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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 05 Jun 2009 16:05:23 -0600

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/2009/Jun/06/t1244239554ci881xylo80qw9g.htm/, Retrieved Mon, 29 Apr 2024 04:51:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41923, Retrieved Mon, 29 Apr 2024 04:51:22 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

165

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

-       [Exponential Smoothing] [Ken Soltvedt Siga...] [2009-06-05 22:05:23] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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3.42
3.42
3.43
3.47
3.51
3.52
3.52
3.52
3.52
3.52
3.52
3.52
3.52
3.52
3.58
3.6
3.61
3.61
3.61
3.63
3.68
3.69
3.69
3.69
3.69
3.69
3.69
3.69
3.69
3.78
3.79
3.79
3.8
3.8
3.8
3.8
3.81
3.95
3.99
4
4.06
4.16
4.19
4.2
4.2
4.2
4.2
4.2
4.23
4.38
4.43
4.44
4.44
4.44
4.44
4.44
4.45
4.45
4.45
4.45
4.45
4.45
4.45
4.45
4.46
4.46
4.46
4.48
4.58
4.67
4.68
4.68

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41923&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41923&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41923&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.873418950693836
beta	0.0296759775106365
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.873418950693836 \tabularnewline
beta & 0.0296759775106365 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41923&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]0.873418950693836[/C][/ROW]
[ROW][C]beta[/C][C]0.0296759775106365[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41923&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41923&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	0.873418950693836
beta	0.0296759775106365
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	3.52	3.46502409710897	0.0549759028910324
14	3.52	3.51637916866576	0.00362083133424251
15	3.58	3.58007339645459	-7.33964545860388e-05
16	3.6	3.59803506364187	0.00196493635812889
17	3.61	3.60741244019217	0.00258755980783043
18	3.61	3.60741060078114	0.00258939921886370
19	3.61	3.64964552079433	-0.039645520794326
20	3.63	3.61742053476775	0.0125794652322471
21	3.68	3.62894473810215	0.051055261897853
22	3.69	3.6739557396976	0.0160442603024031
23	3.69	3.69092692300590	-0.000926923005895475
24	3.69	3.69477467449461	-0.00477467449460711
25	3.69	3.70288088133550	-0.0128808813354953
26	3.69	3.6885750275598	0.00142497244019779
27	3.69	3.75299048235024	-0.0629904823502381
28	3.69	3.71561636123817	-0.0256163612381686
29	3.69	3.69930899812387	-0.0093089981238701
30	3.78	3.68673093869279	0.0932690613072071
31	3.79	3.80424694387552	-0.0142469438755199
32	3.79	3.80185326741977	-0.0118532674197676
33	3.8	3.79707125002915	0.00292874997084658
34	3.8	3.79433025124074	0.00566974875926229
35	3.8	3.7987281476632	0.00127185233679983
36	3.8	3.80280392207294	-0.00280392207293678
37	3.81	3.81066134800965	-0.000661348009649565
38	3.95	3.80782061859225	0.142179381407754
39	3.99	3.99278607106964	-0.00278607106963724
40	4	4.01831319290046	-0.0183131929004636
41	4.06	4.01512783117502	0.0448721688249751
42	4.16	4.06869352788346	0.091306472116539
43	4.19	4.17807196660782	0.0119280333921798
44	4.2	4.20555035994741	-0.00555035994741004
45	4.2	4.21472478598400	-0.0147247859840043
46	4.2	4.20170280812858	-0.00170280812857726
