Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 Aug 2010 13:26:45 +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/19/t1282224442g50s7apxf1e6kqa.htm/, Retrieved Fri, 03 May 2024 07:35:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79293, Retrieved Fri, 03 May 2024 07:35:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPhilippe De Vocht
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Het aantal inschr...] [2010-05-27 12:18:36] [e6858d370c345b8be9ebab3064023a2f]
-    D  [Exponential Smoothing] [Opgave 10 oefenin...] [2010-05-31 15:05:24] [1f3241a8f2363a866734862cbbf73252]
-   PD      [Exponential Smoothing] [stap 33 exponenti...] [2010-08-19 13:26:45] [181f2439255053cc457d7672472fa443] [Current]
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Dataseries X:
73
72
71
69
89
88
73
63
64
64
65
67
69
71
70
72
88
83
76
70
75
71
75
81
87
90
80
85
105
104
98
94
107
112
121
118
120
122
109
112
132
127
116
113
123
125
137
127
123
128
114
120
143
135
119
117
132
139
158
141
139
150
142
149
166
150
139
140
158
169
186
177
175
187
176
185
204
188
171
171
182
185
200
192
185
195
190
195
213
194
171
171
186
182
193
185
172
185
179
182
193
173
155
164
188
186
200
185
173
190
190
193
195
178
163
165
188
182
200
177




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79293&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79293&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79293&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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.666695305515088
beta0.0185297170665319
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.666695305515088 \tabularnewline
beta & 0.0185297170665319 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79293&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]0.666695305515088[/C][/ROW]
[ROW][C]beta[/C][C]0.0185297170665319[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79293&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79293&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
alpha0.666695305515088
beta0.0185297170665319
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
371710
46970-1
58968.320951019104120.6790489808959
68881.35068448009646.64931551990357
77385.1090039904545-12.1090039904545
86376.2116492394221-13.2116492394221
96466.4159536513059-2.41595365130593
106463.78785172441350.212148275586472
116562.91451382552462.08548617447537
126763.3158849286793.68411507132097
136964.82856677427774.1714332257223
147166.71767387765124.28232612234882
157068.73361522141071.26638477858934
167268.75448713603873.24551286396132
178870.134928466562817.8650715334372
188381.48286022510741.51713977489263
197681.9504448776355-5.95044487763555
207077.3659160343971-7.36591603439715
217571.74670308028283.25329691971724
227173.2474597250049-2.2474597250049
237571.05312335003583.94687664996421
248173.03728038994167.96271961005844
258777.79714993223889.20285006776119
269083.49749765122796.50250234877214
278087.477866025888-7.47786602588803
288582.04520930636592.95479069363412
2910583.604458370846921.3955416291531
