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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 11 Aug 2015 13:01:05 +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/11/t1439294484a30gez179yfxhdg.htm/, Retrieved Wed, 15 May 2024 16:24:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280013, Retrieved Wed, 15 May 2024 16:24:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2015-08-11 12:01:05] [d3245c242fac7b2d7caab09de558415e] [Current]
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Dataseries X:
1755000
1690000
1787500
1430000
1852500
1820000
1950000
2015000
2242500
1950000
1852500
2307500
1950000
1462500
1722500
1300000
1820000
1495000
1982500
1787500
1885000
2112500
2080000
2470000
1787500
1495000
1657500
1202500
1722500
1332500
1885000
1787500
1592500
2275000
2047500
2340000
1755000
1625000
1462500
1202500
1592500
1430000
1950000
1885000
1625000
2177500
2015000
2600000
2080000
1267500
1267500
1267500
1495000
1495000
2015000
1852500
1657500
2080000
1917500
2762500
2177500
1267500
1332500
1105000
1527500
1755000
2210000
2177500
1755000
2047500
1820000
2600000
1982500
1592500
1430000
1072500
1592500
1917500
2242500
2112500
1560000
2242500
1755000
2697500
2242500
1625000
1495000
1007500
1592500
1527500
2307500
2307500
1755000
2275000
1690000
2632500
2242500
1657500
1267500
877500
1722500
1657500
2177500
2502500
1852500
2080000
1560000
2697500




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280013&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280013&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280013&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.616435516555755
beta0.0182153483451694
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.616435516555755 \tabularnewline
beta & 0.0182153483451694 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280013&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]0.616435516555755[/C][/ROW]
[ROW][C]beta[/C][C]0.0182153483451694[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280013&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280013&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
alpha0.616435516555755
beta0.0182153483451694
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
317875001625000162500
414300001661995.4169361-231995.4169361
518525001453204.86687705399295.133122953
618200001638047.75354745181952.246452549
719500001690955.83235386259044.167646145
820150001794294.80956939220705.190430607
922425001876478.48714003366021.512859969
1019500002052350.21163633-102350.211636331
1118525001938351.72187861-85851.7218786115
1223075001833559.49359166473940.506408344
1319500002079164.75923753-129164.759237531
1414625001951544.18109499-489044.181094987
1517225001596589.87018179125910.129818211
1613000001622129.03050531-322129.030505308
1718200001367863.88553867452136.114461329
1814950001595960.12515903-100960.125159033
1919825001481974.55898781500525.441012188
2017875001744386.2522938543113.747706153
2118850001725317.23865388159682.761346121
2221125001779898.51703605332601.482963953
2320800001944807.6818103135192.318189702
2424700001989544.84492071480455.15507929
2517875002252509.11606524-465009.116065241
2614950001927434.23521637-432434.235216371
2716575001617584.0421502439915.9578497631
2812025001599355.48417404-396855.48417404
2917225001307429.37012216415070.62987784
3013325001520664.00654629-188164.006546287
3118850001359930.57221882525069.427781181
3217875001644755.34650662142744.653493375
3315925001695504.37191992-103004.371919925
3422750001593608.37628938681391.623710621
3520475001982892.996991664607.0030084024
3623400001992695.11682474347304.883175258
3717550002180661.99377546-425661.99377546
3816250001887365.05163921-262365.051639212
3914625001691784.15539777-229284.155397768
4012025001514020.96127965-311520.961279646
4115925001282066.13882418310433.861175816
