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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 03 Jun 2009 12:02:06 -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/03/t1244052174qjzs0atfyk6be3g.htm/, Retrieved Sat, 11 May 2024 13:38:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41519, Retrieved Sat, 11 May 2024 13:38:08 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

106

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

-       [Exponential Smoothing] [Opgave 10, oefeni...] [2009-06-03 18:02:06] [564a720da86171cdf215ca3dfe587c26] [Current]

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Dataseries X:

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1.54
1.55
1.53
1.55
1.55
1.53
1.54
1.54
1.54
1.53
1.53
1.53
1.54
1.53
1.53
1.54
1.55
1.53
1.53
1.53
1.53
1.52
1.54
1.53
1.52
1.54
1.53
1.54
1.54
1.53
1.54
1.54
1.52
1.52
1.57
1.6
1.59
1.6
1.6
1.62
1.61
1.61
1.62
1.61
1.62
1.61
1.62
1.61
1.61
1.58
1.57
1.57
1.66
1.66
1.67
1.68
1.66
1.66
1.64
1.61
1.58
1.57
1.54
1.61
1.65
1.6
1.57
1.56
1.55
1.54
1.51
1.5
1.5
1.49
1.47
1.47
1.49
1.49
1.49
1.51
1.49
1.48
1.46
1.46
1.45
1.45
1.44
1.47
1.47
1.45
1.43
1.44
1.38
1.4
1.37
1.41

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=41519&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=41519&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41519&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	0.871955057656946
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.871955057656946 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41519&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]0.871955057656946[/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=41519&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41519&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	0.871955057656946
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.54	1.54198183760684	-0.00198183760683746
14	1.53	1.53060050087884	-0.000600500878837451
15	1.53	1.53042362769714	-0.000423627697144102
16	1.54	1.54040097998079	-0.000400979980792471
17	1.55	1.54956474672192	0.000435253278075587
18	1.53	1.52904100461584	0.000958995384159333
19	1.53	1.53439060875473	-0.00439060875473141
20	1.53	1.53090893184159	-0.000908931841587135
21	1.53	1.53046312072199	-0.000463120721986066
22	1.52	1.51998937019621	1.06298037854113e-05
23	1.54	1.51992870883746	0.0200712911625434
24	1.53	1.53694337594374	-0.00694337594374494
25	1.52	1.54056536982035	-0.0205653698203523
26	1.54	1.51315690137134	0.0268430986286596
27	1.53	1.53693226129687	-0.00693226129687274
28	1.54	1.54123727752034	-0.0012372775203362
29	1.54	1.54977890583157	-0.00977890583157404
30	1.53	1.52041593855789	0.00958406144210544
31	1.54	1.53260122291511	0.00739877708488579
32	1.54	1.53984517173109	0.000154828268906115
33	1.52	1.54038399547908	-0.0203839954790761
34	1.52	1.51260079881467	0.00739920118533322
35	1.57	1.52155130586795	0.0484486941320454
36	1.6	1.55985070152463	0.0401492984753724
37	1.59	1.60279116361905	-0.0127911636190485
38	1.6	1.58823186819566	0.0117681318043423
39	1.6	1.59453777054044	0.00546222945956454
40	1.62	1.61037943953537	0.009620560464632
41	1.61	1.62729490228819	-0.0172949022881905
42	1.61	1.59385765391898	0.0161423460810186
