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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 16 Jan 2009 05:12:58 -0700

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/Jan/16/t1232108032wzez2j1dngqof8o.htm/, Retrieved Thu, 31 Oct 2024 23:03:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36912, Retrieved Thu, 31 Oct 2024 23:03:36 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

240

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

-       [Exponential Smoothing] [Bananen - Waerlop...] [2009-01-16 12:12:58] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Boxplots

1.83
1.89
1.9
2.01
2.04
2.04
2.03
2.04
1.87
1.85
1.82
1.79
1.88
2.01
1.9
1.96
1.94
1.92
1.79
1.77
1.74
1.75
1.86
1.84
1.77
1.98
1.94
1.85
1.84
1.82
1.83
1.91
1.85
1.81
1.83
1.79
1.8
1.82
1.88
2.01
1.97
1.92
1.98
2.02
1.9
1.94
1.96
1.84
1.87
1.84
2.07
2.08
2.14
2.15
2.05
2.05
1.95
2.02
2.02
1.88
1.96
1.93
2.03
2.1
1.95
2.07
2.09
2.01
1.92
1.99
2.11
2

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36912&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36912&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36912&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.189436582035874
beta	0
gamma	0.744362208464726

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.189436582035874 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.744362208464726 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36912&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]0.189436582035874[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.744362208464726[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36912&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36912&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	0.189436582035874
beta	0
gamma	0.744362208464726

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.88	1.90227527799859	-0.0222752779985915
14	2.01	2.05216565537804	-0.0421656553780414
15	1.9	1.94953333354587	-0.0495333335458656
16	1.96	2.01172976444937	-0.0517297644493735
17	1.94	1.98416928914675	-0.0441692891467469
18	1.92	1.95149315970507	-0.0314931597050747
19	1.79	1.81623833987934	-0.0262383398793444
20	1.77	1.79666871199340	-0.0266687119934028
21	1.74	1.76085433335414	-0.0208543333541389
22	1.75	1.76978609271535	-0.0197860927153466
23	1.86	1.88596407019132	-0.0259640701913233
24	1.84	1.86927749873068	-0.0292774987306774
25	1.77	1.81724755007505	-0.0472475500750542
26	1.98	1.94455617580194	0.0354438241980597
27	1.94	1.85535251443699	0.0846474855630066
28	1.85	1.94006304763562	-0.0900630476356186
29	1.84	1.91001195080999	-0.0700119508099881
30	1.82	1.88047967667071	-0.0604796766707134
31	1.83	1.74662650483443	0.083373495165572
32	1.91	1.74779040282999	0.162209597170006
33	1.85	1.75119032703091	0.0988096729690888
34	1.81	1.78360806801659	0.0263919319834058
35	1.83	1.90705051993986	-0.0770505199398563
36	1.79	1.87843399063379	-0.0884339906337896
37	1.8	1.8037281799364	-0.00372817993640151
38	1.82	1.99152833346388	-0.171528333463879
39	1.88	1.89282645916319	-0.0128264591631935
40	2.01	1.85379841514258	0.156201584857424
41	1.97	1.88219200395413	0.0878079960458682
42	1.92	1.88782753206184	0.0321724679381643
43	1.98	1.85666170713813	0.123338292861873
44	2.02	1.91243148901862	0.107568510981381
45	1.9	1.86460648426151	0.0353935157384941
46	1.94	1.84058686347180	0.099413136528196
47	1.96	1.91678471635249	0.0432152836475135
48	1.84	1.90268797928788	-0.0626879792878834
49	1.87	1.88365369817882	-0.0136536981788193
50	1.84	1.97042878644653	-0.130428786446534
51	2.07	1.97669132994389	0.0933086700561141
52	2.08	2.06206385664245	0.0179361433575496
53	2.14	2.02062895463934	0.119371045360660
54	2.15	1.99652261921517	0.153477380784831
55	2.05	2.04340358601369	0.00659641398631017
56	2.05	2.06788414170704	-0.0178841417070443
57	1.95	1.94893186022411	0.00106813977588693
58	2.02	1.95664630686942	0.063353693130582
59	2.02	1.99259420093664	0.0274057990633565
60	1.88	1.90929770788939	-0.029297707889389
61	1.96	1.92677640429509	0.0332235957049141
62	1.93	1.95155183104758	-0.0215518310475755
63	2.03	2.12006250596533	-0.0900625059653284
64	2.1	2.12577043605420	-0.0257704360542048
65	1.95	2.1367943578158	-0.186794357815799
66	2.07	2.07411805673626	-0.0041180567362602
67	2.09	2.00402099173862	0.0859790082613823
68	2.01	2.02863466461439	-0.0186346646143853
69	1.92	1.92242522508468	-0.00242522508467768
70	1.99	1.96618513221556	0.0238148677844354
71	2.11	1.97287078172946	0.137129218270541
72	2	1.87703909362869	0.122960906371310

