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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 computationSun, 30 Nov 2014 13:46:29 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/30/t1417355211epipgontar6xr1y.htm/, Retrieved Sun, 19 May 2024 15:20:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261423, Retrieved Sun, 19 May 2024 15:20:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-30 13:46:29] [2f27692a17e58baa8638275162e45e6c] [Current]
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Dataseries X:
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135
124
118
121
121
118
113
107
100
102
130
136
133
120
112
109
110
106
102
98
92
92
120
127
124
114
108
106
111
110
104
100
96
98
122
134
133
125
118
116
118
116
111
108
102
102
129
136
137
126
119
117




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261423&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261423&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261423&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0376243142761576
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0376243142761576 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261423&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]0.0376243142761576[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261423&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261423&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
beta0.0376243142761576
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
39597-2
49390.92475137144772.07524862855232
58489.0028311780495-5.0028311780495
68779.8146030855367.18539691446399
711683.084948717244732.9150512827553
8120113.3233549511236.67664504887703
9117117.574559142752-0.574559142752264
10109114.552941748995-5.55294174899511
11105106.344016123474-1.34401612347372
12107102.2934484384524.70655156154807
13109104.4705292135614.52947078643945
14109106.6409474459342.35905255406577
15108106.7297051806221.27029481937763
16107105.777499152131.22250084786999
1799104.823494908233-5.82349490823313
1810396.60438990562026.39561009437983
19131100.84502034979930.1549796502011
20137129.9795807811497.0204192188508
21135136.24371924019-1.24371924018962
22124134.196925156625-10.1969251566254
23118122.813272839882-4.81327283988207
24121116.6321767498574.36782325014254
25121119.7965131045241.20348689547647
26118119.841793473706-1.84179347370618
27113116.77249725722-3.77249725721968
28107111.630559634808-4.63055963480811
29100105.456338003834-5.45633800383359
3010298.25104702798043.74895297201958
31130100.39209881280629.6079011871938
32136129.5060757921316.49392420786938
33133135.750405237413-2.75040523741305
34120132.646923126374-12.6469231263738
35112119.171091316041-7.17109131604073
36109110.901283922663-1.90128392266298
37110107.8297494188292.17025058117149
38106108.911403608753-2.91140360875252
39102104.801864044392-2.80186404439208
4098100.696445831027-2.69644583102681
419296.5949939056516-4.59499390565162
429290.42211041084831.57788958915165
4312090.481477424643729.5185225753563
44127119.5920915949877.40790840501327
45124126.870809068946-2.87080906894593
46114123.762796846309-9.76279684630907
47108113.395478309549-5.39547830954926
48106107.192477137961-1.19247713796058
49111105.1476110033555.85238899664517
50110110.367803126231-0.367803126230925
51104109.353964785818-5.35396478581787
52100103.152525532093-3.15252553209277
539699.0339139207097-3.03391392070971
