Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 Dec 2016 16:30:14 +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/Dec/21/t14823342710vi61q3iyjx6s36.htm/, Retrieved Fri, 01 Nov 2024 05:25:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302385, Retrieved Fri, 01 Nov 2024 05:25:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2016-12-21 15:30:14] [6f830dc7e8de22be3233942ffbe3aaba] [Current]
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Dataseries X:
4526.1
4616.8
4558
4736.8
4771.1
4611.3
4687.1
4718.3
4731.6
4755.4
4849.8
4697.8
4720.2
4741.1
4794.2
4807.4
4836.9
4853
4902.9
4938
4910.4
4954.6
4937.3
5003.8
5005.6
4984.4
5050
5017.7
4984.8
5036.3
5093.6
5111.2
5090.7
5063.7
5007.5
5122.5
5172.3
5232.8
5183.3
5204.6
5255.4
5294.5
5308.9
5281.3
5413.9
5462.4
5568.7
5579.1
5590.3
5703.2
5717.7
5772.3
5876.6
6134.6
6155.6
6259.5
6180.7
6120.3
6097
6167.5
6207.1
6181.7
6196.2
6183.9
6184
6271.1
6204.9
6284.5
6293.9
6377.9
6400.2
6456.2
6372.8
6368.8
6497.8
6599.4
6696.9
6676.3
6731.7
6732.3
6760.2
6841.4
6917.5
6899.3
6972.9
6969.2
6941.6
6905.5
6971.3
6968.4
7012.2
7049.5
7095.6
7237.5
7230.5
7253.5
7289.4
7364.6
7428.1
7390.2
7279.9
7426.5
7480.1




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=302385&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=302385&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302385&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
alpha0.915843886480235
beta0.109376508578016
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.915843886480235 \tabularnewline
beta & 0.109376508578016 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302385&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]0.915843886480235[/C][/ROW]
[ROW][C]beta[/C][C]0.109376508578016[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302385&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302385&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
alpha0.915843886480235
beta0.109376508578016
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
345584707.5-149.5
44736.84646.305653868790.4943461313023
54771.14813.9736445802-42.8736445801969
64611.34855.20264590876-243.902645908759
74687.14687.88829666434-0.788296664342852
84718.34743.14977278996-24.8497727899594
94731.64773.88544646964-42.285446469642
104755.44784.4169554329-29.0169554329004
114849.84804.1936499441645.6063500558375
124697.84896.88211305858-199.082113058579
134720.24745.53172818954-25.3317281895415
144741.14750.77204609667-9.67204609667442
154794.24769.3853217807424.8146782192598
164807.44822.06878424433-14.6687842443271
174836.94837.12216037363-0.222160373635234
1848534865.38413444919-12.3841344491912
194902.94881.2670977978621.6329022021446
2049384930.47136309777.52863690230333
214910.44967.51248040992-57.112480409919
224954.64939.6313652683814.9686347316174
234937.34979.26473394489-41.9647339448857
245003.84962.552341765141.2476582348963
255005.65026.18136269034-20.5813626903409
264984.45031.12298050898-46.7229805089846
2750505007.4426320934642.5573679065428
285017.75069.79219338896-52.0921933889558
294984.85040.2393634869-55.4393634868984
305036.35002.0675871105334.2324128894661
315093.65049.4502815653244.1497184346808
325111.25110.33823673520.861763264801994
335090.75131.6675071877-40.9675071877
345063.75110.58390680913-46.8839068091274
355007.55079.3853623568-71.8853623568039
365122.55018.08850106506104.411498934944
375172.35128.7111308821843.5888691178234
385232.85187.9961027934344.8038972065715
395183.35252.8819380823-69.5819380823023
405204.65206.03805697014-1.43805697013522
415255.45221.4592800107433.9407199892621
