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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 26 Jan 2009 14:26:35 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jan/26/t1233005240sj05g0f4uaequ1g.htm/, Retrieved Sun, 05 May 2024 15:14:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36979, Retrieved Sun, 05 May 2024 15:14:34 +0000

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No (this computation is public)

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Estimated Impact

204

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

-       [Exponential Smoothing] [tijdreeks - evolu...] [2009-01-26 21:26:35] [d41d8cd98f00b204e9800998ecf8427e] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36979&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36979&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36979&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.425593260268888
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.425593260268888 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36979&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.425593260268888[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36979&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36979&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.425593260268888
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	314.1	295.5	18.6000000000000
4	333.2	332.816034641001	0.383965358998637
5	315.1	352.079447709968	-36.9794477099678
6	321	318.24124399614	2.75875600386019
7	310.9	325.315351958109	-14.4153519581091
8	289	309.080275320334	-20.0802753203339
9	259.3	278.634245479656	-19.3342454796561
10	244.7	240.705720911130	3.99427908886972
11	215.9	227.805659170986	-11.9056591709862
12	215.3	193.938690868756	21.361309131244
13	211.4	202.429920065534	8.9700799344663
14	184.6	202.347525629716	-17.7475256297157
15	177.7	167.994298335259	9.70570166474062
16	184.8	165.224979549954	19.5750204500465
17	172.3	180.655976323119	-8.35597632311897
18	169.6	164.599729117033	5.00027088296687
19	180.3	164.027810704343	16.2721892956574
20	180.9	181.653144798394	-0.753144798393919
21	175.8	181.932611448191	-6.13261144819089
22	175	174.222613347993	0.777386652006953
23	170.4	173.753463867710	-3.35346386771019
24	159.3	167.726252247058	-8.4262522470575
25	139.9	153.040096081384	-13.1400960813843
26	134.5	128.047759749861	6.45224025013852
27	143	125.393789713956	17.6062102860439
28	137.3	141.386874150573	-4.08687415057312
29	140.3	133.947528056522	6.35247194347792
30	131.3	139.651097301713	-8.35109730171348
31	127.8	127.096926574255	0.703073425745458
32	126.5	123.896149885726	2.60385011427405
33	119.2	123.704330945111	-4.50433094511136
34	116	114.487318052851	1.51268194714862
35	110.8	111.931105294488	-1.13110529448825
36	115.4	106.249714504500	9.15028549550041
37	115.1	114.744014340921	0.355985659079252
38	114.1	114.595519438177	-0.49551943817724
39	119.1	113.384629704957	5.71537029504321
40	114	120.817052782468	-6.81705278246818
41	112.1	112.815761063352	-0.71576106335246
42	111.2	110.611137978827	0.588862021173256
43	116	109.961753686266	6.0382463137336
44	109.5	117.331590621235	-7.83159062123488
45	109.5	107.498518435652	2.00148156434771
46	110.2	108.350335499991	1.8496645000089
47	108.8	109.837540244954	-1.03754024495352
48	108.2	107.995970109444	0.204029890556441
49	111.4	107.482803855758	3.91719614424221
