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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, 16 Aug 2017 18:44:45 +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/t1502901941bljqm5rfgevwsv5.htm/, Retrieved Sat, 11 May 2024 10:39:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307455, Retrieved Sat, 11 May 2024 10:39:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Smoothing: bouwen...] [2017-08-16 16:44:45] [de0d54ff4aa383cef5d270d23e3500df] [Current]
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Dataseries X:
336960.00
324480.00
343200.00
274560.00
355680.00
349440.00
374400.00
386880.00
430560.00
374400.00
355680.00
443040.00
374400.00
280800.00
330720.00
249600.00
349440.00
287040.00
380640.00
343200.00
361920.00
405600.00
399360.00
474240.00
343200.00
287040.00
318240.00
230880.00
330720.00
255840.00
361920.00
343200.00
305760.00
436800.00
393120.00
449280.00
336960.00
312000.00
280800.00
230880.00
305760.00
274560.00
374400.00
361920.00
312000.00
418080.00
386880.00
499200.00
399360.00
243360.00
243360.00
243360.00
287040.00
287040.00
386880.00
355680.00
318240.00
399360.00
368160.00
530400.00
418080.00
243360.00
255840.00
212160.00
293280.00
336960.00
424320.00
418080.00
336960.00
393120.00
349440.00
499200.00
380640.00
305760.00
274560.00
205920.00
305760.00
368160.00
430560.00
405600.00
299520.00
430560.00
336960.00
517920.00
430560.00
312000.00
287040.00
193440.00
305760.00
293280.00
443040.00
443040.00
336960.00
436800.00
324480.00
505440.00
430560.00
318240.00
243360.00
168480.00
330720.00
318240.00
418080.00
480480.00
355680.00
399360.00
299520.00
517920.00




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=307455&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=307455&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307455&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
alpha0.00903806239703573
beta1
gamma0.930857409775863

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00903806239703573 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.930857409775863 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307455&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]0.00903806239703573[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.930857409775863[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307455&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307455&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
alpha0.00903806239703573
beta1
gamma0.930857409775863







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13374400388631.082017531-14231.0820175307
14280800291257.805594588-10457.8055945877
15330720345752.081390004-15032.0813900038
16249600260554.484142455-10954.4841424548
17349440359203.890869418-9763.8908694181
18287040290532.363124135-3492.36312413507
19380640363835.20581273316804.7941872672
20343200374107.357615592-30907.3576155918
21361920415859.747582077-53939.7475820773
22405600359828.27805774845771.7219422515
23399360341070.76671900758289.2332809927
24474240426568.18609982847671.8139001717
25343200349381.390912728-6181.3909127278
26287040262102.75070251724937.2492974835
27318240309673.3283812638566.67161873722
28230880234306.120067089-3426.12006708933
29330720328453.0798144462266.92018555355
30255840270258.532027667-14418.5320276671
31361920357488.3706862124431.62931378832
32343200326219.55825978316980.4417402166
33305760347078.715546329-41318.7155463285
34436800382491.62118058754308.3788194127
35393120376976.04550202216143.9544979777
36449280449862.357037864-582.357037863694
