Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 Jan 2009 02:19:12 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jan/27/t12330480166tlfidt6kjosplv.htm/, Retrieved Sun, 05 May 2024 20:36:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36985, Retrieved Sun, 05 May 2024 20:36:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact199
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave10 oefening...] [2009-01-27 09:19:12] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
18,33
18,22
18,21
18,06
18,26
18,21
18,05
18,25
18,27
18,28
18,13
18,01
18,02
17,97
18,06
18,08
18,23
18,06
18,23
18,17
18,27
18,33
18,18
18,29
18,33
18,31
18,44
18,63
18,37
18,59
18,72
18,75
18,87
18,83
18,89
18,78
19,27
19,19
19,43
19,36
19,39
19,07
19,31
19,19
19,06
19,05
19,49
19,25
19,76
20,35
19,61
19,33
18,95
18,97
19,28
19,41
18,99
19,37
19,63
19,53
19,86
20,13
19,47
19,49
18,95
19,33
19,65
19,44
19,73
18,89
19,56
19,56




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36985&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36985&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36985&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.649156349220147
beta0.0720630823717081
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.649156349220147 \tabularnewline
beta & 0.0720630823717081 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36985&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]0.649156349220147[/C][/ROW]
[ROW][C]beta[/C][C]0.0720630823717081[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36985&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36985&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
alpha0.649156349220147
beta0.0720630823717081
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
318.2118.110.100000000000001
418.0618.0695936556686-0.00959365566861337
518.2617.95759510072320.302404899276837
618.2118.06227895259500.147721047405039
718.0518.0734592211471-0.0234592211470499
818.2517.97241930427510.277580695724907
918.2718.07978664334380.190213356656173
1018.2818.13933713982880.140662860171201
1118.1318.1733018546951-0.0433018546951089
1218.0118.0858190371272-0.0758190371271752
1318.0217.97368065383800.0463193461619582
1417.9717.94299600616770.0270039938323237
1518.0617.9010359273290.158964072671012
1618.0817.95217494381120.127825056188787
1718.2317.98907955268340.240920447316611
1818.0618.110671061282-0.0506710612819958
1918.2318.04060368793580.189396312064162
2018.1718.13523757300960.0347624269904045
2118.2718.13111608332980.138883916670220
2218.3318.20108273820140.128917261798602
2318.1818.2706102520355-0.0906102520354963
2418.2918.19339132004690.0966086799530856
2518.3318.24222612054420.0877738794558454
2618.3118.28943183449560.0205681655044465
2718.4418.29397271558100.146027284418981
2818.6318.38678736693820.243212633061759
2918.3718.5540680418511-0.184068041851059
3018.5918.43536601255950.154633987440487
3118.7218.54376836609010.176231633909925
3218.7518.67443512135090.0755648786491463
3318.8718.74328835397910.126711646020944
3418.8318.8512714324780-0.0212714324779668
3518.8918.86219527396770.0278047260322580
