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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 25 Jan 2017 10:23:19 +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/2017/Jan/25/t148533621863vk2vnvos9iibh.htm/, Retrieved Tue, 14 May 2024 16:57:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=306018, Retrieved Tue, 14 May 2024 16:57:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-01-25 09:23:19] [85f5800284aab30c091766186b093bb4] [Current]
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Dataseries X:
3035
2552
2704
2554
2014
1655
1721
1524
1596
2074
2199
2512
2933
2889
2938
2497
1870
1726
1607
1545
1396
1787
2076
2837
2787
3891
3179
2011
1636
1580
1489
1300
1356
1653
2013
2823
3102
2294
2385
2444
1748
1554
1498
1361
1346
1564
1640
2293
2815
3137
2679
1969
1870
1633
1529
1366
1357
1570
1535
2491
3084
2605
2573
2143
1693
1504
1461
1354
1333
1492
1781
1915




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306018&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=306018&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306018&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0441210731237266
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0441210731237266 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306018&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0441210731237266[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306018&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306018&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
alpha1
beta0.0441210731237266
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
520142482.30625-468.30625
616551644.5503256994510.4496743005479
717211716.011376543394.9886234566145
815241549.3564799637-25.3564799637015
91596956.487724857063639.512275142937
1020741254.32869271217819.671307287835
1121992198.493470398430.506529601567763
1225122090.64081902802421.359180971977
1329332027.48163826304905.518361736959
1428892686.05908011611202.940919883886
1529383081.01305128211-143.013051282107
1624972890.82816198884-393.828161988842
1718702037.70204085555-167.70204085555
1817261600.92784684796125.072153152036
1916071892.44616446293-285.446164462927
2015451527.9769733677717.0230266322294
2113961071.9780475706324.021952429402
2217871134.89924382743652.100756172571
2320761984.6706289745691.3293710254438
2428372044.82517883191792.174821168086
2527872446.02678204345340.973217956554
2638912608.695886326141282.30411367386
2731794199.2725198924-1020.2725198924
2820113209.3820014361-1198.3820014361
2916361593.7581015205842.2418984794222
3015801418.24685941227161.753140587726
3114891799.38358155614-310.383581556137
3213001461.81412485789-161.814124857895
331356870.924712022588485.075287977412
3416531145.95175427395507.048245726048
3520131895.32326700089117.676732999112
3628232027.6402907425795.359709257497
3731022477.98241463432624.017585365681
3822942982.13974014873-688.139740148729
3923852573.77827635429-188.778276354285
4024442423.5741762190920.4258237809131
4117482088.72538548374-340.725385483737
4215541575.3172158357-21.3172158356988
4314981810.37667739702-312.376677397018
4413611507.71928317144-146.719283171437
451346969.495870949969376.504129050031
4615641168.73263715917395.267362840829
4716401834.17225737849-194.172257378494
4822931668.7301690121624.269830987902
4928151954.52362387405860.476376125948
5031372712.11376498634424.886235013656
5126793482.86020163065-803.860201630646