3010497.7223830900946.2776169099061
3198101.838810011358-3.83881001135829
329499.1632391829005-5.16323918290045
3310795.540892662509311.4591073374907
34112103.1421486261098.8578513738911
35121109.11858647077811.8814135292222
36118117.2575981361440.742401863856216
37120117.9794544077612.02054559223934
38122119.5784042672032.42159573279731
39109121.474647980217-12.4746479802173
40112113.285528188319-1.28552818831938
41132112.54026103659419.4597389634056
42127125.8661654047291.13383459527054
43116126.988282385836-10.9882823858359
44113119.892895209147-6.89289520914699
45123115.4427308475767.55726915242428
46125120.719783279664.28021672034031
47137123.86491664726913.1350833527311
48127133.075814585494-6.07581458549441
49123129.403838412512-6.40383841251247
50128125.4340593530212.56594064697863
51114127.4760886818-13.4760886817996
52120118.6564931411691.34350685883147
53143119.73364962471423.2663503752856
54135135.714087904054-0.714087904053855
55119135.698058948203-16.6980589482034
56117124.819309133994-7.81930913399405
57132119.76338293301812.2366170669823
58139128.22981577299410.7701842270062
59158135.85163608243622.1483639175637
60141151.332849074934-10.3328490749335
61139145.031341184667-6.03134118466684
62150141.5231191803718.47688081962903
63142147.792181311597-5.79218131159712
64149144.4765719781624.52342802183841
65166148.09421192224517.9057880777547
66150160.855010785671-10.8550107856706
67139154.307020784486-15.3070207844856
68140144.601798651166-4.60179865116598
69158141.97684873192316.0231512680775
70169153.30040090966515.6995990903345
71186164.60219012018821.3978098798116
72177179.967291311006-2.96729131100591
73175179.051636965889-4.05163696588895
74187177.3630018552689.63699814473156
75176184.919567858533-8.91956785853279
76185179.9943689750795.00563102492123
77204184.41487275634519.5851272436547
78188198.797406527676-10.7974065276758
79171192.790660008809-21.7906600088094
80171179.185568261652-8.1855682616521
81182174.5498054603157.45019453968504
82185180.4303696016444.56963039835631
83200184.44692688326515.5530731167351
84192195.978231480081-3.97823148008075
85185194.43896121132-9.43896121131974
86195189.1424422033195.85755779668142
87190194.116402976218-4.11640297621847
88195192.389918218332.61008178167032
89213195.18019337419217.8198066258078
90194208.330860788221-14.3308607882209
91171199.869790366035-28.8697903660349
92171181.359035828613-10.3590358286127
93186175.06134227694710.9386577230526
94182183.097853661088-1.09785366108844
95193183.0961168828999.903883117101
96185190.551535724279-5.551535724279
97172187.634317509139-15.634317509139
98185177.8018147281927.19818527180817
99179183.280558408641-4.28055840864096
100182181.0535969350950.946403064905155
101193182.32311769431310.6768823056866
102173190.211802021856-17.2118020218562
103155179.294602416338-24.2946024163377
104164163.3552054061610.644794593838554
105188164.05075288814623.9492471118537
106186180.5791306859255.42086931407496
107200184.82169364690215.1783063530976
108185195.757001945171-10.7570019451714
109173189.268473443797-16.2684734437969
