Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 05 Aug 2010 14:38:15 +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/2010/Aug/05/t1281019081iga32tinv0upn5w.htm/, Retrieved Sun, 05 May 2024 12:15:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78416, Retrieved Sun, 05 May 2024 12:15:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGhielens Nick
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 2 - sta...] [2010-08-05 14:38:15] [fa169e33c07134f82fd2ac8a5210a945] [Current]
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Dataseries X:
80
79
78
76
74
73
74
76
77
77
78
80
90
90
89
82
78
76
74
78
81
82
88
99
117
113
106
100
97
96
100
104
104
111
117
118
140
147
134
126
116
114
120
122
117
119
132
134
154
152
132
130
123
129
124
128
128
129
141
138
155
160
142
133
131
140
134
134
134
136
145
137
152
168
160
157
147
161
159
164
163
158
175
163




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78416&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78416&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78416&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 time4 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0183448029323068
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0183448029323068 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78416&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]0.0183448029323068[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78416&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78416&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
beta0.0183448029323068
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
378780
47677-1
57474.9816551970677-0.981655197067695
67372.963646925930.0363530740699929
77471.96431381590982.03568618409020
87673.0016580777892.99834192221104
97775.05666206947561.94333793052441
107776.0923122208420.907687779158053
117876.10896357427471.89103642572533
128077.14365426484242.85634573515759
139079.196053364460410.8039466355396
149089.39424963638050.605750363619464
158989.4053620074273-0.405362007427314
168288.3979257212848-6.39792572128482
177881.2805570347523-3.28055703475231
187677.2203758624416-1.22037586244159
197475.1979883077418-1.19798830774175
207873.1760114483214.82398855167898
218177.26450656764933.73549343235072
228280.33303345852071.66696654147933
238881.36361363121896.63638636878113
249987.485356831336811.5146431686632
2511798.696590691101818.3034093088982
26113117.032363127863-4.03236312786285
27106112.958390220931-6.95839022093071
28100105.830739923602-5.83073992360164
299799.7237761487536-2.72377614875363
309696.673809012073-0.673809012073036
3110095.66144811853254.33855188146747
3210499.74103799780964.25896200219036
33104103.8191678164360.180832183563993
34111103.8224851472077.17751485279268
35117110.9541552427266.04584475727449
36118117.0650650733570.934934926642981
37140118.08221627034121.9177837296592
38147140.4842936935746.51570630642567
39134147.603823041730-13.6038230417305
40126134.354263588904-8.35426358890399
41116126.201006269721-10.201006269721
42114116.013870819992-2.01387081999174
43120113.9769267566686.02307324333214
44122120.0874188483641.91258115163636
45117122.122504772682-5.12250477268245
46119117.0285334321081.97146656789221
47132119.06469959778312.9353004022166
48134132.3019951345321.69800486546774
