Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 17 Aug 2008 11:01:50 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Aug/17/t121899257118cf8xghfeybnhx.htm/, Retrieved Tue, 14 May 2024 23:20:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14186, Retrieved Tue, 14 May 2024 23:20:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsAlain Piscaer 2MAR04
Estimated Impact187
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10] [2008-08-17 17:01:50] [a3ab1f5d18edf6efe0d68a62d436c7a5] [Current]
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Dataseries X:
2005/12
2005/11
2005/10
2005/09
2005/08
2005/07
2005/06
2005/05
2005/04
2005/03
2005/02
2005/01
2004/12
2004/11
2004/10
2004/09
2004/08
2004/07
2004/06
2004/05
2004/04
2004/03
2004/02
2004/01
2003/12
2003/11
2003/10
2003/09
2003/08
2003/07
2003/06
2003/05
2003/04
2003/03
2003/02
2003/01
2002/12
2002/11
2002/10
2002/09
2002/08
2002/07
2002/06
2002/05
2002/04
2002/03
2002/02
2002/01
2001/12
2001/11
2001/10
2001/09
2001/08
2001/07
2001/06
2001/05
2001/04
2001/03
2001/02
2001/01
2000/12
2000/11
2000/10
2000/09
2000/08
2000/07
2000/06
2000/05
2000/04
2000/03
2000/02
2000/01
1999/12
1999/11
1999/10
1999/09
1999/08
1999/07
1999/06
1999/05
1999/04
1999/03
1999/02
1999/01
1998/12
1998/11
1998/10
1998/09
1998/08
1998/07
1998/06
1998/05
1998/04
1998/03
1998/02
1998/01




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14186&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14186&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14186&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0587893134639656
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0587893134639656 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14186&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]0.0587893134639656[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14186&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14186&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
alpha0.0587893134639656
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2182.272727272727167.08333333333315.1893939393939
3200.5167.97630737496432.523692625036
4222.777777777778169.88835293570352.8894248420748
5250.625172.99768591167377.6273140883275
6286.428571428571177.561342412977108.867229015595
7334.166666666667183.961572065528150.205094601139
8401192.792026455919208.207973544081
9501.25205.032430278299296.217569721701
10668.333333333333222.446857838202445.886475495131
111002.5248.660217615428753.839782384572
122005292.9779408836421712.02205911636
13167393.626542374258-226.626542374258
14182.181818181818380.303323535363-198.121505353545
15200.4368.655896253181-168.255896253181
16222.666666666667358.764247626192-136.097580959525
17250.5350.763164277475-100.263164277475
18286.285714285714344.868761683877-58.5830473981632
19334341.424704546712-7.42470454671246
20400.8340.98821126373859.8117887362616
21501344.504505260595156.495494739405
22668353.704767956528314.295232043472
231002372.181968873362629.818031126638
242004409.2085385305231594.79146146948
25166.916666666667502.965233668508-336.048567001842
26182.090909090909483.20916912392-301.118260033011
27200.3465.506633345116-265.206633345116
28222.555555555556449.915317444667-227.359761889111
29250.375436.548993133875-186.173993133875
30286.142857142857425.60395189269-139.461094749833
31333.833333333333417.405129877414-83.5717965440808
32400.6412.492001333637-11.8920013336373
33500.75411.7928787395288.9571212604798
34667.666666666667417.022606826155250.644059840512
351001.5431.757799027999569.742200972
362003465.2525518745921537.74744812541