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.88 & 1.90227527799859 & -0.0222752779985915 \tabularnewline
14 & 2.01 & 2.05216565537804 & -0.0421656553780414 \tabularnewline
15 & 1.9 & 1.94953333354587 & -0.0495333335458656 \tabularnewline
16 & 1.96 & 2.01172976444937 & -0.0517297644493735 \tabularnewline
17 & 1.94 & 1.98416928914675 & -0.0441692891467469 \tabularnewline
18 & 1.92 & 1.95149315970507 & -0.0314931597050747 \tabularnewline
19 & 1.79 & 1.81623833987934 & -0.0262383398793444 \tabularnewline
20 & 1.77 & 1.79666871199340 & -0.0266687119934028 \tabularnewline
21 & 1.74 & 1.76085433335414 & -0.0208543333541389 \tabularnewline
22 & 1.75 & 1.76978609271535 & -0.0197860927153466 \tabularnewline
23 & 1.86 & 1.88596407019132 & -0.0259640701913233 \tabularnewline
24 & 1.84 & 1.86927749873068 & -0.0292774987306774 \tabularnewline
25 & 1.77 & 1.81724755007505 & -0.0472475500750542 \tabularnewline
26 & 1.98 & 1.94455617580194 & 0.0354438241980597 \tabularnewline
27 & 1.94 & 1.85535251443699 & 0.0846474855630066 \tabularnewline
28 & 1.85 & 1.94006304763562 & -0.0900630476356186 \tabularnewline
29 & 1.84 & 1.91001195080999 & -0.0700119508099881 \tabularnewline
30 & 1.82 & 1.88047967667071 & -0.0604796766707134 \tabularnewline
31 & 1.83 & 1.74662650483443 & 0.083373495165572 \tabularnewline
32 & 1.91 & 1.74779040282999 & 0.162209597170006 \tabularnewline
33 & 1.85 & 1.75119032703091 & 0.0988096729690888 \tabularnewline
34 & 1.81 & 1.78360806801659 & 0.0263919319834058 \tabularnewline
35 & 1.83 & 1.90705051993986 & -0.0770505199398563 \tabularnewline
36 & 1.79 & 1.87843399063379 & -0.0884339906337896 \tabularnewline
37 & 1.8 & 1.8037281799364 & -0.00372817993640151 \tabularnewline
38 & 1.82 & 1.99152833346388 & -0.171528333463879 \tabularnewline
39 & 1.88 & 1.89282645916319 & -0.0128264591631935 \tabularnewline
40 & 2.01 & 1.85379841514258 & 0.156201584857424 \tabularnewline
41 & 1.97 & 1.88219200395413 & 0.0878079960458682 \tabularnewline
42 & 1.92 & 1.88782753206184 & 0.0321724679381643 \tabularnewline
43 & 1.98 & 1.85666170713813 & 0.123338292861873 \tabularnewline
44 & 2.02 & 1.91243148901862 & 0.107568510981381 \tabularnewline
45 & 1.9 & 1.86460648426151 & 0.0353935157384941 \tabularnewline
46 & 1.94 & 1.84058686347180 & 0.099413136528196 \tabularnewline
47 & 1.96 & 1.91678471635249 & 0.0432152836475135 \tabularnewline
48 & 1.84 & 1.90268797928788 & -0.0626879792878834 \tabularnewline
49 & 1.87 & 1.88365369817882 & -0.0136536981788193 \tabularnewline
50 & 1.84 & 1.97042878644653 & -0.130428786446534 \tabularnewline
51 & 2.07 & 1.97669132994389 & 0.0933086700561141 \tabularnewline
52 & 2.08 & 2.06206385664245 & 0.0179361433575496 \tabularnewline
53 & 2.14 & 2.02062895463934 & 0.119371045360660 \tabularnewline
54 & 2.15 & 1.99652261921517 & 0.153477380784831 \tabularnewline
55 & 2.05 & 2.04340358601369 & 0.00659641398631017 \tabularnewline
56 & 2.05 & 2.06788414170704 & -0.0178841417070443 \tabularnewline
