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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, 10 May 2011 19:36:39 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/10/t13050559735ztx5f7z43bvgz8.htm/, Retrieved Mon, 13 May 2024 01:48:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121451, Retrieved Mon, 13 May 2024 01:48:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Alexander De Raey...] [2011-05-10 19:36:39] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
2435
1379
1511
2021
1614
1680
1630
870
1877
2428
1711
127
3192
1934
2075
1700
1198
1582
1705
911
1817
1168
920
84
2254
1485
1886
1358
1167
1781
1218
779
1418
1641
1196
132
2926
1777
2094
1648
1646
1537
1917
977
1475
2124
1209
135
2917
1981
1398
1171
903
1390
1280
781
1828
1631
1063
186
2275
1342
1070
950
1121
1305
1586
548
1225
1419
880
124
2044
1143
897
1264
1326
1529
1373
587
1137
1426
1016
176
2614




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121451&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121451&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121451&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'Herman Ole Andreas Wold' @ www.yougetit.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.241318956657905
beta0
gamma0.491116881078373

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.241318956657905 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.491116881078373 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121451&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]0.241318956657905[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.491116881078373[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121451&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121451&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
alpha0.241318956657905
beta0
gamma0.491116881078373







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1331923211.64289529915-19.6428952991455
1419341932.208782043411.79121795659466
1520752062.5721266354312.4278733645729
1617001733.71063114617-33.7106311461653
1711981297.17337321995-99.1733732199496
1815821680.13038134319-98.1303813431896
1917051579.7557498446125.244250155402
20911783.452318029758127.547681970242
2118171762.7464146438754.2535853561258
2211682304.85325633389-1136.85325633389
239201332.35677105251-412.356771052509
2484-341.596644965116425.596644965116
2522542807.88668600327-553.886686003271
2614851407.5157920589877.4842079410155
2718861560.10851918255325.891480817446
2813581289.7004783494468.2995216505603
291167853.388716470799313.611283529201
3017811336.34710717206444.652892827941
3112181450.18599529009-232.18599529009
32779568.486130720039210.513869279961
3314181540.4920824362-122.492082436203
3416411596.139162975344.8608370247025
3511961178.7608537604817.2391462395196
36132-79.3005861876447211.300586187645
3729262653.51250850884272.487491491158
3817771687.810838109889.1891618901986
3920941935.78500761612158.214992383879
4016481528.93441251148119.065587488523
4116461196.27688907951449.723110920492
4215371760.90788749864-223.907887498643
4319171461.2194932455455.780506754497
44977910.48942939135466.5105706086464
4514751723.66628214382-248.666282143823
4621241811.22101293278312.778987067223
4712091448.20456067661-239.204560676608
48135200.565892665725-65.5658926657254
4929172889.3641637995327.6358362004694
5019811796.2779940856184.722005914396
5113982093.02514798195-695.025147981953
5211711465.68442236021-294.684422360208
539031156.38452452118-253.384524521181
5413901300.3466926639689.6533073360408
5512801329.57918022557-49.5791802255671
56781511.853850125609269.146149874391
5718281256.49527758593571.504722414073
