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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 06 Aug 2017 19:32:39 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/06/t1502040772j5qrd73dut2bqcu.htm/, Retrieved Sat, 11 May 2024 17:41:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=306975, Retrieved Sat, 11 May 2024 17:41:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-06 17:32:39] [bb1ebaef39f3ee233240b5c77a617fca] [Current]
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Dataseries X:
1755000.00
1690000.00
1787500.00
1430000.00
1852500.00
1820000.00
1950000.00
2015000.00
2242500.00
1950000.00
1852500.00
2307500.00
1950000.00
1462500.00
1722500.00
1300000.00
1820000.00
1495000.00
1982500.00
1787500.00
1885000.00
2112500.00
2080000.00
2470000.00
1787500.00
1495000.00
1657500.00
1202500.00
1722500.00
1332500.00
1885000.00
1787500.00
1592500.00
2275000.00
2047500.00
2340000.00
1755000.00
1625000.00
1462500.00
1202500.00
1592500.00
1430000.00
1950000.00
1885000.00
1625000.00
2177500.00
2015000.00
2600000.00
2080000.00
1267500.00
1267500.00
1267500.00
1495000.00
1495000.00
2015000.00
1852500.00
1657500.00
2080000.00
1917500.00
2762500.00
2177500.00
1267500.00
1332500.00
1105000.00
1527500.00
1755000.00
2210000.00
2177500.00
1755000.00
2047500.00
1820000.00
2600000.00
1982500.00
1592500.00
1430000.00
1072500.00
1592500.00
1917500.00
2242500.00
2112500.00
1560000.00
2242500.00
1755000.00
2697500.00
2242500.00
1625000.00
1495000.00
1007500.00
1592500.00
1527500.00
2307500.00
2307500.00
1755000.00
2275000.00
1690000.00
2632500.00
2242500.00
1657500.00
1267500.00
877500.00
1722500.00
1657500.00
2177500.00
2502500.00
1852500.00
2080000.00
1560000.00
2697500.00




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306975&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=306975&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306975&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
alpha0.00903806239708601
beta1
gamma0.930857409774482

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00903806239708601 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.930857409774482 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306975&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]0.00903806239708601[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.930857409774482[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306975&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306975&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
alpha0.00903806239708601
beta1
gamma0.930857409774482







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1319500002024120.21884131-74120.2188413076
1414625001516967.73747181-54467.7374718066
1517225001800792.09057292-78292.0905729216
1613000001357054.6049086-57054.6049085967
1718200001870853.59827817-50853.5982781702
1814950001513189.39127148-18189.391271482
1919825001894975.0302745687524.969725437
2017875001948475.82091444-160975.820914443
2118850002165936.18532318-280936.18532318
2221125001874105.61488394238394.385116057
2320800001776410.243328303589.756671996
2424700002221709.30260309248290.697396906
2517875001819694.7443371-32194.7443370982
2614950001365118.49324226129881.506757736
2716575001612881.9186524544618.0813475505
2812025001220344.37534948-17844.3753494751
2917225001710693.1240336411806.8759663587
3013325001407596.52097748-75096.5209774841
3118850001861918.5973239623081.4026760357
3217875001699060.1992788439.8007300023
3315925001807701.64347096-215201.643470962
3422750001992143.86031541282856.139684594
3520475001963416.9036561684083.0963438409
