Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 07 Jun 2009 10:45:35 -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/07/t1244393185g0uq1v1qn2kr4ig.htm/, Retrieved Sun, 12 May 2024 19:37:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42189, Retrieved Sun, 12 May 2024 19:37:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsThomas Cammaert
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opdracht 10 oefen...] [2009-06-07 16:45:35] [61792449e3c1c0e0abc5b9baf921991f] [Current]
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Dataseries X:
8.9722
8.8284
8.7446
8.7519
8.6337
8.7272
8.6330
8.5865
8.5968
8.5114
8.3884
8.2671
8.2410
8.3177
8.4070
8.3917
8.4145
8.5245
8.6289
8.6622
8.9055
8.9770
9.1264
9.1120
9.0576
9.2106
9.2637
9.3107
9.6744
9.5780
9.4166
9.4359
9.2275
9.1828
9.0594
9.1358
9.2208
9.1137
9.2689
9.2489
9.1679
9.1051
9.0818
9.0961
9.1733
9.1455
9.2265
9.1541
9.1559
9.1182
9.1856
9.2378
9.0682
9.0105
8.9939
9.0228
9.1368
9.1763
9.2346
9.1653
9.1277
9.1430
9.1962
9.1861
9.0920
9.0620
8.9981
8.9819
9.0476
9.0852
9.0884
9.1670
9.1931
9.2628
9.4276
9.3398
9.3342
9.4223
9.5614
9.4316
9.3111
9.3414
9.4017
9.3346
9.3310
9.2349
9.2170
9.2098
9.2665
9.2533
9.1008
9.0377
9.0795
9.1896
9.2992
9.2372
9.2061
9.3290
9.1842
9.3231
9.2835
9.1735
9.2889
9.4319
9.4314
9.3642
9.4020
9.3699
9.3106
9.3739
9.4566
9.3984
9.5637
9.8506




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42189&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42189&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42189&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.00424858042342793
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00424858042342793 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42189&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.00424858042342793[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42189&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42189&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
alpha1
beta0.00424858042342793
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138.2418.38257243589744-0.141572435897436
148.31778.312217923714750.00548207628524544
158.4078.38850788142340.0184921185765941
168.39178.357040613343050.0346593866569531
178.41458.362100366534680.0523996334653187
188.52458.456518823924950.0679811760750475
198.62898.63212431408545-0.00322431408545398
208.66228.632393948661080.029806051338916
218.90558.70622058206730.199279417932695
228.9778.848396403367790.128603596632209
239.12648.87790945275750.248490547242508
249.1129.023502684831910.0884973151680892
259.05769.09571617279266-0.0381161727926607
269.21069.132354233167120.0782457668328789
279.26379.28525333326697-0.0215533332669668
289.31079.217415928863860.0932840711361411
299.67449.28502475374230.389375246257698
309.5789.72177487912425-0.143774879124253
319.41669.6900807066541-0.273480706654091
329.43599.423402135210950.0124978647890490
339.22759.48315523339463-0.255655233394631
349.18289.171698228241550.0111017717584527
359.05949.08451206167837-0.0251120616783744
369.13588.956142871064730.179657128935268
379.22089.119543658825660.101256341174343
389.11379.29617385453452-0.182473854534521
399.26899.187865266355020.0810347336449784
409.24899.222563715604670.0263362843953274
419.16799.22288810742698-0.0549881074269774
429.10519.21305031936357-0.107950319363574
439.08189.21510835041669-0.133308350416693
449.09619.087125312502160.00897468749783492
459.17339.141863442183780.0314365578162228
469.14559.117226169594560.0282738304054408
479.22659.047012959903580.179487040096417
489.15419.12391302502840.0301869749716062
499.15599.13787877681930.018021223180698
509.11829.23095534143532-0.112755341435316
519.18569.19234295796572-0.00674295796572011
