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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 computationSun, 16 Aug 2015 18:11:53 +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/16/t1439745123z6txyredojqdma2.htm/, Retrieved Sat, 18 May 2024 05:30:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280182, Retrieved Sat, 18 May 2024 05:30:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-08-16 17:11:53] [f898ec974b62c60a8bec4044c4c271e3] [Current]
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Dataseries X:
1544400
1487200
1573000
1258400
1630200
1601600
1716000
1773200
1973400
1716000
1630200
2030600
1716000
1287000
1515800
1144000
1601600
1315600
1744600
1573000
1658800
1859000
1830400
2173600
1573000
1315600
1458600
1058200
1515800
1172600
1658800
1573000
1401400
2002000
1801800
2059200
1544400
1430000
1287000
1058200
1401400
1258400
1716000
1658800
1430000
1916200
1773200
2288000
1830400
1115400
1115400
1115400
1315600
1315600
1773200
1630200
1458600
1830400
1687400
2431000
1916200
1115400
1172600
972400
1344200
1544400
1944800
1916200
1544400
1801800
1601600
2288000
1744600
1401400
1258400
943800
1401400
1687400
1973400
1859000
1372800
1973400
1544400
2373800
1973400
1430000
1315600
886600
1401400
1344200
2030600
2030600
1544400
2002000
1487200
2316600
1973400
1458600
1115400
772200
1515800
1458600
1916200
2202200
1630200
1830400
1372800
2373800




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280182&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]1 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=280182&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280182&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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.616435516555849
beta0.0182153483451373
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.616435516555849 \tabularnewline
beta & 0.0182153483451373 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280182&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]0.616435516555849[/C][/ROW]
[ROW][C]beta[/C][C]0.0182153483451373[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280182&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280182&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
alpha0.616435516555849
beta0.0182153483451373
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
315730001430000143000
412584001462555.96690378-204155.966903779
516302001278820.28285179351379.717148212
616016001441482.02312178160117.976878221
717160001488041.13247141227958.867528592
817732001578979.43242108194220.567578919
919734001651301.06868323322098.931316765
1017160001806068.18623998-90068.1862399823
1116302001705749.51525315-75549.5152531529
1220306001613532.35436062417067.645639378
1317160001829664.98812903-113664.988129026
1412870001717358.87936355-430358.879363553
1515158001404999.0857599110800.914240096
1611440001427473.54684464-283473.546844637
1716016001203720.21927398397879.780726021
1813156001404444.91013995-88844.9101399484
1917446001304137.61190925440462.38809075
2015730001535059.9020185937940.0979814073
2116588001518279.17001539140520.829984605
2218590001566310.6949917292689.3050083
2318304001711430.75999305118969.24000695
2421736001750799.4635302422800.536469803
2515730001982208.0221374-409208.0221374
2613156001696142.12699033-380542.126990328
2714586001423473.9570921235126.0429078839
2810582001407432.8260731-349232.826073097
2915158001150537.84570743365262.154292574
3011726001338184.32576071-165584.325760714
3116588001196738.90355252462061.096447484
3215730001447384.70492583125615.295074173
3314014001492043.84728951-90643.8472895126
3420020001402375.37113461599624.628865394
3518018001744945.837352656854.1626473959
3620592001753571.70280574305628.297194264
3715444001918982.55452237-374582.554522373
3814300001660881.24544242-230881.24544242