37336960328723.3330750188236.6669249821
38312000273272.56037673438727.4396232656
39280800305216.897603135-24416.8976031355
40230880222212.6333448358667.36665516539
41305760318478.828561681-12718.8285616814
42274560247796.81421375526763.185786245
43374400350181.56640036824218.4335996318
44361920332377.23382805529542.7661719451
45312000301547.04360547410452.9563945261
46418080424940.218969777-6860.21896977682
47386880385856.3576003251023.64239967481
48499200443748.38515513655451.6148448642
49399360334013.11461026965346.8853897305
50243360309156.39039599-65796.3903959905
51243360282751.497803324-39391.4978033238
52243360230665.09501780312694.9049821965
53287040308144.565829475-21104.5658294754
54287040274228.97071463712811.029285363
55386880375324.35063226111555.6493677393
56355680362660.45070971-6980.45070971013
57318240313613.88119824626.11880180036
58399360421848.2082788-22488.2082787998
59368160389573.587418484-21413.5874184842
60530400497758.84817772832641.1518222722
61418080395790.11485875522289.8851412454
62243360248414.64345727-5054.64345727043
63255840246673.2075806289166.79241937192
64212160243253.199851303-31093.1998513029
65293280288994.7524013024285.24759869813
66336960286558.47789554150401.5221044593
67424320387546.01911006936773.9808899314
68418080358462.67687217459617.3231278262
69336960321481.37668852915478.623311471
70393120407222.305269318-14102.305269318
71349440376936.518581752-27496.5185817521
72499200539863.802509525-40663.8025095253
73380640426254.378423664-45614.3784236637
74305760249392.34894443256367.6510555675
75274560262407.72137516512152.2786248354
76205920221365.982046835-15445.982046835
77305760303525.8989475232234.1010524765
78368160346202.61855701121957.3814429885
79430560438835.154969644-8275.15496964409
80405600430631.093956588-25031.0939565878
81299520348871.320857808-49351.3208578078
82430560407992.16375767622567.8362423236
83336960363624.213639888-26664.213639888
84517920518832.215456574-912.215456574457
85430560396722.49878849333837.5012115074
86312000312000.440673689-0.440673689183313
87287040282471.0140523424568.98594765842
88193440213474.300878519-20034.3008785186
89305760314429.12324494-8669.12324494001
90293280376238.776731099-82958.7767310995
91443040439654.9591485863385.04085141403
92443040413903.66645027429136.3335497258
93336960307478.05337367929481.9466263207
94436800435299.3745329211500.62546707893
95324480343548.694289477-19068.6942894766
96505440524420.891902239-18980.8919022392
97430560432471.171477826-1911.17147782614
98318240314366.5611561143873.43884388602
99243360288281.346116142-44921.3461161418
100168480195042.754215765-26562.7542157651
101330720305175.60719530125544.3928046989
102318240297726.09777774920513.9022222511
103418080441028.480486283-22948.4804862832
104480480438359.0479506842120.9520493204
105355680332655.41408065323024.5859193471
106399360433551.117966994-34191.1179669944
107299520322814.169069816-23294.1690698161
108517920501013.00849675816906.9915032421

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 374400 & 388631.082017531 & -14231.0820175307 \tabularnewline
14 & 280800 & 291257.805594588 & -10457.8055945877 \tabularnewline
15 & 330720 & 345752.081390004 & -15032.0813900038 \tabularnewline
16 & 249600 & 260554.484142455 & -10954.4841424548 \tabularnewline
17 & 349440 & 359203.890869418 & -9763.8908694181 \tabularnewline
18 & 287040 & 290532.363124135 & -3492.36312413507 \tabularnewline
19 & 380640 & 363835.205812733 & 16804.7941872672 \tabularnewline
20 & 343200 & 374107.357615592 & -30907.3576155918 \tabularnewline
