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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 21 May 2014 03:36:51 -0400

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/2014/May/21/t1400657827bm524smksrqll81.htm/, Retrieved Tue, 14 May 2024 17:57:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235003, Retrieved Tue, 14 May 2024 17:57:19 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

112

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

-     [Standard Deviation Plot] [] [2014-04-28 15:57:15] [ccb4fa85fbb66dbee3adf4746bc114a3]
- RMPD  [Exponential Smoothing] [] [2014-05-20 14:06:52] [ccb4fa85fbb66dbee3adf4746bc114a3]
- R PD      [Exponential Smoothing] [] [2014-05-21 07:36:51] [c97636ecf0aef6cf672ffb6fe15d6b60] [Current]

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Dataseries X:

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Histogram

Boxplots

2.79
3.08
3.89
3.7
4.61
5.07
5.22
4.93
5.15
4.8
3.89
3.54
3.34
2.8
1.6
1.53
0.69
-0.11
-0.67
-0.2
-0.62
-0.58
-0.31
-0.25
-0.08
0.13
0.94
1.05
1.59
2.03
2.15
2.06
2.56
2.55
2.53
2.6
2.71
2.82
2.93
2.88
2.89
3.27
3.32
3.14
3.04
3.08
3.39
3.23
3.38
3.41
3.14
2.96
2.73
2.21
2.23
2.56
2.39
2.49
2.17
2.16
1.48
1.09
1.25
1.26
1.39
1.69
1.55
1.19
1.08
0.93
0.98
1.01

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235003&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235003&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235003&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.729174398512058
beta	0.169192651028085
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.729174398512058 \tabularnewline
beta & 0.169192651028085 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235003&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]0.729174398512058[/C][/ROW]
[ROW][C]beta[/C][C]0.169192651028085[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235003&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235003&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	0.729174398512058
beta	0.169192651028085
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	3.34	4.98116185897436	-1.64116185897436
14	2.8	3.15212661270001	-0.35212661270001
15	1.6	1.55458067221936	0.0454193277806367
16	1.53	1.39293514603231	0.13706485396769
17	0.69	0.479608345795743	0.210391654204257
18	-0.11	-0.380544210827765	0.270544210827765
19	-0.67	1.14779223302765	-1.81779223302765
20	-0.2	-1.21631221398877	1.01631221398877
21	-0.62	-0.760143519323249	0.140143519323249
22	-0.58	-1.41681496653392	0.836814966533921
23	-0.31	-1.95433610658191	1.64433610658191
24	-0.25	-1.01475353154108	0.764753531541079
25	-0.08	-0.834576996504871	0.754576996504871
26	0.13	-0.11723898954433	0.24723898954433
27	0.94	-0.645774887208301	1.5857748872083
28	1.05	1.05492487976504	-0.00492487976503675
29	1.59	0.754741667208607	0.835258332791393
30	2.03	1.14042723449002	0.889572765509977
31	2.15	3.40484910650589	-1.25484910650589
32	2.06	3.13850787242436	-1.07850787242436
33	2.56	2.49118998937597	0.0688100106240279
34	2.55	2.62367146741848	-0.0736714674184791
35	2.53	2.18110778192445	0.34889221807555
36	2.6	2.31821567012198	0.281784329878023
37	2.71	2.46422630411095	0.245773695889054
38	2.82	2.93114524545958	-0.111145245459585
39	2.93	2.71756772099207	0.212432279007928
40	2.88	3.03040160747049	-0.150401607470485
41	2.89	2.87807862232657	0.0119213776734299
42	3.27	2.60293684648229	0.667063153517715
43	3.32	4.02171398754804	-0.701713987548038
44	3.14	4.17207117163895	-1.03207117163895
45	3.04	3.84067446732198	-0.800674467321978
46	3.08	3.164631036084	-0.0846310360839979
47	3.39	2.69123342953146	0.698766570468544
48	3.23	2.97116698662103	0.258833013378966
49	3.38	2.99373876350367	0.386261236496328
50	3.41	3.38681617399094	0.0231838260090629
51	3.14	3.29577469039594	-0.155774690395944
52	2.96	3.13338437573058	-0.173384375730575
53	2.73	2.8969563583529	-0.1669563583529
54	2.21	2.53543456019262	-0.325434560192619
55	2.23	2.60398637769952	-0.373986377699521
56	2.56	2.68845552030226	-0.12845552030226
57	2.39	2.97471084640589	-0.584710846405891
58	2.49	2.57279956822834	-0.0827995682283431
59	2.17	2.23586161579701	-0.0658616157970067
60	2.16	1.66772976612861	0.492270233871387
61	1.48	1.75245534583907	-0.272455345839074
62	1.09	1.34304287309829	-0.253042873098285
63	1.25	0.744199096891276	0.505800903108724
64	1.26	0.883144515643669	0.376855484356331
65	1.39	0.941262704548424	0.448737295451576
66	1.69	0.953312228025605	0.736687771974395
67	1.55	1.88176565000336	-0.331765650003361
68	1.19	2.16730418667994	-0.977304186679941
69	1.08	1.71009898614663	-0.630098986146633
70	0.93	1.40448649660298	-0.474486496602983
71	0.98	0.731669140968781	0.248330859031219
72	1.01	0.527698464050638	0.482301535949362

