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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 18 May 2012 04:04:41 -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/18/t1337328490h5hbsvpor84t65t.htm/, Retrieved Sat, 04 May 2024 05:10:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166644, Retrieved Sat, 04 May 2024 05:10:21 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

136

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

-       [Exponential Smoothing] [] [2012-05-18 08:04:41] [91562a5fde803f4db5c5e8dd5d4cb92f] [Current]

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Dataseries X:

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Histogram

Boxplots

1,45
1,45
1,45
1,44
1,44
1,44
1,44
1,45
1,44
1,45
1,46
1,46
1,47
1,46
1,46
1,45
1,45
1,45
1,44
1,45
1,44
1,45
1,47
1,48
1,5
1,5
1,52
1,54
1,55
1,54
1,55
1,54
1,57
1,61
1,62
1,64
1,63
1,63
1,67
1,7
1,69
1,68
1,67
1,68
1,66
1,65
1,65
1,66
1,67
1,67
1,65
1,65
1,65
1,65
1,66
1,66
1,67
1,67
1,67
1,66

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=166644&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=166644&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166644&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	0.088712332270154
gamma	0.0498388774295448

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.088712332270154 \tabularnewline
gamma & 0.0498388774295448 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166644&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]0.088712332270154[/C][/ROW]
[ROW][C]gamma[/C][C]0.0498388774295448[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166644&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166644&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	0.088712332270154
gamma	0.0498388774295448

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.47	1.46497329059829	0.00502670940171024
14	1.46	1.46095583787458	-0.000955837874577314
15	1.46	1.46087104326745	-0.000871043267450577
16	1.45	1.45079377098769	-0.000793770987687514
17	1.45	1.45030668704541	-0.000306687045414256
18	1.45	1.44944614678901	0.00055385321099477
19	1.44	1.44741194706575	-0.00741194706575476
20	1.45	1.44883774928822	0.00116225071177811
21	1.44	1.43935752192621	0.000642478073786812
22	1.45	1.44941451765457	0.000585482345428989
23	1.47	1.45946645715894	0.0105335428410629
24	1.48	1.47040091231144	0.00959908768856454
25	1.5	1.49166913643462	0.00833086356537982
26	1.5	1.492824853438	0.00717514656200313
27	1.52	1.50346137742389	0.0165386225761086
28	1.54	1.51492855720515	0.0250714427948455
29	1.55	1.5467360367022	0.00326396329780398
30	1.54	1.55619225716546	-0.0161922571654551
31	1.55	1.54267247093426	0.00732752906574374
32	1.54	1.56540584646079	-0.0254058464607889
33	1.57	1.53356870123462	0.0364312987653783
34	1.61	1.58680060671573	0.0231993932842711
35	1.62	1.62885867900123	-0.00885867900122927
36	1.64	1.6280728049262	0.011927195073802
37	1.63	1.6595475608853	-0.0295475608853022
38	1.63	1.62734299451294	0.00265700548706005
39	1.67	1.63757870366655	0.0324212963334494
40	1.7	1.67045487247951	0.0295451275204865
41	1.69	1.71265922298241	-0.0226592229824081
42	1.68	1.69981573713088	-0.0198157371308758
43	1.67	1.68597450354101	-0.0159745035410104
44	1.68	1.68664070140836	-0.0066407014083627
45	1.66	1.67646825596518	-0.0164682559651839
46	1.65	1.67500731857009	-0.0250073185700903
47	1.65	1.66278886101591	-0.0127888610159148
48	1.66	1.65165433132811	0.00834566867188546
49	1.67	1.67281136172702	-0.00281136172701757
50	1.67	1.66297862593803	0.00702137406197378
51	1.65	1.6736015084068	-0.0236015084068042
52	1.65	1.64150776355094	0.00849223644905628
53	1.65	1.65184446298586	-0.00184446298586205
54	1.65	1.65084750303927	-0.000847503039267172
55	1.66	1.64868898573471	0.0113110142652857
56	1.66	1.67177574552386	-0.0117757455238621
57	1.67	1.65114775834089	0.0188522416591128
58	1.67	1.68282018466699	-0.0128201846669875
59	1.67	1.68168287618504	-0.0116828761850449
60	1.66	1.67064646099105	-0.0106464609910464

