Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 04:59:14 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356083984x1b82j2akyi11ld.htm/, Retrieved Thu, 28 Mar 2024 21:06:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203398, Retrieved Thu, 28 Mar 2024 21:06:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2012-12-21 09:59:14] [585de6c888271e2f88a1b417ea6af330] [Current]
Feedback Forum

Post a new message
Dataseries X:
73,97
73,97
73,97
73,97
73,97
73,97
73,96
74,44
75,43
75,77
75,82
75,85
75,85
75,85
77,95
82,07
84,82
85,08
85,34
85,65
85,65
85,72
85,73
85,73
85,73
85,73
85,74
86,32
87,59
87,81
87,87
87,94
87,96
88,01
88,01
88,01
88,01
88,01
88,59
89,43
89,63
89,73
89,88
89,89
89,9
89,91
89,86
90,07
90,17
90,17
90,28
90,87
92,05
92,1
92,16
92,22
92,25
92,29
92,29
92,29
92,29
92,29
91,95
91,82
92,16
92,31
92,33
92,4
92,54
92,49
92,54
92,58




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203398&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203398&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203398&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933722744407
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933722744407 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203398&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]0.999933722744407[/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=203398&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203398&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
alpha0.999933722744407
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
273.9773.970
373.9773.970
473.9773.970
573.9773.970
673.9773.970
773.9673.97-0.0100000000000051
874.4473.96000066277250.479999337227454
975.4374.43996818696120.990031813038769
1075.7775.42993438340850.340065616591502
1175.8275.76997746138420.0500225386157922
1275.8575.81999668464340.0300033153565806
1375.8575.84999801146261.98853740585037e-06
1475.8575.84999999986821.31791466628783e-10
1577.9575.852.10000000000002
1682.0777.94986081776334.12013918223674
1784.8282.06972692848232.75027307151765
1885.0884.81981771944870.260182280551319
1985.3485.07998275583250.260017244167514
2085.6585.33998276677060.31001723322936
2185.6585.64997945290862.05470914096395e-05
2285.7285.64999999863820.070000001361791
2385.7385.7199953605920.0100046394079811
2485.7385.729999336926.63080044205344e-07
2585.7385.7299999999564.39541736341198e-11
2685.7385.730
2785.7485.730.00999999999999091
2886.3285.73999933722740.580000662772548
2987.5986.31996155914781.27003844085218
3087.8187.58991582533760.220084174662361
3187.8787.80998541342490.0600145865750932
3287.9487.86999602239790.0700039776020844
3387.9687.93999536032850.0200046396715123
3488.0187.95999867414740.0500013258526337
3588.0188.00999668604933.31395065700235e-06
3688.0188.00999999978042.19642970478162e-10
3788.0188.011.4210854715202e-14
3888.0188.010
3988.5988.010.579999999999998
4089.4388.58996155919180.840038440808243
4189.6389.42994432455760.200055675442442
4289.7389.62998674085890.100013259141136
4389.8889.72999337139570.150006628604331
4489.8989.87999005797230.0100099420276649
4589.989.88999933656850.010000663431498
4689.9189.89999933718350.0100006628165232
4789.8689.9099993371835-0.0499993371835075
4890.0789.86000331381890.209996686181142
4990.1790.06998608199590.100013918004052
5090.1790.1699933713526.62864800915486e-06
5190.2890.16999999956070.110000000439328
5290.8790.27999270950190.59000729049815
5392.0590.8699608959361.18003910406398