5219692756.51802689325-787.518026893247
5318701617.02188644244252.978113557563
5416331726.80855228941-93.8085522894128
5515291915.66961829422-386.669618294221
5613661561.73433979074-195.734339790738
571357995.348330672006361.651669327994
5815701199.92979041974370.070209580255
5915351859.25768519755-324.257685197548
6024911577.07608815802913.923911841983
6130842178.64939190192905.350608098081
6226053009.21943228442-404.219432284425
6325732942.38483715457-369.384837154572
6421432661.21218174368-518.21218174368
6516931813.59810417936-120.598104179361
6615041555.90218640628-51.9021864062804
6714611794.61220624457-333.612206244568
6813541504.01787769788-150.017877697883
691333995.648927946109337.351072053891
7014921187.15821926457304.841780735434
7117811789.60816576356-8.60816576356115
7219151845.3533642524569.646635747554

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 2014 & 2482.30625 & -468.30625 \tabularnewline
6 & 1655 & 1644.55032569945 & 10.4496743005479 \tabularnewline
7 & 1721 & 1716.01137654339 & 4.9886234566145 \tabularnewline
8 & 1524 & 1549.3564799637 & -25.3564799637015 \tabularnewline
9 & 1596 & 956.487724857063 & 639.512275142937 \tabularnewline
10 & 2074 & 1254.32869271217 & 819.671307287835 \tabularnewline
11 & 2199 & 2198.49347039843 & 0.506529601567763 \tabularnewline
12 & 2512 & 2090.64081902802 & 421.359180971977 \tabularnewline
13 & 2933 & 2027.48163826304 & 905.518361736959 \tabularnewline
14 & 2889 & 2686.05908011611 & 202.940919883886 \tabularnewline
15 & 2938 & 3081.01305128211 & -143.013051282107 \tabularnewline
16 & 2497 & 2890.82816198884 & -393.828161988842 \tabularnewline
17 & 1870 & 2037.70204085555 & -167.70204085555 \tabularnewline
18 & 1726 & 1600.92784684796 & 125.072153152036 \tabularnewline
19 & 1607 & 1892.44616446293 & -285.446164462927 \tabularnewline
20 & 1545 & 1527.97697336777 & 17.0230266322294 \tabularnewline
21 & 1396 & 1071.9780475706 & 324.021952429402 \tabularnewline
22 & 1787 & 1134.89924382743 & 652.100756172571 \tabularnewline
23 & 2076 & 1984.67062897456 & 91.3293710254438 \tabularnewline
24 & 2837 & 2044.82517883191 & 792.174821168086 \tabularnewline
25 & 2787 & 2446.02678204345 & 340.973217956554 \tabularnewline
26 & 3891 & 2608.69588632614 & 1282.30411367386 \tabularnewline
27 & 3179 & 4199.2725198924 & -1020.2725198924 \tabularnewline
28 & 2011 & 3209.3820014361 & -1198.3820014361 \tabularnewline
29 & 1636 & 1593.75810152058 & 42.2418984794222 \tabularnewline
30 & 1580 & 1418.24685941227 & 161.753140587726 \tabularnewline
31 & 1489 & 1799.38358155614 & -310.383581556137 \tabularnewline
32 & 1300 & 1461.81412485789 & -161.814124857895 \tabularnewline
33 & 1356 & 870.924712022588 & 485.075287977412 \tabularnewline
34 & 1653 & 1145.95175427395 & 507.048245726048 \tabularnewline
35 & 2013 & 1895.32326700089 & 117.676732999112 \tabularnewline
36 & 2823 & 2027.6402907425 & 795.359709257497 \tabularnewline
37 & 3102 & 2477.98241463432 & 624.017585365681 \tabularnewline
38 & 2294 & 2982.13974014873 & -688.139740148729 \tabularnewline
39 & 2385 & 2573.77827635429 & -188.778276354285 \tabularnewline
40 & 2444 & 2423.57417621909 & 20.4258237809131 \tabularnewline
41 & 1748 & 2088.72538548374 & -340.725385483737 \tabularnewline
42 & 1554 & 1575.3172158357 & -21.3172158356988 \tabularnewline
43 & 1498 & 1810.37667739702 & -312.376677397018 \tabularnewline
44 & 1361 & 1507.71928317144 & -146.719283171437 \tabularnewline
