Free Statistics

of Irreproducible Research!

Author's title

Opgave 10-Stap 2- Gemiddelde prijs pepersteak-Stap 4 verbetering- Van Lisho...

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 19 May 2011 18:13:11 +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/2011/May/19/t1305828716jh9ppu2hwmljk4z.htm/, Retrieved Sat, 11 May 2024 20:05:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122177, Retrieved Sat, 11 May 2024 20:05:14 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

100

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

-     [Mean versus Median] [Opgave 5 stap 4- ...] [2011-04-05 13:06:33] [5a2e91864be749652d37f2fec149cb5d]
- RMPD    [Exponential Smoothing] [Opgave 10-Stap 2-...] [2011-05-19 18:13:11] [e9fe47e6daef93c4d0b1cb3b475ca7f4] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122177&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122177&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122177&T=0

As an alternative you can also use a QR Code:

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

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.165143187979721
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.165143187979721 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122177&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]0.165143187979721[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122177&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122177&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	0.165143187979721
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	13.91	13.99	-0.08
4	13.94	13.9867885449616	-0.0467885449616237
5	13.96	14.0090617354857	-0.0490617354857257
6	14.01	14.0209595240798	-0.0109595240797979
7	14.01	14.0691496333345	-0.0591496333345187
8	14.06	14.0593814743178	0.000618525682176241
9	14.09	14.1094836196208	-0.0194836196208268
10	14.13	14.1362660325633	-0.00626603256325708
11	14.12	14.1752312399698	-0.0552312399697783
12	14.13	14.1561101769251	-0.0261101769250942
13	14.14	14.161798259069	-0.0217982590689711
14	14.16	14.1681984250739	-0.008198425073914
15	14.21	14.1868445110208	0.0231554889792065
16	14.26	14.2406684822901	0.0193315177099489
17	14.29	14.2938609507532	-0.00386095075315751
18	14.32	14.3232233410371	-0.00322334103714716
19	14.33	14.3526910282223	-0.0226910282223276
20	14.39	14.3589437594832	0.0310562405168451
21	14.48	14.4240724860488	0.0559275139512287
22	14.44	14.5233085339985	-0.0833085339984585
23	14.46	14.469550697108	-0.00955069710803436
24	14.48	14.4879734645402	-0.00797346454018566
25	14.53	14.5066567011868	0.0233432988132236
26	14.58	14.5605116879708	0.0194883120292459
27	14.62	14.6137300499476	0.00626995005239017
28	14.62	14.6547654894877	-0.0347654894877341
29	14.61	14.6490242057221	-0.039024205722054
30	14.65	14.6325796239807	0.0174203760192633
31	14.68	14.6754564804124	0.0045435195876351
32	14.7	14.7062068117217	-0.00620681172171444
33	14.78	14.7251817990468	0.0548182009531999
34	14.84	14.8142346515115	0.0257653484884752
35	14.89	14.8784896233003	0.0115103766996807
36	14.89	14.9303904836034	-0.0403904836033533
37	15.13	14.9237202703771	0.206279729622947
38	15.25	15.1977859625426	0.0522140374574178
39	15.33	15.3264087551456	0.00359124485440887
40	15.36	15.4070018247697	-0.0470018247696657
41	15.4	15.4292397935863	-0.0292397935863367
42	15.4	15.4644110408576	-0.064411040857621
43	15.41	15.4537739962293	-0.0437739962293016
44	15.47	15.4565450189414	0.0134549810586186
45	15.54	15.5187670174076	0.0212329825923891
46	15.55	15.5922734998432	-0.0422734998432333
47	15.59	15.5952923193121	-0.00529231931206375
48	15.65	15.6344183288291	0.0155816711709384
49	15.75	15.6969915356803	0.0530084643197171
50	15.86	15.8057455224679	0.0542544775320497
51	15.89	15.9247052798498	-0.0347052798497653
52	15.94	15.9489739392956	-0.0089739392956485
53	15.93	15.9974919543516	-0.0674919543516275
54	15.95	15.976346117847	-0.0263461178470195
55	15.99	15.9919952359549	-0.00199523595487072
56	15.99	16.0316657363285	-0.0416657363285129
57	16.06	16.0247849238017	0.0352150761982983
58	16.08	16.10060045375	-0.0206004537500348
59	16.07	16.1171984291439	-0.0471984291439256
60	16.11	16.0994039300875	0.010596069912534
61	16.15	16.1411537988529	0.0088462011471222
62	16.18	16.1826146887118	-0.00261468871181947
63	16.3	16.2121828906824	0.0878171093176228
64	16.42	16.3466852880743	0.0733147119257467
65	16.49	16.4787927133275	0.0112072866725121
66	16.5	16.5506435203772	-0.0506435203771858
67	16.58	16.5522800879716	0.0277199120284166
68	16.64	16.6368578426145	0.00314215738552903
69	16.66	16.6973767485023	-0.037376748502254
70	16.81	16.7112042330983	0.0987957669017234
71	16.91	16.8775196810033	0.0324803189966758
72	16.92	16.982883584429	-0.0628835844290343
73	16.95	16.9824987888248	-0.0324987888248351
74	17.11	17.0071318352328	0.10286816476718
75	17.16	17.1841198119041	-0.0241198119040931
76	17.16	17.2301365892728	-0.0701365892727814
77	17.27	17.2185540093263	0.0514459906737486
78	17.34	17.3370499642349	0.00295003576511021
79	17.39	17.4075371425458	-0.0175371425457911
80	17.43	17.4546410029177	-0.0246410029177255
81	17.45	17.4905717091409	-0.0405717091408739
82	17.5	17.5038715677516	-0.00387156775156328
83	17.56	17.5532322047106	0.00676779528940585
84	17.65	17.6143498600003	0.0356501399997207

