Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 May 2017 13:29:07 +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/2017/May/02/t1493728167k78xhyvxakt0xxd.htm/, Retrieved Fri, 17 May 2024 05:02:10 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 05:02:10 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
94
94,45
94,34
94,39
94,68
94,76
94,96
95,01
95,1
95,23
95,26
95,34
95,71
96,07
96,19
96,11
96,31
96,46
96,68
96,69
96,72
96,92
97,04
97,18
97,83
98,25
98,24
98,28
98,53
98,62
98,84
98,94
98,94
99,1
99,15
99,26
99,01
99,43
99,62
99,43
99,81
99,99
100,24
100,32
100,32
100,47
100,62
100,72
100,92
101,13
101,26
101,36
101,52
101,59
101,86
101,74
101,78
101,9
101,83
101,98
102,19
102,59
102,35
102,67
102,61
102,93
103,12
103,2
103,05
103,45
103,66
103,74




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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.999945547882134
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999945547882134 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.999945547882134[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.999945547882134
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
294.45940.450000000000003
394.3494.449975496547-0.109975496546951
494.3994.34000598839870.0499940116012993
594.6894.38999727772020.290002722279823
694.7694.67998420873760.0800157912624115
794.9694.75999564297070.200004357029286
895.0194.95998910933920.050010890660829
995.195.00999727680110.0900027231989071
1095.2395.09999509916110.130004900838912
1195.2695.22999292095780.0300070790421785
1295.3495.2599983660510.0800016339490099
1395.7195.33999564374160.370004356258391
1496.0795.70997985247920.360020147520814
1596.1996.06998039614050.120019603859504
1696.1196.1899934646784-0.0799934646783953
1796.3196.11000435581360.19999564418643
1896.4696.30998910981360.15001089018638
1996.6896.45999183158930.220008168410686
2096.6996.67998802008930.0100119799107148
2196.7296.68999945482650.0300005451735075
2296.9296.71999836640680.200001633593232
2397.0496.91998910948750.120010890512532
2497.1897.03999346515280.14000653484716
2597.8397.17999237634770.650007623652328
2698.2597.82996460570830.420035394291745
2798.2498.2499771281832-0.00997712818319485
2898.2898.24000054327580.0399994567242459
2998.5398.27999782194490.250002178055126
3098.6298.52998638685190.0900136131480735
3198.8498.61999509856810.220004901431878
3298.9498.83998802026720.100011979732813
3398.9498.93999455413595.44586411876935e-06
3499.198.93999999970340.160000000296549
3599.1599.09999128766110.0500087123388937
3699.2699.14999727691970.110002723080285
3799.0199.2599940101188-0.249994010118755
3899.4399.01001361270330.419986387296689
3999.6299.42997713085170.190022869148265
4099.4399.6199896528523-0.189989652852333
4199.8199.4300103453390.379989654661031
4299.9999.80997930875850.180020691241452
43100.2499.98999019749210.25000980250789
44100.32100.2399863864370.0800136135632243
45100.32100.3199956430894.35691070777011e-06
46100.47100.3199999997630.150000000237242
