Free Statistics

of Irreproducible Research!

Author's title

marina cabraja mar205 opgave 10.2 exponential smoothing koffie, thee en cac...

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 18 May 2011 12:38:30 +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/18/t1305722113f85seeykwdcjx0m.htm/, Retrieved Tue, 14 May 2024 22:08:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121813, Retrieved Tue, 14 May 2024 22:08:46 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

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

-       [Exponential Smoothing] [marina cabraja ma...] [2011-05-18 12:38:30] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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

\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' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121813&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' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121813&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121813&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' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0295881156175766
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0295881156175766 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121813&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]0.0295881156175766[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121813&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121813&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	0.0295881156175766
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	106.32	106.02	0.299999999999997
4	105.81	106.128876434685	-0.318876434685265
5	105.92	105.609441481868	0.310558518131913
6	107.54	105.728630323209	1.81136967679141
7	107.34	107.402225338632	-0.0622253386316771
8	107.24	107.200384208118	0.039615791882099
9	107.74	107.101556364748	0.638443635251619
10	105.71	107.620446708844	-1.91044670884351
11	105.41	105.533920190741	-0.123920190741032
12	106.22	105.23025362581	0.989746374189963
13	106.32	106.069538355962	0.250461644038353
14	106.12	106.176949044043	-0.0569490440432077
15	106.22	105.975264029144	0.24473597085624
16	105.92	106.082505305345	-0.162505305345235
17	105.71	105.777697079582	-0.0676970795822172
18	105.71	105.565694050565	0.144305949435449
19	105.92	105.569963791681	0.350036208319253
20	105.71	105.790320703483	-0.0803207034828546
21	105.41	105.577944165222	-0.167944165221712
22	104.49	105.272975013844	-0.782975013843838
23	101.35	104.329808258609	-2.97980825860854
24	99.72	101.101641347335	-1.38164134733462
25	99.01	99.4307611834077	-0.420761183407663
26	97.89	98.7083116528656	-0.818311652865617
27	95.86	97.5640993530694	-1.70409935306941
28	94.95	95.483678264387	-0.53367826438695
29	95.35	94.5578877301977	0.792112269802303
30	95.15	94.9813248396187	0.168675160381312
31	95.46	94.786315619766	0.673684380234107
32	95.56	95.116248671098	0.44375132890201
33	95.05	95.229378436723	-0.179378436723013
34	94.64	94.714070966798	-0.0740709667979473
35	93.63	94.3018793464684	-0.67187934646843
36	93.12	93.271999702684	-0.151999702684037
37	93.53	92.7575023179072	0.77249768209279
38	97.18	93.1903590686393	3.98964093136074
39	96.27	96.958405025789	-0.688405025788995
40	95.15	96.0280364182942	-0.878036418294215
41	97.08	94.8820569752333	2.1979430247667
42	101.95	96.877089967571	5.07291003242906
43	103.07	101.897187816128	1.17281218387198
44	103.68	103.051889118622	0.628110881377893
45	102.87	103.680473736001	-0.810473736000986
46	102.56	102.846493345395	-0.286493345395172
47	103.38	102.528016547168	0.85198345283203
48	103.27	103.373225132075	-0.103225132074613
49	102.89	103.260170894932	-0.370170894932144
50	102.69	102.869218235695	-0.179218235694634
51	101.54	102.663915505816	-1.12391550581611
52	102.9	101.480660963886	1.41933903611435
53	101.53	102.882656531387	-1.35265653138674
54	101.96	101.472633973545	0.487366026454794
