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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 28 Dec 2011 12:22:06 -0500

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/Dec/28/t1325092948yrka59hfmfgt34n.htm/, Retrieved Fri, 03 May 2024 04:21:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160878, Retrieved Fri, 03 May 2024 04:21:46 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

140

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

-       [Exponential Smoothing] [Oefening 10.2] [2011-12-28 17:22:06] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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Boxplots

1,83
1,83
1,87
1,87
1,86
1,87
1,87
1,89
1,89
1,88
1,88
1,87
1,78
1,79
1,8
1,82
1,82
1,83
1,84
1,84
1,83
1,83
1,83
1,84
1,86
1,85
1,85
1,85
1,84
1,85
1,85
1,83
1,82
1,84
1,85
1,88
1,91
1,93
1,91
1,9
1,9
1,89
1,88
1,88
1,92
1,98
2
2
2,02
2,01
2,05
2,07
2,07
2,04
2,05
2,05
2,04
2,03
2,04
2,04
2,1
2,09
2,1
2,09
2,08
2,1
2,11
2,08
2,09
2,1
2,09
2,09

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160878&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160878&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160878&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999944845022461
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999944845022461 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160878&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.999944845022461[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160878&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160878&T=1

As an alternative you can also use a QR Code:

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999944845022461
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	1.83	1.83	0
3	1.87	1.83	0.04
4	1.87	1.8699977938009	2.20619910162867e-06
5	1.86	1.86999999987832	-0.00999999987831712
6	1.87	1.86000055154977	0.00999944845023126
7	1.87	1.86999944848065	5.51519354630159e-07
8	1.89	1.86999999996958	0.0200000000304188
9	1.89	1.88999889690045	1.10309955236865e-06
10	1.88	1.88999999993916	-0.00999999993915868
11	1.88	1.88000055154977	-5.51549772076498e-07
12	1.87	1.88000000003042	-0.0100000000304206
13	1.78	1.87000055154978	-0.090000551549777
14	1.79	1.7800049639784	0.00999503602160079
15	1.8	1.78999944872401	0.0100005512759873
16	1.82	1.79999944841982	0.0200005515801811
17	1.82	1.81999889687003	1.10312997314566e-06
18	1.83	1.81999999993916	0.0100000000608431
19	1.84	1.82999944845022	0.0100005515497787
20	1.84	1.8399994484198	5.51580196184176e-07
21	1.83	1.83999999996958	-0.00999999996957768
22	1.83	1.83000055154977	-5.51549773630811e-07
23	1.83	1.83000000003042	-3.04207770085441e-11
24	1.84	1.83	0.00999999999999823
25	1.86	1.83999944845022	0.0200005515497754
26	1.85	1.85999889687003	-0.00999889687002842
27	1.85	1.85000055148893	-5.51488932298838e-07
28	1.85	1.85000000003042	-3.04174463394702e-11
29	1.84	1.85	-0.0100000000000018
30	1.85	1.84000055154978	0.0099994484502246
31	1.85	1.84999944848065	5.51519354630159e-07
32	1.83	1.84999999996958	-0.019999999969581
33	1.82	1.83000110309955	-0.010001103099549
34	1.84	1.82000055161062	0.0199994483893833
35	1.85	1.83999889693087	0.0100011030691267
36	1.88	1.84999944838938	0.030000551610615
37	1.91	1.87999834532025	0.0300016546797504
38	1.93	1.90999834525941	0.0200016547405901
39	1.91	1.92999889680918	-0.019998896809182
40	1.9	1.9100011030387	-0.0100011030387044
41	1.9	1.90000055161061	-5.51610613408471e-07
42	1.89	1.90000000003042	-0.0100000000304241
43	1.88	1.89000055154978	-0.010000551549777
44	1.88	1.8800005515802	-5.51580196184176e-07
45	1.92	1.88000000003042	0.0399999999695777
46	1.98	1.9199977938009	0.0600022061990999
47	2	1.97999669057966	0.0200033094203351
48	2	1.99999889671792	1.10328208169364e-06
49	2.02	1.99999999993915	0.0200000000608516
50	2.01	2.01999889690045	-0.00999889690044631
51	2.05	2.01000055148893	0.039999448511066
52	2.07	2.04999779383132	0.0200022061686842
53	2.07	2.06999889677877	1.10322123214601e-06
54	2.04	2.06999999993915	-0.0299999999391516
55	2.05	2.04000165464932	0.0099983453506769
56	2.05	2.04999944854149	5.51458513076142e-07
57	2.04	2.04999999996958	-0.00999999996958412
58	2.03	2.04000055154977	-0.0100005515497741
59	2.04	2.0300005515802	0.00999944841980405
60	2.04	2.03999944848065	5.51519352853802e-07
61	2.1	2.03999999996958	0.0600000000304193
62	2.09	2.09999669070135	-0.00999669070134601
63	2.1	2.09000055136725	0.00999944863274926
64	2.09	2.09999944848064	-0.00999944848063539
65	2.08	2.09000055151936	-0.0100005515193562
66	2.1	2.08000055158019	0.0199994484198056
67	2.11	2.09999889693087	0.0100011030691283
68	2.08	2.10999944838938	-0.0299994483893848
69	2.09	2.0800016546189	0.0099983453810979
70	2.1	2.08999944854149	0.0100005514585151
71	2.09	2.09999944841981	-0.00999944841980938
72	2.09	2.09000055151935	-5.51519352853802e-07

