Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 12 Aug 2016 21:31:47 +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/2016/Aug/12/t14710342004opf1mycu8gi6xx.htm/, Retrieved Sun, 05 May 2024 16:32:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296475, Retrieved Sun, 05 May 2024 16:32:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-08-12 20:31:47] [517bf63cbd197750110a40d4d2cd39d6] [Current]
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Dataseries X:
465
455
444
424
630
620
465
362
372
372
382
403
434
424
362
372
661
723
558
465
486
496
548
599
610
506
517
382
765
878
620
537
589
651
744
858
858
785
754
568
878
1023
899
765
785
858
961
1085
1002
951
951
785
1023
1178
1054
920
961
1126
1199
1302
1219
1085
1054
806
971
1147
951
837
951
1064
1126
1292
1209
1002
1023
827
992
1137
971
858
961
1085
1064
1312
1271
1106
1116
899
1033
1240
1085
992
1147
1240
1168
1498
1416
1230
1178
940
1075
1199
1044
1044
1219
1312
1261
1622
1529
1354
1281
1023
1116
1281
1157
1126
1271
1395
1261
1581




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296475&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296475&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296475&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.860261702472379
beta0.00772474680182627
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.860261702472379 \tabularnewline
beta & 0.00772474680182627 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296475&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]0.860261702472379[/C][/ROW]
[ROW][C]beta[/C][C]0.00772474680182627[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296475&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296475&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
alpha0.860261702472379
beta0.00772474680182627
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3444445-1
4424434.133092993693-10.1330929936927
5630415.341998378062214.658001621938
6620591.35654115847528.6434588415245
7465607.540241168874-142.540241168874
8362475.513936761538-113.513936761538
9372367.7035158008614.2964841991386
10372361.26943958772910.7305604122708
11382360.44166056580121.5583394341985
12403369.07186687498833.9281331250116
13434388.56879571703345.4312042829669
14424418.2632802931275.73671970687263
15362413.848242234495-51.8482422344951
16372359.55051945642112.4494805435793
17661360.648395721308300.351604278692
18723611.413370763711111.586629236289
19558700.532594064169-142.532594064169
20465570.095609303282-105.095609303282
21486471.16583653269314.8341634673068
22496475.50563178623420.4943682137664
23548484.8508757149963.1491242850095
24599531.31001783792167.6899821620788
25610582.12530658691127.8746934130888
26506598.8742630593-92.8742630593005
27517511.1303389685175.86966103148313
28382508.371036805836-126.371036805836
29765391.010352849981373.989647150019
30878706.576077560655171.423922439345
31620849.021431118354-229.021431118354
32537645.457066082867-108.457066082867
33589544.88887681314644.111123186854
34651575.86238960379975.1376103962011
35744634.026113353414109.973886646586
36858722.888961308655135.111038691345
37858834.27419238078223.7258076192182
38785849.99664014088-64.9966401408797
39754788.962641521375-34.9626415213748
40568753.533404310558-185.533404310558
41878587.340980516985290.659019483015
421023832.730179417341190.269820582659
43899993.022795930223-94.0227959302231
44765908.124552115042-143.124552115042
45785780.0348417948864.96515820511399
46858779.3740327782578.6259672217499
47961842.60329017326118.39670982674
481085940.832576420082144.167423579918
4910021062.18945708693-60.1894570869251
509511007.34596244936-56.3459624493644
51951955.434443011809-4.43444301180864
52785948.150947442381-163.150947442381
531023803.245533944336219.754466055664
541178989.199318544027188.800681455973
5510541149.77938559854-95.7793855985374
569201064.90963656061-144.909636560608
57961936.81204562360124.1879543763988
