Free Statistics

of Irreproducible Research!

Author's title

Tinneke Hermans - opgave 10 oef 2 - prijzen broodjes - double smoothing add...

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 28 May 2008 02:30:14 -0600

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/2008/May/28/t1211963523zgmkt5wovcnt22x.htm/, Retrieved Tue, 14 May 2024 02:24:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13403, Retrieved Tue, 14 May 2024 02:24:45 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

185

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

-       [Exponential Smoothing] [Tinneke Hermans -...] [2008-05-28 08:30:14] [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	'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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13403&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13403&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13403&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0348836110569791
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0348836110569791 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13403&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]0.0348836110569791[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13403&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13403&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	0.0348836110569791
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	4.09	4.09	0
4	4.08	4.1	-0.0199999999999996
5	4.09	4.08930232777886	0.000697672221139811
6	4.12	4.09932666510527	0.0206733348947328
7	4.14	4.13004782567899	0.00995217432101292
8	4.14	4.15039499345717	-0.0103949934571714
9	4.14	4.15003237854847	-0.0100323785484715
10	4.14	4.14968241295721	-0.0096824129572104
11	4.14	4.14934465542952	-0.00934465542951823
12	4.23	4.14901868010405	0.0809813198959475
13	4.29	4.24184360097018	0.0481563990298151
14	4.32	4.30352347006384	0.0164765299361553
15	4.33	4.33409823092571	-0.00409823092570694
16	4.35	4.34395526983207	0.00604473016792717
17	4.35	4.36416613184819	-0.0141661318481949
18	4.35	4.36367196601462	-0.0136719660146207
19	4.35	4.36319503846978	-0.0131950384697825
20	4.36	4.36273474787992	-0.00273474787992001
21	4.36	4.37263934999854	-0.0126393499985387
22	4.38	4.37219844382918	0.0078015561708229
23	4.4	4.39247059028028	0.00752940971972205
24	4.4	4.41273324328043	-0.0127332432804304
25	4.4	4.41228906177434	-0.0122890617743421
26	4.43	4.41186037492315	0.0181396250768486
27	4.44	4.44249315054905	-0.00249315054904997
28	4.46	4.45240618045499	0.0075938195450087
29	4.47	4.47267108030244	-0.00267108030243612
30	4.49	4.48257790337606	0.00742209662393645
31	4.49	4.50283681290792	-0.0128368129079206
32	4.57	4.50238901851923	0.0676109814807706
33	4.62	4.58474753370039	0.0352524662996148
34	4.64	4.63597726702358	0.00402273297641909
35	4.66	4.65611759447612	0.00388240552388464
36	4.67	4.67625302680038	-0.00625302680037709
37	4.68	4.68603489864554	-0.00603489864554341
38	4.72	4.69582437958842	0.0241756204115759
39	4.74	4.73666771252792	0.00333228747207759
40	4.75	4.75678395474803	-0.00678395474802862