3912870001488770.05674995-201770.056749946
4010582001332338.44592601-274138.445926005
4114014001128218.2021652273181.797834799
4212584001264553.04135441-6153.04135440802
4317160001228626.87469171487373.125308292
4416588001502400.27737332156399.72262668
4514300001573906.06760316-143906.067603156
4619162001458676.84101214457523.158987855
4717732001719327.2892866453872.7107133579
4822880001731758.17942612556241.82057388
4918304002060113.04135019-229713.041350192
5011154001901398.05895161-785998.058951606
5111154001390943.58626507-275543.58626507
5211154001192057.41481302-76657.4148130168
5313156001114910.98869332200689.011306681
5413156001210984.20418077104615.795819228
5517732001249009.16508668524190.83491332
5616302001551561.0046942378638.9953057677
5714586001580341.87075368-121741.870753681
5818304001484233.86486744346166.135132562
5916874001680447.929085776952.07091423357
6024310001667636.45834238763363.541657616
6119162002129675.37774429-213475.377744289
6211154001987159.06627921-871759.066279207
6311726001429064.68613214-256464.686132136
649724001247379.87883337-274979.878833371
6513442001051194.01348172293005.986518282
6615444001208424.85184093335975.148159073
6719448001395915.93395698548884.066043023
6819162001720814.82770241195385.17229759
6915444001829998.34781581-285598.34781581
7018018001639479.67716743162320.322832568
7116016001726896.61161016-125296.611610157
7222880001635609.34851171652390.651488294
7317446002031041.56078322-286441.560783216
7414014001844527.91914732-443127.919147318
7512584001556451.54056842-298051.540568424
769438001354458.69650649-410658.69650649
7714014001078439.68493131322960.315068695
7816874001258275.87592217429124.124077828
7919734001508373.66720609465026.332793914
8018590001785824.4440103573175.5559896517
8113728001822546.14294793-449746.14294793
8219734001531870.32028895441529.679711045
8315444001795566.32448045-251166.324480448
8423738001629439.66641871744360.333581286
8519734002085349.11332538-111949.113325377
8614300002012141.97356333-582141.97356333
8713156001642554.62293519-326954.622935193
888866001426602.57996347-540002.579963475
8914014001073256.74324067328143.256759332
9013442001258751.4191495585448.580850452
9120306001295599.94403023735000.05596977
9220306001741108.08056895289491.919431047
9315444001915239.76422663-370839.764226635
9420020001678155.5385678323844.461432199
9514872001872935.65832163-385735.658321634
9623166001625974.12376174690625.876238262
9719734002050274.82095513-76874.82095513
9814586002000597.63375071-541997.633750707
9911154001658116.35723319-542716.357233193
1007722001309098.09583932-536898.095839321
1011515800957637.810076193558162.189923807
10214586001287478.95030887171121.049691127
10319162001380655.63304188535544.366958125
10422022001704489.19847298497710.80152702
10516302002010589.39982186-380389.399821863
10618304001771126.2142411959273.7857588094
10713728001803352.59247424-430552.592474241
10823738001528798.09668894845001.903311064

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1573000 & 1430000 & 143000 \tabularnewline
4 & 1258400 & 1462555.96690378 & -204155.966903779 \tabularnewline
5 & 1630200 & 1278820.28285179 & 351379.717148212 \tabularnewline
6 & 1601600 & 1441482.02312178 & 160117.976878221 \tabularnewline
7 & 1716000 & 1488041.13247141 & 227958.867528592 \tabularnewline
8 & 1773200 & 1578979.43242108 & 194220.567578919 \tabularnewline
9 & 1973400 & 1651301.06868323 & 322098.931316765 \tabularnewline
10 & 1716000 & 1806068.18623998 & -90068.1862399823 \tabularnewline
11 & 1630200 & 1705749.51525315 & -75549.5152531529 \tabularnewline
12 & 2030600 & 1613532.35436062 & 417067.645639378 \tabularnewline
13 & 1716000 & 1829664.98812903 & -113664.988129026 \tabularnewline
14 & 1287000 & 1717358.87936355 & -430358.879363553 \tabularnewline
15 & 1515800 & 1404999.0857599 & 110800.914240096 \tabularnewline
