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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 computationWed, 26 May 2010 13:24:47 +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/2010/May/26/t1274880539qiquf85xnwiiicr.htm/, Retrieved Fri, 03 May 2024 08:13:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76487, Retrieved Fri, 03 May 2024 08:13:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2010-05-26 13:24:47] [2aa5bad7942f7e33426bcac9d4e6ffec] [Current]
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Dataseries X:
3592,21
5955,74
4652,25
4211,65
4787,85
3599,73
4174,27
5106,33
5325,75
6604,61
5711,90
6919,30
7048,76
8655,98
6658,53
7247,03
8779,57
6602,49
9832,48
9369,49
8582,76
8206,94
6515,83
8618,10
8505,39
9881,64
9375,29
15642,50
12232,73
6288,93
12473,94
11142,82
10236,32
10581,51
8763,71
10819,04
11636,25
14650,13
10671,38
17468,63
13873,19
13077,58
16866,81
14186,64
19919,87
17681,78
9984,28
17423,09
13514,45
12334,57
12274,56
11752,23
13054,00
12460,98
8626,68
13722,62
12066,22
6798,83
6593,82
6606,19
6315,28
7232,95
6747,44
7803,61
6700,31
5369,53
8081,19
10718,39
9447,21
6815,10
5497,80
6805,31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76487&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76487&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76487&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 time3 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.46970488241959
beta0.220607460394909
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.46970488241959 \tabularnewline
beta & 0.220607460394909 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76487&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]0.46970488241959[/C][/ROW]
[ROW][C]beta[/C][C]0.220607460394909[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76487&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76487&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
alpha0.46970488241959
beta0.220607460394909
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
34652.258319.27-3667.02
44211.658580.4047182938-4368.7547182938
54787.858059.23909638813-3271.38909638813
63599.737714.5288140925-4114.79881409250
74174.276547.2877653495-2373.0177653495
85106.335952.27672629837-845.946726298374
95325.755986.88107087961-661.131070879613
106604.616039.78756431809564.822435681908
115711.96727.05753282585-1015.15753282585
126919.36567.01216512138352.287834878615
137048.767085.76676987385-37.0067698738485
148655.987417.833141731341238.14685826866
156658.538477.1426728173-1818.61267281729
167247.037912.23195290176-665.201952901763
178779.577820.15538629656959.414613703439
186602.498590.58408031849-1988.09408031849
199832.487770.546443467372061.93355653262
209369.499066.48494404933303.005055950665
218582.769567.64364555806-984.883645558057
228206.949361.82069742208-1154.88069742208
236515.838956.48010277087-2440.65010277087
248618.17694.30619781219923.793802187813
258505.398108.1519060904397.238093909603
269881.648315.83379800541565.80620199459
279375.299234.6473026514140.642697348596
2815642.59498.62800365056143.8719963495
2912232.7313218.9852981385-986.255298138454
306288.9313488.0908204085-7199.16082040846