3623400002343033.10957213-3033.10957213026
3717550001712100.6930992942899.3069007057
3816250001423294.58529549201705.414704507
3914625001589671.34168316-127171.341683158
4012025001157357.4653378645142.5346621354
4115925001658743.89875898-66243.8987589809
4214300001290608.40736359139391.592636406
4319500001823862.32500216126137.674997836
4418850001731131.42618797153868.573812028
4516250001570557.5187791254442.4812208756
4621775002213230.3071343-35730.3071342972
4720150002009668.529168635331.47083136532
4826000002311189.5060168288810.493983199
4920800001739651.63859549340348.361404513
5012675001610189.53331255-342689.53331255
5112675001472664.05105949-205164.051059493
5212675001201380.7032179366119.2967820738
5314950001604919.61369562-109919.61369562
5414950001428275.8891388366724.1108611699
5520150001954814.3262098860185.6737901215
5618525001888856.51411318-36356.5141131792
5716575001633405.6312408324094.3687591725
5820800002197126.08478575-117126.084785753
5919175002029029.10113817-111529.101138171
6027625002592494.00092551170005.999074492
6121775002061406.84822235116093.151777651
6212675001293826.26800715-26326.2680071502
6313325001284756.2894827947743.7105172062
6411050001266943.74922548-161943.749225484
6515275001505181.002090322318.9979097035
6617550001492492.07237251262507.927627495
6722100002018468.84953152191531.150468476
6821775001866993.1087093310506.891290704
6917550001674382.1702527780617.8297472317
7020475002120949.5066113-73449.5066112978
7118200001963211.03428023-143211.034280235
7226000002811790.63807036-211790.638070357
7319825002220074.88762318-237574.887623184
7415925001298918.48408573293581.515914274
7514300001366706.8821623763293.1178376277
7610725001152947.82316093-80447.8231609317
7715925001580864.0570184911635.942981506
7819175001803138.63831758114361.361682421
7922425002285599.76546687-43099.7654668749
8021125002242870.28102369-130370.281023694
8115600001817038.1294678-257038.129467804
8222425002124959.18623817117540.81376183
8317550001893876.11270809-138876.112708092
8426975002702251.12217008-4751.1221700795
8522425002066263.01452381176236.985476189
8616250001625002.2951751-2.29517510440201
8714950001471203.1981892223796.8018107843
8810075001111845.31707576-104345.317075764
8915925001637651.68356737-45151.6835673749
9015275001959576.96214092-432076.962140915
9123075002289869.5788987917630.4211012051
9223075002155748.26276182151751.737238178
9317550001601448.19465478153551.805345217
9422750002267184.242358587815.75764141791
9516900001789316.11609105-99316.1160910483
9626325002731358.81199055-98858.8119905503
9722425002252454.01811318-9954.01811318425
9816575001637325.8393545220174.1606454784
9912675001501465.34435466-233965.344354663
1008775001015847.67820711-138347.678207108
10117225001589456.28747531133043.71252469
10216575001550656.75925942106843.240740579
10321775002297023.33586565-119523.335865652
10425025002283120.0414092219379.958590801
10518525001732580.2816696119919.718330404
10620800002258078.73941106-178078.739411058
10715600001681323.79723852-121323.797238517
10826975002609442.7525870288057.2474129829

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1950000 & 2024120.21884131 & -74120.2188413076 \tabularnewline
14 & 1462500 & 1516967.73747181 & -54467.7374718066 \tabularnewline
15 & 1722500 & 1800792.09057292 & -78292.0905729216 \tabularnewline
16 & 1300000 & 1357054.6049086 & -57054.6049085967 \tabularnewline
17 & 1820000 & 1870853.59827817 & -50853.5982781702 \tabularnewline
18 & 1495000 & 1513189.39127148 & -18189.391271482 \tabularnewline
19 & 1982500 & 1894975.03027456 & 87524.969725437 \tabularnewline
