Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 31 May 2010 13:30:53 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/May/31/t127531292384vs8nsemsvusdk.htm/, Retrieved Mon, 29 Apr 2024 15:06:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76735, Retrieved Mon, 29 Apr 2024 15:06:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Indicator van het...] [2010-05-31 13:30:53] [181f2439255053cc457d7672472fa443] [Current]
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Dataseries X:
-15
-15
-10
-12
-11
-11
-17
-18
-19
-22
-24
-24
-20
-25
-22
-17
-9
-11
-13
-11
-9
-7
-3
-3
-6
-4
-8
-1
-2
-2
-1
1
2
2
-1
1
-1
-8
1
2
-2
-2
-2
-2
-6
-4
-5
-2
-1
-5
-9
-8
-14
-10
-11
-11
-11
-5
-2
-3
-6
-6
-7
-6
-2
-2
-4
0
-6
-4
-3
-1
-3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76735&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76735&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76735&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.793304674764876
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.793304674764876 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76735&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]0.793304674764876[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76735&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76735&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
ParameterValue
alpha0.793304674764876
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2-15-150
3-10-155
4-12-11.0334766261756-0.966523373824378
5-11-11.80022413690000.80022413690002
6-11-11.16540258823750.165402588237546
7-17-11.0341879417705-5.96581205822951
8-18-15.7668945363326-2.23310546366737
9-19-17.5384275399029-1.46157246009706
10-22-18.6978998050055-3.30210019499446
11-24-21.3174713262367-2.68252867376335
12-24-23.4455338633239-0.554466136676062
13-20-23.88539444154793.88539444154788
14-25-20.8030928677625-4.19690713223752
15-22-24.13251891532062.13251891532055
16-17-22.44078169077225.44078169077224
17-9-18.12458414110759.12458414110748
18-11-10.8860088866815-0.113991113318532
19-13-10.9764385697587-2.02356143024129
20-11-12.58173931204301.58173931204302
21-9-11.32693812153992.32693812153991
22-7-9.48096723183372.4809672318337
23-3-7.512804328881554.51280432888155
24-3-3.932775558480650.93277555848065
25-6-3.19280034743153-2.80719965256847
26-4-5.419764954812431.41976495481243
27-8-4.29345877909239-3.70654122090761
28-1-7.23387525684716.23387525684711
29-2-2.288512873689210.288512873689207
30-2-2.059634262261710.059634262261711
31-1-2.012326123233341.01232612323334
321-1.209243077285732.20924307728573
3320.5433597836169791.45664021638302
3421.698919276724150.301080723275850
35-11.93776802198047-2.93776802198047
361-0.3927770832313981.39277708323140
37-10.712119487801458-1.71211948780146
38-8-0.646112905627483-7.35388709437252
391-6.479985915286297.47998591528629
402-0.5460781215142492.54607812151425
41-21.47373755459958-3.47373755459958
42-2-1.28199468637057-0.718005313629425
43-2-1.85159165817882-0.148408341821181
