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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 20 Dec 2011 13:58:08 -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/2011/Dec/20/t132440757589581n1cker1gex.htm/, Retrieved Mon, 06 May 2024 03:07:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158157, Retrieved Mon, 06 May 2024 03:07:16 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

102

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

-       [Exponential Smoothing] [Gemiddelde prijs ...] [2011-12-20 18:58:08] [442788da29e2c48dd438d3f23a1381bc] [Current]

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Dataseries X:

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Histogram

Boxplots

3,11
3,1
3,13
3,14
3,16
3,17
3,19
3,18
3,17
3,17
3,2
3,21
3,25
3,22
3,25
3,31
3,35
3,37
3,38
3,38
3,39
3,44
3,56
3,65
3,69
3,71
3,71
3,74
3,75
3,77
3,75
3,78
3,8
3,78
3,79
3,8
3,82
3,82
3,84
3,86
3,8
3,85
3,78
3,79
3,77
3,78
3,77
3,76
3,78
3,76
3,75
3,71
3,72
3,7
3,69
3,7
3,72
3,73
3,73
3,69

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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158157&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158157&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158157&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	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.190849902182248
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.190849902182248 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158157&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]0.190849902182248[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158157&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158157&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	0.190849902182248
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	3.13	3.09	0.0399999999999996
4	3.14	3.12763399608729	0.0123660039127103
5	3.16	3.13999404672442	0.0200059532755841
6	3.17	3.16381218095012	0.00618781904987609
7	3.19	3.17499312561051	0.0150068743894858
8	3.18	3.19785718611981	-0.0178571861198087
9	3.17	3.18444914389559	-0.0144491438955936
10	3.17	3.1716915261965	-0.00169152619650204
11	3.2	3.17136869858736	0.0286313014126396
12	3.21	3.20683297966131	0.00316702033868621
13	3.25	3.21743740518316	0.0325625948168389
14	3.22	3.26365197321875	-0.0436519732187546
15	3.25	3.22532099839989	0.0246790016001062
16	3.31	3.26003098344123	0.0499690165587707
17	3.35	3.32956756536361	0.0204324346363864
18	3.37	3.37346709351531	-0.00346709351531338
19	3.38	3.39280539905706	-0.0128053990570591
20	3.38	3.40036148989961	-0.0203614898996145
21	3.39	3.39647550154399	-0.00647550154398813
22	3.44	3.40523965270774	0.0347603472922624
23	3.56	3.46187366158829	0.0981263384117135
24	3.65	3.60060106367566	0.0493989363243359
25	3.69	3.70002884584107	-0.0100288458410707
26	3.71	3.7381148415933	-0.0281148415933017
27	3.71	3.75274912682535	-0.0427491268253504
28	3.74	3.74459046015236	-0.00459046015235565
29	3.75	3.77371437128131	-0.0237143712813075
30	3.77	3.77918848584196	-0.00918848584195642
31	3.75	3.79743486421782	-0.047434864217816
32	3.78	3.76838192502182	0.0116180749781822
33	3.8	3.80059923349495	-0.000599233494949836
34	3.78	3.82048486984105	-0.040484869841054
35	3.79	3.79275833639203	-0.0027583363920276
36	3.8	3.80223190816142	-0.00223190816142393
37	3.82	3.81180594870714	0.00819405129286377
38	3.82	3.83336978259486	-0.0133697825948556
39	3.84	3.83081816089443	0.00918183910557069
40	3.86	3.85257051398958	0.00742948601041915
41	3.8	3.87398843066793	-0.0739884306679337
42	3.85	3.79986774591234	0.0501322540876599
43	3.78	3.85943548170115	-0.0794354817011462
44	3.79	3.77427522778868	0.0157247722113176
45	3.77	3.78727629902705	-0.0172762990270505
46	3.78	3.76397911904767	0.016020880952333
47	3.77	3.77703670261029	-0.00703670261029288
48	3.76	3.76569374860543	-0.00569374860543315
49	3.78	3.75460709724104	0.0253929027589641
50	3.76	3.77945333024871	-0.0194533302487074
51	3.75	3.75574066407362	-0.00574066407362261
52	3.71	3.74464505889671	-0.0346450588967109
53	3.72	3.69803305279518	0.0219669472048252
54	3.7	3.71222544252046	-0.0122254425204589
55	3.69	3.68989221801129	0.000107781988705202
56	3.7	3.6799127881933	0.0200872118067044
57	3.72	3.69374643060172	0.0262535693982806
58	3.73	3.71875692175332	0.0112430782466837
59	3.73	3.73090266213692	-0.000902662136923027
60	3.69	3.73073038915639	-0.0407303891563879