3618.7818.9062779262021-0.126277926202089
3719.2718.84442953884770.425570461152272
3819.1919.16072531041540.0292746895845646
3919.4319.22113264175310.208867358246859
4019.3619.407894552578-0.0478945525780183
4119.3919.4257373216469-0.0357373216469412
4219.0719.4498002350428-0.379800235042786
4319.3119.23274538988560.0772546101143838
4419.1919.3160045860929-0.126004586092900
4519.0619.2614222638658-0.201422263865759
4619.0519.148459501977-0.0984595019770182
4719.4919.09772971477210.39227028522788
4819.2519.3839107700084-0.133910770008423
4919.7619.32225367879580.437746321204198
5020.3519.65216928164400.697830718356027
5119.6120.1835649880172-0.573564988017171
5219.3319.8627946100923-0.532794610092314
5318.9519.5435663394606-0.593566339460612
5418.9719.1571205583516-0.187120558351609
5519.2819.02576809812240.254231901877581
5619.4119.19281541080920.217184589190754
5718.9919.3459731653846-0.355973165384626
5819.3719.11040942594360.259590574056375
5919.6319.2865864972210.343413502778983
6019.5319.5332427097955-0.00324270979552566
6119.8619.55471314634370.305286853656298
6220.1319.79074889027940.339251109720578
6319.4720.0647029839816-0.594702983981598
6419.4919.7045545189056-0.214554518905569
6518.9519.5811449386728-0.631144938672772
6619.3319.15777795125160.172222048748395
6719.6519.26397832763940.386021672360588
6819.4419.5270262610753-0.0870262610753372
6919.7319.47892101848780.251078981512226
7018.8919.6620444676760-0.772044467676032
7119.5619.14488443341690.415115566583118
7219.5619.41779606526460.142203934735427

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 18.21 & 18.11 & 0.100000000000001 \tabularnewline
4 & 18.06 & 18.0695936556686 & -0.00959365566861337 \tabularnewline
5 & 18.26 & 17.9575951007232 & 0.302404899276837 \tabularnewline
6 & 18.21 & 18.0622789525950 & 0.147721047405039 \tabularnewline
7 & 18.05 & 18.0734592211471 & -0.0234592211470499 \tabularnewline
8 & 18.25 & 17.9724193042751 & 0.277580695724907 \tabularnewline
9 & 18.27 & 18.0797866433438 & 0.190213356656173 \tabularnewline
10 & 18.28 & 18.1393371398288 & 0.140662860171201 \tabularnewline
11 & 18.13 & 18.1733018546951 & -0.0433018546951089 \tabularnewline
12 & 18.01 & 18.0858190371272 & -0.0758190371271752 \tabularnewline
13 & 18.02 & 17.9736806538380 & 0.0463193461619582 \tabularnewline
14 & 17.97 & 17.9429960061677 & 0.0270039938323237 \tabularnewline
15 & 18.06 & 17.901035927329 & 0.158964072671012 \tabularnewline
16 & 18.08 & 17.9521749438112 & 0.127825056188787 \tabularnewline
17 & 18.23 & 17.9890795526834 & 0.240920447316611 \tabularnewline
18 & 18.06 & 18.110671061282 & -0.0506710612819958 \tabularnewline
19 & 18.23 & 18.0406036879358 & 0.189396312064162 \tabularnewline
20 & 18.17 & 18.1352375730096 & 0.0347624269904045 \tabularnewline
21 & 18.27 & 18.1311160833298 & 0.138883916670220 \tabularnewline
22 & 18.33 & 18.2010827382014 & 0.128917261798602 \tabularnewline
23 & 18.18 & 18.2706102520355 & -0.0906102520354963 \tabularnewline
24 & 18.29 & 18.1933913200469 & 0.0966086799530856 \tabularnewline
25 & 18.33 & 18.2422261205442 & 0.0877738794558454 \tabularnewline