16 & 1144000 & 1427473.54684464 & -283473.546844637 \tabularnewline
17 & 1601600 & 1203720.21927398 & 397879.780726021 \tabularnewline
18 & 1315600 & 1404444.91013995 & -88844.9101399484 \tabularnewline
19 & 1744600 & 1304137.61190925 & 440462.38809075 \tabularnewline
20 & 1573000 & 1535059.90201859 & 37940.0979814073 \tabularnewline
21 & 1658800 & 1518279.17001539 & 140520.829984605 \tabularnewline
22 & 1859000 & 1566310.6949917 & 292689.3050083 \tabularnewline
23 & 1830400 & 1711430.75999305 & 118969.24000695 \tabularnewline
24 & 2173600 & 1750799.4635302 & 422800.536469803 \tabularnewline
25 & 1573000 & 1982208.0221374 & -409208.0221374 \tabularnewline
26 & 1315600 & 1696142.12699033 & -380542.126990328 \tabularnewline
27 & 1458600 & 1423473.95709212 & 35126.0429078839 \tabularnewline
28 & 1058200 & 1407432.8260731 & -349232.826073097 \tabularnewline
29 & 1515800 & 1150537.84570743 & 365262.154292574 \tabularnewline
30 & 1172600 & 1338184.32576071 & -165584.325760714 \tabularnewline
31 & 1658800 & 1196738.90355252 & 462061.096447484 \tabularnewline
32 & 1573000 & 1447384.70492583 & 125615.295074173 \tabularnewline
33 & 1401400 & 1492043.84728951 & -90643.8472895126 \tabularnewline
34 & 2002000 & 1402375.37113461 & 599624.628865394 \tabularnewline
35 & 1801800 & 1744945.8373526 & 56854.1626473959 \tabularnewline
36 & 2059200 & 1753571.70280574 & 305628.297194264 \tabularnewline
37 & 1544400 & 1918982.55452237 & -374582.554522373 \tabularnewline
38 & 1430000 & 1660881.24544242 & -230881.24544242 \tabularnewline
39 & 1287000 & 1488770.05674995 & -201770.056749946 \tabularnewline
40 & 1058200 & 1332338.44592601 & -274138.445926005 \tabularnewline
41 & 1401400 & 1128218.2021652 & 273181.797834799 \tabularnewline
42 & 1258400 & 1264553.04135441 & -6153.04135440802 \tabularnewline
43 & 1716000 & 1228626.87469171 & 487373.125308292 \tabularnewline
44 & 1658800 & 1502400.27737332 & 156399.72262668 \tabularnewline
45 & 1430000 & 1573906.06760316 & -143906.067603156 \tabularnewline
46 & 1916200 & 1458676.84101214 & 457523.158987855 \tabularnewline
47 & 1773200 & 1719327.28928664 & 53872.7107133579 \tabularnewline
48 & 2288000 & 1731758.17942612 & 556241.82057388 \tabularnewline
49 & 1830400 & 2060113.04135019 & -229713.041350192 \tabularnewline
50 & 1115400 & 1901398.05895161 & -785998.058951606 \tabularnewline
51 & 1115400 & 1390943.58626507 & -275543.58626507 \tabularnewline
52 & 1115400 & 1192057.41481302 & -76657.4148130168 \tabularnewline
53 & 1315600 & 1114910.98869332 & 200689.011306681 \tabularnewline
54 & 1315600 & 1210984.20418077 & 104615.795819228 \tabularnewline
55 & 1773200 & 1249009.16508668 & 524190.83491332 \tabularnewline
56 & 1630200 & 1551561.00469423 & 78638.9953057677 \tabularnewline
57 & 1458600 & 1580341.87075368 & -121741.870753681 \tabularnewline
58 & 1830400 & 1484233.86486744 & 346166.135132562 \tabularnewline
59 & 1687400 & 1680447.92908577 & 6952.07091423357 \tabularnewline
60 & 2431000 & 1667636.45834238 & 763363.541657616 \tabularnewline
61 & 1916200 & 2129675.37774429 & -213475.377744289 \tabularnewline
62 & 1115400 & 1987159.06627921 & -871759.066279207 \tabularnewline
63 & 1172600 & 1429064.68613214 & -256464.686132136 \tabularnewline
64 & 972400 & 1247379.87883337 & -274979.878833371 \tabularnewline
65 & 1344200 & 1051194.01348172 & 293005.986518282 \tabularnewline
66 & 1544400 & 1208424.85184093 & 335975.148159073 \tabularnewline
67 & 1944800 & 1395915.93395698 & 548884.066043023 \tabularnewline
68 & 1916200 & 1720814.82770241 & 195385.17229759 \tabularnewline
69 & 1544400 & 1829998.34781581 & -285598.34781581 \tabularnewline
70 & 1801800 & 1639479.67716743 & 162320.322832568 \tabularnewline
71 & 1601600 & 1726896.61161016 & -125296.611610157 \tabularnewline
72 & 2288000 & 1635609.34851171 & 652390.651488294 \tabularnewline
73 & 1744600 & 2031041.56078322 & -286441.560783216 \tabularnewline
