Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 16 Aug 2017 20:05:46 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/16/t1502906754yt9pxqm8u823a4z.htm/, Retrieved Sat, 11 May 2024 10:26:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307481, Retrieved Sat, 11 May 2024 10:26:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-16 18:05:46] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
43200
41600
44000
35200
45600
44800
48000
49600
55200
48000
45600
56800
48000
36000
42400
32000
44800
36800
48800
44000
46400
52000
51200
60800
44000
36800
40800
29600
42400
32800
46400
44000
39200
56000
50400
57600
43200
40000
36000
29600
39200
35200
48000
46400
40000
53600
49600
64000
51200
31200
31200
31200
36800
36800
49600
45600
40800
51200
47200
68000
53600
31200
32800
27200
37600
43200
54400
53600
43200
50400
44800
64000
48800
39200
35200
26400
39200
47200
55200
52000
38400
55200
43200
66400
55200
40000
36800
24800
39200
37600
56800
56800
43200
56000
41600
64800
55200
40800
31200
21600
42400
40800
53600
61600
45600
51200
38400
66400




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=307481&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=307481&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307481&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
alpha0.548594506058484
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.548594506058484 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307481&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]0.548594506058484[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307481&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307481&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
alpha0.548594506058484
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
24160043200-1600
34400042322.24879030641677.75120969358
43520043242.6538864773-8042.6538864773
54560038830.49815022596769.50184977407
64480042544.20967376472255.79032623526
74800043781.72385355734218.27614644272
84960046095.84697253333504.15302746669
95520048018.20607178977181.79392821026
104800051958.0987644501-3958.09876445007
114560049786.7075278359-4186.70752783589
125680047489.90277959149310.09722040858
134800052597.3709655779-4597.37096557794
143600050075.2785115491-14075.2785115491
154240042353.658048870246.3419511297834
163200042379.08098866-10379.08098866
174480036685.17418034518114.82581965491
183680041136.9230426293-4336.92304262931
194880038757.710888244410042.2891117556
204400044266.8555232045-266.855523204475
214640044120.46004926312279.53995073686
225200045371.00314257826628.99685742179
235120049007.63439923882192.36560076124
246080050210.35412308810589.645876912
254400056019.7756722668-12019.7756722668
263680049425.7927744058-12625.7927744058
274080042499.3522237339-1699.35222373388
282960041567.0969299352-11967.0969299352
294240035002.01330070347397.98669929661
303280039060.5081598313-6260.50815983125
314640035626.027778213510773.9722217865
324400041536.56974751232463.43025248769
333920042887.9940500853-3687.99405008533
345600040864.780775832115135.2192241679
355040049167.87889020141232.12110979862
365760049843.81376183567756.18623816441
374320054098.814920059-10898.814920059
384000048119.7849323664-8119.7849323664
393600043665.3155280937-7665.31552809374
402960039460.1655421767-9860.16554217672
413920034050.93289691145149.06710308861
423520036875.6828209923-1675.68282099228
434800035956.412431499312043.5875685007
444640042563.45840481313836.54159518694
454000044668.1640461975-4668.16404619747
465360042107.234897073811492.7651029262
474960048412.10269195981187.89730804022
486400049063.776628912314936.2233710877
495120057257.7067115534-6057.70671155336
503120053934.4820902816-22734.4820902816