37166.833333333333555.65566863085-388.822335297516
38182532.797070479253-350.797070479253
39200.2512.173951540607-311.973951540607
40222.444444444444493.833217110895-271.38877266645
41250.25477.878457484006-227.628457484006
42286464.496336743659-178.496336743659
43333.666666666667454.002659650667-120.335992984000
44400.4446.928189238133-46.5281892381329
45500.5444.19282893610256.3071710638984
46667.333333333333447.503088866046219.830244467287
471001460.426758016894540.573241983106
482002492.2066877900711509.79331220993
49166.75580.966400087379-414.216400087379
50181.909090909091556.614902300727-374.705811391636
51200.1534.586204898054-334.486204898054
52222.333333333333514.92199054893-292.588657215597
53250.125497.720904263882-247.595904263882
54285.857142857143483.164911035718-197.307768178576
55333.5471.565322803393-138.065322803393
56400.2463.448557262601-63.2485572626005
57500.25459.73021800354640.5197819964541
58667462.112348168827204.887651831173
591000.5474.157552557226526.342447442774
602001505.100863689331495.89913631067
61166.666666666667593.043746924373-426.377080257707
62181.818181818182567.977331099252-386.159149281071
63200545.275299825189-345.275299825189
64222.222222222222524.976801992401-302.754579770179
65250507.178068099641-257.178068099641
66285.714285714286492.058746038074-206.344460323789
67333.333333333333479.927896878546-146.594563545213
68400471.309703130174-71.3097031301735
69500467.11745463983132.8825453601685
70666.666666666667469.050596906503197.616069760163
711000480.668309977151519.331690022849
722000511.1994634936751488.80053650632
73166.583333333333598.725024919665-432.141691586332
74181.727272727273573.319711552148-391.592438824875
75199.9550.298260915954-350.398260915954
76222.111111111111529.698587717737-307.587476606626
77249.875511.61573113792-261.74073113792
78285.571428571429496.228173248766-210.656744677337
79333.166666666667483.843807852631-150.677141185964
80399.8474.985602167595-75.1856021675952
81499.75470.56549223378729.1845077662126
82666.333333333333472.281229409147194.052103924186
83999.5483.689419375088515.810580624912
841999514.0135692874761484.98643071252
85166.5601.31490205237-434.81490205237
86181.636363636364575.75243247681-394.116068840446
87199.8552.582619364563-352.782619364563
88222531.842771370101-309.842771370101
89249.75513.62732755948-263.87732755948
90285.428571428571498.114160633552-212.685589204981
91333485.610520860512-152.610520860512
92399.6476.638653111745-77.0386531117446
93499.5472.10960358511727.3903964148834
94666473.719866185853192.280133814147
95999485.023883245547513.976116754453
961998515.2401862864161482.75981371358

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 182.272727272727 & 167.083333333333 & 15.1893939393939 \tabularnewline
3 & 200.5 & 167.976307374964 & 32.523692625036 \tabularnewline
4 & 222.777777777778 & 169.888352935703 & 52.8894248420748 \tabularnewline
5 & 250.625 & 172.997685911673 & 77.6273140883275 \tabularnewline
6 & 286.428571428571 & 177.561342412977 & 108.867229015595 \tabularnewline
7 & 334.166666666667 & 183.961572065528 & 150.205094601139 \tabularnewline
8 & 401 & 192.792026455919 & 208.207973544081 \tabularnewline
9 & 501.25 & 205.032430278299 & 296.217569721701 \tabularnewline
10 & 668.333333333333 & 222.446857838202 & 445.886475495131 \tabularnewline
11 & 1002.5 & 248.660217615428 & 753.839782384572 \tabularnewline
12 & 2005 & 292.977940883642 & 1712.02205911636 \tabularnewline
13 & 167 & 393.626542374258 & -226.626542374258 \tabularnewline
14 & 182.181818181818 & 380.303323535363 & -198.121505353545 \tabularnewline
15 & 200.4 & 368.655896253181 & -168.255896253181 \tabularnewline
