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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 10 Aug 2016 00:28:40 +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/10/t1470785348lsnh4s6yy3eha4q.htm/, Retrieved Tue, 30 Apr 2024 07:57:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296173, Retrieved Tue, 30 Apr 2024 07:57:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-08-09 23:28:40] [3e69b53d94b342798d3f1a806941de01] [Current]
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Dataseries X:
29054.50
28543.50
28032.00
27009.50
37356.00
36844.50
29054.50
23881.50
24392.50
24392.50
24904.00
25982.00
22859.00
19731.00
17169.50
17169.50
27009.50
28032.00
20242.00
11429.50
16091.50
16091.50
19731.00
21831.50
21320.00
16091.50
18708.50
17681.00
26493.50
24392.50
16091.50
9891.00
15580.00
17169.50
18708.50
20753.50
16602.50
13019.00
14558.00
15069.00
28543.50
28543.50
20753.50
19731.00
22859.00
21320.00
25471.00
30644.00
31671.50
24392.50
22342.50
20242.00
34283.50
35311.00
32694.00
35311.00
34794.50
30644.00
35311.00
40484.00
42584.50
36333.50
32182.50
35311.00
48785.00
52936.00
51913.50
53958.00
53447.00
48274.00
57086.50
59187.00
62259.50
52936.00
49296.50
53447.00
63337.50
72150.00
70049.50
70049.50
71077.00
67488.00
76817.00
76817.00
75227.50
66410.00
67999.50
69027.00
75789.50
84602.00
78350.50
81479.00
78862.00
77328.00
89269.00
86652.00
83012.50
77839.50
83012.50
85629.50
88752.50
92903.00
88752.50
91314.00
88190.50
87679.50
100642.50
101720.50
97570.00
90291.50
96492.00
99104.00
102232.00
106894.00
102232.00
105871.50
104282.00
98592.50
110533.00
110533.00




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296173&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296173&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296173&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.653616535251408
beta0.0529317881405975
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.653616535251408 \tabularnewline
beta & 0.0529317881405975 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296173&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]0.653616535251408[/C][/ROW]
[ROW][C]beta[/C][C]0.0529317881405975[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296173&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296173&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
alpha0.653616535251408
beta0.0529317881405975
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132285927592.9504540598-4733.95045405983
141973121321.260451362-1590.26045136202
1517169.517594.5073290414-425.007329041408
1617169.517003.2205642392166.279435760844
1727009.526513.8280575852495.671942414778
182803227266.4432476464765.556752353554
192024219759.5914827989482.408517201075
2011429.514588.0676146981-3158.56761469812
2116091.512805.92262140923285.57737859077
2216091.514881.26127403031210.2387259697
231973116131.99500755883599.00499244119
2421831.519592.26847842472239.23152157533
252132016336.56359653644983.43640346358
2616091.517922.2590379296-1830.75903792958
2718708.514850.63440417343857.86559582661
281768117820.3890358024-139.389035802385
2926493.527791.6003154287-1298.10031542874
3024392.527949.4982649436-3556.99826494356
3116091.517853.9656981579-1762.4656981579
32989110211.0053746476-320.005374647641
331558012871.56724573572708.43275426431
3417169.514186.07448781862983.42551218137
3518708.517819.831519255888.668480744996
3620753.519340.42138080211413.07861919788
3716602.516769.5342052316-167.034205231612
381301912724.5386696473294.461330352748
391455813182.03156814011375.96843185988
401506913228.72068957321840.2793104268
4128543.524244.73469852374298.76530147633
4228543.527624.2441286433919.25587135669
4320753.521576.7795315312-823.279531531163
441973115580.5421731234150.45782687695
452285922899.9495836532-40.9495836531569
462132023105.4233574333-1785.42335743332
472547123324.35975751042146.64024248958