513120041462.4701174681-10262.4701174681
523120035832.5353924357-4632.53539243573
533680033291.1519270243508.84807297599
543680035216.08670245251583.91329754746
554960036085.012835560113514.9871644399
564560043499.26054342272100.73945657726
574080044651.7146679613-3851.71466796131
585120042538.68516221298661.31483778714
594720047290.2348974657-90.2348974657216
606800047240.732528461320759.2674715387
615360058629.152613146-5029.15261314603
623120055870.1871194444-24670.1871194444
633280042336.2580022824-9536.25800228243
642720037104.719253874-9904.71925387403
653760031671.0446871475928.95531285295
664320034923.63699844448276.36300155555
675440039464.004271243514935.9957287565
685360047657.80947055235942.19052944768
694320050917.6625489601-7717.66254896007
705040046683.79527498733716.20472501274
714480048722.4847705178-3922.48477051783
726400046570.631175313717429.3688246863
734880056132.2871566036-7332.28715660362
743920052109.8347056477-12909.8347056477
753520045027.5703120062-9827.57031200622
762640039636.2192309361-13236.2192309361
773920032374.90207985896825.09792014109
784720036119.113302159511080.8866978405
795520042198.026866851313001.9731331487
805200049330.83789561672669.16210438329
813840050795.1255618609-12395.1255618609
825520043995.227776718911204.7722232811
834320050142.1042600476-6942.10426004764
846640046333.704002500320066.2959974997
855520057341.963743672-2141.96374367199
864000056166.8942017171-16166.8942017171
873680047297.8248626263-10497.8248626263
882480041538.7758174254-16738.7758174254
893920032355.97536584126844.02463415881
903760036110.56967946961489.43032053036
915680036927.662970469519872.3370295305
925680047829.51788741258970.48211258747
934320052750.6750910739-9550.67509107392
945600047511.22720696118488.77279303885
954160052168.121324401-10568.121324401
966480046370.508026475118429.4919735249
975520056480.8260725998-1280.8260725998
984080055778.1719259551-14978.1719259551
993120047561.2290965767-16361.2290965767
1002160038585.5487018305-16985.5487018305
1014240029267.370001617513132.6299983825
1024080036471.8586688294328.14133117103
1035360038846.25322455414753.746775446
1046160046940.077649341814659.9223506582
1054560054982.4305101569-9382.43051015686
1065120049835.28067880931364.7193211907
1073840050583.9582007264-12183.9582007264
1086640043899.905669761722500.0943302383

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 41600 & 43200 & -1600 \tabularnewline
3 & 44000 & 42322.2487903064 & 1677.75120969358 \tabularnewline
4 & 35200 & 43242.6538864773 & -8042.6538864773 \tabularnewline
5 & 45600 & 38830.4981502259 & 6769.50184977407 \tabularnewline
6 & 44800 & 42544.2096737647 & 2255.79032623526 \tabularnewline
7 & 48000 & 43781.7238535573 & 4218.27614644272 \tabularnewline
8 & 49600 & 46095.8469725333 & 3504.15302746669 \tabularnewline
9 & 55200 & 48018.2060717897 & 7181.79392821026 \tabularnewline
10 & 48000 & 51958.0987644501 & -3958.09876445007 \tabularnewline
11 & 45600 & 49786.7075278359 & -4186.70752783589 \tabularnewline
12 & 56800 & 47489.9027795914 & 9310.09722040858 \tabularnewline
13 & 48000 & 52597.3709655779 & -4597.37096557794 \tabularnewline
14 & 36000 & 50075.2785115491 & -14075.2785115491 \tabularnewline
15 & 42400 & 42353.6580488702 & 46.3419511297834 \tabularnewline
16 & 32000 & 42379.08098866 & -10379.08098866 \tabularnewline
17 & 44800 & 36685.1741803451 & 8114.82581965491 \tabularnewline
18 & 36800 & 41136.9230426293 & -4336.92304262931 \tabularnewline
19 & 48800 & 38757.7108882444 & 10042.2891117556 \tabularnewline
20 & 44000 & 44266.8555232045 & -266.855523204475 \tabularnewline
21 & 46400 & 44120.4600492631 & 2279.53995073686 \tabularnewline
22 & 52000 & 45371.0031425782 & 6628.99685742179 \tabularnewline
