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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 25 May 2015 10:31:57 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/May/25/t14325464548nhgb3bz50ww7qh.htm/, Retrieved Tue, 07 May 2024 11:28:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279331, Retrieved Tue, 07 May 2024 11:28:23 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [opgave 10 eigen r...] [2015-05-25 09:31:57] [09743efd8c85782f9ae22fefb9801b71] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279331&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279331&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279331&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.904303758738388
beta	0.016843610741167
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.904303758738388 \tabularnewline
beta & 0.016843610741167 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279331&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]0.904303758738388[/C][/ROW]
[ROW][C]beta[/C][C]0.016843610741167[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279331&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279331&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	0.904303758738388
beta	0.016843610741167
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	544.23	548.497721688035	-4.2677216880345
14	541.6	542.008220899196	-0.408220899196067
15	541.37	541.310163265753	0.0598367342468009
16	540.43	540.185866660481	0.24413333951918
17	540.47	540.267782077088	0.2022179229117
18	540.52	540.329040022502	0.190959977497869
19	540.52	540.79885935172	-0.278859351719802
20	539.7	540.677488448982	-0.977488448982172
21	540.89	537.824039110559	3.06596088944082
22	540.51	540.079629461137	0.430370538863258
23	537.43	538.927984176894	-1.49798417689442
24	538.14	536.793036902083	1.34696309791684
25	538.14	537.59873114271	0.54126885729022
26	537.74	535.871822162855	1.86817783714503
27	540.33	537.356249198593	2.9737508014066
28	540.02	539.008173891524	1.01182610847559
29	539.21	539.915520276107	-0.705520276106995
30	539.84	539.276218039716	0.563781960283791
31	539.84	540.165288699704	-0.325288699704174
32	537.3	540.061435138919	-2.76143513891918
33	536.27	536.080886148256	0.189113851743627
34	536.75	535.538084573166	1.21191542683403
35	536.21	534.97592901344	1.23407098656048
36	536.99	535.692726250919	1.29727374908111
37	536.99	536.484513459033	0.505486540966558
38	536.57	534.959810713786	1.61018928621445
39	536.91	536.420391411552	0.489608588447936
40	536.97	535.703964836975	1.26603516302498
41	540.45	536.746538569159	3.70346143084112
42	542.42	540.35260771888	2.06739228111974
43	542.42	542.67606592879	-0.256065928789894
44	542.98	542.562482911309	0.417517088690602
45	540.19	541.948251981166	-1.75825198116615
46	537.16	539.921879823174	-2.7618798231739
47	537.35	535.887360061278	1.46263993872208
48	537.03	536.939416406186	0.0905835938144719
49	537.03	536.668353198298	0.361646801702364
50	536.27	535.22123569376	1.0487643062404
51	534.71	536.160274988623	-1.4502749886226
52	537.12	533.827750382878	3.29224961712191
53	537.07	537.030597641154	0.0394023588460186