41	4.76	4.76654730590917	-0.0065473059091703
42	4.77	4.77631891223636	-0.00631891223636405
43	4.76	4.78609848575961	-0.0260984857596069
44	4.77	4.77518807633319	-0.00518807633319263
45	4.77	4.78500709749625	-0.0150070974962517
46	4.78	4.7844835957441	-0.00448359574409807
47	4.81	4.79432719173403	0.0156728082659745
48	4.81	4.82487391588174	-0.0148739158817452
49	4.85	4.82435505998523	0.025644940014768
50	4.92	4.86524964809829	0.0547503519017134
51	4.96	4.93715953807926	0.0228404619207412
52	4.95	4.97795629586926	-0.0279562958692638
53	4.96	4.96698107931757	-0.0069810793175673
54	4.97	4.97673755406189	-0.00673755406189525
55	5	4.98650252384652	0.0134974761534759
56	5	5.01697336455491	-0.0169733645549135
57	5.01	5.01638127230745	-0.00638127230745145
58	5.01	5.02615867048623	-0.0161586704862291
59	5.02	5.02559499770979	-0.00559499770978977
60	5.04	5.03539982398582	0.00460017601418361
61	5.04	5.05556029473669	-0.0155602947366891
62	5.19	5.05501749546716	0.134982504532838
63	5.22	5.20972617265478	0.0102738273452161
64	5.22	5.24008456085196	-0.0200845608519602
65	5.22	5.23938393884295	-0.0193839388429504
66	5.24	5.2387077570596	0.00129224294039965
67	5.28	5.25875283515972	0.0212471648402754
68	5.34	5.29949401299408	0.0405059870059237
69	5.36	5.36090700809027	-0.000907008090269557
70	5.38	5.38087536837282	-0.000875368372823537
71	5.39	5.40084483236297	-0.0108448323629746
72	5.41	5.41046652544885	-0.000466525448845623
73	5.44	5.43045025135654	0.00954974864345992
74	5.51	5.46078338107391	0.0492166189260885
75	5.55	5.53250023446607	0.0174997655339322
76	5.56	5.57311068948054	-0.0131106894805422
77	5.57	5.58265334128801	-0.0126533412880132
78	5.58	5.59221194705195	-0.0122119470519522
79	5.58	5.60178595024074	-0.0217859502407425
80	5.59	5.60102597762604	-0.0110259776260380
81	5.61	5.61064135171101	-0.000641351711007765
82	5.63	5.63061897904737	-0.000618979047371404
83	5.64	5.65059738682303	-0.0105973868230302
84	5.64	5.66022771170287	-0.0202277117028746

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 4.09 & 4.09 & 0 \tabularnewline
4 & 4.08 & 4.1 & -0.0199999999999996 \tabularnewline
5 & 4.09 & 4.08930232777886 & 0.000697672221139811 \tabularnewline
6 & 4.12 & 4.09932666510527 & 0.0206733348947328 \tabularnewline
7 & 4.14 & 4.13004782567899 & 0.00995217432101292 \tabularnewline
8 & 4.14 & 4.15039499345717 & -0.0103949934571714 \tabularnewline
9 & 4.14 & 4.15003237854847 & -0.0100323785484715 \tabularnewline
10 & 4.14 & 4.14968241295721 & -0.0096824129572104 \tabularnewline
11 & 4.14 & 4.14934465542952 & -0.00934465542951823 \tabularnewline
12 & 4.23 & 4.14901868010405 & 0.0809813198959475 \tabularnewline
13 & 4.29 & 4.24184360097018 & 0.0481563990298151 \tabularnewline
14 & 4.32 & 4.30352347006384 & 0.0164765299361553 \tabularnewline
15 & 4.33 & 4.33409823092571 & -0.00409823092570694 \tabularnewline
16 & 4.35 & 4.34395526983207 & 0.00604473016792717 \tabularnewline
17 & 4.35 & 4.36416613184819 & -0.0141661318481949 \tabularnewline
18 & 4.35 & 4.36367196601462 & -0.0136719660146207 \tabularnewline
19 & 4.35 & 4.36319503846978 & -0.0131950384697825 \tabularnewline