20 & 1787500 & 1948475.82091444 & -160975.820914443 \tabularnewline
21 & 1885000 & 2165936.18532318 & -280936.18532318 \tabularnewline
22 & 2112500 & 1874105.61488394 & 238394.385116057 \tabularnewline
23 & 2080000 & 1776410.243328 & 303589.756671996 \tabularnewline
24 & 2470000 & 2221709.30260309 & 248290.697396906 \tabularnewline
25 & 1787500 & 1819694.7443371 & -32194.7443370982 \tabularnewline
26 & 1495000 & 1365118.49324226 & 129881.506757736 \tabularnewline
27 & 1657500 & 1612881.91865245 & 44618.0813475505 \tabularnewline
28 & 1202500 & 1220344.37534948 & -17844.3753494751 \tabularnewline
29 & 1722500 & 1710693.12403364 & 11806.8759663587 \tabularnewline
30 & 1332500 & 1407596.52097748 & -75096.5209774841 \tabularnewline
31 & 1885000 & 1861918.59732396 & 23081.4026760357 \tabularnewline
32 & 1787500 & 1699060.19927 & 88439.8007300023 \tabularnewline
33 & 1592500 & 1807701.64347096 & -215201.643470962 \tabularnewline
34 & 2275000 & 1992143.86031541 & 282856.139684594 \tabularnewline
35 & 2047500 & 1963416.90365616 & 84083.0963438409 \tabularnewline
36 & 2340000 & 2343033.10957213 & -3033.10957213026 \tabularnewline
37 & 1755000 & 1712100.69309929 & 42899.3069007057 \tabularnewline
38 & 1625000 & 1423294.58529549 & 201705.414704507 \tabularnewline
39 & 1462500 & 1589671.34168316 & -127171.341683158 \tabularnewline
40 & 1202500 & 1157357.46533786 & 45142.5346621354 \tabularnewline
41 & 1592500 & 1658743.89875898 & -66243.8987589809 \tabularnewline
42 & 1430000 & 1290608.40736359 & 139391.592636406 \tabularnewline
43 & 1950000 & 1823862.32500216 & 126137.674997836 \tabularnewline
44 & 1885000 & 1731131.42618797 & 153868.573812028 \tabularnewline
45 & 1625000 & 1570557.51877912 & 54442.4812208756 \tabularnewline
46 & 2177500 & 2213230.3071343 & -35730.3071342972 \tabularnewline
47 & 2015000 & 2009668.52916863 & 5331.47083136532 \tabularnewline
48 & 2600000 & 2311189.5060168 & 288810.493983199 \tabularnewline
49 & 2080000 & 1739651.63859549 & 340348.361404513 \tabularnewline
50 & 1267500 & 1610189.53331255 & -342689.53331255 \tabularnewline
51 & 1267500 & 1472664.05105949 & -205164.051059493 \tabularnewline
52 & 1267500 & 1201380.70321793 & 66119.2967820738 \tabularnewline
53 & 1495000 & 1604919.61369562 & -109919.61369562 \tabularnewline
54 & 1495000 & 1428275.88913883 & 66724.1108611699 \tabularnewline
55 & 2015000 & 1954814.32620988 & 60185.6737901215 \tabularnewline
56 & 1852500 & 1888856.51411318 & -36356.5141131792 \tabularnewline
57 & 1657500 & 1633405.63124083 & 24094.3687591725 \tabularnewline
58 & 2080000 & 2197126.08478575 & -117126.084785753 \tabularnewline
59 & 1917500 & 2029029.10113817 & -111529.101138171 \tabularnewline
60 & 2762500 & 2592494.00092551 & 170005.999074492 \tabularnewline
61 & 2177500 & 2061406.84822235 & 116093.151777651 \tabularnewline
62 & 1267500 & 1293826.26800715 & -26326.2680071502 \tabularnewline
63 & 1332500 & 1284756.28948279 & 47743.7105172062 \tabularnewline
64 & 1105000 & 1266943.74922548 & -161943.749225484 \tabularnewline
65 & 1527500 & 1505181.0020903 & 22318.9979097035 \tabularnewline
66 & 1755000 & 1492492.07237251 & 262507.927627495 \tabularnewline
67 & 2210000 & 2018468.84953152 & 191531.150468476 \tabularnewline
68 & 2177500 & 1866993.1087093 & 310506.891290704 \tabularnewline
69 & 1755000 & 1674382.17025277 & 80617.8297472317 \tabularnewline
70 & 2047500 & 2120949.5066113 & -73449.5066112978 \tabularnewline
71 & 1820000 & 1963211.03428023 & -143211.034280235 \tabularnewline
72 & 2600000 & 2811790.63807036 & -211790.638070357 \tabularnewline
73 & 1982500 & 2220074.88762318 & -237574.887623184 \tabularnewline
74 & 1592500 & 1298918.48408573 & 293581.515914274 \tabularnewline
