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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 21 Dec 2010 20:45:40 +0000

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/2010/Dec/21/t1292964268obmo3wfx642giiy.htm/, Retrieved Sun, 19 May 2024 18:45:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113967, Retrieved Sun, 19 May 2024 18:45:27 +0000

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No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

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

-       [Exponential Smoothing] [opgave 10 oef 2] [2010-12-21 20:45:40] [3c84fba69796ffa9703fc49b6977555d] [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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113967&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113967&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113967&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.77855541108374
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.77855541108374 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113967&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]0.77855541108374[/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=113967&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113967&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	0.77855541108374
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	96.6	97.7089398501379	-1.10893985013787
14	96.7	96.7897038891088	-0.089703889108776
15	98.9	99.008428293043	-0.108428293043062
16	102	102.059395097890	-0.0593950978896061
17	105.2	105.18678664398	0.0132133560200600
18	106.4	106.360946274092	0.0390537259078485
19	99.3	94.7616345639049	4.53836543609511
20	96.4	98.4338157545798	-2.03381575457982
21	93.1	97.6440661311446	-4.54406613114462
22	95.6	92.2277731320427	3.37222686795727
23	93.3	96.1313235211291	-2.83132352112911
24	96.7	93.6528912554094	3.04710874459056
25	105.6	97.7398345609094	7.86016543909055
26	105.2	104.041996214102	1.15800378589783
27	107	107.422705544400	-0.422705544400458
28	104.9	110.500499711075	-5.60049971107517
29	104.5	109.459383802520	-4.95938380251964
30	105.2	106.772248171377	-1.57224817137711
31	99.7	94.9640902507496	4.7359097492504
32	100.2	97.3359827040107	2.86401729598933
33	98.5	99.772324387962	-1.27232438796197
34	98.4	98.6266956788422	-0.226695678842148
35	97.1	98.3365377411824	-1.23653774118236
36	98.4	98.428954656649	-0.0289546566489065
37	100.6	101.131533757941	-0.531533757941119
38	111.3	99.47421059304	11.8257894069599
39	119	110.880500893443	8.1194991065566
40	117.8	119.621984034453	-1.82198403445284
41	108.8	122.058320044582	-13.2583200445820
42	109.3	113.788979031937	-4.48897903193748
43	103.5	100.620929571758	2.87907042824216
44	103.7	101.063126761092	2.63687323890774
45	110	102.383100044595	7.61689995540515
46	105.5	108.397295902632	-2.89729590263192
47	110.4	105.774847473923	4.62515252607683
48	106.7	110.865527500676	-4.16552750067643
49	110.2	110.480711300359	-0.280711300359158
50	105.2	111.655364126819	-6.4553641268194
51	108	107.857268948042	0.142731051957824
52	108.1	108.162258536412	-0.0622585364121022
53	107.2	109.078464936905	-1.87846493690466
54	106	111.536263536928	-5.53626353692796
55	99.4	99.323422121087	0.076577878912957
56	100.2	97.5926329267454	2.60736707325459
57	100.3	99.8891756125352	0.410824387464814
58	100.8	98.1520713214823	2.64792867851769
59	99.5	101.415569659227	-1.91556965922692
60	100.2	99.485483122993	0.714516877007043
61	103	103.528165322715	-0.528165322714656
62	111	103.078108570833	7.92189142916675
63	120.5	112.037989923223	8.4620100767766
64	109.5	118.789206739553	-9.28920673955265
65	106.6	112.131688191518	-5.53168819151797
66	105.5	110.903813653349	-5.40381365334935
67	103.9	99.9932470725936	3.90675292740639
