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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 27 May 2010 13:08:49 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/May/27/t127496577225qif42t6jshsns.htm/, Retrieved Thu, 02 May 2024 06:33:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76600, Retrieved Thu, 02 May 2024 06:33:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 - Oef 2...] [2010-05-27 13:08:49] [413e0fefcf22560c5655fbc122c1a3c2] [Current]
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Dataseries X:
18450
21845
26488
22394
28057
25451
24872
33424
24052
28449
33533
37351
19969
21701
26249
24493
24603
26485
30723
34569
26689
26157
32064
38870
21337
19419
23166
28286
24570
24001
33151
24878
26804
28967
33311
40226
20504
23060
23562
27562
23940
24584
34303
25517
23494
29095
32903
34379
16991
21109
23740
25552
21752
20294
29009
25500
24166
26960
31222
38641
14672
17543
25453
32683
22449
22316
27595
25451
25421
25288
32568
35110
16052
22146
21198
19543
22084
23816
29961
26773
26635
26972
30207
38687
16974
21697
24179
23757
25013
24019
30345
24488
25156
25650
30923
37240
17466
19463
24352
26805
25236
24735
29356
31234
22724
28496
32857
37198




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76600&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76600&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76600&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0417042970576116
beta0.236464322500064
gamma0.389615920130008

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0417042970576116 \tabularnewline
beta & 0.236464322500064 \tabularnewline
gamma & 0.389615920130008 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76600&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]0.0417042970576116[/C][/ROW]
[ROW][C]beta[/C][C]0.236464322500064[/C][/ROW]
[ROW][C]gamma[/C][C]0.389615920130008[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76600&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76600&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
alpha0.0417042970576116
beta0.236464322500064
gamma0.389615920130008







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131996919924.850961538544.1490384615245
142170121437.2682796208263.731720379161
152624925911.3606167889337.639383211073
162449324231.0732116472261.926788352805
172460324587.294610836915.7053891631185
182648526546.6107329119-61.6107329118859
193072325566.42819472815156.57180527188
203456934405.1765614212163.823438578773
212668925186.57142477081502.42857522918
222615729714.1498581573-3557.14985815730
233206434816.6013508793-2752.60135087927
243887038703.8359796606166.164020339413
252133721143.2097783096193.790221690389
261941922760.522964851-3341.52296485098
272316627092.9720931864-3926.97209318636
282828625145.6243615613140.37563843899
292457025497.405387452-927.405387452018
302400127346.6688183811-3345.66881838112
313315128103.58586698955047.41413301054
322487834998.3370284753-10120.3370284753
332680425673.89541596941130.10458403063
342896728116.4595623729850.540437627114
353331133566.1837072657-255.183707265744
364022638535.03225172111690.96774827888
372050420951.0380417289-447.038041728905
382306021118.06255747811941.93744252192
392356225400.7772352218-1838.77723522178
402756226148.33545724791413.66454275213
412394024861.4038320330-921.403832032975
422458425760.1512279307-1176.15122793065
433430329714.77782255284588.22217744715
442551730896.2375642800-5379.23756428004