21 & 361920 & 415859.747582077 & -53939.7475820773 \tabularnewline
22 & 405600 & 359828.278057748 & 45771.7219422515 \tabularnewline
23 & 399360 & 341070.766719007 & 58289.2332809927 \tabularnewline
24 & 474240 & 426568.186099828 & 47671.8139001717 \tabularnewline
25 & 343200 & 349381.390912728 & -6181.3909127278 \tabularnewline
26 & 287040 & 262102.750702517 & 24937.2492974835 \tabularnewline
27 & 318240 & 309673.328381263 & 8566.67161873722 \tabularnewline
28 & 230880 & 234306.120067089 & -3426.12006708933 \tabularnewline
29 & 330720 & 328453.079814446 & 2266.92018555355 \tabularnewline
30 & 255840 & 270258.532027667 & -14418.5320276671 \tabularnewline
31 & 361920 & 357488.370686212 & 4431.62931378832 \tabularnewline
32 & 343200 & 326219.558259783 & 16980.4417402166 \tabularnewline
33 & 305760 & 347078.715546329 & -41318.7155463285 \tabularnewline
34 & 436800 & 382491.621180587 & 54308.3788194127 \tabularnewline
35 & 393120 & 376976.045502022 & 16143.9544979777 \tabularnewline
36 & 449280 & 449862.357037864 & -582.357037863694 \tabularnewline
37 & 336960 & 328723.333075018 & 8236.6669249821 \tabularnewline
38 & 312000 & 273272.560376734 & 38727.4396232656 \tabularnewline
39 & 280800 & 305216.897603135 & -24416.8976031355 \tabularnewline
40 & 230880 & 222212.633344835 & 8667.36665516539 \tabularnewline
41 & 305760 & 318478.828561681 & -12718.8285616814 \tabularnewline
42 & 274560 & 247796.814213755 & 26763.185786245 \tabularnewline
43 & 374400 & 350181.566400368 & 24218.4335996318 \tabularnewline
44 & 361920 & 332377.233828055 & 29542.7661719451 \tabularnewline
45 & 312000 & 301547.043605474 & 10452.9563945261 \tabularnewline
46 & 418080 & 424940.218969777 & -6860.21896977682 \tabularnewline
47 & 386880 & 385856.357600325 & 1023.64239967481 \tabularnewline
48 & 499200 & 443748.385155136 & 55451.6148448642 \tabularnewline
49 & 399360 & 334013.114610269 & 65346.8853897305 \tabularnewline
50 & 243360 & 309156.39039599 & -65796.3903959905 \tabularnewline
51 & 243360 & 282751.497803324 & -39391.4978033238 \tabularnewline
52 & 243360 & 230665.095017803 & 12694.9049821965 \tabularnewline
53 & 287040 & 308144.565829475 & -21104.5658294754 \tabularnewline
54 & 287040 & 274228.970714637 & 12811.029285363 \tabularnewline
55 & 386880 & 375324.350632261 & 11555.6493677393 \tabularnewline
56 & 355680 & 362660.45070971 & -6980.45070971013 \tabularnewline
57 & 318240 & 313613.8811982 & 4626.11880180036 \tabularnewline
58 & 399360 & 421848.2082788 & -22488.2082787998 \tabularnewline
59 & 368160 & 389573.587418484 & -21413.5874184842 \tabularnewline
60 & 530400 & 497758.848177728 & 32641.1518222722 \tabularnewline
61 & 418080 & 395790.114858755 & 22289.8851412454 \tabularnewline
62 & 243360 & 248414.64345727 & -5054.64345727043 \tabularnewline
63 & 255840 & 246673.207580628 & 9166.79241937192 \tabularnewline
64 & 212160 & 243253.199851303 & -31093.1998513029 \tabularnewline
65 & 293280 & 288994.752401302 & 4285.24759869813 \tabularnewline
66 & 336960 & 286558.477895541 & 50401.5221044593 \tabularnewline
67 & 424320 & 387546.019110069 & 36773.9808899314 \tabularnewline
68 & 418080 & 358462.676872174 & 59617.3231278262 \tabularnewline
69 & 336960 & 321481.376688529 & 15478.623311471 \tabularnewline
70 & 393120 & 407222.305269318 & -14102.305269318 \tabularnewline
71 & 349440 & 376936.518581752 & -27496.5185817521 \tabularnewline
72 & 499200 & 539863.802509525 & -40663.8025095253 \tabularnewline
73 & 380640 & 426254.378423664 & -45614.3784236637 \tabularnewline
74 & 305760 & 249392.348944432 & 56367.6510555675 \tabularnewline
