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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 15 Jan 2010 07:54:39 -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/2010/Jan/15/t1263567353jh7egi6gh97tdez.htm/, Retrieved Fri, 03 May 2024 12:01:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72200, Retrieved Fri, 03 May 2024 12:01:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact177
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [opgave 10_eigen r...] [2009-01-16 14:02:58] [e4a15d75e135371934c77b6a0dd48476]
- RM D    [Exponential Smoothing] [] [2010-01-15 14:54:39] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
6550
8728
12026
14395
14587
13791
9498
8251
7049
9545
9364
8456
7237
9374
11837
13784
15926
13821
11143
7975
7610
1015
12759
8816
10677
10947
15200
17010
20900
16205
12143
8997
5568
11474
12256
10583
10862
10965
14405
20379
20128
17816
12268
8642
7962
13932
15936
12628
12267
12470
18944
21259
22015
18581
15175
10306
10792
14752
13754
11738
12181
12965
19990
23125
23541
21247
15189
14767
10895
17130
17697
16611
12674
12760
20249
22135
20677
19933
15388
15113
13401
16135
17562
14720
12225
11608
20985
19692
24081
22114
14220
13434
13598
17187
16119
13713
13210
14251
20139
21725
26099
21084
18024
16722
14385
21342
17180
14577




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72200&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72200&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72200&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.142162268610765
beta0.0318938520417184
gamma0.336498485279104

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.142162268610765 \tabularnewline
beta & 0.0318938520417184 \tabularnewline
gamma & 0.336498485279104 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72200&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]0.142162268610765[/C][/ROW]
[ROW][C]beta[/C][C]0.0318938520417184[/C][/ROW]
[ROW][C]gamma[/C][C]0.336498485279104[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72200&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72200&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
alpha0.142162268610765
beta0.0318938520417184
gamma0.336498485279104







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1372377082.00026709402154.999732905980
1493749172.19518755744201.804812442559
151183711641.1256946535195.874305346493
161378413938.0178882238-154.017888223778
171592616261.3869475829-335.386947582942
181382113940.0348245903-119.034824590261
19111439465.150094141761677.84990585824
2079758395.98878329206-420.988783292065
2176107108.04299670844501.957003291564
2210159703.95620138403-8688.95620138403
23127598213.205050784434545.79494921557
2488167870.83891453146945.161085468536
25106776741.876349851263935.12365014874
26109479393.334312504381553.66568749562
271520012069.22724221383130.77275778624
281701014712.14884387522297.85115612476
292090017372.64185291813527.3581470819
301620515721.3077341927483.692265807316
311214311911.9605558089231.039444191105
32899710085.8661054921-1088.86610549210
3355689020.96547985179-3452.96547985179
34114748435.220391373083038.77960862692
351225612518.8848619014-262.884861901397
361058310518.556230408764.4437695912638
371086210188.4947637839673.505236216133
381096511735.0708682120-770.07086821202
391440514571.5610188039-166.561018803932
402037916526.03908205673852.96091794326
412012819790.3168617586337.683138241431
421781616820.2770636948995.72293630516