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1.83 & 1.83 & 0 \tabularnewline
3 & 1.87 & 1.83 & 0.04 \tabularnewline
4 & 1.87 & 1.8699977938009 & 2.20619910162867e-06 \tabularnewline
5 & 1.86 & 1.86999999987832 & -0.00999999987831712 \tabularnewline
6 & 1.87 & 1.86000055154977 & 0.00999944845023126 \tabularnewline
7 & 1.87 & 1.86999944848065 & 5.51519354630159e-07 \tabularnewline
8 & 1.89 & 1.86999999996958 & 0.0200000000304188 \tabularnewline
9 & 1.89 & 1.88999889690045 & 1.10309955236865e-06 \tabularnewline
10 & 1.88 & 1.88999999993916 & -0.00999999993915868 \tabularnewline
11 & 1.88 & 1.88000055154977 & -5.51549772076498e-07 \tabularnewline
12 & 1.87 & 1.88000000003042 & -0.0100000000304206 \tabularnewline
13 & 1.78 & 1.87000055154978 & -0.090000551549777 \tabularnewline
14 & 1.79 & 1.7800049639784 & 0.00999503602160079 \tabularnewline
15 & 1.8 & 1.78999944872401 & 0.0100005512759873 \tabularnewline
16 & 1.82 & 1.79999944841982 & 0.0200005515801811 \tabularnewline
17 & 1.82 & 1.81999889687003 & 1.10312997314566e-06 \tabularnewline
18 & 1.83 & 1.81999999993916 & 0.0100000000608431 \tabularnewline
19 & 1.84 & 1.82999944845022 & 0.0100005515497787 \tabularnewline
20 & 1.84 & 1.8399994484198 & 5.51580196184176e-07 \tabularnewline
21 & 1.83 & 1.83999999996958 & -0.00999999996957768 \tabularnewline
22 & 1.83 & 1.83000055154977 & -5.51549773630811e-07 \tabularnewline
23 & 1.83 & 1.83000000003042 & -3.04207770085441e-11 \tabularnewline
24 & 1.84 & 1.83 & 0.00999999999999823 \tabularnewline
25 & 1.86 & 1.83999944845022 & 0.0200005515497754 \tabularnewline
26 & 1.85 & 1.85999889687003 & -0.00999889687002842 \tabularnewline
27 & 1.85 & 1.85000055148893 & -5.51488932298838e-07 \tabularnewline
28 & 1.85 & 1.85000000003042 & -3.04174463394702e-11 \tabularnewline
29 & 1.84 & 1.85 & -0.0100000000000018 \tabularnewline
30 & 1.85 & 1.84000055154978 & 0.0099994484502246 \tabularnewline
31 & 1.85 & 1.84999944848065 & 5.51519354630159e-07 \tabularnewline
32 & 1.83 & 1.84999999996958 & -0.019999999969581 \tabularnewline
33 & 1.82 & 1.83000110309955 & -0.010001103099549 \tabularnewline
34 & 1.84 & 1.82000055161062 & 0.0199994483893833 \tabularnewline
35 & 1.85 & 1.83999889693087 & 0.0100011030691267 \tabularnewline
36 & 1.88 & 1.84999944838938 & 0.030000551610615 \tabularnewline
37 & 1.91 & 1.87999834532025 & 0.0300016546797504 \tabularnewline
38 & 1.93 & 1.90999834525941 & 0.0200016547405901 \tabularnewline
39 & 1.91 & 1.92999889680918 & -0.019998896809182 \tabularnewline
40 & 1.9 & 1.9100011030387 & -0.0100011030387044 \tabularnewline
41 & 1.9 & 1.90000055161061 & -5.51610613408471e-07 \tabularnewline
42 & 1.89 & 1.90000000003042 & -0.0100000000304241 \tabularnewline
43 & 1.88 & 1.89000055154978 & -0.010000551549777 \tabularnewline