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3.13 & 3.09 & 0.0399999999999996 \tabularnewline
4 & 3.14 & 3.12763399608729 & 0.0123660039127103 \tabularnewline
5 & 3.16 & 3.13999404672442 & 0.0200059532755841 \tabularnewline
6 & 3.17 & 3.16381218095012 & 0.00618781904987609 \tabularnewline
7 & 3.19 & 3.17499312561051 & 0.0150068743894858 \tabularnewline
8 & 3.18 & 3.19785718611981 & -0.0178571861198087 \tabularnewline
9 & 3.17 & 3.18444914389559 & -0.0144491438955936 \tabularnewline
10 & 3.17 & 3.1716915261965 & -0.00169152619650204 \tabularnewline
11 & 3.2 & 3.17136869858736 & 0.0286313014126396 \tabularnewline
12 & 3.21 & 3.20683297966131 & 0.00316702033868621 \tabularnewline
13 & 3.25 & 3.21743740518316 & 0.0325625948168389 \tabularnewline
14 & 3.22 & 3.26365197321875 & -0.0436519732187546 \tabularnewline
15 & 3.25 & 3.22532099839989 & 0.0246790016001062 \tabularnewline
16 & 3.31 & 3.26003098344123 & 0.0499690165587707 \tabularnewline
17 & 3.35 & 3.32956756536361 & 0.0204324346363864 \tabularnewline
18 & 3.37 & 3.37346709351531 & -0.00346709351531338 \tabularnewline
19 & 3.38 & 3.39280539905706 & -0.0128053990570591 \tabularnewline
20 & 3.38 & 3.40036148989961 & -0.0203614898996145 \tabularnewline
21 & 3.39 & 3.39647550154399 & -0.00647550154398813 \tabularnewline
22 & 3.44 & 3.40523965270774 & 0.0347603472922624 \tabularnewline
23 & 3.56 & 3.46187366158829 & 0.0981263384117135 \tabularnewline
24 & 3.65 & 3.60060106367566 & 0.0493989363243359 \tabularnewline
25 & 3.69 & 3.70002884584107 & -0.0100288458410707 \tabularnewline
26 & 3.71 & 3.7381148415933 & -0.0281148415933017 \tabularnewline
27 & 3.71 & 3.75274912682535 & -0.0427491268253504 \tabularnewline
28 & 3.74 & 3.74459046015236 & -0.00459046015235565 \tabularnewline
29 & 3.75 & 3.77371437128131 & -0.0237143712813075 \tabularnewline
30 & 3.77 & 3.77918848584196 & -0.00918848584195642 \tabularnewline
31 & 3.75 & 3.79743486421782 & -0.047434864217816 \tabularnewline
32 & 3.78 & 3.76838192502182 & 0.0116180749781822 \tabularnewline
33 & 3.8 & 3.80059923349495 & -0.000599233494949836 \tabularnewline
34 & 3.78 & 3.82048486984105 & -0.040484869841054 \tabularnewline
35 & 3.79 & 3.79275833639203 & -0.0027583363920276 \tabularnewline
36 & 3.8 & 3.80223190816142 & -0.00223190816142393 \tabularnewline
37 & 3.82 & 3.81180594870714 & 0.00819405129286377 \tabularnewline
38 & 3.82 & 3.83336978259486 & -0.0133697825948556 \tabularnewline
39 & 3.84 & 3.83081816089443 & 0.00918183910557069 \tabularnewline
40 & 3.86 & 3.85257051398958 & 0.00742948601041915 \tabularnewline
41 & 3.8 & 3.87398843066793 & -0.0739884306679337 \tabularnewline
42 & 3.85 & 3.79986774591234 & 0.0501322540876599 \tabularnewline
43 & 3.78 & 3.85943548170115 & -0.0794354817011462 \tabularnewline
44 & 3.79 & 3.77427522778868 & 0.0157247722113176 \tabularnewline