43	1.62	1.61148165312713	0.008518346872868
44	1.61	1.61877426547366	-0.00877426547366467
45	1.62	1.60889742826991	0.0111025717300854
46	1.61	1.61212660094679	-0.00212660094678907
47	1.62	1.61802721661031	0.00197278338969276
48	1.61	1.61473901119763	-0.0047390111976322
49	1.61	1.61176012622651	-0.00176012622651056
50	1.58	1.60996409321522	-0.0299640932152201
51	1.57	1.57907393198475	-0.0090739319847546
52	1.57	1.58277317474318	-0.0127731747431823
53	1.66	1.5767159179454	0.083284082054601
54	1.66	1.63526049420743	0.0247395057925683
55	1.67	1.65940461576852	0.0105953842314785
56	1.68	1.66629407979396	0.0137059202060354
57	1.66	1.67856408266441	-0.0185640826644127
58	1.66	1.65423133734559	0.00576866265441289
59	1.64	1.66754117346871	-0.027541173468715
60	1.61	1.63765871275093	-0.02765871275093
61	1.58	1.61507630924480	-0.0350763092447965
62	1.57	1.58061868662197	-0.0106186866219724
63	1.54	1.56927173000321	-0.0292717300032113
64	1.61	1.55488573130020	0.0551142686998036
65	1.65	1.62032292007223	0.0296770799277715
66	1.6	1.62462826281198	-0.0246282628119749
67	1.57	1.60391482562331	-0.0339148256233128
68	1.56	1.57239167544802	-0.0123916754480164
69	1.55	1.55777373713827	-0.00777373713827134
70	1.54	1.54596537314623	-0.00596537314622814
71	1.51	1.54477850136042	-0.0347785013604167
72	1.5	1.50857036567293	-0.00857036567292657
73	1.5	1.50168235722839	-0.00168235722838839
74	1.49	1.49947443484001	-0.00947443484001242
75	1.47	1.48673678648549	-0.0167367864854910
76	1.47	1.49408589551868	-0.0240858955186849
77	1.49	1.48720699716346	0.00279300283653927
78	1.49	1.46111710843304	0.0288828915669626
79	1.49	1.48587389554641	0.00412610445359118
80	1.51	1.49027665727288	0.0197233427271204
81	1.49	1.50425287513230	-0.0142528751323048
82	1.48	1.48702654586020	-0.00702654586020324
83	1.46	1.48122500381848	-0.0212250038184849
84	1.46	1.46019072808465	-0.000190728084646707
85	1.45	1.46149136166068	-0.0114913616606809
86	1.45	1.44973269211848	0.000267307881524737
87	1.44	1.44455949820267	-0.00455949820267088
88	1.47	1.46158563910019	0.00841436089981151
89	1.47	1.48648721069436	-0.0164872106943592
90	1.45	1.44692652056119	0.0030734794388132
91	1.43	1.44600867885574	-0.0160086788557352
92	1.44	1.43485196191626	0.00514803808374298
93	1.38	1.43176868631815	-0.0517686863181535
94	1.4	1.38275555065545	0.0172444493445538
95	1.37	1.39629918490625	-0.0262991849062546
96	1.41	1.37353378393304	0.0364662160669642

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.54 & 1.54198183760684 & -0.00198183760683746 \tabularnewline
14 & 1.53 & 1.53060050087884 & -0.000600500878837451 \tabularnewline
15 & 1.53 & 1.53042362769714 & -0.000423627697144102 \tabularnewline
16 & 1.54 & 1.54040097998079 & -0.000400979980792471 \tabularnewline
17 & 1.55 & 1.54956474672192 & 0.000435253278075587 \tabularnewline
18 & 1.53 & 1.52904100461584 & 0.000958995384159333 \tabularnewline
19 & 1.53 & 1.53439060875473 & -0.00439060875473141 \tabularnewline
20 & 1.53 & 1.53090893184159 & -0.000908931841587135 \tabularnewline
21 & 1.53 & 1.53046312072199 & -0.000463120721986066 \tabularnewline
22 & 1.52 & 1.51998937019621 & 1.06298037854113e-05 \tabularnewline
23 & 1.54 & 1.51992870883746 & 0.0200712911625434 \tabularnewline
