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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, 01 Apr 2015 17:56:05 +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/01/t1427907394tx9gxh8ippda8kx.htm/, Retrieved Thu, 09 May 2024 10:40:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278528, Retrieved Thu, 09 May 2024 10:40:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-04-01 16:56:05] [478e7c199ef13b68c565592d49c085e5] [Current]
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Dataseries X:
4.8
4.81
5.16
5.26
5.29
5.29
5.29
5.3
5.3
5.3
5.3
5.3
5.3
5.3
5.3
5.35
5.44
5.47
5.47
5.48
5.48
5.48
5.48
5.48
5.48
5.48
5.5
5.55
5.57
5.58
5.58
5.58
5.59
5.59
5.59
5.55
5.61
5.61
5.61
5.63
5.69
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.71
5.74
5.77
5.79
5.79
5.8
5.8
5.8
5.8
5.8
5.81
5.81
5.83
5.94
5.98
5.99
6
6.02
6.02
6.02
6.02
6.02
6.02
6.02
6.04
6.06
6.06
6.07
6.14
6.19
6.2
6.22
6.22




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278528&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278528&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278528&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999932742347724
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999932742347724 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278528&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]0.999932742347724[/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=278528&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278528&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
alpha0.999932742347724
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
24.814.80.00999999999999979
35.164.809999327423480.350000672576524
45.265.159976459776470.100023540223533
55.295.259993272651510.0300067273484883
65.295.289997981817972.018182033936e-06
75.295.289999999864261.35738531525931e-10
85.35.289999999999990.0100000000000096
95.35.299999327423486.72576522475765e-07
105.35.299999999954764.52358150937471e-11
115.35.32.66453525910038e-15
125.35.30
135.35.30
145.35.30
155.35.30
165.355.30.0499999999999998
175.445.349996637117390.0900033628826149
185.475.439993946585120.0300060534148834
195.475.469997981863292.01813670663853e-06
205.485.469999999864260.0100000001357357
215.485.479999327423476.72576532245728e-07
225.485.479999999954764.52358150937471e-11
235.485.483.5527136788005e-15
245.485.480
255.485.480
265.485.480
275.55.480.0199999999999996
285.555.499998654846960.0500013451530448
295.575.549996637026910.0200033629730862
305.585.569998654620770.0100013453792309
315.585.579999327332996.72667010093164e-07
325.585.579999999954764.5242032342685e-11
335.595.580.0100000000000033
345.595.589999327423486.72576522475765e-07
355.595.589999999954764.52358150937471e-11
365.555.59-0.0399999999999974
375.615.550002690306090.0599973096939097
385.615.609995964721814.03527819337057e-06
395.615.60999999972862.71403344243026e-10
405.635.609999999999980.0200000000000182
415.695.629998654846950.0600013451530454
425.75.689995964450390.010004035549608
435.75.699999327152066.72847944471755e-07
445.75.699999999954754.52544668405608e-11
455.75.73.5527136788005e-15
465.75.70
475.75.70
485.75.70
