Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 12 Aug 2017 18:33:42 +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/12/t1502555636s38ewcgdzijpit8.htm/, Retrieved Fri, 10 May 2024 07:57:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307136, Retrieved Fri, 10 May 2024 07:57:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-12 16:33:42] [270a72b021b4bbf70c885af1fd2608d6] [Current]
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Dataseries X:
38327240.00
38147255.00
37964735.00
37587020.00
41323610.00
41125880.00
38327240.00
36466550.00
36646535.00
36646535.00
36846800.00
37206770.00
37767005.00
37767005.00
37407035.00
36466550.00
41323610.00
42063830.00
40945895.00
38327240.00
39447710.00
37767005.00
38524970.00
38887475.00
39265190.00
38327240.00
38524970.00
37206770.00
41323610.00
42624065.00
41506130.00
39447710.00
41686115.00
39265190.00
41506130.00
41323610.00
41883845.00
39825425.00
42063830.00
41883845.00
45242720.00
44484755.00
41506130.00
40005410.00
42063830.00
39265190.00
41323610.00
41686115.00
42444080.00
40765910.00
41686115.00
42246350.00
44304770.00
42624065.00
40385660.00
37964735.00
40205675.00
34045625.00
37026785.00
38704955.00
40385660.00
37964735.00
37964735.00
37964735.00
39265190.00
37407035.00
34968365.00
32927690.00
34408130.00
28628330.00
32169725.00
34228145.00
34605860.00
32547440.00
32727425.00
32169725.00
34045625.00
32727425.00
30129050.00
28250615.00
31426970.00
24529235.00
29008580.00
31049255.00
31049255.00
28628330.00
26389925.00
26209940.00
28250615.00
26389925.00
22851065.00
20412395.00
23031050.00
16873535.00
22470815.00
25449440.00
26389925.00
24331505.00
21730595.00
23591285.00
24331505.00
23771270.00
18171455.00
15573080.00
17431235.00
11833955.00
17613755.00
19672175.00
21350345.00
18551705.00
15933050.00
17431235.00
18171455.00
16691015.00
11093735.00
8655065.00
10893470.00
4735955.00
11453705.00
15573080.00




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=307136&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=307136&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307136&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
alpha0.405343002238444
beta0.0645195510983601
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405343002238444 \tabularnewline
beta & 0.0645195510983601 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307136&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]0.405343002238444[/C][/ROW]
[ROW][C]beta[/C][C]0.0645195510983601[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307136&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307136&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
alpha0.405343002238444
beta0.0645195510983601
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133776700537764927.70833342077.29166664183
143776700537660093.4254452106911.574554801
153740703537232973.995664174061.00433597
163646655036287952.7562147178597.243785299
174132361041193777.8977708129832.102229215
184206383041943048.7458002120781.254199773
194094589539148196.50853041797698.49146958
203832724038201928.4607889125311.539211079
213944771038621616.6560271826093.343972944
223776700539197823.7982026-1430818.79820263
233852497038998815.3388008-473845.338800848
243888747539249254.6112696-361779.611269556
253926519039628047.1343634-362857.134363368
263832724039459335.9160887-1132095.91608872
273852497038559227.3855781-34257.3855781406
283720677037516318.2312754-309548.231275395
294132361042166367.2197382-842757.2197382
304262406542461676.6844527162388.315547347
314150613040627621.3213577878508.67864231
323944771038236971.52813431210738.47186571
334168611539464443.43662152221671.56337851
343926519039251836.470114313353.5298857242
354150613040232639.53383541273490.46616455
364132361041329042.5125581-5432.51255814731
374188384541932009.1626975-48164.1626975015
383982542541522025.4179199-1696600.41791992
394206383041119775.1751334944054.824866593
404188384540409138.63179451474706.36820555
414524272045611433.3154091-368713.315409087
424448475546855094.4773433-2370339.47734328
