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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 13:41:13 +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/2014/Nov/30/t14173549457fzazqsh0ngu703.htm/, Retrieved Sun, 19 May 2024 15:39:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261414, Retrieved Sun, 19 May 2024 15:39:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-30 13:41:13] [397b699eae6f3431a51b0bb18afa5c27] [Current]
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Dataseries X:
2011
2203
2523
2565
2596
2545
1935
2386
2478
2457
2194
1736
1881
2520
2381
2419
2541
2514
1737
2221
2648
2159
2184
1745
1770
1871
2137
2283
2042
2099
1653
2254
2302
2233
1974
1684
1842
1592
2175
2366
2569
2894
2159
2877
2419
2305
1812
1514
1557
1606
1988
1901
1993
1993
1420
1927
2029
1899
1759
1496
2091
1850
2326
2212
2083
2048
1642
2014
1844
1846
1743
1337
1682
1512
2050
2108
1948
1927
1641
1916
1921
1858
1823
1367




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261414&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261414&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261414&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.554575585650517
beta0
gamma0.909119074970524

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.554575585650517 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.909119074970524 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261414&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]0.554575585650517[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.909119074970524[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261414&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261414&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
alpha0.554575585650517
beta0
gamma0.909119074970524







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1318811907.43082264957-26.4308226495732
1425202540.76783463186-20.7678346318621
1523812383.91206817727-2.91206817727152
1624192419.50034052814-0.500340528141351
1725412547.92609815246-6.9260981524576
1825142510.996620812353.00337918764762
1917371875.99045585001-138.990455850007
2022212235.98797666289-14.9879766628915
2126482306.25424499309341.745755006913
2221592480.64799815202-321.647998152025
2321842041.51477213595142.48522786405
2417451659.9868350909485.0131649090627
2517701844.84162981291-74.8416298129084
2618712453.62438212665-582.624382126649
2721371992.40727427681144.592725723187
2822832110.77471832616172.225281673836
2920422332.38781812704-290.387818127037
3020992142.27827202185-43.2782720218452
3116531424.10590561953228.894094380466
3222542038.33725537108215.662744628917
3323022380.97390668529-78.9739066852894
3422332053.40959884092179.590401159079
3519742080.19883856255-106.198838562548
3616841537.4838323574146.516167642603
3718421691.7144777744150.285522225599
3815922219.72375896251-627.723758962511
3921752027.97771980756147.02228019244
4023662158.88216853154207.117831468459
4125692212.5135034144356.4864965856
4228942481.21014564386412.789854356143
4321592126.1765484151532.8234515848549
4428772626.31395314457250.686046855429