75 & 274560 & 262407.721375165 & 12152.2786248354 \tabularnewline
76 & 205920 & 221365.982046835 & -15445.982046835 \tabularnewline
77 & 305760 & 303525.898947523 & 2234.1010524765 \tabularnewline
78 & 368160 & 346202.618557011 & 21957.3814429885 \tabularnewline
79 & 430560 & 438835.154969644 & -8275.15496964409 \tabularnewline
80 & 405600 & 430631.093956588 & -25031.0939565878 \tabularnewline
81 & 299520 & 348871.320857808 & -49351.3208578078 \tabularnewline
82 & 430560 & 407992.163757676 & 22567.8362423236 \tabularnewline
83 & 336960 & 363624.213639888 & -26664.213639888 \tabularnewline
84 & 517920 & 518832.215456574 & -912.215456574457 \tabularnewline
85 & 430560 & 396722.498788493 & 33837.5012115074 \tabularnewline
86 & 312000 & 312000.440673689 & -0.440673689183313 \tabularnewline
87 & 287040 & 282471.014052342 & 4568.98594765842 \tabularnewline
88 & 193440 & 213474.300878519 & -20034.3008785186 \tabularnewline
89 & 305760 & 314429.12324494 & -8669.12324494001 \tabularnewline
90 & 293280 & 376238.776731099 & -82958.7767310995 \tabularnewline
91 & 443040 & 439654.959148586 & 3385.04085141403 \tabularnewline
92 & 443040 & 413903.666450274 & 29136.3335497258 \tabularnewline
93 & 336960 & 307478.053373679 & 29481.9466263207 \tabularnewline
94 & 436800 & 435299.374532921 & 1500.62546707893 \tabularnewline
95 & 324480 & 343548.694289477 & -19068.6942894766 \tabularnewline
96 & 505440 & 524420.891902239 & -18980.8919022392 \tabularnewline
97 & 430560 & 432471.171477826 & -1911.17147782614 \tabularnewline
98 & 318240 & 314366.561156114 & 3873.43884388602 \tabularnewline
99 & 243360 & 288281.346116142 & -44921.3461161418 \tabularnewline
100 & 168480 & 195042.754215765 & -26562.7542157651 \tabularnewline
101 & 330720 & 305175.607195301 & 25544.3928046989 \tabularnewline
102 & 318240 & 297726.097777749 & 20513.9022222511 \tabularnewline
103 & 418080 & 441028.480486283 & -22948.4804862832 \tabularnewline
104 & 480480 & 438359.04795068 & 42120.9520493204 \tabularnewline
105 & 355680 & 332655.414080653 & 23024.5859193471 \tabularnewline
106 & 399360 & 433551.117966994 & -34191.1179669944 \tabularnewline
107 & 299520 & 322814.169069816 & -23294.1690698161 \tabularnewline
108 & 517920 & 501013.008496758 & 16906.9915032421 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307455&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]374400[/C][C]388631.082017531[/C][C]-14231.0820175307[/C][/ROW]
[ROW][C]14[/C][C]280800[/C][C]291257.805594588[/C][C]-10457.8055945877[/C][/ROW]
[ROW][C]15[/C][C]330720[/C][C]345752.081390004[/C][C]-15032.0813900038[/C][/ROW]
[ROW][C]16[/C][C]249600[/C][C]260554.484142455[/C][C]-10954.4841424548[/C][/ROW]
[ROW][C]17[/C][C]349440[/C][C]359203.890869418[/C][C]-9763.8908694181[/C][/ROW]
[ROW][C]18[/C][C]287040[/C][C]290532.363124135[/C][C]-3492.36312413507[/C][/ROW]
[ROW][C]19[/C][C]380640[/C][C]363835.205812733[/C][C]16804.7941872672[/C][/ROW]
[ROW][C]20[/C][C]343200[/C][C]374107.357615592[/C][C]-30907.3576155918[/C][/ROW]
[ROW][C]21[/C][C]361920[/C][C]415859.747582077[/C][C]-53939.7475820773[/C][/ROW]
[ROW][C]22[/C][C]405600[/C][C]359828.278057748[/C][C]45771.7219422515[/C][/ROW]
[ROW][C]23[/C][C]399360[/C][C]341070.766719007[/C][C]58289.2332809927[/C][/ROW]
[ROW][C]24[/C][C]474240[/C][C]426568.186099828[/C][C]47671.8139001717[/C][/ROW]
[ROW][C]25[/C][C]343200[/C][C]349381.390912728[/C][C]-6181.3909127278[/C][/ROW]
[ROW][C]26[/C][C]287040[/C][C]262102.750702517[/C][C]24937.2492974835[/C][/ROW]
[ROW][C]27[/C][C]318240[/C][C]309673.328381263[/C][C]8566.67161873722[/C][/ROW]