549894.91976498987013.08023501012988
5512297.035656719935724.9643432800643
56134121.97492301720312.0250769827973
57133134.427358292798-1.42735829279843
58125133.373654915806-8.3736549158055
59118125.058601891613-7.05860189161315
60116117.793026835693-1.79302683569281
61118115.7255654305212.27443456947887
62116117.811139471564-1.81113947156376
63111115.742996590888-4.74299659088769
64108110.564544596541-2.56454459654138
65102107.468055364666-5.46805536466589
66102101.2623235311460.737676468853721
67129101.29007810244527.7099218975554
68136129.3326449124866.66735508751404
69137136.5834995756890.416500424310669
70126137.59917011855-11.5991701185498
71119126.162759296667-7.16275929666681
72117118.893265389805-1.89326538980455

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 95 & 97 & -2 \tabularnewline
4 & 93 & 90.9247513714477 & 2.07524862855232 \tabularnewline
5 & 84 & 89.0028311780495 & -5.0028311780495 \tabularnewline
6 & 87 & 79.814603085536 & 7.18539691446399 \tabularnewline
7 & 116 & 83.0849487172447 & 32.9150512827553 \tabularnewline
8 & 120 & 113.323354951123 & 6.67664504887703 \tabularnewline
9 & 117 & 117.574559142752 & -0.574559142752264 \tabularnewline
10 & 109 & 114.552941748995 & -5.55294174899511 \tabularnewline
11 & 105 & 106.344016123474 & -1.34401612347372 \tabularnewline
12 & 107 & 102.293448438452 & 4.70655156154807 \tabularnewline
13 & 109 & 104.470529213561 & 4.52947078643945 \tabularnewline
14 & 109 & 106.640947445934 & 2.35905255406577 \tabularnewline
15 & 108 & 106.729705180622 & 1.27029481937763 \tabularnewline
16 & 107 & 105.77749915213 & 1.22250084786999 \tabularnewline
17 & 99 & 104.823494908233 & -5.82349490823313 \tabularnewline
18 & 103 & 96.6043899056202 & 6.39561009437983 \tabularnewline
19 & 131 & 100.845020349799 & 30.1549796502011 \tabularnewline
20 & 137 & 129.979580781149 & 7.0204192188508 \tabularnewline
21 & 135 & 136.24371924019 & -1.24371924018962 \tabularnewline
22 & 124 & 134.196925156625 & -10.1969251566254 \tabularnewline
23 & 118 & 122.813272839882 & -4.81327283988207 \tabularnewline
24 & 121 & 116.632176749857 & 4.36782325014254 \tabularnewline
25 & 121 & 119.796513104524 & 1.20348689547647 \tabularnewline
26 & 118 & 119.841793473706 & -1.84179347370618 \tabularnewline
27 & 113 & 116.77249725722 & -3.77249725721968 \tabularnewline
28 & 107 & 111.630559634808 & -4.63055963480811 \tabularnewline
29 & 100 & 105.456338003834 & -5.45633800383359 \tabularnewline
30 & 102 & 98.2510470279804 & 3.74895297201958 \tabularnewline
31 & 130 & 100.392098812806 & 29.6079011871938 \tabularnewline
32 & 136 & 129.506075792131 & 6.49392420786938 \tabularnewline
33 & 133 & 135.750405237413 & -2.75040523741305 \tabularnewline
34 & 120 & 132.646923126374 & -12.6469231263738 \tabularnewline
35 & 112 & 119.171091316041 & -7.17109131604073 \tabularnewline
36 & 109 & 110.901283922663 & -1.90128392266298 \tabularnewline
37 & 110 & 107.829749418829 & 2.17025058117149 \tabularnewline
38 & 106 & 108.911403608753 & -2.91140360875252 \tabularnewline
39 & 102 & 104.801864044392 & -2.80186404439208 \tabularnewline
40 & 98 & 100.696445831027 & -2.69644583102681 \tabularnewline
41 & 92 & 96.5949939056516 & -4.59499390565162 \tabularnewline
42 & 92 & 90.4221104108483 & 1.57788958915165 \tabularnewline
43 & 120 & 90.4814774246437 & 29.5185225753563 \tabularnewline
44 & 127 & 119.592091594987 & 7.40790840501327 \tabularnewline
