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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 01 Jun 2009 09:25:49 -0600
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/Jun/01/t1243869991wd0it4hwgesshmj.htm/, Retrieved Sun, 12 May 2024 22:54:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40977, Retrieved Sun, 12 May 2024 22:54:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Datareeks - Aardo...] [2009-06-01 15:25:49] [900fe54243512ff0c75e5ed1f9ef5c37] [Current]
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Dataseries X:
493395.00
487190.00
519493.00
519453.00
538588.00
438224.00
542034.00
512027.00
619880.00
533737.00
573789.00
589213.00
532168.00
551102.00
593789.00
527106.00
547327.00
601305.00
610872.00
601325.00
642143.00
614216.00
657979.00
673098.00
602297.00
615381.00
703671.00
733852.00
716596.00
745798.00
742027.10
679181.20
739022.70
645410.60
729382.10
671052.70
744954.80
677639.30
778207.20
763316.20
658531.60
831700.10
664156.30
621402.10
683588.70
600023.80
643273.80
653615.90
620177.50
574128.80
599828.00
599369.40
596617.70
616114.60
510226.90
493960.10
634503.30
588556.20
603239.00
617458.20
646543.50
680125.60
731595.80
759600.30
785031.70
849573.30
762342.00
815346.60
929603.20
784057.50
944667.70
1007258.30
664292.70
873207.40
1146510.00
1417266.80
1089387.90
1373379.70
1009397.60
818175.10
1003458.10
961142.70
1121906.60
1141713.30
1042352.60
992223.60
920525.30
1076093.40
967880.40
1236416.10




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40977&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40977&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40977&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.496602762806755
beta0
gamma0.507424910716124

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.496602762806755 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.507424910716124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40977&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]0.496602762806755[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.507424910716124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40977&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40977&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
alpha0.496602762806755
beta0
gamma0.507424910716124







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13532168498335.78712606933832.2128739315
14551102533020.21464982418081.7853501763
15593789585576.5613498958212.43865010526
16527106524229.2215449462876.77845505386
17547327544555.886479072771.11352092994
18601305598445.161248312859.83875169035
19610872606472.4555456094399.54445439111
20601325579909.99694877921415.0030512213
21642143698177.337101558-56034.3371015583
22614216586331.24595690827884.7540430925
23657979645086.14899358912892.8510064112
24673098665291.8648958567806.13510414364
25602297616640.353841763-14343.3538417629
26615381623377.430933972-7996.43093397166
27703671660462.2739921643208.7260078394
28733852615131.265888698118720.734111302
29716596692959.36859656323636.6314034375
30745798757233.180838146-11435.1808381460
31742027.1758554.825637675-16527.7256376750
32679181.2725946.192650208-46764.9926502083
33739022.7790571.785827685-51549.0858276851
34645410.6702389.064842577-56978.4648425775
35729382.1715171.18270623414210.9172937659
36671052.7734732.122088612-63679.422088612
37744954.8644922.902369835100031.897630165
38677639.3710080.279831851-32440.9798318512
39778207.2748105.54810655630101.6518934442
