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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 computationFri, 16 Dec 2016 09:55:08 +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/16/t1481878554ys1lg2v0l81kmbd.htm/, Retrieved Fri, 01 Nov 2024 03:31:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300148, Retrieved Fri, 01 Nov 2024 03:31:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-16 08:55:08] [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 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=300148&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=300148&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300148&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
alpha0.438133149929493
beta0.168647423942594
gamma0.742277494000348

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.438133149929493 \tabularnewline
beta & 0.168647423942594 \tabularnewline
gamma & 0.742277494000348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300148&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]0.438133149929493[/C][/ROW]
[ROW][C]beta[/C][C]0.168647423942594[/C][/ROW]
[ROW][C]gamma[/C][C]0.742277494000348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300148&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300148&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
alpha0.438133149929493
beta0.168647423942594
gamma0.742277494000348







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1340503804.62072649573245.379273504272
1440503934.47097464791115.529025352092
1542004170.1326340364429.867365963556
1644504464.21998124873-14.2199812487324
1744004440.02381868866-40.0238186886609
1844504497.39811183737-47.3981118373686
1942004150.1225682664949.8774317335146
2040504342.90210979286-292.902109792862
2145004468.0226929013431.9773070986621
2246504679.51318903387-29.513189033868
2348504868.13193006821-18.1319300682135
2447004614.5640758062785.4359241937336
2543504604.60708185151-254.607081851507
2645004432.8594067784367.1405932215694
2747004579.63708319307120.362916806929
2848004869.71587216166-69.7158721616579
2947004781.07220925234-81.0722092523392
3046004784.98211053397-184.982110533966
3144004375.4260174763424.5739825236551
3243004369.71930226871-69.7193022687134
3347504700.1692699732649.8307300267352
3448004867.20686289133-67.2068628913285
3550005014.64246525556-14.6424652555634
3649004776.64045168907123.359548310932
3744004615.12538161923-215.12538161923
3846504571.4267400999378.5732599000667
3946504722.81751554508-72.8175155450799
4049004812.1160806971487.8839193028571
4149004762.56387671446137.436123285539
4250004809.79638158531190.20361841469
4345504670.66541487709-120.665414877086
4445004569.91282204479-69.9128220447919
4551004958.03775297122141.962247028779
4650005131.33706923609-131.337069236093
4753505282.5667668994767.4332331005326
4851505154.1137853419-4.11378534190226
4945004802.19418465016-302.194184650157
5046004843.01924729901-243.019247299013
5149004766.78914901006133.210850989944
5250505005.0200033548244.9799966451819
5350004945.808406148354.1915938517041
5453504960.89699306273389.103006937269
5546504776.27673622741-126.27673622741
5646504690.83563054951-40.8356305495145
5752005178.8166704813721.1833295186334
5853005175.04343789275124.95656210725
5957005530.22799628375169.772003716253
6052505433.10011804294-183.100118042936
6149004881.5441970678118.4558029321943
6252005114.330320439585.6696795605039
6352505390.10162207571-140.10162207571
6454505502.67343678944-52.6734367894433