434150613044512508.8169435-3006378.81694348
444000541040735357.3304489-729947.330448866
454206383041717237.8830479346592.116952069
463926519039322244.3226289-57054.3226289377
474132361040912871.4687836410738.531216353
484168611540765494.4927076920620.507292382
494244408041609089.2295168834990.77048324
504076591040490598.4046804275311.595319636
514168611542423269.9433583-737154.943358324
524224635041268091.4457848978258.5542152
534430477045081337.6987843-776567.698784299
544262406544867116.1362629-2243051.13626293
554038566042098948.7844357-1713288.78443568
563796473540134503.9214937-2169768.92149372
574020567541070145.2936405-864470.293640479
583404562537809763.2215972-3764138.22159722
593702678537944514.7947089-917729.794708893
603870495537295703.18181771409251.81818229
614038566038033065.65072742352594.34927259
623796473536983221.6517464981513.3482536
633796473538404859.7655803-440124.765580334
643796473538202714.0572132-237979.057213172
653926519040260190.5257873-995000.525787339
663740703538860404.8636992-1453369.86369915
673496836536523039.1137012-1554674.11370122
683292769034151269.6019616-1223579.60196164
693440813036071223.5311156-1663093.53111558
702862833030566507.6351257-1938177.63512571
713216972532985480.1080761-815755.108076062
723422814533615869.8827404612275.117259637
733460586034424416.4506778181443.549322225
743254744031455675.41997861091764.58002137
753272742531855986.0607129871438.9392871
763216972532119351.629904550373.3700955398
773404562533664753.5219294380871.478070557
783272742532407289.8722114320135.127788637
793012905030632136.8121455-503086.812145542
802825061528814586.3439786-563971.343978599
813142697030688876.0894452738093.910554796
822452923526005009.4620169-1475774.4620169
832900858029302088.6864275-293508.686427493
843104925531030232.085829219022.914170783
853104925531363472.4866778-314217.486677803
862862833028743546.1640889-115216.164088894
872638992528500430.4692294-2110505.46922936
882620994026965680.9540376-755740.954037584
892825061528258628.7154441-8013.71544409543
902638992526675011.1962639-285086.196263898
912285106524016768.4584541-1165703.45845409
922041239521728863.6806787-1316468.68067871
932303105023887174.5125825-856124.512582477
941687353517013675.8096414-140140.809641395
952247081521363183.15541551107631.84458446
962544944023689757.31343981759682.68656021
972638992524420560.0711081969364.92889205
982433150522794488.76483171537016.23516827
992173059522027674.5863372-297079.586337209
1002359128522074123.89368231517161.10631766
1012433150524832979.1478965-501474.147896521
1022377127022971633.8710414799636.128958572
1031817145520344834.8381978-2173379.83819778
1041557308017647892.9098946-2074812.90989463
1051743123519841799.4748036-2410564.47480361
1061183395512792569.9421095-958614.942109469
1071761375517559491.893838954263.1061610952
1081967217519826469.3515895-154294.351589486
1092135034519835720.89624861514624.10375141
1101855170517685908.7441096865796.25589044
1111593305015456492.5577721476557.442227948
1121743123516815743.952919615491.047081046
1131817145517905499.8169403265955.183059655
1141669101517045793.0514185-354778.051418472
1151109373512069796.7579804-976061.757980363
11686550659834766.96625984-1179701.96625984
1171089347012133227.0208721-1239757.02087214
11847359556393991.19544348-1658036.19544348
1191145370511433434.156351420270.8436485827
1201557308013515435.45293122057644.54706883

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 37767005 & 37764927.7083334 & 2077.29166664183 \tabularnewline
14 & 37767005 & 37660093.4254452 & 106911.574554801 \tabularnewline
15 & 37407035 & 37232973.995664 & 174061.00433597 \tabularnewline
16 & 36466550 & 36287952.7562147 & 178597.243785299 \tabularnewline
17 & 41323610 & 41193777.8977708 & 129832.102229215 \tabularnewline
18 & 42063830 & 41943048.7458002 & 120781.254199773 \tabularnewline
19 & 40945895 & 39148196.5085304 & 1797698.49146958 \tabularnewline
20 & 38327240 & 38201928.4607889 & 125311.539211079 \tabularnewline
21 & 39447710 & 38621616.6560271 & 826093.343972944 \tabularnewline
22 & 37767005 & 39197823.7982026 & -1430818.79820263 \tabularnewline