47100.62100.4699918321820.150008167817703
48100.72100.6199918317380.100008168262434
49100.92100.7199945543430.200005445656572
50101.13100.919989109280.210010890720099
51101.26101.1299885644620.130011435537796
52101.36101.2599929206020.100007079397997
53101.52101.3599945544030.160005445597264
54101.59101.5199912873650.0700087126353992
55101.86101.5899961878770.270003812122667
56101.74101.859985297721-0.119985297720604
57101.78101.7400065334540.0399934665464343
58101.9101.7799978222710.120002177728949
59101.83101.899993465627-0.0699934656272774
60101.98101.8300038112920.149996188707561
61102.19101.979991832390.210008167610141
62102.59102.1899885646110.400011435389501
63102.35102.58997821853-0.239978218530183
64102.67102.3500130673220.319986932677764
65102.61102.669982576034-0.0599825760338177
66102.93102.6100032661780.319996733821711
67103.12102.92998257550.190017424499857
68103.2103.1199896531490.0800103468511963
69103.05103.199995643267-0.149995643267175
70103.45103.050008167580.399991832419559
71103.66103.4499782195980.2100217804024
72103.74103.6599885638690.0800114361307322

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 94.45 & 94 & 0.450000000000003 \tabularnewline
3 & 94.34 & 94.449975496547 & -0.109975496546951 \tabularnewline
4 & 94.39 & 94.3400059883987 & 0.0499940116012993 \tabularnewline
5 & 94.68 & 94.3899972777202 & 0.290002722279823 \tabularnewline
6 & 94.76 & 94.6799842087376 & 0.0800157912624115 \tabularnewline
7 & 94.96 & 94.7599956429707 & 0.200004357029286 \tabularnewline
8 & 95.01 & 94.9599891093392 & 0.050010890660829 \tabularnewline
9 & 95.1 & 95.0099972768011 & 0.0900027231989071 \tabularnewline
10 & 95.23 & 95.0999950991611 & 0.130004900838912 \tabularnewline
11 & 95.26 & 95.2299929209578 & 0.0300070790421785 \tabularnewline
12 & 95.34 & 95.259998366051 & 0.0800016339490099 \tabularnewline
13 & 95.71 & 95.3399956437416 & 0.370004356258391 \tabularnewline
14 & 96.07 & 95.7099798524792 & 0.360020147520814 \tabularnewline
15 & 96.19 & 96.0699803961405 & 0.120019603859504 \tabularnewline
16 & 96.11 & 96.1899934646784 & -0.0799934646783953 \tabularnewline
17 & 96.31 & 96.1100043558136 & 0.19999564418643 \tabularnewline
18 & 96.46 & 96.3099891098136 & 0.15001089018638 \tabularnewline
19 & 96.68 & 96.4599918315893 & 0.220008168410686 \tabularnewline
20 & 96.69 & 96.6799880200893 & 0.0100119799107148 \tabularnewline
21 & 96.72 & 96.6899994548265 & 0.0300005451735075 \tabularnewline
22 & 96.92 & 96.7199983664068 & 0.200001633593232 \tabularnewline
23 & 97.04 & 96.9199891094875 & 0.120010890512532 \tabularnewline
24 & 97.18 & 97.0399934651528 & 0.14000653484716 \tabularnewline
25 & 97.83 & 97.1799923763477 & 0.650007623652328 \tabularnewline
26 & 98.25 & 97.8299646057083 & 0.420035394291745 \tabularnewline
27 & 98.24 & 98.2499771281832 & -0.00997712818319485 \tabularnewline
28 & 98.28 & 98.2400005432758 & 0.0399994567242459 \tabularnewline
29 & 98.53 & 98.2799978219449 & 0.250002178055126 \tabularnewline