483064426320.11697114674323.88302885334
4931671.525676.4493086825995.05069131801
5024392.526604.1335684665-2211.63356846647
5122342.526496.6987762337-4154.19877623368
522024223596.7622721687-3354.76227216869
5334283.532396.21025919381887.28974080622
543531133272.92332335772038.07667664232
553269427635.85112096985058.14887903015
563531127692.81138789267618.18861210738
5734794.536433.1025456538-1638.6025456538
583064435540.9446967273-4896.94469672731
593531135531.3691638433-220.36916384333
604048438095.50719905762388.4928009424
6142584.537060.07886156885524.42113843122
6236333.535115.58725668411217.9127433159
6332182.536973.6356253149-4791.13562531486
643531134309.00953839641001.99046160357
654878548297.3055533729487.694446627123
665293648788.47042727224147.52957272783
6751913.546126.27586260145787.22413739862
685395848121.75236148765836.24763851241
695344753004.5132196524442.486780347594
704827452929.5287399848-4655.52873998478
7157086.555291.56221267271794.9377873273
725918760740.2557092608-1553.25570926076
7362259.558741.94692278493517.55307721515
745293654451.8759036103-1515.87590361032
7549296.552804.9047111753-3508.40471117535
765344753392.97950135354.0204986469689
7763337.566958.3696896772-3620.86968967719
787215066264.51775968145885.48224031855
7970049.565599.0712690984450.42873090203
8070049.566984.3582712233065.14172877705
817107768338.27786076322738.72213923675
826748868228.4345161018-740.434516101785
837681775749.37614537561067.62385462435
847681779903.3663080269-3086.36630802686
8575227.578946.8341747744-3719.33417477444
866641068220.1409345869-1810.14093458693
8767999.565717.49702642552282.00297357453
886902771551.4172857383-2524.41728573831
8975789.582296.5443313557-6507.04433135572
908460283047.19842533671554.80157466332
9178350.578942.3540535872-591.854053587173
928147976265.91823715115213.08176284886
937886278698.8501764673163.149823532716
947732875399.49010473191928.5098952681
958926985082.55943400974186.44056599031
968665289735.4682313013-3083.46823130127
9783012.588460.9629579294-5448.46295792944
9877839.577104.954927137734.54507286298
9983012.577610.60899569245401.8910043076
10085629.583854.41235076521775.08764923477
10188752.596214.5383212691-7462.03832126911
1029290399284.7302155296-6381.73021552956
10388752.589125.5380447214-373.038044721368
1049131488487.09479387642826.90520612359
10588190.587412.8516112935777.648388706468
10687679.584949.57161768552729.92838231449
107100642.595789.24003660694853.25996339305
108101720.598233.5556984413486.94430155896
10997570100535.441677108-2965.44167710836
11090291.593131.0305173901-2839.53051739007
1119649292980.60987520523511.39012479482
1129910496730.38878900652373.61121099352
113102232106300.74203852-4068.74203852029
114106894112099.057620716-5205.05762071647
115102232104966.98744103-2734.98744102976
116105871.5103988.1435729091883.35642709119
117104282101649.7097194242632.29028057639
11898592.5101201.414147226-2608.91414722598
119110533109228.8276391661304.17236083376
120110533108699.1575753991833.84242460092

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 22859 & 27592.9504540598 & -4733.95045405983 \tabularnewline
14 & 19731 & 21321.260451362 & -1590.26045136202 \tabularnewline
15 & 17169.5 & 17594.5073290414 & -425.007329041408 \tabularnewline
16 & 17169.5 & 17003.2205642392 & 166.279435760844 \tabularnewline
17 & 27009.5 & 26513.8280575852 & 495.671942414778 \tabularnewline
18 & 28032 & 27266.4432476464 & 765.556752353554 \tabularnewline
19 & 20242 & 19759.5914827989 & 482.408517201075 \tabularnewline
20 & 11429.5 & 14588.0676146981 & -3158.56761469812 \tabularnewline
21 & 16091.5 & 12805.9226214092 & 3285.57737859077 \tabularnewline
22 & 16091.5 & 14881.2612740303 & 1210.2387259697 \tabularnewline
23 & 19731 & 16131.9950075588 & 3599.00499244119 \tabularnewline
24 & 21831.5 & 19592.2684784247 & 2239.23152157533 \tabularnewline
25 & 21320 & 16336.5635965364 & 4983.43640346358 \tabularnewline
