Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 27 May 2010 12:22:32 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/May/27/t1274963056ct0llmevr09urvd.htm/, Retrieved Thu, 02 May 2024 09:19:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76596, Retrieved Thu, 02 May 2024 09:19:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact166
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [De verkoopcijfers...] [2010-05-27 12:22:32] [202f3200e40254c22df549da03ba92fb] [Current]
Feedback Forum

Post a new message
Dataseries X:
68897
38683
44720
39525
45315
50380
40600
36279
42438
38064
31879
11379
70249
39253
47060
41697
38708
49267
39018
32228
40870
39383
34571
12066
70938
34077
45409
40809
37013
44953
37848
32745
43412
34931
33008
8620
68906
39556
50669
36432
40891
48428
36222
33425
39401
37967
34801
12657
69116
41519
51321
38529
41547
52073
38401
40898
40439
41888
37898
8771
68184
50530
47221
41756
45633
48138
39486
39341
41117
41629
29722
7054
56676
34870
35117
30169
30936
35699
33228
27733
33666
35429
27438
8170
62557




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76596&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76596&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76596&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.294870697455103
beta0
gamma0.335511814386048

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.294870697455103 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.335511814386048 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76596&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]0.294870697455103[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.335511814386048[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76596&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76596&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
alpha0.294870697455103
beta0
gamma0.335511814386048







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137024971014.3015814803-765.301581480278
143925339703.6268082511-450.626808251065
154706047620.1628926628-560.162892662767
164169741970.8422031604-273.842203160399
173870838645.108077761862.891922238181
184926748936.740287549330.259712451036
193901839927.344520585-909.344520585044
203222835294.5427433688-3066.54274336876
214087040022.9121377387847.087862261258
223938335879.41468000443503.58531999561
233457130989.10602358413581.89397641593
241206611505.5372144255560.462785574548
257093871920.8782040774-982.878204077395
263407740171.8003070546-6094.80030705463
274540946173.4577239264-764.457723926447
284080940686.3018647619122.698135238097
293701337638.4924524002-625.492452400198
304495347459.781724517-2506.78172451699
313784837772.904467190575.0955328094569
323274533102.5281638041-357.528163804076
334341239422.56119247313989.43880752695
343493136799.3932356376-1868.39323563762
353300830547.68481107672460.31518892329
36862011062.1518262835-2442.15182628345
376890662794.05359643496111.94640356513
383955634971.5034770114584.49652298904
395066945231.25268896015437.74731103993
403643241666.9976341778-5234.99763417777
414089136910.66741890833980.33258109174
424842847836.9858478707591.014152129268