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.47 & 1.46497329059829 & 0.00502670940171024 \tabularnewline
14 & 1.46 & 1.46095583787458 & -0.000955837874577314 \tabularnewline
15 & 1.46 & 1.46087104326745 & -0.000871043267450577 \tabularnewline
16 & 1.45 & 1.45079377098769 & -0.000793770987687514 \tabularnewline
17 & 1.45 & 1.45030668704541 & -0.000306687045414256 \tabularnewline
18 & 1.45 & 1.44944614678901 & 0.00055385321099477 \tabularnewline
19 & 1.44 & 1.44741194706575 & -0.00741194706575476 \tabularnewline
20 & 1.45 & 1.44883774928822 & 0.00116225071177811 \tabularnewline
21 & 1.44 & 1.43935752192621 & 0.000642478073786812 \tabularnewline
22 & 1.45 & 1.44941451765457 & 0.000585482345428989 \tabularnewline
23 & 1.47 & 1.45946645715894 & 0.0105335428410629 \tabularnewline
24 & 1.48 & 1.47040091231144 & 0.00959908768856454 \tabularnewline
25 & 1.5 & 1.49166913643462 & 0.00833086356537982 \tabularnewline
26 & 1.5 & 1.492824853438 & 0.00717514656200313 \tabularnewline
27 & 1.52 & 1.50346137742389 & 0.0165386225761086 \tabularnewline
28 & 1.54 & 1.51492855720515 & 0.0250714427948455 \tabularnewline
29 & 1.55 & 1.5467360367022 & 0.00326396329780398 \tabularnewline
30 & 1.54 & 1.55619225716546 & -0.0161922571654551 \tabularnewline
31 & 1.55 & 1.54267247093426 & 0.00732752906574374 \tabularnewline
32 & 1.54 & 1.56540584646079 & -0.0254058464607889 \tabularnewline
33 & 1.57 & 1.53356870123462 & 0.0364312987653783 \tabularnewline
34 & 1.61 & 1.58680060671573 & 0.0231993932842711 \tabularnewline
35 & 1.62 & 1.62885867900123 & -0.00885867900122927 \tabularnewline
36 & 1.64 & 1.6280728049262 & 0.011927195073802 \tabularnewline
37 & 1.63 & 1.6595475608853 & -0.0295475608853022 \tabularnewline
38 & 1.63 & 1.62734299451294 & 0.00265700548706005 \tabularnewline
39 & 1.67 & 1.63757870366655 & 0.0324212963334494 \tabularnewline
40 & 1.7 & 1.67045487247951 & 0.0295451275204865 \tabularnewline
41 & 1.69 & 1.71265922298241 & -0.0226592229824081 \tabularnewline
42 & 1.68 & 1.69981573713088 & -0.0198157371308758 \tabularnewline
43 & 1.67 & 1.68597450354101 & -0.0159745035410104 \tabularnewline
44 & 1.68 & 1.68664070140836 & -0.0066407014083627 \tabularnewline
45 & 1.66 & 1.67646825596518 & -0.0164682559651839 \tabularnewline
46 & 1.65 & 1.67500731857009 & -0.0250073185700903 \tabularnewline
47 & 1.65 & 1.66278886101591 & -0.0127888610159148 \tabularnewline
48 & 1.66 & 1.65165433132811 & 0.00834566867188546 \tabularnewline
49 & 1.67 & 1.67281136172702 & -0.00281136172701757 \tabularnewline
50 & 1.67 & 1.66297862593803 & 0.00702137406197378 \tabularnewline
51 & 1.65 & 1.6736015084068 & -0.0236015084068042 \tabularnewline
52 & 1.65 & 1.64150776355094 & 0.00849223644905628 \tabularnewline
53 & 1.65 & 1.65184446298586 & -0.00184446298586205 \tabularnewline
54 & 1.65 & 1.65084750303927 & -0.000847503039267172 \tabularnewline
55 & 1.66 & 1.64868898573471 & 0.0113110142652857 \tabularnewline
56 & 1.66 & 1.67177574552386 & -0.0117757455238621 \tabularnewline
57 & 1.67 & 1.65114775834089 & 0.0188522416591128 \tabularnewline
58 & 1.67 & 1.68282018466699 & -0.0128201846669875 \tabularnewline
59 & 1.67 & 1.68168287618504 & -0.0116828761850449 \tabularnewline