55	101.99	101.917054215884	0.0729457841159729
56	101.11	101.949212544178	-0.839212544178253
57	101.75	101.044381826393	0.70561817360661
58	101.71	101.705259738496	0.00474026150406814
59	104.11	101.665399993901	2.44460000609864
60	103.57	104.137731101521	-0.56773110152055
61	103.32	103.580933008049	-0.260933008049065
62	103.64	103.323212492038	0.31678750796155
63	103.68	103.65258563745	0.0274143625497771
64	103.79	103.693396776779	0.0966032232210665
65	103.01	103.806255084117	-0.796255084116638
66	101.54	103.002695396627	-1.46269539662671
67	101.9	101.489416996118	0.410583003881982
68	103.68	101.861565373508	1.8184346264925
69	104.62	103.695369427479	0.92463057252084
70	104.11	104.662727503762	-0.552727503762455
71	105.04	104.136373338476	0.903626661523901
72	104.83	105.093109948612	-0.26310994861241
73	105.05	104.875325021033	0.174674978967275
74	104.68	105.100493324506	-0.420493324505898
75	107.32	104.718051719404	2.60194828059598
76	109.9	107.435038465961	2.46496153403878
77	109.77	110.087972032823	-0.317972032823263
78	110.69	109.948563839553	0.74143616044708
79	110.54	110.890501538391	-0.350501538391271
80	110.89	110.730130858349	0.159869141650773
81	110.95	111.084861084996	-0.134861084996075
82	109.73	111.140870799621	-1.41087079962089
83	110.85	109.87912579128	0.970874208719735
84	110.39	111.027852129618	-0.637852129617968
85	110.58	110.54897928706	0.0310207129400766
86	110.4	110.739897131501	-0.339897131500919
87	111.07	110.549840215876	0.52015978412399
88	110.86	111.235230763708	-0.375230763708259
89	111.38	111.014128392488	0.365871607511593
90	111.44	111.544953843913	-0.104953843912639
91	110.36	111.601848457444	-1.24184845744445
92	110.06	110.485104501706	-0.425104501706073
93	108.34	110.17252646056	-1.83252646056003
94	107.94	108.398305455773	-0.458305455772731
95	107.39	107.984745060959	-0.594745060959141
96	107.1	107.417147675333	-0.317147675332521
97	107.61	107.117763873247	0.492236126753085
98	107.74	107.642328212676	0.0976717873235486
99	106.9	107.775218136812	-0.875218136812336
100	106.71	106.90932208139	-0.199322081389752
101	106.6	106.7134245166	-0.113424516600446
102	108.21	106.600068498889	1.60993150111059
103	110.54	108.257703338281	2.28229666171937
104	110.91	110.655232195781	0.254767804218787
105	109.51	111.032770295028	-1.52277029502805
106	110.27	109.58771439148	0.682285608520218
107	111.39	110.367901936949	1.02209806305113
108	112.13	111.518143892611	0.611856107389059
109	111.64	112.276247561858	-0.636247561857672

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 106.32 & 106.02 & 0.299999999999997 \tabularnewline
4 & 105.81 & 106.128876434685 & -0.318876434685265 \tabularnewline
5 & 105.92 & 105.609441481868 & 0.310558518131913 \tabularnewline
6 & 107.54 & 105.728630323209 & 1.81136967679141 \tabularnewline
7 & 107.34 & 107.402225338632 & -0.0622253386316771 \tabularnewline
8 & 107.24 & 107.200384208118 & 0.039615791882099 \tabularnewline
9 & 107.74 & 107.101556364748 & 0.638443635251619 \tabularnewline
10 & 105.71 & 107.620446708844 & -1.91044670884351 \tabularnewline
11 & 105.41 & 105.533920190741 & -0.123920190741032 \tabularnewline
12 & 106.22 & 105.23025362581 & 0.989746374189963 \tabularnewline
13 & 106.32 & 106.069538355962 & 0.250461644038353 \tabularnewline
14 & 106.12 & 106.176949044043 & -0.0569490440432077 \tabularnewline
15 & 106.22 & 105.975264029144 & 0.24473597085624 \tabularnewline
16 & 105.92 & 106.082505305345 & -0.162505305345235 \tabularnewline
17 & 105.71 & 105.777697079582 & -0.0676970795822172 \tabularnewline
18 & 105.71 & 105.565694050565 & 0.144305949435449 \tabularnewline
19 & 105.92 & 105.569963791681 & 0.350036208319253 \tabularnewline
20 & 105.71 & 105.790320703483 & -0.0803207034828546 \tabularnewline
21 & 105.41 & 105.577944165222 & -0.167944165221712 \tabularnewline
22 & 104.49 & 105.272975013844 & -0.782975013843838 \tabularnewline