431226813026.4455747268-758.445574726766
44864210689.8471672001-2047.84716720013
4579628813.01284266297-851.01284266297
461393210489.69976741173442.30023258830
471593613698.11542369072237.88457630928
481262812179.5755024990448.424497500981
491226712113.4415781884153.558421811591
501247013200.5667293058-730.566729305845
511894416248.23193664952695.76806335050
522125919814.23214480111444.76785519889
532201521754.8401371267260.159862873283
541858118996.7867886545-415.786788654485
551517514522.5885824860652.41141751396
561030612047.4146118136-1741.41461181356
571079210594.0662250223197.933774977661
581475213698.38555614161053.61444385844
591375416247.9210434732-2493.9210434732
601173813547.0636665582-1809.06366655816
611218113071.5623317288-890.562331728797
621296513746.9848144270-781.98481442695
631999017768.10117881462221.89882118542
642312520895.18270406292229.81729593707
652354122598.5670938337942.432906166276
662124719738.60345355471508.3965464453
671518915851.2389526231-662.238952623136
681476712497.14626620362269.85373379635
691089512191.0302334449-1296.03023344493
701713015340.35909969791789.64090030212
711769716984.2246379397712.77536206026
721661114965.20001472161645.79998527843
731267415289.9200790113-2615.92007901128
741276015787.5154883498-3027.51548834982
752024920382.4365910482-133.436591048157
762213523192.2148414611-1057.21484146108
772067724057.0365499997-3380.03654999974
781993320726.7010671808-793.701067180846
791538815855.7977118205-467.797711820498
801511313346.92053155961766.07946844040
811340111908.76286993281492.23713006716
821613516326.7416969967-191.741696996733
831756217350.6467426419211.353257358052
841472015499.9597680745-779.959768074492
851222514208.9299309708-1983.92993097075
861160814639.7188171264-3031.71881712642
872098520031.5912028116953.40879718843
881969222696.2877319095-3004.28773190954
892408122572.04136637421508.95863362576
902211420663.7186611951450.28133880498
911422016196.4826943046-1976.48269430459
921343414101.7024788636-667.702478863637
931359812211.21181459131386.78818540866
941718716100.32907837181086.67092162816
951611917400.3589214253-1281.35892142525
961371315022.5679092203-1309.56790922028
971321013277.563949221-67.5639492210103
981425113655.8764009879595.123599012064
992013920707.6892366457-568.689236645660
1002172522000.6554797930-275.655479792968
1012609923566.57585746522532.42414253480
1022108421790.9135200600-706.913520059981
1031802416022.15147164512001.84852835487
1041672214883.09104129631838.90895870367
1051438513965.7199679191419.280032080871
1062134217649.99761107293692.00238892715
1071718018667.9977448033-1487.99774480328
1081457716282.8992813049-1705.89928130489

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7237 & 7082.00026709402 & 154.999732905980 \tabularnewline
14 & 9374 & 9172.19518755744 & 201.804812442559 \tabularnewline
15 & 11837 & 11641.1256946535 & 195.874305346493 \tabularnewline
16 & 13784 & 13938.0178882238 & -154.017888223778 \tabularnewline
17 & 15926 & 16261.3869475829 & -335.386947582942 \tabularnewline
18 & 13821 & 13940.0348245903 & -119.034824590261 \tabularnewline
19 & 11143 & 9465.15009414176 & 1677.84990585824 \tabularnewline
20 & 7975 & 8395.98878329206 & -420.988783292065 \tabularnewline
21 & 7610 & 7108.04299670844 & 501.957003291564 \tabularnewline
22 & 1015 & 9703.95620138403 & -8688.95620138403 \tabularnewline
23 & 12759 & 8213.20505078443 & 4545.79494921557 \tabularnewline
24 & 8816 & 7870.83891453146 & 945.161085468536 \tabularnewline