4524192869.06237830638-450.062378306377
4623052440.40548550327-135.405485503271
4718122176.77710715507-364.777107155074
4815141592.99628910978-78.9962891097753
4915571623.68960863912-66.6896086391239
5016061716.31972025625-110.319720256245
5119882125.24195845269-137.241958452692
5219012122.83572334293-221.835723342932
5319931999.06580891434-6.06580891434487
5419932089.49949141655-96.4994914165472
5514201298.16140599468121.838594005321
5619271935.8865495424-8.88654954239996
5720291750.91859780553278.081402194473
5818991853.4908363044745.5091636955315
5917591597.31068216961161.689317830386
6014961421.2204695266374.7795304733722
6120911542.17761860355548.822381396454
6218501958.48790800069-108.487908000691
6323262357.52403026259-31.5240302625898
6422122379.49065381334-167.49065381334
6520832373.23388402669-290.233884026695
6620482269.45432795733-221.454327957329
6716421497.23400176342144.765998236581
6820142094.73778343295-80.7377834329545
6918441986.1287934878-142.128793487802
7018461761.4840232517184.515976748294
7117431573.98253207454169.017467925464
7213371366.76275027135-29.7627502713526
7316821621.7040311472460.2959688527631
7415121500.915752101311.0842478986956
7520501997.4297202902552.5702797097499
7621082010.9741495412297.0258504587766
7719482101.70766108699-153.707661086992
7819272101.4940720276-174.494072027599
7916411503.61541934599137.384580654007
8019162005.70928166011-89.7092816601137
8119211867.2650069975953.7349930024138
8218581843.0199125205514.9800874794532
8318231651.17387243673171.826127563266
8413671365.016881505571.98311849443348

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1881 & 1907.43082264957 & -26.4308226495732 \tabularnewline
14 & 2520 & 2540.76783463186 & -20.7678346318621 \tabularnewline
15 & 2381 & 2383.91206817727 & -2.91206817727152 \tabularnewline
16 & 2419 & 2419.50034052814 & -0.500340528141351 \tabularnewline
17 & 2541 & 2547.92609815246 & -6.9260981524576 \tabularnewline
18 & 2514 & 2510.99662081235 & 3.00337918764762 \tabularnewline
19 & 1737 & 1875.99045585001 & -138.990455850007 \tabularnewline
20 & 2221 & 2235.98797666289 & -14.9879766628915 \tabularnewline
21 & 2648 & 2306.25424499309 & 341.745755006913 \tabularnewline
22 & 2159 & 2480.64799815202 & -321.647998152025 \tabularnewline
23 & 2184 & 2041.51477213595 & 142.48522786405 \tabularnewline
24 & 1745 & 1659.98683509094 & 85.0131649090627 \tabularnewline
25 & 1770 & 1844.84162981291 & -74.8416298129084 \tabularnewline
26 & 1871 & 2453.62438212665 & -582.624382126649 \tabularnewline
27 & 2137 & 1992.40727427681 & 144.592725723187 \tabularnewline
28 & 2283 & 2110.77471832616 & 172.225281673836 \tabularnewline
29 & 2042 & 2332.38781812704 & -290.387818127037 \tabularnewline
30 & 2099 & 2142.27827202185 & -43.2782720218452 \tabularnewline
31 & 1653 & 1424.10590561953 & 228.894094380466 \tabularnewline
32 & 2254 & 2038.33725537108 & 215.662744628917 \tabularnewline
33 & 2302 & 2380.97390668529 & -78.9739066852894 \tabularnewline
34 & 2233 & 2053.40959884092 & 179.590401159079 \tabularnewline
35 & 1974 & 2080.19883856255 & -106.198838562548 \tabularnewline
