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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 04 Jun 2009 10:41:39 -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/04/t1244133739ammw1alw4p9m6xe.htm/, Retrieved Tue, 14 May 2024 15:58:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41722, Retrieved Tue, 14 May 2024 15:58:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opdracht 10 reeks...] [2009-06-04 16:41:39] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
1639
1296
1063
1282
1365
1268
1532
1455
1393
1515
1510
1225
1577
1417
1224
1693
1633
1639
1914
1586
1552
2081
1500
1437
1470
1849
1387
1592
1590
1798
1935
1887
2027
2080
1556
1682
1785
1869
1781
2082
2571
1862
1938
1505
1767
1607
1578
1495
1615
1700
1337
1531
1623
1543
1638
1520
1416
1820
1596
1358
1267
1742
1402
1388
1646
1670
1531
1730
1407
1795
1504
1371
1734




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41722&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41722&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41722&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.352262650278532
beta0.0394175072825745
gamma0.365382321391222

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.352262650278532 \tabularnewline
beta & 0.0394175072825745 \tabularnewline
gamma & 0.365382321391222 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41722&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]0.352262650278532[/C][/ROW]
[ROW][C]beta[/C][C]0.0394175072825745[/C][/ROW]
[ROW][C]gamma[/C][C]0.365382321391222[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41722&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41722&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
alpha0.352262650278532
beta0.0394175072825745
gamma0.365382321391222







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315771422.81387939779154.186120602207
1414171331.2094143537485.79058564626
1512241187.1166917629836.8833082370209
1616931656.2357553249236.7642446750838
1716331613.9540438227219.0459561772764
1816391645.68117630928-6.68117630927736
1919141811.03043214306102.969567856944
2015861780.99226298622-194.992262986224
2115521651.07540872186-99.075408721861
2220811753.98738221983327.012617780174
2315001856.20734017917-356.207340179170
2414371398.3672762776738.6327237223311
2514701849.85618427538-379.856184275382
2618491524.11506748975324.884932510254
2713871413.11422752116-26.1142275211616
2815921926.29251852413-334.292518524129
2915901734.92099272508-144.920992725083
3017981692.85946261665105.140537383350
3119351922.9470961917612.0529038082445
3218871774.29703580103112.702964198969
3320271764.41182777473262.588172225274
3420802125.29026122948-45.2902612294765
3515561906.43956399688-350.439563996882
3616821518.47972615291163.520273847091
3717851938.57812999022-153.578129990216
3818691846.1263982576722.8736017423312
3917811515.59035384715265.409646152848
4020822117.50656024182-35.5065602418181
4125712068.91233938390502.087660616095
4218622345.11581640973-483.115816409728
4319382387.90559531103-449.905595311028
4415052076.310187768-571.310187767998
4517671847.5662682562-80.5662682562017
4616071990.12611110514-383.126111105142
4715781592.03715579472-14.0371557947151