26 & 18.31 & 18.2894318344956 & 0.0205681655044465 \tabularnewline
27 & 18.44 & 18.2939727155810 & 0.146027284418981 \tabularnewline
28 & 18.63 & 18.3867873669382 & 0.243212633061759 \tabularnewline
29 & 18.37 & 18.5540680418511 & -0.184068041851059 \tabularnewline
30 & 18.59 & 18.4353660125595 & 0.154633987440487 \tabularnewline
31 & 18.72 & 18.5437683660901 & 0.176231633909925 \tabularnewline
32 & 18.75 & 18.6744351213509 & 0.0755648786491463 \tabularnewline
33 & 18.87 & 18.7432883539791 & 0.126711646020944 \tabularnewline
34 & 18.83 & 18.8512714324780 & -0.0212714324779668 \tabularnewline
35 & 18.89 & 18.8621952739677 & 0.0278047260322580 \tabularnewline
36 & 18.78 & 18.9062779262021 & -0.126277926202089 \tabularnewline
37 & 19.27 & 18.8444295388477 & 0.425570461152272 \tabularnewline
38 & 19.19 & 19.1607253104154 & 0.0292746895845646 \tabularnewline
39 & 19.43 & 19.2211326417531 & 0.208867358246859 \tabularnewline
40 & 19.36 & 19.407894552578 & -0.0478945525780183 \tabularnewline
41 & 19.39 & 19.4257373216469 & -0.0357373216469412 \tabularnewline
42 & 19.07 & 19.4498002350428 & -0.379800235042786 \tabularnewline
43 & 19.31 & 19.2327453898856 & 0.0772546101143838 \tabularnewline
44 & 19.19 & 19.3160045860929 & -0.126004586092900 \tabularnewline
45 & 19.06 & 19.2614222638658 & -0.201422263865759 \tabularnewline
46 & 19.05 & 19.148459501977 & -0.0984595019770182 \tabularnewline
47 & 19.49 & 19.0977297147721 & 0.39227028522788 \tabularnewline
48 & 19.25 & 19.3839107700084 & -0.133910770008423 \tabularnewline
49 & 19.76 & 19.3222536787958 & 0.437746321204198 \tabularnewline
50 & 20.35 & 19.6521692816440 & 0.697830718356027 \tabularnewline
51 & 19.61 & 20.1835649880172 & -0.573564988017171 \tabularnewline
52 & 19.33 & 19.8627946100923 & -0.532794610092314 \tabularnewline
53 & 18.95 & 19.5435663394606 & -0.593566339460612 \tabularnewline
54 & 18.97 & 19.1571205583516 & -0.187120558351609 \tabularnewline
55 & 19.28 & 19.0257680981224 & 0.254231901877581 \tabularnewline
56 & 19.41 & 19.1928154108092 & 0.217184589190754 \tabularnewline
57 & 18.99 & 19.3459731653846 & -0.355973165384626 \tabularnewline
58 & 19.37 & 19.1104094259436 & 0.259590574056375 \tabularnewline
59 & 19.63 & 19.286586497221 & 0.343413502778983 \tabularnewline
60 & 19.53 & 19.5332427097955 & -0.00324270979552566 \tabularnewline
61 & 19.86 & 19.5547131463437 & 0.305286853656298 \tabularnewline
62 & 20.13 & 19.7907488902794 & 0.339251109720578 \tabularnewline
63 & 19.47 & 20.0647029839816 & -0.594702983981598 \tabularnewline
64 & 19.49 & 19.7045545189056 & -0.214554518905569 \tabularnewline
65 & 18.95 & 19.5811449386728 & -0.631144938672772 \tabularnewline
66 & 19.33 & 19.1577779512516 & 0.172222048748395 \tabularnewline
67 & 19.65 & 19.2639783276394 & 0.386021672360588 \tabularnewline
68 & 19.44 & 19.5270262610753 & -0.0870262610753372 \tabularnewline
69 & 19.73 & 19.4789210184878 & 0.251078981512226 \tabularnewline
70 & 18.89 & 19.6620444676760 & -0.772044467676032 \tabularnewline
71 & 19.56 & 19.1448844334169 & 0.415115566583118 \tabularnewline