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3.34 & 4.98116185897436 & -1.64116185897436 \tabularnewline
14 & 2.8 & 3.15212661270001 & -0.35212661270001 \tabularnewline
15 & 1.6 & 1.55458067221936 & 0.0454193277806367 \tabularnewline
16 & 1.53 & 1.39293514603231 & 0.13706485396769 \tabularnewline
17 & 0.69 & 0.479608345795743 & 0.210391654204257 \tabularnewline
18 & -0.11 & -0.380544210827765 & 0.270544210827765 \tabularnewline
19 & -0.67 & 1.14779223302765 & -1.81779223302765 \tabularnewline
20 & -0.2 & -1.21631221398877 & 1.01631221398877 \tabularnewline
21 & -0.62 & -0.760143519323249 & 0.140143519323249 \tabularnewline
22 & -0.58 & -1.41681496653392 & 0.836814966533921 \tabularnewline
23 & -0.31 & -1.95433610658191 & 1.64433610658191 \tabularnewline
24 & -0.25 & -1.01475353154108 & 0.764753531541079 \tabularnewline
25 & -0.08 & -0.834576996504871 & 0.754576996504871 \tabularnewline
26 & 0.13 & -0.11723898954433 & 0.24723898954433 \tabularnewline
27 & 0.94 & -0.645774887208301 & 1.5857748872083 \tabularnewline
28 & 1.05 & 1.05492487976504 & -0.00492487976503675 \tabularnewline
29 & 1.59 & 0.754741667208607 & 0.835258332791393 \tabularnewline
30 & 2.03 & 1.14042723449002 & 0.889572765509977 \tabularnewline
31 & 2.15 & 3.40484910650589 & -1.25484910650589 \tabularnewline
32 & 2.06 & 3.13850787242436 & -1.07850787242436 \tabularnewline
33 & 2.56 & 2.49118998937597 & 0.0688100106240279 \tabularnewline
34 & 2.55 & 2.62367146741848 & -0.0736714674184791 \tabularnewline
35 & 2.53 & 2.18110778192445 & 0.34889221807555 \tabularnewline
36 & 2.6 & 2.31821567012198 & 0.281784329878023 \tabularnewline
37 & 2.71 & 2.46422630411095 & 0.245773695889054 \tabularnewline
38 & 2.82 & 2.93114524545958 & -0.111145245459585 \tabularnewline
39 & 2.93 & 2.71756772099207 & 0.212432279007928 \tabularnewline
40 & 2.88 & 3.03040160747049 & -0.150401607470485 \tabularnewline
41 & 2.89 & 2.87807862232657 & 0.0119213776734299 \tabularnewline
42 & 3.27 & 2.60293684648229 & 0.667063153517715 \tabularnewline
43 & 3.32 & 4.02171398754804 & -0.701713987548038 \tabularnewline
44 & 3.14 & 4.17207117163895 & -1.03207117163895 \tabularnewline
45 & 3.04 & 3.84067446732198 & -0.800674467321978 \tabularnewline
46 & 3.08 & 3.164631036084 & -0.0846310360839979 \tabularnewline
47 & 3.39 & 2.69123342953146 & 0.698766570468544 \tabularnewline
48 & 3.23 & 2.97116698662103 & 0.258833013378966 \tabularnewline
49 & 3.38 & 2.99373876350367 & 0.386261236496328 \tabularnewline
50 & 3.41 & 3.38681617399094 & 0.0231838260090629 \tabularnewline
51 & 3.14 & 3.29577469039594 & -0.155774690395944 \tabularnewline
52 & 2.96 & 3.13338437573058 & -0.173384375730575 \tabularnewline
53 & 2.73 & 2.8969563583529 & -0.1669563583529 \tabularnewline
54 & 2.21 & 2.53543456019262 & -0.325434560192619 \tabularnewline
55 & 2.23 & 2.60398637769952 & -0.373986377699521 \tabularnewline
56 & 2.56 & 2.68845552030226 & -0.12845552030226 \tabularnewline
