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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 21 May 2012 05:12:08 -0400

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/2012/May/21/t13375915535vv3ezuu21cuzxm.htm/, Retrieved Thu, 02 May 2024 23:47:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166891, Retrieved Thu, 02 May 2024 23:47:13 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

137

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

-     [Bootstrap Plot - Central Tendency] [Bootstrap Plot va...] [2012-05-02 19:39:36] [562ee1d5a96d07a2dc4978b28f7ac089]
- RMPD  [Blocked Bootstrap Plot - Central Tendency] [Blocked Bootstrap...] [2012-05-02 19:52:56] [562ee1d5a96d07a2dc4978b28f7ac089]
- RMPD    [Standard Deviation Plot] [Standard Deviatio...] [2012-05-02 20:02:11] [562ee1d5a96d07a2dc4978b28f7ac089]
- RMPD        [Exponential Smoothing] [] [2012-05-21 09:12:08] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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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	'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166891&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166891&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166891&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	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.130443957892895
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.130443957892895 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166891&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]0.130443957892895[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166891&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166891&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	0.130443957892895
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	32.5	32.5	0
4	34.4	33.2	1.2
5	35.5	35.2565327494715	0.243467250528525
6	35.5	36.3882915812477	-0.888291581247714
7	36.6	36.2724193116268	0.327580688373175
8	37.1	37.4151502331475	-0.315150233147499
9	37.9	37.8740407894049	0.0259592105951256
10	38.1	38.6774270115787	-0.577427011578671
11	39	38.8021051467941	0.197894853205909
12	41.5	39.7279193346929	1.7720806653071
13	41.8	42.459076550381	-0.659076550381037
14	41.9	42.6731039965949	-0.773103996594934
15	44.6	42.6722572514163	1.92774274858373
16	46.1	45.6237196453409	0.476280354659131
17	46.4	47.1858475398692	-0.785847539869238
18	47.2	47.3833384764683	-0.183338476468293
19	47.7	48.1594230799637	-0.45942307996372
20	49.2	48.5994941150659	0.600505884934094
21	49.3	50.1778264794347	-0.877826479434695
22	49.3	50.163319319114	-0.863319319114041
23	49.5	50.0507045302034	-0.550704530203404
24	50.1	50.1788684516541	-0.0788684516541238
25	51.9	50.7685805386675	1.13141946133252
26	52.6	52.7161673712407	-0.116167371240735
27	53.2	53.4010140395581	-0.201014039558082
28	53.5	53.9747929726461	-0.474792972646092
29	53.7	54.2128590981144	-0.512859098114397
30	53.7	54.345959727515	-0.645959727514978
31	53.9	54.2616981840185	-0.361698184018515
32	54.1	54.4145168413325	-0.314516841332455