30 & 98.62 & 98.5299863868519 & 0.0900136131480735 \tabularnewline
31 & 98.84 & 98.6199950985681 & 0.220004901431878 \tabularnewline
32 & 98.94 & 98.8399880202672 & 0.100011979732813 \tabularnewline
33 & 98.94 & 98.9399945541359 & 5.44586411876935e-06 \tabularnewline
34 & 99.1 & 98.9399999997034 & 0.160000000296549 \tabularnewline
35 & 99.15 & 99.0999912876611 & 0.0500087123388937 \tabularnewline
36 & 99.26 & 99.1499972769197 & 0.110002723080285 \tabularnewline
37 & 99.01 & 99.2599940101188 & -0.249994010118755 \tabularnewline
38 & 99.43 & 99.0100136127033 & 0.419986387296689 \tabularnewline
39 & 99.62 & 99.4299771308517 & 0.190022869148265 \tabularnewline
40 & 99.43 & 99.6199896528523 & -0.189989652852333 \tabularnewline
41 & 99.81 & 99.430010345339 & 0.379989654661031 \tabularnewline
42 & 99.99 & 99.8099793087585 & 0.180020691241452 \tabularnewline
43 & 100.24 & 99.9899901974921 & 0.25000980250789 \tabularnewline
44 & 100.32 & 100.239986386437 & 0.0800136135632243 \tabularnewline
45 & 100.32 & 100.319995643089 & 4.35691070777011e-06 \tabularnewline
46 & 100.47 & 100.319999999763 & 0.150000000237242 \tabularnewline
47 & 100.62 & 100.469991832182 & 0.150008167817703 \tabularnewline
48 & 100.72 & 100.619991831738 & 0.100008168262434 \tabularnewline
49 & 100.92 & 100.719994554343 & 0.200005445656572 \tabularnewline
50 & 101.13 & 100.91998910928 & 0.210010890720099 \tabularnewline
51 & 101.26 & 101.129988564462 & 0.130011435537796 \tabularnewline
52 & 101.36 & 101.259992920602 & 0.100007079397997 \tabularnewline
53 & 101.52 & 101.359994554403 & 0.160005445597264 \tabularnewline
54 & 101.59 & 101.519991287365 & 0.0700087126353992 \tabularnewline
55 & 101.86 & 101.589996187877 & 0.270003812122667 \tabularnewline
56 & 101.74 & 101.859985297721 & -0.119985297720604 \tabularnewline
57 & 101.78 & 101.740006533454 & 0.0399934665464343 \tabularnewline
58 & 101.9 & 101.779997822271 & 0.120002177728949 \tabularnewline
59 & 101.83 & 101.899993465627 & -0.0699934656272774 \tabularnewline
60 & 101.98 & 101.830003811292 & 0.149996188707561 \tabularnewline
61 & 102.19 & 101.97999183239 & 0.210008167610141 \tabularnewline
62 & 102.59 & 102.189988564611 & 0.400011435389501 \tabularnewline
63 & 102.35 & 102.58997821853 & -0.239978218530183 \tabularnewline
64 & 102.67 & 102.350013067322 & 0.319986932677764 \tabularnewline
65 & 102.61 & 102.669982576034 & -0.0599825760338177 \tabularnewline
66 & 102.93 & 102.610003266178 & 0.319996733821711 \tabularnewline
67 & 103.12 & 102.9299825755 & 0.190017424499857 \tabularnewline
68 & 103.2 & 103.119989653149 & 0.0800103468511963 \tabularnewline
69 & 103.05 & 103.199995643267 & -0.149995643267175 \tabularnewline
70 & 103.45 & 103.05000816758 & 0.399991832419559 \tabularnewline
71 & 103.66 & 103.449978219598 & 0.2100217804024 \tabularnewline
72 & 103.74 & 103.659988563869 & 0.0800114361307322 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]94.45[/C][C]94[/C][C]0.450000000000003[/C][/ROW]
[ROW][C]3[/C][C]94.34[/C][C]94.449975496547[/C][C]-0.109975496546951[/C][/ROW]
