Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 07 Aug 2015 14:38:03 +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/2015/Aug/07/t14389548224yv8p3bo97n2pnv.htm/, Retrieved Wed, 15 May 2024 16:43:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279899, Retrieved Wed, 15 May 2024 16:43:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-08-07 13:38:03] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
1684800.00
1622400.00
1716000.00
1372800.00
1778400.00
1747200.00
1872000.00
1934400.00
2152800.00
1872000.00
1778400.00
2215200.00
1872000.00
1404000.00
1653600.00
1248000.00
1747200.00
1435200.00
1903200.00
1716000.00
1809600.00
2028000.00
1996800.00
2371200.00
1716000.00
1435200.00
1591200.00
1154400.00
1653600.00
1279200.00
1809600.00
1716000.00
1528800.00
2184000.00
1965600.00
2246400.00
1684800.00
1560000.00
1404000.00
1154400.00
1528800.00
1372800.00
1872000.00
1809600.00
1560000.00
2090400.00
1934400.00
2496000.00
1996800.00
1216800.00
1216800.00
1216800.00
1435200.00
1435200.00
1934400.00
1778400.00
1591200.00
1996800.00
1840800.00
2652000.00
2090400.00
1216800.00
1279200.00
1060800.00
1466400.00
1684800.00
2121600.00
2090400.00
1684800.00
1965600.00
1747200.00
2496000.00
1903200.00
1528800.00
1372800.00
1029600.00
1528800.00
1840800.00
2152800.00
2028000.00
1497600.00
2152800.00
1684800.00
2589600.00
2152800.00
1560000.00
1435200.00
967200.00
1528800.00
1466400.00
2215200.00
2215200.00
1684800.00
2184000.00
1622400.00
2527200.00
2152800.00
1591200.00
1216800.00
842400.00
1653600.00
1591200.00
2090400.00
2402400.00
1778400.00
1996800.00
1497600.00
2589600.00




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279899&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279899&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279899&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00926118605786535
beta1
gamma0.929768627343191

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00926118605786535 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.929768627343191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279899&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]0.00926118605786535[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.929768627343191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279899&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279899&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
alpha0.00926118605786535
beta1
gamma0.929768627343191







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1318720001936016.66666667-64016.6666666674
1414040001466458.19887233-62458.1988723313
1516536001729535.72733761-75935.7273376081
1612480001320985.18300485-72985.1830048547
1717472001793186.03485286-45986.034852864
1814352001454011.04561048-18811.045610477
1919032001818213.5164062484986.4835937573
2017160001872164.35106928-156164.351069281
2118096002088835.57587364-279235.575873638
2220280001798680.96254457229319.03745543
2319968001701259.93438262295540.065617385
2423712002145389.24301865225810.756981353
2517160001749394.59486281-33394.5948628134
2614352001282395.17515454152804.824845456
2715912001537884.8105853553315.1894146539
2811544001137279.6643795817120.3356204182
2916536001640050.4261127813549.5738872222
3012792001331875.58088575-52675.5808857456
3118096001796481.0293059913118.9706940132
3217160001632065.4114207483934.5885792614
3315288001744252.92555484-215452.925554837
3421840001930399.51644369253600.483556314
3519656001901679.6776311363920.3223688747
3622464002284763.43127703-38363.431277032
3716848001650437.8212225534362.1787774488
3815600001359097.13145651200902.868543494