23 & 51200 & 49007.6343992388 & 2192.36560076124 \tabularnewline
24 & 60800 & 50210.354123088 & 10589.645876912 \tabularnewline
25 & 44000 & 56019.7756722668 & -12019.7756722668 \tabularnewline
26 & 36800 & 49425.7927744058 & -12625.7927744058 \tabularnewline
27 & 40800 & 42499.3522237339 & -1699.35222373388 \tabularnewline
28 & 29600 & 41567.0969299352 & -11967.0969299352 \tabularnewline
29 & 42400 & 35002.0133007034 & 7397.98669929661 \tabularnewline
30 & 32800 & 39060.5081598313 & -6260.50815983125 \tabularnewline
31 & 46400 & 35626.0277782135 & 10773.9722217865 \tabularnewline
32 & 44000 & 41536.5697475123 & 2463.43025248769 \tabularnewline
33 & 39200 & 42887.9940500853 & -3687.99405008533 \tabularnewline
34 & 56000 & 40864.7807758321 & 15135.2192241679 \tabularnewline
35 & 50400 & 49167.8788902014 & 1232.12110979862 \tabularnewline
36 & 57600 & 49843.8137618356 & 7756.18623816441 \tabularnewline
37 & 43200 & 54098.814920059 & -10898.814920059 \tabularnewline
38 & 40000 & 48119.7849323664 & -8119.7849323664 \tabularnewline
39 & 36000 & 43665.3155280937 & -7665.31552809374 \tabularnewline
40 & 29600 & 39460.1655421767 & -9860.16554217672 \tabularnewline
41 & 39200 & 34050.9328969114 & 5149.06710308861 \tabularnewline
42 & 35200 & 36875.6828209923 & -1675.68282099228 \tabularnewline
43 & 48000 & 35956.4124314993 & 12043.5875685007 \tabularnewline
44 & 46400 & 42563.4584048131 & 3836.54159518694 \tabularnewline
45 & 40000 & 44668.1640461975 & -4668.16404619747 \tabularnewline
46 & 53600 & 42107.2348970738 & 11492.7651029262 \tabularnewline
47 & 49600 & 48412.1026919598 & 1187.89730804022 \tabularnewline
48 & 64000 & 49063.7766289123 & 14936.2233710877 \tabularnewline
49 & 51200 & 57257.7067115534 & -6057.70671155336 \tabularnewline
50 & 31200 & 53934.4820902816 & -22734.4820902816 \tabularnewline
51 & 31200 & 41462.4701174681 & -10262.4701174681 \tabularnewline
52 & 31200 & 35832.5353924357 & -4632.53539243573 \tabularnewline
53 & 36800 & 33291.151927024 & 3508.84807297599 \tabularnewline
54 & 36800 & 35216.0867024525 & 1583.91329754746 \tabularnewline
55 & 49600 & 36085.0128355601 & 13514.9871644399 \tabularnewline
56 & 45600 & 43499.2605434227 & 2100.73945657726 \tabularnewline
57 & 40800 & 44651.7146679613 & -3851.71466796131 \tabularnewline
58 & 51200 & 42538.6851622129 & 8661.31483778714 \tabularnewline
59 & 47200 & 47290.2348974657 & -90.2348974657216 \tabularnewline
60 & 68000 & 47240.7325284613 & 20759.2674715387 \tabularnewline
61 & 53600 & 58629.152613146 & -5029.15261314603 \tabularnewline
62 & 31200 & 55870.1871194444 & -24670.1871194444 \tabularnewline
63 & 32800 & 42336.2580022824 & -9536.25800228243 \tabularnewline
64 & 27200 & 37104.719253874 & -9904.71925387403 \tabularnewline
65 & 37600 & 31671.044687147 & 5928.95531285295 \tabularnewline
66 & 43200 & 34923.6369984444 & 8276.36300155555 \tabularnewline
67 & 54400 & 39464.0042712435 & 14935.9957287565 \tabularnewline
68 & 53600 & 47657.8094705523 & 5942.19052944768 \tabularnewline
69 & 43200 & 50917.6625489601 & -7717.66254896007 \tabularnewline
70 & 50400 & 46683.7952749873 & 3716.20472501274 \tabularnewline
71 & 44800 & 48722.4847705178 & -3922.48477051783 \tabularnewline
72 & 64000 & 46570.6311753137 & 17429.3688246863 \tabularnewline
73 & 48800 & 56132.2871566036 & -7332.28715660362 \tabularnewline
74 & 39200 & 52109.8347056477 & -12909.8347056477 \tabularnewline
75 & 35200 & 45027.5703120062 & -9827.57031200622 \tabularnewline
76 & 26400 & 39636.2192309361 & -13236.2192309361 \tabularnewline
77 & 39200 & 32374.9020798589 & 6825.09792014109 \tabularnewline
78 & 47200 & 36119.1133021595 & 11080.8866978405 \tabularnewline
79 & 55200 & 42198.0268668513 & 13001.9731331487 \tabularnewline
