C]4.7[/C][C]4.8276654678635[/C][C]-0.127665467863503[/C][/ROW]
[ROW][C]41[/C][C]4.72[/C][C]4.80961226479785[/C][C]-0.0896122647978466[/C][/ROW]
[ROW][C]42[/C][C]4.73[/C][C]4.74897597894061[/C][C]-0.0189759789406114[/C][/ROW]
[ROW][C]43[/C][C]4.73[/C][C]4.67508077568115[/C][C]0.0549192243188505[/C][/ROW]
[ROW][C]44[/C][C]4.74[/C][C]4.66684304556095[/C][C]0.0731569544390513[/C][/ROW]
[ROW][C]45[/C][C]4.74[/C][C]4.71172024705726[/C][C]0.0282797529427361[/C][/ROW]
[ROW][C]46[/C][C]4.74[/C][C]4.73467473233064[/C][C]0.00532526766936137[/C][/ROW]
[ROW][C]47[/C][C]4.76[/C][C]4.73341504028999[/C][C]0.0265849597100116[/C][/ROW]
[ROW][C]48[/C][C]4.88[/C][C]4.73656489422204[/C][C]0.14343510577796[/C][/ROW]
[ROW][C]49[/C][C]4.88[/C][C]4.84457201633421[/C][C]0.0354279836657856[/C][/ROW]
[ROW][C]50[/C][C]4.88[/C][C]4.85716941720427[/C][C]0.0228305827957325[/C][/ROW]
[ROW][C]51[/C][C]4.88[/C][C]4.94914031941823[/C][C]-0.0691403194182332[/C][/ROW]
[ROW][C]52[/C][C]4.89[/C][C]5.03044833525241[/C][C]-0.140448335252407[/C][/ROW]
[ROW][C]53[/C][C]4.97[/C][C]5.02246811640765[/C][C]-0.0524681164076499[/C][/ROW]
[ROW][C]54[/C][C]4.97[/C][C]5.01738682966521[/C][C]-0.0473868296652151[/C][/ROW]
[ROW][C]55[/C][C]4.97[/C][C]4.95759900170933[/C][C]0.0124009982906736[/C][/ROW]
[ROW][C]56[/C][C]4.97[/C][C]4.93155905165261[/C][C]0.0384409483473851[/C][/ROW]
[ROW][C]57[/C][C]4.97[/C][C]4.93811082896834[/C][C]0.0318891710316551[/C][/ROW]
[ROW][C]58[/C][C]4.97[/C][C]4.95514695764518[/C][C]0.0148530423548241[/C][/ROW]
[ROW][C]59[/C][C]4.97[/C][C]4.9686817124807[/C][C]0.00131828751929941[/C][/ROW]
[ROW][C]60[/C][C]4.97[/C][C]4.99906279115013[/C][C]-0.0290627911501282[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167682&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167682&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	4.07	3.86178952991453	0.208210470085469
14	4.07	3.99723394681064	0.0727660531893628
15	4.3	4.28376743335781	0.0162325666421861
16	4.44	4.44864202562299	-0.00864202562298999
17	4.52	4.53786148504937	-0.0178614850493748
18	4.52	4.5403267381081	-0.0203267381081007
19	4.52	4.43805667759225	0.081943322407752
20	4.53	4.5389727217484	-0.00897272174839969
21	4.53	4.63279353189752	-0.102793531897524
22	4.53	4.59676017533939	-0.0667601753393905
23	4.53	4.5605291334399	-0.0305291334398978
24	4.53	4.54202863659128	-0.0120286365912756
25	4.53	4.61209555419047	-0.0820955541904702
26	4.53	4.5052232195057	0.024776780494296
27	4.53	4.72823074201218	-0.198230742012176
28	4.61	4.72530011737975	-0.115300117379749
29	4.63	4.7143652838456	-0.0843652838455968
30	4.63	4.64076175474174	-0.0107617547417442
31	4.63	4.54969849929413	0.0803015007058736
32	4.63	4.58268586476777	0.0473141352322264
33	4.63	4.64689071573509	-0.0168907157350944
34	4.63	4.6528977415892	-0.0228977415892029
35	4.63	4.63479850787568	-0.00479850787567759
36	4.63	4.61784729794818	0.0121527020518153
37	4.63	4.65679048396416	-0.0267904839641622
38	4.63	4.60728465927234	0.0227153407276584
39	4.66	4.72859083559195	-0.0685908355919453
40	4.7	4.8276654678635	-0.127665467863503
41	4.72	4.80961226479785	-0.0896122647978466
42	4.73	4.74897597894061	-0.0189759789406114
43	4.73	4.67508077568115	0.0549192243188505
44	4.74	4.66684304556095	0.0731569544390513
45	4.74	4.71172024705726	0.0282797529427361
46	4.74	4.73467473233064	0.00532526766936137
47	4.76	4.73341504028999	0.0265849597100116
48	4.88	4.73656489422204	0.14343510577796
49	4.88	4.84457201633421	0.0354279836657856
50	4.88	4.85716941720427	0.0228305827957325
51	4.88	4.94914031941823	-0.0691403194182332
52	4.89	5.03044833525241	-0.140448335252407
53	4.97	5.02246811640765	-0.0524681164076499
54	4.97	5.01738682966521	-0.0473868296652151
55	4.97	4.95759900170933	0.0124009982906736
56	4.97	4.93155905165261	0.0384409483473851
57	4.97	4.93811082896834	0.0318891710316551
58	4.97	4.95514695764518	0.0148530423548241
59	4.97	4.9686817124807	0.00131828751929941
60	4.97	4.99906279115013	-0.0290627911501282