49154134.33314469916719.6668553008326
50152154.693929283959-2.69392928395933
51132152.644509682132-20.6445096821315
52130132.265790220379-2.26579022037873
53123130.2242247453-7.22422474529992
54129123.0916977660095.90830223399129
55124129.200084406156-5.20008440615578
56128124.1046898824943.8953101175065
57128128.176148578959-0.176148578959385
58129128.1729171679920.827082832008443
59141129.18808983955311.8119101604466
60138141.404777003701-3.40477700370096
61155138.34231704054016.6576829594604
62160155.6478989517404.35210104826024
63142160.727737387812-18.7277373878116
64133142.384180736064-9.38418073606417
65131133.21202978978-2.21202978977993
66140131.1714505392068.82854946079397
67134140.333408539242-6.33340853924241
68134134.217223407700-0.217223407700232
69134134.213238487094-0.213238487093690
70136134.2093266690701.79067333092965
71145136.2421762184428.75782378155759
72137145.402836769831-8.40283676983094
73152137.24868838521614.7513116147839
74168152.51929828978215.4807017102177
75160168.80328871191-8.80328871191008
76157160.641794115334-3.64179411533388
77147157.574986119968-10.5749861199681
78161147.38099008358513.6190099164146
79159161.630828136635-2.63082813663513
80164159.5825661129204.41743388708022
81163164.663603067045-1.66360306704476
82158163.633084596622-5.63308459662224
83175158.52974676979616.4702532302038
84163175.831890319549-12.8318903195495

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 78 & 78 & 0 \tabularnewline
4 & 76 & 77 & -1 \tabularnewline
5 & 74 & 74.9816551970677 & -0.981655197067695 \tabularnewline
6 & 73 & 72.96364692593 & 0.0363530740699929 \tabularnewline
7 & 74 & 71.9643138159098 & 2.03568618409020 \tabularnewline
8 & 76 & 73.001658077789 & 2.99834192221104 \tabularnewline
9 & 77 & 75.0566620694756 & 1.94333793052441 \tabularnewline
10 & 77 & 76.092312220842 & 0.907687779158053 \tabularnewline
11 & 78 & 76.1089635742747 & 1.89103642572533 \tabularnewline
12 & 80 & 77.1436542648424 & 2.85634573515759 \tabularnewline
13 & 90 & 79.1960533644604 & 10.8039466355396 \tabularnewline
14 & 90 & 89.3942496363805 & 0.605750363619464 \tabularnewline
15 & 89 & 89.4053620074273 & -0.405362007427314 \tabularnewline
16 & 82 & 88.3979257212848 & -6.39792572128482 \tabularnewline
17 & 78 & 81.2805570347523 & -3.28055703475231 \tabularnewline
18 & 76 & 77.2203758624416 & -1.22037586244159 \tabularnewline
19 & 74 & 75.1979883077418 & -1.19798830774175 \tabularnewline
20 & 78 & 73.176011448321 & 4.82398855167898 \tabularnewline
21 & 81 & 77.2645065676493 & 3.73549343235072 \tabularnewline
22 & 82 & 80.3330334585207 & 1.66696654147933 \tabularnewline
23 & 88 & 81.3636136312189 & 6.63638636878113 \tabularnewline
24 & 99 & 87.4853568313368 & 11.5146431686632 \tabularnewline
25 & 117 & 98.6965906911018 & 18.3034093088982 \tabularnewline
26 & 113 & 117.032363127863 & -4.03236312786285 \tabularnewline
27 & 106 & 112.958390220931 & -6.95839022093071 \tabularnewline
28 & 100 & 105.830739923602 & -5.83073992360164 \tabularnewline
29 & 97 & 99.7237761487536 & -2.72377614875363 \tabularnewline
30 & 96 & 96.673809012073 & -0.673809012073036 \tabularnewline
31 & 100 & 95.6614481185325 & 4.33855188146747 \tabularnewline
32 & 104 & 99.7410379978096 & 4.25896200219036 \tabularnewline
33 & 104 & 103.819167816436 & 0.180832183563993 \tabularnewline
