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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

Tue, 27 May 2008 13:26:26 -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/27/t1211916446e5e54l289jtzwm8.htm/, Retrieved Mon, 20 May 2024 01:53:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13389, Retrieved Mon, 20 May 2024 01:53:28 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

177

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

-       [Exponential Smoothing] [Joeri Van de Veld...] [2008-05-27 19:26:26] [5e6e1828961460912353a47164e3bace] [Current]

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Dataseries X:

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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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13389&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13389&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13389&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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.981229383786507
beta	0
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.981229383786507 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13389&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]0.981229383786507[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13389&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13389&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	0.981229383786507
beta	0
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	105.18	105.18	0
3	105.18	105.18	0
4	105.18	105.18	0
5	105.18	105.18	0
6	105.18	105.18	0
7	105.18	105.18	0
8	105.18	105.18	0
9	105.18	105.18	0
10	105.18	105.18	0
11	97.82	105.18	-7.36000000000001
12	97.83	97.9581517353313	-0.128151735331301
13	97.82	97.832405487041	-0.0124054870409935
14	97.83	97.8202328586362	0.00976714136382384
15	97.82	97.829816664738	-0.00981666473795428
16	97.82	97.8201842648463	-0.000184264846296855
17	97.8	97.8200034587647	-0.0200034587647053
18	97.8	97.8003754772474	-0.000375477247416711
19	97.44	97.8000070479393	-0.360007047939305
20	97.44	97.446757554131	-0.00675755413101342
21	97.44	97.4401268434551	-0.000126843455134917
22	97.44	97.4400023809298	-2.38092981419413e-06
23	97.7	97.4400000446915	0.259999955308487
24	97.7	97.6951196406234	0.00488035937662801
25	97.7	97.6999083926472	9.16073528429706e-05
26	97.7	97.6999982804735	1.71952646610407e-06
27	97.7	97.6999999677234	3.22765743021591e-08
28	97.7	97.6999999993942	6.05851369073207e-10
29	97.7	97.6999999999886	1.13686837721616e-11
30	97.7	97.6999999999998	2.1316282072803e-13
31	97.7	97.7	1.4210854715202e-14
32	97.7	97.7	0
33	97.7	97.7	0
34	89.38	97.7	-8.32
35	89.38	89.5361715268963	-0.156171526896273
36	89.38	89.3829314357948	-0.00293143579484934
37	89.38	89.3800550248563	-5.50248562660727e-05
38	87.69	89.3800010328505	-1.69000103285046
39	89.21	87.721722360788	1.48827763921196
40	89.21	89.1820641116152	0.0279358883847749
41	89.21	89.2094756261605	0.000524373839454029
42	89.21	89.2099901571799	9.84282009142134e-06
43	89.21	89.2099998152442	1.84755805321402e-07
44	89.21	89.209999996532	3.46797435213375e-09
45	89.21	89.209999999935	6.50999254503404e-11
46	89.21	89.2099999999988	1.22213350550737e-12
