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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 27 May 2012 08:15:49 -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/2012/May/27/t1338120988jgjoiqeoz5uvwf4.htm/, Retrieved Thu, 09 May 2024 00:00:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167691, Retrieved Thu, 09 May 2024 00:00:28 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

143

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

-     [Standard Deviation Plot] [OPG8 OEF3(2)] [2012-04-29 13:29:26] [aedd9af56bfe2946a9f9da3d899aa64c]
- RMPD  [Classical Decomposition] [] [2012-05-07 11:13:11] [aedd9af56bfe2946a9f9da3d899aa64c]
- RMP       [Exponential Smoothing] [OPG10OEF2 double] [2012-05-27 12:15:49] [76c30f62b7052b57088120e90a652e05] [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	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167691&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167691&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167691&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.969392656236537
beta	0.0599857981385038
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.969392656236537 \tabularnewline
beta & 0.0599857981385038 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167691&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]0.969392656236537[/C][/ROW]
[ROW][C]beta[/C][C]0.0599857981385038[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167691&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167691&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	0.969392656236537
beta	0.0599857981385038
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	67.14	67.4	-0.260000000000005
4	67.22	67.2228389634081	-0.00283896340808099
5	67.17	67.2948028620263	-0.124802862026314
6	67.27	67.241278592506	0.0287214074939754
7	67.27	67.3382497662901	-0.0682497662900658
8	67.27	67.3372490866142	-0.0672490866141544
9	67.48	67.3333079380555	0.14669206194452
10	67.38	67.545289880695	-0.165289880694985
11	67.22	67.4452272470471	-0.225227247047144
12	67.2	67.2739648530112	-0.0739648530111623
13	67.2	67.2450340720862	-0.0450340720861675
14	67.19	67.2415298557956	-0.051529855795593
15	67.32	67.2287322240743	0.0912677759257008
16	67.61	67.3596687700757	0.250331229924313
17	67.85	67.6593569692587	0.190643030741299
18	67.74	67.9122697191105	-0.172269719110545
19	67.74	67.8033600660338	-0.0633600660338232
20	67.61	67.7963422561697	-0.186342256169667
21	67.85	67.6592706508667	0.190729349133264
22	67.89	67.8988203626372	-0.00882036263716657
23	67.97	67.9444151470088	0.0255848529912015
24	67.94	68.0248498486316	-0.0848498486315634
25	67.94	67.9932959604419	-0.053295960441929
26	68.07	67.9892310307146	0.0807689692854296
27	67.85	68.1198243581034	-0.269824358103435
28	67.84	67.8948648582434	-0.0548648582434055
29	67.89	67.8750951388304	0.0149048611696116
30	67.86	67.9238263876237	-0.0638263876237204
31	67.86	67.8925246508436	-0.0325246508436408
32	67.89	67.8896752861379	0.000324713862113413
33	67.7	67.9186887363835	-0.218688736383527
34	68.05	67.7226754517682	0.327324548231829
35	68.18	68.0749972899262	0.105002710073833
36	68.19	68.2179078566234	-0.0279078566234148
37	68.19	68.2303530599649	-0.0403530599648718