24 & 1.53 & 1.53694337594374 & -0.00694337594374494 \tabularnewline
25 & 1.52 & 1.54056536982035 & -0.0205653698203523 \tabularnewline
26 & 1.54 & 1.51315690137134 & 0.0268430986286596 \tabularnewline
27 & 1.53 & 1.53693226129687 & -0.00693226129687274 \tabularnewline
28 & 1.54 & 1.54123727752034 & -0.0012372775203362 \tabularnewline
29 & 1.54 & 1.54977890583157 & -0.00977890583157404 \tabularnewline
30 & 1.53 & 1.52041593855789 & 0.00958406144210544 \tabularnewline
31 & 1.54 & 1.53260122291511 & 0.00739877708488579 \tabularnewline
32 & 1.54 & 1.53984517173109 & 0.000154828268906115 \tabularnewline
33 & 1.52 & 1.54038399547908 & -0.0203839954790761 \tabularnewline
34 & 1.52 & 1.51260079881467 & 0.00739920118533322 \tabularnewline
35 & 1.57 & 1.52155130586795 & 0.0484486941320454 \tabularnewline
36 & 1.6 & 1.55985070152463 & 0.0401492984753724 \tabularnewline
37 & 1.59 & 1.60279116361905 & -0.0127911636190485 \tabularnewline
38 & 1.6 & 1.58823186819566 & 0.0117681318043423 \tabularnewline
39 & 1.6 & 1.59453777054044 & 0.00546222945956454 \tabularnewline
40 & 1.62 & 1.61037943953537 & 0.009620560464632 \tabularnewline
41 & 1.61 & 1.62729490228819 & -0.0172949022881905 \tabularnewline
42 & 1.61 & 1.59385765391898 & 0.0161423460810186 \tabularnewline
43 & 1.62 & 1.61148165312713 & 0.008518346872868 \tabularnewline
44 & 1.61 & 1.61877426547366 & -0.00877426547366467 \tabularnewline
45 & 1.62 & 1.60889742826991 & 0.0111025717300854 \tabularnewline
46 & 1.61 & 1.61212660094679 & -0.00212660094678907 \tabularnewline
47 & 1.62 & 1.61802721661031 & 0.00197278338969276 \tabularnewline
48 & 1.61 & 1.61473901119763 & -0.0047390111976322 \tabularnewline
49 & 1.61 & 1.61176012622651 & -0.00176012622651056 \tabularnewline
50 & 1.58 & 1.60996409321522 & -0.0299640932152201 \tabularnewline
51 & 1.57 & 1.57907393198475 & -0.0090739319847546 \tabularnewline
52 & 1.57 & 1.58277317474318 & -0.0127731747431823 \tabularnewline
53 & 1.66 & 1.5767159179454 & 0.083284082054601 \tabularnewline
54 & 1.66 & 1.63526049420743 & 0.0247395057925683 \tabularnewline
55 & 1.67 & 1.65940461576852 & 0.0105953842314785 \tabularnewline
56 & 1.68 & 1.66629407979396 & 0.0137059202060354 \tabularnewline
57 & 1.66 & 1.67856408266441 & -0.0185640826644127 \tabularnewline
58 & 1.66 & 1.65423133734559 & 0.00576866265441289 \tabularnewline
59 & 1.64 & 1.66754117346871 & -0.027541173468715 \tabularnewline
60 & 1.61 & 1.63765871275093 & -0.02765871275093 \tabularnewline
61 & 1.58 & 1.61507630924480 & -0.0350763092447965 \tabularnewline
62 & 1.57 & 1.58061868662197 & -0.0106186866219724 \tabularnewline
63 & 1.54 & 1.56927173000321 & -0.0292717300032113 \tabularnewline
64 & 1.61 & 1.55488573130020 & 0.0551142686998036 \tabularnewline
65 & 1.65 & 1.62032292007223 & 0.0296770799277715 \tabularnewline
66 & 1.6 & 1.62462826281198 & -0.0246282628119749 \tabularnewline
67 & 1.57 & 1.60391482562331 & -0.0339148256233128 \tabularnewline
68 & 1.56 & 1.57239167544802 & -0.0123916754480164 \tabularnewline
69 & 1.55 & 1.55777373713827 & -0.00777373713827134 \tabularnewline
70 & 1.54 & 1.54596537314623 & -0.00596537314622814 \tabularnewline
71 & 1.51 & 1.54477850136042 & -0.0347785013604167 \tabularnewline
72 & 1.5 & 1.50857036567293 & -0.00857036567292657 \tabularnewline