3914040001527344.1579214-123344.157921404
4011544001094083.2936995160316.7063004931
4115288001596686.45081174-67886.4508117402
4213728001228720.97592813144079.02407187
4318720001759545.34199519112454.658004815
4418096001665991.58804574143608.411954256
4515600001508210.7731127251789.2268872836
4620904002136641.74499072-46241.7449907199
4719344001935379.90793802-979.90793802496
4824960002228002.34015692267997.659843076
4919968001670702.24810284326097.751897155
5012168001545371.94284458-328571.942844581
5112168001415027.44103294-198227.44103294
5212168001154554.9465062562245.0534937524
5314352001543399.70217979-108199.702179795
5414352001374260.281534160939.7184658975
5519344001878359.4148686956040.5851313123
5617784001815634.03344899-37234.033448993
5715912001572576.9309880818623.0690119159
5819968002111070.07866473-114270.078664733
5918408001950912.82750346-110112.827503464
6026520002489325.97347617162674.026523827
6120904001982625.00616112107774.99383888
6212168001248251.89550595-31451.8955059499
6312792001239511.8869963939688.1130036146
6410608001222167.38637453-161367.386374528
6514664001450852.1078312515547.8921687519
6616848001438726.30392746246073.696072541
6721216001941805.14175627179794.858243732
6820904001797229.35382365293170.646176349
6916848001614669.4699963470130.5300036597
7019656002037685.15962313-72085.1596231286
7117472001888599.84807855-141399.848078547
7224960002684565.01346091-188565.013460914
7319032002127349.60779324-224149.607793243
7415288001261887.64932227266912.350677733
7513728001324440.345018548359.6549815005
7610296001125050.92585428-95450.9258542773
7715288001521002.104829467797.89517054101
7818408001724772.50270559116027.497294412
7921528002168006.62167028-15206.6216702829
8020280002126668.87882254-98668.8788225418
8114976001732003.03089312-234403.030893123
8221528002015353.02759315137446.972406848
8316848001800456.72795788-115656.727957882
8425896002549550.4202711640049.5797288399
8521528001960127.14840359192672.851596411
8615600001553185.237441666814.76255833544
8714352001411912.9646921523287.0353078451
889672001079492.27195445-112292.271954451
8915288001569913.14953608-41113.1495360842
9014664001871991.35398141-405591.353981406
9122152002183740.7447702231459.2552297842
9222152002060618.87205088154581.127949123
9316848001540276.83651312144523.163486883
9421840002170189.0000817913810.999918208
9516224001720374.50913685-97974.5091368454
9625272002612601.09758554-85401.0975855449
9721528002160983.35670825-8183.35670824535
9815912001577493.6969051913706.3030948099
9912168001448039.69422153-231239.694221535
100842400982595.499780769-140195.499780769
10116536001532290.41517765121309.584822349
10215912001495600.3547506995599.6452493125
10320904002214695.0720958-124295.072095795
10424024002202214.03790245200185.962097545
10517784001672120.36564556106279.634354442
10619968002180008.61205841-183208.612058408
10714976001622309.55053232-124709.550532318
10825896002522535.2053581267064.7946418831

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1872000 & 1936016.66666667 & -64016.6666666674 \tabularnewline
14 & 1404000 & 1466458.19887233 & -62458.1988723313 \tabularnewline
15 & 1653600 & 1729535.72733761 & -75935.7273376081 \tabularnewline
16 & 1248000 & 1320985.18300485 & -72985.1830048547 \tabularnewline
17 & 1747200 & 1793186.03485286 & -45986.034852864 \tabularnewline
18 & 1435200 & 1454011.04561048 & -18811.045610477 \tabularnewline
19 & 1903200 & 1818213.51640624 & 84986.4835937573 \tabularnewline
20 & 1716000 & 1872164.35106928 & -156164.351069281 \tabularnewline
21 & 1809600 & 2088835.57587364 & -279235.575873638 \tabularnewline