47	4.2	4.20408432051875	-0.0040843205187473
48	4.2	4.20816490533	-0.00816490533000191
49	4.23	4.21753393106047	0.0124660689395295
50	4.38	4.25044840952595	0.129551590474050
51	4.43	4.41493866768527	0.0150613323147262
52	4.44	4.46179694593563	-0.0217969459356278
53	4.44	4.47062818506073	-0.0306281850607295
54	4.44	4.46879802914675	-0.0287980291467473
55	4.44	4.4647068575573	-0.0247068575572955
56	4.44	4.45819796749402	-0.0181979674940225
57	4.45	4.45496059279912	-0.00496059279912053
58	4.45	4.45150519670828	-0.00150519670828153
59	4.45	4.45328331929561	-0.00328331929560921
60	4.45	4.45731156450628	-0.00731156450628223
61	4.45	4.47054849457995	-0.0205484945799475
62	4.45	4.48956230108177	-0.0395623010817703
63	4.45	4.48728060425283	-0.0372806042528264
64	4.45	4.47759229284161	-0.0275922928416064
65	4.46	4.47388736617346	-0.0138873661734555
66	4.46	4.48098975504584	-0.0209897550458367
67	4.46	4.47850731393273	-0.0185073139327319
68	4.48	4.47265444591991	0.00734555408009285
69	4.58	4.48847182153645	0.0915281784635482
70	4.67	4.56688434571314	0.103115654286857
71	4.68	4.65940996839529	0.0205900316047112
72	4.68	4.68410351827942	-0.00410351827941913

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3.52 & 3.46502409710897 & 0.0549759028910324 \tabularnewline
14 & 3.52 & 3.51637916866576 & 0.00362083133424251 \tabularnewline
15 & 3.58 & 3.58007339645459 & -7.33964545860388e-05 \tabularnewline
16 & 3.6 & 3.59803506364187 & 0.00196493635812889 \tabularnewline
17 & 3.61 & 3.60741244019217 & 0.00258755980783043 \tabularnewline
18 & 3.61 & 3.60741060078114 & 0.00258939921886370 \tabularnewline
19 & 3.61 & 3.64964552079433 & -0.039645520794326 \tabularnewline
20 & 3.63 & 3.61742053476775 & 0.0125794652322471 \tabularnewline
21 & 3.68 & 3.62894473810215 & 0.051055261897853 \tabularnewline
22 & 3.69 & 3.6739557396976 & 0.0160442603024031 \tabularnewline
23 & 3.69 & 3.69092692300590 & -0.000926923005895475 \tabularnewline
24 & 3.69 & 3.69477467449461 & -0.00477467449460711 \tabularnewline
25 & 3.69 & 3.70288088133550 & -0.0128808813354953 \tabularnewline
26 & 3.69 & 3.6885750275598 & 0.00142497244019779 \tabularnewline
27 & 3.69 & 3.75299048235024 & -0.0629904823502381 \tabularnewline
28 & 3.69 & 3.71561636123817 & -0.0256163612381686 \tabularnewline
29 & 3.69 & 3.69930899812387 & -0.0093089981238701 \tabularnewline
30 & 3.78 & 3.68673093869279 & 0.0932690613072071 \tabularnewline
31 & 3.79 & 3.80424694387552 & -0.0142469438755199 \tabularnewline
32 & 3.79 & 3.80185326741977 & -0.0118532674197676 \tabularnewline
33 & 3.8 & 3.79707125002915 & 0.00292874997084658 \tabularnewline
34 & 3.8 & 3.79433025124074 & 0.00566974875926229 \tabularnewline
35 & 3.8 & 3.7987281476632 & 0.00127185233679983 \tabularnewline
36 & 3.8 & 3.80280392207294 & -0.00280392207293678 \tabularnewline
37 & 3.81 & 3.81066134800965 & -0.000661348009649565 \tabularnewline
38 & 3.95 & 3.80782061859225 & 0.142179381407754 \tabularnewline
39 & 3.99 & 3.99278607106964 & -0.00278607106963724 \tabularnewline
40 & 4 & 4.01831319290046 & -0.0183131929004636 \tabularnewline
41 & 4.06 & 4.01512783117502 & 0.0448721688249751 \tabularnewline
42 & 4.16 & 4.06869352788346 & 0.091306472116539 \tabularnewline
43 & 4.19 & 4.17807196660782 & 0.0119280333921798 \tabularnewline
44 & 4.2 & 4.20555035994741 & -0.00555035994741004 \tabularnewline