44-2-1.96932468951967-0.0306753104803346
45-6-1.99365955672358-4.00634044327642
46-4-5.171908159074351.17190815907435
47-5-4.24222793808557-0.757772061914432
48-2-4.843372057208512.84337205720851
49-1-2.587711712129181.58771171212918
50-5-1.32817258871816-3.67182741128184
51-9-4.24105043901785-4.75894956098215
52-8-8.016347372715240.0163473727152432
53-14-8.00337892552012-5.99662107447988
54-10-12.76052645669862.76052645669858
55-11-10.5705879137875-0.429412086212521
56-11-10.9112425291804-0.0887574708195906
57-11-10.9816542457019-0.0183457542981031
58-5-10.99620801834875.99620801834867
59-2-6.239388166530044.23938816653004
60-3-2.87626171587886-0.123738284121136
61-6-2.97442387511955-3.02557612488045
62-6-5.37462755884421-0.625372441155792
63-7-5.87073843988222-1.12926156011778
64-6-6.766586914555930.766586914555932
65-2-6.158449931625134.15844993162513
66-2-2.859532161091240.859532161091237
67-4-2.17766127958680-1.82233872041320
680-3.623331105495633.62333110549563
69-6-0.748925601284963-5.25107439871504
70-4-4.914627469323760.91462746932376
71-3-4.189049222240851.18904922224085
72-1-3.245770915711642.24577091571164
73-3-1.46419034982660-1.53580965017340

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & -15 & -15 & 0 \tabularnewline
3 & -10 & -15 & 5 \tabularnewline
4 & -12 & -11.0334766261756 & -0.966523373824378 \tabularnewline
5 & -11 & -11.8002241369000 & 0.80022413690002 \tabularnewline
6 & -11 & -11.1654025882375 & 0.165402588237546 \tabularnewline
7 & -17 & -11.0341879417705 & -5.96581205822951 \tabularnewline
8 & -18 & -15.7668945363326 & -2.23310546366737 \tabularnewline
9 & -19 & -17.5384275399029 & -1.46157246009706 \tabularnewline
10 & -22 & -18.6978998050055 & -3.30210019499446 \tabularnewline
11 & -24 & -21.3174713262367 & -2.68252867376335 \tabularnewline
12 & -24 & -23.4455338633239 & -0.554466136676062 \tabularnewline
13 & -20 & -23.8853944415479 & 3.88539444154788 \tabularnewline
14 & -25 & -20.8030928677625 & -4.19690713223752 \tabularnewline
15 & -22 & -24.1325189153206 & 2.13251891532055 \tabularnewline
16 & -17 & -22.4407816907722 & 5.44078169077224 \tabularnewline
17 & -9 & -18.1245841411075 & 9.12458414110748 \tabularnewline
18 & -11 & -10.8860088866815 & -0.113991113318532 \tabularnewline
19 & -13 & -10.9764385697587 & -2.02356143024129 \tabularnewline
20 & -11 & -12.5817393120430 & 1.58173931204302 \tabularnewline
21 & -9 & -11.3269381215399 & 2.32693812153991 \tabularnewline
22 & -7 & -9.4809672318337 & 2.4809672318337 \tabularnewline
23 & -3 & -7.51280432888155 & 4.51280432888155 \tabularnewline
24 & -3 & -3.93277555848065 & 0.93277555848065 \tabularnewline
25 & -6 & -3.19280034743153 & -2.80719965256847 \tabularnewline
26 & -4 & -5.41976495481243 & 1.41976495481243 \tabularnewline
27 & -8 & -4.29345877909239 & -3.70654122090761 \tabularnewline
28 & -1 & -7.2338752568471 & 6.23387525684711 \tabularnewline
29 & -2 & -2.28851287368921 & 0.288512873689207 \tabularnewline
30 & -2 & -2.05963426226171 & 0.059634262261711 \tabularnewline