16 & 222.666666666667 & 358.764247626192 & -136.097580959525 \tabularnewline
17 & 250.5 & 350.763164277475 & -100.263164277475 \tabularnewline
18 & 286.285714285714 & 344.868761683877 & -58.5830473981632 \tabularnewline
19 & 334 & 341.424704546712 & -7.42470454671246 \tabularnewline
20 & 400.8 & 340.988211263738 & 59.8117887362616 \tabularnewline
21 & 501 & 344.504505260595 & 156.495494739405 \tabularnewline
22 & 668 & 353.704767956528 & 314.295232043472 \tabularnewline
23 & 1002 & 372.181968873362 & 629.818031126638 \tabularnewline
24 & 2004 & 409.208538530523 & 1594.79146146948 \tabularnewline
25 & 166.916666666667 & 502.965233668508 & -336.048567001842 \tabularnewline
26 & 182.090909090909 & 483.20916912392 & -301.118260033011 \tabularnewline
27 & 200.3 & 465.506633345116 & -265.206633345116 \tabularnewline
28 & 222.555555555556 & 449.915317444667 & -227.359761889111 \tabularnewline
29 & 250.375 & 436.548993133875 & -186.173993133875 \tabularnewline
30 & 286.142857142857 & 425.60395189269 & -139.461094749833 \tabularnewline
31 & 333.833333333333 & 417.405129877414 & -83.5717965440808 \tabularnewline
32 & 400.6 & 412.492001333637 & -11.8920013336373 \tabularnewline
33 & 500.75 & 411.79287873952 & 88.9571212604798 \tabularnewline
34 & 667.666666666667 & 417.022606826155 & 250.644059840512 \tabularnewline
35 & 1001.5 & 431.757799027999 & 569.742200972 \tabularnewline
36 & 2003 & 465.252551874592 & 1537.74744812541 \tabularnewline
37 & 166.833333333333 & 555.65566863085 & -388.822335297516 \tabularnewline
38 & 182 & 532.797070479253 & -350.797070479253 \tabularnewline
39 & 200.2 & 512.173951540607 & -311.973951540607 \tabularnewline
40 & 222.444444444444 & 493.833217110895 & -271.38877266645 \tabularnewline
41 & 250.25 & 477.878457484006 & -227.628457484006 \tabularnewline
42 & 286 & 464.496336743659 & -178.496336743659 \tabularnewline
43 & 333.666666666667 & 454.002659650667 & -120.335992984000 \tabularnewline
44 & 400.4 & 446.928189238133 & -46.5281892381329 \tabularnewline
45 & 500.5 & 444.192828936102 & 56.3071710638984 \tabularnewline
46 & 667.333333333333 & 447.503088866046 & 219.830244467287 \tabularnewline
47 & 1001 & 460.426758016894 & 540.573241983106 \tabularnewline
48 & 2002 & 492.206687790071 & 1509.79331220993 \tabularnewline
49 & 166.75 & 580.966400087379 & -414.216400087379 \tabularnewline
50 & 181.909090909091 & 556.614902300727 & -374.705811391636 \tabularnewline
51 & 200.1 & 534.586204898054 & -334.486204898054 \tabularnewline
52 & 222.333333333333 & 514.92199054893 & -292.588657215597 \tabularnewline
53 & 250.125 & 497.720904263882 & -247.595904263882 \tabularnewline
54 & 285.857142857143 & 483.164911035718 & -197.307768178576 \tabularnewline
55 & 333.5 & 471.565322803393 & -138.065322803393 \tabularnewline
56 & 400.2 & 463.448557262601 & -63.2485572626005 \tabularnewline
57 & 500.25 & 459.730218003546 & 40.5197819964541 \tabularnewline
58 & 667 & 462.112348168827 & 204.887651831173 \tabularnewline
59 & 1000.5 & 474.157552557226 & 526.342447442774 \tabularnewline
60 & 2001 & 505.10086368933 & 1495.89913631067 \tabularnewline
61 & 166.666666666667 & 593.043746924373 & -426.377080257707 \tabularnewline
62 & 181.818181818182 & 567.977331099252 & -386.159149281071 \tabularnewline
63 & 200 & 545.275299825189 & -345.275299825189 \tabularnewline
64 & 222.222222222222 & 524.976801992401 & -302.754579770179 \tabularnewline
65 & 250 & 507.178068099641 & -257.178068099641 \tabularnewline
66 & 285.714285714286 & 492.058746038074 & -206.344460323789 \tabularnewline
67 & 333.333333333333 & 479.927896878546 & -146.594563545213 \tabularnewline
