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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 25 May 2013 17:58:03 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/25/t1369519110xzds2fy7jurn1ig.htm/, Retrieved Thu, 02 May 2024 16:17:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210560, Retrieved Thu, 02 May 2024 16:17:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [double expo smoot...] [2013-05-25 21:58:03] [b938873e352688ee5cf8a5e46c229f6a] [Current]
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Dataseries X:
6,94
6,98
7,05
7,07
7,08
7,10
7,12
7,13
7,18
7,20
7,21
7,22
7,26
7,29
7,32
7,36
7,41
7,48
7,48
7,51
7,51
7,51
7,51
7,54
7,58
7,64
7,63
7,71
7,77
7,85
7,88
7,89
7,94
8,02
8,08
8,15
8,17
8,17
8,25
8,33
8,41
8,43
8,48
8,52
8,56
8,63
8,70
8,72
8,73
8,82
8,83
8,81
8,82
8,83
8,84
8,83
8,82
8,87
8,87
8,87
8,86
8,95
8,94
8,96
8,96
9,01
9,01
8,96
8,96
8,94
8,93
8,89




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210560&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210560&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210560&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.187341877515482
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.187341877515482 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210560&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.187341877515482[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210560&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210560&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
alpha1
beta0.187341877515482
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
37.057.020.0299999999999994
47.077.09562025632546-0.0256202563254639
57.087.11082050940302-0.0308205094030241
67.17.11504653730548-0.0150465373054782
77.127.13222769075656-0.0122276907565624
87.137.14993693221255-0.0199369322125502
97.187.156201909899950.0237980901000476
107.27.21066028878058-0.0106602887805769
117.217.22866317026557-0.0186631702655671
127.227.23516677690762-0.0151667769076242
137.267.242325404445890.0176745955541087
147.297.285636596361320.00436340363867505
157.327.316454044591350.0035459554086481
167.367.347118350535190.0128816494648056
177.417.389531622931430.0204683770685721
187.487.443366207121150.0366337928788516
197.487.52022925065959-0.0402292506595856
207.517.51269262730998-0.00269262730997877
217.517.54218818545428-0.0321881854542774
227.517.53615799035746-0.0261579903574569
237.517.53125750333186-0.0212575033318592
247.547.527275082746380.0127249172536237
257.587.55965899263590.0203410073641006
267.647.603469715146050.0365302848539528
277.637.67031336729676-0.0403133672967613
287.717.652760985378420.0572390146215849
297.777.743484249844760.0265157501552409
307.857.808451760262570.0415482397374269
317.887.89623548550245-0.0162354855024454
327.897.92319389916604-0.0331938991660428
337.947.926975291774220.0130247082257844
348.027.979415365067330.0405846349326726
358.088.067018566773890.0129814332261073
368.158.129450532847320.0205494671526854
378.178.20330030860564-0.0333003086056411
388.178.21706176626962-0.047061766269616