25 & 10677 & 6741.87634985126 & 3935.12365014874 \tabularnewline
26 & 10947 & 9393.33431250438 & 1553.66568749562 \tabularnewline
27 & 15200 & 12069.2272422138 & 3130.77275778624 \tabularnewline
28 & 17010 & 14712.1488438752 & 2297.85115612476 \tabularnewline
29 & 20900 & 17372.6418529181 & 3527.3581470819 \tabularnewline
30 & 16205 & 15721.3077341927 & 483.692265807316 \tabularnewline
31 & 12143 & 11911.9605558089 & 231.039444191105 \tabularnewline
32 & 8997 & 10085.8661054921 & -1088.86610549210 \tabularnewline
33 & 5568 & 9020.96547985179 & -3452.96547985179 \tabularnewline
34 & 11474 & 8435.22039137308 & 3038.77960862692 \tabularnewline
35 & 12256 & 12518.8848619014 & -262.884861901397 \tabularnewline
36 & 10583 & 10518.5562304087 & 64.4437695912638 \tabularnewline
37 & 10862 & 10188.4947637839 & 673.505236216133 \tabularnewline
38 & 10965 & 11735.0708682120 & -770.07086821202 \tabularnewline
39 & 14405 & 14571.5610188039 & -166.561018803932 \tabularnewline
40 & 20379 & 16526.0390820567 & 3852.96091794326 \tabularnewline
41 & 20128 & 19790.3168617586 & 337.683138241431 \tabularnewline
42 & 17816 & 16820.2770636948 & 995.72293630516 \tabularnewline
43 & 12268 & 13026.4455747268 & -758.445574726766 \tabularnewline
44 & 8642 & 10689.8471672001 & -2047.84716720013 \tabularnewline
45 & 7962 & 8813.01284266297 & -851.01284266297 \tabularnewline
46 & 13932 & 10489.6997674117 & 3442.30023258830 \tabularnewline
47 & 15936 & 13698.1154236907 & 2237.88457630928 \tabularnewline
48 & 12628 & 12179.5755024990 & 448.424497500981 \tabularnewline
49 & 12267 & 12113.4415781884 & 153.558421811591 \tabularnewline
50 & 12470 & 13200.5667293058 & -730.566729305845 \tabularnewline
51 & 18944 & 16248.2319366495 & 2695.76806335050 \tabularnewline
52 & 21259 & 19814.2321448011 & 1444.76785519889 \tabularnewline
53 & 22015 & 21754.8401371267 & 260.159862873283 \tabularnewline
54 & 18581 & 18996.7867886545 & -415.786788654485 \tabularnewline
55 & 15175 & 14522.5885824860 & 652.41141751396 \tabularnewline
56 & 10306 & 12047.4146118136 & -1741.41461181356 \tabularnewline
57 & 10792 & 10594.0662250223 & 197.933774977661 \tabularnewline
58 & 14752 & 13698.3855561416 & 1053.61444385844 \tabularnewline
59 & 13754 & 16247.9210434732 & -2493.9210434732 \tabularnewline
60 & 11738 & 13547.0636665582 & -1809.06366655816 \tabularnewline
61 & 12181 & 13071.5623317288 & -890.562331728797 \tabularnewline
62 & 12965 & 13746.9848144270 & -781.98481442695 \tabularnewline
63 & 19990 & 17768.1011788146 & 2221.89882118542 \tabularnewline
64 & 23125 & 20895.1827040629 & 2229.81729593707 \tabularnewline
65 & 23541 & 22598.5670938337 & 942.432906166276 \tabularnewline
66 & 21247 & 19738.6034535547 & 1508.3965464453 \tabularnewline
67 & 15189 & 15851.2389526231 & -662.238952623136 \tabularnewline
68 & 14767 & 12497.1462662036 & 2269.85373379635 \tabularnewline
69 & 10895 & 12191.0302334449 & -1296.03023344493 \tabularnewline
70 & 17130 & 15340.3590996979 & 1789.64090030212 \tabularnewline
71 & 17697 & 16984.2246379397 & 712.77536206026 \tabularnewline
72 & 16611 & 14965.2000147216 & 1645.79998527843 \tabularnewline
73 & 12674 & 15289.9200790113 & -2615.92007901128 \tabularnewline
74 & 12760 & 15787.5154883498 & -3027.51548834982 \tabularnewline
75 & 20249 & 20382.4365910482 & -133.436591048157 \tabularnewline
76 & 22135 & 23192.2148414611 & -1057.21484146108 \tabularnewline
77 & 20677 & 24057.0365499997 & -3380.03654999974 \tabularnewline