5816311751.16792626116-120.16792626116
5910631078.00351732836-15.0035173283613
60186-50.8332357183974236.833235718397
6122752745.66674126203-470.666741262032
6213421590.86118801742-248.86118801742
6310701455.18176904721-385.181769047214
649501051.77950618361-101.779506183611
651121804.419607482853316.580392517147
6613051213.7413771619691.258622838041
6715861191.48308425614394.516915743859
68548599.683959002229-51.6839590022289
6912251379.56212629246-154.562126292462
7014191441.30311315137-22.3031131513717
71880830.93970986829849.0602901317023
72124-188.602588921406312.602588921406
7320442362.56672247207-318.56672247207
7411431327.11077303898-184.110773038982
758971156.26366260798-259.263662607975
761264888.843811557384375.156188442616
771326912.458882032014413.541117967986
7815291261.22398084633267.776019153669
7913731394.55704558892-21.5570455889231
80587536.09646373699150.9035362630091
8111371302.39842337136-165.39842337136
8214261410.8042558396915.1957441603083
831016836.08011793973179.919882060269
84176-53.6871387335377229.687138733538
8526142242.2987433802371.701256619805

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3192 & 3211.64289529915 & -19.6428952991455 \tabularnewline
14 & 1934 & 1932.20878204341 & 1.79121795659466 \tabularnewline
15 & 2075 & 2062.57212663543 & 12.4278733645729 \tabularnewline
16 & 1700 & 1733.71063114617 & -33.7106311461653 \tabularnewline
17 & 1198 & 1297.17337321995 & -99.1733732199496 \tabularnewline
18 & 1582 & 1680.13038134319 & -98.1303813431896 \tabularnewline
19 & 1705 & 1579.7557498446 & 125.244250155402 \tabularnewline
20 & 911 & 783.452318029758 & 127.547681970242 \tabularnewline
21 & 1817 & 1762.74641464387 & 54.2535853561258 \tabularnewline
22 & 1168 & 2304.85325633389 & -1136.85325633389 \tabularnewline
23 & 920 & 1332.35677105251 & -412.356771052509 \tabularnewline
24 & 84 & -341.596644965116 & 425.596644965116 \tabularnewline
25 & 2254 & 2807.88668600327 & -553.886686003271 \tabularnewline
26 & 1485 & 1407.51579205898 & 77.4842079410155 \tabularnewline
27 & 1886 & 1560.10851918255 & 325.891480817446 \tabularnewline
28 & 1358 & 1289.70047834944 & 68.2995216505603 \tabularnewline
29 & 1167 & 853.388716470799 & 313.611283529201 \tabularnewline
30 & 1781 & 1336.34710717206 & 444.652892827941 \tabularnewline
31 & 1218 & 1450.18599529009 & -232.18599529009 \tabularnewline
32 & 779 & 568.486130720039 & 210.513869279961 \tabularnewline
33 & 1418 & 1540.4920824362 & -122.492082436203 \tabularnewline
34 & 1641 & 1596.1391629753 & 44.8608370247025 \tabularnewline
35 & 1196 & 1178.76085376048 & 17.2391462395196 \tabularnewline
36 & 132 & -79.3005861876447 & 211.300586187645 \tabularnewline
37 & 2926 & 2653.51250850884 & 272.487491491158 \tabularnewline
38 & 1777 & 1687.8108381098 & 89.1891618901986 \tabularnewline
39 & 2094 & 1935.78500761612 & 158.214992383879 \tabularnewline
40 & 1648 & 1528.93441251148 & 119.065587488523 \tabularnewline
41 & 1646 & 1196.27688907951 & 449.723110920492 \tabularnewline
42 & 1537 & 1760.90788749864 & -223.907887498643 \tabularnewline
43 & 1917 & 1461.2194932455 & 455.780506754497 \tabularnewline
44 & 977 & 910.489429391354 & 66.5105706086464 \tabularnewline
45 & 1475 & 1723.66628214382 & -248.666282143823 \tabularnewline
46 & 2124 & 1811.22101293278 & 312.778987067223 \tabularnewline
47 & 1209 & 1448.20456067661 & -239.204560676608 \tabularnewline
48 & 135 & 200.565892665725 & -65.5658926657254 \tabularnewline
49 & 2917 & 2889.36416379953 & 27.6358362004694 \tabularnewline
50 & 1981 & 1796.2779940856 & 184.722005914396 \tabularnewline
51 & 1398 & 2093.02514798195 & -695.025147981953 \tabularnewline