57 & 1.95 & 1.94893186022411 & 0.00106813977588693 \tabularnewline
58 & 2.02 & 1.95664630686942 & 0.063353693130582 \tabularnewline
59 & 2.02 & 1.99259420093664 & 0.0274057990633565 \tabularnewline
60 & 1.88 & 1.90929770788939 & -0.029297707889389 \tabularnewline
61 & 1.96 & 1.92677640429509 & 0.0332235957049141 \tabularnewline
62 & 1.93 & 1.95155183104758 & -0.0215518310475755 \tabularnewline
63 & 2.03 & 2.12006250596533 & -0.0900625059653284 \tabularnewline
64 & 2.1 & 2.12577043605420 & -0.0257704360542048 \tabularnewline
65 & 1.95 & 2.1367943578158 & -0.186794357815799 \tabularnewline
66 & 2.07 & 2.07411805673626 & -0.0041180567362602 \tabularnewline
67 & 2.09 & 2.00402099173862 & 0.0859790082613823 \tabularnewline
68 & 2.01 & 2.02863466461439 & -0.0186346646143853 \tabularnewline
69 & 1.92 & 1.92242522508468 & -0.00242522508467768 \tabularnewline
70 & 1.99 & 1.96618513221556 & 0.0238148677844354 \tabularnewline
71 & 2.11 & 1.97287078172946 & 0.137129218270541 \tabularnewline
72 & 2 & 1.87703909362869 & 0.122960906371310 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36912&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]1.88[/C][C]1.90227527799859[/C][C]-0.0222752779985915[/C][/ROW]
[ROW][C]14[/C][C]2.01[/C][C]2.05216565537804[/C][C]-0.0421656553780414[/C][/ROW]
[ROW][C]15[/C][C]1.9[/C][C]1.94953333354587[/C][C]-0.0495333335458656[/C][/ROW]
[ROW][C]16[/C][C]1.96[/C][C]2.01172976444937[/C][C]-0.0517297644493735[/C][/ROW]
[ROW][C]17[/C][C]1.94[/C][C]1.98416928914675[/C][C]-0.0441692891467469[/C][/ROW]
[ROW][C]18[/C][C]1.92[/C][C]1.95149315970507[/C][C]-0.0314931597050747[/C][/ROW]
[ROW][C]19[/C][C]1.79[/C][C]1.81623833987934[/C][C]-0.0262383398793444[/C][/ROW]
[ROW][C]20[/C][C]1.77[/C][C]1.79666871199340[/C][C]-0.0266687119934028[/C][/ROW]
[ROW][C]21[/C][C]1.74[/C][C]1.76085433335414[/C][C]-0.0208543333541389[/C][/ROW]
[ROW][C]22[/C][C]1.75[/C][C]1.76978609271535[/C][C]-0.0197860927153466[/C][/ROW]
[ROW][C]23[/C][C]1.86[/C][C]1.88596407019132[/C][C]-0.0259640701913233[/C][/ROW]
[ROW][C]24[/C][C]1.84[/C][C]1.86927749873068[/C][C]-0.0292774987306774[/C][/ROW]
[ROW][C]25[/C][C]1.77[/C][C]1.81724755007505[/C][C]-0.0472475500750542[/C][/ROW]
[ROW][C]26[/C][C]1.98[/C][C]1.94455617580194[/C][C]0.0354438241980597[/C][/ROW]
[ROW][C]27[/C][C]1.94[/C][C]1.85535251443699[/C][C]0.0846474855630066[/C][/ROW]
[ROW][C]28[/C][C]1.85[/C][C]1.94006304763562[/C][C]-0.0900630476356186[/C][/ROW]
[ROW][C]29[/C][C]1.84[/C][C]1.91001195080999[/C][C]-0.0700119508099881[/C][/ROW]
[ROW][C]30[/C][C]1.82[/C][C]1.88047967667071[/C][C]-0.0604796766707134[/C][/ROW]
[ROW][C]31[/C][C]1.83[/C][C]1.74662650483443[/C][C]0.083373495165572[/C][/ROW]
[ROW][C]32[/C][C]1.91[/C][C]1.74779040282999[/C][C]0.162209597170006[/C][/ROW]
[ROW][C]33[/C][C]1.85[/C][C]1.75119032703091[/C][C]0.0988096729690888[/C][/ROW]
[ROW][C]34[/C][C]1.81[/C][C]1.78360806801659[/C][C]0.0263919319834058[/C][/ROW]