36 & 1684 & 1537.4838323574 & 146.516167642603 \tabularnewline
37 & 1842 & 1691.7144777744 & 150.285522225599 \tabularnewline
38 & 1592 & 2219.72375896251 & -627.723758962511 \tabularnewline
39 & 2175 & 2027.97771980756 & 147.02228019244 \tabularnewline
40 & 2366 & 2158.88216853154 & 207.117831468459 \tabularnewline
41 & 2569 & 2212.5135034144 & 356.4864965856 \tabularnewline
42 & 2894 & 2481.21014564386 & 412.789854356143 \tabularnewline
43 & 2159 & 2126.17654841515 & 32.8234515848549 \tabularnewline
44 & 2877 & 2626.31395314457 & 250.686046855429 \tabularnewline
45 & 2419 & 2869.06237830638 & -450.062378306377 \tabularnewline
46 & 2305 & 2440.40548550327 & -135.405485503271 \tabularnewline
47 & 1812 & 2176.77710715507 & -364.777107155074 \tabularnewline
48 & 1514 & 1592.99628910978 & -78.9962891097753 \tabularnewline
49 & 1557 & 1623.68960863912 & -66.6896086391239 \tabularnewline
50 & 1606 & 1716.31972025625 & -110.319720256245 \tabularnewline
51 & 1988 & 2125.24195845269 & -137.241958452692 \tabularnewline
52 & 1901 & 2122.83572334293 & -221.835723342932 \tabularnewline
53 & 1993 & 1999.06580891434 & -6.06580891434487 \tabularnewline
54 & 1993 & 2089.49949141655 & -96.4994914165472 \tabularnewline
55 & 1420 & 1298.16140599468 & 121.838594005321 \tabularnewline
56 & 1927 & 1935.8865495424 & -8.88654954239996 \tabularnewline
57 & 2029 & 1750.91859780553 & 278.081402194473 \tabularnewline
58 & 1899 & 1853.49083630447 & 45.5091636955315 \tabularnewline
59 & 1759 & 1597.31068216961 & 161.689317830386 \tabularnewline
60 & 1496 & 1421.22046952663 & 74.7795304733722 \tabularnewline
61 & 2091 & 1542.17761860355 & 548.822381396454 \tabularnewline
62 & 1850 & 1958.48790800069 & -108.487908000691 \tabularnewline
63 & 2326 & 2357.52403026259 & -31.5240302625898 \tabularnewline
64 & 2212 & 2379.49065381334 & -167.49065381334 \tabularnewline
65 & 2083 & 2373.23388402669 & -290.233884026695 \tabularnewline
66 & 2048 & 2269.45432795733 & -221.454327957329 \tabularnewline
67 & 1642 & 1497.23400176342 & 144.765998236581 \tabularnewline
68 & 2014 & 2094.73778343295 & -80.7377834329545 \tabularnewline
69 & 1844 & 1986.1287934878 & -142.128793487802 \tabularnewline
70 & 1846 & 1761.48402325171 & 84.515976748294 \tabularnewline
71 & 1743 & 1573.98253207454 & 169.017467925464 \tabularnewline
72 & 1337 & 1366.76275027135 & -29.7627502713526 \tabularnewline
73 & 1682 & 1621.70403114724 & 60.2959688527631 \tabularnewline
74 & 1512 & 1500.9157521013 & 11.0842478986956 \tabularnewline
75 & 2050 & 1997.42972029025 & 52.5702797097499 \tabularnewline
76 & 2108 & 2010.97414954122 & 97.0258504587766 \tabularnewline
77 & 1948 & 2101.70766108699 & -153.707661086992 \tabularnewline
78 & 1927 & 2101.4940720276 & -174.494072027599 \tabularnewline
79 & 1641 & 1503.61541934599 & 137.384580654007 \tabularnewline
80 & 1916 & 2005.70928166011 & -89.7092816601137 \tabularnewline
81 & 1921 & 1867.26500699759 & 53.7349930024138 \tabularnewline
82 & 1858 & 1843.01991252055 & 14.9800874794532 \tabularnewline
83 & 1823 & 1651.17387243673 & 171.826127563266 \tabularnewline