78 & 19933 & 20726.7010671808 & -793.701067180846 \tabularnewline
79 & 15388 & 15855.7977118205 & -467.797711820498 \tabularnewline
80 & 15113 & 13346.9205315596 & 1766.07946844040 \tabularnewline
81 & 13401 & 11908.7628699328 & 1492.23713006716 \tabularnewline
82 & 16135 & 16326.7416969967 & -191.741696996733 \tabularnewline
83 & 17562 & 17350.6467426419 & 211.353257358052 \tabularnewline
84 & 14720 & 15499.9597680745 & -779.959768074492 \tabularnewline
85 & 12225 & 14208.9299309708 & -1983.92993097075 \tabularnewline
86 & 11608 & 14639.7188171264 & -3031.71881712642 \tabularnewline
87 & 20985 & 20031.5912028116 & 953.40879718843 \tabularnewline
88 & 19692 & 22696.2877319095 & -3004.28773190954 \tabularnewline
89 & 24081 & 22572.0413663742 & 1508.95863362576 \tabularnewline
90 & 22114 & 20663.718661195 & 1450.28133880498 \tabularnewline
91 & 14220 & 16196.4826943046 & -1976.48269430459 \tabularnewline
92 & 13434 & 14101.7024788636 & -667.702478863637 \tabularnewline
93 & 13598 & 12211.2118145913 & 1386.78818540866 \tabularnewline
94 & 17187 & 16100.3290783718 & 1086.67092162816 \tabularnewline
95 & 16119 & 17400.3589214253 & -1281.35892142525 \tabularnewline
96 & 13713 & 15022.5679092203 & -1309.56790922028 \tabularnewline
97 & 13210 & 13277.563949221 & -67.5639492210103 \tabularnewline
98 & 14251 & 13655.8764009879 & 595.123599012064 \tabularnewline
99 & 20139 & 20707.6892366457 & -568.689236645660 \tabularnewline
100 & 21725 & 22000.6554797930 & -275.655479792968 \tabularnewline
101 & 26099 & 23566.5758574652 & 2532.42414253480 \tabularnewline
102 & 21084 & 21790.9135200600 & -706.913520059981 \tabularnewline
103 & 18024 & 16022.1514716451 & 2001.84852835487 \tabularnewline
104 & 16722 & 14883.0910412963 & 1838.90895870367 \tabularnewline
105 & 14385 & 13965.7199679191 & 419.280032080871 \tabularnewline
106 & 21342 & 17649.9976110729 & 3692.00238892715 \tabularnewline
107 & 17180 & 18667.9977448033 & -1487.99774480328 \tabularnewline
108 & 14577 & 16282.8992813049 & -1705.89928130489 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72200&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]7237[/C][C]7082.00026709402[/C][C]154.999732905980[/C][/ROW]
[ROW][C]14[/C][C]9374[/C][C]9172.19518755744[/C][C]201.804812442559[/C][/ROW]
[ROW][C]15[/C][C]11837[/C][C]11641.1256946535[/C][C]195.874305346493[/C][/ROW]
[ROW][C]16[/C][C]13784[/C][C]13938.0178882238[/C][C]-154.017888223778[/C][/ROW]
[ROW][C]17[/C][C]15926[/C][C]16261.3869475829[/C][C]-335.386947582942[/C][/ROW]
[ROW][C]18[/C][C]13821[/C][C]13940.0348245903[/C][C]-119.034824590261[/C][/ROW]
[ROW][C]19[/C][C]11143[/C][C]9465.15009414176[/C][C]1677.84990585824[/C][/ROW]
[ROW][C]20[/C][C]7975[/C][C]8395.98878329206[/C][C]-420.988783292065[/C][/ROW]
[ROW][C]21[/C][C]7610[/C][C]7108.04299670844[/C][C]501.957003291564[/C][/ROW]
[ROW][C]22[/C][C]1015[/C][C]9703.95620138403[/C][C]-8688.95620138403[/C][/ROW]
[ROW][C]23[/C][C]12759[/C][C]8213.20505078443[/C][C]4545.79494921557[/C][/ROW]
[ROW][C]24[/C][C]8816[/C][C]7870.83891453146[/C][C]945.161085468536[/C][/ROW]
[ROW][C]25[/C][C]10677[/C][C]6741.87634985126[/C][C]3935.12365014874[/C][/ROW]
[ROW][C]26[/C][C]10947[/C][C]9393.33431250438[/C][C]1553.66568749562[/C][/ROW]
[ROW][C]27[/C][C]15200[/C][C]12069.2272422138[/C][C]3130.77275778624[/C][/ROW]
[ROW][C]28[/C][C]17010[/C][C]14712.1488438752[/C][C]2297.85115612476[/C][/ROW]
[ROW][C]29[/C][C]20900[/C][C]17372.6418529181[/C][C]3527.3581470819[/C][/ROW]
[ROW][C]30[/C][C]16205[/C][C]15721.3077341927[/C][C]483.692265807316[/C][/ROW]
