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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 16 Aug 2015 15:16:17 +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/2015/Aug/16/t1439734633zw0wkmidrisk7tn.htm/, Retrieved Sat, 18 May 2024 23:05:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280151, Retrieved Sat, 18 May 2024 23:05:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2015-08-16 14:16:17] [0d8529ada52922935dd1fcf0fb375c74] [Current]
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Dataseries X:
37800
36400
38500
30800
39900
39200
42000
43400
48300
42000
39900
49700
42000
31500
37100
28000
39200
32200
42700
38500
40600
45500
44800
53200
38500
32200
35700
25900
37100
28700
40600
38500
34300
49000
44100
50400
37800
35000
31500
25900
34300
30800
42000
40600
35000
46900
43400
56000
44800
27300
27300
27300
32200
32200
43400
39900
35700
44800
41300
59500
46900
27300
28700
23800
32900
37800
47600
46900
37800
44100
39200
56000
42700
34300
30800
23100
34300
41300
48300
45500
33600
48300
37800
58100
48300
35000
32200
21700
34300
32900
49700
49700
37800
49000
36400
56700
48300
35700
27300
18900
37100
35700
46900
53900
39900
44800
33600
58100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280151&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280151&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280151&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00903806239705395
beta1
gamma0.930857409776485

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00903806239705395 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.930857409776485 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280151&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]0.00903806239705395[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.930857409776485[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280151&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280151&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
alpha0.00903806239705395
beta1
gamma0.930857409776485







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134200043596.4354827358-1596.43548273584
143150032673.1512686236-1173.15126862359
153710038786.2911815708-1686.29118157083
162800029228.8684134162-1228.86841341625
173920040295.3082706075-1095.30827060746
183220032591.7715043096-391.771504309643
194270040814.84680591491885.15319408505
203850041967.1715273895-3467.17152738947
214060046650.9332223475-6050.93322234751
224550040365.35170519515134.64829480495
234480038261.14370245176538.85629754829
245320047852.20036376175347.79963623831
253850039193.4252626442-693.425262644152
263220029402.55216214022797.44783785978
273570034738.9951709739961.004829026133
282590026284.3403921408-384.340392140843
293710036845.6980561076254.301943892366
302870030317.4635287451-1617.46352874515
314060040102.8620962119497.137903788142
323850036595.14275350061904.85724649938
333430038935.1123209005-4635.11232090055
344900042907.71391449436092.28608550574
354410042288.97946337431811.02053662571
365040050465.3285138692-65.3285138691936
373780036876.0149282891923.985071710908
383500030655.5756832914344.42431670897
393150034239.0750516365-2739.0750516365
402590024927.6992534282972.300746571807
413430035726.7916655755-1426.79166557545
423080027797.71954321033002.28045678973
434200039283.18853850552716.81146149451
444060037285.90764097093314.09235902913
453500033827.39271215161172.60728784843
464690047669.5758459754-769.575845975443