433622239337.2966219577-3115.2966219577
443342533547.8765998168-122.876599816846
453940141074.9660311752-1673.96603117516
463796735507.61495105252459.38504894752
473480131487.58088231543313.41911768465
481265710644.38453327452012.61546672553
496911673910.5935551122-4794.59355511224
504151939543.55760271621975.4423972838
515132149857.80504585551463.19495414446
523852942204.0291188827-3675.02911888271
534154740002.51722085661544.48277914341
545207349740.33833562192332.66166437809
553840140411.0985281166-2010.09852811658
564089835423.53627185445474.46372814564
574043945002.3170290945-4563.31702909454
584188839201.22837299622686.77162700382
593789835038.38799820732859.61200179267
60877111975.9237638124-3204.92376381236
616818468503.046550077-319.046550076993
625053038345.068366553512184.9316334465
634722151867.2284269123-4646.22842691231
644175641198.6804452804557.319554719601
654563341481.28749434034151.71250565973
664813852607.778993799-4469.77899379899
673948640171.5547271417-685.554727141694
683934137247.30868623232093.69131376772
694111743352.2661640744-2235.26616407436
704162939932.99911576081696.00088423921
712972235526.4441982979-5804.44419829791
72705410314.2408547113-3260.24085471126
735667662287.7597579446-5611.75975794459
743487036352.8819143467-1482.88191434673
753511740637.7685070525-5520.7685070525
763016932621.1230168432-2452.12301684317
773093632601.4141913804-1665.4141913804
783569937842.7973402739-2143.79734027387
793322829616.45037597353611.54962402645
802773329066.4756103698-1333.47561036981
813366631982.0502648531683.94973514697
823542931046.37524108644382.62475891363
832743826978.3818160336459.618183966417
8481707906.20965555718263.790344442824
856255756671.50521445055885.49478554955

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 70249 & 71014.3015814803 & -765.301581480278 \tabularnewline
14 & 39253 & 39703.6268082511 & -450.626808251065 \tabularnewline
15 & 47060 & 47620.1628926628 & -560.162892662767 \tabularnewline
16 & 41697 & 41970.8422031604 & -273.842203160399 \tabularnewline
17 & 38708 & 38645.1080777618 & 62.891922238181 \tabularnewline
18 & 49267 & 48936.740287549 & 330.259712451036 \tabularnewline
19 & 39018 & 39927.344520585 & -909.344520585044 \tabularnewline
20 & 32228 & 35294.5427433688 & -3066.54274336876 \tabularnewline
21 & 40870 & 40022.9121377387 & 847.087862261258 \tabularnewline
22 & 39383 & 35879.4146800044 & 3503.58531999561 \tabularnewline
23 & 34571 & 30989.1060235841 & 3581.89397641593 \tabularnewline
24 & 12066 & 11505.5372144255 & 560.462785574548 \tabularnewline
25 & 70938 & 71920.8782040774 & -982.878204077395 \tabularnewline
26 & 34077 & 40171.8003070546 & -6094.80030705463 \tabularnewline
27 & 45409 & 46173.4577239264 & -764.457723926447 \tabularnewline
28 & 40809 & 40686.3018647619 & 122.698135238097 \tabularnewline
29 & 37013 & 37638.4924524002 & -625.492452400198 \tabularnewline
30 & 44953 & 47459.781724517 & -2506.78172451699 \tabularnewline
31 & 37848 & 37772.9044671905 & 75.0955328094569 \tabularnewline
32 & 32745 & 33102.5281638041 & -357.528163804076 \tabularnewline
33 & 43412 & 39422.5611924731 & 3989.43880752695 \tabularnewline
34 & 34931 & 36799.3932356376 & -1868.39323563762 \tabularnewline