3112473.9410092.98435201372380.95564798626
3211142.8211444.4209425648-301.600942564832
3310236.3211504.5955944826-1268.27559448258
3410581.5110979.2992166929-397.789216692929
358763.7110821.6554623859-2057.94546238590
3610819.049670.983079343361148.05692065665
3711636.2510145.14778743611491.10221256395
3814650.1310934.95115359293715.17884640715
3910671.3813154.3824963053-2483.00249630528
4017468.6312205.20808526255263.42191473749
4113873.1915439.9649321112-1566.7749321112
4213077.5815304.1951249811-2226.61512498115
4316866.8114627.77240497322239.03759502684
4414186.6416280.8985447441-2094.25854474408
4519919.8715681.64641997614238.22358002393
4617681.7818495.9584949773-814.178494977332
479984.2818852.7671450685-8868.48714506849
4817423.0914507.47150128342915.61849871662
4913514.4515999.3453720487-2484.89537204871
5012334.5714697.0856546356-2362.51565463564
5112274.5613207.5034679181-932.943467918087
5211752.2312292.7263405878-540.496340587813
531305411506.27709737261547.72290262742
5412460.9811861.0502964455599.929703554539
558626.6811832.8053589912-3206.12535899124
5613722.629684.617779758874038.00222024113
5712066.2211357.4517036547708.768296345341
586798.8311539.9710540372-4741.14105403718
596593.828671.36243541919-2077.54243541919
606606.196838.58331200908-232.393312009085
616315.285848.39905241974466.88094758026
627232.955235.045717832081997.90428216792
636747.445547.845161967261199.59483803274
647803.615609.977260959672193.63273904033
656700.316366.31891997047333.991080029528
665369.536283.78610191817-914.256101918173
678081.195520.209903916482560.98009608352
6810718.396654.338900815834064.05109918417
699447.218915.58629207526531.62370792474
706815.19572.72235279432-2757.62235279431
715497.88399.13754463364-2901.33754463364
726805.316857.41124866409-52.1012486640857

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 4652.25 & 8319.27 & -3667.02 \tabularnewline
4 & 4211.65 & 8580.4047182938 & -4368.7547182938 \tabularnewline
5 & 4787.85 & 8059.23909638813 & -3271.38909638813 \tabularnewline
6 & 3599.73 & 7714.5288140925 & -4114.79881409250 \tabularnewline
7 & 4174.27 & 6547.2877653495 & -2373.0177653495 \tabularnewline
8 & 5106.33 & 5952.27672629837 & -845.946726298374 \tabularnewline
9 & 5325.75 & 5986.88107087961 & -661.131070879613 \tabularnewline
10 & 6604.61 & 6039.78756431809 & 564.822435681908 \tabularnewline
11 & 5711.9 & 6727.05753282585 & -1015.15753282585 \tabularnewline
12 & 6919.3 & 6567.01216512138 & 352.287834878615 \tabularnewline
13 & 7048.76 & 7085.76676987385 & -37.0067698738485 \tabularnewline
14 & 8655.98 & 7417.83314173134 & 1238.14685826866 \tabularnewline
15 & 6658.53 & 8477.1426728173 & -1818.61267281729 \tabularnewline
16 & 7247.03 & 7912.23195290176 & -665.201952901763 \tabularnewline
17 & 8779.57 & 7820.15538629656 & 959.414613703439 \tabularnewline
18 & 6602.49 & 8590.58408031849 & -1988.09408031849 \tabularnewline
19 & 9832.48 & 7770.54644346737 & 2061.93355653262 \tabularnewline
20 & 9369.49 & 9066.48494404933 & 303.005055950665 \tabularnewline
21 & 8582.76 & 9567.64364555806 & -984.883645558057 \tabularnewline
22 & 8206.94 & 9361.82069742208 & -1154.88069742208 \tabularnewline