23 & 101.35 & 104.329808258609 & -2.97980825860854 \tabularnewline
24 & 99.72 & 101.101641347335 & -1.38164134733462 \tabularnewline
25 & 99.01 & 99.4307611834077 & -0.420761183407663 \tabularnewline
26 & 97.89 & 98.7083116528656 & -0.818311652865617 \tabularnewline
27 & 95.86 & 97.5640993530694 & -1.70409935306941 \tabularnewline
28 & 94.95 & 95.483678264387 & -0.53367826438695 \tabularnewline
29 & 95.35 & 94.5578877301977 & 0.792112269802303 \tabularnewline
30 & 95.15 & 94.9813248396187 & 0.168675160381312 \tabularnewline
31 & 95.46 & 94.786315619766 & 0.673684380234107 \tabularnewline
32 & 95.56 & 95.116248671098 & 0.44375132890201 \tabularnewline
33 & 95.05 & 95.229378436723 & -0.179378436723013 \tabularnewline
34 & 94.64 & 94.714070966798 & -0.0740709667979473 \tabularnewline
35 & 93.63 & 94.3018793464684 & -0.67187934646843 \tabularnewline
36 & 93.12 & 93.271999702684 & -0.151999702684037 \tabularnewline
37 & 93.53 & 92.7575023179072 & 0.77249768209279 \tabularnewline
38 & 97.18 & 93.1903590686393 & 3.98964093136074 \tabularnewline
39 & 96.27 & 96.958405025789 & -0.688405025788995 \tabularnewline
40 & 95.15 & 96.0280364182942 & -0.878036418294215 \tabularnewline
41 & 97.08 & 94.8820569752333 & 2.1979430247667 \tabularnewline
42 & 101.95 & 96.877089967571 & 5.07291003242906 \tabularnewline
43 & 103.07 & 101.897187816128 & 1.17281218387198 \tabularnewline
44 & 103.68 & 103.051889118622 & 0.628110881377893 \tabularnewline
45 & 102.87 & 103.680473736001 & -0.810473736000986 \tabularnewline
46 & 102.56 & 102.846493345395 & -0.286493345395172 \tabularnewline
47 & 103.38 & 102.528016547168 & 0.85198345283203 \tabularnewline
48 & 103.27 & 103.373225132075 & -0.103225132074613 \tabularnewline
49 & 102.89 & 103.260170894932 & -0.370170894932144 \tabularnewline
50 & 102.69 & 102.869218235695 & -0.179218235694634 \tabularnewline
51 & 101.54 & 102.663915505816 & -1.12391550581611 \tabularnewline
52 & 102.9 & 101.480660963886 & 1.41933903611435 \tabularnewline
53 & 101.53 & 102.882656531387 & -1.35265653138674 \tabularnewline
54 & 101.96 & 101.472633973545 & 0.487366026454794 \tabularnewline
55 & 101.99 & 101.917054215884 & 0.0729457841159729 \tabularnewline
56 & 101.11 & 101.949212544178 & -0.839212544178253 \tabularnewline
57 & 101.75 & 101.044381826393 & 0.70561817360661 \tabularnewline
58 & 101.71 & 101.705259738496 & 0.00474026150406814 \tabularnewline
59 & 104.11 & 101.665399993901 & 2.44460000609864 \tabularnewline
60 & 103.57 & 104.137731101521 & -0.56773110152055 \tabularnewline
61 & 103.32 & 103.580933008049 & -0.260933008049065 \tabularnewline
62 & 103.64 & 103.323212492038 & 0.31678750796155 \tabularnewline
63 & 103.68 & 103.65258563745 & 0.0274143625497771 \tabularnewline
64 & 103.79 & 103.693396776779 & 0.0966032232210665 \tabularnewline
65 & 103.01 & 103.806255084117 & -0.796255084116638 \tabularnewline
66 & 101.54 & 103.002695396627 & -1.46269539662671 \tabularnewline
67 & 101.9 & 101.489416996118 & 0.410583003881982 \tabularnewline
68 & 103.68 & 101.861565373508 & 1.8184346264925 \tabularnewline
69 & 104.62 & 103.695369427479 & 0.92463057252084 \tabularnewline
70 & 104.11 & 104.662727503762 & -0.552727503762455 \tabularnewline
71 & 105.04 & 104.136373338476 & 0.903626661523901 \tabularnewline
72 & 104.83 & 105.093109948612 & -0.26310994861241 \tabularnewline
73 & 105.05 & 104.875325021033 & 0.174674978967275 \tabularnewline
74 & 104.68 & 105.100493324506 & -0.420493324505898 \tabularnewline
75 & 107.32 & 104.718051719404 & 2.60194828059598 \tabularnewline
76 & 109.9 & 107.435038465961 & 2.46496153403878 \tabularnewline
77 & 109.77 & 110.087972032823 & -0.317972032823263 \tabularnewline
78 & 110.69 & 109.948563839553 & 0.74143616044708 \tabularnewline
79 & 110.54 & 110.890501538391 & -0.350501538391271 \tabularnewline
80 & 110.89 & 110.730130858349 & 0.159869141650773 \tabularnewline
81 & 110.95 & 111.084861084996 & -0.134861084996075 \tabularnewline