33	54.8	54.5734900197251	0.226509980274912
34	55.4	55.3030368780544	0.0969631219456204
35	55.9	55.9156851314506	-0.0156851314506241
36	56.8	56.4136391008241	0.38636089917587
37	58.4	57.3640375456877	1.03596245431231
38	59.3	59.0991725884566	0.200827411543372
39	60.3	60.0253693108717	0.274630689128273
40	60.5	61.0611932249205	-0.561193224920473
41	60.8	61.1879889595192	-0.38798895951917
42	61	61.4373781440207	-0.437378144020741
43	61.1	61.5803248078188	-0.480324807818825
44	61.3	61.6176693388128	-0.317669338812799
45	61.4	61.7762312929568	-0.376231292956831
46	61.5	61.8271541940204	-0.32715419402038
47	63.9	61.8844789061111	2.01552109388889
48	63.9	64.5473914548146	-0.647391454814588
49	64	64.4629431511425	-0.462943151142539
50	64.1	64.5025550142281	-0.402555014228099
51	64.5	64.5500441449025	-0.0500441449025431
52	64.5	64.9435161885721	-0.44351618857209
53	65.9	64.8856621815452	1.01433781845482
54	66.8	66.4179764212249	0.382023578775119
55	68.7	67.3678090888487	1.3321909111513
56	69.2	69.4415853439682	-0.241585343968225
57	69.6	69.9100719955321	-0.310071995532098
58	70.2	70.2696249772031	-0.0696249772031337
59	70.6	70.8605428196086	-0.260542819608574
60	70.7	71.2265565830182	-0.526556583018234
61	70.7	71.2578704582748	-0.557870458274792
62	71	71.1850996277059	-0.185099627705895
63	72.1	71.4609544996634	0.63904550033655
64	73.7	72.644314124001	1.05568587599902
65	77.4	74.3820219679579	3.01797803204208
66	79.7	78.4756989672913	1.22430103270869
67	91.6	80.9354016396502	10.6645983603498
68	93.6	94.2265340591123	-0.626534059112288
69	94.3	96.144806476687	-1.84480647668698
70	97.3	96.6041626183215	0.695837381678515
71	101.7	99.6949304004375	2.00506959956255
72	103	104.356479614855	-1.35647961485513
73	103.1	105.479535045092	-2.3795350450924
74	104.6	105.269139075866	-0.669139075865687
75	107.2	106.681853926429	0.518146073571032
76	107.7	109.349442951032	-1.64944295103224
77	108.3	109.634283084181	-1.33428308418107
78	108.8	110.060233917731	-1.26023391773094
79	113.1	110.395844017631	2.70415598236875
80	113.8	115.048584826731	-1.24858482673118
81	113.8	115.585714480167	-1.78571448016736
82	116.5	115.352778815708	1.14722118429233
83	116.9	118.202426887565	-1.30242688756533
84	117.6	118.432533169485	-0.832533169485203

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 32.5 & 32.5 & 0 \tabularnewline
4 & 34.4 & 33.2 & 1.2 \tabularnewline
5 & 35.5 & 35.2565327494715 & 0.243467250528525 \tabularnewline
6 & 35.5 & 36.3882915812477 & -0.888291581247714 \tabularnewline
7 & 36.6 & 36.2724193116268 & 0.327580688373175 \tabularnewline
8 & 37.1 & 37.4151502331475 & -0.315150233147499 \tabularnewline
9 & 37.9 & 37.8740407894049 & 0.0259592105951256 \tabularnewline
10 & 38.1 & 38.6774270115787 & -0.577427011578671 \tabularnewline
11 & 39 & 38.8021051467941 & 0.197894853205909 \tabularnewline
12 & 41.5 & 39.7279193346929 & 1.7720806653071 \tabularnewline
13 & 41.8 & 42.459076550381 & -0.659076550381037 \tabularnewline
14 & 41.9 & 42.6731039965949 & -0.773103996594934 \tabularnewline
15 & 44.6 & 42.6722572514163 & 1.92774274858373 \tabularnewline
