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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 05 Jun 2009 03:09:23 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/05/t1244193002yw36ruwho9tl01b.htm/, Retrieved Fri, 10 May 2024 06:22:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41765, Retrieved Fri, 10 May 2024 06:22:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact170
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Inschrijvingen ni...] [2009-06-01 20:14:38] [74be16979710d4c4e7c6647856088456]
- RMPD    [Exponential Smoothing] [Aantal bouwvergun...] [2009-06-05 09:09:23] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
1528
1816
1420
1757
1544
1678
1655
1391
1403
1744
1266
1358
1596
1819
1416
1521
1638
1543
1623
1530
1336
1700
1615
1494
1578
1607
1767
1505
1938
1862
2571
2082
1781
1869
1785
1682
1556
2080
2027
1887
1935
1798
1590
1592
1387
1849
1470
1437
1500
2081
1552
1586
1914
1639
1633
1693
1224
1417
1577
1225
1510
1515
1393
1455
1532
1268
1365
1282
1063
1296
1639
1247
1515
1547
1299




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41765&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41765&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41765&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.341994826009028
beta0
gamma0.441083878543025

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.341994826009028 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.441083878543025 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41765&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]0.341994826009028[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.441083878543025[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41765&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41765&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
alpha0.341994826009028
beta0
gamma0.441083878543025







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315961625.57291666667-29.5729166666674
1418191834.00079884334-15.0007988433376
1514161422.87060325291-6.87060325291395
1615211530.14589248886-9.14589248885636
1716381631.30971124516.69028875490062
1815431518.3894220504524.6105779495513
1916231652.88944570762-29.8894457076201
2015301375.70907659000154.290923409997
2113361440.51744076304-104.517440763044
2217001755.77301679438-55.7730167943778
2316151264.61560028645350.384399713548
2414941478.1535854361015.8464145639020
2515781719.94820106751-141.948201067513
2616071894.17366293501-287.173662935014
2717671392.32142721807374.678572781928
2815051629.4241908755-124.424190875499
2919381695.75964960590242.240350394098
3018621668.59736639099193.402633609013
3125711845.00555954260725.994440457398
3220821879.78924533455202.210754665452
3317811885.87057554576-104.870575545763
3418692215.15274231588-346.152742315884
3517851742.5682525001142.4317474998882
3616821753.69323316395-71.6932331639482
3715561919.75214710064-363.752147100644
3820801975.97222623882104.027773761181
3920271800.00185531290226.998144687097
4018871841.7413493518445.2586506481609
4119352072.52651897017-137.526518970166
4217981901.31149345085-103.311493450849
4315902130.82202598402-540.822025984016
4415921580.3404283021711.6595716978263
4513871432.12834434283-45.1283443428267
4618491711.81340097912137.186599020876