398.258.208245126617470.0417548733825299
408.338.296067562992380.0339324370076248
418.418.382424529450060.0275754705499409
428.438.46759056987626-0.037590569876258
438.488.48054828193876-0.000548281938762329
448.528.53044556577095-0.010445565770949
458.568.56848867386771-0.00848867386770635
468.638.606898389767710.0231016102322865
478.78.681226288802260.0187737111977366
488.728.75474339110598-0.0347433911059767
498.738.76823449898493-0.0382344989849308
508.828.771071576159230.0489284238407706
518.838.87023791894543-0.0402379189454329
528.818.87269967166288-0.0626996716628785
538.828.84095339745395-0.0209533974539511
548.838.8470279486346-0.0170279486346008
558.848.85383790076716-0.0138379007671574
568.838.86124548245656-0.0312454824565638
578.828.84539189510927-0.0253918951092746
588.878.830634929805830.0393650701941723
598.878.88800965596453-0.0180096559645317
608.878.88463569320273-0.0146356932027292
618.868.88189381495939-0.0218938149593892
628.958.867792186558920.0822078134410802
638.948.97319315267541-0.0331931526754143
648.968.956974685132540.0030253148674575
658.968.97754145329989-0.0175414532998897
669.018.974255204504340.0357447954956616
679.019.0309517016039-0.0209517016039023
688.969.02702657048828-0.0670265704882826
698.968.96446968692958-0.00446968692958372
708.948.96363232738829-0.0236323273882917
718.938.93920500280531-0.0092050028053059
728.898.92748052029722-0.0374805202972244

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 7.05 & 7.02 & 0.0299999999999994 \tabularnewline
4 & 7.07 & 7.09562025632546 & -0.0256202563254639 \tabularnewline
5 & 7.08 & 7.11082050940302 & -0.0308205094030241 \tabularnewline
6 & 7.1 & 7.11504653730548 & -0.0150465373054782 \tabularnewline
7 & 7.12 & 7.13222769075656 & -0.0122276907565624 \tabularnewline
8 & 7.13 & 7.14993693221255 & -0.0199369322125502 \tabularnewline
9 & 7.18 & 7.15620190989995 & 0.0237980901000476 \tabularnewline
10 & 7.2 & 7.21066028878058 & -0.0106602887805769 \tabularnewline
11 & 7.21 & 7.22866317026557 & -0.0186631702655671 \tabularnewline
12 & 7.22 & 7.23516677690762 & -0.0151667769076242 \tabularnewline
13 & 7.26 & 7.24232540444589 & 0.0176745955541087 \tabularnewline
14 & 7.29 & 7.28563659636132 & 0.00436340363867505 \tabularnewline
15 & 7.32 & 7.31645404459135 & 0.0035459554086481 \tabularnewline
16 & 7.36 & 7.34711835053519 & 0.0128816494648056 \tabularnewline
17 & 7.41 & 7.38953162293143 & 0.0204683770685721 \tabularnewline
18 & 7.48 & 7.44336620712115 & 0.0366337928788516 \tabularnewline
19 & 7.48 & 7.52022925065959 & -0.0402292506595856 \tabularnewline
20 & 7.51 & 7.51269262730998 & -0.00269262730997877 \tabularnewline
21 & 7.51 & 7.54218818545428 & -0.0321881854542774 \tabularnewline
22 & 7.51 & 7.53615799035746 & -0.0261579903574569 \tabularnewline
23 & 7.51 & 7.53125750333186 & -0.0212575033318592 \tabularnewline
24 & 7.54 & 7.52727508274638 & 0.0127249172536237 \tabularnewline
25 & 7.58 & 7.5596589926359 & 0.0203410073641006 \tabularnewline
26 & 7.64 & 7.60346971514605 & 0.0365302848539528 \tabularnewline