26 & 16091.5 & 17922.2590379296 & -1830.75903792958 \tabularnewline
27 & 18708.5 & 14850.6344041734 & 3857.86559582661 \tabularnewline
28 & 17681 & 17820.3890358024 & -139.389035802385 \tabularnewline
29 & 26493.5 & 27791.6003154287 & -1298.10031542874 \tabularnewline
30 & 24392.5 & 27949.4982649436 & -3556.99826494356 \tabularnewline
31 & 16091.5 & 17853.9656981579 & -1762.4656981579 \tabularnewline
32 & 9891 & 10211.0053746476 & -320.005374647641 \tabularnewline
33 & 15580 & 12871.5672457357 & 2708.43275426431 \tabularnewline
34 & 17169.5 & 14186.0744878186 & 2983.42551218137 \tabularnewline
35 & 18708.5 & 17819.831519255 & 888.668480744996 \tabularnewline
36 & 20753.5 & 19340.4213808021 & 1413.07861919788 \tabularnewline
37 & 16602.5 & 16769.5342052316 & -167.034205231612 \tabularnewline
38 & 13019 & 12724.5386696473 & 294.461330352748 \tabularnewline
39 & 14558 & 13182.0315681401 & 1375.96843185988 \tabularnewline
40 & 15069 & 13228.7206895732 & 1840.2793104268 \tabularnewline
41 & 28543.5 & 24244.7346985237 & 4298.76530147633 \tabularnewline
42 & 28543.5 & 27624.2441286433 & 919.25587135669 \tabularnewline
43 & 20753.5 & 21576.7795315312 & -823.279531531163 \tabularnewline
44 & 19731 & 15580.542173123 & 4150.45782687695 \tabularnewline
45 & 22859 & 22899.9495836532 & -40.9495836531569 \tabularnewline
46 & 21320 & 23105.4233574333 & -1785.42335743332 \tabularnewline
47 & 25471 & 23324.3597575104 & 2146.64024248958 \tabularnewline
48 & 30644 & 26320.1169711467 & 4323.88302885334 \tabularnewline
49 & 31671.5 & 25676.449308682 & 5995.05069131801 \tabularnewline
50 & 24392.5 & 26604.1335684665 & -2211.63356846647 \tabularnewline
51 & 22342.5 & 26496.6987762337 & -4154.19877623368 \tabularnewline
52 & 20242 & 23596.7622721687 & -3354.76227216869 \tabularnewline
53 & 34283.5 & 32396.2102591938 & 1887.28974080622 \tabularnewline
54 & 35311 & 33272.9233233577 & 2038.07667664232 \tabularnewline
55 & 32694 & 27635.8511209698 & 5058.14887903015 \tabularnewline
56 & 35311 & 27692.8113878926 & 7618.18861210738 \tabularnewline
57 & 34794.5 & 36433.1025456538 & -1638.6025456538 \tabularnewline
58 & 30644 & 35540.9446967273 & -4896.94469672731 \tabularnewline
59 & 35311 & 35531.3691638433 & -220.36916384333 \tabularnewline
60 & 40484 & 38095.5071990576 & 2388.4928009424 \tabularnewline
61 & 42584.5 & 37060.0788615688 & 5524.42113843122 \tabularnewline
62 & 36333.5 & 35115.5872566841 & 1217.9127433159 \tabularnewline
63 & 32182.5 & 36973.6356253149 & -4791.13562531486 \tabularnewline
64 & 35311 & 34309.0095383964 & 1001.99046160357 \tabularnewline
65 & 48785 & 48297.3055533729 & 487.694446627123 \tabularnewline
66 & 52936 & 48788.4704272722 & 4147.52957272783 \tabularnewline
67 & 51913.5 & 46126.2758626014 & 5787.22413739862 \tabularnewline
68 & 53958 & 48121.7523614876 & 5836.24763851241 \tabularnewline
69 & 53447 & 53004.5132196524 & 442.486780347594 \tabularnewline
70 & 48274 & 52929.5287399848 & -4655.52873998478 \tabularnewline
71 & 57086.5 & 55291.5622126727 & 1794.9377873273 \tabularnewline
72 & 59187 & 60740.2557092608 & -1553.25570926076 \tabularnewline
73 & 62259.5 & 58741.9469227849 & 3517.55307721515 \tabularnewline
74 & 52936 & 54451.8759036103 & -1515.87590361032 \tabularnewline
75 & 49296.5 & 52804.9047111753 & -3508.40471117535 \tabularnewline
76 & 53447 & 53392.979501353 & 54.0204986469689 \tabularnewline
77 & 63337.5 & 66958.3696896772 & -3620.86968967719 \tabularnewline
78 & 72150 & 66264.5177596814 & 5885.48224031855 \tabularnewline
79 & 70049.5 & 65599.071269098 & 4450.42873090203 \tabularnewline
80 & 70049.5 & 66984.358271223 & 3065.14172877705 \tabularnewline
81 & 71077 & 68338.2778607632 & 2738.72213923675 \tabularnewline
82 & 67488 & 68228.4345161018 & -740.434516101785 \tabularnewline
83 & 76817 & 75749.3761453756 & 1067.62385462435 \tabularnewline
84 & 76817 & 79903.3663080269 & -3086.36630802686 \tabularnewline