45 & 4.2 & 4.21472478598400 & -0.0147247859840043 \tabularnewline
46 & 4.2 & 4.20170280812858 & -0.00170280812857726 \tabularnewline
47 & 4.2 & 4.20408432051875 & -0.0040843205187473 \tabularnewline
48 & 4.2 & 4.20816490533 & -0.00816490533000191 \tabularnewline
49 & 4.23 & 4.21753393106047 & 0.0124660689395295 \tabularnewline
50 & 4.38 & 4.25044840952595 & 0.129551590474050 \tabularnewline
51 & 4.43 & 4.41493866768527 & 0.0150613323147262 \tabularnewline
52 & 4.44 & 4.46179694593563 & -0.0217969459356278 \tabularnewline
53 & 4.44 & 4.47062818506073 & -0.0306281850607295 \tabularnewline
54 & 4.44 & 4.46879802914675 & -0.0287980291467473 \tabularnewline
55 & 4.44 & 4.4647068575573 & -0.0247068575572955 \tabularnewline
56 & 4.44 & 4.45819796749402 & -0.0181979674940225 \tabularnewline
57 & 4.45 & 4.45496059279912 & -0.00496059279912053 \tabularnewline
58 & 4.45 & 4.45150519670828 & -0.00150519670828153 \tabularnewline
59 & 4.45 & 4.45328331929561 & -0.00328331929560921 \tabularnewline
60 & 4.45 & 4.45731156450628 & -0.00731156450628223 \tabularnewline
61 & 4.45 & 4.47054849457995 & -0.0205484945799475 \tabularnewline
62 & 4.45 & 4.48956230108177 & -0.0395623010817703 \tabularnewline
63 & 4.45 & 4.48728060425283 & -0.0372806042528264 \tabularnewline
64 & 4.45 & 4.47759229284161 & -0.0275922928416064 \tabularnewline
65 & 4.46 & 4.47388736617346 & -0.0138873661734555 \tabularnewline
66 & 4.46 & 4.48098975504584 & -0.0209897550458367 \tabularnewline
67 & 4.46 & 4.47850731393273 & -0.0185073139327319 \tabularnewline
68 & 4.48 & 4.47265444591991 & 0.00734555408009285 \tabularnewline
69 & 4.58 & 4.48847182153645 & 0.0915281784635482 \tabularnewline
70 & 4.67 & 4.56688434571314 & 0.103115654286857 \tabularnewline
71 & 4.68 & 4.65940996839529 & 0.0205900316047112 \tabularnewline
72 & 4.68 & 4.68410351827942 & -0.00410351827941913 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41923&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]3.52[/C][C]3.46502409710897[/C][C]0.0549759028910324[/C][/ROW]
[ROW][C]14[/C][C]3.52[/C][C]3.51637916866576[/C][C]0.00362083133424251[/C][/ROW]
[ROW][C]15[/C][C]3.58[/C][C]3.58007339645459[/C][C]-7.33964545860388e-05[/C][/ROW]
[ROW][C]16[/C][C]3.6[/C][C]3.59803506364187[/C][C]0.00196493635812889[/C][/ROW]
[ROW][C]17[/C][C]3.61[/C][C]3.60741244019217[/C][C]0.00258755980783043[/C][/ROW]
[ROW][C]18[/C][C]3.61[/C][C]3.60741060078114[/C][C]0.00258939921886370[/C][/ROW]
[ROW][C]19[/C][C]3.61[/C][C]3.64964552079433[/C][C]-0.039645520794326[/C][/ROW]
[ROW][C]20[/C][C]3.63[/C][C]3.61742053476775[/C][C]0.0125794652322471[/C][/ROW]
[ROW][C]21[/C][C]3.68[/C][C]3.62894473810215[/C][C]0.051055261897853[/C][/ROW]
[ROW][C]22[/C][C]3.69[/C][C]3.6739557396976[/C][C]0.0160442603024031[/C][/ROW]
[ROW][C]23[/C][C]3.69[/C][C]3.69092692300590[/C][C]-0.000926923005895475[/C][/ROW]
[ROW][C]24[/C][C]3.69[/C][C]3.69477467449461[/C][C]-0.00477467449460711[/C][/ROW]
[ROW][C]25[/C][C]3.69[/C][C]3.70288088133550[/C][C]-0.0128808813354953[/C][/ROW]
[ROW][C]26[/C][C]3.69[/C][C]3.6885750275598[/C][C]0.00142497244019779[/C][/ROW]
[ROW][C]27[/C][C]3.69[/C][C]3.75299048235024[/C][C]-0.0629904823502381[/C][/ROW]
[ROW][C]28[/C][C]3.69[/C][C]3.71561636123817[/C][C]-0.0256163612381686[/C][/ROW]
[ROW][C]29[/C][C]3.69[/C][C]3.69930899812387[/C][C]-0.0093089981238701[/C][/ROW]