45 & 1346 & 969.495870949969 & 376.504129050031 \tabularnewline
46 & 1564 & 1168.73263715917 & 395.267362840829 \tabularnewline
47 & 1640 & 1834.17225737849 & -194.172257378494 \tabularnewline
48 & 2293 & 1668.7301690121 & 624.269830987902 \tabularnewline
49 & 2815 & 1954.52362387405 & 860.476376125948 \tabularnewline
50 & 3137 & 2712.11376498634 & 424.886235013656 \tabularnewline
51 & 2679 & 3482.86020163065 & -803.860201630646 \tabularnewline
52 & 1969 & 2756.51802689325 & -787.518026893247 \tabularnewline
53 & 1870 & 1617.02188644244 & 252.978113557563 \tabularnewline
54 & 1633 & 1726.80855228941 & -93.8085522894128 \tabularnewline
55 & 1529 & 1915.66961829422 & -386.669618294221 \tabularnewline
56 & 1366 & 1561.73433979074 & -195.734339790738 \tabularnewline
57 & 1357 & 995.348330672006 & 361.651669327994 \tabularnewline
58 & 1570 & 1199.92979041974 & 370.070209580255 \tabularnewline
59 & 1535 & 1859.25768519755 & -324.257685197548 \tabularnewline
60 & 2491 & 1577.07608815802 & 913.923911841983 \tabularnewline
61 & 3084 & 2178.64939190192 & 905.350608098081 \tabularnewline
62 & 2605 & 3009.21943228442 & -404.219432284425 \tabularnewline
63 & 2573 & 2942.38483715457 & -369.384837154572 \tabularnewline
64 & 2143 & 2661.21218174368 & -518.21218174368 \tabularnewline
65 & 1693 & 1813.59810417936 & -120.598104179361 \tabularnewline
66 & 1504 & 1555.90218640628 & -51.9021864062804 \tabularnewline
67 & 1461 & 1794.61220624457 & -333.612206244568 \tabularnewline
68 & 1354 & 1504.01787769788 & -150.017877697883 \tabularnewline
69 & 1333 & 995.648927946109 & 337.351072053891 \tabularnewline
70 & 1492 & 1187.15821926457 & 304.841780735434 \tabularnewline
71 & 1781 & 1789.60816576356 & -8.60816576356115 \tabularnewline
72 & 1915 & 1845.35336425245 & 69.646635747554 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306018&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]5[/C][C]2014[/C][C]2482.30625[/C][C]-468.30625[/C][/ROW]
[ROW][C]6[/C][C]1655[/C][C]1644.55032569945[/C][C]10.4496743005479[/C][/ROW]
[ROW][C]7[/C][C]1721[/C][C]1716.01137654339[/C][C]4.9886234566145[/C][/ROW]
[ROW][C]8[/C][C]1524[/C][C]1549.3564799637[/C][C]-25.3564799637015[/C][/ROW]
[ROW][C]9[/C][C]1596[/C][C]956.487724857063[/C][C]639.512275142937[/C][/ROW]
[ROW][C]10[/C][C]2074[/C][C]1254.32869271217[/C][C]819.671307287835[/C][/ROW]
[ROW][C]11[/C][C]2199[/C][C]2198.49347039843[/C][C]0.506529601567763[/C][/ROW]
[ROW][C]12[/C][C]2512[/C][C]2090.64081902802[/C][C]421.359180971977[/C][/ROW]
[ROW][C]13[/C][C]2933[/C][C]2027.48163826304[/C][C]905.518361736959[/C][/ROW]
[ROW][C]14[/C][C]2889[/C][C]2686.05908011611[/C][C]202.940919883886[/C][/ROW]
[ROW][C]15[/C][C]2938[/C][C]3081.01305128211[/C][C]-143.013051282107[/C][/ROW]
[ROW][C]16[/C][C]2497[/C][C]2890.82816198884[/C][C]-393.828161988842[/C][/ROW]
[ROW][C]17[/C][C]1870[/C][C]2037.70204085555[/C][C]-167.70204085555[/C][/ROW]
[ROW][C]18[/C][C]1726[/C][C]1600.92784684796[/C][C]125.072153152036[/C][/ROW]
[ROW][C]19[/C][C]1607[/C][C]1892.44616446293[/C][C]-285.446164462927[/C][/ROW]
[ROW][C]20[/C][C]1545[/C][C]1527.97697336777[/C][C]17.0230266322294[/C][/ROW]
[ROW][C]21[/C][C]1396[/C][C]1071.9780475706[/C][C]324.021952429402[/C][/ROW]
[ROW][C]22[/C][C]1787[/C][C]1134.89924382743[/C][C]652.100756172571[/C][/ROW]
[ROW][C]23[/C][C]2076[/C][C]1984.67062897456[/C][C]91.3293710254438[/C][/ROW]
[ROW][C]24[/C][C]2837[/C][C]2044.82517883191[/C][C]792.174821168086[/C][/ROW]