44 & 1.88 & 1.8800005515802 & -5.51580196184176e-07 \tabularnewline
45 & 1.92 & 1.88000000003042 & 0.0399999999695777 \tabularnewline
46 & 1.98 & 1.9199977938009 & 0.0600022061990999 \tabularnewline
47 & 2 & 1.97999669057966 & 0.0200033094203351 \tabularnewline
48 & 2 & 1.99999889671792 & 1.10328208169364e-06 \tabularnewline
49 & 2.02 & 1.99999999993915 & 0.0200000000608516 \tabularnewline
50 & 2.01 & 2.01999889690045 & -0.00999889690044631 \tabularnewline
51 & 2.05 & 2.01000055148893 & 0.039999448511066 \tabularnewline
52 & 2.07 & 2.04999779383132 & 0.0200022061686842 \tabularnewline
53 & 2.07 & 2.06999889677877 & 1.10322123214601e-06 \tabularnewline
54 & 2.04 & 2.06999999993915 & -0.0299999999391516 \tabularnewline
55 & 2.05 & 2.04000165464932 & 0.0099983453506769 \tabularnewline
56 & 2.05 & 2.04999944854149 & 5.51458513076142e-07 \tabularnewline
57 & 2.04 & 2.04999999996958 & -0.00999999996958412 \tabularnewline
58 & 2.03 & 2.04000055154977 & -0.0100005515497741 \tabularnewline
59 & 2.04 & 2.0300005515802 & 0.00999944841980405 \tabularnewline
60 & 2.04 & 2.03999944848065 & 5.51519352853802e-07 \tabularnewline
61 & 2.1 & 2.03999999996958 & 0.0600000000304193 \tabularnewline
62 & 2.09 & 2.09999669070135 & -0.00999669070134601 \tabularnewline
63 & 2.1 & 2.09000055136725 & 0.00999944863274926 \tabularnewline
64 & 2.09 & 2.09999944848064 & -0.00999944848063539 \tabularnewline
65 & 2.08 & 2.09000055151936 & -0.0100005515193562 \tabularnewline
66 & 2.1 & 2.08000055158019 & 0.0199994484198056 \tabularnewline
67 & 2.11 & 2.09999889693087 & 0.0100011030691283 \tabularnewline
68 & 2.08 & 2.10999944838938 & -0.0299994483893848 \tabularnewline
69 & 2.09 & 2.0800016546189 & 0.0099983453810979 \tabularnewline
70 & 2.1 & 2.08999944854149 & 0.0100005514585151 \tabularnewline
71 & 2.09 & 2.09999944841981 & -0.00999944841980938 \tabularnewline
72 & 2.09 & 2.09000055151935 & -5.51519352853802e-07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160878&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]2[/C][C]1.83[/C][C]1.83[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]1.87[/C][C]1.83[/C][C]0.04[/C][/ROW]
[ROW][C]4[/C][C]1.87[/C][C]1.8699977938009[/C][C]2.20619910162867e-06[/C][/ROW]
[ROW][C]5[/C][C]1.86[/C][C]1.86999999987832[/C][C]-0.00999999987831712[/C][/ROW]
[ROW][C]6[/C][C]1.87[/C][C]1.86000055154977[/C][C]0.00999944845023126[/C][/ROW]
[ROW][C]7[/C][C]1.87[/C][C]1.86999944848065[/C][C]5.51519354630159e-07[/C][/ROW]
[ROW][C]8[/C][C]1.89[/C][C]1.86999999996958[/C][C]0.0200000000304188[/C][/ROW]
[ROW][C]9[/C][C]1.89[/C][C]1.88999889690045[/C][C]1.10309955236865e-06[/C][/ROW]
[ROW][C]10[/C][C]1.88[/C][C]1.88999999993916[/C][C]-0.00999999993915868[/C][/ROW]
