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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 02 Apr 2015 22:24:58 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Apr/02/t1428009964cxihzbui0ojqc3m.htm/, Retrieved Thu, 09 May 2024 05:45:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278673, Retrieved Thu, 09 May 2024 05:45:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2015-04-02 21:24:58] [bc7b6c6baf6d03f57c49dbed118965bb] [Current]
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Dataseries X:
6.81
6.80
6.80
6.85
6.85
6.85
6.85
6.85
6.85
6.86
6.86
6.88
6.88
6.88
6.91
6.91
6.91
6.91
6.99
6.99
6.99
7.02
7.02
7.05
7.05
7.05
7.05
7.10
7.10
7.10
7.10
7.12
7.13
7.18
7.24
7.24
7.24
7.27
7.27
7.27
7.27
7.30
7.30
7.57
7.76
7.94
7.94
7.96
7.96
7.98
7.99
8.00
8.00
8.04
8.04
8.04
8.04
8.04
8.07
8.07
8.07
8.07
8.11
8.11
8.11
8.12
8.11
8.13
8.15
8.16
8.20
8.20
8.20
8.20
8.23
8.25
8.26
8.31
8.33
8.33
8.36
8.39
8.41
8.50
8.58
8.58
8.66
8.67
8.70
8.71
8.73
8.75
8.76
8.76
8.77
8.78




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278673&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278673&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278673&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999922332723649
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999922332723649 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278673&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]0.999922332723649[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278673&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278673&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
alpha0.999922332723649
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
26.86.81-0.00999999999999979
36.86.80000077667276-7.76672763436181e-07
46.856.800000000060320.0499999999396774
56.856.849996116636193.88336381274001e-06
66.856.849999999698393.01610292297028e-10
76.856.849999999999982.30926389122033e-14
86.856.850
96.856.850
106.866.850.0100000000000007
116.866.859999223327247.76672763436181e-07
126.886.859999999939680.0200000000603211
136.886.879998446654471.55334553220143e-06
146.886.879999999879361.20644827461547e-10
156.916.879999999999990.03000000000001
166.916.909997669981712.33001829030854e-06
176.916.909999999819031.80966353013901e-10
186.916.909999999999991.4210854715202e-14
196.996.910.0800000000000001
206.996.989993786617896.21338210837763e-06
216.996.989999999517424.82576645310928e-10
227.026.989999999999960.0300000000000376
237.027.019997669981712.33001829030854e-06
247.057.019999999819030.0300000001809666
257.057.04999766998172.3300183045194e-06
267.057.049999999819031.80966353013901e-10
277.057.049999999999991.4210854715202e-14
287.17.050.0499999999999998
297.17.099996116636183.88336381718091e-06
307.17.099999999698393.01610292297028e-10
317.17.099999999999982.30926389122033e-14
327.127.10.0200000000000005
337.137.119998446654470.0100015533455275
347.187.129999223206590.0500007767934081
357.247.179996116575850.060003883424149
367.247.23999533966184.66033819623846e-06
377.247.239999999638043.61955798666713e-10
387.277.239999999999970.0300000000000278
397.277.269997669981712.33001829030854e-06
407.277.269999999819031.80966353013901e-10
417.277.269999999999991.4210854715202e-14
427.37.270.0300000000000002
437.37.299997669981712.33001829030854e-06
447.577.299999999819030.270000000180967