4814951441.6774240376653.3225759623408
4916151705.98573198027-90.9857319802734
5017001664.2066213885735.7933786114277
5113371409.49035316494-72.4903531649375
5215311729.06988679182-198.069886791816
5316231705.34642216078-82.3464221607842
5415431553.87141847292-10.8714184729201
5516381690.90420118187-52.9042011818683
5615201502.7267352608417.2732647391574
5714161575.30879091192-159.308790911922
5818201585.80816987033234.191830129669
5915961497.8848690371498.1151309628558
6013581404.46920867185-46.4692086718483
6112671582.58290319862-315.582903198624
6217421482.07714849129259.922851508711
6314021296.1752086595105.8247913405
6413881637.55704132813-249.557041328128
6516461617.2802535742328.7197464257747
6616701522.64508947200147.354910528001
6715311708.82828933741-177.828289337413
6817301494.00592772033235.994072279667
6914071604.05086529555-197.050865295548
7017951699.612145497395.3878545027019
7115041529.12219285863-25.1221928586297
7213711360.2903358468210.7096641531773
7317341487.38376998273246.616230017269

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1577 & 1422.81387939779 & 154.186120602207 \tabularnewline
14 & 1417 & 1331.20941435374 & 85.79058564626 \tabularnewline
15 & 1224 & 1187.11669176298 & 36.8833082370209 \tabularnewline
16 & 1693 & 1656.23575532492 & 36.7642446750838 \tabularnewline
17 & 1633 & 1613.95404382272 & 19.0459561772764 \tabularnewline
18 & 1639 & 1645.68117630928 & -6.68117630927736 \tabularnewline
19 & 1914 & 1811.03043214306 & 102.969567856944 \tabularnewline
20 & 1586 & 1780.99226298622 & -194.992262986224 \tabularnewline
21 & 1552 & 1651.07540872186 & -99.075408721861 \tabularnewline
22 & 2081 & 1753.98738221983 & 327.012617780174 \tabularnewline
23 & 1500 & 1856.20734017917 & -356.207340179170 \tabularnewline
24 & 1437 & 1398.36727627767 & 38.6327237223311 \tabularnewline
25 & 1470 & 1849.85618427538 & -379.856184275382 \tabularnewline
26 & 1849 & 1524.11506748975 & 324.884932510254 \tabularnewline
27 & 1387 & 1413.11422752116 & -26.1142275211616 \tabularnewline
28 & 1592 & 1926.29251852413 & -334.292518524129 \tabularnewline
29 & 1590 & 1734.92099272508 & -144.920992725083 \tabularnewline
30 & 1798 & 1692.85946261665 & 105.140537383350 \tabularnewline
31 & 1935 & 1922.94709619176 & 12.0529038082445 \tabularnewline
32 & 1887 & 1774.29703580103 & 112.702964198969 \tabularnewline
33 & 2027 & 1764.41182777473 & 262.588172225274 \tabularnewline
34 & 2080 & 2125.29026122948 & -45.2902612294765 \tabularnewline
35 & 1556 & 1906.43956399688 & -350.439563996882 \tabularnewline
36 & 1682 & 1518.47972615291 & 163.520273847091 \tabularnewline
37 & 1785 & 1938.57812999022 & -153.578129990216 \tabularnewline
38 & 1869 & 1846.12639825767 & 22.8736017423312 \tabularnewline
39 & 1781 & 1515.59035384715 & 265.409646152848 \tabularnewline
40 & 2082 & 2117.50656024182 & -35.5065602418181 \tabularnewline
41 & 2571 & 2068.91233938390 & 502.087660616095 \tabularnewline
42 & 1862 & 2345.11581640973 & -483.115816409728 \tabularnewline
43 & 1938 & 2387.90559531103 & -449.905595311028 \tabularnewline
44 & 1505 & 2076.310187768 & -571.310187767998 \tabularnewline
45 & 1767 & 1847.5662682562 & -80.5662682562017 \tabularnewline