529.23789.138868476633180.0989315233668187
539.06829.21170129516661-0.143501295166613
549.01059.11288745170656-0.102387451706564
558.99399.12006911705031-0.126169117050308
569.02288.99881641074290.0239835892570994
579.13689.06821830695070.0685816930492944
589.17639.080538848455860.0957611515441368
599.23469.07791236407630.156687635923694
609.16539.132015564098880.033284435901118
619.12779.14909447570166-0.0213944757016584
629.1439.20260357955103-0.059603579551025
639.19629.21721701561644-0.0210170156164438
649.18619.1494818898020.0366181101979954
659.0929.15974996478813-0.0677499647881294
669.0629.13675795694738-0.0747579569473782
678.99819.17175700842166-0.173657008421662
688.98199.00300254598863-0.0211025459886276
699.04769.027112890124860.0204871098751429
709.08528.990929097925470.0942709020745323
719.08848.986396282101190.102003717898810
729.1678.985167153100170.181832846899832
739.19319.150777184573850.0423228154261537
749.26289.26825699645893-0.00545699645892839
759.42769.337500478637270.0900995213627311
769.33989.38183744036656-0.0420374403665598
779.33429.314071340920360.020128659079635
789.42239.379952692480610.0423473075193872
799.56149.5335492750890.0278507249110085
809.43169.56865093446696-0.137050934466963
819.31119.47866866254977-0.167568662549774
829.34149.255485900277150.0859140997228494
839.40179.2436175799060.158082420094003
849.33469.29972670578130.0348732942187073
859.3319.319012367776410.011987632223585
869.23499.406663298196-0.171763298196003
879.2179.30940021467649-0.0924002146764877
889.20989.170261811599960.0395381884000354
899.26659.183442292773170.0830577072268284
909.25339.31189100345545-0.0585910034554473
919.10089.36375874153184-0.262958741531843
929.03779.10602487350374-0.0683248735037374
939.07959.08303458978374-0.00353458978373666
949.18969.022848739461440.166751260538559
959.29929.091123862269220.208076137730785
969.23729.196745390474560.0404546095254421
979.20619.22115476513663-0.0150547651366271
989.3299.281190803756190.0478091962438114
999.18429.40386059163808-0.219660591638075
1009.32319.137281512615310.185818487384687
1019.28359.29718347740312-0.0136834774031218
1029.17359.32892117538224-0.155421175382235
1039.28899.283577522685790.00532247731420910
1049.43199.294883468992040.137016531007957
1059.43149.47886559474337-0.0474655947433735
1069.36429.37619310001343-0.0119931000134255
1079.4029.266408813030160.135591186969840
1089.36999.29992238309270.0699776169072948
1099.31069.35435718862598-0.0437571886259764
1109.37399.386071282691-0.0121712826909981
1119.45669.44888623868430.00771376131570456
1129.39849.41077317788628-0.0123731778862801
1139.56379.372733109444930.190966890555067
1149.85069.6102402809710.240359719028998

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8.241 & 8.38257243589744 & -0.141572435897436 \tabularnewline
14 & 8.3177 & 8.31221792371475 & 0.00548207628524544 \tabularnewline
15 & 8.407 & 8.3885078814234 & 0.0184921185765941 \tabularnewline
16 & 8.3917 & 8.35704061334305 & 0.0346593866569531 \tabularnewline
17 & 8.4145 & 8.36210036653468 & 0.0523996334653187 \tabularnewline
18 & 8.5245 & 8.45651882392495 & 0.0679811760750475 \tabularnewline
19 & 8.6289 & 8.63212431408545 & -0.00322431408545398 \tabularnewline
20 & 8.6622 & 8.63239394866108 & 0.029806051338916 \tabularnewline
21 & 8.9055 & 8.7062205820673 & 0.199279417932695 \tabularnewline
22 & 8.977 & 8.84839640336779 & 0.128603596632209 \tabularnewline
23 & 9.1264 & 8.8779094527575 & 0.248490547242508 \tabularnewline
24 & 9.112 & 9.02350268483191 & 0.0884973151680892 \tabularnewline
25 & 9.0576 & 9.09571617279266 & -0.0381161727926607 \tabularnewline
26 & 9.2106 & 9.13235423316712 & 0.0782457668328789 \tabularnewline
27 & 9.2637 & 9.28525333326697 & -0.0215533332669668 \tabularnewline
