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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 computationSat, 25 Nov 2017 11:56:59 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Nov/25/t15116090697i0mipqt5jqk4t3.htm/, Retrieved Sat, 18 May 2024 15:26:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308210, Retrieved Sat, 18 May 2024 15:26:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-11-25 10:56:59] [18e24160e6ab037d0bc3734a04ac82d7] [Current]
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Dataseries X:
1028
869
2698
2367
1928
1846
1404
1316
1008
865
586
343
1143
1807
2380
2334
2116
1788
1571
1306
952
806
473
278
993
1038
2259
2283
1746
1515
1230
882
1028
704
390
238
594
692
2125
1849
1468
1531
1203
878
818
605
316
136
528
654
1892
1597
1515
1241
1026
758
733
481
280
117
651
611
1898
1385
1047
1007
842
827
711
443
313
202
473
566
1609
1296
1153
1155
859
798
557
402
223
153
548
647
1757
1326
1308
1175
992
808
758
551
310
146
649
602
1801
1481
1400
1319
1153
950
829
636
310
191
679
842
1975
1677
1418
1540
1173
941
989
614
352
405




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308210&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308210&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308210&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.998712421147733
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.998712421147733 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308210&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]0.998712421147733[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308210&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308210&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
alpha0.998712421147733
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
28691028-159
32698869.204725037511828.79527496249
423672695.64528187883-328.645281878833
519282367.42315671484-439.423156714844
618461928.56579196378-82.5657919637824
714041846.10630996765-442.106309967653
813161404.56924673517-88.569246735168
910081316.11403988906-308.114039889057
108651008.39672112185-143.396721121848
11586865.184634585601-279.184634585601
12343586.35947223137-243.35947223137
131143343.313344509944799.686655490056
1418071141.97034037395665.029659626049
1523801806.14372187414573.856278125864
1623342379.26111479204-45.2611147920443
1721162334.05827725424-218.058277254236
1817882116.28076722635-328.280767226354
1915711788.42268737349-217.422687373487
2013061571.27994885427-265.279948854265
219521306.34156885208-354.341568852075
22806952.456242710533-146.456242710533
23473806.188573960897-333.188573960897
24278473.429006561649-195.429006561649
25993278.251630255968714.748369744032
261038992.07970511442545.9202948855745
2722591037.940873999421221.05912600058
2822832257.4277900919925.5722099080053
2917462282.96707376332-536.967073763317
3015151746.69138744854-231.691387448541
3112301515.29832093073-285.298320930731
328821230.36734408462-348.367344084618
331028882.448550425064145.551449574936
347041027.81259103161-323.812591031611
35390704.41693424431-314.41693424431
36238390.404836595328-152.404836595328
37594238.196233244583355.803766755417
38692593.54187459436998.4581254056311
392125691.8732273998941433.12677260011
4018492123.15473627498-274.154736274983
4114681849.35299584068-381.352995840677
4215311468.4910220526962.5089779473069
4312031530.91951476192-327.919514761918
448781203.42222223245-325.422222232453
45818878.419006771404-60.4190067714042
46605818.077794235394-213.077794235394
47316605.274354461745-289.274354461745
48136316.372463541308-180.372463541308
49528136.232243769587391.767756230413
50654527.495568122078126.504431877922
511892653.8371155687961238.1628844312
5215971890.40576765434-293.405767654345
5315151597.37778306156-82.3777830615647
5412411515.10606789137-274.106067891367
5510261241.35293317629-215.352933176295
567581026.27728388253-268.277283882531
57733758.345428157271-25.3454281572707
58481733.032634237297-252.032634237297