74 & 1401400 & 1844527.91914732 & -443127.919147318 \tabularnewline
75 & 1258400 & 1556451.54056842 & -298051.540568424 \tabularnewline
76 & 943800 & 1354458.69650649 & -410658.69650649 \tabularnewline
77 & 1401400 & 1078439.68493131 & 322960.315068695 \tabularnewline
78 & 1687400 & 1258275.87592217 & 429124.124077828 \tabularnewline
79 & 1973400 & 1508373.66720609 & 465026.332793914 \tabularnewline
80 & 1859000 & 1785824.44401035 & 73175.5559896517 \tabularnewline
81 & 1372800 & 1822546.14294793 & -449746.14294793 \tabularnewline
82 & 1973400 & 1531870.32028895 & 441529.679711045 \tabularnewline
83 & 1544400 & 1795566.32448045 & -251166.324480448 \tabularnewline
84 & 2373800 & 1629439.66641871 & 744360.333581286 \tabularnewline
85 & 1973400 & 2085349.11332538 & -111949.113325377 \tabularnewline
86 & 1430000 & 2012141.97356333 & -582141.97356333 \tabularnewline
87 & 1315600 & 1642554.62293519 & -326954.622935193 \tabularnewline
88 & 886600 & 1426602.57996347 & -540002.579963475 \tabularnewline
89 & 1401400 & 1073256.74324067 & 328143.256759332 \tabularnewline
90 & 1344200 & 1258751.41914955 & 85448.580850452 \tabularnewline
91 & 2030600 & 1295599.94403023 & 735000.05596977 \tabularnewline
92 & 2030600 & 1741108.08056895 & 289491.919431047 \tabularnewline
93 & 1544400 & 1915239.76422663 & -370839.764226635 \tabularnewline
94 & 2002000 & 1678155.5385678 & 323844.461432199 \tabularnewline
95 & 1487200 & 1872935.65832163 & -385735.658321634 \tabularnewline
96 & 2316600 & 1625974.12376174 & 690625.876238262 \tabularnewline
97 & 1973400 & 2050274.82095513 & -76874.82095513 \tabularnewline
98 & 1458600 & 2000597.63375071 & -541997.633750707 \tabularnewline
99 & 1115400 & 1658116.35723319 & -542716.357233193 \tabularnewline
100 & 772200 & 1309098.09583932 & -536898.095839321 \tabularnewline
101 & 1515800 & 957637.810076193 & 558162.189923807 \tabularnewline
102 & 1458600 & 1287478.95030887 & 171121.049691127 \tabularnewline
103 & 1916200 & 1380655.63304188 & 535544.366958125 \tabularnewline
104 & 2202200 & 1704489.19847298 & 497710.80152702 \tabularnewline
105 & 1630200 & 2010589.39982186 & -380389.399821863 \tabularnewline
106 & 1830400 & 1771126.21424119 & 59273.7857588094 \tabularnewline
107 & 1372800 & 1803352.59247424 & -430552.592474241 \tabularnewline
108 & 2373800 & 1528798.09668894 & 845001.903311064 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280182&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]1573000[/C][C]1430000[/C][C]143000[/C][/ROW]
[ROW][C]4[/C][C]1258400[/C][C]1462555.96690378[/C][C]-204155.966903779[/C][/ROW]
[ROW][C]5[/C][C]1630200[/C][C]1278820.28285179[/C][C]351379.717148212[/C][/ROW]
[ROW][C]6[/C][C]1601600[/C][C]1441482.02312178[/C][C]160117.976878221[/C][/ROW]
[ROW][C]7[/C][C]1716000[/C][C]1488041.13247141[/C][C]227958.867528592[/C][/ROW]
[ROW][C]8[/C][C]1773200[/C][C]1578979.43242108[/C][C]194220.567578919[/C][/ROW]
[ROW][C]9[/C][C]1973400[/C][C]1651301.06868323[/C][C]322098.931316765[/C][/ROW]
[ROW][C]10[/C][C]1716000[/C][C]1806068.18623998[/C][C]-90068.1862399823[/C][/ROW]
[ROW][C]11[/C][C]1630200[/C][C]1705749.51525315[/C][C]-75549.5152531529[/C][/ROW]
[ROW][C]12[/C][C]2030600[/C][C]1613532.35436062[/C][C]417067.645639378[/C][/ROW]
[ROW][C]13[/C][C]1716000[/C][C]1829664.98812903[/C][C]-113664.988129026[/C][/ROW]
[ROW][C]14[/C][C]1287000[/C][C]1717358.87936355[/C][C]-430358.879363553[/C][/ROW]
[ROW][C]15[/C][C]1515800[/C][C]1404999.0857599[/C][C]110800.914240096[/C][/ROW]
[ROW][C]16[/C][C]1144000[/C][C]1427473.54684464[/C][C]-283473.546844637[/C][/ROW]
[ROW][C]17[/C][C]1601600[/C][C]1203720.21927398[/C][C]397879.780726021[/C][/ROW]
[ROW][C]18[/C][C]1315600[/C][C]1404444.91013995[/C][C]-88844.9101399484[/C][/ROW]
[ROW][C]19[/C][C]1744600[/C][C]1304137.61190925[/C][C]440462.38809075[/C][/ROW]
[ROW][C]20[/C][C]1573000[/C][C]1535059.90201859[/C][C]37940.0979814073[/C][/ROW]