75 & 1430000 & 1366706.88216237 & 63293.1178376277 \tabularnewline
76 & 1072500 & 1152947.82316093 & -80447.8231609317 \tabularnewline
77 & 1592500 & 1580864.05701849 & 11635.942981506 \tabularnewline
78 & 1917500 & 1803138.63831758 & 114361.361682421 \tabularnewline
79 & 2242500 & 2285599.76546687 & -43099.7654668749 \tabularnewline
80 & 2112500 & 2242870.28102369 & -130370.281023694 \tabularnewline
81 & 1560000 & 1817038.1294678 & -257038.129467804 \tabularnewline
82 & 2242500 & 2124959.18623817 & 117540.81376183 \tabularnewline
83 & 1755000 & 1893876.11270809 & -138876.112708092 \tabularnewline
84 & 2697500 & 2702251.12217008 & -4751.1221700795 \tabularnewline
85 & 2242500 & 2066263.01452381 & 176236.985476189 \tabularnewline
86 & 1625000 & 1625002.2951751 & -2.29517510440201 \tabularnewline
87 & 1495000 & 1471203.19818922 & 23796.8018107843 \tabularnewline
88 & 1007500 & 1111845.31707576 & -104345.317075764 \tabularnewline
89 & 1592500 & 1637651.68356737 & -45151.6835673749 \tabularnewline
90 & 1527500 & 1959576.96214092 & -432076.962140915 \tabularnewline
91 & 2307500 & 2289869.57889879 & 17630.4211012051 \tabularnewline
92 & 2307500 & 2155748.26276182 & 151751.737238178 \tabularnewline
93 & 1755000 & 1601448.19465478 & 153551.805345217 \tabularnewline
94 & 2275000 & 2267184.24235858 & 7815.75764141791 \tabularnewline
95 & 1690000 & 1789316.11609105 & -99316.1160910483 \tabularnewline
96 & 2632500 & 2731358.81199055 & -98858.8119905503 \tabularnewline
97 & 2242500 & 2252454.01811318 & -9954.01811318425 \tabularnewline
98 & 1657500 & 1637325.83935452 & 20174.1606454784 \tabularnewline
99 & 1267500 & 1501465.34435466 & -233965.344354663 \tabularnewline
100 & 877500 & 1015847.67820711 & -138347.678207108 \tabularnewline
101 & 1722500 & 1589456.28747531 & 133043.71252469 \tabularnewline
102 & 1657500 & 1550656.75925942 & 106843.240740579 \tabularnewline
103 & 2177500 & 2297023.33586565 & -119523.335865652 \tabularnewline
104 & 2502500 & 2283120.0414092 & 219379.958590801 \tabularnewline
105 & 1852500 & 1732580.2816696 & 119919.718330404 \tabularnewline
106 & 2080000 & 2258078.73941106 & -178078.739411058 \tabularnewline
107 & 1560000 & 1681323.79723852 & -121323.797238517 \tabularnewline
108 & 2697500 & 2609442.75258702 & 88057.2474129829 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306975&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]1950000[/C][C]2024120.21884131[/C][C]-74120.2188413076[/C][/ROW]
[ROW][C]14[/C][C]1462500[/C][C]1516967.73747181[/C][C]-54467.7374718066[/C][/ROW]
[ROW][C]15[/C][C]1722500[/C][C]1800792.09057292[/C][C]-78292.0905729216[/C][/ROW]
[ROW][C]16[/C][C]1300000[/C][C]1357054.6049086[/C][C]-57054.6049085967[/C][/ROW]
[ROW][C]17[/C][C]1820000[/C][C]1870853.59827817[/C][C]-50853.5982781702[/C][/ROW]
[ROW][C]18[/C][C]1495000[/C][C]1513189.39127148[/C][C]-18189.391271482[/C][/ROW]
[ROW][C]19[/C][C]1982500[/C][C]1894975.03027456[/C][C]87524.969725437[/C][/ROW]
[ROW][C]20[/C][C]1787500[/C][C]1948475.82091444[/C][C]-160975.820914443[/C][/ROW]
[ROW][C]21[/C][C]1885000[/C][C]2165936.18532318[/C][C]-280936.18532318[/C][/ROW]
[ROW][C]22[/C][C]2112500[/C][C]1874105.61488394[/C][C]238394.385116057[/C][/ROW]
[ROW][C]23[/C][C]2080000[/C][C]1776410.243328[/C][C]303589.756671996[/C][/ROW]
[ROW][C]24[/C][C]2470000[/C][C]2221709.30260309[/C][C]248290.697396906[/C][/ROW]
[ROW][C]25[/C][C]1787500[/C][C]1819694.7443371[/C][C]-32194.7443370982[/C][/ROW]
[ROW][C]26[/C][C]1495000[/C][C]1365118.49324226[/C][C]129881.506757736[/C][/ROW]
[ROW][C]27[/C][C]1657500[/C][C]1612881.91865245[/C][C]44618.0813475505[/C][/ROW]