20 & 4.36 & 4.36273474787992 & -0.00273474787992001 \tabularnewline
21 & 4.36 & 4.37263934999854 & -0.0126393499985387 \tabularnewline
22 & 4.38 & 4.37219844382918 & 0.0078015561708229 \tabularnewline
23 & 4.4 & 4.39247059028028 & 0.00752940971972205 \tabularnewline
24 & 4.4 & 4.41273324328043 & -0.0127332432804304 \tabularnewline
25 & 4.4 & 4.41228906177434 & -0.0122890617743421 \tabularnewline
26 & 4.43 & 4.41186037492315 & 0.0181396250768486 \tabularnewline
27 & 4.44 & 4.44249315054905 & -0.00249315054904997 \tabularnewline
28 & 4.46 & 4.45240618045499 & 0.0075938195450087 \tabularnewline
29 & 4.47 & 4.47267108030244 & -0.00267108030243612 \tabularnewline
30 & 4.49 & 4.48257790337606 & 0.00742209662393645 \tabularnewline
31 & 4.49 & 4.50283681290792 & -0.0128368129079206 \tabularnewline
32 & 4.57 & 4.50238901851923 & 0.0676109814807706 \tabularnewline
33 & 4.62 & 4.58474753370039 & 0.0352524662996148 \tabularnewline
34 & 4.64 & 4.63597726702358 & 0.00402273297641909 \tabularnewline
35 & 4.66 & 4.65611759447612 & 0.00388240552388464 \tabularnewline
36 & 4.67 & 4.67625302680038 & -0.00625302680037709 \tabularnewline
37 & 4.68 & 4.68603489864554 & -0.00603489864554341 \tabularnewline
38 & 4.72 & 4.69582437958842 & 0.0241756204115759 \tabularnewline
39 & 4.74 & 4.73666771252792 & 0.00333228747207759 \tabularnewline
40 & 4.75 & 4.75678395474803 & -0.00678395474802862 \tabularnewline
41 & 4.76 & 4.76654730590917 & -0.0065473059091703 \tabularnewline
42 & 4.77 & 4.77631891223636 & -0.00631891223636405 \tabularnewline
43 & 4.76 & 4.78609848575961 & -0.0260984857596069 \tabularnewline
44 & 4.77 & 4.77518807633319 & -0.00518807633319263 \tabularnewline
45 & 4.77 & 4.78500709749625 & -0.0150070974962517 \tabularnewline
46 & 4.78 & 4.7844835957441 & -0.00448359574409807 \tabularnewline
47 & 4.81 & 4.79432719173403 & 0.0156728082659745 \tabularnewline
48 & 4.81 & 4.82487391588174 & -0.0148739158817452 \tabularnewline
49 & 4.85 & 4.82435505998523 & 0.025644940014768 \tabularnewline
50 & 4.92 & 4.86524964809829 & 0.0547503519017134 \tabularnewline
51 & 4.96 & 4.93715953807926 & 0.0228404619207412 \tabularnewline
52 & 4.95 & 4.97795629586926 & -0.0279562958692638 \tabularnewline
53 & 4.96 & 4.96698107931757 & -0.0069810793175673 \tabularnewline
54 & 4.97 & 4.97673755406189 & -0.00673755406189525 \tabularnewline
55 & 5 & 4.98650252384652 & 0.0134974761534759 \tabularnewline
56 & 5 & 5.01697336455491 & -0.0169733645549135 \tabularnewline
57 & 5.01 & 5.01638127230745 & -0.00638127230745145 \tabularnewline
58 & 5.01 & 5.02615867048623 & -0.0161586704862291 \tabularnewline
59 & 5.02 & 5.02559499770979 & -0.00559499770978977 \tabularnewline
60 & 5.04 & 5.03539982398582 & 0.00460017601418361 \tabularnewline
61 & 5.04 & 5.05556029473669 & -0.0155602947366891 \tabularnewline
62 & 5.19 & 5.05501749546716 & 0.134982504532838 \tabularnewline
63 & 5.22 & 5.20972617265478 & 0.0102738273452161 \tabularnewline
64 & 5.22 & 5.24008456085196 & -0.0200845608519602 \tabularnewline
65 & 5.22 & 5.23938393884295 & -0.0193839388429504 \tabularnewline
66 & 5.24 & 5.2387077570596 & 0.00129224294039965 \tabularnewline