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	4.94874841015698	4.80813406159269	5.08936275872126
62	4.92263665659189	4.75246453200324	5.09280878118054
63	4.95296838044403	4.75379639149656	5.15214036939151
64	5.04178659181495	4.81370282991785	5.26987035371206
65	5.1530625400754	4.89589773765739	5.4102273424934
66	5.18400560990304	4.89743781600061	5.47057340380547
67	5.18002668892823	4.86363876726319	5.49641461059327
68	5.1590405583078	4.81235423775405	5.50572687886154
69	5.14007267184845	4.76256984538359	5.51757549831331
70	5.13005536507095	4.72119197199049	5.53891875815141
71	5.12771926384869	4.68693462785039	5.568503899847
72	5.14436688272482	4.67109014843737	5.61764361701227

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 4.94874841015698 & 4.80813406159269 & 5.08936275872126 \tabularnewline
62 & 4.92263665659189 & 4.75246453200324 & 5.09280878118054 \tabularnewline
63 & 4.95296838044403 & 4.75379639149656 & 5.15214036939151 \tabularnewline
64 & 5.04178659181495 & 4.81370282991785 & 5.26987035371206 \tabularnewline
65 & 5.1530625400754 & 4.89589773765739 & 5.4102273424934 \tabularnewline
66 & 5.18400560990304 & 4.89743781600061 & 5.47057340380547 \tabularnewline
67 & 5.18002668892823 & 4.86363876726319 & 5.49641461059327 \tabularnewline
68 & 5.1590405583078 & 4.81235423775405 & 5.50572687886154 \tabularnewline
69 & 5.14007267184845 & 4.76256984538359 & 5.51757549831331 \tabularnewline
70 & 5.13005536507095 & 4.72119197199049 & 5.53891875815141 \tabularnewline
71 & 5.12771926384869 & 4.68693462785039 & 5.568503899847 \tabularnewline
72 & 5.14436688272482 & 4.67109014843737 & 5.61764361701227 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167682&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]61[/C][C]4.94874841015698[/C][C]4.80813406159269[/C][C]5.08936275872126[/C][/ROW]
[ROW][C]62[/C][C]4.92263665659189[/C][C]4.75246453200324[/C][C]5.09280878118054[/C][/ROW]
[ROW][C]63[/C][C]4.95296838044403[/C][C]4.75379639149656[/C][C]5.15214036939151[/C][/ROW]
[ROW][C]64[/C][C]5.04178659181495[/C][C]4.81370282991785[/C][C]5.26987035371206[/C][/ROW]
[ROW][C]65[/C][C]5.1530625400754[/C][C]4.89589773765739[/C][C]5.4102273424934[/C][/ROW]
[ROW][C]66[/C][C]5.18400560990304[/C][C]4.89743781600061[/C][C]5.47057340380547[/C][/ROW]
[ROW][C]67[/C][C]5.18002668892823[/C][C]4.86363876726319[/C][C]5.49641461059327[/C][/ROW]
[ROW][C]68[/C][C]5.1590405583078[/C][C]4.81235423775405[/C][C]5.50572687886154[/C][/ROW]
[ROW][C]69[/C][C]5.14007267184845[/C][C]4.76256984538359[/C][C]5.51757549831331[/C][/ROW]
[ROW][C]70[/C][C]5.13005536507095[/C][C]4.72119197199049[/C][C]5.53891875815141[/C][/ROW]
[ROW][C]71[/C][C]5.12771926384869[/C][C]4.68693462785039[/C][C]5.568503899847[/C][/ROW]
[ROW][C]72[/C][C]5.14436688272482[/C][C]4.67109014843737[/C][C]5.61764361701227[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167682&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167682&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
61	4.94874841015698	4.80813406159269	5.08936275872126
62	4.92263665659189	4.75246453200324	5.09280878118054
63	4.95296838044403	4.75379639149656	5.15214036939151
64	5.04178659181495	4.81370282991785	5.26987035371206
65	5.1530625400754	4.89589773765739	5.4102273424934
66	5.18400560990304	4.89743781600061	5.47057340380547
67	5.18002668892823	4.86363876726319	5.49641461059327
68	5.1590405583078	4.81235423775405	5.50572687886154
69	5.14007267184845	4.76256984538359	5.51757549831331
70	5.13005536507095	4.72119197199049	5.53891875815141
71	5.12771926384869	4.68693462785039	5.568503899847
72	5.14436688272482	4.67109014843737	5.61764361701227

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