34 & 111 & 103.822485147207 & 7.17751485279268 \tabularnewline
35 & 117 & 110.954155242726 & 6.04584475727449 \tabularnewline
36 & 118 & 117.065065073357 & 0.934934926642981 \tabularnewline
37 & 140 & 118.082216270341 & 21.9177837296592 \tabularnewline
38 & 147 & 140.484293693574 & 6.51570630642567 \tabularnewline
39 & 134 & 147.603823041730 & -13.6038230417305 \tabularnewline
40 & 126 & 134.354263588904 & -8.35426358890399 \tabularnewline
41 & 116 & 126.201006269721 & -10.201006269721 \tabularnewline
42 & 114 & 116.013870819992 & -2.01387081999174 \tabularnewline
43 & 120 & 113.976926756668 & 6.02307324333214 \tabularnewline
44 & 122 & 120.087418848364 & 1.91258115163636 \tabularnewline
45 & 117 & 122.122504772682 & -5.12250477268245 \tabularnewline
46 & 119 & 117.028533432108 & 1.97146656789221 \tabularnewline
47 & 132 & 119.064699597783 & 12.9353004022166 \tabularnewline
48 & 134 & 132.301995134532 & 1.69800486546774 \tabularnewline
49 & 154 & 134.333144699167 & 19.6668553008326 \tabularnewline
50 & 152 & 154.693929283959 & -2.69392928395933 \tabularnewline
51 & 132 & 152.644509682132 & -20.6445096821315 \tabularnewline
52 & 130 & 132.265790220379 & -2.26579022037873 \tabularnewline
53 & 123 & 130.2242247453 & -7.22422474529992 \tabularnewline
54 & 129 & 123.091697766009 & 5.90830223399129 \tabularnewline
55 & 124 & 129.200084406156 & -5.20008440615578 \tabularnewline
56 & 128 & 124.104689882494 & 3.8953101175065 \tabularnewline
57 & 128 & 128.176148578959 & -0.176148578959385 \tabularnewline
58 & 129 & 128.172917167992 & 0.827082832008443 \tabularnewline
59 & 141 & 129.188089839553 & 11.8119101604466 \tabularnewline
60 & 138 & 141.404777003701 & -3.40477700370096 \tabularnewline
61 & 155 & 138.342317040540 & 16.6576829594604 \tabularnewline
62 & 160 & 155.647898951740 & 4.35210104826024 \tabularnewline
63 & 142 & 160.727737387812 & -18.7277373878116 \tabularnewline
64 & 133 & 142.384180736064 & -9.38418073606417 \tabularnewline
65 & 131 & 133.21202978978 & -2.21202978977993 \tabularnewline
66 & 140 & 131.171450539206 & 8.82854946079397 \tabularnewline
67 & 134 & 140.333408539242 & -6.33340853924241 \tabularnewline
68 & 134 & 134.217223407700 & -0.217223407700232 \tabularnewline
69 & 134 & 134.213238487094 & -0.213238487093690 \tabularnewline
70 & 136 & 134.209326669070 & 1.79067333092965 \tabularnewline
71 & 145 & 136.242176218442 & 8.75782378155759 \tabularnewline
72 & 137 & 145.402836769831 & -8.40283676983094 \tabularnewline
73 & 152 & 137.248688385216 & 14.7513116147839 \tabularnewline
74 & 168 & 152.519298289782 & 15.4807017102177 \tabularnewline
75 & 160 & 168.80328871191 & -8.80328871191008 \tabularnewline
76 & 157 & 160.641794115334 & -3.64179411533388 \tabularnewline
77 & 147 & 157.574986119968 & -10.5749861199681 \tabularnewline
78 & 161 & 147.380990083585 & 13.6190099164146 \tabularnewline
79 & 159 & 161.630828136635 & -2.63082813663513 \tabularnewline
80 & 164 & 159.582566112920 & 4.41743388708022 \tabularnewline
81 & 163 & 164.663603067045 & -1.66360306704476 \tabularnewline
82 & 158 & 163.633084596622 & -5.63308459662224 \tabularnewline
83 & 175 & 158.529746769796 & 16.4702532302038 \tabularnewline