23 & 38524970 & 38998815.3388008 & -473845.338800848 \tabularnewline
24 & 38887475 & 39249254.6112696 & -361779.611269556 \tabularnewline
25 & 39265190 & 39628047.1343634 & -362857.134363368 \tabularnewline
26 & 38327240 & 39459335.9160887 & -1132095.91608872 \tabularnewline
27 & 38524970 & 38559227.3855781 & -34257.3855781406 \tabularnewline
28 & 37206770 & 37516318.2312754 & -309548.231275395 \tabularnewline
29 & 41323610 & 42166367.2197382 & -842757.2197382 \tabularnewline
30 & 42624065 & 42461676.6844527 & 162388.315547347 \tabularnewline
31 & 41506130 & 40627621.3213577 & 878508.67864231 \tabularnewline
32 & 39447710 & 38236971.5281343 & 1210738.47186571 \tabularnewline
33 & 41686115 & 39464443.4366215 & 2221671.56337851 \tabularnewline
34 & 39265190 & 39251836.4701143 & 13353.5298857242 \tabularnewline
35 & 41506130 & 40232639.5338354 & 1273490.46616455 \tabularnewline
36 & 41323610 & 41329042.5125581 & -5432.51255814731 \tabularnewline
37 & 41883845 & 41932009.1626975 & -48164.1626975015 \tabularnewline
38 & 39825425 & 41522025.4179199 & -1696600.41791992 \tabularnewline
39 & 42063830 & 41119775.1751334 & 944054.824866593 \tabularnewline
40 & 41883845 & 40409138.6317945 & 1474706.36820555 \tabularnewline
41 & 45242720 & 45611433.3154091 & -368713.315409087 \tabularnewline
42 & 44484755 & 46855094.4773433 & -2370339.47734328 \tabularnewline
43 & 41506130 & 44512508.8169435 & -3006378.81694348 \tabularnewline
44 & 40005410 & 40735357.3304489 & -729947.330448866 \tabularnewline
45 & 42063830 & 41717237.8830479 & 346592.116952069 \tabularnewline
46 & 39265190 & 39322244.3226289 & -57054.3226289377 \tabularnewline
47 & 41323610 & 40912871.4687836 & 410738.531216353 \tabularnewline
48 & 41686115 & 40765494.4927076 & 920620.507292382 \tabularnewline
49 & 42444080 & 41609089.2295168 & 834990.77048324 \tabularnewline
50 & 40765910 & 40490598.4046804 & 275311.595319636 \tabularnewline
51 & 41686115 & 42423269.9433583 & -737154.943358324 \tabularnewline
52 & 42246350 & 41268091.4457848 & 978258.5542152 \tabularnewline
53 & 44304770 & 45081337.6987843 & -776567.698784299 \tabularnewline
54 & 42624065 & 44867116.1362629 & -2243051.13626293 \tabularnewline
55 & 40385660 & 42098948.7844357 & -1713288.78443568 \tabularnewline
56 & 37964735 & 40134503.9214937 & -2169768.92149372 \tabularnewline
57 & 40205675 & 41070145.2936405 & -864470.293640479 \tabularnewline
58 & 34045625 & 37809763.2215972 & -3764138.22159722 \tabularnewline
59 & 37026785 & 37944514.7947089 & -917729.794708893 \tabularnewline
60 & 38704955 & 37295703.1818177 & 1409251.81818229 \tabularnewline
61 & 40385660 & 38033065.6507274 & 2352594.34927259 \tabularnewline
62 & 37964735 & 36983221.6517464 & 981513.3482536 \tabularnewline
63 & 37964735 & 38404859.7655803 & -440124.765580334 \tabularnewline
64 & 37964735 & 38202714.0572132 & -237979.057213172 \tabularnewline
65 & 39265190 & 40260190.5257873 & -995000.525787339 \tabularnewline
66 & 37407035 & 38860404.8636992 & -1453369.86369915 \tabularnewline
67 & 34968365 & 36523039.1137012 & -1554674.11370122 \tabularnewline
68 & 32927690 & 34151269.6019616 & -1223579.60196164 \tabularnewline
69 & 34408130 & 36071223.5311156 & -1663093.53111558 \tabularnewline
70 & 28628330 & 30566507.6351257 & -1938177.63512571 \tabularnewline
71 & 32169725 & 32985480.1080761 & -815755.108076062 \tabularnewline
72 & 34228145 & 33615869.8827404 & 612275.117259637 \tabularnewline
73 & 34605860 & 34424416.4506778 & 181443.549322225 \tabularnewline
74 & 32547440 & 31455675.4199786 & 1091764.58002137 \tabularnewline
75 & 32727425 & 31855986.0607129 & 871438.9392871 \tabularnewline
76 & 32169725 & 32119351.6299045 & 50373.3700955398 \tabularnewline
77 & 34045625 & 33664753.5219294 & 380871.478070557 \tabularnewline
78 & 32727425 & 32407289.8722114 & 320135.127788637 \tabularnewline
79 & 30129050 & 30632136.8121455 & -503086.812145542 \tabularnewline
80 & 28250615 & 28814586.3439786 & -563971.343978599 \tabularnewline
81 & 31426970 & 30688876.0894452 & 738093.910554796 \tabularnewline