495.75.70
505.75.70
515.75.70
525.715.70.00999999999999979
535.745.709999327423480.0300006725765227
545.775.73999798222520.0300020177748035
555.795.769997982134720.0200020178652798
565.795.789998654711241.34528876216677e-06
575.85.789999999909520.0100000000904803
585.85.799999327423476.72576528693014e-07
595.85.799999999954764.52358150937471e-11
605.85.83.5527136788005e-15
615.85.80
625.815.80.00999999999999979
635.815.809999327423486.72576522475765e-07
645.835.809999999954760.0200000000452363
655.945.829998654846950.110001345153049
665.985.939992601567780.0400073984322225
675.995.979997309196310.0100026908036916
6865.98999932724250.0100006727575002
696.025.999999327378230.0200006726217703
706.026.019998654801711.34519828520752e-06
716.026.019999999909529.0475182901173e-11
726.026.019999999999996.21724893790088e-15
736.026.020
746.026.020
756.026.020
766.046.020.0200000000000005
776.066.039998654846960.0200013451530445
786.066.059998654756481.3452435174699e-06
796.076.059999999909520.0100000000904785
806.146.069999327423470.0700006725765281
816.196.13999529191910.0500047080808956
826.26.189996636800730.0100033631992682
836.226.199999327197280.0200006728027233
846.226.21999865480171.34519829675384e-06

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 4.81 & 4.8 & 0.00999999999999979 \tabularnewline
3 & 5.16 & 4.80999932742348 & 0.350000672576524 \tabularnewline
4 & 5.26 & 5.15997645977647 & 0.100023540223533 \tabularnewline
5 & 5.29 & 5.25999327265151 & 0.0300067273484883 \tabularnewline
6 & 5.29 & 5.28999798181797 & 2.018182033936e-06 \tabularnewline
7 & 5.29 & 5.28999999986426 & 1.35738531525931e-10 \tabularnewline
8 & 5.3 & 5.28999999999999 & 0.0100000000000096 \tabularnewline
9 & 5.3 & 5.29999932742348 & 6.72576522475765e-07 \tabularnewline
10 & 5.3 & 5.29999999995476 & 4.52358150937471e-11 \tabularnewline
11 & 5.3 & 5.3 & 2.66453525910038e-15 \tabularnewline
12 & 5.3 & 5.3 & 0 \tabularnewline
13 & 5.3 & 5.3 & 0 \tabularnewline
14 & 5.3 & 5.3 & 0 \tabularnewline
15 & 5.3 & 5.3 & 0 \tabularnewline
16 & 5.35 & 5.3 & 0.0499999999999998 \tabularnewline
17 & 5.44 & 5.34999663711739 & 0.0900033628826149 \tabularnewline
18 & 5.47 & 5.43999394658512 & 0.0300060534148834 \tabularnewline
19 & 5.47 & 5.46999798186329 & 2.01813670663853e-06 \tabularnewline
20 & 5.48 & 5.46999999986426 & 0.0100000001357357 \tabularnewline
21 & 5.48 & 5.47999932742347 & 6.72576532245728e-07 \tabularnewline
22 & 5.48 & 5.47999999995476 & 4.52358150937471e-11 \tabularnewline
23 & 5.48 & 5.48 & 3.5527136788005e-15 \tabularnewline
24 & 5.48 & 5.48 & 0 \tabularnewline
25 & 5.48 & 5.48 & 0 \tabularnewline
26 & 5.48 & 5.48 & 0 \tabularnewline
27 & 5.5 & 5.48 & 0.0199999999999996 \tabularnewline
28 & 5.55 & 5.49999865484696 & 0.0500013451530448 \tabularnewline
29 & 5.57 & 5.54999663702691 & 0.0200033629730862 \tabularnewline
30 & 5.58 & 5.56999865462077 & 0.0100013453792309 \tabularnewline
31 & 5.58 & 5.57999932733299 & 6.72667010093164e-07 \tabularnewline
32 & 5.58 & 5.57999999995476 & 4.5242032342685e-11 \tabularnewline
33 & 5.59 & 5.58 & 0.0100000000000033 \tabularnewline
34 & 5.59 & 5.58999932742348 & 6.72576522475765e-07 \tabularnewline