31 & -1 & -2.01232612323334 & 1.01232612323334 \tabularnewline
32 & 1 & -1.20924307728573 & 2.20924307728573 \tabularnewline
33 & 2 & 0.543359783616979 & 1.45664021638302 \tabularnewline
34 & 2 & 1.69891927672415 & 0.301080723275850 \tabularnewline
35 & -1 & 1.93776802198047 & -2.93776802198047 \tabularnewline
36 & 1 & -0.392777083231398 & 1.39277708323140 \tabularnewline
37 & -1 & 0.712119487801458 & -1.71211948780146 \tabularnewline
38 & -8 & -0.646112905627483 & -7.35388709437252 \tabularnewline
39 & 1 & -6.47998591528629 & 7.47998591528629 \tabularnewline
40 & 2 & -0.546078121514249 & 2.54607812151425 \tabularnewline
41 & -2 & 1.47373755459958 & -3.47373755459958 \tabularnewline
42 & -2 & -1.28199468637057 & -0.718005313629425 \tabularnewline
43 & -2 & -1.85159165817882 & -0.148408341821181 \tabularnewline
44 & -2 & -1.96932468951967 & -0.0306753104803346 \tabularnewline
45 & -6 & -1.99365955672358 & -4.00634044327642 \tabularnewline
46 & -4 & -5.17190815907435 & 1.17190815907435 \tabularnewline
47 & -5 & -4.24222793808557 & -0.757772061914432 \tabularnewline
48 & -2 & -4.84337205720851 & 2.84337205720851 \tabularnewline
49 & -1 & -2.58771171212918 & 1.58771171212918 \tabularnewline
50 & -5 & -1.32817258871816 & -3.67182741128184 \tabularnewline
51 & -9 & -4.24105043901785 & -4.75894956098215 \tabularnewline
52 & -8 & -8.01634737271524 & 0.0163473727152432 \tabularnewline
53 & -14 & -8.00337892552012 & -5.99662107447988 \tabularnewline
54 & -10 & -12.7605264566986 & 2.76052645669858 \tabularnewline
55 & -11 & -10.5705879137875 & -0.429412086212521 \tabularnewline
56 & -11 & -10.9112425291804 & -0.0887574708195906 \tabularnewline
57 & -11 & -10.9816542457019 & -0.0183457542981031 \tabularnewline
58 & -5 & -10.9962080183487 & 5.99620801834867 \tabularnewline
59 & -2 & -6.23938816653004 & 4.23938816653004 \tabularnewline
60 & -3 & -2.87626171587886 & -0.123738284121136 \tabularnewline
61 & -6 & -2.97442387511955 & -3.02557612488045 \tabularnewline
62 & -6 & -5.37462755884421 & -0.625372441155792 \tabularnewline
63 & -7 & -5.87073843988222 & -1.12926156011778 \tabularnewline
64 & -6 & -6.76658691455593 & 0.766586914555932 \tabularnewline
65 & -2 & -6.15844993162513 & 4.15844993162513 \tabularnewline
66 & -2 & -2.85953216109124 & 0.859532161091237 \tabularnewline
67 & -4 & -2.17766127958680 & -1.82233872041320 \tabularnewline
68 & 0 & -3.62333110549563 & 3.62333110549563 \tabularnewline
69 & -6 & -0.748925601284963 & -5.25107439871504 \tabularnewline
70 & -4 & -4.91462746932376 & 0.91462746932376 \tabularnewline
71 & -3 & -4.18904922224085 & 1.18904922224085 \tabularnewline
72 & -1 & -3.24577091571164 & 2.24577091571164 \tabularnewline
73 & -3 & -1.46419034982660 & -1.53580965017340 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76735&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]-15[/C][C]-15[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-10[/C][C]-15[/C][C]5[/C][/ROW]
[ROW][C]4[/C][C]-12[/C][C]-11.0334766261756[/C][C]-0.966523373824378[/C][/ROW]