67 & 5.28 & 5.25875283515972 & 0.0212471648402754 \tabularnewline
68 & 5.34 & 5.29949401299408 & 0.0405059870059237 \tabularnewline
69 & 5.36 & 5.36090700809027 & -0.000907008090269557 \tabularnewline
70 & 5.38 & 5.38087536837282 & -0.000875368372823537 \tabularnewline
71 & 5.39 & 5.40084483236297 & -0.0108448323629746 \tabularnewline
72 & 5.41 & 5.41046652544885 & -0.000466525448845623 \tabularnewline
73 & 5.44 & 5.43045025135654 & 0.00954974864345992 \tabularnewline
74 & 5.51 & 5.46078338107391 & 0.0492166189260885 \tabularnewline
75 & 5.55 & 5.53250023446607 & 0.0174997655339322 \tabularnewline
76 & 5.56 & 5.57311068948054 & -0.0131106894805422 \tabularnewline
77 & 5.57 & 5.58265334128801 & -0.0126533412880132 \tabularnewline
78 & 5.58 & 5.59221194705195 & -0.0122119470519522 \tabularnewline
79 & 5.58 & 5.60178595024074 & -0.0217859502407425 \tabularnewline
80 & 5.59 & 5.60102597762604 & -0.0110259776260380 \tabularnewline
81 & 5.61 & 5.61064135171101 & -0.000641351711007765 \tabularnewline
82 & 5.63 & 5.63061897904737 & -0.000618979047371404 \tabularnewline
83 & 5.64 & 5.65059738682303 & -0.0105973868230302 \tabularnewline
84 & 5.64 & 5.66022771170287 & -0.0202277117028746 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13403&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]4.09[/C][C]4.09[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]4.08[/C][C]4.1[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]5[/C][C]4.09[/C][C]4.08930232777886[/C][C]0.000697672221139811[/C][/ROW]
[ROW][C]6[/C][C]4.12[/C][C]4.09932666510527[/C][C]0.0206733348947328[/C][/ROW]
[ROW][C]7[/C][C]4.14[/C][C]4.13004782567899[/C][C]0.00995217432101292[/C][/ROW]
[ROW][C]8[/C][C]4.14[/C][C]4.15039499345717[/C][C]-0.0103949934571714[/C][/ROW]
[ROW][C]9[/C][C]4.14[/C][C]4.15003237854847[/C][C]-0.0100323785484715[/C][/ROW]
[ROW][C]10[/C][C]4.14[/C][C]4.14968241295721[/C][C]-0.0096824129572104[/C][/ROW]
[ROW][C]11[/C][C]4.14[/C][C]4.14934465542952[/C][C]-0.00934465542951823[/C][/ROW]
[ROW][C]12[/C][C]4.23[/C][C]4.14901868010405[/C][C]0.0809813198959475[/C][/ROW]
[ROW][C]13[/C][C]4.29[/C][C]4.24184360097018[/C][C]0.0481563990298151[/C][/ROW]
[ROW][C]14[/C][C]4.32[/C][C]4.30352347006384[/C][C]0.0164765299361553[/C][/ROW]
[ROW][C]15[/C][C]4.33[/C][C]4.33409823092571[/C][C]-0.00409823092570694[/C][/ROW]
[ROW][C]16[/C][C]4.35[/C][C]4.34395526983207[/C][C]0.00604473016792717[/C][/ROW]
[ROW][C]17[/C][C]4.35[/C][C]4.36416613184819[/C][C]-0.0141661318481949[/C][/ROW]
[ROW][C]18[/C][C]4.35[/C][C]4.36367196601462[/C][C]-0.0136719660146207[/C][/ROW]
[ROW][C]19[/C][C]4.35[/C][C]4.36319503846978[/C][C]-0.0131950384697825[/C][/ROW]
[ROW][C]20[/C][C]4.36[/C][C]4.36273474787992[/C][C]-0.00273474787992001[/C][/ROW]
[ROW][C]21[/C][C]4.36[/C][C]4.37263934999854[/C][C]-0.0126393499985387[/C][/ROW]
[ROW][C]22[/C][C]4.38[/C][C]4.37219844382918[/C][C]0.0078015561708229[/C][/ROW]
[ROW][C]23[/C][C]4.4[/C][C]4.39247059028028[/C][C]0.00752940971972205[/C][/ROW]
[ROW][C]24[/C][C]4.4[/C][C]4.41273324328043[/C][C]-0.0127332432804304[/C][/ROW]
[ROW][C]25[/C][C]4.4[/C][C]4.41228906177434[/C][C]-0.0122890617743421[/C][/ROW]