[ROW][C]28[/C][C]230880[/C][C]234306.120067089[/C][C]-3426.12006708933[/C][/ROW]
[ROW][C]29[/C][C]330720[/C][C]328453.079814446[/C][C]2266.92018555355[/C][/ROW]
[ROW][C]30[/C][C]255840[/C][C]270258.532027667[/C][C]-14418.5320276671[/C][/ROW]
[ROW][C]31[/C][C]361920[/C][C]357488.370686212[/C][C]4431.62931378832[/C][/ROW]
[ROW][C]32[/C][C]343200[/C][C]326219.558259783[/C][C]16980.4417402166[/C][/ROW]
[ROW][C]33[/C][C]305760[/C][C]347078.715546329[/C][C]-41318.7155463285[/C][/ROW]
[ROW][C]34[/C][C]436800[/C][C]382491.621180587[/C][C]54308.3788194127[/C][/ROW]
[ROW][C]35[/C][C]393120[/C][C]376976.045502022[/C][C]16143.9544979777[/C][/ROW]
[ROW][C]36[/C][C]449280[/C][C]449862.357037864[/C][C]-582.357037863694[/C][/ROW]
[ROW][C]37[/C][C]336960[/C][C]328723.333075018[/C][C]8236.6669249821[/C][/ROW]
[ROW][C]38[/C][C]312000[/C][C]273272.560376734[/C][C]38727.4396232656[/C][/ROW]
[ROW][C]39[/C][C]280800[/C][C]305216.897603135[/C][C]-24416.8976031355[/C][/ROW]
[ROW][C]40[/C][C]230880[/C][C]222212.633344835[/C][C]8667.36665516539[/C][/ROW]
[ROW][C]41[/C][C]305760[/C][C]318478.828561681[/C][C]-12718.8285616814[/C][/ROW]
[ROW][C]42[/C][C]274560[/C][C]247796.814213755[/C][C]26763.185786245[/C][/ROW]
[ROW][C]43[/C][C]374400[/C][C]350181.566400368[/C][C]24218.4335996318[/C][/ROW]
[ROW][C]44[/C][C]361920[/C][C]332377.233828055[/C][C]29542.7661719451[/C][/ROW]
[ROW][C]45[/C][C]312000[/C][C]301547.043605474[/C][C]10452.9563945261[/C][/ROW]
[ROW][C]46[/C][C]418080[/C][C]424940.218969777[/C][C]-6860.21896977682[/C][/ROW]
[ROW][C]47[/C][C]386880[/C][C]385856.357600325[/C][C]1023.64239967481[/C][/ROW]
[ROW][C]48[/C][C]499200[/C][C]443748.385155136[/C][C]55451.6148448642[/C][/ROW]
[ROW][C]49[/C][C]399360[/C][C]334013.114610269[/C][C]65346.8853897305[/C][/ROW]
[ROW][C]50[/C][C]243360[/C][C]309156.39039599[/C][C]-65796.3903959905[/C][/ROW]
[ROW][C]51[/C][C]243360[/C][C]282751.497803324[/C][C]-39391.4978033238[/C][/ROW]
[ROW][C]52[/C][C]243360[/C][C]230665.095017803[/C][C]12694.9049821965[/C][/ROW]
[ROW][C]53[/C][C]287040[/C][C]308144.565829475[/C][C]-21104.5658294754[/C][/ROW]
[ROW][C]54[/C][C]287040[/C][C]274228.970714637[/C][C]12811.029285363[/C][/ROW]
[ROW][C]55[/C][C]386880[/C][C]375324.350632261[/C][C]11555.6493677393[/C][/ROW]
[ROW][C]56[/C][C]355680[/C][C]362660.45070971[/C][C]-6980.45070971013[/C][/ROW]
[ROW][C]57[/C][C]318240[/C][C]313613.8811982[/C][C]4626.11880180036[/C][/ROW]
[ROW][C]58[/C][C]399360[/C][C]421848.2082788[/C][C]-22488.2082787998[/C][/ROW]
[ROW][C]59[/C][C]368160[/C][C]389573.587418484[/C][C]-21413.5874184842[/C][/ROW]
[ROW][C]60[/C][C]530400[/C][C]497758.848177728[/C][C]32641.1518222722[/C][/ROW]
[ROW][C]61[/C][C]418080[/C][C]395790.114858755[/C][C]22289.8851412454[/C][/ROW]
[ROW][C]62[/C][C]243360[/C][C]248414.64345727[/C][C]-5054.64345727043[/C][/ROW]
[ROW][C]63[/C][C]255840[/C][C]246673.207580628[/C][C]9166.79241937192[/C][/ROW]
[ROW][C]64[/C][C]212160[/C][C]243253.199851303[/C][C]-31093.1998513029[/C][/ROW]
[ROW][C]65[/C][C]293280[/C][C]288994.752401302[/C][C]4285.24759869813[/C][/ROW]
[ROW][C]66[/C][C]336960[/C][C]286558.477895541[/C][C]50401.5221044593[/C][/ROW]
[ROW][C]67[/C][C]424320[/C][C]387546.019110069[/C][C]36773.9808899314[/C][/ROW]
[ROW][C]68[/C][C]418080[/C][C]358462.676872174[/C][C]59617.3231278262[/C][/ROW]
[ROW][C]69[/C][C]336960[/C][C]321481.376688529[/C][C]15478.623311471[/C][/ROW]
[ROW][C]70[/C][C]393120[/C][C]407222.305269318[/C][C]-14102.305269318[/C][/ROW]
[ROW][C]71[/C][C]349440[/C][C]376936.518581752[/C][C]-27496.5185817521[/C][/ROW]
[ROW][C]72[/C][C]499200[/C][C]539863.802509525[/C][C]-40663.8025095253[/C][/ROW]