40763316.2715554.03860045147762.1613995489
41658531.6733855.98684741-75324.3868474098
42831700.1740026.87012748891673.2298725117
43664156.3791251.615762852-127095.315762852
44621402.1696011.11649086-74609.0164908601
45683588.7745587.259450212-61998.5594502125
46600023.8650828.440517532-50804.6405175315
47643273.8684860.848837695-41587.0488376948
48653615.9656816.344127681-3200.44412768132
49620177.5638858.965428205-18681.4654282050
50574128.8611224.57739083-37095.7773908296
51599828662913.918661127-63085.9186611273
52599369.4588596.33932983510773.0606701651
53596617.7557088.62572611539529.0742738849
54616114.6662953.308129673-46838.7081296729
55510226.9589511.215225406-79284.3152254063
56493960.1531420.696901841-37460.5969018411
57634503.3602666.0161272931837.2838727098
58588556.2557365.6694528931190.53054711
59603239634471.613757007-31232.6137570074
60617458.2621374.482320561-3916.28232056089
61646543.5599107.20162438447436.2983756161
62680125.6599603.39408210880522.2059178918
63731595.8703063.3253451228532.4746548806
64759600.3693109.95752307466490.342476926
65785031.7696616.92966480188414.7703351992
66849573.3804696.91717862644876.3828213738
67762342768513.006064364-6171.00606436364
68815346.6757414.05485103557932.5451489652
69929603.2893733.06610555935870.1338944414
70784057.5850270.239618636-66212.7396186361
71944667.7863060.31395288381607.386047117
721007258.3912977.42075510294280.879244898
73664292.7952592.434904953-288299.734904953
74873207.4794812.52740488678394.8725951145
751146510883935.954567406262574.045432594
761417266.8999904.094646863417362.705353137
771089387.91183255.54627635-93867.6462763508
781373379.71189692.29755638183687.40244362
791009397.61209402.96624799-200005.366247988
80818175.11118419.71005999-300244.610059994
811003458.11071231.41580464-67773.3158046413
82961142.7950223.2945369110919.4054630904
831121906.61039076.0309102482830.569089763
841141713.31092837.8439777648875.4560222351
851042352.61012179.4236912130173.1763087875
86992223.61106221.15686581-113997.556865809
87920525.31146848.01811857-226322.718118569
881076093.41059567.3169750116526.0830249907
89967880.4913275.4060064354604.9939935703
901236416.11064341.71482013172074.385179875

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 532168 & 498335.787126069 & 33832.2128739315 \tabularnewline
14 & 551102 & 533020.214649824 & 18081.7853501763 \tabularnewline
15 & 593789 & 585576.561349895 & 8212.43865010526 \tabularnewline
16 & 527106 & 524229.221544946 & 2876.77845505386 \tabularnewline
17 & 547327 & 544555.88647907 & 2771.11352092994 \tabularnewline
18 & 601305 & 598445.16124831 & 2859.83875169035 \tabularnewline
19 & 610872 & 606472.455545609 & 4399.54445439111 \tabularnewline
20 & 601325 & 579909.996948779 & 21415.0030512213 \tabularnewline
21 & 642143 & 698177.337101558 & -56034.3371015583 \tabularnewline
22 & 614216 & 586331.245956908 & 27884.7540430925 \tabularnewline
23 & 657979 & 645086.148993589 & 12892.8510064112 \tabularnewline
24 & 673098 & 665291.864895856 & 7806.13510414364 \tabularnewline
25 & 602297 & 616640.353841763 & -14343.3538417629 \tabularnewline
26 & 615381 & 623377.430933972 & -7996.43093397166 \tabularnewline
27 & 703671 & 660462.27399216 & 43208.7260078394 \tabularnewline
28 & 733852 & 615131.265888698 & 118720.734111302 \tabularnewline
29 & 716596 & 692959.368596563 & 23636.6314034375 \tabularnewline
30 & 745798 & 757233.180838146 & -11435.1808381460 \tabularnewline
31 & 742027.1 & 758554.825637675 & -16527.7256376750 \tabularnewline