23 & 6515.83 & 8956.48010277087 & -2440.65010277087 \tabularnewline
24 & 8618.1 & 7694.30619781219 & 923.793802187813 \tabularnewline
25 & 8505.39 & 8108.1519060904 & 397.238093909603 \tabularnewline
26 & 9881.64 & 8315.8337980054 & 1565.80620199459 \tabularnewline
27 & 9375.29 & 9234.6473026514 & 140.642697348596 \tabularnewline
28 & 15642.5 & 9498.6280036505 & 6143.8719963495 \tabularnewline
29 & 12232.73 & 13218.9852981385 & -986.255298138454 \tabularnewline
30 & 6288.93 & 13488.0908204085 & -7199.16082040846 \tabularnewline
31 & 12473.94 & 10092.9843520137 & 2380.95564798626 \tabularnewline
32 & 11142.82 & 11444.4209425648 & -301.600942564832 \tabularnewline
33 & 10236.32 & 11504.5955944826 & -1268.27559448258 \tabularnewline
34 & 10581.51 & 10979.2992166929 & -397.789216692929 \tabularnewline
35 & 8763.71 & 10821.6554623859 & -2057.94546238590 \tabularnewline
36 & 10819.04 & 9670.98307934336 & 1148.05692065665 \tabularnewline
37 & 11636.25 & 10145.1477874361 & 1491.10221256395 \tabularnewline
38 & 14650.13 & 10934.9511535929 & 3715.17884640715 \tabularnewline
39 & 10671.38 & 13154.3824963053 & -2483.00249630528 \tabularnewline
40 & 17468.63 & 12205.2080852625 & 5263.42191473749 \tabularnewline
41 & 13873.19 & 15439.9649321112 & -1566.7749321112 \tabularnewline
42 & 13077.58 & 15304.1951249811 & -2226.61512498115 \tabularnewline
43 & 16866.81 & 14627.7724049732 & 2239.03759502684 \tabularnewline
44 & 14186.64 & 16280.8985447441 & -2094.25854474408 \tabularnewline
45 & 19919.87 & 15681.6464199761 & 4238.22358002393 \tabularnewline
46 & 17681.78 & 18495.9584949773 & -814.178494977332 \tabularnewline
47 & 9984.28 & 18852.7671450685 & -8868.48714506849 \tabularnewline
48 & 17423.09 & 14507.4715012834 & 2915.61849871662 \tabularnewline
49 & 13514.45 & 15999.3453720487 & -2484.89537204871 \tabularnewline
50 & 12334.57 & 14697.0856546356 & -2362.51565463564 \tabularnewline
51 & 12274.56 & 13207.5034679181 & -932.943467918087 \tabularnewline
52 & 11752.23 & 12292.7263405878 & -540.496340587813 \tabularnewline
53 & 13054 & 11506.2770973726 & 1547.72290262742 \tabularnewline
54 & 12460.98 & 11861.0502964455 & 599.929703554539 \tabularnewline
55 & 8626.68 & 11832.8053589912 & -3206.12535899124 \tabularnewline
56 & 13722.62 & 9684.61777975887 & 4038.00222024113 \tabularnewline
57 & 12066.22 & 11357.4517036547 & 708.768296345341 \tabularnewline
58 & 6798.83 & 11539.9710540372 & -4741.14105403718 \tabularnewline
59 & 6593.82 & 8671.36243541919 & -2077.54243541919 \tabularnewline
60 & 6606.19 & 6838.58331200908 & -232.393312009085 \tabularnewline
61 & 6315.28 & 5848.39905241974 & 466.88094758026 \tabularnewline
62 & 7232.95 & 5235.04571783208 & 1997.90428216792 \tabularnewline
63 & 6747.44 & 5547.84516196726 & 1199.59483803274 \tabularnewline
64 & 7803.61 & 5609.97726095967 & 2193.63273904033 \tabularnewline
65 & 6700.31 & 6366.31891997047 & 333.991080029528 \tabularnewline
66 & 5369.53 & 6283.78610191817 & -914.256101918173 \tabularnewline
67 & 8081.19 & 5520.20990391648 & 2560.98009608352 \tabularnewline
68 & 10718.39 & 6654.33890081583 & 4064.05109918417 \tabularnewline
69 & 9447.21 & 8915.58629207526 & 531.62370792474 \tabularnewline
