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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 10 Apr 2015 08:27:01 +0100

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/2015/Apr/10/t14286508472x5l38pbi4put9p.htm/, Retrieved Thu, 09 May 2024 19:22:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278700, Retrieved Thu, 09 May 2024 19:22:10 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

175

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

-       [Exponential Smoothing] [Model exponential...] [2015-04-10 07:27:01] [c5b33e4153b13210102bee47a487e864] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278700&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278700&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278700&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999956082704757
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999956082704757 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278700&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]0.999956082704757[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278700&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278700&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	0.999956082704757
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	100.93	100.64	0.290000000000006
3	101.41	100.929987263984	0.48001273601561
4	102.07	101.409978919139	0.660021080861043
5	102.42	102.069971013659	0.350028986340675
6	102.53	102.419984627674	0.11001537232633
7	102.43	102.529995168422	-0.0999951684223959
8	102.6	102.430004391517	0.169995608482651
9	102.65	102.599992534253	0.0500074657473419
10	102.74	102.649997803807	0.0900021961926285
11	102.82	102.739996047347	0.0800039526530298
12	103.2	102.819996486443	0.380003513557227
13	102.75	103.199983311273	-0.449983311273499
14	103.09	102.75001976205	0.339980237950073
15	103.71	103.089985068988	0.620014931012477
16	104.3	103.709972770621	0.590027229378776
17	104.58	104.2999740876	0.280025912400035
18	104.71	104.579987702019	0.130012297980656
19	104.44	104.709994290212	-0.269994290211514
20	104.57	104.440011857419	0.129988142581041
21	104.95	104.569994291272	0.380005708727651
22	105.49	104.949983311177	0.540016688822888
23	106.03	105.489976283928	0.540023716072369
24	106.48	106.029976283619	0.450023716380969
25	106.25	106.479980236176	-0.229980236175578
26	106.7	106.25001010011	0.44998989989007
27	107.6	106.699980237661	0.900019762339284
28	108.05	107.599960473566	0.450039526433628
29	108.72	108.049980235481	0.670019764518756
30	109.17	108.719970574544	0.450029425455824
31	109.08	109.169980235925	-0.0899802359248554
32	109.04	109.080003951689	-0.0400039516885755
33	109.34	109.040001756865	0.299998243134638
34	109.37	109.339986824889	0.0300131751114208
35	108.96	109.369998681903	-0.409998681902536
36	108.77	108.960018006033	-0.190018006033171
37	108.11	108.770008345077	-0.660008345076861
38	108.67	108.110028985781	0.559971014218647
39	109.05	108.669975407588	0.380024592412354
40	109.43	109.049983310348	0.380016689652237
41	109.62	109.429983310695	0.190016689305153
42	109.85	109.619991654981	0.230008345019044
43	109.34	109.849989898656	-0.50998989865559
44	109.65	109.340022397377	0.30997760262305
45	109.69	109.649986386622	0.0400136133778801
46	109.91	109.68999824271	0.22000175728968
47	110.09	109.909990338118	0.180009661882139
48	110.44	110.089992094463	0.350007905537467
49	109.9	110.439984628599	-0.53998462859947
50	110.25	109.900023714664	0.349976285335629