[ROW][C]31[/C][C]12143[/C][C]11911.9605558089[/C][C]231.039444191105[/C][/ROW]
[ROW][C]32[/C][C]8997[/C][C]10085.8661054921[/C][C]-1088.86610549210[/C][/ROW]
[ROW][C]33[/C][C]5568[/C][C]9020.96547985179[/C][C]-3452.96547985179[/C][/ROW]
[ROW][C]34[/C][C]11474[/C][C]8435.22039137308[/C][C]3038.77960862692[/C][/ROW]
[ROW][C]35[/C][C]12256[/C][C]12518.8848619014[/C][C]-262.884861901397[/C][/ROW]
[ROW][C]36[/C][C]10583[/C][C]10518.5562304087[/C][C]64.4437695912638[/C][/ROW]
[ROW][C]37[/C][C]10862[/C][C]10188.4947637839[/C][C]673.505236216133[/C][/ROW]
[ROW][C]38[/C][C]10965[/C][C]11735.0708682120[/C][C]-770.07086821202[/C][/ROW]
[ROW][C]39[/C][C]14405[/C][C]14571.5610188039[/C][C]-166.561018803932[/C][/ROW]
[ROW][C]40[/C][C]20379[/C][C]16526.0390820567[/C][C]3852.96091794326[/C][/ROW]
[ROW][C]41[/C][C]20128[/C][C]19790.3168617586[/C][C]337.683138241431[/C][/ROW]
[ROW][C]42[/C][C]17816[/C][C]16820.2770636948[/C][C]995.72293630516[/C][/ROW]
[ROW][C]43[/C][C]12268[/C][C]13026.4455747268[/C][C]-758.445574726766[/C][/ROW]
[ROW][C]44[/C][C]8642[/C][C]10689.8471672001[/C][C]-2047.84716720013[/C][/ROW]
[ROW][C]45[/C][C]7962[/C][C]8813.01284266297[/C][C]-851.01284266297[/C][/ROW]
[ROW][C]46[/C][C]13932[/C][C]10489.6997674117[/C][C]3442.30023258830[/C][/ROW]
[ROW][C]47[/C][C]15936[/C][C]13698.1154236907[/C][C]2237.88457630928[/C][/ROW]
[ROW][C]48[/C][C]12628[/C][C]12179.5755024990[/C][C]448.424497500981[/C][/ROW]
[ROW][C]49[/C][C]12267[/C][C]12113.4415781884[/C][C]153.558421811591[/C][/ROW]
[ROW][C]50[/C][C]12470[/C][C]13200.5667293058[/C][C]-730.566729305845[/C][/ROW]
[ROW][C]51[/C][C]18944[/C][C]16248.2319366495[/C][C]2695.76806335050[/C][/ROW]
[ROW][C]52[/C][C]21259[/C][C]19814.2321448011[/C][C]1444.76785519889[/C][/ROW]
[ROW][C]53[/C][C]22015[/C][C]21754.8401371267[/C][C]260.159862873283[/C][/ROW]
[ROW][C]54[/C][C]18581[/C][C]18996.7867886545[/C][C]-415.786788654485[/C][/ROW]
[ROW][C]55[/C][C]15175[/C][C]14522.5885824860[/C][C]652.41141751396[/C][/ROW]
[ROW][C]56[/C][C]10306[/C][C]12047.4146118136[/C][C]-1741.41461181356[/C][/ROW]
[ROW][C]57[/C][C]10792[/C][C]10594.0662250223[/C][C]197.933774977661[/C][/ROW]
[ROW][C]58[/C][C]14752[/C][C]13698.3855561416[/C][C]1053.61444385844[/C][/ROW]
[ROW][C]59[/C][C]13754[/C][C]16247.9210434732[/C][C]-2493.9210434732[/C][/ROW]
[ROW][C]60[/C][C]11738[/C][C]13547.0636665582[/C][C]-1809.06366655816[/C][/ROW]
[ROW][C]61[/C][C]12181[/C][C]13071.5623317288[/C][C]-890.562331728797[/C][/ROW]
[ROW][C]62[/C][C]12965[/C][C]13746.9848144270[/C][C]-781.98481442695[/C][/ROW]
[ROW][C]63[/C][C]19990[/C][C]17768.1011788146[/C][C]2221.89882118542[/C][/ROW]
[ROW][C]64[/C][C]23125[/C][C]20895.1827040629[/C][C]2229.81729593707[/C][/ROW]
[ROW][C]65[/C][C]23541[/C][C]22598.5670938337[/C][C]942.432906166276[/C][/ROW]
[ROW][C]66[/C][C]21247[/C][C]19738.6034535547[/C][C]1508.3965464453[/C][/ROW]
[ROW][C]67[/C][C]15189[/C][C]15851.2389526231[/C][C]-662.238952623136[/C][/ROW]
[ROW][C]68[/C][C]14767[/C][C]12497.1462662036[/C][C]2269.85373379635[/C][/ROW]
[ROW][C]69[/C][C]10895[/C][C]12191.0302334449[/C][C]-1296.03023344493[/C][/ROW]
[ROW][C]70[/C][C]17130[/C][C]15340.3590996979[/C][C]1789.64090030212[/C][/ROW]
[ROW][C]71[/C][C]17697[/C][C]16984.2246379397[/C][C]712.77536206026[/C][/ROW]
[ROW][C]72[/C][C]16611[/C][C]14965.2000147216[/C][C]1645.79998527843[/C][/ROW]
[ROW][C]73[/C][C]12674[/C][C]15289.9200790113[/C][C]-2615.92007901128[/C][/ROW]
[ROW][C]74[/C][C]12760[/C][C]15787.5154883498[/C][C]-3027.51548834982[/C][/ROW]
