Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 15 Aug 2017 22:04:24 +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/15/t1502827563dc898a718kf8usb.htm/, Retrieved Sun, 19 May 2024 23:04:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307330, Retrieved Sun, 19 May 2024 23:04:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact47
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-15 20:04:24] [f8975010d6e80ebfdd11eb899305ce74] [Current]
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Dataseries X:
1474200
1419600
1501500
1201200
1556100
1528800
1638000
1692600
1883700
1638000
1556100
1938300
1638000
1228500
1446900
1092000
1528800
1255800
1665300
1501500
1583400
1774500
1747200
2074800
1501500
1255800
1392300
1010100
1446900
1119300
1583400
1501500
1337700
1911000
1719900
1965600
1474200
1365000
1228500
1010100
1337700
1201200
1638000
1583400
1365000
1829100
1692600
2184000
1747200
1064700
1064700
1064700
1255800
1255800
1692600
1556100
1392300
1747200
1610700
2320500
1829100
1064700
1119300
928200
1283100
1474200
1856400
1829100
1474200
1719900
1528800
2184000
1665300
1337700
1201200
900900
1337700
1610700
1883700
1774500
1310400
1883700
1474200
2265900
1883700
1365000
1255800
846300
1337700
1283100
1938300
1938300
1474200
1911000
1419600
2211300
1883700
1392300
1064700
737100
1446900
1392300
1829100
2102100
1556100
1747200
1310400
2265900




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=307330&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=307330&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307330&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
alpha0.616435516555793
beta0.0182153483451402
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.616435516555793 \tabularnewline
beta & 0.0182153483451402 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307330&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]0.616435516555793[/C][/ROW]
[ROW][C]beta[/C][C]0.0182153483451402[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307330&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307330&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
alpha0.616435516555793
beta0.0182153483451402
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
315015001365000136500
412012001396076.15022633-194876.150226327
515561001220692.08817671335407.911823286
615288001375960.11297986152839.887020136
716380001420402.89917724217597.100822761
816926001507207.64003829185392.359961713
918837001576241.92919762307458.070802383
1016380001723974.17777451-85974.1777745066
1115561001628215.44637801-72115.446378008
1219383001540189.97461696398110.025383038
1316380001746498.39775951-108498.397759506
1412285001639297.11211976-410797.112119756
1514469001341135.49095266105764.509047339
1610920001362588.38562443-270588.385624432
1715288001149005.66385245379794.336147547
1812558001340606.50513357-84806.5051335739
1916653001244858.62954974420441.37045026
2015015001465284.4519268236215.548073183
2115834001449266.48046923134133.519530768
2217745001495114.75431025279385.24568975
2317472001633638.45272062113561.547279379
2420748001671217.66973336403582.33026664
2515015001892107.65749477-390607.657494767
2612558001619044.75758169-363244.757581694
2713923001358770.5954061433529.4045938591
2810101001343458.60670615-333358.60670615
2914469001098240.67090257348659.329097431
3011193001277357.76549886-158057.765498855
3115834001142341.68066377441058.319336227
3215015001381594.49106554119905.508934458
3313377001424223.6724127-86523.6724127049
3419110001338631.03608304572368.963916963
3517199001665630.1174729154269.882527088
3619656001673863.89813274291736.101867262
3714742001831756.07477134-357556.074771339
3813650001585386.64337687-220386.643376873
3912285001421098.69053406-192598.690534062
4010101001271777.60747485-261677.607474846
4113377001076935.55661226260764.443387737