51	111.26	110.249984629988	1.01001537001186
52	111.74	111.259955642857	0.480044357143186
53	111.91	111.73997891775	0.170021082249761
54	111.95	111.909992533134	0.0400074668660721
55	111.63	111.94999824298	-0.319998242980276
56	111.85	111.630014053457	0.219985946542693
57	112.16	111.849990338812	0.310009661187777
58	112.49	112.159986385214	0.330013614785813
59	112.66	112.489985506695	0.170014493305359
60	113.39	112.659992533423	0.730007466576708
61	112.92	113.389967940047	-0.469967940046558
62	113.44	112.920020639721	0.519979360279223
63	114.68	113.439977163913	1.24002283608709
64	115.38	114.679945541551	0.700054458448989
65	115.48	115.379969255502	0.100030744498355
66	115.41	115.47999560692	-0.0699956069202727
67	114.92	115.410003074018	-0.490003074017736
68	115.16	114.92002151961	0.23997848039032
69	115.89	115.159989460794	0.730010539205779
70	116.25	115.889967939912	0.360032060088386
71	116.43	116.249984188366	0.180015811634291
72	116.83	116.429992094192	0.400007905807541
73	116.17	116.829982432735	-0.659982432734694
74	116.78	116.170028984643	0.609971015356649
75	117.98	116.779973211723	1.20002678827717
76	118.53	117.979947298069	0.550052701930753
77	118.43	118.529975843173	-0.0999758431730839
78	118.29	118.430004390669	-0.140004390668622
79	117.85	118.290006148614	-0.44000614861416
80	118.27	117.85001932388	0.419980676120062
81	119	118.269981555585	0.73001844441535
82	119.33	118.999967939564	0.330032060435542
83	119.17	119.329985505885	-0.159985505884563
84	119.57	119.170007026131	0.399992973869303
85	118.62	119.56998243339	-0.94998243339046
86	119.09	118.620041720659	0.469958279341
87	120.19	119.089979360703	1.1000206392965
88	120.17	120.189951690069	-0.0199516900688081
89	120.29	120.170000876224	0.119999123775742
90	120.35	120.289994729963	0.0600052700369247
91	119.88	120.349997364731	-0.469997364730844
92	120.04	119.880020641013	0.159979358986988
93	120.52	120.039992974139	0.480007025860729
94	120.43	120.51997891939	-0.0899789193897078
95	120.34	120.430003951631	-0.0900039516307771
96	120.75	120.34000395273	0.409996047269871

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 100.93 & 100.64 & 0.290000000000006 \tabularnewline
3 & 101.41 & 100.929987263984 & 0.48001273601561 \tabularnewline
4 & 102.07 & 101.409978919139 & 0.660021080861043 \tabularnewline
5 & 102.42 & 102.069971013659 & 0.350028986340675 \tabularnewline
6 & 102.53 & 102.419984627674 & 0.11001537232633 \tabularnewline
7 & 102.43 & 102.529995168422 & -0.0999951684223959 \tabularnewline
8 & 102.6 & 102.430004391517 & 0.169995608482651 \tabularnewline
9 & 102.65 & 102.599992534253 & 0.0500074657473419 \tabularnewline
10 & 102.74 & 102.649997803807 & 0.0900021961926285 \tabularnewline
11 & 102.82 & 102.739996047347 & 0.0800039526530298 \tabularnewline
12 & 103.2 & 102.819996486443 & 0.380003513557227 \tabularnewline
13 & 102.75 & 103.199983311273 & -0.449983311273499 \tabularnewline
14 & 103.09 & 102.75001976205 & 0.339980237950073 \tabularnewline
15 & 103.71 & 103.089985068988 & 0.620014931012477 \tabularnewline
16 & 104.3 & 103.709972770621 & 0.590027229378776 \tabularnewline
17 & 104.58 & 104.2999740876 & 0.280025912400035 \tabularnewline
18 & 104.71 & 104.579987702019 & 0.130012297980656 \tabularnewline
19 & 104.44 & 104.709994290212 & -0.269994290211514 \tabularnewline
20 & 104.57 & 104.440011857419 & 0.129988142581041 \tabularnewline
21 & 104.95 & 104.569994291272 & 0.380005708727651 \tabularnewline
22 & 105.49 & 104.949983311177 & 0.540016688822888 \tabularnewline