54	537.33	537.205576381842	0.124423618157948
55	537.33	537.55895736491	-0.228957364909888
56	538.79	537.544063852804	1.2459361471964
57	539.24	537.49309649958	1.74690350042033
58	537.17	538.616129855505	-1.44612985550498
59	536.46	536.271483208419	0.188516791581492
60	532.3	536.116402265255	-3.81640226525485
61	532.3	532.355024293044	-0.0550242930444256
62	532.89	530.6073649911	2.28263500889977
63	533.47	532.452344408492	1.01765559150829
64	532.54	532.872306235304	-0.332306235303804
65	533.8	532.497846216051	1.30215378394917
66	534.15	533.853783393376	0.296216606624284
67	534.15	534.362228257667	-0.212228257666652
68	534.15	534.537387586752	-0.387387586751629
69	534.28	533.066244652367	1.21375534763274
70	535.63	533.402372583051	2.22762741694942
71	534.21	534.593089447176	-0.383089447176189
72	533.78	533.585882036712	0.194117963287795
73	533.78	533.920304422204	-0.140304422203826
74	534.55	532.427054329294	2.12294567070614
75	536.93	534.11196309768	2.81803690231948
76	536.09	536.163643974555	-0.0736439745551252
77	533.91	536.316258502916	-2.40625850291588
78	533.99	534.302668142467	-0.312668142466578
79	533.99	534.282833641625	-0.292833641624725
80	533.76	534.438105033825	-0.67810503382475
81	532.5	532.922626351369	-0.42262635136899
82	529.5	531.916404737168	-2.41640473716791
83	528.62	528.627346215165	-0.00734621516460265
84	528.7	527.990560762181	0.709439237818742
85	521.27	528.742235748676	-7.47223574867598
86	521.19	520.706847650767	0.483152349233478
87	519.43	520.821996392252	-1.39199639225239
88	516.81	518.572272829993	-1.76227282999275
89	516.78	516.731378222463	0.0486217775369369
90	515.45	516.932232882389	-1.48223288238898
91	516.22	515.632978998977	0.587021001023459
92	517.01	516.336763265817	0.673236734183092
93	518.19	515.878065698536	2.31193430146402
94	516.79	517.005881907408	-0.215881907408402
95	516.87	515.822781533445	1.0472184665548
96	514.1	516.109778651556	-2.00977865155562

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 544.23 & 548.497721688035 & -4.2677216880345 \tabularnewline
14 & 541.6 & 542.008220899196 & -0.408220899196067 \tabularnewline
15 & 541.37 & 541.310163265753 & 0.0598367342468009 \tabularnewline
16 & 540.43 & 540.185866660481 & 0.24413333951918 \tabularnewline
17 & 540.47 & 540.267782077088 & 0.2022179229117 \tabularnewline
18 & 540.52 & 540.329040022502 & 0.190959977497869 \tabularnewline
19 & 540.52 & 540.79885935172 & -0.278859351719802 \tabularnewline
20 & 539.7 & 540.677488448982 & -0.977488448982172 \tabularnewline
21 & 540.89 & 537.824039110559 & 3.06596088944082 \tabularnewline
22 & 540.51 & 540.079629461137 & 0.430370538863258 \tabularnewline
23 & 537.43 & 538.927984176894 & -1.49798417689442 \tabularnewline
24 & 538.14 & 536.793036902083 & 1.34696309791684 \tabularnewline
25 & 538.14 & 537.59873114271 & 0.54126885729022 \tabularnewline
26 & 537.74 & 535.871822162855 & 1.86817783714503 \tabularnewline
27 & 540.33 & 537.356249198593 & 2.9737508014066 \tabularnewline
28 & 540.02 & 539.008173891524 & 1.01182610847559 \tabularnewline
29 & 539.21 & 539.915520276107 & -0.705520276106995 \tabularnewline
30 & 539.84 & 539.276218039716 & 0.563781960283791 \tabularnewline