68 & 400 & 471.309703130174 & -71.3097031301735 \tabularnewline
69 & 500 & 467.117454639831 & 32.8825453601685 \tabularnewline
70 & 666.666666666667 & 469.050596906503 & 197.616069760163 \tabularnewline
71 & 1000 & 480.668309977151 & 519.331690022849 \tabularnewline
72 & 2000 & 511.199463493675 & 1488.80053650632 \tabularnewline
73 & 166.583333333333 & 598.725024919665 & -432.141691586332 \tabularnewline
74 & 181.727272727273 & 573.319711552148 & -391.592438824875 \tabularnewline
75 & 199.9 & 550.298260915954 & -350.398260915954 \tabularnewline
76 & 222.111111111111 & 529.698587717737 & -307.587476606626 \tabularnewline
77 & 249.875 & 511.61573113792 & -261.74073113792 \tabularnewline
78 & 285.571428571429 & 496.228173248766 & -210.656744677337 \tabularnewline
79 & 333.166666666667 & 483.843807852631 & -150.677141185964 \tabularnewline
80 & 399.8 & 474.985602167595 & -75.1856021675952 \tabularnewline
81 & 499.75 & 470.565492233787 & 29.1845077662126 \tabularnewline
82 & 666.333333333333 & 472.281229409147 & 194.052103924186 \tabularnewline
83 & 999.5 & 483.689419375088 & 515.810580624912 \tabularnewline
84 & 1999 & 514.013569287476 & 1484.98643071252 \tabularnewline
85 & 166.5 & 601.31490205237 & -434.81490205237 \tabularnewline
86 & 181.636363636364 & 575.75243247681 & -394.116068840446 \tabularnewline
87 & 199.8 & 552.582619364563 & -352.782619364563 \tabularnewline
88 & 222 & 531.842771370101 & -309.842771370101 \tabularnewline
89 & 249.75 & 513.62732755948 & -263.87732755948 \tabularnewline
90 & 285.428571428571 & 498.114160633552 & -212.685589204981 \tabularnewline
91 & 333 & 485.610520860512 & -152.610520860512 \tabularnewline
92 & 399.6 & 476.638653111745 & -77.0386531117446 \tabularnewline
93 & 499.5 & 472.109603585117 & 27.3903964148834 \tabularnewline
94 & 666 & 473.719866185853 & 192.280133814147 \tabularnewline
95 & 999 & 485.023883245547 & 513.976116754453 \tabularnewline
96 & 1998 & 515.240186286416 & 1482.75981371358 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14186&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]2[/C][C]182.272727272727[/C][C]167.083333333333[/C][C]15.1893939393939[/C][/ROW]
[ROW][C]3[/C][C]200.5[/C][C]167.976307374964[/C][C]32.523692625036[/C][/ROW]
[ROW][C]4[/C][C]222.777777777778[/C][C]169.888352935703[/C][C]52.8894248420748[/C][/ROW]
[ROW][C]5[/C][C]250.625[/C][C]172.997685911673[/C][C]77.6273140883275[/C][/ROW]
[ROW][C]6[/C][C]286.428571428571[/C][C]177.561342412977[/C][C]108.867229015595[/C][/ROW]
[ROW][C]7[/C][C]334.166666666667[/C][C]183.961572065528[/C][C]150.205094601139[/C][/ROW]
[ROW][C]8[/C][C]401[/C][C]192.792026455919[/C][C]208.207973544081[/C][/ROW]
[ROW][C]9[/C][C]501.25[/C][C]205.032430278299[/C][C]296.217569721701[/C][/ROW]
[ROW][C]10[/C][C]668.333333333333[/C][C]222.446857838202[/C][C]445.886475495131[/C][/ROW]
[ROW][C]11[/C][C]1002.5[/C][C]248.660217615428[/C][C]753.839782384572[/C][/ROW]
[ROW][C]12[/C][C]2005[/C][C]292.977940883642[/C][C]1712.02205911636[/C][/ROW]
[ROW][C]13[/C][C]167[/C][C]393.626542374258[/C][C]-226.626542374258[/C][/ROW]
[ROW][C]14[/C][C]182.181818181818[/C][C]380.303323535363[/C][C]-198.121505353545[/C][/ROW]
[ROW][C]15[/C][C]200.4[/C][C]368.655896253181[/C][C]-168.255896253181[/C][/ROW]
[ROW][C]16[/C][C]222.666666666667[/C][C]358.764247626192[/C][C]-136.097580959525[/C][/ROW]
[ROW][C]17[/C][C]250.5[/C][C]350.763164277475[/C][C]-100.263164277475[/C][/ROW]
[ROW][C]18[/C][C]286.285714285714[/C][C]344.868761683877[/C][C]-58.5830473981632[/C][/ROW]
[ROW][C]19[/C][C]334[/C][C]341.424704546712[/C][C]-7.42470454671246[/C][/ROW]