\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 & -0.0467885449616237 \tabularnewline
5 & 13.96 & 14.0090617354857 & -0.0490617354857257 \tabularnewline
6 & 14.01 & 14.0209595240798 & -0.0109595240797979 \tabularnewline
7 & 14.01 & 14.0691496333345 & -0.0591496333345187 \tabularnewline
8 & 14.06 & 14.0593814743178 & 0.000618525682176241 \tabularnewline
9 & 14.09 & 14.1094836196208 & -0.0194836196208268 \tabularnewline
10 & 14.13 & 14.1362660325633 & -0.00626603256325708 \tabularnewline
11 & 14.12 & 14.1752312399698 & -0.0552312399697783 \tabularnewline
12 & 14.13 & 14.1561101769251 & -0.0261101769250942 \tabularnewline
13 & 14.14 & 14.161798259069 & -0.0217982590689711 \tabularnewline
14 & 14.16 & 14.1681984250739 & -0.008198425073914 \tabularnewline
15 & 14.21 & 14.1868445110208 & 0.0231554889792065 \tabularnewline
16 & 14.26 & 14.2406684822901 & 0.0193315177099489 \tabularnewline
17 & 14.29 & 14.2938609507532 & -0.00386095075315751 \tabularnewline
18 & 14.32 & 14.3232233410371 & -0.00322334103714716 \tabularnewline
19 & 14.33 & 14.3526910282223 & -0.0226910282223276 \tabularnewline
20 & 14.39 & 14.3589437594832 & 0.0310562405168451 \tabularnewline
21 & 14.48 & 14.4240724860488 & 0.0559275139512287 \tabularnewline
22 & 14.44 & 14.5233085339985 & -0.0833085339984585 \tabularnewline
23 & 14.46 & 14.469550697108 & -0.00955069710803436 \tabularnewline
24 & 14.48 & 14.4879734645402 & -0.00797346454018566 \tabularnewline
25 & 14.53 & 14.5066567011868 & 0.0233432988132236 \tabularnewline
26 & 14.58 & 14.5605116879708 & 0.0194883120292459 \tabularnewline
27 & 14.62 & 14.6137300499476 & 0.00626995005239017 \tabularnewline
28 & 14.62 & 14.6547654894877 & -0.0347654894877341 \tabularnewline
29 & 14.61 & 14.6490242057221 & -0.039024205722054 \tabularnewline
30 & 14.65 & 14.6325796239807 & 0.0174203760192633 \tabularnewline
31 & 14.68 & 14.6754564804124 & 0.0045435195876351 \tabularnewline
32 & 14.7 & 14.7062068117217 & -0.00620681172171444 \tabularnewline
33 & 14.78 & 14.7251817990468 & 0.0548182009531999 \tabularnewline
34 & 14.84 & 14.8142346515115 & 0.0257653484884752 \tabularnewline
35 & 14.89 & 14.8784896233003 & 0.0115103766996807 \tabularnewline
36 & 14.89 & 14.9303904836034 & -0.0403904836033533 \tabularnewline
37 & 15.13 & 14.9237202703771 & 0.206279729622947 \tabularnewline
38 & 15.25 & 15.1977859625426 & 0.0522140374574178 \tabularnewline
39 & 15.33 & 15.3264087551456 & 0.00359124485440887 \tabularnewline
40 & 15.36 & 15.4070018247697 & -0.0470018247696657 \tabularnewline
41 & 15.4 & 15.4292397935863 & -0.0292397935863367 \tabularnewline
42 & 15.4 & 15.4644110408576 & -0.064411040857621 \tabularnewline
43 & 15.41 & 15.4537739962293 & -0.0437739962293016 \tabularnewline
44 & 15.47 & 15.4565450189414 & 0.0134549810586186 \tabularnewline
45 & 15.54 & 15.5187670174076 & 0.0212329825923891 \tabularnewline
46 & 15.55 & 15.5922734998432 & -0.0422734998432333 \tabularnewline
47 & 15.59 & 15.5952923193121 & -0.00529231931206375 \tabularnewline
48 & 15.65 & 15.6344183288291 & 0.0155816711709384 \tabularnewline
