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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 18 May 2011 12:03:33 +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/2011/May/18/t13057200192zulfhms8dchman.htm/, Retrieved Mon, 13 May 2024 23:56:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121794, Retrieved Mon, 13 May 2024 23:56:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10.2] [2011-05-18 12:03:33] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
814
1150
1225
1691
1759
1754
2100
2062
2012
1897
1964
2186
966
1549
1538
1612
2078
2137
2907
2249
1883
1739
1828
1868
1138
1430
1809
1763
2200
2067
2503
2141
2103
1972
2181
2344
970
1199
1718
1683
2025
2051
2439
2353
2230
1852
2147
2286
1007
1665
1642
1518
1831
2207
2822
2393
2306
1785
2047
2171
1212
1335
2011
1860
1954
2152
2835
2224
2182
1992
2389
2724
891
1247
2017
2257
2255
2255
3057
3330
1896
2096
2374
2535
1041
1728
2201
2455
2204
2660
3670
2665
2639
2226
2586
2684
1185
1749
2459
2618
2585
3310
3923




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121794&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121794&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121794&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.171837101246772
beta0
gamma0.386851263600274

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.171837101246772 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.386851263600274 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121794&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]0.171837101246772[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.386851263600274[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121794&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121794&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
alpha0.171837101246772
beta0
gamma0.386851263600274







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13966890.37487102069575.6251289793047
1415491431.26540160807117.734598391932
1515381453.250790922684.7492090774037
1616121562.718190933649.2818090664045
1720782057.4693081741720.530691825832
1821372160.60990815768-23.6099081576813
1929072327.02923601584579.970763984157
2022492371.90374660748-122.903746607481
2118832275.09132018145-392.09132018145
2217392088.5556874905-349.555687490495
2318282107.37328273892-279.373282738923
2418682276.15735192144-408.157351921438
251138983.685964199098154.314035800902
2614301597.94935199721-167.949351997213
2718091558.76134094957250.23865905043
2817631690.1238408673472.8761591326563
2922002213.09042200071-13.0904220007133
3020672300.85738822245-233.857388222445
3125032634.22289608979-131.222896089791
3221412331.4449766286-190.444976628596
3321032133.963224215-30.9632242150019
3419722016.97246438246-44.9724643824586
3521812112.4553236313168.5446763686859
3623442307.5095100798236.4904899201788
379701149.31718857444-179.317188574435
3811991628.10390677362-429.103906773623
3917181678.6160863352639.3839136647357
4016831716.7851533595-33.785153359499
4120252189.84203542125-164.842035421247
4220512179.49365273091-128.493652730908
4324392558.50852518634-119.508525186343
4423532241.83984809527111.160151904734
4522302145.8827304727384.1172695272658
4618522041.50208807352-189.502088073515