[ROW][C]4[/C][C]94.39[/C][C]94.3400059883987[/C][C]0.0499940116012993[/C][/ROW]
[ROW][C]5[/C][C]94.68[/C][C]94.3899972777202[/C][C]0.290002722279823[/C][/ROW]
[ROW][C]6[/C][C]94.76[/C][C]94.6799842087376[/C][C]0.0800157912624115[/C][/ROW]
[ROW][C]7[/C][C]94.96[/C][C]94.7599956429707[/C][C]0.200004357029286[/C][/ROW]
[ROW][C]8[/C][C]95.01[/C][C]94.9599891093392[/C][C]0.050010890660829[/C][/ROW]
[ROW][C]9[/C][C]95.1[/C][C]95.0099972768011[/C][C]0.0900027231989071[/C][/ROW]
[ROW][C]10[/C][C]95.23[/C][C]95.0999950991611[/C][C]0.130004900838912[/C][/ROW]
[ROW][C]11[/C][C]95.26[/C][C]95.2299929209578[/C][C]0.0300070790421785[/C][/ROW]
[ROW][C]12[/C][C]95.34[/C][C]95.259998366051[/C][C]0.0800016339490099[/C][/ROW]
[ROW][C]13[/C][C]95.71[/C][C]95.3399956437416[/C][C]0.370004356258391[/C][/ROW]
[ROW][C]14[/C][C]96.07[/C][C]95.7099798524792[/C][C]0.360020147520814[/C][/ROW]
[ROW][C]15[/C][C]96.19[/C][C]96.0699803961405[/C][C]0.120019603859504[/C][/ROW]
[ROW][C]16[/C][C]96.11[/C][C]96.1899934646784[/C][C]-0.0799934646783953[/C][/ROW]
[ROW][C]17[/C][C]96.31[/C][C]96.1100043558136[/C][C]0.19999564418643[/C][/ROW]
[ROW][C]18[/C][C]96.46[/C][C]96.3099891098136[/C][C]0.15001089018638[/C][/ROW]
[ROW][C]19[/C][C]96.68[/C][C]96.4599918315893[/C][C]0.220008168410686[/C][/ROW]
[ROW][C]20[/C][C]96.69[/C][C]96.6799880200893[/C][C]0.0100119799107148[/C][/ROW]
[ROW][C]21[/C][C]96.72[/C][C]96.6899994548265[/C][C]0.0300005451735075[/C][/ROW]
[ROW][C]22[/C][C]96.92[/C][C]96.7199983664068[/C][C]0.200001633593232[/C][/ROW]
[ROW][C]23[/C][C]97.04[/C][C]96.9199891094875[/C][C]0.120010890512532[/C][/ROW]
[ROW][C]24[/C][C]97.18[/C][C]97.0399934651528[/C][C]0.14000653484716[/C][/ROW]
[ROW][C]25[/C][C]97.83[/C][C]97.1799923763477[/C][C]0.650007623652328[/C][/ROW]
[ROW][C]26[/C][C]98.25[/C][C]97.8299646057083[/C][C]0.420035394291745[/C][/ROW]
[ROW][C]27[/C][C]98.24[/C][C]98.2499771281832[/C][C]-0.00997712818319485[/C][/ROW]
[ROW][C]28[/C][C]98.28[/C][C]98.2400005432758[/C][C]0.0399994567242459[/C][/ROW]
[ROW][C]29[/C][C]98.53[/C][C]98.2799978219449[/C][C]0.250002178055126[/C][/ROW]
[ROW][C]30[/C][C]98.62[/C][C]98.5299863868519[/C][C]0.0900136131480735[/C][/ROW]
[ROW][C]31[/C][C]98.84[/C][C]98.6199950985681[/C][C]0.220004901431878[/C][/ROW]
[ROW][C]32[/C][C]98.94[/C][C]98.8399880202672[/C][C]0.100011979732813[/C][/ROW]
[ROW][C]33[/C][C]98.94[/C][C]98.9399945541359[/C][C]5.44586411876935e-06[/C][/ROW]
[ROW][C]34[/C][C]99.1[/C][C]98.9399999997034[/C][C]0.160000000296549[/C][/ROW]
[ROW][C]35[/C][C]99.15[/C][C]99.0999912876611[/C][C]0.0500087123388937[/C][/ROW]
[ROW][C]36[/C][C]99.26[/C][C]99.1499972769197[/C][C]0.110002723080285[/C][/ROW]
[ROW][C]37[/C][C]99.01[/C][C]99.2599940101188[/C][C]-0.249994010118755[/C][/ROW]
[ROW][C]38[/C][C]99.43[/C][C]99.0100136127033[/C][C]0.419986387296689[/C][/ROW]
[ROW][C]39[/C][C]99.62[/C][C]99.4299771308517[/C][C]0.190022869148265[/C][/ROW]
[ROW][C]40[/C][C]99.43[/C][C]99.6199896528523[/C][C]-0.189989652852333[/C][/ROW]
