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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 Dec 2016 11:37:46 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/07/t1481107101oac0l3kcppbw7mt.htm/, Retrieved Tue, 07 May 2024 08:39:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297988, Retrieved Tue, 07 May 2024 08:39:21 +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] [] [2016-12-07 10:37:46] [94ac3c9a028ddd47e8862e80eac9f626] [Current]
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Dataseries X:
3500
3600
3750
3800
4100
3900
3650
3800
4050
4250
4450
4200
4050
4050
4200
4450
4400
4450
4200
4050
4500
4650
4850
4700
4350
4500
4700
4800
4700
4600
4400
4300
4750
4800
5000
4900
4400
4650
4650
4900
4900
5000
4550
4500
5100
5000
5350
5150
4500
4600
4900
5050
5000
5350
4650
4650
5200
5300
5700
5250
4900
5200
5250
5450
5750
5450
5100
4950
5550
5800
6050
5650
5500
5600
5550
5900
5900
5850
5350
5150
5850
6000
6250
5800
5550
5700
5850
6150
6050
6050
5550
5100
5900
6050
6150
5700
5200
5400
5550
5750
5700
5650
5400
4950
5900
6050
6350
6350
5500
5800
6100
6350
6400
6850




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297988&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=297988&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297988&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.17091605305629
beta0.271771008090619
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.17091605305629 \tabularnewline
beta & 0.271771008090619 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297988&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]0.17091605305629[/C][/ROW]
[ROW][C]beta[/C][C]0.271771008090619[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297988&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297988&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
alpha0.17091605305629
beta0.271771008090619
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33750370050
438003810.86830405471-10.8683040547135
541003910.8284047961189.171595203901
639004053.76556147375-153.765561473755
736504130.94683824399-480.946838243987
838004129.86758843352-329.867588433524
940504139.28784896781-89.2878489678133
1042504185.6796259288964.3203740711133
1144504261.31319726778188.68680273222
1242004366.96749500344-166.967495003444
1340504404.07911909328-354.079119093281
1440504392.76337790319-342.763377903186
1542004367.46031002071-167.460310020713
1644504364.3408144936685.6591855063389
1744004408.46237566217-8.46237566217224
1844504436.1039735014913.8960264985108
1942004468.21245201123-268.212452011227
2040504439.64558692431-389.64558692431
2145004372.22480127029127.775198729712
2246504399.17469563309250.82530436691
2348504458.80667080004391.193329199962
2447004560.60073585637139.399264143633
2543504625.83425285821-275.834252858214
2645004607.28518725833-107.285187258325
2747004612.5604627408987.4395372591143
2848004655.17888852775144.821111472246
2947004714.33169118566-14.3316911856646
3046004745.61701752303-145.617017523033
3144004747.69965951186-347.699659511859
3243004699.09247500765-399.092475007646
3347504623.16357666959126.836423330407
3448004643.01592524366156.984074756344
3550004675.31290608231324.687093917693
3649004751.35474965768148.645250342315
3744004804.21279220252-404.212792202518
3846504743.80282468405-93.8028246840468
3946504732.08975980655-82.0897598065476
4049004718.56557410246181.434425897542
4149004758.50953627378141.49046372622
4250004798.19867009454201.80132990546
4345504857.56957655127-307.569576551271
4445004815.59420268028-315.594202680277
4551004757.58793182094342.412068179061
4650004827.95054583063172.049454169373
4753504877.18715623551472.812843764488
4851504999.7912279434150.208772056598
4945005074.23428668867-574.23428668867
5046004998.18519845211-398.185198452114
5149004933.7300118887-33.7300118886997
5250504929.99930733065120.000692669353
5350004958.1176835682941.8823164317128
5453504974.82981004077375.170189959227
5546505065.93285023073-415.932850230725
5646505002.50358867545-352.503588675446