31 & 539.84 & 540.165288699704 & -0.325288699704174 \tabularnewline
32 & 537.3 & 540.061435138919 & -2.76143513891918 \tabularnewline
33 & 536.27 & 536.080886148256 & 0.189113851743627 \tabularnewline
34 & 536.75 & 535.538084573166 & 1.21191542683403 \tabularnewline
35 & 536.21 & 534.97592901344 & 1.23407098656048 \tabularnewline
36 & 536.99 & 535.692726250919 & 1.29727374908111 \tabularnewline
37 & 536.99 & 536.484513459033 & 0.505486540966558 \tabularnewline
38 & 536.57 & 534.959810713786 & 1.61018928621445 \tabularnewline
39 & 536.91 & 536.420391411552 & 0.489608588447936 \tabularnewline
40 & 536.97 & 535.703964836975 & 1.26603516302498 \tabularnewline
41 & 540.45 & 536.746538569159 & 3.70346143084112 \tabularnewline
42 & 542.42 & 540.35260771888 & 2.06739228111974 \tabularnewline
43 & 542.42 & 542.67606592879 & -0.256065928789894 \tabularnewline
44 & 542.98 & 542.562482911309 & 0.417517088690602 \tabularnewline
45 & 540.19 & 541.948251981166 & -1.75825198116615 \tabularnewline
46 & 537.16 & 539.921879823174 & -2.7618798231739 \tabularnewline
47 & 537.35 & 535.887360061278 & 1.46263993872208 \tabularnewline
48 & 537.03 & 536.939416406186 & 0.0905835938144719 \tabularnewline
49 & 537.03 & 536.668353198298 & 0.361646801702364 \tabularnewline
50 & 536.27 & 535.22123569376 & 1.0487643062404 \tabularnewline
51 & 534.71 & 536.160274988623 & -1.4502749886226 \tabularnewline
52 & 537.12 & 533.827750382878 & 3.29224961712191 \tabularnewline
53 & 537.07 & 537.030597641154 & 0.0394023588460186 \tabularnewline
54 & 537.33 & 537.205576381842 & 0.124423618157948 \tabularnewline
55 & 537.33 & 537.55895736491 & -0.228957364909888 \tabularnewline
56 & 538.79 & 537.544063852804 & 1.2459361471964 \tabularnewline
57 & 539.24 & 537.49309649958 & 1.74690350042033 \tabularnewline
58 & 537.17 & 538.616129855505 & -1.44612985550498 \tabularnewline
59 & 536.46 & 536.271483208419 & 0.188516791581492 \tabularnewline
60 & 532.3 & 536.116402265255 & -3.81640226525485 \tabularnewline
61 & 532.3 & 532.355024293044 & -0.0550242930444256 \tabularnewline
62 & 532.89 & 530.6073649911 & 2.28263500889977 \tabularnewline
63 & 533.47 & 532.452344408492 & 1.01765559150829 \tabularnewline
64 & 532.54 & 532.872306235304 & -0.332306235303804 \tabularnewline
65 & 533.8 & 532.497846216051 & 1.30215378394917 \tabularnewline
66 & 534.15 & 533.853783393376 & 0.296216606624284 \tabularnewline
67 & 534.15 & 534.362228257667 & -0.212228257666652 \tabularnewline
68 & 534.15 & 534.537387586752 & -0.387387586751629 \tabularnewline
69 & 534.28 & 533.066244652367 & 1.21375534763274 \tabularnewline
70 & 535.63 & 533.402372583051 & 2.22762741694942 \tabularnewline
71 & 534.21 & 534.593089447176 & -0.383089447176189 \tabularnewline
72 & 533.78 & 533.585882036712 & 0.194117963287795 \tabularnewline
73 & 533.78 & 533.920304422204 & -0.140304422203826 \tabularnewline
74 & 534.55 & 532.427054329294 & 2.12294567070614 \tabularnewline
75 & 536.93 & 534.11196309768 & 2.81803690231948 \tabularnewline
76 & 536.09 & 536.163643974555 & -0.0736439745551252 \tabularnewline
77 & 533.91 & 536.316258502916 & -2.40625850291588 \tabularnewline
