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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 computationFri, 09 Aug 2013 09:54:03 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Aug/09/t1376056579jbh9klmgjfi1bhd.htm/, Retrieved Fri, 03 May 2024 17:41:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211010, Retrieved Fri, 03 May 2024 17:41:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsNick Hollevoet
Estimated Impact190
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS (B) - S...] [2013-08-09 13:54:03] [3f9aa5867cfe47c4a12580af2904c765] [Current]
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Dataseries X:
1620
1560
1650
1320
1710
1680
1800
1860
2070
1800
1710
2130
1800
1350
1590
1200
1680
1380
1830
1650
1740
1950
1920
2280
1650
1380
1530
1110
1590
1230
1740
1650
1470
2100
1890
2160
1620
1500
1350
1110
1470
1320
1800
1740
1500
2010
1860
2400
1920
1170
1170
1170
1380
1380
1860
1710
1530
1920
1770
2550
2010
1170
1230
1020
1410
1620
2040
2010
1620
1890
1680
2400
1830
1470
1320
990
1470
1770
2070
1950
1440
2070
1620
2490
2070
1500
1380
930
1470
1410
2130
2130
1620
2100
1560
2430
2070
1530
1170
810
1590
1530
2010
2310
1710
1920
1440
2490




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211010&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]5 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=211010&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211010&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 time5 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.616435516556137
beta0.0182153483451415
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.616435516556137 \tabularnewline
beta & 0.0182153483451415 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211010&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]0.616435516556137[/C][/ROW]
[ROW][C]beta[/C][C]0.0182153483451415[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211010&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211010&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
alpha0.616435516556137
beta0.0182153483451415
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
316501500150
413201534.14961563338-214.149615633379
517101341.41987711721368.580122882786
616801512.04408019776167.955919802239
718001560.88230678828239.117693211724
818601656.27213191033203.72786808967
920701732.13398812937337.86601187063
1018001894.47711843369-94.4771184336896
1117101789.24774327257-79.2477432725686
1221301692.51645562302437.483544376979
1318001919.22900852708-119.229008527079
1413501801.42539793382-451.425397933815
1515901473.77526478299116.224735217007
1612001497.34987431254-297.349874312544
1716801262.64358665094417.356413349063
1813801473.19396168535-93.1939616853499
1918301367.97651598873462.023484011267
2016501610.2026944252439.7973055747605
2117401592.60052798825147.399472011753
2219501642.98324649486307.016753505136
2319201795.20709090192124.792909098077
2422801836.50293377302443.497066226977
2516502079.23918406038-429.23918406038
2613801779.17006327651-399.170063276513
2715301493.1545004461436.8454995538591
2811101476.32813923748-366.328139237476
2915901206.85788011256383.142119887435
3012301403.68985219662-173.689852196621
3117401255.32052820192484.679471798082
3216501518.23570446779131.764295532212
3314701565.08095869539-95.0809586953892
3421001471.02311657478628.976883425224
3518901830.3627664539859.6372335460246
3621601839.41087706905320.589122930947
3716202012.91876348515-392.918763485146
3815001742.1831245899-242.183124589895
3913501561.64691267468-211.646912674681
4011101397.5578104118-287.557810411801
4114701183.44566660674286.554333393264
4213201326.45423918299-6.45423918298707