[ROW][C]73[/C][C]380640[/C][C]426254.378423664[/C][C]-45614.3784236637[/C][/ROW]
[ROW][C]74[/C][C]305760[/C][C]249392.348944432[/C][C]56367.6510555675[/C][/ROW]
[ROW][C]75[/C][C]274560[/C][C]262407.721375165[/C][C]12152.2786248354[/C][/ROW]
[ROW][C]76[/C][C]205920[/C][C]221365.982046835[/C][C]-15445.982046835[/C][/ROW]
[ROW][C]77[/C][C]305760[/C][C]303525.898947523[/C][C]2234.1010524765[/C][/ROW]
[ROW][C]78[/C][C]368160[/C][C]346202.618557011[/C][C]21957.3814429885[/C][/ROW]
[ROW][C]79[/C][C]430560[/C][C]438835.154969644[/C][C]-8275.15496964409[/C][/ROW]
[ROW][C]80[/C][C]405600[/C][C]430631.093956588[/C][C]-25031.0939565878[/C][/ROW]
[ROW][C]81[/C][C]299520[/C][C]348871.320857808[/C][C]-49351.3208578078[/C][/ROW]
[ROW][C]82[/C][C]430560[/C][C]407992.163757676[/C][C]22567.8362423236[/C][/ROW]
[ROW][C]83[/C][C]336960[/C][C]363624.213639888[/C][C]-26664.213639888[/C][/ROW]
[ROW][C]84[/C][C]517920[/C][C]518832.215456574[/C][C]-912.215456574457[/C][/ROW]
[ROW][C]85[/C][C]430560[/C][C]396722.498788493[/C][C]33837.5012115074[/C][/ROW]
[ROW][C]86[/C][C]312000[/C][C]312000.440673689[/C][C]-0.440673689183313[/C][/ROW]
[ROW][C]87[/C][C]287040[/C][C]282471.014052342[/C][C]4568.98594765842[/C][/ROW]
[ROW][C]88[/C][C]193440[/C][C]213474.300878519[/C][C]-20034.3008785186[/C][/ROW]
[ROW][C]89[/C][C]305760[/C][C]314429.12324494[/C][C]-8669.12324494001[/C][/ROW]
[ROW][C]90[/C][C]293280[/C][C]376238.776731099[/C][C]-82958.7767310995[/C][/ROW]
[ROW][C]91[/C][C]443040[/C][C]439654.959148586[/C][C]3385.04085141403[/C][/ROW]
[ROW][C]92[/C][C]443040[/C][C]413903.666450274[/C][C]29136.3335497258[/C][/ROW]
[ROW][C]93[/C][C]336960[/C][C]307478.053373679[/C][C]29481.9466263207[/C][/ROW]
[ROW][C]94[/C][C]436800[/C][C]435299.374532921[/C][C]1500.62546707893[/C][/ROW]
[ROW][C]95[/C][C]324480[/C][C]343548.694289477[/C][C]-19068.6942894766[/C][/ROW]
[ROW][C]96[/C][C]505440[/C][C]524420.891902239[/C][C]-18980.8919022392[/C][/ROW]
[ROW][C]97[/C][C]430560[/C][C]432471.171477826[/C][C]-1911.17147782614[/C][/ROW]
[ROW][C]98[/C][C]318240[/C][C]314366.561156114[/C][C]3873.43884388602[/C][/ROW]
[ROW][C]99[/C][C]243360[/C][C]288281.346116142[/C][C]-44921.3461161418[/C][/ROW]
[ROW][C]100[/C][C]168480[/C][C]195042.754215765[/C][C]-26562.7542157651[/C][/ROW]
[ROW][C]101[/C][C]330720[/C][C]305175.607195301[/C][C]25544.3928046989[/C][/ROW]
[ROW][C]102[/C][C]318240[/C][C]297726.097777749[/C][C]20513.9022222511[/C][/ROW]
[ROW][C]103[/C][C]418080[/C][C]441028.480486283[/C][C]-22948.4804862832[/C][/ROW]
[ROW][C]104[/C][C]480480[/C][C]438359.04795068[/C][C]42120.9520493204[/C][/ROW]
[ROW][C]105[/C][C]355680[/C][C]332655.414080653[/C][C]23024.5859193471[/C][/ROW]
[ROW][C]106[/C][C]399360[/C][C]433551.117966994[/C][C]-34191.1179669944[/C][/ROW]
[ROW][C]107[/C][C]299520[/C][C]322814.169069816[/C][C]-23294.1690698161[/C][/ROW]
[ROW][C]108[/C][C]517920[/C][C]501013.008496758[/C][C]16906.9915032421[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307455&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307455&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
13374400388631.082017531-14231.0820175307
14280800291257.805594588-10457.8055945877
15330720345752.081390004-15032.0813900038
16249600260554.484142455-10954.4841424548
17349440359203.890869418-9763.8908694181
18287040290532.363124135-3492.36312413507
19380640363835.20581273316804.7941872672
20343200374107.357615592-30907.3576155918
21361920415859.747582077-53939.7475820773
22405600359828.27805774845771.7219422515
23399360341070.76671900758289.2332809927
24474240426568.18609982847671.8139001717