78 & 533.99 & 534.302668142467 & -0.312668142466578 \tabularnewline
79 & 533.99 & 534.282833641625 & -0.292833641624725 \tabularnewline
80 & 533.76 & 534.438105033825 & -0.67810503382475 \tabularnewline
81 & 532.5 & 532.922626351369 & -0.42262635136899 \tabularnewline
82 & 529.5 & 531.916404737168 & -2.41640473716791 \tabularnewline
83 & 528.62 & 528.627346215165 & -0.00734621516460265 \tabularnewline
84 & 528.7 & 527.990560762181 & 0.709439237818742 \tabularnewline
85 & 521.27 & 528.742235748676 & -7.47223574867598 \tabularnewline
86 & 521.19 & 520.706847650767 & 0.483152349233478 \tabularnewline
87 & 519.43 & 520.821996392252 & -1.39199639225239 \tabularnewline
88 & 516.81 & 518.572272829993 & -1.76227282999275 \tabularnewline
89 & 516.78 & 516.731378222463 & 0.0486217775369369 \tabularnewline
90 & 515.45 & 516.932232882389 & -1.48223288238898 \tabularnewline
91 & 516.22 & 515.632978998977 & 0.587021001023459 \tabularnewline
92 & 517.01 & 516.336763265817 & 0.673236734183092 \tabularnewline
93 & 518.19 & 515.878065698536 & 2.31193430146402 \tabularnewline
94 & 516.79 & 517.005881907408 & -0.215881907408402 \tabularnewline
95 & 516.87 & 515.822781533445 & 1.0472184665548 \tabularnewline
96 & 514.1 & 516.109778651556 & -2.00977865155562 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279331&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]544.23[/C][C]548.497721688035[/C][C]-4.2677216880345[/C][/ROW]
[ROW][C]14[/C][C]541.6[/C][C]542.008220899196[/C][C]-0.408220899196067[/C][/ROW]
[ROW][C]15[/C][C]541.37[/C][C]541.310163265753[/C][C]0.0598367342468009[/C][/ROW]
[ROW][C]16[/C][C]540.43[/C][C]540.185866660481[/C][C]0.24413333951918[/C][/ROW]
[ROW][C]17[/C][C]540.47[/C][C]540.267782077088[/C][C]0.2022179229117[/C][/ROW]
[ROW][C]18[/C][C]540.52[/C][C]540.329040022502[/C][C]0.190959977497869[/C][/ROW]
[ROW][C]19[/C][C]540.52[/C][C]540.79885935172[/C][C]-0.278859351719802[/C][/ROW]
[ROW][C]20[/C][C]539.7[/C][C]540.677488448982[/C][C]-0.977488448982172[/C][/ROW]
[ROW][C]21[/C][C]540.89[/C][C]537.824039110559[/C][C]3.06596088944082[/C][/ROW]
[ROW][C]22[/C][C]540.51[/C][C]540.079629461137[/C][C]0.430370538863258[/C][/ROW]
[ROW][C]23[/C][C]537.43[/C][C]538.927984176894[/C][C]-1.49798417689442[/C][/ROW]
[ROW][C]24[/C][C]538.14[/C][C]536.793036902083[/C][C]1.34696309791684[/C][/ROW]
[ROW][C]25[/C][C]538.14[/C][C]537.59873114271[/C][C]0.54126885729022[/C][/ROW]
[ROW][C]26[/C][C]537.74[/C][C]535.871822162855[/C][C]1.86817783714503[/C][/ROW]
[ROW][C]27[/C][C]540.33[/C][C]537.356249198593[/C][C]2.9737508014066[/C][/ROW]
[ROW][C]28[/C][C]540.02[/C][C]539.008173891524[/C][C]1.01182610847559[/C][/ROW]
[ROW][C]29[/C][C]539.21[/C][C]539.915520276107[/C][C]-0.705520276106995[/C][/ROW]
[ROW][C]30[/C][C]539.84[/C][C]539.276218039716[/C][C]0.563781960283791[/C][/ROW]
[ROW][C]31[/C][C]539.84[/C][C]540.165288699704[/C][C]-0.325288699704174[/C][/ROW]
[ROW][C]32[/C][C]537.3[/C][C]540.061435138919[/C][C]-2.76143513891918[/C][/ROW]
[ROW][C]33[/C][C]536.27[/C][C]536.080886148256[/C][C]0.189113851743627[/C][/ROW]
[ROW][C]34[/C][C]536.75[/C][C]535.538084573166[/C][C]1.21191542683403[/C][/ROW]
[ROW][C]35[/C][C]536.21[/C][C]534.97592901344[/C][C]1.23407098656048[/C][/ROW]