49 & 15.75 & 15.6969915356803 & 0.0530084643197171 \tabularnewline
50 & 15.86 & 15.8057455224679 & 0.0542544775320497 \tabularnewline
51 & 15.89 & 15.9247052798498 & -0.0347052798497653 \tabularnewline
52 & 15.94 & 15.9489739392956 & -0.0089739392956485 \tabularnewline
53 & 15.93 & 15.9974919543516 & -0.0674919543516275 \tabularnewline
54 & 15.95 & 15.976346117847 & -0.0263461178470195 \tabularnewline
55 & 15.99 & 15.9919952359549 & -0.00199523595487072 \tabularnewline
56 & 15.99 & 16.0316657363285 & -0.0416657363285129 \tabularnewline
57 & 16.06 & 16.0247849238017 & 0.0352150761982983 \tabularnewline
58 & 16.08 & 16.10060045375 & -0.0206004537500348 \tabularnewline
59 & 16.07 & 16.1171984291439 & -0.0471984291439256 \tabularnewline
60 & 16.11 & 16.0994039300875 & 0.010596069912534 \tabularnewline
61 & 16.15 & 16.1411537988529 & 0.0088462011471222 \tabularnewline
62 & 16.18 & 16.1826146887118 & -0.00261468871181947 \tabularnewline
63 & 16.3 & 16.2121828906824 & 0.0878171093176228 \tabularnewline
64 & 16.42 & 16.3466852880743 & 0.0733147119257467 \tabularnewline
65 & 16.49 & 16.4787927133275 & 0.0112072866725121 \tabularnewline
66 & 16.5 & 16.5506435203772 & -0.0506435203771858 \tabularnewline
67 & 16.58 & 16.5522800879716 & 0.0277199120284166 \tabularnewline
68 & 16.64 & 16.6368578426145 & 0.00314215738552903 \tabularnewline
69 & 16.66 & 16.6973767485023 & -0.037376748502254 \tabularnewline
70 & 16.81 & 16.7112042330983 & 0.0987957669017234 \tabularnewline
71 & 16.91 & 16.8775196810033 & 0.0324803189966758 \tabularnewline
72 & 16.92 & 16.982883584429 & -0.0628835844290343 \tabularnewline
73 & 16.95 & 16.9824987888248 & -0.0324987888248351 \tabularnewline
74 & 17.11 & 17.0071318352328 & 0.10286816476718 \tabularnewline
75 & 17.16 & 17.1841198119041 & -0.0241198119040931 \tabularnewline
76 & 17.16 & 17.2301365892728 & -0.0701365892727814 \tabularnewline
77 & 17.27 & 17.2185540093263 & 0.0514459906737486 \tabularnewline
78 & 17.34 & 17.3370499642349 & 0.00295003576511021 \tabularnewline
79 & 17.39 & 17.4075371425458 & -0.0175371425457911 \tabularnewline
80 & 17.43 & 17.4546410029177 & -0.0246410029177255 \tabularnewline
81 & 17.45 & 17.4905717091409 & -0.0405717091408739 \tabularnewline
82 & 17.5 & 17.5038715677516 & -0.00387156775156328 \tabularnewline
83 & 17.56 & 17.5532322047106 & 0.00676779528940585 \tabularnewline
84 & 17.65 & 17.6143498600003 & 0.0356501399997207 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122177&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]-0.0467885449616237[/C][/ROW]
[ROW][C]5[/C][C]13.96[/C][C]14.0090617354857[/C][C]-0.0490617354857257[/C][/ROW]
[ROW][C]6[/C][C]14.01[/C][C]14.0209595240798[/C][C]-0.0109595240797979[/C][/ROW]
[ROW][C]7[/C][C]14.01[/C][C]14.0691496333345[/C][C]-0.0591496333345187[/C][/ROW]
[ROW][C]8[/C][C]14.06[/C][C]14.0593814743178[/C][C]0.000618525682176241[/C][/ROW]
[ROW][C]9[/C][C]14.09[/C][C]14.1094836196208[/C][C]-0.0194836196208268[/C][/ROW]
[ROW][C]10[/C][C]14.13[/C][C]14.1362660325633[/C][C]-0.00626603256325708[/C][/ROW]