46 & 1607 & 1990.12611110514 & -383.126111105142 \tabularnewline
47 & 1578 & 1592.03715579472 & -14.0371557947151 \tabularnewline
48 & 1495 & 1441.67742403766 & 53.3225759623408 \tabularnewline
49 & 1615 & 1705.98573198027 & -90.9857319802734 \tabularnewline
50 & 1700 & 1664.20662138857 & 35.7933786114277 \tabularnewline
51 & 1337 & 1409.49035316494 & -72.4903531649375 \tabularnewline
52 & 1531 & 1729.06988679182 & -198.069886791816 \tabularnewline
53 & 1623 & 1705.34642216078 & -82.3464221607842 \tabularnewline
54 & 1543 & 1553.87141847292 & -10.8714184729201 \tabularnewline
55 & 1638 & 1690.90420118187 & -52.9042011818683 \tabularnewline
56 & 1520 & 1502.72673526084 & 17.2732647391574 \tabularnewline
57 & 1416 & 1575.30879091192 & -159.308790911922 \tabularnewline
58 & 1820 & 1585.80816987033 & 234.191830129669 \tabularnewline
59 & 1596 & 1497.88486903714 & 98.1151309628558 \tabularnewline
60 & 1358 & 1404.46920867185 & -46.4692086718483 \tabularnewline
61 & 1267 & 1582.58290319862 & -315.582903198624 \tabularnewline
62 & 1742 & 1482.07714849129 & 259.922851508711 \tabularnewline
63 & 1402 & 1296.1752086595 & 105.8247913405 \tabularnewline
64 & 1388 & 1637.55704132813 & -249.557041328128 \tabularnewline
65 & 1646 & 1617.28025357423 & 28.7197464257747 \tabularnewline
66 & 1670 & 1522.64508947200 & 147.354910528001 \tabularnewline
67 & 1531 & 1708.82828933741 & -177.828289337413 \tabularnewline
68 & 1730 & 1494.00592772033 & 235.994072279667 \tabularnewline
69 & 1407 & 1604.05086529555 & -197.050865295548 \tabularnewline
70 & 1795 & 1699.6121454973 & 95.3878545027019 \tabularnewline
71 & 1504 & 1529.12219285863 & -25.1221928586297 \tabularnewline
72 & 1371 & 1360.29033584682 & 10.7096641531773 \tabularnewline
73 & 1734 & 1487.38376998273 & 246.616230017269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41722&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]1577[/C][C]1422.81387939779[/C][C]154.186120602207[/C][/ROW]
[ROW][C]14[/C][C]1417[/C][C]1331.20941435374[/C][C]85.79058564626[/C][/ROW]
[ROW][C]15[/C][C]1224[/C][C]1187.11669176298[/C][C]36.8833082370209[/C][/ROW]
[ROW][C]16[/C][C]1693[/C][C]1656.23575532492[/C][C]36.7642446750838[/C][/ROW]
[ROW][C]17[/C][C]1633[/C][C]1613.95404382272[/C][C]19.0459561772764[/C][/ROW]
[ROW][C]18[/C][C]1639[/C][C]1645.68117630928[/C][C]-6.68117630927736[/C][/ROW]
[ROW][C]19[/C][C]1914[/C][C]1811.03043214306[/C][C]102.969567856944[/C][/ROW]
[ROW][C]20[/C][C]1586[/C][C]1780.99226298622[/C][C]-194.992262986224[/C][/ROW]
[ROW][C]21[/C][C]1552[/C][C]1651.07540872186[/C][C]-99.075408721861[/C][/ROW]
[ROW][C]22[/C][C]2081[/C][C]1753.98738221983[/C][C]327.012617780174[/C][/ROW]
[ROW][C]23[/C][C]1500[/C][C]1856.20734017917[/C][C]-356.207340179170[/C][/ROW]
[ROW][C]24[/C][C]1437[/C][C]1398.36727627767[/C][C]38.6327237223311[/C][/ROW]
[ROW][C]25[/C][C]1470[/C][C]1849.85618427538[/C][C]-379.856184275382[/C][/ROW]
[ROW][C]26[/C][C]1849[/C][C]1524.11506748975[/C][C]324.884932510254[/C][/ROW]
[ROW][C]27[/C][C]1387[/C][C]1413.11422752116[/C][C]-26.1142275211616[/C][/ROW]
[ROW][C]28[/C][C]1592[/C][C]1926.29251852413[/C][C]-334.292518524129[/C][/ROW]
[ROW][C]29[/C][C]1590[/C][C]1734.92099272508[/C][C]-144.920992725083[/C][/ROW]