45 & 3.77 & 3.78727629902705 & -0.0172762990270505 \tabularnewline
46 & 3.78 & 3.76397911904767 & 0.016020880952333 \tabularnewline
47 & 3.77 & 3.77703670261029 & -0.00703670261029288 \tabularnewline
48 & 3.76 & 3.76569374860543 & -0.00569374860543315 \tabularnewline
49 & 3.78 & 3.75460709724104 & 0.0253929027589641 \tabularnewline
50 & 3.76 & 3.77945333024871 & -0.0194533302487074 \tabularnewline
51 & 3.75 & 3.75574066407362 & -0.00574066407362261 \tabularnewline
52 & 3.71 & 3.74464505889671 & -0.0346450588967109 \tabularnewline
53 & 3.72 & 3.69803305279518 & 0.0219669472048252 \tabularnewline
54 & 3.7 & 3.71222544252046 & -0.0122254425204589 \tabularnewline
55 & 3.69 & 3.68989221801129 & 0.000107781988705202 \tabularnewline
56 & 3.7 & 3.6799127881933 & 0.0200872118067044 \tabularnewline
57 & 3.72 & 3.69374643060172 & 0.0262535693982806 \tabularnewline
58 & 3.73 & 3.71875692175332 & 0.0112430782466837 \tabularnewline
59 & 3.73 & 3.73090266213692 & -0.000902662136923027 \tabularnewline
60 & 3.69 & 3.73073038915639 & -0.0407303891563879 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158157&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]3.13[/C][C]3.09[/C][C]0.0399999999999996[/C][/ROW]
[ROW][C]4[/C][C]3.14[/C][C]3.12763399608729[/C][C]0.0123660039127103[/C][/ROW]
[ROW][C]5[/C][C]3.16[/C][C]3.13999404672442[/C][C]0.0200059532755841[/C][/ROW]
[ROW][C]6[/C][C]3.17[/C][C]3.16381218095012[/C][C]0.00618781904987609[/C][/ROW]
[ROW][C]7[/C][C]3.19[/C][C]3.17499312561051[/C][C]0.0150068743894858[/C][/ROW]
[ROW][C]8[/C][C]3.18[/C][C]3.19785718611981[/C][C]-0.0178571861198087[/C][/ROW]
[ROW][C]9[/C][C]3.17[/C][C]3.18444914389559[/C][C]-0.0144491438955936[/C][/ROW]
[ROW][C]10[/C][C]3.17[/C][C]3.1716915261965[/C][C]-0.00169152619650204[/C][/ROW]
[ROW][C]11[/C][C]3.2[/C][C]3.17136869858736[/C][C]0.0286313014126396[/C][/ROW]
[ROW][C]12[/C][C]3.21[/C][C]3.20683297966131[/C][C]0.00316702033868621[/C][/ROW]
[ROW][C]13[/C][C]3.25[/C][C]3.21743740518316[/C][C]0.0325625948168389[/C][/ROW]
[ROW][C]14[/C][C]3.22[/C][C]3.26365197321875[/C][C]-0.0436519732187546[/C][/ROW]
[ROW][C]15[/C][C]3.25[/C][C]3.22532099839989[/C][C]0.0246790016001062[/C][/ROW]
[ROW][C]16[/C][C]3.31[/C][C]3.26003098344123[/C][C]0.0499690165587707[/C][/ROW]
[ROW][C]17[/C][C]3.35[/C][C]3.32956756536361[/C][C]0.0204324346363864[/C][/ROW]
[ROW][C]18[/C][C]3.37[/C][C]3.37346709351531[/C][C]-0.00346709351531338[/C][/ROW]
[ROW][C]19[/C][C]3.38[/C][C]3.39280539905706[/C][C]-0.0128053990570591[/C][/ROW]
[ROW][C]20[/C][C]3.38[/C][C]3.40036148989961[/C][C]-0.0203614898996145[/C][/ROW]
[ROW][C]21[/C][C]3.39[/C][C]3.39647550154399[/C][C]-0.00647550154398813[/C][/ROW]
[ROW][C]22[/C][C]3.44[/C][C]3.40523965270774[/C][C]0.0347603472922624[/C][/ROW]
[ROW][C]23[/C][C]3.56[/C][C]3.46187366158829[/C][C]0.0981263384117135[/C][/ROW]