425294.55272.6818428829721.8181571170298
435308.95314.9875948776-6.08759487759926
445281.35331.12622913293-49.826229132932
455413.95302.21591920894111.684080791056
465462.45432.4114353854829.9885646145231
475568.75490.7906212168377.9093787831671
485579.15600.86211497173-21.762114971727
495590.35617.47013014039-27.1701301403928
505703.25626.4035666542576.7964333457485
515717.75738.24698221205-20.5469822120513
525772.35758.880797411613.4192025883967
535876.65811.9665610755364.6334389244657
546134.65918.43101833928216.168981660724
556155.66185.33241344918-29.7324134491764
566259.56224.0481695977935.4518304022122
576180.76326.01379087495-145.313790874946
586120.36247.86997804841-127.569978048414
5960976173.19781253939-76.1978125393925
606167.56137.9416581979629.5583418020378
616207.16202.502543769334.59745623067374
626181.76244.6636903859-62.9636903859027
636196.26218.64218728728-22.4421872872763
646183.96227.48398062552-43.5839806255217
6561846212.59730570302-28.5973057030196
666271.16208.5714416077762.5285583922296
676204.96294.26624170924-89.3662417092401
686284.56231.8971398591252.6028601408752
696293.96304.81889554573-10.9188955457275
706377.96318.4708741342259.4291258657822
716400.26402.50378096734-2.30378096733693
726456.26429.7682085809426.4317914190624
736372.86485.99765479005-113.197654790048
746368.86403.00911272076-34.209112720755
756497.86388.93495538057108.865044619428
766599.46516.7995985603482.600401439664
776696.96628.8841603001668.0158396998422
786676.36734.42480988091-58.1248098809101
796731.76718.6178494862913.0821505137119
806732.36769.33581109647-37.0358110964744
816760.26770.44359985278-10.2435998527753
826841.46795.0627515774846.3372484225183
836917.56876.1428131792441.3571868207637
846899.36956.80473993283-57.5047399328314
856972.96941.1642217702731.7357782297249
866969.27010.43311683571-41.2331168357086
876941.67008.74349964271-67.1434996427051
886905.56976.5981310918-71.0981310917969
896971.36933.7089092600937.5910907399111
906968.46994.1276142447-25.7276142447017
917012.26993.9790887681918.2209112318096
927049.57035.9057732670813.594226732921
937095.67074.9568953055920.643104694409
947237.57122.53154622493114.968453775068
957230.57268.01008916872-37.5100891687198
967253.57270.0846373363-16.5846373363029
977289.47289.66231955091-0.262319550905886
987364.67324.162419699140.4375803008979
997428.17399.9879797844828.1120202155189
1007390.27467.34128287336-77.1412828733573
1017279.97430.57161011941-150.671610119412
1027426.57311.36658928135115.133410718647
1037480.17447.1305935374632.9694064625382

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 4558 & 4707.5 & -149.5 \tabularnewline
4 & 4736.8 & 4646.3056538687 & 90.4943461313023 \tabularnewline
5 & 4771.1 & 4813.9736445802 & -42.8736445801969 \tabularnewline
6 & 4611.3 & 4855.20264590876 & -243.902645908759 \tabularnewline
7 & 4687.1 & 4687.88829666434 & -0.788296664342852 \tabularnewline
8 & 4718.3 & 4743.14977278996 & -24.8497727899594 \tabularnewline
9 & 4731.6 & 4773.88544646964 & -42.285446469642 \tabularnewline
10 & 4755.4 & 4784.4169554329 & -29.0169554329004 \tabularnewline
11 & 4849.8 & 4804.19364994416 & 45.6063500558375 \tabularnewline
12 & 4697.8 & 4896.88211305858 & -199.082113058579 \tabularnewline
13 & 4720.2 & 4745.53172818954 & -25.3317281895415 \tabularnewline
14 & 4741.1 & 4750.77204609667 & -9.67204609667442 \tabularnewline
15 & 4794.2 & 4769.38532178074 & 24.8146782192598 \tabularnewline
16 & 4807.4 & 4822.06878424433 & -14.6687842443271 \tabularnewline
17 & 4836.9 & 4837.12216037363 & -0.222160373635234 \tabularnewline
18 & 4853 & 4865.38413444919 & -12.3841344491912 \tabularnewline