[ROW][C]26[/C][C]4.43[/C][C]4.41186037492315[/C][C]0.0181396250768486[/C][/ROW]
[ROW][C]27[/C][C]4.44[/C][C]4.44249315054905[/C][C]-0.00249315054904997[/C][/ROW]
[ROW][C]28[/C][C]4.46[/C][C]4.45240618045499[/C][C]0.0075938195450087[/C][/ROW]
[ROW][C]29[/C][C]4.47[/C][C]4.47267108030244[/C][C]-0.00267108030243612[/C][/ROW]
[ROW][C]30[/C][C]4.49[/C][C]4.48257790337606[/C][C]0.00742209662393645[/C][/ROW]
[ROW][C]31[/C][C]4.49[/C][C]4.50283681290792[/C][C]-0.0128368129079206[/C][/ROW]
[ROW][C]32[/C][C]4.57[/C][C]4.50238901851923[/C][C]0.0676109814807706[/C][/ROW]
[ROW][C]33[/C][C]4.62[/C][C]4.58474753370039[/C][C]0.0352524662996148[/C][/ROW]
[ROW][C]34[/C][C]4.64[/C][C]4.63597726702358[/C][C]0.00402273297641909[/C][/ROW]
[ROW][C]35[/C][C]4.66[/C][C]4.65611759447612[/C][C]0.00388240552388464[/C][/ROW]
[ROW][C]36[/C][C]4.67[/C][C]4.67625302680038[/C][C]-0.00625302680037709[/C][/ROW]
[ROW][C]37[/C][C]4.68[/C][C]4.68603489864554[/C][C]-0.00603489864554341[/C][/ROW]
[ROW][C]38[/C][C]4.72[/C][C]4.69582437958842[/C][C]0.0241756204115759[/C][/ROW]
[ROW][C]39[/C][C]4.74[/C][C]4.73666771252792[/C][C]0.00333228747207759[/C][/ROW]
[ROW][C]40[/C][C]4.75[/C][C]4.75678395474803[/C][C]-0.00678395474802862[/C][/ROW]
[ROW][C]41[/C][C]4.76[/C][C]4.76654730590917[/C][C]-0.0065473059091703[/C][/ROW]
[ROW][C]42[/C][C]4.77[/C][C]4.77631891223636[/C][C]-0.00631891223636405[/C][/ROW]
[ROW][C]43[/C][C]4.76[/C][C]4.78609848575961[/C][C]-0.0260984857596069[/C][/ROW]
[ROW][C]44[/C][C]4.77[/C][C]4.77518807633319[/C][C]-0.00518807633319263[/C][/ROW]
[ROW][C]45[/C][C]4.77[/C][C]4.78500709749625[/C][C]-0.0150070974962517[/C][/ROW]
[ROW][C]46[/C][C]4.78[/C][C]4.7844835957441[/C][C]-0.00448359574409807[/C][/ROW]
[ROW][C]47[/C][C]4.81[/C][C]4.79432719173403[/C][C]0.0156728082659745[/C][/ROW]
[ROW][C]48[/C][C]4.81[/C][C]4.82487391588174[/C][C]-0.0148739158817452[/C][/ROW]
[ROW][C]49[/C][C]4.85[/C][C]4.82435505998523[/C][C]0.025644940014768[/C][/ROW]
[ROW][C]50[/C][C]4.92[/C][C]4.86524964809829[/C][C]0.0547503519017134[/C][/ROW]
[ROW][C]51[/C][C]4.96[/C][C]4.93715953807926[/C][C]0.0228404619207412[/C][/ROW]
[ROW][C]52[/C][C]4.95[/C][C]4.97795629586926[/C][C]-0.0279562958692638[/C][/ROW]
[ROW][C]53[/C][C]4.96[/C][C]4.96698107931757[/C][C]-0.0069810793175673[/C][/ROW]
[ROW][C]54[/C][C]4.97[/C][C]4.97673755406189[/C][C]-0.00673755406189525[/C][/ROW]
[ROW][C]55[/C][C]5[/C][C]4.98650252384652[/C][C]0.0134974761534759[/C][/ROW]
[ROW][C]56[/C][C]5[/C][C]5.01697336455491[/C][C]-0.0169733645549135[/C][/ROW]
[ROW][C]57[/C][C]5.01[/C][C]5.01638127230745[/C][C]-0.00638127230745145[/C][/ROW]
[ROW][C]58[/C][C]5.01[/C][C]5.02615867048623[/C][C]-0.0161586704862291[/C][/ROW]
[ROW][C]59[/C][C]5.02[/C][C]5.02559499770979[/C][C]-0.00559499770978977[/C][/ROW]
[ROW][C]60[/C][C]5.04[/C][C]5.03539982398582[/C][C]0.00460017601418361[/C][/ROW]
[ROW][C]61[/C][C]5.04[/C][C]5.05556029473669[/C][C]-0.0155602947366891[/C][/ROW]
[ROW][C]62[/C][C]5.19[/C][C]5.05501749546716[/C][C]0.134982504532838[/C][/ROW]
[ROW][C]63[/C][C]5.22[/C][C]5.20972617265478[/C][C]0.0102738273452161[/C][/ROW]