82 & 109.73 & 111.140870799621 & -1.41087079962089 \tabularnewline
83 & 110.85 & 109.87912579128 & 0.970874208719735 \tabularnewline
84 & 110.39 & 111.027852129618 & -0.637852129617968 \tabularnewline
85 & 110.58 & 110.54897928706 & 0.0310207129400766 \tabularnewline
86 & 110.4 & 110.739897131501 & -0.339897131500919 \tabularnewline
87 & 111.07 & 110.549840215876 & 0.52015978412399 \tabularnewline
88 & 110.86 & 111.235230763708 & -0.375230763708259 \tabularnewline
89 & 111.38 & 111.014128392488 & 0.365871607511593 \tabularnewline
90 & 111.44 & 111.544953843913 & -0.104953843912639 \tabularnewline
91 & 110.36 & 111.601848457444 & -1.24184845744445 \tabularnewline
92 & 110.06 & 110.485104501706 & -0.425104501706073 \tabularnewline
93 & 108.34 & 110.17252646056 & -1.83252646056003 \tabularnewline
94 & 107.94 & 108.398305455773 & -0.458305455772731 \tabularnewline
95 & 107.39 & 107.984745060959 & -0.594745060959141 \tabularnewline
96 & 107.1 & 107.417147675333 & -0.317147675332521 \tabularnewline
97 & 107.61 & 107.117763873247 & 0.492236126753085 \tabularnewline
98 & 107.74 & 107.642328212676 & 0.0976717873235486 \tabularnewline
99 & 106.9 & 107.775218136812 & -0.875218136812336 \tabularnewline
100 & 106.71 & 106.90932208139 & -0.199322081389752 \tabularnewline
101 & 106.6 & 106.7134245166 & -0.113424516600446 \tabularnewline
102 & 108.21 & 106.600068498889 & 1.60993150111059 \tabularnewline
103 & 110.54 & 108.257703338281 & 2.28229666171937 \tabularnewline
104 & 110.91 & 110.655232195781 & 0.254767804218787 \tabularnewline
105 & 109.51 & 111.032770295028 & -1.52277029502805 \tabularnewline
106 & 110.27 & 109.58771439148 & 0.682285608520218 \tabularnewline
107 & 111.39 & 110.367901936949 & 1.02209806305113 \tabularnewline
108 & 112.13 & 111.518143892611 & 0.611856107389059 \tabularnewline
109 & 111.64 & 112.276247561858 & -0.636247561857672 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121813&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]106.32[/C][C]106.02[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]4[/C][C]105.81[/C][C]106.128876434685[/C][C]-0.318876434685265[/C][/ROW]
[ROW][C]5[/C][C]105.92[/C][C]105.609441481868[/C][C]0.310558518131913[/C][/ROW]
[ROW][C]6[/C][C]107.54[/C][C]105.728630323209[/C][C]1.81136967679141[/C][/ROW]
[ROW][C]7[/C][C]107.34[/C][C]107.402225338632[/C][C]-0.0622253386316771[/C][/ROW]
[ROW][C]8[/C][C]107.24[/C][C]107.200384208118[/C][C]0.039615791882099[/C][/ROW]
[ROW][C]9[/C][C]107.74[/C][C]107.101556364748[/C][C]0.638443635251619[/C][/ROW]
[ROW][C]10[/C][C]105.71[/C][C]107.620446708844[/C][C]-1.91044670884351[/C][/ROW]
[ROW][C]11[/C][C]105.41[/C][C]105.533920190741[/C][C]-0.123920190741032[/C][/ROW]
[ROW][C]12[/C][C]106.22[/C][C]105.23025362581[/C][C]0.989746374189963[/C][/ROW]
[ROW][C]13[/C][C]106.32[/C][C]106.069538355962[/C][C]0.250461644038353[/C][/ROW]
[ROW][C]14[/C][C]106.12[/C][C]106.176949044043[/C][C]-0.0569490440432077[/C][/ROW]
[ROW][C]15[/C][C]106.22[/C][C]105.975264029144[/C][C]0.24473597085624[/C][/ROW]
[ROW][C]16[/C][C]105.92[/C][C]106.082505305345[/C][C]-0.162505305345235[/C][/ROW]
[ROW][C]17[/C][C]105.71[/C][C]105.777697079582[/C][C]-0.0676970795822172[/C][/ROW]
[ROW][C]18[/C][C]105.71[/C][C]105.565694050565[/C][C]0.144305949435449[/C][/ROW]
[ROW][C]19[/C][C]105.92[/C][C]105.569963791681[/C][C]0.350036208319253[/C][/ROW]
[ROW][C]20[/C][C]105.71[/C][C]105.790320703483[/C][C]-0.0803207034828546[/C][/ROW]
[ROW][C]21[/C][C]105.41[/C][C]105.577944165222[/C][C]-0.167944165221712[/C][/ROW]
[ROW][C]22[/C][C]104.49[/C][C]105.272975013844[/C][C]-0.782975013843838[/C][/ROW]
[ROW][C]23[/C][C]101.35[/C][C]104.329808258609[/C][C]-2.97980825860854[/C][/ROW]
[ROW][C]24[/C][C]99.72[/C][C]101.101641347335[/C][C]-1.38164134733462[/C][/ROW]
[ROW][C]25[/C][C]99.01[/C][C]99.4307611834077[/C][C]-0.420761183407663[/C][/ROW]
[ROW][C]26[/C][C]97.89[/C][C]98.7083116528656[/C][C]-0.818311652865617[/C][/ROW]