110190178.90449732794311.0955026720569
111190186.9210258669533.07897413304687
112193189.6310091094233.36899089057707
113195192.5759645824822.42403541751816
114178194.920868424391-16.9208684243911
115163184.159580773583-21.1595807735828
116165170.310964906069-5.31096490606942
117188166.96293689993121.0370631000692
118182181.4409005235680.559099476431896
119200182.27320886625517.7267911337449
120177194.770127666612-17.7701276666124

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 71 & 71 & 0 \tabularnewline
4 & 69 & 70 & -1 \tabularnewline
5 & 89 & 68.3209510191041 & 20.6790489808959 \tabularnewline
6 & 88 & 81.3506844800964 & 6.64931551990357 \tabularnewline
7 & 73 & 85.1090039904545 & -12.1090039904545 \tabularnewline
8 & 63 & 76.2116492394221 & -13.2116492394221 \tabularnewline
9 & 64 & 66.4159536513059 & -2.41595365130593 \tabularnewline
10 & 64 & 63.7878517244135 & 0.212148275586472 \tabularnewline
11 & 65 & 62.9145138255246 & 2.08548617447537 \tabularnewline
12 & 67 & 63.315884928679 & 3.68411507132097 \tabularnewline
13 & 69 & 64.8285667742777 & 4.1714332257223 \tabularnewline
14 & 71 & 66.7176738776512 & 4.28232612234882 \tabularnewline
15 & 70 & 68.7336152214107 & 1.26638477858934 \tabularnewline
16 & 72 & 68.7544871360387 & 3.24551286396132 \tabularnewline
17 & 88 & 70.1349284665628 & 17.8650715334372 \tabularnewline
18 & 83 & 81.4828602251074 & 1.51713977489263 \tabularnewline
19 & 76 & 81.9504448776355 & -5.95044487763555 \tabularnewline
20 & 70 & 77.3659160343971 & -7.36591603439715 \tabularnewline
21 & 75 & 71.7467030802828 & 3.25329691971724 \tabularnewline
22 & 71 & 73.2474597250049 & -2.2474597250049 \tabularnewline
23 & 75 & 71.0531233500358 & 3.94687664996421 \tabularnewline
24 & 81 & 73.0372803899416 & 7.96271961005844 \tabularnewline
25 & 87 & 77.7971499322388 & 9.20285006776119 \tabularnewline
26 & 90 & 83.4974976512279 & 6.50250234877214 \tabularnewline
27 & 80 & 87.477866025888 & -7.47786602588803 \tabularnewline
28 & 85 & 82.0452093063659 & 2.95479069363412 \tabularnewline
29 & 105 & 83.6044583708469 & 21.3955416291531 \tabularnewline
30 & 104 & 97.722383090094 & 6.2776169099061 \tabularnewline
31 & 98 & 101.838810011358 & -3.83881001135829 \tabularnewline
32 & 94 & 99.1632391829005 & -5.16323918290045 \tabularnewline
33 & 107 & 95.5408926625093 & 11.4591073374907 \tabularnewline
34 & 112 & 103.142148626109 & 8.8578513738911 \tabularnewline
35 & 121 & 109.118586470778 & 11.8814135292222 \tabularnewline
36 & 118 & 117.257598136144 & 0.742401863856216 \tabularnewline
37 & 120 & 117.979454407761 & 2.02054559223934 \tabularnewline
38 & 122 & 119.578404267203 & 2.42159573279731 \tabularnewline
39 & 109 & 121.474647980217 & -12.4746479802173 \tabularnewline
40 & 112 & 113.285528188319 & -1.28552818831938 \tabularnewline
41 & 132 & 112.540261036594 & 19.4597389634056 \tabularnewline
42 & 127 & 125.866165404729 & 1.13383459527054 \tabularnewline
43 & 116 & 126.988282385836 & -10.9882823858359 \tabularnewline
44 & 113 & 119.892895209147 & -6.89289520914699 \tabularnewline