72 & 19.56 & 19.4177960652646 & 0.142203934735427 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36985&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]18.21[/C][C]18.11[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]4[/C][C]18.06[/C][C]18.0695936556686[/C][C]-0.00959365566861337[/C][/ROW]
[ROW][C]5[/C][C]18.26[/C][C]17.9575951007232[/C][C]0.302404899276837[/C][/ROW]
[ROW][C]6[/C][C]18.21[/C][C]18.0622789525950[/C][C]0.147721047405039[/C][/ROW]
[ROW][C]7[/C][C]18.05[/C][C]18.0734592211471[/C][C]-0.0234592211470499[/C][/ROW]
[ROW][C]8[/C][C]18.25[/C][C]17.9724193042751[/C][C]0.277580695724907[/C][/ROW]
[ROW][C]9[/C][C]18.27[/C][C]18.0797866433438[/C][C]0.190213356656173[/C][/ROW]
[ROW][C]10[/C][C]18.28[/C][C]18.1393371398288[/C][C]0.140662860171201[/C][/ROW]
[ROW][C]11[/C][C]18.13[/C][C]18.1733018546951[/C][C]-0.0433018546951089[/C][/ROW]
[ROW][C]12[/C][C]18.01[/C][C]18.0858190371272[/C][C]-0.0758190371271752[/C][/ROW]
[ROW][C]13[/C][C]18.02[/C][C]17.9736806538380[/C][C]0.0463193461619582[/C][/ROW]
[ROW][C]14[/C][C]17.97[/C][C]17.9429960061677[/C][C]0.0270039938323237[/C][/ROW]
[ROW][C]15[/C][C]18.06[/C][C]17.901035927329[/C][C]0.158964072671012[/C][/ROW]
[ROW][C]16[/C][C]18.08[/C][C]17.9521749438112[/C][C]0.127825056188787[/C][/ROW]
[ROW][C]17[/C][C]18.23[/C][C]17.9890795526834[/C][C]0.240920447316611[/C][/ROW]
[ROW][C]18[/C][C]18.06[/C][C]18.110671061282[/C][C]-0.0506710612819958[/C][/ROW]
[ROW][C]19[/C][C]18.23[/C][C]18.0406036879358[/C][C]0.189396312064162[/C][/ROW]
[ROW][C]20[/C][C]18.17[/C][C]18.1352375730096[/C][C]0.0347624269904045[/C][/ROW]
[ROW][C]21[/C][C]18.27[/C][C]18.1311160833298[/C][C]0.138883916670220[/C][/ROW]
[ROW][C]22[/C][C]18.33[/C][C]18.2010827382014[/C][C]0.128917261798602[/C][/ROW]
[ROW][C]23[/C][C]18.18[/C][C]18.2706102520355[/C][C]-0.0906102520354963[/C][/ROW]
[ROW][C]24[/C][C]18.29[/C][C]18.1933913200469[/C][C]0.0966086799530856[/C][/ROW]
[ROW][C]25[/C][C]18.33[/C][C]18.2422261205442[/C][C]0.0877738794558454[/C][/ROW]
[ROW][C]26[/C][C]18.31[/C][C]18.2894318344956[/C][C]0.0205681655044465[/C][/ROW]
[ROW][C]27[/C][C]18.44[/C][C]18.2939727155810[/C][C]0.146027284418981[/C][/ROW]
[ROW][C]28[/C][C]18.63[/C][C]18.3867873669382[/C][C]0.243212633061759[/C][/ROW]
[ROW][C]29[/C][C]18.37[/C][C]18.5540680418511[/C][C]-0.184068041851059[/C][/ROW]
[ROW][C]30[/C][C]18.59[/C][C]18.4353660125595[/C][C]0.154633987440487[/C][/ROW]
[ROW][C]31[/C][C]18.72[/C][C]18.5437683660901[/C][C]0.176231633909925[/C][/ROW]
[ROW][C]32[/C][C]18.75[/C][C]18.6744351213509[/C][C]0.0755648786491463[/C][/ROW]
[ROW][C]33[/C][C]18.87[/C][C]18.7432883539791[/C][C]0.126711646020944[/C][/ROW]
[ROW][C]34[/C][C]18.83[/C][C]18.8512714324780[/C][C]-0.0212714324779668[/C][/ROW]
[ROW][C]35[/C][C]18.89[/C][C]18.8621952739677[/C][C]0.0278047260322580[/C][/ROW]
[ROW][C]36[/C][C]18.78[/C][C]18.9062779262021[/C][C]-0.126277926202089[/C][/ROW]
[ROW][C]37[/C][C]19.27[/C][C]18.8444295388477[/C][C]0.425570461152272[/C][/ROW]
[ROW][C]38[/C][C]19.19[/C][C]19.1607253104154[/C][C]0.0292746895845646[/C][/ROW]
[ROW][C]39[/C][C]19.43[/C][C]19.2211326417531[/C][C]0.208867358246859[/C][/ROW]