59280481.324511889925-201.324511889925
60117280.259221183952-163.259221183952
61651117.210209120634533.789790879366
62611650.312703553708-39.3127035537078
631898611.0506182057211286.94938179428
6413851896.34295119206-511.342951192064
6510471385.65839437021-338.658394370211
6610071047.43604938673-40.4360493867337
678421007.05206460206-165.05206460206
68827842.212517547905-15.2125175479046
69711827.019587315884-116.019587315884
70443711.149384367077-268.149384367077
71313443.345263476559-130.345263476559
72202313.167829804746-111.167829804746
73473202.143137346709270.856862653291
74566472.65125043165693.3487495683437
751609565.879806124171043.12019387583
7612961607.65690049799-311.656900497993
7711531296.40128283424-143.401282834244
7811551153.184640459171.81535954083461
798591154.99766258145-295.997662581446
80798859.38112033066-61.3811203306602
81557798.079033032466-241.079033032466
82402557.310408264658-155.310408264658
83223402.199974397218-179.199974397218
84153223.230734097361-70.2307340973606
85548153.090427608003394.909572391997
86647547.4915227860399.5084772139696
871757646.8718749891181110.12812501088
8813261755.57062250293-429.570622502929
8913081326.55310604909-18.5531060490898
9011751308.02388858699-133.023888586993
919921175.17127874579-183.171278745791
92808992.235847464856-184.235847464856
93758808.237218181025-50.2372181810252
94551758.064684379727-207.064684379727
95310551.266612108659-241.266612108659
96146310.310649787509-164.310649787509
97649146.211562917869502.788437082131
98602648.352620241249-46.3526202412488
991801602.059682653571198.94031734643
10014811799.45626980225-318.456269802255
10114001481.41003755837-81.4100375583691
10213191400.10482184272-81.1048218427225
10311531319.10442885342-166.104428853422
1049501153.21387254986-203.21387254986
105829950.261653884782-121.261653884782
106636829.156133941133-193.156133941133
107310636.248703753248-326.248703753248
108191310.420070931532-119.420070931532
109679191.153762757868487.846237242132
110842678.371859501769163.628140498231
1111975841.7893158666591133.21068413334
11216771973.54090188795-296.540901887947
11314181677.3818197941-259.381819794103
11415401418.33397454583121.666025454171
11511731539.84334539859-366.843345398586
1169411173.47233973363-232.47233973363
117989941.29932646837847.700673531622
118614988.938581621522-374.938581621522
119352614.482762988595-262.482762988595
120405352.33796725470952.6620327452914

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 869 & 1028 & -159 \tabularnewline
3 & 2698 & 869.20472503751 & 1828.79527496249 \tabularnewline
4 & 2367 & 2695.64528187883 & -328.645281878833 \tabularnewline
5 & 1928 & 2367.42315671484 & -439.423156714844 \tabularnewline
6 & 1846 & 1928.56579196378 & -82.5657919637824 \tabularnewline
7 & 1404 & 1846.10630996765 & -442.106309967653 \tabularnewline
8 & 1316 & 1404.56924673517 & -88.569246735168 \tabularnewline
9 & 1008 & 1316.11403988906 & -308.114039889057 \tabularnewline
10 & 865 & 1008.39672112185 & -143.396721121848 \tabularnewline
11 & 586 & 865.184634585601 & -279.184634585601 \tabularnewline
12 & 343 & 586.35947223137 & -243.35947223137 \tabularnewline
13 & 1143 & 343.313344509944 & 799.686655490056 \tabularnewline
14 & 1807 & 1141.97034037395 & 665.029659626049 \tabularnewline
15 & 2380 & 1806.14372187414 & 573.856278125864 \tabularnewline
16 & 2334 & 2379.26111479204 & -45.2611147920443 \tabularnewline
17 & 2116 & 2334.05827725424 & -218.058277254236 \tabularnewline
18 & 1788 & 2116.28076722635 & -328.280767226354 \tabularnewline
19 & 1571 & 1788.42268737349 & -217.422687373487 \tabularnewline
20 & 1306 & 1571.27994885427 & -265.279948854265 \tabularnewline
21 & 952 & 1306.34156885208 & -354.341568852075 \tabularnewline
22 & 806 & 952.456242710533 & -146.456242710533 \tabularnewline
23 & 473 & 806.188573960897 & -333.188573960897 \tabularnewline
24 & 278 & 473.429006561649 & -195.429006561649 \tabularnewline
25 & 993 & 278.251630255968 & 714.748369744032 \tabularnewline