57 & 2.39 & 2.97471084640589 & -0.584710846405891 \tabularnewline
58 & 2.49 & 2.57279956822834 & -0.0827995682283431 \tabularnewline
59 & 2.17 & 2.23586161579701 & -0.0658616157970067 \tabularnewline
60 & 2.16 & 1.66772976612861 & 0.492270233871387 \tabularnewline
61 & 1.48 & 1.75245534583907 & -0.272455345839074 \tabularnewline
62 & 1.09 & 1.34304287309829 & -0.253042873098285 \tabularnewline
63 & 1.25 & 0.744199096891276 & 0.505800903108724 \tabularnewline
64 & 1.26 & 0.883144515643669 & 0.376855484356331 \tabularnewline
65 & 1.39 & 0.941262704548424 & 0.448737295451576 \tabularnewline
66 & 1.69 & 0.953312228025605 & 0.736687771974395 \tabularnewline
67 & 1.55 & 1.88176565000336 & -0.331765650003361 \tabularnewline
68 & 1.19 & 2.16730418667994 & -0.977304186679941 \tabularnewline
69 & 1.08 & 1.71009898614663 & -0.630098986146633 \tabularnewline
70 & 0.93 & 1.40448649660298 & -0.474486496602983 \tabularnewline
71 & 0.98 & 0.731669140968781 & 0.248330859031219 \tabularnewline
72 & 1.01 & 0.527698464050638 & 0.482301535949362 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235003&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]13[/C][C]3.34[/C][C]4.98116185897436[/C][C]-1.64116185897436[/C][/ROW]
[ROW][C]14[/C][C]2.8[/C][C]3.15212661270001[/C][C]-0.35212661270001[/C][/ROW]
[ROW][C]15[/C][C]1.6[/C][C]1.55458067221936[/C][C]0.0454193277806367[/C][/ROW]
[ROW][C]16[/C][C]1.53[/C][C]1.39293514603231[/C][C]0.13706485396769[/C][/ROW]
[ROW][C]17[/C][C]0.69[/C][C]0.479608345795743[/C][C]0.210391654204257[/C][/ROW]
[ROW][C]18[/C][C]-0.11[/C][C]-0.380544210827765[/C][C]0.270544210827765[/C][/ROW]
[ROW][C]19[/C][C]-0.67[/C][C]1.14779223302765[/C][C]-1.81779223302765[/C][/ROW]
[ROW][C]20[/C][C]-0.2[/C][C]-1.21631221398877[/C][C]1.01631221398877[/C][/ROW]
[ROW][C]21[/C][C]-0.62[/C][C]-0.760143519323249[/C][C]0.140143519323249[/C][/ROW]
[ROW][C]22[/C][C]-0.58[/C][C]-1.41681496653392[/C][C]0.836814966533921[/C][/ROW]
[ROW][C]23[/C][C]-0.31[/C][C]-1.95433610658191[/C][C]1.64433610658191[/C][/ROW]
[ROW][C]24[/C][C]-0.25[/C][C]-1.01475353154108[/C][C]0.764753531541079[/C][/ROW]
[ROW][C]25[/C][C]-0.08[/C][C]-0.834576996504871[/C][C]0.754576996504871[/C][/ROW]
[ROW][C]26[/C][C]0.13[/C][C]-0.11723898954433[/C][C]0.24723898954433[/C][/ROW]
[ROW][C]27[/C][C]0.94[/C][C]-0.645774887208301[/C][C]1.5857748872083[/C][/ROW]
[ROW][C]28[/C][C]1.05[/C][C]1.05492487976504[/C][C]-0.00492487976503675[/C][/ROW]
[ROW][C]29[/C][C]1.59[/C][C]0.754741667208607[/C][C]0.835258332791393[/C][/ROW]
[ROW][C]30[/C][C]2.03[/C][C]1.14042723449002[/C][C]0.889572765509977[/C][/ROW]
[ROW][C]31[/C][C]2.15[/C][C]3.40484910650589[/C][C]-1.25484910650589[/C][/ROW]
[ROW][C]32[/C][C]2.06[/C][C]3.13850787242436[/C][C]-1.07850787242436[/C][/ROW]
[ROW][C]33[/C][C]2.56[/C][C]2.49118998937597[/C][C]0.0688100106240279[/C][/ROW]
[ROW][C]34[/C][C]2.55[/C][C]2.62367146741848[/C][C]-0.0736714674184791[/C][/ROW]
