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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 09 Jan 2013 13:57:10 -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/2013/Jan/09/t1357757942no6ryds2nxozsrr.htm/, Retrieved Mon, 29 Apr 2024 12:57:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205120, Retrieved Mon, 29 Apr 2024 12:57:33 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

114

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

-       [Exponential Smoothing] [Prijs per 150 cl ...] [2013-01-09 18:57:10] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

1.26
1.27
1.24
1.25
1.27
1.25
1.26
1.27
1.26
1.26
1.28
1.27
1.28
1.27
1.26
1.27
1.27
1.28
1.27
1.26
1.3
1.31
1.28
1.29
1.31
1.29
1.29
1.32
1.3
1.29
1.31
1.29
1.33
1.35
1.32
1.33
1.34
1.34
1.33
1.33
1.35
1.32
1.35
1.32
1.36
1.37
1.34
1.32
1.34
1.32
1.33
1.35
1.33
1.33
1.35
1.33
1.36
1.39
1.37
1.37
1.39
1.37
1.39
1.39
1.39
1.37
1.38
1.37
1.41
1.41
1.42
1.42

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205120&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205120&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205120&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.288014681387039
beta	0.0200262579833585
gamma	0.753447853707694

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.288014681387039 \tabularnewline
beta & 0.0200262579833585 \tabularnewline
gamma & 0.753447853707694 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205120&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]0.288014681387039[/C][/ROW]
[ROW][C]beta[/C][C]0.0200262579833585[/C][/ROW]
[ROW][C]gamma[/C][C]0.753447853707694[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205120&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205120&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	0.288014681387039
beta	0.0200262579833585
gamma	0.753447853707694

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.28	1.27188034188034	0.00811965811965831
14	1.27	1.26564104702328	0.00435895297672162
15	1.26	1.25709375568712	0.00290624431287578
16	1.27	1.26564482572761	0.00435517427239018
17	1.27	1.26630499555482	0.00369500444517734
18	1.28	1.2780463390343	0.00195366096569738
19	1.27	1.27513075179542	-0.00513075179542222
20	1.26	1.28431182289987	-0.0243118228998691
21	1.3	1.26782823682033	0.0321717631796739
22	1.31	1.27696498156309	0.0330350184369139
23	1.28	1.30737423106667	-0.0273742310666718
24	1.29	1.28981017252353	0.000189827476470672
25	1.31	1.30412513608944	0.00587486391056347
26	1.29	1.29540487831523	-0.00540487831522762
27	1.29	1.28339282504135	0.00660717495865248
28	1.32	1.29393509477862	0.0260649052213773
29	1.3	1.30076706826717	-0.000767068267170323
30	1.29	1.31053662620739	-0.0205366262073923
31	1.31	1.29746088579703	0.0125391142029743
32	1.29	1.30166125720612	-0.0116612572061219
33	1.33	1.31941414289416	0.0105858571058413
34	1.35	1.32296506630213	0.0270349336978717
35	1.32	1.31937357629699	0.000626423703008028
36	1.33	1.32495573071778	0.0050442692822239
37	1.34	1.3440415918351	-0.00404159183510244
38	1.34	1.3266801490652	0.0133198509348034
39	1.33	1.32687873363829	0.00312126636170929
40	1.33	1.347208732553	-0.0172087325530035
41	1.35	1.32728756389958	0.0227124361004158
42	1.32	1.33345388017674	-0.0134538801767419
43	1.35	1.34044177643383	0.00955822356617375
44	1.32	1.33106470039638	-0.0110647003963793
45	1.36	1.36119040309183	-0.00119040309183061
46	1.37	1.3703723453362	-0.000372345336195679
47	1.34	1.34476114296635	-0.004761142966345
48	1.32	1.35117111839108	-0.0311711183910828
49	1.34	1.3547530704438	-0.0147530704438019
50	1.32	1.34335892904941	-0.0233589290494109
51	1.33	1.32704988695665	0.00295011304334825
52	1.35	1.33595106996819	0.0140489300318074
53	1.33	1.34615470141484	-0.0161547014148398
54	1.33	1.32120800544625	0.00879199455374735
55	1.35	1.34655854233316	0.00344145766683757
56	1.33	1.3239322288748	0.00606777112520351
57	1.36	1.36396367906806	-0.00396367906805684
58	1.39	1.37244406178001	0.0175559382199917
59	1.37	1.34940387537196	0.0205961246280408
60	1.37	1.34885765578446	0.0211423442155365
61	1.39	1.3765237573185	0.0134762426814961
62	1.37	1.36901607961117	0.000983920388829329
63	1.39	1.37434443102541	0.015655568974585
64	1.39	1.39344511949641	-0.00344511949640847
65	1.39	1.38289300948725	0.00710699051274877
66	1.37	1.37864804582089	-0.00864804582088907
67	1.38	1.39662426387121	-0.0166242638712109
68	1.37	1.37003079264637	-3.0792646373401e-05
69	1.41	1.40329247696597	0.0067075230340321
70	1.41	1.42681995739463	-0.0168199573946284
71	1.42	1.39574119166925	0.024258808330748
72	1.42	1.39679531483656	0.0232046851634413