[ROW][C]28[/C][C]1202500[/C][C]1220344.37534948[/C][C]-17844.3753494751[/C][/ROW]
[ROW][C]29[/C][C]1722500[/C][C]1710693.12403364[/C][C]11806.8759663587[/C][/ROW]
[ROW][C]30[/C][C]1332500[/C][C]1407596.52097748[/C][C]-75096.5209774841[/C][/ROW]
[ROW][C]31[/C][C]1885000[/C][C]1861918.59732396[/C][C]23081.4026760357[/C][/ROW]
[ROW][C]32[/C][C]1787500[/C][C]1699060.19927[/C][C]88439.8007300023[/C][/ROW]
[ROW][C]33[/C][C]1592500[/C][C]1807701.64347096[/C][C]-215201.643470962[/C][/ROW]
[ROW][C]34[/C][C]2275000[/C][C]1992143.86031541[/C][C]282856.139684594[/C][/ROW]
[ROW][C]35[/C][C]2047500[/C][C]1963416.90365616[/C][C]84083.0963438409[/C][/ROW]
[ROW][C]36[/C][C]2340000[/C][C]2343033.10957213[/C][C]-3033.10957213026[/C][/ROW]
[ROW][C]37[/C][C]1755000[/C][C]1712100.69309929[/C][C]42899.3069007057[/C][/ROW]
[ROW][C]38[/C][C]1625000[/C][C]1423294.58529549[/C][C]201705.414704507[/C][/ROW]
[ROW][C]39[/C][C]1462500[/C][C]1589671.34168316[/C][C]-127171.341683158[/C][/ROW]
[ROW][C]40[/C][C]1202500[/C][C]1157357.46533786[/C][C]45142.5346621354[/C][/ROW]
[ROW][C]41[/C][C]1592500[/C][C]1658743.89875898[/C][C]-66243.8987589809[/C][/ROW]
[ROW][C]42[/C][C]1430000[/C][C]1290608.40736359[/C][C]139391.592636406[/C][/ROW]
[ROW][C]43[/C][C]1950000[/C][C]1823862.32500216[/C][C]126137.674997836[/C][/ROW]
[ROW][C]44[/C][C]1885000[/C][C]1731131.42618797[/C][C]153868.573812028[/C][/ROW]
[ROW][C]45[/C][C]1625000[/C][C]1570557.51877912[/C][C]54442.4812208756[/C][/ROW]
[ROW][C]46[/C][C]2177500[/C][C]2213230.3071343[/C][C]-35730.3071342972[/C][/ROW]
[ROW][C]47[/C][C]2015000[/C][C]2009668.52916863[/C][C]5331.47083136532[/C][/ROW]
[ROW][C]48[/C][C]2600000[/C][C]2311189.5060168[/C][C]288810.493983199[/C][/ROW]
[ROW][C]49[/C][C]2080000[/C][C]1739651.63859549[/C][C]340348.361404513[/C][/ROW]
[ROW][C]50[/C][C]1267500[/C][C]1610189.53331255[/C][C]-342689.53331255[/C][/ROW]
[ROW][C]51[/C][C]1267500[/C][C]1472664.05105949[/C][C]-205164.051059493[/C][/ROW]
[ROW][C]52[/C][C]1267500[/C][C]1201380.70321793[/C][C]66119.2967820738[/C][/ROW]
[ROW][C]53[/C][C]1495000[/C][C]1604919.61369562[/C][C]-109919.61369562[/C][/ROW]
[ROW][C]54[/C][C]1495000[/C][C]1428275.88913883[/C][C]66724.1108611699[/C][/ROW]
[ROW][C]55[/C][C]2015000[/C][C]1954814.32620988[/C][C]60185.6737901215[/C][/ROW]
[ROW][C]56[/C][C]1852500[/C][C]1888856.51411318[/C][C]-36356.5141131792[/C][/ROW]
[ROW][C]57[/C][C]1657500[/C][C]1633405.63124083[/C][C]24094.3687591725[/C][/ROW]
[ROW][C]58[/C][C]2080000[/C][C]2197126.08478575[/C][C]-117126.084785753[/C][/ROW]
[ROW][C]59[/C][C]1917500[/C][C]2029029.10113817[/C][C]-111529.101138171[/C][/ROW]
[ROW][C]60[/C][C]2762500[/C][C]2592494.00092551[/C][C]170005.999074492[/C][/ROW]
[ROW][C]61[/C][C]2177500[/C][C]2061406.84822235[/C][C]116093.151777651[/C][/ROW]
[ROW][C]62[/C][C]1267500[/C][C]1293826.26800715[/C][C]-26326.2680071502[/C][/ROW]
[ROW][C]63[/C][C]1332500[/C][C]1284756.28948279[/C][C]47743.7105172062[/C][/ROW]
[ROW][C]64[/C][C]1105000[/C][C]1266943.74922548[/C][C]-161943.749225484[/C][/ROW]
[ROW][C]65[/C][C]1527500[/C][C]1505181.0020903[/C][C]22318.9979097035[/C][/ROW]
[ROW][C]66[/C][C]1755000[/C][C]1492492.07237251[/C][C]262507.927627495[/C][/ROW]
[ROW][C]67[/C][C]2210000[/C][C]2018468.84953152[/C][C]191531.150468476[/C][/ROW]
[ROW][C]68[/C][C]2177500[/C][C]1866993.1087093[/C][C]310506.891290704[/C][/ROW]
[ROW][C]69[/C][C]1755000[/C][C]1674382.17025277[/C][C]80617.8297472317[/C][/ROW]
[ROW][C]70[/C][C]2047500[/C][C]2120949.5066113[/C][C]-73449.5066112978[/C][/ROW]
[ROW][C]71[/C][C]1820000[/C][C]1963211.03428023[/C][C]-143211.034280235[/C][/ROW]
[ROW][C]72[/C][C]2600000[/C][C]2811790.63807036[/C][C]-211790.638070357[/C][/ROW]