38	68.27	68.2283874525304	0.0416125474695832
39	68.22	68.3082984639949	-0.0882984639949029
40	68.14	68.2571401576491	-0.117140157649104
41	68.36	68.1712112494566	0.188788750543367
42	68.34	68.3928256048091	-0.0528256048090583
43	68.34	68.3771489804994	-0.037148980499353
44	68.24	68.3745089551738	-0.134508955173814
45	68.14	68.2696672175959	-0.129667217595866
46	68.23	68.1619789031118	0.0680210968881596
47	68.09	68.2498836015613	-0.159883601561262
48	68.03	68.107561960806	-0.0775619608060225
49	68.03	68.0405321021452	-0.0105321021452198
50	67.89	68.0378680566676	-0.147868056667647
51	67.63	67.8934730486715	-0.263473048671457
52	67.61	67.6216905073735	-0.0116905073735296
53	67.41	67.593304312004	-0.183304312003997
54	67.29	67.3878978470656	-0.0978978470655676
55	67.29	67.2595910425705	0.0304089574295148
56	67.49	67.2574321866535	0.23256781334652
57	67.68	67.4647684110727	0.21523158892731
58	68.05	67.6678146990228	0.382185300977241
59	67.7	68.0549286851969	-0.354928685196867
60	67.86	67.7068507570767	0.153149242923305

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 67.14 & 67.4 & -0.260000000000005 \tabularnewline
4 & 67.22 & 67.2228389634081 & -0.00283896340808099 \tabularnewline
5 & 67.17 & 67.2948028620263 & -0.124802862026314 \tabularnewline
6 & 67.27 & 67.241278592506 & 0.0287214074939754 \tabularnewline
7 & 67.27 & 67.3382497662901 & -0.0682497662900658 \tabularnewline
8 & 67.27 & 67.3372490866142 & -0.0672490866141544 \tabularnewline
9 & 67.48 & 67.3333079380555 & 0.14669206194452 \tabularnewline
10 & 67.38 & 67.545289880695 & -0.165289880694985 \tabularnewline
11 & 67.22 & 67.4452272470471 & -0.225227247047144 \tabularnewline
12 & 67.2 & 67.2739648530112 & -0.0739648530111623 \tabularnewline
13 & 67.2 & 67.2450340720862 & -0.0450340720861675 \tabularnewline
14 & 67.19 & 67.2415298557956 & -0.051529855795593 \tabularnewline
15 & 67.32 & 67.2287322240743 & 0.0912677759257008 \tabularnewline
16 & 67.61 & 67.3596687700757 & 0.250331229924313 \tabularnewline
17 & 67.85 & 67.6593569692587 & 0.190643030741299 \tabularnewline
18 & 67.74 & 67.9122697191105 & -0.172269719110545 \tabularnewline
19 & 67.74 & 67.8033600660338 & -0.0633600660338232 \tabularnewline
20 & 67.61 & 67.7963422561697 & -0.186342256169667 \tabularnewline
21 & 67.85 & 67.6592706508667 & 0.190729349133264 \tabularnewline
22 & 67.89 & 67.8988203626372 & -0.00882036263716657 \tabularnewline
23 & 67.97 & 67.9444151470088 & 0.0255848529912015 \tabularnewline
24 & 67.94 & 68.0248498486316 & -0.0848498486315634 \tabularnewline
25 & 67.94 & 67.9932959604419 & -0.053295960441929 \tabularnewline
26 & 68.07 & 67.9892310307146 & 0.0807689692854296 \tabularnewline
27 & 67.85 & 68.1198243581034 & -0.269824358103435 \tabularnewline
28 & 67.84 & 67.8948648582434 & -0.0548648582434055 \tabularnewline
29 & 67.89 & 67.8750951388304 & 0.0149048611696116 \tabularnewline
30 & 67.86 & 67.9238263876237 & -0.0638263876237204 \tabularnewline
31 & 67.86 & 67.8925246508436 & -0.0325246508436408 \tabularnewline
32 & 67.89 & 67.8896752861379 & 0.000324713862113413 \tabularnewline
33 & 67.7 & 67.9186887363835 & -0.218688736383527 \tabularnewline
34 & 68.05 & 67.7226754517682 & 0.327324548231829 \tabularnewline