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.28 & 1.27188034188034 & 0.00811965811965831 \tabularnewline
14 & 1.27 & 1.26564104702328 & 0.00435895297672162 \tabularnewline
15 & 1.26 & 1.25709375568712 & 0.00290624431287578 \tabularnewline
16 & 1.27 & 1.26564482572761 & 0.00435517427239018 \tabularnewline
17 & 1.27 & 1.26630499555482 & 0.00369500444517734 \tabularnewline
18 & 1.28 & 1.2780463390343 & 0.00195366096569738 \tabularnewline
19 & 1.27 & 1.27513075179542 & -0.00513075179542222 \tabularnewline
20 & 1.26 & 1.28431182289987 & -0.0243118228998691 \tabularnewline
21 & 1.3 & 1.26782823682033 & 0.0321717631796739 \tabularnewline
22 & 1.31 & 1.27696498156309 & 0.0330350184369139 \tabularnewline
23 & 1.28 & 1.30737423106667 & -0.0273742310666718 \tabularnewline
24 & 1.29 & 1.28981017252353 & 0.000189827476470672 \tabularnewline
25 & 1.31 & 1.30412513608944 & 0.00587486391056347 \tabularnewline
26 & 1.29 & 1.29540487831523 & -0.00540487831522762 \tabularnewline
27 & 1.29 & 1.28339282504135 & 0.00660717495865248 \tabularnewline
28 & 1.32 & 1.29393509477862 & 0.0260649052213773 \tabularnewline
29 & 1.3 & 1.30076706826717 & -0.000767068267170323 \tabularnewline
30 & 1.29 & 1.31053662620739 & -0.0205366262073923 \tabularnewline
31 & 1.31 & 1.29746088579703 & 0.0125391142029743 \tabularnewline
32 & 1.29 & 1.30166125720612 & -0.0116612572061219 \tabularnewline
33 & 1.33 & 1.31941414289416 & 0.0105858571058413 \tabularnewline
34 & 1.35 & 1.32296506630213 & 0.0270349336978717 \tabularnewline
35 & 1.32 & 1.31937357629699 & 0.000626423703008028 \tabularnewline
36 & 1.33 & 1.32495573071778 & 0.0050442692822239 \tabularnewline
37 & 1.34 & 1.3440415918351 & -0.00404159183510244 \tabularnewline
38 & 1.34 & 1.3266801490652 & 0.0133198509348034 \tabularnewline
39 & 1.33 & 1.32687873363829 & 0.00312126636170929 \tabularnewline
40 & 1.33 & 1.347208732553 & -0.0172087325530035 \tabularnewline
41 & 1.35 & 1.32728756389958 & 0.0227124361004158 \tabularnewline
42 & 1.32 & 1.33345388017674 & -0.0134538801767419 \tabularnewline
43 & 1.35 & 1.34044177643383 & 0.00955822356617375 \tabularnewline
44 & 1.32 & 1.33106470039638 & -0.0110647003963793 \tabularnewline
45 & 1.36 & 1.36119040309183 & -0.00119040309183061 \tabularnewline
46 & 1.37 & 1.3703723453362 & -0.000372345336195679 \tabularnewline
47 & 1.34 & 1.34476114296635 & -0.004761142966345 \tabularnewline
48 & 1.32 & 1.35117111839108 & -0.0311711183910828 \tabularnewline
49 & 1.34 & 1.3547530704438 & -0.0147530704438019 \tabularnewline
50 & 1.32 & 1.34335892904941 & -0.0233589290494109 \tabularnewline
51 & 1.33 & 1.32704988695665 & 0.00295011304334825 \tabularnewline
52 & 1.35 & 1.33595106996819 & 0.0140489300318074 \tabularnewline
53 & 1.33 & 1.34615470141484 & -0.0161547014148398 \tabularnewline
54 & 1.33 & 1.32120800544625 & 0.00879199455374735 \tabularnewline
55 & 1.35 & 1.34655854233316 & 0.00344145766683757 \tabularnewline
56 & 1.33 & 1.3239322288748 & 0.00606777112520351 \tabularnewline