73 & 1.5 & 1.50168235722839 & -0.00168235722838839 \tabularnewline
74 & 1.49 & 1.49947443484001 & -0.00947443484001242 \tabularnewline
75 & 1.47 & 1.48673678648549 & -0.0167367864854910 \tabularnewline
76 & 1.47 & 1.49408589551868 & -0.0240858955186849 \tabularnewline
77 & 1.49 & 1.48720699716346 & 0.00279300283653927 \tabularnewline
78 & 1.49 & 1.46111710843304 & 0.0288828915669626 \tabularnewline
79 & 1.49 & 1.48587389554641 & 0.00412610445359118 \tabularnewline
80 & 1.51 & 1.49027665727288 & 0.0197233427271204 \tabularnewline
81 & 1.49 & 1.50425287513230 & -0.0142528751323048 \tabularnewline
82 & 1.48 & 1.48702654586020 & -0.00702654586020324 \tabularnewline
83 & 1.46 & 1.48122500381848 & -0.0212250038184849 \tabularnewline
84 & 1.46 & 1.46019072808465 & -0.000190728084646707 \tabularnewline
85 & 1.45 & 1.46149136166068 & -0.0114913616606809 \tabularnewline
86 & 1.45 & 1.44973269211848 & 0.000267307881524737 \tabularnewline
87 & 1.44 & 1.44455949820267 & -0.00455949820267088 \tabularnewline
88 & 1.47 & 1.46158563910019 & 0.00841436089981151 \tabularnewline
89 & 1.47 & 1.48648721069436 & -0.0164872106943592 \tabularnewline
90 & 1.45 & 1.44692652056119 & 0.0030734794388132 \tabularnewline
91 & 1.43 & 1.44600867885574 & -0.0160086788557352 \tabularnewline
92 & 1.44 & 1.43485196191626 & 0.00514803808374298 \tabularnewline
93 & 1.38 & 1.43176868631815 & -0.0517686863181535 \tabularnewline
94 & 1.4 & 1.38275555065545 & 0.0172444493445538 \tabularnewline
95 & 1.37 & 1.39629918490625 & -0.0262991849062546 \tabularnewline
96 & 1.41 & 1.37353378393304 & 0.0364662160669642 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41519&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]1.54[/C][C]1.54198183760684[/C][C]-0.00198183760683746[/C][/ROW]
[ROW][C]14[/C][C]1.53[/C][C]1.53060050087884[/C][C]-0.000600500878837451[/C][/ROW]
[ROW][C]15[/C][C]1.53[/C][C]1.53042362769714[/C][C]-0.000423627697144102[/C][/ROW]
[ROW][C]16[/C][C]1.54[/C][C]1.54040097998079[/C][C]-0.000400979980792471[/C][/ROW]
[ROW][C]17[/C][C]1.55[/C][C]1.54956474672192[/C][C]0.000435253278075587[/C][/ROW]
[ROW][C]18[/C][C]1.53[/C][C]1.52904100461584[/C][C]0.000958995384159333[/C][/ROW]
[ROW][C]19[/C][C]1.53[/C][C]1.53439060875473[/C][C]-0.00439060875473141[/C][/ROW]
[ROW][C]20[/C][C]1.53[/C][C]1.53090893184159[/C][C]-0.000908931841587135[/C][/ROW]
[ROW][C]21[/C][C]1.53[/C][C]1.53046312072199[/C][C]-0.000463120721986066[/C][/ROW]
[ROW][C]22[/C][C]1.52[/C][C]1.51998937019621[/C][C]1.06298037854113e-05[/C][/ROW]
[ROW][C]23[/C][C]1.54[/C][C]1.51992870883746[/C][C]0.0200712911625434[/C][/ROW]
[ROW][C]24[/C][C]1.53[/C][C]1.53694337594374[/C][C]-0.00694337594374494[/C][/ROW]
[ROW][C]25[/C][C]1.52[/C][C]1.54056536982035[/C][C]-0.0205653698203523[/C][/ROW]
[ROW][C]26[/C][C]1.54[/C][C]1.51315690137134[/C][C]0.0268430986286596[/C][/ROW]
[ROW][C]27[/C][C]1.53[/C][C]1.53693226129687[/C][C]-0.00693226129687274[/C][/ROW]
[ROW][C]28[/C][C]1.54[/C][C]1.54123727752034[/C][C]-0.0012372775203362[/C][/ROW]
[ROW][C]29[/C][C]1.54[/C][C]1.54977890583157[/C][C]-0.00977890583157404[/C][/ROW]
[ROW][C]30[/C][C]1.53[/C][C]1.52041593855789[/C][C]0.00958406144210544[/C][/ROW]
[ROW][C]31[/C][C]1.54[/C][C]1.53260122291511[/C][C]0.00739877708488579[/C][/ROW]