80 & 52000 & 49330.8378956167 & 2669.16210438329 \tabularnewline
81 & 38400 & 50795.1255618609 & -12395.1255618609 \tabularnewline
82 & 55200 & 43995.2277767189 & 11204.7722232811 \tabularnewline
83 & 43200 & 50142.1042600476 & -6942.10426004764 \tabularnewline
84 & 66400 & 46333.7040025003 & 20066.2959974997 \tabularnewline
85 & 55200 & 57341.963743672 & -2141.96374367199 \tabularnewline
86 & 40000 & 56166.8942017171 & -16166.8942017171 \tabularnewline
87 & 36800 & 47297.8248626263 & -10497.8248626263 \tabularnewline
88 & 24800 & 41538.7758174254 & -16738.7758174254 \tabularnewline
89 & 39200 & 32355.9753658412 & 6844.02463415881 \tabularnewline
90 & 37600 & 36110.5696794696 & 1489.43032053036 \tabularnewline
91 & 56800 & 36927.6629704695 & 19872.3370295305 \tabularnewline
92 & 56800 & 47829.5178874125 & 8970.48211258747 \tabularnewline
93 & 43200 & 52750.6750910739 & -9550.67509107392 \tabularnewline
94 & 56000 & 47511.2272069611 & 8488.77279303885 \tabularnewline
95 & 41600 & 52168.121324401 & -10568.121324401 \tabularnewline
96 & 64800 & 46370.5080264751 & 18429.4919735249 \tabularnewline
97 & 55200 & 56480.8260725998 & -1280.8260725998 \tabularnewline
98 & 40800 & 55778.1719259551 & -14978.1719259551 \tabularnewline
99 & 31200 & 47561.2290965767 & -16361.2290965767 \tabularnewline
100 & 21600 & 38585.5487018305 & -16985.5487018305 \tabularnewline
101 & 42400 & 29267.3700016175 & 13132.6299983825 \tabularnewline
102 & 40800 & 36471.858668829 & 4328.14133117103 \tabularnewline
103 & 53600 & 38846.253224554 & 14753.746775446 \tabularnewline
104 & 61600 & 46940.0776493418 & 14659.9223506582 \tabularnewline
105 & 45600 & 54982.4305101569 & -9382.43051015686 \tabularnewline
106 & 51200 & 49835.2806788093 & 1364.7193211907 \tabularnewline
107 & 38400 & 50583.9582007264 & -12183.9582007264 \tabularnewline
108 & 66400 & 43899.9056697617 & 22500.0943302383 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307481&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]41600[/C][C]43200[/C][C]-1600[/C][/ROW]
[ROW][C]3[/C][C]44000[/C][C]42322.2487903064[/C][C]1677.75120969358[/C][/ROW]
[ROW][C]4[/C][C]35200[/C][C]43242.6538864773[/C][C]-8042.6538864773[/C][/ROW]
[ROW][C]5[/C][C]45600[/C][C]38830.4981502259[/C][C]6769.50184977407[/C][/ROW]
[ROW][C]6[/C][C]44800[/C][C]42544.2096737647[/C][C]2255.79032623526[/C][/ROW]
[ROW][C]7[/C][C]48000[/C][C]43781.7238535573[/C][C]4218.27614644272[/C][/ROW]
[ROW][C]8[/C][C]49600[/C][C]46095.8469725333[/C][C]3504.15302746669[/C][/ROW]
[ROW][C]9[/C][C]55200[/C][C]48018.2060717897[/C][C]7181.79392821026[/C][/ROW]
[ROW][C]10[/C][C]48000[/C][C]51958.0987644501[/C][C]-3958.09876445007[/C][/ROW]
[ROW][C]11[/C][C]45600[/C][C]49786.7075278359[/C][C]-4186.70752783589[/C][/ROW]
[ROW][C]12[/C][C]56800[/C][C]47489.9027795914[/C][C]9310.09722040858[/C][/ROW]
[ROW][C]13[/C][C]48000[/C][C]52597.3709655779[/C][C]-4597.37096557794[/C][/ROW]
[ROW][C]14[/C][C]36000[/C][C]50075.2785115491[/C][C]-14075.2785115491[/C][/ROW]
[ROW][C]15[/C][C]42400[/C][C]42353.6580488702[/C][C]46.3419511297834[/C][/ROW]
[ROW][C]16[/C][C]32000[/C][C]42379.08098866[/C][C]-10379.08098866[/C][/ROW]
[ROW][C]17[/C][C]44800[/C][C]36685.1741803451[/C][C]8114.82581965491[/C][/ROW]
[ROW][C]18[/C][C]36800[/C][C]41136.9230426293[/C][C]-4336.92304262931[/C][/ROW]
[ROW][C]19[/C][C]48800[/C][C]38757.7108882444[/C][C]10042.2891117556[/C][/ROW]
[ROW][C]20[/C][C]44000[/C][C]44266.8555232045[/C][C]-266.855523204475[/C][/ROW]
[ROW][C]21[/C][C]46400[/C][C]44120.4600492631[/C][C]2279.53995073686[/C][/ROW]
[ROW][C]22[/C][C]52000[/C][C]45371.0031425782[/C][C]6628.99685742179[/C][/ROW]
[ROW][C]23[/C][C]51200[/C][C]49007.6343992388[/C][C]2192.36560076124[/C][/ROW]