57 & 1.36 & 1.36396367906806 & -0.00396367906805684 \tabularnewline
58 & 1.39 & 1.37244406178001 & 0.0175559382199917 \tabularnewline
59 & 1.37 & 1.34940387537196 & 0.0205961246280408 \tabularnewline
60 & 1.37 & 1.34885765578446 & 0.0211423442155365 \tabularnewline
61 & 1.39 & 1.3765237573185 & 0.0134762426814961 \tabularnewline
62 & 1.37 & 1.36901607961117 & 0.000983920388829329 \tabularnewline
63 & 1.39 & 1.37434443102541 & 0.015655568974585 \tabularnewline
64 & 1.39 & 1.39344511949641 & -0.00344511949640847 \tabularnewline
65 & 1.39 & 1.38289300948725 & 0.00710699051274877 \tabularnewline
66 & 1.37 & 1.37864804582089 & -0.00864804582088907 \tabularnewline
67 & 1.38 & 1.39662426387121 & -0.0166242638712109 \tabularnewline
68 & 1.37 & 1.37003079264637 & -3.0792646373401e-05 \tabularnewline
69 & 1.41 & 1.40329247696597 & 0.0067075230340321 \tabularnewline
70 & 1.41 & 1.42681995739463 & -0.0168199573946284 \tabularnewline
71 & 1.42 & 1.39574119166925 & 0.024258808330748 \tabularnewline
72 & 1.42 & 1.39679531483656 & 0.0232046851634413 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205120&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]1.28[/C][C]1.27188034188034[/C][C]0.00811965811965831[/C][/ROW]
[ROW][C]14[/C][C]1.27[/C][C]1.26564104702328[/C][C]0.00435895297672162[/C][/ROW]
[ROW][C]15[/C][C]1.26[/C][C]1.25709375568712[/C][C]0.00290624431287578[/C][/ROW]
[ROW][C]16[/C][C]1.27[/C][C]1.26564482572761[/C][C]0.00435517427239018[/C][/ROW]
[ROW][C]17[/C][C]1.27[/C][C]1.26630499555482[/C][C]0.00369500444517734[/C][/ROW]
[ROW][C]18[/C][C]1.28[/C][C]1.2780463390343[/C][C]0.00195366096569738[/C][/ROW]
[ROW][C]19[/C][C]1.27[/C][C]1.27513075179542[/C][C]-0.00513075179542222[/C][/ROW]
[ROW][C]20[/C][C]1.26[/C][C]1.28431182289987[/C][C]-0.0243118228998691[/C][/ROW]
[ROW][C]21[/C][C]1.3[/C][C]1.26782823682033[/C][C]0.0321717631796739[/C][/ROW]
[ROW][C]22[/C][C]1.31[/C][C]1.27696498156309[/C][C]0.0330350184369139[/C][/ROW]
[ROW][C]23[/C][C]1.28[/C][C]1.30737423106667[/C][C]-0.0273742310666718[/C][/ROW]
[ROW][C]24[/C][C]1.29[/C][C]1.28981017252353[/C][C]0.000189827476470672[/C][/ROW]
[ROW][C]25[/C][C]1.31[/C][C]1.30412513608944[/C][C]0.00587486391056347[/C][/ROW]
[ROW][C]26[/C][C]1.29[/C][C]1.29540487831523[/C][C]-0.00540487831522762[/C][/ROW]
[ROW][C]27[/C][C]1.29[/C][C]1.28339282504135[/C][C]0.00660717495865248[/C][/ROW]
[ROW][C]28[/C][C]1.32[/C][C]1.29393509477862[/C][C]0.0260649052213773[/C][/ROW]
[ROW][C]29[/C][C]1.3[/C][C]1.30076706826717[/C][C]-0.000767068267170323[/C][/ROW]
[ROW][C]30[/C][C]1.29[/C][C]1.31053662620739[/C][C]-0.0205366262073923[/C][/ROW]
[ROW][C]31[/C][C]1.31[/C][C]1.29746088579703[/C][C]0.0125391142029743[/C][/ROW]
[ROW][C]32[/C][C]1.29[/C][C]1.30166125720612[/C][C]-0.0116612572061219[/C][/ROW]
[ROW][C]33[/C][C]1.33[/C][C]1.31941414289416[/C][C]0.0105858571058413[/C][/ROW]
[ROW][C]34[/C][C]1.35[/C][C]1.32296506630213[/C][C]0.0270349336978717[/C][/ROW]