452349425985.8220585579-2491.8220585579
462909528152.9935916037942.00640839626
473290333174.6304539567-271.630453956706
483437938850.1995380444-4471.19953804443
491699120130.9636085841-3139.96360858411
502110920971.0987993930137.901200607033
512374023642.643688377497.3563116225669
522555225580.0569757276-28.0569757276498
532175223241.6983276031-1489.69832760314
542029423896.5638280095-3602.56382800948
552900929753.2314133507-744.231413350717
562550026789.1998708837-1289.19987088374
572416622966.17525891441199.82474108557
582696026444.5412489753515.458751024737
593122230866.2083247087355.791675291282
603864134877.10072541193763.89927458807
611467216956.6935179304-2284.69351793037
621754319023.1286695400-1480.12866954005
632545321562.88441131563890.11558868438
643268323599.87722060509083.12277939496
652244921173.84588098411275.15411901591
662231621260.48960229791055.51039770208
672759528529.9094106494-934.90941064943
682545125503.8547735041-52.8547735040884
692542122823.30606141392597.69393858611
702528826279.8292364979-991.82923649788
713256830739.53711747521828.46288252484
723511036259.3605514502-1149.36055145023
731605216002.288782315849.7112176841747
742214618616.08374816613529.91625183393
752119823568.8671685197-2370.86716851967
761954327420.9196792999-7877.91967929986
772208421342.3081661458741.691833854205
782381621289.44372340912526.55627659088
792996127856.30898649192104.69101350815
802677325295.57844556561477.42155443435
812663523692.79725986222942.20274013776
822697225851.19520514711120.80479485288
833020731500.5653688285-1293.56536882849
843868735796.1285193432890.87148065702
851697416212.8524878368761.14751216318
862169720220.33447133691476.66552866307
872417922928.70331314761250.29668685243
882375724955.7053393662-1198.70533936620
892501322519.87865163652493.12134836352
902401923369.6902909646649.309709035435
913034529845.4670083883499.532991611715
922448827112.4745894691-2624.47458946912
932515625973.9588685829-817.958868582908
942565027346.8412441745-1696.84124417454
953092332000.8199366293-1077.81993662930
963724037893.4031727671-653.403172767066
971746617357.8851532992108.114846700802
981946321589.5826406051-2126.58264060513
992435224011.9268908782340.073109121793
1002680525026.38031535841778.61968464160
1012523624062.27803529531173.72196470474
1022473524124.7847249024610.215275097609
1032935630498.7623583523-1142.76235835233
1043123426470.43442965484763.56557034523
1052272426326.9407162732-3602.94071627317
1062849627240.48231608401255.51768391603
1073285732262.7751126759594.22488732406
1083719838414.1078886004-1216.10788860044

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 19969 & 19924.8509615385 & 44.1490384615245 \tabularnewline
14 & 21701 & 21437.2682796208 & 263.731720379161 \tabularnewline
15 & 26249 & 25911.3606167889 & 337.639383211073 \tabularnewline
16 & 24493 & 24231.0732116472 & 261.926788352805 \tabularnewline
17 & 24603 & 24587.2946108369 & 15.7053891631185 \tabularnewline
18 & 26485 & 26546.6107329119 & -61.6107329118859 \tabularnewline
19 & 30723 & 25566.4281947281 & 5156.57180527188 \tabularnewline
20 & 34569 & 34405.1765614212 & 163.823438578773 \tabularnewline
21 & 26689 & 25186.5714247708 & 1502.42857522918 \tabularnewline
22 & 26157 & 29714.1498581573 & -3557.14985815730 \tabularnewline
23 & 32064 & 34816.6013508793 & -2752.60135087927 \tabularnewline
24 & 38870 & 38703.8359796606 & 166.164020339413 \tabularnewline
25 & 21337 & 21143.2097783096 & 193.790221690389 \tabularnewline