85 & 75227.5 & 78946.8341747744 & -3719.33417477444 \tabularnewline
86 & 66410 & 68220.1409345869 & -1810.14093458693 \tabularnewline
87 & 67999.5 & 65717.4970264255 & 2282.00297357453 \tabularnewline
88 & 69027 & 71551.4172857383 & -2524.41728573831 \tabularnewline
89 & 75789.5 & 82296.5443313557 & -6507.04433135572 \tabularnewline
90 & 84602 & 83047.1984253367 & 1554.80157466332 \tabularnewline
91 & 78350.5 & 78942.3540535872 & -591.854053587173 \tabularnewline
92 & 81479 & 76265.9182371511 & 5213.08176284886 \tabularnewline
93 & 78862 & 78698.8501764673 & 163.149823532716 \tabularnewline
94 & 77328 & 75399.4901047319 & 1928.5098952681 \tabularnewline
95 & 89269 & 85082.5594340097 & 4186.44056599031 \tabularnewline
96 & 86652 & 89735.4682313013 & -3083.46823130127 \tabularnewline
97 & 83012.5 & 88460.9629579294 & -5448.46295792944 \tabularnewline
98 & 77839.5 & 77104.954927137 & 734.54507286298 \tabularnewline
99 & 83012.5 & 77610.6089956924 & 5401.8910043076 \tabularnewline
100 & 85629.5 & 83854.4123507652 & 1775.08764923477 \tabularnewline
101 & 88752.5 & 96214.5383212691 & -7462.03832126911 \tabularnewline
102 & 92903 & 99284.7302155296 & -6381.73021552956 \tabularnewline
103 & 88752.5 & 89125.5380447214 & -373.038044721368 \tabularnewline
104 & 91314 & 88487.0947938764 & 2826.90520612359 \tabularnewline
105 & 88190.5 & 87412.8516112935 & 777.648388706468 \tabularnewline
106 & 87679.5 & 84949.5716176855 & 2729.92838231449 \tabularnewline
107 & 100642.5 & 95789.2400366069 & 4853.25996339305 \tabularnewline
108 & 101720.5 & 98233.555698441 & 3486.94430155896 \tabularnewline
109 & 97570 & 100535.441677108 & -2965.44167710836 \tabularnewline
110 & 90291.5 & 93131.0305173901 & -2839.53051739007 \tabularnewline
111 & 96492 & 92980.6098752052 & 3511.39012479482 \tabularnewline
112 & 99104 & 96730.3887890065 & 2373.61121099352 \tabularnewline
113 & 102232 & 106300.74203852 & -4068.74203852029 \tabularnewline
114 & 106894 & 112099.057620716 & -5205.05762071647 \tabularnewline
115 & 102232 & 104966.98744103 & -2734.98744102976 \tabularnewline
116 & 105871.5 & 103988.143572909 & 1883.35642709119 \tabularnewline
117 & 104282 & 101649.709719424 & 2632.29028057639 \tabularnewline
118 & 98592.5 & 101201.414147226 & -2608.91414722598 \tabularnewline
119 & 110533 & 109228.827639166 & 1304.17236083376 \tabularnewline
120 & 110533 & 108699.157575399 & 1833.84242460092 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296173&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]22859[/C][C]27592.9504540598[/C][C]-4733.95045405983[/C][/ROW]
[ROW][C]14[/C][C]19731[/C][C]21321.260451362[/C][C]-1590.26045136202[/C][/ROW]
[ROW][C]15[/C][C]17169.5[/C][C]17594.5073290414[/C][C]-425.007329041408[/C][/ROW]
[ROW][C]16[/C][C]17169.5[/C][C]17003.2205642392[/C][C]166.279435760844[/C][/ROW]
[ROW][C]17[/C][C]27009.5[/C][C]26513.8280575852[/C][C]495.671942414778[/C][/ROW]
[ROW][C]18[/C][C]28032[/C][C]27266.4432476464[/C][C]765.556752353554[/C][/ROW]
[ROW][C]19[/C][C]20242[/C][C]19759.5914827989[/C][C]482.408517201075[/C][/ROW]
[ROW][C]20[/C][C]11429.5[/C][C]14588.0676146981[/C][C]-3158.56761469812[/C][/ROW]
[ROW][C]21[/C][C]16091.5[/C][C]12805.9226214092[/C][C]3285.57737859077[/C][/ROW]
[ROW][C]22[/C][C]16091.5[/C][C]14881.2612740303[/C][C]1210.2387259697[/C][/ROW]
[ROW][C]23[/C][C]19731[/C][C]16131.9950075588[/C][C]3599.00499244119[/C][/ROW]
[ROW][C]24[/C][C]21831.5[/C][C]19592.2684784247[/C][C]2239.23152157533[/C][/ROW]
[ROW][C]25[/C][C]21320[/C][C]16336.5635965364[/C][C]4983.43640346358[/C][/ROW]
[ROW][C]26[/C][C]16091.5[/C][C]17922.2590379296[/C][C]-1830.75903792958[/C][/ROW]
[ROW][C]27[/C][C]18708.5[/C][C]14850.6344041734[/C][C]3857.86559582661[/C][/ROW]
[ROW][C]28[/C][C]17681[/C][C]17820.3890358024[/C][C]-139.389035802385[/C][/ROW]
[ROW][C]29[/C][C]26493.5[/C][C]27791.6003154287[/C][C]-1298.10031542874[/C][/ROW]