47	89.21	89.21	2.8421709430404e-14
48	89.21	89.21	0
49	89.21	89.21	0
50	89.21	89.21	0
51	89.21	89.21	0
52	89.21	89.21	0
53	89.21	89.21	0
54	89.21	89.21	0
55	89.21	89.21	0
56	89.21	89.21	0
57	89.21	89.21	0
58	89.21	89.21	0
59	89.21	89.21	0
60	89.21	89.21	0
61	89.21	89.21	0
62	89.21	89.21	0
63	89.21	89.21	0
64	89.21	89.21	0
65	89.21	89.21	0
66	89.21	89.21	0
67	89.21	89.21	0
68	89.21	89.21	0
69	89.21	89.21	0
70	89.21	89.21	0
71	92.07	89.21	2.86
72	92.07	92.0163160376294	0.0536839623705845
73	92.07	92.0689923189455	0.00100768105447457
74	92.07	92.0699810852057	1.89147943387979e-05
75	92.07	92.0699996449576	3.5504234574546e-07
76	92.07	92.0699999933356	6.66435084895056e-09
77	92.07	92.0699999998749	1.25083943203208e-10
78	92.07	92.0699999999976	2.34479102800833e-12
79	92.07	92.07	4.2632564145606e-14
80	92.07	92.07	0
81	94	92.07	1.93000000000001
82	94	93.963772710708	0.036227289292043
83	94	93.9993199914562	0.000680008543753274
84	94	93.9999872358206	1.27641793881139e-05
85	94	93.9999997604085	2.39591500417191e-07
86	94	93.9999999955027	4.49728077001055e-09
87	94	93.9999999999156	8.44124770082999e-11
88	94	93.9999999999984	1.57740487338742e-12
89	94	94	2.8421709430404e-14
90	94	94	0
91	94	94	0
92	94	94	0
93	94	94	0
94	94	94	0
95	94	94	0
96	94	94	0

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 105.18 & 105.18 & 0 \tabularnewline
3 & 105.18 & 105.18 & 0 \tabularnewline
4 & 105.18 & 105.18 & 0 \tabularnewline
5 & 105.18 & 105.18 & 0 \tabularnewline
6 & 105.18 & 105.18 & 0 \tabularnewline
7 & 105.18 & 105.18 & 0 \tabularnewline
8 & 105.18 & 105.18 & 0 \tabularnewline
9 & 105.18 & 105.18 & 0 \tabularnewline
10 & 105.18 & 105.18 & 0 \tabularnewline
11 & 97.82 & 105.18 & -7.36000000000001 \tabularnewline
12 & 97.83 & 97.9581517353313 & -0.128151735331301 \tabularnewline
13 & 97.82 & 97.832405487041 & -0.0124054870409935 \tabularnewline
14 & 97.83 & 97.8202328586362 & 0.00976714136382384 \tabularnewline
15 & 97.82 & 97.829816664738 & -0.00981666473795428 \tabularnewline
16 & 97.82 & 97.8201842648463 & -0.000184264846296855 \tabularnewline
17 & 97.8 & 97.8200034587647 & -0.0200034587647053 \tabularnewline
18 & 97.8 & 97.8003754772474 & -0.000375477247416711 \tabularnewline
19 & 97.44 & 97.8000070479393 & -0.360007047939305 \tabularnewline
20 & 97.44 & 97.446757554131 & -0.00675755413101342 \tabularnewline
21 & 97.44 & 97.4401268434551 & -0.000126843455134917 \tabularnewline
22 & 97.44 & 97.4400023809298 & -2.38092981419413e-06 \tabularnewline
23 & 97.7 & 97.4400000446915 & 0.259999955308487 \tabularnewline
24 & 97.7 & 97.6951196406234 & 0.00488035937662801 \tabularnewline
25 & 97.7 & 97.6999083926472 & 9.16073528429706e-05 \tabularnewline
26 & 97.7 & 97.6999982804735 & 1.71952646610407e-06 \tabularnewline
27 & 97.7 & 97.6999999677234 & 3.22765743021591e-08 \tabularnewline
28 & 97.7 & 97.6999999993942 & 6.05851369073207e-10 \tabularnewline
29 & 97.7 & 97.6999999999886 & 1.13686837721616e-11 \tabularnewline
30 & 97.7 & 97.6999999999998 & 2.1316282072803e-13 \tabularnewline
31 & 97.7 & 97.7 & 1.4210854715202e-14 \tabularnewline
32 & 97.7 & 97.7 & 0 \tabularnewline
33 & 97.7 & 97.7 & 0 \tabularnewline
34 & 89.38 & 97.7 & -8.32 \tabularnewline