35 & 33008 & 30547.6848110767 & 2460.31518892329 \tabularnewline
36 & 8620 & 11062.1518262835 & -2442.15182628345 \tabularnewline
37 & 68906 & 62794.0535964349 & 6111.94640356513 \tabularnewline
38 & 39556 & 34971.503477011 & 4584.49652298904 \tabularnewline
39 & 50669 & 45231.2526889601 & 5437.74731103993 \tabularnewline
40 & 36432 & 41666.9976341778 & -5234.99763417777 \tabularnewline
41 & 40891 & 36910.6674189083 & 3980.33258109174 \tabularnewline
42 & 48428 & 47836.9858478707 & 591.014152129268 \tabularnewline
43 & 36222 & 39337.2966219577 & -3115.2966219577 \tabularnewline
44 & 33425 & 33547.8765998168 & -122.876599816846 \tabularnewline
45 & 39401 & 41074.9660311752 & -1673.96603117516 \tabularnewline
46 & 37967 & 35507.6149510525 & 2459.38504894752 \tabularnewline
47 & 34801 & 31487.5808823154 & 3313.41911768465 \tabularnewline
48 & 12657 & 10644.3845332745 & 2012.61546672553 \tabularnewline
49 & 69116 & 73910.5935551122 & -4794.59355511224 \tabularnewline
50 & 41519 & 39543.5576027162 & 1975.4423972838 \tabularnewline
51 & 51321 & 49857.8050458555 & 1463.19495414446 \tabularnewline
52 & 38529 & 42204.0291188827 & -3675.02911888271 \tabularnewline
53 & 41547 & 40002.5172208566 & 1544.48277914341 \tabularnewline
54 & 52073 & 49740.3383356219 & 2332.66166437809 \tabularnewline
55 & 38401 & 40411.0985281166 & -2010.09852811658 \tabularnewline
56 & 40898 & 35423.5362718544 & 5474.46372814564 \tabularnewline
57 & 40439 & 45002.3170290945 & -4563.31702909454 \tabularnewline
58 & 41888 & 39201.2283729962 & 2686.77162700382 \tabularnewline
59 & 37898 & 35038.3879982073 & 2859.61200179267 \tabularnewline
60 & 8771 & 11975.9237638124 & -3204.92376381236 \tabularnewline
61 & 68184 & 68503.046550077 & -319.046550076993 \tabularnewline
62 & 50530 & 38345.0683665535 & 12184.9316334465 \tabularnewline
63 & 47221 & 51867.2284269123 & -4646.22842691231 \tabularnewline
64 & 41756 & 41198.6804452804 & 557.319554719601 \tabularnewline
65 & 45633 & 41481.2874943403 & 4151.71250565973 \tabularnewline
66 & 48138 & 52607.778993799 & -4469.77899379899 \tabularnewline
67 & 39486 & 40171.5547271417 & -685.554727141694 \tabularnewline
68 & 39341 & 37247.3086862323 & 2093.69131376772 \tabularnewline
69 & 41117 & 43352.2661640744 & -2235.26616407436 \tabularnewline
70 & 41629 & 39932.9991157608 & 1696.00088423921 \tabularnewline
71 & 29722 & 35526.4441982979 & -5804.44419829791 \tabularnewline
72 & 7054 & 10314.2408547113 & -3260.24085471126 \tabularnewline
73 & 56676 & 62287.7597579446 & -5611.75975794459 \tabularnewline
74 & 34870 & 36352.8819143467 & -1482.88191434673 \tabularnewline
75 & 35117 & 40637.7685070525 & -5520.7685070525 \tabularnewline
76 & 30169 & 32621.1230168432 & -2452.12301684317 \tabularnewline
77 & 30936 & 32601.4141913804 & -1665.4141913804 \tabularnewline
78 & 35699 & 37842.7973402739 & -2143.79734027387 \tabularnewline
79 & 33228 & 29616.4503759735 & 3611.54962402645 \tabularnewline
80 & 27733 & 29066.4756103698 & -1333.47561036981 \tabularnewline
81 & 33666 & 31982.050264853 & 1683.94973514697 \tabularnewline
82 & 35429 & 31046.3752410864 & 4382.62475891363 \tabularnewline
83 & 27438 & 26978.3818160336 & 459.618183966417 \tabularnewline