581126954.343372456018171.656627543982
5911991099.8770615742399.1229384257724
6013021183.67149784785118.328502152148
6112191284.7740739188-65.7740739188007
6210851227.06316576375-142.063165763755
6310541102.77962067785-48.7796206778478
648061058.42018149985-252.420181499846
65971837.199157976553133.800842023447
661147949.118436928645197.881563071355
679511117.478889175-166.478889175004
68837971.287695657638-134.287695657638
69951851.89697054120599.1030294587952
701064933.941917696411130.058082303589
7111261043.4805867850982.5194132149054
7212921112.67192604337179.328073956633
7312091266.33573814296-57.3357381429598
7410021216.0257229316-214.025722931595
7510231029.49904868822-6.49904868822205
768271021.45643638471-194.456436384713
77992850.429059646729141.570940353271
781137969.413948011532167.586051988468
799711111.89230083559-140.892300835594
80858988.062268536302-130.062268536302
81961872.68459496874988.315405031251
821085945.755753346112139.244246653888
8310641063.564364048990.435635951011363
8413121061.96413792404250.035862075961
8512711276.74699153595-5.74699153594679
8611061271.45146153154-165.451461531538
8711161127.66881704447-11.668817044467
888991116.10194927989-217.101949279894
891033926.366117018124106.633882981876
9012401015.83643752069224.163562479313
9110851207.90267518014-122.902675180138
929921100.58439474129-108.584394741292
9311471004.86200631446142.137993685541
9412401125.77103675816114.228963241841
9511681223.4300833255-55.4300833254965
9614981174.76959990768323.230400092316
9714161454.00419283118-38.0041928311844
9812301422.22995044603-192.229950446034
9911781256.50376882316-78.5037688231578
1009401188.09018442284-248.090184422845
1011075972.139266768609102.860733231391
10211991058.78152384485140.218476155147
10310441178.49301082653-134.493010826532
10410441060.98697940802-16.9869794080191
10512191044.45400298897174.545997011035
10613121193.84942212707118.150577872926
10712611295.51516847403-34.5151684740254
10816221265.61905617791356.380943822091
10915291574.36415858815-45.3641585881526
11013541537.20187662199-183.201876621987
11112811380.24565254185-99.2456525418488
11210231294.85423520661-271.854235206609
11311161059.1677106950856.8322893049165
11412811106.61528316964174.384716830363
11511571256.34754650449-99.3475465044937
11611261169.93823232951-43.9382323295142
11712711130.90344619573140.096553804269
11813951251.11772266179143.882277338211
11912611375.54485354962-114.544853549617
12015811276.89583550027304.104164499733

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 444 & 445 & -1 \tabularnewline
4 & 424 & 434.133092993693 & -10.1330929936927 \tabularnewline
5 & 630 & 415.341998378062 & 214.658001621938 \tabularnewline
6 & 620 & 591.356541158475 & 28.6434588415245 \tabularnewline
7 & 465 & 607.540241168874 & -142.540241168874 \tabularnewline
8 & 362 & 475.513936761538 & -113.513936761538 \tabularnewline
9 & 372 & 367.703515800861 & 4.2964841991386 \tabularnewline
10 & 372 & 361.269439587729 & 10.7305604122708 \tabularnewline
11 & 382 & 360.441660565801 & 21.5583394341985 \tabularnewline
12 & 403 & 369.071866874988 & 33.9281331250116 \tabularnewline
13 & 434 & 388.568795717033 & 45.4312042829669 \tabularnewline
14 & 424 & 418.263280293127 & 5.73671970687263 \tabularnewline
15 & 362 & 413.848242234495 & -51.8482422344951 \tabularnewline
16 & 372 & 359.550519456421 & 12.4494805435793 \tabularnewline
17 & 661 & 360.648395721308 & 300.351604278692 \tabularnewline
18 & 723 & 611.413370763711 & 111.586629236289 \tabularnewline
19 & 558 & 700.532594064169 & -142.532594064169 \tabularnewline
20 & 465 & 570.095609303282 & -105.095609303282 \tabularnewline
21 & 486 & 471.165836532693 & 14.8341634673068 \tabularnewline
22 & 496 & 475.505631786234 & 20.4943682137664 \tabularnewline
23 & 548 & 484.85087571499 & 63.1491242850095 \tabularnewline
24 & 599 & 531.310017837921 & 67.6899821620788 \tabularnewline
25 & 610 & 582.125306586911 & 27.8746934130888 \tabularnewline