50	110.8	112.349936133899	-1.54993613389856
51	117.2	111.090293761464	6.10970623853591
52	130.7	120.090543558808	10.6094564411922
53	137.4	138.105856715295	-0.705856715295482
54	141.4	144.505448854550	-3.10544885455022
55	137.1	147.183790751944	-10.0837907519439
56	129.8	138.592197369955	-8.7921973699548
57	127.3	127.550297426348	-0.25029742634824
58	121.7	124.943772528632	-3.24377252863177
59	117.6	117.963244802601	-0.363244802600732
60	111.2	113.708650262786	-2.50865026278613
61	113	106.240985618573	6.7590143814274
62	111.1	110.917576585369	0.182423414631415
63	103.7	109.095214761151	-5.39521476115094
64	110.8	99.3990477211019	11.4009522788981
65	115.3	111.351216171648	3.94878382835186
66	111.4	117.531791955253	-6.13179195525346
67	112.5	111.022142625727	1.47785737427338
68	115.5	112.751108763856	2.74889123614396
69	114.9	116.921018347171	-2.02101834717111
70	119.9	115.460886559735	4.43911344026468
71	125.6	122.350143321481	3.24985667851898
72	131.8	129.433260420699	2.36673957930151
73	134.2	136.640528834461	-2.44052883446088
74	124.5	138.001856211022	-13.5018562110224
75	114.4	122.555557206492	-8.15555720649166
76	103.8	108.984607025671	-5.18460702567147
77	98.5	96.178073218403	2.32192678159704
78	97	91.8662696074885	5.13373039251151
79	98.1	92.551150662579	5.54884933742106
80	99	96.0127035428328	2.98729645716718
81	99.7	98.1840767814283	1.5159232185717
82	98.6	99.5292434863375	-0.92924348633754
83	97.4	98.0337637214035	-0.633763721403497
84	97.8	96.5640381529713	1.23596184702873
85	100.3	97.4900551850162	2.80994481498382
86	101.2	101.185948760001	0.0140512399992048
87	100.7	102.091928873043	-1.39192887304289
88	96.3	100.999533325902	-4.69953332590217
89	98.4	94.5994436159892	3.80055638401085
90	99.5	98.316934798296	1.18306520170391
91	101.4	99.9204393746	1.47956062540008
92	101.1	102.450130404929	-1.35013040492943
93	104.7	101.575524004107	3.12447599589267
94	102.3	106.505279929831	-4.20527992983119
95	100.8	102.315541134151	-1.51554113415101
96	98.5	100.170537041796	-1.67053704179607

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 314.1 & 295.5 & 18.6000000000000 \tabularnewline
4 & 333.2 & 332.816034641001 & 0.383965358998637 \tabularnewline
5 & 315.1 & 352.079447709968 & -36.9794477099678 \tabularnewline
6 & 321 & 318.24124399614 & 2.75875600386019 \tabularnewline
7 & 310.9 & 325.315351958109 & -14.4153519581091 \tabularnewline
8 & 289 & 309.080275320334 & -20.0802753203339 \tabularnewline
9 & 259.3 & 278.634245479656 & -19.3342454796561 \tabularnewline
10 & 244.7 & 240.705720911130 & 3.99427908886972 \tabularnewline
11 & 215.9 & 227.805659170986 & -11.9056591709862 \tabularnewline
12 & 215.3 & 193.938690868756 & 21.361309131244 \tabularnewline
13 & 211.4 & 202.429920065534 & 8.9700799344663 \tabularnewline
14 & 184.6 & 202.347525629716 & -17.7475256297157 \tabularnewline
15 & 177.7 & 167.994298335259 & 9.70570166474062 \tabularnewline
16 & 184.8 & 165.224979549954 & 19.5750204500465 \tabularnewline
17 & 172.3 & 180.655976323119 & -8.35597632311897 \tabularnewline
18 & 169.6 & 164.599729117033 & 5.00027088296687 \tabularnewline
19 & 180.3 & 164.027810704343 & 16.2721892956574 \tabularnewline
20 & 180.9 & 181.653144798394 & -0.753144798393919 \tabularnewline
21 & 175.8 & 181.932611448191 & -6.13261144819089 \tabularnewline
22 & 175 & 174.222613347993 & 0.777386652006953 \tabularnewline