4714701517.30946879319-47.3094687931896
4814371464.62029991883-27.6202999188304
4915001560.98607159841-60.9860715984094
5020811856.51690922318224.483090776825
5115521757.43199740569-205.431997405693
5215861598.53537199705-12.5353719970512
5319141756.50454450728157.495455492719
5416391696.11592197115-57.115921971153
5516331814.44402403782-181.444024037822
5616931547.21760211804145.782397881960
5712241428.39296301991-204.392963019913
5814171706.52460815152-289.524608151518
5915771312.54034717415264.459652825853
6012251372.18910006863-147.189100068626
6115101417.9790301778892.0209698221165
6215151848.69076203581-333.690762035807
6313931433.93667103901-40.9366710390102
6414551387.2820397062467.7179602937615
6515321622.04641448273-90.046414482727
6612681414.71191827773-146.711918277729
6713651466.31422751109-101.314227511086
6812821321.46449716409-39.4644971640889
6910631037.6530664856025.3469335144041
7012961369.64634416173-73.6463441617313
7116391210.27721722589428.722782774113
7212471206.6280396479040.3719603521026
7315151385.99013006081129.009869939194
7415471705.79522799096-158.795227990956
7512991435.82212716730-136.822127167295

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1596 & 1625.57291666667 & -29.5729166666674 \tabularnewline
14 & 1819 & 1834.00079884334 & -15.0007988433376 \tabularnewline
15 & 1416 & 1422.87060325291 & -6.87060325291395 \tabularnewline
16 & 1521 & 1530.14589248886 & -9.14589248885636 \tabularnewline
17 & 1638 & 1631.3097112451 & 6.69028875490062 \tabularnewline
18 & 1543 & 1518.38942205045 & 24.6105779495513 \tabularnewline
19 & 1623 & 1652.88944570762 & -29.8894457076201 \tabularnewline
20 & 1530 & 1375.70907659000 & 154.290923409997 \tabularnewline
21 & 1336 & 1440.51744076304 & -104.517440763044 \tabularnewline
22 & 1700 & 1755.77301679438 & -55.7730167943778 \tabularnewline
23 & 1615 & 1264.61560028645 & 350.384399713548 \tabularnewline
24 & 1494 & 1478.15358543610 & 15.8464145639020 \tabularnewline
25 & 1578 & 1719.94820106751 & -141.948201067513 \tabularnewline
26 & 1607 & 1894.17366293501 & -287.173662935014 \tabularnewline
27 & 1767 & 1392.32142721807 & 374.678572781928 \tabularnewline
28 & 1505 & 1629.4241908755 & -124.424190875499 \tabularnewline
29 & 1938 & 1695.75964960590 & 242.240350394098 \tabularnewline
30 & 1862 & 1668.59736639099 & 193.402633609013 \tabularnewline
31 & 2571 & 1845.00555954260 & 725.994440457398 \tabularnewline
32 & 2082 & 1879.78924533455 & 202.210754665452 \tabularnewline
33 & 1781 & 1885.87057554576 & -104.870575545763 \tabularnewline
34 & 1869 & 2215.15274231588 & -346.152742315884 \tabularnewline
35 & 1785 & 1742.56825250011 & 42.4317474998882 \tabularnewline
36 & 1682 & 1753.69323316395 & -71.6932331639482 \tabularnewline
37 & 1556 & 1919.75214710064 & -363.752147100644 \tabularnewline
38 & 2080 & 1975.97222623882 & 104.027773761181 \tabularnewline
39 & 2027 & 1800.00185531290 & 226.998144687097 \tabularnewline
40 & 1887 & 1841.74134935184 & 45.2586506481609 \tabularnewline
41 & 1935 & 2072.52651897017 & -137.526518970166 \tabularnewline
42 & 1798 & 1901.31149345085 & -103.311493450849 \tabularnewline
43 & 1590 & 2130.82202598402 & -540.822025984016 \tabularnewline
44 & 1592 & 1580.34042830217 & 11.6595716978263 \tabularnewline
45 & 1387 & 1432.12834434283 & -45.1283443428267 \tabularnewline