26 & 19419 & 22760.522964851 & -3341.52296485098 \tabularnewline
27 & 23166 & 27092.9720931864 & -3926.97209318636 \tabularnewline
28 & 28286 & 25145.624361561 & 3140.37563843899 \tabularnewline
29 & 24570 & 25497.405387452 & -927.405387452018 \tabularnewline
30 & 24001 & 27346.6688183811 & -3345.66881838112 \tabularnewline
31 & 33151 & 28103.5858669895 & 5047.41413301054 \tabularnewline
32 & 24878 & 34998.3370284753 & -10120.3370284753 \tabularnewline
33 & 26804 & 25673.8954159694 & 1130.10458403063 \tabularnewline
34 & 28967 & 28116.4595623729 & 850.540437627114 \tabularnewline
35 & 33311 & 33566.1837072657 & -255.183707265744 \tabularnewline
36 & 40226 & 38535.0322517211 & 1690.96774827888 \tabularnewline
37 & 20504 & 20951.0380417289 & -447.038041728905 \tabularnewline
38 & 23060 & 21118.0625574781 & 1941.93744252192 \tabularnewline
39 & 23562 & 25400.7772352218 & -1838.77723522178 \tabularnewline
40 & 27562 & 26148.3354572479 & 1413.66454275213 \tabularnewline
41 & 23940 & 24861.4038320330 & -921.403832032975 \tabularnewline
42 & 24584 & 25760.1512279307 & -1176.15122793065 \tabularnewline
43 & 34303 & 29714.7778225528 & 4588.22217744715 \tabularnewline
44 & 25517 & 30896.2375642800 & -5379.23756428004 \tabularnewline
45 & 23494 & 25985.8220585579 & -2491.8220585579 \tabularnewline
46 & 29095 & 28152.9935916037 & 942.00640839626 \tabularnewline
47 & 32903 & 33174.6304539567 & -271.630453956706 \tabularnewline
48 & 34379 & 38850.1995380444 & -4471.19953804443 \tabularnewline
49 & 16991 & 20130.9636085841 & -3139.96360858411 \tabularnewline
50 & 21109 & 20971.0987993930 & 137.901200607033 \tabularnewline
51 & 23740 & 23642.6436883774 & 97.3563116225669 \tabularnewline
52 & 25552 & 25580.0569757276 & -28.0569757276498 \tabularnewline
53 & 21752 & 23241.6983276031 & -1489.69832760314 \tabularnewline
54 & 20294 & 23896.5638280095 & -3602.56382800948 \tabularnewline
55 & 29009 & 29753.2314133507 & -744.231413350717 \tabularnewline
56 & 25500 & 26789.1998708837 & -1289.19987088374 \tabularnewline
57 & 24166 & 22966.1752589144 & 1199.82474108557 \tabularnewline
58 & 26960 & 26444.5412489753 & 515.458751024737 \tabularnewline
59 & 31222 & 30866.2083247087 & 355.791675291282 \tabularnewline
60 & 38641 & 34877.1007254119 & 3763.89927458807 \tabularnewline
61 & 14672 & 16956.6935179304 & -2284.69351793037 \tabularnewline
62 & 17543 & 19023.1286695400 & -1480.12866954005 \tabularnewline
63 & 25453 & 21562.8844113156 & 3890.11558868438 \tabularnewline
64 & 32683 & 23599.8772206050 & 9083.12277939496 \tabularnewline
65 & 22449 & 21173.8458809841 & 1275.15411901591 \tabularnewline
66 & 22316 & 21260.4896022979 & 1055.51039770208 \tabularnewline
67 & 27595 & 28529.9094106494 & -934.90941064943 \tabularnewline
68 & 25451 & 25503.8547735041 & -52.8547735040884 \tabularnewline
69 & 25421 & 22823.3060614139 & 2597.69393858611 \tabularnewline
70 & 25288 & 26279.8292364979 & -991.82923649788 \tabularnewline
71 & 32568 & 30739.5371174752 & 1828.46288252484 \tabularnewline
72 & 35110 & 36259.3605514502 & -1149.36055145023 \tabularnewline
73 & 16052 & 16002.2887823158 & 49.7112176841747 \tabularnewline
74 & 22146 & 18616.0837481661 & 3529.91625183393 \tabularnewline
75 & 21198 & 23568.8671685197 & -2370.86716851967 \tabularnewline
76 & 19543 & 27420.9196792999 & -7877.91967929986 \tabularnewline
77 & 22084 & 21342.3081661458 & 741.691833854205 \tabularnewline
78 & 23816 & 21289.4437234091 & 2526.55627659088 \tabularnewline