26 & 1038 & 992.079705114425 & 45.9202948855745 \tabularnewline
27 & 2259 & 1037.94087399942 & 1221.05912600058 \tabularnewline
28 & 2283 & 2257.42779009199 & 25.5722099080053 \tabularnewline
29 & 1746 & 2282.96707376332 & -536.967073763317 \tabularnewline
30 & 1515 & 1746.69138744854 & -231.691387448541 \tabularnewline
31 & 1230 & 1515.29832093073 & -285.298320930731 \tabularnewline
32 & 882 & 1230.36734408462 & -348.367344084618 \tabularnewline
33 & 1028 & 882.448550425064 & 145.551449574936 \tabularnewline
34 & 704 & 1027.81259103161 & -323.812591031611 \tabularnewline
35 & 390 & 704.41693424431 & -314.41693424431 \tabularnewline
36 & 238 & 390.404836595328 & -152.404836595328 \tabularnewline
37 & 594 & 238.196233244583 & 355.803766755417 \tabularnewline
38 & 692 & 593.541874594369 & 98.4581254056311 \tabularnewline
39 & 2125 & 691.873227399894 & 1433.12677260011 \tabularnewline
40 & 1849 & 2123.15473627498 & -274.154736274983 \tabularnewline
41 & 1468 & 1849.35299584068 & -381.352995840677 \tabularnewline
42 & 1531 & 1468.49102205269 & 62.5089779473069 \tabularnewline
43 & 1203 & 1530.91951476192 & -327.919514761918 \tabularnewline
44 & 878 & 1203.42222223245 & -325.422222232453 \tabularnewline
45 & 818 & 878.419006771404 & -60.4190067714042 \tabularnewline
46 & 605 & 818.077794235394 & -213.077794235394 \tabularnewline
47 & 316 & 605.274354461745 & -289.274354461745 \tabularnewline
48 & 136 & 316.372463541308 & -180.372463541308 \tabularnewline
49 & 528 & 136.232243769587 & 391.767756230413 \tabularnewline
50 & 654 & 527.495568122078 & 126.504431877922 \tabularnewline
51 & 1892 & 653.837115568796 & 1238.1628844312 \tabularnewline
52 & 1597 & 1890.40576765434 & -293.405767654345 \tabularnewline
53 & 1515 & 1597.37778306156 & -82.3777830615647 \tabularnewline
54 & 1241 & 1515.10606789137 & -274.106067891367 \tabularnewline
55 & 1026 & 1241.35293317629 & -215.352933176295 \tabularnewline
56 & 758 & 1026.27728388253 & -268.277283882531 \tabularnewline
57 & 733 & 758.345428157271 & -25.3454281572707 \tabularnewline
58 & 481 & 733.032634237297 & -252.032634237297 \tabularnewline
59 & 280 & 481.324511889925 & -201.324511889925 \tabularnewline
60 & 117 & 280.259221183952 & -163.259221183952 \tabularnewline
61 & 651 & 117.210209120634 & 533.789790879366 \tabularnewline
62 & 611 & 650.312703553708 & -39.3127035537078 \tabularnewline
63 & 1898 & 611.050618205721 & 1286.94938179428 \tabularnewline
64 & 1385 & 1896.34295119206 & -511.342951192064 \tabularnewline
65 & 1047 & 1385.65839437021 & -338.658394370211 \tabularnewline
66 & 1007 & 1047.43604938673 & -40.4360493867337 \tabularnewline
67 & 842 & 1007.05206460206 & -165.05206460206 \tabularnewline
68 & 827 & 842.212517547905 & -15.2125175479046 \tabularnewline
69 & 711 & 827.019587315884 & -116.019587315884 \tabularnewline
70 & 443 & 711.149384367077 & -268.149384367077 \tabularnewline
71 & 313 & 443.345263476559 & -130.345263476559 \tabularnewline
72 & 202 & 313.167829804746 & -111.167829804746 \tabularnewline
73 & 473 & 202.143137346709 & 270.856862653291 \tabularnewline
74 & 566 & 472.651250431656 & 93.3487495683437 \tabularnewline
75 & 1609 & 565.87980612417 & 1043.12019387583 \tabularnewline
76 & 1296 & 1607.65690049799 & -311.656900497993 \tabularnewline
77 & 1153 & 1296.40128283424 & -143.401282834244 \tabularnewline
78 & 1155 & 1153.18464045917 & 1.81535954083461 \tabularnewline
79 & 859 & 1154.99766258145 & -295.997662581446 \tabularnewline
80 & 798 & 859.38112033066 & -61.3811203306602 \tabularnewline
81 & 557 & 798.079033032466 & -241.079033032466 \tabularnewline
82 & 402 & 557.310408264658 & -155.310408264658 \tabularnewline
83 & 223 & 402.199974397218 & -179.199974397218 \tabularnewline
84 & 153 & 223.230734097361 & -70.2307340973606 \tabularnewline
85 & 548 & 153.090427608003 & 394.909572391997 \tabularnewline
86 & 647 & 547.49152278603 & 99.5084772139696 \tabularnewline
87 & 1757 & 646.871874989118 & 1110.12812501088 \tabularnewline
88 & 1326 & 1755.57062250293 & -429.570622502929 \tabularnewline