52 & 1171 & 1465.68442236021 & -294.684422360208 \tabularnewline
53 & 903 & 1156.38452452118 & -253.384524521181 \tabularnewline
54 & 1390 & 1300.34669266396 & 89.6533073360408 \tabularnewline
55 & 1280 & 1329.57918022557 & -49.5791802255671 \tabularnewline
56 & 781 & 511.853850125609 & 269.146149874391 \tabularnewline
57 & 1828 & 1256.49527758593 & 571.504722414073 \tabularnewline
58 & 1631 & 1751.16792626116 & -120.16792626116 \tabularnewline
59 & 1063 & 1078.00351732836 & -15.0035173283613 \tabularnewline
60 & 186 & -50.8332357183974 & 236.833235718397 \tabularnewline
61 & 2275 & 2745.66674126203 & -470.666741262032 \tabularnewline
62 & 1342 & 1590.86118801742 & -248.86118801742 \tabularnewline
63 & 1070 & 1455.18176904721 & -385.181769047214 \tabularnewline
64 & 950 & 1051.77950618361 & -101.779506183611 \tabularnewline
65 & 1121 & 804.419607482853 & 316.580392517147 \tabularnewline
66 & 1305 & 1213.74137716196 & 91.258622838041 \tabularnewline
67 & 1586 & 1191.48308425614 & 394.516915743859 \tabularnewline
68 & 548 & 599.683959002229 & -51.6839590022289 \tabularnewline
69 & 1225 & 1379.56212629246 & -154.562126292462 \tabularnewline
70 & 1419 & 1441.30311315137 & -22.3031131513717 \tabularnewline
71 & 880 & 830.939709868298 & 49.0602901317023 \tabularnewline
72 & 124 & -188.602588921406 & 312.602588921406 \tabularnewline
73 & 2044 & 2362.56672247207 & -318.56672247207 \tabularnewline
74 & 1143 & 1327.11077303898 & -184.110773038982 \tabularnewline
75 & 897 & 1156.26366260798 & -259.263662607975 \tabularnewline
76 & 1264 & 888.843811557384 & 375.156188442616 \tabularnewline
77 & 1326 & 912.458882032014 & 413.541117967986 \tabularnewline
78 & 1529 & 1261.22398084633 & 267.776019153669 \tabularnewline
79 & 1373 & 1394.55704558892 & -21.5570455889231 \tabularnewline
80 & 587 & 536.096463736991 & 50.9035362630091 \tabularnewline
81 & 1137 & 1302.39842337136 & -165.39842337136 \tabularnewline
82 & 1426 & 1410.80425583969 & 15.1957441603083 \tabularnewline
83 & 1016 & 836.08011793973 & 179.919882060269 \tabularnewline
84 & 176 & -53.6871387335377 & 229.687138733538 \tabularnewline
85 & 2614 & 2242.2987433802 & 371.701256619805 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121451&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]3192[/C][C]3211.64289529915[/C][C]-19.6428952991455[/C][/ROW]
[ROW][C]14[/C][C]1934[/C][C]1932.20878204341[/C][C]1.79121795659466[/C][/ROW]
[ROW][C]15[/C][C]2075[/C][C]2062.57212663543[/C][C]12.4278733645729[/C][/ROW]
[ROW][C]16[/C][C]1700[/C][C]1733.71063114617[/C][C]-33.7106311461653[/C][/ROW]
[ROW][C]17[/C][C]1198[/C][C]1297.17337321995[/C][C]-99.1733732199496[/C][/ROW]
[ROW][C]18[/C][C]1582[/C][C]1680.13038134319[/C][C]-98.1303813431896[/C][/ROW]
[ROW][C]19[/C][C]1705[/C][C]1579.7557498446[/C][C]125.244250155402[/C][/ROW]
[ROW][C]20[/C][C]911[/C][C]783.452318029758[/C][C]127.547681970242[/C][/ROW]
[ROW][C]21[/C][C]1817[/C][C]1762.74641464387[/C][C]54.2535853561258[/C][/ROW]
[ROW][C]22[/C][C]1168[/C][C]2304.85325633389[/C][C]-1136.85325633389[/C][/ROW]
[ROW][C]23[/C][C]920[/C][C]1332.35677105251[/C][C]-412.356771052509[/C][/ROW]
[ROW][C]24[/C][C]84[/C][C]-341.596644965116[/C][C]425.596644965116[/C][/ROW]
[ROW][C]25[/C][C]2254[/C][C]2807.88668600327[/C][C]-553.886686003271[/C][/ROW]
[ROW][C]26[/C][C]1485[/C][C]1407.51579205898[/C][C]77.4842079410155[/C][/ROW]
[ROW][C]27[/C][C]1886[/C][C]1560.10851918255[/C][C]325.891480817446[/C][/ROW]
[ROW][C]28[/C][C]1358[/C][C]1289.70047834944[/C][C]68.2995216505603[/C][/ROW]
[ROW][C]29[/C][C]1167[/C][C]853.388716470799[/C][C]313.611283529201[/C][/ROW]
[ROW][C]30[/C][C]1781[/C][C]1336.34710717206[/C][C]444.652892827941[/C][/ROW]