[ROW][C]11[/C][C]14.12[/C][C]14.1752312399698[/C][C]-0.0552312399697783[/C][/ROW]
[ROW][C]12[/C][C]14.13[/C][C]14.1561101769251[/C][C]-0.0261101769250942[/C][/ROW]
[ROW][C]13[/C][C]14.14[/C][C]14.161798259069[/C][C]-0.0217982590689711[/C][/ROW]
[ROW][C]14[/C][C]14.16[/C][C]14.1681984250739[/C][C]-0.008198425073914[/C][/ROW]
[ROW][C]15[/C][C]14.21[/C][C]14.1868445110208[/C][C]0.0231554889792065[/C][/ROW]
[ROW][C]16[/C][C]14.26[/C][C]14.2406684822901[/C][C]0.0193315177099489[/C][/ROW]
[ROW][C]17[/C][C]14.29[/C][C]14.2938609507532[/C][C]-0.00386095075315751[/C][/ROW]
[ROW][C]18[/C][C]14.32[/C][C]14.3232233410371[/C][C]-0.00322334103714716[/C][/ROW]
[ROW][C]19[/C][C]14.33[/C][C]14.3526910282223[/C][C]-0.0226910282223276[/C][/ROW]
[ROW][C]20[/C][C]14.39[/C][C]14.3589437594832[/C][C]0.0310562405168451[/C][/ROW]
[ROW][C]21[/C][C]14.48[/C][C]14.4240724860488[/C][C]0.0559275139512287[/C][/ROW]
[ROW][C]22[/C][C]14.44[/C][C]14.5233085339985[/C][C]-0.0833085339984585[/C][/ROW]
[ROW][C]23[/C][C]14.46[/C][C]14.469550697108[/C][C]-0.00955069710803436[/C][/ROW]
[ROW][C]24[/C][C]14.48[/C][C]14.4879734645402[/C][C]-0.00797346454018566[/C][/ROW]
[ROW][C]25[/C][C]14.53[/C][C]14.5066567011868[/C][C]0.0233432988132236[/C][/ROW]
[ROW][C]26[/C][C]14.58[/C][C]14.5605116879708[/C][C]0.0194883120292459[/C][/ROW]
[ROW][C]27[/C][C]14.62[/C][C]14.6137300499476[/C][C]0.00626995005239017[/C][/ROW]
[ROW][C]28[/C][C]14.62[/C][C]14.6547654894877[/C][C]-0.0347654894877341[/C][/ROW]
[ROW][C]29[/C][C]14.61[/C][C]14.6490242057221[/C][C]-0.039024205722054[/C][/ROW]
[ROW][C]30[/C][C]14.65[/C][C]14.6325796239807[/C][C]0.0174203760192633[/C][/ROW]
[ROW][C]31[/C][C]14.68[/C][C]14.6754564804124[/C][C]0.0045435195876351[/C][/ROW]
[ROW][C]32[/C][C]14.7[/C][C]14.7062068117217[/C][C]-0.00620681172171444[/C][/ROW]
[ROW][C]33[/C][C]14.78[/C][C]14.7251817990468[/C][C]0.0548182009531999[/C][/ROW]
[ROW][C]34[/C][C]14.84[/C][C]14.8142346515115[/C][C]0.0257653484884752[/C][/ROW]
[ROW][C]35[/C][C]14.89[/C][C]14.8784896233003[/C][C]0.0115103766996807[/C][/ROW]
[ROW][C]36[/C][C]14.89[/C][C]14.9303904836034[/C][C]-0.0403904836033533[/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]0.0522140374574178[/C][/ROW]
[ROW][C]39[/C][C]15.33[/C][C]15.3264087551456[/C][C]0.00359124485440887[/C][/ROW]
[ROW][C]40[/C][C]15.36[/C][C]15.4070018247697[/C][C]-0.0470018247696657[/C][/ROW]
[ROW][C]41[/C][C]15.4[/C][C]15.4292397935863[/C][C]-0.0292397935863367[/C][/ROW]
[ROW][C]42[/C][C]15.4[/C][C]15.4644110408576[/C][C]-0.064411040857621[/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]0.0134549810586186[/C][/ROW]
[ROW][C]45[/C][C]15.54[/C][C]15.5187670174076[/C][C]0.0212329825923891[/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]-0.00529231931206375[/C][/ROW]
[ROW][C]48[/C][C]15.65[/C][C]15.6344183288291[/C][C]0.0155816711709384[/C][/ROW]
[ROW][C]49[/C][C]15.75[/C][C]15.6969915356803[/C][C]0.0530084643197171[/C][/ROW]
[ROW][C]50[/C][C]15.86[/C][C]15.8057455224679[/C][C]0.0542544775320497[/C][/ROW]
[ROW][C]51[/C][C]15.89[/C][C]15.9247052798498[/C][C]-0.0347052798497653[/C][/ROW]