68	104.9	101.747717439540	3.15228256045957
69	104.8	103.973011866593	0.826988133407127
70	99.6	102.975518176800	-3.3755181768005
71	97	100.531705543012	-3.53170554301244
72	95.4	97.9224402468721	-2.52244024687209
73	99.3	99.033411199412	0.266588800588096
74	103.9	100.911035861822	2.98896413817772
75	107.4	105.849557387799	1.55044261220125
76	107.4	103.590697163785	3.80930283621491
77	111	107.877749064313	3.12225093568661
78	113.2	113.475033976598	-0.275033976597953
79	108.5	108.250411405929	0.249588594070985
80	113.3	106.909733238539	6.39026676146052
81	113.8	111.090321123654	2.70967887634609
82	105.3	110.400689552354	-5.10068955235367
83	107.5	106.565908549835	0.934091450164686
84	109.4	107.682976115507	1.71702388449324
85	118.9	113.239230879872	5.66076912012845
86	119	120.321643898434	-1.32164389843385
87	115	121.920810426206	-6.9208104262064
88	124.1	113.289160211407	10.8108397885933
89	120.5	123.013621652757	-2.51362165275742
90	117.7	123.689352238269	-5.98935223826882
91	117.1	113.879980463688	3.22001953631215
92	118.1	116.131534877619	1.96846512238109
93	119.6	115.980845541884	3.61915445811552
94	118.8	114.026806056171	4.77319394382938
95	124.9	119.388223994573	5.51177600542707
96	124	124.322050280934	-0.322050280933666
97	124.9	129.793813980514	-4.8938139805139
98	121.7	127.177267622756	-5.4772676227563
99	121.6	124.273599698928	-2.6735996989277
100	125.1	122.742024549008	2.35797545099160
101	127.9	122.919473485239	4.98052651476061
102	129	128.702815230009	0.297184769990992
103	130.1	125.513848834900	4.58615116510025
104	130.3	128.49109982425	1.80890017574998
105	127.9	128.429155155938	-0.529155155938128
106	124.1	123.147434118408	0.952565881591767
107	125.7	125.731156537994	-0.0311565379938656
108	129.2	125.053293887754	4.14670611224612
109	129.2	133.120574075532	-3.92057407553236
110	132.6	131.132765709815	1.46723429018539
111	131.5	134.417858232361	-2.9178582323612
112	131	133.946299047731	-2.94629904773143
113	125.8	130.482888123026	-4.68288812302639
114	127.2	127.698289009671	-0.498289009671254
115	127.3	124.844406723115	2.45559327688485
116	127.5	125.574717873833	1.92528212616745
117	122	125.134490760238	-3.13449076023811
118	118.4	118.336136079827	0.0638639201727642
119	118.3	119.935325135947	-1.635325135947
120	115.5	118.896673067673	-3.39667306767285

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 96.6 & 97.7089398501379 & -1.10893985013787 \tabularnewline
14 & 96.7 & 96.7897038891088 & -0.089703889108776 \tabularnewline
15 & 98.9 & 99.008428293043 & -0.108428293043062 \tabularnewline
16 & 102 & 102.059395097890 & -0.0593950978896061 \tabularnewline
17 & 105.2 & 105.18678664398 & 0.0132133560200600 \tabularnewline
18 & 106.4 & 106.360946274092 & 0.0390537259078485 \tabularnewline
19 & 99.3 & 94.7616345639049 & 4.53836543609511 \tabularnewline
20 & 96.4 & 98.4338157545798 & -2.03381575457982 \tabularnewline
21 & 93.1 & 97.6440661311446 & -4.54406613114462 \tabularnewline
22 & 95.6 & 92.2277731320427 & 3.37222686795727 \tabularnewline
23 & 93.3 & 96.1313235211291 & -2.83132352112911 \tabularnewline
24 & 96.7 & 93.6528912554094 & 3.04710874459056 \tabularnewline
25 & 105.6 & 97.7398345609094 & 7.86016543909055 \tabularnewline
26 & 105.2 & 104.041996214102 & 1.15800378589783 \tabularnewline
27 & 107 & 107.422705544400 & -0.422705544400458 \tabularnewline
28 & 104.9 & 110.500499711075 & -5.60049971107517 \tabularnewline
29 & 104.5 & 109.459383802520 & -4.95938380251964 \tabularnewline
30 & 105.2 & 106.772248171377 & -1.57224817137711 \tabularnewline
31 & 99.7 & 94.9640902507496 & 4.7359097492504 \tabularnewline
32 & 100.2 & 97.3359827040107 & 2.86401729598933 \tabularnewline
33 & 98.5 & 99.772324387962 & -1.27232438796197 \tabularnewline
34 & 98.4 & 98.6266956788422 & -0.226695678842148 \tabularnewline