28 & 9.3107 & 9.21741592886386 & 0.0932840711361411 \tabularnewline
29 & 9.6744 & 9.2850247537423 & 0.389375246257698 \tabularnewline
30 & 9.578 & 9.72177487912425 & -0.143774879124253 \tabularnewline
31 & 9.4166 & 9.6900807066541 & -0.273480706654091 \tabularnewline
32 & 9.4359 & 9.42340213521095 & 0.0124978647890490 \tabularnewline
33 & 9.2275 & 9.48315523339463 & -0.255655233394631 \tabularnewline
34 & 9.1828 & 9.17169822824155 & 0.0111017717584527 \tabularnewline
35 & 9.0594 & 9.08451206167837 & -0.0251120616783744 \tabularnewline
36 & 9.1358 & 8.95614287106473 & 0.179657128935268 \tabularnewline
37 & 9.2208 & 9.11954365882566 & 0.101256341174343 \tabularnewline
38 & 9.1137 & 9.29617385453452 & -0.182473854534521 \tabularnewline
39 & 9.2689 & 9.18786526635502 & 0.0810347336449784 \tabularnewline
40 & 9.2489 & 9.22256371560467 & 0.0263362843953274 \tabularnewline
41 & 9.1679 & 9.22288810742698 & -0.0549881074269774 \tabularnewline
42 & 9.1051 & 9.21305031936357 & -0.107950319363574 \tabularnewline
43 & 9.0818 & 9.21510835041669 & -0.133308350416693 \tabularnewline
44 & 9.0961 & 9.08712531250216 & 0.00897468749783492 \tabularnewline
45 & 9.1733 & 9.14186344218378 & 0.0314365578162228 \tabularnewline
46 & 9.1455 & 9.11722616959456 & 0.0282738304054408 \tabularnewline
47 & 9.2265 & 9.04701295990358 & 0.179487040096417 \tabularnewline
48 & 9.1541 & 9.1239130250284 & 0.0301869749716062 \tabularnewline
49 & 9.1559 & 9.1378787768193 & 0.018021223180698 \tabularnewline
50 & 9.1182 & 9.23095534143532 & -0.112755341435316 \tabularnewline
51 & 9.1856 & 9.19234295796572 & -0.00674295796572011 \tabularnewline
52 & 9.2378 & 9.13886847663318 & 0.0989315233668187 \tabularnewline
53 & 9.0682 & 9.21170129516661 & -0.143501295166613 \tabularnewline
54 & 9.0105 & 9.11288745170656 & -0.102387451706564 \tabularnewline
55 & 8.9939 & 9.12006911705031 & -0.126169117050308 \tabularnewline
56 & 9.0228 & 8.9988164107429 & 0.0239835892570994 \tabularnewline
57 & 9.1368 & 9.0682183069507 & 0.0685816930492944 \tabularnewline
58 & 9.1763 & 9.08053884845586 & 0.0957611515441368 \tabularnewline
59 & 9.2346 & 9.0779123640763 & 0.156687635923694 \tabularnewline
60 & 9.1653 & 9.13201556409888 & 0.033284435901118 \tabularnewline
61 & 9.1277 & 9.14909447570166 & -0.0213944757016584 \tabularnewline
62 & 9.143 & 9.20260357955103 & -0.059603579551025 \tabularnewline
63 & 9.1962 & 9.21721701561644 & -0.0210170156164438 \tabularnewline
64 & 9.1861 & 9.149481889802 & 0.0366181101979954 \tabularnewline
65 & 9.092 & 9.15974996478813 & -0.0677499647881294 \tabularnewline
66 & 9.062 & 9.13675795694738 & -0.0747579569473782 \tabularnewline
67 & 8.9981 & 9.17175700842166 & -0.173657008421662 \tabularnewline
68 & 8.9819 & 9.00300254598863 & -0.0211025459886276 \tabularnewline
69 & 9.0476 & 9.02711289012486 & 0.0204871098751429 \tabularnewline
70 & 9.0852 & 8.99092909792547 & 0.0942709020745323 \tabularnewline
71 & 9.0884 & 8.98639628210119 & 0.102003717898810 \tabularnewline
72 & 9.167 & 8.98516715310017 & 0.181832846899832 \tabularnewline
73 & 9.1931 & 9.15077718457385 & 0.0423228154261537 \tabularnewline
74 & 9.2628 & 9.26825699645893 & -0.00545699645892839 \tabularnewline
75 & 9.4276 & 9.33750047863727 & 0.0900995213627311 \tabularnewline
76 & 9.3398 & 9.38183744036656 & -0.0420374403665598 \tabularnewline
77 & 9.3342 & 9.31407134092036 & 0.020128659079635 \tabularnewline
78 & 9.4223 & 9.37995269248061 & 0.0423473075193872 \tabularnewline
79 & 9.5614 & 9.533549275089 & 0.0278507249110085 \tabularnewline
80 & 9.4316 & 9.56865093446696 & -0.137050934466963 \tabularnewline
81 & 9.3111 & 9.47866866254977 & -0.167568662549774 \tabularnewline
82 & 9.3414 & 9.25548590027715 & 0.0859140997228494 \tabularnewline
83 & 9.4017 & 9.243617579906 & 0.158082420094003 \tabularnewline