16 & 46.1 & 45.6237196453409 & 0.476280354659131 \tabularnewline
17 & 46.4 & 47.1858475398692 & -0.785847539869238 \tabularnewline
18 & 47.2 & 47.3833384764683 & -0.183338476468293 \tabularnewline
19 & 47.7 & 48.1594230799637 & -0.45942307996372 \tabularnewline
20 & 49.2 & 48.5994941150659 & 0.600505884934094 \tabularnewline
21 & 49.3 & 50.1778264794347 & -0.877826479434695 \tabularnewline
22 & 49.3 & 50.163319319114 & -0.863319319114041 \tabularnewline
23 & 49.5 & 50.0507045302034 & -0.550704530203404 \tabularnewline
24 & 50.1 & 50.1788684516541 & -0.0788684516541238 \tabularnewline
25 & 51.9 & 50.7685805386675 & 1.13141946133252 \tabularnewline
26 & 52.6 & 52.7161673712407 & -0.116167371240735 \tabularnewline
27 & 53.2 & 53.4010140395581 & -0.201014039558082 \tabularnewline
28 & 53.5 & 53.9747929726461 & -0.474792972646092 \tabularnewline
29 & 53.7 & 54.2128590981144 & -0.512859098114397 \tabularnewline
30 & 53.7 & 54.345959727515 & -0.645959727514978 \tabularnewline
31 & 53.9 & 54.2616981840185 & -0.361698184018515 \tabularnewline
32 & 54.1 & 54.4145168413325 & -0.314516841332455 \tabularnewline
33 & 54.8 & 54.5734900197251 & 0.226509980274912 \tabularnewline
34 & 55.4 & 55.3030368780544 & 0.0969631219456204 \tabularnewline
35 & 55.9 & 55.9156851314506 & -0.0156851314506241 \tabularnewline
36 & 56.8 & 56.4136391008241 & 0.38636089917587 \tabularnewline
37 & 58.4 & 57.3640375456877 & 1.03596245431231 \tabularnewline
38 & 59.3 & 59.0991725884566 & 0.200827411543372 \tabularnewline
39 & 60.3 & 60.0253693108717 & 0.274630689128273 \tabularnewline
40 & 60.5 & 61.0611932249205 & -0.561193224920473 \tabularnewline
41 & 60.8 & 61.1879889595192 & -0.38798895951917 \tabularnewline
42 & 61 & 61.4373781440207 & -0.437378144020741 \tabularnewline
43 & 61.1 & 61.5803248078188 & -0.480324807818825 \tabularnewline
44 & 61.3 & 61.6176693388128 & -0.317669338812799 \tabularnewline
45 & 61.4 & 61.7762312929568 & -0.376231292956831 \tabularnewline
46 & 61.5 & 61.8271541940204 & -0.32715419402038 \tabularnewline
47 & 63.9 & 61.8844789061111 & 2.01552109388889 \tabularnewline
48 & 63.9 & 64.5473914548146 & -0.647391454814588 \tabularnewline
49 & 64 & 64.4629431511425 & -0.462943151142539 \tabularnewline
50 & 64.1 & 64.5025550142281 & -0.402555014228099 \tabularnewline
51 & 64.5 & 64.5500441449025 & -0.0500441449025431 \tabularnewline
52 & 64.5 & 64.9435161885721 & -0.44351618857209 \tabularnewline
53 & 65.9 & 64.8856621815452 & 1.01433781845482 \tabularnewline
54 & 66.8 & 66.4179764212249 & 0.382023578775119 \tabularnewline
55 & 68.7 & 67.3678090888487 & 1.3321909111513 \tabularnewline
56 & 69.2 & 69.4415853439682 & -0.241585343968225 \tabularnewline
57 & 69.6 & 69.9100719955321 & -0.310071995532098 \tabularnewline
58 & 70.2 & 70.2696249772031 & -0.0696249772031337 \tabularnewline
59 & 70.6 & 70.8605428196086 & -0.260542819608574 \tabularnewline
60 & 70.7 & 71.2265565830182 & -0.526556583018234 \tabularnewline
61 & 70.7 & 71.2578704582748 & -0.557870458274792 \tabularnewline
62 & 71 & 71.1850996277059 & -0.185099627705895 \tabularnewline