[ROW][C]11[/C][C]1.88[/C][C]1.88000055154977[/C][C]-5.51549772076498e-07[/C][/ROW]
[ROW][C]12[/C][C]1.87[/C][C]1.88000000003042[/C][C]-0.0100000000304206[/C][/ROW]
[ROW][C]13[/C][C]1.78[/C][C]1.87000055154978[/C][C]-0.090000551549777[/C][/ROW]
[ROW][C]14[/C][C]1.79[/C][C]1.7800049639784[/C][C]0.00999503602160079[/C][/ROW]
[ROW][C]15[/C][C]1.8[/C][C]1.78999944872401[/C][C]0.0100005512759873[/C][/ROW]
[ROW][C]16[/C][C]1.82[/C][C]1.79999944841982[/C][C]0.0200005515801811[/C][/ROW]
[ROW][C]17[/C][C]1.82[/C][C]1.81999889687003[/C][C]1.10312997314566e-06[/C][/ROW]
[ROW][C]18[/C][C]1.83[/C][C]1.81999999993916[/C][C]0.0100000000608431[/C][/ROW]
[ROW][C]19[/C][C]1.84[/C][C]1.82999944845022[/C][C]0.0100005515497787[/C][/ROW]
[ROW][C]20[/C][C]1.84[/C][C]1.8399994484198[/C][C]5.51580196184176e-07[/C][/ROW]
[ROW][C]21[/C][C]1.83[/C][C]1.83999999996958[/C][C]-0.00999999996957768[/C][/ROW]
[ROW][C]22[/C][C]1.83[/C][C]1.83000055154977[/C][C]-5.51549773630811e-07[/C][/ROW]
[ROW][C]23[/C][C]1.83[/C][C]1.83000000003042[/C][C]-3.04207770085441e-11[/C][/ROW]
[ROW][C]24[/C][C]1.84[/C][C]1.83[/C][C]0.00999999999999823[/C][/ROW]
[ROW][C]25[/C][C]1.86[/C][C]1.83999944845022[/C][C]0.0200005515497754[/C][/ROW]
[ROW][C]26[/C][C]1.85[/C][C]1.85999889687003[/C][C]-0.00999889687002842[/C][/ROW]
[ROW][C]27[/C][C]1.85[/C][C]1.85000055148893[/C][C]-5.51488932298838e-07[/C][/ROW]
[ROW][C]28[/C][C]1.85[/C][C]1.85000000003042[/C][C]-3.04174463394702e-11[/C][/ROW]
[ROW][C]29[/C][C]1.84[/C][C]1.85[/C][C]-0.0100000000000018[/C][/ROW]
[ROW][C]30[/C][C]1.85[/C][C]1.84000055154978[/C][C]0.0099994484502246[/C][/ROW]
[ROW][C]31[/C][C]1.85[/C][C]1.84999944848065[/C][C]5.51519354630159e-07[/C][/ROW]
[ROW][C]32[/C][C]1.83[/C][C]1.84999999996958[/C][C]-0.019999999969581[/C][/ROW]
[ROW][C]33[/C][C]1.82[/C][C]1.83000110309955[/C][C]-0.010001103099549[/C][/ROW]
[ROW][C]34[/C][C]1.84[/C][C]1.82000055161062[/C][C]0.0199994483893833[/C][/ROW]
[ROW][C]35[/C][C]1.85[/C][C]1.83999889693087[/C][C]0.0100011030691267[/C][/ROW]
[ROW][C]36[/C][C]1.88[/C][C]1.84999944838938[/C][C]0.030000551610615[/C][/ROW]
[ROW][C]37[/C][C]1.91[/C][C]1.87999834532025[/C][C]0.0300016546797504[/C][/ROW]
[ROW][C]38[/C][C]1.93[/C][C]1.90999834525941[/C][C]0.0200016547405901[/C][/ROW]
[ROW][C]39[/C][C]1.91[/C][C]1.92999889680918[/C][C]-0.019998896809182[/C][/ROW]
[ROW][C]40[/C][C]1.9[/C][C]1.9100011030387[/C][C]-0.0100011030387044[/C][/ROW]
[ROW][C]41[/C][C]1.9[/C][C]1.90000055161061[/C][C]-5.51610613408471e-07[/C][/ROW]
[ROW][C]42[/C][C]1.89[/C][C]1.90000000003042[/C][C]-0.0100000000304241[/C][/ROW]
[ROW][C]43[/C][C]1.88[/C][C]1.89000055154978[/C][C]-0.010000551549777[/C][/ROW]
[ROW][C]44[/C][C]1.88[/C][C]1.8800005515802[/C][C]-5.51580196184176e-07[/C][/ROW]