45 & 124 & 126.870809068946 & -2.87080906894593 \tabularnewline
46 & 114 & 123.762796846309 & -9.76279684630907 \tabularnewline
47 & 108 & 113.395478309549 & -5.39547830954926 \tabularnewline
48 & 106 & 107.192477137961 & -1.19247713796058 \tabularnewline
49 & 111 & 105.147611003355 & 5.85238899664517 \tabularnewline
50 & 110 & 110.367803126231 & -0.367803126230925 \tabularnewline
51 & 104 & 109.353964785818 & -5.35396478581787 \tabularnewline
52 & 100 & 103.152525532093 & -3.15252553209277 \tabularnewline
53 & 96 & 99.0339139207097 & -3.03391392070971 \tabularnewline
54 & 98 & 94.9197649898701 & 3.08023501012988 \tabularnewline
55 & 122 & 97.0356567199357 & 24.9643432800643 \tabularnewline
56 & 134 & 121.974923017203 & 12.0250769827973 \tabularnewline
57 & 133 & 134.427358292798 & -1.42735829279843 \tabularnewline
58 & 125 & 133.373654915806 & -8.3736549158055 \tabularnewline
59 & 118 & 125.058601891613 & -7.05860189161315 \tabularnewline
60 & 116 & 117.793026835693 & -1.79302683569281 \tabularnewline
61 & 118 & 115.725565430521 & 2.27443456947887 \tabularnewline
62 & 116 & 117.811139471564 & -1.81113947156376 \tabularnewline
63 & 111 & 115.742996590888 & -4.74299659088769 \tabularnewline
64 & 108 & 110.564544596541 & -2.56454459654138 \tabularnewline
65 & 102 & 107.468055364666 & -5.46805536466589 \tabularnewline
66 & 102 & 101.262323531146 & 0.737676468853721 \tabularnewline
67 & 129 & 101.290078102445 & 27.7099218975554 \tabularnewline
68 & 136 & 129.332644912486 & 6.66735508751404 \tabularnewline
69 & 137 & 136.583499575689 & 0.416500424310669 \tabularnewline
70 & 126 & 137.59917011855 & -11.5991701185498 \tabularnewline
71 & 119 & 126.162759296667 & -7.16275929666681 \tabularnewline
72 & 117 & 118.893265389805 & -1.89326538980455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261423&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]95[/C][C]97[/C][C]-2[/C][/ROW]
[ROW][C]4[/C][C]93[/C][C]90.9247513714477[/C][C]2.07524862855232[/C][/ROW]
[ROW][C]5[/C][C]84[/C][C]89.0028311780495[/C][C]-5.0028311780495[/C][/ROW]
[ROW][C]6[/C][C]87[/C][C]79.814603085536[/C][C]7.18539691446399[/C][/ROW]
[ROW][C]7[/C][C]116[/C][C]83.0849487172447[/C][C]32.9150512827553[/C][/ROW]
[ROW][C]8[/C][C]120[/C][C]113.323354951123[/C][C]6.67664504887703[/C][/ROW]
[ROW][C]9[/C][C]117[/C][C]117.574559142752[/C][C]-0.574559142752264[/C][/ROW]
[ROW][C]10[/C][C]109[/C][C]114.552941748995[/C][C]-5.55294174899511[/C][/ROW]
[ROW][C]11[/C][C]105[/C][C]106.344016123474[/C][C]-1.34401612347372[/C][/ROW]
[ROW][C]12[/C][C]107[/C][C]102.293448438452[/C][C]4.70655156154807[/C][/ROW]
[ROW][C]13[/C][C]109[/C][C]104.470529213561[/C][C]4.52947078643945[/C][/ROW]
[ROW][C]14[/C][C]109[/C][C]106.640947445934[/C][C]2.35905255406577[/C][/ROW]
[ROW][C]15[/C][C]108[/C][C]106.729705180622[/C][C]1.27029481937763[/C][/ROW]
[ROW][C]16[/C][C]107[/C][C]105.77749915213[/C][C]1.22250084786999[/C][/ROW]
[ROW][C]17[/C][C]99[/C][C]104.823494908233[/C][C]-5.82349490823313[/C][/ROW]
[ROW][C]18[/C][C]103[/C][C]96.6043899056202[/C][C]6.39561009437983[/C][/ROW]
[ROW][C]19[/C][C]131[/C][C]100.845020349799[/C][C]30.1549796502011[/C][/ROW]
[ROW][C]20[/C][C]137[/C][C]129.979580781149[/C][C]7.0204192188508[/C][/ROW]
[ROW][C]21[/C][C]135[/C][C]136.24371924019[/C][C]-1.24371924018962[/C][/ROW]
[ROW][C]22[/C][C]124[/C][C]134.196925156625[/C][C]-10.1969251566254[/C][/ROW]
[ROW][C]23[/C][C]118[/C][C]122.813272839882[/C][C]-4.81327283988207[/C][/ROW]