46 & 1849 & 1711.81340097912 & 137.186599020876 \tabularnewline
47 & 1470 & 1517.30946879319 & -47.3094687931896 \tabularnewline
48 & 1437 & 1464.62029991883 & -27.6202999188304 \tabularnewline
49 & 1500 & 1560.98607159841 & -60.9860715984094 \tabularnewline
50 & 2081 & 1856.51690922318 & 224.483090776825 \tabularnewline
51 & 1552 & 1757.43199740569 & -205.431997405693 \tabularnewline
52 & 1586 & 1598.53537199705 & -12.5353719970512 \tabularnewline
53 & 1914 & 1756.50454450728 & 157.495455492719 \tabularnewline
54 & 1639 & 1696.11592197115 & -57.115921971153 \tabularnewline
55 & 1633 & 1814.44402403782 & -181.444024037822 \tabularnewline
56 & 1693 & 1547.21760211804 & 145.782397881960 \tabularnewline
57 & 1224 & 1428.39296301991 & -204.392963019913 \tabularnewline
58 & 1417 & 1706.52460815152 & -289.524608151518 \tabularnewline
59 & 1577 & 1312.54034717415 & 264.459652825853 \tabularnewline
60 & 1225 & 1372.18910006863 & -147.189100068626 \tabularnewline
61 & 1510 & 1417.97903017788 & 92.0209698221165 \tabularnewline
62 & 1515 & 1848.69076203581 & -333.690762035807 \tabularnewline
63 & 1393 & 1433.93667103901 & -40.9366710390102 \tabularnewline
64 & 1455 & 1387.28203970624 & 67.7179602937615 \tabularnewline
65 & 1532 & 1622.04641448273 & -90.046414482727 \tabularnewline
66 & 1268 & 1414.71191827773 & -146.711918277729 \tabularnewline
67 & 1365 & 1466.31422751109 & -101.314227511086 \tabularnewline
68 & 1282 & 1321.46449716409 & -39.4644971640889 \tabularnewline
69 & 1063 & 1037.65306648560 & 25.3469335144041 \tabularnewline
70 & 1296 & 1369.64634416173 & -73.6463441617313 \tabularnewline
71 & 1639 & 1210.27721722589 & 428.722782774113 \tabularnewline
72 & 1247 & 1206.62803964790 & 40.3719603521026 \tabularnewline
73 & 1515 & 1385.99013006081 & 129.009869939194 \tabularnewline
74 & 1547 & 1705.79522799096 & -158.795227990956 \tabularnewline
75 & 1299 & 1435.82212716730 & -136.822127167295 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41765&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]1596[/C][C]1625.57291666667[/C][C]-29.5729166666674[/C][/ROW]
[ROW][C]14[/C][C]1819[/C][C]1834.00079884334[/C][C]-15.0007988433376[/C][/ROW]
[ROW][C]15[/C][C]1416[/C][C]1422.87060325291[/C][C]-6.87060325291395[/C][/ROW]
[ROW][C]16[/C][C]1521[/C][C]1530.14589248886[/C][C]-9.14589248885636[/C][/ROW]
[ROW][C]17[/C][C]1638[/C][C]1631.3097112451[/C][C]6.69028875490062[/C][/ROW]
[ROW][C]18[/C][C]1543[/C][C]1518.38942205045[/C][C]24.6105779495513[/C][/ROW]
[ROW][C]19[/C][C]1623[/C][C]1652.88944570762[/C][C]-29.8894457076201[/C][/ROW]
[ROW][C]20[/C][C]1530[/C][C]1375.70907659000[/C][C]154.290923409997[/C][/ROW]
[ROW][C]21[/C][C]1336[/C][C]1440.51744076304[/C][C]-104.517440763044[/C][/ROW]
[ROW][C]22[/C][C]1700[/C][C]1755.77301679438[/C][C]-55.7730167943778[/C][/ROW]
[ROW][C]23[/C][C]1615[/C][C]1264.61560028645[/C][C]350.384399713548[/C][/ROW]
[ROW][C]24[/C][C]1494[/C][C]1478.15358543610[/C][C]15.8464145639020[/C][/ROW]
[ROW][C]25[/C][C]1578[/C][C]1719.94820106751[/C][C]-141.948201067513[/C][/ROW]
[ROW][C]26[/C][C]1607[/C][C]1894.17366293501[/C][C]-287.173662935014[/C][/ROW]
[ROW][C]27[/C][C]1767[/C][C]1392.32142721807[/C][C]374.678572781928[/C][/ROW]
[ROW][C]28[/C][C]1505[/C][C]1629.4241908755[/C][C]-124.424190875499[/C][/ROW]
[ROW][C]29[/C][C]1938[/C][C]1695.75964960590[/C][C]242.240350394098[/C][/ROW]