23 & 106.03 & 105.489976283928 & 0.540023716072369 \tabularnewline
24 & 106.48 & 106.029976283619 & 0.450023716380969 \tabularnewline
25 & 106.25 & 106.479980236176 & -0.229980236175578 \tabularnewline
26 & 106.7 & 106.25001010011 & 0.44998989989007 \tabularnewline
27 & 107.6 & 106.699980237661 & 0.900019762339284 \tabularnewline
28 & 108.05 & 107.599960473566 & 0.450039526433628 \tabularnewline
29 & 108.72 & 108.049980235481 & 0.670019764518756 \tabularnewline
30 & 109.17 & 108.719970574544 & 0.450029425455824 \tabularnewline
31 & 109.08 & 109.169980235925 & -0.0899802359248554 \tabularnewline
32 & 109.04 & 109.080003951689 & -0.0400039516885755 \tabularnewline
33 & 109.34 & 109.040001756865 & 0.299998243134638 \tabularnewline
34 & 109.37 & 109.339986824889 & 0.0300131751114208 \tabularnewline
35 & 108.96 & 109.369998681903 & -0.409998681902536 \tabularnewline
36 & 108.77 & 108.960018006033 & -0.190018006033171 \tabularnewline
37 & 108.11 & 108.770008345077 & -0.660008345076861 \tabularnewline
38 & 108.67 & 108.110028985781 & 0.559971014218647 \tabularnewline
39 & 109.05 & 108.669975407588 & 0.380024592412354 \tabularnewline
40 & 109.43 & 109.049983310348 & 0.380016689652237 \tabularnewline
41 & 109.62 & 109.429983310695 & 0.190016689305153 \tabularnewline
42 & 109.85 & 109.619991654981 & 0.230008345019044 \tabularnewline
43 & 109.34 & 109.849989898656 & -0.50998989865559 \tabularnewline
44 & 109.65 & 109.340022397377 & 0.30997760262305 \tabularnewline
45 & 109.69 & 109.649986386622 & 0.0400136133778801 \tabularnewline
46 & 109.91 & 109.68999824271 & 0.22000175728968 \tabularnewline
47 & 110.09 & 109.909990338118 & 0.180009661882139 \tabularnewline
48 & 110.44 & 110.089992094463 & 0.350007905537467 \tabularnewline
49 & 109.9 & 110.439984628599 & -0.53998462859947 \tabularnewline
50 & 110.25 & 109.900023714664 & 0.349976285335629 \tabularnewline
51 & 111.26 & 110.249984629988 & 1.01001537001186 \tabularnewline
52 & 111.74 & 111.259955642857 & 0.480044357143186 \tabularnewline
53 & 111.91 & 111.73997891775 & 0.170021082249761 \tabularnewline
54 & 111.95 & 111.909992533134 & 0.0400074668660721 \tabularnewline
55 & 111.63 & 111.94999824298 & -0.319998242980276 \tabularnewline
56 & 111.85 & 111.630014053457 & 0.219985946542693 \tabularnewline
57 & 112.16 & 111.849990338812 & 0.310009661187777 \tabularnewline
58 & 112.49 & 112.159986385214 & 0.330013614785813 \tabularnewline
59 & 112.66 & 112.489985506695 & 0.170014493305359 \tabularnewline
60 & 113.39 & 112.659992533423 & 0.730007466576708 \tabularnewline
61 & 112.92 & 113.389967940047 & -0.469967940046558 \tabularnewline
62 & 113.44 & 112.920020639721 & 0.519979360279223 \tabularnewline
63 & 114.68 & 113.439977163913 & 1.24002283608709 \tabularnewline
64 & 115.38 & 114.679945541551 & 0.700054458448989 \tabularnewline
65 & 115.48 & 115.379969255502 & 0.100030744498355 \tabularnewline
66 & 115.41 & 115.47999560692 & -0.0699956069202727 \tabularnewline
67 & 114.92 & 115.410003074018 & -0.490003074017736 \tabularnewline
68 & 115.16 & 114.92002151961 & 0.23997848039032 \tabularnewline
69 & 115.89 & 115.159989460794 & 0.730010539205779 \tabularnewline
70 & 116.25 & 115.889967939912 & 0.360032060088386 \tabularnewline
71 & 116.43 & 116.249984188366 & 0.180015811634291 \tabularnewline
72 & 116.83 & 116.429992094192 & 0.400007905807541 \tabularnewline
73 & 116.17 & 116.829982432735 & -0.659982432734694 \tabularnewline
74 & 116.78 & 116.170028984643 & 0.609971015356649 \tabularnewline