6557505428.18869118745321.811308812551
6654505743.65356194102-293.653561941015
6751005037.9459529565562.0540470434471
6849505077.56452186099-127.564521860993
6955505553.9156083836-3.91560838360238
7058005581.07407035664218.925929643363
7160506001.7124919523548.2875080476524
7256505700.80448492397-50.8044849239741
7355005297.66362932867202.33637067133
7456005659.02398497045-59.0239849704494
7555505786.5261108781-236.526110878097
7659005895.475595776074.52440422392738
7759006008.62203545289-108.622035452893
7858505853.3964796127-3.39647961270475
7953505419.24219405423-69.2421940542326
8051505308.58177300327-158.581773003269
8158505806.9492400418943.0507599581097
8260005935.1310244426364.8689755573687
8362506193.229322844956.7706771551011
8458005831.46146385307-31.4614638530657
8555505520.550699213229.4493007867977
8657005662.5656901946637.4343098053369
8758505730.83289749135119.167102508647
8861506094.9710885739355.0289114260731
8960506185.60294692543-135.602946925434
9060506062.99472738927-12.994727389274
9155505597.01730940175-47.0173094017464
9251005460.320345118-360.320345118
9359005940.97213971976-40.9721397197573
9460506021.8113755826228.188624417382
9561506238.12213846543-88.1221384654255
9657005743.02843201847-43.0284320184674
9752005418.5533167317-218.553316731697
9854005403.01546635496-3.01546635496106
9955505432.43411047042117.565889529585
10057505713.7891525595236.2108474404768
10157005659.9485312774540.0514687225532
10256505621.6920386214128.307961378594
10354005118.92964189088281.070358109119
10449504978.86309349141-28.8630934914117
10559005745.96724934248154.032750657524
10660505963.5400064159186.4599935840861
10763506183.62951289525166.370487104754
10863505864.40558252812485.594417471882
10955005782.95430232628-282.954302326278
11058005908.95535689863-108.955356898629
11161006014.2827716117885.7172283882182
11263506317.4352897954632.5647102045396
11364006333.0109906294766.9890093705308
11468506373.06142472617476.938575273828

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4050 & 3804.62072649573 & 245.379273504272 \tabularnewline
14 & 4050 & 3934.47097464791 & 115.529025352092 \tabularnewline
15 & 4200 & 4170.13263403644 & 29.867365963556 \tabularnewline
16 & 4450 & 4464.21998124873 & -14.2199812487324 \tabularnewline
17 & 4400 & 4440.02381868866 & -40.0238186886609 \tabularnewline
18 & 4450 & 4497.39811183737 & -47.3981118373686 \tabularnewline
19 & 4200 & 4150.12256826649 & 49.8774317335146 \tabularnewline
20 & 4050 & 4342.90210979286 & -292.902109792862 \tabularnewline
21 & 4500 & 4468.02269290134 & 31.9773070986621 \tabularnewline
22 & 4650 & 4679.51318903387 & -29.513189033868 \tabularnewline
23 & 4850 & 4868.13193006821 & -18.1319300682135 \tabularnewline
24 & 4700 & 4614.56407580627 & 85.4359241937336 \tabularnewline
25 & 4350 & 4604.60708185151 & -254.607081851507 \tabularnewline
26 & 4500 & 4432.85940677843 & 67.1405932215694 \tabularnewline
27 & 4700 & 4579.63708319307 & 120.362916806929 \tabularnewline
28 & 4800 & 4869.71587216166 & -69.7158721616579 \tabularnewline
29 & 4700 & 4781.07220925234 & -81.0722092523392 \tabularnewline
30 & 4600 & 4784.98211053397 & -184.982110533966 \tabularnewline
31 & 4400 & 4375.42601747634 & 24.5739825236551 \tabularnewline
32 & 4300 & 4369.71930226871 & -69.7193022687134 \tabularnewline
33 & 4750 & 4700.16926997326 & 49.8307300267352 \tabularnewline
34 & 4800 & 4867.20686289133 & -67.2068628913285 \tabularnewline
35 & 5000 & 5014.64246525556 & -14.6424652555634 \tabularnewline