[ROW][C]24[/C][C]121[/C][C]116.632176749857[/C][C]4.36782325014254[/C][/ROW]
[ROW][C]25[/C][C]121[/C][C]119.796513104524[/C][C]1.20348689547647[/C][/ROW]
[ROW][C]26[/C][C]118[/C][C]119.841793473706[/C][C]-1.84179347370618[/C][/ROW]
[ROW][C]27[/C][C]113[/C][C]116.77249725722[/C][C]-3.77249725721968[/C][/ROW]
[ROW][C]28[/C][C]107[/C][C]111.630559634808[/C][C]-4.63055963480811[/C][/ROW]
[ROW][C]29[/C][C]100[/C][C]105.456338003834[/C][C]-5.45633800383359[/C][/ROW]
[ROW][C]30[/C][C]102[/C][C]98.2510470279804[/C][C]3.74895297201958[/C][/ROW]
[ROW][C]31[/C][C]130[/C][C]100.392098812806[/C][C]29.6079011871938[/C][/ROW]
[ROW][C]32[/C][C]136[/C][C]129.506075792131[/C][C]6.49392420786938[/C][/ROW]
[ROW][C]33[/C][C]133[/C][C]135.750405237413[/C][C]-2.75040523741305[/C][/ROW]
[ROW][C]34[/C][C]120[/C][C]132.646923126374[/C][C]-12.6469231263738[/C][/ROW]
[ROW][C]35[/C][C]112[/C][C]119.171091316041[/C][C]-7.17109131604073[/C][/ROW]
[ROW][C]36[/C][C]109[/C][C]110.901283922663[/C][C]-1.90128392266298[/C][/ROW]
[ROW][C]37[/C][C]110[/C][C]107.829749418829[/C][C]2.17025058117149[/C][/ROW]
[ROW][C]38[/C][C]106[/C][C]108.911403608753[/C][C]-2.91140360875252[/C][/ROW]
[ROW][C]39[/C][C]102[/C][C]104.801864044392[/C][C]-2.80186404439208[/C][/ROW]
[ROW][C]40[/C][C]98[/C][C]100.696445831027[/C][C]-2.69644583102681[/C][/ROW]
[ROW][C]41[/C][C]92[/C][C]96.5949939056516[/C][C]-4.59499390565162[/C][/ROW]
[ROW][C]42[/C][C]92[/C][C]90.4221104108483[/C][C]1.57788958915165[/C][/ROW]
[ROW][C]43[/C][C]120[/C][C]90.4814774246437[/C][C]29.5185225753563[/C][/ROW]
[ROW][C]44[/C][C]127[/C][C]119.592091594987[/C][C]7.40790840501327[/C][/ROW]
[ROW][C]45[/C][C]124[/C][C]126.870809068946[/C][C]-2.87080906894593[/C][/ROW]
[ROW][C]46[/C][C]114[/C][C]123.762796846309[/C][C]-9.76279684630907[/C][/ROW]
[ROW][C]47[/C][C]108[/C][C]113.395478309549[/C][C]-5.39547830954926[/C][/ROW]
[ROW][C]48[/C][C]106[/C][C]107.192477137961[/C][C]-1.19247713796058[/C][/ROW]
[ROW][C]49[/C][C]111[/C][C]105.147611003355[/C][C]5.85238899664517[/C][/ROW]
[ROW][C]50[/C][C]110[/C][C]110.367803126231[/C][C]-0.367803126230925[/C][/ROW]
[ROW][C]51[/C][C]104[/C][C]109.353964785818[/C][C]-5.35396478581787[/C][/ROW]
[ROW][C]52[/C][C]100[/C][C]103.152525532093[/C][C]-3.15252553209277[/C][/ROW]
[ROW][C]53[/C][C]96[/C][C]99.0339139207097[/C][C]-3.03391392070971[/C][/ROW]
[ROW][C]54[/C][C]98[/C][C]94.9197649898701[/C][C]3.08023501012988[/C][/ROW]
[ROW][C]55[/C][C]122[/C][C]97.0356567199357[/C][C]24.9643432800643[/C][/ROW]
[ROW][C]56[/C][C]134[/C][C]121.974923017203[/C][C]12.0250769827973[/C][/ROW]
[ROW][C]57[/C][C]133[/C][C]134.427358292798[/C][C]-1.42735829279843[/C][/ROW]
[ROW][C]58[/C][C]125[/C][C]133.373654915806[/C][C]-8.3736549158055[/C][/ROW]
[ROW][C]59[/C][C]118[/C][C]125.058601891613[/C][C]-7.05860189161315[/C][/ROW]
[ROW][C]60[/C][C]116[/C][C]117.793026835693[/C][C]-1.79302683569281[/C][/ROW]
[ROW][C]61[/C][C]118[/C][C]115.725565430521[/C][C]2.27443456947887[/C][/ROW]
[ROW][C]62[/C][C]116[/C][C]117.811139471564[/C][C]-1.81113947156376[/C][/ROW]
[ROW][C]63[/C][C]111[/C][C]115.742996590888[/C][C]-4.74299659088769[/C][/ROW]
[ROW][C]64[/C][C]108[/C][C]110.564544596541[/C][C]-2.56454459654138[/C][/ROW]
[ROW][C]65[/C][C]102[/C][C]107.468055364666[/C][C]-5.46805536466589[/C][/ROW]
[ROW][C]66[/C][C]102[/C][C]101.262323531146[/C][C]0.737676468853721[/C][/ROW]
[ROW][C]67[/C][C]129[/C][C]101.290078102445[/C][C]27.7099218975554[/C][/ROW]