[ROW][C]30[/C][C]1798[/C][C]1692.85946261665[/C][C]105.140537383350[/C][/ROW]
[ROW][C]31[/C][C]1935[/C][C]1922.94709619176[/C][C]12.0529038082445[/C][/ROW]
[ROW][C]32[/C][C]1887[/C][C]1774.29703580103[/C][C]112.702964198969[/C][/ROW]
[ROW][C]33[/C][C]2027[/C][C]1764.41182777473[/C][C]262.588172225274[/C][/ROW]
[ROW][C]34[/C][C]2080[/C][C]2125.29026122948[/C][C]-45.2902612294765[/C][/ROW]
[ROW][C]35[/C][C]1556[/C][C]1906.43956399688[/C][C]-350.439563996882[/C][/ROW]
[ROW][C]36[/C][C]1682[/C][C]1518.47972615291[/C][C]163.520273847091[/C][/ROW]
[ROW][C]37[/C][C]1785[/C][C]1938.57812999022[/C][C]-153.578129990216[/C][/ROW]
[ROW][C]38[/C][C]1869[/C][C]1846.12639825767[/C][C]22.8736017423312[/C][/ROW]
[ROW][C]39[/C][C]1781[/C][C]1515.59035384715[/C][C]265.409646152848[/C][/ROW]
[ROW][C]40[/C][C]2082[/C][C]2117.50656024182[/C][C]-35.5065602418181[/C][/ROW]
[ROW][C]41[/C][C]2571[/C][C]2068.91233938390[/C][C]502.087660616095[/C][/ROW]
[ROW][C]42[/C][C]1862[/C][C]2345.11581640973[/C][C]-483.115816409728[/C][/ROW]
[ROW][C]43[/C][C]1938[/C][C]2387.90559531103[/C][C]-449.905595311028[/C][/ROW]
[ROW][C]44[/C][C]1505[/C][C]2076.310187768[/C][C]-571.310187767998[/C][/ROW]
[ROW][C]45[/C][C]1767[/C][C]1847.5662682562[/C][C]-80.5662682562017[/C][/ROW]
[ROW][C]46[/C][C]1607[/C][C]1990.12611110514[/C][C]-383.126111105142[/C][/ROW]
[ROW][C]47[/C][C]1578[/C][C]1592.03715579472[/C][C]-14.0371557947151[/C][/ROW]
[ROW][C]48[/C][C]1495[/C][C]1441.67742403766[/C][C]53.3225759623408[/C][/ROW]
[ROW][C]49[/C][C]1615[/C][C]1705.98573198027[/C][C]-90.9857319802734[/C][/ROW]
[ROW][C]50[/C][C]1700[/C][C]1664.20662138857[/C][C]35.7933786114277[/C][/ROW]
[ROW][C]51[/C][C]1337[/C][C]1409.49035316494[/C][C]-72.4903531649375[/C][/ROW]
[ROW][C]52[/C][C]1531[/C][C]1729.06988679182[/C][C]-198.069886791816[/C][/ROW]
[ROW][C]53[/C][C]1623[/C][C]1705.34642216078[/C][C]-82.3464221607842[/C][/ROW]
[ROW][C]54[/C][C]1543[/C][C]1553.87141847292[/C][C]-10.8714184729201[/C][/ROW]
[ROW][C]55[/C][C]1638[/C][C]1690.90420118187[/C][C]-52.9042011818683[/C][/ROW]
[ROW][C]56[/C][C]1520[/C][C]1502.72673526084[/C][C]17.2732647391574[/C][/ROW]
[ROW][C]57[/C][C]1416[/C][C]1575.30879091192[/C][C]-159.308790911922[/C][/ROW]
[ROW][C]58[/C][C]1820[/C][C]1585.80816987033[/C][C]234.191830129669[/C][/ROW]
[ROW][C]59[/C][C]1596[/C][C]1497.88486903714[/C][C]98.1151309628558[/C][/ROW]
[ROW][C]60[/C][C]1358[/C][C]1404.46920867185[/C][C]-46.4692086718483[/C][/ROW]
[ROW][C]61[/C][C]1267[/C][C]1582.58290319862[/C][C]-315.582903198624[/C][/ROW]
[ROW][C]62[/C][C]1742[/C][C]1482.07714849129[/C][C]259.922851508711[/C][/ROW]
[ROW][C]63[/C][C]1402[/C][C]1296.1752086595[/C][C]105.8247913405[/C][/ROW]
[ROW][C]64[/C][C]1388[/C][C]1637.55704132813[/C][C]-249.557041328128[/C][/ROW]
[ROW][C]65[/C][C]1646[/C][C]1617.28025357423[/C][C]28.7197464257747[/C][/ROW]
[ROW][C]66[/C][C]1670[/C][C]1522.64508947200[/C][C]147.354910528001[/C][/ROW]
[ROW][C]67[/C][C]1531[/C][C]1708.82828933741[/C][C]-177.828289337413[/C][/ROW]
[ROW][C]68[/C][C]1730[/C][C]1494.00592772033[/C][C]235.994072279667[/C][/ROW]
[ROW][C]69[/C][C]1407[/C][C]1604.05086529555[/C][C]-197.050865295548[/C][/ROW]
[ROW][C]70[/C][C]1795[/C][C]1699.6121454973[/C][C]95.3878545027019[/C][/ROW]