82 & 24529235 & 26005009.4620169 & -1475774.4620169 \tabularnewline
83 & 29008580 & 29302088.6864275 & -293508.686427493 \tabularnewline
84 & 31049255 & 31030232.0858292 & 19022.914170783 \tabularnewline
85 & 31049255 & 31363472.4866778 & -314217.486677803 \tabularnewline
86 & 28628330 & 28743546.1640889 & -115216.164088894 \tabularnewline
87 & 26389925 & 28500430.4692294 & -2110505.46922936 \tabularnewline
88 & 26209940 & 26965680.9540376 & -755740.954037584 \tabularnewline
89 & 28250615 & 28258628.7154441 & -8013.71544409543 \tabularnewline
90 & 26389925 & 26675011.1962639 & -285086.196263898 \tabularnewline
91 & 22851065 & 24016768.4584541 & -1165703.45845409 \tabularnewline
92 & 20412395 & 21728863.6806787 & -1316468.68067871 \tabularnewline
93 & 23031050 & 23887174.5125825 & -856124.512582477 \tabularnewline
94 & 16873535 & 17013675.8096414 & -140140.809641395 \tabularnewline
95 & 22470815 & 21363183.1554155 & 1107631.84458446 \tabularnewline
96 & 25449440 & 23689757.3134398 & 1759682.68656021 \tabularnewline
97 & 26389925 & 24420560.071108 & 1969364.92889205 \tabularnewline
98 & 24331505 & 22794488.7648317 & 1537016.23516827 \tabularnewline
99 & 21730595 & 22027674.5863372 & -297079.586337209 \tabularnewline
100 & 23591285 & 22074123.8936823 & 1517161.10631766 \tabularnewline
101 & 24331505 & 24832979.1478965 & -501474.147896521 \tabularnewline
102 & 23771270 & 22971633.8710414 & 799636.128958572 \tabularnewline
103 & 18171455 & 20344834.8381978 & -2173379.83819778 \tabularnewline
104 & 15573080 & 17647892.9098946 & -2074812.90989463 \tabularnewline
105 & 17431235 & 19841799.4748036 & -2410564.47480361 \tabularnewline
106 & 11833955 & 12792569.9421095 & -958614.942109469 \tabularnewline
107 & 17613755 & 17559491.8938389 & 54263.1061610952 \tabularnewline
108 & 19672175 & 19826469.3515895 & -154294.351589486 \tabularnewline
109 & 21350345 & 19835720.8962486 & 1514624.10375141 \tabularnewline
110 & 18551705 & 17685908.7441096 & 865796.25589044 \tabularnewline
111 & 15933050 & 15456492.5577721 & 476557.442227948 \tabularnewline
112 & 17431235 & 16815743.952919 & 615491.047081046 \tabularnewline
113 & 18171455 & 17905499.8169403 & 265955.183059655 \tabularnewline
114 & 16691015 & 17045793.0514185 & -354778.051418472 \tabularnewline
115 & 11093735 & 12069796.7579804 & -976061.757980363 \tabularnewline
116 & 8655065 & 9834766.96625984 & -1179701.96625984 \tabularnewline
117 & 10893470 & 12133227.0208721 & -1239757.02087214 \tabularnewline
118 & 4735955 & 6393991.19544348 & -1658036.19544348 \tabularnewline
119 & 11453705 & 11433434.1563514 & 20270.8436485827 \tabularnewline
120 & 15573080 & 13515435.4529312 & 2057644.54706883 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307136&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]37767005[/C][C]37764927.7083334[/C][C]2077.29166664183[/C][/ROW]
[ROW][C]14[/C][C]37767005[/C][C]37660093.4254452[/C][C]106911.574554801[/C][/ROW]
[ROW][C]15[/C][C]37407035[/C][C]37232973.995664[/C][C]174061.00433597[/C][/ROW]
[ROW][C]16[/C][C]36466550[/C][C]36287952.7562147[/C][C]178597.243785299[/C][/ROW]
[ROW][C]17[/C][C]41323610[/C][C]41193777.8977708[/C][C]129832.102229215[/C][/ROW]
[ROW][C]18[/C][C]42063830[/C][C]41943048.7458002[/C][C]120781.254199773[/C][/ROW]
[ROW][C]19[/C][C]40945895[/C][C]39148196.5085304[/C][C]1797698.49146958[/C][/ROW]
[ROW][C]20[/C][C]38327240[/C][C]38201928.4607889[/C][C]125311.539211079[/C][/ROW]
[ROW][C]21[/C][C]39447710[/C][C]38621616.6560271[/C][C]826093.343972944[/C][/ROW]
[ROW][C]22[/C][C]37767005[/C][C]39197823.7982026[/C][C]-1430818.79820263[/C][/ROW]
[ROW][C]23[/C][C]38524970[/C][C]38998815.3388008[/C][C]-473845.338800848[/C][/ROW]
[ROW][C]24[/C][C]38887475[/C][C]39249254.6112696[/C][C]-361779.611269556[/C][/ROW]
[ROW][C]25[/C][C]39265190[/C][C]39628047.1343634[/C][C]-362857.134363368[/C][/ROW]
[ROW][C]26[/C][C]38327240[/C][C]39459335.9160887[/C][C]-1132095.91608872[/C][/ROW]
[ROW][C]27[/C][C]38524970[/C][C]38559227.3855781[/C][C]-34257.3855781406[/C][/ROW]
[ROW][C]28[/C][C]37206770[/C][C]37516318.2312754[/C][C]-309548.231275395[/C][/ROW]
