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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 18 Dec 2014 18:59:47 +0000

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/2014/Dec/18/t1418929263x15szdof9l57b7x.htm/, Retrieved Sun, 19 May 2024 18:47:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271206, Retrieved Sun, 19 May 2024 18:47:33 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-     [Exponential Smoothing] [] [2014-11-30 21:58:41] [859c5b1ac426e9908e42a61e45afb281]
- R PD    [Exponential Smoothing] [] [2014-12-18 18:59:47] [d49f5b304cc347c7e802f63d6679cbb3] [Current]

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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	'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271206&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271206&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271206&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.811944161703942
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.811944161703942 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271206&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]0.811944161703942[/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=271206&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271206&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	0.811944161703942
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	104.35	104.021152386529	0.328847613471012
14	104.67	104.609306636396	0.060693363604031
15	104.73	104.72407733832	0.00592266167990374
16	104.86	104.872337472677	-0.0123374726769612
17	104.05	104.069383522859	-0.0193835228590302
18	104.15	104.173234859295	-0.0232348592946323
19	104.27	104.284614933606	-0.0146149336058983
20	104.33	104.331631034102	-0.00163103410203291
21	104.41	104.477577997369	-0.0675779973685593
22	104.4	104.484929091808	-0.0849290918080783
23	104.41	104.406657769026	0.00334223097364372
24	104.6	104.680244205336	-0.0802442053361148
25	104.61	104.74102100641	-0.131021006410194
26	104.65	104.905960214976	-0.255960214975616
27	104.55	104.753327669317	-0.203327669316835
28	104.51	104.728130354146	-0.218130354145515
29	104.74	103.7592409437	0.98075905630013
30	104.89	104.674770207058	0.215229792942225
31	104.91	104.981952260015	-0.0719522600153937
32	104.93	104.984936949616	-0.0549369496155947
33	104.95	105.075700228054	-0.125700228054455
34	104.97	105.032643002464	-0.0626430024640996
35	105.16	104.988837936451	0.171162063548508
36	105.29	105.38437756334	-0.0943775633404442
37	105.35	105.424564361931	-0.0745643619313086
38	105.36	105.613187793356	-0.253187793356133
39	105.45	105.47276305377	-0.0227630537699355
40	105.3	105.592085856303	-0.292085856302833
41	105.73	104.782221671457	0.947778328542825
42	105.86	105.526376166333	0.33362383366719
43	105.85	105.875934310829	-0.0259343108289016
44	105.95	105.91962526148	0.030374738519896
45	105.97	106.067038889815	-0.0970388898148826
46	106.15	106.059328355019	0.0906716449814979
47	105.37	106.183961303385	-0.813961303385042
48	105.39	105.73023275897	-0.340232758970259
49	105.39	105.574629062189	-0.184629062188762
50	105.38	105.640320477511	-0.260320477510561
51	105.23	105.537475583517	-0.307475583516862
52	105.34	105.374797188418	-0.0347971884184943
53	104.98	105.005529232609	-0.0255292326085907