32 & 679181.2 & 725946.192650208 & -46764.9926502083 \tabularnewline
33 & 739022.7 & 790571.785827685 & -51549.0858276851 \tabularnewline
34 & 645410.6 & 702389.064842577 & -56978.4648425775 \tabularnewline
35 & 729382.1 & 715171.182706234 & 14210.9172937659 \tabularnewline
36 & 671052.7 & 734732.122088612 & -63679.422088612 \tabularnewline
37 & 744954.8 & 644922.902369835 & 100031.897630165 \tabularnewline
38 & 677639.3 & 710080.279831851 & -32440.9798318512 \tabularnewline
39 & 778207.2 & 748105.548106556 & 30101.6518934442 \tabularnewline
40 & 763316.2 & 715554.038600451 & 47762.1613995489 \tabularnewline
41 & 658531.6 & 733855.98684741 & -75324.3868474098 \tabularnewline
42 & 831700.1 & 740026.870127488 & 91673.2298725117 \tabularnewline
43 & 664156.3 & 791251.615762852 & -127095.315762852 \tabularnewline
44 & 621402.1 & 696011.11649086 & -74609.0164908601 \tabularnewline
45 & 683588.7 & 745587.259450212 & -61998.5594502125 \tabularnewline
46 & 600023.8 & 650828.440517532 & -50804.6405175315 \tabularnewline
47 & 643273.8 & 684860.848837695 & -41587.0488376948 \tabularnewline
48 & 653615.9 & 656816.344127681 & -3200.44412768132 \tabularnewline
49 & 620177.5 & 638858.965428205 & -18681.4654282050 \tabularnewline
50 & 574128.8 & 611224.57739083 & -37095.7773908296 \tabularnewline
51 & 599828 & 662913.918661127 & -63085.9186611273 \tabularnewline
52 & 599369.4 & 588596.339329835 & 10773.0606701651 \tabularnewline
53 & 596617.7 & 557088.625726115 & 39529.0742738849 \tabularnewline
54 & 616114.6 & 662953.308129673 & -46838.7081296729 \tabularnewline
55 & 510226.9 & 589511.215225406 & -79284.3152254063 \tabularnewline
56 & 493960.1 & 531420.696901841 & -37460.5969018411 \tabularnewline
57 & 634503.3 & 602666.01612729 & 31837.2838727098 \tabularnewline
58 & 588556.2 & 557365.66945289 & 31190.53054711 \tabularnewline
59 & 603239 & 634471.613757007 & -31232.6137570074 \tabularnewline
60 & 617458.2 & 621374.482320561 & -3916.28232056089 \tabularnewline
61 & 646543.5 & 599107.201624384 & 47436.2983756161 \tabularnewline
62 & 680125.6 & 599603.394082108 & 80522.2059178918 \tabularnewline
63 & 731595.8 & 703063.32534512 & 28532.4746548806 \tabularnewline
64 & 759600.3 & 693109.957523074 & 66490.342476926 \tabularnewline
65 & 785031.7 & 696616.929664801 & 88414.7703351992 \tabularnewline
66 & 849573.3 & 804696.917178626 & 44876.3828213738 \tabularnewline
67 & 762342 & 768513.006064364 & -6171.00606436364 \tabularnewline
68 & 815346.6 & 757414.054851035 & 57932.5451489652 \tabularnewline
69 & 929603.2 & 893733.066105559 & 35870.1338944414 \tabularnewline
70 & 784057.5 & 850270.239618636 & -66212.7396186361 \tabularnewline
71 & 944667.7 & 863060.313952883 & 81607.386047117 \tabularnewline
72 & 1007258.3 & 912977.420755102 & 94280.879244898 \tabularnewline
73 & 664292.7 & 952592.434904953 & -288299.734904953 \tabularnewline
74 & 873207.4 & 794812.527404886 & 78394.8725951145 \tabularnewline
75 & 1146510 & 883935.954567406 & 262574.045432594 \tabularnewline
76 & 1417266.8 & 999904.094646863 & 417362.705353137 \tabularnewline
77 & 1089387.9 & 1183255.54627635 & -93867.6462763508 \tabularnewline
78 & 1373379.7 & 1189692.29755638 & 183687.40244362 \tabularnewline
79 & 1009397.6 & 1209402.96624799 & -200005.366247988 \tabularnewline
80 & 818175.1 & 1118419.71005999 & -300244.610059994 \tabularnewline
81 & 1003458.1 & 1071231.41580464 & -67773.3158046413 \tabularnewline
82 & 961142.7 & 950223.29453691 & 10919.4054630904 \tabularnewline
83 & 1121906.6 & 1039076.03091024 & 82830.569089763 \tabularnewline