[ROW][C]73[/C][C]1982500[/C][C]2220074.88762318[/C][C]-237574.887623184[/C][/ROW]
[ROW][C]74[/C][C]1592500[/C][C]1298918.48408573[/C][C]293581.515914274[/C][/ROW]
[ROW][C]75[/C][C]1430000[/C][C]1366706.88216237[/C][C]63293.1178376277[/C][/ROW]
[ROW][C]76[/C][C]1072500[/C][C]1152947.82316093[/C][C]-80447.8231609317[/C][/ROW]
[ROW][C]77[/C][C]1592500[/C][C]1580864.05701849[/C][C]11635.942981506[/C][/ROW]
[ROW][C]78[/C][C]1917500[/C][C]1803138.63831758[/C][C]114361.361682421[/C][/ROW]
[ROW][C]79[/C][C]2242500[/C][C]2285599.76546687[/C][C]-43099.7654668749[/C][/ROW]
[ROW][C]80[/C][C]2112500[/C][C]2242870.28102369[/C][C]-130370.281023694[/C][/ROW]
[ROW][C]81[/C][C]1560000[/C][C]1817038.1294678[/C][C]-257038.129467804[/C][/ROW]
[ROW][C]82[/C][C]2242500[/C][C]2124959.18623817[/C][C]117540.81376183[/C][/ROW]
[ROW][C]83[/C][C]1755000[/C][C]1893876.11270809[/C][C]-138876.112708092[/C][/ROW]
[ROW][C]84[/C][C]2697500[/C][C]2702251.12217008[/C][C]-4751.1221700795[/C][/ROW]
[ROW][C]85[/C][C]2242500[/C][C]2066263.01452381[/C][C]176236.985476189[/C][/ROW]
[ROW][C]86[/C][C]1625000[/C][C]1625002.2951751[/C][C]-2.29517510440201[/C][/ROW]
[ROW][C]87[/C][C]1495000[/C][C]1471203.19818922[/C][C]23796.8018107843[/C][/ROW]
[ROW][C]88[/C][C]1007500[/C][C]1111845.31707576[/C][C]-104345.317075764[/C][/ROW]
[ROW][C]89[/C][C]1592500[/C][C]1637651.68356737[/C][C]-45151.6835673749[/C][/ROW]
[ROW][C]90[/C][C]1527500[/C][C]1959576.96214092[/C][C]-432076.962140915[/C][/ROW]
[ROW][C]91[/C][C]2307500[/C][C]2289869.57889879[/C][C]17630.4211012051[/C][/ROW]
[ROW][C]92[/C][C]2307500[/C][C]2155748.26276182[/C][C]151751.737238178[/C][/ROW]
[ROW][C]93[/C][C]1755000[/C][C]1601448.19465478[/C][C]153551.805345217[/C][/ROW]
[ROW][C]94[/C][C]2275000[/C][C]2267184.24235858[/C][C]7815.75764141791[/C][/ROW]
[ROW][C]95[/C][C]1690000[/C][C]1789316.11609105[/C][C]-99316.1160910483[/C][/ROW]
[ROW][C]96[/C][C]2632500[/C][C]2731358.81199055[/C][C]-98858.8119905503[/C][/ROW]
[ROW][C]97[/C][C]2242500[/C][C]2252454.01811318[/C][C]-9954.01811318425[/C][/ROW]
[ROW][C]98[/C][C]1657500[/C][C]1637325.83935452[/C][C]20174.1606454784[/C][/ROW]
[ROW][C]99[/C][C]1267500[/C][C]1501465.34435466[/C][C]-233965.344354663[/C][/ROW]
[ROW][C]100[/C][C]877500[/C][C]1015847.67820711[/C][C]-138347.678207108[/C][/ROW]
[ROW][C]101[/C][C]1722500[/C][C]1589456.28747531[/C][C]133043.71252469[/C][/ROW]
[ROW][C]102[/C][C]1657500[/C][C]1550656.75925942[/C][C]106843.240740579[/C][/ROW]
[ROW][C]103[/C][C]2177500[/C][C]2297023.33586565[/C][C]-119523.335865652[/C][/ROW]
[ROW][C]104[/C][C]2502500[/C][C]2283120.0414092[/C][C]219379.958590801[/C][/ROW]
[ROW][C]105[/C][C]1852500[/C][C]1732580.2816696[/C][C]119919.718330404[/C][/ROW]
[ROW][C]106[/C][C]2080000[/C][C]2258078.73941106[/C][C]-178078.739411058[/C][/ROW]
[ROW][C]107[/C][C]1560000[/C][C]1681323.79723852[/C][C]-121323.797238517[/C][/ROW]
[ROW][C]108[/C][C]2697500[/C][C]2609442.75258702[/C][C]88057.2474129829[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306975&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306975&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
1319500002024120.21884131-74120.2188413076
1414625001516967.73747181-54467.7374718066
1517225001800792.09057292-78292.0905729216
1613000001357054.6049086-57054.6049085967
1718200001870853.59827817-50853.5982781702
1814950001513189.39127148-18189.391271482
1919825001894975.0302745687524.969725437
2017875001948475.82091444-160975.820914443
2118850002165936.18532318-280936.18532318
2221125001874105.61488394238394.385116057
2320800001776410.243328303589.756671996
2424700002221709.30260309248290.697396906