4212012001207073.35765648-5873.35765647818
4316380001172780.19856936465219.80143064
4415834001434109.35567451149290.64432549
4513650001502364.88271209-137364.882712089
4618291001392373.34823887436726.651761129
4716926001641176.048864551423.9511354968
4821840001653041.89854311530958.101456892
4917472001966471.53947061-219271.539470609
5010647001814970.87445381-750270.874453811
5110647001327718.87779852-263018.877798525
5210647001137872.98686701-73172.9868670073
5312558001064233.21648001191566.783519993
5412558001155939.467627199860.5323728998
5516926001192236.0212191500363.9787809
5615561001481035.5044808375064.4955191689
5713923001508508.14935577-116208.149355775
5817472001416768.68919165330431.310808349
5916107001604063.932309136636.06769087259
6023205001591834.801145728665.198854999
6118291002032871.95148315-203771.951483147
6210647001896833.65417561-832133.654175608
6311193001364107.20039891-244807.200398909
649282001190680.79343189-262480.793431891
6512831001003412.4674144279687.532585601
6614742001153496.44948452320703.550515481
6718564001332465.20968619523934.79031381
6818291001642595.97189772186504.028102277
6914742001746816.60473325-272616.604733254
7017199001564957.87365983154942.126340166
7115288001648401.31108242-119601.311082422
7221840001561263.46903391622736.530966088
7316653001938721.4898385-273421.489838497
7413377001760685.74100427-422985.741004268
7512012001485703.74326989-284503.743269891
769009001292892.39211986-391992.392119863
7713377001029419.69925265308280.300747353
7816107001201081.51792571409618.482074291
7918837001439811.22778761443888.772212393
8017745001704650.6056462169849.3943537883
8113104001739703.13645029-429303.136450285
8218837001462239.85118493421460.148815066
8314742001713949.67336769-239749.673367689
8422659001555374.22703606710525.772963942
8518837001990560.5172651-106860.517265101
8613650001920680.97476499-555680.974764994
8712558001567893.04916545-312093.049165446
888463001361757.00814699-515457.008146987
8913377001024472.34582068313227.654179318
9012831001201535.4455518481564.5544481575
9119383001236709.0374834701590.9625166
9219383001661966.80417942276333.195820583
9314742001828183.41130722-353983.411307215
9419110001601875.74136019309124.258639813
9514196001787802.21930701-368202.219307005
9622113001552066.20904532659233.790954683
9718837001957080.51091169-73380.5109116891
9813923001909661.37767113-517361.377671127
9910647001582747.43190444-518047.431904443
1007371001249593.63693758-512493.636937578
1011446900914108.818709141532791.181290859
10213923001228957.17984028163342.820159723
10318291001317898.55881269511201.441187312
10421021001627012.41672418475087.583275822
10515561001919198.9725572-363098.972557197
10617472001690620.4772302456579.5227697624
10713104001721382.02008905-410982.020089052
10822659001459307.27411219806592.725887806

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1501500 & 1365000 & 136500 \tabularnewline
4 & 1201200 & 1396076.15022633 & -194876.150226327 \tabularnewline
5 & 1556100 & 1220692.08817671 & 335407.911823286 \tabularnewline
6 & 1528800 & 1375960.11297986 & 152839.887020136 \tabularnewline
7 & 1638000 & 1420402.89917724 & 217597.100822761 \tabularnewline
8 & 1692600 & 1507207.64003829 & 185392.359961713 \tabularnewline
9 & 1883700 & 1576241.92919762 & 307458.070802383 \tabularnewline
10 & 1638000 & 1723974.17777451 & -85974.1777745066 \tabularnewline
11 & 1556100 & 1628215.44637801 & -72115.446378008 \tabularnewline
12 & 1938300 & 1540189.97461696 & 398110.025383038 \tabularnewline
13 & 1638000 & 1746498.39775951 & -108498.397759506 \tabularnewline
14 & 1228500 & 1639297.11211976 & -410797.112119756 \tabularnewline
15 & 1446900 & 1341135.49095266 & 105764.509047339 \tabularnewline
16 & 1092000 & 1362588.38562443 & -270588.385624432 \tabularnewline
17 & 1528800 & 1149005.66385245 & 379794.336147547 \tabularnewline