4318001288.76944897733511.230551022666
4417401575.94434689525164.055653104748
4515001650.95042056287-150.950420562867
4620101530.0806024603479.919397539703
4718601803.4901635875456.5098364124647
4824001816.52955883867583.470441161332
4919202160.95773568223-240.957735682229
5011701994.47348841079-824.473488410793
5111701459.03173384425-289.031733844249
5211701250.40987567782-80.4098756778185
5313801169.48705107682210.512948923179
5413801270.2631512386109.736848761397
5518601310.14947386719549.850526132805
5617101627.5115433857482.4884566142571
5715301657.70126302844-127.701263028438
5819201556.88866944138363.111330558625
5917701762.707617922257.29238207775302
6025501749.26901224731800.730987752692
6120102233.92522141035-223.925221410354
6211702084.4325870062-914.432587006204
6312301499.01890153696-269.018901536959
6410201308.44043234252-288.440432342525
6514101102.65106309256307.348936907438
6616201267.57851591709352.421484082909
6720401464.24748317178575.752516828224
6820101805.05051856918204.949481430817
6916201919.57868652023-299.578686520233
7018901719.73392709868170.266072901318
7116801811.43001217853-131.430012178533
7224001715.67414179548684.325858204519
7318302130.46317564693-300.463175646932
7414701934.81949560907-464.819495609072
7513201632.64147612059-312.641476120592
769901420.76087046121-430.760870461214
7714701131.23043873895338.769561261046
7817701319.8697999184450.130200081605
7920701582.21014042611487.789859573886
8019501873.2424237872876.7575762127151
8114401911.76168840703-471.761688407028
8220701606.85697932399463.143020676013
8316201883.46117952505-263.461179525051
8424901709.20244729233780.797552707674
8520702187.42913985202-117.429139852017
8615002110.63843380775-610.638433807747
8713801722.95939468711-342.959394687114
889301496.4362726888-566.436272688803
8914701125.79378661586344.20621338414
9014101320.3686214855689.6313785144444
9121301359.02092031147770.979079688534
9221301826.3371474502303.662852549805
9316202008.99275967848-388.992759678478
9421001760.30301248367339.696987516327
9515601964.61782341439-404.617823414392
9624301705.56726268706724.432737312941
9720702150.63792407899-80.6379240789947
9815302098.52898645185-568.528986451845
9911701739.28289220251-569.282892202509
1008101373.17982081026-563.179820810257
10115901004.51518539436585.484814605641
10215301350.50239542896179.497604571036
10320101448.24017451954561.759825480465
10423101787.92573266417522.074267335832
10517102109.00985995324-399.00985995324
10619201857.8247002529862.1752997470226
10714401891.62859350446-451.628593504464
10824901603.6343671561886.365632843896

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1650 & 1500 & 150 \tabularnewline
4 & 1320 & 1534.14961563338 & -214.149615633379 \tabularnewline
5 & 1710 & 1341.41987711721 & 368.580122882786 \tabularnewline
6 & 1680 & 1512.04408019776 & 167.955919802239 \tabularnewline
7 & 1800 & 1560.88230678828 & 239.117693211724 \tabularnewline
8 & 1860 & 1656.27213191033 & 203.72786808967 \tabularnewline
9 & 2070 & 1732.13398812937 & 337.86601187063 \tabularnewline
10 & 1800 & 1894.47711843369 & -94.4771184336896 \tabularnewline
11 & 1710 & 1789.24774327257 & -79.2477432725686 \tabularnewline
12 & 2130 & 1692.51645562302 & 437.483544376979 \tabularnewline
13 & 1800 & 1919.22900852708 & -119.229008527079 \tabularnewline
14 & 1350 & 1801.42539793382 & -451.425397933815 \tabularnewline
15 & 1590 & 1473.77526478299 & 116.224735217007 \tabularnewline
16 & 1200 & 1497.34987431254 & -297.349874312544 \tabularnewline
17 & 1680 & 1262.64358665094 & 417.356413349063 \tabularnewline
18 & 1380 & 1473.19396168535 & -93.1939616853499 \tabularnewline