[ROW][C]30[/C][C]24392.5[/C][C]27949.4982649436[/C][C]-3556.99826494356[/C][/ROW]
[ROW][C]31[/C][C]16091.5[/C][C]17853.9656981579[/C][C]-1762.4656981579[/C][/ROW]
[ROW][C]32[/C][C]9891[/C][C]10211.0053746476[/C][C]-320.005374647641[/C][/ROW]
[ROW][C]33[/C][C]15580[/C][C]12871.5672457357[/C][C]2708.43275426431[/C][/ROW]
[ROW][C]34[/C][C]17169.5[/C][C]14186.0744878186[/C][C]2983.42551218137[/C][/ROW]
[ROW][C]35[/C][C]18708.5[/C][C]17819.831519255[/C][C]888.668480744996[/C][/ROW]
[ROW][C]36[/C][C]20753.5[/C][C]19340.4213808021[/C][C]1413.07861919788[/C][/ROW]
[ROW][C]37[/C][C]16602.5[/C][C]16769.5342052316[/C][C]-167.034205231612[/C][/ROW]
[ROW][C]38[/C][C]13019[/C][C]12724.5386696473[/C][C]294.461330352748[/C][/ROW]
[ROW][C]39[/C][C]14558[/C][C]13182.0315681401[/C][C]1375.96843185988[/C][/ROW]
[ROW][C]40[/C][C]15069[/C][C]13228.7206895732[/C][C]1840.2793104268[/C][/ROW]
[ROW][C]41[/C][C]28543.5[/C][C]24244.7346985237[/C][C]4298.76530147633[/C][/ROW]
[ROW][C]42[/C][C]28543.5[/C][C]27624.2441286433[/C][C]919.25587135669[/C][/ROW]
[ROW][C]43[/C][C]20753.5[/C][C]21576.7795315312[/C][C]-823.279531531163[/C][/ROW]
[ROW][C]44[/C][C]19731[/C][C]15580.542173123[/C][C]4150.45782687695[/C][/ROW]
[ROW][C]45[/C][C]22859[/C][C]22899.9495836532[/C][C]-40.9495836531569[/C][/ROW]
[ROW][C]46[/C][C]21320[/C][C]23105.4233574333[/C][C]-1785.42335743332[/C][/ROW]
[ROW][C]47[/C][C]25471[/C][C]23324.3597575104[/C][C]2146.64024248958[/C][/ROW]
[ROW][C]48[/C][C]30644[/C][C]26320.1169711467[/C][C]4323.88302885334[/C][/ROW]
[ROW][C]49[/C][C]31671.5[/C][C]25676.449308682[/C][C]5995.05069131801[/C][/ROW]
[ROW][C]50[/C][C]24392.5[/C][C]26604.1335684665[/C][C]-2211.63356846647[/C][/ROW]
[ROW][C]51[/C][C]22342.5[/C][C]26496.6987762337[/C][C]-4154.19877623368[/C][/ROW]
[ROW][C]52[/C][C]20242[/C][C]23596.7622721687[/C][C]-3354.76227216869[/C][/ROW]
[ROW][C]53[/C][C]34283.5[/C][C]32396.2102591938[/C][C]1887.28974080622[/C][/ROW]
[ROW][C]54[/C][C]35311[/C][C]33272.9233233577[/C][C]2038.07667664232[/C][/ROW]
[ROW][C]55[/C][C]32694[/C][C]27635.8511209698[/C][C]5058.14887903015[/C][/ROW]
[ROW][C]56[/C][C]35311[/C][C]27692.8113878926[/C][C]7618.18861210738[/C][/ROW]
[ROW][C]57[/C][C]34794.5[/C][C]36433.1025456538[/C][C]-1638.6025456538[/C][/ROW]
[ROW][C]58[/C][C]30644[/C][C]35540.9446967273[/C][C]-4896.94469672731[/C][/ROW]
[ROW][C]59[/C][C]35311[/C][C]35531.3691638433[/C][C]-220.36916384333[/C][/ROW]
[ROW][C]60[/C][C]40484[/C][C]38095.5071990576[/C][C]2388.4928009424[/C][/ROW]
[ROW][C]61[/C][C]42584.5[/C][C]37060.0788615688[/C][C]5524.42113843122[/C][/ROW]
[ROW][C]62[/C][C]36333.5[/C][C]35115.5872566841[/C][C]1217.9127433159[/C][/ROW]
[ROW][C]63[/C][C]32182.5[/C][C]36973.6356253149[/C][C]-4791.13562531486[/C][/ROW]
[ROW][C]64[/C][C]35311[/C][C]34309.0095383964[/C][C]1001.99046160357[/C][/ROW]
[ROW][C]65[/C][C]48785[/C][C]48297.3055533729[/C][C]487.694446627123[/C][/ROW]
[ROW][C]66[/C][C]52936[/C][C]48788.4704272722[/C][C]4147.52957272783[/C][/ROW]
[ROW][C]67[/C][C]51913.5[/C][C]46126.2758626014[/C][C]5787.22413739862[/C][/ROW]
[ROW][C]68[/C][C]53958[/C][C]48121.7523614876[/C][C]5836.24763851241[/C][/ROW]
[ROW][C]69[/C][C]53447[/C][C]53004.5132196524[/C][C]442.486780347594[/C][/ROW]
[ROW][C]70[/C][C]48274[/C][C]52929.5287399848[/C][C]-4655.52873998478[/C][/ROW]
[ROW][C]71[/C][C]57086.5[/C][C]55291.5622126727[/C][C]1794.9377873273[/C][/ROW]
[ROW][C]72[/C][C]59187[/C][C]60740.2557092608[/C][C]-1553.25570926076[/C][/ROW]
[ROW][C]73[/C][C]62259.5[/C][C]58741.9469227849[/C][C]3517.55307721515[/C][/ROW]
[ROW][C]74[/C][C]52936[/C][C]54451.8759036103[/C][C]-1515.87590361032[/C][/ROW]
[ROW][C]75[/C][C]49296.5[/C][C]52804.9047111753[/C][C]-3508.40471117535[/C][/ROW]
[ROW][C]76[/C][C]53447[/C][C]53392.979501353[/C][C]54.0204986469689[/C][/ROW]
[ROW][C]77[/C][C]63337.5[/C][C]66958.3696896772[/C][C]-3620.86968967719[/C][/ROW]
[ROW][C]78[/C][C]72150[/C][C]66264.5177596814[/C][C]5885.48224031855[/C][/ROW]