26 & 506 & 598.8742630593 & -92.8742630593005 \tabularnewline
27 & 517 & 511.130338968517 & 5.86966103148313 \tabularnewline
28 & 382 & 508.371036805836 & -126.371036805836 \tabularnewline
29 & 765 & 391.010352849981 & 373.989647150019 \tabularnewline
30 & 878 & 706.576077560655 & 171.423922439345 \tabularnewline
31 & 620 & 849.021431118354 & -229.021431118354 \tabularnewline
32 & 537 & 645.457066082867 & -108.457066082867 \tabularnewline
33 & 589 & 544.888876813146 & 44.111123186854 \tabularnewline
34 & 651 & 575.862389603799 & 75.1376103962011 \tabularnewline
35 & 744 & 634.026113353414 & 109.973886646586 \tabularnewline
36 & 858 & 722.888961308655 & 135.111038691345 \tabularnewline
37 & 858 & 834.274192380782 & 23.7258076192182 \tabularnewline
38 & 785 & 849.99664014088 & -64.9966401408797 \tabularnewline
39 & 754 & 788.962641521375 & -34.9626415213748 \tabularnewline
40 & 568 & 753.533404310558 & -185.533404310558 \tabularnewline
41 & 878 & 587.340980516985 & 290.659019483015 \tabularnewline
42 & 1023 & 832.730179417341 & 190.269820582659 \tabularnewline
43 & 899 & 993.022795930223 & -94.0227959302231 \tabularnewline
44 & 765 & 908.124552115042 & -143.124552115042 \tabularnewline
45 & 785 & 780.034841794886 & 4.96515820511399 \tabularnewline
46 & 858 & 779.37403277825 & 78.6259672217499 \tabularnewline
47 & 961 & 842.60329017326 & 118.39670982674 \tabularnewline
48 & 1085 & 940.832576420082 & 144.167423579918 \tabularnewline
49 & 1002 & 1062.18945708693 & -60.1894570869251 \tabularnewline
50 & 951 & 1007.34596244936 & -56.3459624493644 \tabularnewline
51 & 951 & 955.434443011809 & -4.43444301180864 \tabularnewline
52 & 785 & 948.150947442381 & -163.150947442381 \tabularnewline
53 & 1023 & 803.245533944336 & 219.754466055664 \tabularnewline
54 & 1178 & 989.199318544027 & 188.800681455973 \tabularnewline
55 & 1054 & 1149.77938559854 & -95.7793855985374 \tabularnewline
56 & 920 & 1064.90963656061 & -144.909636560608 \tabularnewline
57 & 961 & 936.812045623601 & 24.1879543763988 \tabularnewline
58 & 1126 & 954.343372456018 & 171.656627543982 \tabularnewline
59 & 1199 & 1099.87706157423 & 99.1229384257724 \tabularnewline
60 & 1302 & 1183.67149784785 & 118.328502152148 \tabularnewline
61 & 1219 & 1284.7740739188 & -65.7740739188007 \tabularnewline
62 & 1085 & 1227.06316576375 & -142.063165763755 \tabularnewline
63 & 1054 & 1102.77962067785 & -48.7796206778478 \tabularnewline
64 & 806 & 1058.42018149985 & -252.420181499846 \tabularnewline
65 & 971 & 837.199157976553 & 133.800842023447 \tabularnewline
66 & 1147 & 949.118436928645 & 197.881563071355 \tabularnewline
67 & 951 & 1117.478889175 & -166.478889175004 \tabularnewline
68 & 837 & 971.287695657638 & -134.287695657638 \tabularnewline
69 & 951 & 851.896970541205 & 99.1030294587952 \tabularnewline
70 & 1064 & 933.941917696411 & 130.058082303589 \tabularnewline
71 & 1126 & 1043.48058678509 & 82.5194132149054 \tabularnewline
72 & 1292 & 1112.67192604337 & 179.328073956633 \tabularnewline
73 & 1209 & 1266.33573814296 & -57.3357381429598 \tabularnewline
74 & 1002 & 1216.0257229316 & -214.025722931595 \tabularnewline
75 & 1023 & 1029.49904868822 & -6.49904868822205 \tabularnewline
76 & 827 & 1021.45643638471 & -194.456436384713 \tabularnewline
77 & 992 & 850.429059646729 & 141.570940353271 \tabularnewline
78 & 1137 & 969.413948011532 & 167.586051988468 \tabularnewline
79 & 971 & 1111.89230083559 & -140.892300835594 \tabularnewline
80 & 858 & 988.062268536302 & -130.062268536302 \tabularnewline
81 & 961 & 872.684594968749 & 88.315405031251 \tabularnewline
82 & 1085 & 945.755753346112 & 139.244246653888 \tabularnewline
83 & 1064 & 1063.56436404899 & 0.435635951011363 \tabularnewline
84 & 1312 & 1061.96413792404 & 250.035862075961 \tabularnewline
85 & 1271 & 1276.74699153595 & -5.74699153594679 \tabularnewline
86 & 1106 & 1271.45146153154 & -165.451461531538 \tabularnewline
87 & 1116 & 1127.66881704447 & -11.668817044467 \tabularnewline