23 & 170.4 & 173.753463867710 & -3.35346386771019 \tabularnewline
24 & 159.3 & 167.726252247058 & -8.4262522470575 \tabularnewline
25 & 139.9 & 153.040096081384 & -13.1400960813843 \tabularnewline
26 & 134.5 & 128.047759749861 & 6.45224025013852 \tabularnewline
27 & 143 & 125.393789713956 & 17.6062102860439 \tabularnewline
28 & 137.3 & 141.386874150573 & -4.08687415057312 \tabularnewline
29 & 140.3 & 133.947528056522 & 6.35247194347792 \tabularnewline
30 & 131.3 & 139.651097301713 & -8.35109730171348 \tabularnewline
31 & 127.8 & 127.096926574255 & 0.703073425745458 \tabularnewline
32 & 126.5 & 123.896149885726 & 2.60385011427405 \tabularnewline
33 & 119.2 & 123.704330945111 & -4.50433094511136 \tabularnewline
34 & 116 & 114.487318052851 & 1.51268194714862 \tabularnewline
35 & 110.8 & 111.931105294488 & -1.13110529448825 \tabularnewline
36 & 115.4 & 106.249714504500 & 9.15028549550041 \tabularnewline
37 & 115.1 & 114.744014340921 & 0.355985659079252 \tabularnewline
38 & 114.1 & 114.595519438177 & -0.49551943817724 \tabularnewline
39 & 119.1 & 113.384629704957 & 5.71537029504321 \tabularnewline
40 & 114 & 120.817052782468 & -6.81705278246818 \tabularnewline
41 & 112.1 & 112.815761063352 & -0.71576106335246 \tabularnewline
42 & 111.2 & 110.611137978827 & 0.588862021173256 \tabularnewline
43 & 116 & 109.961753686266 & 6.0382463137336 \tabularnewline
44 & 109.5 & 117.331590621235 & -7.83159062123488 \tabularnewline
45 & 109.5 & 107.498518435652 & 2.00148156434771 \tabularnewline
46 & 110.2 & 108.350335499991 & 1.8496645000089 \tabularnewline
47 & 108.8 & 109.837540244954 & -1.03754024495352 \tabularnewline
48 & 108.2 & 107.995970109444 & 0.204029890556441 \tabularnewline
49 & 111.4 & 107.482803855758 & 3.91719614424221 \tabularnewline
50 & 110.8 & 112.349936133899 & -1.54993613389856 \tabularnewline
51 & 117.2 & 111.090293761464 & 6.10970623853591 \tabularnewline
52 & 130.7 & 120.090543558808 & 10.6094564411922 \tabularnewline
53 & 137.4 & 138.105856715295 & -0.705856715295482 \tabularnewline
54 & 141.4 & 144.505448854550 & -3.10544885455022 \tabularnewline
55 & 137.1 & 147.183790751944 & -10.0837907519439 \tabularnewline
56 & 129.8 & 138.592197369955 & -8.7921973699548 \tabularnewline
57 & 127.3 & 127.550297426348 & -0.25029742634824 \tabularnewline
58 & 121.7 & 124.943772528632 & -3.24377252863177 \tabularnewline
59 & 117.6 & 117.963244802601 & -0.363244802600732 \tabularnewline
60 & 111.2 & 113.708650262786 & -2.50865026278613 \tabularnewline
61 & 113 & 106.240985618573 & 6.7590143814274 \tabularnewline
62 & 111.1 & 110.917576585369 & 0.182423414631415 \tabularnewline
63 & 103.7 & 109.095214761151 & -5.39521476115094 \tabularnewline
64 & 110.8 & 99.3990477211019 & 11.4009522788981 \tabularnewline
65 & 115.3 & 111.351216171648 & 3.94878382835186 \tabularnewline
66 & 111.4 & 117.531791955253 & -6.13179195525346 \tabularnewline
67 & 112.5 & 111.022142625727 & 1.47785737427338 \tabularnewline
68 & 115.5 & 112.751108763856 & 2.74889123614396 \tabularnewline
69 & 114.9 & 116.921018347171 & -2.02101834717111 \tabularnewline
70 & 119.9 & 115.460886559735 & 4.43911344026468 \tabularnewline
71 & 125.6 & 122.350143321481 & 3.24985667851898 \tabularnewline
72 & 131.8 & 129.433260420699 & 2.36673957930151 \tabularnewline
73 & 134.2 & 136.640528834461 & -2.44052883446088 \tabularnewline
74 & 124.5 & 138.001856211022 & -13.5018562110224 \tabularnewline