22 & 2028000 & 1798680.96254457 & 229319.03745543 \tabularnewline
23 & 1996800 & 1701259.93438262 & 295540.065617385 \tabularnewline
24 & 2371200 & 2145389.24301865 & 225810.756981353 \tabularnewline
25 & 1716000 & 1749394.59486281 & -33394.5948628134 \tabularnewline
26 & 1435200 & 1282395.17515454 & 152804.824845456 \tabularnewline
27 & 1591200 & 1537884.81058535 & 53315.1894146539 \tabularnewline
28 & 1154400 & 1137279.66437958 & 17120.3356204182 \tabularnewline
29 & 1653600 & 1640050.42611278 & 13549.5738872222 \tabularnewline
30 & 1279200 & 1331875.58088575 & -52675.5808857456 \tabularnewline
31 & 1809600 & 1796481.02930599 & 13118.9706940132 \tabularnewline
32 & 1716000 & 1632065.41142074 & 83934.5885792614 \tabularnewline
33 & 1528800 & 1744252.92555484 & -215452.925554837 \tabularnewline
34 & 2184000 & 1930399.51644369 & 253600.483556314 \tabularnewline
35 & 1965600 & 1901679.67763113 & 63920.3223688747 \tabularnewline
36 & 2246400 & 2284763.43127703 & -38363.431277032 \tabularnewline
37 & 1684800 & 1650437.82122255 & 34362.1787774488 \tabularnewline
38 & 1560000 & 1359097.13145651 & 200902.868543494 \tabularnewline
39 & 1404000 & 1527344.1579214 & -123344.157921404 \tabularnewline
40 & 1154400 & 1094083.29369951 & 60316.7063004931 \tabularnewline
41 & 1528800 & 1596686.45081174 & -67886.4508117402 \tabularnewline
42 & 1372800 & 1228720.97592813 & 144079.02407187 \tabularnewline
43 & 1872000 & 1759545.34199519 & 112454.658004815 \tabularnewline
44 & 1809600 & 1665991.58804574 & 143608.411954256 \tabularnewline
45 & 1560000 & 1508210.77311272 & 51789.2268872836 \tabularnewline
46 & 2090400 & 2136641.74499072 & -46241.7449907199 \tabularnewline
47 & 1934400 & 1935379.90793802 & -979.90793802496 \tabularnewline
48 & 2496000 & 2228002.34015692 & 267997.659843076 \tabularnewline
49 & 1996800 & 1670702.24810284 & 326097.751897155 \tabularnewline
50 & 1216800 & 1545371.94284458 & -328571.942844581 \tabularnewline
51 & 1216800 & 1415027.44103294 & -198227.44103294 \tabularnewline
52 & 1216800 & 1154554.94650625 & 62245.0534937524 \tabularnewline
53 & 1435200 & 1543399.70217979 & -108199.702179795 \tabularnewline
54 & 1435200 & 1374260.2815341 & 60939.7184658975 \tabularnewline
55 & 1934400 & 1878359.41486869 & 56040.5851313123 \tabularnewline
56 & 1778400 & 1815634.03344899 & -37234.033448993 \tabularnewline
57 & 1591200 & 1572576.93098808 & 18623.0690119159 \tabularnewline
58 & 1996800 & 2111070.07866473 & -114270.078664733 \tabularnewline
59 & 1840800 & 1950912.82750346 & -110112.827503464 \tabularnewline
60 & 2652000 & 2489325.97347617 & 162674.026523827 \tabularnewline
61 & 2090400 & 1982625.00616112 & 107774.99383888 \tabularnewline
62 & 1216800 & 1248251.89550595 & -31451.8955059499 \tabularnewline
63 & 1279200 & 1239511.88699639 & 39688.1130036146 \tabularnewline
64 & 1060800 & 1222167.38637453 & -161367.386374528 \tabularnewline
65 & 1466400 & 1450852.10783125 & 15547.8921687519 \tabularnewline
66 & 1684800 & 1438726.30392746 & 246073.696072541 \tabularnewline
67 & 2121600 & 1941805.14175627 & 179794.858243732 \tabularnewline
68 & 2090400 & 1797229.35382365 & 293170.646176349 \tabularnewline
69 & 1684800 & 1614669.46999634 & 70130.5300036597 \tabularnewline
70 & 1965600 & 2037685.15962313 & -72085.1596231286 \tabularnewline
71 & 1747200 & 1888599.84807855 & -141399.848078547 \tabularnewline
72 & 2496000 & 2684565.01346091 & -188565.013460914 \tabularnewline
73 & 1903200 & 2127349.60779324 & -224149.607793243 \tabularnewline
74 & 1528800 & 1261887.64932227 & 266912.350677733 \tabularnewline