75 & 117.98 & 116.779973211723 & 1.20002678827717 \tabularnewline
76 & 118.53 & 117.979947298069 & 0.550052701930753 \tabularnewline
77 & 118.43 & 118.529975843173 & -0.0999758431730839 \tabularnewline
78 & 118.29 & 118.430004390669 & -0.140004390668622 \tabularnewline
79 & 117.85 & 118.290006148614 & -0.44000614861416 \tabularnewline
80 & 118.27 & 117.85001932388 & 0.419980676120062 \tabularnewline
81 & 119 & 118.269981555585 & 0.73001844441535 \tabularnewline
82 & 119.33 & 118.999967939564 & 0.330032060435542 \tabularnewline
83 & 119.17 & 119.329985505885 & -0.159985505884563 \tabularnewline
84 & 119.57 & 119.170007026131 & 0.399992973869303 \tabularnewline
85 & 118.62 & 119.56998243339 & -0.94998243339046 \tabularnewline
86 & 119.09 & 118.620041720659 & 0.469958279341 \tabularnewline
87 & 120.19 & 119.089979360703 & 1.1000206392965 \tabularnewline
88 & 120.17 & 120.189951690069 & -0.0199516900688081 \tabularnewline
89 & 120.29 & 120.170000876224 & 0.119999123775742 \tabularnewline
90 & 120.35 & 120.289994729963 & 0.0600052700369247 \tabularnewline
91 & 119.88 & 120.349997364731 & -0.469997364730844 \tabularnewline
92 & 120.04 & 119.880020641013 & 0.159979358986988 \tabularnewline
93 & 120.52 & 120.039992974139 & 0.480007025860729 \tabularnewline
94 & 120.43 & 120.51997891939 & -0.0899789193897078 \tabularnewline
95 & 120.34 & 120.430003951631 & -0.0900039516307771 \tabularnewline
96 & 120.75 & 120.34000395273 & 0.409996047269871 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278700&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]2[/C][C]100.93[/C][C]100.64[/C][C]0.290000000000006[/C][/ROW]
[ROW][C]3[/C][C]101.41[/C][C]100.929987263984[/C][C]0.48001273601561[/C][/ROW]
[ROW][C]4[/C][C]102.07[/C][C]101.409978919139[/C][C]0.660021080861043[/C][/ROW]
[ROW][C]5[/C][C]102.42[/C][C]102.069971013659[/C][C]0.350028986340675[/C][/ROW]
[ROW][C]6[/C][C]102.53[/C][C]102.419984627674[/C][C]0.11001537232633[/C][/ROW]
[ROW][C]7[/C][C]102.43[/C][C]102.529995168422[/C][C]-0.0999951684223959[/C][/ROW]
[ROW][C]8[/C][C]102.6[/C][C]102.430004391517[/C][C]0.169995608482651[/C][/ROW]
[ROW][C]9[/C][C]102.65[/C][C]102.599992534253[/C][C]0.0500074657473419[/C][/ROW]
[ROW][C]10[/C][C]102.74[/C][C]102.649997803807[/C][C]0.0900021961926285[/C][/ROW]
[ROW][C]11[/C][C]102.82[/C][C]102.739996047347[/C][C]0.0800039526530298[/C][/ROW]
[ROW][C]12[/C][C]103.2[/C][C]102.819996486443[/C][C]0.380003513557227[/C][/ROW]
[ROW][C]13[/C][C]102.75[/C][C]103.199983311273[/C][C]-0.449983311273499[/C][/ROW]
[ROW][C]14[/C][C]103.09[/C][C]102.75001976205[/C][C]0.339980237950073[/C][/ROW]
[ROW][C]15[/C][C]103.71[/C][C]103.089985068988[/C][C]0.620014931012477[/C][/ROW]
[ROW][C]16[/C][C]104.3[/C][C]103.709972770621[/C][C]0.590027229378776[/C][/ROW]
[ROW][C]17[/C][C]104.58[/C][C]104.2999740876[/C][C]0.280025912400035[/C][/ROW]
[ROW][C]18[/C][C]104.71[/C][C]104.579987702019[/C][C]0.130012297980656[/C][/ROW]
[ROW][C]19[/C][C]104.44[/C][C]104.709994290212[/C][C]-0.269994290211514[/C][/ROW]
[ROW][C]20[/C][C]104.57[/C][C]104.440011857419[/C][C]0.129988142581041[/C][/ROW]
[ROW][C]21[/C][C]104.95[/C][C]104.569994291272[/C][C]0.380005708727651[/C][/ROW]
[ROW][C]22[/C][C]105.49[/C][C]104.949983311177[/C][C]0.540016688822888[/C][/ROW]
[ROW][C]23[/C][C]106.03[/C][C]105.489976283928[/C][C]0.540023716072369[/C][/ROW]
[ROW][C]24[/C][C]106.48[/C][C]106.029976283619[/C][C]0.450023716380969[/C][/ROW]
[ROW][C]25[/C][C]106.25[/C][C]106.479980236176[/C][C]-0.229980236175578[/C][/ROW]