75 & 114.4 & 122.555557206492 & -8.15555720649166 \tabularnewline
76 & 103.8 & 108.984607025671 & -5.18460702567147 \tabularnewline
77 & 98.5 & 96.178073218403 & 2.32192678159704 \tabularnewline
78 & 97 & 91.8662696074885 & 5.13373039251151 \tabularnewline
79 & 98.1 & 92.551150662579 & 5.54884933742106 \tabularnewline
80 & 99 & 96.0127035428328 & 2.98729645716718 \tabularnewline
81 & 99.7 & 98.1840767814283 & 1.5159232185717 \tabularnewline
82 & 98.6 & 99.5292434863375 & -0.92924348633754 \tabularnewline
83 & 97.4 & 98.0337637214035 & -0.633763721403497 \tabularnewline
84 & 97.8 & 96.5640381529713 & 1.23596184702873 \tabularnewline
85 & 100.3 & 97.4900551850162 & 2.80994481498382 \tabularnewline
86 & 101.2 & 101.185948760001 & 0.0140512399992048 \tabularnewline
87 & 100.7 & 102.091928873043 & -1.39192887304289 \tabularnewline
88 & 96.3 & 100.999533325902 & -4.69953332590217 \tabularnewline
89 & 98.4 & 94.5994436159892 & 3.80055638401085 \tabularnewline
90 & 99.5 & 98.316934798296 & 1.18306520170391 \tabularnewline
91 & 101.4 & 99.9204393746 & 1.47956062540008 \tabularnewline
92 & 101.1 & 102.450130404929 & -1.35013040492943 \tabularnewline
93 & 104.7 & 101.575524004107 & 3.12447599589267 \tabularnewline
94 & 102.3 & 106.505279929831 & -4.20527992983119 \tabularnewline
95 & 100.8 & 102.315541134151 & -1.51554113415101 \tabularnewline
96 & 98.5 & 100.170537041796 & -1.67053704179607 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36979&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]3[/C][C]314.1[/C][C]295.5[/C][C]18.6000000000000[/C][/ROW]
[ROW][C]4[/C][C]333.2[/C][C]332.816034641001[/C][C]0.383965358998637[/C][/ROW]
[ROW][C]5[/C][C]315.1[/C][C]352.079447709968[/C][C]-36.9794477099678[/C][/ROW]
[ROW][C]6[/C][C]321[/C][C]318.24124399614[/C][C]2.75875600386019[/C][/ROW]
[ROW][C]7[/C][C]310.9[/C][C]325.315351958109[/C][C]-14.4153519581091[/C][/ROW]
[ROW][C]8[/C][C]289[/C][C]309.080275320334[/C][C]-20.0802753203339[/C][/ROW]
[ROW][C]9[/C][C]259.3[/C][C]278.634245479656[/C][C]-19.3342454796561[/C][/ROW]
[ROW][C]10[/C][C]244.7[/C][C]240.705720911130[/C][C]3.99427908886972[/C][/ROW]
[ROW][C]11[/C][C]215.9[/C][C]227.805659170986[/C][C]-11.9056591709862[/C][/ROW]
[ROW][C]12[/C][C]215.3[/C][C]193.938690868756[/C][C]21.361309131244[/C][/ROW]
[ROW][C]13[/C][C]211.4[/C][C]202.429920065534[/C][C]8.9700799344663[/C][/ROW]
[ROW][C]14[/C][C]184.6[/C][C]202.347525629716[/C][C]-17.7475256297157[/C][/ROW]
[ROW][C]15[/C][C]177.7[/C][C]167.994298335259[/C][C]9.70570166474062[/C][/ROW]
[ROW][C]16[/C][C]184.8[/C][C]165.224979549954[/C][C]19.5750204500465[/C][/ROW]
[ROW][C]17[/C][C]172.3[/C][C]180.655976323119[/C][C]-8.35597632311897[/C][/ROW]
[ROW][C]18[/C][C]169.6[/C][C]164.599729117033[/C][C]5.00027088296687[/C][/ROW]
[ROW][C]19[/C][C]180.3[/C][C]164.027810704343[/C][C]16.2721892956574[/C][/ROW]
[ROW][C]20[/C][C]180.9[/C][C]181.653144798394[/C][C]-0.753144798393919[/C][/ROW]
[ROW][C]21[/C][C]175.8[/C][C]181.932611448191[/C][C]-6.13261144819089[/C][/ROW]
[ROW][C]22[/C][C]175[/C][C]174.222613347993[/C][C]0.777386652006953[/C][/ROW]
[ROW][C]23[/C][C]170.4[/C][C]173.753463867710[/C][C]-3.35346386771019[/C][/ROW]
[ROW][C]24[/C][C]159.3[/C][C]167.726252247058[/C][C]-8.4262522470575[/C][/ROW]
[ROW][C]25[/C][C]139.9[/C][C]153.040096081384[/C][C]-13.1400960813843[/C][/ROW]
[ROW][C]26[/C][C]134.5[/C][C]128.047759749861[/C][C]6.45224025013852[/C][/ROW]