75 & 1372800 & 1324440.3450185 & 48359.6549815005 \tabularnewline
76 & 1029600 & 1125050.92585428 & -95450.9258542773 \tabularnewline
77 & 1528800 & 1521002.10482946 & 7797.89517054101 \tabularnewline
78 & 1840800 & 1724772.50270559 & 116027.497294412 \tabularnewline
79 & 2152800 & 2168006.62167028 & -15206.6216702829 \tabularnewline
80 & 2028000 & 2126668.87882254 & -98668.8788225418 \tabularnewline
81 & 1497600 & 1732003.03089312 & -234403.030893123 \tabularnewline
82 & 2152800 & 2015353.02759315 & 137446.972406848 \tabularnewline
83 & 1684800 & 1800456.72795788 & -115656.727957882 \tabularnewline
84 & 2589600 & 2549550.42027116 & 40049.5797288399 \tabularnewline
85 & 2152800 & 1960127.14840359 & 192672.851596411 \tabularnewline
86 & 1560000 & 1553185.23744166 & 6814.76255833544 \tabularnewline
87 & 1435200 & 1411912.96469215 & 23287.0353078451 \tabularnewline
88 & 967200 & 1079492.27195445 & -112292.271954451 \tabularnewline
89 & 1528800 & 1569913.14953608 & -41113.1495360842 \tabularnewline
90 & 1466400 & 1871991.35398141 & -405591.353981406 \tabularnewline
91 & 2215200 & 2183740.74477022 & 31459.2552297842 \tabularnewline
92 & 2215200 & 2060618.87205088 & 154581.127949123 \tabularnewline
93 & 1684800 & 1540276.83651312 & 144523.163486883 \tabularnewline
94 & 2184000 & 2170189.00008179 & 13810.999918208 \tabularnewline
95 & 1622400 & 1720374.50913685 & -97974.5091368454 \tabularnewline
96 & 2527200 & 2612601.09758554 & -85401.0975855449 \tabularnewline
97 & 2152800 & 2160983.35670825 & -8183.35670824535 \tabularnewline
98 & 1591200 & 1577493.69690519 & 13706.3030948099 \tabularnewline
99 & 1216800 & 1448039.69422153 & -231239.694221535 \tabularnewline
100 & 842400 & 982595.499780769 & -140195.499780769 \tabularnewline
101 & 1653600 & 1532290.41517765 & 121309.584822349 \tabularnewline
102 & 1591200 & 1495600.35475069 & 95599.6452493125 \tabularnewline
103 & 2090400 & 2214695.0720958 & -124295.072095795 \tabularnewline
104 & 2402400 & 2202214.03790245 & 200185.962097545 \tabularnewline
105 & 1778400 & 1672120.36564556 & 106279.634354442 \tabularnewline
106 & 1996800 & 2180008.61205841 & -183208.612058408 \tabularnewline
107 & 1497600 & 1622309.55053232 & -124709.550532318 \tabularnewline
108 & 2589600 & 2522535.20535812 & 67064.7946418831 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279899&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]1872000[/C][C]1936016.66666667[/C][C]-64016.6666666674[/C][/ROW]
[ROW][C]14[/C][C]1404000[/C][C]1466458.19887233[/C][C]-62458.1988723313[/C][/ROW]
[ROW][C]15[/C][C]1653600[/C][C]1729535.72733761[/C][C]-75935.7273376081[/C][/ROW]
[ROW][C]16[/C][C]1248000[/C][C]1320985.18300485[/C][C]-72985.1830048547[/C][/ROW]
[ROW][C]17[/C][C]1747200[/C][C]1793186.03485286[/C][C]-45986.034852864[/C][/ROW]
[ROW][C]18[/C][C]1435200[/C][C]1454011.04561048[/C][C]-18811.045610477[/C][/ROW]
[ROW][C]19[/C][C]1903200[/C][C]1818213.51640624[/C][C]84986.4835937573[/C][/ROW]
[ROW][C]20[/C][C]1716000[/C][C]1872164.35106928[/C][C]-156164.351069281[/C][/ROW]
[ROW][C]21[/C][C]1809600[/C][C]2088835.57587364[/C][C]-279235.575873638[/C][/ROW]
[ROW][C]22[/C][C]2028000[/C][C]1798680.96254457[/C][C]229319.03745543[/C][/ROW]
[ROW][C]23[/C][C]1996800[/C][C]1701259.93438262[/C][C]295540.065617385[/C][/ROW]
[ROW][C]24[/C][C]2371200[/C][C]2145389.24301865[/C][C]225810.756981353[/C][/ROW]
[ROW][C]25[/C][C]1716000[/C][C]1749394.59486281[/C][C]-33394.5948628134[/C][/ROW]
[ROW][C]26[/C][C]1435200[/C][C]1282395.17515454[/C][C]152804.824845456[/C][/ROW]
[ROW][C]27[/C][C]1591200[/C][C]1537884.81058535[/C][C]53315.1894146539[/C][/ROW]