[ROW][C]26[/C][C]106.7[/C][C]106.25001010011[/C][C]0.44998989989007[/C][/ROW]
[ROW][C]27[/C][C]107.6[/C][C]106.699980237661[/C][C]0.900019762339284[/C][/ROW]
[ROW][C]28[/C][C]108.05[/C][C]107.599960473566[/C][C]0.450039526433628[/C][/ROW]
[ROW][C]29[/C][C]108.72[/C][C]108.049980235481[/C][C]0.670019764518756[/C][/ROW]
[ROW][C]30[/C][C]109.17[/C][C]108.719970574544[/C][C]0.450029425455824[/C][/ROW]
[ROW][C]31[/C][C]109.08[/C][C]109.169980235925[/C][C]-0.0899802359248554[/C][/ROW]
[ROW][C]32[/C][C]109.04[/C][C]109.080003951689[/C][C]-0.0400039516885755[/C][/ROW]
[ROW][C]33[/C][C]109.34[/C][C]109.040001756865[/C][C]0.299998243134638[/C][/ROW]
[ROW][C]34[/C][C]109.37[/C][C]109.339986824889[/C][C]0.0300131751114208[/C][/ROW]
[ROW][C]35[/C][C]108.96[/C][C]109.369998681903[/C][C]-0.409998681902536[/C][/ROW]
[ROW][C]36[/C][C]108.77[/C][C]108.960018006033[/C][C]-0.190018006033171[/C][/ROW]
[ROW][C]37[/C][C]108.11[/C][C]108.770008345077[/C][C]-0.660008345076861[/C][/ROW]
[ROW][C]38[/C][C]108.67[/C][C]108.110028985781[/C][C]0.559971014218647[/C][/ROW]
[ROW][C]39[/C][C]109.05[/C][C]108.669975407588[/C][C]0.380024592412354[/C][/ROW]
[ROW][C]40[/C][C]109.43[/C][C]109.049983310348[/C][C]0.380016689652237[/C][/ROW]
[ROW][C]41[/C][C]109.62[/C][C]109.429983310695[/C][C]0.190016689305153[/C][/ROW]
[ROW][C]42[/C][C]109.85[/C][C]109.619991654981[/C][C]0.230008345019044[/C][/ROW]
[ROW][C]43[/C][C]109.34[/C][C]109.849989898656[/C][C]-0.50998989865559[/C][/ROW]
[ROW][C]44[/C][C]109.65[/C][C]109.340022397377[/C][C]0.30997760262305[/C][/ROW]
[ROW][C]45[/C][C]109.69[/C][C]109.649986386622[/C][C]0.0400136133778801[/C][/ROW]
[ROW][C]46[/C][C]109.91[/C][C]109.68999824271[/C][C]0.22000175728968[/C][/ROW]
[ROW][C]47[/C][C]110.09[/C][C]109.909990338118[/C][C]0.180009661882139[/C][/ROW]
[ROW][C]48[/C][C]110.44[/C][C]110.089992094463[/C][C]0.350007905537467[/C][/ROW]
[ROW][C]49[/C][C]109.9[/C][C]110.439984628599[/C][C]-0.53998462859947[/C][/ROW]
[ROW][C]50[/C][C]110.25[/C][C]109.900023714664[/C][C]0.349976285335629[/C][/ROW]
[ROW][C]51[/C][C]111.26[/C][C]110.249984629988[/C][C]1.01001537001186[/C][/ROW]
[ROW][C]52[/C][C]111.74[/C][C]111.259955642857[/C][C]0.480044357143186[/C][/ROW]
[ROW][C]53[/C][C]111.91[/C][C]111.73997891775[/C][C]0.170021082249761[/C][/ROW]
[ROW][C]54[/C][C]111.95[/C][C]111.909992533134[/C][C]0.0400074668660721[/C][/ROW]
[ROW][C]55[/C][C]111.63[/C][C]111.94999824298[/C][C]-0.319998242980276[/C][/ROW]
[ROW][C]56[/C][C]111.85[/C][C]111.630014053457[/C][C]0.219985946542693[/C][/ROW]
[ROW][C]57[/C][C]112.16[/C][C]111.849990338812[/C][C]0.310009661187777[/C][/ROW]
[ROW][C]58[/C][C]112.49[/C][C]112.159986385214[/C][C]0.330013614785813[/C][/ROW]
[ROW][C]59[/C][C]112.66[/C][C]112.489985506695[/C][C]0.170014493305359[/C][/ROW]
[ROW][C]60[/C][C]113.39[/C][C]112.659992533423[/C][C]0.730007466576708[/C][/ROW]
[ROW][C]61[/C][C]112.92[/C][C]113.389967940047[/C][C]-0.469967940046558[/C][/ROW]
[ROW][C]62[/C][C]113.44[/C][C]112.920020639721[/C][C]0.519979360279223[/C][/ROW]
[ROW][C]63[/C][C]114.68[/C][C]113.439977163913[/C][C]1.24002283608709[/C][/ROW]
[ROW][C]64[/C][C]115.38[/C][C]114.679945541551[/C][C]0.700054458448989[/C][/ROW]
[ROW][C]65[/C][C]115.48[/C][C]115.379969255502[/C][C]0.100030744498355[/C][/ROW]
[ROW][C]66[/C][C]115.41[/C][C]115.47999560692[/C][C]-0.0699956069202727[/C][/ROW]
[ROW][C]67[/C][C]114.92[/C][C]115.410003074018[/C][C]-0.490003074017736[/C][/ROW]
[ROW][C]68[/C][C]115.16[/C][C]114.92002151961[/C][C]0.23997848039032[/C][/ROW]