4214300001436992.09244823-6992.0924482285
4319500001396166.90305881553833.096941194
4418850001707273.04246969177726.957530313
4516250001788529.62227634-163529.622276342
4621775001657587.31933205519912.680667951
4720150001953781.0105530361218.989446972
4826000001967907.02207519632092.97792481
4920800002341037.54698888-261037.546988876
5012675002160679.6124451-893179.612445095
5112675001580617.71166501-313117.711665009
5212675001354610.69865128-87110.6986512763
5314950001266944.3053334228055.6946666
5414950001376118.41384183118881.586158172
5520150001419328.59668945595671.403310553
5618525001763137.5053343689362.4946656439
5716575001795843.0349474-138343.034947401
5820800001686629.39189488393370.608105115
5919175001909599.919415687900.08058431908
6027625001895041.42993459867458.570065412
6121775002420085.6565276-242585.656527605
6212675002258135.30259009-990635.302590091
6313325001623937.14333214-291437.143332138
6411050001417477.13503804-312477.135038045
6515275001194538.65168387332961.348316128
6617550001373210.05891018381789.941089818
6722100001586268.10676931623731.893230692
6821775001955471.39511637222028.60488363
6917550002079543.57706345-324543.577063449
7020475001863045.08769035184454.912309648
7118200001962382.51319343-142382.513193425
7226000001858646.9869452741353.013054796
7319825002308001.77361731-325501.77361731
7415925002096054.45357659-503554.453576588
7514300001768694.93246424-338694.932464242
7610725001539157.60966658-466657.60966658
7715925001225499.6419675367000.358032495
7819175001429858.9499116487641.050088403
7922425001714060.98546147528439.014538532
8021125002029345.9591026783154.0408973319
8115600002071075.16244087-511075.16244087
8222425001740761.72760119501738.272398812
8317550002040416.27781873-285416.27781873
8426975001851635.9845668845864.015433196
8522425002369714.90150612-127214.901506118
8616250002286524.9699584-661524.969958398
8714950001866539.34424467-371539.344244666
8810075001621139.29541316-613639.295413156
8915925001219609.93550088372890.064499119
9015275001430399.3399427197100.6600572949
9123075001472272.66367075835227.336329252
9223075001978531.90973742328968.090262578
9317550002176408.82298482-421408.822984819
9422750001906994.93019077368005.069809234
9516900002128335.97536554-438335.975365536
9626325001847697.86791116784802.132088839
9722425002329857.75108539-87357.751085388
9816575002273406.4019895-615906.401989501
9912675001884223.13321966-616723.133219656
1008775001487611.47254481-610111.472544811
10117225001088224.78417761634275.215822389
10216575001463044.26171464194455.738285364
10321775001568926.85572941608573.144270586
10425025001936919.54371928565580.456280721
10518525002284760.68161574-432260.68161574
10620800002012643.4252741567356.5747258451
10715600002049264.30962988-489264.309629881
10826975001737270.56441935960229.435580654

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1787500 & 1625000 & 162500 \tabularnewline
4 & 1430000 & 1661995.4169361 & -231995.4169361 \tabularnewline
5 & 1852500 & 1453204.86687705 & 399295.133122953 \tabularnewline
6 & 1820000 & 1638047.75354745 & 181952.246452549 \tabularnewline
7 & 1950000 & 1690955.83235386 & 259044.167646145 \tabularnewline
8 & 2015000 & 1794294.80956939 & 220705.190430607 \tabularnewline
9 & 2242500 & 1876478.48714003 & 366021.512859969 \tabularnewline
10 & 1950000 & 2052350.21163633 & -102350.211636331 \tabularnewline
11 & 1852500 & 1938351.72187861 & -85851.7218786115 \tabularnewline
12 & 2307500 & 1833559.49359166 & 473940.506408344 \tabularnewline
13 & 1950000 & 2079164.75923753 & -129164.759237531 \tabularnewline
14 & 1462500 & 1951544.18109499 & -489044.181094987 \tabularnewline
15 & 1722500 & 1596589.87018179 & 125910.129818211 \tabularnewline
16 & 1300000 & 1622129.03050531 & -322129.030505308 \tabularnewline
17 & 1820000 & 1367863.88553867 & 452136.114461329 \tabularnewline