[ROW][C]21[/C][C]1658800[/C][C]1518279.17001539[/C][C]140520.829984605[/C][/ROW]
[ROW][C]22[/C][C]1859000[/C][C]1566310.6949917[/C][C]292689.3050083[/C][/ROW]
[ROW][C]23[/C][C]1830400[/C][C]1711430.75999305[/C][C]118969.24000695[/C][/ROW]
[ROW][C]24[/C][C]2173600[/C][C]1750799.4635302[/C][C]422800.536469803[/C][/ROW]
[ROW][C]25[/C][C]1573000[/C][C]1982208.0221374[/C][C]-409208.0221374[/C][/ROW]
[ROW][C]26[/C][C]1315600[/C][C]1696142.12699033[/C][C]-380542.126990328[/C][/ROW]
[ROW][C]27[/C][C]1458600[/C][C]1423473.95709212[/C][C]35126.0429078839[/C][/ROW]
[ROW][C]28[/C][C]1058200[/C][C]1407432.8260731[/C][C]-349232.826073097[/C][/ROW]
[ROW][C]29[/C][C]1515800[/C][C]1150537.84570743[/C][C]365262.154292574[/C][/ROW]
[ROW][C]30[/C][C]1172600[/C][C]1338184.32576071[/C][C]-165584.325760714[/C][/ROW]
[ROW][C]31[/C][C]1658800[/C][C]1196738.90355252[/C][C]462061.096447484[/C][/ROW]
[ROW][C]32[/C][C]1573000[/C][C]1447384.70492583[/C][C]125615.295074173[/C][/ROW]
[ROW][C]33[/C][C]1401400[/C][C]1492043.84728951[/C][C]-90643.8472895126[/C][/ROW]
[ROW][C]34[/C][C]2002000[/C][C]1402375.37113461[/C][C]599624.628865394[/C][/ROW]
[ROW][C]35[/C][C]1801800[/C][C]1744945.8373526[/C][C]56854.1626473959[/C][/ROW]
[ROW][C]36[/C][C]2059200[/C][C]1753571.70280574[/C][C]305628.297194264[/C][/ROW]
[ROW][C]37[/C][C]1544400[/C][C]1918982.55452237[/C][C]-374582.554522373[/C][/ROW]
[ROW][C]38[/C][C]1430000[/C][C]1660881.24544242[/C][C]-230881.24544242[/C][/ROW]
[ROW][C]39[/C][C]1287000[/C][C]1488770.05674995[/C][C]-201770.056749946[/C][/ROW]
[ROW][C]40[/C][C]1058200[/C][C]1332338.44592601[/C][C]-274138.445926005[/C][/ROW]
[ROW][C]41[/C][C]1401400[/C][C]1128218.2021652[/C][C]273181.797834799[/C][/ROW]
[ROW][C]42[/C][C]1258400[/C][C]1264553.04135441[/C][C]-6153.04135440802[/C][/ROW]
[ROW][C]43[/C][C]1716000[/C][C]1228626.87469171[/C][C]487373.125308292[/C][/ROW]
[ROW][C]44[/C][C]1658800[/C][C]1502400.27737332[/C][C]156399.72262668[/C][/ROW]
[ROW][C]45[/C][C]1430000[/C][C]1573906.06760316[/C][C]-143906.067603156[/C][/ROW]
[ROW][C]46[/C][C]1916200[/C][C]1458676.84101214[/C][C]457523.158987855[/C][/ROW]
[ROW][C]47[/C][C]1773200[/C][C]1719327.28928664[/C][C]53872.7107133579[/C][/ROW]
[ROW][C]48[/C][C]2288000[/C][C]1731758.17942612[/C][C]556241.82057388[/C][/ROW]
[ROW][C]49[/C][C]1830400[/C][C]2060113.04135019[/C][C]-229713.041350192[/C][/ROW]
[ROW][C]50[/C][C]1115400[/C][C]1901398.05895161[/C][C]-785998.058951606[/C][/ROW]
[ROW][C]51[/C][C]1115400[/C][C]1390943.58626507[/C][C]-275543.58626507[/C][/ROW]
[ROW][C]52[/C][C]1115400[/C][C]1192057.41481302[/C][C]-76657.4148130168[/C][/ROW]
[ROW][C]53[/C][C]1315600[/C][C]1114910.98869332[/C][C]200689.011306681[/C][/ROW]
[ROW][C]54[/C][C]1315600[/C][C]1210984.20418077[/C][C]104615.795819228[/C][/ROW]
[ROW][C]55[/C][C]1773200[/C][C]1249009.16508668[/C][C]524190.83491332[/C][/ROW]
[ROW][C]56[/C][C]1630200[/C][C]1551561.00469423[/C][C]78638.9953057677[/C][/ROW]
[ROW][C]57[/C][C]1458600[/C][C]1580341.87075368[/C][C]-121741.870753681[/C][/ROW]
[ROW][C]58[/C][C]1830400[/C][C]1484233.86486744[/C][C]346166.135132562[/C][/ROW]
[ROW][C]59[/C][C]1687400[/C][C]1680447.92908577[/C][C]6952.07091423357[/C][/ROW]
[ROW][C]60[/C][C]2431000[/C][C]1667636.45834238[/C][C]763363.541657616[/C][/ROW]
[ROW][C]61[/C][C]1916200[/C][C]2129675.37774429[/C][C]-213475.377744289[/C][/ROW]
[ROW][C]62[/C][C]1115400[/C][C]1987159.06627921[/C][C]-871759.066279207[/C][/ROW]
[ROW][C]63[/C][C]1172600[/C][C]1429064.68613214[/C][C]-256464.686132136[/C][/ROW]
[ROW][C]64[/C][C]972400[/C][C]1247379.87883337[/C][C]-274979.878833371[/C][/ROW]
[ROW][C]65[/C][C]1344200[/C][C]1051194.01348172[/C][C]293005.986518282[/C][/ROW]
[ROW][C]66[/C][C]1544400[/C][C]1208424.85184093[/C][C]335975.148159073[/C][/ROW]
[ROW][C]67[/C][C]1944800[/C][C]1395915.93395698[/C][C]548884.066043023[/C][/ROW]