18 & 1255800 & 1340606.50513357 & -84806.5051335739 \tabularnewline
19 & 1665300 & 1244858.62954974 & 420441.37045026 \tabularnewline
20 & 1501500 & 1465284.45192682 & 36215.548073183 \tabularnewline
21 & 1583400 & 1449266.48046923 & 134133.519530768 \tabularnewline
22 & 1774500 & 1495114.75431025 & 279385.24568975 \tabularnewline
23 & 1747200 & 1633638.45272062 & 113561.547279379 \tabularnewline
24 & 2074800 & 1671217.66973336 & 403582.33026664 \tabularnewline
25 & 1501500 & 1892107.65749477 & -390607.657494767 \tabularnewline
26 & 1255800 & 1619044.75758169 & -363244.757581694 \tabularnewline
27 & 1392300 & 1358770.59540614 & 33529.4045938591 \tabularnewline
28 & 1010100 & 1343458.60670615 & -333358.60670615 \tabularnewline
29 & 1446900 & 1098240.67090257 & 348659.329097431 \tabularnewline
30 & 1119300 & 1277357.76549886 & -158057.765498855 \tabularnewline
31 & 1583400 & 1142341.68066377 & 441058.319336227 \tabularnewline
32 & 1501500 & 1381594.49106554 & 119905.508934458 \tabularnewline
33 & 1337700 & 1424223.6724127 & -86523.6724127049 \tabularnewline
34 & 1911000 & 1338631.03608304 & 572368.963916963 \tabularnewline
35 & 1719900 & 1665630.11747291 & 54269.882527088 \tabularnewline
36 & 1965600 & 1673863.89813274 & 291736.101867262 \tabularnewline
37 & 1474200 & 1831756.07477134 & -357556.074771339 \tabularnewline
38 & 1365000 & 1585386.64337687 & -220386.643376873 \tabularnewline
39 & 1228500 & 1421098.69053406 & -192598.690534062 \tabularnewline
40 & 1010100 & 1271777.60747485 & -261677.607474846 \tabularnewline
41 & 1337700 & 1076935.55661226 & 260764.443387737 \tabularnewline
42 & 1201200 & 1207073.35765648 & -5873.35765647818 \tabularnewline
43 & 1638000 & 1172780.19856936 & 465219.80143064 \tabularnewline
44 & 1583400 & 1434109.35567451 & 149290.64432549 \tabularnewline
45 & 1365000 & 1502364.88271209 & -137364.882712089 \tabularnewline
46 & 1829100 & 1392373.34823887 & 436726.651761129 \tabularnewline
47 & 1692600 & 1641176.0488645 & 51423.9511354968 \tabularnewline
48 & 2184000 & 1653041.89854311 & 530958.101456892 \tabularnewline
49 & 1747200 & 1966471.53947061 & -219271.539470609 \tabularnewline
50 & 1064700 & 1814970.87445381 & -750270.874453811 \tabularnewline
51 & 1064700 & 1327718.87779852 & -263018.877798525 \tabularnewline
52 & 1064700 & 1137872.98686701 & -73172.9868670073 \tabularnewline
53 & 1255800 & 1064233.21648001 & 191566.783519993 \tabularnewline
54 & 1255800 & 1155939.4676271 & 99860.5323728998 \tabularnewline
55 & 1692600 & 1192236.0212191 & 500363.9787809 \tabularnewline
56 & 1556100 & 1481035.50448083 & 75064.4955191689 \tabularnewline
57 & 1392300 & 1508508.14935577 & -116208.149355775 \tabularnewline
58 & 1747200 & 1416768.68919165 & 330431.310808349 \tabularnewline
59 & 1610700 & 1604063.93230913 & 6636.06769087259 \tabularnewline
60 & 2320500 & 1591834.801145 & 728665.198854999 \tabularnewline
61 & 1829100 & 2032871.95148315 & -203771.951483147 \tabularnewline
62 & 1064700 & 1896833.65417561 & -832133.654175608 \tabularnewline
63 & 1119300 & 1364107.20039891 & -244807.200398909 \tabularnewline
64 & 928200 & 1190680.79343189 & -262480.793431891 \tabularnewline
65 & 1283100 & 1003412.4674144 & 279687.532585601 \tabularnewline
66 & 1474200 & 1153496.44948452 & 320703.550515481 \tabularnewline
67 & 1856400 & 1332465.20968619 & 523934.79031381 \tabularnewline
68 & 1829100 & 1642595.97189772 & 186504.028102277 \tabularnewline
69 & 1474200 & 1746816.60473325 & -272616.604733254 \tabularnewline
70 & 1719900 & 1564957.87365983 & 154942.126340166 \tabularnewline
71 & 1528800 & 1648401.31108242 & -119601.311082422 \tabularnewline
72 & 2184000 & 1561263.46903391 & 622736.530966088 \tabularnewline
73 & 1665300 & 1938721.4898385 & -273421.489838497 \tabularnewline
74 & 1337700 & 1760685.74100427 & -422985.741004268 \tabularnewline