[ROW][C]40[/C][C]19.36[/C][C]19.407894552578[/C][C]-0.0478945525780183[/C][/ROW]
[ROW][C]41[/C][C]19.39[/C][C]19.4257373216469[/C][C]-0.0357373216469412[/C][/ROW]
[ROW][C]42[/C][C]19.07[/C][C]19.4498002350428[/C][C]-0.379800235042786[/C][/ROW]
[ROW][C]43[/C][C]19.31[/C][C]19.2327453898856[/C][C]0.0772546101143838[/C][/ROW]
[ROW][C]44[/C][C]19.19[/C][C]19.3160045860929[/C][C]-0.126004586092900[/C][/ROW]
[ROW][C]45[/C][C]19.06[/C][C]19.2614222638658[/C][C]-0.201422263865759[/C][/ROW]
[ROW][C]46[/C][C]19.05[/C][C]19.148459501977[/C][C]-0.0984595019770182[/C][/ROW]
[ROW][C]47[/C][C]19.49[/C][C]19.0977297147721[/C][C]0.39227028522788[/C][/ROW]
[ROW][C]48[/C][C]19.25[/C][C]19.3839107700084[/C][C]-0.133910770008423[/C][/ROW]
[ROW][C]49[/C][C]19.76[/C][C]19.3222536787958[/C][C]0.437746321204198[/C][/ROW]
[ROW][C]50[/C][C]20.35[/C][C]19.6521692816440[/C][C]0.697830718356027[/C][/ROW]
[ROW][C]51[/C][C]19.61[/C][C]20.1835649880172[/C][C]-0.573564988017171[/C][/ROW]
[ROW][C]52[/C][C]19.33[/C][C]19.8627946100923[/C][C]-0.532794610092314[/C][/ROW]
[ROW][C]53[/C][C]18.95[/C][C]19.5435663394606[/C][C]-0.593566339460612[/C][/ROW]
[ROW][C]54[/C][C]18.97[/C][C]19.1571205583516[/C][C]-0.187120558351609[/C][/ROW]
[ROW][C]55[/C][C]19.28[/C][C]19.0257680981224[/C][C]0.254231901877581[/C][/ROW]
[ROW][C]56[/C][C]19.41[/C][C]19.1928154108092[/C][C]0.217184589190754[/C][/ROW]
[ROW][C]57[/C][C]18.99[/C][C]19.3459731653846[/C][C]-0.355973165384626[/C][/ROW]
[ROW][C]58[/C][C]19.37[/C][C]19.1104094259436[/C][C]0.259590574056375[/C][/ROW]
[ROW][C]59[/C][C]19.63[/C][C]19.286586497221[/C][C]0.343413502778983[/C][/ROW]
[ROW][C]60[/C][C]19.53[/C][C]19.5332427097955[/C][C]-0.00324270979552566[/C][/ROW]
[ROW][C]61[/C][C]19.86[/C][C]19.5547131463437[/C][C]0.305286853656298[/C][/ROW]
[ROW][C]62[/C][C]20.13[/C][C]19.7907488902794[/C][C]0.339251109720578[/C][/ROW]
[ROW][C]63[/C][C]19.47[/C][C]20.0647029839816[/C][C]-0.594702983981598[/C][/ROW]
[ROW][C]64[/C][C]19.49[/C][C]19.7045545189056[/C][C]-0.214554518905569[/C][/ROW]
[ROW][C]65[/C][C]18.95[/C][C]19.5811449386728[/C][C]-0.631144938672772[/C][/ROW]
[ROW][C]66[/C][C]19.33[/C][C]19.1577779512516[/C][C]0.172222048748395[/C][/ROW]
[ROW][C]67[/C][C]19.65[/C][C]19.2639783276394[/C][C]0.386021672360588[/C][/ROW]
[ROW][C]68[/C][C]19.44[/C][C]19.5270262610753[/C][C]-0.0870262610753372[/C][/ROW]
[ROW][C]69[/C][C]19.73[/C][C]19.4789210184878[/C][C]0.251078981512226[/C][/ROW]
[ROW][C]70[/C][C]18.89[/C][C]19.6620444676760[/C][C]-0.772044467676032[/C][/ROW]
[ROW][C]71[/C][C]19.56[/C][C]19.1448844334169[/C][C]0.415115566583118[/C][/ROW]
[ROW][C]72[/C][C]19.56[/C][C]19.4177960652646[/C][C]0.142203934735427[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36985&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36985&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
318.2118.110.100000000000001
418.0618.0695936556686-0.00959365566861337
518.2617.95759510072320.302404899276837
618.2118.06227895259500.147721047405039
718.0518.0734592211471-0.0234592211470499
818.2517.97241930427510.277580695724907
918.2718.07978664334380.190213356656173
1018.2818.13933713982880.140662860171201