54	105.16	104.845090934529	0.314909065470687
55	105.27	105.1121027937	0.157897206300248
56	105.27	105.315486875058	-0.0454868750584012
57	105.33	105.377010939337	-0.0470109393369427
58	105.33	105.444862997852	-0.114862997852057
59	105.46	105.232799285699	0.227200714301162
60	105.54	105.7134670967	-0.173467096699682
61	105.59	105.722656367153	-0.132656367152919
62	105.57	105.816540409327	-0.246540409327054
63	105.62	105.715993623799	-0.0959936237991172
64	105.57	105.776651538468	-0.206651538467526
65	105.33	105.268599945911	0.0614000540893755
66	105.34	105.242220400611	0.0977795993891135
67	105.5	105.303269822239	0.196730177761467
68	105.47	105.499912699381	-0.0299126993809011
69	105.59	105.573889675861	0.0161103241385376
70	105.65	105.680323121781	-0.0303231217805688
71	105.8	105.600835362481	0.199164637519303
72	105.87	105.983842668467	-0.113842668466631

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 104.35 & 104.021152386529 & 0.328847613471012 \tabularnewline
14 & 104.67 & 104.609306636396 & 0.060693363604031 \tabularnewline
15 & 104.73 & 104.72407733832 & 0.00592266167990374 \tabularnewline
16 & 104.86 & 104.872337472677 & -0.0123374726769612 \tabularnewline
17 & 104.05 & 104.069383522859 & -0.0193835228590302 \tabularnewline
18 & 104.15 & 104.173234859295 & -0.0232348592946323 \tabularnewline
19 & 104.27 & 104.284614933606 & -0.0146149336058983 \tabularnewline
20 & 104.33 & 104.331631034102 & -0.00163103410203291 \tabularnewline
21 & 104.41 & 104.477577997369 & -0.0675779973685593 \tabularnewline
22 & 104.4 & 104.484929091808 & -0.0849290918080783 \tabularnewline
23 & 104.41 & 104.406657769026 & 0.00334223097364372 \tabularnewline
24 & 104.6 & 104.680244205336 & -0.0802442053361148 \tabularnewline
25 & 104.61 & 104.74102100641 & -0.131021006410194 \tabularnewline
26 & 104.65 & 104.905960214976 & -0.255960214975616 \tabularnewline
27 & 104.55 & 104.753327669317 & -0.203327669316835 \tabularnewline
28 & 104.51 & 104.728130354146 & -0.218130354145515 \tabularnewline
29 & 104.74 & 103.7592409437 & 0.98075905630013 \tabularnewline
30 & 104.89 & 104.674770207058 & 0.215229792942225 \tabularnewline
31 & 104.91 & 104.981952260015 & -0.0719522600153937 \tabularnewline
32 & 104.93 & 104.984936949616 & -0.0549369496155947 \tabularnewline
33 & 104.95 & 105.075700228054 & -0.125700228054455 \tabularnewline
34 & 104.97 & 105.032643002464 & -0.0626430024640996 \tabularnewline
35 & 105.16 & 104.988837936451 & 0.171162063548508 \tabularnewline
36 & 105.29 & 105.38437756334 & -0.0943775633404442 \tabularnewline
37 & 105.35 & 105.424564361931 & -0.0745643619313086 \tabularnewline
38 & 105.36 & 105.613187793356 & -0.253187793356133 \tabularnewline
39 & 105.45 & 105.47276305377 & -0.0227630537699355 \tabularnewline
40 & 105.3 & 105.592085856303 & -0.292085856302833 \tabularnewline
41 & 105.73 & 104.782221671457 & 0.947778328542825 \tabularnewline
42 & 105.86 & 105.526376166333 & 0.33362383366719 \tabularnewline
43 & 105.85 & 105.875934310829 & -0.0259343108289016 \tabularnewline
44 & 105.95 & 105.91962526148 & 0.030374738519896 \tabularnewline
45 & 105.97 & 106.067038889815 & -0.0970388898148826 \tabularnewline
46 & 106.15 & 106.059328355019 & 0.0906716449814979 \tabularnewline
47 & 105.37 & 106.183961303385 & -0.813961303385042 \tabularnewline