75 & 1201200 & 1485703.74326989 & -284503.743269891 \tabularnewline
76 & 900900 & 1292892.39211986 & -391992.392119863 \tabularnewline
77 & 1337700 & 1029419.69925265 & 308280.300747353 \tabularnewline
78 & 1610700 & 1201081.51792571 & 409618.482074291 \tabularnewline
79 & 1883700 & 1439811.22778761 & 443888.772212393 \tabularnewline
80 & 1774500 & 1704650.60564621 & 69849.3943537883 \tabularnewline
81 & 1310400 & 1739703.13645029 & -429303.136450285 \tabularnewline
82 & 1883700 & 1462239.85118493 & 421460.148815066 \tabularnewline
83 & 1474200 & 1713949.67336769 & -239749.673367689 \tabularnewline
84 & 2265900 & 1555374.22703606 & 710525.772963942 \tabularnewline
85 & 1883700 & 1990560.5172651 & -106860.517265101 \tabularnewline
86 & 1365000 & 1920680.97476499 & -555680.974764994 \tabularnewline
87 & 1255800 & 1567893.04916545 & -312093.049165446 \tabularnewline
88 & 846300 & 1361757.00814699 & -515457.008146987 \tabularnewline
89 & 1337700 & 1024472.34582068 & 313227.654179318 \tabularnewline
90 & 1283100 & 1201535.44555184 & 81564.5544481575 \tabularnewline
91 & 1938300 & 1236709.0374834 & 701590.9625166 \tabularnewline
92 & 1938300 & 1661966.80417942 & 276333.195820583 \tabularnewline
93 & 1474200 & 1828183.41130722 & -353983.411307215 \tabularnewline
94 & 1911000 & 1601875.74136019 & 309124.258639813 \tabularnewline
95 & 1419600 & 1787802.21930701 & -368202.219307005 \tabularnewline
96 & 2211300 & 1552066.20904532 & 659233.790954683 \tabularnewline
97 & 1883700 & 1957080.51091169 & -73380.5109116891 \tabularnewline
98 & 1392300 & 1909661.37767113 & -517361.377671127 \tabularnewline
99 & 1064700 & 1582747.43190444 & -518047.431904443 \tabularnewline
100 & 737100 & 1249593.63693758 & -512493.636937578 \tabularnewline
101 & 1446900 & 914108.818709141 & 532791.181290859 \tabularnewline
102 & 1392300 & 1228957.17984028 & 163342.820159723 \tabularnewline
103 & 1829100 & 1317898.55881269 & 511201.441187312 \tabularnewline
104 & 2102100 & 1627012.41672418 & 475087.583275822 \tabularnewline
105 & 1556100 & 1919198.9725572 & -363098.972557197 \tabularnewline
106 & 1747200 & 1690620.47723024 & 56579.5227697624 \tabularnewline
107 & 1310400 & 1721382.02008905 & -410982.020089052 \tabularnewline
108 & 2265900 & 1459307.27411219 & 806592.725887806 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307330&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]1501500[/C][C]1365000[/C][C]136500[/C][/ROW]
[ROW][C]4[/C][C]1201200[/C][C]1396076.15022633[/C][C]-194876.150226327[/C][/ROW]
[ROW][C]5[/C][C]1556100[/C][C]1220692.08817671[/C][C]335407.911823286[/C][/ROW]
[ROW][C]6[/C][C]1528800[/C][C]1375960.11297986[/C][C]152839.887020136[/C][/ROW]
[ROW][C]7[/C][C]1638000[/C][C]1420402.89917724[/C][C]217597.100822761[/C][/ROW]
[ROW][C]8[/C][C]1692600[/C][C]1507207.64003829[/C][C]185392.359961713[/C][/ROW]
[ROW][C]9[/C][C]1883700[/C][C]1576241.92919762[/C][C]307458.070802383[/C][/ROW]
[ROW][C]10[/C][C]1638000[/C][C]1723974.17777451[/C][C]-85974.1777745066[/C][/ROW]
[ROW][C]11[/C][C]1556100[/C][C]1628215.44637801[/C][C]-72115.446378008[/C][/ROW]
[ROW][C]12[/C][C]1938300[/C][C]1540189.97461696[/C][C]398110.025383038[/C][/ROW]
[ROW][C]13[/C][C]1638000[/C][C]1746498.39775951[/C][C]-108498.397759506[/C][/ROW]
[ROW][C]14[/C][C]1228500[/C][C]1639297.11211976[/C][C]-410797.112119756[/C][/ROW]
[ROW][C]15[/C][C]1446900[/C][C]1341135.49095266[/C][C]105764.509047339[/C][/ROW]
[ROW][C]16[/C][C]1092000[/C][C]1362588.38562443[/C][C]-270588.385624432[/C][/ROW]
[ROW][C]17[/C][C]1528800[/C][C]1149005.66385245[/C][C]379794.336147547[/C][/ROW]
[ROW][C]18[/C][C]1255800[/C][C]1340606.50513357[/C][C]-84806.5051335739[/C][/ROW]
[ROW][C]19[/C][C]1665300[/C][C]1244858.62954974[/C][C]420441.37045026[/C][/ROW]
[ROW][C]20[/C][C]1501500[/C][C]1465284.45192682[/C][C]36215.548073183[/C][/ROW]
[ROW][C]21[/C][C]1583400[/C][C]1449266.48046923[/C][C]134133.519530768[/C][/ROW]