[ROW][C]52[/C][C]15.94[/C][C]15.9489739392956[/C][C]-0.0089739392956485[/C][/ROW]
[ROW][C]53[/C][C]15.93[/C][C]15.9974919543516[/C][C]-0.0674919543516275[/C][/ROW]
[ROW][C]54[/C][C]15.95[/C][C]15.976346117847[/C][C]-0.0263461178470195[/C][/ROW]
[ROW][C]55[/C][C]15.99[/C][C]15.9919952359549[/C][C]-0.00199523595487072[/C][/ROW]
[ROW][C]56[/C][C]15.99[/C][C]16.0316657363285[/C][C]-0.0416657363285129[/C][/ROW]
[ROW][C]57[/C][C]16.06[/C][C]16.0247849238017[/C][C]0.0352150761982983[/C][/ROW]
[ROW][C]58[/C][C]16.08[/C][C]16.10060045375[/C][C]-0.0206004537500348[/C][/ROW]
[ROW][C]59[/C][C]16.07[/C][C]16.1171984291439[/C][C]-0.0471984291439256[/C][/ROW]
[ROW][C]60[/C][C]16.11[/C][C]16.0994039300875[/C][C]0.010596069912534[/C][/ROW]
[ROW][C]61[/C][C]16.15[/C][C]16.1411537988529[/C][C]0.0088462011471222[/C][/ROW]
[ROW][C]62[/C][C]16.18[/C][C]16.1826146887118[/C][C]-0.00261468871181947[/C][/ROW]
[ROW][C]63[/C][C]16.3[/C][C]16.2121828906824[/C][C]0.0878171093176228[/C][/ROW]
[ROW][C]64[/C][C]16.42[/C][C]16.3466852880743[/C][C]0.0733147119257467[/C][/ROW]
[ROW][C]65[/C][C]16.49[/C][C]16.4787927133275[/C][C]0.0112072866725121[/C][/ROW]
[ROW][C]66[/C][C]16.5[/C][C]16.5506435203772[/C][C]-0.0506435203771858[/C][/ROW]
[ROW][C]67[/C][C]16.58[/C][C]16.5522800879716[/C][C]0.0277199120284166[/C][/ROW]
[ROW][C]68[/C][C]16.64[/C][C]16.6368578426145[/C][C]0.00314215738552903[/C][/ROW]
[ROW][C]69[/C][C]16.66[/C][C]16.6973767485023[/C][C]-0.037376748502254[/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]0.0324803189966758[/C][/ROW]
[ROW][C]72[/C][C]16.92[/C][C]16.982883584429[/C][C]-0.0628835844290343[/C][/ROW]
[ROW][C]73[/C][C]16.95[/C][C]16.9824987888248[/C][C]-0.0324987888248351[/C][/ROW]
[ROW][C]74[/C][C]17.11[/C][C]17.0071318352328[/C][C]0.10286816476718[/C][/ROW]
[ROW][C]75[/C][C]17.16[/C][C]17.1841198119041[/C][C]-0.0241198119040931[/C][/ROW]
[ROW][C]76[/C][C]17.16[/C][C]17.2301365892728[/C][C]-0.0701365892727814[/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]0.00295003576511021[/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]-0.0405717091408739[/C][/ROW]
[ROW][C]82[/C][C]17.5[/C][C]17.5038715677516[/C][C]-0.00387156775156328[/C][/ROW]
[ROW][C]83[/C][C]17.56[/C][C]17.5532322047106[/C][C]0.00676779528940585[/C][/ROW]
[ROW][C]84[/C][C]17.65[/C][C]17.6143498600003[/C][C]0.0356501399997207[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122177&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122177&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	-0.0467885449616237
5	13.96	14.0090617354857	-0.0490617354857257
6	14.01	14.0209595240798	-0.0109595240797979
7	14.01	14.0691496333345	-0.0591496333345187
8	14.06	14.0593814743178	0.000618525682176241
9	14.09	14.1094836196208	-0.0194836196208268
10	14.13	14.1362660325633	-0.00626603256325708
11	14.12	14.1752312399698	-0.0552312399697783
12	14.13	14.1561101769251	-0.0261101769250942
13	14.14	14.161798259069	-0.0217982590689711
14	14.16	14.1681984250739	-0.008198425073914
15	14.21	14.1868445110208	0.0231554889792065
16	14.26	14.2406684822901	0.0193315177099489
17	14.29	14.2938609507532	-0.00386095075315751