[ROW][C]29[/C][C]41323610[/C][C]42166367.2197382[/C][C]-842757.2197382[/C][/ROW]
[ROW][C]30[/C][C]42624065[/C][C]42461676.6844527[/C][C]162388.315547347[/C][/ROW]
[ROW][C]31[/C][C]41506130[/C][C]40627621.3213577[/C][C]878508.67864231[/C][/ROW]
[ROW][C]32[/C][C]39447710[/C][C]38236971.5281343[/C][C]1210738.47186571[/C][/ROW]
[ROW][C]33[/C][C]41686115[/C][C]39464443.4366215[/C][C]2221671.56337851[/C][/ROW]
[ROW][C]34[/C][C]39265190[/C][C]39251836.4701143[/C][C]13353.5298857242[/C][/ROW]
[ROW][C]35[/C][C]41506130[/C][C]40232639.5338354[/C][C]1273490.46616455[/C][/ROW]
[ROW][C]36[/C][C]41323610[/C][C]41329042.5125581[/C][C]-5432.51255814731[/C][/ROW]
[ROW][C]37[/C][C]41883845[/C][C]41932009.1626975[/C][C]-48164.1626975015[/C][/ROW]
[ROW][C]38[/C][C]39825425[/C][C]41522025.4179199[/C][C]-1696600.41791992[/C][/ROW]
[ROW][C]39[/C][C]42063830[/C][C]41119775.1751334[/C][C]944054.824866593[/C][/ROW]
[ROW][C]40[/C][C]41883845[/C][C]40409138.6317945[/C][C]1474706.36820555[/C][/ROW]
[ROW][C]41[/C][C]45242720[/C][C]45611433.3154091[/C][C]-368713.315409087[/C][/ROW]
[ROW][C]42[/C][C]44484755[/C][C]46855094.4773433[/C][C]-2370339.47734328[/C][/ROW]
[ROW][C]43[/C][C]41506130[/C][C]44512508.8169435[/C][C]-3006378.81694348[/C][/ROW]
[ROW][C]44[/C][C]40005410[/C][C]40735357.3304489[/C][C]-729947.330448866[/C][/ROW]
[ROW][C]45[/C][C]42063830[/C][C]41717237.8830479[/C][C]346592.116952069[/C][/ROW]
[ROW][C]46[/C][C]39265190[/C][C]39322244.3226289[/C][C]-57054.3226289377[/C][/ROW]
[ROW][C]47[/C][C]41323610[/C][C]40912871.4687836[/C][C]410738.531216353[/C][/ROW]
[ROW][C]48[/C][C]41686115[/C][C]40765494.4927076[/C][C]920620.507292382[/C][/ROW]
[ROW][C]49[/C][C]42444080[/C][C]41609089.2295168[/C][C]834990.77048324[/C][/ROW]
[ROW][C]50[/C][C]40765910[/C][C]40490598.4046804[/C][C]275311.595319636[/C][/ROW]
[ROW][C]51[/C][C]41686115[/C][C]42423269.9433583[/C][C]-737154.943358324[/C][/ROW]
[ROW][C]52[/C][C]42246350[/C][C]41268091.4457848[/C][C]978258.5542152[/C][/ROW]
[ROW][C]53[/C][C]44304770[/C][C]45081337.6987843[/C][C]-776567.698784299[/C][/ROW]
[ROW][C]54[/C][C]42624065[/C][C]44867116.1362629[/C][C]-2243051.13626293[/C][/ROW]
[ROW][C]55[/C][C]40385660[/C][C]42098948.7844357[/C][C]-1713288.78443568[/C][/ROW]
[ROW][C]56[/C][C]37964735[/C][C]40134503.9214937[/C][C]-2169768.92149372[/C][/ROW]
[ROW][C]57[/C][C]40205675[/C][C]41070145.2936405[/C][C]-864470.293640479[/C][/ROW]
[ROW][C]58[/C][C]34045625[/C][C]37809763.2215972[/C][C]-3764138.22159722[/C][/ROW]
[ROW][C]59[/C][C]37026785[/C][C]37944514.7947089[/C][C]-917729.794708893[/C][/ROW]
[ROW][C]60[/C][C]38704955[/C][C]37295703.1818177[/C][C]1409251.81818229[/C][/ROW]
[ROW][C]61[/C][C]40385660[/C][C]38033065.6507274[/C][C]2352594.34927259[/C][/ROW]
[ROW][C]62[/C][C]37964735[/C][C]36983221.6517464[/C][C]981513.3482536[/C][/ROW]
[ROW][C]63[/C][C]37964735[/C][C]38404859.7655803[/C][C]-440124.765580334[/C][/ROW]
[ROW][C]64[/C][C]37964735[/C][C]38202714.0572132[/C][C]-237979.057213172[/C][/ROW]
[ROW][C]65[/C][C]39265190[/C][C]40260190.5257873[/C][C]-995000.525787339[/C][/ROW]
[ROW][C]66[/C][C]37407035[/C][C]38860404.8636992[/C][C]-1453369.86369915[/C][/ROW]
[ROW][C]67[/C][C]34968365[/C][C]36523039.1137012[/C][C]-1554674.11370122[/C][/ROW]
[ROW][C]68[/C][C]32927690[/C][C]34151269.6019616[/C][C]-1223579.60196164[/C][/ROW]
[ROW][C]69[/C][C]34408130[/C][C]36071223.5311156[/C][C]-1663093.53111558[/C][/ROW]
[ROW][C]70[/C][C]28628330[/C][C]30566507.6351257[/C][C]-1938177.63512571[/C][/ROW]
[ROW][C]71[/C][C]32169725[/C][C]32985480.1080761[/C][C]-815755.108076062[/C][/ROW]
[ROW][C]72[/C][C]34228145[/C][C]33615869.8827404[/C][C]612275.117259637[/C][/ROW]
[ROW][C]73[/C][C]34605860[/C][C]34424416.4506778[/C][C]181443.549322225[/C][/ROW]
[ROW][C]74[/C][C]32547440[/C][C]31455675.4199786[/C][C]1091764.58002137[/C][/ROW]
[ROW][C]75[/C][C]32727425[/C][C]31855986.0607129[/C][C]871438.9392871[/C][/ROW]
[ROW][C]76[/C][C]32169725[/C][C]32119351.6299045[/C][C]50373.3700955398[/C][/ROW]
[ROW][C]77[/C][C]34045625[/C][C]33664753.5219294[/C][C]380871.478070557[/C][/ROW]
[ROW][C]78[/C][C]32727425[/C][C]32407289.8722114[/C][C]320135.127788637[/C][/ROW]