[ROW][C]30[/C][C]3.78[/C][C]3.68673093869279[/C][C]0.0932690613072071[/C][/ROW]
[ROW][C]31[/C][C]3.79[/C][C]3.80424694387552[/C][C]-0.0142469438755199[/C][/ROW]
[ROW][C]32[/C][C]3.79[/C][C]3.80185326741977[/C][C]-0.0118532674197676[/C][/ROW]
[ROW][C]33[/C][C]3.8[/C][C]3.79707125002915[/C][C]0.00292874997084658[/C][/ROW]
[ROW][C]34[/C][C]3.8[/C][C]3.79433025124074[/C][C]0.00566974875926229[/C][/ROW]
[ROW][C]35[/C][C]3.8[/C][C]3.7987281476632[/C][C]0.00127185233679983[/C][/ROW]
[ROW][C]36[/C][C]3.8[/C][C]3.80280392207294[/C][C]-0.00280392207293678[/C][/ROW]
[ROW][C]37[/C][C]3.81[/C][C]3.81066134800965[/C][C]-0.000661348009649565[/C][/ROW]
[ROW][C]38[/C][C]3.95[/C][C]3.80782061859225[/C][C]0.142179381407754[/C][/ROW]
[ROW][C]39[/C][C]3.99[/C][C]3.99278607106964[/C][C]-0.00278607106963724[/C][/ROW]
[ROW][C]40[/C][C]4[/C][C]4.01831319290046[/C][C]-0.0183131929004636[/C][/ROW]
[ROW][C]41[/C][C]4.06[/C][C]4.01512783117502[/C][C]0.0448721688249751[/C][/ROW]
[ROW][C]42[/C][C]4.16[/C][C]4.06869352788346[/C][C]0.091306472116539[/C][/ROW]
[ROW][C]43[/C][C]4.19[/C][C]4.17807196660782[/C][C]0.0119280333921798[/C][/ROW]
[ROW][C]44[/C][C]4.2[/C][C]4.20555035994741[/C][C]-0.00555035994741004[/C][/ROW]
[ROW][C]45[/C][C]4.2[/C][C]4.21472478598400[/C][C]-0.0147247859840043[/C][/ROW]
[ROW][C]46[/C][C]4.2[/C][C]4.20170280812858[/C][C]-0.00170280812857726[/C][/ROW]
[ROW][C]47[/C][C]4.2[/C][C]4.20408432051875[/C][C]-0.0040843205187473[/C][/ROW]
[ROW][C]48[/C][C]4.2[/C][C]4.20816490533[/C][C]-0.00816490533000191[/C][/ROW]
[ROW][C]49[/C][C]4.23[/C][C]4.21753393106047[/C][C]0.0124660689395295[/C][/ROW]
[ROW][C]50[/C][C]4.38[/C][C]4.25044840952595[/C][C]0.129551590474050[/C][/ROW]
[ROW][C]51[/C][C]4.43[/C][C]4.41493866768527[/C][C]0.0150613323147262[/C][/ROW]
[ROW][C]52[/C][C]4.44[/C][C]4.46179694593563[/C][C]-0.0217969459356278[/C][/ROW]
[ROW][C]53[/C][C]4.44[/C][C]4.47062818506073[/C][C]-0.0306281850607295[/C][/ROW]
[ROW][C]54[/C][C]4.44[/C][C]4.46879802914675[/C][C]-0.0287980291467473[/C][/ROW]
[ROW][C]55[/C][C]4.44[/C][C]4.4647068575573[/C][C]-0.0247068575572955[/C][/ROW]
[ROW][C]56[/C][C]4.44[/C][C]4.45819796749402[/C][C]-0.0181979674940225[/C][/ROW]
[ROW][C]57[/C][C]4.45[/C][C]4.45496059279912[/C][C]-0.00496059279912053[/C][/ROW]
[ROW][C]58[/C][C]4.45[/C][C]4.45150519670828[/C][C]-0.00150519670828153[/C][/ROW]
[ROW][C]59[/C][C]4.45[/C][C]4.45328331929561[/C][C]-0.00328331929560921[/C][/ROW]
[ROW][C]60[/C][C]4.45[/C][C]4.45731156450628[/C][C]-0.00731156450628223[/C][/ROW]
[ROW][C]61[/C][C]4.45[/C][C]4.47054849457995[/C][C]-0.0205484945799475[/C][/ROW]
[ROW][C]62[/C][C]4.45[/C][C]4.48956230108177[/C][C]-0.0395623010817703[/C][/ROW]
[ROW][C]63[/C][C]4.45[/C][C]4.48728060425283[/C][C]-0.0372806042528264[/C][/ROW]
[ROW][C]64[/C][C]4.45[/C][C]4.47759229284161[/C][C]-0.0275922928416064[/C][/ROW]
[ROW][C]65[/C][C]4.46[/C][C]4.47388736617346[/C][C]-0.0138873661734555[/C][/ROW]
[ROW][C]66[/C][C]4.46[/C][C]4.48098975504584[/C][C]-0.0209897550458367[/C][/ROW]
[ROW][C]67[/C][C]4.46[/C][C]4.47850731393273[/C][C]-0.0185073139327319[/C][/ROW]
[ROW][C]68[/C][C]4.48[/C][C]4.47265444591991[/C][C]0.00734555408009285[/C][/ROW]
[ROW][C]69[/C][C]4.58[/C][C]4.48847182153645[/C][C]0.0915281784635482[/C][/ROW]
[ROW][C]70[/C][C]4.67[/C][C]4.56688434571314[/C][C]0.103115654286857[/C][/ROW]
[ROW][C]71[/C][C]4.68[/C][C]4.65940996839529[/C][C]0.0205900316047112[/C][/ROW]