[ROW][C]35[/C][C]1.83[/C][C]1.90705051993986[/C][C]-0.0770505199398563[/C][/ROW]
[ROW][C]36[/C][C]1.79[/C][C]1.87843399063379[/C][C]-0.0884339906337896[/C][/ROW]
[ROW][C]37[/C][C]1.8[/C][C]1.8037281799364[/C][C]-0.00372817993640151[/C][/ROW]
[ROW][C]38[/C][C]1.82[/C][C]1.99152833346388[/C][C]-0.171528333463879[/C][/ROW]
[ROW][C]39[/C][C]1.88[/C][C]1.89282645916319[/C][C]-0.0128264591631935[/C][/ROW]
[ROW][C]40[/C][C]2.01[/C][C]1.85379841514258[/C][C]0.156201584857424[/C][/ROW]
[ROW][C]41[/C][C]1.97[/C][C]1.88219200395413[/C][C]0.0878079960458682[/C][/ROW]
[ROW][C]42[/C][C]1.92[/C][C]1.88782753206184[/C][C]0.0321724679381643[/C][/ROW]
[ROW][C]43[/C][C]1.98[/C][C]1.85666170713813[/C][C]0.123338292861873[/C][/ROW]
[ROW][C]44[/C][C]2.02[/C][C]1.91243148901862[/C][C]0.107568510981381[/C][/ROW]
[ROW][C]45[/C][C]1.9[/C][C]1.86460648426151[/C][C]0.0353935157384941[/C][/ROW]
[ROW][C]46[/C][C]1.94[/C][C]1.84058686347180[/C][C]0.099413136528196[/C][/ROW]
[ROW][C]47[/C][C]1.96[/C][C]1.91678471635249[/C][C]0.0432152836475135[/C][/ROW]
[ROW][C]48[/C][C]1.84[/C][C]1.90268797928788[/C][C]-0.0626879792878834[/C][/ROW]
[ROW][C]49[/C][C]1.87[/C][C]1.88365369817882[/C][C]-0.0136536981788193[/C][/ROW]
[ROW][C]50[/C][C]1.84[/C][C]1.97042878644653[/C][C]-0.130428786446534[/C][/ROW]
[ROW][C]51[/C][C]2.07[/C][C]1.97669132994389[/C][C]0.0933086700561141[/C][/ROW]
[ROW][C]52[/C][C]2.08[/C][C]2.06206385664245[/C][C]0.0179361433575496[/C][/ROW]
[ROW][C]53[/C][C]2.14[/C][C]2.02062895463934[/C][C]0.119371045360660[/C][/ROW]
[ROW][C]54[/C][C]2.15[/C][C]1.99652261921517[/C][C]0.153477380784831[/C][/ROW]
[ROW][C]55[/C][C]2.05[/C][C]2.04340358601369[/C][C]0.00659641398631017[/C][/ROW]
[ROW][C]56[/C][C]2.05[/C][C]2.06788414170704[/C][C]-0.0178841417070443[/C][/ROW]
[ROW][C]57[/C][C]1.95[/C][C]1.94893186022411[/C][C]0.00106813977588693[/C][/ROW]
[ROW][C]58[/C][C]2.02[/C][C]1.95664630686942[/C][C]0.063353693130582[/C][/ROW]
[ROW][C]59[/C][C]2.02[/C][C]1.99259420093664[/C][C]0.0274057990633565[/C][/ROW]
[ROW][C]60[/C][C]1.88[/C][C]1.90929770788939[/C][C]-0.029297707889389[/C][/ROW]
[ROW][C]61[/C][C]1.96[/C][C]1.92677640429509[/C][C]0.0332235957049141[/C][/ROW]
[ROW][C]62[/C][C]1.93[/C][C]1.95155183104758[/C][C]-0.0215518310475755[/C][/ROW]
[ROW][C]63[/C][C]2.03[/C][C]2.12006250596533[/C][C]-0.0900625059653284[/C][/ROW]
[ROW][C]64[/C][C]2.1[/C][C]2.12577043605420[/C][C]-0.0257704360542048[/C][/ROW]
[ROW][C]65[/C][C]1.95[/C][C]2.1367943578158[/C][C]-0.186794357815799[/C][/ROW]
[ROW][C]66[/C][C]2.07[/C][C]2.07411805673626[/C][C]-0.0041180567362602[/C][/ROW]
[ROW][C]67[/C][C]2.09[/C][C]2.00402099173862[/C][C]0.0859790082613823[/C][/ROW]
[ROW][C]68[/C][C]2.01[/C][C]2.02863466461439[/C][C]-0.0186346646143853[/C][/ROW]
[ROW][C]69[/C][C]1.92[/C][C]1.92242522508468[/C][C]-0.00242522508467768[/C][/ROW]
[ROW][C]70[/C][C]1.99[/C][C]1.96618513221556[/C][C]0.0238148677844354[/C][/ROW]