[ROW][C]28[/C][C]1154400[/C][C]1137279.66437958[/C][C]17120.3356204182[/C][/ROW]
[ROW][C]29[/C][C]1653600[/C][C]1640050.42611278[/C][C]13549.5738872222[/C][/ROW]
[ROW][C]30[/C][C]1279200[/C][C]1331875.58088575[/C][C]-52675.5808857456[/C][/ROW]
[ROW][C]31[/C][C]1809600[/C][C]1796481.02930599[/C][C]13118.9706940132[/C][/ROW]
[ROW][C]32[/C][C]1716000[/C][C]1632065.41142074[/C][C]83934.5885792614[/C][/ROW]
[ROW][C]33[/C][C]1528800[/C][C]1744252.92555484[/C][C]-215452.925554837[/C][/ROW]
[ROW][C]34[/C][C]2184000[/C][C]1930399.51644369[/C][C]253600.483556314[/C][/ROW]
[ROW][C]35[/C][C]1965600[/C][C]1901679.67763113[/C][C]63920.3223688747[/C][/ROW]
[ROW][C]36[/C][C]2246400[/C][C]2284763.43127703[/C][C]-38363.431277032[/C][/ROW]
[ROW][C]37[/C][C]1684800[/C][C]1650437.82122255[/C][C]34362.1787774488[/C][/ROW]
[ROW][C]38[/C][C]1560000[/C][C]1359097.13145651[/C][C]200902.868543494[/C][/ROW]
[ROW][C]39[/C][C]1404000[/C][C]1527344.1579214[/C][C]-123344.157921404[/C][/ROW]
[ROW][C]40[/C][C]1154400[/C][C]1094083.29369951[/C][C]60316.7063004931[/C][/ROW]
[ROW][C]41[/C][C]1528800[/C][C]1596686.45081174[/C][C]-67886.4508117402[/C][/ROW]
[ROW][C]42[/C][C]1372800[/C][C]1228720.97592813[/C][C]144079.02407187[/C][/ROW]
[ROW][C]43[/C][C]1872000[/C][C]1759545.34199519[/C][C]112454.658004815[/C][/ROW]
[ROW][C]44[/C][C]1809600[/C][C]1665991.58804574[/C][C]143608.411954256[/C][/ROW]
[ROW][C]45[/C][C]1560000[/C][C]1508210.77311272[/C][C]51789.2268872836[/C][/ROW]
[ROW][C]46[/C][C]2090400[/C][C]2136641.74499072[/C][C]-46241.7449907199[/C][/ROW]
[ROW][C]47[/C][C]1934400[/C][C]1935379.90793802[/C][C]-979.90793802496[/C][/ROW]
[ROW][C]48[/C][C]2496000[/C][C]2228002.34015692[/C][C]267997.659843076[/C][/ROW]
[ROW][C]49[/C][C]1996800[/C][C]1670702.24810284[/C][C]326097.751897155[/C][/ROW]
[ROW][C]50[/C][C]1216800[/C][C]1545371.94284458[/C][C]-328571.942844581[/C][/ROW]
[ROW][C]51[/C][C]1216800[/C][C]1415027.44103294[/C][C]-198227.44103294[/C][/ROW]
[ROW][C]52[/C][C]1216800[/C][C]1154554.94650625[/C][C]62245.0534937524[/C][/ROW]
[ROW][C]53[/C][C]1435200[/C][C]1543399.70217979[/C][C]-108199.702179795[/C][/ROW]
[ROW][C]54[/C][C]1435200[/C][C]1374260.2815341[/C][C]60939.7184658975[/C][/ROW]
[ROW][C]55[/C][C]1934400[/C][C]1878359.41486869[/C][C]56040.5851313123[/C][/ROW]
[ROW][C]56[/C][C]1778400[/C][C]1815634.03344899[/C][C]-37234.033448993[/C][/ROW]
[ROW][C]57[/C][C]1591200[/C][C]1572576.93098808[/C][C]18623.0690119159[/C][/ROW]
[ROW][C]58[/C][C]1996800[/C][C]2111070.07866473[/C][C]-114270.078664733[/C][/ROW]
[ROW][C]59[/C][C]1840800[/C][C]1950912.82750346[/C][C]-110112.827503464[/C][/ROW]
[ROW][C]60[/C][C]2652000[/C][C]2489325.97347617[/C][C]162674.026523827[/C][/ROW]
[ROW][C]61[/C][C]2090400[/C][C]1982625.00616112[/C][C]107774.99383888[/C][/ROW]
[ROW][C]62[/C][C]1216800[/C][C]1248251.89550595[/C][C]-31451.8955059499[/C][/ROW]
[ROW][C]63[/C][C]1279200[/C][C]1239511.88699639[/C][C]39688.1130036146[/C][/ROW]
[ROW][C]64[/C][C]1060800[/C][C]1222167.38637453[/C][C]-161367.386374528[/C][/ROW]
[ROW][C]65[/C][C]1466400[/C][C]1450852.10783125[/C][C]15547.8921687519[/C][/ROW]
[ROW][C]66[/C][C]1684800[/C][C]1438726.30392746[/C][C]246073.696072541[/C][/ROW]
[ROW][C]67[/C][C]2121600[/C][C]1941805.14175627[/C][C]179794.858243732[/C][/ROW]
[ROW][C]68[/C][C]2090400[/C][C]1797229.35382365[/C][C]293170.646176349[/C][/ROW]
[ROW][C]69[/C][C]1684800[/C][C]1614669.46999634[/C][C]70130.5300036597[/C][/ROW]
[ROW][C]70[/C][C]1965600[/C][C]2037685.15962313[/C][C]-72085.1596231286[/C][/ROW]
[ROW][C]71[/C][C]1747200[/C][C]1888599.84807855[/C][C]-141399.848078547[/C][/ROW]
[ROW][C]72[/C][C]2496000[/C][C]2684565.01346091[/C][C]-188565.013460914[/C][/ROW]