[ROW][C]45[/C][C]1.92[/C][C]1.88000000003042[/C][C]0.0399999999695777[/C][/ROW]
[ROW][C]46[/C][C]1.98[/C][C]1.9199977938009[/C][C]0.0600022061990999[/C][/ROW]
[ROW][C]47[/C][C]2[/C][C]1.97999669057966[/C][C]0.0200033094203351[/C][/ROW]
[ROW][C]48[/C][C]2[/C][C]1.99999889671792[/C][C]1.10328208169364e-06[/C][/ROW]
[ROW][C]49[/C][C]2.02[/C][C]1.99999999993915[/C][C]0.0200000000608516[/C][/ROW]
[ROW][C]50[/C][C]2.01[/C][C]2.01999889690045[/C][C]-0.00999889690044631[/C][/ROW]
[ROW][C]51[/C][C]2.05[/C][C]2.01000055148893[/C][C]0.039999448511066[/C][/ROW]
[ROW][C]52[/C][C]2.07[/C][C]2.04999779383132[/C][C]0.0200022061686842[/C][/ROW]
[ROW][C]53[/C][C]2.07[/C][C]2.06999889677877[/C][C]1.10322123214601e-06[/C][/ROW]
[ROW][C]54[/C][C]2.04[/C][C]2.06999999993915[/C][C]-0.0299999999391516[/C][/ROW]
[ROW][C]55[/C][C]2.05[/C][C]2.04000165464932[/C][C]0.0099983453506769[/C][/ROW]
[ROW][C]56[/C][C]2.05[/C][C]2.04999944854149[/C][C]5.51458513076142e-07[/C][/ROW]
[ROW][C]57[/C][C]2.04[/C][C]2.04999999996958[/C][C]-0.00999999996958412[/C][/ROW]
[ROW][C]58[/C][C]2.03[/C][C]2.04000055154977[/C][C]-0.0100005515497741[/C][/ROW]
[ROW][C]59[/C][C]2.04[/C][C]2.0300005515802[/C][C]0.00999944841980405[/C][/ROW]
[ROW][C]60[/C][C]2.04[/C][C]2.03999944848065[/C][C]5.51519352853802e-07[/C][/ROW]
[ROW][C]61[/C][C]2.1[/C][C]2.03999999996958[/C][C]0.0600000000304193[/C][/ROW]
[ROW][C]62[/C][C]2.09[/C][C]2.09999669070135[/C][C]-0.00999669070134601[/C][/ROW]
[ROW][C]63[/C][C]2.1[/C][C]2.09000055136725[/C][C]0.00999944863274926[/C][/ROW]
[ROW][C]64[/C][C]2.09[/C][C]2.09999944848064[/C][C]-0.00999944848063539[/C][/ROW]
[ROW][C]65[/C][C]2.08[/C][C]2.09000055151936[/C][C]-0.0100005515193562[/C][/ROW]
[ROW][C]66[/C][C]2.1[/C][C]2.08000055158019[/C][C]0.0199994484198056[/C][/ROW]
[ROW][C]67[/C][C]2.11[/C][C]2.09999889693087[/C][C]0.0100011030691283[/C][/ROW]
[ROW][C]68[/C][C]2.08[/C][C]2.10999944838938[/C][C]-0.0299994483893848[/C][/ROW]
[ROW][C]69[/C][C]2.09[/C][C]2.0800016546189[/C][C]0.0099983453810979[/C][/ROW]
[ROW][C]70[/C][C]2.1[/C][C]2.08999944854149[/C][C]0.0100005514585151[/C][/ROW]
[ROW][C]71[/C][C]2.09[/C][C]2.09999944841981[/C][C]-0.00999944841980938[/C][/ROW]
[ROW][C]72[/C][C]2.09[/C][C]2.09000055151935[/C][C]-5.51519352853802e-07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160878&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160878&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
2	1.83	1.83	0
3	1.87	1.83	0.04
4	1.87	1.8699977938009	2.20619910162867e-06
5	1.86	1.86999999987832	-0.00999999987831712
6	1.87	1.86000055154977	0.00999944845023126
7	1.87	1.86999944848065	5.51519354630159e-07
8	1.89	1.86999999996958	0.0200000000304188
9	1.89	1.88999889690045	1.10309955236865e-06
10	1.88	1.88999999993916	-0.00999999993915868