84 & 163 & 175.831890319549 & -12.8318903195495 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78416&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]78[/C][C]78[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]76[/C][C]77[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]74[/C][C]74.9816551970677[/C][C]-0.981655197067695[/C][/ROW]
[ROW][C]6[/C][C]73[/C][C]72.96364692593[/C][C]0.0363530740699929[/C][/ROW]
[ROW][C]7[/C][C]74[/C][C]71.9643138159098[/C][C]2.03568618409020[/C][/ROW]
[ROW][C]8[/C][C]76[/C][C]73.001658077789[/C][C]2.99834192221104[/C][/ROW]
[ROW][C]9[/C][C]77[/C][C]75.0566620694756[/C][C]1.94333793052441[/C][/ROW]
[ROW][C]10[/C][C]77[/C][C]76.092312220842[/C][C]0.907687779158053[/C][/ROW]
[ROW][C]11[/C][C]78[/C][C]76.1089635742747[/C][C]1.89103642572533[/C][/ROW]
[ROW][C]12[/C][C]80[/C][C]77.1436542648424[/C][C]2.85634573515759[/C][/ROW]
[ROW][C]13[/C][C]90[/C][C]79.1960533644604[/C][C]10.8039466355396[/C][/ROW]
[ROW][C]14[/C][C]90[/C][C]89.3942496363805[/C][C]0.605750363619464[/C][/ROW]
[ROW][C]15[/C][C]89[/C][C]89.4053620074273[/C][C]-0.405362007427314[/C][/ROW]
[ROW][C]16[/C][C]82[/C][C]88.3979257212848[/C][C]-6.39792572128482[/C][/ROW]
[ROW][C]17[/C][C]78[/C][C]81.2805570347523[/C][C]-3.28055703475231[/C][/ROW]
[ROW][C]18[/C][C]76[/C][C]77.2203758624416[/C][C]-1.22037586244159[/C][/ROW]
[ROW][C]19[/C][C]74[/C][C]75.1979883077418[/C][C]-1.19798830774175[/C][/ROW]
[ROW][C]20[/C][C]78[/C][C]73.176011448321[/C][C]4.82398855167898[/C][/ROW]
[ROW][C]21[/C][C]81[/C][C]77.2645065676493[/C][C]3.73549343235072[/C][/ROW]
[ROW][C]22[/C][C]82[/C][C]80.3330334585207[/C][C]1.66696654147933[/C][/ROW]
[ROW][C]23[/C][C]88[/C][C]81.3636136312189[/C][C]6.63638636878113[/C][/ROW]
[ROW][C]24[/C][C]99[/C][C]87.4853568313368[/C][C]11.5146431686632[/C][/ROW]
[ROW][C]25[/C][C]117[/C][C]98.6965906911018[/C][C]18.3034093088982[/C][/ROW]
[ROW][C]26[/C][C]113[/C][C]117.032363127863[/C][C]-4.03236312786285[/C][/ROW]
[ROW][C]27[/C][C]106[/C][C]112.958390220931[/C][C]-6.95839022093071[/C][/ROW]
[ROW][C]28[/C][C]100[/C][C]105.830739923602[/C][C]-5.83073992360164[/C][/ROW]
[ROW][C]29[/C][C]97[/C][C]99.7237761487536[/C][C]-2.72377614875363[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]96.673809012073[/C][C]-0.673809012073036[/C][/ROW]
[ROW][C]31[/C][C]100[/C][C]95.6614481185325[/C][C]4.33855188146747[/C][/ROW]
[ROW][C]32[/C][C]104[/C][C]99.7410379978096[/C][C]4.25896200219036[/C][/ROW]
[ROW][C]33[/C][C]104[/C][C]103.819167816436[/C][C]0.180832183563993[/C][/ROW]
[ROW][C]34[/C][C]111[/C][C]103.822485147207[/C][C]7.17751485279268[/C][/ROW]
[ROW][C]35[/C][C]117[/C][C]110.954155242726[/C][C]6.04584475727449[/C][/ROW]
[ROW][C]36[/C][C]118[/C][C]117.065065073357[/C][C]0.934934926642981[/C][/ROW]
[ROW][C]37[/C][C]140[/C][C]118.082216270341[/C][C]21.9177837296592[/C][/ROW]
[ROW][C]38[/C][C]147[/C][C]140.484293693574[/C][C]6.51570630642567[/C][/ROW]
[ROW][C]39[/C][C]134[/C][C]147.603823041730[/C][C]-13.6038230417305[/C][/ROW]
[ROW][C]40[/C][C]126[/C][C]134.354263588904[/C][C]-8.35426358890399[/C][/ROW]
[ROW][C]41[/C][C]116[/C][C]126.201006269721[/C][C]-10.201006269721[/C][/ROW]
[ROW][C]42[/C][C]114[/C][C]116.013870819992[/C][C]-2.01387081999174[/C][/ROW]
[ROW][C]43[/C][C]120[/C][C]113.976926756668[/C][C]6.02307324333214[/C][/ROW]
[ROW][C]44[/C][C]122[/C][C]120.087418848364[/C][C]1.91258115163636[/C][/ROW]
[ROW][C]45[/C][C]117[/C][C]122.122504772682[/C][C]-5.12250477268245[/C][/ROW]