36 & 4900 & 4776.64045168907 & 123.359548310932 \tabularnewline
37 & 4400 & 4615.12538161923 & -215.12538161923 \tabularnewline
38 & 4650 & 4571.42674009993 & 78.5732599000667 \tabularnewline
39 & 4650 & 4722.81751554508 & -72.8175155450799 \tabularnewline
40 & 4900 & 4812.11608069714 & 87.8839193028571 \tabularnewline
41 & 4900 & 4762.56387671446 & 137.436123285539 \tabularnewline
42 & 5000 & 4809.79638158531 & 190.20361841469 \tabularnewline
43 & 4550 & 4670.66541487709 & -120.665414877086 \tabularnewline
44 & 4500 & 4569.91282204479 & -69.9128220447919 \tabularnewline
45 & 5100 & 4958.03775297122 & 141.962247028779 \tabularnewline
46 & 5000 & 5131.33706923609 & -131.337069236093 \tabularnewline
47 & 5350 & 5282.56676689947 & 67.4332331005326 \tabularnewline
48 & 5150 & 5154.1137853419 & -4.11378534190226 \tabularnewline
49 & 4500 & 4802.19418465016 & -302.194184650157 \tabularnewline
50 & 4600 & 4843.01924729901 & -243.019247299013 \tabularnewline
51 & 4900 & 4766.78914901006 & 133.210850989944 \tabularnewline
52 & 5050 & 5005.02000335482 & 44.9799966451819 \tabularnewline
53 & 5000 & 4945.8084061483 & 54.1915938517041 \tabularnewline
54 & 5350 & 4960.89699306273 & 389.103006937269 \tabularnewline
55 & 4650 & 4776.27673622741 & -126.27673622741 \tabularnewline
56 & 4650 & 4690.83563054951 & -40.8356305495145 \tabularnewline
57 & 5200 & 5178.81667048137 & 21.1833295186334 \tabularnewline
58 & 5300 & 5175.04343789275 & 124.95656210725 \tabularnewline
59 & 5700 & 5530.22799628375 & 169.772003716253 \tabularnewline
60 & 5250 & 5433.10011804294 & -183.100118042936 \tabularnewline
61 & 4900 & 4881.54419706781 & 18.4558029321943 \tabularnewline
62 & 5200 & 5114.3303204395 & 85.6696795605039 \tabularnewline
63 & 5250 & 5390.10162207571 & -140.10162207571 \tabularnewline
64 & 5450 & 5502.67343678944 & -52.6734367894433 \tabularnewline
65 & 5750 & 5428.18869118745 & 321.811308812551 \tabularnewline
66 & 5450 & 5743.65356194102 & -293.653561941015 \tabularnewline
67 & 5100 & 5037.94595295655 & 62.0540470434471 \tabularnewline
68 & 4950 & 5077.56452186099 & -127.564521860993 \tabularnewline
69 & 5550 & 5553.9156083836 & -3.91560838360238 \tabularnewline
70 & 5800 & 5581.07407035664 & 218.925929643363 \tabularnewline
71 & 6050 & 6001.71249195235 & 48.2875080476524 \tabularnewline
72 & 5650 & 5700.80448492397 & -50.8044849239741 \tabularnewline
73 & 5500 & 5297.66362932867 & 202.33637067133 \tabularnewline
74 & 5600 & 5659.02398497045 & -59.0239849704494 \tabularnewline
75 & 5550 & 5786.5261108781 & -236.526110878097 \tabularnewline
76 & 5900 & 5895.47559577607 & 4.52440422392738 \tabularnewline
77 & 5900 & 6008.62203545289 & -108.622035452893 \tabularnewline
78 & 5850 & 5853.3964796127 & -3.39647961270475 \tabularnewline
79 & 5350 & 5419.24219405423 & -69.2421940542326 \tabularnewline
80 & 5150 & 5308.58177300327 & -158.581773003269 \tabularnewline
81 & 5850 & 5806.94924004189 & 43.0507599581097 \tabularnewline
82 & 6000 & 5935.13102444263 & 64.8689755573687 \tabularnewline
83 & 6250 & 6193.2293228449 & 56.7706771551011 \tabularnewline
84 & 5800 & 5831.46146385307 & -31.4614638530657 \tabularnewline
85 & 5550 & 5520.5506992132 & 29.4493007867977 \tabularnewline
86 & 5700 & 5662.56569019466 & 37.4343098053369 \tabularnewline
87 & 5850 & 5730.83289749135 & 119.167102508647 \tabularnewline
88 & 6150 & 6094.97108857393 & 55.0289114260731 \tabularnewline
89 & 6050 & 6185.60294692543 & -135.602946925434 \tabularnewline
90 & 6050 & 6062.99472738927 & -12.994727389274 \tabularnewline