[ROW][C]24[/C][C]60800[/C][C]50210.354123088[/C][C]10589.645876912[/C][/ROW]
[ROW][C]25[/C][C]44000[/C][C]56019.7756722668[/C][C]-12019.7756722668[/C][/ROW]
[ROW][C]26[/C][C]36800[/C][C]49425.7927744058[/C][C]-12625.7927744058[/C][/ROW]
[ROW][C]27[/C][C]40800[/C][C]42499.3522237339[/C][C]-1699.35222373388[/C][/ROW]
[ROW][C]28[/C][C]29600[/C][C]41567.0969299352[/C][C]-11967.0969299352[/C][/ROW]
[ROW][C]29[/C][C]42400[/C][C]35002.0133007034[/C][C]7397.98669929661[/C][/ROW]
[ROW][C]30[/C][C]32800[/C][C]39060.5081598313[/C][C]-6260.50815983125[/C][/ROW]
[ROW][C]31[/C][C]46400[/C][C]35626.0277782135[/C][C]10773.9722217865[/C][/ROW]
[ROW][C]32[/C][C]44000[/C][C]41536.5697475123[/C][C]2463.43025248769[/C][/ROW]
[ROW][C]33[/C][C]39200[/C][C]42887.9940500853[/C][C]-3687.99405008533[/C][/ROW]
[ROW][C]34[/C][C]56000[/C][C]40864.7807758321[/C][C]15135.2192241679[/C][/ROW]
[ROW][C]35[/C][C]50400[/C][C]49167.8788902014[/C][C]1232.12110979862[/C][/ROW]
[ROW][C]36[/C][C]57600[/C][C]49843.8137618356[/C][C]7756.18623816441[/C][/ROW]
[ROW][C]37[/C][C]43200[/C][C]54098.814920059[/C][C]-10898.814920059[/C][/ROW]
[ROW][C]38[/C][C]40000[/C][C]48119.7849323664[/C][C]-8119.7849323664[/C][/ROW]
[ROW][C]39[/C][C]36000[/C][C]43665.3155280937[/C][C]-7665.31552809374[/C][/ROW]
[ROW][C]40[/C][C]29600[/C][C]39460.1655421767[/C][C]-9860.16554217672[/C][/ROW]
[ROW][C]41[/C][C]39200[/C][C]34050.9328969114[/C][C]5149.06710308861[/C][/ROW]
[ROW][C]42[/C][C]35200[/C][C]36875.6828209923[/C][C]-1675.68282099228[/C][/ROW]
[ROW][C]43[/C][C]48000[/C][C]35956.4124314993[/C][C]12043.5875685007[/C][/ROW]
[ROW][C]44[/C][C]46400[/C][C]42563.4584048131[/C][C]3836.54159518694[/C][/ROW]
[ROW][C]45[/C][C]40000[/C][C]44668.1640461975[/C][C]-4668.16404619747[/C][/ROW]
[ROW][C]46[/C][C]53600[/C][C]42107.2348970738[/C][C]11492.7651029262[/C][/ROW]
[ROW][C]47[/C][C]49600[/C][C]48412.1026919598[/C][C]1187.89730804022[/C][/ROW]
[ROW][C]48[/C][C]64000[/C][C]49063.7766289123[/C][C]14936.2233710877[/C][/ROW]
[ROW][C]49[/C][C]51200[/C][C]57257.7067115534[/C][C]-6057.70671155336[/C][/ROW]
[ROW][C]50[/C][C]31200[/C][C]53934.4820902816[/C][C]-22734.4820902816[/C][/ROW]
[ROW][C]51[/C][C]31200[/C][C]41462.4701174681[/C][C]-10262.4701174681[/C][/ROW]
[ROW][C]52[/C][C]31200[/C][C]35832.5353924357[/C][C]-4632.53539243573[/C][/ROW]
[ROW][C]53[/C][C]36800[/C][C]33291.151927024[/C][C]3508.84807297599[/C][/ROW]
[ROW][C]54[/C][C]36800[/C][C]35216.0867024525[/C][C]1583.91329754746[/C][/ROW]
[ROW][C]55[/C][C]49600[/C][C]36085.0128355601[/C][C]13514.9871644399[/C][/ROW]
[ROW][C]56[/C][C]45600[/C][C]43499.2605434227[/C][C]2100.73945657726[/C][/ROW]
[ROW][C]57[/C][C]40800[/C][C]44651.7146679613[/C][C]-3851.71466796131[/C][/ROW]
[ROW][C]58[/C][C]51200[/C][C]42538.6851622129[/C][C]8661.31483778714[/C][/ROW]
[ROW][C]59[/C][C]47200[/C][C]47290.2348974657[/C][C]-90.2348974657216[/C][/ROW]
[ROW][C]60[/C][C]68000[/C][C]47240.7325284613[/C][C]20759.2674715387[/C][/ROW]
[ROW][C]61[/C][C]53600[/C][C]58629.152613146[/C][C]-5029.15261314603[/C][/ROW]
[ROW][C]62[/C][C]31200[/C][C]55870.1871194444[/C][C]-24670.1871194444[/C][/ROW]
[ROW][C]63[/C][C]32800[/C][C]42336.2580022824[/C][C]-9536.25800228243[/C][/ROW]
[ROW][C]64[/C][C]27200[/C][C]37104.719253874[/C][C]-9904.71925387403[/C][/ROW]
[ROW][C]65[/C][C]37600[/C][C]31671.044687147[/C][C]5928.95531285295[/C][/ROW]
[ROW][C]66[/C][C]43200[/C][C]34923.6369984444[/C][C]8276.36300155555[/C][/ROW]
[ROW][C]67[/C][C]54400[/C][C]39464.0042712435[/C][C]14935.9957287565[/C][/ROW]
[ROW][C]68[/C][C]53600[/C][C]47657.8094705523[/C][C]5942.19052944768[/C][/ROW]
[ROW][C]69[/C][C]43200[/C][C]50917.6625489601[/C][C]-7717.66254896007[/C][/ROW]
[ROW][C]70[/C][C]50400[/C][C]46683.7952749873[/C][C]3716.20472501274[/C][/ROW]