5492.192.04992179024670.050078209753309
5592.1692.09999668095370.0600033190463165
5692.2292.15999602314470.0600039768553131
5792.2592.21999602310110.0300039768989109
5892.2992.24999801141880.0400019885812526
5992.2992.2899973487782.6512220188124e-06
6092.2992.28999999982431.75717218553473e-10
6192.2992.291.4210854715202e-14
6292.2992.290
6391.9592.29-0.340000000000003
6491.8291.9500225342669-0.130022534266914
6592.1691.82000861753670.339991382463268
6692.3192.15997746630420.150022533695761
6792.3392.30999005691820.0200099430818028
6892.492.32999867379590.070001326204121
6992.5492.39999536050420.140004639495785
7092.4992.5399907208767-0.0499907208767354
7192.5492.49000331324780.0499966867522232
7292.5892.53999668635680.040003313643183

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 73.97 & 73.97 & 0 \tabularnewline
3 & 73.97 & 73.97 & 0 \tabularnewline
4 & 73.97 & 73.97 & 0 \tabularnewline
5 & 73.97 & 73.97 & 0 \tabularnewline
6 & 73.97 & 73.97 & 0 \tabularnewline
7 & 73.96 & 73.97 & -0.0100000000000051 \tabularnewline
8 & 74.44 & 73.9600006627725 & 0.479999337227454 \tabularnewline
9 & 75.43 & 74.4399681869612 & 0.990031813038769 \tabularnewline
10 & 75.77 & 75.4299343834085 & 0.340065616591502 \tabularnewline
11 & 75.82 & 75.7699774613842 & 0.0500225386157922 \tabularnewline
12 & 75.85 & 75.8199966846434 & 0.0300033153565806 \tabularnewline
13 & 75.85 & 75.8499980114626 & 1.98853740585037e-06 \tabularnewline
14 & 75.85 & 75.8499999998682 & 1.31791466628783e-10 \tabularnewline
15 & 77.95 & 75.85 & 2.10000000000002 \tabularnewline
16 & 82.07 & 77.9498608177633 & 4.12013918223674 \tabularnewline
17 & 84.82 & 82.0697269284823 & 2.75027307151765 \tabularnewline
18 & 85.08 & 84.8198177194487 & 0.260182280551319 \tabularnewline
19 & 85.34 & 85.0799827558325 & 0.260017244167514 \tabularnewline
20 & 85.65 & 85.3399827667706 & 0.31001723322936 \tabularnewline
21 & 85.65 & 85.6499794529086 & 2.05470914096395e-05 \tabularnewline
22 & 85.72 & 85.6499999986382 & 0.070000001361791 \tabularnewline
23 & 85.73 & 85.719995360592 & 0.0100046394079811 \tabularnewline
24 & 85.73 & 85.72999933692 & 6.63080044205344e-07 \tabularnewline
25 & 85.73 & 85.729999999956 & 4.39541736341198e-11 \tabularnewline
26 & 85.73 & 85.73 & 0 \tabularnewline
27 & 85.74 & 85.73 & 0.00999999999999091 \tabularnewline
28 & 86.32 & 85.7399993372274 & 0.580000662772548 \tabularnewline
29 & 87.59 & 86.3199615591478 & 1.27003844085218 \tabularnewline
30 & 87.81 & 87.5899158253376 & 0.220084174662361 \tabularnewline
31 & 87.87 & 87.8099854134249 & 0.0600145865750932 \tabularnewline
32 & 87.94 & 87.8699960223979 & 0.0700039776020844 \tabularnewline
33 & 87.96 & 87.9399953603285 & 0.0200046396715123 \tabularnewline
34 & 88.01 & 87.9599986741474 & 0.0500013258526337 \tabularnewline
35 & 88.01 & 88.0099966860493 & 3.31395065700235e-06 \tabularnewline
36 & 88.01 & 88.0099999997804 & 2.19642970478162e-10 \tabularnewline
37 & 88.01 & 88.01 & 1.4210854715202e-14 \tabularnewline
38 & 88.01 & 88.01 & 0 \tabularnewline
39 & 88.59 & 88.01 & 0.579999999999998 \tabularnewline
40 & 89.43 & 88.5899615591918 & 0.840038440808243 \tabularnewline
41 & 89.63 & 89.4299443245576 & 0.200055675442442 \tabularnewline
42 & 89.73 & 89.6299867408589 & 0.100013259141136 \tabularnewline
43 & 89.88 & 89.7299933713957 & 0.150006628604331 \tabularnewline
44 & 89.89 & 89.8799900579723 & 0.0100099420276649 \tabularnewline
45 & 89.9 & 89.8899993365685 & 0.010000663431498 \tabularnewline