4721472149.25232240628-2.25232240627884
4822862322.03079251129-36.0307925112884
4910071085.80783155629-78.8078315562923
5016651499.65495782406165.345042175942
5116421822.70552670598-180.705526705982
5215181799.1924568875-281.192456887499
5318312199.51454663209-368.514546632086
5422072165.5291468775141.4708531224892
5528222586.49209911449235.507900885514
5623932392.085853964470.914146035534031
5723062262.4011392128643.5988607871395
5817852053.94526409419-268.945264094192
5920472213.59360536566-166.593605365655
6021712349.72746842407-178.72746842407
6112121066.95664625435145.043353745648
6213351617.56743478251-282.567434782512
6320111750.50001777202260.499982227984
6418601766.6588291947893.341170805217
6519542229.20033358206-275.20033358206
6621522354.07089111243-202.070891112428
6728352821.7843869921413.2156130078597
6822242499.17192715494-275.171927154935
6921822332.32640922816-150.326409228161
7019921985.121302973156.87869702685134
7123892231.67363751923157.326362480774
7227242427.23706486073296.762935139272
738911217.94263141972-326.942631419722
7412471555.33432394767-308.33432394767
7520171861.20428215139155.795717848615
7622571805.07154481788451.928455182124
7722552221.230976563133.7690234368979
7822552432.88275703902-177.882757039023
7930573009.6714612563647.3285387436449
8033302569.47036879694760.529631203062
8118962606.04087332991-710.040873329906
8220962184.33339151501-88.333391515012
8323742487.07905491054-113.079054910535
8425352692.03977051495-157.039770514949
8510411147.34045999992-106.340459999922
8617281551.32916861704176.670831382963
8722012150.8776534646150.1223465353878
8824552164.4052766606290.594723339399
8922042436.13220717465-232.132207174655
9026602542.01819880033117.981801199671
9136703302.50843006674367.491569933263
9226653106.32350670552-441.323506705517
9326392436.59954952698202.400450473016
9422262359.57132754962-133.571327549615
9525862673.00752314577-87.0075231457672
9626842885.60415105108-201.604151051084
9711851212.50477919223-27.5047791922266
9817491771.11376805478-22.113768054784
9924592336.29249633475122.707503665255
10026182442.56242295145175.437577048554
10125852528.4235315344656.5764684655405
10233102818.10536968948491.894630310517
10339233813.00610020984109.993899790165

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 966 & 890.374871020695 & 75.6251289793047 \tabularnewline
14 & 1549 & 1431.26540160807 & 117.734598391932 \tabularnewline
15 & 1538 & 1453.2507909226 & 84.7492090774037 \tabularnewline
16 & 1612 & 1562.7181909336 & 49.2818090664045 \tabularnewline
17 & 2078 & 2057.46930817417 & 20.530691825832 \tabularnewline
18 & 2137 & 2160.60990815768 & -23.6099081576813 \tabularnewline
19 & 2907 & 2327.02923601584 & 579.970763984157 \tabularnewline
20 & 2249 & 2371.90374660748 & -122.903746607481 \tabularnewline
21 & 1883 & 2275.09132018145 & -392.09132018145 \tabularnewline
22 & 1739 & 2088.5556874905 & -349.555687490495 \tabularnewline
23 & 1828 & 2107.37328273892 & -279.373282738923 \tabularnewline
24 & 1868 & 2276.15735192144 & -408.157351921438 \tabularnewline
25 & 1138 & 983.685964199098 & 154.314035800902 \tabularnewline
26 & 1430 & 1597.94935199721 & -167.949351997213 \tabularnewline
27 & 1809 & 1558.76134094957 & 250.23865905043 \tabularnewline