84 & 1141713.3 & 1092837.84397776 & 48875.4560222351 \tabularnewline
85 & 1042352.6 & 1012179.42369121 & 30173.1763087875 \tabularnewline
86 & 992223.6 & 1106221.15686581 & -113997.556865809 \tabularnewline
87 & 920525.3 & 1146848.01811857 & -226322.718118569 \tabularnewline
88 & 1076093.4 & 1059567.31697501 & 16526.0830249907 \tabularnewline
89 & 967880.4 & 913275.40600643 & 54604.9939935703 \tabularnewline
90 & 1236416.1 & 1064341.71482013 & 172074.385179875 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40977&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]532168[/C][C]498335.787126069[/C][C]33832.2128739315[/C][/ROW]
[ROW][C]14[/C][C]551102[/C][C]533020.214649824[/C][C]18081.7853501763[/C][/ROW]
[ROW][C]15[/C][C]593789[/C][C]585576.561349895[/C][C]8212.43865010526[/C][/ROW]
[ROW][C]16[/C][C]527106[/C][C]524229.221544946[/C][C]2876.77845505386[/C][/ROW]
[ROW][C]17[/C][C]547327[/C][C]544555.88647907[/C][C]2771.11352092994[/C][/ROW]
[ROW][C]18[/C][C]601305[/C][C]598445.16124831[/C][C]2859.83875169035[/C][/ROW]
[ROW][C]19[/C][C]610872[/C][C]606472.455545609[/C][C]4399.54445439111[/C][/ROW]
[ROW][C]20[/C][C]601325[/C][C]579909.996948779[/C][C]21415.0030512213[/C][/ROW]
[ROW][C]21[/C][C]642143[/C][C]698177.337101558[/C][C]-56034.3371015583[/C][/ROW]
[ROW][C]22[/C][C]614216[/C][C]586331.245956908[/C][C]27884.7540430925[/C][/ROW]
[ROW][C]23[/C][C]657979[/C][C]645086.148993589[/C][C]12892.8510064112[/C][/ROW]
[ROW][C]24[/C][C]673098[/C][C]665291.864895856[/C][C]7806.13510414364[/C][/ROW]
[ROW][C]25[/C][C]602297[/C][C]616640.353841763[/C][C]-14343.3538417629[/C][/ROW]
[ROW][C]26[/C][C]615381[/C][C]623377.430933972[/C][C]-7996.43093397166[/C][/ROW]
[ROW][C]27[/C][C]703671[/C][C]660462.27399216[/C][C]43208.7260078394[/C][/ROW]
[ROW][C]28[/C][C]733852[/C][C]615131.265888698[/C][C]118720.734111302[/C][/ROW]
[ROW][C]29[/C][C]716596[/C][C]692959.368596563[/C][C]23636.6314034375[/C][/ROW]
[ROW][C]30[/C][C]745798[/C][C]757233.180838146[/C][C]-11435.1808381460[/C][/ROW]
[ROW][C]31[/C][C]742027.1[/C][C]758554.825637675[/C][C]-16527.7256376750[/C][/ROW]
[ROW][C]32[/C][C]679181.2[/C][C]725946.192650208[/C][C]-46764.9926502083[/C][/ROW]
[ROW][C]33[/C][C]739022.7[/C][C]790571.785827685[/C][C]-51549.0858276851[/C][/ROW]
[ROW][C]34[/C][C]645410.6[/C][C]702389.064842577[/C][C]-56978.4648425775[/C][/ROW]
[ROW][C]35[/C][C]729382.1[/C][C]715171.182706234[/C][C]14210.9172937659[/C][/ROW]
[ROW][C]36[/C][C]671052.7[/C][C]734732.122088612[/C][C]-63679.422088612[/C][/ROW]
[ROW][C]37[/C][C]744954.8[/C][C]644922.902369835[/C][C]100031.897630165[/C][/ROW]
[ROW][C]38[/C][C]677639.3[/C][C]710080.279831851[/C][C]-32440.9798318512[/C][/ROW]
[ROW][C]39[/C][C]778207.2[/C][C]748105.548106556[/C][C]30101.6518934442[/C][/ROW]
[ROW][C]40[/C][C]763316.2[/C][C]715554.038600451[/C][C]47762.1613995489[/C][/ROW]
[ROW][C]41[/C][C]658531.6[/C][C]733855.98684741[/C][C]-75324.3868474098[/C][/ROW]
[ROW][C]42[/C][C]831700.1[/C][C]740026.870127488[/C][C]91673.2298725117[/C][/ROW]
[ROW][C]43[/C][C]664156.3[/C][C]791251.615762852[/C][C]-127095.315762852[/C][/ROW]
[ROW][C]44[/C][C]621402.1[/C][C]696011.11649086[/C][C]-74609.0164908601[/C][/ROW]
[ROW][C]45[/C][C]683588.7[/C][C]745587.259450212[/C][C]-61998.5594502125[/C][/ROW]
[ROW][C]46[/C][C]600023.8[/C][C]650828.440517532[/C][C]-50804.6405175315[/C][/ROW]
[ROW][C]47[/C][C]643273.8[/C][C]684860.848837695[/C][C]-41587.0488376948[/C][/ROW]
[ROW][C]48[/C][C]653615.9[/C][C]656816.344127681[/C][C]-3200.44412768132[/C][/ROW]
[ROW][C]49[/C][C]620177.5[/C][C]638858.965428205[/C][C]-18681.4654282050[/C][/ROW]