[ROW][C]71[/C][C]44800[/C][C]48722.4847705178[/C][C]-3922.48477051783[/C][/ROW]
[ROW][C]72[/C][C]64000[/C][C]46570.6311753137[/C][C]17429.3688246863[/C][/ROW]
[ROW][C]73[/C][C]48800[/C][C]56132.2871566036[/C][C]-7332.28715660362[/C][/ROW]
[ROW][C]74[/C][C]39200[/C][C]52109.8347056477[/C][C]-12909.8347056477[/C][/ROW]
[ROW][C]75[/C][C]35200[/C][C]45027.5703120062[/C][C]-9827.57031200622[/C][/ROW]
[ROW][C]76[/C][C]26400[/C][C]39636.2192309361[/C][C]-13236.2192309361[/C][/ROW]
[ROW][C]77[/C][C]39200[/C][C]32374.9020798589[/C][C]6825.09792014109[/C][/ROW]
[ROW][C]78[/C][C]47200[/C][C]36119.1133021595[/C][C]11080.8866978405[/C][/ROW]
[ROW][C]79[/C][C]55200[/C][C]42198.0268668513[/C][C]13001.9731331487[/C][/ROW]
[ROW][C]80[/C][C]52000[/C][C]49330.8378956167[/C][C]2669.16210438329[/C][/ROW]
[ROW][C]81[/C][C]38400[/C][C]50795.1255618609[/C][C]-12395.1255618609[/C][/ROW]
[ROW][C]82[/C][C]55200[/C][C]43995.2277767189[/C][C]11204.7722232811[/C][/ROW]
[ROW][C]83[/C][C]43200[/C][C]50142.1042600476[/C][C]-6942.10426004764[/C][/ROW]
[ROW][C]84[/C][C]66400[/C][C]46333.7040025003[/C][C]20066.2959974997[/C][/ROW]
[ROW][C]85[/C][C]55200[/C][C]57341.963743672[/C][C]-2141.96374367199[/C][/ROW]
[ROW][C]86[/C][C]40000[/C][C]56166.8942017171[/C][C]-16166.8942017171[/C][/ROW]
[ROW][C]87[/C][C]36800[/C][C]47297.8248626263[/C][C]-10497.8248626263[/C][/ROW]
[ROW][C]88[/C][C]24800[/C][C]41538.7758174254[/C][C]-16738.7758174254[/C][/ROW]
[ROW][C]89[/C][C]39200[/C][C]32355.9753658412[/C][C]6844.02463415881[/C][/ROW]
[ROW][C]90[/C][C]37600[/C][C]36110.5696794696[/C][C]1489.43032053036[/C][/ROW]
[ROW][C]91[/C][C]56800[/C][C]36927.6629704695[/C][C]19872.3370295305[/C][/ROW]
[ROW][C]92[/C][C]56800[/C][C]47829.5178874125[/C][C]8970.48211258747[/C][/ROW]
[ROW][C]93[/C][C]43200[/C][C]52750.6750910739[/C][C]-9550.67509107392[/C][/ROW]
[ROW][C]94[/C][C]56000[/C][C]47511.2272069611[/C][C]8488.77279303885[/C][/ROW]
[ROW][C]95[/C][C]41600[/C][C]52168.121324401[/C][C]-10568.121324401[/C][/ROW]
[ROW][C]96[/C][C]64800[/C][C]46370.5080264751[/C][C]18429.4919735249[/C][/ROW]
[ROW][C]97[/C][C]55200[/C][C]56480.8260725998[/C][C]-1280.8260725998[/C][/ROW]
[ROW][C]98[/C][C]40800[/C][C]55778.1719259551[/C][C]-14978.1719259551[/C][/ROW]
[ROW][C]99[/C][C]31200[/C][C]47561.2290965767[/C][C]-16361.2290965767[/C][/ROW]
[ROW][C]100[/C][C]21600[/C][C]38585.5487018305[/C][C]-16985.5487018305[/C][/ROW]
[ROW][C]101[/C][C]42400[/C][C]29267.3700016175[/C][C]13132.6299983825[/C][/ROW]
[ROW][C]102[/C][C]40800[/C][C]36471.858668829[/C][C]4328.14133117103[/C][/ROW]
[ROW][C]103[/C][C]53600[/C][C]38846.253224554[/C][C]14753.746775446[/C][/ROW]
[ROW][C]104[/C][C]61600[/C][C]46940.0776493418[/C][C]14659.9223506582[/C][/ROW]
[ROW][C]105[/C][C]45600[/C][C]54982.4305101569[/C][C]-9382.43051015686[/C][/ROW]
[ROW][C]106[/C][C]51200[/C][C]49835.2806788093[/C][C]1364.7193211907[/C][/ROW]
[ROW][C]107[/C][C]38400[/C][C]50583.9582007264[/C][C]-12183.9582007264[/C][/ROW]
[ROW][C]108[/C][C]66400[/C][C]43899.9056697617[/C][C]22500.0943302383[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307481&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307481&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
24160043200-1600
34400042322.24879030641677.75120969358
43520043242.6538864773-8042.6538864773
54560038830.49815022596769.50184977407
64480042544.20967376472255.79032623526
74800043781.72385355734218.27614644272
84960046095.84697253333504.15302746669
95520048018.20607178977181.79392821026
104800051958.0987644501-3958.09876445007
114560049786.7075278359-4186.70752783589
125680047489.90277959149310.09722040858
134800052597.3709655779-4597.37096557794
143600050075.2785115491-14075.2785115491
154240042353.658048870246.3419511297834