[ROW][C]22[/C][C]1774500[/C][C]1495114.75431025[/C][C]279385.24568975[/C][/ROW]
[ROW][C]23[/C][C]1747200[/C][C]1633638.45272062[/C][C]113561.547279379[/C][/ROW]
[ROW][C]24[/C][C]2074800[/C][C]1671217.66973336[/C][C]403582.33026664[/C][/ROW]
[ROW][C]25[/C][C]1501500[/C][C]1892107.65749477[/C][C]-390607.657494767[/C][/ROW]
[ROW][C]26[/C][C]1255800[/C][C]1619044.75758169[/C][C]-363244.757581694[/C][/ROW]
[ROW][C]27[/C][C]1392300[/C][C]1358770.59540614[/C][C]33529.4045938591[/C][/ROW]
[ROW][C]28[/C][C]1010100[/C][C]1343458.60670615[/C][C]-333358.60670615[/C][/ROW]
[ROW][C]29[/C][C]1446900[/C][C]1098240.67090257[/C][C]348659.329097431[/C][/ROW]
[ROW][C]30[/C][C]1119300[/C][C]1277357.76549886[/C][C]-158057.765498855[/C][/ROW]
[ROW][C]31[/C][C]1583400[/C][C]1142341.68066377[/C][C]441058.319336227[/C][/ROW]
[ROW][C]32[/C][C]1501500[/C][C]1381594.49106554[/C][C]119905.508934458[/C][/ROW]
[ROW][C]33[/C][C]1337700[/C][C]1424223.6724127[/C][C]-86523.6724127049[/C][/ROW]
[ROW][C]34[/C][C]1911000[/C][C]1338631.03608304[/C][C]572368.963916963[/C][/ROW]
[ROW][C]35[/C][C]1719900[/C][C]1665630.11747291[/C][C]54269.882527088[/C][/ROW]
[ROW][C]36[/C][C]1965600[/C][C]1673863.89813274[/C][C]291736.101867262[/C][/ROW]
[ROW][C]37[/C][C]1474200[/C][C]1831756.07477134[/C][C]-357556.074771339[/C][/ROW]
[ROW][C]38[/C][C]1365000[/C][C]1585386.64337687[/C][C]-220386.643376873[/C][/ROW]
[ROW][C]39[/C][C]1228500[/C][C]1421098.69053406[/C][C]-192598.690534062[/C][/ROW]
[ROW][C]40[/C][C]1010100[/C][C]1271777.60747485[/C][C]-261677.607474846[/C][/ROW]
[ROW][C]41[/C][C]1337700[/C][C]1076935.55661226[/C][C]260764.443387737[/C][/ROW]
[ROW][C]42[/C][C]1201200[/C][C]1207073.35765648[/C][C]-5873.35765647818[/C][/ROW]
[ROW][C]43[/C][C]1638000[/C][C]1172780.19856936[/C][C]465219.80143064[/C][/ROW]
[ROW][C]44[/C][C]1583400[/C][C]1434109.35567451[/C][C]149290.64432549[/C][/ROW]
[ROW][C]45[/C][C]1365000[/C][C]1502364.88271209[/C][C]-137364.882712089[/C][/ROW]
[ROW][C]46[/C][C]1829100[/C][C]1392373.34823887[/C][C]436726.651761129[/C][/ROW]
[ROW][C]47[/C][C]1692600[/C][C]1641176.0488645[/C][C]51423.9511354968[/C][/ROW]
[ROW][C]48[/C][C]2184000[/C][C]1653041.89854311[/C][C]530958.101456892[/C][/ROW]
[ROW][C]49[/C][C]1747200[/C][C]1966471.53947061[/C][C]-219271.539470609[/C][/ROW]
[ROW][C]50[/C][C]1064700[/C][C]1814970.87445381[/C][C]-750270.874453811[/C][/ROW]
[ROW][C]51[/C][C]1064700[/C][C]1327718.87779852[/C][C]-263018.877798525[/C][/ROW]
[ROW][C]52[/C][C]1064700[/C][C]1137872.98686701[/C][C]-73172.9868670073[/C][/ROW]
[ROW][C]53[/C][C]1255800[/C][C]1064233.21648001[/C][C]191566.783519993[/C][/ROW]
[ROW][C]54[/C][C]1255800[/C][C]1155939.4676271[/C][C]99860.5323728998[/C][/ROW]
[ROW][C]55[/C][C]1692600[/C][C]1192236.0212191[/C][C]500363.9787809[/C][/ROW]
[ROW][C]56[/C][C]1556100[/C][C]1481035.50448083[/C][C]75064.4955191689[/C][/ROW]
[ROW][C]57[/C][C]1392300[/C][C]1508508.14935577[/C][C]-116208.149355775[/C][/ROW]
[ROW][C]58[/C][C]1747200[/C][C]1416768.68919165[/C][C]330431.310808349[/C][/ROW]
[ROW][C]59[/C][C]1610700[/C][C]1604063.93230913[/C][C]6636.06769087259[/C][/ROW]
[ROW][C]60[/C][C]2320500[/C][C]1591834.801145[/C][C]728665.198854999[/C][/ROW]
[ROW][C]61[/C][C]1829100[/C][C]2032871.95148315[/C][C]-203771.951483147[/C][/ROW]
[ROW][C]62[/C][C]1064700[/C][C]1896833.65417561[/C][C]-832133.654175608[/C][/ROW]
[ROW][C]63[/C][C]1119300[/C][C]1364107.20039891[/C][C]-244807.200398909[/C][/ROW]
[ROW][C]64[/C][C]928200[/C][C]1190680.79343189[/C][C]-262480.793431891[/C][/ROW]
[ROW][C]65[/C][C]1283100[/C][C]1003412.4674144[/C][C]279687.532585601[/C][/ROW]
[ROW][C]66[/C][C]1474200[/C][C]1153496.44948452[/C][C]320703.550515481[/C][/ROW]
[ROW][C]67[/C][C]1856400[/C][C]1332465.20968619[/C][C]523934.79031381[/C][/ROW]
[ROW][C]68[/C][C]1829100[/C][C]1642595.97189772[/C][C]186504.028102277[/C][/ROW]
[ROW][C]69[/C][C]1474200[/C][C]1746816.60473325[/C][C]-272616.604733254[/C][/ROW]