[ROW][C]27[/C][C]143[/C][C]125.393789713956[/C][C]17.6062102860439[/C][/ROW]
[ROW][C]28[/C][C]137.3[/C][C]141.386874150573[/C][C]-4.08687415057312[/C][/ROW]
[ROW][C]29[/C][C]140.3[/C][C]133.947528056522[/C][C]6.35247194347792[/C][/ROW]
[ROW][C]30[/C][C]131.3[/C][C]139.651097301713[/C][C]-8.35109730171348[/C][/ROW]
[ROW][C]31[/C][C]127.8[/C][C]127.096926574255[/C][C]0.703073425745458[/C][/ROW]
[ROW][C]32[/C][C]126.5[/C][C]123.896149885726[/C][C]2.60385011427405[/C][/ROW]
[ROW][C]33[/C][C]119.2[/C][C]123.704330945111[/C][C]-4.50433094511136[/C][/ROW]
[ROW][C]34[/C][C]116[/C][C]114.487318052851[/C][C]1.51268194714862[/C][/ROW]
[ROW][C]35[/C][C]110.8[/C][C]111.931105294488[/C][C]-1.13110529448825[/C][/ROW]
[ROW][C]36[/C][C]115.4[/C][C]106.249714504500[/C][C]9.15028549550041[/C][/ROW]
[ROW][C]37[/C][C]115.1[/C][C]114.744014340921[/C][C]0.355985659079252[/C][/ROW]
[ROW][C]38[/C][C]114.1[/C][C]114.595519438177[/C][C]-0.49551943817724[/C][/ROW]
[ROW][C]39[/C][C]119.1[/C][C]113.384629704957[/C][C]5.71537029504321[/C][/ROW]
[ROW][C]40[/C][C]114[/C][C]120.817052782468[/C][C]-6.81705278246818[/C][/ROW]
[ROW][C]41[/C][C]112.1[/C][C]112.815761063352[/C][C]-0.71576106335246[/C][/ROW]
[ROW][C]42[/C][C]111.2[/C][C]110.611137978827[/C][C]0.588862021173256[/C][/ROW]
[ROW][C]43[/C][C]116[/C][C]109.961753686266[/C][C]6.0382463137336[/C][/ROW]
[ROW][C]44[/C][C]109.5[/C][C]117.331590621235[/C][C]-7.83159062123488[/C][/ROW]
[ROW][C]45[/C][C]109.5[/C][C]107.498518435652[/C][C]2.00148156434771[/C][/ROW]
[ROW][C]46[/C][C]110.2[/C][C]108.350335499991[/C][C]1.8496645000089[/C][/ROW]
[ROW][C]47[/C][C]108.8[/C][C]109.837540244954[/C][C]-1.03754024495352[/C][/ROW]
[ROW][C]48[/C][C]108.2[/C][C]107.995970109444[/C][C]0.204029890556441[/C][/ROW]
[ROW][C]49[/C][C]111.4[/C][C]107.482803855758[/C][C]3.91719614424221[/C][/ROW]
[ROW][C]50[/C][C]110.8[/C][C]112.349936133899[/C][C]-1.54993613389856[/C][/ROW]
[ROW][C]51[/C][C]117.2[/C][C]111.090293761464[/C][C]6.10970623853591[/C][/ROW]
[ROW][C]52[/C][C]130.7[/C][C]120.090543558808[/C][C]10.6094564411922[/C][/ROW]
[ROW][C]53[/C][C]137.4[/C][C]138.105856715295[/C][C]-0.705856715295482[/C][/ROW]
[ROW][C]54[/C][C]141.4[/C][C]144.505448854550[/C][C]-3.10544885455022[/C][/ROW]
[ROW][C]55[/C][C]137.1[/C][C]147.183790751944[/C][C]-10.0837907519439[/C][/ROW]
[ROW][C]56[/C][C]129.8[/C][C]138.592197369955[/C][C]-8.7921973699548[/C][/ROW]
[ROW][C]57[/C][C]127.3[/C][C]127.550297426348[/C][C]-0.25029742634824[/C][/ROW]
[ROW][C]58[/C][C]121.7[/C][C]124.943772528632[/C][C]-3.24377252863177[/C][/ROW]
[ROW][C]59[/C][C]117.6[/C][C]117.963244802601[/C][C]-0.363244802600732[/C][/ROW]
[ROW][C]60[/C][C]111.2[/C][C]113.708650262786[/C][C]-2.50865026278613[/C][/ROW]
[ROW][C]61[/C][C]113[/C][C]106.240985618573[/C][C]6.7590143814274[/C][/ROW]
[ROW][C]62[/C][C]111.1[/C][C]110.917576585369[/C][C]0.182423414631415[/C][/ROW]
[ROW][C]63[/C][C]103.7[/C][C]109.095214761151[/C][C]-5.39521476115094[/C][/ROW]
[ROW][C]64[/C][C]110.8[/C][C]99.3990477211019[/C][C]11.4009522788981[/C][/ROW]
[ROW][C]65[/C][C]115.3[/C][C]111.351216171648[/C][C]3.94878382835186[/C][/ROW]
[ROW][C]66[/C][C]111.4[/C][C]117.531791955253[/C][C]-6.13179195525346[/C][/ROW]
[ROW][C]67[/C][C]112.5[/C][C]111.022142625727[/C][C]1.47785737427338[/C][/ROW]
[ROW][C]68[/C][C]115.5[/C][C]112.751108763856[/C][C]2.74889123614396[/C][/ROW]
[ROW][C]69[/C][C]114.9[/C][C]116.921018347171[/C][C]-2.02101834717111[/C][/ROW]