[ROW][C]30[/C][C]1862[/C][C]1668.59736639099[/C][C]193.402633609013[/C][/ROW]
[ROW][C]31[/C][C]2571[/C][C]1845.00555954260[/C][C]725.994440457398[/C][/ROW]
[ROW][C]32[/C][C]2082[/C][C]1879.78924533455[/C][C]202.210754665452[/C][/ROW]
[ROW][C]33[/C][C]1781[/C][C]1885.87057554576[/C][C]-104.870575545763[/C][/ROW]
[ROW][C]34[/C][C]1869[/C][C]2215.15274231588[/C][C]-346.152742315884[/C][/ROW]
[ROW][C]35[/C][C]1785[/C][C]1742.56825250011[/C][C]42.4317474998882[/C][/ROW]
[ROW][C]36[/C][C]1682[/C][C]1753.69323316395[/C][C]-71.6932331639482[/C][/ROW]
[ROW][C]37[/C][C]1556[/C][C]1919.75214710064[/C][C]-363.752147100644[/C][/ROW]
[ROW][C]38[/C][C]2080[/C][C]1975.97222623882[/C][C]104.027773761181[/C][/ROW]
[ROW][C]39[/C][C]2027[/C][C]1800.00185531290[/C][C]226.998144687097[/C][/ROW]
[ROW][C]40[/C][C]1887[/C][C]1841.74134935184[/C][C]45.2586506481609[/C][/ROW]
[ROW][C]41[/C][C]1935[/C][C]2072.52651897017[/C][C]-137.526518970166[/C][/ROW]
[ROW][C]42[/C][C]1798[/C][C]1901.31149345085[/C][C]-103.311493450849[/C][/ROW]
[ROW][C]43[/C][C]1590[/C][C]2130.82202598402[/C][C]-540.822025984016[/C][/ROW]
[ROW][C]44[/C][C]1592[/C][C]1580.34042830217[/C][C]11.6595716978263[/C][/ROW]
[ROW][C]45[/C][C]1387[/C][C]1432.12834434283[/C][C]-45.1283443428267[/C][/ROW]
[ROW][C]46[/C][C]1849[/C][C]1711.81340097912[/C][C]137.186599020876[/C][/ROW]
[ROW][C]47[/C][C]1470[/C][C]1517.30946879319[/C][C]-47.3094687931896[/C][/ROW]
[ROW][C]48[/C][C]1437[/C][C]1464.62029991883[/C][C]-27.6202999188304[/C][/ROW]
[ROW][C]49[/C][C]1500[/C][C]1560.98607159841[/C][C]-60.9860715984094[/C][/ROW]
[ROW][C]50[/C][C]2081[/C][C]1856.51690922318[/C][C]224.483090776825[/C][/ROW]
[ROW][C]51[/C][C]1552[/C][C]1757.43199740569[/C][C]-205.431997405693[/C][/ROW]
[ROW][C]52[/C][C]1586[/C][C]1598.53537199705[/C][C]-12.5353719970512[/C][/ROW]
[ROW][C]53[/C][C]1914[/C][C]1756.50454450728[/C][C]157.495455492719[/C][/ROW]
[ROW][C]54[/C][C]1639[/C][C]1696.11592197115[/C][C]-57.115921971153[/C][/ROW]
[ROW][C]55[/C][C]1633[/C][C]1814.44402403782[/C][C]-181.444024037822[/C][/ROW]
[ROW][C]56[/C][C]1693[/C][C]1547.21760211804[/C][C]145.782397881960[/C][/ROW]
[ROW][C]57[/C][C]1224[/C][C]1428.39296301991[/C][C]-204.392963019913[/C][/ROW]
[ROW][C]58[/C][C]1417[/C][C]1706.52460815152[/C][C]-289.524608151518[/C][/ROW]
[ROW][C]59[/C][C]1577[/C][C]1312.54034717415[/C][C]264.459652825853[/C][/ROW]
[ROW][C]60[/C][C]1225[/C][C]1372.18910006863[/C][C]-147.189100068626[/C][/ROW]
[ROW][C]61[/C][C]1510[/C][C]1417.97903017788[/C][C]92.0209698221165[/C][/ROW]
[ROW][C]62[/C][C]1515[/C][C]1848.69076203581[/C][C]-333.690762035807[/C][/ROW]
[ROW][C]63[/C][C]1393[/C][C]1433.93667103901[/C][C]-40.9366710390102[/C][/ROW]
[ROW][C]64[/C][C]1455[/C][C]1387.28203970624[/C][C]67.7179602937615[/C][/ROW]
[ROW][C]65[/C][C]1532[/C][C]1622.04641448273[/C][C]-90.046414482727[/C][/ROW]
[ROW][C]66[/C][C]1268[/C][C]1414.71191827773[/C][C]-146.711918277729[/C][/ROW]
[ROW][C]67[/C][C]1365[/C][C]1466.31422751109[/C][C]-101.314227511086[/C][/ROW]
[ROW][C]68[/C][C]1282[/C][C]1321.46449716409[/C][C]-39.4644971640889[/C][/ROW]
[ROW][C]69[/C][C]1063[/C][C]1037.65306648560[/C][C]25.3469335144041[/C][/ROW]
[ROW][C]70[/C][C]1296[/C][C]1369.64634416173[/C][C]-73.6463441617313[/C][/ROW]
[ROW][C]71[/C][C]1639[/C][C]1210.27721722589[/C][C]428.722782774113[/C][/ROW]