11	1.88	1.88000055154977	-5.51549772076498e-07
12	1.87	1.88000000003042	-0.0100000000304206
13	1.78	1.87000055154978	-0.090000551549777
14	1.79	1.7800049639784	0.00999503602160079
15	1.8	1.78999944872401	0.0100005512759873
16	1.82	1.79999944841982	0.0200005515801811
17	1.82	1.81999889687003	1.10312997314566e-06
18	1.83	1.81999999993916	0.0100000000608431
19	1.84	1.82999944845022	0.0100005515497787
20	1.84	1.8399994484198	5.51580196184176e-07
21	1.83	1.83999999996958	-0.00999999996957768
22	1.83	1.83000055154977	-5.51549773630811e-07
23	1.83	1.83000000003042	-3.04207770085441e-11
24	1.84	1.83	0.00999999999999823
25	1.86	1.83999944845022	0.0200005515497754
26	1.85	1.85999889687003	-0.00999889687002842
27	1.85	1.85000055148893	-5.51488932298838e-07
28	1.85	1.85000000003042	-3.04174463394702e-11
29	1.84	1.85	-0.0100000000000018
30	1.85	1.84000055154978	0.0099994484502246
31	1.85	1.84999944848065	5.51519354630159e-07
32	1.83	1.84999999996958	-0.019999999969581
33	1.82	1.83000110309955	-0.010001103099549
34	1.84	1.82000055161062	0.0199994483893833
35	1.85	1.83999889693087	0.0100011030691267
36	1.88	1.84999944838938	0.030000551610615
37	1.91	1.87999834532025	0.0300016546797504
38	1.93	1.90999834525941	0.0200016547405901
39	1.91	1.92999889680918	-0.019998896809182
40	1.9	1.9100011030387	-0.0100011030387044
41	1.9	1.90000055161061	-5.51610613408471e-07
42	1.89	1.90000000003042	-0.0100000000304241
43	1.88	1.89000055154978	-0.010000551549777
44	1.88	1.8800005515802	-5.51580196184176e-07
45	1.92	1.88000000003042	0.0399999999695777
46	1.98	1.9199977938009	0.0600022061990999
47	2	1.97999669057966	0.0200033094203351
48	2	1.99999889671792	1.10328208169364e-06
49	2.02	1.99999999993915	0.0200000000608516
50	2.01	2.01999889690045	-0.00999889690044631
51	2.05	2.01000055148893	0.039999448511066
52	2.07	2.04999779383132	0.0200022061686842
53	2.07	2.06999889677877	1.10322123214601e-06
54	2.04	2.06999999993915	-0.0299999999391516
55	2.05	2.04000165464932	0.0099983453506769
56	2.05	2.04999944854149	5.51458513076142e-07
57	2.04	2.04999999996958	-0.00999999996958412
58	2.03	2.04000055154977	-0.0100005515497741
59	2.04	2.0300005515802	0.00999944841980405
60	2.04	2.03999944848065	5.51519352853802e-07
61	2.1	2.03999999996958	0.0600000000304193
62	2.09	2.09999669070135	-0.00999669070134601
63	2.1	2.09000055136725	0.00999944863274926
64	2.09	2.09999944848064	-0.00999944848063539
65	2.08	2.09000055151936	-0.0100005515193562
66	2.1	2.08000055158019	0.0199994484198056
67	2.11	2.09999889693087	0.0100011030691283
68	2.08	2.10999944838938	-0.0299994483893848
69	2.09	2.0800016546189	0.0099983453810979
70	2.1	2.08999944854149	0.0100005514585151
71	2.09	2.09999944841981	-0.00999944841980938
72	2.09	2.09000055151935	-5.51519352853802e-07