474340043285.1683205534114.831679446645
485600049779.4662834326220.53371656802
494480037469.41990820637330.58009179369
502730034681.0053328888-7381.00533288882
512730031718.9180228093-4418.91802280926
522730025875.89206930711424.10793069292
533220034567.4993718976-2367.49937189757
543220030762.86530453011437.13469546989
554340042103.69317990491296.3068200951
563990040683.0633809009-783.063380900901
573570035181.0443651844518.955634815589
584480047322.7156723024-2522.71567230237
594130043702.1652552797-2402.16525527965
605950055838.33232763393661.66767236607
614690044399.53211556972500.46788443029
622730027867.027310907-567.027310907029
632870027671.67392731071028.32607268926
642380027288.0192140889-3488.01921408887
653290032419.2831219386480.716878061408
663780032145.98309725635654.01690274368
674760043474.71368221924125.28631778082
684690040212.15926450576687.84073549435
693780036063.61597467491736.38402532515
704410045681.9893731593-1581.98937315926
713920042284.5453537213-3084.54535372129
725600060561.6445122904-4561.64451229038
734270047816.9975795808-5116.9975795808
743430027976.70581107436323.29418892575
753080029436.76361580531363.23638419473
762310024832.7223449965-1732.72234499649
773430034049.379689628250.620310372018
784130038836.8322099272463.16779007304
794830049228.3026408309-928.302640830865
804550048307.9752835983-2807.97528359825
813360039136.205865462-5536.20586546197
824830045768.35170358572531.64829641431
833780040791.1778121658-2991.17781216578
845810058202.3318621139-102.331862113868
854830044504.12646665523795.8735333448
863500035000.0494345527-0.0494345526894904
873220031687.4534994623512.546500537741
882170023947.4375985503-2247.43759855034
893430035272.4977999128-972.497799912773
903290042206.2730307332-9306.27303073315
914970049320.2678532045379.732146795483
924970046431.50104409773268.49895590225
933780034492.73034640143307.26965359861
944900048831.660604654168.339395345982
953640038539.1163465723-2139.11634657229
965670058829.2667197998-2129.26671979979
974830048514.3942362947-214.394236294676
983570035265.4796168705434.520383129486
992730032339.25357072-5039.25357072003
1001890021879.7961459968-2979.7961459968
1013710034234.44311485522865.55688514484
1023570033398.76096865062301.2390313494
1034690049474.3487724982-2574.34877249815
1045390049174.89319959584725.10680040422
1053990037317.11375904842582.88624095164
1064480048635.5420796299-3835.54207962986
1073360036213.127940522-2613.127940522
1085810056203.38236341581896.61763658416

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 42000 & 43596.4354827358 & -1596.43548273584 \tabularnewline
14 & 31500 & 32673.1512686236 & -1173.15126862359 \tabularnewline
15 & 37100 & 38786.2911815708 & -1686.29118157083 \tabularnewline
16 & 28000 & 29228.8684134162 & -1228.86841341625 \tabularnewline
17 & 39200 & 40295.3082706075 & -1095.30827060746 \tabularnewline
18 & 32200 & 32591.7715043096 & -391.771504309643 \tabularnewline
19 & 42700 & 40814.8468059149 & 1885.15319408505 \tabularnewline
20 & 38500 & 41967.1715273895 & -3467.17152738947 \tabularnewline
21 & 40600 & 46650.9332223475 & -6050.93322234751 \tabularnewline
22 & 45500 & 40365.3517051951 & 5134.64829480495 \tabularnewline
23 & 44800 & 38261.1437024517 & 6538.85629754829 \tabularnewline
24 & 53200 & 47852.2003637617 & 5347.79963623831 \tabularnewline
25 & 38500 & 39193.4252626442 & -693.425262644152 \tabularnewline
26 & 32200 & 29402.5521621402 & 2797.44783785978 \tabularnewline