63 & 72.1 & 71.4609544996634 & 0.63904550033655 \tabularnewline
64 & 73.7 & 72.644314124001 & 1.05568587599902 \tabularnewline
65 & 77.4 & 74.3820219679579 & 3.01797803204208 \tabularnewline
66 & 79.7 & 78.4756989672913 & 1.22430103270869 \tabularnewline
67 & 91.6 & 80.9354016396502 & 10.6645983603498 \tabularnewline
68 & 93.6 & 94.2265340591123 & -0.626534059112288 \tabularnewline
69 & 94.3 & 96.144806476687 & -1.84480647668698 \tabularnewline
70 & 97.3 & 96.6041626183215 & 0.695837381678515 \tabularnewline
71 & 101.7 & 99.6949304004375 & 2.00506959956255 \tabularnewline
72 & 103 & 104.356479614855 & -1.35647961485513 \tabularnewline
73 & 103.1 & 105.479535045092 & -2.3795350450924 \tabularnewline
74 & 104.6 & 105.269139075866 & -0.669139075865687 \tabularnewline
75 & 107.2 & 106.681853926429 & 0.518146073571032 \tabularnewline
76 & 107.7 & 109.349442951032 & -1.64944295103224 \tabularnewline
77 & 108.3 & 109.634283084181 & -1.33428308418107 \tabularnewline
78 & 108.8 & 110.060233917731 & -1.26023391773094 \tabularnewline
79 & 113.1 & 110.395844017631 & 2.70415598236875 \tabularnewline
80 & 113.8 & 115.048584826731 & -1.24858482673118 \tabularnewline
81 & 113.8 & 115.585714480167 & -1.78571448016736 \tabularnewline
82 & 116.5 & 115.352778815708 & 1.14722118429233 \tabularnewline
83 & 116.9 & 118.202426887565 & -1.30242688756533 \tabularnewline
84 & 117.6 & 118.432533169485 & -0.832533169485203 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166891&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]32.5[/C][C]32.5[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]34.4[/C][C]33.2[/C][C]1.2[/C][/ROW]
[ROW][C]5[/C][C]35.5[/C][C]35.2565327494715[/C][C]0.243467250528525[/C][/ROW]
[ROW][C]6[/C][C]35.5[/C][C]36.3882915812477[/C][C]-0.888291581247714[/C][/ROW]
[ROW][C]7[/C][C]36.6[/C][C]36.2724193116268[/C][C]0.327580688373175[/C][/ROW]
[ROW][C]8[/C][C]37.1[/C][C]37.4151502331475[/C][C]-0.315150233147499[/C][/ROW]
[ROW][C]9[/C][C]37.9[/C][C]37.8740407894049[/C][C]0.0259592105951256[/C][/ROW]
[ROW][C]10[/C][C]38.1[/C][C]38.6774270115787[/C][C]-0.577427011578671[/C][/ROW]
[ROW][C]11[/C][C]39[/C][C]38.8021051467941[/C][C]0.197894853205909[/C][/ROW]
[ROW][C]12[/C][C]41.5[/C][C]39.7279193346929[/C][C]1.7720806653071[/C][/ROW]
[ROW][C]13[/C][C]41.8[/C][C]42.459076550381[/C][C]-0.659076550381037[/C][/ROW]
[ROW][C]14[/C][C]41.9[/C][C]42.6731039965949[/C][C]-0.773103996594934[/C][/ROW]
[ROW][C]15[/C][C]44.6[/C][C]42.6722572514163[/C][C]1.92774274858373[/C][/ROW]
[ROW][C]16[/C][C]46.1[/C][C]45.6237196453409[/C][C]0.476280354659131[/C][/ROW]
[ROW][C]17[/C][C]46.4[/C][C]47.1858475398692[/C][C]-0.785847539869238[/C][/ROW]
[ROW][C]18[/C][C]47.2[/C][C]47.3833384764683[/C][C]-0.183338476468293[/C][/ROW]
[ROW][C]19[/C][C]47.7[/C][C]48.1594230799637[/C][C]-0.45942307996372[/C][/ROW]
[ROW][C]20[/C][C]49.2[/C][C]48.5994941150659[/C][C]0.600505884934094[/C][/ROW]
[ROW][C]21[/C][C]49.3[/C][C]50.1778264794347[/C][C]-0.877826479434695[/C][/ROW]
[ROW][C]22[/C][C]49.3[/C][C]50.163319319114[/C][C]-0.863319319114041[/C][/ROW]
[ROW][C]23[/C][C]49.5[/C][C]50.0507045302034[/C][C]-0.550704530203404[/C][/ROW]