25343200349381.390912728-6181.3909127278
26287040262102.75070251724937.2492974835
27318240309673.3283812638566.67161873722
28230880234306.120067089-3426.12006708933
29330720328453.0798144462266.92018555355
30255840270258.532027667-14418.5320276671
31361920357488.3706862124431.62931378832
32343200326219.55825978316980.4417402166
33305760347078.715546329-41318.7155463285
34436800382491.62118058754308.3788194127
35393120376976.04550202216143.9544979777
36449280449862.357037864-582.357037863694
37336960328723.3330750188236.6669249821
38312000273272.56037673438727.4396232656
39280800305216.897603135-24416.8976031355
40230880222212.6333448358667.36665516539
41305760318478.828561681-12718.8285616814
42274560247796.81421375526763.185786245
43374400350181.56640036824218.4335996318
44361920332377.23382805529542.7661719451
45312000301547.04360547410452.9563945261
46418080424940.218969777-6860.21896977682
47386880385856.3576003251023.64239967481
48499200443748.38515513655451.6148448642
49399360334013.11461026965346.8853897305
50243360309156.39039599-65796.3903959905
51243360282751.497803324-39391.4978033238
52243360230665.09501780312694.9049821965
53287040308144.565829475-21104.5658294754
54287040274228.97071463712811.029285363
55386880375324.35063226111555.6493677393
56355680362660.45070971-6980.45070971013
57318240313613.88119824626.11880180036
58399360421848.2082788-22488.2082787998
59368160389573.587418484-21413.5874184842
60530400497758.84817772832641.1518222722
61418080395790.11485875522289.8851412454
62243360248414.64345727-5054.64345727043
63255840246673.2075806289166.79241937192
64212160243253.199851303-31093.1998513029
65293280288994.7524013024285.24759869813
66336960286558.47789554150401.5221044593
67424320387546.01911006936773.9808899314
68418080358462.67687217459617.3231278262
69336960321481.37668852915478.623311471
70393120407222.305269318-14102.305269318
71349440376936.518581752-27496.5185817521
72499200539863.802509525-40663.8025095253
73380640426254.378423664-45614.3784236637
74305760249392.34894443256367.6510555675
75274560262407.72137516512152.2786248354
76205920221365.982046835-15445.982046835
77305760303525.8989475232234.1010524765
78368160346202.61855701121957.3814429885
79430560438835.154969644-8275.15496964409
80405600430631.093956588-25031.0939565878
81299520348871.320857808-49351.3208578078
82430560407992.16375767622567.8362423236
83336960363624.213639888-26664.213639888
84517920518832.215456574-912.215456574457
85430560396722.49878849333837.5012115074
86312000312000.440673689-0.440673689183313
87287040282471.0140523424568.98594765842
88193440213474.300878519-20034.3008785186
89305760314429.12324494-8669.12324494001
90293280376238.776731099-82958.7767310995
91443040439654.9591485863385.04085141403
92443040413903.66645027429136.3335497258
93336960307478.05337367929481.9466263207
94436800435299.3745329211500.62546707893
95324480343548.694289477-19068.6942894766
96505440524420.891902239-18980.8919022392
97430560432471.171477826-1911.17147782614
98318240314366.5611561143873.43884388602
99243360288281.346116142-44921.3461161418
100168480195042.754215765-26562.7542157651
101330720305175.60719530125544.3928046989
102318240297726.09777774920513.9022222511
103418080441028.480486283-22948.4804862832
104480480438359.0479506842120.9520493204
105355680332655.41408065323024.5859193471
106399360433551.117966994-34191.1179669944
107299520322814.169069816-23294.1690698161
108517920501013.00849675816906.9915032421







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109425439.786618781371945.706870111478933.866367452