35 & 68.18 & 68.0749972899262 & 0.105002710073833 \tabularnewline
36 & 68.19 & 68.2179078566234 & -0.0279078566234148 \tabularnewline
37 & 68.19 & 68.2303530599649 & -0.0403530599648718 \tabularnewline
38 & 68.27 & 68.2283874525304 & 0.0416125474695832 \tabularnewline
39 & 68.22 & 68.3082984639949 & -0.0882984639949029 \tabularnewline
40 & 68.14 & 68.2571401576491 & -0.117140157649104 \tabularnewline
41 & 68.36 & 68.1712112494566 & 0.188788750543367 \tabularnewline
42 & 68.34 & 68.3928256048091 & -0.0528256048090583 \tabularnewline
43 & 68.34 & 68.3771489804994 & -0.037148980499353 \tabularnewline
44 & 68.24 & 68.3745089551738 & -0.134508955173814 \tabularnewline
45 & 68.14 & 68.2696672175959 & -0.129667217595866 \tabularnewline
46 & 68.23 & 68.1619789031118 & 0.0680210968881596 \tabularnewline
47 & 68.09 & 68.2498836015613 & -0.159883601561262 \tabularnewline
48 & 68.03 & 68.107561960806 & -0.0775619608060225 \tabularnewline
49 & 68.03 & 68.0405321021452 & -0.0105321021452198 \tabularnewline
50 & 67.89 & 68.0378680566676 & -0.147868056667647 \tabularnewline
51 & 67.63 & 67.8934730486715 & -0.263473048671457 \tabularnewline
52 & 67.61 & 67.6216905073735 & -0.0116905073735296 \tabularnewline
53 & 67.41 & 67.593304312004 & -0.183304312003997 \tabularnewline
54 & 67.29 & 67.3878978470656 & -0.0978978470655676 \tabularnewline
55 & 67.29 & 67.2595910425705 & 0.0304089574295148 \tabularnewline
56 & 67.49 & 67.2574321866535 & 0.23256781334652 \tabularnewline
57 & 67.68 & 67.4647684110727 & 0.21523158892731 \tabularnewline
58 & 68.05 & 67.6678146990228 & 0.382185300977241 \tabularnewline
59 & 67.7 & 68.0549286851969 & -0.354928685196867 \tabularnewline
60 & 67.86 & 67.7068507570767 & 0.153149242923305 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167691&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]67.14[/C][C]67.4[/C][C]-0.260000000000005[/C][/ROW]
[ROW][C]4[/C][C]67.22[/C][C]67.2228389634081[/C][C]-0.00283896340808099[/C][/ROW]
[ROW][C]5[/C][C]67.17[/C][C]67.2948028620263[/C][C]-0.124802862026314[/C][/ROW]
[ROW][C]6[/C][C]67.27[/C][C]67.241278592506[/C][C]0.0287214074939754[/C][/ROW]
[ROW][C]7[/C][C]67.27[/C][C]67.3382497662901[/C][C]-0.0682497662900658[/C][/ROW]
[ROW][C]8[/C][C]67.27[/C][C]67.3372490866142[/C][C]-0.0672490866141544[/C][/ROW]
[ROW][C]9[/C][C]67.48[/C][C]67.3333079380555[/C][C]0.14669206194452[/C][/ROW]
[ROW][C]10[/C][C]67.38[/C][C]67.545289880695[/C][C]-0.165289880694985[/C][/ROW]
[ROW][C]11[/C][C]67.22[/C][C]67.4452272470471[/C][C]-0.225227247047144[/C][/ROW]
[ROW][C]12[/C][C]67.2[/C][C]67.2739648530112[/C][C]-0.0739648530111623[/C][/ROW]
[ROW][C]13[/C][C]67.2[/C][C]67.2450340720862[/C][C]-0.0450340720861675[/C][/ROW]
[ROW][C]14[/C][C]67.19[/C][C]67.2415298557956[/C][C]-0.051529855795593[/C][/ROW]
[ROW][C]15[/C][C]67.32[/C][C]67.2287322240743[/C][C]0.0912677759257008[/C][/ROW]
[ROW][C]16[/C][C]67.61[/C][C]67.3596687700757[/C][C]0.250331229924313[/C][/ROW]
[ROW][C]17[/C][C]67.85[/C][C]67.6593569692587[/C][C]0.190643030741299[/C][/ROW]
[ROW][C]18[/C][C]67.74[/C][C]67.9122697191105[/C][C]-0.172269719110545[/C][/ROW]
[ROW][C]19[/C][C]67.74[/C][C]67.8033600660338[/C][C]-0.0633600660338232[/C][/ROW]
[ROW][C]20[/C][C]67.61[/C][C]67.7963422561697[/C][C]-0.186342256169667[/C][/ROW]