457.767.569979029835370.190020970164628
467.947.75998524158880.180014758411203
477.947.939986018744011.39812559885044e-05
487.967.939999998914110.0200000010858856
497.967.959998446654391.55334561124931e-06
507.987.959999999879360.0200000001206453
517.997.979998446654460.0100015533455364
5287.989999223206590.0100007767934072
5387.999999223266917.76733094731696e-07
548.047.999999999939670.040000000060326
558.048.039996893308943.1066910590738e-06
568.048.039999999758712.41289654923094e-10
578.048.039999999999981.95399252334028e-14
588.048.040
598.078.040.0300000000000011
608.078.069997669981712.33001829030854e-06
618.078.069999999819031.80966353013901e-10
628.078.069999999999991.4210854715202e-14
638.118.070.0399999999999991
648.118.109996893308953.10669105374473e-06
658.118.109999999758712.41287878566254e-10
668.128.109999999999980.0100000000000193
678.118.11999922332724-0.00999922332723635
688.138.110000776612440.0199992233875594
698.158.129998446714790.0200015532852085
708.168.149998446533830.0100015534661662
718.28.159999223206580.0400007767934163
728.28.199996893248623.10675138415206e-06
738.28.199999999758712.41291431279933e-10
748.28.199999999999981.77635683940025e-14
758.238.20.0300000000000011
768.258.229997669981710.0200023300182899
778.268.249998446473510.010001553526493
788.318.259999223206580.0500007767934232
798.338.309996116575850.0200038834241489
808.338.329998446352861.55364714160555e-06
818.368.329999999879330.0300000001206673
828.398.35999766998170.0300023300183003
838.418.389997669800740.0200023301992562
848.58.409998446473490.0900015535265073
858.588.499993009824470.08000699017553
868.588.579993786074986.21392501543028e-06
878.668.579999999517380.0800000004826185
888.678.659993786617860.0100062133821446
898.78.669999222844660.0300007771553386
908.718.699997669921350.0100023300786507
918.738.709999223146270.0200007768537329
928.758.729998446594140.020001553405864
938.768.749998446533820.0100015534661768
948.768.759999223206587.76793417145427e-07
958.778.759999999939670.010000000060332
968.788.769999223327230.0100007766727686

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 6.8 & 6.81 & -0.00999999999999979 \tabularnewline
3 & 6.8 & 6.80000077667276 & -7.76672763436181e-07 \tabularnewline
4 & 6.85 & 6.80000000006032 & 0.0499999999396774 \tabularnewline
5 & 6.85 & 6.84999611663619 & 3.88336381274001e-06 \tabularnewline
6 & 6.85 & 6.84999999969839 & 3.01610292297028e-10 \tabularnewline
7 & 6.85 & 6.84999999999998 & 2.30926389122033e-14 \tabularnewline
8 & 6.85 & 6.85 & 0 \tabularnewline
9 & 6.85 & 6.85 & 0 \tabularnewline
10 & 6.86 & 6.85 & 0.0100000000000007 \tabularnewline
11 & 6.86 & 6.85999922332724 & 7.76672763436181e-07 \tabularnewline
12 & 6.88 & 6.85999999993968 & 0.0200000000603211 \tabularnewline
13 & 6.88 & 6.87999844665447 & 1.55334553220143e-06 \tabularnewline
14 & 6.88 & 6.87999999987936 & 1.20644827461547e-10 \tabularnewline
15 & 6.91 & 6.87999999999999 & 0.03000000000001 \tabularnewline
16 & 6.91 & 6.90999766998171 & 2.33001829030854e-06 \tabularnewline
17 & 6.91 & 6.90999999981903 & 1.80966353013901e-10 \tabularnewline
18 & 6.91 & 6.90999999999999 & 1.4210854715202e-14 \tabularnewline
19 & 6.99 & 6.91 & 0.0800000000000001 \tabularnewline
20 & 6.99 & 6.98999378661789 & 6.21338210837763e-06 \tabularnewline
21 & 6.99 & 6.98999999951742 & 4.82576645310928e-10 \tabularnewline