[ROW][C]79[/C][C]70049.5[/C][C]65599.071269098[/C][C]4450.42873090203[/C][/ROW]
[ROW][C]80[/C][C]70049.5[/C][C]66984.358271223[/C][C]3065.14172877705[/C][/ROW]
[ROW][C]81[/C][C]71077[/C][C]68338.2778607632[/C][C]2738.72213923675[/C][/ROW]
[ROW][C]82[/C][C]67488[/C][C]68228.4345161018[/C][C]-740.434516101785[/C][/ROW]
[ROW][C]83[/C][C]76817[/C][C]75749.3761453756[/C][C]1067.62385462435[/C][/ROW]
[ROW][C]84[/C][C]76817[/C][C]79903.3663080269[/C][C]-3086.36630802686[/C][/ROW]
[ROW][C]85[/C][C]75227.5[/C][C]78946.8341747744[/C][C]-3719.33417477444[/C][/ROW]
[ROW][C]86[/C][C]66410[/C][C]68220.1409345869[/C][C]-1810.14093458693[/C][/ROW]
[ROW][C]87[/C][C]67999.5[/C][C]65717.4970264255[/C][C]2282.00297357453[/C][/ROW]
[ROW][C]88[/C][C]69027[/C][C]71551.4172857383[/C][C]-2524.41728573831[/C][/ROW]
[ROW][C]89[/C][C]75789.5[/C][C]82296.5443313557[/C][C]-6507.04433135572[/C][/ROW]
[ROW][C]90[/C][C]84602[/C][C]83047.1984253367[/C][C]1554.80157466332[/C][/ROW]
[ROW][C]91[/C][C]78350.5[/C][C]78942.3540535872[/C][C]-591.854053587173[/C][/ROW]
[ROW][C]92[/C][C]81479[/C][C]76265.9182371511[/C][C]5213.08176284886[/C][/ROW]
[ROW][C]93[/C][C]78862[/C][C]78698.8501764673[/C][C]163.149823532716[/C][/ROW]
[ROW][C]94[/C][C]77328[/C][C]75399.4901047319[/C][C]1928.5098952681[/C][/ROW]
[ROW][C]95[/C][C]89269[/C][C]85082.5594340097[/C][C]4186.44056599031[/C][/ROW]
[ROW][C]96[/C][C]86652[/C][C]89735.4682313013[/C][C]-3083.46823130127[/C][/ROW]
[ROW][C]97[/C][C]83012.5[/C][C]88460.9629579294[/C][C]-5448.46295792944[/C][/ROW]
[ROW][C]98[/C][C]77839.5[/C][C]77104.954927137[/C][C]734.54507286298[/C][/ROW]
[ROW][C]99[/C][C]83012.5[/C][C]77610.6089956924[/C][C]5401.8910043076[/C][/ROW]
[ROW][C]100[/C][C]85629.5[/C][C]83854.4123507652[/C][C]1775.08764923477[/C][/ROW]
[ROW][C]101[/C][C]88752.5[/C][C]96214.5383212691[/C][C]-7462.03832126911[/C][/ROW]
[ROW][C]102[/C][C]92903[/C][C]99284.7302155296[/C][C]-6381.73021552956[/C][/ROW]
[ROW][C]103[/C][C]88752.5[/C][C]89125.5380447214[/C][C]-373.038044721368[/C][/ROW]
[ROW][C]104[/C][C]91314[/C][C]88487.0947938764[/C][C]2826.90520612359[/C][/ROW]
[ROW][C]105[/C][C]88190.5[/C][C]87412.8516112935[/C][C]777.648388706468[/C][/ROW]
[ROW][C]106[/C][C]87679.5[/C][C]84949.5716176855[/C][C]2729.92838231449[/C][/ROW]
[ROW][C]107[/C][C]100642.5[/C][C]95789.2400366069[/C][C]4853.25996339305[/C][/ROW]
[ROW][C]108[/C][C]101720.5[/C][C]98233.555698441[/C][C]3486.94430155896[/C][/ROW]
[ROW][C]109[/C][C]97570[/C][C]100535.441677108[/C][C]-2965.44167710836[/C][/ROW]
[ROW][C]110[/C][C]90291.5[/C][C]93131.0305173901[/C][C]-2839.53051739007[/C][/ROW]
[ROW][C]111[/C][C]96492[/C][C]92980.6098752052[/C][C]3511.39012479482[/C][/ROW]
[ROW][C]112[/C][C]99104[/C][C]96730.3887890065[/C][C]2373.61121099352[/C][/ROW]
[ROW][C]113[/C][C]102232[/C][C]106300.74203852[/C][C]-4068.74203852029[/C][/ROW]
[ROW][C]114[/C][C]106894[/C][C]112099.057620716[/C][C]-5205.05762071647[/C][/ROW]
[ROW][C]115[/C][C]102232[/C][C]104966.98744103[/C][C]-2734.98744102976[/C][/ROW]
[ROW][C]116[/C][C]105871.5[/C][C]103988.143572909[/C][C]1883.35642709119[/C][/ROW]
[ROW][C]117[/C][C]104282[/C][C]101649.709719424[/C][C]2632.29028057639[/C][/ROW]
[ROW][C]118[/C][C]98592.5[/C][C]101201.414147226[/C][C]-2608.91414722598[/C][/ROW]
[ROW][C]119[/C][C]110533[/C][C]109228.827639166[/C][C]1304.17236083376[/C][/ROW]
[ROW][C]120[/C][C]110533[/C][C]108699.157575399[/C][C]1833.84242460092[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296173&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296173&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
132285927592.9504540598-4733.95045405983
141973121321.260451362-1590.26045136202
1517169.517594.5073290414-425.007329041408
1617169.517003.2205642392166.279435760844
1727009.526513.8280575852495.671942414778
182803227266.4432476464765.556752353554
192024219759.5914827989482.408517201075
2011429.514588.0676146981-3158.56761469812
2116091.512805.92262140923285.57737859077