28 & 1763 & 1690.12384086734 & 72.8761591326563 \tabularnewline
29 & 2200 & 2213.09042200071 & -13.0904220007133 \tabularnewline
30 & 2067 & 2300.85738822245 & -233.857388222445 \tabularnewline
31 & 2503 & 2634.22289608979 & -131.222896089791 \tabularnewline
32 & 2141 & 2331.4449766286 & -190.444976628596 \tabularnewline
33 & 2103 & 2133.963224215 & -30.9632242150019 \tabularnewline
34 & 1972 & 2016.97246438246 & -44.9724643824586 \tabularnewline
35 & 2181 & 2112.45532363131 & 68.5446763686859 \tabularnewline
36 & 2344 & 2307.50951007982 & 36.4904899201788 \tabularnewline
37 & 970 & 1149.31718857444 & -179.317188574435 \tabularnewline
38 & 1199 & 1628.10390677362 & -429.103906773623 \tabularnewline
39 & 1718 & 1678.61608633526 & 39.3839136647357 \tabularnewline
40 & 1683 & 1716.7851533595 & -33.785153359499 \tabularnewline
41 & 2025 & 2189.84203542125 & -164.842035421247 \tabularnewline
42 & 2051 & 2179.49365273091 & -128.493652730908 \tabularnewline
43 & 2439 & 2558.50852518634 & -119.508525186343 \tabularnewline
44 & 2353 & 2241.83984809527 & 111.160151904734 \tabularnewline
45 & 2230 & 2145.88273047273 & 84.1172695272658 \tabularnewline
46 & 1852 & 2041.50208807352 & -189.502088073515 \tabularnewline
47 & 2147 & 2149.25232240628 & -2.25232240627884 \tabularnewline
48 & 2286 & 2322.03079251129 & -36.0307925112884 \tabularnewline
49 & 1007 & 1085.80783155629 & -78.8078315562923 \tabularnewline
50 & 1665 & 1499.65495782406 & 165.345042175942 \tabularnewline
51 & 1642 & 1822.70552670598 & -180.705526705982 \tabularnewline
52 & 1518 & 1799.1924568875 & -281.192456887499 \tabularnewline
53 & 1831 & 2199.51454663209 & -368.514546632086 \tabularnewline
54 & 2207 & 2165.52914687751 & 41.4708531224892 \tabularnewline
55 & 2822 & 2586.49209911449 & 235.507900885514 \tabularnewline
56 & 2393 & 2392.08585396447 & 0.914146035534031 \tabularnewline
57 & 2306 & 2262.40113921286 & 43.5988607871395 \tabularnewline
58 & 1785 & 2053.94526409419 & -268.945264094192 \tabularnewline
59 & 2047 & 2213.59360536566 & -166.593605365655 \tabularnewline
60 & 2171 & 2349.72746842407 & -178.72746842407 \tabularnewline
61 & 1212 & 1066.95664625435 & 145.043353745648 \tabularnewline
62 & 1335 & 1617.56743478251 & -282.567434782512 \tabularnewline
63 & 2011 & 1750.50001777202 & 260.499982227984 \tabularnewline
64 & 1860 & 1766.65882919478 & 93.341170805217 \tabularnewline
65 & 1954 & 2229.20033358206 & -275.20033358206 \tabularnewline
66 & 2152 & 2354.07089111243 & -202.070891112428 \tabularnewline
67 & 2835 & 2821.78438699214 & 13.2156130078597 \tabularnewline
68 & 2224 & 2499.17192715494 & -275.171927154935 \tabularnewline
69 & 2182 & 2332.32640922816 & -150.326409228161 \tabularnewline
70 & 1992 & 1985.12130297315 & 6.87869702685134 \tabularnewline
71 & 2389 & 2231.67363751923 & 157.326362480774 \tabularnewline
72 & 2724 & 2427.23706486073 & 296.762935139272 \tabularnewline
73 & 891 & 1217.94263141972 & -326.942631419722 \tabularnewline
74 & 1247 & 1555.33432394767 & -308.33432394767 \tabularnewline
75 & 2017 & 1861.20428215139 & 155.795717848615 \tabularnewline
76 & 2257 & 1805.07154481788 & 451.928455182124 \tabularnewline
77 & 2255 & 2221.2309765631 & 33.7690234368979 \tabularnewline
78 & 2255 & 2432.88275703902 & -177.882757039023 \tabularnewline