19 & 4902.9 & 4881.26709779786 & 21.6329022021446 \tabularnewline
20 & 4938 & 4930.4713630977 & 7.52863690230333 \tabularnewline
21 & 4910.4 & 4967.51248040992 & -57.112480409919 \tabularnewline
22 & 4954.6 & 4939.63136526838 & 14.9686347316174 \tabularnewline
23 & 4937.3 & 4979.26473394489 & -41.9647339448857 \tabularnewline
24 & 5003.8 & 4962.5523417651 & 41.2476582348963 \tabularnewline
25 & 5005.6 & 5026.18136269034 & -20.5813626903409 \tabularnewline
26 & 4984.4 & 5031.12298050898 & -46.7229805089846 \tabularnewline
27 & 5050 & 5007.44263209346 & 42.5573679065428 \tabularnewline
28 & 5017.7 & 5069.79219338896 & -52.0921933889558 \tabularnewline
29 & 4984.8 & 5040.2393634869 & -55.4393634868984 \tabularnewline
30 & 5036.3 & 5002.06758711053 & 34.2324128894661 \tabularnewline
31 & 5093.6 & 5049.45028156532 & 44.1497184346808 \tabularnewline
32 & 5111.2 & 5110.3382367352 & 0.861763264801994 \tabularnewline
33 & 5090.7 & 5131.6675071877 & -40.9675071877 \tabularnewline
34 & 5063.7 & 5110.58390680913 & -46.8839068091274 \tabularnewline
35 & 5007.5 & 5079.3853623568 & -71.8853623568039 \tabularnewline
36 & 5122.5 & 5018.08850106506 & 104.411498934944 \tabularnewline
37 & 5172.3 & 5128.71113088218 & 43.5888691178234 \tabularnewline
38 & 5232.8 & 5187.99610279343 & 44.8038972065715 \tabularnewline
39 & 5183.3 & 5252.8819380823 & -69.5819380823023 \tabularnewline
40 & 5204.6 & 5206.03805697014 & -1.43805697013522 \tabularnewline
41 & 5255.4 & 5221.45928001074 & 33.9407199892621 \tabularnewline
42 & 5294.5 & 5272.68184288297 & 21.8181571170298 \tabularnewline
43 & 5308.9 & 5314.9875948776 & -6.08759487759926 \tabularnewline
44 & 5281.3 & 5331.12622913293 & -49.826229132932 \tabularnewline
45 & 5413.9 & 5302.21591920894 & 111.684080791056 \tabularnewline
46 & 5462.4 & 5432.41143538548 & 29.9885646145231 \tabularnewline
47 & 5568.7 & 5490.79062121683 & 77.9093787831671 \tabularnewline
48 & 5579.1 & 5600.86211497173 & -21.762114971727 \tabularnewline
49 & 5590.3 & 5617.47013014039 & -27.1701301403928 \tabularnewline
50 & 5703.2 & 5626.40356665425 & 76.7964333457485 \tabularnewline
51 & 5717.7 & 5738.24698221205 & -20.5469822120513 \tabularnewline
52 & 5772.3 & 5758.8807974116 & 13.4192025883967 \tabularnewline
53 & 5876.6 & 5811.96656107553 & 64.6334389244657 \tabularnewline
54 & 6134.6 & 5918.43101833928 & 216.168981660724 \tabularnewline
55 & 6155.6 & 6185.33241344918 & -29.7324134491764 \tabularnewline
56 & 6259.5 & 6224.04816959779 & 35.4518304022122 \tabularnewline
57 & 6180.7 & 6326.01379087495 & -145.313790874946 \tabularnewline
58 & 6120.3 & 6247.86997804841 & -127.569978048414 \tabularnewline
59 & 6097 & 6173.19781253939 & -76.1978125393925 \tabularnewline
60 & 6167.5 & 6137.94165819796 & 29.5583418020378 \tabularnewline
61 & 6207.1 & 6202.50254376933 & 4.59745623067374 \tabularnewline
62 & 6181.7 & 6244.6636903859 & -62.9636903859027 \tabularnewline
63 & 6196.2 & 6218.64218728728 & -22.4421872872763 \tabularnewline
64 & 6183.9 & 6227.48398062552 & -43.5839806255217 \tabularnewline
65 & 6184 & 6212.59730570302 & -28.5973057030196 \tabularnewline
66 & 6271.1 & 6208.57144160777 & 62.5285583922296 \tabularnewline
67 & 6204.9 & 6294.26624170924 & -89.3662417092401 \tabularnewline
68 & 6284.5 & 6231.89713985912 & 52.6028601408752 \tabularnewline
69 & 6293.9 & 6304.81889554573 & -10.9188955457275 \tabularnewline
70 & 6377.9 & 6318.47087413422 & 59.4291258657822 \tabularnewline
71 & 6400.2 & 6402.50378096734 & -2.30378096733693 \tabularnewline
72 & 6456.2 & 6429.76820858094 & 26.4317914190624 \tabularnewline
73 & 6372.8 & 6485.99765479005 & -113.197654790048 \tabularnewline