18	14.32	14.3232233410371	-0.00322334103714716
19	14.33	14.3526910282223	-0.0226910282223276
20	14.39	14.3589437594832	0.0310562405168451
21	14.48	14.4240724860488	0.0559275139512287
22	14.44	14.5233085339985	-0.0833085339984585
23	14.46	14.469550697108	-0.00955069710803436
24	14.48	14.4879734645402	-0.00797346454018566
25	14.53	14.5066567011868	0.0233432988132236
26	14.58	14.5605116879708	0.0194883120292459
27	14.62	14.6137300499476	0.00626995005239017
28	14.62	14.6547654894877	-0.0347654894877341
29	14.61	14.6490242057221	-0.039024205722054
30	14.65	14.6325796239807	0.0174203760192633
31	14.68	14.6754564804124	0.0045435195876351
32	14.7	14.7062068117217	-0.00620681172171444
33	14.78	14.7251817990468	0.0548182009531999
34	14.84	14.8142346515115	0.0257653484884752
35	14.89	14.8784896233003	0.0115103766996807
36	14.89	14.9303904836034	-0.0403904836033533
37	15.13	14.9237202703771	0.206279729622947
38	15.25	15.1977859625426	0.0522140374574178
39	15.33	15.3264087551456	0.00359124485440887
40	15.36	15.4070018247697	-0.0470018247696657
41	15.4	15.4292397935863	-0.0292397935863367
42	15.4	15.4644110408576	-0.064411040857621
43	15.41	15.4537739962293	-0.0437739962293016
44	15.47	15.4565450189414	0.0134549810586186
45	15.54	15.5187670174076	0.0212329825923891
46	15.55	15.5922734998432	-0.0422734998432333
47	15.59	15.5952923193121	-0.00529231931206375
48	15.65	15.6344183288291	0.0155816711709384
49	15.75	15.6969915356803	0.0530084643197171
50	15.86	15.8057455224679	0.0542544775320497
51	15.89	15.9247052798498	-0.0347052798497653
52	15.94	15.9489739392956	-0.0089739392956485
53	15.93	15.9974919543516	-0.0674919543516275
54	15.95	15.976346117847	-0.0263461178470195
55	15.99	15.9919952359549	-0.00199523595487072
56	15.99	16.0316657363285	-0.0416657363285129
57	16.06	16.0247849238017	0.0352150761982983
58	16.08	16.10060045375	-0.0206004537500348
59	16.07	16.1171984291439	-0.0471984291439256
60	16.11	16.0994039300875	0.010596069912534
61	16.15	16.1411537988529	0.0088462011471222
62	16.18	16.1826146887118	-0.00261468871181947
63	16.3	16.2121828906824	0.0878171093176228
64	16.42	16.3466852880743	0.0733147119257467
65	16.49	16.4787927133275	0.0112072866725121
66	16.5	16.5506435203772	-0.0506435203771858
67	16.58	16.5522800879716	0.0277199120284166
68	16.64	16.6368578426145	0.00314215738552903
69	16.66	16.6973767485023	-0.037376748502254
70	16.81	16.7112042330983	0.0987957669017234
71	16.91	16.8775196810033	0.0324803189966758
72	16.92	16.982883584429	-0.0628835844290343
73	16.95	16.9824987888248	-0.0324987888248351
74	17.11	17.0071318352328	0.10286816476718
75	17.16	17.1841198119041	-0.0241198119040931
76	17.16	17.2301365892728	-0.0701365892727814
77	17.27	17.2185540093263	0.0514459906737486
78	17.34	17.3370499642349	0.00295003576511021
79	17.39	17.4075371425458	-0.0175371425457911
80	17.43	17.4546410029177	-0.0246410029177255
81	17.45	17.4905717091409	-0.0405717091408739
82	17.5	17.5038715677516	-0.00387156775156328
83	17.56	17.5532322047106	0.00676779528940585
84	17.65	17.6143498600003	0.0356501399997207