[ROW][C]27[/C][C]95.86[/C][C]97.5640993530694[/C][C]-1.70409935306941[/C][/ROW]
[ROW][C]28[/C][C]94.95[/C][C]95.483678264387[/C][C]-0.53367826438695[/C][/ROW]
[ROW][C]29[/C][C]95.35[/C][C]94.5578877301977[/C][C]0.792112269802303[/C][/ROW]
[ROW][C]30[/C][C]95.15[/C][C]94.9813248396187[/C][C]0.168675160381312[/C][/ROW]
[ROW][C]31[/C][C]95.46[/C][C]94.786315619766[/C][C]0.673684380234107[/C][/ROW]
[ROW][C]32[/C][C]95.56[/C][C]95.116248671098[/C][C]0.44375132890201[/C][/ROW]
[ROW][C]33[/C][C]95.05[/C][C]95.229378436723[/C][C]-0.179378436723013[/C][/ROW]
[ROW][C]34[/C][C]94.64[/C][C]94.714070966798[/C][C]-0.0740709667979473[/C][/ROW]
[ROW][C]35[/C][C]93.63[/C][C]94.3018793464684[/C][C]-0.67187934646843[/C][/ROW]
[ROW][C]36[/C][C]93.12[/C][C]93.271999702684[/C][C]-0.151999702684037[/C][/ROW]
[ROW][C]37[/C][C]93.53[/C][C]92.7575023179072[/C][C]0.77249768209279[/C][/ROW]
[ROW][C]38[/C][C]97.18[/C][C]93.1903590686393[/C][C]3.98964093136074[/C][/ROW]
[ROW][C]39[/C][C]96.27[/C][C]96.958405025789[/C][C]-0.688405025788995[/C][/ROW]
[ROW][C]40[/C][C]95.15[/C][C]96.0280364182942[/C][C]-0.878036418294215[/C][/ROW]
[ROW][C]41[/C][C]97.08[/C][C]94.8820569752333[/C][C]2.1979430247667[/C][/ROW]
[ROW][C]42[/C][C]101.95[/C][C]96.877089967571[/C][C]5.07291003242906[/C][/ROW]
[ROW][C]43[/C][C]103.07[/C][C]101.897187816128[/C][C]1.17281218387198[/C][/ROW]
[ROW][C]44[/C][C]103.68[/C][C]103.051889118622[/C][C]0.628110881377893[/C][/ROW]
[ROW][C]45[/C][C]102.87[/C][C]103.680473736001[/C][C]-0.810473736000986[/C][/ROW]
[ROW][C]46[/C][C]102.56[/C][C]102.846493345395[/C][C]-0.286493345395172[/C][/ROW]
[ROW][C]47[/C][C]103.38[/C][C]102.528016547168[/C][C]0.85198345283203[/C][/ROW]
[ROW][C]48[/C][C]103.27[/C][C]103.373225132075[/C][C]-0.103225132074613[/C][/ROW]
[ROW][C]49[/C][C]102.89[/C][C]103.260170894932[/C][C]-0.370170894932144[/C][/ROW]
[ROW][C]50[/C][C]102.69[/C][C]102.869218235695[/C][C]-0.179218235694634[/C][/ROW]
[ROW][C]51[/C][C]101.54[/C][C]102.663915505816[/C][C]-1.12391550581611[/C][/ROW]
[ROW][C]52[/C][C]102.9[/C][C]101.480660963886[/C][C]1.41933903611435[/C][/ROW]
[ROW][C]53[/C][C]101.53[/C][C]102.882656531387[/C][C]-1.35265653138674[/C][/ROW]
[ROW][C]54[/C][C]101.96[/C][C]101.472633973545[/C][C]0.487366026454794[/C][/ROW]
[ROW][C]55[/C][C]101.99[/C][C]101.917054215884[/C][C]0.0729457841159729[/C][/ROW]
[ROW][C]56[/C][C]101.11[/C][C]101.949212544178[/C][C]-0.839212544178253[/C][/ROW]
[ROW][C]57[/C][C]101.75[/C][C]101.044381826393[/C][C]0.70561817360661[/C][/ROW]
[ROW][C]58[/C][C]101.71[/C][C]101.705259738496[/C][C]0.00474026150406814[/C][/ROW]
[ROW][C]59[/C][C]104.11[/C][C]101.665399993901[/C][C]2.44460000609864[/C][/ROW]
[ROW][C]60[/C][C]103.57[/C][C]104.137731101521[/C][C]-0.56773110152055[/C][/ROW]
[ROW][C]61[/C][C]103.32[/C][C]103.580933008049[/C][C]-0.260933008049065[/C][/ROW]
[ROW][C]62[/C][C]103.64[/C][C]103.323212492038[/C][C]0.31678750796155[/C][/ROW]
[ROW][C]63[/C][C]103.68[/C][C]103.65258563745[/C][C]0.0274143625497771[/C][/ROW]
[ROW][C]64[/C][C]103.79[/C][C]103.693396776779[/C][C]0.0966032232210665[/C][/ROW]
[ROW][C]65[/C][C]103.01[/C][C]103.806255084117[/C][C]-0.796255084116638[/C][/ROW]
[ROW][C]66[/C][C]101.54[/C][C]103.002695396627[/C][C]-1.46269539662671[/C][/ROW]
[ROW][C]67[/C][C]101.9[/C][C]101.489416996118[/C][C]0.410583003881982[/C][/ROW]
[ROW][C]68[/C][C]103.68[/C][C]101.861565373508[/C][C]1.8184346264925[/C][/ROW]
[ROW][C]69[/C][C]104.62[/C][C]103.695369427479[/C][C]0.92463057252084[/C][/ROW]
[ROW][C]70[/C][C]104.11[/C][C]104.662727503762[/C][C]-0.552727503762455[/C][/ROW]
[ROW][C]71[/C][C]105.04[/C][C]104.136373338476[/C][C]0.903626661523901[/C][/ROW]
[ROW][C]72[/C][C]104.83[/C][C]105.093109948612[/C][C]-0.26310994861241[/C][/ROW]
[ROW][C]73[/C][C]105.05[/C][C]104.875325021033[/C][C]0.174674978967275[/C][/ROW]
[ROW][C]74[/C][C]104.68[/C][C]105.100493324506[/C][C]-0.420493324505898[/C][/ROW]