[ROW][C]35[/C][C]1.32[/C][C]1.31937357629699[/C][C]0.000626423703008028[/C][/ROW]
[ROW][C]36[/C][C]1.33[/C][C]1.32495573071778[/C][C]0.0050442692822239[/C][/ROW]
[ROW][C]37[/C][C]1.34[/C][C]1.3440415918351[/C][C]-0.00404159183510244[/C][/ROW]
[ROW][C]38[/C][C]1.34[/C][C]1.3266801490652[/C][C]0.0133198509348034[/C][/ROW]
[ROW][C]39[/C][C]1.33[/C][C]1.32687873363829[/C][C]0.00312126636170929[/C][/ROW]
[ROW][C]40[/C][C]1.33[/C][C]1.347208732553[/C][C]-0.0172087325530035[/C][/ROW]
[ROW][C]41[/C][C]1.35[/C][C]1.32728756389958[/C][C]0.0227124361004158[/C][/ROW]
[ROW][C]42[/C][C]1.32[/C][C]1.33345388017674[/C][C]-0.0134538801767419[/C][/ROW]
[ROW][C]43[/C][C]1.35[/C][C]1.34044177643383[/C][C]0.00955822356617375[/C][/ROW]
[ROW][C]44[/C][C]1.32[/C][C]1.33106470039638[/C][C]-0.0110647003963793[/C][/ROW]
[ROW][C]45[/C][C]1.36[/C][C]1.36119040309183[/C][C]-0.00119040309183061[/C][/ROW]
[ROW][C]46[/C][C]1.37[/C][C]1.3703723453362[/C][C]-0.000372345336195679[/C][/ROW]
[ROW][C]47[/C][C]1.34[/C][C]1.34476114296635[/C][C]-0.004761142966345[/C][/ROW]
[ROW][C]48[/C][C]1.32[/C][C]1.35117111839108[/C][C]-0.0311711183910828[/C][/ROW]
[ROW][C]49[/C][C]1.34[/C][C]1.3547530704438[/C][C]-0.0147530704438019[/C][/ROW]
[ROW][C]50[/C][C]1.32[/C][C]1.34335892904941[/C][C]-0.0233589290494109[/C][/ROW]
[ROW][C]51[/C][C]1.33[/C][C]1.32704988695665[/C][C]0.00295011304334825[/C][/ROW]
[ROW][C]52[/C][C]1.35[/C][C]1.33595106996819[/C][C]0.0140489300318074[/C][/ROW]
[ROW][C]53[/C][C]1.33[/C][C]1.34615470141484[/C][C]-0.0161547014148398[/C][/ROW]
[ROW][C]54[/C][C]1.33[/C][C]1.32120800544625[/C][C]0.00879199455374735[/C][/ROW]
[ROW][C]55[/C][C]1.35[/C][C]1.34655854233316[/C][C]0.00344145766683757[/C][/ROW]
[ROW][C]56[/C][C]1.33[/C][C]1.3239322288748[/C][C]0.00606777112520351[/C][/ROW]
[ROW][C]57[/C][C]1.36[/C][C]1.36396367906806[/C][C]-0.00396367906805684[/C][/ROW]
[ROW][C]58[/C][C]1.39[/C][C]1.37244406178001[/C][C]0.0175559382199917[/C][/ROW]
[ROW][C]59[/C][C]1.37[/C][C]1.34940387537196[/C][C]0.0205961246280408[/C][/ROW]
[ROW][C]60[/C][C]1.37[/C][C]1.34885765578446[/C][C]0.0211423442155365[/C][/ROW]
[ROW][C]61[/C][C]1.39[/C][C]1.3765237573185[/C][C]0.0134762426814961[/C][/ROW]
[ROW][C]62[/C][C]1.37[/C][C]1.36901607961117[/C][C]0.000983920388829329[/C][/ROW]
[ROW][C]63[/C][C]1.39[/C][C]1.37434443102541[/C][C]0.015655568974585[/C][/ROW]
[ROW][C]64[/C][C]1.39[/C][C]1.39344511949641[/C][C]-0.00344511949640847[/C][/ROW]
[ROW][C]65[/C][C]1.39[/C][C]1.38289300948725[/C][C]0.00710699051274877[/C][/ROW]
[ROW][C]66[/C][C]1.37[/C][C]1.37864804582089[/C][C]-0.00864804582088907[/C][/ROW]
[ROW][C]67[/C][C]1.38[/C][C]1.39662426387121[/C][C]-0.0166242638712109[/C][/ROW]
[ROW][C]68[/C][C]1.37[/C][C]1.37003079264637[/C][C]-3.0792646373401e-05[/C][/ROW]
[ROW][C]69[/C][C]1.41[/C][C]1.40329247696597[/C][C]0.0067075230340321[/C][/ROW]
[ROW][C]70[/C][C]1.41[/C][C]1.42681995739463[/C][C]-0.0168199573946284[/C][/ROW]
[ROW][C]71[/C][C]1.42[/C][C]1.39574119166925[/C][C]0.024258808330748[/C][/ROW]