[ROW][C]68[/C][C]136[/C][C]129.332644912486[/C][C]6.66735508751404[/C][/ROW]
[ROW][C]69[/C][C]137[/C][C]136.583499575689[/C][C]0.416500424310669[/C][/ROW]
[ROW][C]70[/C][C]126[/C][C]137.59917011855[/C][C]-11.5991701185498[/C][/ROW]
[ROW][C]71[/C][C]119[/C][C]126.162759296667[/C][C]-7.16275929666681[/C][/ROW]
[ROW][C]72[/C][C]117[/C][C]118.893265389805[/C][C]-1.89326538980455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261423&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261423&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
39597-2
49390.92475137144772.07524862855232
58489.0028311780495-5.0028311780495
68779.8146030855367.18539691446399
711683.084948717244732.9150512827553
8120113.3233549511236.67664504887703
9117117.574559142752-0.574559142752264
10109114.552941748995-5.55294174899511
11105106.344016123474-1.34401612347372
12107102.2934484384524.70655156154807
13109104.4705292135614.52947078643945
14109106.6409474459342.35905255406577
15108106.7297051806221.27029481937763
16107105.777499152131.22250084786999
1799104.823494908233-5.82349490823313
1810396.60438990562026.39561009437983
19131100.84502034979930.1549796502011
20137129.9795807811497.0204192188508
21135136.24371924019-1.24371924018962
22124134.196925156625-10.1969251566254
23118122.813272839882-4.81327283988207
24121116.6321767498574.36782325014254
25121119.7965131045241.20348689547647
26118119.841793473706-1.84179347370618
27113116.77249725722-3.77249725721968
28107111.630559634808-4.63055963480811
29100105.456338003834-5.45633800383359
3010298.25104702798043.74895297201958
31130100.39209881280629.6079011871938
32136129.5060757921316.49392420786938
33133135.750405237413-2.75040523741305
34120132.646923126374-12.6469231263738
35112119.171091316041-7.17109131604073
36109110.901283922663-1.90128392266298
37110107.8297494188292.17025058117149
38106108.911403608753-2.91140360875252
39102104.801864044392-2.80186404439208
4098100.696445831027-2.69644583102681
419296.5949939056516-4.59499390565162
429290.42211041084831.57788958915165
4312090.481477424643729.5185225753563
44127119.5920915949877.40790840501327
45124126.870809068946-2.87080906894593
46114123.762796846309-9.76279684630907
47108113.395478309549-5.39547830954926
48106107.192477137961-1.19247713796058
49111105.1476110033555.85238899664517
50110110.367803126231-0.367803126230925
51104109.353964785818-5.35396478581787
52100103.152525532093-3.15252553209277
539699.0339139207097-3.03391392070971
549894.91976498987013.08023501012988
5512297.035656719935724.9643432800643
56134121.97492301720312.0250769827973
57133134.427358292798-1.42735829279843
58125133.373654915806-8.3736549158055
59118125.058601891613-7.05860189161315
60116117.793026835693-1.79302683569281
61118115.7255654305212.27443456947887
62116117.811139471564-1.81113947156376
63111115.742996590888-4.74299659088769
64108110.564544596541-2.56454459654138
65102107.468055364666-5.46805536466589
66102101.2623235311460.737676468853721
67129101.29007810244527.7099218975554
68136129.3326449124866.66735508751404
69137136.5834995756890.416500424310669
70126137.59917011855-11.5991701185498
71119126.162759296667-7.16275929666681
72117118.893265389805-1.89326538980455







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73116.8220325777797.4746887720019136.169376383539
74116.64406515554188.7633127885882144.524817522493
75116.46609773331181.6794668763392151.252728590283