[ROW][C]75[/C][C]20249[/C][C]20382.4365910482[/C][C]-133.436591048157[/C][/ROW]
[ROW][C]76[/C][C]22135[/C][C]23192.2148414611[/C][C]-1057.21484146108[/C][/ROW]
[ROW][C]77[/C][C]20677[/C][C]24057.0365499997[/C][C]-3380.03654999974[/C][/ROW]
[ROW][C]78[/C][C]19933[/C][C]20726.7010671808[/C][C]-793.701067180846[/C][/ROW]
[ROW][C]79[/C][C]15388[/C][C]15855.7977118205[/C][C]-467.797711820498[/C][/ROW]
[ROW][C]80[/C][C]15113[/C][C]13346.9205315596[/C][C]1766.07946844040[/C][/ROW]
[ROW][C]81[/C][C]13401[/C][C]11908.7628699328[/C][C]1492.23713006716[/C][/ROW]
[ROW][C]82[/C][C]16135[/C][C]16326.7416969967[/C][C]-191.741696996733[/C][/ROW]
[ROW][C]83[/C][C]17562[/C][C]17350.6467426419[/C][C]211.353257358052[/C][/ROW]
[ROW][C]84[/C][C]14720[/C][C]15499.9597680745[/C][C]-779.959768074492[/C][/ROW]
[ROW][C]85[/C][C]12225[/C][C]14208.9299309708[/C][C]-1983.92993097075[/C][/ROW]
[ROW][C]86[/C][C]11608[/C][C]14639.7188171264[/C][C]-3031.71881712642[/C][/ROW]
[ROW][C]87[/C][C]20985[/C][C]20031.5912028116[/C][C]953.40879718843[/C][/ROW]
[ROW][C]88[/C][C]19692[/C][C]22696.2877319095[/C][C]-3004.28773190954[/C][/ROW]
[ROW][C]89[/C][C]24081[/C][C]22572.0413663742[/C][C]1508.95863362576[/C][/ROW]
[ROW][C]90[/C][C]22114[/C][C]20663.718661195[/C][C]1450.28133880498[/C][/ROW]
[ROW][C]91[/C][C]14220[/C][C]16196.4826943046[/C][C]-1976.48269430459[/C][/ROW]
[ROW][C]92[/C][C]13434[/C][C]14101.7024788636[/C][C]-667.702478863637[/C][/ROW]
[ROW][C]93[/C][C]13598[/C][C]12211.2118145913[/C][C]1386.78818540866[/C][/ROW]
[ROW][C]94[/C][C]17187[/C][C]16100.3290783718[/C][C]1086.67092162816[/C][/ROW]
[ROW][C]95[/C][C]16119[/C][C]17400.3589214253[/C][C]-1281.35892142525[/C][/ROW]
[ROW][C]96[/C][C]13713[/C][C]15022.5679092203[/C][C]-1309.56790922028[/C][/ROW]
[ROW][C]97[/C][C]13210[/C][C]13277.563949221[/C][C]-67.5639492210103[/C][/ROW]
[ROW][C]98[/C][C]14251[/C][C]13655.8764009879[/C][C]595.123599012064[/C][/ROW]
[ROW][C]99[/C][C]20139[/C][C]20707.6892366457[/C][C]-568.689236645660[/C][/ROW]
[ROW][C]100[/C][C]21725[/C][C]22000.6554797930[/C][C]-275.655479792968[/C][/ROW]
[ROW][C]101[/C][C]26099[/C][C]23566.5758574652[/C][C]2532.42414253480[/C][/ROW]
[ROW][C]102[/C][C]21084[/C][C]21790.9135200600[/C][C]-706.913520059981[/C][/ROW]
[ROW][C]103[/C][C]18024[/C][C]16022.1514716451[/C][C]2001.84852835487[/C][/ROW]
[ROW][C]104[/C][C]16722[/C][C]14883.0910412963[/C][C]1838.90895870367[/C][/ROW]
[ROW][C]105[/C][C]14385[/C][C]13965.7199679191[/C][C]419.280032080871[/C][/ROW]
[ROW][C]106[/C][C]21342[/C][C]17649.9976110729[/C][C]3692.00238892715[/C][/ROW]
[ROW][C]107[/C][C]17180[/C][C]18667.9977448033[/C][C]-1487.99774480328[/C][/ROW]
[ROW][C]108[/C][C]14577[/C][C]16282.8992813049[/C][C]-1705.89928130489[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72200&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72200&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
1372377082.00026709402154.999732905980
1493749172.19518755744201.804812442559
151183711641.1256946535195.874305346493
161378413938.0178882238-154.017888223778
171592616261.3869475829-335.386947582942
181382113940.0348245903-119.034824590261
19111439465.150094141761677.84990585824
2079758395.98878329206-420.988783292065
2176107108.04299670844501.957003291564
2210159703.95620138403-8688.95620138403
23127598213.205050784434545.79494921557
2488167870.83891453146945.161085468536
25106776741.876349851263935.12365014874
26109479393.334312504381553.66568749562
271520012069.22724221383130.77275778624