[ROW][C]35[/C][C]2.53[/C][C]2.18110778192445[/C][C]0.34889221807555[/C][/ROW]
[ROW][C]36[/C][C]2.6[/C][C]2.31821567012198[/C][C]0.281784329878023[/C][/ROW]
[ROW][C]37[/C][C]2.71[/C][C]2.46422630411095[/C][C]0.245773695889054[/C][/ROW]
[ROW][C]38[/C][C]2.82[/C][C]2.93114524545958[/C][C]-0.111145245459585[/C][/ROW]
[ROW][C]39[/C][C]2.93[/C][C]2.71756772099207[/C][C]0.212432279007928[/C][/ROW]
[ROW][C]40[/C][C]2.88[/C][C]3.03040160747049[/C][C]-0.150401607470485[/C][/ROW]
[ROW][C]41[/C][C]2.89[/C][C]2.87807862232657[/C][C]0.0119213776734299[/C][/ROW]
[ROW][C]42[/C][C]3.27[/C][C]2.60293684648229[/C][C]0.667063153517715[/C][/ROW]
[ROW][C]43[/C][C]3.32[/C][C]4.02171398754804[/C][C]-0.701713987548038[/C][/ROW]
[ROW][C]44[/C][C]3.14[/C][C]4.17207117163895[/C][C]-1.03207117163895[/C][/ROW]
[ROW][C]45[/C][C]3.04[/C][C]3.84067446732198[/C][C]-0.800674467321978[/C][/ROW]
[ROW][C]46[/C][C]3.08[/C][C]3.164631036084[/C][C]-0.0846310360839979[/C][/ROW]
[ROW][C]47[/C][C]3.39[/C][C]2.69123342953146[/C][C]0.698766570468544[/C][/ROW]
[ROW][C]48[/C][C]3.23[/C][C]2.97116698662103[/C][C]0.258833013378966[/C][/ROW]
[ROW][C]49[/C][C]3.38[/C][C]2.99373876350367[/C][C]0.386261236496328[/C][/ROW]
[ROW][C]50[/C][C]3.41[/C][C]3.38681617399094[/C][C]0.0231838260090629[/C][/ROW]
[ROW][C]51[/C][C]3.14[/C][C]3.29577469039594[/C][C]-0.155774690395944[/C][/ROW]
[ROW][C]52[/C][C]2.96[/C][C]3.13338437573058[/C][C]-0.173384375730575[/C][/ROW]
[ROW][C]53[/C][C]2.73[/C][C]2.8969563583529[/C][C]-0.1669563583529[/C][/ROW]
[ROW][C]54[/C][C]2.21[/C][C]2.53543456019262[/C][C]-0.325434560192619[/C][/ROW]
[ROW][C]55[/C][C]2.23[/C][C]2.60398637769952[/C][C]-0.373986377699521[/C][/ROW]
[ROW][C]56[/C][C]2.56[/C][C]2.68845552030226[/C][C]-0.12845552030226[/C][/ROW]
[ROW][C]57[/C][C]2.39[/C][C]2.97471084640589[/C][C]-0.584710846405891[/C][/ROW]
[ROW][C]58[/C][C]2.49[/C][C]2.57279956822834[/C][C]-0.0827995682283431[/C][/ROW]
[ROW][C]59[/C][C]2.17[/C][C]2.23586161579701[/C][C]-0.0658616157970067[/C][/ROW]
[ROW][C]60[/C][C]2.16[/C][C]1.66772976612861[/C][C]0.492270233871387[/C][/ROW]
[ROW][C]61[/C][C]1.48[/C][C]1.75245534583907[/C][C]-0.272455345839074[/C][/ROW]
[ROW][C]62[/C][C]1.09[/C][C]1.34304287309829[/C][C]-0.253042873098285[/C][/ROW]
[ROW][C]63[/C][C]1.25[/C][C]0.744199096891276[/C][C]0.505800903108724[/C][/ROW]
[ROW][C]64[/C][C]1.26[/C][C]0.883144515643669[/C][C]0.376855484356331[/C][/ROW]
[ROW][C]65[/C][C]1.39[/C][C]0.941262704548424[/C][C]0.448737295451576[/C][/ROW]
[ROW][C]66[/C][C]1.69[/C][C]0.953312228025605[/C][C]0.736687771974395[/C][/ROW]
[ROW][C]67[/C][C]1.55[/C][C]1.88176565000336[/C][C]-0.331765650003361[/C][/ROW]
[ROW][C]68[/C][C]1.19[/C][C]2.16730418667994[/C][C]-0.977304186679941[/C][/ROW]
[ROW][C]69[/C][C]1.08[/C][C]1.71009898614663[/C][C]-0.630098986146633[/C][/ROW]
[ROW][C]70[/C][C]0.93[/C][C]1.40448649660298[/C][C]-0.474486496602983[/C][/ROW]