35 & 89.38 & 89.5361715268963 & -0.156171526896273 \tabularnewline
36 & 89.38 & 89.3829314357948 & -0.00293143579484934 \tabularnewline
37 & 89.38 & 89.3800550248563 & -5.50248562660727e-05 \tabularnewline
38 & 87.69 & 89.3800010328505 & -1.69000103285046 \tabularnewline
39 & 89.21 & 87.721722360788 & 1.48827763921196 \tabularnewline
40 & 89.21 & 89.1820641116152 & 0.0279358883847749 \tabularnewline
41 & 89.21 & 89.2094756261605 & 0.000524373839454029 \tabularnewline
42 & 89.21 & 89.2099901571799 & 9.84282009142134e-06 \tabularnewline
43 & 89.21 & 89.2099998152442 & 1.84755805321402e-07 \tabularnewline
44 & 89.21 & 89.209999996532 & 3.46797435213375e-09 \tabularnewline
45 & 89.21 & 89.209999999935 & 6.50999254503404e-11 \tabularnewline
46 & 89.21 & 89.2099999999988 & 1.22213350550737e-12 \tabularnewline
47 & 89.21 & 89.21 & 2.8421709430404e-14 \tabularnewline
48 & 89.21 & 89.21 & 0 \tabularnewline
49 & 89.21 & 89.21 & 0 \tabularnewline
50 & 89.21 & 89.21 & 0 \tabularnewline
51 & 89.21 & 89.21 & 0 \tabularnewline
52 & 89.21 & 89.21 & 0 \tabularnewline
53 & 89.21 & 89.21 & 0 \tabularnewline
54 & 89.21 & 89.21 & 0 \tabularnewline
55 & 89.21 & 89.21 & 0 \tabularnewline
56 & 89.21 & 89.21 & 0 \tabularnewline
57 & 89.21 & 89.21 & 0 \tabularnewline
58 & 89.21 & 89.21 & 0 \tabularnewline
59 & 89.21 & 89.21 & 0 \tabularnewline
60 & 89.21 & 89.21 & 0 \tabularnewline
61 & 89.21 & 89.21 & 0 \tabularnewline
62 & 89.21 & 89.21 & 0 \tabularnewline
63 & 89.21 & 89.21 & 0 \tabularnewline
64 & 89.21 & 89.21 & 0 \tabularnewline
65 & 89.21 & 89.21 & 0 \tabularnewline
66 & 89.21 & 89.21 & 0 \tabularnewline
67 & 89.21 & 89.21 & 0 \tabularnewline
68 & 89.21 & 89.21 & 0 \tabularnewline
69 & 89.21 & 89.21 & 0 \tabularnewline
70 & 89.21 & 89.21 & 0 \tabularnewline
71 & 92.07 & 89.21 & 2.86 \tabularnewline
72 & 92.07 & 92.0163160376294 & 0.0536839623705845 \tabularnewline
73 & 92.07 & 92.0689923189455 & 0.00100768105447457 \tabularnewline
74 & 92.07 & 92.0699810852057 & 1.89147943387979e-05 \tabularnewline
75 & 92.07 & 92.0699996449576 & 3.5504234574546e-07 \tabularnewline
76 & 92.07 & 92.0699999933356 & 6.66435084895056e-09 \tabularnewline
77 & 92.07 & 92.0699999998749 & 1.25083943203208e-10 \tabularnewline
78 & 92.07 & 92.0699999999976 & 2.34479102800833e-12 \tabularnewline
79 & 92.07 & 92.07 & 4.2632564145606e-14 \tabularnewline
80 & 92.07 & 92.07 & 0 \tabularnewline
81 & 94 & 92.07 & 1.93000000000001 \tabularnewline
82 & 94 & 93.963772710708 & 0.036227289292043 \tabularnewline
83 & 94 & 93.9993199914562 & 0.000680008543753274 \tabularnewline
84 & 94 & 93.9999872358206 & 1.27641793881139e-05 \tabularnewline
85 & 94 & 93.9999997604085 & 2.39591500417191e-07 \tabularnewline
86 & 94 & 93.9999999955027 & 4.49728077001055e-09 \tabularnewline
87 & 94 & 93.9999999999156 & 8.44124770082999e-11 \tabularnewline
88 & 94 & 93.9999999999984 & 1.57740487338742e-12 \tabularnewline
89 & 94 & 94 & 2.8421709430404e-14 \tabularnewline
90 & 94 & 94 & 0 \tabularnewline
91 & 94 & 94 & 0 \tabularnewline
92 & 94 & 94 & 0 \tabularnewline
93 & 94 & 94 & 0 \tabularnewline
94 & 94 & 94 & 0 \tabularnewline
95 & 94 & 94 & 0 \tabularnewline