19 & 1830 & 1367.97651598873 & 462.023484011267 \tabularnewline
20 & 1650 & 1610.20269442524 & 39.7973055747605 \tabularnewline
21 & 1740 & 1592.60052798825 & 147.399472011753 \tabularnewline
22 & 1950 & 1642.98324649486 & 307.016753505136 \tabularnewline
23 & 1920 & 1795.20709090192 & 124.792909098077 \tabularnewline
24 & 2280 & 1836.50293377302 & 443.497066226977 \tabularnewline
25 & 1650 & 2079.23918406038 & -429.23918406038 \tabularnewline
26 & 1380 & 1779.17006327651 & -399.170063276513 \tabularnewline
27 & 1530 & 1493.15450044614 & 36.8454995538591 \tabularnewline
28 & 1110 & 1476.32813923748 & -366.328139237476 \tabularnewline
29 & 1590 & 1206.85788011256 & 383.142119887435 \tabularnewline
30 & 1230 & 1403.68985219662 & -173.689852196621 \tabularnewline
31 & 1740 & 1255.32052820192 & 484.679471798082 \tabularnewline
32 & 1650 & 1518.23570446779 & 131.764295532212 \tabularnewline
33 & 1470 & 1565.08095869539 & -95.0809586953892 \tabularnewline
34 & 2100 & 1471.02311657478 & 628.976883425224 \tabularnewline
35 & 1890 & 1830.36276645398 & 59.6372335460246 \tabularnewline
36 & 2160 & 1839.41087706905 & 320.589122930947 \tabularnewline
37 & 1620 & 2012.91876348515 & -392.918763485146 \tabularnewline
38 & 1500 & 1742.1831245899 & -242.183124589895 \tabularnewline
39 & 1350 & 1561.64691267468 & -211.646912674681 \tabularnewline
40 & 1110 & 1397.5578104118 & -287.557810411801 \tabularnewline
41 & 1470 & 1183.44566660674 & 286.554333393264 \tabularnewline
42 & 1320 & 1326.45423918299 & -6.45423918298707 \tabularnewline
43 & 1800 & 1288.76944897733 & 511.230551022666 \tabularnewline
44 & 1740 & 1575.94434689525 & 164.055653104748 \tabularnewline
45 & 1500 & 1650.95042056287 & -150.950420562867 \tabularnewline
46 & 2010 & 1530.0806024603 & 479.919397539703 \tabularnewline
47 & 1860 & 1803.49016358754 & 56.5098364124647 \tabularnewline
48 & 2400 & 1816.52955883867 & 583.470441161332 \tabularnewline
49 & 1920 & 2160.95773568223 & -240.957735682229 \tabularnewline
50 & 1170 & 1994.47348841079 & -824.473488410793 \tabularnewline
51 & 1170 & 1459.03173384425 & -289.031733844249 \tabularnewline
52 & 1170 & 1250.40987567782 & -80.4098756778185 \tabularnewline
53 & 1380 & 1169.48705107682 & 210.512948923179 \tabularnewline
54 & 1380 & 1270.2631512386 & 109.736848761397 \tabularnewline
55 & 1860 & 1310.14947386719 & 549.850526132805 \tabularnewline
56 & 1710 & 1627.51154338574 & 82.4884566142571 \tabularnewline
57 & 1530 & 1657.70126302844 & -127.701263028438 \tabularnewline
58 & 1920 & 1556.88866944138 & 363.111330558625 \tabularnewline
59 & 1770 & 1762.70761792225 & 7.29238207775302 \tabularnewline
60 & 2550 & 1749.26901224731 & 800.730987752692 \tabularnewline
61 & 2010 & 2233.92522141035 & -223.925221410354 \tabularnewline
62 & 1170 & 2084.4325870062 & -914.432587006204 \tabularnewline
63 & 1230 & 1499.01890153696 & -269.018901536959 \tabularnewline
64 & 1020 & 1308.44043234252 & -288.440432342525 \tabularnewline
65 & 1410 & 1102.65106309256 & 307.348936907438 \tabularnewline
66 & 1620 & 1267.57851591709 & 352.421484082909 \tabularnewline
67 & 2040 & 1464.24748317178 & 575.752516828224 \tabularnewline
68 & 2010 & 1805.05051856918 & 204.949481430817 \tabularnewline
69 & 1620 & 1919.57868652023 & -299.578686520233 \tabularnewline
70 & 1890 & 1719.73392709868 & 170.266072901318 \tabularnewline
71 & 1680 & 1811.43001217853 & -131.430012178533 \tabularnewline
72 & 2400 & 1715.67414179548 & 684.325858204519 \tabularnewline
73 & 1830 & 2130.46317564693 & -300.463175646932 \tabularnewline
74 & 1470 & 1934.81949560907 & -464.819495609072 \tabularnewline
75 & 1320 & 1632.64147612059 & -312.641476120592 \tabularnewline
76 & 990 & 1420.76087046121 & -430.760870461214 \tabularnewline