74 & 6368.8 & 6403.00911272076 & -34.209112720755 \tabularnewline
75 & 6497.8 & 6388.93495538057 & 108.865044619428 \tabularnewline
76 & 6599.4 & 6516.79959856034 & 82.600401439664 \tabularnewline
77 & 6696.9 & 6628.88416030016 & 68.0158396998422 \tabularnewline
78 & 6676.3 & 6734.42480988091 & -58.1248098809101 \tabularnewline
79 & 6731.7 & 6718.61784948629 & 13.0821505137119 \tabularnewline
80 & 6732.3 & 6769.33581109647 & -37.0358110964744 \tabularnewline
81 & 6760.2 & 6770.44359985278 & -10.2435998527753 \tabularnewline
82 & 6841.4 & 6795.06275157748 & 46.3372484225183 \tabularnewline
83 & 6917.5 & 6876.14281317924 & 41.3571868207637 \tabularnewline
84 & 6899.3 & 6956.80473993283 & -57.5047399328314 \tabularnewline
85 & 6972.9 & 6941.16422177027 & 31.7357782297249 \tabularnewline
86 & 6969.2 & 7010.43311683571 & -41.2331168357086 \tabularnewline
87 & 6941.6 & 7008.74349964271 & -67.1434996427051 \tabularnewline
88 & 6905.5 & 6976.5981310918 & -71.0981310917969 \tabularnewline
89 & 6971.3 & 6933.70890926009 & 37.5910907399111 \tabularnewline
90 & 6968.4 & 6994.1276142447 & -25.7276142447017 \tabularnewline
91 & 7012.2 & 6993.97908876819 & 18.2209112318096 \tabularnewline
92 & 7049.5 & 7035.90577326708 & 13.594226732921 \tabularnewline
93 & 7095.6 & 7074.95689530559 & 20.643104694409 \tabularnewline
94 & 7237.5 & 7122.53154622493 & 114.968453775068 \tabularnewline
95 & 7230.5 & 7268.01008916872 & -37.5100891687198 \tabularnewline
96 & 7253.5 & 7270.0846373363 & -16.5846373363029 \tabularnewline
97 & 7289.4 & 7289.66231955091 & -0.262319550905886 \tabularnewline
98 & 7364.6 & 7324.1624196991 & 40.4375803008979 \tabularnewline
99 & 7428.1 & 7399.98797978448 & 28.1120202155189 \tabularnewline
100 & 7390.2 & 7467.34128287336 & -77.1412828733573 \tabularnewline
101 & 7279.9 & 7430.57161011941 & -150.671610119412 \tabularnewline
102 & 7426.5 & 7311.36658928135 & 115.133410718647 \tabularnewline
103 & 7480.1 & 7447.13059353746 & 32.9694064625382 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302385&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]4558[/C][C]4707.5[/C][C]-149.5[/C][/ROW]
[ROW][C]4[/C][C]4736.8[/C][C]4646.3056538687[/C][C]90.4943461313023[/C][/ROW]
[ROW][C]5[/C][C]4771.1[/C][C]4813.9736445802[/C][C]-42.8736445801969[/C][/ROW]
[ROW][C]6[/C][C]4611.3[/C][C]4855.20264590876[/C][C]-243.902645908759[/C][/ROW]
[ROW][C]7[/C][C]4687.1[/C][C]4687.88829666434[/C][C]-0.788296664342852[/C][/ROW]
[ROW][C]8[/C][C]4718.3[/C][C]4743.14977278996[/C][C]-24.8497727899594[/C][/ROW]
[ROW][C]9[/C][C]4731.6[/C][C]4773.88544646964[/C][C]-42.285446469642[/C][/ROW]
[ROW][C]10[/C][C]4755.4[/C][C]4784.4169554329[/C][C]-29.0169554329004[/C][/ROW]
[ROW][C]11[/C][C]4849.8[/C][C]4804.19364994416[/C][C]45.6063500558375[/C][/ROW]
[ROW][C]12[/C][C]4697.8[/C][C]4896.88211305858[/C][C]-199.082113058579[/C][/ROW]
[ROW][C]13[/C][C]4720.2[/C][C]4745.53172818954[/C][C]-25.3317281895415[/C][/ROW]
[ROW][C]14[/C][C]4741.1[/C][C]4750.77204609667[/C][C]-9.67204609667442[/C][/ROW]
[ROW][C]15[/C][C]4794.2[/C][C]4769.38532178074[/C][C]24.8146782192598[/C][/ROW]
[ROW][C]16[/C][C]4807.4[/C][C]4822.06878424433[/C][C]-14.6687842443271[/C][/ROW]
[ROW][C]17[/C][C]4836.9[/C][C]4837.12216037363[/C][C]-0.222160373635234[/C][/ROW]
[ROW][C]18[/C][C]4853[/C][C]4865.38413444919[/C][C]-12.3841344491912[/C][/ROW]
[ROW][C]19[/C][C]4902.9[/C][C]4881.26709779786[/C][C]21.6329022021446[/C][/ROW]
[ROW][C]20[/C][C]4938[/C][C]4930.4713630977[/C][C]7.52863690230333[/C][/ROW]
[ROW][C]21[/C][C]4910.4[/C][C]4967.51248040992[/C][C]-57.112480409919[/C][/ROW]
[ROW][C]22[/C][C]4954.6[/C][C]4939.63136526838[/C][C]14.9686347316174[/C][/ROW]