[ROW][C]20[/C][C]400.8[/C][C]340.988211263738[/C][C]59.8117887362616[/C][/ROW]
[ROW][C]21[/C][C]501[/C][C]344.504505260595[/C][C]156.495494739405[/C][/ROW]
[ROW][C]22[/C][C]668[/C][C]353.704767956528[/C][C]314.295232043472[/C][/ROW]
[ROW][C]23[/C][C]1002[/C][C]372.181968873362[/C][C]629.818031126638[/C][/ROW]
[ROW][C]24[/C][C]2004[/C][C]409.208538530523[/C][C]1594.79146146948[/C][/ROW]
[ROW][C]25[/C][C]166.916666666667[/C][C]502.965233668508[/C][C]-336.048567001842[/C][/ROW]
[ROW][C]26[/C][C]182.090909090909[/C][C]483.20916912392[/C][C]-301.118260033011[/C][/ROW]
[ROW][C]27[/C][C]200.3[/C][C]465.506633345116[/C][C]-265.206633345116[/C][/ROW]
[ROW][C]28[/C][C]222.555555555556[/C][C]449.915317444667[/C][C]-227.359761889111[/C][/ROW]
[ROW][C]29[/C][C]250.375[/C][C]436.548993133875[/C][C]-186.173993133875[/C][/ROW]
[ROW][C]30[/C][C]286.142857142857[/C][C]425.60395189269[/C][C]-139.461094749833[/C][/ROW]
[ROW][C]31[/C][C]333.833333333333[/C][C]417.405129877414[/C][C]-83.5717965440808[/C][/ROW]
[ROW][C]32[/C][C]400.6[/C][C]412.492001333637[/C][C]-11.8920013336373[/C][/ROW]
[ROW][C]33[/C][C]500.75[/C][C]411.79287873952[/C][C]88.9571212604798[/C][/ROW]
[ROW][C]34[/C][C]667.666666666667[/C][C]417.022606826155[/C][C]250.644059840512[/C][/ROW]
[ROW][C]35[/C][C]1001.5[/C][C]431.757799027999[/C][C]569.742200972[/C][/ROW]
[ROW][C]36[/C][C]2003[/C][C]465.252551874592[/C][C]1537.74744812541[/C][/ROW]
[ROW][C]37[/C][C]166.833333333333[/C][C]555.65566863085[/C][C]-388.822335297516[/C][/ROW]
[ROW][C]38[/C][C]182[/C][C]532.797070479253[/C][C]-350.797070479253[/C][/ROW]
[ROW][C]39[/C][C]200.2[/C][C]512.173951540607[/C][C]-311.973951540607[/C][/ROW]
[ROW][C]40[/C][C]222.444444444444[/C][C]493.833217110895[/C][C]-271.38877266645[/C][/ROW]
[ROW][C]41[/C][C]250.25[/C][C]477.878457484006[/C][C]-227.628457484006[/C][/ROW]
[ROW][C]42[/C][C]286[/C][C]464.496336743659[/C][C]-178.496336743659[/C][/ROW]
[ROW][C]43[/C][C]333.666666666667[/C][C]454.002659650667[/C][C]-120.335992984000[/C][/ROW]
[ROW][C]44[/C][C]400.4[/C][C]446.928189238133[/C][C]-46.5281892381329[/C][/ROW]
[ROW][C]45[/C][C]500.5[/C][C]444.192828936102[/C][C]56.3071710638984[/C][/ROW]
[ROW][C]46[/C][C]667.333333333333[/C][C]447.503088866046[/C][C]219.830244467287[/C][/ROW]
[ROW][C]47[/C][C]1001[/C][C]460.426758016894[/C][C]540.573241983106[/C][/ROW]
[ROW][C]48[/C][C]2002[/C][C]492.206687790071[/C][C]1509.79331220993[/C][/ROW]
[ROW][C]49[/C][C]166.75[/C][C]580.966400087379[/C][C]-414.216400087379[/C][/ROW]
[ROW][C]50[/C][C]181.909090909091[/C][C]556.614902300727[/C][C]-374.705811391636[/C][/ROW]
[ROW][C]51[/C][C]200.1[/C][C]534.586204898054[/C][C]-334.486204898054[/C][/ROW]
[ROW][C]52[/C][C]222.333333333333[/C][C]514.92199054893[/C][C]-292.588657215597[/C][/ROW]
[ROW][C]53[/C][C]250.125[/C][C]497.720904263882[/C][C]-247.595904263882[/C][/ROW]
[ROW][C]54[/C][C]285.857142857143[/C][C]483.164911035718[/C][C]-197.307768178576[/C][/ROW]
[ROW][C]55[/C][C]333.5[/C][C]471.565322803393[/C][C]-138.065322803393[/C][/ROW]
[ROW][C]56[/C][C]400.2[/C][C]463.448557262601[/C][C]-63.2485572626005[/C][/ROW]
[ROW][C]57[/C][C]500.25[/C][C]459.730218003546[/C][C]40.5197819964541[/C][/ROW]
[ROW][C]58[/C][C]667[/C][C]462.112348168827[/C][C]204.887651831173[/C][/ROW]
[ROW][C]59[/C][C]1000.5[/C][C]474.157552557226[/C][C]526.342447442774[/C][/ROW]
[ROW][C]60[/C][C]2001[/C][C]505.10086368933[/C][C]1495.89913631067[/C][/ROW]
[ROW][C]61[/C][C]166.666666666667[/C][C]593.043746924373[/C][C]-426.377080257707[/C][/ROW]
[ROW][C]62[/C][C]181.818181818182[/C][C]567.977331099252[/C][C]-386.159149281071[/C][/ROW]
[ROW][C]63[/C][C]200[/C][C]545.275299825189[/C][C]-345.275299825189[/C][/ROW]