18 & 1495000 & 1595960.12515903 & -100960.125159033 \tabularnewline
19 & 1982500 & 1481974.55898781 & 500525.441012188 \tabularnewline
20 & 1787500 & 1744386.25229385 & 43113.747706153 \tabularnewline
21 & 1885000 & 1725317.23865388 & 159682.761346121 \tabularnewline
22 & 2112500 & 1779898.51703605 & 332601.482963953 \tabularnewline
23 & 2080000 & 1944807.6818103 & 135192.318189702 \tabularnewline
24 & 2470000 & 1989544.84492071 & 480455.15507929 \tabularnewline
25 & 1787500 & 2252509.11606524 & -465009.116065241 \tabularnewline
26 & 1495000 & 1927434.23521637 & -432434.235216371 \tabularnewline
27 & 1657500 & 1617584.04215024 & 39915.9578497631 \tabularnewline
28 & 1202500 & 1599355.48417404 & -396855.48417404 \tabularnewline
29 & 1722500 & 1307429.37012216 & 415070.62987784 \tabularnewline
30 & 1332500 & 1520664.00654629 & -188164.006546287 \tabularnewline
31 & 1885000 & 1359930.57221882 & 525069.427781181 \tabularnewline
32 & 1787500 & 1644755.34650662 & 142744.653493375 \tabularnewline
33 & 1592500 & 1695504.37191992 & -103004.371919925 \tabularnewline
34 & 2275000 & 1593608.37628938 & 681391.623710621 \tabularnewline
35 & 2047500 & 1982892.9969916 & 64607.0030084024 \tabularnewline
36 & 2340000 & 1992695.11682474 & 347304.883175258 \tabularnewline
37 & 1755000 & 2180661.99377546 & -425661.99377546 \tabularnewline
38 & 1625000 & 1887365.05163921 & -262365.051639212 \tabularnewline
39 & 1462500 & 1691784.15539777 & -229284.155397768 \tabularnewline
40 & 1202500 & 1514020.96127965 & -311520.961279646 \tabularnewline
41 & 1592500 & 1282066.13882418 & 310433.861175816 \tabularnewline
42 & 1430000 & 1436992.09244823 & -6992.0924482285 \tabularnewline
43 & 1950000 & 1396166.90305881 & 553833.096941194 \tabularnewline
44 & 1885000 & 1707273.04246969 & 177726.957530313 \tabularnewline
45 & 1625000 & 1788529.62227634 & -163529.622276342 \tabularnewline
46 & 2177500 & 1657587.31933205 & 519912.680667951 \tabularnewline
47 & 2015000 & 1953781.01055303 & 61218.989446972 \tabularnewline
48 & 2600000 & 1967907.02207519 & 632092.97792481 \tabularnewline
49 & 2080000 & 2341037.54698888 & -261037.546988876 \tabularnewline
50 & 1267500 & 2160679.6124451 & -893179.612445095 \tabularnewline
51 & 1267500 & 1580617.71166501 & -313117.711665009 \tabularnewline
52 & 1267500 & 1354610.69865128 & -87110.6986512763 \tabularnewline
53 & 1495000 & 1266944.3053334 & 228055.6946666 \tabularnewline
54 & 1495000 & 1376118.41384183 & 118881.586158172 \tabularnewline
55 & 2015000 & 1419328.59668945 & 595671.403310553 \tabularnewline
56 & 1852500 & 1763137.50533436 & 89362.4946656439 \tabularnewline
57 & 1657500 & 1795843.0349474 & -138343.034947401 \tabularnewline
58 & 2080000 & 1686629.39189488 & 393370.608105115 \tabularnewline
59 & 1917500 & 1909599.91941568 & 7900.08058431908 \tabularnewline
60 & 2762500 & 1895041.42993459 & 867458.570065412 \tabularnewline
61 & 2177500 & 2420085.6565276 & -242585.656527605 \tabularnewline
62 & 1267500 & 2258135.30259009 & -990635.302590091 \tabularnewline
63 & 1332500 & 1623937.14333214 & -291437.143332138 \tabularnewline
64 & 1105000 & 1417477.13503804 & -312477.135038045 \tabularnewline
65 & 1527500 & 1194538.65168387 & 332961.348316128 \tabularnewline
66 & 1755000 & 1373210.05891018 & 381789.941089818 \tabularnewline
67 & 2210000 & 1586268.10676931 & 623731.893230692 \tabularnewline
68 & 2177500 & 1955471.39511637 & 222028.60488363 \tabularnewline
69 & 1755000 & 2079543.57706345 & -324543.577063449 \tabularnewline
70 & 2047500 & 1863045.08769035 & 184454.912309648 \tabularnewline
71 & 1820000 & 1962382.51319343 & -142382.513193425 \tabularnewline
72 & 2600000 & 1858646.9869452 & 741353.013054796 \tabularnewline
73 & 1982500 & 2308001.77361731 & -325501.77361731 \tabularnewline
74 & 1592500 & 2096054.45357659 & -503554.453576588 \tabularnewline