96 & 94 & 94 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13389&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]105.18[/C][C]105.18[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]105.18[/C][C]105.18[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]105.18[/C][C]105.18[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]105.18[/C][C]105.18[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]105.18[/C][C]105.18[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]105.18[/C][C]105.18[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]105.18[/C][C]105.18[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]105.18[/C][C]105.18[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]105.18[/C][C]105.18[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]97.82[/C][C]105.18[/C][C]-7.36000000000001[/C][/ROW]
[ROW][C]12[/C][C]97.83[/C][C]97.9581517353313[/C][C]-0.128151735331301[/C][/ROW]
[ROW][C]13[/C][C]97.82[/C][C]97.832405487041[/C][C]-0.0124054870409935[/C][/ROW]
[ROW][C]14[/C][C]97.83[/C][C]97.8202328586362[/C][C]0.00976714136382384[/C][/ROW]
[ROW][C]15[/C][C]97.82[/C][C]97.829816664738[/C][C]-0.00981666473795428[/C][/ROW]
[ROW][C]16[/C][C]97.82[/C][C]97.8201842648463[/C][C]-0.000184264846296855[/C][/ROW]
[ROW][C]17[/C][C]97.8[/C][C]97.8200034587647[/C][C]-0.0200034587647053[/C][/ROW]
[ROW][C]18[/C][C]97.8[/C][C]97.8003754772474[/C][C]-0.000375477247416711[/C][/ROW]
[ROW][C]19[/C][C]97.44[/C][C]97.8000070479393[/C][C]-0.360007047939305[/C][/ROW]
[ROW][C]20[/C][C]97.44[/C][C]97.446757554131[/C][C]-0.00675755413101342[/C][/ROW]
[ROW][C]21[/C][C]97.44[/C][C]97.4401268434551[/C][C]-0.000126843455134917[/C][/ROW]
[ROW][C]22[/C][C]97.44[/C][C]97.4400023809298[/C][C]-2.38092981419413e-06[/C][/ROW]
[ROW][C]23[/C][C]97.7[/C][C]97.4400000446915[/C][C]0.259999955308487[/C][/ROW]
[ROW][C]24[/C][C]97.7[/C][C]97.6951196406234[/C][C]0.00488035937662801[/C][/ROW]
[ROW][C]25[/C][C]97.7[/C][C]97.6999083926472[/C][C]9.16073528429706e-05[/C][/ROW]
[ROW][C]26[/C][C]97.7[/C][C]97.6999982804735[/C][C]1.71952646610407e-06[/C][/ROW]
[ROW][C]27[/C][C]97.7[/C][C]97.6999999677234[/C][C]3.22765743021591e-08[/C][/ROW]
[ROW][C]28[/C][C]97.7[/C][C]97.6999999993942[/C][C]6.05851369073207e-10[/C][/ROW]
[ROW][C]29[/C][C]97.7[/C][C]97.6999999999886[/C][C]1.13686837721616e-11[/C][/ROW]
[ROW][C]30[/C][C]97.7[/C][C]97.6999999999998[/C][C]2.1316282072803e-13[/C][/ROW]
[ROW][C]31[/C][C]97.7[/C][C]97.7[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]32[/C][C]97.7[/C][C]97.7[/C][C]0[/C][/ROW]
[ROW][C]33[/C][C]97.7[/C][C]97.7[/C][C]0[/C][/ROW]
[ROW][C]34[/C][C]89.38[/C][C]97.7[/C][C]-8.32[/C][/ROW]
[ROW][C]35[/C][C]89.38[/C][C]89.5361715268963[/C][C]-0.156171526896273[/C][/ROW]
[ROW][C]36[/C][C]89.38[/C][C]89.3829314357948[/C][C]-0.00293143579484934[/C][/ROW]
[ROW][C]37[/C][C]89.38[/C][C]89.3800550248563[/C][C]-5.50248562660727e-05[/C][/ROW]
[ROW][C]38[/C][C]87.69[/C][C]89.3800010328505[/C][C]-1.69000103285046[/C][/ROW]
[ROW][C]39[/C][C]89.21[/C][C]87.721722360788[/C][C]1.48827763921196[/C][/ROW]
[ROW][C]40[/C][C]89.21[/C][C]89.1820641116152[/C][C]0.0279358883847749[/C][/ROW]
[ROW][C]41[/C][C]89.21[/C][C]89.2094756261605[/C][C]0.000524373839454029[/C][/ROW]
[ROW][C]42[/C][C]89.21[/C][C]89.2099901571799[/C][C]9.84282009142134e-06[/C][/ROW]