[ROW][C]71[/C][C]2.11[/C][C]1.97287078172946[/C][C]0.137129218270541[/C][/ROW]
[ROW][C]72[/C][C]2[/C][C]1.87703909362869[/C][C]0.122960906371310[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36912&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36912&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	1.88	1.90227527799859	-0.0222752779985915
14	2.01	2.05216565537804	-0.0421656553780414
15	1.9	1.94953333354587	-0.0495333335458656
16	1.96	2.01172976444937	-0.0517297644493735
17	1.94	1.98416928914675	-0.0441692891467469
18	1.92	1.95149315970507	-0.0314931597050747
19	1.79	1.81623833987934	-0.0262383398793444
20	1.77	1.79666871199340	-0.0266687119934028
21	1.74	1.76085433335414	-0.0208543333541389
22	1.75	1.76978609271535	-0.0197860927153466
23	1.86	1.88596407019132	-0.0259640701913233
24	1.84	1.86927749873068	-0.0292774987306774
25	1.77	1.81724755007505	-0.0472475500750542
26	1.98	1.94455617580194	0.0354438241980597
27	1.94	1.85535251443699	0.0846474855630066
28	1.85	1.94006304763562	-0.0900630476356186
29	1.84	1.91001195080999	-0.0700119508099881
30	1.82	1.88047967667071	-0.0604796766707134
31	1.83	1.74662650483443	0.083373495165572
32	1.91	1.74779040282999	0.162209597170006
33	1.85	1.75119032703091	0.0988096729690888
34	1.81	1.78360806801659	0.0263919319834058
35	1.83	1.90705051993986	-0.0770505199398563
36	1.79	1.87843399063379	-0.0884339906337896
37	1.8	1.8037281799364	-0.00372817993640151
38	1.82	1.99152833346388	-0.171528333463879
39	1.88	1.89282645916319	-0.0128264591631935
40	2.01	1.85379841514258	0.156201584857424
41	1.97	1.88219200395413	0.0878079960458682
42	1.92	1.88782753206184	0.0321724679381643
43	1.98	1.85666170713813	0.123338292861873
44	2.02	1.91243148901862	0.107568510981381
45	1.9	1.86460648426151	0.0353935157384941
46	1.94	1.84058686347180	0.099413136528196
47	1.96	1.91678471635249	0.0432152836475135
48	1.84	1.90268797928788	-0.0626879792878834
49	1.87	1.88365369817882	-0.0136536981788193
50	1.84	1.97042878644653	-0.130428786446534
51	2.07	1.97669132994389	0.0933086700561141
52	2.08	2.06206385664245	0.0179361433575496
53	2.14	2.02062895463934	0.119371045360660
54	2.15	1.99652261921517	0.153477380784831
55	2.05	2.04340358601369	0.00659641398631017
56	2.05	2.06788414170704	-0.0178841417070443
57	1.95	1.94893186022411	0.00106813977588693
58	2.02	1.95664630686942	0.063353693130582
59	2.02	1.99259420093664	0.0274057990633565
60	1.88	1.90929770788939	-0.029297707889389
61	1.96	1.92677640429509	0.0332235957049141
62	1.93	1.95155183104758	-0.0215518310475755
63	2.03	2.12006250596533	-0.0900625059653284
64	2.1	2.12577043605420	-0.0257704360542048
65	1.95	2.1367943578158	-0.186794357815799
66	2.07	2.07411805673626	-0.0041180567362602
67	2.09	2.00402099173862	0.0859790082613823
68	2.01	2.02863466461439	-0.0186346646143853
69	1.92	1.92242522508468	-0.00242522508467768
70	1.99	1.96618513221556	0.0238148677844354
71	2.11	1.97287078172946	0.137129218270541
72	2	1.87703909362869	0.122960906371310