79 & 3057 & 3009.67146125636 & 47.3285387436449 \tabularnewline
80 & 3330 & 2569.47036879694 & 760.529631203062 \tabularnewline
81 & 1896 & 2606.04087332991 & -710.040873329906 \tabularnewline
82 & 2096 & 2184.33339151501 & -88.333391515012 \tabularnewline
83 & 2374 & 2487.07905491054 & -113.079054910535 \tabularnewline
84 & 2535 & 2692.03977051495 & -157.039770514949 \tabularnewline
85 & 1041 & 1147.34045999992 & -106.340459999922 \tabularnewline
86 & 1728 & 1551.32916861704 & 176.670831382963 \tabularnewline
87 & 2201 & 2150.87765346461 & 50.1223465353878 \tabularnewline
88 & 2455 & 2164.4052766606 & 290.594723339399 \tabularnewline
89 & 2204 & 2436.13220717465 & -232.132207174655 \tabularnewline
90 & 2660 & 2542.01819880033 & 117.981801199671 \tabularnewline
91 & 3670 & 3302.50843006674 & 367.491569933263 \tabularnewline
92 & 2665 & 3106.32350670552 & -441.323506705517 \tabularnewline
93 & 2639 & 2436.59954952698 & 202.400450473016 \tabularnewline
94 & 2226 & 2359.57132754962 & -133.571327549615 \tabularnewline
95 & 2586 & 2673.00752314577 & -87.0075231457672 \tabularnewline
96 & 2684 & 2885.60415105108 & -201.604151051084 \tabularnewline
97 & 1185 & 1212.50477919223 & -27.5047791922266 \tabularnewline
98 & 1749 & 1771.11376805478 & -22.113768054784 \tabularnewline
99 & 2459 & 2336.29249633475 & 122.707503665255 \tabularnewline
100 & 2618 & 2442.56242295145 & 175.437577048554 \tabularnewline
101 & 2585 & 2528.42353153446 & 56.5764684655405 \tabularnewline
102 & 3310 & 2818.10536968948 & 491.894630310517 \tabularnewline
103 & 3923 & 3813.00610020984 & 109.993899790165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121794&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]966[/C][C]890.374871020695[/C][C]75.6251289793047[/C][/ROW]
[ROW][C]14[/C][C]1549[/C][C]1431.26540160807[/C][C]117.734598391932[/C][/ROW]
[ROW][C]15[/C][C]1538[/C][C]1453.2507909226[/C][C]84.7492090774037[/C][/ROW]
[ROW][C]16[/C][C]1612[/C][C]1562.7181909336[/C][C]49.2818090664045[/C][/ROW]
[ROW][C]17[/C][C]2078[/C][C]2057.46930817417[/C][C]20.530691825832[/C][/ROW]
[ROW][C]18[/C][C]2137[/C][C]2160.60990815768[/C][C]-23.6099081576813[/C][/ROW]
[ROW][C]19[/C][C]2907[/C][C]2327.02923601584[/C][C]579.970763984157[/C][/ROW]
[ROW][C]20[/C][C]2249[/C][C]2371.90374660748[/C][C]-122.903746607481[/C][/ROW]
[ROW][C]21[/C][C]1883[/C][C]2275.09132018145[/C][C]-392.09132018145[/C][/ROW]
[ROW][C]22[/C][C]1739[/C][C]2088.5556874905[/C][C]-349.555687490495[/C][/ROW]
[ROW][C]23[/C][C]1828[/C][C]2107.37328273892[/C][C]-279.373282738923[/C][/ROW]
[ROW][C]24[/C][C]1868[/C][C]2276.15735192144[/C][C]-408.157351921438[/C][/ROW]
[ROW][C]25[/C][C]1138[/C][C]983.685964199098[/C][C]154.314035800902[/C][/ROW]
[ROW][C]26[/C][C]1430[/C][C]1597.94935199721[/C][C]-167.949351997213[/C][/ROW]
[ROW][C]27[/C][C]1809[/C][C]1558.76134094957[/C][C]250.23865905043[/C][/ROW]
[ROW][C]28[/C][C]1763[/C][C]1690.12384086734[/C][C]72.8761591326563[/C][/ROW]
[ROW][C]29[/C][C]2200[/C][C]2213.09042200071[/C][C]-13.0904220007133[/C][/ROW]
[ROW][C]30[/C][C]2067[/C][C]2300.85738822245[/C][C]-233.857388222445[/C][/ROW]
[ROW][C]31[/C][C]2503[/C][C]2634.22289608979[/C][C]-131.222896089791[/C][/ROW]
[ROW][C]32[/C][C]2141[/C][C]2331.4449766286[/C][C]-190.444976628596[/C][/ROW]