48 & 105.39 & 105.73023275897 & -0.340232758970259 \tabularnewline
49 & 105.39 & 105.574629062189 & -0.184629062188762 \tabularnewline
50 & 105.38 & 105.640320477511 & -0.260320477510561 \tabularnewline
51 & 105.23 & 105.537475583517 & -0.307475583516862 \tabularnewline
52 & 105.34 & 105.374797188418 & -0.0347971884184943 \tabularnewline
53 & 104.98 & 105.005529232609 & -0.0255292326085907 \tabularnewline
54 & 105.16 & 104.845090934529 & 0.314909065470687 \tabularnewline
55 & 105.27 & 105.1121027937 & 0.157897206300248 \tabularnewline
56 & 105.27 & 105.315486875058 & -0.0454868750584012 \tabularnewline
57 & 105.33 & 105.377010939337 & -0.0470109393369427 \tabularnewline
58 & 105.33 & 105.444862997852 & -0.114862997852057 \tabularnewline
59 & 105.46 & 105.232799285699 & 0.227200714301162 \tabularnewline
60 & 105.54 & 105.7134670967 & -0.173467096699682 \tabularnewline
61 & 105.59 & 105.722656367153 & -0.132656367152919 \tabularnewline
62 & 105.57 & 105.816540409327 & -0.246540409327054 \tabularnewline
63 & 105.62 & 105.715993623799 & -0.0959936237991172 \tabularnewline
64 & 105.57 & 105.776651538468 & -0.206651538467526 \tabularnewline
65 & 105.33 & 105.268599945911 & 0.0614000540893755 \tabularnewline
66 & 105.34 & 105.242220400611 & 0.0977795993891135 \tabularnewline
67 & 105.5 & 105.303269822239 & 0.196730177761467 \tabularnewline
68 & 105.47 & 105.499912699381 & -0.0299126993809011 \tabularnewline
69 & 105.59 & 105.573889675861 & 0.0161103241385376 \tabularnewline
70 & 105.65 & 105.680323121781 & -0.0303231217805688 \tabularnewline
71 & 105.8 & 105.600835362481 & 0.199164637519303 \tabularnewline
72 & 105.87 & 105.983842668467 & -0.113842668466631 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271206&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]104.35[/C][C]104.021152386529[/C][C]0.328847613471012[/C][/ROW]
[ROW][C]14[/C][C]104.67[/C][C]104.609306636396[/C][C]0.060693363604031[/C][/ROW]
[ROW][C]15[/C][C]104.73[/C][C]104.72407733832[/C][C]0.00592266167990374[/C][/ROW]
[ROW][C]16[/C][C]104.86[/C][C]104.872337472677[/C][C]-0.0123374726769612[/C][/ROW]
[ROW][C]17[/C][C]104.05[/C][C]104.069383522859[/C][C]-0.0193835228590302[/C][/ROW]
[ROW][C]18[/C][C]104.15[/C][C]104.173234859295[/C][C]-0.0232348592946323[/C][/ROW]
[ROW][C]19[/C][C]104.27[/C][C]104.284614933606[/C][C]-0.0146149336058983[/C][/ROW]
[ROW][C]20[/C][C]104.33[/C][C]104.331631034102[/C][C]-0.00163103410203291[/C][/ROW]
[ROW][C]21[/C][C]104.41[/C][C]104.477577997369[/C][C]-0.0675779973685593[/C][/ROW]
[ROW][C]22[/C][C]104.4[/C][C]104.484929091808[/C][C]-0.0849290918080783[/C][/ROW]
[ROW][C]23[/C][C]104.41[/C][C]104.406657769026[/C][C]0.00334223097364372[/C][/ROW]
[ROW][C]24[/C][C]104.6[/C][C]104.680244205336[/C][C]-0.0802442053361148[/C][/ROW]
[ROW][C]25[/C][C]104.61[/C][C]104.74102100641[/C][C]-0.131021006410194[/C][/ROW]
[ROW][C]26[/C][C]104.65[/C][C]104.905960214976[/C][C]-0.255960214975616[/C][/ROW]
[ROW][C]27[/C][C]104.55[/C][C]104.753327669317[/C][C]-0.203327669316835[/C][/ROW]
[ROW][C]28[/C][C]104.51[/C][C]104.728130354146[/C][C]-0.218130354145515[/C][/ROW]
[ROW][C]29[/C][C]104.74[/C][C]103.7592409437[/C][C]0.98075905630013[/C][/ROW]
[ROW][C]30[/C][C]104.89[/C][C]104.674770207058[/C][C]0.215229792942225[/C][/ROW]
[ROW][C]31[/C][C]104.91[/C][C]104.981952260015[/C][C]-0.0719522600153937[/C][/ROW]