27 & 7.63 & 7.67031336729676 & -0.0403133672967613 \tabularnewline
28 & 7.71 & 7.65276098537842 & 0.0572390146215849 \tabularnewline
29 & 7.77 & 7.74348424984476 & 0.0265157501552409 \tabularnewline
30 & 7.85 & 7.80845176026257 & 0.0415482397374269 \tabularnewline
31 & 7.88 & 7.89623548550245 & -0.0162354855024454 \tabularnewline
32 & 7.89 & 7.92319389916604 & -0.0331938991660428 \tabularnewline
33 & 7.94 & 7.92697529177422 & 0.0130247082257844 \tabularnewline
34 & 8.02 & 7.97941536506733 & 0.0405846349326726 \tabularnewline
35 & 8.08 & 8.06701856677389 & 0.0129814332261073 \tabularnewline
36 & 8.15 & 8.12945053284732 & 0.0205494671526854 \tabularnewline
37 & 8.17 & 8.20330030860564 & -0.0333003086056411 \tabularnewline
38 & 8.17 & 8.21706176626962 & -0.047061766269616 \tabularnewline
39 & 8.25 & 8.20824512661747 & 0.0417548733825299 \tabularnewline
40 & 8.33 & 8.29606756299238 & 0.0339324370076248 \tabularnewline
41 & 8.41 & 8.38242452945006 & 0.0275754705499409 \tabularnewline
42 & 8.43 & 8.46759056987626 & -0.037590569876258 \tabularnewline
43 & 8.48 & 8.48054828193876 & -0.000548281938762329 \tabularnewline
44 & 8.52 & 8.53044556577095 & -0.010445565770949 \tabularnewline
45 & 8.56 & 8.56848867386771 & -0.00848867386770635 \tabularnewline
46 & 8.63 & 8.60689838976771 & 0.0231016102322865 \tabularnewline
47 & 8.7 & 8.68122628880226 & 0.0187737111977366 \tabularnewline
48 & 8.72 & 8.75474339110598 & -0.0347433911059767 \tabularnewline
49 & 8.73 & 8.76823449898493 & -0.0382344989849308 \tabularnewline
50 & 8.82 & 8.77107157615923 & 0.0489284238407706 \tabularnewline
51 & 8.83 & 8.87023791894543 & -0.0402379189454329 \tabularnewline
52 & 8.81 & 8.87269967166288 & -0.0626996716628785 \tabularnewline
53 & 8.82 & 8.84095339745395 & -0.0209533974539511 \tabularnewline
54 & 8.83 & 8.8470279486346 & -0.0170279486346008 \tabularnewline
55 & 8.84 & 8.85383790076716 & -0.0138379007671574 \tabularnewline
56 & 8.83 & 8.86124548245656 & -0.0312454824565638 \tabularnewline
57 & 8.82 & 8.84539189510927 & -0.0253918951092746 \tabularnewline
58 & 8.87 & 8.83063492980583 & 0.0393650701941723 \tabularnewline
59 & 8.87 & 8.88800965596453 & -0.0180096559645317 \tabularnewline
60 & 8.87 & 8.88463569320273 & -0.0146356932027292 \tabularnewline
61 & 8.86 & 8.88189381495939 & -0.0218938149593892 \tabularnewline
62 & 8.95 & 8.86779218655892 & 0.0822078134410802 \tabularnewline
63 & 8.94 & 8.97319315267541 & -0.0331931526754143 \tabularnewline
64 & 8.96 & 8.95697468513254 & 0.0030253148674575 \tabularnewline
65 & 8.96 & 8.97754145329989 & -0.0175414532998897 \tabularnewline
66 & 9.01 & 8.97425520450434 & 0.0357447954956616 \tabularnewline
67 & 9.01 & 9.0309517016039 & -0.0209517016039023 \tabularnewline
68 & 8.96 & 9.02702657048828 & -0.0670265704882826 \tabularnewline
69 & 8.96 & 8.96446968692958 & -0.00446968692958372 \tabularnewline
70 & 8.94 & 8.96363232738829 & -0.0236323273882917 \tabularnewline
71 & 8.93 & 8.93920500280531 & -0.0092050028053059 \tabularnewline
72 & 8.89 & 8.92748052029722 & -0.0374805202972244 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210560&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]7.05[/C][C]7.02[/C][C]0.0299999999999994[/C][/ROW]