[ROW][C]36[/C][C]536.99[/C][C]535.692726250919[/C][C]1.29727374908111[/C][/ROW]
[ROW][C]37[/C][C]536.99[/C][C]536.484513459033[/C][C]0.505486540966558[/C][/ROW]
[ROW][C]38[/C][C]536.57[/C][C]534.959810713786[/C][C]1.61018928621445[/C][/ROW]
[ROW][C]39[/C][C]536.91[/C][C]536.420391411552[/C][C]0.489608588447936[/C][/ROW]
[ROW][C]40[/C][C]536.97[/C][C]535.703964836975[/C][C]1.26603516302498[/C][/ROW]
[ROW][C]41[/C][C]540.45[/C][C]536.746538569159[/C][C]3.70346143084112[/C][/ROW]
[ROW][C]42[/C][C]542.42[/C][C]540.35260771888[/C][C]2.06739228111974[/C][/ROW]
[ROW][C]43[/C][C]542.42[/C][C]542.67606592879[/C][C]-0.256065928789894[/C][/ROW]
[ROW][C]44[/C][C]542.98[/C][C]542.562482911309[/C][C]0.417517088690602[/C][/ROW]
[ROW][C]45[/C][C]540.19[/C][C]541.948251981166[/C][C]-1.75825198116615[/C][/ROW]
[ROW][C]46[/C][C]537.16[/C][C]539.921879823174[/C][C]-2.7618798231739[/C][/ROW]
[ROW][C]47[/C][C]537.35[/C][C]535.887360061278[/C][C]1.46263993872208[/C][/ROW]
[ROW][C]48[/C][C]537.03[/C][C]536.939416406186[/C][C]0.0905835938144719[/C][/ROW]
[ROW][C]49[/C][C]537.03[/C][C]536.668353198298[/C][C]0.361646801702364[/C][/ROW]
[ROW][C]50[/C][C]536.27[/C][C]535.22123569376[/C][C]1.0487643062404[/C][/ROW]
[ROW][C]51[/C][C]534.71[/C][C]536.160274988623[/C][C]-1.4502749886226[/C][/ROW]
[ROW][C]52[/C][C]537.12[/C][C]533.827750382878[/C][C]3.29224961712191[/C][/ROW]
[ROW][C]53[/C][C]537.07[/C][C]537.030597641154[/C][C]0.0394023588460186[/C][/ROW]
[ROW][C]54[/C][C]537.33[/C][C]537.205576381842[/C][C]0.124423618157948[/C][/ROW]
[ROW][C]55[/C][C]537.33[/C][C]537.55895736491[/C][C]-0.228957364909888[/C][/ROW]
[ROW][C]56[/C][C]538.79[/C][C]537.544063852804[/C][C]1.2459361471964[/C][/ROW]
[ROW][C]57[/C][C]539.24[/C][C]537.49309649958[/C][C]1.74690350042033[/C][/ROW]
[ROW][C]58[/C][C]537.17[/C][C]538.616129855505[/C][C]-1.44612985550498[/C][/ROW]
[ROW][C]59[/C][C]536.46[/C][C]536.271483208419[/C][C]0.188516791581492[/C][/ROW]
[ROW][C]60[/C][C]532.3[/C][C]536.116402265255[/C][C]-3.81640226525485[/C][/ROW]
[ROW][C]61[/C][C]532.3[/C][C]532.355024293044[/C][C]-0.0550242930444256[/C][/ROW]
[ROW][C]62[/C][C]532.89[/C][C]530.6073649911[/C][C]2.28263500889977[/C][/ROW]
[ROW][C]63[/C][C]533.47[/C][C]532.452344408492[/C][C]1.01765559150829[/C][/ROW]
[ROW][C]64[/C][C]532.54[/C][C]532.872306235304[/C][C]-0.332306235303804[/C][/ROW]
[ROW][C]65[/C][C]533.8[/C][C]532.497846216051[/C][C]1.30215378394917[/C][/ROW]
[ROW][C]66[/C][C]534.15[/C][C]533.853783393376[/C][C]0.296216606624284[/C][/ROW]
[ROW][C]67[/C][C]534.15[/C][C]534.362228257667[/C][C]-0.212228257666652[/C][/ROW]
[ROW][C]68[/C][C]534.15[/C][C]534.537387586752[/C][C]-0.387387586751629[/C][/ROW]
[ROW][C]69[/C][C]534.28[/C][C]533.066244652367[/C][C]1.21375534763274[/C][/ROW]
[ROW][C]70[/C][C]535.63[/C][C]533.402372583051[/C][C]2.22762741694942[/C][/ROW]
[ROW][C]71[/C][C]534.21[/C][C]534.593089447176[/C][C]-0.383089447176189[/C][/ROW]
[ROW][C]72[/C][C]533.78[/C][C]533.585882036712[/C][C]0.194117963287795[/C][/ROW]
[ROW][C]73[/C][C]533.78[/C][C]533.920304422204[/C][C]-0.140304422203826[/C][/ROW]
[ROW][C]74[/C][C]534.55[/C][C]532.427054329294[/C][C]2.12294567070614[/C][/ROW]