[ROW][C]71[/C][C]1504[/C][C]1529.12219285863[/C][C]-25.1221928586297[/C][/ROW]
[ROW][C]72[/C][C]1371[/C][C]1360.29033584682[/C][C]10.7096641531773[/C][/ROW]
[ROW][C]73[/C][C]1734[/C][C]1487.38376998273[/C][C]246.616230017269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41722&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41722&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
1315771422.81387939779154.186120602207
1414171331.2094143537485.79058564626
1512241187.1166917629836.8833082370209
1616931656.2357553249236.7642446750838
1716331613.9540438227219.0459561772764
1816391645.68117630928-6.68117630927736
1919141811.03043214306102.969567856944
2015861780.99226298622-194.992262986224
2115521651.07540872186-99.075408721861
2220811753.98738221983327.012617780174
2315001856.20734017917-356.207340179170
2414371398.3672762776738.6327237223311
2514701849.85618427538-379.856184275382
2618491524.11506748975324.884932510254
2713871413.11422752116-26.1142275211616
2815921926.29251852413-334.292518524129
2915901734.92099272508-144.920992725083
3017981692.85946261665105.140537383350
3119351922.9470961917612.0529038082445
3218871774.29703580103112.702964198969
3320271764.41182777473262.588172225274
3420802125.29026122948-45.2902612294765
3515561906.43956399688-350.439563996882
3616821518.47972615291163.520273847091
3717851938.57812999022-153.578129990216
3818691846.1263982576722.8736017423312
3917811515.59035384715265.409646152848
4020822117.50656024182-35.5065602418181
4125712068.91233938390502.087660616095
4218622345.11581640973-483.115816409728
4319382387.90559531103-449.905595311028
4415052076.310187768-571.310187767998
4517671847.5662682562-80.5662682562017
4616071990.12611110514-383.126111105142
4715781592.03715579472-14.0371557947151
4814951441.6774240376653.3225759623408
4916151705.98573198027-90.9857319802734
5017001664.2066213885735.7933786114277
5113371409.49035316494-72.4903531649375
5215311729.06988679182-198.069886791816
5316231705.34642216078-82.3464221607842
5415431553.87141847292-10.8714184729201
5516381690.90420118187-52.9042011818683
5615201502.7267352608417.2732647391574
5714161575.30879091192-159.308790911922
5818201585.80816987033234.191830129669
5915961497.8848690371498.1151309628558
6013581404.46920867185-46.4692086718483
6112671582.58290319862-315.582903198624
6217421482.07714849129259.922851508711
6314021296.1752086595105.8247913405
6413881637.55704132813-249.557041328128
6516461617.2802535742328.7197464257747
6616701522.64508947200147.354910528001
6715311708.82828933741-177.828289337413
6817301494.00592772033235.994072279667
6914071604.05086529555-197.050865295548
7017951699.612145497395.3878545027019
7115041529.12219285863-25.1221928586297
7213711360.2903358468210.7096641531773
7317341487.38376998273246.616230017269







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
741743.826950653211494.748266897771992.90563440864
751411.408462410991132.715213559021690.10171126296
761638.322187060251296.619698853951980.02467526654
771790.846337727201390.153877057812191.53879839660
781710.710928425011286.544763230482134.87709361954
791772.927485520791300.897227601452244.95774344013
801715.128896860941220.390986663542209.86680705834