[ROW][C]33[/C][C]2103[/C][C]2133.963224215[/C][C]-30.9632242150019[/C][/ROW]
[ROW][C]34[/C][C]1972[/C][C]2016.97246438246[/C][C]-44.9724643824586[/C][/ROW]
[ROW][C]35[/C][C]2181[/C][C]2112.45532363131[/C][C]68.5446763686859[/C][/ROW]
[ROW][C]36[/C][C]2344[/C][C]2307.50951007982[/C][C]36.4904899201788[/C][/ROW]
[ROW][C]37[/C][C]970[/C][C]1149.31718857444[/C][C]-179.317188574435[/C][/ROW]
[ROW][C]38[/C][C]1199[/C][C]1628.10390677362[/C][C]-429.103906773623[/C][/ROW]
[ROW][C]39[/C][C]1718[/C][C]1678.61608633526[/C][C]39.3839136647357[/C][/ROW]
[ROW][C]40[/C][C]1683[/C][C]1716.7851533595[/C][C]-33.785153359499[/C][/ROW]
[ROW][C]41[/C][C]2025[/C][C]2189.84203542125[/C][C]-164.842035421247[/C][/ROW]
[ROW][C]42[/C][C]2051[/C][C]2179.49365273091[/C][C]-128.493652730908[/C][/ROW]
[ROW][C]43[/C][C]2439[/C][C]2558.50852518634[/C][C]-119.508525186343[/C][/ROW]
[ROW][C]44[/C][C]2353[/C][C]2241.83984809527[/C][C]111.160151904734[/C][/ROW]
[ROW][C]45[/C][C]2230[/C][C]2145.88273047273[/C][C]84.1172695272658[/C][/ROW]
[ROW][C]46[/C][C]1852[/C][C]2041.50208807352[/C][C]-189.502088073515[/C][/ROW]
[ROW][C]47[/C][C]2147[/C][C]2149.25232240628[/C][C]-2.25232240627884[/C][/ROW]
[ROW][C]48[/C][C]2286[/C][C]2322.03079251129[/C][C]-36.0307925112884[/C][/ROW]
[ROW][C]49[/C][C]1007[/C][C]1085.80783155629[/C][C]-78.8078315562923[/C][/ROW]
[ROW][C]50[/C][C]1665[/C][C]1499.65495782406[/C][C]165.345042175942[/C][/ROW]
[ROW][C]51[/C][C]1642[/C][C]1822.70552670598[/C][C]-180.705526705982[/C][/ROW]
[ROW][C]52[/C][C]1518[/C][C]1799.1924568875[/C][C]-281.192456887499[/C][/ROW]
[ROW][C]53[/C][C]1831[/C][C]2199.51454663209[/C][C]-368.514546632086[/C][/ROW]
[ROW][C]54[/C][C]2207[/C][C]2165.52914687751[/C][C]41.4708531224892[/C][/ROW]
[ROW][C]55[/C][C]2822[/C][C]2586.49209911449[/C][C]235.507900885514[/C][/ROW]
[ROW][C]56[/C][C]2393[/C][C]2392.08585396447[/C][C]0.914146035534031[/C][/ROW]
[ROW][C]57[/C][C]2306[/C][C]2262.40113921286[/C][C]43.5988607871395[/C][/ROW]
[ROW][C]58[/C][C]1785[/C][C]2053.94526409419[/C][C]-268.945264094192[/C][/ROW]
[ROW][C]59[/C][C]2047[/C][C]2213.59360536566[/C][C]-166.593605365655[/C][/ROW]
[ROW][C]60[/C][C]2171[/C][C]2349.72746842407[/C][C]-178.72746842407[/C][/ROW]
[ROW][C]61[/C][C]1212[/C][C]1066.95664625435[/C][C]145.043353745648[/C][/ROW]
[ROW][C]62[/C][C]1335[/C][C]1617.56743478251[/C][C]-282.567434782512[/C][/ROW]
[ROW][C]63[/C][C]2011[/C][C]1750.50001777202[/C][C]260.499982227984[/C][/ROW]
[ROW][C]64[/C][C]1860[/C][C]1766.65882919478[/C][C]93.341170805217[/C][/ROW]
[ROW][C]65[/C][C]1954[/C][C]2229.20033358206[/C][C]-275.20033358206[/C][/ROW]
[ROW][C]66[/C][C]2152[/C][C]2354.07089111243[/C][C]-202.070891112428[/C][/ROW]
[ROW][C]67[/C][C]2835[/C][C]2821.78438699214[/C][C]13.2156130078597[/C][/ROW]
[ROW][C]68[/C][C]2224[/C][C]2499.17192715494[/C][C]-275.171927154935[/C][/ROW]
[ROW][C]69[/C][C]2182[/C][C]2332.32640922816[/C][C]-150.326409228161[/C][/ROW]
[ROW][C]70[/C][C]1992[/C][C]1985.12130297315[/C][C]6.87869702685134[/C][/ROW]
[ROW][C]71[/C][C]2389[/C][C]2231.67363751923[/C][C]157.326362480774[/C][/ROW]
[ROW][C]72[/C][C]2724[/C][C]2427.23706486073[/C][C]296.762935139272[/C][/ROW]
[ROW][C]73[/C][C]891[/C][C]1217.94263141972[/C][C]-326.942631419722[/C][/ROW]