[ROW][C]43[/C][C]89.21[/C][C]89.2099998152442[/C][C]1.84755805321402e-07[/C][/ROW]
[ROW][C]44[/C][C]89.21[/C][C]89.209999996532[/C][C]3.46797435213375e-09[/C][/ROW]
[ROW][C]45[/C][C]89.21[/C][C]89.209999999935[/C][C]6.50999254503404e-11[/C][/ROW]
[ROW][C]46[/C][C]89.21[/C][C]89.2099999999988[/C][C]1.22213350550737e-12[/C][/ROW]
[ROW][C]47[/C][C]89.21[/C][C]89.21[/C][C]2.8421709430404e-14[/C][/ROW]
[ROW][C]48[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]51[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]52[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]53[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]54[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]55[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]56[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]57[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]58[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]59[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]60[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]61[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]63[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]64[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]65[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]66[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]67[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]68[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]69[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]70[/C][C]89.21[/C][C]89.21[/C][C]0[/C][/ROW]
[ROW][C]71[/C][C]92.07[/C][C]89.21[/C][C]2.86[/C][/ROW]
[ROW][C]72[/C][C]92.07[/C][C]92.0163160376294[/C][C]0.0536839623705845[/C][/ROW]
[ROW][C]73[/C][C]92.07[/C][C]92.0689923189455[/C][C]0.00100768105447457[/C][/ROW]
[ROW][C]74[/C][C]92.07[/C][C]92.0699810852057[/C][C]1.89147943387979e-05[/C][/ROW]
[ROW][C]75[/C][C]92.07[/C][C]92.0699996449576[/C][C]3.5504234574546e-07[/C][/ROW]
[ROW][C]76[/C][C]92.07[/C][C]92.0699999933356[/C][C]6.66435084895056e-09[/C][/ROW]
[ROW][C]77[/C][C]92.07[/C][C]92.0699999998749[/C][C]1.25083943203208e-10[/C][/ROW]
[ROW][C]78[/C][C]92.07[/C][C]92.0699999999976[/C][C]2.34479102800833e-12[/C][/ROW]
[ROW][C]79[/C][C]92.07[/C][C]92.07[/C][C]4.2632564145606e-14[/C][/ROW]
[ROW][C]80[/C][C]92.07[/C][C]92.07[/C][C]0[/C][/ROW]
[ROW][C]81[/C][C]94[/C][C]92.07[/C][C]1.93000000000001[/C][/ROW]
[ROW][C]82[/C][C]94[/C][C]93.963772710708[/C][C]0.036227289292043[/C][/ROW]
[ROW][C]83[/C][C]94[/C][C]93.9993199914562[/C][C]0.000680008543753274[/C][/ROW]
[ROW][C]84[/C][C]94[/C][C]93.9999872358206[/C][C]1.27641793881139e-05[/C][/ROW]
[ROW][C]85[/C][C]94[/C][C]93.9999997604085[/C][C]2.39591500417191e-07[/C][/ROW]
[ROW][C]86[/C][C]94[/C][C]93.9999999955027[/C][C]4.49728077001055e-09[/C][/ROW]
[ROW][C]87[/C][C]94[/C][C]93.9999999999156[/C][C]8.44124770082999e-11[/C][/ROW]
[ROW][C]88[/C][C]94[/C][C]93.9999999999984[/C][C]1.57740487338742e-12[/C][/ROW]
[ROW][C]89[/C][C]94[/C][C]94[/C][C]2.8421709430404e-14[/C][/ROW]
[ROW][C]90[/C][C]94[/C][C]94[/C][C]0[/C][/ROW]
[ROW][C]91[/C][C]94[/C][C]94[/C][C]0[/C][/ROW]
[ROW][C]92[/C][C]94[/C][C]94[/C][C]0[/C][/ROW]
[ROW][C]93[/C][C]94[/C][C]94[/C][C]0[/C][/ROW]