[ROW][C]64[/C][C]222.222222222222[/C][C]524.976801992401[/C][C]-302.754579770179[/C][/ROW]
[ROW][C]65[/C][C]250[/C][C]507.178068099641[/C][C]-257.178068099641[/C][/ROW]
[ROW][C]66[/C][C]285.714285714286[/C][C]492.058746038074[/C][C]-206.344460323789[/C][/ROW]
[ROW][C]67[/C][C]333.333333333333[/C][C]479.927896878546[/C][C]-146.594563545213[/C][/ROW]
[ROW][C]68[/C][C]400[/C][C]471.309703130174[/C][C]-71.3097031301735[/C][/ROW]
[ROW][C]69[/C][C]500[/C][C]467.117454639831[/C][C]32.8825453601685[/C][/ROW]
[ROW][C]70[/C][C]666.666666666667[/C][C]469.050596906503[/C][C]197.616069760163[/C][/ROW]
[ROW][C]71[/C][C]1000[/C][C]480.668309977151[/C][C]519.331690022849[/C][/ROW]
[ROW][C]72[/C][C]2000[/C][C]511.199463493675[/C][C]1488.80053650632[/C][/ROW]
[ROW][C]73[/C][C]166.583333333333[/C][C]598.725024919665[/C][C]-432.141691586332[/C][/ROW]
[ROW][C]74[/C][C]181.727272727273[/C][C]573.319711552148[/C][C]-391.592438824875[/C][/ROW]
[ROW][C]75[/C][C]199.9[/C][C]550.298260915954[/C][C]-350.398260915954[/C][/ROW]
[ROW][C]76[/C][C]222.111111111111[/C][C]529.698587717737[/C][C]-307.587476606626[/C][/ROW]
[ROW][C]77[/C][C]249.875[/C][C]511.61573113792[/C][C]-261.74073113792[/C][/ROW]
[ROW][C]78[/C][C]285.571428571429[/C][C]496.228173248766[/C][C]-210.656744677337[/C][/ROW]
[ROW][C]79[/C][C]333.166666666667[/C][C]483.843807852631[/C][C]-150.677141185964[/C][/ROW]
[ROW][C]80[/C][C]399.8[/C][C]474.985602167595[/C][C]-75.1856021675952[/C][/ROW]
[ROW][C]81[/C][C]499.75[/C][C]470.565492233787[/C][C]29.1845077662126[/C][/ROW]
[ROW][C]82[/C][C]666.333333333333[/C][C]472.281229409147[/C][C]194.052103924186[/C][/ROW]
[ROW][C]83[/C][C]999.5[/C][C]483.689419375088[/C][C]515.810580624912[/C][/ROW]
[ROW][C]84[/C][C]1999[/C][C]514.013569287476[/C][C]1484.98643071252[/C][/ROW]
[ROW][C]85[/C][C]166.5[/C][C]601.31490205237[/C][C]-434.81490205237[/C][/ROW]
[ROW][C]86[/C][C]181.636363636364[/C][C]575.75243247681[/C][C]-394.116068840446[/C][/ROW]
[ROW][C]87[/C][C]199.8[/C][C]552.582619364563[/C][C]-352.782619364563[/C][/ROW]
[ROW][C]88[/C][C]222[/C][C]531.842771370101[/C][C]-309.842771370101[/C][/ROW]
[ROW][C]89[/C][C]249.75[/C][C]513.62732755948[/C][C]-263.87732755948[/C][/ROW]
[ROW][C]90[/C][C]285.428571428571[/C][C]498.114160633552[/C][C]-212.685589204981[/C][/ROW]
[ROW][C]91[/C][C]333[/C][C]485.610520860512[/C][C]-152.610520860512[/C][/ROW]
[ROW][C]92[/C][C]399.6[/C][C]476.638653111745[/C][C]-77.0386531117446[/C][/ROW]
[ROW][C]93[/C][C]499.5[/C][C]472.109603585117[/C][C]27.3903964148834[/C][/ROW]
[ROW][C]94[/C][C]666[/C][C]473.719866185853[/C][C]192.280133814147[/C][/ROW]
[ROW][C]95[/C][C]999[/C][C]485.023883245547[/C][C]513.976116754453[/C][/ROW]
[ROW][C]96[/C][C]1998[/C][C]515.240186286416[/C][C]1482.75981371358[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14186&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14186&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
2182.272727272727167.08333333333315.1893939393939
3200.5167.97630737496432.523692625036
4222.777777777778169.88835293570352.8894248420748
5250.625172.99768591167377.6273140883275
6286.428571428571177.561342412977108.867229015595
7334.166666666667183.961572065528150.205094601139
8401192.792026455919208.207973544081
9501.25205.032430278299296.217569721701
10668.333333333333222.446857838202445.886475495131
111002.5248.660217615428753.839782384572
122005292.9779408836421712.02205911636
13167393.626542374258-226.626542374258
14182.181818181818380.303323535363-198.121505353545
15200.4368.655896253181-168.255896253181
16222.666666666667358.764247626192-136.097580959525