27 & 35700 & 34738.9951709739 & 961.004829026133 \tabularnewline
28 & 25900 & 26284.3403921408 & -384.340392140843 \tabularnewline
29 & 37100 & 36845.6980561076 & 254.301943892366 \tabularnewline
30 & 28700 & 30317.4635287451 & -1617.46352874515 \tabularnewline
31 & 40600 & 40102.8620962119 & 497.137903788142 \tabularnewline
32 & 38500 & 36595.1427535006 & 1904.85724649938 \tabularnewline
33 & 34300 & 38935.1123209005 & -4635.11232090055 \tabularnewline
34 & 49000 & 42907.7139144943 & 6092.28608550574 \tabularnewline
35 & 44100 & 42288.9794633743 & 1811.02053662571 \tabularnewline
36 & 50400 & 50465.3285138692 & -65.3285138691936 \tabularnewline
37 & 37800 & 36876.0149282891 & 923.985071710908 \tabularnewline
38 & 35000 & 30655.575683291 & 4344.42431670897 \tabularnewline
39 & 31500 & 34239.0750516365 & -2739.0750516365 \tabularnewline
40 & 25900 & 24927.6992534282 & 972.300746571807 \tabularnewline
41 & 34300 & 35726.7916655755 & -1426.79166557545 \tabularnewline
42 & 30800 & 27797.7195432103 & 3002.28045678973 \tabularnewline
43 & 42000 & 39283.1885385055 & 2716.81146149451 \tabularnewline
44 & 40600 & 37285.9076409709 & 3314.09235902913 \tabularnewline
45 & 35000 & 33827.3927121516 & 1172.60728784843 \tabularnewline
46 & 46900 & 47669.5758459754 & -769.575845975443 \tabularnewline
47 & 43400 & 43285.1683205534 & 114.831679446645 \tabularnewline
48 & 56000 & 49779.466283432 & 6220.53371656802 \tabularnewline
49 & 44800 & 37469.4199082063 & 7330.58009179369 \tabularnewline
50 & 27300 & 34681.0053328888 & -7381.00533288882 \tabularnewline
51 & 27300 & 31718.9180228093 & -4418.91802280926 \tabularnewline
52 & 27300 & 25875.8920693071 & 1424.10793069292 \tabularnewline
53 & 32200 & 34567.4993718976 & -2367.49937189757 \tabularnewline
54 & 32200 & 30762.8653045301 & 1437.13469546989 \tabularnewline
55 & 43400 & 42103.6931799049 & 1296.3068200951 \tabularnewline
56 & 39900 & 40683.0633809009 & -783.063380900901 \tabularnewline
57 & 35700 & 35181.0443651844 & 518.955634815589 \tabularnewline
58 & 44800 & 47322.7156723024 & -2522.71567230237 \tabularnewline
59 & 41300 & 43702.1652552797 & -2402.16525527965 \tabularnewline
60 & 59500 & 55838.3323276339 & 3661.66767236607 \tabularnewline
61 & 46900 & 44399.5321155697 & 2500.46788443029 \tabularnewline
62 & 27300 & 27867.027310907 & -567.027310907029 \tabularnewline
63 & 28700 & 27671.6739273107 & 1028.32607268926 \tabularnewline
64 & 23800 & 27288.0192140889 & -3488.01921408887 \tabularnewline
65 & 32900 & 32419.2831219386 & 480.716878061408 \tabularnewline
66 & 37800 & 32145.9830972563 & 5654.01690274368 \tabularnewline
67 & 47600 & 43474.7136822192 & 4125.28631778082 \tabularnewline
68 & 46900 & 40212.1592645057 & 6687.84073549435 \tabularnewline
69 & 37800 & 36063.6159746749 & 1736.38402532515 \tabularnewline
70 & 44100 & 45681.9893731593 & -1581.98937315926 \tabularnewline
71 & 39200 & 42284.5453537213 & -3084.54535372129 \tabularnewline
72 & 56000 & 60561.6445122904 & -4561.64451229038 \tabularnewline
73 & 42700 & 47816.9975795808 & -5116.9975795808 \tabularnewline
74 & 34300 & 27976.7058110743 & 6323.29418892575 \tabularnewline
75 & 30800 & 29436.7636158053 & 1363.23638419473 \tabularnewline
76 & 23100 & 24832.7223449965 & -1732.72234499649 \tabularnewline
77 & 34300 & 34049.379689628 & 250.620310372018 \tabularnewline
78 & 41300 & 38836.832209927 & 2463.16779007304 \tabularnewline
79 & 48300 & 49228.3026408309 & -928.302640830865 \tabularnewline