[ROW][C]64[/C][C]5.22[/C][C]5.24008456085196[/C][C]-0.0200845608519602[/C][/ROW]
[ROW][C]65[/C][C]5.22[/C][C]5.23938393884295[/C][C]-0.0193839388429504[/C][/ROW]
[ROW][C]66[/C][C]5.24[/C][C]5.2387077570596[/C][C]0.00129224294039965[/C][/ROW]
[ROW][C]67[/C][C]5.28[/C][C]5.25875283515972[/C][C]0.0212471648402754[/C][/ROW]
[ROW][C]68[/C][C]5.34[/C][C]5.29949401299408[/C][C]0.0405059870059237[/C][/ROW]
[ROW][C]69[/C][C]5.36[/C][C]5.36090700809027[/C][C]-0.000907008090269557[/C][/ROW]
[ROW][C]70[/C][C]5.38[/C][C]5.38087536837282[/C][C]-0.000875368372823537[/C][/ROW]
[ROW][C]71[/C][C]5.39[/C][C]5.40084483236297[/C][C]-0.0108448323629746[/C][/ROW]
[ROW][C]72[/C][C]5.41[/C][C]5.41046652544885[/C][C]-0.000466525448845623[/C][/ROW]
[ROW][C]73[/C][C]5.44[/C][C]5.43045025135654[/C][C]0.00954974864345992[/C][/ROW]
[ROW][C]74[/C][C]5.51[/C][C]5.46078338107391[/C][C]0.0492166189260885[/C][/ROW]
[ROW][C]75[/C][C]5.55[/C][C]5.53250023446607[/C][C]0.0174997655339322[/C][/ROW]
[ROW][C]76[/C][C]5.56[/C][C]5.57311068948054[/C][C]-0.0131106894805422[/C][/ROW]
[ROW][C]77[/C][C]5.57[/C][C]5.58265334128801[/C][C]-0.0126533412880132[/C][/ROW]
[ROW][C]78[/C][C]5.58[/C][C]5.59221194705195[/C][C]-0.0122119470519522[/C][/ROW]
[ROW][C]79[/C][C]5.58[/C][C]5.60178595024074[/C][C]-0.0217859502407425[/C][/ROW]
[ROW][C]80[/C][C]5.59[/C][C]5.60102597762604[/C][C]-0.0110259776260380[/C][/ROW]
[ROW][C]81[/C][C]5.61[/C][C]5.61064135171101[/C][C]-0.000641351711007765[/C][/ROW]
[ROW][C]82[/C][C]5.63[/C][C]5.63061897904737[/C][C]-0.000618979047371404[/C][/ROW]
[ROW][C]83[/C][C]5.64[/C][C]5.65059738682303[/C][C]-0.0105973868230302[/C][/ROW]
[ROW][C]84[/C][C]5.64[/C][C]5.66022771170287[/C][C]-0.0202277117028746[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13403&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13403&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	4.09	4.09	0
4	4.08	4.1	-0.0199999999999996
5	4.09	4.08930232777886	0.000697672221139811
6	4.12	4.09932666510527	0.0206733348947328
7	4.14	4.13004782567899	0.00995217432101292
8	4.14	4.15039499345717	-0.0103949934571714
9	4.14	4.15003237854847	-0.0100323785484715
10	4.14	4.14968241295721	-0.0096824129572104
11	4.14	4.14934465542952	-0.00934465542951823
12	4.23	4.14901868010405	0.0809813198959475
13	4.29	4.24184360097018	0.0481563990298151
14	4.32	4.30352347006384	0.0164765299361553
15	4.33	4.33409823092571	-0.00409823092570694
16	4.35	4.34395526983207	0.00604473016792717
17	4.35	4.36416613184819	-0.0141661318481949
18	4.35	4.36367196601462	-0.0136719660146207
19	4.35	4.36319503846978	-0.0131950384697825
20	4.36	4.36273474787992	-0.00273474787992001
21	4.36	4.37263934999854	-0.0126393499985387
22	4.38	4.37219844382918	0.0078015561708229
23	4.4	4.39247059028028	0.00752940971972205
24	4.4	4.41273324328043	-0.0127332432804304
25	4.4	4.41228906177434	-0.0122890617743421
26	4.43	4.41186037492315	0.0181396250768486
27	4.44	4.44249315054905	-0.00249315054904997
28	4.46	4.45240618045499	0.0075938195450087
29	4.47	4.47267108030244	-0.00267108030243612
30	4.49	4.48257790337606	0.00742209662393645
31	4.49	4.50283681290792	-0.0128368129079206