89 & 1308 & 1326.55310604909 & -18.5531060490898 \tabularnewline
90 & 1175 & 1308.02388858699 & -133.023888586993 \tabularnewline
91 & 992 & 1175.17127874579 & -183.171278745791 \tabularnewline
92 & 808 & 992.235847464856 & -184.235847464856 \tabularnewline
93 & 758 & 808.237218181025 & -50.2372181810252 \tabularnewline
94 & 551 & 758.064684379727 & -207.064684379727 \tabularnewline
95 & 310 & 551.266612108659 & -241.266612108659 \tabularnewline
96 & 146 & 310.310649787509 & -164.310649787509 \tabularnewline
97 & 649 & 146.211562917869 & 502.788437082131 \tabularnewline
98 & 602 & 648.352620241249 & -46.3526202412488 \tabularnewline
99 & 1801 & 602.05968265357 & 1198.94031734643 \tabularnewline
100 & 1481 & 1799.45626980225 & -318.456269802255 \tabularnewline
101 & 1400 & 1481.41003755837 & -81.4100375583691 \tabularnewline
102 & 1319 & 1400.10482184272 & -81.1048218427225 \tabularnewline
103 & 1153 & 1319.10442885342 & -166.104428853422 \tabularnewline
104 & 950 & 1153.21387254986 & -203.21387254986 \tabularnewline
105 & 829 & 950.261653884782 & -121.261653884782 \tabularnewline
106 & 636 & 829.156133941133 & -193.156133941133 \tabularnewline
107 & 310 & 636.248703753248 & -326.248703753248 \tabularnewline
108 & 191 & 310.420070931532 & -119.420070931532 \tabularnewline
109 & 679 & 191.153762757868 & 487.846237242132 \tabularnewline
110 & 842 & 678.371859501769 & 163.628140498231 \tabularnewline
111 & 1975 & 841.789315866659 & 1133.21068413334 \tabularnewline
112 & 1677 & 1973.54090188795 & -296.540901887947 \tabularnewline
113 & 1418 & 1677.3818197941 & -259.381819794103 \tabularnewline
114 & 1540 & 1418.33397454583 & 121.666025454171 \tabularnewline
115 & 1173 & 1539.84334539859 & -366.843345398586 \tabularnewline
116 & 941 & 1173.47233973363 & -232.47233973363 \tabularnewline
117 & 989 & 941.299326468378 & 47.700673531622 \tabularnewline
118 & 614 & 988.938581621522 & -374.938581621522 \tabularnewline
119 & 352 & 614.482762988595 & -262.482762988595 \tabularnewline
120 & 405 & 352.337967254709 & 52.6620327452914 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308210&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]2[/C][C]869[/C][C]1028[/C][C]-159[/C][/ROW]
[ROW][C]3[/C][C]2698[/C][C]869.20472503751[/C][C]1828.79527496249[/C][/ROW]
[ROW][C]4[/C][C]2367[/C][C]2695.64528187883[/C][C]-328.645281878833[/C][/ROW]
[ROW][C]5[/C][C]1928[/C][C]2367.42315671484[/C][C]-439.423156714844[/C][/ROW]
[ROW][C]6[/C][C]1846[/C][C]1928.56579196378[/C][C]-82.5657919637824[/C][/ROW]
[ROW][C]7[/C][C]1404[/C][C]1846.10630996765[/C][C]-442.106309967653[/C][/ROW]
[ROW][C]8[/C][C]1316[/C][C]1404.56924673517[/C][C]-88.569246735168[/C][/ROW]
[ROW][C]9[/C][C]1008[/C][C]1316.11403988906[/C][C]-308.114039889057[/C][/ROW]
[ROW][C]10[/C][C]865[/C][C]1008.39672112185[/C][C]-143.396721121848[/C][/ROW]
[ROW][C]11[/C][C]586[/C][C]865.184634585601[/C][C]-279.184634585601[/C][/ROW]
[ROW][C]12[/C][C]343[/C][C]586.35947223137[/C][C]-243.35947223137[/C][/ROW]
[ROW][C]13[/C][C]1143[/C][C]343.313344509944[/C][C]799.686655490056[/C][/ROW]
[ROW][C]14[/C][C]1807[/C][C]1141.97034037395[/C][C]665.029659626049[/C][/ROW]
[ROW][C]15[/C][C]2380[/C][C]1806.14372187414[/C][C]573.856278125864[/C][/ROW]
[ROW][C]16[/C][C]2334[/C][C]2379.26111479204[/C][C]-45.2611147920443[/C][/ROW]
[ROW][C]17[/C][C]2116[/C][C]2334.05827725424[/C][C]-218.058277254236[/C][/ROW]
[ROW][C]18[/C][C]1788[/C][C]2116.28076722635[/C][C]-328.280767226354[/C][/ROW]
[ROW][C]19[/C][C]1571[/C][C]1788.42268737349[/C][C]-217.422687373487[/C][/ROW]
[ROW][C]20[/C][C]1306[/C][C]1571.27994885427[/C][C]-265.279948854265[/C][/ROW]
[ROW][C]21[/C][C]952[/C][C]1306.34156885208[/C][C]-354.341568852075[/C][/ROW]
[ROW][C]22[/C][C]806[/C][C]952.456242710533[/C][C]-146.456242710533[/C][/ROW]
[ROW][C]23[/C][C]473[/C][C]806.188573960897[/C][C]-333.188573960897[/C][/ROW]
[ROW][C]24[/C][C]278[/C][C]473.429006561649[/C][C]-195.429006561649[/C][/ROW]
[ROW][C]25[/C][C]993[/C][C]278.251630255968[/C][C]714.748369744032[/C][/ROW]