[ROW][C]75[/C][C]107.32[/C][C]104.718051719404[/C][C]2.60194828059598[/C][/ROW]
[ROW][C]76[/C][C]109.9[/C][C]107.435038465961[/C][C]2.46496153403878[/C][/ROW]
[ROW][C]77[/C][C]109.77[/C][C]110.087972032823[/C][C]-0.317972032823263[/C][/ROW]
[ROW][C]78[/C][C]110.69[/C][C]109.948563839553[/C][C]0.74143616044708[/C][/ROW]
[ROW][C]79[/C][C]110.54[/C][C]110.890501538391[/C][C]-0.350501538391271[/C][/ROW]
[ROW][C]80[/C][C]110.89[/C][C]110.730130858349[/C][C]0.159869141650773[/C][/ROW]
[ROW][C]81[/C][C]110.95[/C][C]111.084861084996[/C][C]-0.134861084996075[/C][/ROW]
[ROW][C]82[/C][C]109.73[/C][C]111.140870799621[/C][C]-1.41087079962089[/C][/ROW]
[ROW][C]83[/C][C]110.85[/C][C]109.87912579128[/C][C]0.970874208719735[/C][/ROW]
[ROW][C]84[/C][C]110.39[/C][C]111.027852129618[/C][C]-0.637852129617968[/C][/ROW]
[ROW][C]85[/C][C]110.58[/C][C]110.54897928706[/C][C]0.0310207129400766[/C][/ROW]
[ROW][C]86[/C][C]110.4[/C][C]110.739897131501[/C][C]-0.339897131500919[/C][/ROW]
[ROW][C]87[/C][C]111.07[/C][C]110.549840215876[/C][C]0.52015978412399[/C][/ROW]
[ROW][C]88[/C][C]110.86[/C][C]111.235230763708[/C][C]-0.375230763708259[/C][/ROW]
[ROW][C]89[/C][C]111.38[/C][C]111.014128392488[/C][C]0.365871607511593[/C][/ROW]
[ROW][C]90[/C][C]111.44[/C][C]111.544953843913[/C][C]-0.104953843912639[/C][/ROW]
[ROW][C]91[/C][C]110.36[/C][C]111.601848457444[/C][C]-1.24184845744445[/C][/ROW]
[ROW][C]92[/C][C]110.06[/C][C]110.485104501706[/C][C]-0.425104501706073[/C][/ROW]
[ROW][C]93[/C][C]108.34[/C][C]110.17252646056[/C][C]-1.83252646056003[/C][/ROW]
[ROW][C]94[/C][C]107.94[/C][C]108.398305455773[/C][C]-0.458305455772731[/C][/ROW]
[ROW][C]95[/C][C]107.39[/C][C]107.984745060959[/C][C]-0.594745060959141[/C][/ROW]
[ROW][C]96[/C][C]107.1[/C][C]107.417147675333[/C][C]-0.317147675332521[/C][/ROW]
[ROW][C]97[/C][C]107.61[/C][C]107.117763873247[/C][C]0.492236126753085[/C][/ROW]
[ROW][C]98[/C][C]107.74[/C][C]107.642328212676[/C][C]0.0976717873235486[/C][/ROW]
[ROW][C]99[/C][C]106.9[/C][C]107.775218136812[/C][C]-0.875218136812336[/C][/ROW]
[ROW][C]100[/C][C]106.71[/C][C]106.90932208139[/C][C]-0.199322081389752[/C][/ROW]
[ROW][C]101[/C][C]106.6[/C][C]106.7134245166[/C][C]-0.113424516600446[/C][/ROW]
[ROW][C]102[/C][C]108.21[/C][C]106.600068498889[/C][C]1.60993150111059[/C][/ROW]
[ROW][C]103[/C][C]110.54[/C][C]108.257703338281[/C][C]2.28229666171937[/C][/ROW]
[ROW][C]104[/C][C]110.91[/C][C]110.655232195781[/C][C]0.254767804218787[/C][/ROW]
[ROW][C]105[/C][C]109.51[/C][C]111.032770295028[/C][C]-1.52277029502805[/C][/ROW]
[ROW][C]106[/C][C]110.27[/C][C]109.58771439148[/C][C]0.682285608520218[/C][/ROW]
[ROW][C]107[/C][C]111.39[/C][C]110.367901936949[/C][C]1.02209806305113[/C][/ROW]
[ROW][C]108[/C][C]112.13[/C][C]111.518143892611[/C][C]0.611856107389059[/C][/ROW]
[ROW][C]109[/C][C]111.64[/C][C]112.276247561858[/C][C]-0.636247561857672[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121813&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121813&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	106.32	106.02	0.299999999999997
4	105.81	106.128876434685	-0.318876434685265
5	105.92	105.609441481868	0.310558518131913
6	107.54	105.728630323209	1.81136967679141
7	107.34	107.402225338632	-0.0622253386316771
8	107.24	107.200384208118	0.039615791882099
9	107.74	107.101556364748	0.638443635251619
10	105.71	107.620446708844	-1.91044670884351
11	105.41	105.533920190741	-0.123920190741032
12	106.22	105.23025362581	0.989746374189963
13	106.32	106.069538355962	0.250461644038353
14	106.12	106.176949044043	-0.0569490440432077
15	106.22	105.975264029144	0.24473597085624
16	105.92	106.082505305345	-0.162505305345235
17	105.71	105.777697079582	-0.0676970795822172
18	105.71	105.565694050565	0.144305949435449
19	105.92	105.569963791681	0.350036208319253
20	105.71	105.790320703483	-0.0803207034828546
21	105.41	105.577944165222	-0.167944165221712
22	104.49	105.272975013844	-0.782975013843838