2216091.514881.26127403031210.2387259697
231973116131.99500755883599.00499244119
2421831.519592.26847842472239.23152157533
252132016336.56359653644983.43640346358
2616091.517922.2590379296-1830.75903792958
2718708.514850.63440417343857.86559582661
281768117820.3890358024-139.389035802385
2926493.527791.6003154287-1298.10031542874
3024392.527949.4982649436-3556.99826494356
3116091.517853.9656981579-1762.4656981579
32989110211.0053746476-320.005374647641
331558012871.56724573572708.43275426431
3417169.514186.07448781862983.42551218137
3518708.517819.831519255888.668480744996
3620753.519340.42138080211413.07861919788
3716602.516769.5342052316-167.034205231612
381301912724.5386696473294.461330352748
391455813182.03156814011375.96843185988
401506913228.72068957321840.2793104268
4128543.524244.73469852374298.76530147633
4228543.527624.2441286433919.25587135669
4320753.521576.7795315312-823.279531531163
441973115580.5421731234150.45782687695
452285922899.9495836532-40.9495836531569
462132023105.4233574333-1785.42335743332
472547123324.35975751042146.64024248958
483064426320.11697114674323.88302885334
4931671.525676.4493086825995.05069131801
5024392.526604.1335684665-2211.63356846647
5122342.526496.6987762337-4154.19877623368
522024223596.7622721687-3354.76227216869
5334283.532396.21025919381887.28974080622
543531133272.92332335772038.07667664232
553269427635.85112096985058.14887903015
563531127692.81138789267618.18861210738
5734794.536433.1025456538-1638.6025456538
583064435540.9446967273-4896.94469672731
593531135531.3691638433-220.36916384333
604048438095.50719905762388.4928009424
6142584.537060.07886156885524.42113843122
6236333.535115.58725668411217.9127433159
6332182.536973.6356253149-4791.13562531486
643531134309.00953839641001.99046160357
654878548297.3055533729487.694446627123
665293648788.47042727224147.52957272783
6751913.546126.27586260145787.22413739862
685395848121.75236148765836.24763851241
695344753004.5132196524442.486780347594
704827452929.5287399848-4655.52873998478
7157086.555291.56221267271794.9377873273
725918760740.2557092608-1553.25570926076
7362259.558741.94692278493517.55307721515
745293654451.8759036103-1515.87590361032
7549296.552804.9047111753-3508.40471117535
765344753392.97950135354.0204986469689
7763337.566958.3696896772-3620.86968967719
787215066264.51775968145885.48224031855
7970049.565599.0712690984450.42873090203
8070049.566984.3582712233065.14172877705
817107768338.27786076322738.72213923675
826748868228.4345161018-740.434516101785
837681775749.37614537561067.62385462435
847681779903.3663080269-3086.36630802686
8575227.578946.8341747744-3719.33417477444
866641068220.1409345869-1810.14093458693
8767999.565717.49702642552282.00297357453
886902771551.4172857383-2524.41728573831
8975789.582296.5443313557-6507.04433135572
908460283047.19842533671554.80157466332
9178350.578942.3540535872-591.854053587173
928147976265.91823715115213.08176284886
937886278698.8501764673163.149823532716
947732875399.49010473191928.5098952681
958926985082.55943400974186.44056599031
968665289735.4682313013-3083.46823130127
9783012.588460.9629579294-5448.46295792944
9877839.577104.954927137734.54507286298
9983012.577610.60899569245401.8910043076
10085629.583854.41235076521775.08764923477
10188752.596214.5383212691-7462.03832126911
1029290399284.7302155296-6381.73021552956
10388752.589125.5380447214-373.038044721368
1049131488487.09479387642826.90520612359
10588190.587412.8516112935777.648388706468
10687679.584949.57161768552729.92838231449
107100642.595789.24003660694853.25996339305
108101720.598233.5556984413486.94430155896
10997570100535.441677108-2965.44167710836
11090291.593131.0305173901-2839.53051739007
1119649292980.60987520523511.39012479482
1129910496730.38878900652373.61121099352
113102232106300.74203852-4068.74203852029
114106894112099.057620716-5205.05762071647
115102232104966.98744103-2734.98744102976
