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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 20 Dec 2010 10:32:37 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/20/t1292841244mfv8xf7uol6ze6o.htm/, Retrieved Fri, 03 May 2024 22:55:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112837, Retrieved Fri, 03 May 2024 22:55:35 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

194

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

-       [Exponential Smoothing] [Opgave 10; Opdrac...] [2010-12-20 10:32:37] [516d1a4ad1f0b8513272cbee80fe4619] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112837&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112837&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112837&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.165143187979639
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.165143187979639 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112837&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]0.165143187979639[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112837&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112837&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	0.165143187979639
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	13.91	13.99	-0.08
4	13.94	13.9867885449616	-0.046788544961629
5	13.96	14.0090617354857	-0.0490617354857346
6	14.01	14.0209595240798	-0.0109595240798104
7	14.01	14.0691496333345	-0.0591496333345294
8	14.06	14.0593814743178	0.00061852568216203
9	14.09	14.1094836196208	-0.0194836196208392
10	14.13	14.1362660325633	-0.00626603256326952
11	14.12	14.1752312399698	-0.055231239969789
12	14.13	14.1561101769251	-0.0261101769251066
13	14.14	14.1617982590690	-0.0217982590689836
14	14.16	14.1681984250739	-0.00819842507392643
15	14.21	14.1868445110208	0.0231554889791958
16	14.26	14.2406684822901	0.0193315177099418
17	14.29	14.2938609507532	-0.00386095075316284
18	14.32	14.3232233410372	-0.00322334103715072
19	14.33	14.3526910282223	-0.0226910282223312
20	14.39	14.3589437594832	0.0310562405168415
21	14.48	14.4240724860488	0.055927513951227
22	14.44	14.5233085339985	-0.083308533998455
23	14.46	14.4695506971080	-0.0095506971080379
24	14.48	14.4879734645402	-0.00797346454019099
25	14.53	14.5066567011868	0.0233432988132183
26	14.58	14.5605116879708	0.0194883120292442
27	14.62	14.6137300499476	0.00626995005239195
28	14.62	14.6547654894877	-0.0347654894877323
29	14.61	14.6490242057221	-0.0390242057220558
30	14.65	14.6325796239807	0.0174203760192579
31	14.68	14.6754564804124	0.00454351958763333
32	14.7	14.7062068117217	-0.00620681172171622
33	14.78	14.7251817990468	0.0548182009531981
34	14.84	14.8142346515115	0.0257653484884788
35	14.89	14.8784896233003	0.0115103766996842
36	14.89	14.9303904836033	-0.040390483603348
37	15.13	14.9237202703771	0.206279729622947
38	15.25	15.1977859625426	0.0522140374574356
39	15.33	15.3264087551456	0.00359124485442663
40	15.36	15.4070018247696	-0.0470018247696498
41	15.4	15.4292397935863	-0.0292397935863278
42	15.4	15.4644110408576	-0.0644110408576157
43	15.41	15.4537739962293	-0.0437739962293016