[ROW][C]4[/C][C]7.07[/C][C]7.09562025632546[/C][C]-0.0256202563254639[/C][/ROW]
[ROW][C]5[/C][C]7.08[/C][C]7.11082050940302[/C][C]-0.0308205094030241[/C][/ROW]
[ROW][C]6[/C][C]7.1[/C][C]7.11504653730548[/C][C]-0.0150465373054782[/C][/ROW]
[ROW][C]7[/C][C]7.12[/C][C]7.13222769075656[/C][C]-0.0122276907565624[/C][/ROW]
[ROW][C]8[/C][C]7.13[/C][C]7.14993693221255[/C][C]-0.0199369322125502[/C][/ROW]
[ROW][C]9[/C][C]7.18[/C][C]7.15620190989995[/C][C]0.0237980901000476[/C][/ROW]
[ROW][C]10[/C][C]7.2[/C][C]7.21066028878058[/C][C]-0.0106602887805769[/C][/ROW]
[ROW][C]11[/C][C]7.21[/C][C]7.22866317026557[/C][C]-0.0186631702655671[/C][/ROW]
[ROW][C]12[/C][C]7.22[/C][C]7.23516677690762[/C][C]-0.0151667769076242[/C][/ROW]
[ROW][C]13[/C][C]7.26[/C][C]7.24232540444589[/C][C]0.0176745955541087[/C][/ROW]
[ROW][C]14[/C][C]7.29[/C][C]7.28563659636132[/C][C]0.00436340363867505[/C][/ROW]
[ROW][C]15[/C][C]7.32[/C][C]7.31645404459135[/C][C]0.0035459554086481[/C][/ROW]
[ROW][C]16[/C][C]7.36[/C][C]7.34711835053519[/C][C]0.0128816494648056[/C][/ROW]
[ROW][C]17[/C][C]7.41[/C][C]7.38953162293143[/C][C]0.0204683770685721[/C][/ROW]
[ROW][C]18[/C][C]7.48[/C][C]7.44336620712115[/C][C]0.0366337928788516[/C][/ROW]
[ROW][C]19[/C][C]7.48[/C][C]7.52022925065959[/C][C]-0.0402292506595856[/C][/ROW]
[ROW][C]20[/C][C]7.51[/C][C]7.51269262730998[/C][C]-0.00269262730997877[/C][/ROW]
[ROW][C]21[/C][C]7.51[/C][C]7.54218818545428[/C][C]-0.0321881854542774[/C][/ROW]
[ROW][C]22[/C][C]7.51[/C][C]7.53615799035746[/C][C]-0.0261579903574569[/C][/ROW]
[ROW][C]23[/C][C]7.51[/C][C]7.53125750333186[/C][C]-0.0212575033318592[/C][/ROW]
[ROW][C]24[/C][C]7.54[/C][C]7.52727508274638[/C][C]0.0127249172536237[/C][/ROW]
[ROW][C]25[/C][C]7.58[/C][C]7.5596589926359[/C][C]0.0203410073641006[/C][/ROW]
[ROW][C]26[/C][C]7.64[/C][C]7.60346971514605[/C][C]0.0365302848539528[/C][/ROW]
[ROW][C]27[/C][C]7.63[/C][C]7.67031336729676[/C][C]-0.0403133672967613[/C][/ROW]
[ROW][C]28[/C][C]7.71[/C][C]7.65276098537842[/C][C]0.0572390146215849[/C][/ROW]
[ROW][C]29[/C][C]7.77[/C][C]7.74348424984476[/C][C]0.0265157501552409[/C][/ROW]
[ROW][C]30[/C][C]7.85[/C][C]7.80845176026257[/C][C]0.0415482397374269[/C][/ROW]
[ROW][C]31[/C][C]7.88[/C][C]7.89623548550245[/C][C]-0.0162354855024454[/C][/ROW]
[ROW][C]32[/C][C]7.89[/C][C]7.92319389916604[/C][C]-0.0331938991660428[/C][/ROW]
[ROW][C]33[/C][C]7.94[/C][C]7.92697529177422[/C][C]0.0130247082257844[/C][/ROW]
[ROW][C]34[/C][C]8.02[/C][C]7.97941536506733[/C][C]0.0405846349326726[/C][/ROW]
[ROW][C]35[/C][C]8.08[/C][C]8.06701856677389[/C][C]0.0129814332261073[/C][/ROW]
[ROW][C]36[/C][C]8.15[/C][C]8.12945053284732[/C][C]0.0205494671526854[/C][/ROW]
[ROW][C]37[/C][C]8.17[/C][C]8.20330030860564[/C][C]-0.0333003086056411[/C][/ROW]
[ROW][C]38[/C][C]8.17[/C][C]8.21706176626962[/C][C]-0.047061766269616[/C][/ROW]
[ROW][C]39[/C][C]8.25[/C][C]8.20824512661747[/C][C]0.0417548733825299[/C][/ROW]
[ROW][C]40[/C][C]8.33[/C][C]8.29606756299238[/C][C]0.0339324370076248[/C][/ROW]