35 & 97.1 & 98.3365377411824 & -1.23653774118236 \tabularnewline
36 & 98.4 & 98.428954656649 & -0.0289546566489065 \tabularnewline
37 & 100.6 & 101.131533757941 & -0.531533757941119 \tabularnewline
38 & 111.3 & 99.47421059304 & 11.8257894069599 \tabularnewline
39 & 119 & 110.880500893443 & 8.1194991065566 \tabularnewline
40 & 117.8 & 119.621984034453 & -1.82198403445284 \tabularnewline
41 & 108.8 & 122.058320044582 & -13.2583200445820 \tabularnewline
42 & 109.3 & 113.788979031937 & -4.48897903193748 \tabularnewline
43 & 103.5 & 100.620929571758 & 2.87907042824216 \tabularnewline
44 & 103.7 & 101.063126761092 & 2.63687323890774 \tabularnewline
45 & 110 & 102.383100044595 & 7.61689995540515 \tabularnewline
46 & 105.5 & 108.397295902632 & -2.89729590263192 \tabularnewline
47 & 110.4 & 105.774847473923 & 4.62515252607683 \tabularnewline
48 & 106.7 & 110.865527500676 & -4.16552750067643 \tabularnewline
49 & 110.2 & 110.480711300359 & -0.280711300359158 \tabularnewline
50 & 105.2 & 111.655364126819 & -6.4553641268194 \tabularnewline
51 & 108 & 107.857268948042 & 0.142731051957824 \tabularnewline
52 & 108.1 & 108.162258536412 & -0.0622585364121022 \tabularnewline
53 & 107.2 & 109.078464936905 & -1.87846493690466 \tabularnewline
54 & 106 & 111.536263536928 & -5.53626353692796 \tabularnewline
55 & 99.4 & 99.323422121087 & 0.076577878912957 \tabularnewline
56 & 100.2 & 97.5926329267454 & 2.60736707325459 \tabularnewline
57 & 100.3 & 99.8891756125352 & 0.410824387464814 \tabularnewline
58 & 100.8 & 98.1520713214823 & 2.64792867851769 \tabularnewline
59 & 99.5 & 101.415569659227 & -1.91556965922692 \tabularnewline
60 & 100.2 & 99.485483122993 & 0.714516877007043 \tabularnewline
61 & 103 & 103.528165322715 & -0.528165322714656 \tabularnewline
62 & 111 & 103.078108570833 & 7.92189142916675 \tabularnewline
63 & 120.5 & 112.037989923223 & 8.4620100767766 \tabularnewline
64 & 109.5 & 118.789206739553 & -9.28920673955265 \tabularnewline
65 & 106.6 & 112.131688191518 & -5.53168819151797 \tabularnewline
66 & 105.5 & 110.903813653349 & -5.40381365334935 \tabularnewline
67 & 103.9 & 99.9932470725936 & 3.90675292740639 \tabularnewline
68 & 104.9 & 101.747717439540 & 3.15228256045957 \tabularnewline
69 & 104.8 & 103.973011866593 & 0.826988133407127 \tabularnewline
70 & 99.6 & 102.975518176800 & -3.3755181768005 \tabularnewline
71 & 97 & 100.531705543012 & -3.53170554301244 \tabularnewline
72 & 95.4 & 97.9224402468721 & -2.52244024687209 \tabularnewline
73 & 99.3 & 99.033411199412 & 0.266588800588096 \tabularnewline
74 & 103.9 & 100.911035861822 & 2.98896413817772 \tabularnewline
75 & 107.4 & 105.849557387799 & 1.55044261220125 \tabularnewline
76 & 107.4 & 103.590697163785 & 3.80930283621491 \tabularnewline
77 & 111 & 107.877749064313 & 3.12225093568661 \tabularnewline
78 & 113.2 & 113.475033976598 & -0.275033976597953 \tabularnewline
79 & 108.5 & 108.250411405929 & 0.249588594070985 \tabularnewline
80 & 113.3 & 106.909733238539 & 6.39026676146052 \tabularnewline
81 & 113.8 & 111.090321123654 & 2.70967887634609 \tabularnewline
82 & 105.3 & 110.400689552354 & -5.10068955235367 \tabularnewline
83 & 107.5 & 106.565908549835 & 0.934091450164686 \tabularnewline
84 & 109.4 & 107.682976115507 & 1.71702388449324 \tabularnewline
85 & 118.9 & 113.239230879872 & 5.66076912012845 \tabularnewline
86 & 119 & 120.321643898434 & -1.32164389843385 \tabularnewline
87 & 115 & 121.920810426206 & -6.9208104262064 \tabularnewline
88 & 124.1 & 113.289160211407 & 10.8108397885933 \tabularnewline
89 & 120.5 & 123.013621652757 & -2.51362165275742 \tabularnewline
90 & 117.7 & 123.689352238269 & -5.98935223826882 \tabularnewline
91 & 117.1 & 113.879980463688 & 3.22001953631215 \tabularnewline
92 & 118.1 & 116.131534877619 & 1.96846512238109 \tabularnewline