[ROW][C]69[/C][C]115.89[/C][C]115.159989460794[/C][C]0.730010539205779[/C][/ROW]
[ROW][C]70[/C][C]116.25[/C][C]115.889967939912[/C][C]0.360032060088386[/C][/ROW]
[ROW][C]71[/C][C]116.43[/C][C]116.249984188366[/C][C]0.180015811634291[/C][/ROW]
[ROW][C]72[/C][C]116.83[/C][C]116.429992094192[/C][C]0.400007905807541[/C][/ROW]
[ROW][C]73[/C][C]116.17[/C][C]116.829982432735[/C][C]-0.659982432734694[/C][/ROW]
[ROW][C]74[/C][C]116.78[/C][C]116.170028984643[/C][C]0.609971015356649[/C][/ROW]
[ROW][C]75[/C][C]117.98[/C][C]116.779973211723[/C][C]1.20002678827717[/C][/ROW]
[ROW][C]76[/C][C]118.53[/C][C]117.979947298069[/C][C]0.550052701930753[/C][/ROW]
[ROW][C]77[/C][C]118.43[/C][C]118.529975843173[/C][C]-0.0999758431730839[/C][/ROW]
[ROW][C]78[/C][C]118.29[/C][C]118.430004390669[/C][C]-0.140004390668622[/C][/ROW]
[ROW][C]79[/C][C]117.85[/C][C]118.290006148614[/C][C]-0.44000614861416[/C][/ROW]
[ROW][C]80[/C][C]118.27[/C][C]117.85001932388[/C][C]0.419980676120062[/C][/ROW]
[ROW][C]81[/C][C]119[/C][C]118.269981555585[/C][C]0.73001844441535[/C][/ROW]
[ROW][C]82[/C][C]119.33[/C][C]118.999967939564[/C][C]0.330032060435542[/C][/ROW]
[ROW][C]83[/C][C]119.17[/C][C]119.329985505885[/C][C]-0.159985505884563[/C][/ROW]
[ROW][C]84[/C][C]119.57[/C][C]119.170007026131[/C][C]0.399992973869303[/C][/ROW]
[ROW][C]85[/C][C]118.62[/C][C]119.56998243339[/C][C]-0.94998243339046[/C][/ROW]
[ROW][C]86[/C][C]119.09[/C][C]118.620041720659[/C][C]0.469958279341[/C][/ROW]
[ROW][C]87[/C][C]120.19[/C][C]119.089979360703[/C][C]1.1000206392965[/C][/ROW]
[ROW][C]88[/C][C]120.17[/C][C]120.189951690069[/C][C]-0.0199516900688081[/C][/ROW]
[ROW][C]89[/C][C]120.29[/C][C]120.170000876224[/C][C]0.119999123775742[/C][/ROW]
[ROW][C]90[/C][C]120.35[/C][C]120.289994729963[/C][C]0.0600052700369247[/C][/ROW]
[ROW][C]91[/C][C]119.88[/C][C]120.349997364731[/C][C]-0.469997364730844[/C][/ROW]
[ROW][C]92[/C][C]120.04[/C][C]119.880020641013[/C][C]0.159979358986988[/C][/ROW]
[ROW][C]93[/C][C]120.52[/C][C]120.039992974139[/C][C]0.480007025860729[/C][/ROW]
[ROW][C]94[/C][C]120.43[/C][C]120.51997891939[/C][C]-0.0899789193897078[/C][/ROW]
[ROW][C]95[/C][C]120.34[/C][C]120.430003951631[/C][C]-0.0900039516307771[/C][/ROW]
[ROW][C]96[/C][C]120.75[/C][C]120.34000395273[/C][C]0.409996047269871[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278700&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278700&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
2	100.93	100.64	0.290000000000006
3	101.41	100.929987263984	0.48001273601561
4	102.07	101.409978919139	0.660021080861043
5	102.42	102.069971013659	0.350028986340675
6	102.53	102.419984627674	0.11001537232633
7	102.43	102.529995168422	-0.0999951684223959
8	102.6	102.430004391517	0.169995608482651
9	102.65	102.599992534253	0.0500074657473419
10	102.74	102.649997803807	0.0900021961926285
11	102.82	102.739996047347	0.0800039526530298
12	103.2	102.819996486443	0.380003513557227
13	102.75	103.199983311273	-0.449983311273499
14	103.09	102.75001976205	0.339980237950073
15	103.71	103.089985068988	0.620014931012477
16	104.3	103.709972770621	0.590027229378776
17	104.58	104.2999740876	0.280025912400035
18	104.71	104.579987702019	0.130012297980656
19	104.44	104.709994290212	-0.269994290211514
20	104.57	104.440011857419	0.129988142581041
21	104.95	104.569994291272	0.380005708727651
22	105.49	104.949983311177	0.540016688822888
23	106.03	105.489976283928	0.540023716072369
24	106.48	106.029976283619	0.450023716380969
25	106.25	106.479980236176	-0.229980236175578