[ROW][C]21[/C][C]67.85[/C][C]67.6592706508667[/C][C]0.190729349133264[/C][/ROW]
[ROW][C]22[/C][C]67.89[/C][C]67.8988203626372[/C][C]-0.00882036263716657[/C][/ROW]
[ROW][C]23[/C][C]67.97[/C][C]67.9444151470088[/C][C]0.0255848529912015[/C][/ROW]
[ROW][C]24[/C][C]67.94[/C][C]68.0248498486316[/C][C]-0.0848498486315634[/C][/ROW]
[ROW][C]25[/C][C]67.94[/C][C]67.9932959604419[/C][C]-0.053295960441929[/C][/ROW]
[ROW][C]26[/C][C]68.07[/C][C]67.9892310307146[/C][C]0.0807689692854296[/C][/ROW]
[ROW][C]27[/C][C]67.85[/C][C]68.1198243581034[/C][C]-0.269824358103435[/C][/ROW]
[ROW][C]28[/C][C]67.84[/C][C]67.8948648582434[/C][C]-0.0548648582434055[/C][/ROW]
[ROW][C]29[/C][C]67.89[/C][C]67.8750951388304[/C][C]0.0149048611696116[/C][/ROW]
[ROW][C]30[/C][C]67.86[/C][C]67.9238263876237[/C][C]-0.0638263876237204[/C][/ROW]
[ROW][C]31[/C][C]67.86[/C][C]67.8925246508436[/C][C]-0.0325246508436408[/C][/ROW]
[ROW][C]32[/C][C]67.89[/C][C]67.8896752861379[/C][C]0.000324713862113413[/C][/ROW]
[ROW][C]33[/C][C]67.7[/C][C]67.9186887363835[/C][C]-0.218688736383527[/C][/ROW]
[ROW][C]34[/C][C]68.05[/C][C]67.7226754517682[/C][C]0.327324548231829[/C][/ROW]
[ROW][C]35[/C][C]68.18[/C][C]68.0749972899262[/C][C]0.105002710073833[/C][/ROW]
[ROW][C]36[/C][C]68.19[/C][C]68.2179078566234[/C][C]-0.0279078566234148[/C][/ROW]
[ROW][C]37[/C][C]68.19[/C][C]68.2303530599649[/C][C]-0.0403530599648718[/C][/ROW]
[ROW][C]38[/C][C]68.27[/C][C]68.2283874525304[/C][C]0.0416125474695832[/C][/ROW]
[ROW][C]39[/C][C]68.22[/C][C]68.3082984639949[/C][C]-0.0882984639949029[/C][/ROW]
[ROW][C]40[/C][C]68.14[/C][C]68.2571401576491[/C][C]-0.117140157649104[/C][/ROW]
[ROW][C]41[/C][C]68.36[/C][C]68.1712112494566[/C][C]0.188788750543367[/C][/ROW]
[ROW][C]42[/C][C]68.34[/C][C]68.3928256048091[/C][C]-0.0528256048090583[/C][/ROW]
[ROW][C]43[/C][C]68.34[/C][C]68.3771489804994[/C][C]-0.037148980499353[/C][/ROW]
[ROW][C]44[/C][C]68.24[/C][C]68.3745089551738[/C][C]-0.134508955173814[/C][/ROW]
[ROW][C]45[/C][C]68.14[/C][C]68.2696672175959[/C][C]-0.129667217595866[/C][/ROW]
[ROW][C]46[/C][C]68.23[/C][C]68.1619789031118[/C][C]0.0680210968881596[/C][/ROW]
[ROW][C]47[/C][C]68.09[/C][C]68.2498836015613[/C][C]-0.159883601561262[/C][/ROW]
[ROW][C]48[/C][C]68.03[/C][C]68.107561960806[/C][C]-0.0775619608060225[/C][/ROW]
[ROW][C]49[/C][C]68.03[/C][C]68.0405321021452[/C][C]-0.0105321021452198[/C][/ROW]
[ROW][C]50[/C][C]67.89[/C][C]68.0378680566676[/C][C]-0.147868056667647[/C][/ROW]
[ROW][C]51[/C][C]67.63[/C][C]67.8934730486715[/C][C]-0.263473048671457[/C][/ROW]
[ROW][C]52[/C][C]67.61[/C][C]67.6216905073735[/C][C]-0.0116905073735296[/C][/ROW]
[ROW][C]53[/C][C]67.41[/C][C]67.593304312004[/C][C]-0.183304312003997[/C][/ROW]
[ROW][C]54[/C][C]67.29[/C][C]67.3878978470656[/C][C]-0.0978978470655676[/C][/ROW]
[ROW][C]55[/C][C]67.29[/C][C]67.2595910425705[/C][C]0.0304089574295148[/C][/ROW]
[ROW][C]56[/C][C]67.49[/C][C]67.2574321866535[/C][C]0.23256781334652[/C][/ROW]
[ROW][C]57[/C][C]67.68[/C][C]67.4647684110727[/C][C]0.21523158892731[/C][/ROW]
[ROW][C]58[/C][C]68.05[/C][C]67.6678146990228[/C][C]0.382185300977241[/C][/ROW]
[ROW][C]59[/C][C]67.7[/C][C]68.0549286851969[/C][C]-0.354928685196867[/C][/ROW]