5752004933.54160457601266.458395423992
5853004982.74715972913317.252840270866
5957005055.37070423838644.629295761617
6052505213.891189245936.1088107541018
6149005270.08301002398-370.083010023976
6252005239.65976181893-39.6597618189253
6352505263.86895398665-13.8689539866509
6454505291.84199593266158.158004067336
6557505356.5636502919393.436349708096
6654505479.77328033278-29.7732803327772
6751005529.26662108541-429.266621085411
6849505490.54069022915-540.540690229149
6955505407.68810445051142.311895549487
7058005448.15637899086351.843621009144
7160505540.7801350977509.219864902305
7256505683.95529465778-33.9552946577842
7355005732.71587543875-232.715875438751
7456005736.69542331045-136.695423310446
7555505750.73690162716-200.736901627158
7659005744.50842852925155.49157147075
7759005806.3877078939993.6122921060087
7858505862.03911865677-12.0391186567667
7953505899.07378989298-549.07378989298
8051505818.81612183167-668.81612183167
8158505687.02603940031162.97396059969
8260005704.9723798688295.027620131199
8362505759.19285184313490.807148156871
8458005869.67319380995-69.6731938099529
8555505881.1221261062-331.122126106199
8657005832.50460677696-132.504606776963
8758505811.6791672193638.3208327806406
8861505821.83054130965328.169458690353
8960505896.76517908159153.234820918414
9060505948.91844075077101.081559249232
9155505996.85311404269-446.853114042692
9251005930.38061596673-830.380615966732
9359005759.78590812953140.214091870472
9460505761.59436537189288.405634628114
9561505802.12758601349347.872413986513
9657005868.98331725431-168.983317254309
9752005839.65082708751-639.650827087512
9854005700.16190498546-300.161904985462
9955505604.75456060292-54.7545606029207
10057505548.74792003806201.252079961942
10157005545.84508879167154.154911208326
10256505542.05309529962107.946904700385
10354005535.37754846557-135.377548465566
10449505480.82565556237-530.825655562374
10559005334.02846642146565.971533578536
10660505400.98091745517649.019082544828
10763505512.27448235559837.725517644413
10863505694.73338011226655.266619887742
10955005876.44427608549-376.444276085494
11058005864.33337064491-64.3333706449093
11161005902.57894240782197.42105759218
11263505994.73276157546355.267238424535
11364006130.36720014678269.63279985322
11468506263.88978958493586.110210415065

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3750 & 3700 & 50 \tabularnewline
4 & 3800 & 3810.86830405471 & -10.8683040547135 \tabularnewline
5 & 4100 & 3910.8284047961 & 189.171595203901 \tabularnewline
6 & 3900 & 4053.76556147375 & -153.765561473755 \tabularnewline
7 & 3650 & 4130.94683824399 & -480.946838243987 \tabularnewline
8 & 3800 & 4129.86758843352 & -329.867588433524 \tabularnewline
9 & 4050 & 4139.28784896781 & -89.2878489678133 \tabularnewline
10 & 4250 & 4185.67962592889 & 64.3203740711133 \tabularnewline
11 & 4450 & 4261.31319726778 & 188.68680273222 \tabularnewline
12 & 4200 & 4366.96749500344 & -166.967495003444 \tabularnewline
13 & 4050 & 4404.07911909328 & -354.079119093281 \tabularnewline
14 & 4050 & 4392.76337790319 & -342.763377903186 \tabularnewline
15 & 4200 & 4367.46031002071 & -167.460310020713 \tabularnewline
16 & 4450 & 4364.34081449366 & 85.6591855063389 \tabularnewline
17 & 4400 & 4408.46237566217 & -8.46237566217224 \tabularnewline
18 & 4450 & 4436.10397350149 & 13.8960264985108 \tabularnewline
19 & 4200 & 4468.21245201123 & -268.212452011227 \tabularnewline
20 & 4050 & 4439.64558692431 & -389.64558692431 \tabularnewline
21 & 4500 & 4372.22480127029 & 127.775198729712 \tabularnewline
22 & 4650 & 4399.17469563309 & 250.82530436691 \tabularnewline
23 & 4850 & 4458.80667080004 & 391.193329199962 \tabularnewline
24 & 4700 & 4560.60073585637 & 139.399264143633 \tabularnewline
25 & 4350 & 4625.83425285821 & -275.834252858214 \tabularnewline
26 & 4500 & 4607.28518725833 & -107.285187258325 \tabularnewline
27 & 4700 & 4612.56046274089 & 87.4395372591143 \tabularnewline
28 & 4800 & 4655.17888852775 & 144.821111472246 \tabularnewline
29 & 4700 & 4714.33169118566 & -14.3316911856646 \tabularnewline