[ROW][C]79[/C][C]30129050[/C][C]30632136.8121455[/C][C]-503086.812145542[/C][/ROW]
[ROW][C]80[/C][C]28250615[/C][C]28814586.3439786[/C][C]-563971.343978599[/C][/ROW]
[ROW][C]81[/C][C]31426970[/C][C]30688876.0894452[/C][C]738093.910554796[/C][/ROW]
[ROW][C]82[/C][C]24529235[/C][C]26005009.4620169[/C][C]-1475774.4620169[/C][/ROW]
[ROW][C]83[/C][C]29008580[/C][C]29302088.6864275[/C][C]-293508.686427493[/C][/ROW]
[ROW][C]84[/C][C]31049255[/C][C]31030232.0858292[/C][C]19022.914170783[/C][/ROW]
[ROW][C]85[/C][C]31049255[/C][C]31363472.4866778[/C][C]-314217.486677803[/C][/ROW]
[ROW][C]86[/C][C]28628330[/C][C]28743546.1640889[/C][C]-115216.164088894[/C][/ROW]
[ROW][C]87[/C][C]26389925[/C][C]28500430.4692294[/C][C]-2110505.46922936[/C][/ROW]
[ROW][C]88[/C][C]26209940[/C][C]26965680.9540376[/C][C]-755740.954037584[/C][/ROW]
[ROW][C]89[/C][C]28250615[/C][C]28258628.7154441[/C][C]-8013.71544409543[/C][/ROW]
[ROW][C]90[/C][C]26389925[/C][C]26675011.1962639[/C][C]-285086.196263898[/C][/ROW]
[ROW][C]91[/C][C]22851065[/C][C]24016768.4584541[/C][C]-1165703.45845409[/C][/ROW]
[ROW][C]92[/C][C]20412395[/C][C]21728863.6806787[/C][C]-1316468.68067871[/C][/ROW]
[ROW][C]93[/C][C]23031050[/C][C]23887174.5125825[/C][C]-856124.512582477[/C][/ROW]
[ROW][C]94[/C][C]16873535[/C][C]17013675.8096414[/C][C]-140140.809641395[/C][/ROW]
[ROW][C]95[/C][C]22470815[/C][C]21363183.1554155[/C][C]1107631.84458446[/C][/ROW]
[ROW][C]96[/C][C]25449440[/C][C]23689757.3134398[/C][C]1759682.68656021[/C][/ROW]
[ROW][C]97[/C][C]26389925[/C][C]24420560.071108[/C][C]1969364.92889205[/C][/ROW]
[ROW][C]98[/C][C]24331505[/C][C]22794488.7648317[/C][C]1537016.23516827[/C][/ROW]
[ROW][C]99[/C][C]21730595[/C][C]22027674.5863372[/C][C]-297079.586337209[/C][/ROW]
[ROW][C]100[/C][C]23591285[/C][C]22074123.8936823[/C][C]1517161.10631766[/C][/ROW]
[ROW][C]101[/C][C]24331505[/C][C]24832979.1478965[/C][C]-501474.147896521[/C][/ROW]
[ROW][C]102[/C][C]23771270[/C][C]22971633.8710414[/C][C]799636.128958572[/C][/ROW]
[ROW][C]103[/C][C]18171455[/C][C]20344834.8381978[/C][C]-2173379.83819778[/C][/ROW]
[ROW][C]104[/C][C]15573080[/C][C]17647892.9098946[/C][C]-2074812.90989463[/C][/ROW]
[ROW][C]105[/C][C]17431235[/C][C]19841799.4748036[/C][C]-2410564.47480361[/C][/ROW]
[ROW][C]106[/C][C]11833955[/C][C]12792569.9421095[/C][C]-958614.942109469[/C][/ROW]
[ROW][C]107[/C][C]17613755[/C][C]17559491.8938389[/C][C]54263.1061610952[/C][/ROW]
[ROW][C]108[/C][C]19672175[/C][C]19826469.3515895[/C][C]-154294.351589486[/C][/ROW]
[ROW][C]109[/C][C]21350345[/C][C]19835720.8962486[/C][C]1514624.10375141[/C][/ROW]
[ROW][C]110[/C][C]18551705[/C][C]17685908.7441096[/C][C]865796.25589044[/C][/ROW]
[ROW][C]111[/C][C]15933050[/C][C]15456492.5577721[/C][C]476557.442227948[/C][/ROW]
[ROW][C]112[/C][C]17431235[/C][C]16815743.952919[/C][C]615491.047081046[/C][/ROW]
[ROW][C]113[/C][C]18171455[/C][C]17905499.8169403[/C][C]265955.183059655[/C][/ROW]
[ROW][C]114[/C][C]16691015[/C][C]17045793.0514185[/C][C]-354778.051418472[/C][/ROW]
[ROW][C]115[/C][C]11093735[/C][C]12069796.7579804[/C][C]-976061.757980363[/C][/ROW]
[ROW][C]116[/C][C]8655065[/C][C]9834766.96625984[/C][C]-1179701.96625984[/C][/ROW]
[ROW][C]117[/C][C]10893470[/C][C]12133227.0208721[/C][C]-1239757.02087214[/C][/ROW]
[ROW][C]118[/C][C]4735955[/C][C]6393991.19544348[/C][C]-1658036.19544348[/C][/ROW]
[ROW][C]119[/C][C]11453705[/C][C]11433434.1563514[/C][C]20270.8436485827[/C][/ROW]
[ROW][C]120[/C][C]15573080[/C][C]13515435.4529312[/C][C]2057644.54706883[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307136&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307136&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
133776700537764927.70833342077.29166664183
143776700537660093.4254452106911.574554801
153740703537232973.995664174061.00433597
163646655036287952.7562147178597.243785299
174132361041193777.8977708129832.102229215
184206383041943048.7458002120781.254199773
194094589539148196.50853041797698.49146958
203832724038201928.4607889125311.539211079
213944771038621616.6560271826093.343972944