[ROW][C]50[/C][C]574128.8[/C][C]611224.57739083[/C][C]-37095.7773908296[/C][/ROW]
[ROW][C]51[/C][C]599828[/C][C]662913.918661127[/C][C]-63085.9186611273[/C][/ROW]
[ROW][C]52[/C][C]599369.4[/C][C]588596.339329835[/C][C]10773.0606701651[/C][/ROW]
[ROW][C]53[/C][C]596617.7[/C][C]557088.625726115[/C][C]39529.0742738849[/C][/ROW]
[ROW][C]54[/C][C]616114.6[/C][C]662953.308129673[/C][C]-46838.7081296729[/C][/ROW]
[ROW][C]55[/C][C]510226.9[/C][C]589511.215225406[/C][C]-79284.3152254063[/C][/ROW]
[ROW][C]56[/C][C]493960.1[/C][C]531420.696901841[/C][C]-37460.5969018411[/C][/ROW]
[ROW][C]57[/C][C]634503.3[/C][C]602666.01612729[/C][C]31837.2838727098[/C][/ROW]
[ROW][C]58[/C][C]588556.2[/C][C]557365.66945289[/C][C]31190.53054711[/C][/ROW]
[ROW][C]59[/C][C]603239[/C][C]634471.613757007[/C][C]-31232.6137570074[/C][/ROW]
[ROW][C]60[/C][C]617458.2[/C][C]621374.482320561[/C][C]-3916.28232056089[/C][/ROW]
[ROW][C]61[/C][C]646543.5[/C][C]599107.201624384[/C][C]47436.2983756161[/C][/ROW]
[ROW][C]62[/C][C]680125.6[/C][C]599603.394082108[/C][C]80522.2059178918[/C][/ROW]
[ROW][C]63[/C][C]731595.8[/C][C]703063.32534512[/C][C]28532.4746548806[/C][/ROW]
[ROW][C]64[/C][C]759600.3[/C][C]693109.957523074[/C][C]66490.342476926[/C][/ROW]
[ROW][C]65[/C][C]785031.7[/C][C]696616.929664801[/C][C]88414.7703351992[/C][/ROW]
[ROW][C]66[/C][C]849573.3[/C][C]804696.917178626[/C][C]44876.3828213738[/C][/ROW]
[ROW][C]67[/C][C]762342[/C][C]768513.006064364[/C][C]-6171.00606436364[/C][/ROW]
[ROW][C]68[/C][C]815346.6[/C][C]757414.054851035[/C][C]57932.5451489652[/C][/ROW]
[ROW][C]69[/C][C]929603.2[/C][C]893733.066105559[/C][C]35870.1338944414[/C][/ROW]
[ROW][C]70[/C][C]784057.5[/C][C]850270.239618636[/C][C]-66212.7396186361[/C][/ROW]
[ROW][C]71[/C][C]944667.7[/C][C]863060.313952883[/C][C]81607.386047117[/C][/ROW]
[ROW][C]72[/C][C]1007258.3[/C][C]912977.420755102[/C][C]94280.879244898[/C][/ROW]
[ROW][C]73[/C][C]664292.7[/C][C]952592.434904953[/C][C]-288299.734904953[/C][/ROW]
[ROW][C]74[/C][C]873207.4[/C][C]794812.527404886[/C][C]78394.8725951145[/C][/ROW]
[ROW][C]75[/C][C]1146510[/C][C]883935.954567406[/C][C]262574.045432594[/C][/ROW]
[ROW][C]76[/C][C]1417266.8[/C][C]999904.094646863[/C][C]417362.705353137[/C][/ROW]
[ROW][C]77[/C][C]1089387.9[/C][C]1183255.54627635[/C][C]-93867.6462763508[/C][/ROW]
[ROW][C]78[/C][C]1373379.7[/C][C]1189692.29755638[/C][C]183687.40244362[/C][/ROW]
[ROW][C]79[/C][C]1009397.6[/C][C]1209402.96624799[/C][C]-200005.366247988[/C][/ROW]
[ROW][C]80[/C][C]818175.1[/C][C]1118419.71005999[/C][C]-300244.610059994[/C][/ROW]
[ROW][C]81[/C][C]1003458.1[/C][C]1071231.41580464[/C][C]-67773.3158046413[/C][/ROW]
[ROW][C]82[/C][C]961142.7[/C][C]950223.29453691[/C][C]10919.4054630904[/C][/ROW]
[ROW][C]83[/C][C]1121906.6[/C][C]1039076.03091024[/C][C]82830.569089763[/C][/ROW]
[ROW][C]84[/C][C]1141713.3[/C][C]1092837.84397776[/C][C]48875.4560222351[/C][/ROW]
[ROW][C]85[/C][C]1042352.6[/C][C]1012179.42369121[/C][C]30173.1763087875[/C][/ROW]
[ROW][C]86[/C][C]992223.6[/C][C]1106221.15686581[/C][C]-113997.556865809[/C][/ROW]
[ROW][C]87[/C][C]920525.3[/C][C]1146848.01811857[/C][C]-226322.718118569[/C][/ROW]
[ROW][C]88[/C][C]1076093.4[/C][C]1059567.31697501[/C][C]16526.0830249907[/C][/ROW]
[ROW][C]89[/C][C]967880.4[/C][C]913275.40600643[/C][C]54604.9939935703[/C][/ROW]
[ROW][C]90[/C][C]1236416.1[/C][C]1064341.71482013[/C][C]172074.385179875[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40977&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40977&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