46 & 89.91 & 89.8999993371835 & 0.0100006628165232 \tabularnewline
47 & 89.86 & 89.9099993371835 & -0.0499993371835075 \tabularnewline
48 & 90.07 & 89.8600033138189 & 0.209996686181142 \tabularnewline
49 & 90.17 & 90.0699860819959 & 0.100013918004052 \tabularnewline
50 & 90.17 & 90.169993371352 & 6.62864800915486e-06 \tabularnewline
51 & 90.28 & 90.1699999995607 & 0.110000000439328 \tabularnewline
52 & 90.87 & 90.2799927095019 & 0.59000729049815 \tabularnewline
53 & 92.05 & 90.869960895936 & 1.18003910406398 \tabularnewline
54 & 92.1 & 92.0499217902467 & 0.050078209753309 \tabularnewline
55 & 92.16 & 92.0999966809537 & 0.0600033190463165 \tabularnewline
56 & 92.22 & 92.1599960231447 & 0.0600039768553131 \tabularnewline
57 & 92.25 & 92.2199960231011 & 0.0300039768989109 \tabularnewline
58 & 92.29 & 92.2499980114188 & 0.0400019885812526 \tabularnewline
59 & 92.29 & 92.289997348778 & 2.6512220188124e-06 \tabularnewline
60 & 92.29 & 92.2899999998243 & 1.75717218553473e-10 \tabularnewline
61 & 92.29 & 92.29 & 1.4210854715202e-14 \tabularnewline
62 & 92.29 & 92.29 & 0 \tabularnewline
63 & 91.95 & 92.29 & -0.340000000000003 \tabularnewline
64 & 91.82 & 91.9500225342669 & -0.130022534266914 \tabularnewline
65 & 92.16 & 91.8200086175367 & 0.339991382463268 \tabularnewline
66 & 92.31 & 92.1599774663042 & 0.150022533695761 \tabularnewline
67 & 92.33 & 92.3099900569182 & 0.0200099430818028 \tabularnewline
68 & 92.4 & 92.3299986737959 & 0.070001326204121 \tabularnewline
69 & 92.54 & 92.3999953605042 & 0.140004639495785 \tabularnewline
70 & 92.49 & 92.5399907208767 & -0.0499907208767354 \tabularnewline
71 & 92.54 & 92.4900033132478 & 0.0499966867522232 \tabularnewline
72 & 92.58 & 92.5399966863568 & 0.040003313643183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203398&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]73.97[/C][C]73.97[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]73.97[/C][C]73.97[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]73.97[/C][C]73.97[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]73.97[/C][C]73.97[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]73.97[/C][C]73.97[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]73.96[/C][C]73.97[/C][C]-0.0100000000000051[/C][/ROW]
[ROW][C]8[/C][C]74.44[/C][C]73.9600006627725[/C][C]0.479999337227454[/C][/ROW]
[ROW][C]9[/C][C]75.43[/C][C]74.4399681869612[/C][C]0.990031813038769[/C][/ROW]
[ROW][C]10[/C][C]75.77[/C][C]75.4299343834085[/C][C]0.340065616591502[/C][/ROW]
[ROW][C]11[/C][C]75.82[/C][C]75.7699774613842[/C][C]0.0500225386157922[/C][/ROW]
[ROW][C]12[/C][C]75.85[/C][C]75.8199966846434[/C][C]0.0300033153565806[/C][/ROW]
[ROW][C]13[/C][C]75.85[/C][C]75.8499980114626[/C][C]1.98853740585037e-06[/C][/ROW]
[ROW][C]14[/C][C]75.85[/C][C]75.8499999998682[/C][C]1.31791466628783e-10[/C][/ROW]
[ROW][C]15[/C][C]77.95[/C][C]75.85[/C][C]2.10000000000002[/C][/ROW]
[ROW][C]16[/C][C]82.07[/C][C]77.9498608177633[/C][C]4.12013918223674[/C][/ROW]
[ROW][C]17[/C][C]84.82[/C][C]82.0697269284823[/C][C]2.75027307151765[/C][/ROW]
[ROW][C]18[/C][C]85.08[/C][C]84.8198177194487[/C][C]0.260182280551319[/C][/ROW]
[ROW][C]19[/C][C]85.34[/C][C]85.0799827558325[/C][C]0.260017244167514[/C][/ROW]
[ROW][C]20[/C][C]85.65[/C][C]85.3399827667706[/C][C]0.31001723322936[/C][/ROW]
[ROW][C]21[/C][C]85.65[/C][C]85.6499794529086[/C][C]2.05470914096395e-05[/C][/ROW]
[ROW][C]22[/C][C]85.72[/C][C]85.6499999986382[/C][C]0.070000001361791[/C][/ROW]