223776700539197823.7982026-1430818.79820263
233852497038998815.3388008-473845.338800848
243888747539249254.6112696-361779.611269556
253926519039628047.1343634-362857.134363368
263832724039459335.9160887-1132095.91608872
273852497038559227.3855781-34257.3855781406
283720677037516318.2312754-309548.231275395
294132361042166367.2197382-842757.2197382
304262406542461676.6844527162388.315547347
314150613040627621.3213577878508.67864231
323944771038236971.52813431210738.47186571
334168611539464443.43662152221671.56337851
343926519039251836.470114313353.5298857242
354150613040232639.53383541273490.46616455
364132361041329042.5125581-5432.51255814731
374188384541932009.1626975-48164.1626975015
383982542541522025.4179199-1696600.41791992
394206383041119775.1751334944054.824866593
404188384540409138.63179451474706.36820555
414524272045611433.3154091-368713.315409087
424448475546855094.4773433-2370339.47734328
434150613044512508.8169435-3006378.81694348
444000541040735357.3304489-729947.330448866
454206383041717237.8830479346592.116952069
463926519039322244.3226289-57054.3226289377
474132361040912871.4687836410738.531216353
484168611540765494.4927076920620.507292382
494244408041609089.2295168834990.77048324
504076591040490598.4046804275311.595319636
514168611542423269.9433583-737154.943358324
524224635041268091.4457848978258.5542152
534430477045081337.6987843-776567.698784299
544262406544867116.1362629-2243051.13626293
554038566042098948.7844357-1713288.78443568
563796473540134503.9214937-2169768.92149372
574020567541070145.2936405-864470.293640479
583404562537809763.2215972-3764138.22159722
593702678537944514.7947089-917729.794708893
603870495537295703.18181771409251.81818229
614038566038033065.65072742352594.34927259
623796473536983221.6517464981513.3482536
633796473538404859.7655803-440124.765580334
643796473538202714.0572132-237979.057213172
653926519040260190.5257873-995000.525787339
663740703538860404.8636992-1453369.86369915
673496836536523039.1137012-1554674.11370122
683292769034151269.6019616-1223579.60196164
693440813036071223.5311156-1663093.53111558
702862833030566507.6351257-1938177.63512571
713216972532985480.1080761-815755.108076062
723422814533615869.8827404612275.117259637
733460586034424416.4506778181443.549322225
743254744031455675.41997861091764.58002137
753272742531855986.0607129871438.9392871
763216972532119351.629904550373.3700955398
773404562533664753.5219294380871.478070557
783272742532407289.8722114320135.127788637
793012905030632136.8121455-503086.812145542
802825061528814586.3439786-563971.343978599
813142697030688876.0894452738093.910554796
822452923526005009.4620169-1475774.4620169
832900858029302088.6864275-293508.686427493
843104925531030232.085829219022.914170783
853104925531363472.4866778-314217.486677803
862862833028743546.1640889-115216.164088894
872638992528500430.4692294-2110505.46922936
882620994026965680.9540376-755740.954037584
892825061528258628.7154441-8013.71544409543
902638992526675011.1962639-285086.196263898
912285106524016768.4584541-1165703.45845409
922041239521728863.6806787-1316468.68067871
932303105023887174.5125825-856124.512582477
941687353517013675.8096414-140140.809641395
952247081521363183.15541551107631.84458446
962544944023689757.31343981759682.68656021
972638992524420560.0711081969364.92889205
982433150522794488.76483171537016.23516827
992173059522027674.5863372-297079.586337209
1002359128522074123.89368231517161.10631766
1012433150524832979.1478965-501474.147896521
1022377127022971633.8710414799636.128958572
1031817145520344834.8381978-2173379.83819778
1041557308017647892.9098946-2074812.90989463
1051743123519841799.4748036-2410564.47480361
1061183395512792569.9421095-958614.942109469
1071761375517559491.893838954263.1061610952
1081967217519826469.3515895-154294.351589486
1092135034519835720.89624861514624.10375141
1101855170517685908.7441096865796.25589044
1111593305015456492.5577721476557.442227948
1121743123516815743.952919615491.047081046
1131817145517905499.8169403265955.183059655
1141669101517045793.0514185-354778.051418472
1151109373512069796.7579804-976061.757980363