80 & 45500 & 48307.9752835983 & -2807.97528359825 \tabularnewline
81 & 33600 & 39136.205865462 & -5536.20586546197 \tabularnewline
82 & 48300 & 45768.3517035857 & 2531.64829641431 \tabularnewline
83 & 37800 & 40791.1778121658 & -2991.17781216578 \tabularnewline
84 & 58100 & 58202.3318621139 & -102.331862113868 \tabularnewline
85 & 48300 & 44504.1264666552 & 3795.8735333448 \tabularnewline
86 & 35000 & 35000.0494345527 & -0.0494345526894904 \tabularnewline
87 & 32200 & 31687.4534994623 & 512.546500537741 \tabularnewline
88 & 21700 & 23947.4375985503 & -2247.43759855034 \tabularnewline
89 & 34300 & 35272.4977999128 & -972.497799912773 \tabularnewline
90 & 32900 & 42206.2730307332 & -9306.27303073315 \tabularnewline
91 & 49700 & 49320.2678532045 & 379.732146795483 \tabularnewline
92 & 49700 & 46431.5010440977 & 3268.49895590225 \tabularnewline
93 & 37800 & 34492.7303464014 & 3307.26965359861 \tabularnewline
94 & 49000 & 48831.660604654 & 168.339395345982 \tabularnewline
95 & 36400 & 38539.1163465723 & -2139.11634657229 \tabularnewline
96 & 56700 & 58829.2667197998 & -2129.26671979979 \tabularnewline
97 & 48300 & 48514.3942362947 & -214.394236294676 \tabularnewline
98 & 35700 & 35265.4796168705 & 434.520383129486 \tabularnewline
99 & 27300 & 32339.25357072 & -5039.25357072003 \tabularnewline
100 & 18900 & 21879.7961459968 & -2979.7961459968 \tabularnewline
101 & 37100 & 34234.4431148552 & 2865.55688514484 \tabularnewline
102 & 35700 & 33398.7609686506 & 2301.2390313494 \tabularnewline
103 & 46900 & 49474.3487724982 & -2574.34877249815 \tabularnewline
104 & 53900 & 49174.8931995958 & 4725.10680040422 \tabularnewline
105 & 39900 & 37317.1137590484 & 2582.88624095164 \tabularnewline
106 & 44800 & 48635.5420796299 & -3835.54207962986 \tabularnewline
107 & 33600 & 36213.127940522 & -2613.127940522 \tabularnewline
108 & 58100 & 56203.3823634158 & 1896.61763658416 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280151&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]42000[/C][C]43596.4354827358[/C][C]-1596.43548273584[/C][/ROW]
[ROW][C]14[/C][C]31500[/C][C]32673.1512686236[/C][C]-1173.15126862359[/C][/ROW]
[ROW][C]15[/C][C]37100[/C][C]38786.2911815708[/C][C]-1686.29118157083[/C][/ROW]
[ROW][C]16[/C][C]28000[/C][C]29228.8684134162[/C][C]-1228.86841341625[/C][/ROW]
[ROW][C]17[/C][C]39200[/C][C]40295.3082706075[/C][C]-1095.30827060746[/C][/ROW]
[ROW][C]18[/C][C]32200[/C][C]32591.7715043096[/C][C]-391.771504309643[/C][/ROW]
[ROW][C]19[/C][C]42700[/C][C]40814.8468059149[/C][C]1885.15319408505[/C][/ROW]
[ROW][C]20[/C][C]38500[/C][C]41967.1715273895[/C][C]-3467.17152738947[/C][/ROW]
[ROW][C]21[/C][C]40600[/C][C]46650.9332223475[/C][C]-6050.93322234751[/C][/ROW]
[ROW][C]22[/C][C]45500[/C][C]40365.3517051951[/C][C]5134.64829480495[/C][/ROW]
[ROW][C]23[/C][C]44800[/C][C]38261.1437024517[/C][C]6538.85629754829[/C][/ROW]
[ROW][C]24[/C][C]53200[/C][C]47852.2003637617[/C][C]5347.79963623831[/C][/ROW]
[ROW][C]25[/C][C]38500[/C][C]39193.4252626442[/C][C]-693.425262644152[/C][/ROW]
[ROW][C]26[/C][C]32200[/C][C]29402.5521621402[/C][C]2797.44783785978[/C][/ROW]
[ROW][C]27[/C][C]35700[/C][C]34738.9951709739[/C][C]961.004829026133[/C][/ROW]
[ROW][C]28[/C][C]25900[/C][C]26284.3403921408[/C][C]-384.340392140843[/C][/ROW]
[ROW][C]29[/C][C]37100[/C][C]36845.6980561076[/C][C]254.301943892366[/C][/ROW]
[ROW][C]30[/C][C]28700[/C][C]30317.4635287451[/C][C]-1617.46352874515[/C][/ROW]
[ROW][C]31[/C][C]40600[/C][C]40102.8620962119[/C][C]497.137903788142[/C][/ROW]