84 & 1367 & 1365.01688150557 & 1.98311849443348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261414&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]1881[/C][C]1907.43082264957[/C][C]-26.4308226495732[/C][/ROW]
[ROW][C]14[/C][C]2520[/C][C]2540.76783463186[/C][C]-20.7678346318621[/C][/ROW]
[ROW][C]15[/C][C]2381[/C][C]2383.91206817727[/C][C]-2.91206817727152[/C][/ROW]
[ROW][C]16[/C][C]2419[/C][C]2419.50034052814[/C][C]-0.500340528141351[/C][/ROW]
[ROW][C]17[/C][C]2541[/C][C]2547.92609815246[/C][C]-6.9260981524576[/C][/ROW]
[ROW][C]18[/C][C]2514[/C][C]2510.99662081235[/C][C]3.00337918764762[/C][/ROW]
[ROW][C]19[/C][C]1737[/C][C]1875.99045585001[/C][C]-138.990455850007[/C][/ROW]
[ROW][C]20[/C][C]2221[/C][C]2235.98797666289[/C][C]-14.9879766628915[/C][/ROW]
[ROW][C]21[/C][C]2648[/C][C]2306.25424499309[/C][C]341.745755006913[/C][/ROW]
[ROW][C]22[/C][C]2159[/C][C]2480.64799815202[/C][C]-321.647998152025[/C][/ROW]
[ROW][C]23[/C][C]2184[/C][C]2041.51477213595[/C][C]142.48522786405[/C][/ROW]
[ROW][C]24[/C][C]1745[/C][C]1659.98683509094[/C][C]85.0131649090627[/C][/ROW]
[ROW][C]25[/C][C]1770[/C][C]1844.84162981291[/C][C]-74.8416298129084[/C][/ROW]
[ROW][C]26[/C][C]1871[/C][C]2453.62438212665[/C][C]-582.624382126649[/C][/ROW]
[ROW][C]27[/C][C]2137[/C][C]1992.40727427681[/C][C]144.592725723187[/C][/ROW]
[ROW][C]28[/C][C]2283[/C][C]2110.77471832616[/C][C]172.225281673836[/C][/ROW]
[ROW][C]29[/C][C]2042[/C][C]2332.38781812704[/C][C]-290.387818127037[/C][/ROW]
[ROW][C]30[/C][C]2099[/C][C]2142.27827202185[/C][C]-43.2782720218452[/C][/ROW]
[ROW][C]31[/C][C]1653[/C][C]1424.10590561953[/C][C]228.894094380466[/C][/ROW]
[ROW][C]32[/C][C]2254[/C][C]2038.33725537108[/C][C]215.662744628917[/C][/ROW]
[ROW][C]33[/C][C]2302[/C][C]2380.97390668529[/C][C]-78.9739066852894[/C][/ROW]
[ROW][C]34[/C][C]2233[/C][C]2053.40959884092[/C][C]179.590401159079[/C][/ROW]
[ROW][C]35[/C][C]1974[/C][C]2080.19883856255[/C][C]-106.198838562548[/C][/ROW]
[ROW][C]36[/C][C]1684[/C][C]1537.4838323574[/C][C]146.516167642603[/C][/ROW]
[ROW][C]37[/C][C]1842[/C][C]1691.7144777744[/C][C]150.285522225599[/C][/ROW]
[ROW][C]38[/C][C]1592[/C][C]2219.72375896251[/C][C]-627.723758962511[/C][/ROW]
[ROW][C]39[/C][C]2175[/C][C]2027.97771980756[/C][C]147.02228019244[/C][/ROW]
[ROW][C]40[/C][C]2366[/C][C]2158.88216853154[/C][C]207.117831468459[/C][/ROW]
[ROW][C]41[/C][C]2569[/C][C]2212.5135034144[/C][C]356.4864965856[/C][/ROW]
[ROW][C]42[/C][C]2894[/C][C]2481.21014564386[/C][C]412.789854356143[/C][/ROW]
[ROW][C]43[/C][C]2159[/C][C]2126.17654841515[/C][C]32.8234515848549[/C][/ROW]
[ROW][C]44[/C][C]2877[/C][C]2626.31395314457[/C][C]250.686046855429[/C][/ROW]
[ROW][C]45[/C][C]2419[/C][C]2869.06237830638[/C][C]-450.062378306377[/C][/ROW]
[ROW][C]46[/C][C]2305[/C][C]2440.40548550327[/C][C]-135.405485503271[/C][/ROW]
[ROW][C]47[/C][C]1812[/C][C]2176.77710715507[/C][C]-364.777107155074[/C][/ROW]
[ROW][C]48[/C][C]1514[/C][C]1592.99628910978[/C][C]-78.9962891097753[/C][/ROW]
[ROW][C]49[/C][C]1557[/C][C]1623.68960863912[/C][C]-66.6896086391239[/C][/ROW]
[ROW][C]50[/C][C]1606[/C][C]1716.31972025625[/C][C]-110.319720256245[/C][/ROW]