88 & 899 & 1116.10194927989 & -217.101949279894 \tabularnewline
89 & 1033 & 926.366117018124 & 106.633882981876 \tabularnewline
90 & 1240 & 1015.83643752069 & 224.163562479313 \tabularnewline
91 & 1085 & 1207.90267518014 & -122.902675180138 \tabularnewline
92 & 992 & 1100.58439474129 & -108.584394741292 \tabularnewline
93 & 1147 & 1004.86200631446 & 142.137993685541 \tabularnewline
94 & 1240 & 1125.77103675816 & 114.228963241841 \tabularnewline
95 & 1168 & 1223.4300833255 & -55.4300833254965 \tabularnewline
96 & 1498 & 1174.76959990768 & 323.230400092316 \tabularnewline
97 & 1416 & 1454.00419283118 & -38.0041928311844 \tabularnewline
98 & 1230 & 1422.22995044603 & -192.229950446034 \tabularnewline
99 & 1178 & 1256.50376882316 & -78.5037688231578 \tabularnewline
100 & 940 & 1188.09018442284 & -248.090184422845 \tabularnewline
101 & 1075 & 972.139266768609 & 102.860733231391 \tabularnewline
102 & 1199 & 1058.78152384485 & 140.218476155147 \tabularnewline
103 & 1044 & 1178.49301082653 & -134.493010826532 \tabularnewline
104 & 1044 & 1060.98697940802 & -16.9869794080191 \tabularnewline
105 & 1219 & 1044.45400298897 & 174.545997011035 \tabularnewline
106 & 1312 & 1193.84942212707 & 118.150577872926 \tabularnewline
107 & 1261 & 1295.51516847403 & -34.5151684740254 \tabularnewline
108 & 1622 & 1265.61905617791 & 356.380943822091 \tabularnewline
109 & 1529 & 1574.36415858815 & -45.3641585881526 \tabularnewline
110 & 1354 & 1537.20187662199 & -183.201876621987 \tabularnewline
111 & 1281 & 1380.24565254185 & -99.2456525418488 \tabularnewline
112 & 1023 & 1294.85423520661 & -271.854235206609 \tabularnewline
113 & 1116 & 1059.16771069508 & 56.8322893049165 \tabularnewline
114 & 1281 & 1106.61528316964 & 174.384716830363 \tabularnewline
115 & 1157 & 1256.34754650449 & -99.3475465044937 \tabularnewline
116 & 1126 & 1169.93823232951 & -43.9382323295142 \tabularnewline
117 & 1271 & 1130.90344619573 & 140.096553804269 \tabularnewline
118 & 1395 & 1251.11772266179 & 143.882277338211 \tabularnewline
119 & 1261 & 1375.54485354962 & -114.544853549617 \tabularnewline
120 & 1581 & 1276.89583550027 & 304.104164499733 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296475&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]3[/C][C]444[/C][C]445[/C][C]-1[/C][/ROW]
[ROW][C]4[/C][C]424[/C][C]434.133092993693[/C][C]-10.1330929936927[/C][/ROW]
[ROW][C]5[/C][C]630[/C][C]415.341998378062[/C][C]214.658001621938[/C][/ROW]
[ROW][C]6[/C][C]620[/C][C]591.356541158475[/C][C]28.6434588415245[/C][/ROW]
[ROW][C]7[/C][C]465[/C][C]607.540241168874[/C][C]-142.540241168874[/C][/ROW]
[ROW][C]8[/C][C]362[/C][C]475.513936761538[/C][C]-113.513936761538[/C][/ROW]
[ROW][C]9[/C][C]372[/C][C]367.703515800861[/C][C]4.2964841991386[/C][/ROW]
[ROW][C]10[/C][C]372[/C][C]361.269439587729[/C][C]10.7305604122708[/C][/ROW]
[ROW][C]11[/C][C]382[/C][C]360.441660565801[/C][C]21.5583394341985[/C][/ROW]
[ROW][C]12[/C][C]403[/C][C]369.071866874988[/C][C]33.9281331250116[/C][/ROW]
[ROW][C]13[/C][C]434[/C][C]388.568795717033[/C][C]45.4312042829669[/C][/ROW]
[ROW][C]14[/C][C]424[/C][C]418.263280293127[/C][C]5.73671970687263[/C][/ROW]
[ROW][C]15[/C][C]362[/C][C]413.848242234495[/C][C]-51.8482422344951[/C][/ROW]
[ROW][C]16[/C][C]372[/C][C]359.550519456421[/C][C]12.4494805435793[/C][/ROW]
[ROW][C]17[/C][C]661[/C][C]360.648395721308[/C][C]300.351604278692[/C][/ROW]
[ROW][C]18[/C][C]723[/C][C]611.413370763711[/C][C]111.586629236289[/C][/ROW]
[ROW][C]19[/C][C]558[/C][C]700.532594064169[/C][C]-142.532594064169[/C][/ROW]
[ROW][C]20[/C][C]465[/C][C]570.095609303282[/C][C]-105.095609303282[/C][/ROW]
[ROW][C]21[/C][C]486[/C][C]471.165836532693[/C][C]14.8341634673068[/C][/ROW]
[ROW][C]22[/C][C]496[/C][C]475.505631786234[/C][C]20.4943682137664[/C][/ROW]
[ROW][C]23[/C][C]548[/C][C]484.85087571499[/C][C]63.1491242850095[/C][/ROW]
[ROW][C]24[/C][C]599[/C][C]531.310017837921[/C][C]67.6899821620788[/C][/ROW]
[ROW][C]25[/C][C]610[/C][C]582.125306586911[/C][C]27.8746934130888[/C][/ROW]