44	15.47	15.4565450189414	0.0134549810586133
45	15.54	15.5187670174076	0.0212329825923874
46	15.55	15.5922734998432	-0.0422734998432333
47	15.59	15.5952923193121	-0.00529231931206731
48	15.65	15.6344183288291	0.0155816711709349
49	15.75	15.6969915356803	0.0530084643197153
50	15.86	15.8057455224679	0.0542544775320533
51	15.89	15.9247052798498	-0.0347052798497582
52	15.94	15.9489739392956	-0.00897393929564672
53	15.93	15.9974919543516	-0.0674919543516257
54	15.95	15.9763461178470	-0.026346117847023
55	15.99	15.9919952359549	-0.00199523595487605
56	15.99	16.0316657363285	-0.0416657363285164
57	16.06	16.0247849238017	0.0352150761982912
58	16.08	16.1006004537500	-0.0206004537500384
59	16.07	16.1171984291439	-0.0471984291439291
60	16.11	16.0994039300875	0.0105960699125269
61	16.15	16.1411537988529	0.00884620114711865
62	16.18	16.1826146887118	-0.00261468871182302
63	16.3	16.2121828906824	0.0878171093176192
64	16.42	16.3466852880742	0.0733147119257538
65	16.49	16.4787927133275	0.0112072866725192
66	16.5	16.5506435203772	-0.0506435203771751
67	16.58	16.5522800879716	0.0277199120284202
68	16.64	16.6368578426145	0.00314215738553614
69	16.66	16.6973767485023	-0.0373767485022505
70	16.81	16.7112042330983	0.0987957669017234
71	16.91	16.8775196810033	0.0324803189966829
72	16.92	16.9828835844290	-0.0628835844290236
73	16.95	16.9824987888248	-0.0324987888248316
74	17.11	17.0071318352328	0.102868164767180
75	17.16	17.1841198119041	-0.0241198119040860
76	17.16	17.2301365892728	-0.0701365892727779
77	17.27	17.2185540093263	0.0514459906737486
78	17.34	17.3370499642349	0.00295003576511377
79	17.39	17.4075371425458	-0.0175371425457911
80	17.43	17.4546410029177	-0.0246410029177255
81	17.45	17.4905717091409	-0.0405717091408775
82	17.5	17.5038715677516	-0.00387156775157038
83	17.56	17.5532322047106	0.0067677952894023
84	17.65	17.6143498600003	0.0356501399997171

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 13.91 & 13.99 & -0.08 \tabularnewline
4 & 13.94 & 13.9867885449616 & -0.046788544961629 \tabularnewline
5 & 13.96 & 14.0090617354857 & -0.0490617354857346 \tabularnewline
6 & 14.01 & 14.0209595240798 & -0.0109595240798104 \tabularnewline
7 & 14.01 & 14.0691496333345 & -0.0591496333345294 \tabularnewline
8 & 14.06 & 14.0593814743178 & 0.00061852568216203 \tabularnewline
9 & 14.09 & 14.1094836196208 & -0.0194836196208392 \tabularnewline
10 & 14.13 & 14.1362660325633 & -0.00626603256326952 \tabularnewline
11 & 14.12 & 14.1752312399698 & -0.055231239969789 \tabularnewline
12 & 14.13 & 14.1561101769251 & -0.0261101769251066 \tabularnewline
13 & 14.14 & 14.1617982590690 & -0.0217982590689836 \tabularnewline
14 & 14.16 & 14.1681984250739 & -0.00819842507392643 \tabularnewline
15 & 14.21 & 14.1868445110208 & 0.0231554889791958 \tabularnewline
16 & 14.26 & 14.2406684822901 & 0.0193315177099418 \tabularnewline
17 & 14.29 & 14.2938609507532 & -0.00386095075316284 \tabularnewline
18 & 14.32 & 14.3232233410372 & -0.00322334103715072 \tabularnewline
19 & 14.33 & 14.3526910282223 & -0.0226910282223312 \tabularnewline
20 & 14.39 & 14.3589437594832 & 0.0310562405168415 \tabularnewline