32	4.57	4.50238901851923	0.0676109814807706
33	4.62	4.58474753370039	0.0352524662996148
34	4.64	4.63597726702358	0.00402273297641909
35	4.66	4.65611759447612	0.00388240552388464
36	4.67	4.67625302680038	-0.00625302680037709
37	4.68	4.68603489864554	-0.00603489864554341
38	4.72	4.69582437958842	0.0241756204115759
39	4.74	4.73666771252792	0.00333228747207759
40	4.75	4.75678395474803	-0.00678395474802862
41	4.76	4.76654730590917	-0.0065473059091703
42	4.77	4.77631891223636	-0.00631891223636405
43	4.76	4.78609848575961	-0.0260984857596069
44	4.77	4.77518807633319	-0.00518807633319263
45	4.77	4.78500709749625	-0.0150070974962517
46	4.78	4.7844835957441	-0.00448359574409807
47	4.81	4.79432719173403	0.0156728082659745
48	4.81	4.82487391588174	-0.0148739158817452
49	4.85	4.82435505998523	0.025644940014768
50	4.92	4.86524964809829	0.0547503519017134
51	4.96	4.93715953807926	0.0228404619207412
52	4.95	4.97795629586926	-0.0279562958692638
53	4.96	4.96698107931757	-0.0069810793175673
54	4.97	4.97673755406189	-0.00673755406189525
55	5	4.98650252384652	0.0134974761534759
56	5	5.01697336455491	-0.0169733645549135
57	5.01	5.01638127230745	-0.00638127230745145
58	5.01	5.02615867048623	-0.0161586704862291
59	5.02	5.02559499770979	-0.00559499770978977
60	5.04	5.03539982398582	0.00460017601418361
61	5.04	5.05556029473669	-0.0155602947366891
62	5.19	5.05501749546716	0.134982504532838
63	5.22	5.20972617265478	0.0102738273452161
64	5.22	5.24008456085196	-0.0200845608519602
65	5.22	5.23938393884295	-0.0193839388429504
66	5.24	5.2387077570596	0.00129224294039965
67	5.28	5.25875283515972	0.0212471648402754
68	5.34	5.29949401299408	0.0405059870059237
69	5.36	5.36090700809027	-0.000907008090269557
70	5.38	5.38087536837282	-0.000875368372823537
71	5.39	5.40084483236297	-0.0108448323629746
72	5.41	5.41046652544885	-0.000466525448845623
73	5.44	5.43045025135654	0.00954974864345992
74	5.51	5.46078338107391	0.0492166189260885
75	5.55	5.53250023446607	0.0174997655339322
76	5.56	5.57311068948054	-0.0131106894805422
77	5.57	5.58265334128801	-0.0126533412880132
78	5.58	5.59221194705195	-0.0122119470519522
79	5.58	5.60178595024074	-0.0217859502407425
80	5.59	5.60102597762604	-0.0110259776260380
81	5.61	5.61064135171101	-0.000641351711007765
82	5.63	5.63061897904737	-0.000618979047371404
83	5.64	5.65059738682303	-0.0105973868230302
84	5.64	5.66022771170287	-0.0202277117028746

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	5.65952209607526	5.61019181607674	5.70885237607378
86	5.67904419215052	5.60805340991579	5.75003497438525
87	5.69856628822578	5.6101097093639	5.78702286708766
88	5.71808838430104	5.61419408945801	5.82198267914406
89	5.7376104803763	5.61948348064934	5.85573748010325
90	5.75713257645156	5.62556366117943	5.88870149172368
91	5.77665467252681	5.63219318583796	5.92111615921567
92	5.79617676860207	5.63921774367152	5.95313579353263
93	5.81569886467733	5.64653224560157	5.98486548375309
94	5.83522096075259	5.65406171568152	6.01638020582366
95	5.85474305682785	5.66175072761762	6.04773538603808
96	5.87426515290311	5.66955714470954	6.07897316109669