77 & 1470 & 1131.23043873895 & 338.769561261046 \tabularnewline
78 & 1770 & 1319.8697999184 & 450.130200081605 \tabularnewline
79 & 2070 & 1582.21014042611 & 487.789859573886 \tabularnewline
80 & 1950 & 1873.24242378728 & 76.7575762127151 \tabularnewline
81 & 1440 & 1911.76168840703 & -471.761688407028 \tabularnewline
82 & 2070 & 1606.85697932399 & 463.143020676013 \tabularnewline
83 & 1620 & 1883.46117952505 & -263.461179525051 \tabularnewline
84 & 2490 & 1709.20244729233 & 780.797552707674 \tabularnewline
85 & 2070 & 2187.42913985202 & -117.429139852017 \tabularnewline
86 & 1500 & 2110.63843380775 & -610.638433807747 \tabularnewline
87 & 1380 & 1722.95939468711 & -342.959394687114 \tabularnewline
88 & 930 & 1496.4362726888 & -566.436272688803 \tabularnewline
89 & 1470 & 1125.79378661586 & 344.20621338414 \tabularnewline
90 & 1410 & 1320.36862148556 & 89.6313785144444 \tabularnewline
91 & 2130 & 1359.02092031147 & 770.979079688534 \tabularnewline
92 & 2130 & 1826.3371474502 & 303.662852549805 \tabularnewline
93 & 1620 & 2008.99275967848 & -388.992759678478 \tabularnewline
94 & 2100 & 1760.30301248367 & 339.696987516327 \tabularnewline
95 & 1560 & 1964.61782341439 & -404.617823414392 \tabularnewline
96 & 2430 & 1705.56726268706 & 724.432737312941 \tabularnewline
97 & 2070 & 2150.63792407899 & -80.6379240789947 \tabularnewline
98 & 1530 & 2098.52898645185 & -568.528986451845 \tabularnewline
99 & 1170 & 1739.28289220251 & -569.282892202509 \tabularnewline
100 & 810 & 1373.17982081026 & -563.179820810257 \tabularnewline
101 & 1590 & 1004.51518539436 & 585.484814605641 \tabularnewline
102 & 1530 & 1350.50239542896 & 179.497604571036 \tabularnewline
103 & 2010 & 1448.24017451954 & 561.759825480465 \tabularnewline
104 & 2310 & 1787.92573266417 & 522.074267335832 \tabularnewline
105 & 1710 & 2109.00985995324 & -399.00985995324 \tabularnewline
106 & 1920 & 1857.82470025298 & 62.1752997470226 \tabularnewline
107 & 1440 & 1891.62859350446 & -451.628593504464 \tabularnewline
108 & 2490 & 1603.6343671561 & 886.365632843896 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211010&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]3[/C][C]1650[/C][C]1500[/C][C]150[/C][/ROW]
[ROW][C]4[/C][C]1320[/C][C]1534.14961563338[/C][C]-214.149615633379[/C][/ROW]
[ROW][C]5[/C][C]1710[/C][C]1341.41987711721[/C][C]368.580122882786[/C][/ROW]
[ROW][C]6[/C][C]1680[/C][C]1512.04408019776[/C][C]167.955919802239[/C][/ROW]
[ROW][C]7[/C][C]1800[/C][C]1560.88230678828[/C][C]239.117693211724[/C][/ROW]
[ROW][C]8[/C][C]1860[/C][C]1656.27213191033[/C][C]203.72786808967[/C][/ROW]
[ROW][C]9[/C][C]2070[/C][C]1732.13398812937[/C][C]337.86601187063[/C][/ROW]
[ROW][C]10[/C][C]1800[/C][C]1894.47711843369[/C][C]-94.4771184336896[/C][/ROW]
[ROW][C]11[/C][C]1710[/C][C]1789.24774327257[/C][C]-79.2477432725686[/C][/ROW]
[ROW][C]12[/C][C]2130[/C][C]1692.51645562302[/C][C]437.483544376979[/C][/ROW]
[ROW][C]13[/C][C]1800[/C][C]1919.22900852708[/C][C]-119.229008527079[/C][/ROW]
[ROW][C]14[/C][C]1350[/C][C]1801.42539793382[/C][C]-451.425397933815[/C][/ROW]
[ROW][C]15[/C][C]1590[/C][C]1473.77526478299[/C][C]116.224735217007[/C][/ROW]
[ROW][C]16[/C][C]1200[/C][C]1497.34987431254[/C][C]-297.349874312544[/C][/ROW]
[ROW][C]17[/C][C]1680[/C][C]1262.64358665094[/C][C]417.356413349063[/C][/ROW]
[ROW][C]18[/C][C]1380[/C][C]1473.19396168535[/C][C]-93.1939616853499[/C][/ROW]
[ROW][C]19[/C][C]1830[/C][C]1367.97651598873[/C][C]462.023484011267[/C][/ROW]
[ROW][C]20[/C][C]1650[/C][C]1610.20269442524[/C][C]39.7973055747605[/C][/ROW]
[ROW][C]21[/C][C]1740[/C][C]1592.60052798825[/C][C]147.399472011753[/C][/ROW]
[ROW][C]22[/C][C]1950[/C][C]1642.98324649486[/C][C]307.016753505136[/C][/ROW]