30 & 4600 & 4745.61701752303 & -145.617017523033 \tabularnewline
31 & 4400 & 4747.69965951186 & -347.699659511859 \tabularnewline
32 & 4300 & 4699.09247500765 & -399.092475007646 \tabularnewline
33 & 4750 & 4623.16357666959 & 126.836423330407 \tabularnewline
34 & 4800 & 4643.01592524366 & 156.984074756344 \tabularnewline
35 & 5000 & 4675.31290608231 & 324.687093917693 \tabularnewline
36 & 4900 & 4751.35474965768 & 148.645250342315 \tabularnewline
37 & 4400 & 4804.21279220252 & -404.212792202518 \tabularnewline
38 & 4650 & 4743.80282468405 & -93.8028246840468 \tabularnewline
39 & 4650 & 4732.08975980655 & -82.0897598065476 \tabularnewline
40 & 4900 & 4718.56557410246 & 181.434425897542 \tabularnewline
41 & 4900 & 4758.50953627378 & 141.49046372622 \tabularnewline
42 & 5000 & 4798.19867009454 & 201.80132990546 \tabularnewline
43 & 4550 & 4857.56957655127 & -307.569576551271 \tabularnewline
44 & 4500 & 4815.59420268028 & -315.594202680277 \tabularnewline
45 & 5100 & 4757.58793182094 & 342.412068179061 \tabularnewline
46 & 5000 & 4827.95054583063 & 172.049454169373 \tabularnewline
47 & 5350 & 4877.18715623551 & 472.812843764488 \tabularnewline
48 & 5150 & 4999.7912279434 & 150.208772056598 \tabularnewline
49 & 4500 & 5074.23428668867 & -574.23428668867 \tabularnewline
50 & 4600 & 4998.18519845211 & -398.185198452114 \tabularnewline
51 & 4900 & 4933.7300118887 & -33.7300118886997 \tabularnewline
52 & 5050 & 4929.99930733065 & 120.000692669353 \tabularnewline
53 & 5000 & 4958.11768356829 & 41.8823164317128 \tabularnewline
54 & 5350 & 4974.82981004077 & 375.170189959227 \tabularnewline
55 & 4650 & 5065.93285023073 & -415.932850230725 \tabularnewline
56 & 4650 & 5002.50358867545 & -352.503588675446 \tabularnewline
57 & 5200 & 4933.54160457601 & 266.458395423992 \tabularnewline
58 & 5300 & 4982.74715972913 & 317.252840270866 \tabularnewline
59 & 5700 & 5055.37070423838 & 644.629295761617 \tabularnewline
60 & 5250 & 5213.8911892459 & 36.1088107541018 \tabularnewline
61 & 4900 & 5270.08301002398 & -370.083010023976 \tabularnewline
62 & 5200 & 5239.65976181893 & -39.6597618189253 \tabularnewline
63 & 5250 & 5263.86895398665 & -13.8689539866509 \tabularnewline
64 & 5450 & 5291.84199593266 & 158.158004067336 \tabularnewline
65 & 5750 & 5356.5636502919 & 393.436349708096 \tabularnewline
66 & 5450 & 5479.77328033278 & -29.7732803327772 \tabularnewline
67 & 5100 & 5529.26662108541 & -429.266621085411 \tabularnewline
68 & 4950 & 5490.54069022915 & -540.540690229149 \tabularnewline
69 & 5550 & 5407.68810445051 & 142.311895549487 \tabularnewline
70 & 5800 & 5448.15637899086 & 351.843621009144 \tabularnewline
71 & 6050 & 5540.7801350977 & 509.219864902305 \tabularnewline
72 & 5650 & 5683.95529465778 & -33.9552946577842 \tabularnewline
73 & 5500 & 5732.71587543875 & -232.715875438751 \tabularnewline
74 & 5600 & 5736.69542331045 & -136.695423310446 \tabularnewline
75 & 5550 & 5750.73690162716 & -200.736901627158 \tabularnewline
76 & 5900 & 5744.50842852925 & 155.49157147075 \tabularnewline
77 & 5900 & 5806.38770789399 & 93.6122921060087 \tabularnewline
78 & 5850 & 5862.03911865677 & -12.0391186567667 \tabularnewline
79 & 5350 & 5899.07378989298 & -549.07378989298 \tabularnewline
80 & 5150 & 5818.81612183167 & -668.81612183167 \tabularnewline
81 & 5850 & 5687.02603940031 & 162.97396059969 \tabularnewline
82 & 6000 & 5704.9723798688 & 295.027620131199 \tabularnewline
83 & 6250 & 5759.19285184313 & 490.807148156871 \tabularnewline
84 & 5800 & 5869.67319380995 & -69.6731938099529 \tabularnewline
85 & 5550 & 5881.1221261062 & -331.122126106199 \tabularnewline
86 & 5700 & 5832.50460677696 & -132.504606776963 \tabularnewline
87 & 5850 & 5811.67916721936 & 38.3208327806406 \tabularnewline
88 & 6150 & 5821.83054130965 & 328.169458690353 \tabularnewline
89 & 6050 & 5896.76517908159 & 153.234820918414 \tabularnewline
90 & 6050 & 5948.91844075077 & 101.081559249232 \tabularnewline
91 & 5550 & 5996.85311404269 & -446.853114042692 \tabularnewline
92 & 5100 & 5930.38061596673 & -830.380615966732 \tabularnewline