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	17.890948951087	17.6626667155827	18.1192311865913
89	17.9511861888588	17.6778827762073	18.2244896015103
90	18.0114234266305	17.6920621793521	18.3307846739089
91	18.0716606644023	17.7049864047221	18.4383349240825
92	18.131897902174	17.7165466584179	18.5472491459302
93	18.1921351399458	17.7266910335562	18.6575792463355
94	18.2523723777176	17.7353990949092	18.769345660526
95	18.3126096154893	17.7426685540096	18.8825506769691
96	18.3728468532611	17.7485078328418	18.9971858736804

\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 & 17.890948951087 & 17.6626667155827 & 18.1192311865913 \tabularnewline
89 & 17.9511861888588 & 17.6778827762073 & 18.2244896015103 \tabularnewline
90 & 18.0114234266305 & 17.6920621793521 & 18.3307846739089 \tabularnewline
91 & 18.0716606644023 & 17.7049864047221 & 18.4383349240825 \tabularnewline
92 & 18.131897902174 & 17.7165466584179 & 18.5472491459302 \tabularnewline
93 & 18.1921351399458 & 17.7266910335562 & 18.6575792463355 \tabularnewline
94 & 18.2523723777176 & 17.7353990949092 & 18.769345660526 \tabularnewline
95 & 18.3126096154893 & 17.7426685540096 & 18.8825506769691 \tabularnewline
96 & 18.3728468532611 & 17.7485078328418 & 18.9971858736804 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122177&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]17.890948951087[/C][C]17.6626667155827[/C][C]18.1192311865913[/C][/ROW]
[ROW][C]89[/C][C]17.9511861888588[/C][C]17.6778827762073[/C][C]18.2244896015103[/C][/ROW]
[ROW][C]90[/C][C]18.0114234266305[/C][C]17.6920621793521[/C][C]18.3307846739089[/C][/ROW]
[ROW][C]91[/C][C]18.0716606644023[/C][C]17.7049864047221[/C][C]18.4383349240825[/C][/ROW]
[ROW][C]92[/C][C]18.131897902174[/C][C]17.7165466584179[/C][C]18.5472491459302[/C][/ROW]
[ROW][C]93[/C][C]18.1921351399458[/C][C]17.7266910335562[/C][C]18.6575792463355[/C][/ROW]
[ROW][C]94[/C][C]18.2523723777176[/C][C]17.7353990949092[/C][C]18.769345660526[/C][/ROW]
[ROW][C]95[/C][C]18.3126096154893[/C][C]17.7426685540096[/C][C]18.8825506769691[/C][/ROW]
[ROW][C]96[/C][C]18.3728468532611[/C][C]17.7485078328418[/C][C]18.9971858736804[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122177&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122177&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	17.890948951087	17.6626667155827	18.1192311865913
89	17.9511861888588	17.6778827762073	18.2244896015103
90	18.0114234266305	17.6920621793521	18.3307846739089
91	18.0716606644023	17.7049864047221	18.4383349240825
92	18.131897902174	17.7165466584179	18.5472491459302
93	18.1921351399458	17.7266910335562	18.6575792463355
94	18.2523723777176	17.7353990949092	18.769345660526
95	18.3126096154893	17.7426685540096	18.8825506769691
96	18.3728468532611	17.7485078328418	18.9971858736804

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

Opgave 10-Stap 2- Gemiddelde prijs pepersteak-Stap 4 verbetering- Van Lisho...

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code