[ROW][C]72[/C][C]1247[/C][C]1206.62803964790[/C][C]40.3719603521026[/C][/ROW]
[ROW][C]73[/C][C]1515[/C][C]1385.99013006081[/C][C]129.009869939194[/C][/ROW]
[ROW][C]74[/C][C]1547[/C][C]1705.79522799096[/C][C]-158.795227990956[/C][/ROW]
[ROW][C]75[/C][C]1299[/C][C]1435.82212716730[/C][C]-136.822127167295[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41765&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41765&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
1315961625.57291666667-29.5729166666674
1418191834.00079884334-15.0007988433376
1514161422.87060325291-6.87060325291395
1615211530.14589248886-9.14589248885636
1716381631.30971124516.69028875490062
1815431518.3894220504524.6105779495513
1916231652.88944570762-29.8894457076201
2015301375.70907659000154.290923409997
2113361440.51744076304-104.517440763044
2217001755.77301679438-55.7730167943778
2316151264.61560028645350.384399713548
2414941478.1535854361015.8464145639020
2515781719.94820106751-141.948201067513
2616071894.17366293501-287.173662935014
2717671392.32142721807374.678572781928
2815051629.4241908755-124.424190875499
2919381695.75964960590242.240350394098
3018621668.59736639099193.402633609013
3125711845.00555954260725.994440457398
3220821879.78924533455202.210754665452
3317811885.87057554576-104.870575545763
3418692215.15274231588-346.152742315884
3517851742.5682525001142.4317474998882
3616821753.69323316395-71.6932331639482
3715561919.75214710064-363.752147100644
3820801975.97222623882104.027773761181
3920271800.00185531290226.998144687097
4018871841.7413493518445.2586506481609
4119352072.52651897017-137.526518970166
4217981901.31149345085-103.311493450849
4315902130.82202598402-540.822025984016
4415921580.3404283021711.6595716978263
4513871432.12834434283-45.1283443428267
4618491711.81340097912137.186599020876
4714701517.30946879319-47.3094687931896
4814371464.62029991883-27.6202999188304
4915001560.98607159841-60.9860715984094
5020811856.51690922318224.483090776825
5115521757.43199740569-205.431997405693
5215861598.53537199705-12.5353719970512
5319141756.50454450728157.495455492719
5416391696.11592197115-57.115921971153
5516331814.44402403782-181.444024037822
5616931547.21760211804145.782397881960
5712241428.39296301991-204.392963019913
5814171706.52460815152-289.524608151518
5915771312.54034717415264.459652825853
6012251372.18910006863-147.189100068626
6115101417.9790301778892.0209698221165
6215151848.69076203581-333.690762035807
6313931433.93667103901-40.9366710390102
6414551387.2820397062467.7179602937615
6515321622.04641448273-90.046414482727
6612681414.71191827773-146.711918277729
6713651466.31422751109-101.314227511086
6812821321.46449716409-39.4644971640889
6910631037.6530664856025.3469335144041
7012961369.64634416173-73.6463441617313
7116391210.27721722589428.722782774113
7212471206.6280396479040.3719603521026
7315151385.99013006081129.009869939194
7415471705.79522799096-158.795227990956
7512991435.82212716730-136.822127167295







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
761387.91059440295988.157047309231787.66414149667
771553.726958998821131.242025439811976.21189255783
781360.74153128029916.6873231539511804.79573940662
791475.694577787781011.071332109041940.31782346653
801383.44477486989899.1252717571161867.76427798266