22 & 7.02 & 6.98999999999996 & 0.0300000000000376 \tabularnewline
23 & 7.02 & 7.01999766998171 & 2.33001829030854e-06 \tabularnewline
24 & 7.05 & 7.01999999981903 & 0.0300000001809666 \tabularnewline
25 & 7.05 & 7.0499976699817 & 2.3300183045194e-06 \tabularnewline
26 & 7.05 & 7.04999999981903 & 1.80966353013901e-10 \tabularnewline
27 & 7.05 & 7.04999999999999 & 1.4210854715202e-14 \tabularnewline
28 & 7.1 & 7.05 & 0.0499999999999998 \tabularnewline
29 & 7.1 & 7.09999611663618 & 3.88336381718091e-06 \tabularnewline
30 & 7.1 & 7.09999999969839 & 3.01610292297028e-10 \tabularnewline
31 & 7.1 & 7.09999999999998 & 2.30926389122033e-14 \tabularnewline
32 & 7.12 & 7.1 & 0.0200000000000005 \tabularnewline
33 & 7.13 & 7.11999844665447 & 0.0100015533455275 \tabularnewline
34 & 7.18 & 7.12999922320659 & 0.0500007767934081 \tabularnewline
35 & 7.24 & 7.17999611657585 & 0.060003883424149 \tabularnewline
36 & 7.24 & 7.2399953396618 & 4.66033819623846e-06 \tabularnewline
37 & 7.24 & 7.23999999963804 & 3.61955798666713e-10 \tabularnewline
38 & 7.27 & 7.23999999999997 & 0.0300000000000278 \tabularnewline
39 & 7.27 & 7.26999766998171 & 2.33001829030854e-06 \tabularnewline
40 & 7.27 & 7.26999999981903 & 1.80966353013901e-10 \tabularnewline
41 & 7.27 & 7.26999999999999 & 1.4210854715202e-14 \tabularnewline
42 & 7.3 & 7.27 & 0.0300000000000002 \tabularnewline
43 & 7.3 & 7.29999766998171 & 2.33001829030854e-06 \tabularnewline
44 & 7.57 & 7.29999999981903 & 0.270000000180967 \tabularnewline
45 & 7.76 & 7.56997902983537 & 0.190020970164628 \tabularnewline
46 & 7.94 & 7.7599852415888 & 0.180014758411203 \tabularnewline
47 & 7.94 & 7.93998601874401 & 1.39812559885044e-05 \tabularnewline
48 & 7.96 & 7.93999999891411 & 0.0200000010858856 \tabularnewline
49 & 7.96 & 7.95999844665439 & 1.55334561124931e-06 \tabularnewline
50 & 7.98 & 7.95999999987936 & 0.0200000001206453 \tabularnewline
51 & 7.99 & 7.97999844665446 & 0.0100015533455364 \tabularnewline
52 & 8 & 7.98999922320659 & 0.0100007767934072 \tabularnewline
53 & 8 & 7.99999922326691 & 7.76733094731696e-07 \tabularnewline
54 & 8.04 & 7.99999999993967 & 0.040000000060326 \tabularnewline
55 & 8.04 & 8.03999689330894 & 3.1066910590738e-06 \tabularnewline
56 & 8.04 & 8.03999999975871 & 2.41289654923094e-10 \tabularnewline
57 & 8.04 & 8.03999999999998 & 1.95399252334028e-14 \tabularnewline
58 & 8.04 & 8.04 & 0 \tabularnewline
59 & 8.07 & 8.04 & 0.0300000000000011 \tabularnewline
60 & 8.07 & 8.06999766998171 & 2.33001829030854e-06 \tabularnewline
61 & 8.07 & 8.06999999981903 & 1.80966353013901e-10 \tabularnewline
62 & 8.07 & 8.06999999999999 & 1.4210854715202e-14 \tabularnewline
63 & 8.11 & 8.07 & 0.0399999999999991 \tabularnewline
64 & 8.11 & 8.10999689330895 & 3.10669105374473e-06 \tabularnewline
65 & 8.11 & 8.10999999975871 & 2.41287878566254e-10 \tabularnewline
66 & 8.12 & 8.10999999999998 & 0.0100000000000193 \tabularnewline
67 & 8.11 & 8.11999922332724 & -0.00999922332723635 \tabularnewline
68 & 8.13 & 8.11000077661244 & 0.0199992233875594 \tabularnewline
69 & 8.15 & 8.12999844671479 & 0.0200015532852085 \tabularnewline
70 & 8.16 & 8.14999844653383 & 0.0100015534661662 \tabularnewline
71 & 8.2 & 8.15999922320658 & 0.0400007767934163 \tabularnewline
72 & 8.2 & 8.19999689324862 & 3.10675138415206e-06 \tabularnewline
73 & 8.2 & 8.19999999975871 & 2.41291431279933e-10 \tabularnewline