[ROW][C]32[/C][C]1.54[/C][C]1.53984517173109[/C][C]0.000154828268906115[/C][/ROW]
[ROW][C]33[/C][C]1.52[/C][C]1.54038399547908[/C][C]-0.0203839954790761[/C][/ROW]
[ROW][C]34[/C][C]1.52[/C][C]1.51260079881467[/C][C]0.00739920118533322[/C][/ROW]
[ROW][C]35[/C][C]1.57[/C][C]1.52155130586795[/C][C]0.0484486941320454[/C][/ROW]
[ROW][C]36[/C][C]1.6[/C][C]1.55985070152463[/C][C]0.0401492984753724[/C][/ROW]
[ROW][C]37[/C][C]1.59[/C][C]1.60279116361905[/C][C]-0.0127911636190485[/C][/ROW]
[ROW][C]38[/C][C]1.6[/C][C]1.58823186819566[/C][C]0.0117681318043423[/C][/ROW]
[ROW][C]39[/C][C]1.6[/C][C]1.59453777054044[/C][C]0.00546222945956454[/C][/ROW]
[ROW][C]40[/C][C]1.62[/C][C]1.61037943953537[/C][C]0.009620560464632[/C][/ROW]
[ROW][C]41[/C][C]1.61[/C][C]1.62729490228819[/C][C]-0.0172949022881905[/C][/ROW]
[ROW][C]42[/C][C]1.61[/C][C]1.59385765391898[/C][C]0.0161423460810186[/C][/ROW]
[ROW][C]43[/C][C]1.62[/C][C]1.61148165312713[/C][C]0.008518346872868[/C][/ROW]
[ROW][C]44[/C][C]1.61[/C][C]1.61877426547366[/C][C]-0.00877426547366467[/C][/ROW]
[ROW][C]45[/C][C]1.62[/C][C]1.60889742826991[/C][C]0.0111025717300854[/C][/ROW]
[ROW][C]46[/C][C]1.61[/C][C]1.61212660094679[/C][C]-0.00212660094678907[/C][/ROW]
[ROW][C]47[/C][C]1.62[/C][C]1.61802721661031[/C][C]0.00197278338969276[/C][/ROW]
[ROW][C]48[/C][C]1.61[/C][C]1.61473901119763[/C][C]-0.0047390111976322[/C][/ROW]
[ROW][C]49[/C][C]1.61[/C][C]1.61176012622651[/C][C]-0.00176012622651056[/C][/ROW]
[ROW][C]50[/C][C]1.58[/C][C]1.60996409321522[/C][C]-0.0299640932152201[/C][/ROW]
[ROW][C]51[/C][C]1.57[/C][C]1.57907393198475[/C][C]-0.0090739319847546[/C][/ROW]
[ROW][C]52[/C][C]1.57[/C][C]1.58277317474318[/C][C]-0.0127731747431823[/C][/ROW]
[ROW][C]53[/C][C]1.66[/C][C]1.5767159179454[/C][C]0.083284082054601[/C][/ROW]
[ROW][C]54[/C][C]1.66[/C][C]1.63526049420743[/C][C]0.0247395057925683[/C][/ROW]
[ROW][C]55[/C][C]1.67[/C][C]1.65940461576852[/C][C]0.0105953842314785[/C][/ROW]
[ROW][C]56[/C][C]1.68[/C][C]1.66629407979396[/C][C]0.0137059202060354[/C][/ROW]
[ROW][C]57[/C][C]1.66[/C][C]1.67856408266441[/C][C]-0.0185640826644127[/C][/ROW]
[ROW][C]58[/C][C]1.66[/C][C]1.65423133734559[/C][C]0.00576866265441289[/C][/ROW]
[ROW][C]59[/C][C]1.64[/C][C]1.66754117346871[/C][C]-0.027541173468715[/C][/ROW]
[ROW][C]60[/C][C]1.61[/C][C]1.63765871275093[/C][C]-0.02765871275093[/C][/ROW]
[ROW][C]61[/C][C]1.58[/C][C]1.61507630924480[/C][C]-0.0350763092447965[/C][/ROW]
[ROW][C]62[/C][C]1.57[/C][C]1.58061868662197[/C][C]-0.0106186866219724[/C][/ROW]
[ROW][C]63[/C][C]1.54[/C][C]1.56927173000321[/C][C]-0.0292717300032113[/C][/ROW]
[ROW][C]64[/C][C]1.61[/C][C]1.55488573130020[/C][C]0.0551142686998036[/C][/ROW]
[ROW][C]65[/C][C]1.65[/C][C]1.62032292007223[/C][C]0.0296770799277715[/C][/ROW]
[ROW][C]66[/C][C]1.6[/C][C]1.62462826281198[/C][C]-0.0246282628119749[/C][/ROW]
[ROW][C]67[/C][C]1.57[/C][C]1.60391482562331[/C][C]-0.0339148256233128[/C][/ROW]
[ROW][C]68[/C][C]1.56[/C][C]1.57239167544802[/C][C]-0.0123916754480164[/C][/ROW]
[ROW][C]69[/C][C]1.55[/C][C]1.55777373713827[/C][C]-0.00777373713827134[/C][/ROW]
[ROW][C]70[/C][C]1.54[/C][C]1.54596537314623[/C][C]-0.00596537314622814[/C][/ROW]
[ROW][C]71[/C][C]1.51[/C][C]1.54477850136042[/C][C]-0.0347785013604167[/C][/ROW]