[ROW][C]46[/C][C]119[/C][C]117.028533432108[/C][C]1.97146656789221[/C][/ROW]
[ROW][C]47[/C][C]132[/C][C]119.064699597783[/C][C]12.9353004022166[/C][/ROW]
[ROW][C]48[/C][C]134[/C][C]132.301995134532[/C][C]1.69800486546774[/C][/ROW]
[ROW][C]49[/C][C]154[/C][C]134.333144699167[/C][C]19.6668553008326[/C][/ROW]
[ROW][C]50[/C][C]152[/C][C]154.693929283959[/C][C]-2.69392928395933[/C][/ROW]
[ROW][C]51[/C][C]132[/C][C]152.644509682132[/C][C]-20.6445096821315[/C][/ROW]
[ROW][C]52[/C][C]130[/C][C]132.265790220379[/C][C]-2.26579022037873[/C][/ROW]
[ROW][C]53[/C][C]123[/C][C]130.2242247453[/C][C]-7.22422474529992[/C][/ROW]
[ROW][C]54[/C][C]129[/C][C]123.091697766009[/C][C]5.90830223399129[/C][/ROW]
[ROW][C]55[/C][C]124[/C][C]129.200084406156[/C][C]-5.20008440615578[/C][/ROW]
[ROW][C]56[/C][C]128[/C][C]124.104689882494[/C][C]3.8953101175065[/C][/ROW]
[ROW][C]57[/C][C]128[/C][C]128.176148578959[/C][C]-0.176148578959385[/C][/ROW]
[ROW][C]58[/C][C]129[/C][C]128.172917167992[/C][C]0.827082832008443[/C][/ROW]
[ROW][C]59[/C][C]141[/C][C]129.188089839553[/C][C]11.8119101604466[/C][/ROW]
[ROW][C]60[/C][C]138[/C][C]141.404777003701[/C][C]-3.40477700370096[/C][/ROW]
[ROW][C]61[/C][C]155[/C][C]138.342317040540[/C][C]16.6576829594604[/C][/ROW]
[ROW][C]62[/C][C]160[/C][C]155.647898951740[/C][C]4.35210104826024[/C][/ROW]
[ROW][C]63[/C][C]142[/C][C]160.727737387812[/C][C]-18.7277373878116[/C][/ROW]
[ROW][C]64[/C][C]133[/C][C]142.384180736064[/C][C]-9.38418073606417[/C][/ROW]
[ROW][C]65[/C][C]131[/C][C]133.21202978978[/C][C]-2.21202978977993[/C][/ROW]
[ROW][C]66[/C][C]140[/C][C]131.171450539206[/C][C]8.82854946079397[/C][/ROW]
[ROW][C]67[/C][C]134[/C][C]140.333408539242[/C][C]-6.33340853924241[/C][/ROW]
[ROW][C]68[/C][C]134[/C][C]134.217223407700[/C][C]-0.217223407700232[/C][/ROW]
[ROW][C]69[/C][C]134[/C][C]134.213238487094[/C][C]-0.213238487093690[/C][/ROW]
[ROW][C]70[/C][C]136[/C][C]134.209326669070[/C][C]1.79067333092965[/C][/ROW]
[ROW][C]71[/C][C]145[/C][C]136.242176218442[/C][C]8.75782378155759[/C][/ROW]
[ROW][C]72[/C][C]137[/C][C]145.402836769831[/C][C]-8.40283676983094[/C][/ROW]
[ROW][C]73[/C][C]152[/C][C]137.248688385216[/C][C]14.7513116147839[/C][/ROW]
[ROW][C]74[/C][C]168[/C][C]152.519298289782[/C][C]15.4807017102177[/C][/ROW]
[ROW][C]75[/C][C]160[/C][C]168.80328871191[/C][C]-8.80328871191008[/C][/ROW]
[ROW][C]76[/C][C]157[/C][C]160.641794115334[/C][C]-3.64179411533388[/C][/ROW]
[ROW][C]77[/C][C]147[/C][C]157.574986119968[/C][C]-10.5749861199681[/C][/ROW]
[ROW][C]78[/C][C]161[/C][C]147.380990083585[/C][C]13.6190099164146[/C][/ROW]
[ROW][C]79[/C][C]159[/C][C]161.630828136635[/C][C]-2.63082813663513[/C][/ROW]
[ROW][C]80[/C][C]164[/C][C]159.582566112920[/C][C]4.41743388708022[/C][/ROW]
[ROW][C]81[/C][C]163[/C][C]164.663603067045[/C][C]-1.66360306704476[/C][/ROW]
[ROW][C]82[/C][C]158[/C][C]163.633084596622[/C][C]-5.63308459662224[/C][/ROW]
[ROW][C]83[/C][C]175[/C][C]158.529746769796[/C][C]16.4702532302038[/C][/ROW]
[ROW][C]84[/C][C]163[/C][C]175.831890319549[/C][C]-12.8318903195495[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78416&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78416&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
378780
47677-1
57474.9816551970677-0.981655197067695
67372.963646925930.0363530740699929