[ROW][C]26[/C][C]506[/C][C]598.8742630593[/C][C]-92.8742630593005[/C][/ROW]
[ROW][C]27[/C][C]517[/C][C]511.130338968517[/C][C]5.86966103148313[/C][/ROW]
[ROW][C]28[/C][C]382[/C][C]508.371036805836[/C][C]-126.371036805836[/C][/ROW]
[ROW][C]29[/C][C]765[/C][C]391.010352849981[/C][C]373.989647150019[/C][/ROW]
[ROW][C]30[/C][C]878[/C][C]706.576077560655[/C][C]171.423922439345[/C][/ROW]
[ROW][C]31[/C][C]620[/C][C]849.021431118354[/C][C]-229.021431118354[/C][/ROW]
[ROW][C]32[/C][C]537[/C][C]645.457066082867[/C][C]-108.457066082867[/C][/ROW]
[ROW][C]33[/C][C]589[/C][C]544.888876813146[/C][C]44.111123186854[/C][/ROW]
[ROW][C]34[/C][C]651[/C][C]575.862389603799[/C][C]75.1376103962011[/C][/ROW]
[ROW][C]35[/C][C]744[/C][C]634.026113353414[/C][C]109.973886646586[/C][/ROW]
[ROW][C]36[/C][C]858[/C][C]722.888961308655[/C][C]135.111038691345[/C][/ROW]
[ROW][C]37[/C][C]858[/C][C]834.274192380782[/C][C]23.7258076192182[/C][/ROW]
[ROW][C]38[/C][C]785[/C][C]849.99664014088[/C][C]-64.9966401408797[/C][/ROW]
[ROW][C]39[/C][C]754[/C][C]788.962641521375[/C][C]-34.9626415213748[/C][/ROW]
[ROW][C]40[/C][C]568[/C][C]753.533404310558[/C][C]-185.533404310558[/C][/ROW]
[ROW][C]41[/C][C]878[/C][C]587.340980516985[/C][C]290.659019483015[/C][/ROW]
[ROW][C]42[/C][C]1023[/C][C]832.730179417341[/C][C]190.269820582659[/C][/ROW]
[ROW][C]43[/C][C]899[/C][C]993.022795930223[/C][C]-94.0227959302231[/C][/ROW]
[ROW][C]44[/C][C]765[/C][C]908.124552115042[/C][C]-143.124552115042[/C][/ROW]
[ROW][C]45[/C][C]785[/C][C]780.034841794886[/C][C]4.96515820511399[/C][/ROW]
[ROW][C]46[/C][C]858[/C][C]779.37403277825[/C][C]78.6259672217499[/C][/ROW]
[ROW][C]47[/C][C]961[/C][C]842.60329017326[/C][C]118.39670982674[/C][/ROW]
[ROW][C]48[/C][C]1085[/C][C]940.832576420082[/C][C]144.167423579918[/C][/ROW]
[ROW][C]49[/C][C]1002[/C][C]1062.18945708693[/C][C]-60.1894570869251[/C][/ROW]
[ROW][C]50[/C][C]951[/C][C]1007.34596244936[/C][C]-56.3459624493644[/C][/ROW]
[ROW][C]51[/C][C]951[/C][C]955.434443011809[/C][C]-4.43444301180864[/C][/ROW]
[ROW][C]52[/C][C]785[/C][C]948.150947442381[/C][C]-163.150947442381[/C][/ROW]
[ROW][C]53[/C][C]1023[/C][C]803.245533944336[/C][C]219.754466055664[/C][/ROW]
[ROW][C]54[/C][C]1178[/C][C]989.199318544027[/C][C]188.800681455973[/C][/ROW]
[ROW][C]55[/C][C]1054[/C][C]1149.77938559854[/C][C]-95.7793855985374[/C][/ROW]
[ROW][C]56[/C][C]920[/C][C]1064.90963656061[/C][C]-144.909636560608[/C][/ROW]
[ROW][C]57[/C][C]961[/C][C]936.812045623601[/C][C]24.1879543763988[/C][/ROW]
[ROW][C]58[/C][C]1126[/C][C]954.343372456018[/C][C]171.656627543982[/C][/ROW]
[ROW][C]59[/C][C]1199[/C][C]1099.87706157423[/C][C]99.1229384257724[/C][/ROW]
[ROW][C]60[/C][C]1302[/C][C]1183.67149784785[/C][C]118.328502152148[/C][/ROW]
[ROW][C]61[/C][C]1219[/C][C]1284.7740739188[/C][C]-65.7740739188007[/C][/ROW]
[ROW][C]62[/C][C]1085[/C][C]1227.06316576375[/C][C]-142.063165763755[/C][/ROW]
[ROW][C]63[/C][C]1054[/C][C]1102.77962067785[/C][C]-48.7796206778478[/C][/ROW]
[ROW][C]64[/C][C]806[/C][C]1058.42018149985[/C][C]-252.420181499846[/C][/ROW]
[ROW][C]65[/C][C]971[/C][C]837.199157976553[/C][C]133.800842023447[/C][/ROW]
[ROW][C]66[/C][C]1147[/C][C]949.118436928645[/C][C]197.881563071355[/C][/ROW]
[ROW][C]67[/C][C]951[/C][C]1117.478889175[/C][C]-166.478889175004[/C][/ROW]
[ROW][C]68[/C][C]837[/C][C]971.287695657638[/C][C]-134.287695657638[/C][/ROW]
[ROW][C]69[/C][C]951[/C][C]851.896970541205[/C][C]99.1030294587952[/C][/ROW]
[ROW][C]70[/C][C]1064[/C][C]933.941917696411[/C][C]130.058082303589[/C][/ROW]
[ROW][C]71[/C][C]1126[/C][C]1043.48058678509[/C][C]82.5194132149054[/C][/ROW]
[ROW][C]72[/C][C]1292[/C][C]1112.67192604337[/C][C]179.328073956633[/C][/ROW]
[ROW][C]73[/C][C]1209[/C][C]1266.33573814296[/C][C]-57.3357381429598[/C][/ROW]
[ROW][C]74[/C][C]1002[/C][C]1216.0257229316[/C][C]-214.025722931595[/C][/ROW]
[ROW][C]75[/C][C]1023[/C][C]1029.49904868822[/C][C]-6.49904868822205[/C][/ROW]
[ROW][C]76[/C][C]827[/C][C]1021.45643638471[/C][C]-194.456436384713[/C][/ROW]