[ROW][C]73[/C][C]1903200[/C][C]2127349.60779324[/C][C]-224149.607793243[/C][/ROW]
[ROW][C]74[/C][C]1528800[/C][C]1261887.64932227[/C][C]266912.350677733[/C][/ROW]
[ROW][C]75[/C][C]1372800[/C][C]1324440.3450185[/C][C]48359.6549815005[/C][/ROW]
[ROW][C]76[/C][C]1029600[/C][C]1125050.92585428[/C][C]-95450.9258542773[/C][/ROW]
[ROW][C]77[/C][C]1528800[/C][C]1521002.10482946[/C][C]7797.89517054101[/C][/ROW]
[ROW][C]78[/C][C]1840800[/C][C]1724772.50270559[/C][C]116027.497294412[/C][/ROW]
[ROW][C]79[/C][C]2152800[/C][C]2168006.62167028[/C][C]-15206.6216702829[/C][/ROW]
[ROW][C]80[/C][C]2028000[/C][C]2126668.87882254[/C][C]-98668.8788225418[/C][/ROW]
[ROW][C]81[/C][C]1497600[/C][C]1732003.03089312[/C][C]-234403.030893123[/C][/ROW]
[ROW][C]82[/C][C]2152800[/C][C]2015353.02759315[/C][C]137446.972406848[/C][/ROW]
[ROW][C]83[/C][C]1684800[/C][C]1800456.72795788[/C][C]-115656.727957882[/C][/ROW]
[ROW][C]84[/C][C]2589600[/C][C]2549550.42027116[/C][C]40049.5797288399[/C][/ROW]
[ROW][C]85[/C][C]2152800[/C][C]1960127.14840359[/C][C]192672.851596411[/C][/ROW]
[ROW][C]86[/C][C]1560000[/C][C]1553185.23744166[/C][C]6814.76255833544[/C][/ROW]
[ROW][C]87[/C][C]1435200[/C][C]1411912.96469215[/C][C]23287.0353078451[/C][/ROW]
[ROW][C]88[/C][C]967200[/C][C]1079492.27195445[/C][C]-112292.271954451[/C][/ROW]
[ROW][C]89[/C][C]1528800[/C][C]1569913.14953608[/C][C]-41113.1495360842[/C][/ROW]
[ROW][C]90[/C][C]1466400[/C][C]1871991.35398141[/C][C]-405591.353981406[/C][/ROW]
[ROW][C]91[/C][C]2215200[/C][C]2183740.74477022[/C][C]31459.2552297842[/C][/ROW]
[ROW][C]92[/C][C]2215200[/C][C]2060618.87205088[/C][C]154581.127949123[/C][/ROW]
[ROW][C]93[/C][C]1684800[/C][C]1540276.83651312[/C][C]144523.163486883[/C][/ROW]
[ROW][C]94[/C][C]2184000[/C][C]2170189.00008179[/C][C]13810.999918208[/C][/ROW]
[ROW][C]95[/C][C]1622400[/C][C]1720374.50913685[/C][C]-97974.5091368454[/C][/ROW]
[ROW][C]96[/C][C]2527200[/C][C]2612601.09758554[/C][C]-85401.0975855449[/C][/ROW]
[ROW][C]97[/C][C]2152800[/C][C]2160983.35670825[/C][C]-8183.35670824535[/C][/ROW]
[ROW][C]98[/C][C]1591200[/C][C]1577493.69690519[/C][C]13706.3030948099[/C][/ROW]
[ROW][C]99[/C][C]1216800[/C][C]1448039.69422153[/C][C]-231239.694221535[/C][/ROW]
[ROW][C]100[/C][C]842400[/C][C]982595.499780769[/C][C]-140195.499780769[/C][/ROW]
[ROW][C]101[/C][C]1653600[/C][C]1532290.41517765[/C][C]121309.584822349[/C][/ROW]
[ROW][C]102[/C][C]1591200[/C][C]1495600.35475069[/C][C]95599.6452493125[/C][/ROW]
[ROW][C]103[/C][C]2090400[/C][C]2214695.0720958[/C][C]-124295.072095795[/C][/ROW]
[ROW][C]104[/C][C]2402400[/C][C]2202214.03790245[/C][C]200185.962097545[/C][/ROW]
[ROW][C]105[/C][C]1778400[/C][C]1672120.36564556[/C][C]106279.634354442[/C][/ROW]
[ROW][C]106[/C][C]1996800[/C][C]2180008.61205841[/C][C]-183208.612058408[/C][/ROW]
[ROW][C]107[/C][C]1497600[/C][C]1622309.55053232[/C][C]-124709.550532318[/C][/ROW]
[ROW][C]108[/C][C]2589600[/C][C]2522535.20535812[/C][C]67064.7946418831[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279899&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279899&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
1318720001936016.66666667-64016.6666666674
1414040001466458.19887233-62458.1988723313
1516536001729535.72733761-75935.7273376081
1612480001320985.18300485-72985.1830048547
1717472001793186.03485286-45986.034852864
1814352001454011.04561048-18811.045610477
1919032001818213.5164062484986.4835937573
2017160001872164.35106928-156164.351069281
2118096002088835.57587364-279235.575873638
2220280001798680.96254457229319.03745543
2319968001701259.93438262295540.065617385
2423712002145389.24301865225810.756981353