23	101.35	104.329808258609	-2.97980825860854
24	99.72	101.101641347335	-1.38164134733462
25	99.01	99.4307611834077	-0.420761183407663
26	97.89	98.7083116528656	-0.818311652865617
27	95.86	97.5640993530694	-1.70409935306941
28	94.95	95.483678264387	-0.53367826438695
29	95.35	94.5578877301977	0.792112269802303
30	95.15	94.9813248396187	0.168675160381312
31	95.46	94.786315619766	0.673684380234107
32	95.56	95.116248671098	0.44375132890201
33	95.05	95.229378436723	-0.179378436723013
34	94.64	94.714070966798	-0.0740709667979473
35	93.63	94.3018793464684	-0.67187934646843
36	93.12	93.271999702684	-0.151999702684037
37	93.53	92.7575023179072	0.77249768209279
38	97.18	93.1903590686393	3.98964093136074
39	96.27	96.958405025789	-0.688405025788995
40	95.15	96.0280364182942	-0.878036418294215
41	97.08	94.8820569752333	2.1979430247667
42	101.95	96.877089967571	5.07291003242906
43	103.07	101.897187816128	1.17281218387198
44	103.68	103.051889118622	0.628110881377893
45	102.87	103.680473736001	-0.810473736000986
46	102.56	102.846493345395	-0.286493345395172
47	103.38	102.528016547168	0.85198345283203
48	103.27	103.373225132075	-0.103225132074613
49	102.89	103.260170894932	-0.370170894932144
50	102.69	102.869218235695	-0.179218235694634
51	101.54	102.663915505816	-1.12391550581611
52	102.9	101.480660963886	1.41933903611435
53	101.53	102.882656531387	-1.35265653138674
54	101.96	101.472633973545	0.487366026454794
55	101.99	101.917054215884	0.0729457841159729
56	101.11	101.949212544178	-0.839212544178253
57	101.75	101.044381826393	0.70561817360661
58	101.71	101.705259738496	0.00474026150406814
59	104.11	101.665399993901	2.44460000609864
60	103.57	104.137731101521	-0.56773110152055
61	103.32	103.580933008049	-0.260933008049065
62	103.64	103.323212492038	0.31678750796155
63	103.68	103.65258563745	0.0274143625497771
64	103.79	103.693396776779	0.0966032232210665
65	103.01	103.806255084117	-0.796255084116638
66	101.54	103.002695396627	-1.46269539662671
67	101.9	101.489416996118	0.410583003881982
68	103.68	101.861565373508	1.8184346264925
69	104.62	103.695369427479	0.92463057252084
70	104.11	104.662727503762	-0.552727503762455
71	105.04	104.136373338476	0.903626661523901
72	104.83	105.093109948612	-0.26310994861241
73	105.05	104.875325021033	0.174674978967275
74	104.68	105.100493324506	-0.420493324505898
75	107.32	104.718051719404	2.60194828059598
76	109.9	107.435038465961	2.46496153403878
77	109.77	110.087972032823	-0.317972032823263
78	110.69	109.948563839553	0.74143616044708
79	110.54	110.890501538391	-0.350501538391271
80	110.89	110.730130858349	0.159869141650773
81	110.95	111.084861084996	-0.134861084996075
82	109.73	111.140870799621	-1.41087079962089
83	110.85	109.87912579128	0.970874208719735
84	110.39	111.027852129618	-0.637852129617968
85	110.58	110.54897928706	0.0310207129400766
86	110.4	110.739897131501	-0.339897131500919
87	111.07	110.549840215876	0.52015978412399
88	110.86	111.235230763708	-0.375230763708259
89	111.38	111.014128392488	0.365871607511593
90	111.44	111.544953843913	-0.104953843912639
91	110.36	111.601848457444	-1.24184845744445
92	110.06	110.485104501706	-0.425104501706073
93	108.34	110.17252646056	-1.83252646056003
94	107.94	108.398305455773	-0.458305455772731
95	107.39	107.984745060959	-0.594745060959141
96	107.1	107.417147675333	-0.317147675332521
97	107.61	107.117763873247	0.492236126753085
98	107.74	107.642328212676	0.0976717873235486
99	106.9	107.775218136812	-0.875218136812336
100	106.71	106.90932208139	-0.199322081389752
101	106.6	106.7134245166	-0.113424516600446
102	108.21	106.600068498889	1.60993150111059
103	110.54	108.257703338281	2.28229666171937
104	110.91	110.655232195781	0.254767804218787
105	109.51	111.032770295028	-1.52277029502805
106	110.27	109.58771439148	0.682285608520218
107	111.39	110.367901936949	1.02209806305113
108	112.13	111.518143892611	0.611856107389059
109	111.64	112.276247561858	-0.636247561857672