17250.5350.763164277475-100.263164277475
18286.285714285714344.868761683877-58.5830473981632
19334341.424704546712-7.42470454671246
20400.8340.98821126373859.8117887362616
21501344.504505260595156.495494739405
22668353.704767956528314.295232043472
231002372.181968873362629.818031126638
242004409.2085385305231594.79146146948
25166.916666666667502.965233668508-336.048567001842
26182.090909090909483.20916912392-301.118260033011
27200.3465.506633345116-265.206633345116
28222.555555555556449.915317444667-227.359761889111
29250.375436.548993133875-186.173993133875
30286.142857142857425.60395189269-139.461094749833
31333.833333333333417.405129877414-83.5717965440808
32400.6412.492001333637-11.8920013336373
33500.75411.7928787395288.9571212604798
34667.666666666667417.022606826155250.644059840512
351001.5431.757799027999569.742200972
362003465.2525518745921537.74744812541
37166.833333333333555.65566863085-388.822335297516
38182532.797070479253-350.797070479253
39200.2512.173951540607-311.973951540607
40222.444444444444493.833217110895-271.38877266645
41250.25477.878457484006-227.628457484006
42286464.496336743659-178.496336743659
43333.666666666667454.002659650667-120.335992984000
44400.4446.928189238133-46.5281892381329
45500.5444.19282893610256.3071710638984
46667.333333333333447.503088866046219.830244467287
471001460.426758016894540.573241983106
482002492.2066877900711509.79331220993
49166.75580.966400087379-414.216400087379
50181.909090909091556.614902300727-374.705811391636
51200.1534.586204898054-334.486204898054
52222.333333333333514.92199054893-292.588657215597
53250.125497.720904263882-247.595904263882
54285.857142857143483.164911035718-197.307768178576
55333.5471.565322803393-138.065322803393
56400.2463.448557262601-63.2485572626005
57500.25459.73021800354640.5197819964541
58667462.112348168827204.887651831173
591000.5474.157552557226526.342447442774
602001505.100863689331495.89913631067
61166.666666666667593.043746924373-426.377080257707
62181.818181818182567.977331099252-386.159149281071
63200545.275299825189-345.275299825189
64222.222222222222524.976801992401-302.754579770179
65250507.178068099641-257.178068099641
66285.714285714286492.058746038074-206.344460323789
67333.333333333333479.927896878546-146.594563545213
68400471.309703130174-71.3097031301735
69500467.11745463983132.8825453601685
70666.666666666667469.050596906503197.616069760163
711000480.668309977151519.331690022849
722000511.1994634936751488.80053650632
73166.583333333333598.725024919665-432.141691586332
74181.727272727273573.319711552148-391.592438824875
75199.9550.298260915954-350.398260915954
76222.111111111111529.698587717737-307.587476606626
77249.875511.61573113792-261.74073113792
78285.571428571429496.228173248766-210.656744677337
79333.166666666667483.843807852631-150.677141185964
80399.8474.985602167595-75.1856021675952
81499.75470.56549223378729.1845077662126
82666.333333333333472.281229409147194.052103924186
83999.5483.689419375088515.810580624912
841999514.0135692874761484.98643071252
85166.5601.31490205237-434.81490205237
86181.636363636364575.75243247681-394.116068840446
87199.8552.582619364563-352.782619364563
88222531.842771370101-309.842771370101
89249.75513.62732755948-263.87732755948
90285.428571428571498.114160633552-212.685589204981
91333485.610520860512-152.610520860512
92399.6476.638653111745-77.0386531117446
93499.5472.10960358511727.3903964148834
94666473.719866185853192.280133814147
95999485.023883245547513.976116754453
961998515.2401862864161482.75981371358







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97602.410617766595-421.2695465711621626.09078210435