79 & 29961 & 27856.3089864919 & 2104.69101350815 \tabularnewline
80 & 26773 & 25295.5784455656 & 1477.42155443435 \tabularnewline
81 & 26635 & 23692.7972598622 & 2942.20274013776 \tabularnewline
82 & 26972 & 25851.1952051471 & 1120.80479485288 \tabularnewline
83 & 30207 & 31500.5653688285 & -1293.56536882849 \tabularnewline
84 & 38687 & 35796.128519343 & 2890.87148065702 \tabularnewline
85 & 16974 & 16212.8524878368 & 761.14751216318 \tabularnewline
86 & 21697 & 20220.3344713369 & 1476.66552866307 \tabularnewline
87 & 24179 & 22928.7033131476 & 1250.29668685243 \tabularnewline
88 & 23757 & 24955.7053393662 & -1198.70533936620 \tabularnewline
89 & 25013 & 22519.8786516365 & 2493.12134836352 \tabularnewline
90 & 24019 & 23369.6902909646 & 649.309709035435 \tabularnewline
91 & 30345 & 29845.4670083883 & 499.532991611715 \tabularnewline
92 & 24488 & 27112.4745894691 & -2624.47458946912 \tabularnewline
93 & 25156 & 25973.9588685829 & -817.958868582908 \tabularnewline
94 & 25650 & 27346.8412441745 & -1696.84124417454 \tabularnewline
95 & 30923 & 32000.8199366293 & -1077.81993662930 \tabularnewline
96 & 37240 & 37893.4031727671 & -653.403172767066 \tabularnewline
97 & 17466 & 17357.8851532992 & 108.114846700802 \tabularnewline
98 & 19463 & 21589.5826406051 & -2126.58264060513 \tabularnewline
99 & 24352 & 24011.9268908782 & 340.073109121793 \tabularnewline
100 & 26805 & 25026.3803153584 & 1778.61968464160 \tabularnewline
101 & 25236 & 24062.2780352953 & 1173.72196470474 \tabularnewline
102 & 24735 & 24124.7847249024 & 610.215275097609 \tabularnewline
103 & 29356 & 30498.7623583523 & -1142.76235835233 \tabularnewline
104 & 31234 & 26470.4344296548 & 4763.56557034523 \tabularnewline
105 & 22724 & 26326.9407162732 & -3602.94071627317 \tabularnewline
106 & 28496 & 27240.4823160840 & 1255.51768391603 \tabularnewline
107 & 32857 & 32262.7751126759 & 594.22488732406 \tabularnewline
108 & 37198 & 38414.1078886004 & -1216.10788860044 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76600&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]19969[/C][C]19924.8509615385[/C][C]44.1490384615245[/C][/ROW]
[ROW][C]14[/C][C]21701[/C][C]21437.2682796208[/C][C]263.731720379161[/C][/ROW]
[ROW][C]15[/C][C]26249[/C][C]25911.3606167889[/C][C]337.639383211073[/C][/ROW]
[ROW][C]16[/C][C]24493[/C][C]24231.0732116472[/C][C]261.926788352805[/C][/ROW]
[ROW][C]17[/C][C]24603[/C][C]24587.2946108369[/C][C]15.7053891631185[/C][/ROW]
[ROW][C]18[/C][C]26485[/C][C]26546.6107329119[/C][C]-61.6107329118859[/C][/ROW]
[ROW][C]19[/C][C]30723[/C][C]25566.4281947281[/C][C]5156.57180527188[/C][/ROW]
[ROW][C]20[/C][C]34569[/C][C]34405.1765614212[/C][C]163.823438578773[/C][/ROW]
[ROW][C]21[/C][C]26689[/C][C]25186.5714247708[/C][C]1502.42857522918[/C][/ROW]
[ROW][C]22[/C][C]26157[/C][C]29714.1498581573[/C][C]-3557.14985815730[/C][/ROW]
[ROW][C]23[/C][C]32064[/C][C]34816.6013508793[/C][C]-2752.60135087927[/C][/ROW]
[ROW][C]24[/C][C]38870[/C][C]38703.8359796606[/C][C]166.164020339413[/C][/ROW]
[ROW][C]25[/C][C]21337[/C][C]21143.2097783096[/C][C]193.790221690389[/C][/ROW]
[ROW][C]26[/C][C]19419[/C][C]22760.522964851[/C][C]-3341.52296485098[/C][/ROW]
[ROW][C]27[/C][C]23166[/C][C]27092.9720931864[/C][C]-3926.97209318636[/C][/ROW]
[ROW][C]28[/C][C]28286[/C][C]25145.624361561[/C][C]3140.37563843899[/C][/ROW]
[ROW][C]29[/C][C]24570[/C][C]25497.405387452[/C][C]-927.405387452018[/C][/ROW]
[ROW][C]30[/C][C]24001[/C][C]27346.6688183811[/C][C]-3345.66881838112[/C][/ROW]