[ROW][C]23[/C][C]4937.3[/C][C]4979.26473394489[/C][C]-41.9647339448857[/C][/ROW]
[ROW][C]24[/C][C]5003.8[/C][C]4962.5523417651[/C][C]41.2476582348963[/C][/ROW]
[ROW][C]25[/C][C]5005.6[/C][C]5026.18136269034[/C][C]-20.5813626903409[/C][/ROW]
[ROW][C]26[/C][C]4984.4[/C][C]5031.12298050898[/C][C]-46.7229805089846[/C][/ROW]
[ROW][C]27[/C][C]5050[/C][C]5007.44263209346[/C][C]42.5573679065428[/C][/ROW]
[ROW][C]28[/C][C]5017.7[/C][C]5069.79219338896[/C][C]-52.0921933889558[/C][/ROW]
[ROW][C]29[/C][C]4984.8[/C][C]5040.2393634869[/C][C]-55.4393634868984[/C][/ROW]
[ROW][C]30[/C][C]5036.3[/C][C]5002.06758711053[/C][C]34.2324128894661[/C][/ROW]
[ROW][C]31[/C][C]5093.6[/C][C]5049.45028156532[/C][C]44.1497184346808[/C][/ROW]
[ROW][C]32[/C][C]5111.2[/C][C]5110.3382367352[/C][C]0.861763264801994[/C][/ROW]
[ROW][C]33[/C][C]5090.7[/C][C]5131.6675071877[/C][C]-40.9675071877[/C][/ROW]
[ROW][C]34[/C][C]5063.7[/C][C]5110.58390680913[/C][C]-46.8839068091274[/C][/ROW]
[ROW][C]35[/C][C]5007.5[/C][C]5079.3853623568[/C][C]-71.8853623568039[/C][/ROW]
[ROW][C]36[/C][C]5122.5[/C][C]5018.08850106506[/C][C]104.411498934944[/C][/ROW]
[ROW][C]37[/C][C]5172.3[/C][C]5128.71113088218[/C][C]43.5888691178234[/C][/ROW]
[ROW][C]38[/C][C]5232.8[/C][C]5187.99610279343[/C][C]44.8038972065715[/C][/ROW]
[ROW][C]39[/C][C]5183.3[/C][C]5252.8819380823[/C][C]-69.5819380823023[/C][/ROW]
[ROW][C]40[/C][C]5204.6[/C][C]5206.03805697014[/C][C]-1.43805697013522[/C][/ROW]
[ROW][C]41[/C][C]5255.4[/C][C]5221.45928001074[/C][C]33.9407199892621[/C][/ROW]
[ROW][C]42[/C][C]5294.5[/C][C]5272.68184288297[/C][C]21.8181571170298[/C][/ROW]
[ROW][C]43[/C][C]5308.9[/C][C]5314.9875948776[/C][C]-6.08759487759926[/C][/ROW]
[ROW][C]44[/C][C]5281.3[/C][C]5331.12622913293[/C][C]-49.826229132932[/C][/ROW]
[ROW][C]45[/C][C]5413.9[/C][C]5302.21591920894[/C][C]111.684080791056[/C][/ROW]
[ROW][C]46[/C][C]5462.4[/C][C]5432.41143538548[/C][C]29.9885646145231[/C][/ROW]
[ROW][C]47[/C][C]5568.7[/C][C]5490.79062121683[/C][C]77.9093787831671[/C][/ROW]
[ROW][C]48[/C][C]5579.1[/C][C]5600.86211497173[/C][C]-21.762114971727[/C][/ROW]
[ROW][C]49[/C][C]5590.3[/C][C]5617.47013014039[/C][C]-27.1701301403928[/C][/ROW]
[ROW][C]50[/C][C]5703.2[/C][C]5626.40356665425[/C][C]76.7964333457485[/C][/ROW]
[ROW][C]51[/C][C]5717.7[/C][C]5738.24698221205[/C][C]-20.5469822120513[/C][/ROW]
[ROW][C]52[/C][C]5772.3[/C][C]5758.8807974116[/C][C]13.4192025883967[/C][/ROW]
[ROW][C]53[/C][C]5876.6[/C][C]5811.96656107553[/C][C]64.6334389244657[/C][/ROW]
[ROW][C]54[/C][C]6134.6[/C][C]5918.43101833928[/C][C]216.168981660724[/C][/ROW]
[ROW][C]55[/C][C]6155.6[/C][C]6185.33241344918[/C][C]-29.7324134491764[/C][/ROW]
[ROW][C]56[/C][C]6259.5[/C][C]6224.04816959779[/C][C]35.4518304022122[/C][/ROW]
[ROW][C]57[/C][C]6180.7[/C][C]6326.01379087495[/C][C]-145.313790874946[/C][/ROW]
[ROW][C]58[/C][C]6120.3[/C][C]6247.86997804841[/C][C]-127.569978048414[/C][/ROW]
[ROW][C]59[/C][C]6097[/C][C]6173.19781253939[/C][C]-76.1978125393925[/C][/ROW]
[ROW][C]60[/C][C]6167.5[/C][C]6137.94165819796[/C][C]29.5583418020378[/C][/ROW]
[ROW][C]61[/C][C]6207.1[/C][C]6202.50254376933[/C][C]4.59745623067374[/C][/ROW]
[ROW][C]62[/C][C]6181.7[/C][C]6244.6636903859[/C][C]-62.9636903859027[/C][/ROW]
[ROW][C]63[/C][C]6196.2[/C][C]6218.64218728728[/C][C]-22.4421872872763[/C][/ROW]
[ROW][C]64[/C][C]6183.9[/C][C]6227.48398062552[/C][C]-43.5839806255217[/C][/ROW]
[ROW][C]65[/C][C]6184[/C][C]6212.59730570302[/C][C]-28.5973057030196[/C][/ROW]
[ROW][C]66[/C][C]6271.1[/C][C]6208.57144160777[/C][C]62.5285583922296[/C][/ROW]
[ROW][C]67[/C][C]6204.9[/C][C]6294.26624170924[/C][C]-89.3662417092401[/C][/ROW]