84 & 8170 & 7906.20965555718 & 263.790344442824 \tabularnewline
85 & 62557 & 56671.5052144505 & 5885.49478554955 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76596&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]70249[/C][C]71014.3015814803[/C][C]-765.301581480278[/C][/ROW]
[ROW][C]14[/C][C]39253[/C][C]39703.6268082511[/C][C]-450.626808251065[/C][/ROW]
[ROW][C]15[/C][C]47060[/C][C]47620.1628926628[/C][C]-560.162892662767[/C][/ROW]
[ROW][C]16[/C][C]41697[/C][C]41970.8422031604[/C][C]-273.842203160399[/C][/ROW]
[ROW][C]17[/C][C]38708[/C][C]38645.1080777618[/C][C]62.891922238181[/C][/ROW]
[ROW][C]18[/C][C]49267[/C][C]48936.740287549[/C][C]330.259712451036[/C][/ROW]
[ROW][C]19[/C][C]39018[/C][C]39927.344520585[/C][C]-909.344520585044[/C][/ROW]
[ROW][C]20[/C][C]32228[/C][C]35294.5427433688[/C][C]-3066.54274336876[/C][/ROW]
[ROW][C]21[/C][C]40870[/C][C]40022.9121377387[/C][C]847.087862261258[/C][/ROW]
[ROW][C]22[/C][C]39383[/C][C]35879.4146800044[/C][C]3503.58531999561[/C][/ROW]
[ROW][C]23[/C][C]34571[/C][C]30989.1060235841[/C][C]3581.89397641593[/C][/ROW]
[ROW][C]24[/C][C]12066[/C][C]11505.5372144255[/C][C]560.462785574548[/C][/ROW]
[ROW][C]25[/C][C]70938[/C][C]71920.8782040774[/C][C]-982.878204077395[/C][/ROW]
[ROW][C]26[/C][C]34077[/C][C]40171.8003070546[/C][C]-6094.80030705463[/C][/ROW]
[ROW][C]27[/C][C]45409[/C][C]46173.4577239264[/C][C]-764.457723926447[/C][/ROW]
[ROW][C]28[/C][C]40809[/C][C]40686.3018647619[/C][C]122.698135238097[/C][/ROW]
[ROW][C]29[/C][C]37013[/C][C]37638.4924524002[/C][C]-625.492452400198[/C][/ROW]
[ROW][C]30[/C][C]44953[/C][C]47459.781724517[/C][C]-2506.78172451699[/C][/ROW]
[ROW][C]31[/C][C]37848[/C][C]37772.9044671905[/C][C]75.0955328094569[/C][/ROW]
[ROW][C]32[/C][C]32745[/C][C]33102.5281638041[/C][C]-357.528163804076[/C][/ROW]
[ROW][C]33[/C][C]43412[/C][C]39422.5611924731[/C][C]3989.43880752695[/C][/ROW]
[ROW][C]34[/C][C]34931[/C][C]36799.3932356376[/C][C]-1868.39323563762[/C][/ROW]
[ROW][C]35[/C][C]33008[/C][C]30547.6848110767[/C][C]2460.31518892329[/C][/ROW]
[ROW][C]36[/C][C]8620[/C][C]11062.1518262835[/C][C]-2442.15182628345[/C][/ROW]
[ROW][C]37[/C][C]68906[/C][C]62794.0535964349[/C][C]6111.94640356513[/C][/ROW]
[ROW][C]38[/C][C]39556[/C][C]34971.503477011[/C][C]4584.49652298904[/C][/ROW]
[ROW][C]39[/C][C]50669[/C][C]45231.2526889601[/C][C]5437.74731103993[/C][/ROW]
[ROW][C]40[/C][C]36432[/C][C]41666.9976341778[/C][C]-5234.99763417777[/C][/ROW]
[ROW][C]41[/C][C]40891[/C][C]36910.6674189083[/C][C]3980.33258109174[/C][/ROW]
[ROW][C]42[/C][C]48428[/C][C]47836.9858478707[/C][C]591.014152129268[/C][/ROW]
[ROW][C]43[/C][C]36222[/C][C]39337.2966219577[/C][C]-3115.2966219577[/C][/ROW]
[ROW][C]44[/C][C]33425[/C][C]33547.8765998168[/C][C]-122.876599816846[/C][/ROW]
[ROW][C]45[/C][C]39401[/C][C]41074.9660311752[/C][C]-1673.96603117516[/C][/ROW]
[ROW][C]46[/C][C]37967[/C][C]35507.6149510525[/C][C]2459.38504894752[/C][/ROW]
[ROW][C]47[/C][C]34801[/C][C]31487.5808823154[/C][C]3313.41911768465[/C][/ROW]
[ROW][C]48[/C][C]12657[/C][C]10644.3845332745[/C][C]2012.61546672553[/C][/ROW]
[ROW][C]49[/C][C]69116[/C][C]73910.5935551122[/C][C]-4794.59355511224[/C][/ROW]