[ROW][C]74[/C][C]1247[/C][C]1555.33432394767[/C][C]-308.33432394767[/C][/ROW]
[ROW][C]75[/C][C]2017[/C][C]1861.20428215139[/C][C]155.795717848615[/C][/ROW]
[ROW][C]76[/C][C]2257[/C][C]1805.07154481788[/C][C]451.928455182124[/C][/ROW]
[ROW][C]77[/C][C]2255[/C][C]2221.2309765631[/C][C]33.7690234368979[/C][/ROW]
[ROW][C]78[/C][C]2255[/C][C]2432.88275703902[/C][C]-177.882757039023[/C][/ROW]
[ROW][C]79[/C][C]3057[/C][C]3009.67146125636[/C][C]47.3285387436449[/C][/ROW]
[ROW][C]80[/C][C]3330[/C][C]2569.47036879694[/C][C]760.529631203062[/C][/ROW]
[ROW][C]81[/C][C]1896[/C][C]2606.04087332991[/C][C]-710.040873329906[/C][/ROW]
[ROW][C]82[/C][C]2096[/C][C]2184.33339151501[/C][C]-88.333391515012[/C][/ROW]
[ROW][C]83[/C][C]2374[/C][C]2487.07905491054[/C][C]-113.079054910535[/C][/ROW]
[ROW][C]84[/C][C]2535[/C][C]2692.03977051495[/C][C]-157.039770514949[/C][/ROW]
[ROW][C]85[/C][C]1041[/C][C]1147.34045999992[/C][C]-106.340459999922[/C][/ROW]
[ROW][C]86[/C][C]1728[/C][C]1551.32916861704[/C][C]176.670831382963[/C][/ROW]
[ROW][C]87[/C][C]2201[/C][C]2150.87765346461[/C][C]50.1223465353878[/C][/ROW]
[ROW][C]88[/C][C]2455[/C][C]2164.4052766606[/C][C]290.594723339399[/C][/ROW]
[ROW][C]89[/C][C]2204[/C][C]2436.13220717465[/C][C]-232.132207174655[/C][/ROW]
[ROW][C]90[/C][C]2660[/C][C]2542.01819880033[/C][C]117.981801199671[/C][/ROW]
[ROW][C]91[/C][C]3670[/C][C]3302.50843006674[/C][C]367.491569933263[/C][/ROW]
[ROW][C]92[/C][C]2665[/C][C]3106.32350670552[/C][C]-441.323506705517[/C][/ROW]
[ROW][C]93[/C][C]2639[/C][C]2436.59954952698[/C][C]202.400450473016[/C][/ROW]
[ROW][C]94[/C][C]2226[/C][C]2359.57132754962[/C][C]-133.571327549615[/C][/ROW]
[ROW][C]95[/C][C]2586[/C][C]2673.00752314577[/C][C]-87.0075231457672[/C][/ROW]
[ROW][C]96[/C][C]2684[/C][C]2885.60415105108[/C][C]-201.604151051084[/C][/ROW]
[ROW][C]97[/C][C]1185[/C][C]1212.50477919223[/C][C]-27.5047791922266[/C][/ROW]
[ROW][C]98[/C][C]1749[/C][C]1771.11376805478[/C][C]-22.113768054784[/C][/ROW]
[ROW][C]99[/C][C]2459[/C][C]2336.29249633475[/C][C]122.707503665255[/C][/ROW]
[ROW][C]100[/C][C]2618[/C][C]2442.56242295145[/C][C]175.437577048554[/C][/ROW]
[ROW][C]101[/C][C]2585[/C][C]2528.42353153446[/C][C]56.5764684655405[/C][/ROW]
[ROW][C]102[/C][C]3310[/C][C]2818.10536968948[/C][C]491.894630310517[/C][/ROW]
[ROW][C]103[/C][C]3923[/C][C]3813.00610020984[/C][C]109.993899790165[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121794&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121794&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
13966890.37487102069575.6251289793047
1415491431.26540160807117.734598391932
1515381453.250790922684.7492090774037
1616121562.718190933649.2818090664045
1720782057.4693081741720.530691825832
1821372160.60990815768-23.6099081576813
1929072327.02923601584579.970763984157
2022492371.90374660748-122.903746607481
2118832275.09132018145-392.09132018145
2217392088.5556874905-349.555687490495
2318282107.37328273892-279.373282738923
2418682276.15735192144-408.157351921438
251138983.685964199098154.314035800902
2614301597.94935199721-167.949351997213
2718091558.76134094957250.23865905043
2817631690.1238408673472.8761591326563
2922002213.09042200071-13.0904220007133
3020672300.85738822245-233.857388222445
3125032634.22289608979-131.222896089791