281701014712.14884387522297.85115612476
292090017372.64185291813527.3581470819
301620515721.3077341927483.692265807316
311214311911.9605558089231.039444191105
32899710085.8661054921-1088.86610549210
3355689020.96547985179-3452.96547985179
34114748435.220391373083038.77960862692
351225612518.8848619014-262.884861901397
361058310518.556230408764.4437695912638
371086210188.4947637839673.505236216133
381096511735.0708682120-770.07086821202
391440514571.5610188039-166.561018803932
402037916526.03908205673852.96091794326
412012819790.3168617586337.683138241431
421781616820.2770636948995.72293630516
431226813026.4455747268-758.445574726766
44864210689.8471672001-2047.84716720013
4579628813.01284266297-851.01284266297
461393210489.69976741173442.30023258830
471593613698.11542369072237.88457630928
481262812179.5755024990448.424497500981
491226712113.4415781884153.558421811591
501247013200.5667293058-730.566729305845
511894416248.23193664952695.76806335050
522125919814.23214480111444.76785519889
532201521754.8401371267260.159862873283
541858118996.7867886545-415.786788654485
551517514522.5885824860652.41141751396
561030612047.4146118136-1741.41461181356
571079210594.0662250223197.933774977661
581475213698.38555614161053.61444385844
591375416247.9210434732-2493.9210434732
601173813547.0636665582-1809.06366655816
611218113071.5623317288-890.562331728797
621296513746.9848144270-781.98481442695
631999017768.10117881462221.89882118542
642312520895.18270406292229.81729593707
652354122598.5670938337942.432906166276
662124719738.60345355471508.3965464453
671518915851.2389526231-662.238952623136
681476712497.14626620362269.85373379635
691089512191.0302334449-1296.03023344493
701713015340.35909969791789.64090030212
711769716984.2246379397712.77536206026
721661114965.20001472161645.79998527843
731267415289.9200790113-2615.92007901128
741276015787.5154883498-3027.51548834982
752024920382.4365910482-133.436591048157
762213523192.2148414611-1057.21484146108
772067724057.0365499997-3380.03654999974
781993320726.7010671808-793.701067180846
791538815855.7977118205-467.797711820498
801511313346.92053155961766.07946844040
811340111908.76286993281492.23713006716
821613516326.7416969967-191.741696996733
831756217350.6467426419211.353257358052
841472015499.9597680745-779.959768074492
851222514208.9299309708-1983.92993097075
861160814639.7188171264-3031.71881712642
872098520031.5912028116953.40879718843
881969222696.2877319095-3004.28773190954
892408122572.04136637421508.95863362576
902211420663.7186611951450.28133880498
911422016196.4826943046-1976.48269430459
921343414101.7024788636-667.702478863637
931359812211.21181459131386.78818540866
941718716100.32907837181086.67092162816
951611917400.3589214253-1281.35892142525
961371315022.5679092203-1309.56790922028
971321013277.563949221-67.5639492210103
981425113655.8764009879595.123599012064
992013920707.6892366457-568.689236645660
1002172522000.6554797930-275.655479792968
1012609923566.57585746522532.42414253480
1022108421790.9135200600-706.913520059981
1031802416022.15147164512001.84852835487
1041672214883.09104129631838.90895870367
1051438513965.7199679191419.280032080871
1062134217649.99761107293692.00238892715
1071718018667.9977448033-1487.99774480328
1081457716282.8992813049-1705.89928130489







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10914868.484803162811028.178665821918708.7909405037
11015476.415378860811595.007829810719357.822927911
11122133.699216996618209.082053243526058.3163807497