[ROW][C]5[/C][C]-11[/C][C]-11.8002241369000[/C][C]0.80022413690002[/C][/ROW]
[ROW][C]6[/C][C]-11[/C][C]-11.1654025882375[/C][C]0.165402588237546[/C][/ROW]
[ROW][C]7[/C][C]-17[/C][C]-11.0341879417705[/C][C]-5.96581205822951[/C][/ROW]
[ROW][C]8[/C][C]-18[/C][C]-15.7668945363326[/C][C]-2.23310546366737[/C][/ROW]
[ROW][C]9[/C][C]-19[/C][C]-17.5384275399029[/C][C]-1.46157246009706[/C][/ROW]
[ROW][C]10[/C][C]-22[/C][C]-18.6978998050055[/C][C]-3.30210019499446[/C][/ROW]
[ROW][C]11[/C][C]-24[/C][C]-21.3174713262367[/C][C]-2.68252867376335[/C][/ROW]
[ROW][C]12[/C][C]-24[/C][C]-23.4455338633239[/C][C]-0.554466136676062[/C][/ROW]
[ROW][C]13[/C][C]-20[/C][C]-23.8853944415479[/C][C]3.88539444154788[/C][/ROW]
[ROW][C]14[/C][C]-25[/C][C]-20.8030928677625[/C][C]-4.19690713223752[/C][/ROW]
[ROW][C]15[/C][C]-22[/C][C]-24.1325189153206[/C][C]2.13251891532055[/C][/ROW]
[ROW][C]16[/C][C]-17[/C][C]-22.4407816907722[/C][C]5.44078169077224[/C][/ROW]
[ROW][C]17[/C][C]-9[/C][C]-18.1245841411075[/C][C]9.12458414110748[/C][/ROW]
[ROW][C]18[/C][C]-11[/C][C]-10.8860088866815[/C][C]-0.113991113318532[/C][/ROW]
[ROW][C]19[/C][C]-13[/C][C]-10.9764385697587[/C][C]-2.02356143024129[/C][/ROW]
[ROW][C]20[/C][C]-11[/C][C]-12.5817393120430[/C][C]1.58173931204302[/C][/ROW]
[ROW][C]21[/C][C]-9[/C][C]-11.3269381215399[/C][C]2.32693812153991[/C][/ROW]
[ROW][C]22[/C][C]-7[/C][C]-9.4809672318337[/C][C]2.4809672318337[/C][/ROW]
[ROW][C]23[/C][C]-3[/C][C]-7.51280432888155[/C][C]4.51280432888155[/C][/ROW]
[ROW][C]24[/C][C]-3[/C][C]-3.93277555848065[/C][C]0.93277555848065[/C][/ROW]
[ROW][C]25[/C][C]-6[/C][C]-3.19280034743153[/C][C]-2.80719965256847[/C][/ROW]
[ROW][C]26[/C][C]-4[/C][C]-5.41976495481243[/C][C]1.41976495481243[/C][/ROW]
[ROW][C]27[/C][C]-8[/C][C]-4.29345877909239[/C][C]-3.70654122090761[/C][/ROW]
[ROW][C]28[/C][C]-1[/C][C]-7.2338752568471[/C][C]6.23387525684711[/C][/ROW]
[ROW][C]29[/C][C]-2[/C][C]-2.28851287368921[/C][C]0.288512873689207[/C][/ROW]
[ROW][C]30[/C][C]-2[/C][C]-2.05963426226171[/C][C]0.059634262261711[/C][/ROW]
[ROW][C]31[/C][C]-1[/C][C]-2.01232612323334[/C][C]1.01232612323334[/C][/ROW]
[ROW][C]32[/C][C]1[/C][C]-1.20924307728573[/C][C]2.20924307728573[/C][/ROW]
[ROW][C]33[/C][C]2[/C][C]0.543359783616979[/C][C]1.45664021638302[/C][/ROW]
[ROW][C]34[/C][C]2[/C][C]1.69891927672415[/C][C]0.301080723275850[/C][/ROW]
[ROW][C]35[/C][C]-1[/C][C]1.93776802198047[/C][C]-2.93776802198047[/C][/ROW]
[ROW][C]36[/C][C]1[/C][C]-0.392777083231398[/C][C]1.39277708323140[/C][/ROW]
[ROW][C]37[/C][C]-1[/C][C]0.712119487801458[/C][C]-1.71211948780146[/C][/ROW]
[ROW][C]38[/C][C]-8[/C][C]-0.646112905627483[/C][C]-7.35388709437252[/C][/ROW]
[ROW][C]39[/C][C]1[/C][C]-6.47998591528629[/C][C]7.47998591528629[/C][/ROW]
[ROW][C]40[/C][C]2[/C][C]-0.546078121514249[/C][C]2.54607812151425[/C][/ROW]
[ROW][C]41[/C][C]-2[/C][C]1.47373755459958[/C][C]-3.47373755459958[/C][/ROW]
[ROW][C]42[/C][C]-2[/C][C]-1.28199468637057[/C][C]-0.718005313629425[/C][/ROW]
[ROW][C]43[/C][C]-2[/C][C]-1.85159165817882[/C][C]-0.148408341821181[/C][/ROW]