[ROW][C]26[/C][C]1038[/C][C]992.079705114425[/C][C]45.9202948855745[/C][/ROW]
[ROW][C]27[/C][C]2259[/C][C]1037.94087399942[/C][C]1221.05912600058[/C][/ROW]
[ROW][C]28[/C][C]2283[/C][C]2257.42779009199[/C][C]25.5722099080053[/C][/ROW]
[ROW][C]29[/C][C]1746[/C][C]2282.96707376332[/C][C]-536.967073763317[/C][/ROW]
[ROW][C]30[/C][C]1515[/C][C]1746.69138744854[/C][C]-231.691387448541[/C][/ROW]
[ROW][C]31[/C][C]1230[/C][C]1515.29832093073[/C][C]-285.298320930731[/C][/ROW]
[ROW][C]32[/C][C]882[/C][C]1230.36734408462[/C][C]-348.367344084618[/C][/ROW]
[ROW][C]33[/C][C]1028[/C][C]882.448550425064[/C][C]145.551449574936[/C][/ROW]
[ROW][C]34[/C][C]704[/C][C]1027.81259103161[/C][C]-323.812591031611[/C][/ROW]
[ROW][C]35[/C][C]390[/C][C]704.41693424431[/C][C]-314.41693424431[/C][/ROW]
[ROW][C]36[/C][C]238[/C][C]390.404836595328[/C][C]-152.404836595328[/C][/ROW]
[ROW][C]37[/C][C]594[/C][C]238.196233244583[/C][C]355.803766755417[/C][/ROW]
[ROW][C]38[/C][C]692[/C][C]593.541874594369[/C][C]98.4581254056311[/C][/ROW]
[ROW][C]39[/C][C]2125[/C][C]691.873227399894[/C][C]1433.12677260011[/C][/ROW]
[ROW][C]40[/C][C]1849[/C][C]2123.15473627498[/C][C]-274.154736274983[/C][/ROW]
[ROW][C]41[/C][C]1468[/C][C]1849.35299584068[/C][C]-381.352995840677[/C][/ROW]
[ROW][C]42[/C][C]1531[/C][C]1468.49102205269[/C][C]62.5089779473069[/C][/ROW]
[ROW][C]43[/C][C]1203[/C][C]1530.91951476192[/C][C]-327.919514761918[/C][/ROW]
[ROW][C]44[/C][C]878[/C][C]1203.42222223245[/C][C]-325.422222232453[/C][/ROW]
[ROW][C]45[/C][C]818[/C][C]878.419006771404[/C][C]-60.4190067714042[/C][/ROW]
[ROW][C]46[/C][C]605[/C][C]818.077794235394[/C][C]-213.077794235394[/C][/ROW]
[ROW][C]47[/C][C]316[/C][C]605.274354461745[/C][C]-289.274354461745[/C][/ROW]
[ROW][C]48[/C][C]136[/C][C]316.372463541308[/C][C]-180.372463541308[/C][/ROW]
[ROW][C]49[/C][C]528[/C][C]136.232243769587[/C][C]391.767756230413[/C][/ROW]
[ROW][C]50[/C][C]654[/C][C]527.495568122078[/C][C]126.504431877922[/C][/ROW]
[ROW][C]51[/C][C]1892[/C][C]653.837115568796[/C][C]1238.1628844312[/C][/ROW]
[ROW][C]52[/C][C]1597[/C][C]1890.40576765434[/C][C]-293.405767654345[/C][/ROW]
[ROW][C]53[/C][C]1515[/C][C]1597.37778306156[/C][C]-82.3777830615647[/C][/ROW]
[ROW][C]54[/C][C]1241[/C][C]1515.10606789137[/C][C]-274.106067891367[/C][/ROW]
[ROW][C]55[/C][C]1026[/C][C]1241.35293317629[/C][C]-215.352933176295[/C][/ROW]
[ROW][C]56[/C][C]758[/C][C]1026.27728388253[/C][C]-268.277283882531[/C][/ROW]
[ROW][C]57[/C][C]733[/C][C]758.345428157271[/C][C]-25.3454281572707[/C][/ROW]
[ROW][C]58[/C][C]481[/C][C]733.032634237297[/C][C]-252.032634237297[/C][/ROW]
[ROW][C]59[/C][C]280[/C][C]481.324511889925[/C][C]-201.324511889925[/C][/ROW]
[ROW][C]60[/C][C]117[/C][C]280.259221183952[/C][C]-163.259221183952[/C][/ROW]
[ROW][C]61[/C][C]651[/C][C]117.210209120634[/C][C]533.789790879366[/C][/ROW]
[ROW][C]62[/C][C]611[/C][C]650.312703553708[/C][C]-39.3127035537078[/C][/ROW]
[ROW][C]63[/C][C]1898[/C][C]611.050618205721[/C][C]1286.94938179428[/C][/ROW]
[ROW][C]64[/C][C]1385[/C][C]1896.34295119206[/C][C]-511.342951192064[/C][/ROW]
[ROW][C]65[/C][C]1047[/C][C]1385.65839437021[/C][C]-338.658394370211[/C][/ROW]
[ROW][C]66[/C][C]1007[/C][C]1047.43604938673[/C][C]-40.4360493867337[/C][/ROW]
[ROW][C]67[/C][C]842[/C][C]1007.05206460206[/C][C]-165.05206460206[/C][/ROW]
[ROW][C]68[/C][C]827[/C][C]842.212517547905[/C][C]-15.2125175479046[/C][/ROW]
[ROW][C]69[/C][C]711[/C][C]827.019587315884[/C][C]-116.019587315884[/C][/ROW]
[ROW][C]70[/C][C]443[/C][C]711.149384367077[/C][C]-268.149384367077[/C][/ROW]
[ROW][C]71[/C][C]313[/C][C]443.345263476559[/C][C]-130.345263476559[/C][/ROW]
[ROW][C]72[/C][C]202[/C][C]313.167829804746[/C][C]-111.167829804746[/C][/ROW]
[ROW][C]73[/C][C]473[/C][C]202.143137346709[/C][C]270.856862653291[/C][/ROW]
[ROW][C]74[/C][C]566[/C][C]472.651250431656[/C][C]93.3487495683437[/C][/ROW]
[ROW][C]75[/C][C]1609[/C][C]565.87980612417[/C][C]1043.12019387583[/C][/ROW]
[ROW][C]76[/C][C]1296[/C][C]1607.65690049799[/C][C]-311.656900497993[/C][/ROW]