3221412331.4449766286-190.444976628596
3321032133.963224215-30.9632242150019
3419722016.97246438246-44.9724643824586
3521812112.4553236313168.5446763686859
3623442307.5095100798236.4904899201788
379701149.31718857444-179.317188574435
3811991628.10390677362-429.103906773623
3917181678.6160863352639.3839136647357
4016831716.7851533595-33.785153359499
4120252189.84203542125-164.842035421247
4220512179.49365273091-128.493652730908
4324392558.50852518634-119.508525186343
4423532241.83984809527111.160151904734
4522302145.8827304727384.1172695272658
4618522041.50208807352-189.502088073515
4721472149.25232240628-2.25232240627884
4822862322.03079251129-36.0307925112884
4910071085.80783155629-78.8078315562923
5016651499.65495782406165.345042175942
5116421822.70552670598-180.705526705982
5215181799.1924568875-281.192456887499
5318312199.51454663209-368.514546632086
5422072165.5291468775141.4708531224892
5528222586.49209911449235.507900885514
5623932392.085853964470.914146035534031
5723062262.4011392128643.5988607871395
5817852053.94526409419-268.945264094192
5920472213.59360536566-166.593605365655
6021712349.72746842407-178.72746842407
6112121066.95664625435145.043353745648
6213351617.56743478251-282.567434782512
6320111750.50001777202260.499982227984
6418601766.6588291947893.341170805217
6519542229.20033358206-275.20033358206
6621522354.07089111243-202.070891112428
6728352821.7843869921413.2156130078597
6822242499.17192715494-275.171927154935
6921822332.32640922816-150.326409228161
7019921985.121302973156.87869702685134
7123892231.67363751923157.326362480774
7227242427.23706486073296.762935139272
738911217.94263141972-326.942631419722
7412471555.33432394767-308.33432394767
7520171861.20428215139155.795717848615
7622571805.07154481788451.928455182124
7722552221.230976563133.7690234368979
7822552432.88275703902-177.882757039023
7930573009.6714612563647.3285387436449
8033302569.47036879694760.529631203062
8118962606.04087332991-710.040873329906
8220962184.33339151501-88.333391515012
8323742487.07905491054-113.079054910535
8425352692.03977051495-157.039770514949
8510411147.34045999992-106.340459999922
8617281551.32916861704176.670831382963
8722012150.8776534646150.1223465353878
8824552164.4052766606290.594723339399
8922042436.13220717465-232.132207174655
9026602542.01819880033117.981801199671
9136703302.50843006674367.491569933263
9226653106.32350670552-441.323506705517
9326392436.59954952698202.400450473016
9422262359.57132754962-133.571327549615
9525862673.00752314577-87.0075231457672
9626842885.60415105108-201.604151051084
9711851212.50477919223-27.5047791922266
9817491771.11376805478-22.113768054784
9924592336.29249633475122.707503665255
10026182442.56242295145175.437577048554
10125852528.4235315344656.5764684655405
10233102818.10536968948491.894630310517
10339233813.00610020984109.993899790165







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1043255.692451156113030.533199346783480.85170296544
1052815.648745149312580.569785012593050.72770528603
1062569.848938695392325.842555833692813.8553215571
1072961.113770957882695.781197341073226.44634457468
1083172.691748711542889.747385352433455.63611207065
1091369.414318431861130.166757588071608.66187927566
1102013.101606751491734.058619857032292.14459364596