75 & 1430000 & 1768694.93246424 & -338694.932464242 \tabularnewline
76 & 1072500 & 1539157.60966658 & -466657.60966658 \tabularnewline
77 & 1592500 & 1225499.6419675 & 367000.358032495 \tabularnewline
78 & 1917500 & 1429858.9499116 & 487641.050088403 \tabularnewline
79 & 2242500 & 1714060.98546147 & 528439.014538532 \tabularnewline
80 & 2112500 & 2029345.95910267 & 83154.0408973319 \tabularnewline
81 & 1560000 & 2071075.16244087 & -511075.16244087 \tabularnewline
82 & 2242500 & 1740761.72760119 & 501738.272398812 \tabularnewline
83 & 1755000 & 2040416.27781873 & -285416.27781873 \tabularnewline
84 & 2697500 & 1851635.9845668 & 845864.015433196 \tabularnewline
85 & 2242500 & 2369714.90150612 & -127214.901506118 \tabularnewline
86 & 1625000 & 2286524.9699584 & -661524.969958398 \tabularnewline
87 & 1495000 & 1866539.34424467 & -371539.344244666 \tabularnewline
88 & 1007500 & 1621139.29541316 & -613639.295413156 \tabularnewline
89 & 1592500 & 1219609.93550088 & 372890.064499119 \tabularnewline
90 & 1527500 & 1430399.33994271 & 97100.6600572949 \tabularnewline
91 & 2307500 & 1472272.66367075 & 835227.336329252 \tabularnewline
92 & 2307500 & 1978531.90973742 & 328968.090262578 \tabularnewline
93 & 1755000 & 2176408.82298482 & -421408.822984819 \tabularnewline
94 & 2275000 & 1906994.93019077 & 368005.069809234 \tabularnewline
95 & 1690000 & 2128335.97536554 & -438335.975365536 \tabularnewline
96 & 2632500 & 1847697.86791116 & 784802.132088839 \tabularnewline
97 & 2242500 & 2329857.75108539 & -87357.751085388 \tabularnewline
98 & 1657500 & 2273406.4019895 & -615906.401989501 \tabularnewline
99 & 1267500 & 1884223.13321966 & -616723.133219656 \tabularnewline
100 & 877500 & 1487611.47254481 & -610111.472544811 \tabularnewline
101 & 1722500 & 1088224.78417761 & 634275.215822389 \tabularnewline
102 & 1657500 & 1463044.26171464 & 194455.738285364 \tabularnewline
103 & 2177500 & 1568926.85572941 & 608573.144270586 \tabularnewline
104 & 2502500 & 1936919.54371928 & 565580.456280721 \tabularnewline
105 & 1852500 & 2284760.68161574 & -432260.68161574 \tabularnewline
106 & 2080000 & 2012643.42527415 & 67356.5747258451 \tabularnewline
107 & 1560000 & 2049264.30962988 & -489264.309629881 \tabularnewline
108 & 2697500 & 1737270.56441935 & 960229.435580654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280013&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]1787500[/C][C]1625000[/C][C]162500[/C][/ROW]
[ROW][C]4[/C][C]1430000[/C][C]1661995.4169361[/C][C]-231995.4169361[/C][/ROW]
[ROW][C]5[/C][C]1852500[/C][C]1453204.86687705[/C][C]399295.133122953[/C][/ROW]
[ROW][C]6[/C][C]1820000[/C][C]1638047.75354745[/C][C]181952.246452549[/C][/ROW]
[ROW][C]7[/C][C]1950000[/C][C]1690955.83235386[/C][C]259044.167646145[/C][/ROW]
[ROW][C]8[/C][C]2015000[/C][C]1794294.80956939[/C][C]220705.190430607[/C][/ROW]
[ROW][C]9[/C][C]2242500[/C][C]1876478.48714003[/C][C]366021.512859969[/C][/ROW]
[ROW][C]10[/C][C]1950000[/C][C]2052350.21163633[/C][C]-102350.211636331[/C][/ROW]
[ROW][C]11[/C][C]1852500[/C][C]1938351.72187861[/C][C]-85851.7218786115[/C][/ROW]
[ROW][C]12[/C][C]2307500[/C][C]1833559.49359166[/C][C]473940.506408344[/C][/ROW]
[ROW][C]13[/C][C]1950000[/C][C]2079164.75923753[/C][C]-129164.759237531[/C][/ROW]
[ROW][C]14[/C][C]1462500[/C][C]1951544.18109499[/C][C]-489044.181094987[/C][/ROW]
[ROW][C]15[/C][C]1722500[/C][C]1596589.87018179[/C][C]125910.129818211[/C][/ROW]
[ROW][C]16[/C][C]1300000[/C][C]1622129.03050531[/C][C]-322129.030505308[/C][/ROW]
[ROW][C]17[/C][C]1820000[/C][C]1367863.88553867[/C][C]452136.114461329[/C][/ROW]
[ROW][C]18[/C][C]1495000[/C][C]1595960.12515903[/C][C]-100960.125159033[/C][/ROW]
[ROW][C]19[/C][C]1982500[/C][C]1481974.55898781[/C][C]500525.441012188[/C][/ROW]
[ROW][C]20[/C][C]1787500[/C][C]1744386.25229385[/C][C]43113.747706153[/C][/ROW]
[ROW][C]21[/C][C]1885000[/C][C]1725317.23865388[/C][C]159682.761346121[/C][/ROW]