[ROW][C]25[/C][C]2787[/C][C]2446.02678204345[/C][C]340.973217956554[/C][/ROW]
[ROW][C]26[/C][C]3891[/C][C]2608.69588632614[/C][C]1282.30411367386[/C][/ROW]
[ROW][C]27[/C][C]3179[/C][C]4199.2725198924[/C][C]-1020.2725198924[/C][/ROW]
[ROW][C]28[/C][C]2011[/C][C]3209.3820014361[/C][C]-1198.3820014361[/C][/ROW]
[ROW][C]29[/C][C]1636[/C][C]1593.75810152058[/C][C]42.2418984794222[/C][/ROW]
[ROW][C]30[/C][C]1580[/C][C]1418.24685941227[/C][C]161.753140587726[/C][/ROW]
[ROW][C]31[/C][C]1489[/C][C]1799.38358155614[/C][C]-310.383581556137[/C][/ROW]
[ROW][C]32[/C][C]1300[/C][C]1461.81412485789[/C][C]-161.814124857895[/C][/ROW]
[ROW][C]33[/C][C]1356[/C][C]870.924712022588[/C][C]485.075287977412[/C][/ROW]
[ROW][C]34[/C][C]1653[/C][C]1145.95175427395[/C][C]507.048245726048[/C][/ROW]
[ROW][C]35[/C][C]2013[/C][C]1895.32326700089[/C][C]117.676732999112[/C][/ROW]
[ROW][C]36[/C][C]2823[/C][C]2027.6402907425[/C][C]795.359709257497[/C][/ROW]
[ROW][C]37[/C][C]3102[/C][C]2477.98241463432[/C][C]624.017585365681[/C][/ROW]
[ROW][C]38[/C][C]2294[/C][C]2982.13974014873[/C][C]-688.139740148729[/C][/ROW]
[ROW][C]39[/C][C]2385[/C][C]2573.77827635429[/C][C]-188.778276354285[/C][/ROW]
[ROW][C]40[/C][C]2444[/C][C]2423.57417621909[/C][C]20.4258237809131[/C][/ROW]
[ROW][C]41[/C][C]1748[/C][C]2088.72538548374[/C][C]-340.725385483737[/C][/ROW]
[ROW][C]42[/C][C]1554[/C][C]1575.3172158357[/C][C]-21.3172158356988[/C][/ROW]
[ROW][C]43[/C][C]1498[/C][C]1810.37667739702[/C][C]-312.376677397018[/C][/ROW]
[ROW][C]44[/C][C]1361[/C][C]1507.71928317144[/C][C]-146.719283171437[/C][/ROW]
[ROW][C]45[/C][C]1346[/C][C]969.495870949969[/C][C]376.504129050031[/C][/ROW]
[ROW][C]46[/C][C]1564[/C][C]1168.73263715917[/C][C]395.267362840829[/C][/ROW]
[ROW][C]47[/C][C]1640[/C][C]1834.17225737849[/C][C]-194.172257378494[/C][/ROW]
[ROW][C]48[/C][C]2293[/C][C]1668.7301690121[/C][C]624.269830987902[/C][/ROW]
[ROW][C]49[/C][C]2815[/C][C]1954.52362387405[/C][C]860.476376125948[/C][/ROW]
[ROW][C]50[/C][C]3137[/C][C]2712.11376498634[/C][C]424.886235013656[/C][/ROW]
[ROW][C]51[/C][C]2679[/C][C]3482.86020163065[/C][C]-803.860201630646[/C][/ROW]
[ROW][C]52[/C][C]1969[/C][C]2756.51802689325[/C][C]-787.518026893247[/C][/ROW]
[ROW][C]53[/C][C]1870[/C][C]1617.02188644244[/C][C]252.978113557563[/C][/ROW]
[ROW][C]54[/C][C]1633[/C][C]1726.80855228941[/C][C]-93.8085522894128[/C][/ROW]
[ROW][C]55[/C][C]1529[/C][C]1915.66961829422[/C][C]-386.669618294221[/C][/ROW]
[ROW][C]56[/C][C]1366[/C][C]1561.73433979074[/C][C]-195.734339790738[/C][/ROW]
[ROW][C]57[/C][C]1357[/C][C]995.348330672006[/C][C]361.651669327994[/C][/ROW]
[ROW][C]58[/C][C]1570[/C][C]1199.92979041974[/C][C]370.070209580255[/C][/ROW]
[ROW][C]59[/C][C]1535[/C][C]1859.25768519755[/C][C]-324.257685197548[/C][/ROW]
[ROW][C]60[/C][C]2491[/C][C]1577.07608815802[/C][C]913.923911841983[/C][/ROW]
[ROW][C]61[/C][C]3084[/C][C]2178.64939190192[/C][C]905.350608098081[/C][/ROW]
[ROW][C]62[/C][C]2605[/C][C]3009.21943228442[/C][C]-404.219432284425[/C][/ROW]
[ROW][C]63[/C][C]2573[/C][C]2942.38483715457[/C][C]-369.384837154572[/C][/ROW]
[ROW][C]64[/C][C]2143[/C][C]2661.21218174368[/C][C]-518.21218174368[/C][/ROW]
[ROW][C]65[/C][C]1693[/C][C]1813.59810417936[/C][C]-120.598104179361[/C][/ROW]
[ROW][C]66[/C][C]1504[/C][C]1555.90218640628[/C][C]-51.9021864062804[/C][/ROW]
[ROW][C]67[/C][C]1461[/C][C]1794.61220624457[/C][C]-333.612206244568[/C][/ROW]
[ROW][C]68[/C][C]1354[/C][C]1504.01787769788[/C][C]-150.017877697883[/C][/ROW]