[ROW][C]60[/C][C]67.86[/C][C]67.7068507570767[/C][C]0.153149242923305[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167691&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167691&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	67.14	67.4	-0.260000000000005
4	67.22	67.2228389634081	-0.00283896340808099
5	67.17	67.2948028620263	-0.124802862026314
6	67.27	67.241278592506	0.0287214074939754
7	67.27	67.3382497662901	-0.0682497662900658
8	67.27	67.3372490866142	-0.0672490866141544
9	67.48	67.3333079380555	0.14669206194452
10	67.38	67.545289880695	-0.165289880694985
11	67.22	67.4452272470471	-0.225227247047144
12	67.2	67.2739648530112	-0.0739648530111623
13	67.2	67.2450340720862	-0.0450340720861675
14	67.19	67.2415298557956	-0.051529855795593
15	67.32	67.2287322240743	0.0912677759257008
16	67.61	67.3596687700757	0.250331229924313
17	67.85	67.6593569692587	0.190643030741299
18	67.74	67.9122697191105	-0.172269719110545
19	67.74	67.8033600660338	-0.0633600660338232
20	67.61	67.7963422561697	-0.186342256169667
21	67.85	67.6592706508667	0.190729349133264
22	67.89	67.8988203626372	-0.00882036263716657
23	67.97	67.9444151470088	0.0255848529912015
24	67.94	68.0248498486316	-0.0848498486315634
25	67.94	67.9932959604419	-0.053295960441929
26	68.07	67.9892310307146	0.0807689692854296
27	67.85	68.1198243581034	-0.269824358103435
28	67.84	67.8948648582434	-0.0548648582434055
29	67.89	67.8750951388304	0.0149048611696116
30	67.86	67.9238263876237	-0.0638263876237204
31	67.86	67.8925246508436	-0.0325246508436408
32	67.89	67.8896752861379	0.000324713862113413
33	67.7	67.9186887363835	-0.218688736383527
34	68.05	67.7226754517682	0.327324548231829
35	68.18	68.0749972899262	0.105002710073833
36	68.19	68.2179078566234	-0.0279078566234148
37	68.19	68.2303530599649	-0.0403530599648718
38	68.27	68.2283874525304	0.0416125474695832
39	68.22	68.3082984639949	-0.0882984639949029
40	68.14	68.2571401576491	-0.117140157649104
41	68.36	68.1712112494566	0.188788750543367
42	68.34	68.3928256048091	-0.0528256048090583
43	68.34	68.3771489804994	-0.037148980499353
44	68.24	68.3745089551738	-0.134508955173814
45	68.14	68.2696672175959	-0.129667217595866
46	68.23	68.1619789031118	0.0680210968881596
47	68.09	68.2498836015613	-0.159883601561262
48	68.03	68.107561960806	-0.0775619608060225
49	68.03	68.0405321021452	-0.0105321021452198
50	67.89	68.0378680566676	-0.147868056667647
51	67.63	67.8934730486715	-0.263473048671457
52	67.61	67.6216905073735	-0.0116905073735296
53	67.41	67.593304312004	-0.183304312003997
54	67.29	67.3878978470656	-0.0978978470655676
55	67.29	67.2595910425705	0.0304089574295148
56	67.49	67.2574321866535	0.23256781334652
57	67.68	67.4647684110727	0.21523158892731
58	68.05	67.6678146990228	0.382185300977241
59	67.7	68.0549286851969	-0.354928685196867
60	67.86	67.7068507570767	0.153149242923305

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	67.8602054379227	67.562996761926	68.1574141139195
62	67.8650983673707	67.4389542410173	68.2912424937241
63	67.8699912968187	67.3354640648311	68.4045185288063
64	67.8748842262667	67.2414080932371	68.5083603592964
65	67.8797771557147	67.1525123190361	68.6070419923933
66	67.8846700851627	67.0666339401866	68.7027062301388
67	67.8895630146107	66.9825369043632	68.7965891248583
68	67.8944559440587	66.8994427726296	68.8894691154879