[ROW][C]22[/C][C]2112500[/C][C]1779898.51703605[/C][C]332601.482963953[/C][/ROW]
[ROW][C]23[/C][C]2080000[/C][C]1944807.6818103[/C][C]135192.318189702[/C][/ROW]
[ROW][C]24[/C][C]2470000[/C][C]1989544.84492071[/C][C]480455.15507929[/C][/ROW]
[ROW][C]25[/C][C]1787500[/C][C]2252509.11606524[/C][C]-465009.116065241[/C][/ROW]
[ROW][C]26[/C][C]1495000[/C][C]1927434.23521637[/C][C]-432434.235216371[/C][/ROW]
[ROW][C]27[/C][C]1657500[/C][C]1617584.04215024[/C][C]39915.9578497631[/C][/ROW]
[ROW][C]28[/C][C]1202500[/C][C]1599355.48417404[/C][C]-396855.48417404[/C][/ROW]
[ROW][C]29[/C][C]1722500[/C][C]1307429.37012216[/C][C]415070.62987784[/C][/ROW]
[ROW][C]30[/C][C]1332500[/C][C]1520664.00654629[/C][C]-188164.006546287[/C][/ROW]
[ROW][C]31[/C][C]1885000[/C][C]1359930.57221882[/C][C]525069.427781181[/C][/ROW]
[ROW][C]32[/C][C]1787500[/C][C]1644755.34650662[/C][C]142744.653493375[/C][/ROW]
[ROW][C]33[/C][C]1592500[/C][C]1695504.37191992[/C][C]-103004.371919925[/C][/ROW]
[ROW][C]34[/C][C]2275000[/C][C]1593608.37628938[/C][C]681391.623710621[/C][/ROW]
[ROW][C]35[/C][C]2047500[/C][C]1982892.9969916[/C][C]64607.0030084024[/C][/ROW]
[ROW][C]36[/C][C]2340000[/C][C]1992695.11682474[/C][C]347304.883175258[/C][/ROW]
[ROW][C]37[/C][C]1755000[/C][C]2180661.99377546[/C][C]-425661.99377546[/C][/ROW]
[ROW][C]38[/C][C]1625000[/C][C]1887365.05163921[/C][C]-262365.051639212[/C][/ROW]
[ROW][C]39[/C][C]1462500[/C][C]1691784.15539777[/C][C]-229284.155397768[/C][/ROW]
[ROW][C]40[/C][C]1202500[/C][C]1514020.96127965[/C][C]-311520.961279646[/C][/ROW]
[ROW][C]41[/C][C]1592500[/C][C]1282066.13882418[/C][C]310433.861175816[/C][/ROW]
[ROW][C]42[/C][C]1430000[/C][C]1436992.09244823[/C][C]-6992.0924482285[/C][/ROW]
[ROW][C]43[/C][C]1950000[/C][C]1396166.90305881[/C][C]553833.096941194[/C][/ROW]
[ROW][C]44[/C][C]1885000[/C][C]1707273.04246969[/C][C]177726.957530313[/C][/ROW]
[ROW][C]45[/C][C]1625000[/C][C]1788529.62227634[/C][C]-163529.622276342[/C][/ROW]
[ROW][C]46[/C][C]2177500[/C][C]1657587.31933205[/C][C]519912.680667951[/C][/ROW]
[ROW][C]47[/C][C]2015000[/C][C]1953781.01055303[/C][C]61218.989446972[/C][/ROW]
[ROW][C]48[/C][C]2600000[/C][C]1967907.02207519[/C][C]632092.97792481[/C][/ROW]
[ROW][C]49[/C][C]2080000[/C][C]2341037.54698888[/C][C]-261037.546988876[/C][/ROW]
[ROW][C]50[/C][C]1267500[/C][C]2160679.6124451[/C][C]-893179.612445095[/C][/ROW]
[ROW][C]51[/C][C]1267500[/C][C]1580617.71166501[/C][C]-313117.711665009[/C][/ROW]
[ROW][C]52[/C][C]1267500[/C][C]1354610.69865128[/C][C]-87110.6986512763[/C][/ROW]
[ROW][C]53[/C][C]1495000[/C][C]1266944.3053334[/C][C]228055.6946666[/C][/ROW]
[ROW][C]54[/C][C]1495000[/C][C]1376118.41384183[/C][C]118881.586158172[/C][/ROW]
[ROW][C]55[/C][C]2015000[/C][C]1419328.59668945[/C][C]595671.403310553[/C][/ROW]
[ROW][C]56[/C][C]1852500[/C][C]1763137.50533436[/C][C]89362.4946656439[/C][/ROW]
[ROW][C]57[/C][C]1657500[/C][C]1795843.0349474[/C][C]-138343.034947401[/C][/ROW]
[ROW][C]58[/C][C]2080000[/C][C]1686629.39189488[/C][C]393370.608105115[/C][/ROW]
[ROW][C]59[/C][C]1917500[/C][C]1909599.91941568[/C][C]7900.08058431908[/C][/ROW]
[ROW][C]60[/C][C]2762500[/C][C]1895041.42993459[/C][C]867458.570065412[/C][/ROW]
[ROW][C]61[/C][C]2177500[/C][C]2420085.6565276[/C][C]-242585.656527605[/C][/ROW]
[ROW][C]62[/C][C]1267500[/C][C]2258135.30259009[/C][C]-990635.302590091[/C][/ROW]
[ROW][C]63[/C][C]1332500[/C][C]1623937.14333214[/C][C]-291437.143332138[/C][/ROW]
[ROW][C]64[/C][C]1105000[/C][C]1417477.13503804[/C][C]-312477.135038045[/C][/ROW]
[ROW][C]65[/C][C]1527500[/C][C]1194538.65168387[/C][C]332961.348316128[/C][/ROW]
[ROW][C]66[/C][C]1755000[/C][C]1373210.05891018[/C][C]381789.941089818[/C][/ROW]
[ROW][C]67[/C][C]2210000[/C][C]1586268.10676931[/C][C]623731.893230692[/C][/ROW]
[ROW][C]68[/C][C]2177500[/C][C]1955471.39511637[/C][C]222028.60488363[/C][/ROW]