[ROW][C]24[/C][C]50.1[/C][C]50.1788684516541[/C][C]-0.0788684516541238[/C][/ROW]
[ROW][C]25[/C][C]51.9[/C][C]50.7685805386675[/C][C]1.13141946133252[/C][/ROW]
[ROW][C]26[/C][C]52.6[/C][C]52.7161673712407[/C][C]-0.116167371240735[/C][/ROW]
[ROW][C]27[/C][C]53.2[/C][C]53.4010140395581[/C][C]-0.201014039558082[/C][/ROW]
[ROW][C]28[/C][C]53.5[/C][C]53.9747929726461[/C][C]-0.474792972646092[/C][/ROW]
[ROW][C]29[/C][C]53.7[/C][C]54.2128590981144[/C][C]-0.512859098114397[/C][/ROW]
[ROW][C]30[/C][C]53.7[/C][C]54.345959727515[/C][C]-0.645959727514978[/C][/ROW]
[ROW][C]31[/C][C]53.9[/C][C]54.2616981840185[/C][C]-0.361698184018515[/C][/ROW]
[ROW][C]32[/C][C]54.1[/C][C]54.4145168413325[/C][C]-0.314516841332455[/C][/ROW]
[ROW][C]33[/C][C]54.8[/C][C]54.5734900197251[/C][C]0.226509980274912[/C][/ROW]
[ROW][C]34[/C][C]55.4[/C][C]55.3030368780544[/C][C]0.0969631219456204[/C][/ROW]
[ROW][C]35[/C][C]55.9[/C][C]55.9156851314506[/C][C]-0.0156851314506241[/C][/ROW]
[ROW][C]36[/C][C]56.8[/C][C]56.4136391008241[/C][C]0.38636089917587[/C][/ROW]
[ROW][C]37[/C][C]58.4[/C][C]57.3640375456877[/C][C]1.03596245431231[/C][/ROW]
[ROW][C]38[/C][C]59.3[/C][C]59.0991725884566[/C][C]0.200827411543372[/C][/ROW]
[ROW][C]39[/C][C]60.3[/C][C]60.0253693108717[/C][C]0.274630689128273[/C][/ROW]
[ROW][C]40[/C][C]60.5[/C][C]61.0611932249205[/C][C]-0.561193224920473[/C][/ROW]
[ROW][C]41[/C][C]60.8[/C][C]61.1879889595192[/C][C]-0.38798895951917[/C][/ROW]
[ROW][C]42[/C][C]61[/C][C]61.4373781440207[/C][C]-0.437378144020741[/C][/ROW]
[ROW][C]43[/C][C]61.1[/C][C]61.5803248078188[/C][C]-0.480324807818825[/C][/ROW]
[ROW][C]44[/C][C]61.3[/C][C]61.6176693388128[/C][C]-0.317669338812799[/C][/ROW]
[ROW][C]45[/C][C]61.4[/C][C]61.7762312929568[/C][C]-0.376231292956831[/C][/ROW]
[ROW][C]46[/C][C]61.5[/C][C]61.8271541940204[/C][C]-0.32715419402038[/C][/ROW]
[ROW][C]47[/C][C]63.9[/C][C]61.8844789061111[/C][C]2.01552109388889[/C][/ROW]
[ROW][C]48[/C][C]63.9[/C][C]64.5473914548146[/C][C]-0.647391454814588[/C][/ROW]
[ROW][C]49[/C][C]64[/C][C]64.4629431511425[/C][C]-0.462943151142539[/C][/ROW]
[ROW][C]50[/C][C]64.1[/C][C]64.5025550142281[/C][C]-0.402555014228099[/C][/ROW]
[ROW][C]51[/C][C]64.5[/C][C]64.5500441449025[/C][C]-0.0500441449025431[/C][/ROW]
[ROW][C]52[/C][C]64.5[/C][C]64.9435161885721[/C][C]-0.44351618857209[/C][/ROW]
[ROW][C]53[/C][C]65.9[/C][C]64.8856621815452[/C][C]1.01433781845482[/C][/ROW]
[ROW][C]54[/C][C]66.8[/C][C]66.4179764212249[/C][C]0.382023578775119[/C][/ROW]
[ROW][C]55[/C][C]68.7[/C][C]67.3678090888487[/C][C]1.3321909111513[/C][/ROW]
[ROW][C]56[/C][C]69.2[/C][C]69.4415853439682[/C][C]-0.241585343968225[/C][/ROW]
[ROW][C]57[/C][C]69.6[/C][C]69.9100719955321[/C][C]-0.310071995532098[/C][/ROW]
[ROW][C]58[/C][C]70.2[/C][C]70.2696249772031[/C][C]-0.0696249772031337[/C][/ROW]
[ROW][C]59[/C][C]70.6[/C][C]70.8605428196086[/C][C]-0.260542819608574[/C][/ROW]
[ROW][C]60[/C][C]70.7[/C][C]71.2265565830182[/C][C]-0.526556583018234[/C][/ROW]
[ROW][C]61[/C][C]70.7[/C][C]71.2578704582748[/C][C]-0.557870458274792[/C][/ROW]