[ROW][C]72[/C][C]4.68[/C][C]4.68410351827942[/C][C]-0.00410351827941913[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41923&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41923&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	3.52	3.46502409710897	0.0549759028910324
14	3.52	3.51637916866576	0.00362083133424251
15	3.58	3.58007339645459	-7.33964545860388e-05
16	3.6	3.59803506364187	0.00196493635812889
17	3.61	3.60741244019217	0.00258755980783043
18	3.61	3.60741060078114	0.00258939921886370
19	3.61	3.64964552079433	-0.039645520794326
20	3.63	3.61742053476775	0.0125794652322471
21	3.68	3.62894473810215	0.051055261897853
22	3.69	3.6739557396976	0.0160442603024031
23	3.69	3.69092692300590	-0.000926923005895475
24	3.69	3.69477467449461	-0.00477467449460711
25	3.69	3.70288088133550	-0.0128808813354953
26	3.69	3.6885750275598	0.00142497244019779
27	3.69	3.75299048235024	-0.0629904823502381
28	3.69	3.71561636123817	-0.0256163612381686
29	3.69	3.69930899812387	-0.0093089981238701
30	3.78	3.68673093869279	0.0932690613072071
31	3.79	3.80424694387552	-0.0142469438755199
32	3.79	3.80185326741977	-0.0118532674197676
33	3.8	3.79707125002915	0.00292874997084658
34	3.8	3.79433025124074	0.00566974875926229
35	3.8	3.7987281476632	0.00127185233679983
36	3.8	3.80280392207294	-0.00280392207293678
37	3.81	3.81066134800965	-0.000661348009649565
38	3.95	3.80782061859225	0.142179381407754
39	3.99	3.99278607106964	-0.00278607106963724
40	4	4.01831319290046	-0.0183131929004636
41	4.06	4.01512783117502	0.0448721688249751
42	4.16	4.06869352788346	0.091306472116539
43	4.19	4.17807196660782	0.0119280333921798
44	4.2	4.20555035994741	-0.00555035994741004
45	4.2	4.21472478598400	-0.0147247859840043
46	4.2	4.20170280812858	-0.00170280812857726
47	4.2	4.20408432051875	-0.0040843205187473
48	4.2	4.20816490533	-0.00816490533000191
49	4.23	4.21753393106047	0.0124660689395295
50	4.38	4.25044840952595	0.129551590474050
51	4.43	4.41493866768527	0.0150613323147262
52	4.44	4.46179694593563	-0.0217969459356278
53	4.44	4.47062818506073	-0.0306281850607295
54	4.44	4.46879802914675	-0.0287980291467473
55	4.44	4.4647068575573	-0.0247068575572955
56	4.44	4.45819796749402	-0.0181979674940225
57	4.45	4.45496059279912	-0.00496059279912053
58	4.45	4.45150519670828	-0.00150519670828153
59	4.45	4.45328331929561	-0.00328331929560921
60	4.45	4.45731156450628	-0.00731156450628223
61	4.45	4.47054849457995	-0.0205484945799475
62	4.45	4.48956230108177	-0.0395623010817703
63	4.45	4.48728060425283	-0.0372806042528264
64	4.45	4.47759229284161	-0.0275922928416064
65	4.46	4.47388736617346	-0.0138873661734555
66	4.46	4.48098975504584	-0.0209897550458367
67	4.46	4.47850731393273	-0.0185073139327319
68	4.48	4.47265444591991	0.00734555408009285
69	4.58	4.48847182153645	0.0915281784635482
70	4.67	4.56688434571314	0.103115654286857
71	4.68	4.65940996839529	0.0205900316047112
72	4.68	4.68410351827942	-0.00410351827941913

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	4.6994642720259	4.62041017000297	4.77851837404882
74	4.73647951725077	4.62998053074079	4.84297850376076
75	4.77261180698504	4.64312143238524	4.90210218158483
76	4.80085150748046	4.65089424252500	4.95080877243591
77	4.8278078425174	4.65889446600094	4.99672121903386
78	4.85106451220569	4.66431315058774	5.03781587382363