[ROW][C]32[/C][C]104.93[/C][C]104.984936949616[/C][C]-0.0549369496155947[/C][/ROW]
[ROW][C]33[/C][C]104.95[/C][C]105.075700228054[/C][C]-0.125700228054455[/C][/ROW]
[ROW][C]34[/C][C]104.97[/C][C]105.032643002464[/C][C]-0.0626430024640996[/C][/ROW]
[ROW][C]35[/C][C]105.16[/C][C]104.988837936451[/C][C]0.171162063548508[/C][/ROW]
[ROW][C]36[/C][C]105.29[/C][C]105.38437756334[/C][C]-0.0943775633404442[/C][/ROW]
[ROW][C]37[/C][C]105.35[/C][C]105.424564361931[/C][C]-0.0745643619313086[/C][/ROW]
[ROW][C]38[/C][C]105.36[/C][C]105.613187793356[/C][C]-0.253187793356133[/C][/ROW]
[ROW][C]39[/C][C]105.45[/C][C]105.47276305377[/C][C]-0.0227630537699355[/C][/ROW]
[ROW][C]40[/C][C]105.3[/C][C]105.592085856303[/C][C]-0.292085856302833[/C][/ROW]
[ROW][C]41[/C][C]105.73[/C][C]104.782221671457[/C][C]0.947778328542825[/C][/ROW]
[ROW][C]42[/C][C]105.86[/C][C]105.526376166333[/C][C]0.33362383366719[/C][/ROW]
[ROW][C]43[/C][C]105.85[/C][C]105.875934310829[/C][C]-0.0259343108289016[/C][/ROW]
[ROW][C]44[/C][C]105.95[/C][C]105.91962526148[/C][C]0.030374738519896[/C][/ROW]
[ROW][C]45[/C][C]105.97[/C][C]106.067038889815[/C][C]-0.0970388898148826[/C][/ROW]
[ROW][C]46[/C][C]106.15[/C][C]106.059328355019[/C][C]0.0906716449814979[/C][/ROW]
[ROW][C]47[/C][C]105.37[/C][C]106.183961303385[/C][C]-0.813961303385042[/C][/ROW]
[ROW][C]48[/C][C]105.39[/C][C]105.73023275897[/C][C]-0.340232758970259[/C][/ROW]
[ROW][C]49[/C][C]105.39[/C][C]105.574629062189[/C][C]-0.184629062188762[/C][/ROW]
[ROW][C]50[/C][C]105.38[/C][C]105.640320477511[/C][C]-0.260320477510561[/C][/ROW]
[ROW][C]51[/C][C]105.23[/C][C]105.537475583517[/C][C]-0.307475583516862[/C][/ROW]
[ROW][C]52[/C][C]105.34[/C][C]105.374797188418[/C][C]-0.0347971884184943[/C][/ROW]
[ROW][C]53[/C][C]104.98[/C][C]105.005529232609[/C][C]-0.0255292326085907[/C][/ROW]
[ROW][C]54[/C][C]105.16[/C][C]104.845090934529[/C][C]0.314909065470687[/C][/ROW]
[ROW][C]55[/C][C]105.27[/C][C]105.1121027937[/C][C]0.157897206300248[/C][/ROW]
[ROW][C]56[/C][C]105.27[/C][C]105.315486875058[/C][C]-0.0454868750584012[/C][/ROW]
[ROW][C]57[/C][C]105.33[/C][C]105.377010939337[/C][C]-0.0470109393369427[/C][/ROW]
[ROW][C]58[/C][C]105.33[/C][C]105.444862997852[/C][C]-0.114862997852057[/C][/ROW]
[ROW][C]59[/C][C]105.46[/C][C]105.232799285699[/C][C]0.227200714301162[/C][/ROW]
[ROW][C]60[/C][C]105.54[/C][C]105.7134670967[/C][C]-0.173467096699682[/C][/ROW]
[ROW][C]61[/C][C]105.59[/C][C]105.722656367153[/C][C]-0.132656367152919[/C][/ROW]
[ROW][C]62[/C][C]105.57[/C][C]105.816540409327[/C][C]-0.246540409327054[/C][/ROW]
[ROW][C]63[/C][C]105.62[/C][C]105.715993623799[/C][C]-0.0959936237991172[/C][/ROW]
[ROW][C]64[/C][C]105.57[/C][C]105.776651538468[/C][C]-0.206651538467526[/C][/ROW]
[ROW][C]65[/C][C]105.33[/C][C]105.268599945911[/C][C]0.0614000540893755[/C][/ROW]
[ROW][C]66[/C][C]105.34[/C][C]105.242220400611[/C][C]0.0977795993891135[/C][/ROW]
[ROW][C]67[/C][C]105.5[/C][C]105.303269822239[/C][C]0.196730177761467[/C][/ROW]
[ROW][C]68[/C][C]105.47[/C][C]105.499912699381[/C][C]-0.0299126993809011[/C][/ROW]
[ROW][C]69[/C][C]105.59[/C][C]105.573889675861[/C][C]0.0161103241385376[/C][/ROW]
[ROW][C]70[/C][C]105.65[/C][C]105.680323121781[/C][C]-0.0303231217805688[/C][/ROW]
[ROW][C]71[/C][C]105.8[/C][C]105.600835362481[/C][C]0.199164637519303[/C][/ROW]