[ROW][C]51[/C][C]1988[/C][C]2125.24195845269[/C][C]-137.241958452692[/C][/ROW]
[ROW][C]52[/C][C]1901[/C][C]2122.83572334293[/C][C]-221.835723342932[/C][/ROW]
[ROW][C]53[/C][C]1993[/C][C]1999.06580891434[/C][C]-6.06580891434487[/C][/ROW]
[ROW][C]54[/C][C]1993[/C][C]2089.49949141655[/C][C]-96.4994914165472[/C][/ROW]
[ROW][C]55[/C][C]1420[/C][C]1298.16140599468[/C][C]121.838594005321[/C][/ROW]
[ROW][C]56[/C][C]1927[/C][C]1935.8865495424[/C][C]-8.88654954239996[/C][/ROW]
[ROW][C]57[/C][C]2029[/C][C]1750.91859780553[/C][C]278.081402194473[/C][/ROW]
[ROW][C]58[/C][C]1899[/C][C]1853.49083630447[/C][C]45.5091636955315[/C][/ROW]
[ROW][C]59[/C][C]1759[/C][C]1597.31068216961[/C][C]161.689317830386[/C][/ROW]
[ROW][C]60[/C][C]1496[/C][C]1421.22046952663[/C][C]74.7795304733722[/C][/ROW]
[ROW][C]61[/C][C]2091[/C][C]1542.17761860355[/C][C]548.822381396454[/C][/ROW]
[ROW][C]62[/C][C]1850[/C][C]1958.48790800069[/C][C]-108.487908000691[/C][/ROW]
[ROW][C]63[/C][C]2326[/C][C]2357.52403026259[/C][C]-31.5240302625898[/C][/ROW]
[ROW][C]64[/C][C]2212[/C][C]2379.49065381334[/C][C]-167.49065381334[/C][/ROW]
[ROW][C]65[/C][C]2083[/C][C]2373.23388402669[/C][C]-290.233884026695[/C][/ROW]
[ROW][C]66[/C][C]2048[/C][C]2269.45432795733[/C][C]-221.454327957329[/C][/ROW]
[ROW][C]67[/C][C]1642[/C][C]1497.23400176342[/C][C]144.765998236581[/C][/ROW]
[ROW][C]68[/C][C]2014[/C][C]2094.73778343295[/C][C]-80.7377834329545[/C][/ROW]
[ROW][C]69[/C][C]1844[/C][C]1986.1287934878[/C][C]-142.128793487802[/C][/ROW]
[ROW][C]70[/C][C]1846[/C][C]1761.48402325171[/C][C]84.515976748294[/C][/ROW]
[ROW][C]71[/C][C]1743[/C][C]1573.98253207454[/C][C]169.017467925464[/C][/ROW]
[ROW][C]72[/C][C]1337[/C][C]1366.76275027135[/C][C]-29.7627502713526[/C][/ROW]
[ROW][C]73[/C][C]1682[/C][C]1621.70403114724[/C][C]60.2959688527631[/C][/ROW]
[ROW][C]74[/C][C]1512[/C][C]1500.9157521013[/C][C]11.0842478986956[/C][/ROW]
[ROW][C]75[/C][C]2050[/C][C]1997.42972029025[/C][C]52.5702797097499[/C][/ROW]
[ROW][C]76[/C][C]2108[/C][C]2010.97414954122[/C][C]97.0258504587766[/C][/ROW]
[ROW][C]77[/C][C]1948[/C][C]2101.70766108699[/C][C]-153.707661086992[/C][/ROW]
[ROW][C]78[/C][C]1927[/C][C]2101.4940720276[/C][C]-174.494072027599[/C][/ROW]
[ROW][C]79[/C][C]1641[/C][C]1503.61541934599[/C][C]137.384580654007[/C][/ROW]
[ROW][C]80[/C][C]1916[/C][C]2005.70928166011[/C][C]-89.7092816601137[/C][/ROW]
[ROW][C]81[/C][C]1921[/C][C]1867.26500699759[/C][C]53.7349930024138[/C][/ROW]
[ROW][C]82[/C][C]1858[/C][C]1843.01991252055[/C][C]14.9800874794532[/C][/ROW]
[ROW][C]83[/C][C]1823[/C][C]1651.17387243673[/C][C]171.826127563266[/C][/ROW]
[ROW][C]84[/C][C]1367[/C][C]1365.01688150557[/C][C]1.98311849443348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261414&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261414&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
1318811907.43082264957-26.4308226495732
1425202540.76783463186-20.7678346318621
1523812383.91206817727-2.91206817727152
1624192419.50034052814-0.500340528141351
1725412547.92609815246-6.9260981524576
1825142510.996620812353.00337918764762