45 & 123 & 115.442730847576 & 7.55726915242428 \tabularnewline
46 & 125 & 120.71978327966 & 4.28021672034031 \tabularnewline
47 & 137 & 123.864916647269 & 13.1350833527311 \tabularnewline
48 & 127 & 133.075814585494 & -6.07581458549441 \tabularnewline
49 & 123 & 129.403838412512 & -6.40383841251247 \tabularnewline
50 & 128 & 125.434059353021 & 2.56594064697863 \tabularnewline
51 & 114 & 127.4760886818 & -13.4760886817996 \tabularnewline
52 & 120 & 118.656493141169 & 1.34350685883147 \tabularnewline
53 & 143 & 119.733649624714 & 23.2663503752856 \tabularnewline
54 & 135 & 135.714087904054 & -0.714087904053855 \tabularnewline
55 & 119 & 135.698058948203 & -16.6980589482034 \tabularnewline
56 & 117 & 124.819309133994 & -7.81930913399405 \tabularnewline
57 & 132 & 119.763382933018 & 12.2366170669823 \tabularnewline
58 & 139 & 128.229815772994 & 10.7701842270062 \tabularnewline
59 & 158 & 135.851636082436 & 22.1483639175637 \tabularnewline
60 & 141 & 151.332849074934 & -10.3328490749335 \tabularnewline
61 & 139 & 145.031341184667 & -6.03134118466684 \tabularnewline
62 & 150 & 141.523119180371 & 8.47688081962903 \tabularnewline
63 & 142 & 147.792181311597 & -5.79218131159712 \tabularnewline
64 & 149 & 144.476571978162 & 4.52342802183841 \tabularnewline
65 & 166 & 148.094211922245 & 17.9057880777547 \tabularnewline
66 & 150 & 160.855010785671 & -10.8550107856706 \tabularnewline
67 & 139 & 154.307020784486 & -15.3070207844856 \tabularnewline
68 & 140 & 144.601798651166 & -4.60179865116598 \tabularnewline
69 & 158 & 141.976848731923 & 16.0231512680775 \tabularnewline
70 & 169 & 153.300400909665 & 15.6995990903345 \tabularnewline
71 & 186 & 164.602190120188 & 21.3978098798116 \tabularnewline
72 & 177 & 179.967291311006 & -2.96729131100591 \tabularnewline
73 & 175 & 179.051636965889 & -4.05163696588895 \tabularnewline
74 & 187 & 177.363001855268 & 9.63699814473156 \tabularnewline
75 & 176 & 184.919567858533 & -8.91956785853279 \tabularnewline
76 & 185 & 179.994368975079 & 5.00563102492123 \tabularnewline
77 & 204 & 184.414872756345 & 19.5851272436547 \tabularnewline
78 & 188 & 198.797406527676 & -10.7974065276758 \tabularnewline
79 & 171 & 192.790660008809 & -21.7906600088094 \tabularnewline
80 & 171 & 179.185568261652 & -8.1855682616521 \tabularnewline
81 & 182 & 174.549805460315 & 7.45019453968504 \tabularnewline
82 & 185 & 180.430369601644 & 4.56963039835631 \tabularnewline
83 & 200 & 184.446926883265 & 15.5530731167351 \tabularnewline
84 & 192 & 195.978231480081 & -3.97823148008075 \tabularnewline
85 & 185 & 194.43896121132 & -9.43896121131974 \tabularnewline
86 & 195 & 189.142442203319 & 5.85755779668142 \tabularnewline
87 & 190 & 194.116402976218 & -4.11640297621847 \tabularnewline
88 & 195 & 192.38991821833 & 2.61008178167032 \tabularnewline
89 & 213 & 195.180193374192 & 17.8198066258078 \tabularnewline
90 & 194 & 208.330860788221 & -14.3308607882209 \tabularnewline
91 & 171 & 199.869790366035 & -28.8697903660349 \tabularnewline
92 & 171 & 181.359035828613 & -10.3590358286127 \tabularnewline
93 & 186 & 175.061342276947 & 10.9386577230526 \tabularnewline