93 & 5900 & 5759.78590812953 & 140.214091870472 \tabularnewline
94 & 6050 & 5761.59436537189 & 288.405634628114 \tabularnewline
95 & 6150 & 5802.12758601349 & 347.872413986513 \tabularnewline
96 & 5700 & 5868.98331725431 & -168.983317254309 \tabularnewline
97 & 5200 & 5839.65082708751 & -639.650827087512 \tabularnewline
98 & 5400 & 5700.16190498546 & -300.161904985462 \tabularnewline
99 & 5550 & 5604.75456060292 & -54.7545606029207 \tabularnewline
100 & 5750 & 5548.74792003806 & 201.252079961942 \tabularnewline
101 & 5700 & 5545.84508879167 & 154.154911208326 \tabularnewline
102 & 5650 & 5542.05309529962 & 107.946904700385 \tabularnewline
103 & 5400 & 5535.37754846557 & -135.377548465566 \tabularnewline
104 & 4950 & 5480.82565556237 & -530.825655562374 \tabularnewline
105 & 5900 & 5334.02846642146 & 565.971533578536 \tabularnewline
106 & 6050 & 5400.98091745517 & 649.019082544828 \tabularnewline
107 & 6350 & 5512.27448235559 & 837.725517644413 \tabularnewline
108 & 6350 & 5694.73338011226 & 655.266619887742 \tabularnewline
109 & 5500 & 5876.44427608549 & -376.444276085494 \tabularnewline
110 & 5800 & 5864.33337064491 & -64.3333706449093 \tabularnewline
111 & 6100 & 5902.57894240782 & 197.42105759218 \tabularnewline
112 & 6350 & 5994.73276157546 & 355.267238424535 \tabularnewline
113 & 6400 & 6130.36720014678 & 269.63279985322 \tabularnewline
114 & 6850 & 6263.88978958493 & 586.110210415065 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297988&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]3[/C][C]3750[/C][C]3700[/C][C]50[/C][/ROW]
[ROW][C]4[/C][C]3800[/C][C]3810.86830405471[/C][C]-10.8683040547135[/C][/ROW]
[ROW][C]5[/C][C]4100[/C][C]3910.8284047961[/C][C]189.171595203901[/C][/ROW]
[ROW][C]6[/C][C]3900[/C][C]4053.76556147375[/C][C]-153.765561473755[/C][/ROW]
[ROW][C]7[/C][C]3650[/C][C]4130.94683824399[/C][C]-480.946838243987[/C][/ROW]
[ROW][C]8[/C][C]3800[/C][C]4129.86758843352[/C][C]-329.867588433524[/C][/ROW]
[ROW][C]9[/C][C]4050[/C][C]4139.28784896781[/C][C]-89.2878489678133[/C][/ROW]
[ROW][C]10[/C][C]4250[/C][C]4185.67962592889[/C][C]64.3203740711133[/C][/ROW]
[ROW][C]11[/C][C]4450[/C][C]4261.31319726778[/C][C]188.68680273222[/C][/ROW]
[ROW][C]12[/C][C]4200[/C][C]4366.96749500344[/C][C]-166.967495003444[/C][/ROW]
[ROW][C]13[/C][C]4050[/C][C]4404.07911909328[/C][C]-354.079119093281[/C][/ROW]
[ROW][C]14[/C][C]4050[/C][C]4392.76337790319[/C][C]-342.763377903186[/C][/ROW]
[ROW][C]15[/C][C]4200[/C][C]4367.46031002071[/C][C]-167.460310020713[/C][/ROW]
[ROW][C]16[/C][C]4450[/C][C]4364.34081449366[/C][C]85.6591855063389[/C][/ROW]
[ROW][C]17[/C][C]4400[/C][C]4408.46237566217[/C][C]-8.46237566217224[/C][/ROW]
[ROW][C]18[/C][C]4450[/C][C]4436.10397350149[/C][C]13.8960264985108[/C][/ROW]
[ROW][C]19[/C][C]4200[/C][C]4468.21245201123[/C][C]-268.212452011227[/C][/ROW]
[ROW][C]20[/C][C]4050[/C][C]4439.64558692431[/C][C]-389.64558692431[/C][/ROW]
[ROW][C]21[/C][C]4500[/C][C]4372.22480127029[/C][C]127.775198729712[/C][/ROW]
[ROW][C]22[/C][C]4650[/C][C]4399.17469563309[/C][C]250.82530436691[/C][/ROW]
[ROW][C]23[/C][C]4850[/C][C]4458.80667080004[/C][C]391.193329199962[/C][/ROW]
[ROW][C]24[/C][C]4700[/C][C]4560.60073585637[/C][C]139.399264143633[/C][/ROW]
[ROW][C]25[/C][C]4350[/C][C]4625.83425285821[/C][C]-275.834252858214[/C][/ROW]
[ROW][C]26[/C][C]4500[/C][C]4607.28518725833[/C][C]-107.285187258325[/C][/ROW]
[ROW][C]27[/C][C]4700[/C][C]4612.56046274089[/C][C]87.4395372591143[/C][/ROW]
[ROW][C]28[/C][C]4800[/C][C]4655.17888852775[/C][C]144.821111472246[/C][/ROW]
[ROW][C]29[/C][C]4700[/C][C]4714.33169118566[/C][C]-14.3316911856646[/C][/ROW]
[ROW][C]30[/C][C]4600[/C][C]4745.61701752303[/C][C]-145.617017523033[/C][/ROW]
[ROW][C]31[/C][C]4400[/C][C]4747.69965951186[/C][C]-347.699659511859[/C][/ROW]
[ROW][C]32[/C][C]4300[/C][C]4699.09247500765[/C][C]-399.092475007646[/C][/ROW]
[ROW][C]33[/C][C]4750[/C][C]4623.16357666959[/C][C]126.836423330407[/C][/ROW]
[ROW][C]34[/C][C]4800[/C][C]4643.01592524366[/C][C]156.984074756344[/C][/ROW]