[ROW][C]41[/C][C]8.41[/C][C]8.38242452945006[/C][C]0.0275754705499409[/C][/ROW]
[ROW][C]42[/C][C]8.43[/C][C]8.46759056987626[/C][C]-0.037590569876258[/C][/ROW]
[ROW][C]43[/C][C]8.48[/C][C]8.48054828193876[/C][C]-0.000548281938762329[/C][/ROW]
[ROW][C]44[/C][C]8.52[/C][C]8.53044556577095[/C][C]-0.010445565770949[/C][/ROW]
[ROW][C]45[/C][C]8.56[/C][C]8.56848867386771[/C][C]-0.00848867386770635[/C][/ROW]
[ROW][C]46[/C][C]8.63[/C][C]8.60689838976771[/C][C]0.0231016102322865[/C][/ROW]
[ROW][C]47[/C][C]8.7[/C][C]8.68122628880226[/C][C]0.0187737111977366[/C][/ROW]
[ROW][C]48[/C][C]8.72[/C][C]8.75474339110598[/C][C]-0.0347433911059767[/C][/ROW]
[ROW][C]49[/C][C]8.73[/C][C]8.76823449898493[/C][C]-0.0382344989849308[/C][/ROW]
[ROW][C]50[/C][C]8.82[/C][C]8.77107157615923[/C][C]0.0489284238407706[/C][/ROW]
[ROW][C]51[/C][C]8.83[/C][C]8.87023791894543[/C][C]-0.0402379189454329[/C][/ROW]
[ROW][C]52[/C][C]8.81[/C][C]8.87269967166288[/C][C]-0.0626996716628785[/C][/ROW]
[ROW][C]53[/C][C]8.82[/C][C]8.84095339745395[/C][C]-0.0209533974539511[/C][/ROW]
[ROW][C]54[/C][C]8.83[/C][C]8.8470279486346[/C][C]-0.0170279486346008[/C][/ROW]
[ROW][C]55[/C][C]8.84[/C][C]8.85383790076716[/C][C]-0.0138379007671574[/C][/ROW]
[ROW][C]56[/C][C]8.83[/C][C]8.86124548245656[/C][C]-0.0312454824565638[/C][/ROW]
[ROW][C]57[/C][C]8.82[/C][C]8.84539189510927[/C][C]-0.0253918951092746[/C][/ROW]
[ROW][C]58[/C][C]8.87[/C][C]8.83063492980583[/C][C]0.0393650701941723[/C][/ROW]
[ROW][C]59[/C][C]8.87[/C][C]8.88800965596453[/C][C]-0.0180096559645317[/C][/ROW]
[ROW][C]60[/C][C]8.87[/C][C]8.88463569320273[/C][C]-0.0146356932027292[/C][/ROW]
[ROW][C]61[/C][C]8.86[/C][C]8.88189381495939[/C][C]-0.0218938149593892[/C][/ROW]
[ROW][C]62[/C][C]8.95[/C][C]8.86779218655892[/C][C]0.0822078134410802[/C][/ROW]
[ROW][C]63[/C][C]8.94[/C][C]8.97319315267541[/C][C]-0.0331931526754143[/C][/ROW]
[ROW][C]64[/C][C]8.96[/C][C]8.95697468513254[/C][C]0.0030253148674575[/C][/ROW]
[ROW][C]65[/C][C]8.96[/C][C]8.97754145329989[/C][C]-0.0175414532998897[/C][/ROW]
[ROW][C]66[/C][C]9.01[/C][C]8.97425520450434[/C][C]0.0357447954956616[/C][/ROW]
[ROW][C]67[/C][C]9.01[/C][C]9.0309517016039[/C][C]-0.0209517016039023[/C][/ROW]
[ROW][C]68[/C][C]8.96[/C][C]9.02702657048828[/C][C]-0.0670265704882826[/C][/ROW]
[ROW][C]69[/C][C]8.96[/C][C]8.96446968692958[/C][C]-0.00446968692958372[/C][/ROW]
[ROW][C]70[/C][C]8.94[/C][C]8.96363232738829[/C][C]-0.0236323273882917[/C][/ROW]
[ROW][C]71[/C][C]8.93[/C][C]8.93920500280531[/C][C]-0.0092050028053059[/C][/ROW]
[ROW][C]72[/C][C]8.89[/C][C]8.92748052029722[/C][C]-0.0374805202972244[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210560&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210560&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
37.057.020.0299999999999994
47.077.09562025632546-0.0256202563254639
57.087.11082050940302-0.0308205094030241
67.17.11504653730548-0.0150465373054782
77.127.13222769075656-0.0122276907565624
87.137.14993693221255-0.0199369322125502
97.187.156201909899950.0237980901000476
107.27.21066028878058-0.0106602887805769
117.217.22866317026557-0.0186631702655671