[ROW][C]75[/C][C]536.93[/C][C]534.11196309768[/C][C]2.81803690231948[/C][/ROW]
[ROW][C]76[/C][C]536.09[/C][C]536.163643974555[/C][C]-0.0736439745551252[/C][/ROW]
[ROW][C]77[/C][C]533.91[/C][C]536.316258502916[/C][C]-2.40625850291588[/C][/ROW]
[ROW][C]78[/C][C]533.99[/C][C]534.302668142467[/C][C]-0.312668142466578[/C][/ROW]
[ROW][C]79[/C][C]533.99[/C][C]534.282833641625[/C][C]-0.292833641624725[/C][/ROW]
[ROW][C]80[/C][C]533.76[/C][C]534.438105033825[/C][C]-0.67810503382475[/C][/ROW]
[ROW][C]81[/C][C]532.5[/C][C]532.922626351369[/C][C]-0.42262635136899[/C][/ROW]
[ROW][C]82[/C][C]529.5[/C][C]531.916404737168[/C][C]-2.41640473716791[/C][/ROW]
[ROW][C]83[/C][C]528.62[/C][C]528.627346215165[/C][C]-0.00734621516460265[/C][/ROW]
[ROW][C]84[/C][C]528.7[/C][C]527.990560762181[/C][C]0.709439237818742[/C][/ROW]
[ROW][C]85[/C][C]521.27[/C][C]528.742235748676[/C][C]-7.47223574867598[/C][/ROW]
[ROW][C]86[/C][C]521.19[/C][C]520.706847650767[/C][C]0.483152349233478[/C][/ROW]
[ROW][C]87[/C][C]519.43[/C][C]520.821996392252[/C][C]-1.39199639225239[/C][/ROW]
[ROW][C]88[/C][C]516.81[/C][C]518.572272829993[/C][C]-1.76227282999275[/C][/ROW]
[ROW][C]89[/C][C]516.78[/C][C]516.731378222463[/C][C]0.0486217775369369[/C][/ROW]
[ROW][C]90[/C][C]515.45[/C][C]516.932232882389[/C][C]-1.48223288238898[/C][/ROW]
[ROW][C]91[/C][C]516.22[/C][C]515.632978998977[/C][C]0.587021001023459[/C][/ROW]
[ROW][C]92[/C][C]517.01[/C][C]516.336763265817[/C][C]0.673236734183092[/C][/ROW]
[ROW][C]93[/C][C]518.19[/C][C]515.878065698536[/C][C]2.31193430146402[/C][/ROW]
[ROW][C]94[/C][C]516.79[/C][C]517.005881907408[/C][C]-0.215881907408402[/C][/ROW]
[ROW][C]95[/C][C]516.87[/C][C]515.822781533445[/C][C]1.0472184665548[/C][/ROW]
[ROW][C]96[/C][C]514.1[/C][C]516.109778651556[/C][C]-2.00977865155562[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279331&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279331&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	544.23	548.497721688035	-4.2677216880345
14	541.6	542.008220899196	-0.408220899196067
15	541.37	541.310163265753	0.0598367342468009
16	540.43	540.185866660481	0.24413333951918
17	540.47	540.267782077088	0.2022179229117
18	540.52	540.329040022502	0.190959977497869
19	540.52	540.79885935172	-0.278859351719802
20	539.7	540.677488448982	-0.977488448982172
21	540.89	537.824039110559	3.06596088944082
22	540.51	540.079629461137	0.430370538863258
23	537.43	538.927984176894	-1.49798417689442
24	538.14	536.793036902083	1.34696309791684
25	538.14	537.59873114271	0.54126885729022
26	537.74	535.871822162855	1.86817783714503
27	540.33	537.356249198593	2.9737508014066
28	540.02	539.008173891524	1.01182610847559
29	539.21	539.915520276107	-0.705520276106995
30	539.84	539.276218039716	0.563781960283791
31	539.84	540.165288699704	-0.325288699704174
32	537.3	540.061435138919	-2.76143513891918
33	536.27	536.080886148256	0.189113851743627
34	536.75	535.538084573166	1.21191542683403
35	536.21	534.97592901344	1.23407098656048
36	536.99	535.692726250919	1.29727374908111
37	536.99	536.484513459033	0.505486540966558
38	536.57	534.959810713786	1.61018928621445
39	536.91	536.420391411552	0.489608588447936