74 & 8.2 & 8.19999999999998 & 1.77635683940025e-14 \tabularnewline
75 & 8.23 & 8.2 & 0.0300000000000011 \tabularnewline
76 & 8.25 & 8.22999766998171 & 0.0200023300182899 \tabularnewline
77 & 8.26 & 8.24999844647351 & 0.010001553526493 \tabularnewline
78 & 8.31 & 8.25999922320658 & 0.0500007767934232 \tabularnewline
79 & 8.33 & 8.30999611657585 & 0.0200038834241489 \tabularnewline
80 & 8.33 & 8.32999844635286 & 1.55364714160555e-06 \tabularnewline
81 & 8.36 & 8.32999999987933 & 0.0300000001206673 \tabularnewline
82 & 8.39 & 8.3599976699817 & 0.0300023300183003 \tabularnewline
83 & 8.41 & 8.38999766980074 & 0.0200023301992562 \tabularnewline
84 & 8.5 & 8.40999844647349 & 0.0900015535265073 \tabularnewline
85 & 8.58 & 8.49999300982447 & 0.08000699017553 \tabularnewline
86 & 8.58 & 8.57999378607498 & 6.21392501543028e-06 \tabularnewline
87 & 8.66 & 8.57999999951738 & 0.0800000004826185 \tabularnewline
88 & 8.67 & 8.65999378661786 & 0.0100062133821446 \tabularnewline
89 & 8.7 & 8.66999922284466 & 0.0300007771553386 \tabularnewline
90 & 8.71 & 8.69999766992135 & 0.0100023300786507 \tabularnewline
91 & 8.73 & 8.70999922314627 & 0.0200007768537329 \tabularnewline
92 & 8.75 & 8.72999844659414 & 0.020001553405864 \tabularnewline
93 & 8.76 & 8.74999844653382 & 0.0100015534661768 \tabularnewline
94 & 8.76 & 8.75999922320658 & 7.76793417145427e-07 \tabularnewline
95 & 8.77 & 8.75999999993967 & 0.010000000060332 \tabularnewline
96 & 8.78 & 8.76999922332723 & 0.0100007766727686 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278673&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]6.8[/C][C]6.81[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]3[/C][C]6.8[/C][C]6.80000077667276[/C][C]-7.76672763436181e-07[/C][/ROW]
[ROW][C]4[/C][C]6.85[/C][C]6.80000000006032[/C][C]0.0499999999396774[/C][/ROW]
[ROW][C]5[/C][C]6.85[/C][C]6.84999611663619[/C][C]3.88336381274001e-06[/C][/ROW]
[ROW][C]6[/C][C]6.85[/C][C]6.84999999969839[/C][C]3.01610292297028e-10[/C][/ROW]
[ROW][C]7[/C][C]6.85[/C][C]6.84999999999998[/C][C]2.30926389122033e-14[/C][/ROW]
[ROW][C]8[/C][C]6.85[/C][C]6.85[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]6.85[/C][C]6.85[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]6.86[/C][C]6.85[/C][C]0.0100000000000007[/C][/ROW]
[ROW][C]11[/C][C]6.86[/C][C]6.85999922332724[/C][C]7.76672763436181e-07[/C][/ROW]
[ROW][C]12[/C][C]6.88[/C][C]6.85999999993968[/C][C]0.0200000000603211[/C][/ROW]
[ROW][C]13[/C][C]6.88[/C][C]6.87999844665447[/C][C]1.55334553220143e-06[/C][/ROW]
[ROW][C]14[/C][C]6.88[/C][C]6.87999999987936[/C][C]1.20644827461547e-10[/C][/ROW]
[ROW][C]15[/C][C]6.91[/C][C]6.87999999999999[/C][C]0.03000000000001[/C][/ROW]
[ROW][C]16[/C][C]6.91[/C][C]6.90999766998171[/C][C]2.33001829030854e-06[/C][/ROW]
[ROW][C]17[/C][C]6.91[/C][C]6.90999999981903[/C][C]1.80966353013901e-10[/C][/ROW]
[ROW][C]18[/C][C]6.91[/C][C]6.90999999999999[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]19[/C][C]6.99[/C][C]6.91[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]20[/C][C]6.99[/C][C]6.98999378661789[/C][C]6.21338210837763e-06[/C][/ROW]
[ROW][C]21[/C][C]6.99[/C][C]6.98999999951742[/C][C]4.82576645310928e-10[/C][/ROW]
[ROW][C]22[/C][C]7.02[/C][C]6.98999999999996[/C][C]0.0300000000000376[/C][/ROW]
[ROW][C]23[/C][C]7.02[/C][C]7.01999766998171[/C][C]2.33001829030854e-06[/C][/ROW]