70 & 6815.1 & 9572.72235279432 & -2757.62235279431 \tabularnewline
71 & 5497.8 & 8399.13754463364 & -2901.33754463364 \tabularnewline
72 & 6805.31 & 6857.41124866409 & -52.1012486640857 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76487&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]4652.25[/C][C]8319.27[/C][C]-3667.02[/C][/ROW]
[ROW][C]4[/C][C]4211.65[/C][C]8580.4047182938[/C][C]-4368.7547182938[/C][/ROW]
[ROW][C]5[/C][C]4787.85[/C][C]8059.23909638813[/C][C]-3271.38909638813[/C][/ROW]
[ROW][C]6[/C][C]3599.73[/C][C]7714.5288140925[/C][C]-4114.79881409250[/C][/ROW]
[ROW][C]7[/C][C]4174.27[/C][C]6547.2877653495[/C][C]-2373.0177653495[/C][/ROW]
[ROW][C]8[/C][C]5106.33[/C][C]5952.27672629837[/C][C]-845.946726298374[/C][/ROW]
[ROW][C]9[/C][C]5325.75[/C][C]5986.88107087961[/C][C]-661.131070879613[/C][/ROW]
[ROW][C]10[/C][C]6604.61[/C][C]6039.78756431809[/C][C]564.822435681908[/C][/ROW]
[ROW][C]11[/C][C]5711.9[/C][C]6727.05753282585[/C][C]-1015.15753282585[/C][/ROW]
[ROW][C]12[/C][C]6919.3[/C][C]6567.01216512138[/C][C]352.287834878615[/C][/ROW]
[ROW][C]13[/C][C]7048.76[/C][C]7085.76676987385[/C][C]-37.0067698738485[/C][/ROW]
[ROW][C]14[/C][C]8655.98[/C][C]7417.83314173134[/C][C]1238.14685826866[/C][/ROW]
[ROW][C]15[/C][C]6658.53[/C][C]8477.1426728173[/C][C]-1818.61267281729[/C][/ROW]
[ROW][C]16[/C][C]7247.03[/C][C]7912.23195290176[/C][C]-665.201952901763[/C][/ROW]
[ROW][C]17[/C][C]8779.57[/C][C]7820.15538629656[/C][C]959.414613703439[/C][/ROW]
[ROW][C]18[/C][C]6602.49[/C][C]8590.58408031849[/C][C]-1988.09408031849[/C][/ROW]
[ROW][C]19[/C][C]9832.48[/C][C]7770.54644346737[/C][C]2061.93355653262[/C][/ROW]
[ROW][C]20[/C][C]9369.49[/C][C]9066.48494404933[/C][C]303.005055950665[/C][/ROW]
[ROW][C]21[/C][C]8582.76[/C][C]9567.64364555806[/C][C]-984.883645558057[/C][/ROW]
[ROW][C]22[/C][C]8206.94[/C][C]9361.82069742208[/C][C]-1154.88069742208[/C][/ROW]
[ROW][C]23[/C][C]6515.83[/C][C]8956.48010277087[/C][C]-2440.65010277087[/C][/ROW]
[ROW][C]24[/C][C]8618.1[/C][C]7694.30619781219[/C][C]923.793802187813[/C][/ROW]
[ROW][C]25[/C][C]8505.39[/C][C]8108.1519060904[/C][C]397.238093909603[/C][/ROW]
[ROW][C]26[/C][C]9881.64[/C][C]8315.8337980054[/C][C]1565.80620199459[/C][/ROW]
[ROW][C]27[/C][C]9375.29[/C][C]9234.6473026514[/C][C]140.642697348596[/C][/ROW]
[ROW][C]28[/C][C]15642.5[/C][C]9498.6280036505[/C][C]6143.8719963495[/C][/ROW]
[ROW][C]29[/C][C]12232.73[/C][C]13218.9852981385[/C][C]-986.255298138454[/C][/ROW]
[ROW][C]30[/C][C]6288.93[/C][C]13488.0908204085[/C][C]-7199.16082040846[/C][/ROW]
[ROW][C]31[/C][C]12473.94[/C][C]10092.9843520137[/C][C]2380.95564798626[/C][/ROW]
[ROW][C]32[/C][C]11142.82[/C][C]11444.4209425648[/C][C]-301.600942564832[/C][/ROW]
[ROW][C]33[/C][C]10236.32[/C][C]11504.5955944826[/C][C]-1268.27559448258[/C][/ROW]
[ROW][C]34[/C][C]10581.51[/C][C]10979.2992166929[/C][C]-397.789216692929[/C][/ROW]
[ROW][C]35[/C][C]8763.71[/C][C]10821.6554623859[/C][C]-2057.94546238590[/C][/ROW]
[ROW][C]36[/C][C]10819.04[/C][C]9670.98307934336[/C][C]1148.05692065665[/C][/ROW]
[ROW][C]37[/C][C]11636.25[/C][C]10145.1477874361[/C][C]1491.10221256395[/C][/ROW]
[ROW][C]38[/C][C]14650.13[/C][C]10934.9511535929[/C][C]3715.17884640715[/C][/ROW]