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 5.65952209607526 & 5.61019181607674 & 5.70885237607378 \tabularnewline
86 & 5.67904419215052 & 5.60805340991579 & 5.75003497438525 \tabularnewline
87 & 5.69856628822578 & 5.6101097093639 & 5.78702286708766 \tabularnewline
88 & 5.71808838430104 & 5.61419408945801 & 5.82198267914406 \tabularnewline
89 & 5.7376104803763 & 5.61948348064934 & 5.85573748010325 \tabularnewline
90 & 5.75713257645156 & 5.62556366117943 & 5.88870149172368 \tabularnewline
91 & 5.77665467252681 & 5.63219318583796 & 5.92111615921567 \tabularnewline
92 & 5.79617676860207 & 5.63921774367152 & 5.95313579353263 \tabularnewline
93 & 5.81569886467733 & 5.64653224560157 & 5.98486548375309 \tabularnewline
94 & 5.83522096075259 & 5.65406171568152 & 6.01638020582366 \tabularnewline
95 & 5.85474305682785 & 5.66175072761762 & 6.04773538603808 \tabularnewline
96 & 5.87426515290311 & 5.66955714470954 & 6.07897316109669 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13403&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]5.65952209607526[/C][C]5.61019181607674[/C][C]5.70885237607378[/C][/ROW]
[ROW][C]86[/C][C]5.67904419215052[/C][C]5.60805340991579[/C][C]5.75003497438525[/C][/ROW]
[ROW][C]87[/C][C]5.69856628822578[/C][C]5.6101097093639[/C][C]5.78702286708766[/C][/ROW]
[ROW][C]88[/C][C]5.71808838430104[/C][C]5.61419408945801[/C][C]5.82198267914406[/C][/ROW]
[ROW][C]89[/C][C]5.7376104803763[/C][C]5.61948348064934[/C][C]5.85573748010325[/C][/ROW]
[ROW][C]90[/C][C]5.75713257645156[/C][C]5.62556366117943[/C][C]5.88870149172368[/C][/ROW]
[ROW][C]91[/C][C]5.77665467252681[/C][C]5.63219318583796[/C][C]5.92111615921567[/C][/ROW]
[ROW][C]92[/C][C]5.79617676860207[/C][C]5.63921774367152[/C][C]5.95313579353263[/C][/ROW]
[ROW][C]93[/C][C]5.81569886467733[/C][C]5.64653224560157[/C][C]5.98486548375309[/C][/ROW]
[ROW][C]94[/C][C]5.83522096075259[/C][C]5.65406171568152[/C][C]6.01638020582366[/C][/ROW]
[ROW][C]95[/C][C]5.85474305682785[/C][C]5.66175072761762[/C][C]6.04773538603808[/C][/ROW]
[ROW][C]96[/C][C]5.87426515290311[/C][C]5.66955714470954[/C][C]6.07897316109669[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13403&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13403&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	5.65952209607526	5.61019181607674	5.70885237607378
86	5.67904419215052	5.60805340991579	5.75003497438525
87	5.69856628822578	5.6101097093639	5.78702286708766
88	5.71808838430104	5.61419408945801	5.82198267914406
89	5.7376104803763	5.61948348064934	5.85573748010325
90	5.75713257645156	5.62556366117943	5.88870149172368
91	5.77665467252681	5.63219318583796	5.92111615921567
92	5.79617676860207	5.63921774367152	5.95313579353263
93	5.81569886467733	5.64653224560157	5.98486548375309
94	5.83522096075259	5.65406171568152	6.01638020582366
95	5.85474305682785	5.66175072761762	6.04773538603808
96	5.87426515290311	5.66955714470954	6.07897316109669

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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

Tinneke Hermans - opgave 10 oef 2 - prijzen broodjes - double smoothing add...

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code