26	106.7	106.25001010011	0.44998989989007
27	107.6	106.699980237661	0.900019762339284
28	108.05	107.599960473566	0.450039526433628
29	108.72	108.049980235481	0.670019764518756
30	109.17	108.719970574544	0.450029425455824
31	109.08	109.169980235925	-0.0899802359248554
32	109.04	109.080003951689	-0.0400039516885755
33	109.34	109.040001756865	0.299998243134638
34	109.37	109.339986824889	0.0300131751114208
35	108.96	109.369998681903	-0.409998681902536
36	108.77	108.960018006033	-0.190018006033171
37	108.11	108.770008345077	-0.660008345076861
38	108.67	108.110028985781	0.559971014218647
39	109.05	108.669975407588	0.380024592412354
40	109.43	109.049983310348	0.380016689652237
41	109.62	109.429983310695	0.190016689305153
42	109.85	109.619991654981	0.230008345019044
43	109.34	109.849989898656	-0.50998989865559
44	109.65	109.340022397377	0.30997760262305
45	109.69	109.649986386622	0.0400136133778801
46	109.91	109.68999824271	0.22000175728968
47	110.09	109.909990338118	0.180009661882139
48	110.44	110.089992094463	0.350007905537467
49	109.9	110.439984628599	-0.53998462859947
50	110.25	109.900023714664	0.349976285335629
51	111.26	110.249984629988	1.01001537001186
52	111.74	111.259955642857	0.480044357143186
53	111.91	111.73997891775	0.170021082249761
54	111.95	111.909992533134	0.0400074668660721
55	111.63	111.94999824298	-0.319998242980276
56	111.85	111.630014053457	0.219985946542693
57	112.16	111.849990338812	0.310009661187777
58	112.49	112.159986385214	0.330013614785813
59	112.66	112.489985506695	0.170014493305359
60	113.39	112.659992533423	0.730007466576708
61	112.92	113.389967940047	-0.469967940046558
62	113.44	112.920020639721	0.519979360279223
63	114.68	113.439977163913	1.24002283608709
64	115.38	114.679945541551	0.700054458448989
65	115.48	115.379969255502	0.100030744498355
66	115.41	115.47999560692	-0.0699956069202727
67	114.92	115.410003074018	-0.490003074017736
68	115.16	114.92002151961	0.23997848039032
69	115.89	115.159989460794	0.730010539205779
70	116.25	115.889967939912	0.360032060088386
71	116.43	116.249984188366	0.180015811634291
72	116.83	116.429992094192	0.400007905807541
73	116.17	116.829982432735	-0.659982432734694
74	116.78	116.170028984643	0.609971015356649
75	117.98	116.779973211723	1.20002678827717
76	118.53	117.979947298069	0.550052701930753
77	118.43	118.529975843173	-0.0999758431730839
78	118.29	118.430004390669	-0.140004390668622
79	117.85	118.290006148614	-0.44000614861416
80	118.27	117.85001932388	0.419980676120062
81	119	118.269981555585	0.73001844441535
82	119.33	118.999967939564	0.330032060435542
83	119.17	119.329985505885	-0.159985505884563
84	119.57	119.170007026131	0.399992973869303
85	118.62	119.56998243339	-0.94998243339046
86	119.09	118.620041720659	0.469958279341
87	120.19	119.089979360703	1.1000206392965
88	120.17	120.189951690069	-0.0199516900688081
89	120.29	120.170000876224	0.119999123775742
90	120.35	120.289994729963	0.0600052700369247
91	119.88	120.349997364731	-0.469997364730844
92	120.04	119.880020641013	0.159979358986988
93	120.52	120.039992974139	0.480007025860729
94	120.43	120.51997891939	-0.0899789193897078
95	120.34	120.430003951631	-0.0900039516307771
96	120.75	120.34000395273	0.409996047269871

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	120.749981994083	119.941476330496	121.558487657669
98	120.749981994083	119.606607426618	121.893356561547
99	120.749981994083	119.349650106637	122.150313881529
100	120.749981994083	119.13302392769	122.366940060475