[ROW][C]35[/C][C]5000[/C][C]4675.31290608231[/C][C]324.687093917693[/C][/ROW]
[ROW][C]36[/C][C]4900[/C][C]4751.35474965768[/C][C]148.645250342315[/C][/ROW]
[ROW][C]37[/C][C]4400[/C][C]4804.21279220252[/C][C]-404.212792202518[/C][/ROW]
[ROW][C]38[/C][C]4650[/C][C]4743.80282468405[/C][C]-93.8028246840468[/C][/ROW]
[ROW][C]39[/C][C]4650[/C][C]4732.08975980655[/C][C]-82.0897598065476[/C][/ROW]
[ROW][C]40[/C][C]4900[/C][C]4718.56557410246[/C][C]181.434425897542[/C][/ROW]
[ROW][C]41[/C][C]4900[/C][C]4758.50953627378[/C][C]141.49046372622[/C][/ROW]
[ROW][C]42[/C][C]5000[/C][C]4798.19867009454[/C][C]201.80132990546[/C][/ROW]
[ROW][C]43[/C][C]4550[/C][C]4857.56957655127[/C][C]-307.569576551271[/C][/ROW]
[ROW][C]44[/C][C]4500[/C][C]4815.59420268028[/C][C]-315.594202680277[/C][/ROW]
[ROW][C]45[/C][C]5100[/C][C]4757.58793182094[/C][C]342.412068179061[/C][/ROW]
[ROW][C]46[/C][C]5000[/C][C]4827.95054583063[/C][C]172.049454169373[/C][/ROW]
[ROW][C]47[/C][C]5350[/C][C]4877.18715623551[/C][C]472.812843764488[/C][/ROW]
[ROW][C]48[/C][C]5150[/C][C]4999.7912279434[/C][C]150.208772056598[/C][/ROW]
[ROW][C]49[/C][C]4500[/C][C]5074.23428668867[/C][C]-574.23428668867[/C][/ROW]
[ROW][C]50[/C][C]4600[/C][C]4998.18519845211[/C][C]-398.185198452114[/C][/ROW]
[ROW][C]51[/C][C]4900[/C][C]4933.7300118887[/C][C]-33.7300118886997[/C][/ROW]
[ROW][C]52[/C][C]5050[/C][C]4929.99930733065[/C][C]120.000692669353[/C][/ROW]
[ROW][C]53[/C][C]5000[/C][C]4958.11768356829[/C][C]41.8823164317128[/C][/ROW]
[ROW][C]54[/C][C]5350[/C][C]4974.82981004077[/C][C]375.170189959227[/C][/ROW]
[ROW][C]55[/C][C]4650[/C][C]5065.93285023073[/C][C]-415.932850230725[/C][/ROW]
[ROW][C]56[/C][C]4650[/C][C]5002.50358867545[/C][C]-352.503588675446[/C][/ROW]
[ROW][C]57[/C][C]5200[/C][C]4933.54160457601[/C][C]266.458395423992[/C][/ROW]
[ROW][C]58[/C][C]5300[/C][C]4982.74715972913[/C][C]317.252840270866[/C][/ROW]
[ROW][C]59[/C][C]5700[/C][C]5055.37070423838[/C][C]644.629295761617[/C][/ROW]
[ROW][C]60[/C][C]5250[/C][C]5213.8911892459[/C][C]36.1088107541018[/C][/ROW]
[ROW][C]61[/C][C]4900[/C][C]5270.08301002398[/C][C]-370.083010023976[/C][/ROW]
[ROW][C]62[/C][C]5200[/C][C]5239.65976181893[/C][C]-39.6597618189253[/C][/ROW]
[ROW][C]63[/C][C]5250[/C][C]5263.86895398665[/C][C]-13.8689539866509[/C][/ROW]
[ROW][C]64[/C][C]5450[/C][C]5291.84199593266[/C][C]158.158004067336[/C][/ROW]
[ROW][C]65[/C][C]5750[/C][C]5356.5636502919[/C][C]393.436349708096[/C][/ROW]
[ROW][C]66[/C][C]5450[/C][C]5479.77328033278[/C][C]-29.7732803327772[/C][/ROW]
[ROW][C]67[/C][C]5100[/C][C]5529.26662108541[/C][C]-429.266621085411[/C][/ROW]
[ROW][C]68[/C][C]4950[/C][C]5490.54069022915[/C][C]-540.540690229149[/C][/ROW]
[ROW][C]69[/C][C]5550[/C][C]5407.68810445051[/C][C]142.311895549487[/C][/ROW]
[ROW][C]70[/C][C]5800[/C][C]5448.15637899086[/C][C]351.843621009144[/C][/ROW]
[ROW][C]71[/C][C]6050[/C][C]5540.7801350977[/C][C]509.219864902305[/C][/ROW]
[ROW][C]72[/C][C]5650[/C][C]5683.95529465778[/C][C]-33.9552946577842[/C][/ROW]
[ROW][C]73[/C][C]5500[/C][C]5732.71587543875[/C][C]-232.715875438751[/C][/ROW]
[ROW][C]74[/C][C]5600[/C][C]5736.69542331045[/C][C]-136.695423310446[/C][/ROW]
[ROW][C]75[/C][C]5550[/C][C]5750.73690162716[/C][C]-200.736901627158[/C][/ROW]
[ROW][C]76[/C][C]5900[/C][C]5744.50842852925[/C][C]155.49157147075[/C][/ROW]
[ROW][C]77[/C][C]5900[/C][C]5806.38770789399[/C][C]93.6122921060087[/C][/ROW]
[ROW][C]78[/C][C]5850[/C][C]5862.03911865677[/C][C]-12.0391186567667[/C][/ROW]
[ROW][C]79[/C][C]5350[/C][C]5899.07378989298[/C][C]-549.07378989298[/C][/ROW]
[ROW][C]80[/C][C]5150[/C][C]5818.81612183167[/C][C]-668.81612183167[/C][/ROW]
[ROW][C]81[/C][C]5850[/C][C]5687.02603940031[/C][C]162.97396059969[/C][/ROW]
[ROW][C]82[/C][C]6000[/C][C]5704.9723798688[/C][C]295.027620131199[/C][/ROW]
[ROW][C]83[/C][C]6250[/C][C]5759.19285184313[/C][C]490.807148156871[/C][/ROW]
[ROW][C]84[/C][C]5800[/C][C]5869.67319380995[/C][C]-69.6731938099529[/C][/ROW]
[ROW][C]85[/C][C]5550[/C][C]5881.1221261062[/C][C]-331.122126106199[/C][/ROW]
[ROW][C]86[/C][C]5700[/C][C]5832.50460677696[/C][C]-132.504606776963[/C][/ROW]