[ROW][C]32[/C][C]38500[/C][C]36595.1427535006[/C][C]1904.85724649938[/C][/ROW]
[ROW][C]33[/C][C]34300[/C][C]38935.1123209005[/C][C]-4635.11232090055[/C][/ROW]
[ROW][C]34[/C][C]49000[/C][C]42907.7139144943[/C][C]6092.28608550574[/C][/ROW]
[ROW][C]35[/C][C]44100[/C][C]42288.9794633743[/C][C]1811.02053662571[/C][/ROW]
[ROW][C]36[/C][C]50400[/C][C]50465.3285138692[/C][C]-65.3285138691936[/C][/ROW]
[ROW][C]37[/C][C]37800[/C][C]36876.0149282891[/C][C]923.985071710908[/C][/ROW]
[ROW][C]38[/C][C]35000[/C][C]30655.575683291[/C][C]4344.42431670897[/C][/ROW]
[ROW][C]39[/C][C]31500[/C][C]34239.0750516365[/C][C]-2739.0750516365[/C][/ROW]
[ROW][C]40[/C][C]25900[/C][C]24927.6992534282[/C][C]972.300746571807[/C][/ROW]
[ROW][C]41[/C][C]34300[/C][C]35726.7916655755[/C][C]-1426.79166557545[/C][/ROW]
[ROW][C]42[/C][C]30800[/C][C]27797.7195432103[/C][C]3002.28045678973[/C][/ROW]
[ROW][C]43[/C][C]42000[/C][C]39283.1885385055[/C][C]2716.81146149451[/C][/ROW]
[ROW][C]44[/C][C]40600[/C][C]37285.9076409709[/C][C]3314.09235902913[/C][/ROW]
[ROW][C]45[/C][C]35000[/C][C]33827.3927121516[/C][C]1172.60728784843[/C][/ROW]
[ROW][C]46[/C][C]46900[/C][C]47669.5758459754[/C][C]-769.575845975443[/C][/ROW]
[ROW][C]47[/C][C]43400[/C][C]43285.1683205534[/C][C]114.831679446645[/C][/ROW]
[ROW][C]48[/C][C]56000[/C][C]49779.466283432[/C][C]6220.53371656802[/C][/ROW]
[ROW][C]49[/C][C]44800[/C][C]37469.4199082063[/C][C]7330.58009179369[/C][/ROW]
[ROW][C]50[/C][C]27300[/C][C]34681.0053328888[/C][C]-7381.00533288882[/C][/ROW]
[ROW][C]51[/C][C]27300[/C][C]31718.9180228093[/C][C]-4418.91802280926[/C][/ROW]
[ROW][C]52[/C][C]27300[/C][C]25875.8920693071[/C][C]1424.10793069292[/C][/ROW]
[ROW][C]53[/C][C]32200[/C][C]34567.4993718976[/C][C]-2367.49937189757[/C][/ROW]
[ROW][C]54[/C][C]32200[/C][C]30762.8653045301[/C][C]1437.13469546989[/C][/ROW]
[ROW][C]55[/C][C]43400[/C][C]42103.6931799049[/C][C]1296.3068200951[/C][/ROW]
[ROW][C]56[/C][C]39900[/C][C]40683.0633809009[/C][C]-783.063380900901[/C][/ROW]
[ROW][C]57[/C][C]35700[/C][C]35181.0443651844[/C][C]518.955634815589[/C][/ROW]
[ROW][C]58[/C][C]44800[/C][C]47322.7156723024[/C][C]-2522.71567230237[/C][/ROW]
[ROW][C]59[/C][C]41300[/C][C]43702.1652552797[/C][C]-2402.16525527965[/C][/ROW]
[ROW][C]60[/C][C]59500[/C][C]55838.3323276339[/C][C]3661.66767236607[/C][/ROW]
[ROW][C]61[/C][C]46900[/C][C]44399.5321155697[/C][C]2500.46788443029[/C][/ROW]
[ROW][C]62[/C][C]27300[/C][C]27867.027310907[/C][C]-567.027310907029[/C][/ROW]
[ROW][C]63[/C][C]28700[/C][C]27671.6739273107[/C][C]1028.32607268926[/C][/ROW]
[ROW][C]64[/C][C]23800[/C][C]27288.0192140889[/C][C]-3488.01921408887[/C][/ROW]
[ROW][C]65[/C][C]32900[/C][C]32419.2831219386[/C][C]480.716878061408[/C][/ROW]
[ROW][C]66[/C][C]37800[/C][C]32145.9830972563[/C][C]5654.01690274368[/C][/ROW]
[ROW][C]67[/C][C]47600[/C][C]43474.7136822192[/C][C]4125.28631778082[/C][/ROW]
[ROW][C]68[/C][C]46900[/C][C]40212.1592645057[/C][C]6687.84073549435[/C][/ROW]
[ROW][C]69[/C][C]37800[/C][C]36063.6159746749[/C][C]1736.38402532515[/C][/ROW]
[ROW][C]70[/C][C]44100[/C][C]45681.9893731593[/C][C]-1581.98937315926[/C][/ROW]
[ROW][C]71[/C][C]39200[/C][C]42284.5453537213[/C][C]-3084.54535372129[/C][/ROW]
[ROW][C]72[/C][C]56000[/C][C]60561.6445122904[/C][C]-4561.64451229038[/C][/ROW]
[ROW][C]73[/C][C]42700[/C][C]47816.9975795808[/C][C]-5116.9975795808[/C][/ROW]
[ROW][C]74[/C][C]34300[/C][C]27976.7058110743[/C][C]6323.29418892575[/C][/ROW]
[ROW][C]75[/C][C]30800[/C][C]29436.7636158053[/C][C]1363.23638419473[/C][/ROW]