91 & 5550 & 5597.01730940175 & -47.0173094017464 \tabularnewline
92 & 5100 & 5460.320345118 & -360.320345118 \tabularnewline
93 & 5900 & 5940.97213971976 & -40.9721397197573 \tabularnewline
94 & 6050 & 6021.81137558262 & 28.188624417382 \tabularnewline
95 & 6150 & 6238.12213846543 & -88.1221384654255 \tabularnewline
96 & 5700 & 5743.02843201847 & -43.0284320184674 \tabularnewline
97 & 5200 & 5418.5533167317 & -218.553316731697 \tabularnewline
98 & 5400 & 5403.01546635496 & -3.01546635496106 \tabularnewline
99 & 5550 & 5432.43411047042 & 117.565889529585 \tabularnewline
100 & 5750 & 5713.78915255952 & 36.2108474404768 \tabularnewline
101 & 5700 & 5659.94853127745 & 40.0514687225532 \tabularnewline
102 & 5650 & 5621.69203862141 & 28.307961378594 \tabularnewline
103 & 5400 & 5118.92964189088 & 281.070358109119 \tabularnewline
104 & 4950 & 4978.86309349141 & -28.8630934914117 \tabularnewline
105 & 5900 & 5745.96724934248 & 154.032750657524 \tabularnewline
106 & 6050 & 5963.54000641591 & 86.4599935840861 \tabularnewline
107 & 6350 & 6183.62951289525 & 166.370487104754 \tabularnewline
108 & 6350 & 5864.40558252812 & 485.594417471882 \tabularnewline
109 & 5500 & 5782.95430232628 & -282.954302326278 \tabularnewline
110 & 5800 & 5908.95535689863 & -108.955356898629 \tabularnewline
111 & 6100 & 6014.28277161178 & 85.7172283882182 \tabularnewline
112 & 6350 & 6317.43528979546 & 32.5647102045396 \tabularnewline
113 & 6400 & 6333.01099062947 & 66.9890093705308 \tabularnewline
114 & 6850 & 6373.06142472617 & 476.938575273828 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300148&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]4050[/C][C]3804.62072649573[/C][C]245.379273504272[/C][/ROW]
[ROW][C]14[/C][C]4050[/C][C]3934.47097464791[/C][C]115.529025352092[/C][/ROW]
[ROW][C]15[/C][C]4200[/C][C]4170.13263403644[/C][C]29.867365963556[/C][/ROW]
[ROW][C]16[/C][C]4450[/C][C]4464.21998124873[/C][C]-14.2199812487324[/C][/ROW]
[ROW][C]17[/C][C]4400[/C][C]4440.02381868866[/C][C]-40.0238186886609[/C][/ROW]
[ROW][C]18[/C][C]4450[/C][C]4497.39811183737[/C][C]-47.3981118373686[/C][/ROW]
[ROW][C]19[/C][C]4200[/C][C]4150.12256826649[/C][C]49.8774317335146[/C][/ROW]
[ROW][C]20[/C][C]4050[/C][C]4342.90210979286[/C][C]-292.902109792862[/C][/ROW]
[ROW][C]21[/C][C]4500[/C][C]4468.02269290134[/C][C]31.9773070986621[/C][/ROW]
[ROW][C]22[/C][C]4650[/C][C]4679.51318903387[/C][C]-29.513189033868[/C][/ROW]
[ROW][C]23[/C][C]4850[/C][C]4868.13193006821[/C][C]-18.1319300682135[/C][/ROW]
[ROW][C]24[/C][C]4700[/C][C]4614.56407580627[/C][C]85.4359241937336[/C][/ROW]
[ROW][C]25[/C][C]4350[/C][C]4604.60708185151[/C][C]-254.607081851507[/C][/ROW]
[ROW][C]26[/C][C]4500[/C][C]4432.85940677843[/C][C]67.1405932215694[/C][/ROW]
[ROW][C]27[/C][C]4700[/C][C]4579.63708319307[/C][C]120.362916806929[/C][/ROW]
[ROW][C]28[/C][C]4800[/C][C]4869.71587216166[/C][C]-69.7158721616579[/C][/ROW]
[ROW][C]29[/C][C]4700[/C][C]4781.07220925234[/C][C]-81.0722092523392[/C][/ROW]
[ROW][C]30[/C][C]4600[/C][C]4784.98211053397[/C][C]-184.982110533966[/C][/ROW]
[ROW][C]31[/C][C]4400[/C][C]4375.42601747634[/C][C]24.5739825236551[/C][/ROW]
[ROW][C]32[/C][C]4300[/C][C]4369.71930226871[/C][C]-69.7193022687134[/C][/ROW]
[ROW][C]33[/C][C]4750[/C][C]4700.16926997326[/C][C]49.8307300267352[/C][/ROW]
[ROW][C]34[/C][C]4800[/C][C]4867.20686289133[/C][C]-67.2068628913285[/C][/ROW]
[ROW][C]35[/C][C]5000[/C][C]5014.64246525556[/C][C]-14.6424652555634[/C][/ROW]
[ROW][C]36[/C][C]4900[/C][C]4776.64045168907[/C][C]123.359548310932[/C][/ROW]