[ROW][C]24[/C][C]7.05[/C][C]7.01999999981903[/C][C]0.0300000001809666[/C][/ROW]
[ROW][C]25[/C][C]7.05[/C][C]7.0499976699817[/C][C]2.3300183045194e-06[/C][/ROW]
[ROW][C]26[/C][C]7.05[/C][C]7.04999999981903[/C][C]1.80966353013901e-10[/C][/ROW]
[ROW][C]27[/C][C]7.05[/C][C]7.04999999999999[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]28[/C][C]7.1[/C][C]7.05[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]29[/C][C]7.1[/C][C]7.09999611663618[/C][C]3.88336381718091e-06[/C][/ROW]
[ROW][C]30[/C][C]7.1[/C][C]7.09999999969839[/C][C]3.01610292297028e-10[/C][/ROW]
[ROW][C]31[/C][C]7.1[/C][C]7.09999999999998[/C][C]2.30926389122033e-14[/C][/ROW]
[ROW][C]32[/C][C]7.12[/C][C]7.1[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]33[/C][C]7.13[/C][C]7.11999844665447[/C][C]0.0100015533455275[/C][/ROW]
[ROW][C]34[/C][C]7.18[/C][C]7.12999922320659[/C][C]0.0500007767934081[/C][/ROW]
[ROW][C]35[/C][C]7.24[/C][C]7.17999611657585[/C][C]0.060003883424149[/C][/ROW]
[ROW][C]36[/C][C]7.24[/C][C]7.2399953396618[/C][C]4.66033819623846e-06[/C][/ROW]
[ROW][C]37[/C][C]7.24[/C][C]7.23999999963804[/C][C]3.61955798666713e-10[/C][/ROW]
[ROW][C]38[/C][C]7.27[/C][C]7.23999999999997[/C][C]0.0300000000000278[/C][/ROW]
[ROW][C]39[/C][C]7.27[/C][C]7.26999766998171[/C][C]2.33001829030854e-06[/C][/ROW]
[ROW][C]40[/C][C]7.27[/C][C]7.26999999981903[/C][C]1.80966353013901e-10[/C][/ROW]
[ROW][C]41[/C][C]7.27[/C][C]7.26999999999999[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]42[/C][C]7.3[/C][C]7.27[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]43[/C][C]7.3[/C][C]7.29999766998171[/C][C]2.33001829030854e-06[/C][/ROW]
[ROW][C]44[/C][C]7.57[/C][C]7.29999999981903[/C][C]0.270000000180967[/C][/ROW]
[ROW][C]45[/C][C]7.76[/C][C]7.56997902983537[/C][C]0.190020970164628[/C][/ROW]
[ROW][C]46[/C][C]7.94[/C][C]7.7599852415888[/C][C]0.180014758411203[/C][/ROW]
[ROW][C]47[/C][C]7.94[/C][C]7.93998601874401[/C][C]1.39812559885044e-05[/C][/ROW]
[ROW][C]48[/C][C]7.96[/C][C]7.93999999891411[/C][C]0.0200000010858856[/C][/ROW]
[ROW][C]49[/C][C]7.96[/C][C]7.95999844665439[/C][C]1.55334561124931e-06[/C][/ROW]
[ROW][C]50[/C][C]7.98[/C][C]7.95999999987936[/C][C]0.0200000001206453[/C][/ROW]
[ROW][C]51[/C][C]7.99[/C][C]7.97999844665446[/C][C]0.0100015533455364[/C][/ROW]
[ROW][C]52[/C][C]8[/C][C]7.98999922320659[/C][C]0.0100007767934072[/C][/ROW]
[ROW][C]53[/C][C]8[/C][C]7.99999922326691[/C][C]7.76733094731696e-07[/C][/ROW]
[ROW][C]54[/C][C]8.04[/C][C]7.99999999993967[/C][C]0.040000000060326[/C][/ROW]
[ROW][C]55[/C][C]8.04[/C][C]8.03999689330894[/C][C]3.1066910590738e-06[/C][/ROW]
[ROW][C]56[/C][C]8.04[/C][C]8.03999999975871[/C][C]2.41289654923094e-10[/C][/ROW]
[ROW][C]57[/C][C]8.04[/C][C]8.03999999999998[/C][C]1.95399252334028e-14[/C][/ROW]
[ROW][C]58[/C][C]8.04[/C][C]8.04[/C][C]0[/C][/ROW]
[ROW][C]59[/C][C]8.07[/C][C]8.04[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]60[/C][C]8.07[/C][C]8.06999766998171[/C][C]2.33001829030854e-06[/C][/ROW]
[ROW][C]61[/C][C]8.07[/C][C]8.06999999981903[/C][C]1.80966353013901e-10[/C][/ROW]
[ROW][C]62[/C][C]8.07[/C][C]8.06999999999999[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]63[/C][C]8.11[/C][C]8.07[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]64[/C][C]8.11[/C][C]8.10999689330895[/C][C]3.10669105374473e-06[/C][/ROW]
[ROW][C]65[/C][C]8.11[/C][C]8.10999999975871[/C][C]2.41287878566254e-10[/C][/ROW]