69	67.8993488735067	66.8168309510105	68.981866796003
70	67.9042418029547	66.7343378468997	69.0741457590097
71	67.9091347324027	66.6517011432943	69.1665683215112
72	67.9140276618507	66.5687268313675	69.2593284923339

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 67.8602054379227 & 67.562996761926 & 68.1574141139195 \tabularnewline
62 & 67.8650983673707 & 67.4389542410173 & 68.2912424937241 \tabularnewline
63 & 67.8699912968187 & 67.3354640648311 & 68.4045185288063 \tabularnewline
64 & 67.8748842262667 & 67.2414080932371 & 68.5083603592964 \tabularnewline
65 & 67.8797771557147 & 67.1525123190361 & 68.6070419923933 \tabularnewline
66 & 67.8846700851627 & 67.0666339401866 & 68.7027062301388 \tabularnewline
67 & 67.8895630146107 & 66.9825369043632 & 68.7965891248583 \tabularnewline
68 & 67.8944559440587 & 66.8994427726296 & 68.8894691154879 \tabularnewline
69 & 67.8993488735067 & 66.8168309510105 & 68.981866796003 \tabularnewline
70 & 67.9042418029547 & 66.7343378468997 & 69.0741457590097 \tabularnewline
71 & 67.9091347324027 & 66.6517011432943 & 69.1665683215112 \tabularnewline
72 & 67.9140276618507 & 66.5687268313675 & 69.2593284923339 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167691&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]61[/C][C]67.8602054379227[/C][C]67.562996761926[/C][C]68.1574141139195[/C][/ROW]
[ROW][C]62[/C][C]67.8650983673707[/C][C]67.4389542410173[/C][C]68.2912424937241[/C][/ROW]
[ROW][C]63[/C][C]67.8699912968187[/C][C]67.3354640648311[/C][C]68.4045185288063[/C][/ROW]
[ROW][C]64[/C][C]67.8748842262667[/C][C]67.2414080932371[/C][C]68.5083603592964[/C][/ROW]
[ROW][C]65[/C][C]67.8797771557147[/C][C]67.1525123190361[/C][C]68.6070419923933[/C][/ROW]
[ROW][C]66[/C][C]67.8846700851627[/C][C]67.0666339401866[/C][C]68.7027062301388[/C][/ROW]
[ROW][C]67[/C][C]67.8895630146107[/C][C]66.9825369043632[/C][C]68.7965891248583[/C][/ROW]
[ROW][C]68[/C][C]67.8944559440587[/C][C]66.8994427726296[/C][C]68.8894691154879[/C][/ROW]
[ROW][C]69[/C][C]67.8993488735067[/C][C]66.8168309510105[/C][C]68.981866796003[/C][/ROW]
[ROW][C]70[/C][C]67.9042418029547[/C][C]66.7343378468997[/C][C]69.0741457590097[/C][/ROW]
[ROW][C]71[/C][C]67.9091347324027[/C][C]66.6517011432943[/C][C]69.1665683215112[/C][/ROW]
[ROW][C]72[/C][C]67.9140276618507[/C][C]66.5687268313675[/C][C]69.2593284923339[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167691&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167691&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
61	67.8602054379227	67.562996761926	68.1574141139195
62	67.8650983673707	67.4389542410173	68.2912424937241
63	67.8699912968187	67.3354640648311	68.4045185288063
64	67.8748842262667	67.2414080932371	68.5083603592964
65	67.8797771557147	67.1525123190361	68.6070419923933
66	67.8846700851627	67.0666339401866	68.7027062301388
67	67.8895630146107	66.9825369043632	68.7965891248583
68	67.8944559440587	66.8994427726296	68.8894691154879
69	67.8993488735067	66.8168309510105	68.981866796003
70	67.9042418029547	66.7343378468997	69.0741457590097
71	67.9091347324027	66.6517011432943	69.1665683215112
72	67.9140276618507	66.5687268313675	69.2593284923339

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code