[ROW][C]41[/C][C]99.81[/C][C]99.430010345339[/C][C]0.379989654661031[/C][/ROW]
[ROW][C]42[/C][C]99.99[/C][C]99.8099793087585[/C][C]0.180020691241452[/C][/ROW]
[ROW][C]43[/C][C]100.24[/C][C]99.9899901974921[/C][C]0.25000980250789[/C][/ROW]
[ROW][C]44[/C][C]100.32[/C][C]100.239986386437[/C][C]0.0800136135632243[/C][/ROW]
[ROW][C]45[/C][C]100.32[/C][C]100.319995643089[/C][C]4.35691070777011e-06[/C][/ROW]
[ROW][C]46[/C][C]100.47[/C][C]100.319999999763[/C][C]0.150000000237242[/C][/ROW]
[ROW][C]47[/C][C]100.62[/C][C]100.469991832182[/C][C]0.150008167817703[/C][/ROW]
[ROW][C]48[/C][C]100.72[/C][C]100.619991831738[/C][C]0.100008168262434[/C][/ROW]
[ROW][C]49[/C][C]100.92[/C][C]100.719994554343[/C][C]0.200005445656572[/C][/ROW]
[ROW][C]50[/C][C]101.13[/C][C]100.91998910928[/C][C]0.210010890720099[/C][/ROW]
[ROW][C]51[/C][C]101.26[/C][C]101.129988564462[/C][C]0.130011435537796[/C][/ROW]
[ROW][C]52[/C][C]101.36[/C][C]101.259992920602[/C][C]0.100007079397997[/C][/ROW]
[ROW][C]53[/C][C]101.52[/C][C]101.359994554403[/C][C]0.160005445597264[/C][/ROW]
[ROW][C]54[/C][C]101.59[/C][C]101.519991287365[/C][C]0.0700087126353992[/C][/ROW]
[ROW][C]55[/C][C]101.86[/C][C]101.589996187877[/C][C]0.270003812122667[/C][/ROW]
[ROW][C]56[/C][C]101.74[/C][C]101.859985297721[/C][C]-0.119985297720604[/C][/ROW]
[ROW][C]57[/C][C]101.78[/C][C]101.740006533454[/C][C]0.0399934665464343[/C][/ROW]
[ROW][C]58[/C][C]101.9[/C][C]101.779997822271[/C][C]0.120002177728949[/C][/ROW]
[ROW][C]59[/C][C]101.83[/C][C]101.899993465627[/C][C]-0.0699934656272774[/C][/ROW]
[ROW][C]60[/C][C]101.98[/C][C]101.830003811292[/C][C]0.149996188707561[/C][/ROW]
[ROW][C]61[/C][C]102.19[/C][C]101.97999183239[/C][C]0.210008167610141[/C][/ROW]
[ROW][C]62[/C][C]102.59[/C][C]102.189988564611[/C][C]0.400011435389501[/C][/ROW]
[ROW][C]63[/C][C]102.35[/C][C]102.58997821853[/C][C]-0.239978218530183[/C][/ROW]
[ROW][C]64[/C][C]102.67[/C][C]102.350013067322[/C][C]0.319986932677764[/C][/ROW]
[ROW][C]65[/C][C]102.61[/C][C]102.669982576034[/C][C]-0.0599825760338177[/C][/ROW]
[ROW][C]66[/C][C]102.93[/C][C]102.610003266178[/C][C]0.319996733821711[/C][/ROW]
[ROW][C]67[/C][C]103.12[/C][C]102.9299825755[/C][C]0.190017424499857[/C][/ROW]
[ROW][C]68[/C][C]103.2[/C][C]103.119989653149[/C][C]0.0800103468511963[/C][/ROW]
[ROW][C]69[/C][C]103.05[/C][C]103.199995643267[/C][C]-0.149995643267175[/C][/ROW]
[ROW][C]70[/C][C]103.45[/C][C]103.05000816758[/C][C]0.399991832419559[/C][/ROW]
[ROW][C]71[/C][C]103.66[/C][C]103.449978219598[/C][C]0.2100217804024[/C][/ROW]
[ROW][C]72[/C][C]103.74[/C][C]103.659988563869[/C][C]0.0800114361307322[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
294.45940.450000000000003
394.3494.449975496547-0.109975496546951
494.3994.34000598839870.0499940116012993
594.6894.38999727772020.290002722279823
694.7694.67998420873760.0800157912624115
794.9694.75999564297070.200004357029286
895.0194.95998910933920.050010890660829
995.195.00999727680110.0900027231989071
1095.2395.09999509916110.130004900838912
1195.2695.22999292095780.0300070790421785