[ROW][C]66[/C][C]8.12[/C][C]8.10999999999998[/C][C]0.0100000000000193[/C][/ROW]
[ROW][C]67[/C][C]8.11[/C][C]8.11999922332724[/C][C]-0.00999922332723635[/C][/ROW]
[ROW][C]68[/C][C]8.13[/C][C]8.11000077661244[/C][C]0.0199992233875594[/C][/ROW]
[ROW][C]69[/C][C]8.15[/C][C]8.12999844671479[/C][C]0.0200015532852085[/C][/ROW]
[ROW][C]70[/C][C]8.16[/C][C]8.14999844653383[/C][C]0.0100015534661662[/C][/ROW]
[ROW][C]71[/C][C]8.2[/C][C]8.15999922320658[/C][C]0.0400007767934163[/C][/ROW]
[ROW][C]72[/C][C]8.2[/C][C]8.19999689324862[/C][C]3.10675138415206e-06[/C][/ROW]
[ROW][C]73[/C][C]8.2[/C][C]8.19999999975871[/C][C]2.41291431279933e-10[/C][/ROW]
[ROW][C]74[/C][C]8.2[/C][C]8.19999999999998[/C][C]1.77635683940025e-14[/C][/ROW]
[ROW][C]75[/C][C]8.23[/C][C]8.2[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]76[/C][C]8.25[/C][C]8.22999766998171[/C][C]0.0200023300182899[/C][/ROW]
[ROW][C]77[/C][C]8.26[/C][C]8.24999844647351[/C][C]0.010001553526493[/C][/ROW]
[ROW][C]78[/C][C]8.31[/C][C]8.25999922320658[/C][C]0.0500007767934232[/C][/ROW]
[ROW][C]79[/C][C]8.33[/C][C]8.30999611657585[/C][C]0.0200038834241489[/C][/ROW]
[ROW][C]80[/C][C]8.33[/C][C]8.32999844635286[/C][C]1.55364714160555e-06[/C][/ROW]
[ROW][C]81[/C][C]8.36[/C][C]8.32999999987933[/C][C]0.0300000001206673[/C][/ROW]
[ROW][C]82[/C][C]8.39[/C][C]8.3599976699817[/C][C]0.0300023300183003[/C][/ROW]
[ROW][C]83[/C][C]8.41[/C][C]8.38999766980074[/C][C]0.0200023301992562[/C][/ROW]
[ROW][C]84[/C][C]8.5[/C][C]8.40999844647349[/C][C]0.0900015535265073[/C][/ROW]
[ROW][C]85[/C][C]8.58[/C][C]8.49999300982447[/C][C]0.08000699017553[/C][/ROW]
[ROW][C]86[/C][C]8.58[/C][C]8.57999378607498[/C][C]6.21392501543028e-06[/C][/ROW]
[ROW][C]87[/C][C]8.66[/C][C]8.57999999951738[/C][C]0.0800000004826185[/C][/ROW]
[ROW][C]88[/C][C]8.67[/C][C]8.65999378661786[/C][C]0.0100062133821446[/C][/ROW]
[ROW][C]89[/C][C]8.7[/C][C]8.66999922284466[/C][C]0.0300007771553386[/C][/ROW]
[ROW][C]90[/C][C]8.71[/C][C]8.69999766992135[/C][C]0.0100023300786507[/C][/ROW]
[ROW][C]91[/C][C]8.73[/C][C]8.70999922314627[/C][C]0.0200007768537329[/C][/ROW]
[ROW][C]92[/C][C]8.75[/C][C]8.72999844659414[/C][C]0.020001553405864[/C][/ROW]
[ROW][C]93[/C][C]8.76[/C][C]8.74999844653382[/C][C]0.0100015534661768[/C][/ROW]
[ROW][C]94[/C][C]8.76[/C][C]8.75999922320658[/C][C]7.76793417145427e-07[/C][/ROW]
[ROW][C]95[/C][C]8.77[/C][C]8.75999999993967[/C][C]0.010000000060332[/C][/ROW]
[ROW][C]96[/C][C]8.78[/C][C]8.76999922332723[/C][C]0.0100007766727686[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278673&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278673&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
26.86.81-0.00999999999999979
36.86.80000077667276-7.76672763436181e-07
46.856.800000000060320.0499999999396774
56.856.849996116636193.88336381274001e-06
66.856.849999999698393.01610292297028e-10
76.856.849999999999982.30926389122033e-14
86.856.850
96.856.850
106.866.850.0100000000000007
116.866.859999223327247.76672763436181e-07
126.886.859999999939680.0200000000603211
136.886.879998446654471.55334553220143e-06
146.886.879999999879361.20644827461547e-10
156.916.879999999999990.03000000000001
166.916.909997669981712.33001829030854e-06
176.916.909999999819031.80966353013901e-10
186.916.909999999999991.4210854715202e-14
196.996.910.0800000000000001
206.996.989993786617896.21338210837763e-06
216.996.989999999517424.82576645310928e-10