[ROW][C]31[/C][C]33151[/C][C]28103.5858669895[/C][C]5047.41413301054[/C][/ROW]
[ROW][C]32[/C][C]24878[/C][C]34998.3370284753[/C][C]-10120.3370284753[/C][/ROW]
[ROW][C]33[/C][C]26804[/C][C]25673.8954159694[/C][C]1130.10458403063[/C][/ROW]
[ROW][C]34[/C][C]28967[/C][C]28116.4595623729[/C][C]850.540437627114[/C][/ROW]
[ROW][C]35[/C][C]33311[/C][C]33566.1837072657[/C][C]-255.183707265744[/C][/ROW]
[ROW][C]36[/C][C]40226[/C][C]38535.0322517211[/C][C]1690.96774827888[/C][/ROW]
[ROW][C]37[/C][C]20504[/C][C]20951.0380417289[/C][C]-447.038041728905[/C][/ROW]
[ROW][C]38[/C][C]23060[/C][C]21118.0625574781[/C][C]1941.93744252192[/C][/ROW]
[ROW][C]39[/C][C]23562[/C][C]25400.7772352218[/C][C]-1838.77723522178[/C][/ROW]
[ROW][C]40[/C][C]27562[/C][C]26148.3354572479[/C][C]1413.66454275213[/C][/ROW]
[ROW][C]41[/C][C]23940[/C][C]24861.4038320330[/C][C]-921.403832032975[/C][/ROW]
[ROW][C]42[/C][C]24584[/C][C]25760.1512279307[/C][C]-1176.15122793065[/C][/ROW]
[ROW][C]43[/C][C]34303[/C][C]29714.7778225528[/C][C]4588.22217744715[/C][/ROW]
[ROW][C]44[/C][C]25517[/C][C]30896.2375642800[/C][C]-5379.23756428004[/C][/ROW]
[ROW][C]45[/C][C]23494[/C][C]25985.8220585579[/C][C]-2491.8220585579[/C][/ROW]
[ROW][C]46[/C][C]29095[/C][C]28152.9935916037[/C][C]942.00640839626[/C][/ROW]
[ROW][C]47[/C][C]32903[/C][C]33174.6304539567[/C][C]-271.630453956706[/C][/ROW]
[ROW][C]48[/C][C]34379[/C][C]38850.1995380444[/C][C]-4471.19953804443[/C][/ROW]
[ROW][C]49[/C][C]16991[/C][C]20130.9636085841[/C][C]-3139.96360858411[/C][/ROW]
[ROW][C]50[/C][C]21109[/C][C]20971.0987993930[/C][C]137.901200607033[/C][/ROW]
[ROW][C]51[/C][C]23740[/C][C]23642.6436883774[/C][C]97.3563116225669[/C][/ROW]
[ROW][C]52[/C][C]25552[/C][C]25580.0569757276[/C][C]-28.0569757276498[/C][/ROW]
[ROW][C]53[/C][C]21752[/C][C]23241.6983276031[/C][C]-1489.69832760314[/C][/ROW]
[ROW][C]54[/C][C]20294[/C][C]23896.5638280095[/C][C]-3602.56382800948[/C][/ROW]
[ROW][C]55[/C][C]29009[/C][C]29753.2314133507[/C][C]-744.231413350717[/C][/ROW]
[ROW][C]56[/C][C]25500[/C][C]26789.1998708837[/C][C]-1289.19987088374[/C][/ROW]
[ROW][C]57[/C][C]24166[/C][C]22966.1752589144[/C][C]1199.82474108557[/C][/ROW]
[ROW][C]58[/C][C]26960[/C][C]26444.5412489753[/C][C]515.458751024737[/C][/ROW]
[ROW][C]59[/C][C]31222[/C][C]30866.2083247087[/C][C]355.791675291282[/C][/ROW]
[ROW][C]60[/C][C]38641[/C][C]34877.1007254119[/C][C]3763.89927458807[/C][/ROW]
[ROW][C]61[/C][C]14672[/C][C]16956.6935179304[/C][C]-2284.69351793037[/C][/ROW]
[ROW][C]62[/C][C]17543[/C][C]19023.1286695400[/C][C]-1480.12866954005[/C][/ROW]
[ROW][C]63[/C][C]25453[/C][C]21562.8844113156[/C][C]3890.11558868438[/C][/ROW]
[ROW][C]64[/C][C]32683[/C][C]23599.8772206050[/C][C]9083.12277939496[/C][/ROW]
[ROW][C]65[/C][C]22449[/C][C]21173.8458809841[/C][C]1275.15411901591[/C][/ROW]
[ROW][C]66[/C][C]22316[/C][C]21260.4896022979[/C][C]1055.51039770208[/C][/ROW]
[ROW][C]67[/C][C]27595[/C][C]28529.9094106494[/C][C]-934.90941064943[/C][/ROW]
[ROW][C]68[/C][C]25451[/C][C]25503.8547735041[/C][C]-52.8547735040884[/C][/ROW]
[ROW][C]69[/C][C]25421[/C][C]22823.3060614139[/C][C]2597.69393858611[/C][/ROW]
[ROW][C]70[/C][C]25288[/C][C]26279.8292364979[/C][C]-991.82923649788[/C][/ROW]
[ROW][C]71[/C][C]32568[/C][C]30739.5371174752[/C][C]1828.46288252484[/C][/ROW]
[ROW][C]72[/C][C]35110[/C][C]36259.3605514502[/C][C]-1149.36055145023[/C][/ROW]
[ROW][C]73[/C][C]16052[/C][C]16002.2887823158[/C][C]49.7112176841747[/C][/ROW]
[ROW][C]74[/C][C]22146[/C][C]18616.0837481661[/C][C]3529.91625183393[/C][/ROW]