[ROW][C]23[/C][C]85.73[/C][C]85.719995360592[/C][C]0.0100046394079811[/C][/ROW]
[ROW][C]24[/C][C]85.73[/C][C]85.72999933692[/C][C]6.63080044205344e-07[/C][/ROW]
[ROW][C]25[/C][C]85.73[/C][C]85.729999999956[/C][C]4.39541736341198e-11[/C][/ROW]
[ROW][C]26[/C][C]85.73[/C][C]85.73[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]85.74[/C][C]85.73[/C][C]0.00999999999999091[/C][/ROW]
[ROW][C]28[/C][C]86.32[/C][C]85.7399993372274[/C][C]0.580000662772548[/C][/ROW]
[ROW][C]29[/C][C]87.59[/C][C]86.3199615591478[/C][C]1.27003844085218[/C][/ROW]
[ROW][C]30[/C][C]87.81[/C][C]87.5899158253376[/C][C]0.220084174662361[/C][/ROW]
[ROW][C]31[/C][C]87.87[/C][C]87.8099854134249[/C][C]0.0600145865750932[/C][/ROW]
[ROW][C]32[/C][C]87.94[/C][C]87.8699960223979[/C][C]0.0700039776020844[/C][/ROW]
[ROW][C]33[/C][C]87.96[/C][C]87.9399953603285[/C][C]0.0200046396715123[/C][/ROW]
[ROW][C]34[/C][C]88.01[/C][C]87.9599986741474[/C][C]0.0500013258526337[/C][/ROW]
[ROW][C]35[/C][C]88.01[/C][C]88.0099966860493[/C][C]3.31395065700235e-06[/C][/ROW]
[ROW][C]36[/C][C]88.01[/C][C]88.0099999997804[/C][C]2.19642970478162e-10[/C][/ROW]
[ROW][C]37[/C][C]88.01[/C][C]88.01[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]38[/C][C]88.01[/C][C]88.01[/C][C]0[/C][/ROW]
[ROW][C]39[/C][C]88.59[/C][C]88.01[/C][C]0.579999999999998[/C][/ROW]
[ROW][C]40[/C][C]89.43[/C][C]88.5899615591918[/C][C]0.840038440808243[/C][/ROW]
[ROW][C]41[/C][C]89.63[/C][C]89.4299443245576[/C][C]0.200055675442442[/C][/ROW]
[ROW][C]42[/C][C]89.73[/C][C]89.6299867408589[/C][C]0.100013259141136[/C][/ROW]
[ROW][C]43[/C][C]89.88[/C][C]89.7299933713957[/C][C]0.150006628604331[/C][/ROW]
[ROW][C]44[/C][C]89.89[/C][C]89.8799900579723[/C][C]0.0100099420276649[/C][/ROW]
[ROW][C]45[/C][C]89.9[/C][C]89.8899993365685[/C][C]0.010000663431498[/C][/ROW]
[ROW][C]46[/C][C]89.91[/C][C]89.8999993371835[/C][C]0.0100006628165232[/C][/ROW]
[ROW][C]47[/C][C]89.86[/C][C]89.9099993371835[/C][C]-0.0499993371835075[/C][/ROW]
[ROW][C]48[/C][C]90.07[/C][C]89.8600033138189[/C][C]0.209996686181142[/C][/ROW]
[ROW][C]49[/C][C]90.17[/C][C]90.0699860819959[/C][C]0.100013918004052[/C][/ROW]
[ROW][C]50[/C][C]90.17[/C][C]90.169993371352[/C][C]6.62864800915486e-06[/C][/ROW]
[ROW][C]51[/C][C]90.28[/C][C]90.1699999995607[/C][C]0.110000000439328[/C][/ROW]
[ROW][C]52[/C][C]90.87[/C][C]90.2799927095019[/C][C]0.59000729049815[/C][/ROW]
[ROW][C]53[/C][C]92.05[/C][C]90.869960895936[/C][C]1.18003910406398[/C][/ROW]
[ROW][C]54[/C][C]92.1[/C][C]92.0499217902467[/C][C]0.050078209753309[/C][/ROW]
[ROW][C]55[/C][C]92.16[/C][C]92.0999966809537[/C][C]0.0600033190463165[/C][/ROW]
[ROW][C]56[/C][C]92.22[/C][C]92.1599960231447[/C][C]0.0600039768553131[/C][/ROW]
[ROW][C]57[/C][C]92.25[/C][C]92.2199960231011[/C][C]0.0300039768989109[/C][/ROW]
[ROW][C]58[/C][C]92.29[/C][C]92.2499980114188[/C][C]0.0400019885812526[/C][/ROW]
[ROW][C]59[/C][C]92.29[/C][C]92.289997348778[/C][C]2.6512220188124e-06[/C][/ROW]
[ROW][C]60[/C][C]92.29[/C][C]92.2899999998243[/C][C]1.75717218553473e-10[/C][/ROW]
[ROW][C]61[/C][C]92.29[/C][C]92.29[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]62[/C][C]92.29[/C][C]92.29[/C][C]0[/C][/ROW]
[ROW][C]63[/C][C]91.95[/C][C]92.29[/C][C]-0.340000000000003[/C][/ROW]
[ROW][C]64[/C][C]91.82[/C][C]91.9500225342669[/C][C]-0.130022534266914[/C][/ROW]
[ROW][C]65[/C][C]92.16[/C][C]91.8200086175367[/C][C]0.339991382463268[/C][/ROW]
[ROW][C]66[/C][C]92.31[/C][C]92.1599774663042[/C][C]0.150022533695761[/C][/ROW]