21 & 14.48 & 14.4240724860488 & 0.055927513951227 \tabularnewline
22 & 14.44 & 14.5233085339985 & -0.083308533998455 \tabularnewline
23 & 14.46 & 14.4695506971080 & -0.0095506971080379 \tabularnewline
24 & 14.48 & 14.4879734645402 & -0.00797346454019099 \tabularnewline
25 & 14.53 & 14.5066567011868 & 0.0233432988132183 \tabularnewline
26 & 14.58 & 14.5605116879708 & 0.0194883120292442 \tabularnewline
27 & 14.62 & 14.6137300499476 & 0.00626995005239195 \tabularnewline
28 & 14.62 & 14.6547654894877 & -0.0347654894877323 \tabularnewline
29 & 14.61 & 14.6490242057221 & -0.0390242057220558 \tabularnewline
30 & 14.65 & 14.6325796239807 & 0.0174203760192579 \tabularnewline
31 & 14.68 & 14.6754564804124 & 0.00454351958763333 \tabularnewline
32 & 14.7 & 14.7062068117217 & -0.00620681172171622 \tabularnewline
33 & 14.78 & 14.7251817990468 & 0.0548182009531981 \tabularnewline
34 & 14.84 & 14.8142346515115 & 0.0257653484884788 \tabularnewline
35 & 14.89 & 14.8784896233003 & 0.0115103766996842 \tabularnewline
36 & 14.89 & 14.9303904836033 & -0.040390483603348 \tabularnewline
37 & 15.13 & 14.9237202703771 & 0.206279729622947 \tabularnewline
38 & 15.25 & 15.1977859625426 & 0.0522140374574356 \tabularnewline
39 & 15.33 & 15.3264087551456 & 0.00359124485442663 \tabularnewline
40 & 15.36 & 15.4070018247696 & -0.0470018247696498 \tabularnewline
41 & 15.4 & 15.4292397935863 & -0.0292397935863278 \tabularnewline
42 & 15.4 & 15.4644110408576 & -0.0644110408576157 \tabularnewline
43 & 15.41 & 15.4537739962293 & -0.0437739962293016 \tabularnewline
44 & 15.47 & 15.4565450189414 & 0.0134549810586133 \tabularnewline
45 & 15.54 & 15.5187670174076 & 0.0212329825923874 \tabularnewline
46 & 15.55 & 15.5922734998432 & -0.0422734998432333 \tabularnewline
47 & 15.59 & 15.5952923193121 & -0.00529231931206731 \tabularnewline
48 & 15.65 & 15.6344183288291 & 0.0155816711709349 \tabularnewline
49 & 15.75 & 15.6969915356803 & 0.0530084643197153 \tabularnewline
50 & 15.86 & 15.8057455224679 & 0.0542544775320533 \tabularnewline
51 & 15.89 & 15.9247052798498 & -0.0347052798497582 \tabularnewline
52 & 15.94 & 15.9489739392956 & -0.00897393929564672 \tabularnewline
53 & 15.93 & 15.9974919543516 & -0.0674919543516257 \tabularnewline
54 & 15.95 & 15.9763461178470 & -0.026346117847023 \tabularnewline
55 & 15.99 & 15.9919952359549 & -0.00199523595487605 \tabularnewline
56 & 15.99 & 16.0316657363285 & -0.0416657363285164 \tabularnewline
57 & 16.06 & 16.0247849238017 & 0.0352150761982912 \tabularnewline
58 & 16.08 & 16.1006004537500 & -0.0206004537500384 \tabularnewline
59 & 16.07 & 16.1171984291439 & -0.0471984291439291 \tabularnewline
60 & 16.11 & 16.0994039300875 & 0.0105960699125269 \tabularnewline
61 & 16.15 & 16.1411537988529 & 0.00884620114711865 \tabularnewline
62 & 16.18 & 16.1826146887118 & -0.00261468871182302 \tabularnewline
63 & 16.3 & 16.2121828906824 & 0.0878171093176192 \tabularnewline
64 & 16.42 & 16.3466852880742 & 0.0733147119257538 \tabularnewline
65 & 16.49 & 16.4787927133275 & 0.0112072866725192 \tabularnewline
66 & 16.5 & 16.5506435203772 & -0.0506435203771751 \tabularnewline