13532168498335.78712606933832.2128739315
14551102533020.21464982418081.7853501763
15593789585576.5613498958212.43865010526
16527106524229.2215449462876.77845505386
17547327544555.886479072771.11352092994
18601305598445.161248312859.83875169035
19610872606472.4555456094399.54445439111
20601325579909.99694877921415.0030512213
21642143698177.337101558-56034.3371015583
22614216586331.24595690827884.7540430925
23657979645086.14899358912892.8510064112
24673098665291.8648958567806.13510414364
25602297616640.353841763-14343.3538417629
26615381623377.430933972-7996.43093397166
27703671660462.2739921643208.7260078394
28733852615131.265888698118720.734111302
29716596692959.36859656323636.6314034375
30745798757233.180838146-11435.1808381460
31742027.1758554.825637675-16527.7256376750
32679181.2725946.192650208-46764.9926502083
33739022.7790571.785827685-51549.0858276851
34645410.6702389.064842577-56978.4648425775
35729382.1715171.18270623414210.9172937659
36671052.7734732.122088612-63679.422088612
37744954.8644922.902369835100031.897630165
38677639.3710080.279831851-32440.9798318512
39778207.2748105.54810655630101.6518934442
40763316.2715554.03860045147762.1613995489
41658531.6733855.98684741-75324.3868474098
42831700.1740026.87012748891673.2298725117
43664156.3791251.615762852-127095.315762852
44621402.1696011.11649086-74609.0164908601
45683588.7745587.259450212-61998.5594502125
46600023.8650828.440517532-50804.6405175315
47643273.8684860.848837695-41587.0488376948
48653615.9656816.344127681-3200.44412768132
49620177.5638858.965428205-18681.4654282050
50574128.8611224.57739083-37095.7773908296
51599828662913.918661127-63085.9186611273
52599369.4588596.33932983510773.0606701651
53596617.7557088.62572611539529.0742738849
54616114.6662953.308129673-46838.7081296729
55510226.9589511.215225406-79284.3152254063
56493960.1531420.696901841-37460.5969018411
57634503.3602666.0161272931837.2838727098
58588556.2557365.6694528931190.53054711
59603239634471.613757007-31232.6137570074
60617458.2621374.482320561-3916.28232056089
61646543.5599107.20162438447436.2983756161
62680125.6599603.39408210880522.2059178918
63731595.8703063.3253451228532.4746548806
64759600.3693109.95752307466490.342476926
65785031.7696616.92966480188414.7703351992
66849573.3804696.91717862644876.3828213738
67762342768513.006064364-6171.00606436364
68815346.6757414.05485103557932.5451489652
69929603.2893733.06610555935870.1338944414
70784057.5850270.239618636-66212.7396186361
71944667.7863060.31395288381607.386047117
721007258.3912977.42075510294280.879244898
73664292.7952592.434904953-288299.734904953
74873207.4794812.52740488678394.8725951145
751146510883935.954567406262574.045432594
761417266.8999904.094646863417362.705353137
771089387.91183255.54627635-93867.6462763508
781373379.71189692.29755638183687.40244362
791009397.61209402.96624799-200005.366247988
80818175.11118419.71005999-300244.610059994
811003458.11071231.41580464-67773.3158046413
82961142.7950223.2945369110919.4054630904
831121906.61039076.0309102482830.569089763
841141713.31092837.8439777648875.4560222351
851042352.61012179.4236912130173.1763087875
86992223.61106221.15686581-113997.556865809
87920525.31146848.01811857-226322.718118569
881076093.41059567.3169750116526.0830249907
89967880.4913275.4060064354604.9939935703
901236416.11064341.71482013172074.385179875







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
91980276.266597313783146.7177526251177405.815442
92963011.486496802742912.6327076721183110.34028593