811131.94057435205628.6951056533761635.18604305072
821426.53397101763905.048954515631948.01898751963
831438.15685454201899.0490331310781977.26467595294
841175.17351834387619.0010057393841731.34603094836
851366.45447292564793.725492999591939.18345285169
861558.60761374451969.7875180298012147.42770945922
871349.31903262688744.8360090539841953.80205619977

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 1387.91059440295 & 988.15704730923 & 1787.66414149667 \tabularnewline
77 & 1553.72695899882 & 1131.24202543981 & 1976.21189255783 \tabularnewline
78 & 1360.74153128029 & 916.687323153951 & 1804.79573940662 \tabularnewline
79 & 1475.69457778778 & 1011.07133210904 & 1940.31782346653 \tabularnewline
80 & 1383.44477486989 & 899.125271757116 & 1867.76427798266 \tabularnewline
81 & 1131.94057435205 & 628.695105653376 & 1635.18604305072 \tabularnewline
82 & 1426.53397101763 & 905.04895451563 & 1948.01898751963 \tabularnewline
83 & 1438.15685454201 & 899.049033131078 & 1977.26467595294 \tabularnewline
84 & 1175.17351834387 & 619.001005739384 & 1731.34603094836 \tabularnewline
85 & 1366.45447292564 & 793.72549299959 & 1939.18345285169 \tabularnewline
86 & 1558.60761374451 & 969.787518029801 & 2147.42770945922 \tabularnewline
87 & 1349.31903262688 & 744.836009053984 & 1953.80205619977 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41765&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]76[/C][C]1387.91059440295[/C][C]988.15704730923[/C][C]1787.66414149667[/C][/ROW]
[ROW][C]77[/C][C]1553.72695899882[/C][C]1131.24202543981[/C][C]1976.21189255783[/C][/ROW]
[ROW][C]78[/C][C]1360.74153128029[/C][C]916.687323153951[/C][C]1804.79573940662[/C][/ROW]
[ROW][C]79[/C][C]1475.69457778778[/C][C]1011.07133210904[/C][C]1940.31782346653[/C][/ROW]
[ROW][C]80[/C][C]1383.44477486989[/C][C]899.125271757116[/C][C]1867.76427798266[/C][/ROW]
[ROW][C]81[/C][C]1131.94057435205[/C][C]628.695105653376[/C][C]1635.18604305072[/C][/ROW]
[ROW][C]82[/C][C]1426.53397101763[/C][C]905.04895451563[/C][C]1948.01898751963[/C][/ROW]
[ROW][C]83[/C][C]1438.15685454201[/C][C]899.049033131078[/C][C]1977.26467595294[/C][/ROW]
[ROW][C]84[/C][C]1175.17351834387[/C][C]619.001005739384[/C][C]1731.34603094836[/C][/ROW]
[ROW][C]85[/C][C]1366.45447292564[/C][C]793.72549299959[/C][C]1939.18345285169[/C][/ROW]
[ROW][C]86[/C][C]1558.60761374451[/C][C]969.787518029801[/C][C]2147.42770945922[/C][/ROW]
[ROW][C]87[/C][C]1349.31903262688[/C][C]744.836009053984[/C][C]1953.80205619977[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41765&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41765&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
761387.91059440295988.157047309231787.66414149667
771553.726958998821131.242025439811976.21189255783
781360.74153128029916.6873231539511804.79573940662
791475.694577787781011.071332109041940.31782346653
801383.44477486989899.1252717571161867.76427798266
811131.94057435205628.6951056533761635.18604305072
821426.53397101763905.048954515631948.01898751963
831438.15685454201899.0490331310781977.26467595294
841175.17351834387619.0010057393841731.34603094836
851366.45447292564793.725492999591939.18345285169
861558.60761374451969.7875180298012147.42770945922
871349.31903262688744.8360090539841953.80205619977



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')