1295.3495.2599983660510.0800016339490099
1395.7195.33999564374160.370004356258391
1496.0795.70997985247920.360020147520814
1596.1996.06998039614050.120019603859504
1696.1196.1899934646784-0.0799934646783953
1796.3196.11000435581360.19999564418643
1896.4696.30998910981360.15001089018638
1996.6896.45999183158930.220008168410686
2096.6996.67998802008930.0100119799107148
2196.7296.68999945482650.0300005451735075
2296.9296.71999836640680.200001633593232
2397.0496.91998910948750.120010890512532
2497.1897.03999346515280.14000653484716
2597.8397.17999237634770.650007623652328
2698.2597.82996460570830.420035394291745
2798.2498.2499771281832-0.00997712818319485
2898.2898.24000054327580.0399994567242459
2998.5398.27999782194490.250002178055126
3098.6298.52998638685190.0900136131480735
3198.8498.61999509856810.220004901431878
3298.9498.83998802026720.100011979732813
3398.9498.93999455413595.44586411876935e-06
3499.198.93999999970340.160000000296549
3599.1599.09999128766110.0500087123388937
3699.2699.14999727691970.110002723080285
3799.0199.2599940101188-0.249994010118755
3899.4399.01001361270330.419986387296689
3999.6299.42997713085170.190022869148265
4099.4399.6199896528523-0.189989652852333
4199.8199.4300103453390.379989654661031
4299.9999.80997930875850.180020691241452
43100.2499.98999019749210.25000980250789
44100.32100.2399863864370.0800136135632243
45100.32100.3199956430894.35691070777011e-06
46100.47100.3199999997630.150000000237242
47100.62100.4699918321820.150008167817703
48100.72100.6199918317380.100008168262434
49100.92100.7199945543430.200005445656572
50101.13100.919989109280.210010890720099
51101.26101.1299885644620.130011435537796
52101.36101.2599929206020.100007079397997
53101.52101.3599945544030.160005445597264
54101.59101.5199912873650.0700087126353992
55101.86101.5899961878770.270003812122667
56101.74101.859985297721-0.119985297720604
57101.78101.7400065334540.0399934665464343
58101.9101.7799978222710.120002177728949
59101.83101.899993465627-0.0699934656272774
60101.98101.8300038112920.149996188707561
61102.19101.979991832390.210008167610141
62102.59102.1899885646110.400011435389501
63102.35102.58997821853-0.239978218530183
64102.67102.3500130673220.319986932677764
65102.61102.669982576034-0.0599825760338177
66102.93102.6100032661780.319996733821711
67103.12102.92998257550.190017424499857
68103.2103.1199896531490.0800103468511963
69103.05103.199995643267-0.149995643267175
70103.45103.050008167580.399991832419559
71103.66103.4499782195980.2100217804024
72103.74103.6599885638690.0800114361307322







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73103.739995643208103.415497158937104.064494127478
74103.739995643208103.281097979928104.198893306488
75103.739995643208103.177968184418104.302023101998
76103.739995643208103.091025178931104.388966107485
77103.739995643208103.014426582005104.46556470441
78103.739995643208102.945176002255104.534815284161
79103.739995643208102.881493423808104.598497862608