40	536.97	535.703964836975	1.26603516302498
41	540.45	536.746538569159	3.70346143084112
42	542.42	540.35260771888	2.06739228111974
43	542.42	542.67606592879	-0.256065928789894
44	542.98	542.562482911309	0.417517088690602
45	540.19	541.948251981166	-1.75825198116615
46	537.16	539.921879823174	-2.7618798231739
47	537.35	535.887360061278	1.46263993872208
48	537.03	536.939416406186	0.0905835938144719
49	537.03	536.668353198298	0.361646801702364
50	536.27	535.22123569376	1.0487643062404
51	534.71	536.160274988623	-1.4502749886226
52	537.12	533.827750382878	3.29224961712191
53	537.07	537.030597641154	0.0394023588460186
54	537.33	537.205576381842	0.124423618157948
55	537.33	537.55895736491	-0.228957364909888
56	538.79	537.544063852804	1.2459361471964
57	539.24	537.49309649958	1.74690350042033
58	537.17	538.616129855505	-1.44612985550498
59	536.46	536.271483208419	0.188516791581492
60	532.3	536.116402265255	-3.81640226525485
61	532.3	532.355024293044	-0.0550242930444256
62	532.89	530.6073649911	2.28263500889977
63	533.47	532.452344408492	1.01765559150829
64	532.54	532.872306235304	-0.332306235303804
65	533.8	532.497846216051	1.30215378394917
66	534.15	533.853783393376	0.296216606624284
67	534.15	534.362228257667	-0.212228257666652
68	534.15	534.537387586752	-0.387387586751629
69	534.28	533.066244652367	1.21375534763274
70	535.63	533.402372583051	2.22762741694942
71	534.21	534.593089447176	-0.383089447176189
72	533.78	533.585882036712	0.194117963287795
73	533.78	533.920304422204	-0.140304422203826
74	534.55	532.427054329294	2.12294567070614
75	536.93	534.11196309768	2.81803690231948
76	536.09	536.163643974555	-0.0736439745551252
77	533.91	536.316258502916	-2.40625850291588
78	533.99	534.302668142467	-0.312668142466578
79	533.99	534.282833641625	-0.292833641624725
80	533.76	534.438105033825	-0.67810503382475
81	532.5	532.922626351369	-0.42262635136899
82	529.5	531.916404737168	-2.41640473716791
83	528.62	528.627346215165	-0.00734621516460265
84	528.7	527.990560762181	0.709439237818742
85	521.27	528.742235748676	-7.47223574867598
86	521.19	520.706847650767	0.483152349233478
87	519.43	520.821996392252	-1.39199639225239
88	516.81	518.572272829993	-1.76227282999275
89	516.78	516.731378222463	0.0486217775369369
90	515.45	516.932232882389	-1.48223288238898
91	516.22	515.632978998977	0.587021001023459
92	517.01	516.336763265817	0.673236734183092
93	518.19	515.878065698536	2.31193430146402
94	516.79	517.005881907408	-0.215881907408402
95	516.87	515.822781533445	1.0472184665548
96	514.1	516.109778651556	-2.00977865155562

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	513.479622807105	510.110502254897	516.848743359312
98	512.936645148234	508.359666005189	517.513624291279
99	512.402012293275	506.846195280784	517.957829305765
100	511.363424340565	504.951612265768	517.775236415363
101	511.304080070032	504.11473383546	518.493426304604
102	511.328352828253	503.416433639057	519.240272017449
103	511.603968508552	503.010255748869	520.197681268235
104	511.812677625734	502.568638060411	521.056717191056
105	510.919251806155	501.049862883316	520.788640728994
106	509.696524902317	499.222037962283	520.171011842352