67 & 16.58 & 16.5522800879716 & 0.0277199120284202 \tabularnewline
68 & 16.64 & 16.6368578426145 & 0.00314215738553614 \tabularnewline
69 & 16.66 & 16.6973767485023 & -0.0373767485022505 \tabularnewline
70 & 16.81 & 16.7112042330983 & 0.0987957669017234 \tabularnewline
71 & 16.91 & 16.8775196810033 & 0.0324803189966829 \tabularnewline
72 & 16.92 & 16.9828835844290 & -0.0628835844290236 \tabularnewline
73 & 16.95 & 16.9824987888248 & -0.0324987888248316 \tabularnewline
74 & 17.11 & 17.0071318352328 & 0.102868164767180 \tabularnewline
75 & 17.16 & 17.1841198119041 & -0.0241198119040860 \tabularnewline
76 & 17.16 & 17.2301365892728 & -0.0701365892727779 \tabularnewline
77 & 17.27 & 17.2185540093263 & 0.0514459906737486 \tabularnewline
78 & 17.34 & 17.3370499642349 & 0.00295003576511377 \tabularnewline
79 & 17.39 & 17.4075371425458 & -0.0175371425457911 \tabularnewline
80 & 17.43 & 17.4546410029177 & -0.0246410029177255 \tabularnewline
81 & 17.45 & 17.4905717091409 & -0.0405717091408775 \tabularnewline
82 & 17.5 & 17.5038715677516 & -0.00387156775157038 \tabularnewline
83 & 17.56 & 17.5532322047106 & 0.0067677952894023 \tabularnewline
84 & 17.65 & 17.6143498600003 & 0.0356501399997171 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112837&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]13.91[/C][C]13.99[/C][C]-0.08[/C][/ROW]
[ROW][C]4[/C][C]13.94[/C][C]13.9867885449616[/C][C]-0.046788544961629[/C][/ROW]
[ROW][C]5[/C][C]13.96[/C][C]14.0090617354857[/C][C]-0.0490617354857346[/C][/ROW]
[ROW][C]6[/C][C]14.01[/C][C]14.0209595240798[/C][C]-0.0109595240798104[/C][/ROW]
[ROW][C]7[/C][C]14.01[/C][C]14.0691496333345[/C][C]-0.0591496333345294[/C][/ROW]
[ROW][C]8[/C][C]14.06[/C][C]14.0593814743178[/C][C]0.00061852568216203[/C][/ROW]
[ROW][C]9[/C][C]14.09[/C][C]14.1094836196208[/C][C]-0.0194836196208392[/C][/ROW]
[ROW][C]10[/C][C]14.13[/C][C]14.1362660325633[/C][C]-0.00626603256326952[/C][/ROW]
[ROW][C]11[/C][C]14.12[/C][C]14.1752312399698[/C][C]-0.055231239969789[/C][/ROW]
[ROW][C]12[/C][C]14.13[/C][C]14.1561101769251[/C][C]-0.0261101769251066[/C][/ROW]
[ROW][C]13[/C][C]14.14[/C][C]14.1617982590690[/C][C]-0.0217982590689836[/C][/ROW]
[ROW][C]14[/C][C]14.16[/C][C]14.1681984250739[/C][C]-0.00819842507392643[/C][/ROW]
[ROW][C]15[/C][C]14.21[/C][C]14.1868445110208[/C][C]0.0231554889791958[/C][/ROW]
[ROW][C]16[/C][C]14.26[/C][C]14.2406684822901[/C][C]0.0193315177099418[/C][/ROW]
[ROW][C]17[/C][C]14.29[/C][C]14.2938609507532[/C][C]-0.00386095075316284[/C][/ROW]
[ROW][C]18[/C][C]14.32[/C][C]14.3232233410372[/C][C]-0.00322334103715072[/C][/ROW]
[ROW][C]19[/C][C]14.33[/C][C]14.3526910282223[/C][C]-0.0226910282223312[/C][/ROW]
[ROW][C]20[/C][C]14.39[/C][C]14.3589437594832[/C][C]0.0310562405168415[/C][/ROW]
[ROW][C]21[/C][C]14.48[/C][C]14.4240724860488[/C][C]0.055927513951227[/C][/ROW]
[ROW][C]22[/C][C]14.44[/C][C]14.5233085339985[/C][C]-0.083308533998455[/C][/ROW]
[ROW][C]23[/C][C]14.46[/C][C]14.4695506971080[/C][C]-0.0095506971080379[/C][/ROW]
[ROW][C]24[/C][C]14.48[/C][C]14.4879734645402[/C][C]-0.00797346454019099[/C][/ROW]