77471.96431381590982.03568618409020
87673.0016580777892.99834192221104
97775.05666206947561.94333793052441
107776.0923122208420.907687779158053
117876.10896357427471.89103642572533
128077.14365426484242.85634573515759
139079.196053364460410.8039466355396
149089.39424963638050.605750363619464
158989.4053620074273-0.405362007427314
168288.3979257212848-6.39792572128482
177881.2805570347523-3.28055703475231
187677.2203758624416-1.22037586244159
197475.1979883077418-1.19798830774175
207873.1760114483214.82398855167898
218177.26450656764933.73549343235072
228280.33303345852071.66696654147933
238881.36361363121896.63638636878113
249987.485356831336811.5146431686632
2511798.696590691101818.3034093088982
26113117.032363127863-4.03236312786285
27106112.958390220931-6.95839022093071
28100105.830739923602-5.83073992360164
299799.7237761487536-2.72377614875363
309696.673809012073-0.673809012073036
3110095.66144811853254.33855188146747
3210499.74103799780964.25896200219036
33104103.8191678164360.180832183563993
34111103.8224851472077.17751485279268
35117110.9541552427266.04584475727449
36118117.0650650733570.934934926642981
37140118.08221627034121.9177837296592
38147140.4842936935746.51570630642567
39134147.603823041730-13.6038230417305
40126134.354263588904-8.35426358890399
41116126.201006269721-10.201006269721
42114116.013870819992-2.01387081999174
43120113.9769267566686.02307324333214
44122120.0874188483641.91258115163636
45117122.122504772682-5.12250477268245
46119117.0285334321081.97146656789221
47132119.06469959778312.9353004022166
48134132.3019951345321.69800486546774
49154134.33314469916719.6668553008326
50152154.693929283959-2.69392928395933
51132152.644509682132-20.6445096821315
52130132.265790220379-2.26579022037873
53123130.2242247453-7.22422474529992
54129123.0916977660095.90830223399129
55124129.200084406156-5.20008440615578
56128124.1046898824943.8953101175065
57128128.176148578959-0.176148578959385
58129128.1729171679920.827082832008443
59141129.18808983955311.8119101604466
60138141.404777003701-3.40477700370096
61155138.34231704054016.6576829594604
62160155.6478989517404.35210104826024
63142160.727737387812-18.7277373878116
64133142.384180736064-9.38418073606417
65131133.21202978978-2.21202978977993
66140131.1714505392068.82854946079397
67134140.333408539242-6.33340853924241
68134134.217223407700-0.217223407700232
69134134.213238487094-0.213238487093690
70136134.2093266690701.79067333092965
71145136.2421762184428.75782378155759
72137145.402836769831-8.40283676983094
73152137.24868838521614.7513116147839
74168152.51929828978215.4807017102177
75160168.80328871191-8.80328871191008
76157160.641794115334-3.64179411533388
77147157.574986119968-10.5749861199681
78161147.38099008358513.6190099164146
79159161.630828136635-2.63082813663513
80164159.5825661129204.41743388708022
81163164.663603067045-1.66360306704476
82158163.633084596622-5.63308459662224
83175158.52974676979616.4702532302038
84163175.831890319549-12.8318903195495







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85163.596491820388147.477366090804179.715617549973
86164.192983640777141.187054193133187.19891308842
87164.789475461165136.355084207689193.223866714641
88165.385967281553132.254010767216198.517923795890
89165.982459101942128.604879206357203.360038997527