1917371875.99045585001-138.990455850007
2022212235.98797666289-14.9879766628915
2126482306.25424499309341.745755006913
2221592480.64799815202-321.647998152025
2321842041.51477213595142.48522786405
2417451659.9868350909485.0131649090627
2517701844.84162981291-74.8416298129084
2618712453.62438212665-582.624382126649
2721371992.40727427681144.592725723187
2822832110.77471832616172.225281673836
2920422332.38781812704-290.387818127037
3020992142.27827202185-43.2782720218452
3116531424.10590561953228.894094380466
3222542038.33725537108215.662744628917
3323022380.97390668529-78.9739066852894
3422332053.40959884092179.590401159079
3519742080.19883856255-106.198838562548
3616841537.4838323574146.516167642603
3718421691.7144777744150.285522225599
3815922219.72375896251-627.723758962511
3921752027.97771980756147.02228019244
4023662158.88216853154207.117831468459
4125692212.5135034144356.4864965856
4228942481.21014564386412.789854356143
4321592126.1765484151532.8234515848549
4428772626.31395314457250.686046855429
4524192869.06237830638-450.062378306377
4623052440.40548550327-135.405485503271
4718122176.77710715507-364.777107155074
4815141592.99628910978-78.9962891097753
4915571623.68960863912-66.6896086391239
5016061716.31972025625-110.319720256245
5119882125.24195845269-137.241958452692
5219012122.83572334293-221.835723342932
5319931999.06580891434-6.06580891434487
5419932089.49949141655-96.4994914165472
5514201298.16140599468121.838594005321
5619271935.8865495424-8.88654954239996
5720291750.91859780553278.081402194473
5818991853.4908363044745.5091636955315
5917591597.31068216961161.689317830386
6014961421.2204695266374.7795304733722
6120911542.17761860355548.822381396454
6218501958.48790800069-108.487908000691
6323262357.52403026259-31.5240302625898
6422122379.49065381334-167.49065381334
6520832373.23388402669-290.233884026695
6620482269.45432795733-221.454327957329
6716421497.23400176342144.765998236581
6820142094.73778343295-80.7377834329545
6918441986.1287934878-142.128793487802
7018461761.4840232517184.515976748294
7117431573.98253207454169.017467925464
7213371366.76275027135-29.7627502713526
7316821621.7040311472460.2959688527631
7415121500.915752101311.0842478986956
7520501997.4297202902552.5702797097499
7621082010.9741495412297.0258504587766
7719482101.70766108699-153.707661086992
7819272101.4940720276-174.494072027599
7916411503.61541934599137.384580654007
8019162005.70928166011-89.7092816601137
8119211867.2650069975953.7349930024138
8218581843.0199125205514.9800874794532
8318231651.17387243673171.826127563266
8413671365.016881505571.98311849443348







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
851674.032368930171268.980835836032079.0839020243
861499.87743480541036.707767031011963.04710257978
872007.04386240151492.276402444522521.81132235848
882009.436107147161447.791259832692571.08095446162
891944.828461990011339.928196492292549.72872748773
902021.44006020661376.177533878332666.70258653487
911646.6248963055963.3803393803342329.86945323067
921980.568365618771261.34481118512699.79192005243
931949.961542565891196.475034434182703.4480506976