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
110	111.767422195436	109.553005633928	113.981838756944
111	111.894844390872	108.71651883852	115.073169943224
112	112.022266586308	108.072212956841	115.972320215776
113	112.149688781744	107.521974698767	116.777402864722
114	112.27711097718	107.028417707404	117.525804246956
115	112.404533172616	106.572668998615	118.236397346617
116	112.531955368052	106.143692725182	118.920218010922
117	112.659377563488	105.734412116629	119.584343010347
118	112.786799758924	105.339990634824	120.233608883025
119	112.91422195436	104.95696460555	120.871479303171
120	113.041644149796	104.582763169281	121.500525130312
121	113.169066345232	104.215423468622	122.122709221842

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
110 & 111.767422195436 & 109.553005633928 & 113.981838756944 \tabularnewline
111 & 111.894844390872 & 108.71651883852 & 115.073169943224 \tabularnewline
112 & 112.022266586308 & 108.072212956841 & 115.972320215776 \tabularnewline
113 & 112.149688781744 & 107.521974698767 & 116.777402864722 \tabularnewline
114 & 112.27711097718 & 107.028417707404 & 117.525804246956 \tabularnewline
115 & 112.404533172616 & 106.572668998615 & 118.236397346617 \tabularnewline
116 & 112.531955368052 & 106.143692725182 & 118.920218010922 \tabularnewline
117 & 112.659377563488 & 105.734412116629 & 119.584343010347 \tabularnewline
118 & 112.786799758924 & 105.339990634824 & 120.233608883025 \tabularnewline
119 & 112.91422195436 & 104.95696460555 & 120.871479303171 \tabularnewline
120 & 113.041644149796 & 104.582763169281 & 121.500525130312 \tabularnewline
121 & 113.169066345232 & 104.215423468622 & 122.122709221842 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121813&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]110[/C][C]111.767422195436[/C][C]109.553005633928[/C][C]113.981838756944[/C][/ROW]
[ROW][C]111[/C][C]111.894844390872[/C][C]108.71651883852[/C][C]115.073169943224[/C][/ROW]
[ROW][C]112[/C][C]112.022266586308[/C][C]108.072212956841[/C][C]115.972320215776[/C][/ROW]
[ROW][C]113[/C][C]112.149688781744[/C][C]107.521974698767[/C][C]116.777402864722[/C][/ROW]
[ROW][C]114[/C][C]112.27711097718[/C][C]107.028417707404[/C][C]117.525804246956[/C][/ROW]
[ROW][C]115[/C][C]112.404533172616[/C][C]106.572668998615[/C][C]118.236397346617[/C][/ROW]
[ROW][C]116[/C][C]112.531955368052[/C][C]106.143692725182[/C][C]118.920218010922[/C][/ROW]
[ROW][C]117[/C][C]112.659377563488[/C][C]105.734412116629[/C][C]119.584343010347[/C][/ROW]
[ROW][C]118[/C][C]112.786799758924[/C][C]105.339990634824[/C][C]120.233608883025[/C][/ROW]
[ROW][C]119[/C][C]112.91422195436[/C][C]104.95696460555[/C][C]120.871479303171[/C][/ROW]
[ROW][C]120[/C][C]113.041644149796[/C][C]104.582763169281[/C][C]121.500525130312[/C][/ROW]
[ROW][C]121[/C][C]113.169066345232[/C][C]104.215423468622[/C][C]122.122709221842[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121813&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121813&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
110	111.767422195436	109.553005633928	113.981838756944
111	111.894844390872	108.71651883852	115.073169943224
112	112.022266586308	108.072212956841	115.972320215776
113	112.149688781744	107.521974698767	116.777402864722
114	112.27711097718	107.028417707404	117.525804246956
115	112.404533172616	106.572668998615	118.236397346617
116	112.531955368052	106.143692725182	118.920218010922
117	112.659377563488	105.734412116629	119.584343010347
118	112.786799758924	105.339990634824	120.233608883025
119	112.91422195436	104.95696460555	120.871479303171
120	113.041644149796	104.582763169281	121.500525130312
121	113.169066345232	104.215423468622	122.122709221842

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

marina cabraja mar205 opgave 10.2 exponential smoothing koffie, thee en cac...

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code