[ROW][C]31[/C][C]1218[/C][C]1450.18599529009[/C][C]-232.18599529009[/C][/ROW]
[ROW][C]32[/C][C]779[/C][C]568.486130720039[/C][C]210.513869279961[/C][/ROW]
[ROW][C]33[/C][C]1418[/C][C]1540.4920824362[/C][C]-122.492082436203[/C][/ROW]
[ROW][C]34[/C][C]1641[/C][C]1596.1391629753[/C][C]44.8608370247025[/C][/ROW]
[ROW][C]35[/C][C]1196[/C][C]1178.76085376048[/C][C]17.2391462395196[/C][/ROW]
[ROW][C]36[/C][C]132[/C][C]-79.3005861876447[/C][C]211.300586187645[/C][/ROW]
[ROW][C]37[/C][C]2926[/C][C]2653.51250850884[/C][C]272.487491491158[/C][/ROW]
[ROW][C]38[/C][C]1777[/C][C]1687.8108381098[/C][C]89.1891618901986[/C][/ROW]
[ROW][C]39[/C][C]2094[/C][C]1935.78500761612[/C][C]158.214992383879[/C][/ROW]
[ROW][C]40[/C][C]1648[/C][C]1528.93441251148[/C][C]119.065587488523[/C][/ROW]
[ROW][C]41[/C][C]1646[/C][C]1196.27688907951[/C][C]449.723110920492[/C][/ROW]
[ROW][C]42[/C][C]1537[/C][C]1760.90788749864[/C][C]-223.907887498643[/C][/ROW]
[ROW][C]43[/C][C]1917[/C][C]1461.2194932455[/C][C]455.780506754497[/C][/ROW]
[ROW][C]44[/C][C]977[/C][C]910.489429391354[/C][C]66.5105706086464[/C][/ROW]
[ROW][C]45[/C][C]1475[/C][C]1723.66628214382[/C][C]-248.666282143823[/C][/ROW]
[ROW][C]46[/C][C]2124[/C][C]1811.22101293278[/C][C]312.778987067223[/C][/ROW]
[ROW][C]47[/C][C]1209[/C][C]1448.20456067661[/C][C]-239.204560676608[/C][/ROW]
[ROW][C]48[/C][C]135[/C][C]200.565892665725[/C][C]-65.5658926657254[/C][/ROW]
[ROW][C]49[/C][C]2917[/C][C]2889.36416379953[/C][C]27.6358362004694[/C][/ROW]
[ROW][C]50[/C][C]1981[/C][C]1796.2779940856[/C][C]184.722005914396[/C][/ROW]
[ROW][C]51[/C][C]1398[/C][C]2093.02514798195[/C][C]-695.025147981953[/C][/ROW]
[ROW][C]52[/C][C]1171[/C][C]1465.68442236021[/C][C]-294.684422360208[/C][/ROW]
[ROW][C]53[/C][C]903[/C][C]1156.38452452118[/C][C]-253.384524521181[/C][/ROW]
[ROW][C]54[/C][C]1390[/C][C]1300.34669266396[/C][C]89.6533073360408[/C][/ROW]
[ROW][C]55[/C][C]1280[/C][C]1329.57918022557[/C][C]-49.5791802255671[/C][/ROW]
[ROW][C]56[/C][C]781[/C][C]511.853850125609[/C][C]269.146149874391[/C][/ROW]
[ROW][C]57[/C][C]1828[/C][C]1256.49527758593[/C][C]571.504722414073[/C][/ROW]
[ROW][C]58[/C][C]1631[/C][C]1751.16792626116[/C][C]-120.16792626116[/C][/ROW]
[ROW][C]59[/C][C]1063[/C][C]1078.00351732836[/C][C]-15.0035173283613[/C][/ROW]
[ROW][C]60[/C][C]186[/C][C]-50.8332357183974[/C][C]236.833235718397[/C][/ROW]
[ROW][C]61[/C][C]2275[/C][C]2745.66674126203[/C][C]-470.666741262032[/C][/ROW]
[ROW][C]62[/C][C]1342[/C][C]1590.86118801742[/C][C]-248.86118801742[/C][/ROW]
[ROW][C]63[/C][C]1070[/C][C]1455.18176904721[/C][C]-385.181769047214[/C][/ROW]
[ROW][C]64[/C][C]950[/C][C]1051.77950618361[/C][C]-101.779506183611[/C][/ROW]
[ROW][C]65[/C][C]1121[/C][C]804.419607482853[/C][C]316.580392517147[/C][/ROW]
[ROW][C]66[/C][C]1305[/C][C]1213.74137716196[/C][C]91.258622838041[/C][/ROW]
[ROW][C]67[/C][C]1586[/C][C]1191.48308425614[/C][C]394.516915743859[/C][/ROW]
[ROW][C]68[/C][C]548[/C][C]599.683959002229[/C][C]-51.6839590022289[/C][/ROW]
[ROW][C]69[/C][C]1225[/C][C]1379.56212629246[/C][C]-154.562126292462[/C][/ROW]
[ROW][C]70[/C][C]1419[/C][C]1441.30311315137[/C][C]-22.3031131513717[/C][/ROW]
[ROW][C]71[/C][C]880[/C][C]830.939709868298[/C][C]49.0602901317023[/C][/ROW]
[ROW][C]72[/C][C]124[/C][C]-188.602588921406[/C][C]312.602588921406[/C][/ROW]
[ROW][C]73[/C][C]2044[/C][C]2362.56672247207[/C][C]-318.56672247207[/C][/ROW]
[ROW][C]74[/C][C]1143[/C][C]1327.11077303898[/C][C]-184.110773038982[/C][/ROW]
[ROW][C]75[/C][C]897[/C][C]1156.26366260798[/C][C]-259.263662607975[/C][/ROW]
[ROW][C]76[/C][C]1264[/C][C]888.843811557384[/C][C]375.156188442616[/C][/ROW]
[ROW][C]77[/C][C]1326[/C][C]912.458882032014[/C][C]413.541117967986[/C][/ROW]