[ROW][C]77[/C][C]992[/C][C]850.429059646729[/C][C]141.570940353271[/C][/ROW]
[ROW][C]78[/C][C]1137[/C][C]969.413948011532[/C][C]167.586051988468[/C][/ROW]
[ROW][C]79[/C][C]971[/C][C]1111.89230083559[/C][C]-140.892300835594[/C][/ROW]
[ROW][C]80[/C][C]858[/C][C]988.062268536302[/C][C]-130.062268536302[/C][/ROW]
[ROW][C]81[/C][C]961[/C][C]872.684594968749[/C][C]88.315405031251[/C][/ROW]
[ROW][C]82[/C][C]1085[/C][C]945.755753346112[/C][C]139.244246653888[/C][/ROW]
[ROW][C]83[/C][C]1064[/C][C]1063.56436404899[/C][C]0.435635951011363[/C][/ROW]
[ROW][C]84[/C][C]1312[/C][C]1061.96413792404[/C][C]250.035862075961[/C][/ROW]
[ROW][C]85[/C][C]1271[/C][C]1276.74699153595[/C][C]-5.74699153594679[/C][/ROW]
[ROW][C]86[/C][C]1106[/C][C]1271.45146153154[/C][C]-165.451461531538[/C][/ROW]
[ROW][C]87[/C][C]1116[/C][C]1127.66881704447[/C][C]-11.668817044467[/C][/ROW]
[ROW][C]88[/C][C]899[/C][C]1116.10194927989[/C][C]-217.101949279894[/C][/ROW]
[ROW][C]89[/C][C]1033[/C][C]926.366117018124[/C][C]106.633882981876[/C][/ROW]
[ROW][C]90[/C][C]1240[/C][C]1015.83643752069[/C][C]224.163562479313[/C][/ROW]
[ROW][C]91[/C][C]1085[/C][C]1207.90267518014[/C][C]-122.902675180138[/C][/ROW]
[ROW][C]92[/C][C]992[/C][C]1100.58439474129[/C][C]-108.584394741292[/C][/ROW]
[ROW][C]93[/C][C]1147[/C][C]1004.86200631446[/C][C]142.137993685541[/C][/ROW]
[ROW][C]94[/C][C]1240[/C][C]1125.77103675816[/C][C]114.228963241841[/C][/ROW]
[ROW][C]95[/C][C]1168[/C][C]1223.4300833255[/C][C]-55.4300833254965[/C][/ROW]
[ROW][C]96[/C][C]1498[/C][C]1174.76959990768[/C][C]323.230400092316[/C][/ROW]
[ROW][C]97[/C][C]1416[/C][C]1454.00419283118[/C][C]-38.0041928311844[/C][/ROW]
[ROW][C]98[/C][C]1230[/C][C]1422.22995044603[/C][C]-192.229950446034[/C][/ROW]
[ROW][C]99[/C][C]1178[/C][C]1256.50376882316[/C][C]-78.5037688231578[/C][/ROW]
[ROW][C]100[/C][C]940[/C][C]1188.09018442284[/C][C]-248.090184422845[/C][/ROW]
[ROW][C]101[/C][C]1075[/C][C]972.139266768609[/C][C]102.860733231391[/C][/ROW]
[ROW][C]102[/C][C]1199[/C][C]1058.78152384485[/C][C]140.218476155147[/C][/ROW]
[ROW][C]103[/C][C]1044[/C][C]1178.49301082653[/C][C]-134.493010826532[/C][/ROW]
[ROW][C]104[/C][C]1044[/C][C]1060.98697940802[/C][C]-16.9869794080191[/C][/ROW]
[ROW][C]105[/C][C]1219[/C][C]1044.45400298897[/C][C]174.545997011035[/C][/ROW]
[ROW][C]106[/C][C]1312[/C][C]1193.84942212707[/C][C]118.150577872926[/C][/ROW]
[ROW][C]107[/C][C]1261[/C][C]1295.51516847403[/C][C]-34.5151684740254[/C][/ROW]
[ROW][C]108[/C][C]1622[/C][C]1265.61905617791[/C][C]356.380943822091[/C][/ROW]
[ROW][C]109[/C][C]1529[/C][C]1574.36415858815[/C][C]-45.3641585881526[/C][/ROW]
[ROW][C]110[/C][C]1354[/C][C]1537.20187662199[/C][C]-183.201876621987[/C][/ROW]
[ROW][C]111[/C][C]1281[/C][C]1380.24565254185[/C][C]-99.2456525418488[/C][/ROW]
[ROW][C]112[/C][C]1023[/C][C]1294.85423520661[/C][C]-271.854235206609[/C][/ROW]
[ROW][C]113[/C][C]1116[/C][C]1059.16771069508[/C][C]56.8322893049165[/C][/ROW]
[ROW][C]114[/C][C]1281[/C][C]1106.61528316964[/C][C]174.384716830363[/C][/ROW]
[ROW][C]115[/C][C]1157[/C][C]1256.34754650449[/C][C]-99.3475465044937[/C][/ROW]
[ROW][C]116[/C][C]1126[/C][C]1169.93823232951[/C][C]-43.9382323295142[/C][/ROW]
[ROW][C]117[/C][C]1271[/C][C]1130.90344619573[/C][C]140.096553804269[/C][/ROW]
[ROW][C]118[/C][C]1395[/C][C]1251.11772266179[/C][C]143.882277338211[/C][/ROW]
[ROW][C]119[/C][C]1261[/C][C]1375.54485354962[/C][C]-114.544853549617[/C][/ROW]
[ROW][C]120[/C][C]1581[/C][C]1276.89583550027[/C][C]304.104164499733[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296475&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296475&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
3444445-1
4424434.133092993693-10.1330929936927
5630415.341998378062214.658001621938
6620591.35654115847528.6434588415245
7465607.540241168874-142.540241168874
8362475.513936761538-113.513936761538
9372367.7035158008614.2964841991386
10372361.26943958772910.7305604122708
11382360.44166056580121.5583394341985