[ROW][C]69[/C][C]1333[/C][C]995.648927946109[/C][C]337.351072053891[/C][/ROW]
[ROW][C]70[/C][C]1492[/C][C]1187.15821926457[/C][C]304.841780735434[/C][/ROW]
[ROW][C]71[/C][C]1781[/C][C]1789.60816576356[/C][C]-8.60816576356115[/C][/ROW]
[ROW][C]72[/C][C]1915[/C][C]1845.35336425245[/C][C]69.646635747554[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306018&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306018&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
520142482.30625-468.30625
616551644.5503256994510.4496743005479
717211716.011376543394.9886234566145
815241549.3564799637-25.3564799637015
91596956.487724857063639.512275142937
1020741254.32869271217819.671307287835
1121992198.493470398430.506529601567763
1225122090.64081902802421.359180971977
1329332027.48163826304905.518361736959
1428892686.05908011611202.940919883886
1529383081.01305128211-143.013051282107
1624972890.82816198884-393.828161988842
1718702037.70204085555-167.70204085555
1817261600.92784684796125.072153152036
1916071892.44616446293-285.446164462927
2015451527.9769733677717.0230266322294
2113961071.9780475706324.021952429402
2217871134.89924382743652.100756172571
2320761984.6706289745691.3293710254438
2428372044.82517883191792.174821168086
2527872446.02678204345340.973217956554
2638912608.695886326141282.30411367386
2731794199.2725198924-1020.2725198924
2820113209.3820014361-1198.3820014361
2916361593.7581015205842.2418984794222
3015801418.24685941227161.753140587726
3114891799.38358155614-310.383581556137
3213001461.81412485789-161.814124857895
331356870.924712022588485.075287977412
3416531145.95175427395507.048245726048
3520131895.32326700089117.676732999112
3628232027.6402907425795.359709257497
3731022477.98241463432624.017585365681
3822942982.13974014873-688.139740148729
3923852573.77827635429-188.778276354285
4024442423.5741762190920.4258237809131
4117482088.72538548374-340.725385483737
4215541575.3172158357-21.3172158356988
4314981810.37667739702-312.376677397018
4413611507.71928317144-146.719283171437
451346969.495870949969376.504129050031
4615641168.73263715917395.267362840829
4716401834.17225737849-194.172257378494
4822931668.7301690121624.269830987902
4928151954.52362387405860.476376125948
5031372712.11376498634424.886235013656
5126793482.86020163065-803.860201630646
5219692756.51802689325-787.518026893247
5318701617.02188644244252.978113557563
5416331726.80855228941-93.8085522894128
5515291915.66961829422-386.669618294221
5613661561.73433979074-195.734339790738
571357995.348330672006361.651669327994
5815701199.92979041974370.070209580255
5915351859.25768519755-324.257685197548
6024911577.07608815802913.923911841983
6130842178.64939190192905.350608098081
6226053009.21943228442-404.219432284425
6325732942.38483715457-369.384837154572
6421432661.21218174368-518.21218174368
6516931813.59810417936-120.598104179361
6615041555.90218640628-51.9021864062804
6714611794.61220624457-333.612206244568
6813541504.01787769788-150.017877697883
691333995.648927946109337.351072053891
7014921187.15821926457304.841780735434
7117811789.60816576356-8.60816576356115
7219151845.3533642524569.646635747554







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731587.67624856109622.7869342753182552.56556284685
741457.9774971221762.99018826496582852.96480597938
751758.2787456832612.26633125367063504.29116011284
761825.70499424434-233.9904709699583885.40045945864