[ROW][C]78[/C][C]1529[/C][C]1261.22398084633[/C][C]267.776019153669[/C][/ROW]
[ROW][C]79[/C][C]1373[/C][C]1394.55704558892[/C][C]-21.5570455889231[/C][/ROW]
[ROW][C]80[/C][C]587[/C][C]536.096463736991[/C][C]50.9035362630091[/C][/ROW]
[ROW][C]81[/C][C]1137[/C][C]1302.39842337136[/C][C]-165.39842337136[/C][/ROW]
[ROW][C]82[/C][C]1426[/C][C]1410.80425583969[/C][C]15.1957441603083[/C][/ROW]
[ROW][C]83[/C][C]1016[/C][C]836.08011793973[/C][C]179.919882060269[/C][/ROW]
[ROW][C]84[/C][C]176[/C][C]-53.6871387335377[/C][C]229.687138733538[/C][/ROW]
[ROW][C]85[/C][C]2614[/C][C]2242.2987433802[/C][C]371.701256619805[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121451&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121451&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
1331923211.64289529915-19.6428952991455
1419341932.208782043411.79121795659466
1520752062.5721266354312.4278733645729
1617001733.71063114617-33.7106311461653
1711981297.17337321995-99.1733732199496
1815821680.13038134319-98.1303813431896
1917051579.7557498446125.244250155402
20911783.452318029758127.547681970242
2118171762.7464146438754.2535853561258
2211682304.85325633389-1136.85325633389
239201332.35677105251-412.356771052509
2484-341.596644965116425.596644965116
2522542807.88668600327-553.886686003271
2614851407.5157920589877.4842079410155
2718861560.10851918255325.891480817446
2813581289.7004783494468.2995216505603
291167853.388716470799313.611283529201
3017811336.34710717206444.652892827941
3112181450.18599529009-232.18599529009
32779568.486130720039210.513869279961
3314181540.4920824362-122.492082436203
3416411596.139162975344.8608370247025
3511961178.7608537604817.2391462395196
36132-79.3005861876447211.300586187645
3729262653.51250850884272.487491491158
3817771687.810838109889.1891618901986
3920941935.78500761612158.214992383879
4016481528.93441251148119.065587488523
4116461196.27688907951449.723110920492
4215371760.90788749864-223.907887498643
4319171461.2194932455455.780506754497
44977910.48942939135466.5105706086464
4514751723.66628214382-248.666282143823
4621241811.22101293278312.778987067223
4712091448.20456067661-239.204560676608
48135200.565892665725-65.5658926657254
4929172889.3641637995327.6358362004694
5019811796.2779940856184.722005914396
5113982093.02514798195-695.025147981953
5211711465.68442236021-294.684422360208
539031156.38452452118-253.384524521181
5413901300.3466926639689.6533073360408
5512801329.57918022557-49.5791802255671
56781511.853850125609269.146149874391
5718281256.49527758593571.504722414073
5816311751.16792626116-120.16792626116
5910631078.00351732836-15.0035173283613
60186-50.8332357183974236.833235718397
6122752745.66674126203-470.666741262032
6213421590.86118801742-248.86118801742
6310701455.18176904721-385.181769047214
649501051.77950618361-101.779506183611
651121804.419607482853316.580392517147
6613051213.7413771619691.258622838041
6715861191.48308425614394.516915743859
68548599.683959002229-51.6839590022289
6912251379.56212629246-154.562126292462
7014191441.30311315137-22.3031131513717
71880830.93970986829849.0602901317023
72124-188.602588921406312.602588921406
7320442362.56672247207-318.56672247207
7411431327.11077303898-184.110773038982
758971156.26366260798-259.263662607975
761264888.843811557384375.156188442616
771326912.458882032014413.541117967986
7815291261.22398084633267.776019153669
7913731394.55704558892-21.5570455889231
80587536.09646373699150.9035362630091
8111371302.39842337136-165.39842337136
8214261410.8042558396915.1957441603083
831016836.08011793973179.919882060269
84176-53.6871387335377229.687138733538
8526142242.2987433802371.701256619805