[ROW][C]23[/C][C]1920[/C][C]1795.20709090192[/C][C]124.792909098077[/C][/ROW]
[ROW][C]24[/C][C]2280[/C][C]1836.50293377302[/C][C]443.497066226977[/C][/ROW]
[ROW][C]25[/C][C]1650[/C][C]2079.23918406038[/C][C]-429.23918406038[/C][/ROW]
[ROW][C]26[/C][C]1380[/C][C]1779.17006327651[/C][C]-399.170063276513[/C][/ROW]
[ROW][C]27[/C][C]1530[/C][C]1493.15450044614[/C][C]36.8454995538591[/C][/ROW]
[ROW][C]28[/C][C]1110[/C][C]1476.32813923748[/C][C]-366.328139237476[/C][/ROW]
[ROW][C]29[/C][C]1590[/C][C]1206.85788011256[/C][C]383.142119887435[/C][/ROW]
[ROW][C]30[/C][C]1230[/C][C]1403.68985219662[/C][C]-173.689852196621[/C][/ROW]
[ROW][C]31[/C][C]1740[/C][C]1255.32052820192[/C][C]484.679471798082[/C][/ROW]
[ROW][C]32[/C][C]1650[/C][C]1518.23570446779[/C][C]131.764295532212[/C][/ROW]
[ROW][C]33[/C][C]1470[/C][C]1565.08095869539[/C][C]-95.0809586953892[/C][/ROW]
[ROW][C]34[/C][C]2100[/C][C]1471.02311657478[/C][C]628.976883425224[/C][/ROW]
[ROW][C]35[/C][C]1890[/C][C]1830.36276645398[/C][C]59.6372335460246[/C][/ROW]
[ROW][C]36[/C][C]2160[/C][C]1839.41087706905[/C][C]320.589122930947[/C][/ROW]
[ROW][C]37[/C][C]1620[/C][C]2012.91876348515[/C][C]-392.918763485146[/C][/ROW]
[ROW][C]38[/C][C]1500[/C][C]1742.1831245899[/C][C]-242.183124589895[/C][/ROW]
[ROW][C]39[/C][C]1350[/C][C]1561.64691267468[/C][C]-211.646912674681[/C][/ROW]
[ROW][C]40[/C][C]1110[/C][C]1397.5578104118[/C][C]-287.557810411801[/C][/ROW]
[ROW][C]41[/C][C]1470[/C][C]1183.44566660674[/C][C]286.554333393264[/C][/ROW]
[ROW][C]42[/C][C]1320[/C][C]1326.45423918299[/C][C]-6.45423918298707[/C][/ROW]
[ROW][C]43[/C][C]1800[/C][C]1288.76944897733[/C][C]511.230551022666[/C][/ROW]
[ROW][C]44[/C][C]1740[/C][C]1575.94434689525[/C][C]164.055653104748[/C][/ROW]
[ROW][C]45[/C][C]1500[/C][C]1650.95042056287[/C][C]-150.950420562867[/C][/ROW]
[ROW][C]46[/C][C]2010[/C][C]1530.0806024603[/C][C]479.919397539703[/C][/ROW]
[ROW][C]47[/C][C]1860[/C][C]1803.49016358754[/C][C]56.5098364124647[/C][/ROW]
[ROW][C]48[/C][C]2400[/C][C]1816.52955883867[/C][C]583.470441161332[/C][/ROW]
[ROW][C]49[/C][C]1920[/C][C]2160.95773568223[/C][C]-240.957735682229[/C][/ROW]
[ROW][C]50[/C][C]1170[/C][C]1994.47348841079[/C][C]-824.473488410793[/C][/ROW]
[ROW][C]51[/C][C]1170[/C][C]1459.03173384425[/C][C]-289.031733844249[/C][/ROW]
[ROW][C]52[/C][C]1170[/C][C]1250.40987567782[/C][C]-80.4098756778185[/C][/ROW]
[ROW][C]53[/C][C]1380[/C][C]1169.48705107682[/C][C]210.512948923179[/C][/ROW]
[ROW][C]54[/C][C]1380[/C][C]1270.2631512386[/C][C]109.736848761397[/C][/ROW]
[ROW][C]55[/C][C]1860[/C][C]1310.14947386719[/C][C]549.850526132805[/C][/ROW]
[ROW][C]56[/C][C]1710[/C][C]1627.51154338574[/C][C]82.4884566142571[/C][/ROW]
[ROW][C]57[/C][C]1530[/C][C]1657.70126302844[/C][C]-127.701263028438[/C][/ROW]
[ROW][C]58[/C][C]1920[/C][C]1556.88866944138[/C][C]363.111330558625[/C][/ROW]
[ROW][C]59[/C][C]1770[/C][C]1762.70761792225[/C][C]7.29238207775302[/C][/ROW]
[ROW][C]60[/C][C]2550[/C][C]1749.26901224731[/C][C]800.730987752692[/C][/ROW]
[ROW][C]61[/C][C]2010[/C][C]2233.92522141035[/C][C]-223.925221410354[/C][/ROW]
[ROW][C]62[/C][C]1170[/C][C]2084.4325870062[/C][C]-914.432587006204[/C][/ROW]
[ROW][C]63[/C][C]1230[/C][C]1499.01890153696[/C][C]-269.018901536959[/C][/ROW]
[ROW][C]64[/C][C]1020[/C][C]1308.44043234252[/C][C]-288.440432342525[/C][/ROW]
[ROW][C]65[/C][C]1410[/C][C]1102.65106309256[/C][C]307.348936907438[/C][/ROW]
[ROW][C]66[/C][C]1620[/C][C]1267.57851591709[/C][C]352.421484082909[/C][/ROW]
[ROW][C]67[/C][C]2040[/C][C]1464.24748317178[/C][C]575.752516828224[/C][/ROW]
[ROW][C]68[/C][C]2010[/C][C]1805.05051856918[/C][C]204.949481430817[/C][/ROW]
[ROW][C]69[/C][C]1620[/C][C]1919.57868652023[/C][C]-299.578686520233[/C][/ROW]