163200042379.08098866-10379.08098866
174480036685.17418034518114.82581965491
183680041136.9230426293-4336.92304262931
194880038757.710888244410042.2891117556
204400044266.8555232045-266.855523204475
214640044120.46004926312279.53995073686
225200045371.00314257826628.99685742179
235120049007.63439923882192.36560076124
246080050210.35412308810589.645876912
254400056019.7756722668-12019.7756722668
263680049425.7927744058-12625.7927744058
274080042499.3522237339-1699.35222373388
282960041567.0969299352-11967.0969299352
294240035002.01330070347397.98669929661
303280039060.5081598313-6260.50815983125
314640035626.027778213510773.9722217865
324400041536.56974751232463.43025248769
333920042887.9940500853-3687.99405008533
345600040864.780775832115135.2192241679
355040049167.87889020141232.12110979862
365760049843.81376183567756.18623816441
374320054098.814920059-10898.814920059
384000048119.7849323664-8119.7849323664
393600043665.3155280937-7665.31552809374
402960039460.1655421767-9860.16554217672
413920034050.93289691145149.06710308861
423520036875.6828209923-1675.68282099228
434800035956.412431499312043.5875685007
444640042563.45840481313836.54159518694
454000044668.1640461975-4668.16404619747
465360042107.234897073811492.7651029262
474960048412.10269195981187.89730804022
486400049063.776628912314936.2233710877
495120057257.7067115534-6057.70671155336
503120053934.4820902816-22734.4820902816
513120041462.4701174681-10262.4701174681
523120035832.5353924357-4632.53539243573
533680033291.1519270243508.84807297599
543680035216.08670245251583.91329754746
554960036085.012835560113514.9871644399
564560043499.26054342272100.73945657726
574080044651.7146679613-3851.71466796131
585120042538.68516221298661.31483778714
594720047290.2348974657-90.2348974657216
606800047240.732528461320759.2674715387
615360058629.152613146-5029.15261314603
623120055870.1871194444-24670.1871194444
633280042336.2580022824-9536.25800228243
642720037104.719253874-9904.71925387403
653760031671.0446871475928.95531285295
664320034923.63699844448276.36300155555
675440039464.004271243514935.9957287565
685360047657.80947055235942.19052944768
694320050917.6625489601-7717.66254896007
705040046683.79527498733716.20472501274
714480048722.4847705178-3922.48477051783
726400046570.631175313717429.3688246863
734880056132.2871566036-7332.28715660362
743920052109.8347056477-12909.8347056477
753520045027.5703120062-9827.57031200622
762640039636.2192309361-13236.2192309361
773920032374.90207985896825.09792014109
784720036119.113302159511080.8866978405
795520042198.026866851313001.9731331487
805200049330.83789561672669.16210438329
813840050795.1255618609-12395.1255618609
825520043995.227776718911204.7722232811
834320050142.1042600476-6942.10426004764
846640046333.704002500320066.2959974997
855520057341.963743672-2141.96374367199
864000056166.8942017171-16166.8942017171
873680047297.8248626263-10497.8248626263
882480041538.7758174254-16738.7758174254
893920032355.97536584126844.02463415881
903760036110.56967946961489.43032053036
915680036927.662970469519872.3370295305
925680047829.51788741258970.48211258747
934320052750.6750910739-9550.67509107392
945600047511.22720696118488.77279303885
954160052168.121324401-10568.121324401
966480046370.508026475118429.4919735249
975520056480.8260725998-1280.8260725998
984080055778.1719259551-14978.1719259551
993120047561.2290965767-16361.2290965767
1002160038585.5487018305-16985.5487018305
1014240029267.370001617513132.6299983825
1024080036471.8586688294328.14133117103
1035360038846.25322455414753.746775446
1046160046940.077649341814659.9223506582
1054560054982.4305101569-9382.43051015686
1065120049835.28067880931364.7193211907
1073840050583.9582007264-12183.9582007264