84 & 9.3346 & 9.2997267057813 & 0.0348732942187073 \tabularnewline
85 & 9.331 & 9.31901236777641 & 0.011987632223585 \tabularnewline
86 & 9.2349 & 9.406663298196 & -0.171763298196003 \tabularnewline
87 & 9.217 & 9.30940021467649 & -0.0924002146764877 \tabularnewline
88 & 9.2098 & 9.17026181159996 & 0.0395381884000354 \tabularnewline
89 & 9.2665 & 9.18344229277317 & 0.0830577072268284 \tabularnewline
90 & 9.2533 & 9.31189100345545 & -0.0585910034554473 \tabularnewline
91 & 9.1008 & 9.36375874153184 & -0.262958741531843 \tabularnewline
92 & 9.0377 & 9.10602487350374 & -0.0683248735037374 \tabularnewline
93 & 9.0795 & 9.08303458978374 & -0.00353458978373666 \tabularnewline
94 & 9.1896 & 9.02284873946144 & 0.166751260538559 \tabularnewline
95 & 9.2992 & 9.09112386226922 & 0.208076137730785 \tabularnewline
96 & 9.2372 & 9.19674539047456 & 0.0404546095254421 \tabularnewline
97 & 9.2061 & 9.22115476513663 & -0.0150547651366271 \tabularnewline
98 & 9.329 & 9.28119080375619 & 0.0478091962438114 \tabularnewline
99 & 9.1842 & 9.40386059163808 & -0.219660591638075 \tabularnewline
100 & 9.3231 & 9.13728151261531 & 0.185818487384687 \tabularnewline
101 & 9.2835 & 9.29718347740312 & -0.0136834774031218 \tabularnewline
102 & 9.1735 & 9.32892117538224 & -0.155421175382235 \tabularnewline
103 & 9.2889 & 9.28357752268579 & 0.00532247731420910 \tabularnewline
104 & 9.4319 & 9.29488346899204 & 0.137016531007957 \tabularnewline
105 & 9.4314 & 9.47886559474337 & -0.0474655947433735 \tabularnewline
106 & 9.3642 & 9.37619310001343 & -0.0119931000134255 \tabularnewline
107 & 9.402 & 9.26640881303016 & 0.135591186969840 \tabularnewline
108 & 9.3699 & 9.2999223830927 & 0.0699776169072948 \tabularnewline
109 & 9.3106 & 9.35435718862598 & -0.0437571886259764 \tabularnewline
110 & 9.3739 & 9.386071282691 & -0.0121712826909981 \tabularnewline
111 & 9.4566 & 9.4488862386843 & 0.00771376131570456 \tabularnewline
112 & 9.3984 & 9.41077317788628 & -0.0123731778862801 \tabularnewline
113 & 9.5637 & 9.37273310944493 & 0.190966890555067 \tabularnewline
114 & 9.8506 & 9.610240280971 & 0.240359719028998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42189&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]8.241[/C][C]8.38257243589744[/C][C]-0.141572435897436[/C][/ROW]
[ROW][C]14[/C][C]8.3177[/C][C]8.31221792371475[/C][C]0.00548207628524544[/C][/ROW]
[ROW][C]15[/C][C]8.407[/C][C]8.3885078814234[/C][C]0.0184921185765941[/C][/ROW]
[ROW][C]16[/C][C]8.3917[/C][C]8.35704061334305[/C][C]0.0346593866569531[/C][/ROW]
[ROW][C]17[/C][C]8.4145[/C][C]8.36210036653468[/C][C]0.0523996334653187[/C][/ROW]
[ROW][C]18[/C][C]8.5245[/C][C]8.45651882392495[/C][C]0.0679811760750475[/C][/ROW]
[ROW][C]19[/C][C]8.6289[/C][C]8.63212431408545[/C][C]-0.00322431408545398[/C][/ROW]
[ROW][C]20[/C][C]8.6622[/C][C]8.63239394866108[/C][C]0.029806051338916[/C][/ROW]
[ROW][C]21[/C][C]8.9055[/C][C]8.7062205820673[/C][C]0.199279417932695[/C][/ROW]
[ROW][C]22[/C][C]8.977[/C][C]8.84839640336779[/C][C]0.128603596632209[/C][/ROW]
[ROW][C]23[/C][C]9.1264[/C][C]8.8779094527575[/C][C]0.248490547242508[/C][/ROW]
[ROW][C]24[/C][C]9.112[/C][C]9.02350268483191[/C][C]0.0884973151680892[/C][/ROW]
[ROW][C]25[/C][C]9.0576[/C][C]9.09571617279266[/C][C]-0.0381161727926607[/C][/ROW]
[ROW][C]26[/C][C]9.2106[/C][C]9.13235423316712[/C][C]0.0782457668328789[/C][/ROW]
[ROW][C]27[/C][C]9.2637[/C][C]9.28525333326697[/C][C]-0.0215533332669668[/C][/ROW]
[ROW][C]28[/C][C]9.3107[/C][C]9.21741592886386[/C][C]0.0932840711361411[/C][/ROW]
[ROW][C]29[/C][C]9.6744[/C][C]9.2850247537423[/C][C]0.389375246257698[/C][/ROW]
[ROW][C]30[/C][C]9.578[/C][C]9.72177487912425[/C][C]-0.143774879124253[/C][/ROW]
[ROW][C]31[/C][C]9.4166[/C][C]9.6900807066541[/C][C]-0.273480706654091[/C][/ROW]