[ROW][C]68[/C][C]6284.5[/C][C]6231.89713985912[/C][C]52.6028601408752[/C][/ROW]
[ROW][C]69[/C][C]6293.9[/C][C]6304.81889554573[/C][C]-10.9188955457275[/C][/ROW]
[ROW][C]70[/C][C]6377.9[/C][C]6318.47087413422[/C][C]59.4291258657822[/C][/ROW]
[ROW][C]71[/C][C]6400.2[/C][C]6402.50378096734[/C][C]-2.30378096733693[/C][/ROW]
[ROW][C]72[/C][C]6456.2[/C][C]6429.76820858094[/C][C]26.4317914190624[/C][/ROW]
[ROW][C]73[/C][C]6372.8[/C][C]6485.99765479005[/C][C]-113.197654790048[/C][/ROW]
[ROW][C]74[/C][C]6368.8[/C][C]6403.00911272076[/C][C]-34.209112720755[/C][/ROW]
[ROW][C]75[/C][C]6497.8[/C][C]6388.93495538057[/C][C]108.865044619428[/C][/ROW]
[ROW][C]76[/C][C]6599.4[/C][C]6516.79959856034[/C][C]82.600401439664[/C][/ROW]
[ROW][C]77[/C][C]6696.9[/C][C]6628.88416030016[/C][C]68.0158396998422[/C][/ROW]
[ROW][C]78[/C][C]6676.3[/C][C]6734.42480988091[/C][C]-58.1248098809101[/C][/ROW]
[ROW][C]79[/C][C]6731.7[/C][C]6718.61784948629[/C][C]13.0821505137119[/C][/ROW]
[ROW][C]80[/C][C]6732.3[/C][C]6769.33581109647[/C][C]-37.0358110964744[/C][/ROW]
[ROW][C]81[/C][C]6760.2[/C][C]6770.44359985278[/C][C]-10.2435998527753[/C][/ROW]
[ROW][C]82[/C][C]6841.4[/C][C]6795.06275157748[/C][C]46.3372484225183[/C][/ROW]
[ROW][C]83[/C][C]6917.5[/C][C]6876.14281317924[/C][C]41.3571868207637[/C][/ROW]
[ROW][C]84[/C][C]6899.3[/C][C]6956.80473993283[/C][C]-57.5047399328314[/C][/ROW]
[ROW][C]85[/C][C]6972.9[/C][C]6941.16422177027[/C][C]31.7357782297249[/C][/ROW]
[ROW][C]86[/C][C]6969.2[/C][C]7010.43311683571[/C][C]-41.2331168357086[/C][/ROW]
[ROW][C]87[/C][C]6941.6[/C][C]7008.74349964271[/C][C]-67.1434996427051[/C][/ROW]
[ROW][C]88[/C][C]6905.5[/C][C]6976.5981310918[/C][C]-71.0981310917969[/C][/ROW]
[ROW][C]89[/C][C]6971.3[/C][C]6933.70890926009[/C][C]37.5910907399111[/C][/ROW]
[ROW][C]90[/C][C]6968.4[/C][C]6994.1276142447[/C][C]-25.7276142447017[/C][/ROW]
[ROW][C]91[/C][C]7012.2[/C][C]6993.97908876819[/C][C]18.2209112318096[/C][/ROW]
[ROW][C]92[/C][C]7049.5[/C][C]7035.90577326708[/C][C]13.594226732921[/C][/ROW]
[ROW][C]93[/C][C]7095.6[/C][C]7074.95689530559[/C][C]20.643104694409[/C][/ROW]
[ROW][C]94[/C][C]7237.5[/C][C]7122.53154622493[/C][C]114.968453775068[/C][/ROW]
[ROW][C]95[/C][C]7230.5[/C][C]7268.01008916872[/C][C]-37.5100891687198[/C][/ROW]
[ROW][C]96[/C][C]7253.5[/C][C]7270.0846373363[/C][C]-16.5846373363029[/C][/ROW]
[ROW][C]97[/C][C]7289.4[/C][C]7289.66231955091[/C][C]-0.262319550905886[/C][/ROW]
[ROW][C]98[/C][C]7364.6[/C][C]7324.1624196991[/C][C]40.4375803008979[/C][/ROW]
[ROW][C]99[/C][C]7428.1[/C][C]7399.98797978448[/C][C]28.1120202155189[/C][/ROW]
[ROW][C]100[/C][C]7390.2[/C][C]7467.34128287336[/C][C]-77.1412828733573[/C][/ROW]
[ROW][C]101[/C][C]7279.9[/C][C]7430.57161011941[/C][C]-150.671610119412[/C][/ROW]
[ROW][C]102[/C][C]7426.5[/C][C]7311.36658928135[/C][C]115.133410718647[/C][/ROW]
[ROW][C]103[/C][C]7480.1[/C][C]7447.13059353746[/C][C]32.9694064625382[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302385&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302385&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
345584707.5-149.5
44736.84646.305653868790.4943461313023
54771.14813.9736445802-42.8736445801969
64611.34855.20264590876-243.902645908759
74687.14687.88829666434-0.788296664342852
84718.34743.14977278996-24.8497727899594
94731.64773.88544646964-42.285446469642
104755.44784.4169554329-29.0169554329004
114849.84804.1936499441645.6063500558375
124697.84896.88211305858-199.082113058579
134720.24745.53172818954-25.3317281895415
144741.14750.77204609667-9.67204609667442
154794.24769.3853217807424.8146782192598
164807.44822.06878424433-14.6687842443271
174836.94837.12216037363-0.222160373635234