1086640043899.905669761722500.0943302383







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10956243.333805128135945.427495701876541.2401145543
11056243.333805128133091.652451363479395.0151588927
11156243.333805128130552.952366421181933.7152438351
11256243.333805128128243.493672972584243.1739372836
11356243.333805128126110.521185223586376.1464250326
11456243.333805128124118.861119241388367.8064910149
11556243.333805128122243.670655233690242.9969550226
11656243.333805128120466.631284265492020.0363259907
11756243.333805128118773.775598147493712.8920121087
11856243.333805128117154.164701828995332.5029084272
11956243.333805128115599.041584124696887.6260261316
12056243.333805128114101.266472042398385.4011382138

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 56243.3338051281 & 35945.4274957018 & 76541.2401145543 \tabularnewline
110 & 56243.3338051281 & 33091.6524513634 & 79395.0151588927 \tabularnewline
111 & 56243.3338051281 & 30552.9523664211 & 81933.7152438351 \tabularnewline
112 & 56243.3338051281 & 28243.4936729725 & 84243.1739372836 \tabularnewline
113 & 56243.3338051281 & 26110.5211852235 & 86376.1464250326 \tabularnewline
114 & 56243.3338051281 & 24118.8611192413 & 88367.8064910149 \tabularnewline
115 & 56243.3338051281 & 22243.6706552336 & 90242.9969550226 \tabularnewline
116 & 56243.3338051281 & 20466.6312842654 & 92020.0363259907 \tabularnewline
117 & 56243.3338051281 & 18773.7755981474 & 93712.8920121087 \tabularnewline
118 & 56243.3338051281 & 17154.1647018289 & 95332.5029084272 \tabularnewline
119 & 56243.3338051281 & 15599.0415841246 & 96887.6260261316 \tabularnewline
120 & 56243.3338051281 & 14101.2664720423 & 98385.4011382138 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307481&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]56243.3338051281[/C][C]35945.4274957018[/C][C]76541.2401145543[/C][/ROW]
[ROW][C]110[/C][C]56243.3338051281[/C][C]33091.6524513634[/C][C]79395.0151588927[/C][/ROW]
[ROW][C]111[/C][C]56243.3338051281[/C][C]30552.9523664211[/C][C]81933.7152438351[/C][/ROW]
[ROW][C]112[/C][C]56243.3338051281[/C][C]28243.4936729725[/C][C]84243.1739372836[/C][/ROW]
[ROW][C]113[/C][C]56243.3338051281[/C][C]26110.5211852235[/C][C]86376.1464250326[/C][/ROW]
[ROW][C]114[/C][C]56243.3338051281[/C][C]24118.8611192413[/C][C]88367.8064910149[/C][/ROW]
[ROW][C]115[/C][C]56243.3338051281[/C][C]22243.6706552336[/C][C]90242.9969550226[/C][/ROW]
[ROW][C]116[/C][C]56243.3338051281[/C][C]20466.6312842654[/C][C]92020.0363259907[/C][/ROW]
[ROW][C]117[/C][C]56243.3338051281[/C][C]18773.7755981474[/C][C]93712.8920121087[/C][/ROW]
[ROW][C]118[/C][C]56243.3338051281[/C][C]17154.1647018289[/C][C]95332.5029084272[/C][/ROW]
[ROW][C]119[/C][C]56243.3338051281[/C][C]15599.0415841246[/C][C]96887.6260261316[/C][/ROW]
[ROW][C]120[/C][C]56243.3338051281[/C][C]14101.2664720423[/C][C]98385.4011382138[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307481&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307481&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
10956243.333805128135945.427495701876541.2401145543
11056243.333805128133091.652451363479395.0151588927
11156243.333805128130552.952366421181933.7152438351
11256243.333805128128243.493672972584243.1739372836
11356243.333805128126110.521185223586376.1464250326
11456243.333805128124118.861119241388367.8064910149
11556243.333805128122243.670655233690242.9969550226
11656243.333805128120466.631284265492020.0363259907
11756243.333805128118773.775598147493712.8920121087
11856243.333805128117154.164701828995332.5029084272
11956243.333805128115599.041584124696887.6260261316
12056243.333805128114101.266472042398385.4011382138



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