[ROW][C]72[/C][C]105.87[/C][C]105.983842668467[/C][C]-0.113842668466631[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271206&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271206&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	104.35	104.021152386529	0.328847613471012
14	104.67	104.609306636396	0.060693363604031
15	104.73	104.72407733832	0.00592266167990374
16	104.86	104.872337472677	-0.0123374726769612
17	104.05	104.069383522859	-0.0193835228590302
18	104.15	104.173234859295	-0.0232348592946323
19	104.27	104.284614933606	-0.0146149336058983
20	104.33	104.331631034102	-0.00163103410203291
21	104.41	104.477577997369	-0.0675779973685593
22	104.4	104.484929091808	-0.0849290918080783
23	104.41	104.406657769026	0.00334223097364372
24	104.6	104.680244205336	-0.0802442053361148
25	104.61	104.74102100641	-0.131021006410194
26	104.65	104.905960214976	-0.255960214975616
27	104.55	104.753327669317	-0.203327669316835
28	104.51	104.728130354146	-0.218130354145515
29	104.74	103.7592409437	0.98075905630013
30	104.89	104.674770207058	0.215229792942225
31	104.91	104.981952260015	-0.0719522600153937
32	104.93	104.984936949616	-0.0549369496155947
33	104.95	105.075700228054	-0.125700228054455
34	104.97	105.032643002464	-0.0626430024640996
35	105.16	104.988837936451	0.171162063548508
36	105.29	105.38437756334	-0.0943775633404442
37	105.35	105.424564361931	-0.0745643619313086
38	105.36	105.613187793356	-0.253187793356133
39	105.45	105.47276305377	-0.0227630537699355
40	105.3	105.592085856303	-0.292085856302833
41	105.73	104.782221671457	0.947778328542825
42	105.86	105.526376166333	0.33362383366719
43	105.85	105.875934310829	-0.0259343108289016
44	105.95	105.91962526148	0.030374738519896
45	105.97	106.067038889815	-0.0970388898148826
46	106.15	106.059328355019	0.0906716449814979
47	105.37	106.183961303385	-0.813961303385042
48	105.39	105.73023275897	-0.340232758970259
49	105.39	105.574629062189	-0.184629062188762
50	105.38	105.640320477511	-0.260320477510561
51	105.23	105.537475583517	-0.307475583516862
52	105.34	105.374797188418	-0.0347971884184943
53	104.98	105.005529232609	-0.0255292326085907
54	105.16	104.845090934529	0.314909065470687
55	105.27	105.1121027937	0.157897206300248
56	105.27	105.315486875058	-0.0454868750584012
57	105.33	105.377010939337	-0.0470109393369427
58	105.33	105.444862997852	-0.114862997852057
59	105.46	105.232799285699	0.227200714301162
60	105.54	105.7134670967	-0.173467096699682
61	105.59	105.722656367153	-0.132656367152919
62	105.57	105.816540409327	-0.246540409327054
63	105.62	105.715993623799	-0.0959936237991172
64	105.57	105.776651538468	-0.206651538467526
65	105.33	105.268599945911	0.0614000540893755
66	105.34	105.242220400611	0.0977795993891135
67	105.5	105.303269822239	0.196730177761467
68	105.47	105.499912699381	-0.0299126993809011
69	105.59	105.573889675861	0.0161103241385376
70	105.65	105.680323121781	-0.0303231217805688
71	105.8	105.600835362481	0.199164637519303
72	105.87	105.983842668467	-0.113842668466631

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	106.049456695112	105.540398814824	106.558514575401
74	106.230118523279	105.574066005279	106.886171041279
75	106.358543192456	105.582812181185	107.134274203726
76	106.476754663621	105.597396801058	107.356112526184
77	106.183990457786	105.214595423951	107.153385491622
78	106.113630346418	105.060699657579	107.166561035257