94 & 182 & 183.097853661088 & -1.09785366108844 \tabularnewline
95 & 193 & 183.096116882899 & 9.903883117101 \tabularnewline
96 & 185 & 190.551535724279 & -5.551535724279 \tabularnewline
97 & 172 & 187.634317509139 & -15.634317509139 \tabularnewline
98 & 185 & 177.801814728192 & 7.19818527180817 \tabularnewline
99 & 179 & 183.280558408641 & -4.28055840864096 \tabularnewline
100 & 182 & 181.053596935095 & 0.946403064905155 \tabularnewline
101 & 193 & 182.323117694313 & 10.6768823056866 \tabularnewline
102 & 173 & 190.211802021856 & -17.2118020218562 \tabularnewline
103 & 155 & 179.294602416338 & -24.2946024163377 \tabularnewline
104 & 164 & 163.355205406161 & 0.644794593838554 \tabularnewline
105 & 188 & 164.050752888146 & 23.9492471118537 \tabularnewline
106 & 186 & 180.579130685925 & 5.42086931407496 \tabularnewline
107 & 200 & 184.821693646902 & 15.1783063530976 \tabularnewline
108 & 185 & 195.757001945171 & -10.7570019451714 \tabularnewline
109 & 173 & 189.268473443797 & -16.2684734437969 \tabularnewline
110 & 190 & 178.904497327943 & 11.0955026720569 \tabularnewline
111 & 190 & 186.921025866953 & 3.07897413304687 \tabularnewline
112 & 193 & 189.631009109423 & 3.36899089057707 \tabularnewline
113 & 195 & 192.575964582482 & 2.42403541751816 \tabularnewline
114 & 178 & 194.920868424391 & -16.9208684243911 \tabularnewline
115 & 163 & 184.159580773583 & -21.1595807735828 \tabularnewline
116 & 165 & 170.310964906069 & -5.31096490606942 \tabularnewline
117 & 188 & 166.962936899931 & 21.0370631000692 \tabularnewline
118 & 182 & 181.440900523568 & 0.559099476431896 \tabularnewline
119 & 200 & 182.273208866255 & 17.7267911337449 \tabularnewline
120 & 177 & 194.770127666612 & -17.7701276666124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79293&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]71[/C][C]71[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]69[/C][C]70[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]89[/C][C]68.3209510191041[/C][C]20.6790489808959[/C][/ROW]
[ROW][C]6[/C][C]88[/C][C]81.3506844800964[/C][C]6.64931551990357[/C][/ROW]
[ROW][C]7[/C][C]73[/C][C]85.1090039904545[/C][C]-12.1090039904545[/C][/ROW]
[ROW][C]8[/C][C]63[/C][C]76.2116492394221[/C][C]-13.2116492394221[/C][/ROW]
[ROW][C]9[/C][C]64[/C][C]66.4159536513059[/C][C]-2.41595365130593[/C][/ROW]
[ROW][C]10[/C][C]64[/C][C]63.7878517244135[/C][C]0.212148275586472[/C][/ROW]
[ROW][C]11[/C][C]65[/C][C]62.9145138255246[/C][C]2.08548617447537[/C][/ROW]
[ROW][C]12[/C][C]67[/C][C]63.315884928679[/C][C]3.68411507132097[/C][/ROW]
[ROW][C]13[/C][C]69[/C][C]64.8285667742777[/C][C]4.1714332257223[/C][/ROW]
[ROW][C]14[/C][C]71[/C][C]66.7176738776512[/C][C]4.28232612234882[/C][/ROW]
[ROW][C]15[/C][C]70[/C][C]68.7336152214107[/C][C]1.26638477858934[/C][/ROW]
[ROW][C]16[/C][C]72[/C][C]68.7544871360387[/C][C]3.24551286396132[/C][/ROW]
[ROW][C]17[/C][C]88[/C][C]70.1349284665628[/C][C]17.8650715334372[/C][/ROW]
[ROW][C]18[/C][C]83[/C][C]81.4828602251074[/C][C]1.51713977489263[/C][/ROW]
[ROW][C]19[/C][C]76[/C][C]81.9504448776355[/C][C]-5.95044487763555[/C][/ROW]