[ROW][C]72[/C][C]1.42[/C][C]1.39679531483656[/C][C]0.0232046851634413[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205120&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205120&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	1.28	1.27188034188034	0.00811965811965831
14	1.27	1.26564104702328	0.00435895297672162
15	1.26	1.25709375568712	0.00290624431287578
16	1.27	1.26564482572761	0.00435517427239018
17	1.27	1.26630499555482	0.00369500444517734
18	1.28	1.2780463390343	0.00195366096569738
19	1.27	1.27513075179542	-0.00513075179542222
20	1.26	1.28431182289987	-0.0243118228998691
21	1.3	1.26782823682033	0.0321717631796739
22	1.31	1.27696498156309	0.0330350184369139
23	1.28	1.30737423106667	-0.0273742310666718
24	1.29	1.28981017252353	0.000189827476470672
25	1.31	1.30412513608944	0.00587486391056347
26	1.29	1.29540487831523	-0.00540487831522762
27	1.29	1.28339282504135	0.00660717495865248
28	1.32	1.29393509477862	0.0260649052213773
29	1.3	1.30076706826717	-0.000767068267170323
30	1.29	1.31053662620739	-0.0205366262073923
31	1.31	1.29746088579703	0.0125391142029743
32	1.29	1.30166125720612	-0.0116612572061219
33	1.33	1.31941414289416	0.0105858571058413
34	1.35	1.32296506630213	0.0270349336978717
35	1.32	1.31937357629699	0.000626423703008028
36	1.33	1.32495573071778	0.0050442692822239
37	1.34	1.3440415918351	-0.00404159183510244
38	1.34	1.3266801490652	0.0133198509348034
39	1.33	1.32687873363829	0.00312126636170929
40	1.33	1.347208732553	-0.0172087325530035
41	1.35	1.32728756389958	0.0227124361004158
42	1.32	1.33345388017674	-0.0134538801767419
43	1.35	1.34044177643383	0.00955822356617375
44	1.32	1.33106470039638	-0.0110647003963793
45	1.36	1.36119040309183	-0.00119040309183061
46	1.37	1.3703723453362	-0.000372345336195679
47	1.34	1.34476114296635	-0.004761142966345
48	1.32	1.35117111839108	-0.0311711183910828
49	1.34	1.3547530704438	-0.0147530704438019
50	1.32	1.34335892904941	-0.0233589290494109
51	1.33	1.32704988695665	0.00295011304334825
52	1.35	1.33595106996819	0.0140489300318074
53	1.33	1.34615470141484	-0.0161547014148398
54	1.33	1.32120800544625	0.00879199455374735
55	1.35	1.34655854233316	0.00344145766683757
56	1.33	1.3239322288748	0.00606777112520351
57	1.36	1.36396367906806	-0.00396367906805684
58	1.39	1.37244406178001	0.0175559382199917
59	1.37	1.34940387537196	0.0205961246280408
60	1.37	1.34885765578446	0.0211423442155365
61	1.39	1.3765237573185	0.0134762426814961
62	1.37	1.36901607961117	0.000983920388829329
63	1.39	1.37434443102541	0.015655568974585
64	1.39	1.39344511949641	-0.00344511949640847
65	1.39	1.38289300948725	0.00710699051274877
66	1.37	1.37864804582089	-0.00864804582088907
67	1.38	1.39662426387121	-0.0166242638712109
68	1.37	1.37003079264637	-3.0792646373401e-05
69	1.41	1.40329247696597	0.0067075230340321
70	1.41	1.42681995739463	-0.0168199573946284
71	1.42	1.39574119166925	0.024258808330748
72	1.42	1.39679531483656	0.0232046851634413