80103.739995643208102.822219058311104.657772228104
81103.739995643208102.766547309266104.71344397715
82103.739995643208102.713891624151104.766099662265
83103.739995643208102.663809201649104.816182084766
84103.739995643208102.615956028219104.864035258197

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 103.739995643208 & 103.415497158937 & 104.064494127478 \tabularnewline
74 & 103.739995643208 & 103.281097979928 & 104.198893306488 \tabularnewline
75 & 103.739995643208 & 103.177968184418 & 104.302023101998 \tabularnewline
76 & 103.739995643208 & 103.091025178931 & 104.388966107485 \tabularnewline
77 & 103.739995643208 & 103.014426582005 & 104.46556470441 \tabularnewline
78 & 103.739995643208 & 102.945176002255 & 104.534815284161 \tabularnewline
79 & 103.739995643208 & 102.881493423808 & 104.598497862608 \tabularnewline
80 & 103.739995643208 & 102.822219058311 & 104.657772228104 \tabularnewline
81 & 103.739995643208 & 102.766547309266 & 104.71344397715 \tabularnewline
82 & 103.739995643208 & 102.713891624151 & 104.766099662265 \tabularnewline
83 & 103.739995643208 & 102.663809201649 & 104.816182084766 \tabularnewline
84 & 103.739995643208 & 102.615956028219 & 104.864035258197 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]103.739995643208[/C][C]103.415497158937[/C][C]104.064494127478[/C][/ROW]
[ROW][C]74[/C][C]103.739995643208[/C][C]103.281097979928[/C][C]104.198893306488[/C][/ROW]
[ROW][C]75[/C][C]103.739995643208[/C][C]103.177968184418[/C][C]104.302023101998[/C][/ROW]
[ROW][C]76[/C][C]103.739995643208[/C][C]103.091025178931[/C][C]104.388966107485[/C][/ROW]
[ROW][C]77[/C][C]103.739995643208[/C][C]103.014426582005[/C][C]104.46556470441[/C][/ROW]
[ROW][C]78[/C][C]103.739995643208[/C][C]102.945176002255[/C][C]104.534815284161[/C][/ROW]
[ROW][C]79[/C][C]103.739995643208[/C][C]102.881493423808[/C][C]104.598497862608[/C][/ROW]
[ROW][C]80[/C][C]103.739995643208[/C][C]102.822219058311[/C][C]104.657772228104[/C][/ROW]
[ROW][C]81[/C][C]103.739995643208[/C][C]102.766547309266[/C][C]104.71344397715[/C][/ROW]
[ROW][C]82[/C][C]103.739995643208[/C][C]102.713891624151[/C][C]104.766099662265[/C][/ROW]
[ROW][C]83[/C][C]103.739995643208[/C][C]102.663809201649[/C][C]104.816182084766[/C][/ROW]
[ROW][C]84[/C][C]103.739995643208[/C][C]102.615956028219[/C][C]104.864035258197[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
73103.739995643208103.415497158937104.064494127478
74103.739995643208103.281097979928104.198893306488
75103.739995643208103.177968184418104.302023101998
76103.739995643208103.091025178931104.388966107485
77103.739995643208103.014426582005104.46556470441
78103.739995643208102.945176002255104.534815284161
79103.739995643208102.881493423808104.598497862608
80103.739995643208102.822219058311104.657772228104
81103.739995643208102.766547309266104.71344397715
82103.739995643208102.713891624151104.766099662265
83103.739995643208102.663809201649104.816182084766
84103.739995643208102.615956028219104.864035258197



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')