[ROW][C]39[/C][C]10671.38[/C][C]13154.3824963053[/C][C]-2483.00249630528[/C][/ROW]
[ROW][C]40[/C][C]17468.63[/C][C]12205.2080852625[/C][C]5263.42191473749[/C][/ROW]
[ROW][C]41[/C][C]13873.19[/C][C]15439.9649321112[/C][C]-1566.7749321112[/C][/ROW]
[ROW][C]42[/C][C]13077.58[/C][C]15304.1951249811[/C][C]-2226.61512498115[/C][/ROW]
[ROW][C]43[/C][C]16866.81[/C][C]14627.7724049732[/C][C]2239.03759502684[/C][/ROW]
[ROW][C]44[/C][C]14186.64[/C][C]16280.8985447441[/C][C]-2094.25854474408[/C][/ROW]
[ROW][C]45[/C][C]19919.87[/C][C]15681.6464199761[/C][C]4238.22358002393[/C][/ROW]
[ROW][C]46[/C][C]17681.78[/C][C]18495.9584949773[/C][C]-814.178494977332[/C][/ROW]
[ROW][C]47[/C][C]9984.28[/C][C]18852.7671450685[/C][C]-8868.48714506849[/C][/ROW]
[ROW][C]48[/C][C]17423.09[/C][C]14507.4715012834[/C][C]2915.61849871662[/C][/ROW]
[ROW][C]49[/C][C]13514.45[/C][C]15999.3453720487[/C][C]-2484.89537204871[/C][/ROW]
[ROW][C]50[/C][C]12334.57[/C][C]14697.0856546356[/C][C]-2362.51565463564[/C][/ROW]
[ROW][C]51[/C][C]12274.56[/C][C]13207.5034679181[/C][C]-932.943467918087[/C][/ROW]
[ROW][C]52[/C][C]11752.23[/C][C]12292.7263405878[/C][C]-540.496340587813[/C][/ROW]
[ROW][C]53[/C][C]13054[/C][C]11506.2770973726[/C][C]1547.72290262742[/C][/ROW]
[ROW][C]54[/C][C]12460.98[/C][C]11861.0502964455[/C][C]599.929703554539[/C][/ROW]
[ROW][C]55[/C][C]8626.68[/C][C]11832.8053589912[/C][C]-3206.12535899124[/C][/ROW]
[ROW][C]56[/C][C]13722.62[/C][C]9684.61777975887[/C][C]4038.00222024113[/C][/ROW]
[ROW][C]57[/C][C]12066.22[/C][C]11357.4517036547[/C][C]708.768296345341[/C][/ROW]
[ROW][C]58[/C][C]6798.83[/C][C]11539.9710540372[/C][C]-4741.14105403718[/C][/ROW]
[ROW][C]59[/C][C]6593.82[/C][C]8671.36243541919[/C][C]-2077.54243541919[/C][/ROW]
[ROW][C]60[/C][C]6606.19[/C][C]6838.58331200908[/C][C]-232.393312009085[/C][/ROW]
[ROW][C]61[/C][C]6315.28[/C][C]5848.39905241974[/C][C]466.88094758026[/C][/ROW]
[ROW][C]62[/C][C]7232.95[/C][C]5235.04571783208[/C][C]1997.90428216792[/C][/ROW]
[ROW][C]63[/C][C]6747.44[/C][C]5547.84516196726[/C][C]1199.59483803274[/C][/ROW]
[ROW][C]64[/C][C]7803.61[/C][C]5609.97726095967[/C][C]2193.63273904033[/C][/ROW]
[ROW][C]65[/C][C]6700.31[/C][C]6366.31891997047[/C][C]333.991080029528[/C][/ROW]
[ROW][C]66[/C][C]5369.53[/C][C]6283.78610191817[/C][C]-914.256101918173[/C][/ROW]
[ROW][C]67[/C][C]8081.19[/C][C]5520.20990391648[/C][C]2560.98009608352[/C][/ROW]
[ROW][C]68[/C][C]10718.39[/C][C]6654.33890081583[/C][C]4064.05109918417[/C][/ROW]
[ROW][C]69[/C][C]9447.21[/C][C]8915.58629207526[/C][C]531.62370792474[/C][/ROW]
[ROW][C]70[/C][C]6815.1[/C][C]9572.72235279432[/C][C]-2757.62235279431[/C][/ROW]
[ROW][C]71[/C][C]5497.8[/C][C]8399.13754463364[/C][C]-2901.33754463364[/C][/ROW]
[ROW][C]72[/C][C]6805.31[/C][C]6857.41124866409[/C][C]-52.1012486640857[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76487&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76487&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
34652.258319.27-3667.02
44211.658580.4047182938-4368.7547182938
54787.858059.23909638813-3271.38909638813
63599.737714.5288140925-4114.79881409250
74174.276547.2877653495-2373.0177653495
85106.335952.27672629837-845.946726298374