110313684.095696199260184.528778696367183.662613703
111243134.672932948189627.097312992296642.248552904
112168239.660732154114727.862832368221751.458631939
113325175.284300184271522.354266377378828.214333991
114313164.192576815259402.359927121366926.025226508
115414965.338577537360710.985869718469219.691285356
116472048.751807411417094.696021373527002.807593449
117349615.644965028294990.448241809404240.841688247
118396469.555920797341023.566184933451915.545656662
119297279.657952389242343.637343655352215.678561123
120510170.713453169485919.956896876534421.470009462

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 425439.786618781 & 371945.706870111 & 478933.866367452 \tabularnewline
110 & 313684.095696199 & 260184.528778696 & 367183.662613703 \tabularnewline
111 & 243134.672932948 & 189627.097312992 & 296642.248552904 \tabularnewline
112 & 168239.660732154 & 114727.862832368 & 221751.458631939 \tabularnewline
113 & 325175.284300184 & 271522.354266377 & 378828.214333991 \tabularnewline
114 & 313164.192576815 & 259402.359927121 & 366926.025226508 \tabularnewline
115 & 414965.338577537 & 360710.985869718 & 469219.691285356 \tabularnewline
116 & 472048.751807411 & 417094.696021373 & 527002.807593449 \tabularnewline
117 & 349615.644965028 & 294990.448241809 & 404240.841688247 \tabularnewline
118 & 396469.555920797 & 341023.566184933 & 451915.545656662 \tabularnewline
119 & 297279.657952389 & 242343.637343655 & 352215.678561123 \tabularnewline
120 & 510170.713453169 & 485919.956896876 & 534421.470009462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307455&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]425439.786618781[/C][C]371945.706870111[/C][C]478933.866367452[/C][/ROW]
[ROW][C]110[/C][C]313684.095696199[/C][C]260184.528778696[/C][C]367183.662613703[/C][/ROW]
[ROW][C]111[/C][C]243134.672932948[/C][C]189627.097312992[/C][C]296642.248552904[/C][/ROW]
[ROW][C]112[/C][C]168239.660732154[/C][C]114727.862832368[/C][C]221751.458631939[/C][/ROW]
[ROW][C]113[/C][C]325175.284300184[/C][C]271522.354266377[/C][C]378828.214333991[/C][/ROW]
[ROW][C]114[/C][C]313164.192576815[/C][C]259402.359927121[/C][C]366926.025226508[/C][/ROW]
[ROW][C]115[/C][C]414965.338577537[/C][C]360710.985869718[/C][C]469219.691285356[/C][/ROW]
[ROW][C]116[/C][C]472048.751807411[/C][C]417094.696021373[/C][C]527002.807593449[/C][/ROW]
[ROW][C]117[/C][C]349615.644965028[/C][C]294990.448241809[/C][C]404240.841688247[/C][/ROW]
[ROW][C]118[/C][C]396469.555920797[/C][C]341023.566184933[/C][C]451915.545656662[/C][/ROW]
[ROW][C]119[/C][C]297279.657952389[/C][C]242343.637343655[/C][C]352215.678561123[/C][/ROW]
[ROW][C]120[/C][C]510170.713453169[/C][C]485919.956896876[/C][C]534421.470009462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307455&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307455&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
109425439.786618781371945.706870111478933.866367452
110313684.095696199260184.528778696367183.662613703
111243134.672932948189627.097312992296642.248552904
112168239.660732154114727.862832368221751.458631939
113325175.284300184271522.354266377378828.214333991
114313164.192576815259402.359927121366926.025226508
115414965.338577537360710.985869718469219.691285356
116472048.751807411417094.696021373527002.807593449
117349615.644965028294990.448241809404240.841688247
118396469.555920797341023.566184933451915.545656662
119297279.657952389242343.637343655352215.678561123
120510170.713453169485919.956896876534421.470009462



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