[ROW][C]76[/C][C]23100[/C][C]24832.7223449965[/C][C]-1732.72234499649[/C][/ROW]
[ROW][C]77[/C][C]34300[/C][C]34049.379689628[/C][C]250.620310372018[/C][/ROW]
[ROW][C]78[/C][C]41300[/C][C]38836.832209927[/C][C]2463.16779007304[/C][/ROW]
[ROW][C]79[/C][C]48300[/C][C]49228.3026408309[/C][C]-928.302640830865[/C][/ROW]
[ROW][C]80[/C][C]45500[/C][C]48307.9752835983[/C][C]-2807.97528359825[/C][/ROW]
[ROW][C]81[/C][C]33600[/C][C]39136.205865462[/C][C]-5536.20586546197[/C][/ROW]
[ROW][C]82[/C][C]48300[/C][C]45768.3517035857[/C][C]2531.64829641431[/C][/ROW]
[ROW][C]83[/C][C]37800[/C][C]40791.1778121658[/C][C]-2991.17781216578[/C][/ROW]
[ROW][C]84[/C][C]58100[/C][C]58202.3318621139[/C][C]-102.331862113868[/C][/ROW]
[ROW][C]85[/C][C]48300[/C][C]44504.1264666552[/C][C]3795.8735333448[/C][/ROW]
[ROW][C]86[/C][C]35000[/C][C]35000.0494345527[/C][C]-0.0494345526894904[/C][/ROW]
[ROW][C]87[/C][C]32200[/C][C]31687.4534994623[/C][C]512.546500537741[/C][/ROW]
[ROW][C]88[/C][C]21700[/C][C]23947.4375985503[/C][C]-2247.43759855034[/C][/ROW]
[ROW][C]89[/C][C]34300[/C][C]35272.4977999128[/C][C]-972.497799912773[/C][/ROW]
[ROW][C]90[/C][C]32900[/C][C]42206.2730307332[/C][C]-9306.27303073315[/C][/ROW]
[ROW][C]91[/C][C]49700[/C][C]49320.2678532045[/C][C]379.732146795483[/C][/ROW]
[ROW][C]92[/C][C]49700[/C][C]46431.5010440977[/C][C]3268.49895590225[/C][/ROW]
[ROW][C]93[/C][C]37800[/C][C]34492.7303464014[/C][C]3307.26965359861[/C][/ROW]
[ROW][C]94[/C][C]49000[/C][C]48831.660604654[/C][C]168.339395345982[/C][/ROW]
[ROW][C]95[/C][C]36400[/C][C]38539.1163465723[/C][C]-2139.11634657229[/C][/ROW]
[ROW][C]96[/C][C]56700[/C][C]58829.2667197998[/C][C]-2129.26671979979[/C][/ROW]
[ROW][C]97[/C][C]48300[/C][C]48514.3942362947[/C][C]-214.394236294676[/C][/ROW]
[ROW][C]98[/C][C]35700[/C][C]35265.4796168705[/C][C]434.520383129486[/C][/ROW]
[ROW][C]99[/C][C]27300[/C][C]32339.25357072[/C][C]-5039.25357072003[/C][/ROW]
[ROW][C]100[/C][C]18900[/C][C]21879.7961459968[/C][C]-2979.7961459968[/C][/ROW]
[ROW][C]101[/C][C]37100[/C][C]34234.4431148552[/C][C]2865.55688514484[/C][/ROW]
[ROW][C]102[/C][C]35700[/C][C]33398.7609686506[/C][C]2301.2390313494[/C][/ROW]
[ROW][C]103[/C][C]46900[/C][C]49474.3487724982[/C][C]-2574.34877249815[/C][/ROW]
[ROW][C]104[/C][C]53900[/C][C]49174.8931995958[/C][C]4725.10680040422[/C][/ROW]
[ROW][C]105[/C][C]39900[/C][C]37317.1137590484[/C][C]2582.88624095164[/C][/ROW]
[ROW][C]106[/C][C]44800[/C][C]48635.5420796299[/C][C]-3835.54207962986[/C][/ROW]
[ROW][C]107[/C][C]33600[/C][C]36213.127940522[/C][C]-2613.127940522[/C][/ROW]
[ROW][C]108[/C][C]58100[/C][C]56203.3823634158[/C][C]1896.61763658416[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280151&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280151&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
134200043596.4354827358-1596.43548273584
143150032673.1512686236-1173.15126862359
153710038786.2911815708-1686.29118157083
162800029228.8684134162-1228.86841341625
173920040295.3082706075-1095.30827060746
183220032591.7715043096-391.771504309643
194270040814.84680591491885.15319408505
203850041967.1715273895-3467.17152738947
214060046650.9332223475-6050.93322234751
224550040365.35170519515134.64829480495
234480038261.14370245176538.85629754829
245320047852.20036376175347.79963623831
253850039193.4252626442-693.425262644152
263220029402.55216214022797.44783785978
273570034738.9951709739961.004829026133
282590026284.3403921408-384.340392140843