[ROW][C]71[/C][C]0.98[/C][C]0.731669140968781[/C][C]0.248330859031219[/C][/ROW]
[ROW][C]72[/C][C]1.01[/C][C]0.527698464050638[/C][C]0.482301535949362[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235003&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235003&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
13	3.34	4.98116185897436	-1.64116185897436
14	2.8	3.15212661270001	-0.35212661270001
15	1.6	1.55458067221936	0.0454193277806367
16	1.53	1.39293514603231	0.13706485396769
17	0.69	0.479608345795743	0.210391654204257
18	-0.11	-0.380544210827765	0.270544210827765
19	-0.67	1.14779223302765	-1.81779223302765
20	-0.2	-1.21631221398877	1.01631221398877
21	-0.62	-0.760143519323249	0.140143519323249
22	-0.58	-1.41681496653392	0.836814966533921
23	-0.31	-1.95433610658191	1.64433610658191
24	-0.25	-1.01475353154108	0.764753531541079
25	-0.08	-0.834576996504871	0.754576996504871
26	0.13	-0.11723898954433	0.24723898954433
27	0.94	-0.645774887208301	1.5857748872083
28	1.05	1.05492487976504	-0.00492487976503675
29	1.59	0.754741667208607	0.835258332791393
30	2.03	1.14042723449002	0.889572765509977
31	2.15	3.40484910650589	-1.25484910650589
32	2.06	3.13850787242436	-1.07850787242436
33	2.56	2.49118998937597	0.0688100106240279
34	2.55	2.62367146741848	-0.0736714674184791
35	2.53	2.18110778192445	0.34889221807555
36	2.6	2.31821567012198	0.281784329878023
37	2.71	2.46422630411095	0.245773695889054
38	2.82	2.93114524545958	-0.111145245459585
39	2.93	2.71756772099207	0.212432279007928
40	2.88	3.03040160747049	-0.150401607470485
41	2.89	2.87807862232657	0.0119213776734299
42	3.27	2.60293684648229	0.667063153517715
43	3.32	4.02171398754804	-0.701713987548038
44	3.14	4.17207117163895	-1.03207117163895
45	3.04	3.84067446732198	-0.800674467321978
46	3.08	3.164631036084	-0.0846310360839979
47	3.39	2.69123342953146	0.698766570468544
48	3.23	2.97116698662103	0.258833013378966
49	3.38	2.99373876350367	0.386261236496328
50	3.41	3.38681617399094	0.0231838260090629
51	3.14	3.29577469039594	-0.155774690395944
52	2.96	3.13338437573058	-0.173384375730575
53	2.73	2.8969563583529	-0.1669563583529
54	2.21	2.53543456019262	-0.325434560192619
55	2.23	2.60398637769952	-0.373986377699521
56	2.56	2.68845552030226	-0.12845552030226
57	2.39	2.97471084640589	-0.584710846405891
58	2.49	2.57279956822834	-0.0827995682283431
59	2.17	2.23586161579701	-0.0658616157970067
60	2.16	1.66772976612861	0.492270233871387
61	1.48	1.75245534583907	-0.272455345839074
62	1.09	1.34304287309829	-0.253042873098285
63	1.25	0.744199096891276	0.505800903108724
64	1.26	0.883144515643669	0.376855484356331
65	1.39	0.941262704548424	0.448737295451576
66	1.69	0.953312228025605	0.736687771974395
67	1.55	1.88176565000336	-0.331765650003361
68	1.19	2.16730418667994	-0.977304186679941
69	1.08	1.71009898614663	-0.630098986146633
70	0.93	1.40448649660298	-0.474486496602983
71	0.98	0.731669140968781	0.248330859031219
72	1.01	0.527698464050638	0.482301535949362