1112714.192816365162381.616923336643046.76870939369
1122826.833741811222478.191612775933175.47587084651
1132844.525221590722487.039944400193202.01049878125
1143303.992547690612901.799490199663706.18560518156
1154152.704628369213724.447971624744580.96128511368

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
104 & 3255.69245115611 & 3030.53319934678 & 3480.85170296544 \tabularnewline
105 & 2815.64874514931 & 2580.56978501259 & 3050.72770528603 \tabularnewline
106 & 2569.84893869539 & 2325.84255583369 & 2813.8553215571 \tabularnewline
107 & 2961.11377095788 & 2695.78119734107 & 3226.44634457468 \tabularnewline
108 & 3172.69174871154 & 2889.74738535243 & 3455.63611207065 \tabularnewline
109 & 1369.41431843186 & 1130.16675758807 & 1608.66187927566 \tabularnewline
110 & 2013.10160675149 & 1734.05861985703 & 2292.14459364596 \tabularnewline
111 & 2714.19281636516 & 2381.61692333664 & 3046.76870939369 \tabularnewline
112 & 2826.83374181122 & 2478.19161277593 & 3175.47587084651 \tabularnewline
113 & 2844.52522159072 & 2487.03994440019 & 3202.01049878125 \tabularnewline
114 & 3303.99254769061 & 2901.79949019966 & 3706.18560518156 \tabularnewline
115 & 4152.70462836921 & 3724.44797162474 & 4580.96128511368 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121794&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]104[/C][C]3255.69245115611[/C][C]3030.53319934678[/C][C]3480.85170296544[/C][/ROW]
[ROW][C]105[/C][C]2815.64874514931[/C][C]2580.56978501259[/C][C]3050.72770528603[/C][/ROW]
[ROW][C]106[/C][C]2569.84893869539[/C][C]2325.84255583369[/C][C]2813.8553215571[/C][/ROW]
[ROW][C]107[/C][C]2961.11377095788[/C][C]2695.78119734107[/C][C]3226.44634457468[/C][/ROW]
[ROW][C]108[/C][C]3172.69174871154[/C][C]2889.74738535243[/C][C]3455.63611207065[/C][/ROW]
[ROW][C]109[/C][C]1369.41431843186[/C][C]1130.16675758807[/C][C]1608.66187927566[/C][/ROW]
[ROW][C]110[/C][C]2013.10160675149[/C][C]1734.05861985703[/C][C]2292.14459364596[/C][/ROW]
[ROW][C]111[/C][C]2714.19281636516[/C][C]2381.61692333664[/C][C]3046.76870939369[/C][/ROW]
[ROW][C]112[/C][C]2826.83374181122[/C][C]2478.19161277593[/C][C]3175.47587084651[/C][/ROW]
[ROW][C]113[/C][C]2844.52522159072[/C][C]2487.03994440019[/C][C]3202.01049878125[/C][/ROW]
[ROW][C]114[/C][C]3303.99254769061[/C][C]2901.79949019966[/C][C]3706.18560518156[/C][/ROW]
[ROW][C]115[/C][C]4152.70462836921[/C][C]3724.44797162474[/C][C]4580.96128511368[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121794&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121794&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
1043255.692451156113030.533199346783480.85170296544
1052815.648745149312580.569785012593050.72770528603
1062569.848938695392325.842555833692813.8553215571
1072961.113770957882695.781197341073226.44634457468
1083172.691748711542889.747385352433455.63611207065
1091369.414318431861130.166757588071608.66187927566
1102013.101606751491734.058619857032292.14459364596
1112714.192816365162381.616923336643046.76870939369
1122826.833741811222478.191612775933175.47587084651
1132844.525221590722487.039944400193202.01049878125
1143303.992547690612901.799490199663706.18560518156
1154152.704628369213724.447971624744580.96128511368



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')