1848534865.38413444919-12.3841344491912
194902.94881.2670977978621.6329022021446
2049384930.47136309777.52863690230333
214910.44967.51248040992-57.112480409919
224954.64939.6313652683814.9686347316174
234937.34979.26473394489-41.9647339448857
245003.84962.552341765141.2476582348963
255005.65026.18136269034-20.5813626903409
264984.45031.12298050898-46.7229805089846
2750505007.4426320934642.5573679065428
285017.75069.79219338896-52.0921933889558
294984.85040.2393634869-55.4393634868984
305036.35002.0675871105334.2324128894661
315093.65049.4502815653244.1497184346808
325111.25110.33823673520.861763264801994
335090.75131.6675071877-40.9675071877
345063.75110.58390680913-46.8839068091274
355007.55079.3853623568-71.8853623568039
365122.55018.08850106506104.411498934944
375172.35128.7111308821843.5888691178234
385232.85187.9961027934344.8038972065715
395183.35252.8819380823-69.5819380823023
405204.65206.03805697014-1.43805697013522
415255.45221.4592800107433.9407199892621
425294.55272.6818428829721.8181571170298
435308.95314.9875948776-6.08759487759926
445281.35331.12622913293-49.826229132932
455413.95302.21591920894111.684080791056
465462.45432.4114353854829.9885646145231
475568.75490.7906212168377.9093787831671
485579.15600.86211497173-21.762114971727
495590.35617.47013014039-27.1701301403928
505703.25626.4035666542576.7964333457485
515717.75738.24698221205-20.5469822120513
525772.35758.880797411613.4192025883967
535876.65811.9665610755364.6334389244657
546134.65918.43101833928216.168981660724
556155.66185.33241344918-29.7324134491764
566259.56224.0481695977935.4518304022122
576180.76326.01379087495-145.313790874946
586120.36247.86997804841-127.569978048414
5960976173.19781253939-76.1978125393925
606167.56137.9416581979629.5583418020378
616207.16202.502543769334.59745623067374
626181.76244.6636903859-62.9636903859027
636196.26218.64218728728-22.4421872872763
646183.96227.48398062552-43.5839806255217
6561846212.59730570302-28.5973057030196
666271.16208.5714416077762.5285583922296
676204.96294.26624170924-89.3662417092401
686284.56231.8971398591252.6028601408752
696293.96304.81889554573-10.9188955457275
706377.96318.4708741342259.4291258657822
716400.26402.50378096734-2.30378096733693
726456.26429.7682085809426.4317914190624
736372.86485.99765479005-113.197654790048
746368.86403.00911272076-34.209112720755
756497.86388.93495538057108.865044619428
766599.46516.7995985603482.600401439664
776696.96628.8841603001668.0158396998422
786676.36734.42480988091-58.1248098809101
796731.76718.6178494862913.0821505137119
806732.36769.33581109647-37.0358110964744
816760.26770.44359985278-10.2435998527753
826841.46795.0627515774846.3372484225183
836917.56876.1428131792441.3571868207637
846899.36956.80473993283-57.5047399328314
856972.96941.1642217702731.7357782297249
866969.27010.43311683571-41.2331168357086
876941.67008.74349964271-67.1434996427051
886905.56976.5981310918-71.0981310917969
896971.36933.7089092600937.5910907399111
906968.46994.1276142447-25.7276142447017
917012.26993.9790887681918.2209112318096
927049.57035.9057732670813.594226732921
937095.67074.9568953055920.643104694409
947237.57122.53154622493114.968453775068
957230.57268.01008916872-37.5100891687198
967253.57270.0846373363-16.5846373363029
977289.47289.66231955091-0.262319550905886
987364.67324.162419699140.4375803008979
997428.17399.9879797844828.1120202155189
1007390.27467.34128287336-77.1412828733573
1017279.97430.57161011941-150.671610119412
1027426.57311.36658928135115.133410718647
1037480.17447.1305935374632.9694064625382







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1047510.947801818257377.35962815637644.53597548019