2517160001749394.59486281-33394.5948628134
2614352001282395.17515454152804.824845456
2715912001537884.8105853553315.1894146539
2811544001137279.6643795817120.3356204182
2916536001640050.4261127813549.5738872222
3012792001331875.58088575-52675.5808857456
3118096001796481.0293059913118.9706940132
3217160001632065.4114207483934.5885792614
3315288001744252.92555484-215452.925554837
3421840001930399.51644369253600.483556314
3519656001901679.6776311363920.3223688747
3622464002284763.43127703-38363.431277032
3716848001650437.8212225534362.1787774488
3815600001359097.13145651200902.868543494
3914040001527344.1579214-123344.157921404
4011544001094083.2936995160316.7063004931
4115288001596686.45081174-67886.4508117402
4213728001228720.97592813144079.02407187
4318720001759545.34199519112454.658004815
4418096001665991.58804574143608.411954256
4515600001508210.7731127251789.2268872836
4620904002136641.74499072-46241.7449907199
4719344001935379.90793802-979.90793802496
4824960002228002.34015692267997.659843076
4919968001670702.24810284326097.751897155
5012168001545371.94284458-328571.942844581
5112168001415027.44103294-198227.44103294
5212168001154554.9465062562245.0534937524
5314352001543399.70217979-108199.702179795
5414352001374260.281534160939.7184658975
5519344001878359.4148686956040.5851313123
5617784001815634.03344899-37234.033448993
5715912001572576.9309880818623.0690119159
5819968002111070.07866473-114270.078664733
5918408001950912.82750346-110112.827503464
6026520002489325.97347617162674.026523827
6120904001982625.00616112107774.99383888
6212168001248251.89550595-31451.8955059499
6312792001239511.8869963939688.1130036146
6410608001222167.38637453-161367.386374528
6514664001450852.1078312515547.8921687519
6616848001438726.30392746246073.696072541
6721216001941805.14175627179794.858243732
6820904001797229.35382365293170.646176349
6916848001614669.4699963470130.5300036597
7019656002037685.15962313-72085.1596231286
7117472001888599.84807855-141399.848078547
7224960002684565.01346091-188565.013460914
7319032002127349.60779324-224149.607793243
7415288001261887.64932227266912.350677733
7513728001324440.345018548359.6549815005
7610296001125050.92585428-95450.9258542773
7715288001521002.104829467797.89517054101
7818408001724772.50270559116027.497294412
7921528002168006.62167028-15206.6216702829
8020280002126668.87882254-98668.8788225418
8114976001732003.03089312-234403.030893123
8221528002015353.02759315137446.972406848
8316848001800456.72795788-115656.727957882
8425896002549550.4202711640049.5797288399
8521528001960127.14840359192672.851596411
8615600001553185.237441666814.76255833544
8714352001411912.9646921523287.0353078451
889672001079492.27195445-112292.271954451
8915288001569913.14953608-41113.1495360842
9014664001871991.35398141-405591.353981406
9122152002183740.7447702231459.2552297842
9222152002060618.87205088154581.127949123
9316848001540276.83651312144523.163486883
9421840002170189.0000817913810.999918208
9516224001720374.50913685-97974.5091368454
9625272002612601.09758554-85401.0975855449
9721528002160983.35670825-8183.35670824535
9815912001577493.6969051913706.3030948099
9912168001448039.69422153-231239.694221535
100842400982595.499780769-140195.499780769
10116536001532290.41517765121309.584822349
10215912001495600.3547506995599.6452493125
10320904002214695.0720958-124295.072095795
10424024002202214.03790245200185.962097545
10517784001672120.36564556106279.634354442
10619968002180008.61205841-183208.612058408
10714976001622309.55053232-124709.550532318
10825896002522535.2053581267064.7946418831