[ROW][C]70[/C][C]1890[/C][C]1719.73392709868[/C][C]170.266072901318[/C][/ROW]
[ROW][C]71[/C][C]1680[/C][C]1811.43001217853[/C][C]-131.430012178533[/C][/ROW]
[ROW][C]72[/C][C]2400[/C][C]1715.67414179548[/C][C]684.325858204519[/C][/ROW]
[ROW][C]73[/C][C]1830[/C][C]2130.46317564693[/C][C]-300.463175646932[/C][/ROW]
[ROW][C]74[/C][C]1470[/C][C]1934.81949560907[/C][C]-464.819495609072[/C][/ROW]
[ROW][C]75[/C][C]1320[/C][C]1632.64147612059[/C][C]-312.641476120592[/C][/ROW]
[ROW][C]76[/C][C]990[/C][C]1420.76087046121[/C][C]-430.760870461214[/C][/ROW]
[ROW][C]77[/C][C]1470[/C][C]1131.23043873895[/C][C]338.769561261046[/C][/ROW]
[ROW][C]78[/C][C]1770[/C][C]1319.8697999184[/C][C]450.130200081605[/C][/ROW]
[ROW][C]79[/C][C]2070[/C][C]1582.21014042611[/C][C]487.789859573886[/C][/ROW]
[ROW][C]80[/C][C]1950[/C][C]1873.24242378728[/C][C]76.7575762127151[/C][/ROW]
[ROW][C]81[/C][C]1440[/C][C]1911.76168840703[/C][C]-471.761688407028[/C][/ROW]
[ROW][C]82[/C][C]2070[/C][C]1606.85697932399[/C][C]463.143020676013[/C][/ROW]
[ROW][C]83[/C][C]1620[/C][C]1883.46117952505[/C][C]-263.461179525051[/C][/ROW]
[ROW][C]84[/C][C]2490[/C][C]1709.20244729233[/C][C]780.797552707674[/C][/ROW]
[ROW][C]85[/C][C]2070[/C][C]2187.42913985202[/C][C]-117.429139852017[/C][/ROW]
[ROW][C]86[/C][C]1500[/C][C]2110.63843380775[/C][C]-610.638433807747[/C][/ROW]
[ROW][C]87[/C][C]1380[/C][C]1722.95939468711[/C][C]-342.959394687114[/C][/ROW]
[ROW][C]88[/C][C]930[/C][C]1496.4362726888[/C][C]-566.436272688803[/C][/ROW]
[ROW][C]89[/C][C]1470[/C][C]1125.79378661586[/C][C]344.20621338414[/C][/ROW]
[ROW][C]90[/C][C]1410[/C][C]1320.36862148556[/C][C]89.6313785144444[/C][/ROW]
[ROW][C]91[/C][C]2130[/C][C]1359.02092031147[/C][C]770.979079688534[/C][/ROW]
[ROW][C]92[/C][C]2130[/C][C]1826.3371474502[/C][C]303.662852549805[/C][/ROW]
[ROW][C]93[/C][C]1620[/C][C]2008.99275967848[/C][C]-388.992759678478[/C][/ROW]
[ROW][C]94[/C][C]2100[/C][C]1760.30301248367[/C][C]339.696987516327[/C][/ROW]
[ROW][C]95[/C][C]1560[/C][C]1964.61782341439[/C][C]-404.617823414392[/C][/ROW]
[ROW][C]96[/C][C]2430[/C][C]1705.56726268706[/C][C]724.432737312941[/C][/ROW]
[ROW][C]97[/C][C]2070[/C][C]2150.63792407899[/C][C]-80.6379240789947[/C][/ROW]
[ROW][C]98[/C][C]1530[/C][C]2098.52898645185[/C][C]-568.528986451845[/C][/ROW]
[ROW][C]99[/C][C]1170[/C][C]1739.28289220251[/C][C]-569.282892202509[/C][/ROW]
[ROW][C]100[/C][C]810[/C][C]1373.17982081026[/C][C]-563.179820810257[/C][/ROW]
[ROW][C]101[/C][C]1590[/C][C]1004.51518539436[/C][C]585.484814605641[/C][/ROW]
[ROW][C]102[/C][C]1530[/C][C]1350.50239542896[/C][C]179.497604571036[/C][/ROW]
[ROW][C]103[/C][C]2010[/C][C]1448.24017451954[/C][C]561.759825480465[/C][/ROW]
[ROW][C]104[/C][C]2310[/C][C]1787.92573266417[/C][C]522.074267335832[/C][/ROW]
[ROW][C]105[/C][C]1710[/C][C]2109.00985995324[/C][C]-399.00985995324[/C][/ROW]
[ROW][C]106[/C][C]1920[/C][C]1857.82470025298[/C][C]62.1752997470226[/C][/ROW]
[ROW][C]107[/C][C]1440[/C][C]1891.62859350446[/C][C]-451.628593504464[/C][/ROW]
[ROW][C]108[/C][C]2490[/C][C]1603.6343671561[/C][C]886.365632843896[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211010&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211010&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
316501500150
413201534.14961563338-214.149615633379
517101341.41987711721368.580122882786
616801512.04408019776167.955919802239
718001560.88230678828239.117693211724
818601656.27213191033203.72786808967
920701732.13398812937337.86601187063
1018001894.47711843369-94.4771184336896
1117101789.24774327257-79.2477432725686
1221301692.51645562302437.483544376979
1318001919.22900852708-119.229008527079
1413501801.42539793382-451.425397933815