[ROW][C]37[/C][C]4400[/C][C]4615.12538161923[/C][C]-215.12538161923[/C][/ROW]
[ROW][C]38[/C][C]4650[/C][C]4571.42674009993[/C][C]78.5732599000667[/C][/ROW]
[ROW][C]39[/C][C]4650[/C][C]4722.81751554508[/C][C]-72.8175155450799[/C][/ROW]
[ROW][C]40[/C][C]4900[/C][C]4812.11608069714[/C][C]87.8839193028571[/C][/ROW]
[ROW][C]41[/C][C]4900[/C][C]4762.56387671446[/C][C]137.436123285539[/C][/ROW]
[ROW][C]42[/C][C]5000[/C][C]4809.79638158531[/C][C]190.20361841469[/C][/ROW]
[ROW][C]43[/C][C]4550[/C][C]4670.66541487709[/C][C]-120.665414877086[/C][/ROW]
[ROW][C]44[/C][C]4500[/C][C]4569.91282204479[/C][C]-69.9128220447919[/C][/ROW]
[ROW][C]45[/C][C]5100[/C][C]4958.03775297122[/C][C]141.962247028779[/C][/ROW]
[ROW][C]46[/C][C]5000[/C][C]5131.33706923609[/C][C]-131.337069236093[/C][/ROW]
[ROW][C]47[/C][C]5350[/C][C]5282.56676689947[/C][C]67.4332331005326[/C][/ROW]
[ROW][C]48[/C][C]5150[/C][C]5154.1137853419[/C][C]-4.11378534190226[/C][/ROW]
[ROW][C]49[/C][C]4500[/C][C]4802.19418465016[/C][C]-302.194184650157[/C][/ROW]
[ROW][C]50[/C][C]4600[/C][C]4843.01924729901[/C][C]-243.019247299013[/C][/ROW]
[ROW][C]51[/C][C]4900[/C][C]4766.78914901006[/C][C]133.210850989944[/C][/ROW]
[ROW][C]52[/C][C]5050[/C][C]5005.02000335482[/C][C]44.9799966451819[/C][/ROW]
[ROW][C]53[/C][C]5000[/C][C]4945.8084061483[/C][C]54.1915938517041[/C][/ROW]
[ROW][C]54[/C][C]5350[/C][C]4960.89699306273[/C][C]389.103006937269[/C][/ROW]
[ROW][C]55[/C][C]4650[/C][C]4776.27673622741[/C][C]-126.27673622741[/C][/ROW]
[ROW][C]56[/C][C]4650[/C][C]4690.83563054951[/C][C]-40.8356305495145[/C][/ROW]
[ROW][C]57[/C][C]5200[/C][C]5178.81667048137[/C][C]21.1833295186334[/C][/ROW]
[ROW][C]58[/C][C]5300[/C][C]5175.04343789275[/C][C]124.95656210725[/C][/ROW]
[ROW][C]59[/C][C]5700[/C][C]5530.22799628375[/C][C]169.772003716253[/C][/ROW]
[ROW][C]60[/C][C]5250[/C][C]5433.10011804294[/C][C]-183.100118042936[/C][/ROW]
[ROW][C]61[/C][C]4900[/C][C]4881.54419706781[/C][C]18.4558029321943[/C][/ROW]
[ROW][C]62[/C][C]5200[/C][C]5114.3303204395[/C][C]85.6696795605039[/C][/ROW]
[ROW][C]63[/C][C]5250[/C][C]5390.10162207571[/C][C]-140.10162207571[/C][/ROW]
[ROW][C]64[/C][C]5450[/C][C]5502.67343678944[/C][C]-52.6734367894433[/C][/ROW]
[ROW][C]65[/C][C]5750[/C][C]5428.18869118745[/C][C]321.811308812551[/C][/ROW]
[ROW][C]66[/C][C]5450[/C][C]5743.65356194102[/C][C]-293.653561941015[/C][/ROW]
[ROW][C]67[/C][C]5100[/C][C]5037.94595295655[/C][C]62.0540470434471[/C][/ROW]
[ROW][C]68[/C][C]4950[/C][C]5077.56452186099[/C][C]-127.564521860993[/C][/ROW]
[ROW][C]69[/C][C]5550[/C][C]5553.9156083836[/C][C]-3.91560838360238[/C][/ROW]
[ROW][C]70[/C][C]5800[/C][C]5581.07407035664[/C][C]218.925929643363[/C][/ROW]
[ROW][C]71[/C][C]6050[/C][C]6001.71249195235[/C][C]48.2875080476524[/C][/ROW]
[ROW][C]72[/C][C]5650[/C][C]5700.80448492397[/C][C]-50.8044849239741[/C][/ROW]
[ROW][C]73[/C][C]5500[/C][C]5297.66362932867[/C][C]202.33637067133[/C][/ROW]
[ROW][C]74[/C][C]5600[/C][C]5659.02398497045[/C][C]-59.0239849704494[/C][/ROW]
[ROW][C]75[/C][C]5550[/C][C]5786.5261108781[/C][C]-236.526110878097[/C][/ROW]
[ROW][C]76[/C][C]5900[/C][C]5895.47559577607[/C][C]4.52440422392738[/C][/ROW]
[ROW][C]77[/C][C]5900[/C][C]6008.62203545289[/C][C]-108.622035452893[/C][/ROW]
[ROW][C]78[/C][C]5850[/C][C]5853.3964796127[/C][C]-3.39647961270475[/C][/ROW]
[ROW][C]79[/C][C]5350[/C][C]5419.24219405423[/C][C]-69.2421940542326[/C][/ROW]
[ROW][C]80[/C][C]5150[/C][C]5308.58177300327[/C][C]-158.581773003269[/C][/ROW]
[ROW][C]81[/C][C]5850[/C][C]5806.94924004189[/C][C]43.0507599581097[/C][/ROW]