[ROW][C]44[/C][C]-2[/C][C]-1.96932468951967[/C][C]-0.0306753104803346[/C][/ROW]
[ROW][C]45[/C][C]-6[/C][C]-1.99365955672358[/C][C]-4.00634044327642[/C][/ROW]
[ROW][C]46[/C][C]-4[/C][C]-5.17190815907435[/C][C]1.17190815907435[/C][/ROW]
[ROW][C]47[/C][C]-5[/C][C]-4.24222793808557[/C][C]-0.757772061914432[/C][/ROW]
[ROW][C]48[/C][C]-2[/C][C]-4.84337205720851[/C][C]2.84337205720851[/C][/ROW]
[ROW][C]49[/C][C]-1[/C][C]-2.58771171212918[/C][C]1.58771171212918[/C][/ROW]
[ROW][C]50[/C][C]-5[/C][C]-1.32817258871816[/C][C]-3.67182741128184[/C][/ROW]
[ROW][C]51[/C][C]-9[/C][C]-4.24105043901785[/C][C]-4.75894956098215[/C][/ROW]
[ROW][C]52[/C][C]-8[/C][C]-8.01634737271524[/C][C]0.0163473727152432[/C][/ROW]
[ROW][C]53[/C][C]-14[/C][C]-8.00337892552012[/C][C]-5.99662107447988[/C][/ROW]
[ROW][C]54[/C][C]-10[/C][C]-12.7605264566986[/C][C]2.76052645669858[/C][/ROW]
[ROW][C]55[/C][C]-11[/C][C]-10.5705879137875[/C][C]-0.429412086212521[/C][/ROW]
[ROW][C]56[/C][C]-11[/C][C]-10.9112425291804[/C][C]-0.0887574708195906[/C][/ROW]
[ROW][C]57[/C][C]-11[/C][C]-10.9816542457019[/C][C]-0.0183457542981031[/C][/ROW]
[ROW][C]58[/C][C]-5[/C][C]-10.9962080183487[/C][C]5.99620801834867[/C][/ROW]
[ROW][C]59[/C][C]-2[/C][C]-6.23938816653004[/C][C]4.23938816653004[/C][/ROW]
[ROW][C]60[/C][C]-3[/C][C]-2.87626171587886[/C][C]-0.123738284121136[/C][/ROW]
[ROW][C]61[/C][C]-6[/C][C]-2.97442387511955[/C][C]-3.02557612488045[/C][/ROW]
[ROW][C]62[/C][C]-6[/C][C]-5.37462755884421[/C][C]-0.625372441155792[/C][/ROW]
[ROW][C]63[/C][C]-7[/C][C]-5.87073843988222[/C][C]-1.12926156011778[/C][/ROW]
[ROW][C]64[/C][C]-6[/C][C]-6.76658691455593[/C][C]0.766586914555932[/C][/ROW]
[ROW][C]65[/C][C]-2[/C][C]-6.15844993162513[/C][C]4.15844993162513[/C][/ROW]
[ROW][C]66[/C][C]-2[/C][C]-2.85953216109124[/C][C]0.859532161091237[/C][/ROW]
[ROW][C]67[/C][C]-4[/C][C]-2.17766127958680[/C][C]-1.82233872041320[/C][/ROW]
[ROW][C]68[/C][C]0[/C][C]-3.62333110549563[/C][C]3.62333110549563[/C][/ROW]
[ROW][C]69[/C][C]-6[/C][C]-0.748925601284963[/C][C]-5.25107439871504[/C][/ROW]
[ROW][C]70[/C][C]-4[/C][C]-4.91462746932376[/C][C]0.91462746932376[/C][/ROW]
[ROW][C]71[/C][C]-3[/C][C]-4.18904922224085[/C][C]1.18904922224085[/C][/ROW]
[ROW][C]72[/C][C]-1[/C][C]-3.24577091571164[/C][C]2.24577091571164[/C][/ROW]
[ROW][C]73[/C][C]-3[/C][C]-1.46419034982660[/C][C]-1.53580965017340[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76735&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76735&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
tObservedFittedResiduals
2-15-150
3-10-155
4-12-11.0334766261756-0.966523373824378
5-11-11.80022413690000.80022413690002
6-11-11.16540258823750.165402588237546
7-17-11.0341879417705-5.96581205822951
8-18-15.7668945363326-2.23310546366737
9-19-17.5384275399029-1.46157246009706
10-22-18.6978998050055-3.30210019499446
11-24-21.3174713262367-2.68252867376335
12-24-23.4455338633239-0.554466136676062
13-20-23.88539444154793.88539444154788
14-25-20.8030928677625-4.19690713223752
15-22-24.13251891532062.13251891532055