771498.38124280543-853.420727665693850.18321327654
781368.68249136651-1261.53905637383998.90403910683
791668.9837399276-1230.541875974784568.50935582998
801736.40998848868-1426.207198547154899.02717552451
811409.08623704977-2012.373415755064830.5458898546
821279.38748561085-2398.055864269294956.83083549099
831579.68873417194-2351.899052123335511.27652046721
841647.11498273302-2537.546256515575831.77622198162

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1587.67624856109 & 622.786934275318 & 2552.56556284685 \tabularnewline
74 & 1457.97749712217 & 62.9901882649658 & 2852.96480597938 \tabularnewline
75 & 1758.27874568326 & 12.2663312536706 & 3504.29116011284 \tabularnewline
76 & 1825.70499424434 & -233.990470969958 & 3885.40045945864 \tabularnewline
77 & 1498.38124280543 & -853.42072766569 & 3850.18321327654 \tabularnewline
78 & 1368.68249136651 & -1261.5390563738 & 3998.90403910683 \tabularnewline
79 & 1668.9837399276 & -1230.54187597478 & 4568.50935582998 \tabularnewline
80 & 1736.40998848868 & -1426.20719854715 & 4899.02717552451 \tabularnewline
81 & 1409.08623704977 & -2012.37341575506 & 4830.5458898546 \tabularnewline
82 & 1279.38748561085 & -2398.05586426929 & 4956.83083549099 \tabularnewline
83 & 1579.68873417194 & -2351.89905212333 & 5511.27652046721 \tabularnewline
84 & 1647.11498273302 & -2537.54625651557 & 5831.77622198162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306018&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]73[/C][C]1587.67624856109[/C][C]622.786934275318[/C][C]2552.56556284685[/C][/ROW]
[ROW][C]74[/C][C]1457.97749712217[/C][C]62.9901882649658[/C][C]2852.96480597938[/C][/ROW]
[ROW][C]75[/C][C]1758.27874568326[/C][C]12.2663312536706[/C][C]3504.29116011284[/C][/ROW]
[ROW][C]76[/C][C]1825.70499424434[/C][C]-233.990470969958[/C][C]3885.40045945864[/C][/ROW]
[ROW][C]77[/C][C]1498.38124280543[/C][C]-853.42072766569[/C][C]3850.18321327654[/C][/ROW]
[ROW][C]78[/C][C]1368.68249136651[/C][C]-1261.5390563738[/C][C]3998.90403910683[/C][/ROW]
[ROW][C]79[/C][C]1668.9837399276[/C][C]-1230.54187597478[/C][C]4568.50935582998[/C][/ROW]
[ROW][C]80[/C][C]1736.40998848868[/C][C]-1426.20719854715[/C][C]4899.02717552451[/C][/ROW]
[ROW][C]81[/C][C]1409.08623704977[/C][C]-2012.37341575506[/C][C]4830.5458898546[/C][/ROW]
[ROW][C]82[/C][C]1279.38748561085[/C][C]-2398.05586426929[/C][C]4956.83083549099[/C][/ROW]
[ROW][C]83[/C][C]1579.68873417194[/C][C]-2351.89905212333[/C][C]5511.27652046721[/C][/ROW]
[ROW][C]84[/C][C]1647.11498273302[/C][C]-2537.54625651557[/C][C]5831.77622198162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306018&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306018&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
731587.67624856109622.7869342753182552.56556284685
741457.9774971221762.99018826496582852.96480597938
751758.2787456832612.26633125367063504.29116011284
761825.70499424434-233.9904709699583885.40045945864
771498.38124280543-853.420727665693850.18321327654
781368.68249136651-1261.53905637383998.90403910683
791668.9837399276-1230.541875974784568.50935582998
801736.40998848868-1426.207198547154899.02717552451
811409.08623704977-2012.373415755064830.5458898546
821279.38748561085-2398.055864269294956.83083549099
831579.68873417194-2351.899052123335511.27652046721
841647.11498273302-2537.546256515575831.77622198162



Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 4 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')