93 & 119.6 & 115.980845541884 & 3.61915445811552 \tabularnewline
94 & 118.8 & 114.026806056171 & 4.77319394382938 \tabularnewline
95 & 124.9 & 119.388223994573 & 5.51177600542707 \tabularnewline
96 & 124 & 124.322050280934 & -0.322050280933666 \tabularnewline
97 & 124.9 & 129.793813980514 & -4.8938139805139 \tabularnewline
98 & 121.7 & 127.177267622756 & -5.4772676227563 \tabularnewline
99 & 121.6 & 124.273599698928 & -2.6735996989277 \tabularnewline
100 & 125.1 & 122.742024549008 & 2.35797545099160 \tabularnewline
101 & 127.9 & 122.919473485239 & 4.98052651476061 \tabularnewline
102 & 129 & 128.702815230009 & 0.297184769990992 \tabularnewline
103 & 130.1 & 125.513848834900 & 4.58615116510025 \tabularnewline
104 & 130.3 & 128.49109982425 & 1.80890017574998 \tabularnewline
105 & 127.9 & 128.429155155938 & -0.529155155938128 \tabularnewline
106 & 124.1 & 123.147434118408 & 0.952565881591767 \tabularnewline
107 & 125.7 & 125.731156537994 & -0.0311565379938656 \tabularnewline
108 & 129.2 & 125.053293887754 & 4.14670611224612 \tabularnewline
109 & 129.2 & 133.120574075532 & -3.92057407553236 \tabularnewline
110 & 132.6 & 131.132765709815 & 1.46723429018539 \tabularnewline
111 & 131.5 & 134.417858232361 & -2.9178582323612 \tabularnewline
112 & 131 & 133.946299047731 & -2.94629904773143 \tabularnewline
113 & 125.8 & 130.482888123026 & -4.68288812302639 \tabularnewline
114 & 127.2 & 127.698289009671 & -0.498289009671254 \tabularnewline
115 & 127.3 & 124.844406723115 & 2.45559327688485 \tabularnewline
116 & 127.5 & 125.574717873833 & 1.92528212616745 \tabularnewline
117 & 122 & 125.134490760238 & -3.13449076023811 \tabularnewline
118 & 118.4 & 118.336136079827 & 0.0638639201727642 \tabularnewline
119 & 118.3 & 119.935325135947 & -1.635325135947 \tabularnewline
120 & 115.5 & 118.896673067673 & -3.39667306767285 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113967&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]96.6[/C][C]97.7089398501379[/C][C]-1.10893985013787[/C][/ROW]
[ROW][C]14[/C][C]96.7[/C][C]96.7897038891088[/C][C]-0.089703889108776[/C][/ROW]
[ROW][C]15[/C][C]98.9[/C][C]99.008428293043[/C][C]-0.108428293043062[/C][/ROW]
[ROW][C]16[/C][C]102[/C][C]102.059395097890[/C][C]-0.0593950978896061[/C][/ROW]
[ROW][C]17[/C][C]105.2[/C][C]105.18678664398[/C][C]0.0132133560200600[/C][/ROW]
[ROW][C]18[/C][C]106.4[/C][C]106.360946274092[/C][C]0.0390537259078485[/C][/ROW]
[ROW][C]19[/C][C]99.3[/C][C]94.7616345639049[/C][C]4.53836543609511[/C][/ROW]
[ROW][C]20[/C][C]96.4[/C][C]98.4338157545798[/C][C]-2.03381575457982[/C][/ROW]
[ROW][C]21[/C][C]93.1[/C][C]97.6440661311446[/C][C]-4.54406613114462[/C][/ROW]
[ROW][C]22[/C][C]95.6[/C][C]92.2277731320427[/C][C]3.37222686795727[/C][/ROW]
[ROW][C]23[/C][C]93.3[/C][C]96.1313235211291[/C][C]-2.83132352112911[/C][/ROW]
[ROW][C]24[/C][C]96.7[/C][C]93.6528912554094[/C][C]3.04710874459056[/C][/ROW]
[ROW][C]25[/C][C]105.6[/C][C]97.7398345609094[/C][C]7.86016543909055[/C][/ROW]
[ROW][C]26[/C][C]105.2[/C][C]104.041996214102[/C][C]1.15800378589783[/C][/ROW]
[ROW][C]27[/C][C]107[/C][C]107.422705544400[/C][C]-0.422705544400458[/C][/ROW]
[ROW][C]28[/C][C]104.9[/C][C]110.500499711075[/C][C]-5.60049971107517[/C][/ROW]
[ROW][C]29[/C][C]104.5[/C][C]109.459383802520[/C][C]-4.95938380251964[/C][/ROW]
[ROW][C]30[/C][C]105.2[/C][C]106.772248171377[/C][C]-1.57224817137711[/C][/ROW]
[ROW][C]31[/C][C]99.7[/C][C]94.9640902507496[/C][C]4.7359097492504[/C][/ROW]
[ROW][C]32[/C][C]100.2[/C][C]97.3359827040107[/C][C]2.86401729598933[/C][/ROW]
[ROW][C]33[/C][C]98.5[/C][C]99.772324387962[/C][C]-1.27232438796197[/C][/ROW]
[ROW][C]34[/C][C]98.4[/C][C]98.6266956788422[/C][C]-0.226695678842148[/C][/ROW]
[ROW][C]35[/C][C]97.1[/C][C]98.3365377411824[/C][C]-1.23653774118236[/C][/ROW]
[ROW][C]36[/C][C]98.4[/C][C]98.428954656649[/C][C]-0.0289546566489065[/C][/ROW]