[ROW][C]24[/C][C]3.65[/C][C]3.60060106367566[/C][C]0.0493989363243359[/C][/ROW]
[ROW][C]25[/C][C]3.69[/C][C]3.70002884584107[/C][C]-0.0100288458410707[/C][/ROW]
[ROW][C]26[/C][C]3.71[/C][C]3.7381148415933[/C][C]-0.0281148415933017[/C][/ROW]
[ROW][C]27[/C][C]3.71[/C][C]3.75274912682535[/C][C]-0.0427491268253504[/C][/ROW]
[ROW][C]28[/C][C]3.74[/C][C]3.74459046015236[/C][C]-0.00459046015235565[/C][/ROW]
[ROW][C]29[/C][C]3.75[/C][C]3.77371437128131[/C][C]-0.0237143712813075[/C][/ROW]
[ROW][C]30[/C][C]3.77[/C][C]3.77918848584196[/C][C]-0.00918848584195642[/C][/ROW]
[ROW][C]31[/C][C]3.75[/C][C]3.79743486421782[/C][C]-0.047434864217816[/C][/ROW]
[ROW][C]32[/C][C]3.78[/C][C]3.76838192502182[/C][C]0.0116180749781822[/C][/ROW]
[ROW][C]33[/C][C]3.8[/C][C]3.80059923349495[/C][C]-0.000599233494949836[/C][/ROW]
[ROW][C]34[/C][C]3.78[/C][C]3.82048486984105[/C][C]-0.040484869841054[/C][/ROW]
[ROW][C]35[/C][C]3.79[/C][C]3.79275833639203[/C][C]-0.0027583363920276[/C][/ROW]
[ROW][C]36[/C][C]3.8[/C][C]3.80223190816142[/C][C]-0.00223190816142393[/C][/ROW]
[ROW][C]37[/C][C]3.82[/C][C]3.81180594870714[/C][C]0.00819405129286377[/C][/ROW]
[ROW][C]38[/C][C]3.82[/C][C]3.83336978259486[/C][C]-0.0133697825948556[/C][/ROW]
[ROW][C]39[/C][C]3.84[/C][C]3.83081816089443[/C][C]0.00918183910557069[/C][/ROW]
[ROW][C]40[/C][C]3.86[/C][C]3.85257051398958[/C][C]0.00742948601041915[/C][/ROW]
[ROW][C]41[/C][C]3.8[/C][C]3.87398843066793[/C][C]-0.0739884306679337[/C][/ROW]
[ROW][C]42[/C][C]3.85[/C][C]3.79986774591234[/C][C]0.0501322540876599[/C][/ROW]
[ROW][C]43[/C][C]3.78[/C][C]3.85943548170115[/C][C]-0.0794354817011462[/C][/ROW]
[ROW][C]44[/C][C]3.79[/C][C]3.77427522778868[/C][C]0.0157247722113176[/C][/ROW]
[ROW][C]45[/C][C]3.77[/C][C]3.78727629902705[/C][C]-0.0172762990270505[/C][/ROW]
[ROW][C]46[/C][C]3.78[/C][C]3.76397911904767[/C][C]0.016020880952333[/C][/ROW]
[ROW][C]47[/C][C]3.77[/C][C]3.77703670261029[/C][C]-0.00703670261029288[/C][/ROW]
[ROW][C]48[/C][C]3.76[/C][C]3.76569374860543[/C][C]-0.00569374860543315[/C][/ROW]
[ROW][C]49[/C][C]3.78[/C][C]3.75460709724104[/C][C]0.0253929027589641[/C][/ROW]
[ROW][C]50[/C][C]3.76[/C][C]3.77945333024871[/C][C]-0.0194533302487074[/C][/ROW]
[ROW][C]51[/C][C]3.75[/C][C]3.75574066407362[/C][C]-0.00574066407362261[/C][/ROW]
[ROW][C]52[/C][C]3.71[/C][C]3.74464505889671[/C][C]-0.0346450588967109[/C][/ROW]
[ROW][C]53[/C][C]3.72[/C][C]3.69803305279518[/C][C]0.0219669472048252[/C][/ROW]
[ROW][C]54[/C][C]3.7[/C][C]3.71222544252046[/C][C]-0.0122254425204589[/C][/ROW]
[ROW][C]55[/C][C]3.69[/C][C]3.68989221801129[/C][C]0.000107781988705202[/C][/ROW]
[ROW][C]56[/C][C]3.7[/C][C]3.6799127881933[/C][C]0.0200872118067044[/C][/ROW]
[ROW][C]57[/C][C]3.72[/C][C]3.69374643060172[/C][C]0.0262535693982806[/C][/ROW]
[ROW][C]58[/C][C]3.73[/C][C]3.71875692175332[/C][C]0.0112430782466837[/C][/ROW]
[ROW][C]59[/C][C]3.73[/C][C]3.73090266213692[/C][C]-0.000902662136923027[/C][/ROW]