[ROW][C]67[/C][C]92.33[/C][C]92.3099900569182[/C][C]0.0200099430818028[/C][/ROW]
[ROW][C]68[/C][C]92.4[/C][C]92.3299986737959[/C][C]0.070001326204121[/C][/ROW]
[ROW][C]69[/C][C]92.54[/C][C]92.3999953605042[/C][C]0.140004639495785[/C][/ROW]
[ROW][C]70[/C][C]92.49[/C][C]92.5399907208767[/C][C]-0.0499907208767354[/C][/ROW]
[ROW][C]71[/C][C]92.54[/C][C]92.4900033132478[/C][C]0.0499966867522232[/C][/ROW]
[ROW][C]72[/C][C]92.58[/C][C]92.5399966863568[/C][C]0.040003313643183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203398&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203398&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
273.9773.970
373.9773.970
473.9773.970
573.9773.970
673.9773.970
773.9673.97-0.0100000000000051
874.4473.96000066277250.479999337227454
975.4374.43996818696120.990031813038769
1075.7775.42993438340850.340065616591502
1175.8275.76997746138420.0500225386157922
1275.8575.81999668464340.0300033153565806
1375.8575.84999801146261.98853740585037e-06
1475.8575.84999999986821.31791466628783e-10
1577.9575.852.10000000000002
1682.0777.94986081776334.12013918223674
1784.8282.06972692848232.75027307151765
1885.0884.81981771944870.260182280551319
1985.3485.07998275583250.260017244167514
2085.6585.33998276677060.31001723322936
2185.6585.64997945290862.05470914096395e-05
2285.7285.64999999863820.070000001361791
2385.7385.7199953605920.0100046394079811
2485.7385.729999336926.63080044205344e-07
2585.7385.7299999999564.39541736341198e-11
2685.7385.730
2785.7485.730.00999999999999091
2886.3285.73999933722740.580000662772548
2987.5986.31996155914781.27003844085218
3087.8187.58991582533760.220084174662361
3187.8787.80998541342490.0600145865750932
3287.9487.86999602239790.0700039776020844
3387.9687.93999536032850.0200046396715123
3488.0187.95999867414740.0500013258526337
3588.0188.00999668604933.31395065700235e-06
3688.0188.00999999978042.19642970478162e-10
3788.0188.011.4210854715202e-14
3888.0188.010
3988.5988.010.579999999999998
4089.4388.58996155919180.840038440808243
4189.6389.42994432455760.200055675442442
4289.7389.62998674085890.100013259141136
4389.8889.72999337139570.150006628604331
4489.8989.87999005797230.0100099420276649
4589.989.88999933656850.010000663431498
4689.9189.89999933718350.0100006628165232
4789.8689.9099993371835-0.0499993371835075
4890.0789.86000331381890.209996686181142
4990.1790.06998608199590.100013918004052
5090.1790.1699933713526.62864800915486e-06
5190.2890.16999999956070.110000000439328
5290.8790.27999270950190.59000729049815
5392.0590.8699608959361.18003910406398
5492.192.04992179024670.050078209753309
5592.1692.09999668095370.0600033190463165
5692.2292.15999602314470.0600039768553131
5792.2592.21999602310110.0300039768989109
5892.2992.24999801141880.0400019885812526
5992.2992.2899973487782.6512220188124e-06
6092.2992.28999999982431.75717218553473e-10
6192.2992.291.4210854715202e-14
6292.2992.290
6391.9592.29-0.340000000000003
6491.8291.9500225342669-0.130022534266914
6592.1691.82000861753670.339991382463268
6692.3192.15997746630420.150022533695761
6792.3392.30999005691820.0200099430818028
6892.492.32999867379590.070001326204121
6992.5492.39999536050420.140004639495785
7092.4992.5399907208767-0.0499907208767354
7192.5492.49000331324780.0499966867522232
7292.5892.53999668635680.040003313643183







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7392.579997348690291.278112452039693.8818822453407
7492.579997348690290.738915083149194.4210796142312