[ROW][C]82[/C][C]6000[/C][C]5935.13102444263[/C][C]64.8689755573687[/C][/ROW]
[ROW][C]83[/C][C]6250[/C][C]6193.2293228449[/C][C]56.7706771551011[/C][/ROW]
[ROW][C]84[/C][C]5800[/C][C]5831.46146385307[/C][C]-31.4614638530657[/C][/ROW]
[ROW][C]85[/C][C]5550[/C][C]5520.5506992132[/C][C]29.4493007867977[/C][/ROW]
[ROW][C]86[/C][C]5700[/C][C]5662.56569019466[/C][C]37.4343098053369[/C][/ROW]
[ROW][C]87[/C][C]5850[/C][C]5730.83289749135[/C][C]119.167102508647[/C][/ROW]
[ROW][C]88[/C][C]6150[/C][C]6094.97108857393[/C][C]55.0289114260731[/C][/ROW]
[ROW][C]89[/C][C]6050[/C][C]6185.60294692543[/C][C]-135.602946925434[/C][/ROW]
[ROW][C]90[/C][C]6050[/C][C]6062.99472738927[/C][C]-12.994727389274[/C][/ROW]
[ROW][C]91[/C][C]5550[/C][C]5597.01730940175[/C][C]-47.0173094017464[/C][/ROW]
[ROW][C]92[/C][C]5100[/C][C]5460.320345118[/C][C]-360.320345118[/C][/ROW]
[ROW][C]93[/C][C]5900[/C][C]5940.97213971976[/C][C]-40.9721397197573[/C][/ROW]
[ROW][C]94[/C][C]6050[/C][C]6021.81137558262[/C][C]28.188624417382[/C][/ROW]
[ROW][C]95[/C][C]6150[/C][C]6238.12213846543[/C][C]-88.1221384654255[/C][/ROW]
[ROW][C]96[/C][C]5700[/C][C]5743.02843201847[/C][C]-43.0284320184674[/C][/ROW]
[ROW][C]97[/C][C]5200[/C][C]5418.5533167317[/C][C]-218.553316731697[/C][/ROW]
[ROW][C]98[/C][C]5400[/C][C]5403.01546635496[/C][C]-3.01546635496106[/C][/ROW]
[ROW][C]99[/C][C]5550[/C][C]5432.43411047042[/C][C]117.565889529585[/C][/ROW]
[ROW][C]100[/C][C]5750[/C][C]5713.78915255952[/C][C]36.2108474404768[/C][/ROW]
[ROW][C]101[/C][C]5700[/C][C]5659.94853127745[/C][C]40.0514687225532[/C][/ROW]
[ROW][C]102[/C][C]5650[/C][C]5621.69203862141[/C][C]28.307961378594[/C][/ROW]
[ROW][C]103[/C][C]5400[/C][C]5118.92964189088[/C][C]281.070358109119[/C][/ROW]
[ROW][C]104[/C][C]4950[/C][C]4978.86309349141[/C][C]-28.8630934914117[/C][/ROW]
[ROW][C]105[/C][C]5900[/C][C]5745.96724934248[/C][C]154.032750657524[/C][/ROW]
[ROW][C]106[/C][C]6050[/C][C]5963.54000641591[/C][C]86.4599935840861[/C][/ROW]
[ROW][C]107[/C][C]6350[/C][C]6183.62951289525[/C][C]166.370487104754[/C][/ROW]
[ROW][C]108[/C][C]6350[/C][C]5864.40558252812[/C][C]485.594417471882[/C][/ROW]
[ROW][C]109[/C][C]5500[/C][C]5782.95430232628[/C][C]-282.954302326278[/C][/ROW]
[ROW][C]110[/C][C]5800[/C][C]5908.95535689863[/C][C]-108.955356898629[/C][/ROW]
[ROW][C]111[/C][C]6100[/C][C]6014.28277161178[/C][C]85.7172283882182[/C][/ROW]
[ROW][C]112[/C][C]6350[/C][C]6317.43528979546[/C][C]32.5647102045396[/C][/ROW]
[ROW][C]113[/C][C]6400[/C][C]6333.01099062947[/C][C]66.9890093705308[/C][/ROW]
[ROW][C]114[/C][C]6850[/C][C]6373.06142472617[/C][C]476.938575273828[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300148&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300148&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
1340503804.62072649573245.379273504272
1440503934.47097464791115.529025352092
1542004170.1326340364429.867365963556
1644504464.21998124873-14.2199812487324
1744004440.02381868866-40.0238186886609
1844504497.39811183737-47.3981118373686
1942004150.1225682664949.8774317335146
2040504342.90210979286-292.902109792862
2145004468.0226929013431.9773070986621
2246504679.51318903387-29.513189033868
2348504868.13193006821-18.1319300682135
2447004614.5640758062785.4359241937336
2543504604.60708185151-254.607081851507
2645004432.8594067784367.1405932215694
2747004579.63708319307120.362916806929
2848004869.71587216166-69.7158721616579
2947004781.07220925234-81.0722092523392
3046004784.98211053397-184.982110533966