[ROW][C]77[/C][C]1153[/C][C]1296.40128283424[/C][C]-143.401282834244[/C][/ROW]
[ROW][C]78[/C][C]1155[/C][C]1153.18464045917[/C][C]1.81535954083461[/C][/ROW]
[ROW][C]79[/C][C]859[/C][C]1154.99766258145[/C][C]-295.997662581446[/C][/ROW]
[ROW][C]80[/C][C]798[/C][C]859.38112033066[/C][C]-61.3811203306602[/C][/ROW]
[ROW][C]81[/C][C]557[/C][C]798.079033032466[/C][C]-241.079033032466[/C][/ROW]
[ROW][C]82[/C][C]402[/C][C]557.310408264658[/C][C]-155.310408264658[/C][/ROW]
[ROW][C]83[/C][C]223[/C][C]402.199974397218[/C][C]-179.199974397218[/C][/ROW]
[ROW][C]84[/C][C]153[/C][C]223.230734097361[/C][C]-70.2307340973606[/C][/ROW]
[ROW][C]85[/C][C]548[/C][C]153.090427608003[/C][C]394.909572391997[/C][/ROW]
[ROW][C]86[/C][C]647[/C][C]547.49152278603[/C][C]99.5084772139696[/C][/ROW]
[ROW][C]87[/C][C]1757[/C][C]646.871874989118[/C][C]1110.12812501088[/C][/ROW]
[ROW][C]88[/C][C]1326[/C][C]1755.57062250293[/C][C]-429.570622502929[/C][/ROW]
[ROW][C]89[/C][C]1308[/C][C]1326.55310604909[/C][C]-18.5531060490898[/C][/ROW]
[ROW][C]90[/C][C]1175[/C][C]1308.02388858699[/C][C]-133.023888586993[/C][/ROW]
[ROW][C]91[/C][C]992[/C][C]1175.17127874579[/C][C]-183.171278745791[/C][/ROW]
[ROW][C]92[/C][C]808[/C][C]992.235847464856[/C][C]-184.235847464856[/C][/ROW]
[ROW][C]93[/C][C]758[/C][C]808.237218181025[/C][C]-50.2372181810252[/C][/ROW]
[ROW][C]94[/C][C]551[/C][C]758.064684379727[/C][C]-207.064684379727[/C][/ROW]
[ROW][C]95[/C][C]310[/C][C]551.266612108659[/C][C]-241.266612108659[/C][/ROW]
[ROW][C]96[/C][C]146[/C][C]310.310649787509[/C][C]-164.310649787509[/C][/ROW]
[ROW][C]97[/C][C]649[/C][C]146.211562917869[/C][C]502.788437082131[/C][/ROW]
[ROW][C]98[/C][C]602[/C][C]648.352620241249[/C][C]-46.3526202412488[/C][/ROW]
[ROW][C]99[/C][C]1801[/C][C]602.05968265357[/C][C]1198.94031734643[/C][/ROW]
[ROW][C]100[/C][C]1481[/C][C]1799.45626980225[/C][C]-318.456269802255[/C][/ROW]
[ROW][C]101[/C][C]1400[/C][C]1481.41003755837[/C][C]-81.4100375583691[/C][/ROW]
[ROW][C]102[/C][C]1319[/C][C]1400.10482184272[/C][C]-81.1048218427225[/C][/ROW]
[ROW][C]103[/C][C]1153[/C][C]1319.10442885342[/C][C]-166.104428853422[/C][/ROW]
[ROW][C]104[/C][C]950[/C][C]1153.21387254986[/C][C]-203.21387254986[/C][/ROW]
[ROW][C]105[/C][C]829[/C][C]950.261653884782[/C][C]-121.261653884782[/C][/ROW]
[ROW][C]106[/C][C]636[/C][C]829.156133941133[/C][C]-193.156133941133[/C][/ROW]
[ROW][C]107[/C][C]310[/C][C]636.248703753248[/C][C]-326.248703753248[/C][/ROW]
[ROW][C]108[/C][C]191[/C][C]310.420070931532[/C][C]-119.420070931532[/C][/ROW]
[ROW][C]109[/C][C]679[/C][C]191.153762757868[/C][C]487.846237242132[/C][/ROW]
[ROW][C]110[/C][C]842[/C][C]678.371859501769[/C][C]163.628140498231[/C][/ROW]
[ROW][C]111[/C][C]1975[/C][C]841.789315866659[/C][C]1133.21068413334[/C][/ROW]
[ROW][C]112[/C][C]1677[/C][C]1973.54090188795[/C][C]-296.540901887947[/C][/ROW]
[ROW][C]113[/C][C]1418[/C][C]1677.3818197941[/C][C]-259.381819794103[/C][/ROW]
[ROW][C]114[/C][C]1540[/C][C]1418.33397454583[/C][C]121.666025454171[/C][/ROW]
[ROW][C]115[/C][C]1173[/C][C]1539.84334539859[/C][C]-366.843345398586[/C][/ROW]
[ROW][C]116[/C][C]941[/C][C]1173.47233973363[/C][C]-232.47233973363[/C][/ROW]
[ROW][C]117[/C][C]989[/C][C]941.299326468378[/C][C]47.700673531622[/C][/ROW]
[ROW][C]118[/C][C]614[/C][C]988.938581621522[/C][C]-374.938581621522[/C][/ROW]
[ROW][C]119[/C][C]352[/C][C]614.482762988595[/C][C]-262.482762988595[/C][/ROW]
[ROW][C]120[/C][C]405[/C][C]352.337967254709[/C][C]52.6620327452914[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308210&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308210&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
28691028-159
32698869.204725037511828.79527496249
423672695.64528187883-328.645281878833
519282367.42315671484-439.423156714844
618461928.56579196378-82.5657919637824
714041846.10630996765-442.106309967653
813161404.56924673517-88.569246735168
910081316.11403988906-308.114039889057
108651008.39672112185-143.396721121848
11586865.184634585601-279.184634585601
12343586.35947223137-243.35947223137