7592.579997348690290.325166194733794.8348285026467
7692.579997348690289.976356982353995.1836377150264
7792.579997348690289.669048571817195.4909461255632
7892.579997348690289.391219776337195.7687749210432
7992.579997348690289.135729352394796.0242653449856
8092.579997348690288.897924338188196.2620703591923
8192.579997348690288.674572752179496.4854219452009
8292.579997348690288.463321395521996.6966733018584
8392.579997348690288.262393785629296.8976009117512
8492.579997348690288.070409767533897.0895849298466

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 92.5799973486902 & 91.2781124520396 & 93.8818822453407 \tabularnewline
74 & 92.5799973486902 & 90.7389150831491 & 94.4210796142312 \tabularnewline
75 & 92.5799973486902 & 90.3251661947337 & 94.8348285026467 \tabularnewline
76 & 92.5799973486902 & 89.9763569823539 & 95.1836377150264 \tabularnewline
77 & 92.5799973486902 & 89.6690485718171 & 95.4909461255632 \tabularnewline
78 & 92.5799973486902 & 89.3912197763371 & 95.7687749210432 \tabularnewline
79 & 92.5799973486902 & 89.1357293523947 & 96.0242653449856 \tabularnewline
80 & 92.5799973486902 & 88.8979243381881 & 96.2620703591923 \tabularnewline
81 & 92.5799973486902 & 88.6745727521794 & 96.4854219452009 \tabularnewline
82 & 92.5799973486902 & 88.4633213955219 & 96.6966733018584 \tabularnewline
83 & 92.5799973486902 & 88.2623937856292 & 96.8976009117512 \tabularnewline
84 & 92.5799973486902 & 88.0704097675338 & 97.0895849298466 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203398&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]92.5799973486902[/C][C]91.2781124520396[/C][C]93.8818822453407[/C][/ROW]
[ROW][C]74[/C][C]92.5799973486902[/C][C]90.7389150831491[/C][C]94.4210796142312[/C][/ROW]
[ROW][C]75[/C][C]92.5799973486902[/C][C]90.3251661947337[/C][C]94.8348285026467[/C][/ROW]
[ROW][C]76[/C][C]92.5799973486902[/C][C]89.9763569823539[/C][C]95.1836377150264[/C][/ROW]
[ROW][C]77[/C][C]92.5799973486902[/C][C]89.6690485718171[/C][C]95.4909461255632[/C][/ROW]
[ROW][C]78[/C][C]92.5799973486902[/C][C]89.3912197763371[/C][C]95.7687749210432[/C][/ROW]
[ROW][C]79[/C][C]92.5799973486902[/C][C]89.1357293523947[/C][C]96.0242653449856[/C][/ROW]
[ROW][C]80[/C][C]92.5799973486902[/C][C]88.8979243381881[/C][C]96.2620703591923[/C][/ROW]
[ROW][C]81[/C][C]92.5799973486902[/C][C]88.6745727521794[/C][C]96.4854219452009[/C][/ROW]
[ROW][C]82[/C][C]92.5799973486902[/C][C]88.4633213955219[/C][C]96.6966733018584[/C][/ROW]
[ROW][C]83[/C][C]92.5799973486902[/C][C]88.2623937856292[/C][C]96.8976009117512[/C][/ROW]
[ROW][C]84[/C][C]92.5799973486902[/C][C]88.0704097675338[/C][C]97.0895849298466[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203398&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203398&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
7392.579997348690291.278112452039693.8818822453407
7492.579997348690290.738915083149194.4210796142312
7592.579997348690290.325166194733794.8348285026467
7692.579997348690289.976356982353995.1836377150264
7792.579997348690289.669048571817195.4909461255632
7892.579997348690289.391219776337195.7687749210432
7992.579997348690289.135729352394796.0242653449856
8092.579997348690288.897924338188196.2620703591923
8192.579997348690288.674572752179496.4854219452009
8292.579997348690288.463321395521996.6966733018584
8392.579997348690288.262393785629296.8976009117512
8492.579997348690288.070409767533897.0895849298466



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')