[ROW][C]94[/C][C]94[/C][C]94[/C][C]0[/C][/ROW]
[ROW][C]95[/C][C]94[/C][C]94[/C][C]0[/C][/ROW]
[ROW][C]96[/C][C]94[/C][C]94[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13389&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13389&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	105.18	105.18	0
3	105.18	105.18	0
4	105.18	105.18	0
5	105.18	105.18	0
6	105.18	105.18	0
7	105.18	105.18	0
8	105.18	105.18	0
9	105.18	105.18	0
10	105.18	105.18	0
11	97.82	105.18	-7.36000000000001
12	97.83	97.9581517353313	-0.128151735331301
13	97.82	97.832405487041	-0.0124054870409935
14	97.83	97.8202328586362	0.00976714136382384
15	97.82	97.829816664738	-0.00981666473795428
16	97.82	97.8201842648463	-0.000184264846296855
17	97.8	97.8200034587647	-0.0200034587647053
18	97.8	97.8003754772474	-0.000375477247416711
19	97.44	97.8000070479393	-0.360007047939305
20	97.44	97.446757554131	-0.00675755413101342
21	97.44	97.4401268434551	-0.000126843455134917
22	97.44	97.4400023809298	-2.38092981419413e-06
23	97.7	97.4400000446915	0.259999955308487
24	97.7	97.6951196406234	0.00488035937662801
25	97.7	97.6999083926472	9.16073528429706e-05
26	97.7	97.6999982804735	1.71952646610407e-06
27	97.7	97.6999999677234	3.22765743021591e-08
28	97.7	97.6999999993942	6.05851369073207e-10
29	97.7	97.6999999999886	1.13686837721616e-11
30	97.7	97.6999999999998	2.1316282072803e-13
31	97.7	97.7	1.4210854715202e-14
32	97.7	97.7	0
33	97.7	97.7	0
34	89.38	97.7	-8.32
35	89.38	89.5361715268963	-0.156171526896273
36	89.38	89.3829314357948	-0.00293143579484934
37	89.38	89.3800550248563	-5.50248562660727e-05
38	87.69	89.3800010328505	-1.69000103285046
39	89.21	87.721722360788	1.48827763921196
40	89.21	89.1820641116152	0.0279358883847749
41	89.21	89.2094756261605	0.000524373839454029
42	89.21	89.2099901571799	9.84282009142134e-06
43	89.21	89.2099998152442	1.84755805321402e-07
44	89.21	89.209999996532	3.46797435213375e-09
45	89.21	89.209999999935	6.50999254503404e-11
46	89.21	89.2099999999988	1.22213350550737e-12
47	89.21	89.21	2.8421709430404e-14
48	89.21	89.21	0
49	89.21	89.21	0
50	89.21	89.21	0
51	89.21	89.21	0
52	89.21	89.21	0
53	89.21	89.21	0
54	89.21	89.21	0
55	89.21	89.21	0
56	89.21	89.21	0
57	89.21	89.21	0
58	89.21	89.21	0
59	89.21	89.21	0
60	89.21	89.21	0
61	89.21	89.21	0
62	89.21	89.21	0
63	89.21	89.21	0
64	89.21	89.21	0
65	89.21	89.21	0
66	89.21	89.21	0
67	89.21	89.21	0
68	89.21	89.21	0
69	89.21	89.21	0
70	89.21	89.21	0
71	92.07	89.21	2.86
72	92.07	92.0163160376294	0.0536839623705845
73	92.07	92.0689923189455	0.00100768105447457
74	92.07	92.0699810852057	1.89147943387979e-05
75	92.07	92.0699996449576	3.5504234574546e-07
76	92.07	92.0699999933356	6.66435084895056e-09
77	92.07	92.0699999998749	1.25083943203208e-10
78	92.07	92.0699999999976	2.34479102800833e-12
79	92.07	92.07	4.2632564145606e-14
80	92.07	92.07	0
81	94	92.07	1.93000000000001
82	94	93.963772710708	0.036227289292043
83	94	93.9993199914562	0.000680008543753274
84	94	93.9999872358206	1.27641793881139e-05
85	94	93.9999997604085	2.39591500417191e-07
86	94	93.9999999955027	4.49728077001055e-09
87	94	93.9999999999156	8.44124770082999e-11
88	94	93.9999999999984	1.57740487338742e-12
89	94	94	2.8421709430404e-14
90	94	94	0
91	94	94	0