[ROW][C]68[/C][C]1916200[/C][C]1720814.82770241[/C][C]195385.17229759[/C][/ROW]
[ROW][C]69[/C][C]1544400[/C][C]1829998.34781581[/C][C]-285598.34781581[/C][/ROW]
[ROW][C]70[/C][C]1801800[/C][C]1639479.67716743[/C][C]162320.322832568[/C][/ROW]
[ROW][C]71[/C][C]1601600[/C][C]1726896.61161016[/C][C]-125296.611610157[/C][/ROW]
[ROW][C]72[/C][C]2288000[/C][C]1635609.34851171[/C][C]652390.651488294[/C][/ROW]
[ROW][C]73[/C][C]1744600[/C][C]2031041.56078322[/C][C]-286441.560783216[/C][/ROW]
[ROW][C]74[/C][C]1401400[/C][C]1844527.91914732[/C][C]-443127.919147318[/C][/ROW]
[ROW][C]75[/C][C]1258400[/C][C]1556451.54056842[/C][C]-298051.540568424[/C][/ROW]
[ROW][C]76[/C][C]943800[/C][C]1354458.69650649[/C][C]-410658.69650649[/C][/ROW]
[ROW][C]77[/C][C]1401400[/C][C]1078439.68493131[/C][C]322960.315068695[/C][/ROW]
[ROW][C]78[/C][C]1687400[/C][C]1258275.87592217[/C][C]429124.124077828[/C][/ROW]
[ROW][C]79[/C][C]1973400[/C][C]1508373.66720609[/C][C]465026.332793914[/C][/ROW]
[ROW][C]80[/C][C]1859000[/C][C]1785824.44401035[/C][C]73175.5559896517[/C][/ROW]
[ROW][C]81[/C][C]1372800[/C][C]1822546.14294793[/C][C]-449746.14294793[/C][/ROW]
[ROW][C]82[/C][C]1973400[/C][C]1531870.32028895[/C][C]441529.679711045[/C][/ROW]
[ROW][C]83[/C][C]1544400[/C][C]1795566.32448045[/C][C]-251166.324480448[/C][/ROW]
[ROW][C]84[/C][C]2373800[/C][C]1629439.66641871[/C][C]744360.333581286[/C][/ROW]
[ROW][C]85[/C][C]1973400[/C][C]2085349.11332538[/C][C]-111949.113325377[/C][/ROW]
[ROW][C]86[/C][C]1430000[/C][C]2012141.97356333[/C][C]-582141.97356333[/C][/ROW]
[ROW][C]87[/C][C]1315600[/C][C]1642554.62293519[/C][C]-326954.622935193[/C][/ROW]
[ROW][C]88[/C][C]886600[/C][C]1426602.57996347[/C][C]-540002.579963475[/C][/ROW]
[ROW][C]89[/C][C]1401400[/C][C]1073256.74324067[/C][C]328143.256759332[/C][/ROW]
[ROW][C]90[/C][C]1344200[/C][C]1258751.41914955[/C][C]85448.580850452[/C][/ROW]
[ROW][C]91[/C][C]2030600[/C][C]1295599.94403023[/C][C]735000.05596977[/C][/ROW]
[ROW][C]92[/C][C]2030600[/C][C]1741108.08056895[/C][C]289491.919431047[/C][/ROW]
[ROW][C]93[/C][C]1544400[/C][C]1915239.76422663[/C][C]-370839.764226635[/C][/ROW]
[ROW][C]94[/C][C]2002000[/C][C]1678155.5385678[/C][C]323844.461432199[/C][/ROW]
[ROW][C]95[/C][C]1487200[/C][C]1872935.65832163[/C][C]-385735.658321634[/C][/ROW]
[ROW][C]96[/C][C]2316600[/C][C]1625974.12376174[/C][C]690625.876238262[/C][/ROW]
[ROW][C]97[/C][C]1973400[/C][C]2050274.82095513[/C][C]-76874.82095513[/C][/ROW]
[ROW][C]98[/C][C]1458600[/C][C]2000597.63375071[/C][C]-541997.633750707[/C][/ROW]
[ROW][C]99[/C][C]1115400[/C][C]1658116.35723319[/C][C]-542716.357233193[/C][/ROW]
[ROW][C]100[/C][C]772200[/C][C]1309098.09583932[/C][C]-536898.095839321[/C][/ROW]
[ROW][C]101[/C][C]1515800[/C][C]957637.810076193[/C][C]558162.189923807[/C][/ROW]
[ROW][C]102[/C][C]1458600[/C][C]1287478.95030887[/C][C]171121.049691127[/C][/ROW]
[ROW][C]103[/C][C]1916200[/C][C]1380655.63304188[/C][C]535544.366958125[/C][/ROW]
[ROW][C]104[/C][C]2202200[/C][C]1704489.19847298[/C][C]497710.80152702[/C][/ROW]
[ROW][C]105[/C][C]1630200[/C][C]2010589.39982186[/C][C]-380389.399821863[/C][/ROW]
[ROW][C]106[/C][C]1830400[/C][C]1771126.21424119[/C][C]59273.7857588094[/C][/ROW]
[ROW][C]107[/C][C]1372800[/C][C]1803352.59247424[/C][C]-430552.592474241[/C][/ROW]
[ROW][C]108[/C][C]2373800[/C][C]1528798.09668894[/C][C]845001.903311064[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280182&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280182&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
315730001430000143000
412584001462555.96690378-204155.966903779
516302001278820.28285179351379.717148212
616016001441482.02312178160117.976878221
717160001488041.13247141227958.867528592
817732001578979.43242108194220.567578919
919734001651301.06868323322098.931316765
1017160001806068.18623998-90068.1862399823
1116302001705749.51525315-75549.5152531529
1220306001613532.35436062417067.645639378