60 & 1.66 & 1.67064646099105 & -0.0106464609910464 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166644&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]1.47[/C][C]1.46497329059829[/C][C]0.00502670940171024[/C][/ROW]
[ROW][C]14[/C][C]1.46[/C][C]1.46095583787458[/C][C]-0.000955837874577314[/C][/ROW]
[ROW][C]15[/C][C]1.46[/C][C]1.46087104326745[/C][C]-0.000871043267450577[/C][/ROW]
[ROW][C]16[/C][C]1.45[/C][C]1.45079377098769[/C][C]-0.000793770987687514[/C][/ROW]
[ROW][C]17[/C][C]1.45[/C][C]1.45030668704541[/C][C]-0.000306687045414256[/C][/ROW]
[ROW][C]18[/C][C]1.45[/C][C]1.44944614678901[/C][C]0.00055385321099477[/C][/ROW]
[ROW][C]19[/C][C]1.44[/C][C]1.44741194706575[/C][C]-0.00741194706575476[/C][/ROW]
[ROW][C]20[/C][C]1.45[/C][C]1.44883774928822[/C][C]0.00116225071177811[/C][/ROW]
[ROW][C]21[/C][C]1.44[/C][C]1.43935752192621[/C][C]0.000642478073786812[/C][/ROW]
[ROW][C]22[/C][C]1.45[/C][C]1.44941451765457[/C][C]0.000585482345428989[/C][/ROW]
[ROW][C]23[/C][C]1.47[/C][C]1.45946645715894[/C][C]0.0105335428410629[/C][/ROW]
[ROW][C]24[/C][C]1.48[/C][C]1.47040091231144[/C][C]0.00959908768856454[/C][/ROW]
[ROW][C]25[/C][C]1.5[/C][C]1.49166913643462[/C][C]0.00833086356537982[/C][/ROW]
[ROW][C]26[/C][C]1.5[/C][C]1.492824853438[/C][C]0.00717514656200313[/C][/ROW]
[ROW][C]27[/C][C]1.52[/C][C]1.50346137742389[/C][C]0.0165386225761086[/C][/ROW]
[ROW][C]28[/C][C]1.54[/C][C]1.51492855720515[/C][C]0.0250714427948455[/C][/ROW]
[ROW][C]29[/C][C]1.55[/C][C]1.5467360367022[/C][C]0.00326396329780398[/C][/ROW]
[ROW][C]30[/C][C]1.54[/C][C]1.55619225716546[/C][C]-0.0161922571654551[/C][/ROW]
[ROW][C]31[/C][C]1.55[/C][C]1.54267247093426[/C][C]0.00732752906574374[/C][/ROW]
[ROW][C]32[/C][C]1.54[/C][C]1.56540584646079[/C][C]-0.0254058464607889[/C][/ROW]
[ROW][C]33[/C][C]1.57[/C][C]1.53356870123462[/C][C]0.0364312987653783[/C][/ROW]
[ROW][C]34[/C][C]1.61[/C][C]1.58680060671573[/C][C]0.0231993932842711[/C][/ROW]
[ROW][C]35[/C][C]1.62[/C][C]1.62885867900123[/C][C]-0.00885867900122927[/C][/ROW]
[ROW][C]36[/C][C]1.64[/C][C]1.6280728049262[/C][C]0.011927195073802[/C][/ROW]
[ROW][C]37[/C][C]1.63[/C][C]1.6595475608853[/C][C]-0.0295475608853022[/C][/ROW]
[ROW][C]38[/C][C]1.63[/C][C]1.62734299451294[/C][C]0.00265700548706005[/C][/ROW]
[ROW][C]39[/C][C]1.67[/C][C]1.63757870366655[/C][C]0.0324212963334494[/C][/ROW]
[ROW][C]40[/C][C]1.7[/C][C]1.67045487247951[/C][C]0.0295451275204865[/C][/ROW]
[ROW][C]41[/C][C]1.69[/C][C]1.71265922298241[/C][C]-0.0226592229824081[/C][/ROW]
[ROW][C]42[/C][C]1.68[/C][C]1.69981573713088[/C][C]-0.0198157371308758[/C][/ROW]
[ROW][C]43[/C][C]1.67[/C][C]1.68597450354101[/C][C]-0.0159745035410104[/C][/ROW]
[ROW][C]44[/C][C]1.68[/C][C]1.68664070140836[/C][C]-0.0066407014083627[/C][/ROW]
[ROW][C]45[/C][C]1.66[/C][C]1.67646825596518[/C][C]-0.0164682559651839[/C][/ROW]
[ROW][C]46[/C][C]1.65[/C][C]1.67500731857009[/C][C]-0.0250073185700903[/C][/ROW]
[ROW][C]47[/C][C]1.65[/C][C]1.66278886101591[/C][C]-0.0127888610159148[/C][/ROW]
[ROW][C]48[/C][C]1.66[/C][C]1.65165433132811[/C][C]0.00834566867188546[/C][/ROW]
[ROW][C]49[/C][C]1.67[/C][C]1.67281136172702[/C][C]-0.00281136172701757[/C][/ROW]