[ROW][C]25[/C][C]14.53[/C][C]14.5066567011868[/C][C]0.0233432988132183[/C][/ROW]
[ROW][C]26[/C][C]14.58[/C][C]14.5605116879708[/C][C]0.0194883120292442[/C][/ROW]
[ROW][C]27[/C][C]14.62[/C][C]14.6137300499476[/C][C]0.00626995005239195[/C][/ROW]
[ROW][C]28[/C][C]14.62[/C][C]14.6547654894877[/C][C]-0.0347654894877323[/C][/ROW]
[ROW][C]29[/C][C]14.61[/C][C]14.6490242057221[/C][C]-0.0390242057220558[/C][/ROW]
[ROW][C]30[/C][C]14.65[/C][C]14.6325796239807[/C][C]0.0174203760192579[/C][/ROW]
[ROW][C]31[/C][C]14.68[/C][C]14.6754564804124[/C][C]0.00454351958763333[/C][/ROW]
[ROW][C]32[/C][C]14.7[/C][C]14.7062068117217[/C][C]-0.00620681172171622[/C][/ROW]
[ROW][C]33[/C][C]14.78[/C][C]14.7251817990468[/C][C]0.0548182009531981[/C][/ROW]
[ROW][C]34[/C][C]14.84[/C][C]14.8142346515115[/C][C]0.0257653484884788[/C][/ROW]
[ROW][C]35[/C][C]14.89[/C][C]14.8784896233003[/C][C]0.0115103766996842[/C][/ROW]
[ROW][C]36[/C][C]14.89[/C][C]14.9303904836033[/C][C]-0.040390483603348[/C][/ROW]
[ROW][C]37[/C][C]15.13[/C][C]14.9237202703771[/C][C]0.206279729622947[/C][/ROW]
[ROW][C]38[/C][C]15.25[/C][C]15.1977859625426[/C][C]0.0522140374574356[/C][/ROW]
[ROW][C]39[/C][C]15.33[/C][C]15.3264087551456[/C][C]0.00359124485442663[/C][/ROW]
[ROW][C]40[/C][C]15.36[/C][C]15.4070018247696[/C][C]-0.0470018247696498[/C][/ROW]
[ROW][C]41[/C][C]15.4[/C][C]15.4292397935863[/C][C]-0.0292397935863278[/C][/ROW]
[ROW][C]42[/C][C]15.4[/C][C]15.4644110408576[/C][C]-0.0644110408576157[/C][/ROW]
[ROW][C]43[/C][C]15.41[/C][C]15.4537739962293[/C][C]-0.0437739962293016[/C][/ROW]
[ROW][C]44[/C][C]15.47[/C][C]15.4565450189414[/C][C]0.0134549810586133[/C][/ROW]
[ROW][C]45[/C][C]15.54[/C][C]15.5187670174076[/C][C]0.0212329825923874[/C][/ROW]
[ROW][C]46[/C][C]15.55[/C][C]15.5922734998432[/C][C]-0.0422734998432333[/C][/ROW]
[ROW][C]47[/C][C]15.59[/C][C]15.5952923193121[/C][C]-0.00529231931206731[/C][/ROW]
[ROW][C]48[/C][C]15.65[/C][C]15.6344183288291[/C][C]0.0155816711709349[/C][/ROW]
[ROW][C]49[/C][C]15.75[/C][C]15.6969915356803[/C][C]0.0530084643197153[/C][/ROW]
[ROW][C]50[/C][C]15.86[/C][C]15.8057455224679[/C][C]0.0542544775320533[/C][/ROW]
[ROW][C]51[/C][C]15.89[/C][C]15.9247052798498[/C][C]-0.0347052798497582[/C][/ROW]
[ROW][C]52[/C][C]15.94[/C][C]15.9489739392956[/C][C]-0.00897393929564672[/C][/ROW]
[ROW][C]53[/C][C]15.93[/C][C]15.9974919543516[/C][C]-0.0674919543516257[/C][/ROW]
[ROW][C]54[/C][C]15.95[/C][C]15.9763461178470[/C][C]-0.026346117847023[/C][/ROW]
[ROW][C]55[/C][C]15.99[/C][C]15.9919952359549[/C][C]-0.00199523595487605[/C][/ROW]
[ROW][C]56[/C][C]15.99[/C][C]16.0316657363285[/C][C]-0.0416657363285164[/C][/ROW]
[ROW][C]57[/C][C]16.06[/C][C]16.0247849238017[/C][C]0.0352150761982912[/C][/ROW]
[ROW][C]58[/C][C]16.08[/C][C]16.1006004537500[/C][C]-0.0206004537500384[/C][/ROW]
[ROW][C]59[/C][C]16.07[/C][C]16.1171984291439[/C][C]-0.0471984291439291[/C][/ROW]
[ROW][C]60[/C][C]16.11[/C][C]16.0994039300875[/C][C]0.0105960699125269[/C][/ROW]
[ROW][C]61[/C][C]16.15[/C][C]16.1411537988529[/C][C]0.00884620114711865[/C][/ROW]
[ROW][C]62[/C][C]16.18[/C][C]16.1826146887118[/C][C]-0.00261468871182302[/C][/ROW]