[ROW][C]69[/C][C]1755000[/C][C]2079543.57706345[/C][C]-324543.577063449[/C][/ROW]
[ROW][C]70[/C][C]2047500[/C][C]1863045.08769035[/C][C]184454.912309648[/C][/ROW]
[ROW][C]71[/C][C]1820000[/C][C]1962382.51319343[/C][C]-142382.513193425[/C][/ROW]
[ROW][C]72[/C][C]2600000[/C][C]1858646.9869452[/C][C]741353.013054796[/C][/ROW]
[ROW][C]73[/C][C]1982500[/C][C]2308001.77361731[/C][C]-325501.77361731[/C][/ROW]
[ROW][C]74[/C][C]1592500[/C][C]2096054.45357659[/C][C]-503554.453576588[/C][/ROW]
[ROW][C]75[/C][C]1430000[/C][C]1768694.93246424[/C][C]-338694.932464242[/C][/ROW]
[ROW][C]76[/C][C]1072500[/C][C]1539157.60966658[/C][C]-466657.60966658[/C][/ROW]
[ROW][C]77[/C][C]1592500[/C][C]1225499.6419675[/C][C]367000.358032495[/C][/ROW]
[ROW][C]78[/C][C]1917500[/C][C]1429858.9499116[/C][C]487641.050088403[/C][/ROW]
[ROW][C]79[/C][C]2242500[/C][C]1714060.98546147[/C][C]528439.014538532[/C][/ROW]
[ROW][C]80[/C][C]2112500[/C][C]2029345.95910267[/C][C]83154.0408973319[/C][/ROW]
[ROW][C]81[/C][C]1560000[/C][C]2071075.16244087[/C][C]-511075.16244087[/C][/ROW]
[ROW][C]82[/C][C]2242500[/C][C]1740761.72760119[/C][C]501738.272398812[/C][/ROW]
[ROW][C]83[/C][C]1755000[/C][C]2040416.27781873[/C][C]-285416.27781873[/C][/ROW]
[ROW][C]84[/C][C]2697500[/C][C]1851635.9845668[/C][C]845864.015433196[/C][/ROW]
[ROW][C]85[/C][C]2242500[/C][C]2369714.90150612[/C][C]-127214.901506118[/C][/ROW]
[ROW][C]86[/C][C]1625000[/C][C]2286524.9699584[/C][C]-661524.969958398[/C][/ROW]
[ROW][C]87[/C][C]1495000[/C][C]1866539.34424467[/C][C]-371539.344244666[/C][/ROW]
[ROW][C]88[/C][C]1007500[/C][C]1621139.29541316[/C][C]-613639.295413156[/C][/ROW]
[ROW][C]89[/C][C]1592500[/C][C]1219609.93550088[/C][C]372890.064499119[/C][/ROW]
[ROW][C]90[/C][C]1527500[/C][C]1430399.33994271[/C][C]97100.6600572949[/C][/ROW]
[ROW][C]91[/C][C]2307500[/C][C]1472272.66367075[/C][C]835227.336329252[/C][/ROW]
[ROW][C]92[/C][C]2307500[/C][C]1978531.90973742[/C][C]328968.090262578[/C][/ROW]
[ROW][C]93[/C][C]1755000[/C][C]2176408.82298482[/C][C]-421408.822984819[/C][/ROW]
[ROW][C]94[/C][C]2275000[/C][C]1906994.93019077[/C][C]368005.069809234[/C][/ROW]
[ROW][C]95[/C][C]1690000[/C][C]2128335.97536554[/C][C]-438335.975365536[/C][/ROW]
[ROW][C]96[/C][C]2632500[/C][C]1847697.86791116[/C][C]784802.132088839[/C][/ROW]
[ROW][C]97[/C][C]2242500[/C][C]2329857.75108539[/C][C]-87357.751085388[/C][/ROW]
[ROW][C]98[/C][C]1657500[/C][C]2273406.4019895[/C][C]-615906.401989501[/C][/ROW]
[ROW][C]99[/C][C]1267500[/C][C]1884223.13321966[/C][C]-616723.133219656[/C][/ROW]
[ROW][C]100[/C][C]877500[/C][C]1487611.47254481[/C][C]-610111.472544811[/C][/ROW]
[ROW][C]101[/C][C]1722500[/C][C]1088224.78417761[/C][C]634275.215822389[/C][/ROW]
[ROW][C]102[/C][C]1657500[/C][C]1463044.26171464[/C][C]194455.738285364[/C][/ROW]
[ROW][C]103[/C][C]2177500[/C][C]1568926.85572941[/C][C]608573.144270586[/C][/ROW]
[ROW][C]104[/C][C]2502500[/C][C]1936919.54371928[/C][C]565580.456280721[/C][/ROW]
[ROW][C]105[/C][C]1852500[/C][C]2284760.68161574[/C][C]-432260.68161574[/C][/ROW]
[ROW][C]106[/C][C]2080000[/C][C]2012643.42527415[/C][C]67356.5747258451[/C][/ROW]
[ROW][C]107[/C][C]1560000[/C][C]2049264.30962988[/C][C]-489264.309629881[/C][/ROW]
[ROW][C]108[/C][C]2697500[/C][C]1737270.56441935[/C][C]960229.435580654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280013&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280013&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
317875001625000162500
414300001661995.4169361-231995.4169361
518525001453204.86687705399295.133122953
618200001638047.75354745181952.246452549
719500001690955.83235386259044.167646145
820150001794294.80956939220705.190430607
922425001876478.48714003366021.512859969
1019500002052350.21163633-102350.211636331
1118525001938351.72187861-85851.7218786115
1223075001833559.49359166473940.506408344
1319500002079164.75923753-129164.759237531