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	2.09000000003042	2.04925735256752	2.13074264749332
74	2.09000000003042	2.03238278438142	2.14761721567942
75	2.09000000003042	2.01943425936259	2.16056574069825
76	2.09000000003042	2.00851807582108	2.17148192423976
77	2.09000000003042	1.99890069053955	2.18109930952129
78	2.09000000003042	1.99020588995087	2.18979411010997
79	2.09000000003042	1.98221018314855	2.19778981691229
80	2.09000000003042	1.97476795222998	2.20523204783086
81	2.09000000003042	1.9677780500495	2.21222195001134
82	2.09000000003042	1.96116683165365	2.21883316840719
83	2.09000000003042	1.954878700855	2.22512129920584
84	2.09000000003042	1.94887046482354	2.2311295352373

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 2.09000000003042 & 2.04925735256752 & 2.13074264749332 \tabularnewline
74 & 2.09000000003042 & 2.03238278438142 & 2.14761721567942 \tabularnewline
75 & 2.09000000003042 & 2.01943425936259 & 2.16056574069825 \tabularnewline
76 & 2.09000000003042 & 2.00851807582108 & 2.17148192423976 \tabularnewline
77 & 2.09000000003042 & 1.99890069053955 & 2.18109930952129 \tabularnewline
78 & 2.09000000003042 & 1.99020588995087 & 2.18979411010997 \tabularnewline
79 & 2.09000000003042 & 1.98221018314855 & 2.19778981691229 \tabularnewline
80 & 2.09000000003042 & 1.97476795222998 & 2.20523204783086 \tabularnewline
81 & 2.09000000003042 & 1.9677780500495 & 2.21222195001134 \tabularnewline
82 & 2.09000000003042 & 1.96116683165365 & 2.21883316840719 \tabularnewline
83 & 2.09000000003042 & 1.954878700855 & 2.22512129920584 \tabularnewline
84 & 2.09000000003042 & 1.94887046482354 & 2.2311295352373 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160878&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]73[/C][C]2.09000000003042[/C][C]2.04925735256752[/C][C]2.13074264749332[/C][/ROW]
[ROW][C]74[/C][C]2.09000000003042[/C][C]2.03238278438142[/C][C]2.14761721567942[/C][/ROW]
[ROW][C]75[/C][C]2.09000000003042[/C][C]2.01943425936259[/C][C]2.16056574069825[/C][/ROW]
[ROW][C]76[/C][C]2.09000000003042[/C][C]2.00851807582108[/C][C]2.17148192423976[/C][/ROW]
[ROW][C]77[/C][C]2.09000000003042[/C][C]1.99890069053955[/C][C]2.18109930952129[/C][/ROW]
[ROW][C]78[/C][C]2.09000000003042[/C][C]1.99020588995087[/C][C]2.18979411010997[/C][/ROW]
[ROW][C]79[/C][C]2.09000000003042[/C][C]1.98221018314855[/C][C]2.19778981691229[/C][/ROW]
[ROW][C]80[/C][C]2.09000000003042[/C][C]1.97476795222998[/C][C]2.20523204783086[/C][/ROW]
[ROW][C]81[/C][C]2.09000000003042[/C][C]1.9677780500495[/C][C]2.21222195001134[/C][/ROW]
[ROW][C]82[/C][C]2.09000000003042[/C][C]1.96116683165365[/C][C]2.21883316840719[/C][/ROW]
[ROW][C]83[/C][C]2.09000000003042[/C][C]1.954878700855[/C][C]2.22512129920584[/C][/ROW]
[ROW][C]84[/C][C]2.09000000003042[/C][C]1.94887046482354[/C][C]2.2311295352373[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160878&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160878&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
73	2.09000000003042	2.04925735256752	2.13074264749332
74	2.09000000003042	2.03238278438142	2.14761721567942
75	2.09000000003042	2.01943425936259	2.16056574069825
76	2.09000000003042	2.00851807582108	2.17148192423976
77	2.09000000003042	1.99890069053955	2.18109930952129
78	2.09000000003042	1.99020588995087	2.18979411010997
79	2.09000000003042	1.98221018314855	2.19778981691229
80	2.09000000003042	1.97476795222998	2.20523204783086
81	2.09000000003042	1.9677780500495	2.21222195001134
82	2.09000000003042	1.96116683165365	2.21883316840719
83	2.09000000003042	1.954878700855	2.22512129920584
84	2.09000000003042	1.94887046482354	2.2311295352373

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = additive ;

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

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code