92	94	94	0
93	94	94	0
94	94	94	0
95	94	94	0
96	94	94	0

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	94	91.6145311220365	96.3854688779635
98	94	90.657949500329	97.342050499671
99	94	89.919786608893	98.080213391107
100	94	89.2960674864973	98.7039325135027
101	94	88.7458758231075	99.2541241768925
102	94	88.2480733105485	99.7519266894515
103	94	87.7900482759169	100.209951724083
104	94	87.3635596747909	100.636440325209
105	94	86.962871326693	101.037128673307
106	94	86.5838001820812	101.416199817919
107	94	86.2231844875993	101.776815512401
108	94	85.878565441467	102.121434558533

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 94 & 91.6145311220365 & 96.3854688779635 \tabularnewline
98 & 94 & 90.657949500329 & 97.342050499671 \tabularnewline
99 & 94 & 89.919786608893 & 98.080213391107 \tabularnewline
100 & 94 & 89.2960674864973 & 98.7039325135027 \tabularnewline
101 & 94 & 88.7458758231075 & 99.2541241768925 \tabularnewline
102 & 94 & 88.2480733105485 & 99.7519266894515 \tabularnewline
103 & 94 & 87.7900482759169 & 100.209951724083 \tabularnewline
104 & 94 & 87.3635596747909 & 100.636440325209 \tabularnewline
105 & 94 & 86.962871326693 & 101.037128673307 \tabularnewline
106 & 94 & 86.5838001820812 & 101.416199817919 \tabularnewline
107 & 94 & 86.2231844875993 & 101.776815512401 \tabularnewline
108 & 94 & 85.878565441467 & 102.121434558533 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13389&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]97[/C][C]94[/C][C]91.6145311220365[/C][C]96.3854688779635[/C][/ROW]
[ROW][C]98[/C][C]94[/C][C]90.657949500329[/C][C]97.342050499671[/C][/ROW]
[ROW][C]99[/C][C]94[/C][C]89.919786608893[/C][C]98.080213391107[/C][/ROW]
[ROW][C]100[/C][C]94[/C][C]89.2960674864973[/C][C]98.7039325135027[/C][/ROW]
[ROW][C]101[/C][C]94[/C][C]88.7458758231075[/C][C]99.2541241768925[/C][/ROW]
[ROW][C]102[/C][C]94[/C][C]88.2480733105485[/C][C]99.7519266894515[/C][/ROW]
[ROW][C]103[/C][C]94[/C][C]87.7900482759169[/C][C]100.209951724083[/C][/ROW]
[ROW][C]104[/C][C]94[/C][C]87.3635596747909[/C][C]100.636440325209[/C][/ROW]
[ROW][C]105[/C][C]94[/C][C]86.962871326693[/C][C]101.037128673307[/C][/ROW]
[ROW][C]106[/C][C]94[/C][C]86.5838001820812[/C][C]101.416199817919[/C][/ROW]
[ROW][C]107[/C][C]94[/C][C]86.2231844875993[/C][C]101.776815512401[/C][/ROW]
[ROW][C]108[/C][C]94[/C][C]85.878565441467[/C][C]102.121434558533[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13389&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13389&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
97	94	91.6145311220365	96.3854688779635
98	94	90.657949500329	97.342050499671
99	94	89.919786608893	98.080213391107
100	94	89.2960674864973	98.7039325135027
101	94	88.7458758231075	99.2541241768925
102	94	88.2480733105485	99.7519266894515
103	94	87.7900482759169	100.209951724083
104	94	87.3635596747909	100.636440325209
105	94	86.962871326693	101.037128673307
106	94	86.5838001820812	101.416199817919
107	94	86.2231844875993	101.776815512401
108	94	85.878565441467	102.121434558533

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=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

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code