95325.755986.88107087961-661.131070879613
106604.616039.78756431809564.822435681908
115711.96727.05753282585-1015.15753282585
126919.36567.01216512138352.287834878615
137048.767085.76676987385-37.0067698738485
148655.987417.833141731341238.14685826866
156658.538477.1426728173-1818.61267281729
167247.037912.23195290176-665.201952901763
178779.577820.15538629656959.414613703439
186602.498590.58408031849-1988.09408031849
199832.487770.546443467372061.93355653262
209369.499066.48494404933303.005055950665
218582.769567.64364555806-984.883645558057
228206.949361.82069742208-1154.88069742208
236515.838956.48010277087-2440.65010277087
248618.17694.30619781219923.793802187813
258505.398108.1519060904397.238093909603
269881.648315.83379800541565.80620199459
279375.299234.6473026514140.642697348596
2815642.59498.62800365056143.8719963495
2912232.7313218.9852981385-986.255298138454
306288.9313488.0908204085-7199.16082040846
3112473.9410092.98435201372380.95564798626
3211142.8211444.4209425648-301.600942564832
3310236.3211504.5955944826-1268.27559448258
3410581.5110979.2992166929-397.789216692929
358763.7110821.6554623859-2057.94546238590
3610819.049670.983079343361148.05692065665
3711636.2510145.14778743611491.10221256395
3814650.1310934.95115359293715.17884640715
3910671.3813154.3824963053-2483.00249630528
4017468.6312205.20808526255263.42191473749
4113873.1915439.9649321112-1566.7749321112
4213077.5815304.1951249811-2226.61512498115
4316866.8114627.77240497322239.03759502684
4414186.6416280.8985447441-2094.25854474408
4519919.8715681.64641997614238.22358002393
4617681.7818495.9584949773-814.178494977332
479984.2818852.7671450685-8868.48714506849
4817423.0914507.47150128342915.61849871662
4913514.4515999.3453720487-2484.89537204871
5012334.5714697.0856546356-2362.51565463564
5112274.5613207.5034679181-932.943467918087
5211752.2312292.7263405878-540.496340587813
531305411506.27709737261547.72290262742
5412460.9811861.0502964455599.929703554539
558626.6811832.8053589912-3206.12535899124
5613722.629684.617779758874038.00222024113
5712066.2211357.4517036547708.768296345341
586798.8311539.9710540372-4741.14105403718
596593.828671.36243541919-2077.54243541919
606606.196838.58331200908-232.393312009085
616315.285848.39905241974466.88094758026
627232.955235.045717832081997.90428216792
636747.445547.845161967261199.59483803274
647803.615609.977260959672193.63273904033
656700.316366.31891997047333.991080029528
665369.536283.78610191817-914.256101918173
678081.195520.209903916482560.98009608352
6810718.396654.338900815834064.05109918417
699447.218915.58629207526531.62370792474
706815.19572.72235279432-2757.62235279431
715497.88399.13754463364-2901.33754463364
726805.316857.41124866409-52.1012486640857







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
736648.586399786561465.4681705797411831.7046289934
746464.23376178672489.68802263024212438.7795009432
756279.88112378688-648.76224519510713208.5244927689
766095.52848578704-1927.8326535213914118.8896250955
775911.17584778719-3328.7795016171215151.1311971915
785726.82320978735-4836.8103769210216290.4567964957
795542.47057178751-6440.5159514270117525.4570950020
805358.11793378766-8131.0819016711218847.3177692465