1414625001951544.18109499-489044.181094987
1517225001596589.87018179125910.129818211
1613000001622129.03050531-322129.030505308
1718200001367863.88553867452136.114461329
1814950001595960.12515903-100960.125159033
1919825001481974.55898781500525.441012188
2017875001744386.2522938543113.747706153
2118850001725317.23865388159682.761346121
2221125001779898.51703605332601.482963953
2320800001944807.6818103135192.318189702
2424700001989544.84492071480455.15507929
2517875002252509.11606524-465009.116065241
2614950001927434.23521637-432434.235216371
2716575001617584.0421502439915.9578497631
2812025001599355.48417404-396855.48417404
2917225001307429.37012216415070.62987784
3013325001520664.00654629-188164.006546287
3118850001359930.57221882525069.427781181
3217875001644755.34650662142744.653493375
3315925001695504.37191992-103004.371919925
3422750001593608.37628938681391.623710621
3520475001982892.996991664607.0030084024
3623400001992695.11682474347304.883175258
3717550002180661.99377546-425661.99377546
3816250001887365.05163921-262365.051639212
3914625001691784.15539777-229284.155397768
4012025001514020.96127965-311520.961279646
4115925001282066.13882418310433.861175816
4214300001436992.09244823-6992.0924482285
4319500001396166.90305881553833.096941194
4418850001707273.04246969177726.957530313
4516250001788529.62227634-163529.622276342
4621775001657587.31933205519912.680667951
4720150001953781.0105530361218.989446972
4826000001967907.02207519632092.97792481
4920800002341037.54698888-261037.546988876
5012675002160679.6124451-893179.612445095
5112675001580617.71166501-313117.711665009
5212675001354610.69865128-87110.6986512763
5314950001266944.3053334228055.6946666
5414950001376118.41384183118881.586158172
5520150001419328.59668945595671.403310553
5618525001763137.5053343689362.4946656439
5716575001795843.0349474-138343.034947401
5820800001686629.39189488393370.608105115
5919175001909599.919415687900.08058431908
6027625001895041.42993459867458.570065412
6121775002420085.6565276-242585.656527605
6212675002258135.30259009-990635.302590091
6313325001623937.14333214-291437.143332138
6411050001417477.13503804-312477.135038045
6515275001194538.65168387332961.348316128
6617550001373210.05891018381789.941089818
6722100001586268.10676931623731.893230692
6821775001955471.39511637222028.60488363
6917550002079543.57706345-324543.577063449
7020475001863045.08769035184454.912309648
7118200001962382.51319343-142382.513193425
7226000001858646.9869452741353.013054796
7319825002308001.77361731-325501.77361731
7415925002096054.45357659-503554.453576588
7514300001768694.93246424-338694.932464242
7610725001539157.60966658-466657.60966658
7715925001225499.6419675367000.358032495
7819175001429858.9499116487641.050088403
7922425001714060.98546147528439.014538532
8021125002029345.9591026783154.0408973319
8115600002071075.16244087-511075.16244087
8222425001740761.72760119501738.272398812
8317550002040416.27781873-285416.27781873
8426975001851635.9845668845864.015433196
8522425002369714.90150612-127214.901506118
8616250002286524.9699584-661524.969958398
8714950001866539.34424467-371539.344244666
8810075001621139.29541316-613639.295413156
8915925001219609.93550088372890.064499119
9015275001430399.3399427197100.6600572949
9123075001472272.66367075835227.336329252
9223075001978531.90973742328968.090262578
9317550002176408.82298482-421408.822984819
9422750001906994.93019077368005.069809234
9516900002128335.97536554-438335.975365536
9626325001847697.86791116784802.132088839
9722425002329857.75108539-87357.751085388
9816575002273406.4019895-615906.401989501
9912675001884223.13321966-616723.133219656
1008775001487611.47254481-610111.472544811
10117225001088224.78417761634275.215822389
10216575001463044.26171464194455.738285364
10321775001568926.85572941608573.144270586
10425025001936919.54371928565580.456280721
10518525002284760.68161574-432260.68161574