98602.410617766595-423.0370338823451627.85826941554
99602.410617766595-424.8014799454971629.62271547869
100602.410617766595-426.5629004056791631.38413593887
101602.410617766595-428.3213107742731633.14254630746
102602.410617766595-430.0767264305761634.89796196377
103602.410617766595-431.8291626233681636.65039815656
104602.410617766595-433.5786344724561638.39987000565
105602.410617766595-435.3251569702011640.14639250339
106602.410617766595-437.0687449830121641.88998051620
107602.410617766595-438.8094132528241643.63064878601
108602.410617766595-440.5471763985531645.36841193174

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 602.410617766595 & -421.269546571162 & 1626.09078210435 \tabularnewline
98 & 602.410617766595 & -423.037033882345 & 1627.85826941554 \tabularnewline
99 & 602.410617766595 & -424.801479945497 & 1629.62271547869 \tabularnewline
100 & 602.410617766595 & -426.562900405679 & 1631.38413593887 \tabularnewline
101 & 602.410617766595 & -428.321310774273 & 1633.14254630746 \tabularnewline
102 & 602.410617766595 & -430.076726430576 & 1634.89796196377 \tabularnewline
103 & 602.410617766595 & -431.829162623368 & 1636.65039815656 \tabularnewline
104 & 602.410617766595 & -433.578634472456 & 1638.39987000565 \tabularnewline
105 & 602.410617766595 & -435.325156970201 & 1640.14639250339 \tabularnewline
106 & 602.410617766595 & -437.068744983012 & 1641.88998051620 \tabularnewline
107 & 602.410617766595 & -438.809413252824 & 1643.63064878601 \tabularnewline
108 & 602.410617766595 & -440.547176398553 & 1645.36841193174 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14186&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]97[/C][C]602.410617766595[/C][C]-421.269546571162[/C][C]1626.09078210435[/C][/ROW]
[ROW][C]98[/C][C]602.410617766595[/C][C]-423.037033882345[/C][C]1627.85826941554[/C][/ROW]
[ROW][C]99[/C][C]602.410617766595[/C][C]-424.801479945497[/C][C]1629.62271547869[/C][/ROW]
[ROW][C]100[/C][C]602.410617766595[/C][C]-426.562900405679[/C][C]1631.38413593887[/C][/ROW]
[ROW][C]101[/C][C]602.410617766595[/C][C]-428.321310774273[/C][C]1633.14254630746[/C][/ROW]
[ROW][C]102[/C][C]602.410617766595[/C][C]-430.076726430576[/C][C]1634.89796196377[/C][/ROW]
[ROW][C]103[/C][C]602.410617766595[/C][C]-431.829162623368[/C][C]1636.65039815656[/C][/ROW]
[ROW][C]104[/C][C]602.410617766595[/C][C]-433.578634472456[/C][C]1638.39987000565[/C][/ROW]
[ROW][C]105[/C][C]602.410617766595[/C][C]-435.325156970201[/C][C]1640.14639250339[/C][/ROW]
[ROW][C]106[/C][C]602.410617766595[/C][C]-437.068744983012[/C][C]1641.88998051620[/C][/ROW]
[ROW][C]107[/C][C]602.410617766595[/C][C]-438.809413252824[/C][C]1643.63064878601[/C][/ROW]
[ROW][C]108[/C][C]602.410617766595[/C][C]-440.547176398553[/C][C]1645.36841193174[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14186&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14186&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
97602.410617766595-421.2695465711621626.09078210435
98602.410617766595-423.0370338823451627.85826941554
99602.410617766595-424.8014799454971629.62271547869
100602.410617766595-426.5629004056791631.38413593887
101602.410617766595-428.3213107742731633.14254630746
102602.410617766595-430.0767264305761634.89796196377
103602.410617766595-431.8291626233681636.65039815656
104602.410617766595-433.5786344724561638.39987000565
105602.410617766595-435.3251569702011640.14639250339
106602.410617766595-437.0687449830121641.88998051620
107602.410617766595-438.8094132528241643.63064878601
108602.410617766595-440.5471763985531645.36841193174



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')