107	508.814859839834	497.751964589886	519.877755089782
108	507.831697801777	496.194325733337	519.469069870218

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 513.479622807105 & 510.110502254897 & 516.848743359312 \tabularnewline
98 & 512.936645148234 & 508.359666005189 & 517.513624291279 \tabularnewline
99 & 512.402012293275 & 506.846195280784 & 517.957829305765 \tabularnewline
100 & 511.363424340565 & 504.951612265768 & 517.775236415363 \tabularnewline
101 & 511.304080070032 & 504.11473383546 & 518.493426304604 \tabularnewline
102 & 511.328352828253 & 503.416433639057 & 519.240272017449 \tabularnewline
103 & 511.603968508552 & 503.010255748869 & 520.197681268235 \tabularnewline
104 & 511.812677625734 & 502.568638060411 & 521.056717191056 \tabularnewline
105 & 510.919251806155 & 501.049862883316 & 520.788640728994 \tabularnewline
106 & 509.696524902317 & 499.222037962283 & 520.171011842352 \tabularnewline
107 & 508.814859839834 & 497.751964589886 & 519.877755089782 \tabularnewline
108 & 507.831697801777 & 496.194325733337 & 519.469069870218 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279331&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]513.479622807105[/C][C]510.110502254897[/C][C]516.848743359312[/C][/ROW]
[ROW][C]98[/C][C]512.936645148234[/C][C]508.359666005189[/C][C]517.513624291279[/C][/ROW]
[ROW][C]99[/C][C]512.402012293275[/C][C]506.846195280784[/C][C]517.957829305765[/C][/ROW]
[ROW][C]100[/C][C]511.363424340565[/C][C]504.951612265768[/C][C]517.775236415363[/C][/ROW]
[ROW][C]101[/C][C]511.304080070032[/C][C]504.11473383546[/C][C]518.493426304604[/C][/ROW]
[ROW][C]102[/C][C]511.328352828253[/C][C]503.416433639057[/C][C]519.240272017449[/C][/ROW]
[ROW][C]103[/C][C]511.603968508552[/C][C]503.010255748869[/C][C]520.197681268235[/C][/ROW]
[ROW][C]104[/C][C]511.812677625734[/C][C]502.568638060411[/C][C]521.056717191056[/C][/ROW]
[ROW][C]105[/C][C]510.919251806155[/C][C]501.049862883316[/C][C]520.788640728994[/C][/ROW]
[ROW][C]106[/C][C]509.696524902317[/C][C]499.222037962283[/C][C]520.171011842352[/C][/ROW]
[ROW][C]107[/C][C]508.814859839834[/C][C]497.751964589886[/C][C]519.877755089782[/C][/ROW]
[ROW][C]108[/C][C]507.831697801777[/C][C]496.194325733337[/C][C]519.469069870218[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279331&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279331&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	513.479622807105	510.110502254897	516.848743359312
98	512.936645148234	508.359666005189	517.513624291279
99	512.402012293275	506.846195280784	517.957829305765
100	511.363424340565	504.951612265768	517.775236415363
101	511.304080070032	504.11473383546	518.493426304604
102	511.328352828253	503.416433639057	519.240272017449
103	511.603968508552	503.010255748869	520.197681268235
104	511.812677625734	502.568638060411	521.056717191056
105	510.919251806155	501.049862883316	520.788640728994
106	509.696524902317	499.222037962283	520.171011842352
107	508.814859839834	497.751964589886	519.877755089782
108	507.831697801777	496.194325733337	519.469069870218

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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