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.42120728337016	1.39219009323734	1.45022447350298
74	1.40330340716521	1.37305991895241	1.43354689537801
75	1.41639980123297	1.38493201821051	1.44786758425544
76	1.42083562192288	1.38814446541485	1.45352677843091
77	1.41704685399032	1.38313231965559	1.45096138832505
78	1.40237277187912	1.36723405864582	1.43751148511241
79	1.41868033285875	1.38231595024477	1.45504471547273
80	1.40599161655868	1.36839947471802	1.44358375839935
81	1.44309233289251	1.40426981871678	1.48191484706823
82	1.45224352447966	1.41218756633886	1.49229948262045
83	1.44831936563803	1.40702648878812	1.48961224248793
84	1.44195495929465	1.39942133355888	1.48448858503043

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.42120728337016 & 1.39219009323734 & 1.45022447350298 \tabularnewline
74 & 1.40330340716521 & 1.37305991895241 & 1.43354689537801 \tabularnewline
75 & 1.41639980123297 & 1.38493201821051 & 1.44786758425544 \tabularnewline
76 & 1.42083562192288 & 1.38814446541485 & 1.45352677843091 \tabularnewline
77 & 1.41704685399032 & 1.38313231965559 & 1.45096138832505 \tabularnewline
78 & 1.40237277187912 & 1.36723405864582 & 1.43751148511241 \tabularnewline
79 & 1.41868033285875 & 1.38231595024477 & 1.45504471547273 \tabularnewline
80 & 1.40599161655868 & 1.36839947471802 & 1.44358375839935 \tabularnewline
81 & 1.44309233289251 & 1.40426981871678 & 1.48191484706823 \tabularnewline
82 & 1.45224352447966 & 1.41218756633886 & 1.49229948262045 \tabularnewline
83 & 1.44831936563803 & 1.40702648878812 & 1.48961224248793 \tabularnewline
84 & 1.44195495929465 & 1.39942133355888 & 1.48448858503043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205120&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]1.42120728337016[/C][C]1.39219009323734[/C][C]1.45022447350298[/C][/ROW]
[ROW][C]74[/C][C]1.40330340716521[/C][C]1.37305991895241[/C][C]1.43354689537801[/C][/ROW]
[ROW][C]75[/C][C]1.41639980123297[/C][C]1.38493201821051[/C][C]1.44786758425544[/C][/ROW]
[ROW][C]76[/C][C]1.42083562192288[/C][C]1.38814446541485[/C][C]1.45352677843091[/C][/ROW]
[ROW][C]77[/C][C]1.41704685399032[/C][C]1.38313231965559[/C][C]1.45096138832505[/C][/ROW]
[ROW][C]78[/C][C]1.40237277187912[/C][C]1.36723405864582[/C][C]1.43751148511241[/C][/ROW]
[ROW][C]79[/C][C]1.41868033285875[/C][C]1.38231595024477[/C][C]1.45504471547273[/C][/ROW]
[ROW][C]80[/C][C]1.40599161655868[/C][C]1.36839947471802[/C][C]1.44358375839935[/C][/ROW]
[ROW][C]81[/C][C]1.44309233289251[/C][C]1.40426981871678[/C][C]1.48191484706823[/C][/ROW]
[ROW][C]82[/C][C]1.45224352447966[/C][C]1.41218756633886[/C][C]1.49229948262045[/C][/ROW]
[ROW][C]83[/C][C]1.44831936563803[/C][C]1.40702648878812[/C][C]1.48961224248793[/C][/ROW]
[ROW][C]84[/C][C]1.44195495929465[/C][C]1.39942133355888[/C][C]1.48448858503043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205120&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205120&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	1.42120728337016	1.39219009323734	1.45022447350298
74	1.40330340716521	1.37305991895241	1.43354689537801
75	1.41639980123297	1.38493201821051	1.44786758425544
76	1.42083562192288	1.38814446541485	1.45352677843091
77	1.41704685399032	1.38313231965559	1.45096138832505
78	1.40237277187912	1.36723405864582	1.43751148511241
79	1.41868033285875	1.38231595024477	1.45504471547273
80	1.40599161655868	1.36839947471802	1.44358375839935
81	1.44309233289251	1.40426981871678	1.48191484706823
82	1.45224352447966	1.41218756633886	1.49229948262045
83	1.44831936563803	1.40702648878812	1.48961224248793
84	1.44195495929465	1.39942133355888	1.48448858503043

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