[ROW][C]72[/C][C]1.5[/C][C]1.50857036567293[/C][C]-0.00857036567292657[/C][/ROW]
[ROW][C]73[/C][C]1.5[/C][C]1.50168235722839[/C][C]-0.00168235722838839[/C][/ROW]
[ROW][C]74[/C][C]1.49[/C][C]1.49947443484001[/C][C]-0.00947443484001242[/C][/ROW]
[ROW][C]75[/C][C]1.47[/C][C]1.48673678648549[/C][C]-0.0167367864854910[/C][/ROW]
[ROW][C]76[/C][C]1.47[/C][C]1.49408589551868[/C][C]-0.0240858955186849[/C][/ROW]
[ROW][C]77[/C][C]1.49[/C][C]1.48720699716346[/C][C]0.00279300283653927[/C][/ROW]
[ROW][C]78[/C][C]1.49[/C][C]1.46111710843304[/C][C]0.0288828915669626[/C][/ROW]
[ROW][C]79[/C][C]1.49[/C][C]1.48587389554641[/C][C]0.00412610445359118[/C][/ROW]
[ROW][C]80[/C][C]1.51[/C][C]1.49027665727288[/C][C]0.0197233427271204[/C][/ROW]
[ROW][C]81[/C][C]1.49[/C][C]1.50425287513230[/C][C]-0.0142528751323048[/C][/ROW]
[ROW][C]82[/C][C]1.48[/C][C]1.48702654586020[/C][C]-0.00702654586020324[/C][/ROW]
[ROW][C]83[/C][C]1.46[/C][C]1.48122500381848[/C][C]-0.0212250038184849[/C][/ROW]
[ROW][C]84[/C][C]1.46[/C][C]1.46019072808465[/C][C]-0.000190728084646707[/C][/ROW]
[ROW][C]85[/C][C]1.45[/C][C]1.46149136166068[/C][C]-0.0114913616606809[/C][/ROW]
[ROW][C]86[/C][C]1.45[/C][C]1.44973269211848[/C][C]0.000267307881524737[/C][/ROW]
[ROW][C]87[/C][C]1.44[/C][C]1.44455949820267[/C][C]-0.00455949820267088[/C][/ROW]
[ROW][C]88[/C][C]1.47[/C][C]1.46158563910019[/C][C]0.00841436089981151[/C][/ROW]
[ROW][C]89[/C][C]1.47[/C][C]1.48648721069436[/C][C]-0.0164872106943592[/C][/ROW]
[ROW][C]90[/C][C]1.45[/C][C]1.44692652056119[/C][C]0.0030734794388132[/C][/ROW]
[ROW][C]91[/C][C]1.43[/C][C]1.44600867885574[/C][C]-0.0160086788557352[/C][/ROW]
[ROW][C]92[/C][C]1.44[/C][C]1.43485196191626[/C][C]0.00514803808374298[/C][/ROW]
[ROW][C]93[/C][C]1.38[/C][C]1.43176868631815[/C][C]-0.0517686863181535[/C][/ROW]
[ROW][C]94[/C][C]1.4[/C][C]1.38275555065545[/C][C]0.0172444493445538[/C][/ROW]
[ROW][C]95[/C][C]1.37[/C][C]1.39629918490625[/C][C]-0.0262991849062546[/C][/ROW]
[ROW][C]96[/C][C]1.41[/C][C]1.37353378393304[/C][C]0.0364662160669642[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41519&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41519&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	1.54	1.54198183760684	-0.00198183760683746
14	1.53	1.53060050087884	-0.000600500878837451
15	1.53	1.53042362769714	-0.000423627697144102
16	1.54	1.54040097998079	-0.000400979980792471
17	1.55	1.54956474672192	0.000435253278075587
18	1.53	1.52904100461584	0.000958995384159333
19	1.53	1.53439060875473	-0.00439060875473141
20	1.53	1.53090893184159	-0.000908931841587135
21	1.53	1.53046312072199	-0.000463120721986066
22	1.52	1.51998937019621	1.06298037854113e-05
23	1.54	1.51992870883746	0.0200712911625434
24	1.53	1.53694337594374	-0.00694337594374494
25	1.52	1.54056536982035	-0.0205653698203523
26	1.54	1.51315690137134	0.0268430986286596
27	1.53	1.53693226129687	-0.00693226129687274
28	1.54	1.54123727752034	-0.0012372775203362
29	1.54	1.54977890583157	-0.00977890583157404
30	1.53	1.52041593855789	0.00958406144210544
31	1.54	1.53260122291511	0.00739877708488579
32	1.54	1.53984517173109	0.000154828268906115
33	1.52	1.54038399547908	-0.0203839954790761
34	1.52	1.51260079881467	0.00739920118533322
35	1.57	1.52155130586795	0.0484486941320454
36	1.6	1.55985070152463	0.0401492984753724