[ROW][C]87[/C][C]5850[/C][C]5811.67916721936[/C][C]38.3208327806406[/C][/ROW]
[ROW][C]88[/C][C]6150[/C][C]5821.83054130965[/C][C]328.169458690353[/C][/ROW]
[ROW][C]89[/C][C]6050[/C][C]5896.76517908159[/C][C]153.234820918414[/C][/ROW]
[ROW][C]90[/C][C]6050[/C][C]5948.91844075077[/C][C]101.081559249232[/C][/ROW]
[ROW][C]91[/C][C]5550[/C][C]5996.85311404269[/C][C]-446.853114042692[/C][/ROW]
[ROW][C]92[/C][C]5100[/C][C]5930.38061596673[/C][C]-830.380615966732[/C][/ROW]
[ROW][C]93[/C][C]5900[/C][C]5759.78590812953[/C][C]140.214091870472[/C][/ROW]
[ROW][C]94[/C][C]6050[/C][C]5761.59436537189[/C][C]288.405634628114[/C][/ROW]
[ROW][C]95[/C][C]6150[/C][C]5802.12758601349[/C][C]347.872413986513[/C][/ROW]
[ROW][C]96[/C][C]5700[/C][C]5868.98331725431[/C][C]-168.983317254309[/C][/ROW]
[ROW][C]97[/C][C]5200[/C][C]5839.65082708751[/C][C]-639.650827087512[/C][/ROW]
[ROW][C]98[/C][C]5400[/C][C]5700.16190498546[/C][C]-300.161904985462[/C][/ROW]
[ROW][C]99[/C][C]5550[/C][C]5604.75456060292[/C][C]-54.7545606029207[/C][/ROW]
[ROW][C]100[/C][C]5750[/C][C]5548.74792003806[/C][C]201.252079961942[/C][/ROW]
[ROW][C]101[/C][C]5700[/C][C]5545.84508879167[/C][C]154.154911208326[/C][/ROW]
[ROW][C]102[/C][C]5650[/C][C]5542.05309529962[/C][C]107.946904700385[/C][/ROW]
[ROW][C]103[/C][C]5400[/C][C]5535.37754846557[/C][C]-135.377548465566[/C][/ROW]
[ROW][C]104[/C][C]4950[/C][C]5480.82565556237[/C][C]-530.825655562374[/C][/ROW]
[ROW][C]105[/C][C]5900[/C][C]5334.02846642146[/C][C]565.971533578536[/C][/ROW]
[ROW][C]106[/C][C]6050[/C][C]5400.98091745517[/C][C]649.019082544828[/C][/ROW]
[ROW][C]107[/C][C]6350[/C][C]5512.27448235559[/C][C]837.725517644413[/C][/ROW]
[ROW][C]108[/C][C]6350[/C][C]5694.73338011226[/C][C]655.266619887742[/C][/ROW]
[ROW][C]109[/C][C]5500[/C][C]5876.44427608549[/C][C]-376.444276085494[/C][/ROW]
[ROW][C]110[/C][C]5800[/C][C]5864.33337064491[/C][C]-64.3333706449093[/C][/ROW]
[ROW][C]111[/C][C]6100[/C][C]5902.57894240782[/C][C]197.42105759218[/C][/ROW]
[ROW][C]112[/C][C]6350[/C][C]5994.73276157546[/C][C]355.267238424535[/C][/ROW]
[ROW][C]113[/C][C]6400[/C][C]6130.36720014678[/C][C]269.63279985322[/C][/ROW]
[ROW][C]114[/C][C]6850[/C][C]6263.88978958493[/C][C]586.110210415065[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297988&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297988&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
33750370050
438003810.86830405471-10.8683040547135
541003910.8284047961189.171595203901
639004053.76556147375-153.765561473755
736504130.94683824399-480.946838243987
838004129.86758843352-329.867588433524
940504139.28784896781-89.2878489678133
1042504185.6796259288964.3203740711133
1144504261.31319726778188.68680273222
1242004366.96749500344-166.967495003444
1340504404.07911909328-354.079119093281
1440504392.76337790319-342.763377903186
1542004367.46031002071-167.460310020713
1644504364.3408144936685.6591855063389
1744004408.46237566217-8.46237566217224
1844504436.1039735014913.8960264985108
1942004468.21245201123-268.212452011227
2040504439.64558692431-389.64558692431
2145004372.22480127029127.775198729712
2246504399.17469563309250.82530436691
2348504458.80667080004391.193329199962
2447004560.60073585637139.399264143633
2543504625.83425285821-275.834252858214
2645004607.28518725833-107.285187258325
2747004612.5604627408987.4395372591143
2848004655.17888852775144.821111472246
2947004714.33169118566-14.3316911856646
3046004745.61701752303-145.617017523033
3144004747.69965951186-347.699659511859
3243004699.09247500765-399.092475007646
3347504623.16357666959126.836423330407
3448004643.01592524366156.984074756344
3550004675.31290608231324.687093917693
3649004751.35474965768148.645250342315
3744004804.21279220252-404.212792202518
3846504743.80282468405-93.8028246840468
3946504732.08975980655-82.0897598065476
4049004718.56557410246181.434425897542
4149004758.50953627378141.49046372622
4250004798.19867009454201.80132990546
4345504857.56957655127-307.569576551271
4445004815.59420268028-315.594202680277
4551004757.58793182094342.412068179061