1057544.570180749437354.129104573077735.0112569258
1067578.192559680627336.32186809587820.06325126544
1077611.814938611817320.430609130147903.19926809348
1087645.437317542997305.090237311467985.78439777453
1097679.059696474187289.632556203648068.48683674472
1107712.682075405377273.68884242048151.67530839033
1117746.304454336557257.040761046678235.56814762644
1127779.926833267747239.553490159368320.30017637612
1137813.549212198937221.141947569588405.95647682827
1147847.171591130117201.752226089238492.590956171
1157880.79397006137181.350718494598580.23722162801

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
104 & 7510.94780181825 & 7377.3596281563 & 7644.53597548019 \tabularnewline
105 & 7544.57018074943 & 7354.12910457307 & 7735.0112569258 \tabularnewline
106 & 7578.19255968062 & 7336.3218680958 & 7820.06325126544 \tabularnewline
107 & 7611.81493861181 & 7320.43060913014 & 7903.19926809348 \tabularnewline
108 & 7645.43731754299 & 7305.09023731146 & 7985.78439777453 \tabularnewline
109 & 7679.05969647418 & 7289.63255620364 & 8068.48683674472 \tabularnewline
110 & 7712.68207540537 & 7273.6888424204 & 8151.67530839033 \tabularnewline
111 & 7746.30445433655 & 7257.04076104667 & 8235.56814762644 \tabularnewline
112 & 7779.92683326774 & 7239.55349015936 & 8320.30017637612 \tabularnewline
113 & 7813.54921219893 & 7221.14194756958 & 8405.95647682827 \tabularnewline
114 & 7847.17159113011 & 7201.75222608923 & 8492.590956171 \tabularnewline
115 & 7880.7939700613 & 7181.35071849459 & 8580.23722162801 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302385&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]104[/C][C]7510.94780181825[/C][C]7377.3596281563[/C][C]7644.53597548019[/C][/ROW]
[ROW][C]105[/C][C]7544.57018074943[/C][C]7354.12910457307[/C][C]7735.0112569258[/C][/ROW]
[ROW][C]106[/C][C]7578.19255968062[/C][C]7336.3218680958[/C][C]7820.06325126544[/C][/ROW]
[ROW][C]107[/C][C]7611.81493861181[/C][C]7320.43060913014[/C][C]7903.19926809348[/C][/ROW]
[ROW][C]108[/C][C]7645.43731754299[/C][C]7305.09023731146[/C][C]7985.78439777453[/C][/ROW]
[ROW][C]109[/C][C]7679.05969647418[/C][C]7289.63255620364[/C][C]8068.48683674472[/C][/ROW]
[ROW][C]110[/C][C]7712.68207540537[/C][C]7273.6888424204[/C][C]8151.67530839033[/C][/ROW]
[ROW][C]111[/C][C]7746.30445433655[/C][C]7257.04076104667[/C][C]8235.56814762644[/C][/ROW]
[ROW][C]112[/C][C]7779.92683326774[/C][C]7239.55349015936[/C][C]8320.30017637612[/C][/ROW]
[ROW][C]113[/C][C]7813.54921219893[/C][C]7221.14194756958[/C][C]8405.95647682827[/C][/ROW]
[ROW][C]114[/C][C]7847.17159113011[/C][C]7201.75222608923[/C][C]8492.590956171[/C][/ROW]
[ROW][C]115[/C][C]7880.7939700613[/C][C]7181.35071849459[/C][C]8580.23722162801[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302385&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302385&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
1047510.947801818257377.35962815637644.53597548019
1057544.570180749437354.129104573077735.0112569258
1067578.192559680627336.32186809587820.06325126544
1077611.814938611817320.430609130147903.19926809348
1087645.437317542997305.090237311467985.78439777453
1097679.059696474187289.632556203648068.48683674472
1107712.682075405377273.68884242048151.67530839033
1117746.304454336557257.040761046678235.56814762644
1127779.926833267747239.553490159368320.30017637612
1137813.549212198937221.141947569588405.95647682827
1147847.171591130117201.752226089238492.590956171
1157880.79397006137181.350718494598580.23722162801



Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
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')