[ROW][C]70[/C][C]119.9[/C][C]115.460886559735[/C][C]4.43911344026468[/C][/ROW]
[ROW][C]71[/C][C]125.6[/C][C]122.350143321481[/C][C]3.24985667851898[/C][/ROW]
[ROW][C]72[/C][C]131.8[/C][C]129.433260420699[/C][C]2.36673957930151[/C][/ROW]
[ROW][C]73[/C][C]134.2[/C][C]136.640528834461[/C][C]-2.44052883446088[/C][/ROW]
[ROW][C]74[/C][C]124.5[/C][C]138.001856211022[/C][C]-13.5018562110224[/C][/ROW]
[ROW][C]75[/C][C]114.4[/C][C]122.555557206492[/C][C]-8.15555720649166[/C][/ROW]
[ROW][C]76[/C][C]103.8[/C][C]108.984607025671[/C][C]-5.18460702567147[/C][/ROW]
[ROW][C]77[/C][C]98.5[/C][C]96.178073218403[/C][C]2.32192678159704[/C][/ROW]
[ROW][C]78[/C][C]97[/C][C]91.8662696074885[/C][C]5.13373039251151[/C][/ROW]
[ROW][C]79[/C][C]98.1[/C][C]92.551150662579[/C][C]5.54884933742106[/C][/ROW]
[ROW][C]80[/C][C]99[/C][C]96.0127035428328[/C][C]2.98729645716718[/C][/ROW]
[ROW][C]81[/C][C]99.7[/C][C]98.1840767814283[/C][C]1.5159232185717[/C][/ROW]
[ROW][C]82[/C][C]98.6[/C][C]99.5292434863375[/C][C]-0.92924348633754[/C][/ROW]
[ROW][C]83[/C][C]97.4[/C][C]98.0337637214035[/C][C]-0.633763721403497[/C][/ROW]
[ROW][C]84[/C][C]97.8[/C][C]96.5640381529713[/C][C]1.23596184702873[/C][/ROW]
[ROW][C]85[/C][C]100.3[/C][C]97.4900551850162[/C][C]2.80994481498382[/C][/ROW]
[ROW][C]86[/C][C]101.2[/C][C]101.185948760001[/C][C]0.0140512399992048[/C][/ROW]
[ROW][C]87[/C][C]100.7[/C][C]102.091928873043[/C][C]-1.39192887304289[/C][/ROW]
[ROW][C]88[/C][C]96.3[/C][C]100.999533325902[/C][C]-4.69953332590217[/C][/ROW]
[ROW][C]89[/C][C]98.4[/C][C]94.5994436159892[/C][C]3.80055638401085[/C][/ROW]
[ROW][C]90[/C][C]99.5[/C][C]98.316934798296[/C][C]1.18306520170391[/C][/ROW]
[ROW][C]91[/C][C]101.4[/C][C]99.9204393746[/C][C]1.47956062540008[/C][/ROW]
[ROW][C]92[/C][C]101.1[/C][C]102.450130404929[/C][C]-1.35013040492943[/C][/ROW]
[ROW][C]93[/C][C]104.7[/C][C]101.575524004107[/C][C]3.12447599589267[/C][/ROW]
[ROW][C]94[/C][C]102.3[/C][C]106.505279929831[/C][C]-4.20527992983119[/C][/ROW]
[ROW][C]95[/C][C]100.8[/C][C]102.315541134151[/C][C]-1.51554113415101[/C][/ROW]
[ROW][C]96[/C][C]98.5[/C][C]100.170537041796[/C][C]-1.67053704179607[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36979&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36979&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
3	314.1	295.5	18.6000000000000
4	333.2	332.816034641001	0.383965358998637
5	315.1	352.079447709968	-36.9794477099678
6	321	318.24124399614	2.75875600386019
7	310.9	325.315351958109	-14.4153519581091
8	289	309.080275320334	-20.0802753203339
9	259.3	278.634245479656	-19.3342454796561
10	244.7	240.705720911130	3.99427908886972
11	215.9	227.805659170986	-11.9056591709862
12	215.3	193.938690868756	21.361309131244
13	211.4	202.429920065534	8.9700799344663
14	184.6	202.347525629716	-17.7475256297157
15	177.7	167.994298335259	9.70570166474062
16	184.8	165.224979549954	19.5750204500465
17	172.3	180.655976323119	-8.35597632311897
18	169.6	164.599729117033	5.00027088296687
19	180.3	164.027810704343	16.2721892956574
20	180.9	181.653144798394	-0.753144798393919
21	175.8	181.932611448191	-6.13261144819089
22	175	174.222613347993	0.777386652006953
23	170.4	173.753463867710	-3.35346386771019
24	159.3	167.726252247058	-8.4262522470575
25	139.9	153.040096081384	-13.1400960813843
26	134.5	128.047759749861	6.45224025013852
27	143	125.393789713956	17.6062102860439