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.96147715700842	1.84017738173516	2.08277693228167
74	1.94682017292012	1.82163550291125	2.07200484292900
75	2.07847205943309	1.94954999858896	2.20739412027722
76	2.14089137062812	2.00955865787017	2.27222408338607
77	2.05634108309776	1.92078409285136	2.19189807334417
78	2.14208809817020	2.00370747789487	2.28046871844553
79	2.12618436431985	1.98577820082501	2.26659052781469
80	2.06994353285057	1.92842467147988	2.21146239422126
81	1.97445676016745	1.82865433646939	2.12025918386551
82	2.03616138029112	1.88574742858209	2.18657533200015
83	2.10741699674723	1.95776544461701	2.25706854887745
84	1.97452119164158	NA	NA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.96147715700842 & 1.84017738173516 & 2.08277693228167 \tabularnewline
74 & 1.94682017292012 & 1.82163550291125 & 2.07200484292900 \tabularnewline
75 & 2.07847205943309 & 1.94954999858896 & 2.20739412027722 \tabularnewline
76 & 2.14089137062812 & 2.00955865787017 & 2.27222408338607 \tabularnewline
77 & 2.05634108309776 & 1.92078409285136 & 2.19189807334417 \tabularnewline
78 & 2.14208809817020 & 2.00370747789487 & 2.28046871844553 \tabularnewline
79 & 2.12618436431985 & 1.98577820082501 & 2.26659052781469 \tabularnewline
80 & 2.06994353285057 & 1.92842467147988 & 2.21146239422126 \tabularnewline
81 & 1.97445676016745 & 1.82865433646939 & 2.12025918386551 \tabularnewline
82 & 2.03616138029112 & 1.88574742858209 & 2.18657533200015 \tabularnewline
83 & 2.10741699674723 & 1.95776544461701 & 2.25706854887745 \tabularnewline
84 & 1.97452119164158 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36912&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]1.96147715700842[/C][C]1.84017738173516[/C][C]2.08277693228167[/C][/ROW]
[ROW][C]74[/C][C]1.94682017292012[/C][C]1.82163550291125[/C][C]2.07200484292900[/C][/ROW]
[ROW][C]75[/C][C]2.07847205943309[/C][C]1.94954999858896[/C][C]2.20739412027722[/C][/ROW]
[ROW][C]76[/C][C]2.14089137062812[/C][C]2.00955865787017[/C][C]2.27222408338607[/C][/ROW]
[ROW][C]77[/C][C]2.05634108309776[/C][C]1.92078409285136[/C][C]2.19189807334417[/C][/ROW]
[ROW][C]78[/C][C]2.14208809817020[/C][C]2.00370747789487[/C][C]2.28046871844553[/C][/ROW]
[ROW][C]79[/C][C]2.12618436431985[/C][C]1.98577820082501[/C][C]2.26659052781469[/C][/ROW]
[ROW][C]80[/C][C]2.06994353285057[/C][C]1.92842467147988[/C][C]2.21146239422126[/C][/ROW]
[ROW][C]81[/C][C]1.97445676016745[/C][C]1.82865433646939[/C][C]2.12025918386551[/C][/ROW]
[ROW][C]82[/C][C]2.03616138029112[/C][C]1.88574742858209[/C][C]2.18657533200015[/C][/ROW]
[ROW][C]83[/C][C]2.10741699674723[/C][C]1.95776544461701[/C][C]2.25706854887745[/C][/ROW]
[ROW][C]84[/C][C]1.97452119164158[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36912&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36912&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	1.96147715700842	1.84017738173516	2.08277693228167
74	1.94682017292012	1.82163550291125	2.07200484292900
75	2.07847205943309	1.94954999858896	2.20739412027722
76	2.14089137062812	2.00955865787017	2.27222408338607
77	2.05634108309776	1.92078409285136	2.19189807334417
78	2.14208809817020	2.00370747789487	2.28046871844553
79	2.12618436431985	1.98577820082501	2.26659052781469
80	2.06994353285057	1.92842467147988	2.21146239422126
81	1.97445676016745	1.82865433646939	2.12025918386551
82	2.03616138029112	1.88574742858209	2.18657533200015
83	2.10741699674723	1.95776544461701	2.25706854887745
84	1.97452119164158	NA	NA

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