1515901473.77526478299116.224735217007
1612001497.34987431254-297.349874312544
1716801262.64358665094417.356413349063
1813801473.19396168535-93.1939616853499
1918301367.97651598873462.023484011267
2016501610.2026944252439.7973055747605
2117401592.60052798825147.399472011753
2219501642.98324649486307.016753505136
2319201795.20709090192124.792909098077
2422801836.50293377302443.497066226977
2516502079.23918406038-429.23918406038
2613801779.17006327651-399.170063276513
2715301493.1545004461436.8454995538591
2811101476.32813923748-366.328139237476
2915901206.85788011256383.142119887435
3012301403.68985219662-173.689852196621
3117401255.32052820192484.679471798082
3216501518.23570446779131.764295532212
3314701565.08095869539-95.0809586953892
3421001471.02311657478628.976883425224
3518901830.3627664539859.6372335460246
3621601839.41087706905320.589122930947
3716202012.91876348515-392.918763485146
3815001742.1831245899-242.183124589895
3913501561.64691267468-211.646912674681
4011101397.5578104118-287.557810411801
4114701183.44566660674286.554333393264
4213201326.45423918299-6.45423918298707
4318001288.76944897733511.230551022666
4417401575.94434689525164.055653104748
4515001650.95042056287-150.950420562867
4620101530.0806024603479.919397539703
4718601803.4901635875456.5098364124647
4824001816.52955883867583.470441161332
4919202160.95773568223-240.957735682229
5011701994.47348841079-824.473488410793
5111701459.03173384425-289.031733844249
5211701250.40987567782-80.4098756778185
5313801169.48705107682210.512948923179
5413801270.2631512386109.736848761397
5518601310.14947386719549.850526132805
5617101627.5115433857482.4884566142571
5715301657.70126302844-127.701263028438
5819201556.88866944138363.111330558625
5917701762.707617922257.29238207775302
6025501749.26901224731800.730987752692
6120102233.92522141035-223.925221410354
6211702084.4325870062-914.432587006204
6312301499.01890153696-269.018901536959
6410201308.44043234252-288.440432342525
6514101102.65106309256307.348936907438
6616201267.57851591709352.421484082909
6720401464.24748317178575.752516828224
6820101805.05051856918204.949481430817
6916201919.57868652023-299.578686520233
7018901719.73392709868170.266072901318
7116801811.43001217853-131.430012178533
7224001715.67414179548684.325858204519
7318302130.46317564693-300.463175646932
7414701934.81949560907-464.819495609072
7513201632.64147612059-312.641476120592
769901420.76087046121-430.760870461214
7714701131.23043873895338.769561261046
7817701319.8697999184450.130200081605
7920701582.21014042611487.789859573886
8019501873.2424237872876.7575762127151
8114401911.76168840703-471.761688407028
8220701606.85697932399463.143020676013
8316201883.46117952505-263.461179525051
8424901709.20244729233780.797552707674
8520702187.42913985202-117.429139852017
8615002110.63843380775-610.638433807747
8713801722.95939468711-342.959394687114
889301496.4362726888-566.436272688803
8914701125.79378661586344.20621338414
9014101320.3686214855689.6313785144444
9121301359.02092031147770.979079688534
9221301826.3371474502303.662852549805
9316202008.99275967848-388.992759678478
9421001760.30301248367339.696987516327
9515601964.61782341439-404.617823414392
9624301705.56726268706724.432737312941
9720702150.63792407899-80.6379240789947
9815302098.52898645185-568.528986451845
9911701739.28289220251-569.282892202509
1008101373.17982081026-563.179820810257
10115901004.51518539436585.484814605641
10215301350.50239542896179.497604571036
10320101448.24017451954561.759825480465
10423101787.92573266417522.074267335832
10517102109.00985995324-399.00985995324
10619201857.8247002529862.1752997470226
10714401891.62859350446-451.628593504464