[ROW][C]75[/C][C]21198[/C][C]23568.8671685197[/C][C]-2370.86716851967[/C][/ROW]
[ROW][C]76[/C][C]19543[/C][C]27420.9196792999[/C][C]-7877.91967929986[/C][/ROW]
[ROW][C]77[/C][C]22084[/C][C]21342.3081661458[/C][C]741.691833854205[/C][/ROW]
[ROW][C]78[/C][C]23816[/C][C]21289.4437234091[/C][C]2526.55627659088[/C][/ROW]
[ROW][C]79[/C][C]29961[/C][C]27856.3089864919[/C][C]2104.69101350815[/C][/ROW]
[ROW][C]80[/C][C]26773[/C][C]25295.5784455656[/C][C]1477.42155443435[/C][/ROW]
[ROW][C]81[/C][C]26635[/C][C]23692.7972598622[/C][C]2942.20274013776[/C][/ROW]
[ROW][C]82[/C][C]26972[/C][C]25851.1952051471[/C][C]1120.80479485288[/C][/ROW]
[ROW][C]83[/C][C]30207[/C][C]31500.5653688285[/C][C]-1293.56536882849[/C][/ROW]
[ROW][C]84[/C][C]38687[/C][C]35796.128519343[/C][C]2890.87148065702[/C][/ROW]
[ROW][C]85[/C][C]16974[/C][C]16212.8524878368[/C][C]761.14751216318[/C][/ROW]
[ROW][C]86[/C][C]21697[/C][C]20220.3344713369[/C][C]1476.66552866307[/C][/ROW]
[ROW][C]87[/C][C]24179[/C][C]22928.7033131476[/C][C]1250.29668685243[/C][/ROW]
[ROW][C]88[/C][C]23757[/C][C]24955.7053393662[/C][C]-1198.70533936620[/C][/ROW]
[ROW][C]89[/C][C]25013[/C][C]22519.8786516365[/C][C]2493.12134836352[/C][/ROW]
[ROW][C]90[/C][C]24019[/C][C]23369.6902909646[/C][C]649.309709035435[/C][/ROW]
[ROW][C]91[/C][C]30345[/C][C]29845.4670083883[/C][C]499.532991611715[/C][/ROW]
[ROW][C]92[/C][C]24488[/C][C]27112.4745894691[/C][C]-2624.47458946912[/C][/ROW]
[ROW][C]93[/C][C]25156[/C][C]25973.9588685829[/C][C]-817.958868582908[/C][/ROW]
[ROW][C]94[/C][C]25650[/C][C]27346.8412441745[/C][C]-1696.84124417454[/C][/ROW]
[ROW][C]95[/C][C]30923[/C][C]32000.8199366293[/C][C]-1077.81993662930[/C][/ROW]
[ROW][C]96[/C][C]37240[/C][C]37893.4031727671[/C][C]-653.403172767066[/C][/ROW]
[ROW][C]97[/C][C]17466[/C][C]17357.8851532992[/C][C]108.114846700802[/C][/ROW]
[ROW][C]98[/C][C]19463[/C][C]21589.5826406051[/C][C]-2126.58264060513[/C][/ROW]
[ROW][C]99[/C][C]24352[/C][C]24011.9268908782[/C][C]340.073109121793[/C][/ROW]
[ROW][C]100[/C][C]26805[/C][C]25026.3803153584[/C][C]1778.61968464160[/C][/ROW]
[ROW][C]101[/C][C]25236[/C][C]24062.2780352953[/C][C]1173.72196470474[/C][/ROW]
[ROW][C]102[/C][C]24735[/C][C]24124.7847249024[/C][C]610.215275097609[/C][/ROW]
[ROW][C]103[/C][C]29356[/C][C]30498.7623583523[/C][C]-1142.76235835233[/C][/ROW]
[ROW][C]104[/C][C]31234[/C][C]26470.4344296548[/C][C]4763.56557034523[/C][/ROW]
[ROW][C]105[/C][C]22724[/C][C]26326.9407162732[/C][C]-3602.94071627317[/C][/ROW]
[ROW][C]106[/C][C]28496[/C][C]27240.4823160840[/C][C]1255.51768391603[/C][/ROW]
[ROW][C]107[/C][C]32857[/C][C]32262.7751126759[/C][C]594.22488732406[/C][/ROW]
[ROW][C]108[/C][C]37198[/C][C]38414.1078886004[/C][C]-1216.10788860044[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76600&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76600&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
131996919924.850961538544.1490384615245
142170121437.2682796208263.731720379161
152624925911.3606167889337.639383211073
162449324231.0732116472261.926788352805
172460324587.294610836915.7053891631185
182648526546.6107329119-61.6107329118859
193072325566.42819472815156.57180527188
203456934405.1765614212163.823438578773
212668925186.57142477081502.42857522918
222615729714.1498581573-3557.14985815730
233206434816.6013508793-2752.60135087927
243887038703.8359796606166.164020339413
252133721143.2097783096193.790221690389
261941922760.522964851-3341.52296485098
272316627092.9720931864-3926.97209318636