[ROW][C]63[/C][C]16.3[/C][C]16.2121828906824[/C][C]0.0878171093176192[/C][/ROW]
[ROW][C]64[/C][C]16.42[/C][C]16.3466852880742[/C][C]0.0733147119257538[/C][/ROW]
[ROW][C]65[/C][C]16.49[/C][C]16.4787927133275[/C][C]0.0112072866725192[/C][/ROW]
[ROW][C]66[/C][C]16.5[/C][C]16.5506435203772[/C][C]-0.0506435203771751[/C][/ROW]
[ROW][C]67[/C][C]16.58[/C][C]16.5522800879716[/C][C]0.0277199120284202[/C][/ROW]
[ROW][C]68[/C][C]16.64[/C][C]16.6368578426145[/C][C]0.00314215738553614[/C][/ROW]
[ROW][C]69[/C][C]16.66[/C][C]16.6973767485023[/C][C]-0.0373767485022505[/C][/ROW]
[ROW][C]70[/C][C]16.81[/C][C]16.7112042330983[/C][C]0.0987957669017234[/C][/ROW]
[ROW][C]71[/C][C]16.91[/C][C]16.8775196810033[/C][C]0.0324803189966829[/C][/ROW]
[ROW][C]72[/C][C]16.92[/C][C]16.9828835844290[/C][C]-0.0628835844290236[/C][/ROW]
[ROW][C]73[/C][C]16.95[/C][C]16.9824987888248[/C][C]-0.0324987888248316[/C][/ROW]
[ROW][C]74[/C][C]17.11[/C][C]17.0071318352328[/C][C]0.102868164767180[/C][/ROW]
[ROW][C]75[/C][C]17.16[/C][C]17.1841198119041[/C][C]-0.0241198119040860[/C][/ROW]
[ROW][C]76[/C][C]17.16[/C][C]17.2301365892728[/C][C]-0.0701365892727779[/C][/ROW]
[ROW][C]77[/C][C]17.27[/C][C]17.2185540093263[/C][C]0.0514459906737486[/C][/ROW]
[ROW][C]78[/C][C]17.34[/C][C]17.3370499642349[/C][C]0.00295003576511377[/C][/ROW]
[ROW][C]79[/C][C]17.39[/C][C]17.4075371425458[/C][C]-0.0175371425457911[/C][/ROW]
[ROW][C]80[/C][C]17.43[/C][C]17.4546410029177[/C][C]-0.0246410029177255[/C][/ROW]
[ROW][C]81[/C][C]17.45[/C][C]17.4905717091409[/C][C]-0.0405717091408775[/C][/ROW]
[ROW][C]82[/C][C]17.5[/C][C]17.5038715677516[/C][C]-0.00387156775157038[/C][/ROW]
[ROW][C]83[/C][C]17.56[/C][C]17.5532322047106[/C][C]0.0067677952894023[/C][/ROW]
[ROW][C]84[/C][C]17.65[/C][C]17.6143498600003[/C][C]0.0356501399997171[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112837&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112837&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	13.91	13.99	-0.08
4	13.94	13.9867885449616	-0.046788544961629
5	13.96	14.0090617354857	-0.0490617354857346
6	14.01	14.0209595240798	-0.0109595240798104
7	14.01	14.0691496333345	-0.0591496333345294
8	14.06	14.0593814743178	0.00061852568216203
9	14.09	14.1094836196208	-0.0194836196208392
10	14.13	14.1362660325633	-0.00626603256326952
11	14.12	14.1752312399698	-0.055231239969789
12	14.13	14.1561101769251	-0.0261101769251066
13	14.14	14.1617982590690	-0.0217982590689836
14	14.16	14.1681984250739	-0.00819842507392643
15	14.21	14.1868445110208	0.0231554889791958
16	14.26	14.2406684822901	0.0193315177099418
17	14.29	14.2938609507532	-0.00386095075316284
18	14.32	14.3232233410372	-0.00322334103715072
19	14.33	14.3526910282223	-0.0226910282223312
20	14.39	14.3589437594832	0.0310562405168415
21	14.48	14.4240724860488	0.055927513951227
22	14.44	14.5233085339985	-0.083308533998455
23	14.46	14.4695506971080	-0.0095506971080379
24	14.48	14.4879734645402	-0.00797346454019099
25	14.53	14.5066567011868	0.0233432988132183
26	14.58	14.5605116879708	0.0194883120292442
27	14.62	14.6137300499476	0.00626995005239195
28	14.62	14.6547654894877	-0.0347654894877323