90166.578950922330125.265995391784207.891906452876
91167.175442742719122.153982643268212.196902842169
92167.771934563107119.215028948480216.328840177733
93168.368426383495116.412109978487220.324742788504
94168.964918203884113.718525167057224.21131124071
95169.561410024272111.114311293551228.008508754993
96170.157901844660108.584109421917231.731694267404

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 163.596491820388 & 147.477366090804 & 179.715617549973 \tabularnewline
86 & 164.192983640777 & 141.187054193133 & 187.19891308842 \tabularnewline
87 & 164.789475461165 & 136.355084207689 & 193.223866714641 \tabularnewline
88 & 165.385967281553 & 132.254010767216 & 198.517923795890 \tabularnewline
89 & 165.982459101942 & 128.604879206357 & 203.360038997527 \tabularnewline
90 & 166.578950922330 & 125.265995391784 & 207.891906452876 \tabularnewline
91 & 167.175442742719 & 122.153982643268 & 212.196902842169 \tabularnewline
92 & 167.771934563107 & 119.215028948480 & 216.328840177733 \tabularnewline
93 & 168.368426383495 & 116.412109978487 & 220.324742788504 \tabularnewline
94 & 168.964918203884 & 113.718525167057 & 224.21131124071 \tabularnewline
95 & 169.561410024272 & 111.114311293551 & 228.008508754993 \tabularnewline
96 & 170.157901844660 & 108.584109421917 & 231.731694267404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78416&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]163.596491820388[/C][C]147.477366090804[/C][C]179.715617549973[/C][/ROW]
[ROW][C]86[/C][C]164.192983640777[/C][C]141.187054193133[/C][C]187.19891308842[/C][/ROW]
[ROW][C]87[/C][C]164.789475461165[/C][C]136.355084207689[/C][C]193.223866714641[/C][/ROW]
[ROW][C]88[/C][C]165.385967281553[/C][C]132.254010767216[/C][C]198.517923795890[/C][/ROW]
[ROW][C]89[/C][C]165.982459101942[/C][C]128.604879206357[/C][C]203.360038997527[/C][/ROW]
[ROW][C]90[/C][C]166.578950922330[/C][C]125.265995391784[/C][C]207.891906452876[/C][/ROW]
[ROW][C]91[/C][C]167.175442742719[/C][C]122.153982643268[/C][C]212.196902842169[/C][/ROW]
[ROW][C]92[/C][C]167.771934563107[/C][C]119.215028948480[/C][C]216.328840177733[/C][/ROW]
[ROW][C]93[/C][C]168.368426383495[/C][C]116.412109978487[/C][C]220.324742788504[/C][/ROW]
[ROW][C]94[/C][C]168.964918203884[/C][C]113.718525167057[/C][C]224.21131124071[/C][/ROW]
[ROW][C]95[/C][C]169.561410024272[/C][C]111.114311293551[/C][C]228.008508754993[/C][/ROW]
[ROW][C]96[/C][C]170.157901844660[/C][C]108.584109421917[/C][C]231.731694267404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78416&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78416&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
85163.596491820388147.477366090804179.715617549973
86164.192983640777141.187054193133187.19891308842
87164.789475461165136.355084207689193.223866714641
88165.385967281553132.254010767216198.517923795890
89165.982459101942128.604879206357203.360038997527
90166.578950922330125.265995391784207.891906452876
91167.175442742719122.153982643268212.196902842169
92167.771934563107119.215028948480216.328840177733
93168.368426383495116.412109978487220.324742788504
94168.964918203884113.718525167057224.21131124071
95169.561410024272111.114311293551228.008508754993
96170.157901844660108.584109421917231.731694267404



Parameters (Session):
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')