35 & 5.59 & 5.58999999995476 & 4.52358150937471e-11 \tabularnewline
36 & 5.55 & 5.59 & -0.0399999999999974 \tabularnewline
37 & 5.61 & 5.55000269030609 & 0.0599973096939097 \tabularnewline
38 & 5.61 & 5.60999596472181 & 4.03527819337057e-06 \tabularnewline
39 & 5.61 & 5.6099999997286 & 2.71403344243026e-10 \tabularnewline
40 & 5.63 & 5.60999999999998 & 0.0200000000000182 \tabularnewline
41 & 5.69 & 5.62999865484695 & 0.0600013451530454 \tabularnewline
42 & 5.7 & 5.68999596445039 & 0.010004035549608 \tabularnewline
43 & 5.7 & 5.69999932715206 & 6.72847944471755e-07 \tabularnewline
44 & 5.7 & 5.69999999995475 & 4.52544668405608e-11 \tabularnewline
45 & 5.7 & 5.7 & 3.5527136788005e-15 \tabularnewline
46 & 5.7 & 5.7 & 0 \tabularnewline
47 & 5.7 & 5.7 & 0 \tabularnewline
48 & 5.7 & 5.7 & 0 \tabularnewline
49 & 5.7 & 5.7 & 0 \tabularnewline
50 & 5.7 & 5.7 & 0 \tabularnewline
51 & 5.7 & 5.7 & 0 \tabularnewline
52 & 5.71 & 5.7 & 0.00999999999999979 \tabularnewline
53 & 5.74 & 5.70999932742348 & 0.0300006725765227 \tabularnewline
54 & 5.77 & 5.7399979822252 & 0.0300020177748035 \tabularnewline
55 & 5.79 & 5.76999798213472 & 0.0200020178652798 \tabularnewline
56 & 5.79 & 5.78999865471124 & 1.34528876216677e-06 \tabularnewline
57 & 5.8 & 5.78999999990952 & 0.0100000000904803 \tabularnewline
58 & 5.8 & 5.79999932742347 & 6.72576528693014e-07 \tabularnewline
59 & 5.8 & 5.79999999995476 & 4.52358150937471e-11 \tabularnewline
60 & 5.8 & 5.8 & 3.5527136788005e-15 \tabularnewline
61 & 5.8 & 5.8 & 0 \tabularnewline
62 & 5.81 & 5.8 & 0.00999999999999979 \tabularnewline
63 & 5.81 & 5.80999932742348 & 6.72576522475765e-07 \tabularnewline
64 & 5.83 & 5.80999999995476 & 0.0200000000452363 \tabularnewline
65 & 5.94 & 5.82999865484695 & 0.110001345153049 \tabularnewline
66 & 5.98 & 5.93999260156778 & 0.0400073984322225 \tabularnewline
67 & 5.99 & 5.97999730919631 & 0.0100026908036916 \tabularnewline
68 & 6 & 5.9899993272425 & 0.0100006727575002 \tabularnewline
69 & 6.02 & 5.99999932737823 & 0.0200006726217703 \tabularnewline
70 & 6.02 & 6.01999865480171 & 1.34519828520752e-06 \tabularnewline
71 & 6.02 & 6.01999999990952 & 9.0475182901173e-11 \tabularnewline
72 & 6.02 & 6.01999999999999 & 6.21724893790088e-15 \tabularnewline
73 & 6.02 & 6.02 & 0 \tabularnewline
74 & 6.02 & 6.02 & 0 \tabularnewline
75 & 6.02 & 6.02 & 0 \tabularnewline
76 & 6.04 & 6.02 & 0.0200000000000005 \tabularnewline
77 & 6.06 & 6.03999865484696 & 0.0200013451530445 \tabularnewline
78 & 6.06 & 6.05999865475648 & 1.3452435174699e-06 \tabularnewline
79 & 6.07 & 6.05999999990952 & 0.0100000000904785 \tabularnewline
80 & 6.14 & 6.06999932742347 & 0.0700006725765281 \tabularnewline
81 & 6.19 & 6.1399952919191 & 0.0500047080808956 \tabularnewline
82 & 6.2 & 6.18999663680073 & 0.0100033631992682 \tabularnewline
83 & 6.22 & 6.19999932719728 & 0.0200006728027233 \tabularnewline
84 & 6.22 & 6.2199986548017 & 1.34519829675384e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278528&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]4.81[/C][C]4.8[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]3[/C][C]5.16[/C][C]4.80999932742348[/C][C]0.350000672576524[/C][/ROW]