[ROW][C]70[/C][C]1719900[/C][C]1564957.87365983[/C][C]154942.126340166[/C][/ROW]
[ROW][C]71[/C][C]1528800[/C][C]1648401.31108242[/C][C]-119601.311082422[/C][/ROW]
[ROW][C]72[/C][C]2184000[/C][C]1561263.46903391[/C][C]622736.530966088[/C][/ROW]
[ROW][C]73[/C][C]1665300[/C][C]1938721.4898385[/C][C]-273421.489838497[/C][/ROW]
[ROW][C]74[/C][C]1337700[/C][C]1760685.74100427[/C][C]-422985.741004268[/C][/ROW]
[ROW][C]75[/C][C]1201200[/C][C]1485703.74326989[/C][C]-284503.743269891[/C][/ROW]
[ROW][C]76[/C][C]900900[/C][C]1292892.39211986[/C][C]-391992.392119863[/C][/ROW]
[ROW][C]77[/C][C]1337700[/C][C]1029419.69925265[/C][C]308280.300747353[/C][/ROW]
[ROW][C]78[/C][C]1610700[/C][C]1201081.51792571[/C][C]409618.482074291[/C][/ROW]
[ROW][C]79[/C][C]1883700[/C][C]1439811.22778761[/C][C]443888.772212393[/C][/ROW]
[ROW][C]80[/C][C]1774500[/C][C]1704650.60564621[/C][C]69849.3943537883[/C][/ROW]
[ROW][C]81[/C][C]1310400[/C][C]1739703.13645029[/C][C]-429303.136450285[/C][/ROW]
[ROW][C]82[/C][C]1883700[/C][C]1462239.85118493[/C][C]421460.148815066[/C][/ROW]
[ROW][C]83[/C][C]1474200[/C][C]1713949.67336769[/C][C]-239749.673367689[/C][/ROW]
[ROW][C]84[/C][C]2265900[/C][C]1555374.22703606[/C][C]710525.772963942[/C][/ROW]
[ROW][C]85[/C][C]1883700[/C][C]1990560.5172651[/C][C]-106860.517265101[/C][/ROW]
[ROW][C]86[/C][C]1365000[/C][C]1920680.97476499[/C][C]-555680.974764994[/C][/ROW]
[ROW][C]87[/C][C]1255800[/C][C]1567893.04916545[/C][C]-312093.049165446[/C][/ROW]
[ROW][C]88[/C][C]846300[/C][C]1361757.00814699[/C][C]-515457.008146987[/C][/ROW]
[ROW][C]89[/C][C]1337700[/C][C]1024472.34582068[/C][C]313227.654179318[/C][/ROW]
[ROW][C]90[/C][C]1283100[/C][C]1201535.44555184[/C][C]81564.5544481575[/C][/ROW]
[ROW][C]91[/C][C]1938300[/C][C]1236709.0374834[/C][C]701590.9625166[/C][/ROW]
[ROW][C]92[/C][C]1938300[/C][C]1661966.80417942[/C][C]276333.195820583[/C][/ROW]
[ROW][C]93[/C][C]1474200[/C][C]1828183.41130722[/C][C]-353983.411307215[/C][/ROW]
[ROW][C]94[/C][C]1911000[/C][C]1601875.74136019[/C][C]309124.258639813[/C][/ROW]
[ROW][C]95[/C][C]1419600[/C][C]1787802.21930701[/C][C]-368202.219307005[/C][/ROW]
[ROW][C]96[/C][C]2211300[/C][C]1552066.20904532[/C][C]659233.790954683[/C][/ROW]
[ROW][C]97[/C][C]1883700[/C][C]1957080.51091169[/C][C]-73380.5109116891[/C][/ROW]
[ROW][C]98[/C][C]1392300[/C][C]1909661.37767113[/C][C]-517361.377671127[/C][/ROW]
[ROW][C]99[/C][C]1064700[/C][C]1582747.43190444[/C][C]-518047.431904443[/C][/ROW]
[ROW][C]100[/C][C]737100[/C][C]1249593.63693758[/C][C]-512493.636937578[/C][/ROW]
[ROW][C]101[/C][C]1446900[/C][C]914108.818709141[/C][C]532791.181290859[/C][/ROW]
[ROW][C]102[/C][C]1392300[/C][C]1228957.17984028[/C][C]163342.820159723[/C][/ROW]
[ROW][C]103[/C][C]1829100[/C][C]1317898.55881269[/C][C]511201.441187312[/C][/ROW]
[ROW][C]104[/C][C]2102100[/C][C]1627012.41672418[/C][C]475087.583275822[/C][/ROW]
[ROW][C]105[/C][C]1556100[/C][C]1919198.9725572[/C][C]-363098.972557197[/C][/ROW]
[ROW][C]106[/C][C]1747200[/C][C]1690620.47723024[/C][C]56579.5227697624[/C][/ROW]
[ROW][C]107[/C][C]1310400[/C][C]1721382.02008905[/C][C]-410982.020089052[/C][/ROW]
[ROW][C]108[/C][C]2265900[/C][C]1459307.27411219[/C][C]806592.725887806[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307330&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307330&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
315015001365000136500
412012001396076.15022633-194876.150226327
515561001220692.08817671335407.911823286
615288001375960.11297986152839.887020136
716380001420402.89917724217597.100822761
816926001507207.64003829185392.359961713
918837001576241.92919762307458.070802383
1016380001723974.17777451-85974.1777745066
1115561001628215.44637801-72115.446378008
1219383001540189.97461696398110.025383038
1316380001746498.39775951-108498.397759506
1412285001639297.11211976-410797.112119756