811635.232828965381124.781459084732145.68419884604
821897.322145601131282.222466389752512.42182481251
831649.175451230051071.324085235732227.02681722437
841487.43742457432925.2419579052212049.63289124341
851682.424719872371067.512418117902297.33702162685

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 1743.82695065321 & 1494.74826689777 & 1992.90563440864 \tabularnewline
75 & 1411.40846241099 & 1132.71521355902 & 1690.10171126296 \tabularnewline
76 & 1638.32218706025 & 1296.61969885395 & 1980.02467526654 \tabularnewline
77 & 1790.84633772720 & 1390.15387705781 & 2191.53879839660 \tabularnewline
78 & 1710.71092842501 & 1286.54476323048 & 2134.87709361954 \tabularnewline
79 & 1772.92748552079 & 1300.89722760145 & 2244.95774344013 \tabularnewline
80 & 1715.12889686094 & 1220.39098666354 & 2209.86680705834 \tabularnewline
81 & 1635.23282896538 & 1124.78145908473 & 2145.68419884604 \tabularnewline
82 & 1897.32214560113 & 1282.22246638975 & 2512.42182481251 \tabularnewline
83 & 1649.17545123005 & 1071.32408523573 & 2227.02681722437 \tabularnewline
84 & 1487.43742457432 & 925.241957905221 & 2049.63289124341 \tabularnewline
85 & 1682.42471987237 & 1067.51241811790 & 2297.33702162685 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41722&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]74[/C][C]1743.82695065321[/C][C]1494.74826689777[/C][C]1992.90563440864[/C][/ROW]
[ROW][C]75[/C][C]1411.40846241099[/C][C]1132.71521355902[/C][C]1690.10171126296[/C][/ROW]
[ROW][C]76[/C][C]1638.32218706025[/C][C]1296.61969885395[/C][C]1980.02467526654[/C][/ROW]
[ROW][C]77[/C][C]1790.84633772720[/C][C]1390.15387705781[/C][C]2191.53879839660[/C][/ROW]
[ROW][C]78[/C][C]1710.71092842501[/C][C]1286.54476323048[/C][C]2134.87709361954[/C][/ROW]
[ROW][C]79[/C][C]1772.92748552079[/C][C]1300.89722760145[/C][C]2244.95774344013[/C][/ROW]
[ROW][C]80[/C][C]1715.12889686094[/C][C]1220.39098666354[/C][C]2209.86680705834[/C][/ROW]
[ROW][C]81[/C][C]1635.23282896538[/C][C]1124.78145908473[/C][C]2145.68419884604[/C][/ROW]
[ROW][C]82[/C][C]1897.32214560113[/C][C]1282.22246638975[/C][C]2512.42182481251[/C][/ROW]
[ROW][C]83[/C][C]1649.17545123005[/C][C]1071.32408523573[/C][C]2227.02681722437[/C][/ROW]
[ROW][C]84[/C][C]1487.43742457432[/C][C]925.241957905221[/C][C]2049.63289124341[/C][/ROW]
[ROW][C]85[/C][C]1682.42471987237[/C][C]1067.51241811790[/C][C]2297.33702162685[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41722&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41722&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
741743.826950653211494.748266897771992.90563440864
751411.408462410991132.715213559021690.10171126296
761638.322187060251296.619698853951980.02467526654
771790.846337727201390.153877057812191.53879839660
781710.710928425011286.544763230482134.87709361954
791772.927485520791300.897227601452244.95774344013
801715.128896860941220.390986663542209.86680705834
811635.232828965381124.781459084732145.68419884604
821897.322145601131282.222466389752512.42182481251
831649.175451230051071.324085235732227.02681722437
841487.43742457432925.2419579052212049.63289124341
851682.424719872371067.512418117902297.33702162685



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