[ROW][C]4[/C][C]5.26[/C][C]5.15997645977647[/C][C]0.100023540223533[/C][/ROW]
[ROW][C]5[/C][C]5.29[/C][C]5.25999327265151[/C][C]0.0300067273484883[/C][/ROW]
[ROW][C]6[/C][C]5.29[/C][C]5.28999798181797[/C][C]2.018182033936e-06[/C][/ROW]
[ROW][C]7[/C][C]5.29[/C][C]5.28999999986426[/C][C]1.35738531525931e-10[/C][/ROW]
[ROW][C]8[/C][C]5.3[/C][C]5.28999999999999[/C][C]0.0100000000000096[/C][/ROW]
[ROW][C]9[/C][C]5.3[/C][C]5.29999932742348[/C][C]6.72576522475765e-07[/C][/ROW]
[ROW][C]10[/C][C]5.3[/C][C]5.29999999995476[/C][C]4.52358150937471e-11[/C][/ROW]
[ROW][C]11[/C][C]5.3[/C][C]5.3[/C][C]2.66453525910038e-15[/C][/ROW]
[ROW][C]12[/C][C]5.3[/C][C]5.3[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]5.3[/C][C]5.3[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]5.3[/C][C]5.3[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]5.3[/C][C]5.3[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]5.35[/C][C]5.3[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]17[/C][C]5.44[/C][C]5.34999663711739[/C][C]0.0900033628826149[/C][/ROW]
[ROW][C]18[/C][C]5.47[/C][C]5.43999394658512[/C][C]0.0300060534148834[/C][/ROW]
[ROW][C]19[/C][C]5.47[/C][C]5.46999798186329[/C][C]2.01813670663853e-06[/C][/ROW]
[ROW][C]20[/C][C]5.48[/C][C]5.46999999986426[/C][C]0.0100000001357357[/C][/ROW]
[ROW][C]21[/C][C]5.48[/C][C]5.47999932742347[/C][C]6.72576532245728e-07[/C][/ROW]
[ROW][C]22[/C][C]5.48[/C][C]5.47999999995476[/C][C]4.52358150937471e-11[/C][/ROW]
[ROW][C]23[/C][C]5.48[/C][C]5.48[/C][C]3.5527136788005e-15[/C][/ROW]
[ROW][C]24[/C][C]5.48[/C][C]5.48[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]5.48[/C][C]5.48[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]5.48[/C][C]5.48[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]5.5[/C][C]5.48[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]28[/C][C]5.55[/C][C]5.49999865484696[/C][C]0.0500013451530448[/C][/ROW]
[ROW][C]29[/C][C]5.57[/C][C]5.54999663702691[/C][C]0.0200033629730862[/C][/ROW]
[ROW][C]30[/C][C]5.58[/C][C]5.56999865462077[/C][C]0.0100013453792309[/C][/ROW]
[ROW][C]31[/C][C]5.58[/C][C]5.57999932733299[/C][C]6.72667010093164e-07[/C][/ROW]
[ROW][C]32[/C][C]5.58[/C][C]5.57999999995476[/C][C]4.5242032342685e-11[/C][/ROW]
[ROW][C]33[/C][C]5.59[/C][C]5.58[/C][C]0.0100000000000033[/C][/ROW]
[ROW][C]34[/C][C]5.59[/C][C]5.58999932742348[/C][C]6.72576522475765e-07[/C][/ROW]
[ROW][C]35[/C][C]5.59[/C][C]5.58999999995476[/C][C]4.52358150937471e-11[/C][/ROW]
[ROW][C]36[/C][C]5.55[/C][C]5.59[/C][C]-0.0399999999999974[/C][/ROW]
[ROW][C]37[/C][C]5.61[/C][C]5.55000269030609[/C][C]0.0599973096939097[/C][/ROW]
[ROW][C]38[/C][C]5.61[/C][C]5.60999596472181[/C][C]4.03527819337057e-06[/C][/ROW]
[ROW][C]39[/C][C]5.61[/C][C]5.6099999997286[/C][C]2.71403344243026e-10[/C][/ROW]
[ROW][C]40[/C][C]5.63[/C][C]5.60999999999998[/C][C]0.0200000000000182[/C][/ROW]
[ROW][C]41[/C][C]5.69[/C][C]5.62999865484695[/C][C]0.0600013451530454[/C][/ROW]
[ROW][C]42[/C][C]5.7[/C][C]5.68999596445039[/C][C]0.010004035549608[/C][/ROW]
[ROW][C]43[/C][C]5.7[/C][C]5.69999932715206[/C][C]6.72847944471755e-07[/C][/ROW]
[ROW][C]44[/C][C]5.7[/C][C]5.69999999995475[/C][C]4.52544668405608e-11[/C][/ROW]