1514469001341135.49095266105764.509047339
1610920001362588.38562443-270588.385624432
1715288001149005.66385245379794.336147547
1812558001340606.50513357-84806.5051335739
1916653001244858.62954974420441.37045026
2015015001465284.4519268236215.548073183
2115834001449266.48046923134133.519530768
2217745001495114.75431025279385.24568975
2317472001633638.45272062113561.547279379
2420748001671217.66973336403582.33026664
2515015001892107.65749477-390607.657494767
2612558001619044.75758169-363244.757581694
2713923001358770.5954061433529.4045938591
2810101001343458.60670615-333358.60670615
2914469001098240.67090257348659.329097431
3011193001277357.76549886-158057.765498855
3115834001142341.68066377441058.319336227
3215015001381594.49106554119905.508934458
3313377001424223.6724127-86523.6724127049
3419110001338631.03608304572368.963916963
3517199001665630.1174729154269.882527088
3619656001673863.89813274291736.101867262
3714742001831756.07477134-357556.074771339
3813650001585386.64337687-220386.643376873
3912285001421098.69053406-192598.690534062
4010101001271777.60747485-261677.607474846
4113377001076935.55661226260764.443387737
4212012001207073.35765648-5873.35765647818
4316380001172780.19856936465219.80143064
4415834001434109.35567451149290.64432549
4513650001502364.88271209-137364.882712089
4618291001392373.34823887436726.651761129
4716926001641176.048864551423.9511354968
4821840001653041.89854311530958.101456892
4917472001966471.53947061-219271.539470609
5010647001814970.87445381-750270.874453811
5110647001327718.87779852-263018.877798525
5210647001137872.98686701-73172.9868670073
5312558001064233.21648001191566.783519993
5412558001155939.467627199860.5323728998
5516926001192236.0212191500363.9787809
5615561001481035.5044808375064.4955191689
5713923001508508.14935577-116208.149355775
5817472001416768.68919165330431.310808349
5916107001604063.932309136636.06769087259
6023205001591834.801145728665.198854999
6118291002032871.95148315-203771.951483147
6210647001896833.65417561-832133.654175608
6311193001364107.20039891-244807.200398909
649282001190680.79343189-262480.793431891
6512831001003412.4674144279687.532585601
6614742001153496.44948452320703.550515481
6718564001332465.20968619523934.79031381
6818291001642595.97189772186504.028102277
6914742001746816.60473325-272616.604733254
7017199001564957.87365983154942.126340166
7115288001648401.31108242-119601.311082422
7221840001561263.46903391622736.530966088
7316653001938721.4898385-273421.489838497
7413377001760685.74100427-422985.741004268
7512012001485703.74326989-284503.743269891
769009001292892.39211986-391992.392119863
7713377001029419.69925265308280.300747353
7816107001201081.51792571409618.482074291
7918837001439811.22778761443888.772212393
8017745001704650.6056462169849.3943537883
8113104001739703.13645029-429303.136450285
8218837001462239.85118493421460.148815066
8314742001713949.67336769-239749.673367689
8422659001555374.22703606710525.772963942
8518837001990560.5172651-106860.517265101
8613650001920680.97476499-555680.974764994
8712558001567893.04916545-312093.049165446
888463001361757.00814699-515457.008146987
8913377001024472.34582068313227.654179318
9012831001201535.4455518481564.5544481575
9119383001236709.0374834701590.9625166
9219383001661966.80417942276333.195820583
9314742001828183.41130722-353983.411307215
9419110001601875.74136019309124.258639813
9514196001787802.21930701-368202.219307005
9622113001552066.20904532659233.790954683
9718837001957080.51091169-73380.5109116891
9813923001909661.37767113-517361.377671127
9910647001582747.43190444-518047.431904443
1007371001249593.63693758-512493.636937578
1011446900914108.818709141532791.181290859
10213923001228957.17984028163342.820159723
10318291001317898.55881269511201.441187312
10421021001627012.41672418475087.583275822
10515561001919198.9725572-363098.972557197
10617472001690620.4772302456579.5227697624