16-17-22.44078169077225.44078169077224
17-9-18.12458414110759.12458414110748
18-11-10.8860088866815-0.113991113318532
19-13-10.9764385697587-2.02356143024129
20-11-12.58173931204301.58173931204302
21-9-11.32693812153992.32693812153991
22-7-9.48096723183372.4809672318337
23-3-7.512804328881554.51280432888155
24-3-3.932775558480650.93277555848065
25-6-3.19280034743153-2.80719965256847
26-4-5.419764954812431.41976495481243
27-8-4.29345877909239-3.70654122090761
28-1-7.23387525684716.23387525684711
29-2-2.288512873689210.288512873689207
30-2-2.059634262261710.059634262261711
31-1-2.012326123233341.01232612323334
321-1.209243077285732.20924307728573
3320.5433597836169791.45664021638302
3421.698919276724150.301080723275850
35-11.93776802198047-2.93776802198047
361-0.3927770832313981.39277708323140
37-10.712119487801458-1.71211948780146
38-8-0.646112905627483-7.35388709437252
391-6.479985915286297.47998591528629
402-0.5460781215142492.54607812151425
41-21.47373755459958-3.47373755459958
42-2-1.28199468637057-0.718005313629425
43-2-1.85159165817882-0.148408341821181
44-2-1.96932468951967-0.0306753104803346
45-6-1.99365955672358-4.00634044327642
46-4-5.171908159074351.17190815907435
47-5-4.24222793808557-0.757772061914432
48-2-4.843372057208512.84337205720851
49-1-2.587711712129181.58771171212918
50-5-1.32817258871816-3.67182741128184
51-9-4.24105043901785-4.75894956098215
52-8-8.016347372715240.0163473727152432
53-14-8.00337892552012-5.99662107447988
54-10-12.76052645669862.76052645669858
55-11-10.5705879137875-0.429412086212521
56-11-10.9112425291804-0.0887574708195906
57-11-10.9816542457019-0.0183457542981031
58-5-10.99620801834875.99620801834867
59-2-6.239388166530044.23938816653004
60-3-2.87626171587886-0.123738284121136
61-6-2.97442387511955-3.02557612488045
62-6-5.37462755884421-0.625372441155792
63-7-5.87073843988222-1.12926156011778
64-6-6.766586914555930.766586914555932
65-2-6.158449931625134.15844993162513
66-2-2.859532161091240.859532161091237
67-4-2.17766127958680-1.82233872041320
680-3.623331105495633.62333110549563
69-6-0.748925601284963-5.25107439871504
70-4-4.914627469323760.91462746932376
71-3-4.189049222240851.18904922224085
72-1-3.245770915711642.24577091571164
73-3-1.46419034982660-1.53580965017340







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
74-2.68255532485817-8.97920151644913.61409086673277
75-2.68255532485817-10.71992835900415.35481770928781
76-2.68255532485817-12.14569314050676.78058249079036
77-2.68255532485817-13.38314359587858.01803294616215
78-2.68255532485817-14.49162816627289.12651751655651
79-2.68255532485817-15.504638361626310.13952771191
80-2.68255532485817-16.443275706790211.0781650570738
81-2.68255532485817-17.321853035392611.9567423856763
82-2.68255532485817-18.150607868265112.7854972185488
83-2.68255532485817-18.937162718257113.5720520685408
84-2.68255532485817-19.687374451843314.3222638021270
85-2.68255532485817-20.405858785822215.0407481361059

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & -2.68255532485817 & -8.9792015164491 & 3.61409086673277 \tabularnewline