[ROW][C]50[/C][C]41519[/C][C]39543.5576027162[/C][C]1975.4423972838[/C][/ROW]
[ROW][C]51[/C][C]51321[/C][C]49857.8050458555[/C][C]1463.19495414446[/C][/ROW]
[ROW][C]52[/C][C]38529[/C][C]42204.0291188827[/C][C]-3675.02911888271[/C][/ROW]
[ROW][C]53[/C][C]41547[/C][C]40002.5172208566[/C][C]1544.48277914341[/C][/ROW]
[ROW][C]54[/C][C]52073[/C][C]49740.3383356219[/C][C]2332.66166437809[/C][/ROW]
[ROW][C]55[/C][C]38401[/C][C]40411.0985281166[/C][C]-2010.09852811658[/C][/ROW]
[ROW][C]56[/C][C]40898[/C][C]35423.5362718544[/C][C]5474.46372814564[/C][/ROW]
[ROW][C]57[/C][C]40439[/C][C]45002.3170290945[/C][C]-4563.31702909454[/C][/ROW]
[ROW][C]58[/C][C]41888[/C][C]39201.2283729962[/C][C]2686.77162700382[/C][/ROW]
[ROW][C]59[/C][C]37898[/C][C]35038.3879982073[/C][C]2859.61200179267[/C][/ROW]
[ROW][C]60[/C][C]8771[/C][C]11975.9237638124[/C][C]-3204.92376381236[/C][/ROW]
[ROW][C]61[/C][C]68184[/C][C]68503.046550077[/C][C]-319.046550076993[/C][/ROW]
[ROW][C]62[/C][C]50530[/C][C]38345.0683665535[/C][C]12184.9316334465[/C][/ROW]
[ROW][C]63[/C][C]47221[/C][C]51867.2284269123[/C][C]-4646.22842691231[/C][/ROW]
[ROW][C]64[/C][C]41756[/C][C]41198.6804452804[/C][C]557.319554719601[/C][/ROW]
[ROW][C]65[/C][C]45633[/C][C]41481.2874943403[/C][C]4151.71250565973[/C][/ROW]
[ROW][C]66[/C][C]48138[/C][C]52607.778993799[/C][C]-4469.77899379899[/C][/ROW]
[ROW][C]67[/C][C]39486[/C][C]40171.5547271417[/C][C]-685.554727141694[/C][/ROW]
[ROW][C]68[/C][C]39341[/C][C]37247.3086862323[/C][C]2093.69131376772[/C][/ROW]
[ROW][C]69[/C][C]41117[/C][C]43352.2661640744[/C][C]-2235.26616407436[/C][/ROW]
[ROW][C]70[/C][C]41629[/C][C]39932.9991157608[/C][C]1696.00088423921[/C][/ROW]
[ROW][C]71[/C][C]29722[/C][C]35526.4441982979[/C][C]-5804.44419829791[/C][/ROW]
[ROW][C]72[/C][C]7054[/C][C]10314.2408547113[/C][C]-3260.24085471126[/C][/ROW]
[ROW][C]73[/C][C]56676[/C][C]62287.7597579446[/C][C]-5611.75975794459[/C][/ROW]
[ROW][C]74[/C][C]34870[/C][C]36352.8819143467[/C][C]-1482.88191434673[/C][/ROW]
[ROW][C]75[/C][C]35117[/C][C]40637.7685070525[/C][C]-5520.7685070525[/C][/ROW]
[ROW][C]76[/C][C]30169[/C][C]32621.1230168432[/C][C]-2452.12301684317[/C][/ROW]
[ROW][C]77[/C][C]30936[/C][C]32601.4141913804[/C][C]-1665.4141913804[/C][/ROW]
[ROW][C]78[/C][C]35699[/C][C]37842.7973402739[/C][C]-2143.79734027387[/C][/ROW]
[ROW][C]79[/C][C]33228[/C][C]29616.4503759735[/C][C]3611.54962402645[/C][/ROW]
[ROW][C]80[/C][C]27733[/C][C]29066.4756103698[/C][C]-1333.47561036981[/C][/ROW]
[ROW][C]81[/C][C]33666[/C][C]31982.050264853[/C][C]1683.94973514697[/C][/ROW]
[ROW][C]82[/C][C]35429[/C][C]31046.3752410864[/C][C]4382.62475891363[/C][/ROW]
[ROW][C]83[/C][C]27438[/C][C]26978.3818160336[/C][C]459.618183966417[/C][/ROW]
[ROW][C]84[/C][C]8170[/C][C]7906.20965555718[/C][C]263.790344442824[/C][/ROW]
[ROW][C]85[/C][C]62557[/C][C]56671.5052144505[/C][C]5885.49478554955[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76596&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76596&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
137024971014.3015814803-765.301581480278
143925339703.6268082511-450.626808251065
154706047620.1628926628-560.162892662767
164169741970.8422031604-273.842203160399
173870838645.108077761862.891922238181