[ROW][C]62[/C][C]71[/C][C]71.1850996277059[/C][C]-0.185099627705895[/C][/ROW]
[ROW][C]63[/C][C]72.1[/C][C]71.4609544996634[/C][C]0.63904550033655[/C][/ROW]
[ROW][C]64[/C][C]73.7[/C][C]72.644314124001[/C][C]1.05568587599902[/C][/ROW]
[ROW][C]65[/C][C]77.4[/C][C]74.3820219679579[/C][C]3.01797803204208[/C][/ROW]
[ROW][C]66[/C][C]79.7[/C][C]78.4756989672913[/C][C]1.22430103270869[/C][/ROW]
[ROW][C]67[/C][C]91.6[/C][C]80.9354016396502[/C][C]10.6645983603498[/C][/ROW]
[ROW][C]68[/C][C]93.6[/C][C]94.2265340591123[/C][C]-0.626534059112288[/C][/ROW]
[ROW][C]69[/C][C]94.3[/C][C]96.144806476687[/C][C]-1.84480647668698[/C][/ROW]
[ROW][C]70[/C][C]97.3[/C][C]96.6041626183215[/C][C]0.695837381678515[/C][/ROW]
[ROW][C]71[/C][C]101.7[/C][C]99.6949304004375[/C][C]2.00506959956255[/C][/ROW]
[ROW][C]72[/C][C]103[/C][C]104.356479614855[/C][C]-1.35647961485513[/C][/ROW]
[ROW][C]73[/C][C]103.1[/C][C]105.479535045092[/C][C]-2.3795350450924[/C][/ROW]
[ROW][C]74[/C][C]104.6[/C][C]105.269139075866[/C][C]-0.669139075865687[/C][/ROW]
[ROW][C]75[/C][C]107.2[/C][C]106.681853926429[/C][C]0.518146073571032[/C][/ROW]
[ROW][C]76[/C][C]107.7[/C][C]109.349442951032[/C][C]-1.64944295103224[/C][/ROW]
[ROW][C]77[/C][C]108.3[/C][C]109.634283084181[/C][C]-1.33428308418107[/C][/ROW]
[ROW][C]78[/C][C]108.8[/C][C]110.060233917731[/C][C]-1.26023391773094[/C][/ROW]
[ROW][C]79[/C][C]113.1[/C][C]110.395844017631[/C][C]2.70415598236875[/C][/ROW]
[ROW][C]80[/C][C]113.8[/C][C]115.048584826731[/C][C]-1.24858482673118[/C][/ROW]
[ROW][C]81[/C][C]113.8[/C][C]115.585714480167[/C][C]-1.78571448016736[/C][/ROW]
[ROW][C]82[/C][C]116.5[/C][C]115.352778815708[/C][C]1.14722118429233[/C][/ROW]
[ROW][C]83[/C][C]116.9[/C][C]118.202426887565[/C][C]-1.30242688756533[/C][/ROW]
[ROW][C]84[/C][C]117.6[/C][C]118.432533169485[/C][C]-0.832533169485203[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166891&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166891&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	32.5	32.5	0
4	34.4	33.2	1.2
5	35.5	35.2565327494715	0.243467250528525
6	35.5	36.3882915812477	-0.888291581247714
7	36.6	36.2724193116268	0.327580688373175
8	37.1	37.4151502331475	-0.315150233147499
9	37.9	37.8740407894049	0.0259592105951256
10	38.1	38.6774270115787	-0.577427011578671
11	39	38.8021051467941	0.197894853205909
12	41.5	39.7279193346929	1.7720806653071
13	41.8	42.459076550381	-0.659076550381037
14	41.9	42.6731039965949	-0.773103996594934
15	44.6	42.6722572514163	1.92774274858373
16	46.1	45.6237196453409	0.476280354659131
17	46.4	47.1858475398692	-0.785847539869238
18	47.2	47.3833384764683	-0.183338476468293
19	47.7	48.1594230799637	-0.45942307996372
20	49.2	48.5994941150659	0.600505884934094
21	49.3	50.1778264794347	-0.877826479434695
22	49.3	50.163319319114	-0.863319319114041
23	49.5	50.0507045302034	-0.550704530203404
24	50.1	50.1788684516541	-0.0788684516541238
25	51.9	50.7685805386675	1.13141946133252
26	52.6	52.7161673712407	-0.116167371240735
27	53.2	53.4010140395581	-0.201014039558082
28	53.5	53.9747929726461	-0.474792972646092
29	53.7	54.2128590981144	-0.512859098114397