1118.1318.1733018546951-0.0433018546951089
1218.0118.0858190371272-0.0758190371271752
1318.0217.97368065383800.0463193461619582
1417.9717.94299600616770.0270039938323237
1518.0617.9010359273290.158964072671012
1618.0817.95217494381120.127825056188787
1718.2317.98907955268340.240920447316611
1818.0618.110671061282-0.0506710612819958
1918.2318.04060368793580.189396312064162
2018.1718.13523757300960.0347624269904045
2118.2718.13111608332980.138883916670220
2218.3318.20108273820140.128917261798602
2318.1818.2706102520355-0.0906102520354963
2418.2918.19339132004690.0966086799530856
2518.3318.24222612054420.0877738794558454
2618.3118.28943183449560.0205681655044465
2718.4418.29397271558100.146027284418981
2818.6318.38678736693820.243212633061759
2918.3718.5540680418511-0.184068041851059
3018.5918.43536601255950.154633987440487
3118.7218.54376836609010.176231633909925
3218.7518.67443512135090.0755648786491463
3318.8718.74328835397910.126711646020944
3418.8318.8512714324780-0.0212714324779668
3518.8918.86219527396770.0278047260322580
3618.7818.9062779262021-0.126277926202089
3719.2718.84442953884770.425570461152272
3819.1919.16072531041540.0292746895845646
3919.4319.22113264175310.208867358246859
4019.3619.407894552578-0.0478945525780183
4119.3919.4257373216469-0.0357373216469412
4219.0719.4498002350428-0.379800235042786
4319.3119.23274538988560.0772546101143838
4419.1919.3160045860929-0.126004586092900
4519.0619.2614222638658-0.201422263865759
4619.0519.148459501977-0.0984595019770182
4719.4919.09772971477210.39227028522788
4819.2519.3839107700084-0.133910770008423
4919.7619.32225367879580.437746321204198
5020.3519.65216928164400.697830718356027
5119.6120.1835649880172-0.573564988017171
5219.3319.8627946100923-0.532794610092314
5318.9519.5435663394606-0.593566339460612
5418.9719.1571205583516-0.187120558351609
5519.2819.02576809812240.254231901877581
5619.4119.19281541080920.217184589190754
5718.9919.3459731653846-0.355973165384626
5819.3719.11040942594360.259590574056375
5919.6319.2865864972210.343413502778983
6019.5319.5332427097955-0.00324270979552566
6119.8619.55471314634370.305286853656298
6220.1319.79074889027940.339251109720578
6319.4720.0647029839816-0.594702983981598
6419.4919.7045545189056-0.214554518905569
6518.9519.5811449386728-0.631144938672772
6619.3319.15777795125160.172222048748395
6719.6519.26397832763940.386021672360588
6819.4419.5270262610753-0.0870262610753372
6919.7319.47892101848780.251078981512226
7018.8919.6620444676760-0.772044467676032
7119.5619.14488443341690.415115566583118
7219.5619.41779606526460.142203934735427







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7319.520197708091718.974612487516420.065782928667
7419.530286763801218.865583988734820.1949895388676
7519.540375819510818.761897040029620.3188545989919
7619.550464875220318.660765863837420.4401638866032
7719.560553930929918.560684966204120.5604228956557
7819.570642986639418.460754315383620.6805316578952
7919.580732042349018.360399348401420.8010647362965
8019.590821098058518.259236397106820.9224057990102
8119.600910153768018.157001062641721.0448192448944