293710036845.6980561076254.301943892366
302870030317.4635287451-1617.46352874515
314060040102.8620962119497.137903788142
323850036595.14275350061904.85724649938
333430038935.1123209005-4635.11232090055
344900042907.71391449436092.28608550574
354410042288.97946337431811.02053662571
365040050465.3285138692-65.3285138691936
373780036876.0149282891923.985071710908
383500030655.5756832914344.42431670897
393150034239.0750516365-2739.0750516365
402590024927.6992534282972.300746571807
413430035726.7916655755-1426.79166557545
423080027797.71954321033002.28045678973
434200039283.18853850552716.81146149451
444060037285.90764097093314.09235902913
453500033827.39271215161172.60728784843
464690047669.5758459754-769.575845975443
474340043285.1683205534114.831679446645
485600049779.4662834326220.53371656802
494480037469.41990820637330.58009179369
502730034681.0053328888-7381.00533288882
512730031718.9180228093-4418.91802280926
522730025875.89206930711424.10793069292
533220034567.4993718976-2367.49937189757
543220030762.86530453011437.13469546989
554340042103.69317990491296.3068200951
563990040683.0633809009-783.063380900901
573570035181.0443651844518.955634815589
584480047322.7156723024-2522.71567230237
594130043702.1652552797-2402.16525527965
605950055838.33232763393661.66767236607
614690044399.53211556972500.46788443029
622730027867.027310907-567.027310907029
632870027671.67392731071028.32607268926
642380027288.0192140889-3488.01921408887
653290032419.2831219386480.716878061408
663780032145.98309725635654.01690274368
674760043474.71368221924125.28631778082
684690040212.15926450576687.84073549435
693780036063.61597467491736.38402532515
704410045681.9893731593-1581.98937315926
713920042284.5453537213-3084.54535372129
725600060561.6445122904-4561.64451229038
734270047816.9975795808-5116.9975795808
743430027976.70581107436323.29418892575
753080029436.76361580531363.23638419473
762310024832.7223449965-1732.72234499649
773430034049.379689628250.620310372018
784130038836.8322099272463.16779007304
794830049228.3026408309-928.302640830865
804550048307.9752835983-2807.97528359825
813360039136.205865462-5536.20586546197
824830045768.35170358572531.64829641431
833780040791.1778121658-2991.17781216578
845810058202.3318621139-102.331862113868
854830044504.12646665523795.8735333448
863500035000.0494345527-0.0494345526894904
873220031687.4534994623512.546500537741
882170023947.4375985503-2247.43759855034
893430035272.4977999128-972.497799912773
903290042206.2730307332-9306.27303073315
914970049320.2678532045379.732146795483
924970046431.50104409773268.49895590225
933780034492.73034640143307.26965359861
944900048831.660604654168.339395345982
953640038539.1163465723-2139.11634657229
965670058829.2667197998-2129.26671979979
974830048514.3942362947-214.394236294676
983570035265.4796168705434.520383129486
992730032339.25357072-5039.25357072003
1001890021879.7961459968-2979.7961459968
1013710034234.44311485522865.55688514484
1023570033398.76096865062301.2390313494
1034690049474.3487724982-2574.34877249815
1045390049174.89319959584725.10680040422
1053990037317.11375904842582.88624095164
1064480048635.5420796299-3835.54207962986
1073360036213.127940522-2613.127940522
1085810056203.38236341581896.61763658416







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10947725.617088644541724.678655296153726.555521993
11035188.920991560629187.367010426341190.4749726948
11127274.722925167121272.270531898833277.1753184354
11218873.038864181912870.112817727624875.9649106362