30	53.7	54.345959727515	-0.645959727514978
31	53.9	54.2616981840185	-0.361698184018515
32	54.1	54.4145168413325	-0.314516841332455
33	54.8	54.5734900197251	0.226509980274912
34	55.4	55.3030368780544	0.0969631219456204
35	55.9	55.9156851314506	-0.0156851314506241
36	56.8	56.4136391008241	0.38636089917587
37	58.4	57.3640375456877	1.03596245431231
38	59.3	59.0991725884566	0.200827411543372
39	60.3	60.0253693108717	0.274630689128273
40	60.5	61.0611932249205	-0.561193224920473
41	60.8	61.1879889595192	-0.38798895951917
42	61	61.4373781440207	-0.437378144020741
43	61.1	61.5803248078188	-0.480324807818825
44	61.3	61.6176693388128	-0.317669338812799
45	61.4	61.7762312929568	-0.376231292956831
46	61.5	61.8271541940204	-0.32715419402038
47	63.9	61.8844789061111	2.01552109388889
48	63.9	64.5473914548146	-0.647391454814588
49	64	64.4629431511425	-0.462943151142539
50	64.1	64.5025550142281	-0.402555014228099
51	64.5	64.5500441449025	-0.0500441449025431
52	64.5	64.9435161885721	-0.44351618857209
53	65.9	64.8856621815452	1.01433781845482
54	66.8	66.4179764212249	0.382023578775119
55	68.7	67.3678090888487	1.3321909111513
56	69.2	69.4415853439682	-0.241585343968225
57	69.6	69.9100719955321	-0.310071995532098
58	70.2	70.2696249772031	-0.0696249772031337
59	70.6	70.8605428196086	-0.260542819608574
60	70.7	71.2265565830182	-0.526556583018234
61	70.7	71.2578704582748	-0.557870458274792
62	71	71.1850996277059	-0.185099627705895
63	72.1	71.4609544996634	0.63904550033655
64	73.7	72.644314124001	1.05568587599902
65	77.4	74.3820219679579	3.01797803204208
66	79.7	78.4756989672913	1.22430103270869
67	91.6	80.9354016396502	10.6645983603498
68	93.6	94.2265340591123	-0.626534059112288
69	94.3	96.144806476687	-1.84480647668698
70	97.3	96.6041626183215	0.695837381678515
71	101.7	99.6949304004375	2.00506959956255
72	103	104.356479614855	-1.35647961485513
73	103.1	105.479535045092	-2.3795350450924
74	104.6	105.269139075866	-0.669139075865687
75	107.2	106.681853926429	0.518146073571032
76	107.7	109.349442951032	-1.64944295103224
77	108.3	109.634283084181	-1.33428308418107
78	108.8	110.060233917731	-1.26023391773094
79	113.1	110.395844017631	2.70415598236875
80	113.8	115.048584826731	-1.24858482673118
81	113.8	115.585714480167	-1.78571448016736
82	116.5	115.352778815708	1.14722118429233
83	116.9	118.202426887565	-1.30242688756533
84	117.6	118.432533169485	-0.832533169485203

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	119.02393424778	116.007505961857	122.040362533704
86	120.447868495561	115.895256172758	125.000480818363
87	121.871802743341	115.939521312132	127.80408417455
88	123.295736991122	116.028995179117	130.562478803126
89	124.719671238902	116.124518848295	133.314823629509
90	126.143605486683	116.208066646159	136.079144327206
91	127.567539734463	116.270192976488	138.864886492438
92	128.991473982243	116.305591093019	141.677356871468
93	130.415408230024	116.311177670176	144.519638789872
94	131.839342477804	116.285154177066	147.393530778542
95	133.263276725585	116.226503803057	150.300049648112
96	134.687210973365	116.134703370661	153.239718576069