12403369.07186687498833.9281331250116
13434388.56879571703345.4312042829669
14424418.2632802931275.73671970687263
15362413.848242234495-51.8482422344951
16372359.55051945642112.4494805435793
17661360.648395721308300.351604278692
18723611.413370763711111.586629236289
19558700.532594064169-142.532594064169
20465570.095609303282-105.095609303282
21486471.16583653269314.8341634673068
22496475.50563178623420.4943682137664
23548484.8508757149963.1491242850095
24599531.31001783792167.6899821620788
25610582.12530658691127.8746934130888
26506598.8742630593-92.8742630593005
27517511.1303389685175.86966103148313
28382508.371036805836-126.371036805836
29765391.010352849981373.989647150019
30878706.576077560655171.423922439345
31620849.021431118354-229.021431118354
32537645.457066082867-108.457066082867
33589544.88887681314644.111123186854
34651575.86238960379975.1376103962011
35744634.026113353414109.973886646586
36858722.888961308655135.111038691345
37858834.27419238078223.7258076192182
38785849.99664014088-64.9966401408797
39754788.962641521375-34.9626415213748
40568753.533404310558-185.533404310558
41878587.340980516985290.659019483015
421023832.730179417341190.269820582659
43899993.022795930223-94.0227959302231
44765908.124552115042-143.124552115042
45785780.0348417948864.96515820511399
46858779.3740327782578.6259672217499
47961842.60329017326118.39670982674
481085940.832576420082144.167423579918
4910021062.18945708693-60.1894570869251
509511007.34596244936-56.3459624493644
51951955.434443011809-4.43444301180864
52785948.150947442381-163.150947442381
531023803.245533944336219.754466055664
541178989.199318544027188.800681455973
5510541149.77938559854-95.7793855985374
569201064.90963656061-144.909636560608
57961936.81204562360124.1879543763988
581126954.343372456018171.656627543982
5911991099.8770615742399.1229384257724
6013021183.67149784785118.328502152148
6112191284.7740739188-65.7740739188007
6210851227.06316576375-142.063165763755
6310541102.77962067785-48.7796206778478
648061058.42018149985-252.420181499846
65971837.199157976553133.800842023447
661147949.118436928645197.881563071355
679511117.478889175-166.478889175004
68837971.287695657638-134.287695657638
69951851.89697054120599.1030294587952
701064933.941917696411130.058082303589
7111261043.4805867850982.5194132149054
7212921112.67192604337179.328073956633
7312091266.33573814296-57.3357381429598
7410021216.0257229316-214.025722931595
7510231029.49904868822-6.49904868822205
768271021.45643638471-194.456436384713
77992850.429059646729141.570940353271
781137969.413948011532167.586051988468
799711111.89230083559-140.892300835594
80858988.062268536302-130.062268536302
81961872.68459496874988.315405031251
821085945.755753346112139.244246653888
8310641063.564364048990.435635951011363
8413121061.96413792404250.035862075961
8512711276.74699153595-5.74699153594679
8611061271.45146153154-165.451461531538
8711161127.66881704447-11.668817044467
888991116.10194927989-217.101949279894
891033926.366117018124106.633882981876
9012401015.83643752069224.163562479313
9110851207.90267518014-122.902675180138
929921100.58439474129-108.584394741292
9311471004.86200631446142.137993685541
9412401125.77103675816114.228963241841
9511681223.4300833255-55.4300833254965
9614981174.76959990768323.230400092316
9714161454.00419283118-38.0041928311844
9812301422.22995044603-192.229950446034
9911781256.50376882316-78.5037688231578
1009401188.09018442284-248.090184422845
1011075972.139266768609102.860733231391
10211991058.78152384485140.218476155147
10310441178.49301082653-134.493010826532
10410441060.98697940802-16.9869794080191
10512191044.45400298897174.545997011035
10613121193.84942212707118.150577872926
10712611295.51516847403-34.5151684740254
10816221265.61905617791356.380943822091
10915291574.36415858815-45.3641585881526
11013541537.20187662199-183.201876621987
11112811380.24565254185-99.2456525418488
11210231294.85423520661-271.854235206609
11311161059.1677106950856.8322893049165