227.026.989999999999960.0300000000000376
237.027.019997669981712.33001829030854e-06
247.057.019999999819030.0300000001809666
257.057.04999766998172.3300183045194e-06
267.057.049999999819031.80966353013901e-10
277.057.049999999999991.4210854715202e-14
287.17.050.0499999999999998
297.17.099996116636183.88336381718091e-06
307.17.099999999698393.01610292297028e-10
317.17.099999999999982.30926389122033e-14
327.127.10.0200000000000005
337.137.119998446654470.0100015533455275
347.187.129999223206590.0500007767934081
357.247.179996116575850.060003883424149
367.247.23999533966184.66033819623846e-06
377.247.239999999638043.61955798666713e-10
387.277.239999999999970.0300000000000278
397.277.269997669981712.33001829030854e-06
407.277.269999999819031.80966353013901e-10
417.277.269999999999991.4210854715202e-14
427.37.270.0300000000000002
437.37.299997669981712.33001829030854e-06
447.577.299999999819030.270000000180967
457.767.569979029835370.190020970164628
467.947.75998524158880.180014758411203
477.947.939986018744011.39812559885044e-05
487.967.939999998914110.0200000010858856
497.967.959998446654391.55334561124931e-06
507.987.959999999879360.0200000001206453
517.997.979998446654460.0100015533455364
5287.989999223206590.0100007767934072
5387.999999223266917.76733094731696e-07
548.047.999999999939670.040000000060326
558.048.039996893308943.1066910590738e-06
568.048.039999999758712.41289654923094e-10
578.048.039999999999981.95399252334028e-14
588.048.040
598.078.040.0300000000000011
608.078.069997669981712.33001829030854e-06
618.078.069999999819031.80966353013901e-10
628.078.069999999999991.4210854715202e-14
638.118.070.0399999999999991
648.118.109996893308953.10669105374473e-06
658.118.109999999758712.41287878566254e-10
668.128.109999999999980.0100000000000193
678.118.11999922332724-0.00999922332723635
688.138.110000776612440.0199992233875594
698.158.129998446714790.0200015532852085
708.168.149998446533830.0100015534661662
718.28.159999223206580.0400007767934163
728.28.199996893248623.10675138415206e-06
738.28.199999999758712.41291431279933e-10
748.28.199999999999981.77635683940025e-14
758.238.20.0300000000000011
768.258.229997669981710.0200023300182899
778.268.249998446473510.010001553526493
788.318.259999223206580.0500007767934232
798.338.309996116575850.0200038834241489
808.338.329998446352861.55364714160555e-06
818.368.329999999879330.0300000001206673
828.398.35999766998170.0300023300183003
838.418.389997669800740.0200023301992562
848.58.409998446473490.0900015535265073
858.588.499993009824470.08000699017553
868.588.579993786074986.21392501543028e-06
878.668.579999999517380.0800000004826185
888.678.659993786617860.0100062133821446
898.78.669999222844660.0300007771553386
908.718.699997669921350.0100023300786507
918.738.709999223146270.0200007768537329
928.758.729998446594140.020001553405864
938.768.749998446533820.0100015534661768
948.768.759999223206587.76793417145427e-07
958.778.759999999939670.010000000060332
968.788.769999223327230.0100007766727686







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
978.779999223266918.698870256846278.86112818968756
988.779999223266918.66526999409348.89472845244042
998.779999223266918.639487007210758.92051143932307
1008.779999223266918.617750741932648.94224770460119
1018.779999223266918.598600611007778.96139783552606
1028.779999223266918.58128751409058.97871093244332