8219.610999209477618.053507112552321.1684913064028
8319.621088265187117.948621486255121.2935550441191
8419.631177320896717.842248380843821.4201062609495

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 19.5201977080917 & 18.9746124875164 & 20.065782928667 \tabularnewline
74 & 19.5302867638012 & 18.8655839887348 & 20.1949895388676 \tabularnewline
75 & 19.5403758195108 & 18.7618970400296 & 20.3188545989919 \tabularnewline
76 & 19.5504648752203 & 18.6607658638374 & 20.4401638866032 \tabularnewline
77 & 19.5605539309299 & 18.5606849662041 & 20.5604228956557 \tabularnewline
78 & 19.5706429866394 & 18.4607543153836 & 20.6805316578952 \tabularnewline
79 & 19.5807320423490 & 18.3603993484014 & 20.8010647362965 \tabularnewline
80 & 19.5908210980585 & 18.2592363971068 & 20.9224057990102 \tabularnewline
81 & 19.6009101537680 & 18.1570010626417 & 21.0448192448944 \tabularnewline
82 & 19.6109992094776 & 18.0535071125523 & 21.1684913064028 \tabularnewline
83 & 19.6210882651871 & 17.9486214862551 & 21.2935550441191 \tabularnewline
84 & 19.6311773208967 & 17.8422483808438 & 21.4201062609495 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36985&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]19.5201977080917[/C][C]18.9746124875164[/C][C]20.065782928667[/C][/ROW]
[ROW][C]74[/C][C]19.5302867638012[/C][C]18.8655839887348[/C][C]20.1949895388676[/C][/ROW]
[ROW][C]75[/C][C]19.5403758195108[/C][C]18.7618970400296[/C][C]20.3188545989919[/C][/ROW]
[ROW][C]76[/C][C]19.5504648752203[/C][C]18.6607658638374[/C][C]20.4401638866032[/C][/ROW]
[ROW][C]77[/C][C]19.5605539309299[/C][C]18.5606849662041[/C][C]20.5604228956557[/C][/ROW]
[ROW][C]78[/C][C]19.5706429866394[/C][C]18.4607543153836[/C][C]20.6805316578952[/C][/ROW]
[ROW][C]79[/C][C]19.5807320423490[/C][C]18.3603993484014[/C][C]20.8010647362965[/C][/ROW]
[ROW][C]80[/C][C]19.5908210980585[/C][C]18.2592363971068[/C][C]20.9224057990102[/C][/ROW]
[ROW][C]81[/C][C]19.6009101537680[/C][C]18.1570010626417[/C][C]21.0448192448944[/C][/ROW]
[ROW][C]82[/C][C]19.6109992094776[/C][C]18.0535071125523[/C][C]21.1684913064028[/C][/ROW]
[ROW][C]83[/C][C]19.6210882651871[/C][C]17.9486214862551[/C][C]21.2935550441191[/C][/ROW]
[ROW][C]84[/C][C]19.6311773208967[/C][C]17.8422483808438[/C][C]21.4201062609495[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36985&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36985&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
7319.520197708091718.974612487516420.065782928667
7419.530286763801218.865583988734820.1949895388676
7519.540375819510818.761897040029620.3188545989919
7619.550464875220318.660765863837420.4401638866032
7719.560553930929918.560684966204120.5604228956557
7819.570642986639418.460754315383620.6805316578952
7919.580732042349018.360399348401420.8010647362965
8019.590821098058518.259236397106820.9224057990102
8119.600910153768018.157001062641721.0448192448944
8219.610999209477618.053507112552321.1684913064028
8319.621088265187117.948621486255121.2935550441191
8419.631177320896717.842248380843821.4201062609495



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')