3144004375.4260174763424.5739825236551
3243004369.71930226871-69.7193022687134
3347504700.1692699732649.8307300267352
3448004867.20686289133-67.2068628913285
3550005014.64246525556-14.6424652555634
3649004776.64045168907123.359548310932
3744004615.12538161923-215.12538161923
3846504571.4267400999378.5732599000667
3946504722.81751554508-72.8175155450799
4049004812.1160806971487.8839193028571
4149004762.56387671446137.436123285539
4250004809.79638158531190.20361841469
4345504670.66541487709-120.665414877086
4445004569.91282204479-69.9128220447919
4551004958.03775297122141.962247028779
4650005131.33706923609-131.337069236093
4753505282.5667668994767.4332331005326
4851505154.1137853419-4.11378534190226
4945004802.19418465016-302.194184650157
5046004843.01924729901-243.019247299013
5149004766.78914901006133.210850989944
5250505005.0200033548244.9799966451819
5350004945.808406148354.1915938517041
5453504960.89699306273389.103006937269
5546504776.27673622741-126.27673622741
5646504690.83563054951-40.8356305495145
5752005178.8166704813721.1833295186334
5853005175.04343789275124.95656210725
5957005530.22799628375169.772003716253
6052505433.10011804294-183.100118042936
6149004881.5441970678118.4558029321943
6252005114.330320439585.6696795605039
6352505390.10162207571-140.10162207571
6454505502.67343678944-52.6734367894433
6557505428.18869118745321.811308812551
6654505743.65356194102-293.653561941015
6751005037.9459529565562.0540470434471
6849505077.56452186099-127.564521860993
6955505553.9156083836-3.91560838360238
7058005581.07407035664218.925929643363
7160506001.7124919523548.2875080476524
7256505700.80448492397-50.8044849239741
7355005297.66362932867202.33637067133
7456005659.02398497045-59.0239849704494
7555505786.5261108781-236.526110878097
7659005895.475595776074.52440422392738
7759006008.62203545289-108.622035452893
7858505853.3964796127-3.39647961270475
7953505419.24219405423-69.2421940542326
8051505308.58177300327-158.581773003269
8158505806.9492400418943.0507599581097
8260005935.1310244426364.8689755573687
8362506193.229322844956.7706771551011
8458005831.46146385307-31.4614638530657
8555505520.550699213229.4493007867977
8657005662.5656901946637.4343098053369
8758505730.83289749135119.167102508647
8861506094.9710885739355.0289114260731
8960506185.60294692543-135.602946925434
9060506062.99472738927-12.994727389274
9155505597.01730940175-47.0173094017464
9251005460.320345118-360.320345118
9359005940.97213971976-40.9721397197573
9460506021.8113755826228.188624417382
9561506238.12213846543-88.1221384654255
9657005743.02843201847-43.0284320184674
9752005418.5533167317-218.553316731697
9854005403.01546635496-3.01546635496106
9955505432.43411047042117.565889529585
10057505713.7891525595236.2108474404768
10157005659.9485312774540.0514687225532
10256505621.6920386214128.307961378594
10354005118.92964189088281.070358109119
10449504978.86309349141-28.8630934914117
10559005745.96724934248154.032750657524
10660505963.5400064159186.4599935840861
10763506183.62951289525166.370487104754
10863505864.40558252812485.594417471882
10955005782.95430232628-282.954302326278
11058005908.95535689863-108.955356898629
11161006014.2827716117885.7172283882182
11263506317.4352897954632.5647102045396
11364006333.0109906294766.9890093705308
11468506373.06142472617476.938575273828







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1156276.828125363775979.026832529536574.62941819802
1165968.137633310225633.569082171276302.70618444918
1176910.082596473746532.7480257167287.41716723149