282828625145.6243615613140.37563843899
292457025497.405387452-927.405387452018
302400127346.6688183811-3345.66881838112
313315128103.58586698955047.41413301054
322487834998.3370284753-10120.3370284753
332680425673.89541596941130.10458403063
342896728116.4595623729850.540437627114
353331133566.1837072657-255.183707265744
364022638535.03225172111690.96774827888
372050420951.0380417289-447.038041728905
382306021118.06255747811941.93744252192
392356225400.7772352218-1838.77723522178
402756226148.33545724791413.66454275213
412394024861.4038320330-921.403832032975
422458425760.1512279307-1176.15122793065
433430329714.77782255284588.22217744715
442551730896.2375642800-5379.23756428004
452349425985.8220585579-2491.8220585579
462909528152.9935916037942.00640839626
473290333174.6304539567-271.630453956706
483437938850.1995380444-4471.19953804443
491699120130.9636085841-3139.96360858411
502110920971.0987993930137.901200607033
512374023642.643688377497.3563116225669
522555225580.0569757276-28.0569757276498
532175223241.6983276031-1489.69832760314
542029423896.5638280095-3602.56382800948
552900929753.2314133507-744.231413350717
562550026789.1998708837-1289.19987088374
572416622966.17525891441199.82474108557
582696026444.5412489753515.458751024737
593122230866.2083247087355.791675291282
603864134877.10072541193763.89927458807
611467216956.6935179304-2284.69351793037
621754319023.1286695400-1480.12866954005
632545321562.88441131563890.11558868438
643268323599.87722060509083.12277939496
652244921173.84588098411275.15411901591
662231621260.48960229791055.51039770208
672759528529.9094106494-934.90941064943
682545125503.8547735041-52.8547735040884
692542122823.30606141392597.69393858611
702528826279.8292364979-991.82923649788
713256830739.53711747521828.46288252484
723511036259.3605514502-1149.36055145023
731605216002.288782315849.7112176841747
742214618616.08374816613529.91625183393
752119823568.8671685197-2370.86716851967
761954327420.9196792999-7877.91967929986
772208421342.3081661458741.691833854205
782381621289.44372340912526.55627659088
792996127856.30898649192104.69101350815
802677325295.57844556561477.42155443435
812663523692.79725986222942.20274013776
822697225851.19520514711120.80479485288
833020731500.5653688285-1293.56536882849
843868735796.1285193432890.87148065702
851697416212.8524878368761.14751216318
862169720220.33447133691476.66552866307
872417922928.70331314761250.29668685243
882375724955.7053393662-1198.70533936620
892501322519.87865163652493.12134836352
902401923369.6902909646649.309709035435
913034529845.4670083883499.532991611715
922448827112.4745894691-2624.47458946912
932515625973.9588685829-817.958868582908
942565027346.8412441745-1696.84124417454
953092332000.8199366293-1077.81993662930
963724037893.4031727671-653.403172767066
971746617357.8851532992108.114846700802
981946321589.5826406051-2126.58264060513
992435224011.9268908782340.073109121793
1002680525026.38031535841778.61968464160
1012523624062.27803529531173.72196470474
1022473524124.7847249024610.215275097609
1032935630498.7623583523-1142.76235835233
1043123426470.43442965484763.56557034523
1052272426326.9407162732-3602.94071627317
1062849627240.48231608401255.51768391603
1073285732262.7751126759594.22488732406
1083719838414.1078886004-1216.10788860044







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10918164.454166462112951.262490200623377.6458427235
11021581.219338706316361.101222496526801.3374549161