79	4.8725758773511	4.66877061335302	5.07638114134918
80	4.89180771201712	4.67157531882776	5.11204010520648
81	4.9176855681833	4.68115405196285	5.15421708440374
82	4.91924156963804	4.66783082303564	5.17065231624044
83	4.91023177593882	4.64475346653108	5.17571008534656
84	4.91292529328788	0.885039005800385	8.94081158077537

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 4.6994642720259 & 4.62041017000297 & 4.77851837404882 \tabularnewline
74 & 4.73647951725077 & 4.62998053074079 & 4.84297850376076 \tabularnewline
75 & 4.77261180698504 & 4.64312143238524 & 4.90210218158483 \tabularnewline
76 & 4.80085150748046 & 4.65089424252500 & 4.95080877243591 \tabularnewline
77 & 4.8278078425174 & 4.65889446600094 & 4.99672121903386 \tabularnewline
78 & 4.85106451220569 & 4.66431315058774 & 5.03781587382363 \tabularnewline
79 & 4.8725758773511 & 4.66877061335302 & 5.07638114134918 \tabularnewline
80 & 4.89180771201712 & 4.67157531882776 & 5.11204010520648 \tabularnewline
81 & 4.9176855681833 & 4.68115405196285 & 5.15421708440374 \tabularnewline
82 & 4.91924156963804 & 4.66783082303564 & 5.17065231624044 \tabularnewline
83 & 4.91023177593882 & 4.64475346653108 & 5.17571008534656 \tabularnewline
84 & 4.91292529328788 & 0.885039005800385 & 8.94081158077537 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41923&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]4.6994642720259[/C][C]4.62041017000297[/C][C]4.77851837404882[/C][/ROW]
[ROW][C]74[/C][C]4.73647951725077[/C][C]4.62998053074079[/C][C]4.84297850376076[/C][/ROW]
[ROW][C]75[/C][C]4.77261180698504[/C][C]4.64312143238524[/C][C]4.90210218158483[/C][/ROW]
[ROW][C]76[/C][C]4.80085150748046[/C][C]4.65089424252500[/C][C]4.95080877243591[/C][/ROW]
[ROW][C]77[/C][C]4.8278078425174[/C][C]4.65889446600094[/C][C]4.99672121903386[/C][/ROW]
[ROW][C]78[/C][C]4.85106451220569[/C][C]4.66431315058774[/C][C]5.03781587382363[/C][/ROW]
[ROW][C]79[/C][C]4.8725758773511[/C][C]4.66877061335302[/C][C]5.07638114134918[/C][/ROW]
[ROW][C]80[/C][C]4.89180771201712[/C][C]4.67157531882776[/C][C]5.11204010520648[/C][/ROW]
[ROW][C]81[/C][C]4.9176855681833[/C][C]4.68115405196285[/C][C]5.15421708440374[/C][/ROW]
[ROW][C]82[/C][C]4.91924156963804[/C][C]4.66783082303564[/C][C]5.17065231624044[/C][/ROW]
[ROW][C]83[/C][C]4.91023177593882[/C][C]4.64475346653108[/C][C]5.17571008534656[/C][/ROW]
[ROW][C]84[/C][C]4.91292529328788[/C][C]0.885039005800385[/C][C]8.94081158077537[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41923&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41923&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	4.6994642720259	4.62041017000297	4.77851837404882
74	4.73647951725077	4.62998053074079	4.84297850376076
75	4.77261180698504	4.64312143238524	4.90210218158483
76	4.80085150748046	4.65089424252500	4.95080877243591
77	4.8278078425174	4.65889446600094	4.99672121903386
78	4.85106451220569	4.66431315058774	5.03781587382363
79	4.8725758773511	4.66877061335302	5.07638114134918
80	4.89180771201712	4.67157531882776	5.11204010520648
81	4.9176855681833	4.68115405196285	5.15421708440374
82	4.91924156963804	4.66783082303564	5.17065231624044
83	4.91023177593882	4.64475346653108	5.17571008534656
84	4.91292529328788	0.885039005800385	8.94081158077537

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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