[ROW][C]32[/C][C]9.4359[/C][C]9.42340213521095[/C][C]0.0124978647890490[/C][/ROW]
[ROW][C]33[/C][C]9.2275[/C][C]9.48315523339463[/C][C]-0.255655233394631[/C][/ROW]
[ROW][C]34[/C][C]9.1828[/C][C]9.17169822824155[/C][C]0.0111017717584527[/C][/ROW]
[ROW][C]35[/C][C]9.0594[/C][C]9.08451206167837[/C][C]-0.0251120616783744[/C][/ROW]
[ROW][C]36[/C][C]9.1358[/C][C]8.95614287106473[/C][C]0.179657128935268[/C][/ROW]
[ROW][C]37[/C][C]9.2208[/C][C]9.11954365882566[/C][C]0.101256341174343[/C][/ROW]
[ROW][C]38[/C][C]9.1137[/C][C]9.29617385453452[/C][C]-0.182473854534521[/C][/ROW]
[ROW][C]39[/C][C]9.2689[/C][C]9.18786526635502[/C][C]0.0810347336449784[/C][/ROW]
[ROW][C]40[/C][C]9.2489[/C][C]9.22256371560467[/C][C]0.0263362843953274[/C][/ROW]
[ROW][C]41[/C][C]9.1679[/C][C]9.22288810742698[/C][C]-0.0549881074269774[/C][/ROW]
[ROW][C]42[/C][C]9.1051[/C][C]9.21305031936357[/C][C]-0.107950319363574[/C][/ROW]
[ROW][C]43[/C][C]9.0818[/C][C]9.21510835041669[/C][C]-0.133308350416693[/C][/ROW]
[ROW][C]44[/C][C]9.0961[/C][C]9.08712531250216[/C][C]0.00897468749783492[/C][/ROW]
[ROW][C]45[/C][C]9.1733[/C][C]9.14186344218378[/C][C]0.0314365578162228[/C][/ROW]
[ROW][C]46[/C][C]9.1455[/C][C]9.11722616959456[/C][C]0.0282738304054408[/C][/ROW]
[ROW][C]47[/C][C]9.2265[/C][C]9.04701295990358[/C][C]0.179487040096417[/C][/ROW]
[ROW][C]48[/C][C]9.1541[/C][C]9.1239130250284[/C][C]0.0301869749716062[/C][/ROW]
[ROW][C]49[/C][C]9.1559[/C][C]9.1378787768193[/C][C]0.018021223180698[/C][/ROW]
[ROW][C]50[/C][C]9.1182[/C][C]9.23095534143532[/C][C]-0.112755341435316[/C][/ROW]
[ROW][C]51[/C][C]9.1856[/C][C]9.19234295796572[/C][C]-0.00674295796572011[/C][/ROW]
[ROW][C]52[/C][C]9.2378[/C][C]9.13886847663318[/C][C]0.0989315233668187[/C][/ROW]
[ROW][C]53[/C][C]9.0682[/C][C]9.21170129516661[/C][C]-0.143501295166613[/C][/ROW]
[ROW][C]54[/C][C]9.0105[/C][C]9.11288745170656[/C][C]-0.102387451706564[/C][/ROW]
[ROW][C]55[/C][C]8.9939[/C][C]9.12006911705031[/C][C]-0.126169117050308[/C][/ROW]
[ROW][C]56[/C][C]9.0228[/C][C]8.9988164107429[/C][C]0.0239835892570994[/C][/ROW]
[ROW][C]57[/C][C]9.1368[/C][C]9.0682183069507[/C][C]0.0685816930492944[/C][/ROW]
[ROW][C]58[/C][C]9.1763[/C][C]9.08053884845586[/C][C]0.0957611515441368[/C][/ROW]
[ROW][C]59[/C][C]9.2346[/C][C]9.0779123640763[/C][C]0.156687635923694[/C][/ROW]
[ROW][C]60[/C][C]9.1653[/C][C]9.13201556409888[/C][C]0.033284435901118[/C][/ROW]
[ROW][C]61[/C][C]9.1277[/C][C]9.14909447570166[/C][C]-0.0213944757016584[/C][/ROW]
[ROW][C]62[/C][C]9.143[/C][C]9.20260357955103[/C][C]-0.059603579551025[/C][/ROW]
[ROW][C]63[/C][C]9.1962[/C][C]9.21721701561644[/C][C]-0.0210170156164438[/C][/ROW]
[ROW][C]64[/C][C]9.1861[/C][C]9.149481889802[/C][C]0.0366181101979954[/C][/ROW]
[ROW][C]65[/C][C]9.092[/C][C]9.15974996478813[/C][C]-0.0677499647881294[/C][/ROW]
[ROW][C]66[/C][C]9.062[/C][C]9.13675795694738[/C][C]-0.0747579569473782[/C][/ROW]
[ROW][C]67[/C][C]8.9981[/C][C]9.17175700842166[/C][C]-0.173657008421662[/C][/ROW]
[ROW][C]68[/C][C]8.9819[/C][C]9.00300254598863[/C][C]-0.0211025459886276[/C][/ROW]
[ROW][C]69[/C][C]9.0476[/C][C]9.02711289012486[/C][C]0.0204871098751429[/C][/ROW]
[ROW][C]70[/C][C]9.0852[/C][C]8.99092909792547[/C][C]0.0942709020745323[/C][/ROW]
[ROW][C]71[/C][C]9.0884[/C][C]8.98639628210119[/C][C]0.102003717898810[/C][/ROW]
[ROW][C]72[/C][C]9.167[/C][C]8.98516715310017[/C][C]0.181832846899832[/C][/ROW]
[ROW][C]73[/C][C]9.1931[/C][C]9.15077718457385[/C][C]0.0423228154261537[/C][/ROW]
[ROW][C]74[/C][C]9.2628[/C][C]9.26825699645893[/C][C]-0.00545699645892839[/C][/ROW]
[ROW][C]75[/C][C]9.4276[/C][C]9.33750047863727[/C][C]0.0900995213627311[/C][/ROW]
[ROW][C]76[/C][C]9.3398[/C][C]9.38183744036656[/C][C]-0.0420374403665598[/C][/ROW]
[ROW][C]77[/C][C]9.3342[/C][C]9.31407134092036[/C][C]0.020128659079635[/C][/ROW]