11125058.130609169219828.199215785030288.0620025534
11226637.064944632821393.945530779331880.1843584863
11325396.954802699320136.795526597230657.1140788014
11425212.559769190819931.045622364630494.073916017
11530913.009134556525605.379207279236220.6390618339
11629155.263025275523816.331209556934494.194840994
11725660.046568971520284.225684257731035.8674536853
11828544.084227466223125.413427598033962.7550273344
11933260.978712783427793.153904976938728.80352059
12038699.618022301833176.024907616444223.2111369873

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 18164.4541664621 & 12951.2624902006 & 23377.6458427235 \tabularnewline
110 & 21581.2193387063 & 16361.1012224965 & 26801.3374549161 \tabularnewline
111 & 25058.1306091692 & 19828.1992157850 & 30288.0620025534 \tabularnewline
112 & 26637.0649446328 & 21393.9455307793 & 31880.1843584863 \tabularnewline
113 & 25396.9548026993 & 20136.7955265972 & 30657.1140788014 \tabularnewline
114 & 25212.5597691908 & 19931.0456223646 & 30494.073916017 \tabularnewline
115 & 30913.0091345565 & 25605.3792072792 & 36220.6390618339 \tabularnewline
116 & 29155.2630252755 & 23816.3312095569 & 34494.194840994 \tabularnewline
117 & 25660.0465689715 & 20284.2256842577 & 31035.8674536853 \tabularnewline
118 & 28544.0842274662 & 23125.4134275980 & 33962.7550273344 \tabularnewline
119 & 33260.9787127834 & 27793.1539049769 & 38728.80352059 \tabularnewline
120 & 38699.6180223018 & 33176.0249076164 & 44223.2111369873 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76600&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]18164.4541664621[/C][C]12951.2624902006[/C][C]23377.6458427235[/C][/ROW]
[ROW][C]110[/C][C]21581.2193387063[/C][C]16361.1012224965[/C][C]26801.3374549161[/C][/ROW]
[ROW][C]111[/C][C]25058.1306091692[/C][C]19828.1992157850[/C][C]30288.0620025534[/C][/ROW]
[ROW][C]112[/C][C]26637.0649446328[/C][C]21393.9455307793[/C][C]31880.1843584863[/C][/ROW]
[ROW][C]113[/C][C]25396.9548026993[/C][C]20136.7955265972[/C][C]30657.1140788014[/C][/ROW]
[ROW][C]114[/C][C]25212.5597691908[/C][C]19931.0456223646[/C][C]30494.073916017[/C][/ROW]
[ROW][C]115[/C][C]30913.0091345565[/C][C]25605.3792072792[/C][C]36220.6390618339[/C][/ROW]
[ROW][C]116[/C][C]29155.2630252755[/C][C]23816.3312095569[/C][C]34494.194840994[/C][/ROW]
[ROW][C]117[/C][C]25660.0465689715[/C][C]20284.2256842577[/C][C]31035.8674536853[/C][/ROW]
[ROW][C]118[/C][C]28544.0842274662[/C][C]23125.4134275980[/C][C]33962.7550273344[/C][/ROW]
[ROW][C]119[/C][C]33260.9787127834[/C][C]27793.1539049769[/C][C]38728.80352059[/C][/ROW]
[ROW][C]120[/C][C]38699.6180223018[/C][C]33176.0249076164[/C][C]44223.2111369873[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76600&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76600&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
10918164.454166462112951.262490200623377.6458427235
11021581.219338706316361.101222496526801.3374549161
11125058.130609169219828.199215785030288.0620025534
11226637.064944632821393.945530779331880.1843584863
11325396.954802699320136.795526597230657.1140788014
11425212.559769190819931.045622364630494.073916017
11530913.009134556525605.379207279236220.6390618339
11629155.263025275523816.331209556934494.194840994
11725660.046568971520284.225684257731035.8674536853
11828544.084227466223125.413427598033962.7550273344
11933260.978712783427793.153904976938728.80352059
12038699.618022301833176.024907616444223.2111369873



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