[ROW][C]50[/C][C]1.67[/C][C]1.66297862593803[/C][C]0.00702137406197378[/C][/ROW]
[ROW][C]51[/C][C]1.65[/C][C]1.6736015084068[/C][C]-0.0236015084068042[/C][/ROW]
[ROW][C]52[/C][C]1.65[/C][C]1.64150776355094[/C][C]0.00849223644905628[/C][/ROW]
[ROW][C]53[/C][C]1.65[/C][C]1.65184446298586[/C][C]-0.00184446298586205[/C][/ROW]
[ROW][C]54[/C][C]1.65[/C][C]1.65084750303927[/C][C]-0.000847503039267172[/C][/ROW]
[ROW][C]55[/C][C]1.66[/C][C]1.64868898573471[/C][C]0.0113110142652857[/C][/ROW]
[ROW][C]56[/C][C]1.66[/C][C]1.67177574552386[/C][C]-0.0117757455238621[/C][/ROW]
[ROW][C]57[/C][C]1.67[/C][C]1.65114775834089[/C][C]0.0188522416591128[/C][/ROW]
[ROW][C]58[/C][C]1.67[/C][C]1.68282018466699[/C][C]-0.0128201846669875[/C][/ROW]
[ROW][C]59[/C][C]1.67[/C][C]1.68168287618504[/C][C]-0.0116828761850449[/C][/ROW]
[ROW][C]60[/C][C]1.66[/C][C]1.67064646099105[/C][C]-0.0106464609910464[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166644&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166644&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	1.47	1.46497329059829	0.00502670940171024
14	1.46	1.46095583787458	-0.000955837874577314
15	1.46	1.46087104326745	-0.000871043267450577
16	1.45	1.45079377098769	-0.000793770987687514
17	1.45	1.45030668704541	-0.000306687045414256
18	1.45	1.44944614678901	0.00055385321099477
19	1.44	1.44741194706575	-0.00741194706575476
20	1.45	1.44883774928822	0.00116225071177811
21	1.44	1.43935752192621	0.000642478073786812
22	1.45	1.44941451765457	0.000585482345428989
23	1.47	1.45946645715894	0.0105335428410629
24	1.48	1.47040091231144	0.00959908768856454
25	1.5	1.49166913643462	0.00833086356537982
26	1.5	1.492824853438	0.00717514656200313
27	1.52	1.50346137742389	0.0165386225761086
28	1.54	1.51492855720515	0.0250714427948455
29	1.55	1.5467360367022	0.00326396329780398
30	1.54	1.55619225716546	-0.0161922571654551
31	1.55	1.54267247093426	0.00732752906574374
32	1.54	1.56540584646079	-0.0254058464607889
33	1.57	1.53356870123462	0.0364312987653783
34	1.61	1.58680060671573	0.0231993932842711
35	1.62	1.62885867900123	-0.00885867900122927
36	1.64	1.6280728049262	0.011927195073802
37	1.63	1.6595475608853	-0.0295475608853022
38	1.63	1.62734299451294	0.00265700548706005
39	1.67	1.63757870366655	0.0324212963334494
40	1.7	1.67045487247951	0.0295451275204865
41	1.69	1.71265922298241	-0.0226592229824081
42	1.68	1.69981573713088	-0.0198157371308758
43	1.67	1.68597450354101	-0.0159745035410104
44	1.68	1.68664070140836	-0.0066407014083627
45	1.66	1.67646825596518	-0.0164682559651839
46	1.65	1.67500731857009	-0.0250073185700903
47	1.65	1.66278886101591	-0.0127888610159148
48	1.66	1.65165433132811	0.00834566867188546
49	1.67	1.67281136172702	-0.00281136172701757
50	1.67	1.66297862593803	0.00702137406197378
51	1.65	1.6736015084068	-0.0236015084068042
52	1.65	1.64150776355094	0.00849223644905628
53	1.65	1.65184446298586	-0.00184446298586205
54	1.65	1.65084750303927	-0.000847503039267172
55	1.66	1.64868898573471	0.0113110142652857
56	1.66	1.67177574552386	-0.0117757455238621
57	1.67	1.65114775834089	0.0188522416591128
58	1.67	1.68282018466699	-0.0128201846669875
59	1.67	1.68168287618504	-0.0116828761850449
60	1.66	1.67064646099105	-0.0106464609910464