[ROW][C]45[/C][C]5.7[/C][C]5.7[/C][C]3.5527136788005e-15[/C][/ROW]
[ROW][C]46[/C][C]5.7[/C][C]5.7[/C][C]0[/C][/ROW]
[ROW][C]47[/C][C]5.7[/C][C]5.7[/C][C]0[/C][/ROW]
[ROW][C]48[/C][C]5.7[/C][C]5.7[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]5.7[/C][C]5.7[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]5.7[/C][C]5.7[/C][C]0[/C][/ROW]
[ROW][C]51[/C][C]5.7[/C][C]5.7[/C][C]0[/C][/ROW]
[ROW][C]52[/C][C]5.71[/C][C]5.7[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]53[/C][C]5.74[/C][C]5.70999932742348[/C][C]0.0300006725765227[/C][/ROW]
[ROW][C]54[/C][C]5.77[/C][C]5.7399979822252[/C][C]0.0300020177748035[/C][/ROW]
[ROW][C]55[/C][C]5.79[/C][C]5.76999798213472[/C][C]0.0200020178652798[/C][/ROW]
[ROW][C]56[/C][C]5.79[/C][C]5.78999865471124[/C][C]1.34528876216677e-06[/C][/ROW]
[ROW][C]57[/C][C]5.8[/C][C]5.78999999990952[/C][C]0.0100000000904803[/C][/ROW]
[ROW][C]58[/C][C]5.8[/C][C]5.79999932742347[/C][C]6.72576528693014e-07[/C][/ROW]
[ROW][C]59[/C][C]5.8[/C][C]5.79999999995476[/C][C]4.52358150937471e-11[/C][/ROW]
[ROW][C]60[/C][C]5.8[/C][C]5.8[/C][C]3.5527136788005e-15[/C][/ROW]
[ROW][C]61[/C][C]5.8[/C][C]5.8[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]5.81[/C][C]5.8[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]63[/C][C]5.81[/C][C]5.80999932742348[/C][C]6.72576522475765e-07[/C][/ROW]
[ROW][C]64[/C][C]5.83[/C][C]5.80999999995476[/C][C]0.0200000000452363[/C][/ROW]
[ROW][C]65[/C][C]5.94[/C][C]5.82999865484695[/C][C]0.110001345153049[/C][/ROW]
[ROW][C]66[/C][C]5.98[/C][C]5.93999260156778[/C][C]0.0400073984322225[/C][/ROW]
[ROW][C]67[/C][C]5.99[/C][C]5.97999730919631[/C][C]0.0100026908036916[/C][/ROW]
[ROW][C]68[/C][C]6[/C][C]5.9899993272425[/C][C]0.0100006727575002[/C][/ROW]
[ROW][C]69[/C][C]6.02[/C][C]5.99999932737823[/C][C]0.0200006726217703[/C][/ROW]
[ROW][C]70[/C][C]6.02[/C][C]6.01999865480171[/C][C]1.34519828520752e-06[/C][/ROW]
[ROW][C]71[/C][C]6.02[/C][C]6.01999999990952[/C][C]9.0475182901173e-11[/C][/ROW]
[ROW][C]72[/C][C]6.02[/C][C]6.01999999999999[/C][C]6.21724893790088e-15[/C][/ROW]
[ROW][C]73[/C][C]6.02[/C][C]6.02[/C][C]0[/C][/ROW]
[ROW][C]74[/C][C]6.02[/C][C]6.02[/C][C]0[/C][/ROW]
[ROW][C]75[/C][C]6.02[/C][C]6.02[/C][C]0[/C][/ROW]
[ROW][C]76[/C][C]6.04[/C][C]6.02[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]77[/C][C]6.06[/C][C]6.03999865484696[/C][C]0.0200013451530445[/C][/ROW]
[ROW][C]78[/C][C]6.06[/C][C]6.05999865475648[/C][C]1.3452435174699e-06[/C][/ROW]
[ROW][C]79[/C][C]6.07[/C][C]6.05999999990952[/C][C]0.0100000000904785[/C][/ROW]
[ROW][C]80[/C][C]6.14[/C][C]6.06999932742347[/C][C]0.0700006725765281[/C][/ROW]
[ROW][C]81[/C][C]6.19[/C][C]6.1399952919191[/C][C]0.0500047080808956[/C][/ROW]
[ROW][C]82[/C][C]6.2[/C][C]6.18999663680073[/C][C]0.0100033631992682[/C][/ROW]
[ROW][C]83[/C][C]6.22[/C][C]6.19999932719728[/C][C]0.0200006728027233[/C][/ROW]
[ROW][C]84[/C][C]6.22[/C][C]6.2199986548017[/C][C]1.34519829675384e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278528&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278528&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
24.814.80.00999999999999979
35.164.809999327423480.350000672576524
45.265.159976459776470.100023540223533