79	106.113487060885	104.982748334592	107.244225787179
80	106.107459136914	104.904051252425	107.310867021404
81	106.214732231304	104.941727580417	107.487736882192
82	106.299566236731	104.960748546663	107.638383926799
83	106.287429016685	104.88695265456	107.68790537881
84	106.450369661041	95.8504097714789	117.050329550603

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 106.049456695112 & 105.540398814824 & 106.558514575401 \tabularnewline
74 & 106.230118523279 & 105.574066005279 & 106.886171041279 \tabularnewline
75 & 106.358543192456 & 105.582812181185 & 107.134274203726 \tabularnewline
76 & 106.476754663621 & 105.597396801058 & 107.356112526184 \tabularnewline
77 & 106.183990457786 & 105.214595423951 & 107.153385491622 \tabularnewline
78 & 106.113630346418 & 105.060699657579 & 107.166561035257 \tabularnewline
79 & 106.113487060885 & 104.982748334592 & 107.244225787179 \tabularnewline
80 & 106.107459136914 & 104.904051252425 & 107.310867021404 \tabularnewline
81 & 106.214732231304 & 104.941727580417 & 107.487736882192 \tabularnewline
82 & 106.299566236731 & 104.960748546663 & 107.638383926799 \tabularnewline
83 & 106.287429016685 & 104.88695265456 & 107.68790537881 \tabularnewline
84 & 106.450369661041 & 95.8504097714789 & 117.050329550603 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271206&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]106.049456695112[/C][C]105.540398814824[/C][C]106.558514575401[/C][/ROW]
[ROW][C]74[/C][C]106.230118523279[/C][C]105.574066005279[/C][C]106.886171041279[/C][/ROW]
[ROW][C]75[/C][C]106.358543192456[/C][C]105.582812181185[/C][C]107.134274203726[/C][/ROW]
[ROW][C]76[/C][C]106.476754663621[/C][C]105.597396801058[/C][C]107.356112526184[/C][/ROW]
[ROW][C]77[/C][C]106.183990457786[/C][C]105.214595423951[/C][C]107.153385491622[/C][/ROW]
[ROW][C]78[/C][C]106.113630346418[/C][C]105.060699657579[/C][C]107.166561035257[/C][/ROW]
[ROW][C]79[/C][C]106.113487060885[/C][C]104.982748334592[/C][C]107.244225787179[/C][/ROW]
[ROW][C]80[/C][C]106.107459136914[/C][C]104.904051252425[/C][C]107.310867021404[/C][/ROW]
[ROW][C]81[/C][C]106.214732231304[/C][C]104.941727580417[/C][C]107.487736882192[/C][/ROW]
[ROW][C]82[/C][C]106.299566236731[/C][C]104.960748546663[/C][C]107.638383926799[/C][/ROW]
[ROW][C]83[/C][C]106.287429016685[/C][C]104.88695265456[/C][C]107.68790537881[/C][/ROW]
[ROW][C]84[/C][C]106.450369661041[/C][C]95.8504097714789[/C][C]117.050329550603[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271206&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271206&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	106.049456695112	105.540398814824	106.558514575401
74	106.230118523279	105.574066005279	106.886171041279
75	106.358543192456	105.582812181185	107.134274203726
76	106.476754663621	105.597396801058	107.356112526184
77	106.183990457786	105.214595423951	107.153385491622
78	106.113630346418	105.060699657579	107.166561035257
79	106.113487060885	104.982748334592	107.244225787179
80	106.107459136914	104.904051252425	107.310867021404
81	106.214732231304	104.941727580417	107.487736882192
82	106.299566236731	104.960748546663	107.638383926799
83	106.287429016685	104.88695265456	107.68790537881
84	106.450369661041	95.8504097714789	117.050329550603

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