[ROW][C]60[/C][C]3.69[/C][C]3.73073038915639[/C][C]-0.0407303891563879[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158157&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158157&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	3.13	3.09	0.0399999999999996
4	3.14	3.12763399608729	0.0123660039127103
5	3.16	3.13999404672442	0.0200059532755841
6	3.17	3.16381218095012	0.00618781904987609
7	3.19	3.17499312561051	0.0150068743894858
8	3.18	3.19785718611981	-0.0178571861198087
9	3.17	3.18444914389559	-0.0144491438955936
10	3.17	3.1716915261965	-0.00169152619650204
11	3.2	3.17136869858736	0.0286313014126396
12	3.21	3.20683297966131	0.00316702033868621
13	3.25	3.21743740518316	0.0325625948168389
14	3.22	3.26365197321875	-0.0436519732187546
15	3.25	3.22532099839989	0.0246790016001062
16	3.31	3.26003098344123	0.0499690165587707
17	3.35	3.32956756536361	0.0204324346363864
18	3.37	3.37346709351531	-0.00346709351531338
19	3.38	3.39280539905706	-0.0128053990570591
20	3.38	3.40036148989961	-0.0203614898996145
21	3.39	3.39647550154399	-0.00647550154398813
22	3.44	3.40523965270774	0.0347603472922624
23	3.56	3.46187366158829	0.0981263384117135
24	3.65	3.60060106367566	0.0493989363243359
25	3.69	3.70002884584107	-0.0100288458410707
26	3.71	3.7381148415933	-0.0281148415933017
27	3.71	3.75274912682535	-0.0427491268253504
28	3.74	3.74459046015236	-0.00459046015235565
29	3.75	3.77371437128131	-0.0237143712813075
30	3.77	3.77918848584196	-0.00918848584195642
31	3.75	3.79743486421782	-0.047434864217816
32	3.78	3.76838192502182	0.0116180749781822
33	3.8	3.80059923349495	-0.000599233494949836
34	3.78	3.82048486984105	-0.040484869841054
35	3.79	3.79275833639203	-0.0027583363920276
36	3.8	3.80223190816142	-0.00223190816142393
37	3.82	3.81180594870714	0.00819405129286377
38	3.82	3.83336978259486	-0.0133697825948556
39	3.84	3.83081816089443	0.00918183910557069
40	3.86	3.85257051398958	0.00742948601041915
41	3.8	3.87398843066793	-0.0739884306679337
42	3.85	3.79986774591234	0.0501322540876599
43	3.78	3.85943548170115	-0.0794354817011462
44	3.79	3.77427522778868	0.0157247722113176
45	3.77	3.78727629902705	-0.0172762990270505
46	3.78	3.76397911904767	0.016020880952333
47	3.77	3.77703670261029	-0.00703670261029288
48	3.76	3.76569374860543	-0.00569374860543315
49	3.78	3.75460709724104	0.0253929027589641
50	3.76	3.77945333024871	-0.0194533302487074
51	3.75	3.75574066407362	-0.00574066407362261
52	3.71	3.74464505889671	-0.0346450588967109
53	3.72	3.69803305279518	0.0219669472048252
54	3.7	3.71222544252046	-0.0122254425204589
55	3.69	3.68989221801129	0.000107781988705202
56	3.7	3.6799127881933	0.0200872118067044
57	3.72	3.69374643060172	0.0262535693982806
58	3.73	3.71875692175332	0.0112430782466837
59	3.73	3.73090266213692	-0.000902662136923027
60	3.69	3.73073038915639	-0.0407303891563879