37	1.59	1.60279116361905	-0.0127911636190485
38	1.6	1.58823186819566	0.0117681318043423
39	1.6	1.59453777054044	0.00546222945956454
40	1.62	1.61037943953537	0.009620560464632
41	1.61	1.62729490228819	-0.0172949022881905
42	1.61	1.59385765391898	0.0161423460810186
43	1.62	1.61148165312713	0.008518346872868
44	1.61	1.61877426547366	-0.00877426547366467
45	1.62	1.60889742826991	0.0111025717300854
46	1.61	1.61212660094679	-0.00212660094678907
47	1.62	1.61802721661031	0.00197278338969276
48	1.61	1.61473901119763	-0.0047390111976322
49	1.61	1.61176012622651	-0.00176012622651056
50	1.58	1.60996409321522	-0.0299640932152201
51	1.57	1.57907393198475	-0.0090739319847546
52	1.57	1.58277317474318	-0.0127731747431823
53	1.66	1.5767159179454	0.083284082054601
54	1.66	1.63526049420743	0.0247395057925683
55	1.67	1.65940461576852	0.0105953842314785
56	1.68	1.66629407979396	0.0137059202060354
57	1.66	1.67856408266441	-0.0185640826644127
58	1.66	1.65423133734559	0.00576866265441289
59	1.64	1.66754117346871	-0.027541173468715
60	1.61	1.63765871275093	-0.02765871275093
61	1.58	1.61507630924480	-0.0350763092447965
62	1.57	1.58061868662197	-0.0106186866219724
63	1.54	1.56927173000321	-0.0292717300032113
64	1.61	1.55488573130020	0.0551142686998036
65	1.65	1.62032292007223	0.0296770799277715
66	1.6	1.62462826281198	-0.0246282628119749
67	1.57	1.60391482562331	-0.0339148256233128
68	1.56	1.57239167544802	-0.0123916754480164
69	1.55	1.55777373713827	-0.00777373713827134
70	1.54	1.54596537314623	-0.00596537314622814
71	1.51	1.54477850136042	-0.0347785013604167
72	1.5	1.50857036567293	-0.00857036567292657
73	1.5	1.50168235722839	-0.00168235722838839
74	1.49	1.49947443484001	-0.00947443484001242
75	1.47	1.48673678648549	-0.0167367864854910
76	1.47	1.49408589551868	-0.0240858955186849
77	1.49	1.48720699716346	0.00279300283653927
78	1.49	1.46111710843304	0.0288828915669626
79	1.49	1.48587389554641	0.00412610445359118
80	1.51	1.49027665727288	0.0197233427271204
81	1.49	1.50425287513230	-0.0142528751323048
82	1.48	1.48702654586020	-0.00702654586020324
83	1.46	1.48122500381848	-0.0212250038184849
84	1.46	1.46019072808465	-0.000190728084646707
85	1.45	1.46149136166068	-0.0114913616606809
86	1.45	1.44973269211848	0.000267307881524737
87	1.44	1.44455949820267	-0.00455949820267088
88	1.47	1.46158563910019	0.00841436089981151
89	1.47	1.48648721069436	-0.0164872106943592
90	1.45	1.44692652056119	0.0030734794388132
91	1.43	1.44600867885574	-0.0160086788557352
92	1.44	1.43485196191626	0.00514803808374298
93	1.38	1.43176868631815	-0.0517686863181535
94	1.4	1.38275555065545	0.0172444493445538
95	1.37	1.39629918490625	-0.0262991849062546
96	1.41	1.37353378393304	0.0364662160669642

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	1.40535063638563	1.36424286833719	1.44645840443407
98	1.40511755592638	1.35057720406483	1.45965790778794
99	1.39909323344458	1.33382876096191	1.46435770592725
100	1.42175628890104	1.34729654974155	1.49621602806053
101	1.43613239565264	1.35349430429667	1.51877048700862
102	1.41345245971136	1.32337551743302	1.50352940198971
103	1.40741130820603	1.31046463772439	1.50435797868767
104	1.41292245036190	1.30956163426250	1.51628326646130
105	1.39806241822527	1.28866287667233	1.50746195977820