1317160001829664.98812903-113664.988129026
1412870001717358.87936355-430358.879363553
1515158001404999.0857599110800.914240096
1611440001427473.54684464-283473.546844637
1716016001203720.21927398397879.780726021
1813156001404444.91013995-88844.9101399484
1917446001304137.61190925440462.38809075
2015730001535059.9020185937940.0979814073
2116588001518279.17001539140520.829984605
2218590001566310.6949917292689.3050083
2318304001711430.75999305118969.24000695
2421736001750799.4635302422800.536469803
2515730001982208.0221374-409208.0221374
2613156001696142.12699033-380542.126990328
2714586001423473.9570921235126.0429078839
2810582001407432.8260731-349232.826073097
2915158001150537.84570743365262.154292574
3011726001338184.32576071-165584.325760714
3116588001196738.90355252462061.096447484
3215730001447384.70492583125615.295074173
3314014001492043.84728951-90643.8472895126
3420020001402375.37113461599624.628865394
3518018001744945.837352656854.1626473959
3620592001753571.70280574305628.297194264
3715444001918982.55452237-374582.554522373
3814300001660881.24544242-230881.24544242
3912870001488770.05674995-201770.056749946
4010582001332338.44592601-274138.445926005
4114014001128218.2021652273181.797834799
4212584001264553.04135441-6153.04135440802
4317160001228626.87469171487373.125308292
4416588001502400.27737332156399.72262668
4514300001573906.06760316-143906.067603156
4619162001458676.84101214457523.158987855
4717732001719327.2892866453872.7107133579
4822880001731758.17942612556241.82057388
4918304002060113.04135019-229713.041350192
5011154001901398.05895161-785998.058951606
5111154001390943.58626507-275543.58626507
5211154001192057.41481302-76657.4148130168
5313156001114910.98869332200689.011306681
5413156001210984.20418077104615.795819228
5517732001249009.16508668524190.83491332
5616302001551561.0046942378638.9953057677
5714586001580341.87075368-121741.870753681
5818304001484233.86486744346166.135132562
5916874001680447.929085776952.07091423357
6024310001667636.45834238763363.541657616
6119162002129675.37774429-213475.377744289
6211154001987159.06627921-871759.066279207
6311726001429064.68613214-256464.686132136
649724001247379.87883337-274979.878833371
6513442001051194.01348172293005.986518282
6615444001208424.85184093335975.148159073
6719448001395915.93395698548884.066043023
6819162001720814.82770241195385.17229759
6915444001829998.34781581-285598.34781581
7018018001639479.67716743162320.322832568
7116016001726896.61161016-125296.611610157
7222880001635609.34851171652390.651488294
7317446002031041.56078322-286441.560783216
7414014001844527.91914732-443127.919147318
7512584001556451.54056842-298051.540568424
769438001354458.69650649-410658.69650649
7714014001078439.68493131322960.315068695
7816874001258275.87592217429124.124077828
7919734001508373.66720609465026.332793914
8018590001785824.4440103573175.5559896517
8113728001822546.14294793-449746.14294793
8219734001531870.32028895441529.679711045
8315444001795566.32448045-251166.324480448
8423738001629439.66641871744360.333581286
8519734002085349.11332538-111949.113325377
8614300002012141.97356333-582141.97356333
8713156001642554.62293519-326954.622935193
888866001426602.57996347-540002.579963475
8914014001073256.74324067328143.256759332
9013442001258751.4191495585448.580850452
9120306001295599.94403023735000.05596977
9220306001741108.08056895289491.919431047
9315444001915239.76422663-370839.764226635
9420020001678155.5385678323844.461432199
9514872001872935.65832163-385735.658321634
9623166001625974.12376174690625.876238262
9719734002050274.82095513-76874.82095513
9814586002000597.63375071-541997.633750707
9911154001658116.35723319-542716.357233193
1007722001309098.09583932-536898.095839321
1011515800957637.810076193558162.189923807
10214586001287478.95030887171121.049691127
10319162001380655.63304188535544.366958125