[ROW][C]37[/C][C]100.6[/C][C]101.131533757941[/C][C]-0.531533757941119[/C][/ROW]
[ROW][C]38[/C][C]111.3[/C][C]99.47421059304[/C][C]11.8257894069599[/C][/ROW]
[ROW][C]39[/C][C]119[/C][C]110.880500893443[/C][C]8.1194991065566[/C][/ROW]
[ROW][C]40[/C][C]117.8[/C][C]119.621984034453[/C][C]-1.82198403445284[/C][/ROW]
[ROW][C]41[/C][C]108.8[/C][C]122.058320044582[/C][C]-13.2583200445820[/C][/ROW]
[ROW][C]42[/C][C]109.3[/C][C]113.788979031937[/C][C]-4.48897903193748[/C][/ROW]
[ROW][C]43[/C][C]103.5[/C][C]100.620929571758[/C][C]2.87907042824216[/C][/ROW]
[ROW][C]44[/C][C]103.7[/C][C]101.063126761092[/C][C]2.63687323890774[/C][/ROW]
[ROW][C]45[/C][C]110[/C][C]102.383100044595[/C][C]7.61689995540515[/C][/ROW]
[ROW][C]46[/C][C]105.5[/C][C]108.397295902632[/C][C]-2.89729590263192[/C][/ROW]
[ROW][C]47[/C][C]110.4[/C][C]105.774847473923[/C][C]4.62515252607683[/C][/ROW]
[ROW][C]48[/C][C]106.7[/C][C]110.865527500676[/C][C]-4.16552750067643[/C][/ROW]
[ROW][C]49[/C][C]110.2[/C][C]110.480711300359[/C][C]-0.280711300359158[/C][/ROW]
[ROW][C]50[/C][C]105.2[/C][C]111.655364126819[/C][C]-6.4553641268194[/C][/ROW]
[ROW][C]51[/C][C]108[/C][C]107.857268948042[/C][C]0.142731051957824[/C][/ROW]
[ROW][C]52[/C][C]108.1[/C][C]108.162258536412[/C][C]-0.0622585364121022[/C][/ROW]
[ROW][C]53[/C][C]107.2[/C][C]109.078464936905[/C][C]-1.87846493690466[/C][/ROW]
[ROW][C]54[/C][C]106[/C][C]111.536263536928[/C][C]-5.53626353692796[/C][/ROW]
[ROW][C]55[/C][C]99.4[/C][C]99.323422121087[/C][C]0.076577878912957[/C][/ROW]
[ROW][C]56[/C][C]100.2[/C][C]97.5926329267454[/C][C]2.60736707325459[/C][/ROW]
[ROW][C]57[/C][C]100.3[/C][C]99.8891756125352[/C][C]0.410824387464814[/C][/ROW]
[ROW][C]58[/C][C]100.8[/C][C]98.1520713214823[/C][C]2.64792867851769[/C][/ROW]
[ROW][C]59[/C][C]99.5[/C][C]101.415569659227[/C][C]-1.91556965922692[/C][/ROW]
[ROW][C]60[/C][C]100.2[/C][C]99.485483122993[/C][C]0.714516877007043[/C][/ROW]
[ROW][C]61[/C][C]103[/C][C]103.528165322715[/C][C]-0.528165322714656[/C][/ROW]
[ROW][C]62[/C][C]111[/C][C]103.078108570833[/C][C]7.92189142916675[/C][/ROW]
[ROW][C]63[/C][C]120.5[/C][C]112.037989923223[/C][C]8.4620100767766[/C][/ROW]
[ROW][C]64[/C][C]109.5[/C][C]118.789206739553[/C][C]-9.28920673955265[/C][/ROW]
[ROW][C]65[/C][C]106.6[/C][C]112.131688191518[/C][C]-5.53168819151797[/C][/ROW]
[ROW][C]66[/C][C]105.5[/C][C]110.903813653349[/C][C]-5.40381365334935[/C][/ROW]
[ROW][C]67[/C][C]103.9[/C][C]99.9932470725936[/C][C]3.90675292740639[/C][/ROW]
[ROW][C]68[/C][C]104.9[/C][C]101.747717439540[/C][C]3.15228256045957[/C][/ROW]
[ROW][C]69[/C][C]104.8[/C][C]103.973011866593[/C][C]0.826988133407127[/C][/ROW]
[ROW][C]70[/C][C]99.6[/C][C]102.975518176800[/C][C]-3.3755181768005[/C][/ROW]
[ROW][C]71[/C][C]97[/C][C]100.531705543012[/C][C]-3.53170554301244[/C][/ROW]
[ROW][C]72[/C][C]95.4[/C][C]97.9224402468721[/C][C]-2.52244024687209[/C][/ROW]
[ROW][C]73[/C][C]99.3[/C][C]99.033411199412[/C][C]0.266588800588096[/C][/ROW]
[ROW][C]74[/C][C]103.9[/C][C]100.911035861822[/C][C]2.98896413817772[/C][/ROW]
[ROW][C]75[/C][C]107.4[/C][C]105.849557387799[/C][C]1.55044261220125[/C][/ROW]
[ROW][C]76[/C][C]107.4[/C][C]103.590697163785[/C][C]3.80930283621491[/C][/ROW]
[ROW][C]77[/C][C]111[/C][C]107.877749064313[/C][C]3.12225093568661[/C][/ROW]
[ROW][C]78[/C][C]113.2[/C][C]113.475033976598[/C][C]-0.275033976597953[/C][/ROW]
[ROW][C]79[/C][C]108.5[/C][C]108.250411405929[/C][C]0.249588594070985[/C][/ROW]
[ROW][C]80[/C][C]113.3[/C][C]106.909733238539[/C][C]6.39026676146052[/C][/ROW]
[ROW][C]81[/C][C]113.8[/C][C]111.090321123654[/C][C]2.70967887634609[/C][/ROW]
[ROW][C]82[/C][C]105.3[/C][C]110.400689552354[/C][C]-5.10068955235367[/C][/ROW]
[ROW][C]83[/C][C]107.5[/C][C]106.565908549835[/C][C]0.934091450164686[/C][/ROW]
[ROW][C]84[/C][C]109.4[/C][C]107.682976115507[/C][C]1.71702388449324[/C][/ROW]