[ROW][C]78[/C][C]9.4223[/C][C]9.37995269248061[/C][C]0.0423473075193872[/C][/ROW]
[ROW][C]79[/C][C]9.5614[/C][C]9.533549275089[/C][C]0.0278507249110085[/C][/ROW]
[ROW][C]80[/C][C]9.4316[/C][C]9.56865093446696[/C][C]-0.137050934466963[/C][/ROW]
[ROW][C]81[/C][C]9.3111[/C][C]9.47866866254977[/C][C]-0.167568662549774[/C][/ROW]
[ROW][C]82[/C][C]9.3414[/C][C]9.25548590027715[/C][C]0.0859140997228494[/C][/ROW]
[ROW][C]83[/C][C]9.4017[/C][C]9.243617579906[/C][C]0.158082420094003[/C][/ROW]
[ROW][C]84[/C][C]9.3346[/C][C]9.2997267057813[/C][C]0.0348732942187073[/C][/ROW]
[ROW][C]85[/C][C]9.331[/C][C]9.31901236777641[/C][C]0.011987632223585[/C][/ROW]
[ROW][C]86[/C][C]9.2349[/C][C]9.406663298196[/C][C]-0.171763298196003[/C][/ROW]
[ROW][C]87[/C][C]9.217[/C][C]9.30940021467649[/C][C]-0.0924002146764877[/C][/ROW]
[ROW][C]88[/C][C]9.2098[/C][C]9.17026181159996[/C][C]0.0395381884000354[/C][/ROW]
[ROW][C]89[/C][C]9.2665[/C][C]9.18344229277317[/C][C]0.0830577072268284[/C][/ROW]
[ROW][C]90[/C][C]9.2533[/C][C]9.31189100345545[/C][C]-0.0585910034554473[/C][/ROW]
[ROW][C]91[/C][C]9.1008[/C][C]9.36375874153184[/C][C]-0.262958741531843[/C][/ROW]
[ROW][C]92[/C][C]9.0377[/C][C]9.10602487350374[/C][C]-0.0683248735037374[/C][/ROW]
[ROW][C]93[/C][C]9.0795[/C][C]9.08303458978374[/C][C]-0.00353458978373666[/C][/ROW]
[ROW][C]94[/C][C]9.1896[/C][C]9.02284873946144[/C][C]0.166751260538559[/C][/ROW]
[ROW][C]95[/C][C]9.2992[/C][C]9.09112386226922[/C][C]0.208076137730785[/C][/ROW]
[ROW][C]96[/C][C]9.2372[/C][C]9.19674539047456[/C][C]0.0404546095254421[/C][/ROW]
[ROW][C]97[/C][C]9.2061[/C][C]9.22115476513663[/C][C]-0.0150547651366271[/C][/ROW]
[ROW][C]98[/C][C]9.329[/C][C]9.28119080375619[/C][C]0.0478091962438114[/C][/ROW]
[ROW][C]99[/C][C]9.1842[/C][C]9.40386059163808[/C][C]-0.219660591638075[/C][/ROW]
[ROW][C]100[/C][C]9.3231[/C][C]9.13728151261531[/C][C]0.185818487384687[/C][/ROW]
[ROW][C]101[/C][C]9.2835[/C][C]9.29718347740312[/C][C]-0.0136834774031218[/C][/ROW]
[ROW][C]102[/C][C]9.1735[/C][C]9.32892117538224[/C][C]-0.155421175382235[/C][/ROW]
[ROW][C]103[/C][C]9.2889[/C][C]9.28357752268579[/C][C]0.00532247731420910[/C][/ROW]
[ROW][C]104[/C][C]9.4319[/C][C]9.29488346899204[/C][C]0.137016531007957[/C][/ROW]
[ROW][C]105[/C][C]9.4314[/C][C]9.47886559474337[/C][C]-0.0474655947433735[/C][/ROW]
[ROW][C]106[/C][C]9.3642[/C][C]9.37619310001343[/C][C]-0.0119931000134255[/C][/ROW]
[ROW][C]107[/C][C]9.402[/C][C]9.26640881303016[/C][C]0.135591186969840[/C][/ROW]
[ROW][C]108[/C][C]9.3699[/C][C]9.2999223830927[/C][C]0.0699776169072948[/C][/ROW]
[ROW][C]109[/C][C]9.3106[/C][C]9.35435718862598[/C][C]-0.0437571886259764[/C][/ROW]
[ROW][C]110[/C][C]9.3739[/C][C]9.386071282691[/C][C]-0.0121712826909981[/C][/ROW]
[ROW][C]111[/C][C]9.4566[/C][C]9.4488862386843[/C][C]0.00771376131570456[/C][/ROW]
[ROW][C]112[/C][C]9.3984[/C][C]9.41077317788628[/C][C]-0.0123731778862801[/C][/ROW]
[ROW][C]113[/C][C]9.5637[/C][C]9.37273310944493[/C][C]0.190966890555067[/C][/ROW]
[ROW][C]114[/C][C]9.8506[/C][C]9.610240280971[/C][C]0.240359719028998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42189&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42189&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
138.2418.38257243589744-0.141572435897436
148.31778.312217923714750.00548207628524544
158.4078.38850788142340.0184921185765941
168.39178.357040613343050.0346593866569531
178.41458.362100366534680.0523996334653187
188.52458.456518823924950.0679811760750475
198.62898.63212431408545-0.00322431408545398
208.66228.632393948661080.029806051338916
218.90558.70622058206730.199279417932695
228.9778.848396403367790.128603596632209
239.12648.87790945275750.248490547242508
249.1129.023502684831910.0884973151680892
259.05769.09571617279266-0.0381161727926607
269.21069.132354233167120.0782457668328789