184926748936.740287549330.259712451036
193901839927.344520585-909.344520585044
203222835294.5427433688-3066.54274336876
214087040022.9121377387847.087862261258
223938335879.41468000443503.58531999561
233457130989.10602358413581.89397641593
241206611505.5372144255560.462785574548
257093871920.8782040774-982.878204077395
263407740171.8003070546-6094.80030705463
274540946173.4577239264-764.457723926447
284080940686.3018647619122.698135238097
293701337638.4924524002-625.492452400198
304495347459.781724517-2506.78172451699
313784837772.904467190575.0955328094569
323274533102.5281638041-357.528163804076
334341239422.56119247313989.43880752695
343493136799.3932356376-1868.39323563762
353300830547.68481107672460.31518892329
36862011062.1518262835-2442.15182628345
376890662794.05359643496111.94640356513
383955634971.5034770114584.49652298904
395066945231.25268896015437.74731103993
403643241666.9976341778-5234.99763417777
414089136910.66741890833980.33258109174
424842847836.9858478707591.014152129268
433622239337.2966219577-3115.2966219577
443342533547.8765998168-122.876599816846
453940141074.9660311752-1673.96603117516
463796735507.61495105252459.38504894752
473480131487.58088231543313.41911768465
481265710644.38453327452012.61546672553
496911673910.5935551122-4794.59355511224
504151939543.55760271621975.4423972838
515132149857.80504585551463.19495414446
523852942204.0291188827-3675.02911888271
534154740002.51722085661544.48277914341
545207349740.33833562192332.66166437809
553840140411.0985281166-2010.09852811658
564089835423.53627185445474.46372814564
574043945002.3170290945-4563.31702909454
584188839201.22837299622686.77162700382
593789835038.38799820732859.61200179267
60877111975.9237638124-3204.92376381236
616818468503.046550077-319.046550076993
625053038345.068366553512184.9316334465
634722151867.2284269123-4646.22842691231
644175641198.6804452804557.319554719601
654563341481.28749434034151.71250565973
664813852607.778993799-4469.77899379899
673948640171.5547271417-685.554727141694
683934137247.30868623232093.69131376772
694111743352.2661640744-2235.26616407436
704162939932.99911576081696.00088423921
712972235526.4441982979-5804.44419829791
72705410314.2408547113-3260.24085471126
735667662287.7597579446-5611.75975794459
743487036352.8819143467-1482.88191434673
753511740637.7685070525-5520.7685070525
763016932621.1230168432-2452.12301684317
773093632601.4141913804-1665.4141913804
783569937842.7973402739-2143.79734027387
793322829616.45037597353611.54962402645
802773329066.4756103698-1333.47561036981
813366631982.0502648531683.94973514697
823542931046.37524108644382.62475891363
832743826978.3818160336459.618183966417
8481707906.20965555718263.790344442824
856255756671.50521445055885.49478554955







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8635451.150837307531927.633201859938974.6684727551
8739151.342863950335016.200055934943286.4856719656
8833260.638432154428949.685553922337571.5913103864
8934204.079011988829404.81128746539003.3467365126
9040262.59206345134559.805989137845965.3781377641
9133401.049092861228019.221643865138782.8765418572
9230451.392942887825026.389454082435876.3964316932