2517875001819694.7443371-32194.7443370982
2614950001365118.49324226129881.506757736
2716575001612881.9186524544618.0813475505
2812025001220344.37534948-17844.3753494751
2917225001710693.1240336411806.8759663587
3013325001407596.52097748-75096.5209774841
3118850001861918.5973239623081.4026760357
3217875001699060.1992788439.8007300023
3315925001807701.64347096-215201.643470962
3422750001992143.86031541282856.139684594
3520475001963416.9036561684083.0963438409
3623400002343033.10957213-3033.10957213026
3717550001712100.6930992942899.3069007057
3816250001423294.58529549201705.414704507
3914625001589671.34168316-127171.341683158
4012025001157357.4653378645142.5346621354
4115925001658743.89875898-66243.8987589809
4214300001290608.40736359139391.592636406
4319500001823862.32500216126137.674997836
4418850001731131.42618797153868.573812028
4516250001570557.5187791254442.4812208756
4621775002213230.3071343-35730.3071342972
4720150002009668.529168635331.47083136532
4826000002311189.5060168288810.493983199
4920800001739651.63859549340348.361404513
5012675001610189.53331255-342689.53331255
5112675001472664.05105949-205164.051059493
5212675001201380.7032179366119.2967820738
5314950001604919.61369562-109919.61369562
5414950001428275.8891388366724.1108611699
5520150001954814.3262098860185.6737901215
5618525001888856.51411318-36356.5141131792
5716575001633405.6312408324094.3687591725
5820800002197126.08478575-117126.084785753
5919175002029029.10113817-111529.101138171
6027625002592494.00092551170005.999074492
6121775002061406.84822235116093.151777651
6212675001293826.26800715-26326.2680071502
6313325001284756.2894827947743.7105172062
6411050001266943.74922548-161943.749225484
6515275001505181.002090322318.9979097035
6617550001492492.07237251262507.927627495
6722100002018468.84953152191531.150468476
6821775001866993.1087093310506.891290704
6917550001674382.1702527780617.8297472317
7020475002120949.5066113-73449.5066112978
7118200001963211.03428023-143211.034280235
7226000002811790.63807036-211790.638070357
7319825002220074.88762318-237574.887623184
7415925001298918.48408573293581.515914274
7514300001366706.8821623763293.1178376277
7610725001152947.82316093-80447.8231609317
7715925001580864.0570184911635.942981506
7819175001803138.63831758114361.361682421
7922425002285599.76546687-43099.7654668749
8021125002242870.28102369-130370.281023694
8115600001817038.1294678-257038.129467804
8222425002124959.18623817117540.81376183
8317550001893876.11270809-138876.112708092
8426975002702251.12217008-4751.1221700795
8522425002066263.01452381176236.985476189
8616250001625002.2951751-2.29517510440201
8714950001471203.1981892223796.8018107843
8810075001111845.31707576-104345.317075764
8915925001637651.68356737-45151.6835673749
9015275001959576.96214092-432076.962140915
9123075002289869.5788987917630.4211012051
9223075002155748.26276182151751.737238178
9317550001601448.19465478153551.805345217
9422750002267184.242358587815.75764141791
9516900001789316.11609105-99316.1160910483
9626325002731358.81199055-98858.8119905503
9722425002252454.01811318-9954.01811318425
9816575001637325.8393545220174.1606454784
9912675001501465.34435466-233965.344354663
1008775001015847.67820711-138347.678207108
10117225001589456.28747531133043.71252469
10216575001550656.75925942106843.240740579
10321775002297023.33586565-119523.335865652
10425025002283120.0414092219379.958590801
10518525001732580.2816696119919.718330404
10620800002258078.73941106-178078.739411058
10715600001681323.79723852-121323.797238517
10826975002609442.7525870288057.2474129829







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092215832.221972491937217.223281912494447.22066308