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.67011865527277	1.63981525334178	1.70042205720377
62	1.66065397721221	1.61585724066184	1.70545071376259
63	1.66118929915166	1.60391969055899	1.71845890774432
64	1.6517246210911	1.5827903675272	1.72065887465499
65	1.65184327636387	1.57160880059961	1.73207775212813
66	1.65112859830331	1.55974380095681	1.74251339564981
67	1.64833058690942	1.54582587810765	1.75083529571119
68	1.65761590884886	1.54394917105794	1.77128264663978
69	1.64731789745497	1.5224004414931	1.77223535341683
70	1.65701988606107	1.5207319568236	1.79330781529855
71	1.66672187466718	1.51892245791247	1.81452129142189
72	1.66642386327329	1.5069571633858	1.82589056316078

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.67011865527277 & 1.63981525334178 & 1.70042205720377 \tabularnewline
62 & 1.66065397721221 & 1.61585724066184 & 1.70545071376259 \tabularnewline
63 & 1.66118929915166 & 1.60391969055899 & 1.71845890774432 \tabularnewline
64 & 1.6517246210911 & 1.5827903675272 & 1.72065887465499 \tabularnewline
65 & 1.65184327636387 & 1.57160880059961 & 1.73207775212813 \tabularnewline
66 & 1.65112859830331 & 1.55974380095681 & 1.74251339564981 \tabularnewline
67 & 1.64833058690942 & 1.54582587810765 & 1.75083529571119 \tabularnewline
68 & 1.65761590884886 & 1.54394917105794 & 1.77128264663978 \tabularnewline
69 & 1.64731789745497 & 1.5224004414931 & 1.77223535341683 \tabularnewline
70 & 1.65701988606107 & 1.5207319568236 & 1.79330781529855 \tabularnewline
71 & 1.66672187466718 & 1.51892245791247 & 1.81452129142189 \tabularnewline
72 & 1.66642386327329 & 1.5069571633858 & 1.82589056316078 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166644&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]1.67011865527277[/C][C]1.63981525334178[/C][C]1.70042205720377[/C][/ROW]
[ROW][C]62[/C][C]1.66065397721221[/C][C]1.61585724066184[/C][C]1.70545071376259[/C][/ROW]
[ROW][C]63[/C][C]1.66118929915166[/C][C]1.60391969055899[/C][C]1.71845890774432[/C][/ROW]
[ROW][C]64[/C][C]1.6517246210911[/C][C]1.5827903675272[/C][C]1.72065887465499[/C][/ROW]
[ROW][C]65[/C][C]1.65184327636387[/C][C]1.57160880059961[/C][C]1.73207775212813[/C][/ROW]
[ROW][C]66[/C][C]1.65112859830331[/C][C]1.55974380095681[/C][C]1.74251339564981[/C][/ROW]
[ROW][C]67[/C][C]1.64833058690942[/C][C]1.54582587810765[/C][C]1.75083529571119[/C][/ROW]
[ROW][C]68[/C][C]1.65761590884886[/C][C]1.54394917105794[/C][C]1.77128264663978[/C][/ROW]
[ROW][C]69[/C][C]1.64731789745497[/C][C]1.5224004414931[/C][C]1.77223535341683[/C][/ROW]
[ROW][C]70[/C][C]1.65701988606107[/C][C]1.5207319568236[/C][C]1.79330781529855[/C][/ROW]
[ROW][C]71[/C][C]1.66672187466718[/C][C]1.51892245791247[/C][C]1.81452129142189[/C][/ROW]
[ROW][C]72[/C][C]1.66642386327329[/C][C]1.5069571633858[/C][C]1.82589056316078[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166644&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166644&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	1.67011865527277	1.63981525334178	1.70042205720377
62	1.66065397721221	1.61585724066184	1.70545071376259
63	1.66118929915166	1.60391969055899	1.71845890774432
64	1.6517246210911	1.5827903675272	1.72065887465499
65	1.65184327636387	1.57160880059961	1.73207775212813
66	1.65112859830331	1.55974380095681	1.74251339564981
67	1.64833058690942	1.54582587810765	1.75083529571119
68	1.65761590884886	1.54394917105794	1.77128264663978
69	1.64731789745497	1.5224004414931	1.77223535341683
70	1.65701988606107	1.5207319568236	1.79330781529855
71	1.66672187466718	1.51892245791247	1.81452129142189
72	1.66642386327329	1.5069571633858	1.82589056316078

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