279.26379.28525333326697-0.0215533332669668
289.31079.217415928863860.0932840711361411
299.67449.28502475374230.389375246257698
309.5789.72177487912425-0.143774879124253
319.41669.6900807066541-0.273480706654091
329.43599.423402135210950.0124978647890490
339.22759.48315523339463-0.255655233394631
349.18289.171698228241550.0111017717584527
359.05949.08451206167837-0.0251120616783744
369.13588.956142871064730.179657128935268
379.22089.119543658825660.101256341174343
389.11379.29617385453452-0.182473854534521
399.26899.187865266355020.0810347336449784
409.24899.222563715604670.0263362843953274
419.16799.22288810742698-0.0549881074269774
429.10519.21305031936357-0.107950319363574
439.08189.21510835041669-0.133308350416693
449.09619.087125312502160.00897468749783492
459.17339.141863442183780.0314365578162228
469.14559.117226169594560.0282738304054408
479.22659.047012959903580.179487040096417
489.15419.12391302502840.0301869749716062
499.15599.13787877681930.018021223180698
509.11829.23095534143532-0.112755341435316
519.18569.19234295796572-0.00674295796572011
529.23789.138868476633180.0989315233668187
539.06829.21170129516661-0.143501295166613
549.01059.11288745170656-0.102387451706564
558.99399.12006911705031-0.126169117050308
569.02288.99881641074290.0239835892570994
579.13689.06821830695070.0685816930492944
589.17639.080538848455860.0957611515441368
599.23469.07791236407630.156687635923694
609.16539.132015564098880.033284435901118
619.12779.14909447570166-0.0213944757016584
629.1439.20260357955103-0.059603579551025
639.19629.21721701561644-0.0210170156164438
649.18619.1494818898020.0366181101979954
659.0929.15974996478813-0.0677499647881294
669.0629.13675795694738-0.0747579569473782
678.99819.17175700842166-0.173657008421662
688.98199.00300254598863-0.0211025459886276
699.04769.027112890124860.0204871098751429
709.08528.990929097925470.0942709020745323
719.08848.986396282101190.102003717898810
729.1678.985167153100170.181832846899832
739.19319.150777184573850.0423228154261537
749.26289.26825699645893-0.00545699645892839
759.42769.337500478637270.0900995213627311
769.33989.38183744036656-0.0420374403665598
779.33429.314071340920360.020128659079635
789.42239.379952692480610.0423473075193872
799.56149.5335492750890.0278507249110085
809.43169.56865093446696-0.137050934466963
819.31119.47866866254977-0.167568662549774
829.34149.255485900277150.0859140997228494
839.40179.2436175799060.158082420094003
849.33469.29972670578130.0348732942187073
859.3319.319012367776410.011987632223585
869.23499.406663298196-0.171763298196003
879.2179.30940021467649-0.0924002146764877
889.20989.170261811599960.0395381884000354
899.26659.183442292773170.0830577072268284
909.25339.31189100345545-0.0585910034554473
919.10089.36375874153184-0.262958741531843
929.03779.10602487350374-0.0683248735037374
939.07959.08303458978374-0.00353458978373666
949.18969.022848739461440.166751260538559
959.29929.091123862269220.208076137730785
969.23729.196745390474560.0404546095254421
979.20619.22115476513663-0.0150547651366271
989.3299.281190803756190.0478091962438114
999.18429.40386059163808-0.219660591638075
1009.32319.137281512615310.185818487384687
1019.28359.29718347740312-0.0136834774031218
1029.17359.32892117538224-0.155421175382235
1039.28899.283577522685790.00532247731420910
1049.43199.294883468992040.137016531007957
1059.43149.47886559474337-0.0474655947433735
1069.36429.37619310001343-0.0119931000134255
1079.4029.266408813030160.135591186969840
1089.36999.29992238309270.0699776169072948
1099.31069.35435718862598-0.0437571886259764
1109.37399.386071282691-0.0121712826909981
1119.45669.44888623868430.00771376131570456
1129.39849.41077317788628-0.0123731778862801
1139.56379.372733109444930.190966890555067