[ROW][C]85[/C][C]118.9[/C][C]113.239230879872[/C][C]5.66076912012845[/C][/ROW]
[ROW][C]86[/C][C]119[/C][C]120.321643898434[/C][C]-1.32164389843385[/C][/ROW]
[ROW][C]87[/C][C]115[/C][C]121.920810426206[/C][C]-6.9208104262064[/C][/ROW]
[ROW][C]88[/C][C]124.1[/C][C]113.289160211407[/C][C]10.8108397885933[/C][/ROW]
[ROW][C]89[/C][C]120.5[/C][C]123.013621652757[/C][C]-2.51362165275742[/C][/ROW]
[ROW][C]90[/C][C]117.7[/C][C]123.689352238269[/C][C]-5.98935223826882[/C][/ROW]
[ROW][C]91[/C][C]117.1[/C][C]113.879980463688[/C][C]3.22001953631215[/C][/ROW]
[ROW][C]92[/C][C]118.1[/C][C]116.131534877619[/C][C]1.96846512238109[/C][/ROW]
[ROW][C]93[/C][C]119.6[/C][C]115.980845541884[/C][C]3.61915445811552[/C][/ROW]
[ROW][C]94[/C][C]118.8[/C][C]114.026806056171[/C][C]4.77319394382938[/C][/ROW]
[ROW][C]95[/C][C]124.9[/C][C]119.388223994573[/C][C]5.51177600542707[/C][/ROW]
[ROW][C]96[/C][C]124[/C][C]124.322050280934[/C][C]-0.322050280933666[/C][/ROW]
[ROW][C]97[/C][C]124.9[/C][C]129.793813980514[/C][C]-4.8938139805139[/C][/ROW]
[ROW][C]98[/C][C]121.7[/C][C]127.177267622756[/C][C]-5.4772676227563[/C][/ROW]
[ROW][C]99[/C][C]121.6[/C][C]124.273599698928[/C][C]-2.6735996989277[/C][/ROW]
[ROW][C]100[/C][C]125.1[/C][C]122.742024549008[/C][C]2.35797545099160[/C][/ROW]
[ROW][C]101[/C][C]127.9[/C][C]122.919473485239[/C][C]4.98052651476061[/C][/ROW]
[ROW][C]102[/C][C]129[/C][C]128.702815230009[/C][C]0.297184769990992[/C][/ROW]
[ROW][C]103[/C][C]130.1[/C][C]125.513848834900[/C][C]4.58615116510025[/C][/ROW]
[ROW][C]104[/C][C]130.3[/C][C]128.49109982425[/C][C]1.80890017574998[/C][/ROW]
[ROW][C]105[/C][C]127.9[/C][C]128.429155155938[/C][C]-0.529155155938128[/C][/ROW]
[ROW][C]106[/C][C]124.1[/C][C]123.147434118408[/C][C]0.952565881591767[/C][/ROW]
[ROW][C]107[/C][C]125.7[/C][C]125.731156537994[/C][C]-0.0311565379938656[/C][/ROW]
[ROW][C]108[/C][C]129.2[/C][C]125.053293887754[/C][C]4.14670611224612[/C][/ROW]
[ROW][C]109[/C][C]129.2[/C][C]133.120574075532[/C][C]-3.92057407553236[/C][/ROW]
[ROW][C]110[/C][C]132.6[/C][C]131.132765709815[/C][C]1.46723429018539[/C][/ROW]
[ROW][C]111[/C][C]131.5[/C][C]134.417858232361[/C][C]-2.9178582323612[/C][/ROW]
[ROW][C]112[/C][C]131[/C][C]133.946299047731[/C][C]-2.94629904773143[/C][/ROW]
[ROW][C]113[/C][C]125.8[/C][C]130.482888123026[/C][C]-4.68288812302639[/C][/ROW]
[ROW][C]114[/C][C]127.2[/C][C]127.698289009671[/C][C]-0.498289009671254[/C][/ROW]
[ROW][C]115[/C][C]127.3[/C][C]124.844406723115[/C][C]2.45559327688485[/C][/ROW]
[ROW][C]116[/C][C]127.5[/C][C]125.574717873833[/C][C]1.92528212616745[/C][/ROW]
[ROW][C]117[/C][C]122[/C][C]125.134490760238[/C][C]-3.13449076023811[/C][/ROW]
[ROW][C]118[/C][C]118.4[/C][C]118.336136079827[/C][C]0.0638639201727642[/C][/ROW]
[ROW][C]119[/C][C]118.3[/C][C]119.935325135947[/C][C]-1.635325135947[/C][/ROW]
[ROW][C]120[/C][C]115.5[/C][C]118.896673067673[/C][C]-3.39667306767285[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113967&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113967&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	96.6	97.7089398501379	-1.10893985013787
14	96.7	96.7897038891088	-0.089703889108776
15	98.9	99.008428293043	-0.108428293043062
16	102	102.059395097890	-0.0593950978896061
17	105.2	105.18678664398	0.0132133560200600
18	106.4	106.360946274092	0.0390537259078485
19	99.3	94.7616345639049	4.53836543609511
20	96.4	98.4338157545798	-2.03381575457982
21	93.1	97.6440661311446	-4.54406613114462
22	95.6	92.2277731320427	3.37222686795727
23	93.3	96.1313235211291	-2.83132352112911
24	96.7	93.6528912554094	3.04710874459056
25	105.6	97.7398345609094	7.86016543909055
26	105.2	104.041996214102	1.15800378589783
27	107	107.422705544400	-0.422705544400458
28	104.9	110.500499711075	-5.60049971107517