11336477.996636240330459.238459366942496.7548131137
11435130.598526246329099.623709770141161.5733427224
11546550.598878888940464.373414866552636.8243429114
11652954.186901475646789.469104960359118.9046979909
11739219.703762104333091.877206610545347.5303175981
11844475.751465471838255.848770738750695.654160205
11933348.679577990827185.984958416839511.3741975648
12057230.689009170954501.233612233159960.1444061087

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 47725.6170886445 & 41724.6786552961 & 53726.555521993 \tabularnewline
110 & 35188.9209915606 & 29187.3670104263 & 41190.4749726948 \tabularnewline
111 & 27274.7229251671 & 21272.2705318988 & 33277.1753184354 \tabularnewline
112 & 18873.0388641819 & 12870.1128177276 & 24875.9649106362 \tabularnewline
113 & 36477.9966362403 & 30459.2384593669 & 42496.7548131137 \tabularnewline
114 & 35130.5985262463 & 29099.6237097701 & 41161.5733427224 \tabularnewline
115 & 46550.5988788889 & 40464.3734148665 & 52636.8243429114 \tabularnewline
116 & 52954.1869014756 & 46789.4691049603 & 59118.9046979909 \tabularnewline
117 & 39219.7037621043 & 33091.8772066105 & 45347.5303175981 \tabularnewline
118 & 44475.7514654718 & 38255.8487707387 & 50695.654160205 \tabularnewline
119 & 33348.6795779908 & 27185.9849584168 & 39511.3741975648 \tabularnewline
120 & 57230.6890091709 & 54501.2336122331 & 59960.1444061087 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280151&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]47725.6170886445[/C][C]41724.6786552961[/C][C]53726.555521993[/C][/ROW]
[ROW][C]110[/C][C]35188.9209915606[/C][C]29187.3670104263[/C][C]41190.4749726948[/C][/ROW]
[ROW][C]111[/C][C]27274.7229251671[/C][C]21272.2705318988[/C][C]33277.1753184354[/C][/ROW]
[ROW][C]112[/C][C]18873.0388641819[/C][C]12870.1128177276[/C][C]24875.9649106362[/C][/ROW]
[ROW][C]113[/C][C]36477.9966362403[/C][C]30459.2384593669[/C][C]42496.7548131137[/C][/ROW]
[ROW][C]114[/C][C]35130.5985262463[/C][C]29099.6237097701[/C][C]41161.5733427224[/C][/ROW]
[ROW][C]115[/C][C]46550.5988788889[/C][C]40464.3734148665[/C][C]52636.8243429114[/C][/ROW]
[ROW][C]116[/C][C]52954.1869014756[/C][C]46789.4691049603[/C][C]59118.9046979909[/C][/ROW]
[ROW][C]117[/C][C]39219.7037621043[/C][C]33091.8772066105[/C][C]45347.5303175981[/C][/ROW]
[ROW][C]118[/C][C]44475.7514654718[/C][C]38255.8487707387[/C][C]50695.654160205[/C][/ROW]
[ROW][C]119[/C][C]33348.6795779908[/C][C]27185.9849584168[/C][C]39511.3741975648[/C][/ROW]
[ROW][C]120[/C][C]57230.6890091709[/C][C]54501.2336122331[/C][C]59960.1444061087[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280151&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280151&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
10947725.617088644541724.678655296153726.555521993
11035188.920991560629187.367010426341190.4749726948
11127274.722925167121272.270531898833277.1753184354
11218873.038864181912870.112817727624875.9649106362
11336477.996636240330459.238459366942496.7548131137
11435130.598526246329099.623709770141161.5733427224
11546550.598878888940464.373414866552636.8243429114
11652954.186901475646789.469104960359118.9046979909
11739219.703762104333091.877206610545347.5303175981
11844475.751465471838255.848770738750695.654160205
11933348.679577990827185.984958416839511.3741975648
12057230.689009170954501.233612233159960.1444061087



Parameters (Session):
par1 = 0 ; par2 = no ; par3 = 512 ;
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')