127.227.23516677690762-0.0151667769076242
137.267.242325404445890.0176745955541087
147.297.285636596361320.00436340363867505
157.327.316454044591350.0035459554086481
167.367.347118350535190.0128816494648056
177.417.389531622931430.0204683770685721
187.487.443366207121150.0366337928788516
197.487.52022925065959-0.0402292506595856
207.517.51269262730998-0.00269262730997877
217.517.54218818545428-0.0321881854542774
227.517.53615799035746-0.0261579903574569
237.517.53125750333186-0.0212575033318592
247.547.527275082746380.0127249172536237
257.587.55965899263590.0203410073641006
267.647.603469715146050.0365302848539528
277.637.67031336729676-0.0403133672967613
287.717.652760985378420.0572390146215849
297.777.743484249844760.0265157501552409
307.857.808451760262570.0415482397374269
317.887.89623548550245-0.0162354855024454
327.897.92319389916604-0.0331938991660428
337.947.926975291774220.0130247082257844
348.027.979415365067330.0405846349326726
358.088.067018566773890.0129814332261073
368.158.129450532847320.0205494671526854
378.178.20330030860564-0.0333003086056411
388.178.21706176626962-0.047061766269616
398.258.208245126617470.0417548733825299
408.338.296067562992380.0339324370076248
418.418.382424529450060.0275754705499409
428.438.46759056987626-0.037590569876258
438.488.48054828193876-0.000548281938762329
448.528.53044556577095-0.010445565770949
458.568.56848867386771-0.00848867386770635
468.638.606898389767710.0231016102322865
478.78.681226288802260.0187737111977366
488.728.75474339110598-0.0347433911059767
498.738.76823449898493-0.0382344989849308
508.828.771071576159230.0489284238407706
518.838.87023791894543-0.0402379189454329
528.818.87269967166288-0.0626996716628785
538.828.84095339745395-0.0209533974539511
548.838.8470279486346-0.0170279486346008
558.848.85383790076716-0.0138379007671574
568.838.86124548245656-0.0312454824565638
578.828.84539189510927-0.0253918951092746
588.878.830634929805830.0393650701941723
598.878.88800965596453-0.0180096559645317
608.878.88463569320273-0.0146356932027292
618.868.88189381495939-0.0218938149593892
628.958.867792186558920.0822078134410802
638.948.97319315267541-0.0331931526754143
648.968.956974685132540.0030253148674575
658.968.97754145329989-0.0175414532998897
669.018.974255204504340.0357447954956616
679.019.0309517016039-0.0209517016039023
688.969.02702657048828-0.0670265704882826
698.968.96446968692958-0.00446968692958372
708.948.96363232738829-0.0236323273882917
718.938.93920500280531-0.0092050028053059
728.898.92748052029722-0.0374805202972244







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
738.880458849254498.820647148411868.94027055009711
748.870917698508978.778069193278528.96376620373943
758.861376547763468.737355054706438.98539804082049
768.851835397017958.696561408050219.00710938598568
778.842294246272438.655056423448989.02953206909588
788.832753095526928.612579488298889.05292670275496
798.82321194478148.569014440141919.0774094494209
808.813670794035898.524311192374499.10303039569729
818.804129643290388.478452878555049.12980640802571