10620800002012643.4252741567356.5747258451
10715600002049264.30962988-489264.309629881
10826975001737270.56441935960229.435580654







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092329578.265179281492462.062319633166694.46803893
1102329966.4378051341615.335577943318317.54003207
1112330354.610430731206576.040149583454133.18071189
1122330742.783056461082118.994828813579366.57128411
1132331130.95568219965274.4932467823696987.41811759
1142331519.12830792854169.299879443808868.95673639
1152331907.30093364747535.5044603833916279.0974069
1162332295.47355937644469.9482540944020120.99886465
1172332683.6461851544303.8585049994121063.4338652
1182333071.81881083446526.701677224219616.93594444
1192333459.99143656350739.0448445934316180.93802852
1202333848.16406228256621.9870673394411074.34105723

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2329578.26517928 & 1492462.06231963 & 3166694.46803893 \tabularnewline
110 & 2329966.437805 & 1341615.33557794 & 3318317.54003207 \tabularnewline
111 & 2330354.61043073 & 1206576.04014958 & 3454133.18071189 \tabularnewline
112 & 2330742.78305646 & 1082118.99482881 & 3579366.57128411 \tabularnewline
113 & 2331130.95568219 & 965274.493246782 & 3696987.41811759 \tabularnewline
114 & 2331519.12830792 & 854169.29987944 & 3808868.95673639 \tabularnewline
115 & 2331907.30093364 & 747535.504460383 & 3916279.0974069 \tabularnewline
116 & 2332295.47355937 & 644469.948254094 & 4020120.99886465 \tabularnewline
117 & 2332683.6461851 & 544303.858504999 & 4121063.4338652 \tabularnewline
118 & 2333071.81881083 & 446526.70167722 & 4219616.93594444 \tabularnewline
119 & 2333459.99143656 & 350739.044844593 & 4316180.93802852 \tabularnewline
120 & 2333848.16406228 & 256621.987067339 & 4411074.34105723 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280013&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]2329578.26517928[/C][C]1492462.06231963[/C][C]3166694.46803893[/C][/ROW]
[ROW][C]110[/C][C]2329966.437805[/C][C]1341615.33557794[/C][C]3318317.54003207[/C][/ROW]
[ROW][C]111[/C][C]2330354.61043073[/C][C]1206576.04014958[/C][C]3454133.18071189[/C][/ROW]
[ROW][C]112[/C][C]2330742.78305646[/C][C]1082118.99482881[/C][C]3579366.57128411[/C][/ROW]
[ROW][C]113[/C][C]2331130.95568219[/C][C]965274.493246782[/C][C]3696987.41811759[/C][/ROW]
[ROW][C]114[/C][C]2331519.12830792[/C][C]854169.29987944[/C][C]3808868.95673639[/C][/ROW]
[ROW][C]115[/C][C]2331907.30093364[/C][C]747535.504460383[/C][C]3916279.0974069[/C][/ROW]
[ROW][C]116[/C][C]2332295.47355937[/C][C]644469.948254094[/C][C]4020120.99886465[/C][/ROW]
[ROW][C]117[/C][C]2332683.6461851[/C][C]544303.858504999[/C][C]4121063.4338652[/C][/ROW]
[ROW][C]118[/C][C]2333071.81881083[/C][C]446526.70167722[/C][C]4219616.93594444[/C][/ROW]
[ROW][C]119[/C][C]2333459.99143656[/C][C]350739.044844593[/C][C]4316180.93802852[/C][/ROW]
[ROW][C]120[/C][C]2333848.16406228[/C][C]256621.987067339[/C][C]4411074.34105723[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280013&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280013&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
1092329578.265179281492462.062319633166694.46803893
1102329966.4378051341615.335577943318317.54003207
1112330354.610430731206576.040149583454133.18071189
1122330742.783056461082118.994828813579366.57128411
1132331130.95568219965274.4932467823696987.41811759
1142331519.12830792854169.299879443808868.95673639
1152331907.30093364747535.5044603833916279.0974069
1162332295.47355937644469.9482540944020120.99886465
1172332683.6461851544303.8585049994121063.4338652
1182333071.81881083446526.701677224219616.93594444
1192333459.99143656350739.0448445934316180.93802852
1202333848.16406228256621.9870673394411074.34105723



Parameters (Session):
par1 = 0 ; par2 = no ; par3 = 512 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')