101	120.749981994083	118.942171887366	122.557792100799
102	120.749981994083	118.76962814302	122.730335845145
103	120.749981994083	118.610957597566	122.889006390599
104	120.749981994083	118.463270520729	123.036693467436
105	120.749981994083	118.324559689444	123.175404298721
106	120.749981994083	118.193363651562	123.306600336603
107	120.749981994083	118.06857912566	123.431384862505
108	120.749981994083	117.949348969879	123.550615018286

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 120.749981994083 & 119.941476330496 & 121.558487657669 \tabularnewline
98 & 120.749981994083 & 119.606607426618 & 121.893356561547 \tabularnewline
99 & 120.749981994083 & 119.349650106637 & 122.150313881529 \tabularnewline
100 & 120.749981994083 & 119.13302392769 & 122.366940060475 \tabularnewline
101 & 120.749981994083 & 118.942171887366 & 122.557792100799 \tabularnewline
102 & 120.749981994083 & 118.76962814302 & 122.730335845145 \tabularnewline
103 & 120.749981994083 & 118.610957597566 & 122.889006390599 \tabularnewline
104 & 120.749981994083 & 118.463270520729 & 123.036693467436 \tabularnewline
105 & 120.749981994083 & 118.324559689444 & 123.175404298721 \tabularnewline
106 & 120.749981994083 & 118.193363651562 & 123.306600336603 \tabularnewline
107 & 120.749981994083 & 118.06857912566 & 123.431384862505 \tabularnewline
108 & 120.749981994083 & 117.949348969879 & 123.550615018286 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278700&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]120.749981994083[/C][C]119.941476330496[/C][C]121.558487657669[/C][/ROW]
[ROW][C]98[/C][C]120.749981994083[/C][C]119.606607426618[/C][C]121.893356561547[/C][/ROW]
[ROW][C]99[/C][C]120.749981994083[/C][C]119.349650106637[/C][C]122.150313881529[/C][/ROW]
[ROW][C]100[/C][C]120.749981994083[/C][C]119.13302392769[/C][C]122.366940060475[/C][/ROW]
[ROW][C]101[/C][C]120.749981994083[/C][C]118.942171887366[/C][C]122.557792100799[/C][/ROW]
[ROW][C]102[/C][C]120.749981994083[/C][C]118.76962814302[/C][C]122.730335845145[/C][/ROW]
[ROW][C]103[/C][C]120.749981994083[/C][C]118.610957597566[/C][C]122.889006390599[/C][/ROW]
[ROW][C]104[/C][C]120.749981994083[/C][C]118.463270520729[/C][C]123.036693467436[/C][/ROW]
[ROW][C]105[/C][C]120.749981994083[/C][C]118.324559689444[/C][C]123.175404298721[/C][/ROW]
[ROW][C]106[/C][C]120.749981994083[/C][C]118.193363651562[/C][C]123.306600336603[/C][/ROW]
[ROW][C]107[/C][C]120.749981994083[/C][C]118.06857912566[/C][C]123.431384862505[/C][/ROW]
[ROW][C]108[/C][C]120.749981994083[/C][C]117.949348969879[/C][C]123.550615018286[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278700&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278700&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	120.749981994083	119.941476330496	121.558487657669
98	120.749981994083	119.606607426618	121.893356561547
99	120.749981994083	119.349650106637	122.150313881529
100	120.749981994083	119.13302392769	122.366940060475
101	120.749981994083	118.942171887366	122.557792100799
102	120.749981994083	118.76962814302	122.730335845145
103	120.749981994083	118.610957597566	122.889006390599
104	120.749981994083	118.463270520729	123.036693467436
105	120.749981994083	118.324559689444	123.175404298721
106	120.749981994083	118.193363651562	123.306600336603
107	120.749981994083	118.06857912566	123.431384862505
108	120.749981994083	117.949348969879	123.550615018286

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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