11686550659834766.96625984-1179701.96625984
1171089347012133227.0208721-1239757.02087214
11847359556393991.19544348-1658036.19544348
1191145370511433434.156351420270.8436485827
1201557308013515435.45293122057644.54706883







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12115424385.345384313110002.627740517738768.0630281
12212245859.96697569725213.0483432214766506.885608
1239382452.03927216648314.5119143112116589.5666299
12410567105.15542327612577.1404915713521633.1703547
12511119378.52859877937842.5405984114300914.5165989
1269695646.36879096280731.8147671313110560.9228147
1274416185.56205527761739.867692748070631.25641781
1282403405.39122889-1496529.74223516303340.52469289
1295122895.32948024971687.0011942549274103.65776622
130-351565.390201139-4759672.692531544056541.91212926
1316412310.748305171741822.6266725411082798.8699378
1329751446.578962894813227.7160335414689665.4418922

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 15424385.3453843 & 13110002.6277405 & 17738768.0630281 \tabularnewline
122 & 12245859.9669756 & 9725213.04834322 & 14766506.885608 \tabularnewline
123 & 9382452.0392721 & 6648314.51191431 & 12116589.5666299 \tabularnewline
124 & 10567105.1554232 & 7612577.14049157 & 13521633.1703547 \tabularnewline
125 & 11119378.5285987 & 7937842.54059841 & 14300914.5165989 \tabularnewline
126 & 9695646.3687909 & 6280731.81476713 & 13110560.9228147 \tabularnewline
127 & 4416185.56205527 & 761739.86769274 & 8070631.25641781 \tabularnewline
128 & 2403405.39122889 & -1496529.7422351 & 6303340.52469289 \tabularnewline
129 & 5122895.32948024 & 971687.001194254 & 9274103.65776622 \tabularnewline
130 & -351565.390201139 & -4759672.69253154 & 4056541.91212926 \tabularnewline
131 & 6412310.74830517 & 1741822.62667254 & 11082798.8699378 \tabularnewline
132 & 9751446.57896289 & 4813227.71603354 & 14689665.4418922 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307136&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]121[/C][C]15424385.3453843[/C][C]13110002.6277405[/C][C]17738768.0630281[/C][/ROW]
[ROW][C]122[/C][C]12245859.9669756[/C][C]9725213.04834322[/C][C]14766506.885608[/C][/ROW]
[ROW][C]123[/C][C]9382452.0392721[/C][C]6648314.51191431[/C][C]12116589.5666299[/C][/ROW]
[ROW][C]124[/C][C]10567105.1554232[/C][C]7612577.14049157[/C][C]13521633.1703547[/C][/ROW]
[ROW][C]125[/C][C]11119378.5285987[/C][C]7937842.54059841[/C][C]14300914.5165989[/C][/ROW]
[ROW][C]126[/C][C]9695646.3687909[/C][C]6280731.81476713[/C][C]13110560.9228147[/C][/ROW]
[ROW][C]127[/C][C]4416185.56205527[/C][C]761739.86769274[/C][C]8070631.25641781[/C][/ROW]
[ROW][C]128[/C][C]2403405.39122889[/C][C]-1496529.7422351[/C][C]6303340.52469289[/C][/ROW]
[ROW][C]129[/C][C]5122895.32948024[/C][C]971687.001194254[/C][C]9274103.65776622[/C][/ROW]
[ROW][C]130[/C][C]-351565.390201139[/C][C]-4759672.69253154[/C][C]4056541.91212926[/C][/ROW]
[ROW][C]131[/C][C]6412310.74830517[/C][C]1741822.62667254[/C][C]11082798.8699378[/C][/ROW]
[ROW][C]132[/C][C]9751446.57896289[/C][C]4813227.71603354[/C][C]14689665.4418922[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307136&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307136&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
12115424385.345384313110002.627740517738768.0630281
12212245859.96697569725213.0483432214766506.885608
1239382452.03927216648314.5119143112116589.5666299
12410567105.15542327612577.1404915713521633.1703547
12511119378.52859877937842.5405984114300914.5165989
1269695646.36879096280731.8147671313110560.9228147
1274416185.56205527761739.867692748070631.25641781
1282403405.39122889-1496529.74223516303340.52469289
1295122895.32948024971687.0011942549274103.65776622
130-351565.390201139-4759672.692531544056541.91212926
1316412310.748305171741822.6266725411082798.8699378
1329751446.578962894813227.7160335414689665.4418922



Parameters (Session):
par1 = 48481212additiveadditive12 ; par2 = 111212Triple ; par3 = 01additive ; par4 = 0112 ; par5 = 1212 ; par6 = White NoiseWhite Noise ; par7 = 0.950.95 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')