55.295.259993272651510.0300067273484883
65.295.289997981817972.018182033936e-06
75.295.289999999864261.35738531525931e-10
85.35.289999999999990.0100000000000096
95.35.299999327423486.72576522475765e-07
105.35.299999999954764.52358150937471e-11
115.35.32.66453525910038e-15
125.35.30
135.35.30
145.35.30
155.35.30
165.355.30.0499999999999998
175.445.349996637117390.0900033628826149
185.475.439993946585120.0300060534148834
195.475.469997981863292.01813670663853e-06
205.485.469999999864260.0100000001357357
215.485.479999327423476.72576532245728e-07
225.485.479999999954764.52358150937471e-11
235.485.483.5527136788005e-15
245.485.480
255.485.480
265.485.480
275.55.480.0199999999999996
285.555.499998654846960.0500013451530448
295.575.549996637026910.0200033629730862
305.585.569998654620770.0100013453792309
315.585.579999327332996.72667010093164e-07
325.585.579999999954764.5242032342685e-11
335.595.580.0100000000000033
345.595.589999327423486.72576522475765e-07
355.595.589999999954764.52358150937471e-11
365.555.59-0.0399999999999974
375.615.550002690306090.0599973096939097
385.615.609995964721814.03527819337057e-06
395.615.60999999972862.71403344243026e-10
405.635.609999999999980.0200000000000182
415.695.629998654846950.0600013451530454
425.75.689995964450390.010004035549608
435.75.699999327152066.72847944471755e-07
445.75.699999999954754.52544668405608e-11
455.75.73.5527136788005e-15
465.75.70
475.75.70
485.75.70
495.75.70
505.75.70
515.75.70
525.715.70.00999999999999979
535.745.709999327423480.0300006725765227
545.775.73999798222520.0300020177748035
555.795.769997982134720.0200020178652798
565.795.789998654711241.34528876216677e-06
575.85.789999999909520.0100000000904803
585.85.799999327423476.72576528693014e-07
595.85.799999999954764.52358150937471e-11
605.85.83.5527136788005e-15
615.85.80
625.815.80.00999999999999979
635.815.809999327423486.72576522475765e-07
645.835.809999999954760.0200000000452363
655.945.829998654846950.110001345153049
665.985.939992601567780.0400073984322225
675.995.979997309196310.0100026908036916
6865.98999932724250.0100006727575002
696.025.999999327378230.0200006726217703
706.026.019998654801711.34519828520752e-06
716.026.019999999909529.0475182901173e-11
726.026.019999999999996.21724893790088e-15
736.026.020
746.026.020
756.026.020
766.046.020.0200000000000005
776.066.039998654846960.0200013451530445
786.066.059998654756481.3452435174699e-06
796.076.059999999909520.0100000000904785
806.146.069999327423470.0700006725765281
816.196.13999529191910.0500047080808956
826.26.189996636800730.0100033631992682
836.226.199999327197280.0200006728027233
846.226.21999865480171.34519829675384e-06







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
856.219999999909526.133501374737256.3064986250818
866.219999999909526.09767658472636.34232341509275
876.219999999909526.07018670394596.36981329587315
886.219999999909526.047011476033296.39298852378576
896.219999999909526.026593601002276.41340639881678
906.219999999909526.008134380037716.43186561978134
916.219999999909525.991159342182226.44884065763682
926.219999999909525.975359340217696.46464065960136
936.219999999909525.960519638186616.47948036163244