131143343.313344509944799.686655490056
1418071141.97034037395665.029659626049
1523801806.14372187414573.856278125864
1623342379.26111479204-45.2611147920443
1721162334.05827725424-218.058277254236
1817882116.28076722635-328.280767226354
1915711788.42268737349-217.422687373487
2013061571.27994885427-265.279948854265
219521306.34156885208-354.341568852075
22806952.456242710533-146.456242710533
23473806.188573960897-333.188573960897
24278473.429006561649-195.429006561649
25993278.251630255968714.748369744032
261038992.07970511442545.9202948855745
2722591037.940873999421221.05912600058
2822832257.4277900919925.5722099080053
2917462282.96707376332-536.967073763317
3015151746.69138744854-231.691387448541
3112301515.29832093073-285.298320930731
328821230.36734408462-348.367344084618
331028882.448550425064145.551449574936
347041027.81259103161-323.812591031611
35390704.41693424431-314.41693424431
36238390.404836595328-152.404836595328
37594238.196233244583355.803766755417
38692593.54187459436998.4581254056311
392125691.8732273998941433.12677260011
4018492123.15473627498-274.154736274983
4114681849.35299584068-381.352995840677
4215311468.4910220526962.5089779473069
4312031530.91951476192-327.919514761918
448781203.42222223245-325.422222232453
45818878.419006771404-60.4190067714042
46605818.077794235394-213.077794235394
47316605.274354461745-289.274354461745
48136316.372463541308-180.372463541308
49528136.232243769587391.767756230413
50654527.495568122078126.504431877922
511892653.8371155687961238.1628844312
5215971890.40576765434-293.405767654345
5315151597.37778306156-82.3777830615647
5412411515.10606789137-274.106067891367
5510261241.35293317629-215.352933176295
567581026.27728388253-268.277283882531
57733758.345428157271-25.3454281572707
58481733.032634237297-252.032634237297
59280481.324511889925-201.324511889925
60117280.259221183952-163.259221183952
61651117.210209120634533.789790879366
62611650.312703553708-39.3127035537078
631898611.0506182057211286.94938179428
6413851896.34295119206-511.342951192064
6510471385.65839437021-338.658394370211
6610071047.43604938673-40.4360493867337
678421007.05206460206-165.05206460206
68827842.212517547905-15.2125175479046
69711827.019587315884-116.019587315884
70443711.149384367077-268.149384367077
71313443.345263476559-130.345263476559
72202313.167829804746-111.167829804746
73473202.143137346709270.856862653291
74566472.65125043165693.3487495683437
751609565.879806124171043.12019387583
7612961607.65690049799-311.656900497993
7711531296.40128283424-143.401282834244
7811551153.184640459171.81535954083461
798591154.99766258145-295.997662581446
80798859.38112033066-61.3811203306602
81557798.079033032466-241.079033032466
82402557.310408264658-155.310408264658
83223402.199974397218-179.199974397218
84153223.230734097361-70.2307340973606
85548153.090427608003394.909572391997
86647547.4915227860399.5084772139696
871757646.8718749891181110.12812501088
8813261755.57062250293-429.570622502929
8913081326.55310604909-18.5531060490898
9011751308.02388858699-133.023888586993
919921175.17127874579-183.171278745791
92808992.235847464856-184.235847464856
93758808.237218181025-50.2372181810252
94551758.064684379727-207.064684379727
95310551.266612108659-241.266612108659
96146310.310649787509-164.310649787509
97649146.211562917869502.788437082131
98602648.352620241249-46.3526202412488
991801602.059682653571198.94031734643
10014811799.45626980225-318.456269802255
10114001481.41003755837-81.4100375583691
10213191400.10482184272-81.1048218427225
10311531319.10442885342-166.104428853422
1049501153.21387254986-203.21387254986
105829950.261653884782-121.261653884782
106636829.156133941133-193.156133941133
107310636.248703753248-326.248703753248
108191310.420070931532-119.420070931532
109679191.153762757868487.846237242132
110842678.371859501769163.628140498231
1111975841.7893158666591133.21068413334
11216771973.54090188795-296.540901887947
11314181677.3818197941-259.381819794103
11415401418.33397454583121.666025454171