116105871.5103988.1435729091883.35642709119
117104282101649.7097194242632.29028057639
11898592.5101201.414147226-2608.91414722598
119110533109228.8276391661304.17236083376
120110533108699.1575753991833.84242460092







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121107447.382273348101091.30620644113803.458340255
122101889.27528199994173.4125726721109605.137991326
123105757.34104330896777.2754684517114737.406618164
124106659.09402905196470.0048811095116848.183176992
125112205.555579241100840.735707598123570.375450884
126120169.498425724107648.99242808132690.004423368
127117375.04241674103710.267614756131039.817218724
128119958.083102108105154.541494494134761.624709721
129116757.449581509100816.430002667132698.469160351
130112791.48435062895711.1867185397129871.781982717
131123988.121916902105764.430094188142211.813739615
132122852.937800158103479.968277745142225.90732257

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 107447.382273348 & 101091.30620644 & 113803.458340255 \tabularnewline
122 & 101889.275281999 & 94173.4125726721 & 109605.137991326 \tabularnewline
123 & 105757.341043308 & 96777.2754684517 & 114737.406618164 \tabularnewline
124 & 106659.094029051 & 96470.0048811095 & 116848.183176992 \tabularnewline
125 & 112205.555579241 & 100840.735707598 & 123570.375450884 \tabularnewline
126 & 120169.498425724 & 107648.99242808 & 132690.004423368 \tabularnewline
127 & 117375.04241674 & 103710.267614756 & 131039.817218724 \tabularnewline
128 & 119958.083102108 & 105154.541494494 & 134761.624709721 \tabularnewline
129 & 116757.449581509 & 100816.430002667 & 132698.469160351 \tabularnewline
130 & 112791.484350628 & 95711.1867185397 & 129871.781982717 \tabularnewline
131 & 123988.121916902 & 105764.430094188 & 142211.813739615 \tabularnewline
132 & 122852.937800158 & 103479.968277745 & 142225.90732257 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296173&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]107447.382273348[/C][C]101091.30620644[/C][C]113803.458340255[/C][/ROW]
[ROW][C]122[/C][C]101889.275281999[/C][C]94173.4125726721[/C][C]109605.137991326[/C][/ROW]
[ROW][C]123[/C][C]105757.341043308[/C][C]96777.2754684517[/C][C]114737.406618164[/C][/ROW]
[ROW][C]124[/C][C]106659.094029051[/C][C]96470.0048811095[/C][C]116848.183176992[/C][/ROW]
[ROW][C]125[/C][C]112205.555579241[/C][C]100840.735707598[/C][C]123570.375450884[/C][/ROW]
[ROW][C]126[/C][C]120169.498425724[/C][C]107648.99242808[/C][C]132690.004423368[/C][/ROW]
[ROW][C]127[/C][C]117375.04241674[/C][C]103710.267614756[/C][C]131039.817218724[/C][/ROW]
[ROW][C]128[/C][C]119958.083102108[/C][C]105154.541494494[/C][C]134761.624709721[/C][/ROW]
[ROW][C]129[/C][C]116757.449581509[/C][C]100816.430002667[/C][C]132698.469160351[/C][/ROW]
[ROW][C]130[/C][C]112791.484350628[/C][C]95711.1867185397[/C][C]129871.781982717[/C][/ROW]
[ROW][C]131[/C][C]123988.121916902[/C][C]105764.430094188[/C][C]142211.813739615[/C][/ROW]
[ROW][C]132[/C][C]122852.937800158[/C][C]103479.968277745[/C][C]142225.90732257[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296173&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296173&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
121107447.382273348101091.30620644113803.458340255
122101889.27528199994173.4125726721109605.137991326
123105757.34104330896777.2754684517114737.406618164
124106659.09402905196470.0048811095116848.183176992
125112205.555579241100840.735707598123570.375450884
126120169.498425724107648.99242808132690.004423368
127117375.04241674103710.267614756131039.817218724
128119958.083102108105154.541494494134761.624709721
129116757.449581509100816.430002667132698.469160351
130112791.48435062895711.1867185397129871.781982717
131123988.121916902105764.430094188142211.813739615
132122852.937800158103479.968277745142225.90732257



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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')