29	104.5	109.459383802520	-4.95938380251964
30	105.2	106.772248171377	-1.57224817137711
31	99.7	94.9640902507496	4.7359097492504
32	100.2	97.3359827040107	2.86401729598933
33	98.5	99.772324387962	-1.27232438796197
34	98.4	98.6266956788422	-0.226695678842148
35	97.1	98.3365377411824	-1.23653774118236
36	98.4	98.428954656649	-0.0289546566489065
37	100.6	101.131533757941	-0.531533757941119
38	111.3	99.47421059304	11.8257894069599
39	119	110.880500893443	8.1194991065566
40	117.8	119.621984034453	-1.82198403445284
41	108.8	122.058320044582	-13.2583200445820
42	109.3	113.788979031937	-4.48897903193748
43	103.5	100.620929571758	2.87907042824216
44	103.7	101.063126761092	2.63687323890774
45	110	102.383100044595	7.61689995540515
46	105.5	108.397295902632	-2.89729590263192
47	110.4	105.774847473923	4.62515252607683
48	106.7	110.865527500676	-4.16552750067643
49	110.2	110.480711300359	-0.280711300359158
50	105.2	111.655364126819	-6.4553641268194
51	108	107.857268948042	0.142731051957824
52	108.1	108.162258536412	-0.0622585364121022
53	107.2	109.078464936905	-1.87846493690466
54	106	111.536263536928	-5.53626353692796
55	99.4	99.323422121087	0.076577878912957
56	100.2	97.5926329267454	2.60736707325459
57	100.3	99.8891756125352	0.410824387464814
58	100.8	98.1520713214823	2.64792867851769
59	99.5	101.415569659227	-1.91556965922692
60	100.2	99.485483122993	0.714516877007043
61	103	103.528165322715	-0.528165322714656
62	111	103.078108570833	7.92189142916675
63	120.5	112.037989923223	8.4620100767766
64	109.5	118.789206739553	-9.28920673955265
65	106.6	112.131688191518	-5.53168819151797
66	105.5	110.903813653349	-5.40381365334935
67	103.9	99.9932470725936	3.90675292740639
68	104.9	101.747717439540	3.15228256045957
69	104.8	103.973011866593	0.826988133407127
70	99.6	102.975518176800	-3.3755181768005
71	97	100.531705543012	-3.53170554301244
72	95.4	97.9224402468721	-2.52244024687209
73	99.3	99.033411199412	0.266588800588096
74	103.9	100.911035861822	2.98896413817772
75	107.4	105.849557387799	1.55044261220125
76	107.4	103.590697163785	3.80930283621491
77	111	107.877749064313	3.12225093568661
78	113.2	113.475033976598	-0.275033976597953
79	108.5	108.250411405929	0.249588594070985
80	113.3	106.909733238539	6.39026676146052
81	113.8	111.090321123654	2.70967887634609
82	105.3	110.400689552354	-5.10068955235367
83	107.5	106.565908549835	0.934091450164686
84	109.4	107.682976115507	1.71702388449324
85	118.9	113.239230879872	5.66076912012845
86	119	120.321643898434	-1.32164389843385
87	115	121.920810426206	-6.9208104262064
88	124.1	113.289160211407	10.8108397885933
89	120.5	123.013621652757	-2.51362165275742
90	117.7	123.689352238269	-5.98935223826882
91	117.1	113.879980463688	3.22001953631215
92	118.1	116.131534877619	1.96846512238109
93	119.6	115.980845541884	3.61915445811552
94	118.8	114.026806056171	4.77319394382938
95	124.9	119.388223994573	5.51177600542707
96	124	124.322050280934	-0.322050280933666
97	124.9	129.793813980514	-4.8938139805139
98	121.7	127.177267622756	-5.4772676227563
99	121.6	124.273599698928	-2.6735996989277
100	125.1	122.742024549008	2.35797545099160
101	127.9	122.919473485239	4.98052651476061
102	129	128.702815230009	0.297184769990992
103	130.1	125.513848834900	4.58615116510025
104	130.3	128.49109982425	1.80890017574998
105	127.9	128.429155155938	-0.529155155938128
106	124.1	123.147434118408	0.952565881591767
107	125.7	125.731156537994	-0.0311565379938656
108	129.2	125.053293887754	4.14670611224612
109	129.2	133.120574075532	-3.92057407553236
110	132.6	131.132765709815	1.46723429018539
111	131.5	134.417858232361	-2.9178582323612
112	131	133.946299047731	-2.94629904773143
113	125.8	130.482888123026	-4.68288812302639
114	127.2	127.698289009671	-0.498289009671254
115	127.3	124.844406723115	2.45559327688485
116	127.5	125.574717873833	1.92528212616745