1101633771.331750771355127.754055841912414.9094457
1111266326.42152591987641.131839041545011.71121278
112876248.232980056597540.9522524111154955.5137077
1131693621.272396431414178.928470741973063.61632211
1141631063.503003971351053.957953871911073.04805407
1152161277.80509131878703.051405092443852.5587775
1162458587.24899642172368.208444432744806.28954837
1171820914.817525851536408.584592742105421.05045895
1182064945.60375421776164.407213512353726.80029488
1191548331.551835391262206.444498551834456.65917224
1202657139.132568242530838.256810242783440.00832625

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2215832.22197249 & 1937217.22328191 & 2494447.22066308 \tabularnewline
110 & 1633771.33175077 & 1355127.75405584 & 1912414.9094457 \tabularnewline
111 & 1266326.42152591 & 987641.13183904 & 1545011.71121278 \tabularnewline
112 & 876248.232980056 & 597540.952252411 & 1154955.5137077 \tabularnewline
113 & 1693621.27239643 & 1414178.92847074 & 1973063.61632211 \tabularnewline
114 & 1631063.50300397 & 1351053.95795387 & 1911073.04805407 \tabularnewline
115 & 2161277.8050913 & 1878703.05140509 & 2443852.5587775 \tabularnewline
116 & 2458587.2489964 & 2172368.20844443 & 2744806.28954837 \tabularnewline
117 & 1820914.81752585 & 1536408.58459274 & 2105421.05045895 \tabularnewline
118 & 2064945.6037542 & 1776164.40721351 & 2353726.80029488 \tabularnewline
119 & 1548331.55183539 & 1262206.44449855 & 1834456.65917224 \tabularnewline
120 & 2657139.13256824 & 2530838.25681024 & 2783440.00832625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306975&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]2215832.22197249[/C][C]1937217.22328191[/C][C]2494447.22066308[/C][/ROW]
[ROW][C]110[/C][C]1633771.33175077[/C][C]1355127.75405584[/C][C]1912414.9094457[/C][/ROW]
[ROW][C]111[/C][C]1266326.42152591[/C][C]987641.13183904[/C][C]1545011.71121278[/C][/ROW]
[ROW][C]112[/C][C]876248.232980056[/C][C]597540.952252411[/C][C]1154955.5137077[/C][/ROW]
[ROW][C]113[/C][C]1693621.27239643[/C][C]1414178.92847074[/C][C]1973063.61632211[/C][/ROW]
[ROW][C]114[/C][C]1631063.50300397[/C][C]1351053.95795387[/C][C]1911073.04805407[/C][/ROW]
[ROW][C]115[/C][C]2161277.8050913[/C][C]1878703.05140509[/C][C]2443852.5587775[/C][/ROW]
[ROW][C]116[/C][C]2458587.2489964[/C][C]2172368.20844443[/C][C]2744806.28954837[/C][/ROW]
[ROW][C]117[/C][C]1820914.81752585[/C][C]1536408.58459274[/C][C]2105421.05045895[/C][/ROW]
[ROW][C]118[/C][C]2064945.6037542[/C][C]1776164.40721351[/C][C]2353726.80029488[/C][/ROW]
[ROW][C]119[/C][C]1548331.55183539[/C][C]1262206.44449855[/C][C]1834456.65917224[/C][/ROW]
[ROW][C]120[/C][C]2657139.13256824[/C][C]2530838.25681024[/C][C]2783440.00832625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306975&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306975&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
1092215832.221972491937217.223281912494447.22066308
1101633771.331750771355127.754055841912414.9094457
1111266326.42152591987641.131839041545011.71121278
112876248.232980056597540.9522524111154955.5137077
1131693621.272396431414178.928470741973063.61632211
1141631063.503003971351053.957953871911073.04805407
1152161277.80509131878703.051405092443852.5587775
1162458587.24899642172368.208444432744806.28954837
1171820914.817525851536408.584592742105421.05045895
1182064945.60375421776164.407213512353726.80029488
1191548331.551835391262206.444498551834456.65917224
1202657139.132568242530838.256810242783440.00832625



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; 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')