106	1.40302603340278	1.28790409335983	1.51814797344572
107	1.39595774069404	1.27538468206771	1.51653079932037
108	1.40416083916084	1.27837266859712	1.52994900972456

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 1.40535063638563 & 1.36424286833719 & 1.44645840443407 \tabularnewline
98 & 1.40511755592638 & 1.35057720406483 & 1.45965790778794 \tabularnewline
99 & 1.39909323344458 & 1.33382876096191 & 1.46435770592725 \tabularnewline
100 & 1.42175628890104 & 1.34729654974155 & 1.49621602806053 \tabularnewline
101 & 1.43613239565264 & 1.35349430429667 & 1.51877048700862 \tabularnewline
102 & 1.41345245971136 & 1.32337551743302 & 1.50352940198971 \tabularnewline
103 & 1.40741130820603 & 1.31046463772439 & 1.50435797868767 \tabularnewline
104 & 1.41292245036190 & 1.30956163426250 & 1.51628326646130 \tabularnewline
105 & 1.39806241822527 & 1.28866287667233 & 1.50746195977820 \tabularnewline
106 & 1.40302603340278 & 1.28790409335983 & 1.51814797344572 \tabularnewline
107 & 1.39595774069404 & 1.27538468206771 & 1.51653079932037 \tabularnewline
108 & 1.40416083916084 & 1.27837266859712 & 1.52994900972456 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41519&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]97[/C][C]1.40535063638563[/C][C]1.36424286833719[/C][C]1.44645840443407[/C][/ROW]
[ROW][C]98[/C][C]1.40511755592638[/C][C]1.35057720406483[/C][C]1.45965790778794[/C][/ROW]
[ROW][C]99[/C][C]1.39909323344458[/C][C]1.33382876096191[/C][C]1.46435770592725[/C][/ROW]
[ROW][C]100[/C][C]1.42175628890104[/C][C]1.34729654974155[/C][C]1.49621602806053[/C][/ROW]
[ROW][C]101[/C][C]1.43613239565264[/C][C]1.35349430429667[/C][C]1.51877048700862[/C][/ROW]
[ROW][C]102[/C][C]1.41345245971136[/C][C]1.32337551743302[/C][C]1.50352940198971[/C][/ROW]
[ROW][C]103[/C][C]1.40741130820603[/C][C]1.31046463772439[/C][C]1.50435797868767[/C][/ROW]
[ROW][C]104[/C][C]1.41292245036190[/C][C]1.30956163426250[/C][C]1.51628326646130[/C][/ROW]
[ROW][C]105[/C][C]1.39806241822527[/C][C]1.28866287667233[/C][C]1.50746195977820[/C][/ROW]
[ROW][C]106[/C][C]1.40302603340278[/C][C]1.28790409335983[/C][C]1.51814797344572[/C][/ROW]
[ROW][C]107[/C][C]1.39595774069404[/C][C]1.27538468206771[/C][C]1.51653079932037[/C][/ROW]
[ROW][C]108[/C][C]1.40416083916084[/C][C]1.27837266859712[/C][C]1.52994900972456[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41519&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41519&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
97	1.40535063638563	1.36424286833719	1.44645840443407
98	1.40511755592638	1.35057720406483	1.45965790778794
99	1.39909323344458	1.33382876096191	1.46435770592725
100	1.42175628890104	1.34729654974155	1.49621602806053
101	1.43613239565264	1.35349430429667	1.51877048700862
102	1.41345245971136	1.32337551743302	1.50352940198971
103	1.40741130820603	1.31046463772439	1.50435797868767
104	1.41292245036190	1.30956163426250	1.51628326646130
105	1.39806241822527	1.28866287667233	1.50746195977820
106	1.40302603340278	1.28790409335983	1.51814797344572
107	1.39595774069404	1.27538468206771	1.51653079932037
108	1.40416083916084	1.27837266859712	1.52994900972456

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=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