29	14.61	14.6490242057221	-0.0390242057220558
30	14.65	14.6325796239807	0.0174203760192579
31	14.68	14.6754564804124	0.00454351958763333
32	14.7	14.7062068117217	-0.00620681172171622
33	14.78	14.7251817990468	0.0548182009531981
34	14.84	14.8142346515115	0.0257653484884788
35	14.89	14.8784896233003	0.0115103766996842
36	14.89	14.9303904836033	-0.040390483603348
37	15.13	14.9237202703771	0.206279729622947
38	15.25	15.1977859625426	0.0522140374574356
39	15.33	15.3264087551456	0.00359124485442663
40	15.36	15.4070018247696	-0.0470018247696498
41	15.4	15.4292397935863	-0.0292397935863278
42	15.4	15.4644110408576	-0.0644110408576157
43	15.41	15.4537739962293	-0.0437739962293016
44	15.47	15.4565450189414	0.0134549810586133
45	15.54	15.5187670174076	0.0212329825923874
46	15.55	15.5922734998432	-0.0422734998432333
47	15.59	15.5952923193121	-0.00529231931206731
48	15.65	15.6344183288291	0.0155816711709349
49	15.75	15.6969915356803	0.0530084643197153
50	15.86	15.8057455224679	0.0542544775320533
51	15.89	15.9247052798498	-0.0347052798497582
52	15.94	15.9489739392956	-0.00897393929564672
53	15.93	15.9974919543516	-0.0674919543516257
54	15.95	15.9763461178470	-0.026346117847023
55	15.99	15.9919952359549	-0.00199523595487605
56	15.99	16.0316657363285	-0.0416657363285164
57	16.06	16.0247849238017	0.0352150761982912
58	16.08	16.1006004537500	-0.0206004537500384
59	16.07	16.1171984291439	-0.0471984291439291
60	16.11	16.0994039300875	0.0105960699125269
61	16.15	16.1411537988529	0.00884620114711865
62	16.18	16.1826146887118	-0.00261468871182302
63	16.3	16.2121828906824	0.0878171093176192
64	16.42	16.3466852880742	0.0733147119257538
65	16.49	16.4787927133275	0.0112072866725192
66	16.5	16.5506435203772	-0.0506435203771751
67	16.58	16.5522800879716	0.0277199120284202
68	16.64	16.6368578426145	0.00314215738553614
69	16.66	16.6973767485023	-0.0373767485022505
70	16.81	16.7112042330983	0.0987957669017234
71	16.91	16.8775196810033	0.0324803189966829
72	16.92	16.9828835844290	-0.0628835844290236
73	16.95	16.9824987888248	-0.0324987888248316
74	17.11	17.0071318352328	0.102868164767180
75	17.16	17.1841198119041	-0.0241198119040860
76	17.16	17.2301365892728	-0.0701365892727779
77	17.27	17.2185540093263	0.0514459906737486
78	17.34	17.3370499642349	0.00295003576511377
79	17.39	17.4075371425458	-0.0175371425457911
80	17.43	17.4546410029177	-0.0246410029177255
81	17.45	17.4905717091409	-0.0405717091408775
82	17.5	17.5038715677516	-0.00387156775157038
83	17.56	17.5532322047106	0.0067677952894023
84	17.65	17.6143498600003	0.0356501399997171

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	17.7102372377718	17.6197425540635	17.8007319214801
86	17.7704744755435	17.6315258295282	17.9094231215588
87	17.8307117133153	17.6468666798591	18.0145567467714
88	17.8909489510870	17.6626667155827	18.1192311865913
89	17.9511861888588	17.6778827762073	18.2244896015102
90	18.0114234266305	17.6920621793522	18.3307846739089
91	18.0716606644023	17.7049864047222	18.4383349240824
92	18.1318979021740	17.716546658418	18.5472491459301
93	18.1921351399458	17.7266910335562	18.6575792463353
94	18.2523723777176	17.7353990949093	18.7693456605258