10824901603.6343671561886.365632843896







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092150.379937088781377.657288295272923.1025858823
1102150.738250281731238.414155918143063.06234464532
1112151.096563474681113.762498599513188.43062834985
1122151.45487666762998.8790721494443304.0306811858
1132151.81318986057891.0226091505383412.6037705706
1142152.17150305352788.4639691190483515.87903698798
1152152.52981624646690.0327733475223615.0268591454
1162152.88812943941594.8953368493283710.88092202949
1172153.24644263235502.434330927013804.0585543377
1182153.6047558253412.1784938551443895.03101779546
1192153.96306901825323.7591183172693984.16701971923
1202154.32138221119236.8818342151264071.76093020726

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2150.37993708878 & 1377.65728829527 & 2923.1025858823 \tabularnewline
110 & 2150.73825028173 & 1238.41415591814 & 3063.06234464532 \tabularnewline
111 & 2151.09656347468 & 1113.76249859951 & 3188.43062834985 \tabularnewline
112 & 2151.45487666762 & 998.879072149444 & 3304.0306811858 \tabularnewline
113 & 2151.81318986057 & 891.022609150538 & 3412.6037705706 \tabularnewline
114 & 2152.17150305352 & 788.463969119048 & 3515.87903698798 \tabularnewline
115 & 2152.52981624646 & 690.032773347522 & 3615.0268591454 \tabularnewline
116 & 2152.88812943941 & 594.895336849328 & 3710.88092202949 \tabularnewline
117 & 2153.24644263235 & 502.43433092701 & 3804.0585543377 \tabularnewline
118 & 2153.6047558253 & 412.178493855144 & 3895.03101779546 \tabularnewline
119 & 2153.96306901825 & 323.759118317269 & 3984.16701971923 \tabularnewline
120 & 2154.32138221119 & 236.881834215126 & 4071.76093020726 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211010&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]109[/C][C]2150.37993708878[/C][C]1377.65728829527[/C][C]2923.1025858823[/C][/ROW]
[ROW][C]110[/C][C]2150.73825028173[/C][C]1238.41415591814[/C][C]3063.06234464532[/C][/ROW]
[ROW][C]111[/C][C]2151.09656347468[/C][C]1113.76249859951[/C][C]3188.43062834985[/C][/ROW]
[ROW][C]112[/C][C]2151.45487666762[/C][C]998.879072149444[/C][C]3304.0306811858[/C][/ROW]
[ROW][C]113[/C][C]2151.81318986057[/C][C]891.022609150538[/C][C]3412.6037705706[/C][/ROW]
[ROW][C]114[/C][C]2152.17150305352[/C][C]788.463969119048[/C][C]3515.87903698798[/C][/ROW]
[ROW][C]115[/C][C]2152.52981624646[/C][C]690.032773347522[/C][C]3615.0268591454[/C][/ROW]
[ROW][C]116[/C][C]2152.88812943941[/C][C]594.895336849328[/C][C]3710.88092202949[/C][/ROW]
[ROW][C]117[/C][C]2153.24644263235[/C][C]502.43433092701[/C][C]3804.0585543377[/C][/ROW]
[ROW][C]118[/C][C]2153.6047558253[/C][C]412.178493855144[/C][C]3895.03101779546[/C][/ROW]
[ROW][C]119[/C][C]2153.96306901825[/C][C]323.759118317269[/C][C]3984.16701971923[/C][/ROW]
[ROW][C]120[/C][C]2154.32138221119[/C][C]236.881834215126[/C][C]4071.76093020726[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211010&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211010&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
1092150.379937088781377.657288295272923.1025858823
1102150.738250281731238.414155918143063.06234464532
1112151.096563474681113.762498599513188.43062834985
1122151.45487666762998.8790721494443304.0306811858
1132151.81318986057891.0226091505383412.6037705706
1142152.17150305352788.4639691190483515.87903698798
1152152.52981624646690.0327733475223615.0268591454
1162152.88812943941594.8953368493283710.88092202949
1172153.24644263235502.434330927013804.0585543377
1182153.6047558253412.1784938551443895.03101779546
1192153.96306901825323.7591183172693984.16701971923
1202154.32138221119236.8818342151264071.76093020726



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')