28	137.3	141.386874150573	-4.08687415057312
29	140.3	133.947528056522	6.35247194347792
30	131.3	139.651097301713	-8.35109730171348
31	127.8	127.096926574255	0.703073425745458
32	126.5	123.896149885726	2.60385011427405
33	119.2	123.704330945111	-4.50433094511136
34	116	114.487318052851	1.51268194714862
35	110.8	111.931105294488	-1.13110529448825
36	115.4	106.249714504500	9.15028549550041
37	115.1	114.744014340921	0.355985659079252
38	114.1	114.595519438177	-0.49551943817724
39	119.1	113.384629704957	5.71537029504321
40	114	120.817052782468	-6.81705278246818
41	112.1	112.815761063352	-0.71576106335246
42	111.2	110.611137978827	0.588862021173256
43	116	109.961753686266	6.0382463137336
44	109.5	117.331590621235	-7.83159062123488
45	109.5	107.498518435652	2.00148156434771
46	110.2	108.350335499991	1.8496645000089
47	108.8	109.837540244954	-1.03754024495352
48	108.2	107.995970109444	0.204029890556441
49	111.4	107.482803855758	3.91719614424221
50	110.8	112.349936133899	-1.54993613389856
51	117.2	111.090293761464	6.10970623853591
52	130.7	120.090543558808	10.6094564411922
53	137.4	138.105856715295	-0.705856715295482
54	141.4	144.505448854550	-3.10544885455022
55	137.1	147.183790751944	-10.0837907519439
56	129.8	138.592197369955	-8.7921973699548
57	127.3	127.550297426348	-0.25029742634824
58	121.7	124.943772528632	-3.24377252863177
59	117.6	117.963244802601	-0.363244802600732
60	111.2	113.708650262786	-2.50865026278613
61	113	106.240985618573	6.7590143814274
62	111.1	110.917576585369	0.182423414631415
63	103.7	109.095214761151	-5.39521476115094
64	110.8	99.3990477211019	11.4009522788981
65	115.3	111.351216171648	3.94878382835186
66	111.4	117.531791955253	-6.13179195525346
67	112.5	111.022142625727	1.47785737427338
68	115.5	112.751108763856	2.74889123614396
69	114.9	116.921018347171	-2.02101834717111
70	119.9	115.460886559735	4.43911344026468
71	125.6	122.350143321481	3.24985667851898
72	131.8	129.433260420699	2.36673957930151
73	134.2	136.640528834461	-2.44052883446088
74	124.5	138.001856211022	-13.5018562110224
75	114.4	122.555557206492	-8.15555720649166
76	103.8	108.984607025671	-5.18460702567147
77	98.5	96.178073218403	2.32192678159704
78	97	91.8662696074885	5.13373039251151
79	98.1	92.551150662579	5.54884933742106
80	99	96.0127035428328	2.98729645716718
81	99.7	98.1840767814283	1.5159232185717
82	98.6	99.5292434863375	-0.92924348633754
83	97.4	98.0337637214035	-0.633763721403497
84	97.8	96.5640381529713	1.23596184702873
85	100.3	97.4900551850162	2.80994481498382
86	101.2	101.185948760001	0.0140512399992048
87	100.7	102.091928873043	-1.39192887304289
88	96.3	100.999533325902	-4.69953332590217
89	98.4	94.5994436159892	3.80055638401085
90	99.5	98.316934798296	1.18306520170391
91	101.4	99.9204393746	1.47956062540008
92	101.1	102.450130404929	-1.35013040492943
93	104.7	101.575524004107	3.12447599589267
94	102.3	106.505279929831	-4.20527992983119
95	100.8	102.315541134151	-1.51554113415101
96	98.5	100.170537041796	-1.67053704179607

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	97.1595677357781	80.4723783283844	113.846757143172
98	95.8191354715563	66.7608199947369	124.877450948376
99	94.4787032073344	52.0682591689816	136.889147245687
100	93.1382709431126	36.1986711439238	150.077870742301
101	91.7978386788907	19.1639758939002	164.431701463881
102	90.4574064146688	1.01356204125629	179.901250788081
103	89.116974150447	-18.1982781877222	196.432226488616