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092141535.791563041855548.274391032427523.30873504
1101576438.121872121290401.550855941862474.6928883
1111219248.68368841933101.772269131505395.59510768
112839979.106438694553636.1392878611126322.07358953
1131633325.228415371346676.192633291919974.26419744
1141572170.677621341285081.476258441859259.87898423
1152087278.807316821799591.573849362374966.04078428
1162375454.797338262086988.327903832663921.2667727
1171755758.300684361466308.618368342045207.98300039
1181993767.308161441703108.370392372284426.24593051
1191491117.987611871199002.543797611783233.43142614
1202569774.147093592275934.749101472863613.54508571

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2141535.79156304 & 1855548.27439103 & 2427523.30873504 \tabularnewline
110 & 1576438.12187212 & 1290401.55085594 & 1862474.6928883 \tabularnewline
111 & 1219248.68368841 & 933101.77226913 & 1505395.59510768 \tabularnewline
112 & 839979.106438694 & 553636.139287861 & 1126322.07358953 \tabularnewline
113 & 1633325.22841537 & 1346676.19263329 & 1919974.26419744 \tabularnewline
114 & 1572170.67762134 & 1285081.47625844 & 1859259.87898423 \tabularnewline
115 & 2087278.80731682 & 1799591.57384936 & 2374966.04078428 \tabularnewline
116 & 2375454.79733826 & 2086988.32790383 & 2663921.2667727 \tabularnewline
117 & 1755758.30068436 & 1466308.61836834 & 2045207.98300039 \tabularnewline
118 & 1993767.30816144 & 1703108.37039237 & 2284426.24593051 \tabularnewline
119 & 1491117.98761187 & 1199002.54379761 & 1783233.43142614 \tabularnewline
120 & 2569774.14709359 & 2275934.74910147 & 2863613.54508571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279899&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]2141535.79156304[/C][C]1855548.27439103[/C][C]2427523.30873504[/C][/ROW]
[ROW][C]110[/C][C]1576438.12187212[/C][C]1290401.55085594[/C][C]1862474.6928883[/C][/ROW]
[ROW][C]111[/C][C]1219248.68368841[/C][C]933101.77226913[/C][C]1505395.59510768[/C][/ROW]
[ROW][C]112[/C][C]839979.106438694[/C][C]553636.139287861[/C][C]1126322.07358953[/C][/ROW]
[ROW][C]113[/C][C]1633325.22841537[/C][C]1346676.19263329[/C][C]1919974.26419744[/C][/ROW]
[ROW][C]114[/C][C]1572170.67762134[/C][C]1285081.47625844[/C][C]1859259.87898423[/C][/ROW]
[ROW][C]115[/C][C]2087278.80731682[/C][C]1799591.57384936[/C][C]2374966.04078428[/C][/ROW]
[ROW][C]116[/C][C]2375454.79733826[/C][C]2086988.32790383[/C][C]2663921.2667727[/C][/ROW]
[ROW][C]117[/C][C]1755758.30068436[/C][C]1466308.61836834[/C][C]2045207.98300039[/C][/ROW]
[ROW][C]118[/C][C]1993767.30816144[/C][C]1703108.37039237[/C][C]2284426.24593051[/C][/ROW]
[ROW][C]119[/C][C]1491117.98761187[/C][C]1199002.54379761[/C][C]1783233.43142614[/C][/ROW]
[ROW][C]120[/C][C]2569774.14709359[/C][C]2275934.74910147[/C][C]2863613.54508571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279899&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279899&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
1092141535.791563041855548.274391032427523.30873504
1101576438.121872121290401.550855941862474.6928883
1111219248.68368841933101.772269131505395.59510768
112839979.106438694553636.1392878611126322.07358953
1131633325.228415371346676.192633291919974.26419744
1141572170.677621341285081.476258441859259.87898423
1152087278.807316821799591.573849362374966.04078428
1162375454.797338262086988.327903832663921.2667727
1171755758.300684361466308.618368342045207.98300039
1181993767.308161441703108.370392372284426.24593051
1191491117.987611871199002.543797611783233.43142614
1202569774.147093592275934.749101472863613.54508571



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