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	3.68295699837005	3.62323125341923	3.74268274332086
62	3.67591399674009	3.58303857192662	3.76878942155356
63	3.66887099511014	3.54462970433123	3.79311228588905
64	3.66182799348018	3.5060808118952	3.81757517506517
65	3.65478499185023	3.46677020039114	3.84279978330933
66	3.64774199022028	3.4264438008852	3.86904017955535
67	3.64069898859032	3.38499012382466	3.89640785335599
68	3.63365598696037	3.34236262088581	3.92494935303493
69	3.62661298533042	3.29854721149497	3.95467875916586
70	3.61956998370046	3.25354694807197	3.98559301932896
71	3.61252698207051	3.20737415210909	4.01767981203193
72	3.60548398044055	3.16004614014322	4.05092182073788

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 3.68295699837005 & 3.62323125341923 & 3.74268274332086 \tabularnewline
62 & 3.67591399674009 & 3.58303857192662 & 3.76878942155356 \tabularnewline
63 & 3.66887099511014 & 3.54462970433123 & 3.79311228588905 \tabularnewline
64 & 3.66182799348018 & 3.5060808118952 & 3.81757517506517 \tabularnewline
65 & 3.65478499185023 & 3.46677020039114 & 3.84279978330933 \tabularnewline
66 & 3.64774199022028 & 3.4264438008852 & 3.86904017955535 \tabularnewline
67 & 3.64069898859032 & 3.38499012382466 & 3.89640785335599 \tabularnewline
68 & 3.63365598696037 & 3.34236262088581 & 3.92494935303493 \tabularnewline
69 & 3.62661298533042 & 3.29854721149497 & 3.95467875916586 \tabularnewline
70 & 3.61956998370046 & 3.25354694807197 & 3.98559301932896 \tabularnewline
71 & 3.61252698207051 & 3.20737415210909 & 4.01767981203193 \tabularnewline
72 & 3.60548398044055 & 3.16004614014322 & 4.05092182073788 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158157&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]3.68295699837005[/C][C]3.62323125341923[/C][C]3.74268274332086[/C][/ROW]
[ROW][C]62[/C][C]3.67591399674009[/C][C]3.58303857192662[/C][C]3.76878942155356[/C][/ROW]
[ROW][C]63[/C][C]3.66887099511014[/C][C]3.54462970433123[/C][C]3.79311228588905[/C][/ROW]
[ROW][C]64[/C][C]3.66182799348018[/C][C]3.5060808118952[/C][C]3.81757517506517[/C][/ROW]
[ROW][C]65[/C][C]3.65478499185023[/C][C]3.46677020039114[/C][C]3.84279978330933[/C][/ROW]
[ROW][C]66[/C][C]3.64774199022028[/C][C]3.4264438008852[/C][C]3.86904017955535[/C][/ROW]
[ROW][C]67[/C][C]3.64069898859032[/C][C]3.38499012382466[/C][C]3.89640785335599[/C][/ROW]
[ROW][C]68[/C][C]3.63365598696037[/C][C]3.34236262088581[/C][C]3.92494935303493[/C][/ROW]
[ROW][C]69[/C][C]3.62661298533042[/C][C]3.29854721149497[/C][C]3.95467875916586[/C][/ROW]
[ROW][C]70[/C][C]3.61956998370046[/C][C]3.25354694807197[/C][C]3.98559301932896[/C][/ROW]
[ROW][C]71[/C][C]3.61252698207051[/C][C]3.20737415210909[/C][C]4.01767981203193[/C][/ROW]
[ROW][C]72[/C][C]3.60548398044055[/C][C]3.16004614014322[/C][C]4.05092182073788[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158157&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158157&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	3.68295699837005	3.62323125341923	3.74268274332086
62	3.67591399674009	3.58303857192662	3.76878942155356
63	3.66887099511014	3.54462970433123	3.79311228588905
64	3.66182799348018	3.5060808118952	3.81757517506517
65	3.65478499185023	3.46677020039114	3.84279978330933
66	3.64774199022028	3.4264438008852	3.86904017955535
67	3.64069898859032	3.38499012382466	3.89640785335599
68	3.63365598696037	3.34236262088581	3.92494935303493
69	3.62661298533042	3.29854721149497	3.95467875916586
70	3.61956998370046	3.25354694807197	3.98559301932896
71	3.61252698207051	3.20737415210909	4.01767981203193
72	3.60548398044055	3.16004614014322	4.05092182073788

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 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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