941880.222772941071093.964981487882666.48056439426
951743.58297850408925.8662113376132561.29974567055
961293.35853339638445.3490358142462141.36803097852

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1674.03236893017 & 1268.98083583603 & 2079.0839020243 \tabularnewline
86 & 1499.8774348054 & 1036.70776703101 & 1963.04710257978 \tabularnewline
87 & 2007.0438624015 & 1492.27640244452 & 2521.81132235848 \tabularnewline
88 & 2009.43610714716 & 1447.79125983269 & 2571.08095446162 \tabularnewline
89 & 1944.82846199001 & 1339.92819649229 & 2549.72872748773 \tabularnewline
90 & 2021.4400602066 & 1376.17753387833 & 2666.70258653487 \tabularnewline
91 & 1646.6248963055 & 963.380339380334 & 2329.86945323067 \tabularnewline
92 & 1980.56836561877 & 1261.3448111851 & 2699.79192005243 \tabularnewline
93 & 1949.96154256589 & 1196.47503443418 & 2703.4480506976 \tabularnewline
94 & 1880.22277294107 & 1093.96498148788 & 2666.48056439426 \tabularnewline
95 & 1743.58297850408 & 925.866211337613 & 2561.29974567055 \tabularnewline
96 & 1293.35853339638 & 445.349035814246 & 2141.36803097852 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261414&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]85[/C][C]1674.03236893017[/C][C]1268.98083583603[/C][C]2079.0839020243[/C][/ROW]
[ROW][C]86[/C][C]1499.8774348054[/C][C]1036.70776703101[/C][C]1963.04710257978[/C][/ROW]
[ROW][C]87[/C][C]2007.0438624015[/C][C]1492.27640244452[/C][C]2521.81132235848[/C][/ROW]
[ROW][C]88[/C][C]2009.43610714716[/C][C]1447.79125983269[/C][C]2571.08095446162[/C][/ROW]
[ROW][C]89[/C][C]1944.82846199001[/C][C]1339.92819649229[/C][C]2549.72872748773[/C][/ROW]
[ROW][C]90[/C][C]2021.4400602066[/C][C]1376.17753387833[/C][C]2666.70258653487[/C][/ROW]
[ROW][C]91[/C][C]1646.6248963055[/C][C]963.380339380334[/C][C]2329.86945323067[/C][/ROW]
[ROW][C]92[/C][C]1980.56836561877[/C][C]1261.3448111851[/C][C]2699.79192005243[/C][/ROW]
[ROW][C]93[/C][C]1949.96154256589[/C][C]1196.47503443418[/C][C]2703.4480506976[/C][/ROW]
[ROW][C]94[/C][C]1880.22277294107[/C][C]1093.96498148788[/C][C]2666.48056439426[/C][/ROW]
[ROW][C]95[/C][C]1743.58297850408[/C][C]925.866211337613[/C][C]2561.29974567055[/C][/ROW]
[ROW][C]96[/C][C]1293.35853339638[/C][C]445.349035814246[/C][C]2141.36803097852[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261414&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261414&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
851674.032368930171268.980835836032079.0839020243
861499.87743480541036.707767031011963.04710257978
872007.04386240151492.276402444522521.81132235848
882009.436107147161447.791259832692571.08095446162
891944.828461990011339.928196492292549.72872748773
902021.44006020661376.177533878332666.70258653487
911646.6248963055963.3803393803342329.86945323067
921980.568365618771261.34481118512699.79192005243
931949.961542565891196.475034434182703.4480506976
941880.222772941071093.964981487882666.48056439426
951743.58297850408925.8662113376132561.29974567055
961293.35853339638445.3490358142462141.36803097852



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')