1149.85069.6102402809710.240359719028998







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1159.963478135234529.7350301425419610.1919261279271
1169.972239603802379.6484783233658210.2960008842389
11710.02140107237029.6240340781649210.4187680665755
1189.968591707604749.5087788613981910.4284045538113
1199.873249009505929.3580740614366710.3884239575752
1209.77304381140719.2075046590239110.3385829637903
1219.75907611330839.1469342548581610.3712179717584
1229.836308415209489.1805215007826910.4920953296363
1239.913107383777339.2160759040520910.6101388635026
1249.869060519011859.1327801656815210.6053408723422
1259.845226154246369.0713876787878210.6190646297049
1269.892787622814219.0828453718005610.7027298738279

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
115 & 9.96347813523452 & 9.73503014254196 & 10.1919261279271 \tabularnewline
116 & 9.97223960380237 & 9.64847832336582 & 10.2960008842389 \tabularnewline
117 & 10.0214010723702 & 9.62403407816492 & 10.4187680665755 \tabularnewline
118 & 9.96859170760474 & 9.50877886139819 & 10.4284045538113 \tabularnewline
119 & 9.87324900950592 & 9.35807406143667 & 10.3884239575752 \tabularnewline
120 & 9.7730438114071 & 9.20750465902391 & 10.3385829637903 \tabularnewline
121 & 9.7590761133083 & 9.14693425485816 & 10.3712179717584 \tabularnewline
122 & 9.83630841520948 & 9.18052150078269 & 10.4920953296363 \tabularnewline
123 & 9.91310738377733 & 9.21607590405209 & 10.6101388635026 \tabularnewline
124 & 9.86906051901185 & 9.13278016568152 & 10.6053408723422 \tabularnewline
125 & 9.84522615424636 & 9.07138767878782 & 10.6190646297049 \tabularnewline
126 & 9.89278762281421 & 9.08284537180056 & 10.7027298738279 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42189&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]115[/C][C]9.96347813523452[/C][C]9.73503014254196[/C][C]10.1919261279271[/C][/ROW]
[ROW][C]116[/C][C]9.97223960380237[/C][C]9.64847832336582[/C][C]10.2960008842389[/C][/ROW]
[ROW][C]117[/C][C]10.0214010723702[/C][C]9.62403407816492[/C][C]10.4187680665755[/C][/ROW]
[ROW][C]118[/C][C]9.96859170760474[/C][C]9.50877886139819[/C][C]10.4284045538113[/C][/ROW]
[ROW][C]119[/C][C]9.87324900950592[/C][C]9.35807406143667[/C][C]10.3884239575752[/C][/ROW]
[ROW][C]120[/C][C]9.7730438114071[/C][C]9.20750465902391[/C][C]10.3385829637903[/C][/ROW]
[ROW][C]121[/C][C]9.7590761133083[/C][C]9.14693425485816[/C][C]10.3712179717584[/C][/ROW]
[ROW][C]122[/C][C]9.83630841520948[/C][C]9.18052150078269[/C][C]10.4920953296363[/C][/ROW]
[ROW][C]123[/C][C]9.91310738377733[/C][C]9.21607590405209[/C][C]10.6101388635026[/C][/ROW]
[ROW][C]124[/C][C]9.86906051901185[/C][C]9.13278016568152[/C][C]10.6053408723422[/C][/ROW]
[ROW][C]125[/C][C]9.84522615424636[/C][C]9.07138767878782[/C][C]10.6190646297049[/C][/ROW]
[ROW][C]126[/C][C]9.89278762281421[/C][C]9.08284537180056[/C][C]10.7027298738279[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42189&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42189&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
1159.963478135234529.7350301425419610.1919261279271
1169.972239603802379.6484783233658210.2960008842389
11710.02140107237029.6240340781649210.4187680665755
1189.968591707604749.5087788613981910.4284045538113
1199.873249009505929.3580740614366710.3884239575752
1209.77304381140719.2075046590239110.3385829637903
1219.75907611330839.1469342548581610.3712179717584
1229.836308415209489.1805215007826910.4920953296363
1239.913107383777339.2160759040520910.6101388635026
1249.869060519011859.1327801656815210.6053408723422
1259.845226154246369.0713876787878210.6190646297049
1269.892787622814219.0828453718005610.7027298738279



Parameters (Session):
par1 = additive ; par2 = 12 ;
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')