75 & -2.68255532485817 & -10.7199283590041 & 5.35481770928781 \tabularnewline
76 & -2.68255532485817 & -12.1456931405067 & 6.78058249079036 \tabularnewline
77 & -2.68255532485817 & -13.3831435958785 & 8.01803294616215 \tabularnewline
78 & -2.68255532485817 & -14.4916281662728 & 9.12651751655651 \tabularnewline
79 & -2.68255532485817 & -15.5046383616263 & 10.13952771191 \tabularnewline
80 & -2.68255532485817 & -16.4432757067902 & 11.0781650570738 \tabularnewline
81 & -2.68255532485817 & -17.3218530353926 & 11.9567423856763 \tabularnewline
82 & -2.68255532485817 & -18.1506078682651 & 12.7854972185488 \tabularnewline
83 & -2.68255532485817 & -18.9371627182571 & 13.5720520685408 \tabularnewline
84 & -2.68255532485817 & -19.6873744518433 & 14.3222638021270 \tabularnewline
85 & -2.68255532485817 & -20.4058587858222 & 15.0407481361059 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76735&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]74[/C][C]-2.68255532485817[/C][C]-8.9792015164491[/C][C]3.61409086673277[/C][/ROW]
[ROW][C]75[/C][C]-2.68255532485817[/C][C]-10.7199283590041[/C][C]5.35481770928781[/C][/ROW]
[ROW][C]76[/C][C]-2.68255532485817[/C][C]-12.1456931405067[/C][C]6.78058249079036[/C][/ROW]
[ROW][C]77[/C][C]-2.68255532485817[/C][C]-13.3831435958785[/C][C]8.01803294616215[/C][/ROW]
[ROW][C]78[/C][C]-2.68255532485817[/C][C]-14.4916281662728[/C][C]9.12651751655651[/C][/ROW]
[ROW][C]79[/C][C]-2.68255532485817[/C][C]-15.5046383616263[/C][C]10.13952771191[/C][/ROW]
[ROW][C]80[/C][C]-2.68255532485817[/C][C]-16.4432757067902[/C][C]11.0781650570738[/C][/ROW]
[ROW][C]81[/C][C]-2.68255532485817[/C][C]-17.3218530353926[/C][C]11.9567423856763[/C][/ROW]
[ROW][C]82[/C][C]-2.68255532485817[/C][C]-18.1506078682651[/C][C]12.7854972185488[/C][/ROW]
[ROW][C]83[/C][C]-2.68255532485817[/C][C]-18.9371627182571[/C][C]13.5720520685408[/C][/ROW]
[ROW][C]84[/C][C]-2.68255532485817[/C][C]-19.6873744518433[/C][C]14.3222638021270[/C][/ROW]
[ROW][C]85[/C][C]-2.68255532485817[/C][C]-20.4058587858222[/C][C]15.0407481361059[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76735&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76735&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
tForecast95% Lower Bound95% Upper Bound
74-2.68255532485817-8.97920151644913.61409086673277
75-2.68255532485817-10.71992835900415.35481770928781
76-2.68255532485817-12.14569314050676.78058249079036
77-2.68255532485817-13.38314359587858.01803294616215
78-2.68255532485817-14.49162816627289.12651751655651
79-2.68255532485817-15.504638361626310.13952771191
80-2.68255532485817-16.443275706790211.0781650570738
81-2.68255532485817-17.321853035392611.9567423856763
82-2.68255532485817-18.150607868265112.7854972185488
83-2.68255532485817-18.937162718257113.5720520685408
84-2.68255532485817-19.687374451843314.3222638021270
85-2.68255532485817-20.405858785822215.0407481361059



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
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')