4650004827.95054583063172.049454169373
4753504877.18715623551472.812843764488
4851504999.7912279434150.208772056598
4945005074.23428668867-574.23428668867
5046004998.18519845211-398.185198452114
5149004933.7300118887-33.7300118886997
5250504929.99930733065120.000692669353
5350004958.1176835682941.8823164317128
5453504974.82981004077375.170189959227
5546505065.93285023073-415.932850230725
5646505002.50358867545-352.503588675446
5752004933.54160457601266.458395423992
5853004982.74715972913317.252840270866
5957005055.37070423838644.629295761617
6052505213.891189245936.1088107541018
6149005270.08301002398-370.083010023976
6252005239.65976181893-39.6597618189253
6352505263.86895398665-13.8689539866509
6454505291.84199593266158.158004067336
6557505356.5636502919393.436349708096
6654505479.77328033278-29.7732803327772
6751005529.26662108541-429.266621085411
6849505490.54069022915-540.540690229149
6955505407.68810445051142.311895549487
7058005448.15637899086351.843621009144
7160505540.7801350977509.219864902305
7256505683.95529465778-33.9552946577842
7355005732.71587543875-232.715875438751
7456005736.69542331045-136.695423310446
7555505750.73690162716-200.736901627158
7659005744.50842852925155.49157147075
7759005806.3877078939993.6122921060087
7858505862.03911865677-12.0391186567667
7953505899.07378989298-549.07378989298
8051505818.81612183167-668.81612183167
8158505687.02603940031162.97396059969
8260005704.9723798688295.027620131199
8362505759.19285184313490.807148156871
8458005869.67319380995-69.6731938099529
8555505881.1221261062-331.122126106199
8657005832.50460677696-132.504606776963
8758505811.6791672193638.3208327806406
8861505821.83054130965328.169458690353
8960505896.76517908159153.234820918414
9060505948.91844075077101.081559249232
9155505996.85311404269-446.853114042692
9251005930.38061596673-830.380615966732
9359005759.78590812953140.214091870472
9460505761.59436537189288.405634628114
9561505802.12758601349347.872413986513
9657005868.98331725431-168.983317254309
9752005839.65082708751-639.650827087512
9854005700.16190498546-300.161904985462
9955505604.75456060292-54.7545606029207
10057505548.74792003806201.252079961942
10157005545.84508879167154.154911208326
10256505542.05309529962107.946904700385
10354005535.37754846557-135.377548465566
10449505480.82565556237-530.825655562374
10559005334.02846642146565.971533578536
10660505400.98091745517649.019082544828
10763505512.27448235559837.725517644413
10863505694.73338011226655.266619887742
10955005876.44427608549-376.444276085494
11058005864.33337064491-64.3333706449093
11161005902.57894240782197.42105759218
11263505994.73276157546355.267238424535
11364006130.36720014678269.63279985322
11468506263.88978958493586.110210415065







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1156478.728284624925846.401606016297111.05496323355
1166593.391135844775946.298767103027240.48350458652
1176708.053987064626039.804956527397376.30301760185
1186822.716838284476126.263603172427519.17007339652
1196937.379689504326205.310744552067669.44863445658
1207052.042540724176276.855052410687827.23002903767
1217166.705391944026341.027128243047992.383655645
1227281.368243163876398.11449688128164.62198944654
1237396.031094383726448.498098447688343.56409031976
1247510.693945603576492.600251402928528.78763980423
1257625.356796823426530.847529388638719.86606425822
1267740.019648043286563.647488306648916.39180777991
1277854.682499263136591.37615632539117.98884220095
1287969.345350482986614.372918645869324.31778232009
1298084.008201702836632.939986963849535.07641644181
1308198.671052922686647.344422165659749.9976836797
1318313.333904142536657.821377377349968.84643090772
1328427.996755362386664.5777530844710191.4157576403

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
115 & 6478.72828462492 & 5846.40160601629 & 7111.05496323355 \tabularnewline
116 & 6593.39113584477 & 5946.29876710302 & 7240.48350458652 \tabularnewline
117 & 6708.05398706462 & 6039.80495652739 & 7376.30301760185 \tabularnewline
118 & 6822.71683828447 & 6126.26360317242 & 7519.17007339652 \tabularnewline