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.380721681627523	-0.933583538948421	1.69502690220347
74	0.191520963417761	-1.53559490517194	1.91863683200746
75	0.0302089306576345	-2.12109883000337	2.18151669131864
76	-0.249480541640611	-2.84092205912812	2.3419609758469
77	-0.508077409254871	-3.55731415786172	2.54115933935197
78	-0.862001538625511	-4.38727248787987	2.66326941062885
79	-0.967722656634828	-4.98732761750496	3.05188230423531
80	-0.781803357178963	-5.3138552577563	3.75024854339838
81	-0.478486255476182	-5.54079104509211	4.58381853413975
82	-0.250901887008434	-5.86090308619404	5.35909931217717
83	-0.291839579436637	-6.46659696724552	5.88291780837224
84	-0.554019513356357	-7.31020624600108	6.20216721928837

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.380721681627523 & -0.933583538948421 & 1.69502690220347 \tabularnewline
74 & 0.191520963417761 & -1.53559490517194 & 1.91863683200746 \tabularnewline
75 & 0.0302089306576345 & -2.12109883000337 & 2.18151669131864 \tabularnewline
76 & -0.249480541640611 & -2.84092205912812 & 2.3419609758469 \tabularnewline
77 & -0.508077409254871 & -3.55731415786172 & 2.54115933935197 \tabularnewline
78 & -0.862001538625511 & -4.38727248787987 & 2.66326941062885 \tabularnewline
79 & -0.967722656634828 & -4.98732761750496 & 3.05188230423531 \tabularnewline
80 & -0.781803357178963 & -5.3138552577563 & 3.75024854339838 \tabularnewline
81 & -0.478486255476182 & -5.54079104509211 & 4.58381853413975 \tabularnewline
82 & -0.250901887008434 & -5.86090308619404 & 5.35909931217717 \tabularnewline
83 & -0.291839579436637 & -6.46659696724552 & 5.88291780837224 \tabularnewline
84 & -0.554019513356357 & -7.31020624600108 & 6.20216721928837 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235003&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]0.380721681627523[/C][C]-0.933583538948421[/C][C]1.69502690220347[/C][/ROW]
[ROW][C]74[/C][C]0.191520963417761[/C][C]-1.53559490517194[/C][C]1.91863683200746[/C][/ROW]
[ROW][C]75[/C][C]0.0302089306576345[/C][C]-2.12109883000337[/C][C]2.18151669131864[/C][/ROW]
[ROW][C]76[/C][C]-0.249480541640611[/C][C]-2.84092205912812[/C][C]2.3419609758469[/C][/ROW]
[ROW][C]77[/C][C]-0.508077409254871[/C][C]-3.55731415786172[/C][C]2.54115933935197[/C][/ROW]
[ROW][C]78[/C][C]-0.862001538625511[/C][C]-4.38727248787987[/C][C]2.66326941062885[/C][/ROW]
[ROW][C]79[/C][C]-0.967722656634828[/C][C]-4.98732761750496[/C][C]3.05188230423531[/C][/ROW]
[ROW][C]80[/C][C]-0.781803357178963[/C][C]-5.3138552577563[/C][C]3.75024854339838[/C][/ROW]
[ROW][C]81[/C][C]-0.478486255476182[/C][C]-5.54079104509211[/C][C]4.58381853413975[/C][/ROW]
[ROW][C]82[/C][C]-0.250901887008434[/C][C]-5.86090308619404[/C][C]5.35909931217717[/C][/ROW]
[ROW][C]83[/C][C]-0.291839579436637[/C][C]-6.46659696724552[/C][C]5.88291780837224[/C][/ROW]
[ROW][C]84[/C][C]-0.554019513356357[/C][C]-7.31020624600108[/C][C]6.20216721928837[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235003&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235003&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	0.380721681627523	-0.933583538948421	1.69502690220347
74	0.191520963417761	-1.53559490517194	1.91863683200746
75	0.0302089306576345	-2.12109883000337	2.18151669131864
76	-0.249480541640611	-2.84092205912812	2.3419609758469
77	-0.508077409254871	-3.55731415786172	2.54115933935197
78	-0.862001538625511	-4.38727248787987	2.66326941062885
79	-0.967722656634828	-4.98732761750496	3.05188230423531
80	-0.781803357178963	-5.3138552577563	3.75024854339838
81	-0.478486255476182	-5.54079104509211	4.58381853413975
82	-0.250901887008434	-5.86090308619404	5.35909931217717
83	-0.291839579436637	-6.46659696724552	5.88291780837224
84	-0.554019513356357	-7.31020624600108	6.20216721928837

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 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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