11412811106.61528316964174.384716830363
11511571256.34754650449-99.3475465044937
11611261169.93823232951-43.9382323295142
11712711130.90344619573140.096553804269
11813951251.11772266179143.882277338211
11912611375.54485354962-114.544853549617
12015811276.89583550027304.104164499733







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1211540.4153990271259.975427317751820.85537073625
1221542.325796272261171.176683465641913.47490907887
1231544.236193517511099.526887229971988.94549980505
1241546.146590762771037.523318297992054.76986322754
1251548.05698800802981.8835087678742114.23046724817
1261549.96738525327930.8247206914172169.11004981513
1271551.87778249853883.252124281592220.50344071547
1281553.78817974378838.4370422550742269.13931723249
1291555.69857698904795.8660149087552315.53113906932
1301557.60897423429755.1614467441842360.0565017244
1311559.51937147955716.0362762639062403.00246669519
1321561.4297687248678.2663857135592444.59315173604

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 1540.415399027 & 1259.97542731775 & 1820.85537073625 \tabularnewline
122 & 1542.32579627226 & 1171.17668346564 & 1913.47490907887 \tabularnewline
123 & 1544.23619351751 & 1099.52688722997 & 1988.94549980505 \tabularnewline
124 & 1546.14659076277 & 1037.52331829799 & 2054.76986322754 \tabularnewline
125 & 1548.05698800802 & 981.883508767874 & 2114.23046724817 \tabularnewline
126 & 1549.96738525327 & 930.824720691417 & 2169.11004981513 \tabularnewline
127 & 1551.87778249853 & 883.25212428159 & 2220.50344071547 \tabularnewline
128 & 1553.78817974378 & 838.437042255074 & 2269.13931723249 \tabularnewline
129 & 1555.69857698904 & 795.866014908755 & 2315.53113906932 \tabularnewline
130 & 1557.60897423429 & 755.161446744184 & 2360.0565017244 \tabularnewline
131 & 1559.51937147955 & 716.036276263906 & 2403.00246669519 \tabularnewline
132 & 1561.4297687248 & 678.266385713559 & 2444.59315173604 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296475&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]1540.415399027[/C][C]1259.97542731775[/C][C]1820.85537073625[/C][/ROW]
[ROW][C]122[/C][C]1542.32579627226[/C][C]1171.17668346564[/C][C]1913.47490907887[/C][/ROW]
[ROW][C]123[/C][C]1544.23619351751[/C][C]1099.52688722997[/C][C]1988.94549980505[/C][/ROW]
[ROW][C]124[/C][C]1546.14659076277[/C][C]1037.52331829799[/C][C]2054.76986322754[/C][/ROW]
[ROW][C]125[/C][C]1548.05698800802[/C][C]981.883508767874[/C][C]2114.23046724817[/C][/ROW]
[ROW][C]126[/C][C]1549.96738525327[/C][C]930.824720691417[/C][C]2169.11004981513[/C][/ROW]
[ROW][C]127[/C][C]1551.87778249853[/C][C]883.25212428159[/C][C]2220.50344071547[/C][/ROW]
[ROW][C]128[/C][C]1553.78817974378[/C][C]838.437042255074[/C][C]2269.13931723249[/C][/ROW]
[ROW][C]129[/C][C]1555.69857698904[/C][C]795.866014908755[/C][C]2315.53113906932[/C][/ROW]
[ROW][C]130[/C][C]1557.60897423429[/C][C]755.161446744184[/C][C]2360.0565017244[/C][/ROW]
[ROW][C]131[/C][C]1559.51937147955[/C][C]716.036276263906[/C][C]2403.00246669519[/C][/ROW]
[ROW][C]132[/C][C]1561.4297687248[/C][C]678.266385713559[/C][C]2444.59315173604[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296475&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296475&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
1211540.4153990271259.975427317751820.85537073625
1221542.325796272261171.176683465641913.47490907887
1231544.236193517511099.526887229971988.94549980505
1241546.146590762771037.523318297992054.76986322754
1251548.05698800802981.8835087678742114.23046724817
1261549.96738525327930.8247206914172169.11004981513
1271551.87778249853883.252124281592220.50344071547
1281553.78817974378838.4370422550742269.13931723249
1291555.69857698904795.8660149087552315.53113906932
1301557.60897423429755.1614467441842360.0565017244
1311559.51937147955716.0362762639062403.00246669519
1321561.4297687248678.2663857135592444.59315173604



Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')