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 119.02393424778 & 116.007505961857 & 122.040362533704 \tabularnewline
86 & 120.447868495561 & 115.895256172758 & 125.000480818363 \tabularnewline
87 & 121.871802743341 & 115.939521312132 & 127.80408417455 \tabularnewline
88 & 123.295736991122 & 116.028995179117 & 130.562478803126 \tabularnewline
89 & 124.719671238902 & 116.124518848295 & 133.314823629509 \tabularnewline
90 & 126.143605486683 & 116.208066646159 & 136.079144327206 \tabularnewline
91 & 127.567539734463 & 116.270192976488 & 138.864886492438 \tabularnewline
92 & 128.991473982243 & 116.305591093019 & 141.677356871468 \tabularnewline
93 & 130.415408230024 & 116.311177670176 & 144.519638789872 \tabularnewline
94 & 131.839342477804 & 116.285154177066 & 147.393530778542 \tabularnewline
95 & 133.263276725585 & 116.226503803057 & 150.300049648112 \tabularnewline
96 & 134.687210973365 & 116.134703370661 & 153.239718576069 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166891&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]85[/C][C]119.02393424778[/C][C]116.007505961857[/C][C]122.040362533704[/C][/ROW]
[ROW][C]86[/C][C]120.447868495561[/C][C]115.895256172758[/C][C]125.000480818363[/C][/ROW]
[ROW][C]87[/C][C]121.871802743341[/C][C]115.939521312132[/C][C]127.80408417455[/C][/ROW]
[ROW][C]88[/C][C]123.295736991122[/C][C]116.028995179117[/C][C]130.562478803126[/C][/ROW]
[ROW][C]89[/C][C]124.719671238902[/C][C]116.124518848295[/C][C]133.314823629509[/C][/ROW]
[ROW][C]90[/C][C]126.143605486683[/C][C]116.208066646159[/C][C]136.079144327206[/C][/ROW]
[ROW][C]91[/C][C]127.567539734463[/C][C]116.270192976488[/C][C]138.864886492438[/C][/ROW]
[ROW][C]92[/C][C]128.991473982243[/C][C]116.305591093019[/C][C]141.677356871468[/C][/ROW]
[ROW][C]93[/C][C]130.415408230024[/C][C]116.311177670176[/C][C]144.519638789872[/C][/ROW]
[ROW][C]94[/C][C]131.839342477804[/C][C]116.285154177066[/C][C]147.393530778542[/C][/ROW]
[ROW][C]95[/C][C]133.263276725585[/C][C]116.226503803057[/C][C]150.300049648112[/C][/ROW]
[ROW][C]96[/C][C]134.687210973365[/C][C]116.134703370661[/C][C]153.239718576069[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166891&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166891&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
85	119.02393424778	116.007505961857	122.040362533704
86	120.447868495561	115.895256172758	125.000480818363
87	121.871802743341	115.939521312132	127.80408417455
88	123.295736991122	116.028995179117	130.562478803126
89	124.719671238902	116.124518848295	133.314823629509
90	126.143605486683	116.208066646159	136.079144327206
91	127.567539734463	116.270192976488	138.864886492438
92	128.991473982243	116.305591093019	141.677356871468
93	130.415408230024	116.311177670176	144.519638789872
94	131.839342477804	116.285154177066	147.393530778542
95	133.263276725585	116.226503803057	150.300049648112
96	134.687210973365	116.134703370661	153.239718576069

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 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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