10713104001721382.02008905-410982.020089052
10822659001459307.27411219806592.725887806







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091956845.742750561253668.132348472660023.35315266
1101957171.807756141126956.881885412787386.73362687
1111957497.872761721013523.873725552901471.87179788
1121957823.93776729908979.9556560813006667.9198785
1131958150.00277287810830.5743271513105469.43121858
1141958476.06777844717502.2118985623199449.92365833
1151958802.13278402627929.8237465353289674.4418215
1161959128.19778959541354.7565332363376901.63904595
1171959454.26279517457215.2411439823461693.28444636
1181959780.32780075375082.4294086363544478.22619286
1191960106.39280632294620.7976692193625591.98794343
1201960432.4578119215562.4691363173705302.44648748

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1956845.74275056 & 1253668.13234847 & 2660023.35315266 \tabularnewline
110 & 1957171.80775614 & 1126956.88188541 & 2787386.73362687 \tabularnewline
111 & 1957497.87276172 & 1013523.87372555 & 2901471.87179788 \tabularnewline
112 & 1957823.93776729 & 908979.955656081 & 3006667.9198785 \tabularnewline
113 & 1958150.00277287 & 810830.574327151 & 3105469.43121858 \tabularnewline
114 & 1958476.06777844 & 717502.211898562 & 3199449.92365833 \tabularnewline
115 & 1958802.13278402 & 627929.823746535 & 3289674.4418215 \tabularnewline
116 & 1959128.19778959 & 541354.756533236 & 3376901.63904595 \tabularnewline
117 & 1959454.26279517 & 457215.241143982 & 3461693.28444636 \tabularnewline
118 & 1959780.32780075 & 375082.429408636 & 3544478.22619286 \tabularnewline
119 & 1960106.39280632 & 294620.797669219 & 3625591.98794343 \tabularnewline
120 & 1960432.4578119 & 215562.469136317 & 3705302.44648748 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307330&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]1956845.74275056[/C][C]1253668.13234847[/C][C]2660023.35315266[/C][/ROW]
[ROW][C]110[/C][C]1957171.80775614[/C][C]1126956.88188541[/C][C]2787386.73362687[/C][/ROW]
[ROW][C]111[/C][C]1957497.87276172[/C][C]1013523.87372555[/C][C]2901471.87179788[/C][/ROW]
[ROW][C]112[/C][C]1957823.93776729[/C][C]908979.955656081[/C][C]3006667.9198785[/C][/ROW]
[ROW][C]113[/C][C]1958150.00277287[/C][C]810830.574327151[/C][C]3105469.43121858[/C][/ROW]
[ROW][C]114[/C][C]1958476.06777844[/C][C]717502.211898562[/C][C]3199449.92365833[/C][/ROW]
[ROW][C]115[/C][C]1958802.13278402[/C][C]627929.823746535[/C][C]3289674.4418215[/C][/ROW]
[ROW][C]116[/C][C]1959128.19778959[/C][C]541354.756533236[/C][C]3376901.63904595[/C][/ROW]
[ROW][C]117[/C][C]1959454.26279517[/C][C]457215.241143982[/C][C]3461693.28444636[/C][/ROW]
[ROW][C]118[/C][C]1959780.32780075[/C][C]375082.429408636[/C][C]3544478.22619286[/C][/ROW]
[ROW][C]119[/C][C]1960106.39280632[/C][C]294620.797669219[/C][C]3625591.98794343[/C][/ROW]
[ROW][C]120[/C][C]1960432.4578119[/C][C]215562.469136317[/C][C]3705302.44648748[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307330&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307330&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
1091956845.742750561253668.132348472660023.35315266
1101957171.807756141126956.881885412787386.73362687
1111957497.872761721013523.873725552901471.87179788
1121957823.93776729908979.9556560813006667.9198785
1131958150.00277287810830.5743271513105469.43121858
1141958476.06777844717502.2118985623199449.92365833
1151958802.13278402627929.8237465353289674.4418215
1161959128.19778959541354.7565332363376901.63904595
1171959454.26279517457215.2411439823461693.28444636
1181959780.32780075375082.4294086363544478.22619286
1191960106.39280632294620.7976692193625591.98794343
1201960432.4578119215562.4691363173705302.44648748



Parameters (Session):
par1 = additive ; par2 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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')