931124307.10194291883419.2611313221365194.94275449
941057056.37395933797036.3780696961317076.36984897
951158855.22484304881017.4220263171436693.02765976
961162809.78007093868229.92487781457389.63526405
971053102.43219356742682.1727110571363522.69167605
981095333.64426866769842.9625145431420824.32602278
991163880.08383610823986.5264974221503773.64117477
1001251024.2685674897313.8266351351604734.71049966
1011106252.19516516739244.6705236371473259.71980668
1021260207.45952770880368.0598400481640046.85921535

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
91 & 980276.266597313 & 783146.717752625 & 1177405.815442 \tabularnewline
92 & 963011.486496802 & 742912.632707672 & 1183110.34028593 \tabularnewline
93 & 1124307.10194291 & 883419.261131322 & 1365194.94275449 \tabularnewline
94 & 1057056.37395933 & 797036.378069696 & 1317076.36984897 \tabularnewline
95 & 1158855.22484304 & 881017.422026317 & 1436693.02765976 \tabularnewline
96 & 1162809.78007093 & 868229.9248778 & 1457389.63526405 \tabularnewline
97 & 1053102.43219356 & 742682.172711057 & 1363522.69167605 \tabularnewline
98 & 1095333.64426866 & 769842.962514543 & 1420824.32602278 \tabularnewline
99 & 1163880.08383610 & 823986.526497422 & 1503773.64117477 \tabularnewline
100 & 1251024.2685674 & 897313.826635135 & 1604734.71049966 \tabularnewline
101 & 1106252.19516516 & 739244.670523637 & 1473259.71980668 \tabularnewline
102 & 1260207.45952770 & 880368.059840048 & 1640046.85921535 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40977&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]91[/C][C]980276.266597313[/C][C]783146.717752625[/C][C]1177405.815442[/C][/ROW]
[ROW][C]92[/C][C]963011.486496802[/C][C]742912.632707672[/C][C]1183110.34028593[/C][/ROW]
[ROW][C]93[/C][C]1124307.10194291[/C][C]883419.261131322[/C][C]1365194.94275449[/C][/ROW]
[ROW][C]94[/C][C]1057056.37395933[/C][C]797036.378069696[/C][C]1317076.36984897[/C][/ROW]
[ROW][C]95[/C][C]1158855.22484304[/C][C]881017.422026317[/C][C]1436693.02765976[/C][/ROW]
[ROW][C]96[/C][C]1162809.78007093[/C][C]868229.9248778[/C][C]1457389.63526405[/C][/ROW]
[ROW][C]97[/C][C]1053102.43219356[/C][C]742682.172711057[/C][C]1363522.69167605[/C][/ROW]
[ROW][C]98[/C][C]1095333.64426866[/C][C]769842.962514543[/C][C]1420824.32602278[/C][/ROW]
[ROW][C]99[/C][C]1163880.08383610[/C][C]823986.526497422[/C][C]1503773.64117477[/C][/ROW]
[ROW][C]100[/C][C]1251024.2685674[/C][C]897313.826635135[/C][C]1604734.71049966[/C][/ROW]
[ROW][C]101[/C][C]1106252.19516516[/C][C]739244.670523637[/C][C]1473259.71980668[/C][/ROW]
[ROW][C]102[/C][C]1260207.45952770[/C][C]880368.059840048[/C][C]1640046.85921535[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40977&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40977&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
91980276.266597313783146.7177526251177405.815442
92963011.486496802742912.6327076721183110.34028593
931124307.10194291883419.2611313221365194.94275449
941057056.37395933797036.3780696961317076.36984897
951158855.22484304881017.4220263171436693.02765976
961162809.78007093868229.92487781457389.63526405
971053102.43219356742682.1727110571363522.69167605
981095333.64426866769842.9625145431420824.32602278
991163880.08383610823986.5264974221503773.64117477
1001251024.2685674897313.8266351351604734.71049966
1011106252.19516516739244.6705236371473259.71980668
1021260207.45952770880368.0598400481640046.85921535



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=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')