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
861423.51597279861849.4235501646851997.60839543254
871269.09623512974678.5242490256531859.66822123382
881300.62713453557694.023118874481907.23115019666
891248.01217075773625.7890653836241870.23527613183
901442.6697269915805.2101173638632080.12933661914
911403.57755331851751.2372165679272055.91789006908
92577.317985383771-89.57111783886431244.20708860641
931250.74161564305569.614434389561931.86879689654
941466.35080272204771.2771389372161.42446650708
95949.336033359659240.5902685520011658.08179816732
9634.694031440516-687.465037032646756.853099913678
972328.166664835831592.838927549083063.49440212259

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 1423.51597279861 & 849.423550164685 & 1997.60839543254 \tabularnewline
87 & 1269.09623512974 & 678.524249025653 & 1859.66822123382 \tabularnewline
88 & 1300.62713453557 & 694.02311887448 & 1907.23115019666 \tabularnewline
89 & 1248.01217075773 & 625.789065383624 & 1870.23527613183 \tabularnewline
90 & 1442.6697269915 & 805.210117363863 & 2080.12933661914 \tabularnewline
91 & 1403.57755331851 & 751.237216567927 & 2055.91789006908 \tabularnewline
92 & 577.317985383771 & -89.5711178388643 & 1244.20708860641 \tabularnewline
93 & 1250.74161564305 & 569.61443438956 & 1931.86879689654 \tabularnewline
94 & 1466.35080272204 & 771.277138937 & 2161.42446650708 \tabularnewline
95 & 949.336033359659 & 240.590268552001 & 1658.08179816732 \tabularnewline
96 & 34.694031440516 & -687.465037032646 & 756.853099913678 \tabularnewline
97 & 2328.16666483583 & 1592.83892754908 & 3063.49440212259 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121451&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]86[/C][C]1423.51597279861[/C][C]849.423550164685[/C][C]1997.60839543254[/C][/ROW]
[ROW][C]87[/C][C]1269.09623512974[/C][C]678.524249025653[/C][C]1859.66822123382[/C][/ROW]
[ROW][C]88[/C][C]1300.62713453557[/C][C]694.02311887448[/C][C]1907.23115019666[/C][/ROW]
[ROW][C]89[/C][C]1248.01217075773[/C][C]625.789065383624[/C][C]1870.23527613183[/C][/ROW]
[ROW][C]90[/C][C]1442.6697269915[/C][C]805.210117363863[/C][C]2080.12933661914[/C][/ROW]
[ROW][C]91[/C][C]1403.57755331851[/C][C]751.237216567927[/C][C]2055.91789006908[/C][/ROW]
[ROW][C]92[/C][C]577.317985383771[/C][C]-89.5711178388643[/C][C]1244.20708860641[/C][/ROW]
[ROW][C]93[/C][C]1250.74161564305[/C][C]569.61443438956[/C][C]1931.86879689654[/C][/ROW]
[ROW][C]94[/C][C]1466.35080272204[/C][C]771.277138937[/C][C]2161.42446650708[/C][/ROW]
[ROW][C]95[/C][C]949.336033359659[/C][C]240.590268552001[/C][C]1658.08179816732[/C][/ROW]
[ROW][C]96[/C][C]34.694031440516[/C][C]-687.465037032646[/C][C]756.853099913678[/C][/ROW]
[ROW][C]97[/C][C]2328.16666483583[/C][C]1592.83892754908[/C][C]3063.49440212259[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121451&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121451&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
861423.51597279861849.4235501646851997.60839543254
871269.09623512974678.5242490256531859.66822123382
881300.62713453557694.023118874481907.23115019666
891248.01217075773625.7890653836241870.23527613183
901442.6697269915805.2101173638632080.12933661914
911403.57755331851751.2372165679272055.91789006908
92577.317985383771-89.57111783886431244.20708860641
931250.74161564305569.614434389561931.86879689654
941466.35080272204771.2771389372161.42446650708
95949.336033359659240.5902685520011658.08179816732
9634.694031440516-687.465037032646756.853099913678
972328.166664835831592.838927549083063.49440212259



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=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')