9334770.820896014428468.604759503341073.0370325255
9433892.344252809527401.281848799440383.4066568195
9527507.071509610421623.340310561133390.8027086598
968051.469323409654223.1482921964911879.7903546228
9758059.15754621140259.082023804875859.2330686172

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 35451.1508373075 & 31927.6332018599 & 38974.6684727551 \tabularnewline
87 & 39151.3428639503 & 35016.2000559349 & 43286.4856719656 \tabularnewline
88 & 33260.6384321544 & 28949.6855539223 & 37571.5913103864 \tabularnewline
89 & 34204.0790119888 & 29404.811287465 & 39003.3467365126 \tabularnewline
90 & 40262.592063451 & 34559.8059891378 & 45965.3781377641 \tabularnewline
91 & 33401.0490928612 & 28019.2216438651 & 38782.8765418572 \tabularnewline
92 & 30451.3929428878 & 25026.3894540824 & 35876.3964316932 \tabularnewline
93 & 34770.8208960144 & 28468.6047595033 & 41073.0370325255 \tabularnewline
94 & 33892.3442528095 & 27401.2818487994 & 40383.4066568195 \tabularnewline
95 & 27507.0715096104 & 21623.3403105611 & 33390.8027086598 \tabularnewline
96 & 8051.46932340965 & 4223.14829219649 & 11879.7903546228 \tabularnewline
97 & 58059.157546211 & 40259.0820238048 & 75859.2330686172 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76596&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]86[/C][C]35451.1508373075[/C][C]31927.6332018599[/C][C]38974.6684727551[/C][/ROW]
[ROW][C]87[/C][C]39151.3428639503[/C][C]35016.2000559349[/C][C]43286.4856719656[/C][/ROW]
[ROW][C]88[/C][C]33260.6384321544[/C][C]28949.6855539223[/C][C]37571.5913103864[/C][/ROW]
[ROW][C]89[/C][C]34204.0790119888[/C][C]29404.811287465[/C][C]39003.3467365126[/C][/ROW]
[ROW][C]90[/C][C]40262.592063451[/C][C]34559.8059891378[/C][C]45965.3781377641[/C][/ROW]
[ROW][C]91[/C][C]33401.0490928612[/C][C]28019.2216438651[/C][C]38782.8765418572[/C][/ROW]
[ROW][C]92[/C][C]30451.3929428878[/C][C]25026.3894540824[/C][C]35876.3964316932[/C][/ROW]
[ROW][C]93[/C][C]34770.8208960144[/C][C]28468.6047595033[/C][C]41073.0370325255[/C][/ROW]
[ROW][C]94[/C][C]33892.3442528095[/C][C]27401.2818487994[/C][C]40383.4066568195[/C][/ROW]
[ROW][C]95[/C][C]27507.0715096104[/C][C]21623.3403105611[/C][C]33390.8027086598[/C][/ROW]
[ROW][C]96[/C][C]8051.46932340965[/C][C]4223.14829219649[/C][C]11879.7903546228[/C][/ROW]
[ROW][C]97[/C][C]58059.157546211[/C][C]40259.0820238048[/C][C]75859.2330686172[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76596&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76596&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
8635451.150837307531927.633201859938974.6684727551
8739151.342863950335016.200055934943286.4856719656
8833260.638432154428949.685553922337571.5913103864
8934204.079011988829404.81128746539003.3467365126
9040262.59206345134559.805989137845965.3781377641
9133401.049092861228019.221643865138782.8765418572
9230451.392942887825026.389454082435876.3964316932
9334770.820896014428468.604759503341073.0370325255
9433892.344252809527401.281848799440383.4066568195
9527507.071509610421623.340310561133390.8027086598
968051.469323409654223.1482921964911879.7903546228
9758059.15754621140259.082023804875859.2330686172



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')