117	122	125.134490760238	-3.13449076023811
118	118.4	118.336136079827	0.0638639201727642
119	118.3	119.935325135947	-1.635325135947
120	115.5	118.896673067673	-3.39667306767285

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	118.980330752302	110.84551129802	127.115150206585
122	121.056842234052	110.713119969415	131.400564498688
123	122.116415073612	109.897024073180	134.335806074043
124	123.771709292713	110.116558223922	137.426860361504
125	122.275186176138	107.071037540023	137.479334812253
126	124.012708175293	107.720046410486	140.305369940100
127	122.238295909037	104.89806015235	139.578531665724
128	120.986176406582	102.883255152599	139.089097660565
129	118.069763193211	99.3601554020778	136.779370984345
130	114.537611829211	94.6229844919517	134.452239166471
131	115.668772997793	94.7971668929008	136.540379102686
132	115.5	NA	NA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 118.980330752302 & 110.84551129802 & 127.115150206585 \tabularnewline
122 & 121.056842234052 & 110.713119969415 & 131.400564498688 \tabularnewline
123 & 122.116415073612 & 109.897024073180 & 134.335806074043 \tabularnewline
124 & 123.771709292713 & 110.116558223922 & 137.426860361504 \tabularnewline
125 & 122.275186176138 & 107.071037540023 & 137.479334812253 \tabularnewline
126 & 124.012708175293 & 107.720046410486 & 140.305369940100 \tabularnewline
127 & 122.238295909037 & 104.89806015235 & 139.578531665724 \tabularnewline
128 & 120.986176406582 & 102.883255152599 & 139.089097660565 \tabularnewline
129 & 118.069763193211 & 99.3601554020778 & 136.779370984345 \tabularnewline
130 & 114.537611829211 & 94.6229844919517 & 134.452239166471 \tabularnewline
131 & 115.668772997793 & 94.7971668929008 & 136.540379102686 \tabularnewline
132 & 115.5 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113967&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]121[/C][C]118.980330752302[/C][C]110.84551129802[/C][C]127.115150206585[/C][/ROW]
[ROW][C]122[/C][C]121.056842234052[/C][C]110.713119969415[/C][C]131.400564498688[/C][/ROW]
[ROW][C]123[/C][C]122.116415073612[/C][C]109.897024073180[/C][C]134.335806074043[/C][/ROW]
[ROW][C]124[/C][C]123.771709292713[/C][C]110.116558223922[/C][C]137.426860361504[/C][/ROW]
[ROW][C]125[/C][C]122.275186176138[/C][C]107.071037540023[/C][C]137.479334812253[/C][/ROW]
[ROW][C]126[/C][C]124.012708175293[/C][C]107.720046410486[/C][C]140.305369940100[/C][/ROW]
[ROW][C]127[/C][C]122.238295909037[/C][C]104.89806015235[/C][C]139.578531665724[/C][/ROW]
[ROW][C]128[/C][C]120.986176406582[/C][C]102.883255152599[/C][C]139.089097660565[/C][/ROW]
[ROW][C]129[/C][C]118.069763193211[/C][C]99.3601554020778[/C][C]136.779370984345[/C][/ROW]
[ROW][C]130[/C][C]114.537611829211[/C][C]94.6229844919517[/C][C]134.452239166471[/C][/ROW]
[ROW][C]131[/C][C]115.668772997793[/C][C]94.7971668929008[/C][C]136.540379102686[/C][/ROW]
[ROW][C]132[/C][C]115.5[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113967&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113967&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
121	118.980330752302	110.84551129802	127.115150206585
122	121.056842234052	110.713119969415	131.400564498688
123	122.116415073612	109.897024073180	134.335806074043
124	123.771709292713	110.116558223922	137.426860361504
125	122.275186176138	107.071037540023	137.479334812253
126	124.012708175293	107.720046410486	140.305369940100
127	122.238295909037	104.89806015235	139.578531665724
128	120.986176406582	102.883255152599	139.089097660565
129	118.069763193211	99.3601554020778	136.779370984345
130	114.537611829211	94.6229844919517	134.452239166471
131	115.668772997793	94.7971668929008	136.540379102686
132	115.5	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=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