946.219999999909525.946483887284976.49351611253408
956.219999999909525.933134056286656.5068659435324
966.219999999909525.920378446352316.51962155346674

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 6.21999999990952 & 6.13350137473725 & 6.3064986250818 \tabularnewline
86 & 6.21999999990952 & 6.0976765847263 & 6.34232341509275 \tabularnewline
87 & 6.21999999990952 & 6.0701867039459 & 6.36981329587315 \tabularnewline
88 & 6.21999999990952 & 6.04701147603329 & 6.39298852378576 \tabularnewline
89 & 6.21999999990952 & 6.02659360100227 & 6.41340639881678 \tabularnewline
90 & 6.21999999990952 & 6.00813438003771 & 6.43186561978134 \tabularnewline
91 & 6.21999999990952 & 5.99115934218222 & 6.44884065763682 \tabularnewline
92 & 6.21999999990952 & 5.97535934021769 & 6.46464065960136 \tabularnewline
93 & 6.21999999990952 & 5.96051963818661 & 6.47948036163244 \tabularnewline
94 & 6.21999999990952 & 5.94648388728497 & 6.49351611253408 \tabularnewline
95 & 6.21999999990952 & 5.93313405628665 & 6.5068659435324 \tabularnewline
96 & 6.21999999990952 & 5.92037844635231 & 6.51962155346674 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278528&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]85[/C][C]6.21999999990952[/C][C]6.13350137473725[/C][C]6.3064986250818[/C][/ROW]
[ROW][C]86[/C][C]6.21999999990952[/C][C]6.0976765847263[/C][C]6.34232341509275[/C][/ROW]
[ROW][C]87[/C][C]6.21999999990952[/C][C]6.0701867039459[/C][C]6.36981329587315[/C][/ROW]
[ROW][C]88[/C][C]6.21999999990952[/C][C]6.04701147603329[/C][C]6.39298852378576[/C][/ROW]
[ROW][C]89[/C][C]6.21999999990952[/C][C]6.02659360100227[/C][C]6.41340639881678[/C][/ROW]
[ROW][C]90[/C][C]6.21999999990952[/C][C]6.00813438003771[/C][C]6.43186561978134[/C][/ROW]
[ROW][C]91[/C][C]6.21999999990952[/C][C]5.99115934218222[/C][C]6.44884065763682[/C][/ROW]
[ROW][C]92[/C][C]6.21999999990952[/C][C]5.97535934021769[/C][C]6.46464065960136[/C][/ROW]
[ROW][C]93[/C][C]6.21999999990952[/C][C]5.96051963818661[/C][C]6.47948036163244[/C][/ROW]
[ROW][C]94[/C][C]6.21999999990952[/C][C]5.94648388728497[/C][C]6.49351611253408[/C][/ROW]
[ROW][C]95[/C][C]6.21999999990952[/C][C]5.93313405628665[/C][C]6.5068659435324[/C][/ROW]
[ROW][C]96[/C][C]6.21999999990952[/C][C]5.92037844635231[/C][C]6.51962155346674[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278528&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278528&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
856.219999999909526.133501374737256.3064986250818
866.219999999909526.09767658472636.34232341509275
876.219999999909526.07018670394596.36981329587315
886.219999999909526.047011476033296.39298852378576
896.219999999909526.026593601002276.41340639881678
906.219999999909526.008134380037716.43186561978134
916.219999999909525.991159342182226.44884065763682
926.219999999909525.975359340217696.46464065960136
936.219999999909525.960519638186616.47948036163244
946.219999999909525.946483887284976.49351611253408
956.219999999909525.933134056286656.5068659435324
966.219999999909525.920378446352316.51962155346674



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):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')