11511731539.84334539859-366.843345398586
1169411173.47233973363-232.47233973363
117989941.29932646837847.700673531622
118614988.938581621522-374.938581621522
119352614.482762988595-262.482762988595
120405352.33796725470952.6620327452914







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121404.93219348032-474.4574105125221284.32179747316
122404.93219348032-837.9121236750811647.77651063572
123404.93219348032-1116.908112780581926.77249974122
124404.93219348032-1352.148862941112162.01324990175
125404.93219348032-1559.41751059732369.28189755794
126404.93219348032-1746.812605743012556.67699270365
127404.93219348032-1919.146463118772729.01085007941
128404.93219348032-2079.555182847892889.41956980853
129404.93219348032-2230.217412179483040.08179914012
130404.93219348032-2372.71957830173182.58396526234
131404.93219348032-2508.259404468323318.12379142896
132404.93219348032-2637.76746429623447.63185125684

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 404.93219348032 & -474.457410512522 & 1284.32179747316 \tabularnewline
122 & 404.93219348032 & -837.912123675081 & 1647.77651063572 \tabularnewline
123 & 404.93219348032 & -1116.90811278058 & 1926.77249974122 \tabularnewline
124 & 404.93219348032 & -1352.14886294111 & 2162.01324990175 \tabularnewline
125 & 404.93219348032 & -1559.4175105973 & 2369.28189755794 \tabularnewline
126 & 404.93219348032 & -1746.81260574301 & 2556.67699270365 \tabularnewline
127 & 404.93219348032 & -1919.14646311877 & 2729.01085007941 \tabularnewline
128 & 404.93219348032 & -2079.55518284789 & 2889.41956980853 \tabularnewline
129 & 404.93219348032 & -2230.21741217948 & 3040.08179914012 \tabularnewline
130 & 404.93219348032 & -2372.7195783017 & 3182.58396526234 \tabularnewline
131 & 404.93219348032 & -2508.25940446832 & 3318.12379142896 \tabularnewline
132 & 404.93219348032 & -2637.7674642962 & 3447.63185125684 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308210&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]121[/C][C]404.93219348032[/C][C]-474.457410512522[/C][C]1284.32179747316[/C][/ROW]
[ROW][C]122[/C][C]404.93219348032[/C][C]-837.912123675081[/C][C]1647.77651063572[/C][/ROW]
[ROW][C]123[/C][C]404.93219348032[/C][C]-1116.90811278058[/C][C]1926.77249974122[/C][/ROW]
[ROW][C]124[/C][C]404.93219348032[/C][C]-1352.14886294111[/C][C]2162.01324990175[/C][/ROW]
[ROW][C]125[/C][C]404.93219348032[/C][C]-1559.4175105973[/C][C]2369.28189755794[/C][/ROW]
[ROW][C]126[/C][C]404.93219348032[/C][C]-1746.81260574301[/C][C]2556.67699270365[/C][/ROW]
[ROW][C]127[/C][C]404.93219348032[/C][C]-1919.14646311877[/C][C]2729.01085007941[/C][/ROW]
[ROW][C]128[/C][C]404.93219348032[/C][C]-2079.55518284789[/C][C]2889.41956980853[/C][/ROW]
[ROW][C]129[/C][C]404.93219348032[/C][C]-2230.21741217948[/C][C]3040.08179914012[/C][/ROW]
[ROW][C]130[/C][C]404.93219348032[/C][C]-2372.7195783017[/C][C]3182.58396526234[/C][/ROW]
[ROW][C]131[/C][C]404.93219348032[/C][C]-2508.25940446832[/C][C]3318.12379142896[/C][/ROW]
[ROW][C]132[/C][C]404.93219348032[/C][C]-2637.7674642962[/C][C]3447.63185125684[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308210&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308210&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
121404.93219348032-474.4574105125221284.32179747316
122404.93219348032-837.9121236750811647.77651063572
123404.93219348032-1116.908112780581926.77249974122
124404.93219348032-1352.148862941112162.01324990175
125404.93219348032-1559.41751059732369.28189755794
126404.93219348032-1746.812605743012556.67699270365
127404.93219348032-1919.146463118772729.01085007941
128404.93219348032-2079.555182847892889.41956980853
129404.93219348032-2230.217412179483040.08179914012
130404.93219348032-2372.71957830173182.58396526234
131404.93219348032-2508.259404468323318.12379142896
132404.93219348032-2637.76746429623447.63185125684



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'multiplicative'
par2 <- 'Triple'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')