815173.76529578782-9901.6085326937620249.1391242694
824989.41265778798-11746.597039154521725.4223547304
834805.06001978813-13661.579866288323271.6999058645
844620.70738178829-15642.858527106624884.2732906832

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 6648.58639978656 & 1465.46817057974 & 11831.7046289934 \tabularnewline
74 & 6464.23376178672 & 489.688022630242 & 12438.7795009432 \tabularnewline
75 & 6279.88112378688 & -648.762245195107 & 13208.5244927689 \tabularnewline
76 & 6095.52848578704 & -1927.83265352139 & 14118.8896250955 \tabularnewline
77 & 5911.17584778719 & -3328.77950161712 & 15151.1311971915 \tabularnewline
78 & 5726.82320978735 & -4836.81037692102 & 16290.4567964957 \tabularnewline
79 & 5542.47057178751 & -6440.51595142701 & 17525.4570950020 \tabularnewline
80 & 5358.11793378766 & -8131.08190167112 & 18847.3177692465 \tabularnewline
81 & 5173.76529578782 & -9901.60853269376 & 20249.1391242694 \tabularnewline
82 & 4989.41265778798 & -11746.5970391545 & 21725.4223547304 \tabularnewline
83 & 4805.06001978813 & -13661.5798662883 & 23271.6999058645 \tabularnewline
84 & 4620.70738178829 & -15642.8585271066 & 24884.2732906832 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76487&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]6648.58639978656[/C][C]1465.46817057974[/C][C]11831.7046289934[/C][/ROW]
[ROW][C]74[/C][C]6464.23376178672[/C][C]489.688022630242[/C][C]12438.7795009432[/C][/ROW]
[ROW][C]75[/C][C]6279.88112378688[/C][C]-648.762245195107[/C][C]13208.5244927689[/C][/ROW]
[ROW][C]76[/C][C]6095.52848578704[/C][C]-1927.83265352139[/C][C]14118.8896250955[/C][/ROW]
[ROW][C]77[/C][C]5911.17584778719[/C][C]-3328.77950161712[/C][C]15151.1311971915[/C][/ROW]
[ROW][C]78[/C][C]5726.82320978735[/C][C]-4836.81037692102[/C][C]16290.4567964957[/C][/ROW]
[ROW][C]79[/C][C]5542.47057178751[/C][C]-6440.51595142701[/C][C]17525.4570950020[/C][/ROW]
[ROW][C]80[/C][C]5358.11793378766[/C][C]-8131.08190167112[/C][C]18847.3177692465[/C][/ROW]
[ROW][C]81[/C][C]5173.76529578782[/C][C]-9901.60853269376[/C][C]20249.1391242694[/C][/ROW]
[ROW][C]82[/C][C]4989.41265778798[/C][C]-11746.5970391545[/C][C]21725.4223547304[/C][/ROW]
[ROW][C]83[/C][C]4805.06001978813[/C][C]-13661.5798662883[/C][C]23271.6999058645[/C][/ROW]
[ROW][C]84[/C][C]4620.70738178829[/C][C]-15642.8585271066[/C][C]24884.2732906832[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76487&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76487&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
736648.586399786561465.4681705797411831.7046289934
746464.23376178672489.68802263024212438.7795009432
756279.88112378688-648.76224519510713208.5244927689
766095.52848578704-1927.8326535213914118.8896250955
775911.17584778719-3328.7795016171215151.1311971915
785726.82320978735-4836.8103769210216290.4567964957
795542.47057178751-6440.5159514270117525.4570950020
805358.11793378766-8131.0819016711218847.3177692465
815173.76529578782-9901.6085326937620249.1391242694
824989.41265778798-11746.597039154521725.4223547304
834805.06001978813-13661.579866288323271.6999058645
844620.70738178829-15642.858527106624884.2732906832



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