828.794588492544868.431440294074869.15773669101486
838.785047341799358.383283890740399.1868107928583
848.775506191053838.333999408098659.21701297400902

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 8.88045884925449 & 8.82064714841186 & 8.94027055009711 \tabularnewline
74 & 8.87091769850897 & 8.77806919327852 & 8.96376620373943 \tabularnewline
75 & 8.86137654776346 & 8.73735505470643 & 8.98539804082049 \tabularnewline
76 & 8.85183539701795 & 8.69656140805021 & 9.00710938598568 \tabularnewline
77 & 8.84229424627243 & 8.65505642344898 & 9.02953206909588 \tabularnewline
78 & 8.83275309552692 & 8.61257948829888 & 9.05292670275496 \tabularnewline
79 & 8.8232119447814 & 8.56901444014191 & 9.0774094494209 \tabularnewline
80 & 8.81367079403589 & 8.52431119237449 & 9.10303039569729 \tabularnewline
81 & 8.80412964329038 & 8.47845287855504 & 9.12980640802571 \tabularnewline
82 & 8.79458849254486 & 8.43144029407486 & 9.15773669101486 \tabularnewline
83 & 8.78504734179935 & 8.38328389074039 & 9.1868107928583 \tabularnewline
84 & 8.77550619105383 & 8.33399940809865 & 9.21701297400902 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210560&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]8.88045884925449[/C][C]8.82064714841186[/C][C]8.94027055009711[/C][/ROW]
[ROW][C]74[/C][C]8.87091769850897[/C][C]8.77806919327852[/C][C]8.96376620373943[/C][/ROW]
[ROW][C]75[/C][C]8.86137654776346[/C][C]8.73735505470643[/C][C]8.98539804082049[/C][/ROW]
[ROW][C]76[/C][C]8.85183539701795[/C][C]8.69656140805021[/C][C]9.00710938598568[/C][/ROW]
[ROW][C]77[/C][C]8.84229424627243[/C][C]8.65505642344898[/C][C]9.02953206909588[/C][/ROW]
[ROW][C]78[/C][C]8.83275309552692[/C][C]8.61257948829888[/C][C]9.05292670275496[/C][/ROW]
[ROW][C]79[/C][C]8.8232119447814[/C][C]8.56901444014191[/C][C]9.0774094494209[/C][/ROW]
[ROW][C]80[/C][C]8.81367079403589[/C][C]8.52431119237449[/C][C]9.10303039569729[/C][/ROW]
[ROW][C]81[/C][C]8.80412964329038[/C][C]8.47845287855504[/C][C]9.12980640802571[/C][/ROW]
[ROW][C]82[/C][C]8.79458849254486[/C][C]8.43144029407486[/C][C]9.15773669101486[/C][/ROW]
[ROW][C]83[/C][C]8.78504734179935[/C][C]8.38328389074039[/C][C]9.1868107928583[/C][/ROW]
[ROW][C]84[/C][C]8.77550619105383[/C][C]8.33399940809865[/C][C]9.21701297400902[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210560&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210560&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
738.880458849254498.820647148411868.94027055009711
748.870917698508978.778069193278528.96376620373943
758.861376547763468.737355054706438.98539804082049
768.851835397017958.696561408050219.00710938598568
778.842294246272438.655056423448989.02953206909588
788.832753095526928.612579488298889.05292670275496
798.82321194478148.569014440141919.0774094494209
808.813670794035898.524311192374499.10303039569729
818.804129643290388.478452878555049.12980640802571
828.794588492544868.431440294074869.15773669101486
838.785047341799358.383283890740399.1868107928583
848.775506191053838.333999408098659.21701297400902



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