95	18.3126096154893	17.7426685540097	18.8825506769689
96	18.3728468532611	17.7485078328419	18.9971858736802

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 17.7102372377718 & 17.6197425540635 & 17.8007319214801 \tabularnewline
86 & 17.7704744755435 & 17.6315258295282 & 17.9094231215588 \tabularnewline
87 & 17.8307117133153 & 17.6468666798591 & 18.0145567467714 \tabularnewline
88 & 17.8909489510870 & 17.6626667155827 & 18.1192311865913 \tabularnewline
89 & 17.9511861888588 & 17.6778827762073 & 18.2244896015102 \tabularnewline
90 & 18.0114234266305 & 17.6920621793522 & 18.3307846739089 \tabularnewline
91 & 18.0716606644023 & 17.7049864047222 & 18.4383349240824 \tabularnewline
92 & 18.1318979021740 & 17.716546658418 & 18.5472491459301 \tabularnewline
93 & 18.1921351399458 & 17.7266910335562 & 18.6575792463353 \tabularnewline
94 & 18.2523723777176 & 17.7353990949093 & 18.7693456605258 \tabularnewline
95 & 18.3126096154893 & 17.7426685540097 & 18.8825506769689 \tabularnewline
96 & 18.3728468532611 & 17.7485078328419 & 18.9971858736802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112837&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]17.7102372377718[/C][C]17.6197425540635[/C][C]17.8007319214801[/C][/ROW]
[ROW][C]86[/C][C]17.7704744755435[/C][C]17.6315258295282[/C][C]17.9094231215588[/C][/ROW]
[ROW][C]87[/C][C]17.8307117133153[/C][C]17.6468666798591[/C][C]18.0145567467714[/C][/ROW]
[ROW][C]88[/C][C]17.8909489510870[/C][C]17.6626667155827[/C][C]18.1192311865913[/C][/ROW]
[ROW][C]89[/C][C]17.9511861888588[/C][C]17.6778827762073[/C][C]18.2244896015102[/C][/ROW]
[ROW][C]90[/C][C]18.0114234266305[/C][C]17.6920621793522[/C][C]18.3307846739089[/C][/ROW]
[ROW][C]91[/C][C]18.0716606644023[/C][C]17.7049864047222[/C][C]18.4383349240824[/C][/ROW]
[ROW][C]92[/C][C]18.1318979021740[/C][C]17.716546658418[/C][C]18.5472491459301[/C][/ROW]
[ROW][C]93[/C][C]18.1921351399458[/C][C]17.7266910335562[/C][C]18.6575792463353[/C][/ROW]
[ROW][C]94[/C][C]18.2523723777176[/C][C]17.7353990949093[/C][C]18.7693456605258[/C][/ROW]
[ROW][C]95[/C][C]18.3126096154893[/C][C]17.7426685540097[/C][C]18.8825506769689[/C][/ROW]
[ROW][C]96[/C][C]18.3728468532611[/C][C]17.7485078328419[/C][C]18.9971858736802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112837&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112837&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	17.7102372377718	17.6197425540635	17.8007319214801
86	17.7704744755435	17.6315258295282	17.9094231215588
87	17.8307117133153	17.6468666798591	18.0145567467714
88	17.8909489510870	17.6626667155827	18.1192311865913
89	17.9511861888588	17.6778827762073	18.2244896015102
90	18.0114234266305	17.6920621793522	18.3307846739089
91	18.0716606644023	17.7049864047222	18.4383349240824
92	18.1318979021740	17.716546658418	18.5472491459301
93	18.1921351399458	17.7266910335562	18.6575792463353
94	18.2523723777176	17.7353990949093	18.7693456605258
95	18.3126096154893	17.7426685540097	18.8825506769689
96	18.3728468532611	17.7485078328419	18.9971858736802

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