119 & 6937.37968950432 & 6205.31074455206 & 7669.44863445658 \tabularnewline
120 & 7052.04254072417 & 6276.85505241068 & 7827.23002903767 \tabularnewline
121 & 7166.70539194402 & 6341.02712824304 & 7992.383655645 \tabularnewline
122 & 7281.36824316387 & 6398.1144968812 & 8164.62198944654 \tabularnewline
123 & 7396.03109438372 & 6448.49809844768 & 8343.56409031976 \tabularnewline
124 & 7510.69394560357 & 6492.60025140292 & 8528.78763980423 \tabularnewline
125 & 7625.35679682342 & 6530.84752938863 & 8719.86606425822 \tabularnewline
126 & 7740.01964804328 & 6563.64748830664 & 8916.39180777991 \tabularnewline
127 & 7854.68249926313 & 6591.3761563253 & 9117.98884220095 \tabularnewline
128 & 7969.34535048298 & 6614.37291864586 & 9324.31778232009 \tabularnewline
129 & 8084.00820170283 & 6632.93998696384 & 9535.07641644181 \tabularnewline
130 & 8198.67105292268 & 6647.34442216565 & 9749.9976836797 \tabularnewline
131 & 8313.33390414253 & 6657.82137737734 & 9968.84643090772 \tabularnewline
132 & 8427.99675536238 & 6664.57775308447 & 10191.4157576403 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297988&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]115[/C][C]6478.72828462492[/C][C]5846.40160601629[/C][C]7111.05496323355[/C][/ROW]
[ROW][C]116[/C][C]6593.39113584477[/C][C]5946.29876710302[/C][C]7240.48350458652[/C][/ROW]
[ROW][C]117[/C][C]6708.05398706462[/C][C]6039.80495652739[/C][C]7376.30301760185[/C][/ROW]
[ROW][C]118[/C][C]6822.71683828447[/C][C]6126.26360317242[/C][C]7519.17007339652[/C][/ROW]
[ROW][C]119[/C][C]6937.37968950432[/C][C]6205.31074455206[/C][C]7669.44863445658[/C][/ROW]
[ROW][C]120[/C][C]7052.04254072417[/C][C]6276.85505241068[/C][C]7827.23002903767[/C][/ROW]
[ROW][C]121[/C][C]7166.70539194402[/C][C]6341.02712824304[/C][C]7992.383655645[/C][/ROW]
[ROW][C]122[/C][C]7281.36824316387[/C][C]6398.1144968812[/C][C]8164.62198944654[/C][/ROW]
[ROW][C]123[/C][C]7396.03109438372[/C][C]6448.49809844768[/C][C]8343.56409031976[/C][/ROW]
[ROW][C]124[/C][C]7510.69394560357[/C][C]6492.60025140292[/C][C]8528.78763980423[/C][/ROW]
[ROW][C]125[/C][C]7625.35679682342[/C][C]6530.84752938863[/C][C]8719.86606425822[/C][/ROW]
[ROW][C]126[/C][C]7740.01964804328[/C][C]6563.64748830664[/C][C]8916.39180777991[/C][/ROW]
[ROW][C]127[/C][C]7854.68249926313[/C][C]6591.3761563253[/C][C]9117.98884220095[/C][/ROW]
[ROW][C]128[/C][C]7969.34535048298[/C][C]6614.37291864586[/C][C]9324.31778232009[/C][/ROW]
[ROW][C]129[/C][C]8084.00820170283[/C][C]6632.93998696384[/C][C]9535.07641644181[/C][/ROW]
[ROW][C]130[/C][C]8198.67105292268[/C][C]6647.34442216565[/C][C]9749.9976836797[/C][/ROW]
[ROW][C]131[/C][C]8313.33390414253[/C][C]6657.82137737734[/C][C]9968.84643090772[/C][/ROW]
[ROW][C]132[/C][C]8427.99675536238[/C][C]6664.57775308447[/C][C]10191.4157576403[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297988&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297988&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
1156478.728284624925846.401606016297111.05496323355
1166593.391135844775946.298767103027240.48350458652
1176708.053987064626039.804956527397376.30301760185
1186822.716838284476126.263603172427519.17007339652
1196937.379689504326205.310744552067669.44863445658
1207052.042540724176276.855052410687827.23002903767
1217166.705391944026341.027128243047992.383655645
1227281.368243163876398.11449688128164.62198944654
1237396.031094383726448.498098447688343.56409031976
1247510.693945603576492.600251402928528.78763980423
1257625.356796823426530.847529388638719.86606425822
1267740.019648043286563.647488306648916.39180777991
1277854.682499263136591.37615632539117.98884220095
1287969.345350482986614.372918645869324.31778232009
1298084.008201702836632.939986963849535.07641644181
1308198.671052922686647.344422165659749.9976836797
1318313.333904142536657.821377377349968.84643090772
1328427.996755362386664.5777530844710191.4157576403



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ; par4 = 18 ;
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')