10422022001704489.19847298497710.80152702
10516302002010589.39982186-380389.399821863
10618304001771126.2142411959273.7857588094
10713728001803352.59247424-430552.592474241
10823738001528798.09668894845001.903311064







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092050028.873357771313366.614841292786691.13187425
1102050370.465268371180621.495308542920119.4352282
1112050712.057178971061786.915331523039637.19902642
1122051053.64908957952264.71544923149842.58272994
1132051395.24100017849441.5540569723253348.92794336
1142051736.83291077751668.9838936753351804.68192786
1152052078.42482137657831.2439248733446325.60571786
1162052420.01673197567133.5544633113537706.47900063
1172052761.60864257478987.3954840823626535.82180105
1182053103.20055317392943.4974756143713262.90363072
1192053444.79246377308650.3594628823798239.22546465
1202053786.38437437225827.3486188823881745.42012986

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2050028.87335777 & 1313366.61484129 & 2786691.13187425 \tabularnewline
110 & 2050370.46526837 & 1180621.49530854 & 2920119.4352282 \tabularnewline
111 & 2050712.05717897 & 1061786.91533152 & 3039637.19902642 \tabularnewline
112 & 2051053.64908957 & 952264.7154492 & 3149842.58272994 \tabularnewline
113 & 2051395.24100017 & 849441.554056972 & 3253348.92794336 \tabularnewline
114 & 2051736.83291077 & 751668.983893675 & 3351804.68192786 \tabularnewline
115 & 2052078.42482137 & 657831.243924873 & 3446325.60571786 \tabularnewline
116 & 2052420.01673197 & 567133.554463311 & 3537706.47900063 \tabularnewline
117 & 2052761.60864257 & 478987.395484082 & 3626535.82180105 \tabularnewline
118 & 2053103.20055317 & 392943.497475614 & 3713262.90363072 \tabularnewline
119 & 2053444.79246377 & 308650.359462882 & 3798239.22546465 \tabularnewline
120 & 2053786.38437437 & 225827.348618882 & 3881745.42012986 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280182&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]2050028.87335777[/C][C]1313366.61484129[/C][C]2786691.13187425[/C][/ROW]
[ROW][C]110[/C][C]2050370.46526837[/C][C]1180621.49530854[/C][C]2920119.4352282[/C][/ROW]
[ROW][C]111[/C][C]2050712.05717897[/C][C]1061786.91533152[/C][C]3039637.19902642[/C][/ROW]
[ROW][C]112[/C][C]2051053.64908957[/C][C]952264.7154492[/C][C]3149842.58272994[/C][/ROW]
[ROW][C]113[/C][C]2051395.24100017[/C][C]849441.554056972[/C][C]3253348.92794336[/C][/ROW]
[ROW][C]114[/C][C]2051736.83291077[/C][C]751668.983893675[/C][C]3351804.68192786[/C][/ROW]
[ROW][C]115[/C][C]2052078.42482137[/C][C]657831.243924873[/C][C]3446325.60571786[/C][/ROW]
[ROW][C]116[/C][C]2052420.01673197[/C][C]567133.554463311[/C][C]3537706.47900063[/C][/ROW]
[ROW][C]117[/C][C]2052761.60864257[/C][C]478987.395484082[/C][C]3626535.82180105[/C][/ROW]
[ROW][C]118[/C][C]2053103.20055317[/C][C]392943.497475614[/C][C]3713262.90363072[/C][/ROW]
[ROW][C]119[/C][C]2053444.79246377[/C][C]308650.359462882[/C][C]3798239.22546465[/C][/ROW]
[ROW][C]120[/C][C]2053786.38437437[/C][C]225827.348618882[/C][C]3881745.42012986[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280182&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280182&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
1092050028.873357771313366.614841292786691.13187425
1102050370.465268371180621.495308542920119.4352282
1112050712.057178971061786.915331523039637.19902642
1122051053.64908957952264.71544923149842.58272994
1132051395.24100017849441.5540569723253348.92794336
1142051736.83291077751668.9838936753351804.68192786
1152052078.42482137657831.2439248733446325.60571786
1162052420.01673197567133.5544633113537706.47900063
1172052761.60864257478987.3954840823626535.82180105
1182053103.20055317392943.4974756143713262.90363072
1192053444.79246377308650.3594628823798239.22546465
1202053786.38437437225827.3486188823881745.42012986



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