11223620.700166674519650.757652184927590.642681164
11326066.242656491422048.855196954130083.6301160287
11423013.863082537718946.910715425327080.8154496501
11518149.085595745514030.451281250122267.7199102409
11616690.900842969612518.473544642220863.3281412969
11715106.474175924210878.151723050719334.7966287976
11819678.112105684715391.803832505423964.4203788639
11918661.502825799514315.131985566623007.8736660325
12016417.307078817012008.813033337420825.8011242965

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 14868.4848031628 & 11028.1786658219 & 18708.7909405037 \tabularnewline
110 & 15476.4153788608 & 11595.0078298107 & 19357.822927911 \tabularnewline
111 & 22133.6992169966 & 18209.0820532435 & 26058.3163807497 \tabularnewline
112 & 23620.7001666745 & 19650.7576521849 & 27590.642681164 \tabularnewline
113 & 26066.2426564914 & 22048.8551969541 & 30083.6301160287 \tabularnewline
114 & 23013.8630825377 & 18946.9107154253 & 27080.8154496501 \tabularnewline
115 & 18149.0855957455 & 14030.4512812501 & 22267.7199102409 \tabularnewline
116 & 16690.9008429696 & 12518.4735446422 & 20863.3281412969 \tabularnewline
117 & 15106.4741759242 & 10878.1517230507 & 19334.7966287976 \tabularnewline
118 & 19678.1121056847 & 15391.8038325054 & 23964.4203788639 \tabularnewline
119 & 18661.5028257995 & 14315.1319855666 & 23007.8736660325 \tabularnewline
120 & 16417.3070788170 & 12008.8130333374 & 20825.8011242965 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72200&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]109[/C][C]14868.4848031628[/C][C]11028.1786658219[/C][C]18708.7909405037[/C][/ROW]
[ROW][C]110[/C][C]15476.4153788608[/C][C]11595.0078298107[/C][C]19357.822927911[/C][/ROW]
[ROW][C]111[/C][C]22133.6992169966[/C][C]18209.0820532435[/C][C]26058.3163807497[/C][/ROW]
[ROW][C]112[/C][C]23620.7001666745[/C][C]19650.7576521849[/C][C]27590.642681164[/C][/ROW]
[ROW][C]113[/C][C]26066.2426564914[/C][C]22048.8551969541[/C][C]30083.6301160287[/C][/ROW]
[ROW][C]114[/C][C]23013.8630825377[/C][C]18946.9107154253[/C][C]27080.8154496501[/C][/ROW]
[ROW][C]115[/C][C]18149.0855957455[/C][C]14030.4512812501[/C][C]22267.7199102409[/C][/ROW]
[ROW][C]116[/C][C]16690.9008429696[/C][C]12518.4735446422[/C][C]20863.3281412969[/C][/ROW]
[ROW][C]117[/C][C]15106.4741759242[/C][C]10878.1517230507[/C][C]19334.7966287976[/C][/ROW]
[ROW][C]118[/C][C]19678.1121056847[/C][C]15391.8038325054[/C][C]23964.4203788639[/C][/ROW]
[ROW][C]119[/C][C]18661.5028257995[/C][C]14315.1319855666[/C][C]23007.8736660325[/C][/ROW]
[ROW][C]120[/C][C]16417.3070788170[/C][C]12008.8130333374[/C][C]20825.8011242965[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72200&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72200&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
10914868.484803162811028.178665821918708.7909405037
11015476.415378860811595.007829810719357.822927911
11122133.699216996618209.082053243526058.3163807497
11223620.700166674519650.757652184927590.642681164
11326066.242656491422048.855196954130083.6301160287
11423013.863082537718946.910715425327080.8154496501
11518149.085595745514030.451281250122267.7199102409
11616690.900842969612518.473544642220863.3281412969
11715106.474175924210878.151723050719334.7966287976
11819678.112105684715391.803832505423964.4203788639
11918661.502825799514315.131985566623007.8736660325
12016417.307078817012008.813033337420825.8011242965



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')