1187106.521229728966681.092271264347531.95018819357
1197390.203475324166911.94645582667868.46049482173
1207187.076057424616651.753993301017722.39812154821
1216592.310441898965996.090679000867188.53020479707
1226955.731316180296295.108082596837616.35454976374
1237238.916730170556510.649426475737967.18403386536
1247524.942871726736726.00793547378323.87780797977
1257580.798754137916708.352333428978453.24517484686
1267797.714110837156849.063047689628746.36517398468

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
115 & 6276.82812536377 & 5979.02683252953 & 6574.62941819802 \tabularnewline
116 & 5968.13763331022 & 5633.56908217127 & 6302.70618444918 \tabularnewline
117 & 6910.08259647374 & 6532.748025716 & 7287.41716723149 \tabularnewline
118 & 7106.52122972896 & 6681.09227126434 & 7531.95018819357 \tabularnewline
119 & 7390.20347532416 & 6911.9464558266 & 7868.46049482173 \tabularnewline
120 & 7187.07605742461 & 6651.75399330101 & 7722.39812154821 \tabularnewline
121 & 6592.31044189896 & 5996.09067900086 & 7188.53020479707 \tabularnewline
122 & 6955.73131618029 & 6295.10808259683 & 7616.35454976374 \tabularnewline
123 & 7238.91673017055 & 6510.64942647573 & 7967.18403386536 \tabularnewline
124 & 7524.94287172673 & 6726.0079354737 & 8323.87780797977 \tabularnewline
125 & 7580.79875413791 & 6708.35233342897 & 8453.24517484686 \tabularnewline
126 & 7797.71411083715 & 6849.06304768962 & 8746.36517398468 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300148&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]6276.82812536377[/C][C]5979.02683252953[/C][C]6574.62941819802[/C][/ROW]
[ROW][C]116[/C][C]5968.13763331022[/C][C]5633.56908217127[/C][C]6302.70618444918[/C][/ROW]
[ROW][C]117[/C][C]6910.08259647374[/C][C]6532.748025716[/C][C]7287.41716723149[/C][/ROW]
[ROW][C]118[/C][C]7106.52122972896[/C][C]6681.09227126434[/C][C]7531.95018819357[/C][/ROW]
[ROW][C]119[/C][C]7390.20347532416[/C][C]6911.9464558266[/C][C]7868.46049482173[/C][/ROW]
[ROW][C]120[/C][C]7187.07605742461[/C][C]6651.75399330101[/C][C]7722.39812154821[/C][/ROW]
[ROW][C]121[/C][C]6592.31044189896[/C][C]5996.09067900086[/C][C]7188.53020479707[/C][/ROW]
[ROW][C]122[/C][C]6955.73131618029[/C][C]6295.10808259683[/C][C]7616.35454976374[/C][/ROW]
[ROW][C]123[/C][C]7238.91673017055[/C][C]6510.64942647573[/C][C]7967.18403386536[/C][/ROW]
[ROW][C]124[/C][C]7524.94287172673[/C][C]6726.0079354737[/C][C]8323.87780797977[/C][/ROW]
[ROW][C]125[/C][C]7580.79875413791[/C][C]6708.35233342897[/C][C]8453.24517484686[/C][/ROW]
[ROW][C]126[/C][C]7797.71411083715[/C][C]6849.06304768962[/C][C]8746.36517398468[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300148&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300148&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
1156276.828125363775979.026832529536574.62941819802
1165968.137633310225633.569082171276302.70618444918
1176910.082596473746532.7480257167287.41716723149
1187106.521229728966681.092271264347531.95018819357
1197390.203475324166911.94645582667868.46049482173
1207187.076057424616651.753993301017722.39812154821
1216592.310441898965996.090679000867188.53020479707
1226955.731316180296295.108082596837616.35454976374
1237238.916730170556510.649426475737967.18403386536
1247524.942871726736726.00793547378323.87780797977
1257580.798754137916708.352333428978453.24517484686
1267797.714110837156849.063047689628746.36517398468



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
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')