1038.779999223266918.565366443389118.99463200314472
1048.779999223266918.550547448306819.00945099822701
1058.779999223266918.536629126774759.02336931975908
1068.779999223266918.523464838240529.03653360829331
1078.779999223266918.510943880381599.04905456615223
1088.779999223266918.498980248161319.06101819837251

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 8.77999922326691 & 8.69887025684627 & 8.86112818968756 \tabularnewline
98 & 8.77999922326691 & 8.6652699940934 & 8.89472845244042 \tabularnewline
99 & 8.77999922326691 & 8.63948700721075 & 8.92051143932307 \tabularnewline
100 & 8.77999922326691 & 8.61775074193264 & 8.94224770460119 \tabularnewline
101 & 8.77999922326691 & 8.59860061100777 & 8.96139783552606 \tabularnewline
102 & 8.77999922326691 & 8.5812875140905 & 8.97871093244332 \tabularnewline
103 & 8.77999922326691 & 8.56536644338911 & 8.99463200314472 \tabularnewline
104 & 8.77999922326691 & 8.55054744830681 & 9.00945099822701 \tabularnewline
105 & 8.77999922326691 & 8.53662912677475 & 9.02336931975908 \tabularnewline
106 & 8.77999922326691 & 8.52346483824052 & 9.03653360829331 \tabularnewline
107 & 8.77999922326691 & 8.51094388038159 & 9.04905456615223 \tabularnewline
108 & 8.77999922326691 & 8.49898024816131 & 9.06101819837251 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278673&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]8.77999922326691[/C][C]8.69887025684627[/C][C]8.86112818968756[/C][/ROW]
[ROW][C]98[/C][C]8.77999922326691[/C][C]8.6652699940934[/C][C]8.89472845244042[/C][/ROW]
[ROW][C]99[/C][C]8.77999922326691[/C][C]8.63948700721075[/C][C]8.92051143932307[/C][/ROW]
[ROW][C]100[/C][C]8.77999922326691[/C][C]8.61775074193264[/C][C]8.94224770460119[/C][/ROW]
[ROW][C]101[/C][C]8.77999922326691[/C][C]8.59860061100777[/C][C]8.96139783552606[/C][/ROW]
[ROW][C]102[/C][C]8.77999922326691[/C][C]8.5812875140905[/C][C]8.97871093244332[/C][/ROW]
[ROW][C]103[/C][C]8.77999922326691[/C][C]8.56536644338911[/C][C]8.99463200314472[/C][/ROW]
[ROW][C]104[/C][C]8.77999922326691[/C][C]8.55054744830681[/C][C]9.00945099822701[/C][/ROW]
[ROW][C]105[/C][C]8.77999922326691[/C][C]8.53662912677475[/C][C]9.02336931975908[/C][/ROW]
[ROW][C]106[/C][C]8.77999922326691[/C][C]8.52346483824052[/C][C]9.03653360829331[/C][/ROW]
[ROW][C]107[/C][C]8.77999922326691[/C][C]8.51094388038159[/C][C]9.04905456615223[/C][/ROW]
[ROW][C]108[/C][C]8.77999922326691[/C][C]8.49898024816131[/C][C]9.06101819837251[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278673&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278673&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
978.779999223266918.698870256846278.86112818968756
988.779999223266918.66526999409348.89472845244042
998.779999223266918.639487007210758.92051143932307
1008.779999223266918.617750741932648.94224770460119
1018.779999223266918.598600611007778.96139783552606
1028.779999223266918.58128751409058.97871093244332
1038.779999223266918.565366443389118.99463200314472
1048.779999223266918.550547448306819.00945099822701
1058.779999223266918.536629126774759.02336931975908
1068.779999223266918.523464838240529.03653360829331
1078.779999223266918.510943880381599.04905456615223
1088.779999223266918.498980248161319.06101819837251



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=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')