76116.28813031108175.3772579225907157.199002699572
77116.11016288885269.5358620575474162.684463720156
78115.93219546662263.9940831872497167.870307745995
79115.75422804439358.6581224591601172.850333629625
80115.57626062216353.468140692126177.6843805522
81115.39829319993348.3834654554013182.413120944465
82115.22032577770443.3751396626313187.065511892776
83115.04235835547438.4218048607542191.662911850194
84114.86439093324433.507263076087196.221518790402

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 116.82203257777 & 97.4746887720019 & 136.169376383539 \tabularnewline
74 & 116.644065155541 & 88.7633127885882 & 144.524817522493 \tabularnewline
75 & 116.466097733311 & 81.6794668763392 & 151.252728590283 \tabularnewline
76 & 116.288130311081 & 75.3772579225907 & 157.199002699572 \tabularnewline
77 & 116.110162888852 & 69.5358620575474 & 162.684463720156 \tabularnewline
78 & 115.932195466622 & 63.9940831872497 & 167.870307745995 \tabularnewline
79 & 115.754228044393 & 58.6581224591601 & 172.850333629625 \tabularnewline
80 & 115.576260622163 & 53.468140692126 & 177.6843805522 \tabularnewline
81 & 115.398293199933 & 48.3834654554013 & 182.413120944465 \tabularnewline
82 & 115.220325777704 & 43.3751396626313 & 187.065511892776 \tabularnewline
83 & 115.042358355474 & 38.4218048607542 & 191.662911850194 \tabularnewline
84 & 114.864390933244 & 33.507263076087 & 196.221518790402 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261423&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]116.82203257777[/C][C]97.4746887720019[/C][C]136.169376383539[/C][/ROW]
[ROW][C]74[/C][C]116.644065155541[/C][C]88.7633127885882[/C][C]144.524817522493[/C][/ROW]
[ROW][C]75[/C][C]116.466097733311[/C][C]81.6794668763392[/C][C]151.252728590283[/C][/ROW]
[ROW][C]76[/C][C]116.288130311081[/C][C]75.3772579225907[/C][C]157.199002699572[/C][/ROW]
[ROW][C]77[/C][C]116.110162888852[/C][C]69.5358620575474[/C][C]162.684463720156[/C][/ROW]
[ROW][C]78[/C][C]115.932195466622[/C][C]63.9940831872497[/C][C]167.870307745995[/C][/ROW]
[ROW][C]79[/C][C]115.754228044393[/C][C]58.6581224591601[/C][C]172.850333629625[/C][/ROW]
[ROW][C]80[/C][C]115.576260622163[/C][C]53.468140692126[/C][C]177.6843805522[/C][/ROW]
[ROW][C]81[/C][C]115.398293199933[/C][C]48.3834654554013[/C][C]182.413120944465[/C][/ROW]
[ROW][C]82[/C][C]115.220325777704[/C][C]43.3751396626313[/C][C]187.065511892776[/C][/ROW]
[ROW][C]83[/C][C]115.042358355474[/C][C]38.4218048607542[/C][C]191.662911850194[/C][/ROW]
[ROW][C]84[/C][C]114.864390933244[/C][C]33.507263076087[/C][C]196.221518790402[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261423&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261423&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
73116.8220325777797.4746887720019136.169376383539
74116.64406515554188.7633127885882144.524817522493
75116.46609773331181.6794668763392151.252728590283
76116.28813031108175.3772579225907157.199002699572
77116.11016288885269.5358620575474162.684463720156
78115.93219546662263.9940831872497167.870307745995
79115.75422804439358.6581224591601172.850333629625
80115.57626062216353.468140692126177.6843805522
81115.39829319993348.3834654554013182.413120944465
82115.22032577770443.3751396626313187.065511892776
83115.04235835547438.4218048607542191.662911850194
84114.86439093324433.507263076087196.221518790402



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')