104	87.7765418862251	-38.4202878157595	213.973371588210
105	86.4361096220033	-59.6060286909149	232.478247934921
106	85.0956773577814	-81.7139084949872	251.90526321055
107	83.7552450935596	-104.706715721756	272.217205908875
108	82.4148128293377	-128.551061018514	293.380686677189

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 97.1595677357781 & 80.4723783283844 & 113.846757143172 \tabularnewline
98 & 95.8191354715563 & 66.7608199947369 & 124.877450948376 \tabularnewline
99 & 94.4787032073344 & 52.0682591689816 & 136.889147245687 \tabularnewline
100 & 93.1382709431126 & 36.1986711439238 & 150.077870742301 \tabularnewline
101 & 91.7978386788907 & 19.1639758939002 & 164.431701463881 \tabularnewline
102 & 90.4574064146688 & 1.01356204125629 & 179.901250788081 \tabularnewline
103 & 89.116974150447 & -18.1982781877222 & 196.432226488616 \tabularnewline
104 & 87.7765418862251 & -38.4202878157595 & 213.973371588210 \tabularnewline
105 & 86.4361096220033 & -59.6060286909149 & 232.478247934921 \tabularnewline
106 & 85.0956773577814 & -81.7139084949872 & 251.90526321055 \tabularnewline
107 & 83.7552450935596 & -104.706715721756 & 272.217205908875 \tabularnewline
108 & 82.4148128293377 & -128.551061018514 & 293.380686677189 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36979&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]97.1595677357781[/C][C]80.4723783283844[/C][C]113.846757143172[/C][/ROW]
[ROW][C]98[/C][C]95.8191354715563[/C][C]66.7608199947369[/C][C]124.877450948376[/C][/ROW]
[ROW][C]99[/C][C]94.4787032073344[/C][C]52.0682591689816[/C][C]136.889147245687[/C][/ROW]
[ROW][C]100[/C][C]93.1382709431126[/C][C]36.1986711439238[/C][C]150.077870742301[/C][/ROW]
[ROW][C]101[/C][C]91.7978386788907[/C][C]19.1639758939002[/C][C]164.431701463881[/C][/ROW]
[ROW][C]102[/C][C]90.4574064146688[/C][C]1.01356204125629[/C][C]179.901250788081[/C][/ROW]
[ROW][C]103[/C][C]89.116974150447[/C][C]-18.1982781877222[/C][C]196.432226488616[/C][/ROW]
[ROW][C]104[/C][C]87.7765418862251[/C][C]-38.4202878157595[/C][C]213.973371588210[/C][/ROW]
[ROW][C]105[/C][C]86.4361096220033[/C][C]-59.6060286909149[/C][C]232.478247934921[/C][/ROW]
[ROW][C]106[/C][C]85.0956773577814[/C][C]-81.7139084949872[/C][C]251.90526321055[/C][/ROW]
[ROW][C]107[/C][C]83.7552450935596[/C][C]-104.706715721756[/C][C]272.217205908875[/C][/ROW]
[ROW][C]108[/C][C]82.4148128293377[/C][C]-128.551061018514[/C][C]293.380686677189[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36979&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36979&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	97.1595677357781	80.4723783283844	113.846757143172
98	95.8191354715563	66.7608199947369	124.877450948376
99	94.4787032073344	52.0682591689816	136.889147245687
100	93.1382709431126	36.1986711439238	150.077870742301
101	91.7978386788907	19.1639758939002	164.431701463881
102	90.4574064146688	1.01356204125629	179.901250788081
103	89.116974150447	-18.1982781877222	196.432226488616
104	87.7765418862251	-38.4202878157595	213.973371588210
105	86.4361096220033	-59.6060286909149	232.478247934921
106	85.0956773577814	-81.7139084949872	251.90526321055
107	83.7552450935596	-104.706715721756	272.217205908875
108	82.4148128293377	-128.551061018514	293.380686677189

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 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code