[ROW][C]20[/C][C]70[/C][C]77.3659160343971[/C][C]-7.36591603439715[/C][/ROW]
[ROW][C]21[/C][C]75[/C][C]71.7467030802828[/C][C]3.25329691971724[/C][/ROW]
[ROW][C]22[/C][C]71[/C][C]73.2474597250049[/C][C]-2.2474597250049[/C][/ROW]
[ROW][C]23[/C][C]75[/C][C]71.0531233500358[/C][C]3.94687664996421[/C][/ROW]
[ROW][C]24[/C][C]81[/C][C]73.0372803899416[/C][C]7.96271961005844[/C][/ROW]
[ROW][C]25[/C][C]87[/C][C]77.7971499322388[/C][C]9.20285006776119[/C][/ROW]
[ROW][C]26[/C][C]90[/C][C]83.4974976512279[/C][C]6.50250234877214[/C][/ROW]
[ROW][C]27[/C][C]80[/C][C]87.477866025888[/C][C]-7.47786602588803[/C][/ROW]
[ROW][C]28[/C][C]85[/C][C]82.0452093063659[/C][C]2.95479069363412[/C][/ROW]
[ROW][C]29[/C][C]105[/C][C]83.6044583708469[/C][C]21.3955416291531[/C][/ROW]
[ROW][C]30[/C][C]104[/C][C]97.722383090094[/C][C]6.2776169099061[/C][/ROW]
[ROW][C]31[/C][C]98[/C][C]101.838810011358[/C][C]-3.83881001135829[/C][/ROW]
[ROW][C]32[/C][C]94[/C][C]99.1632391829005[/C][C]-5.16323918290045[/C][/ROW]
[ROW][C]33[/C][C]107[/C][C]95.5408926625093[/C][C]11.4591073374907[/C][/ROW]
[ROW][C]34[/C][C]112[/C][C]103.142148626109[/C][C]8.8578513738911[/C][/ROW]
[ROW][C]35[/C][C]121[/C][C]109.118586470778[/C][C]11.8814135292222[/C][/ROW]
[ROW][C]36[/C][C]118[/C][C]117.257598136144[/C][C]0.742401863856216[/C][/ROW]
[ROW][C]37[/C][C]120[/C][C]117.979454407761[/C][C]2.02054559223934[/C][/ROW]
[ROW][C]38[/C][C]122[/C][C]119.578404267203[/C][C]2.42159573279731[/C][/ROW]
[ROW][C]39[/C][C]109[/C][C]121.474647980217[/C][C]-12.4746479802173[/C][/ROW]
[ROW][C]40[/C][C]112[/C][C]113.285528188319[/C][C]-1.28552818831938[/C][/ROW]
[ROW][C]41[/C][C]132[/C][C]112.540261036594[/C][C]19.4597389634056[/C][/ROW]
[ROW][C]42[/C][C]127[/C][C]125.866165404729[/C][C]1.13383459527054[/C][/ROW]
[ROW][C]43[/C][C]116[/C][C]126.988282385836[/C][C]-10.9882823858359[/C][/ROW]
[ROW][C]44[/C][C]113[/C][C]119.892895209147[/C][C]-6.89289520914699[/C][/ROW]
[ROW][C]45[/C][C]123[/C][C]115.442730847576[/C][C]7.55726915242428[/C][/ROW]
[ROW][C]46[/C][C]125[/C][C]120.71978327966[/C][C]4.28021672034031[/C][/ROW]
[ROW][C]47[/C][C]137[/C][C]123.864916647269[/C][C]13.1350833527311[/C][/ROW]
[ROW][C]48[/C][C]127[/C][C]133.075814585494[/C][C]-6.07581458549441[/C][/ROW]
[ROW][C]49[/C][C]123[/C][C]129.403838412512[/C][C]-6.40383841251247[/C][/ROW]
[ROW][C]50[/C][C]128[/C][C]125.434059353021[/C][C]2.56594064697863[/C][/ROW]
[ROW][C]51[/C][C]114[/C][C]127.4760886818[/C][C]-13.4760886817996[/C][/ROW]
[ROW][C]52[/C][C]120[/C][C]118.656493141169[/C][C]1.34350685883147[/C][/ROW]
[ROW][C]53[/C][C]143[/C][C]119.733649624714[/C][C]23.2663503752856[/C][/ROW]
[ROW][C]54[/C][C]135[/C][C]135.714087904054[/C][C]-0.714087904053855[/C][/ROW]
[ROW][C]55[/C][C]119[/C][C]135.698058948203[/C][C]-16.6980589482034[/C][/ROW]
[ROW][C]56[/C][C]117[/C][C]124.819309133994[/C][C]-7.81930913399405[/C][/ROW]
[ROW][C]57[/C][C]132[/C][C]119.763382933018[/C][C]12.2366170669823[/C][/ROW]
[ROW][C]58[/C][C]139[/C][C]128.229815772994[/C][C]10.7701842270062[/C][/ROW]
[ROW][C]59[/C][C]158[/C][C]135.851636082436[/C][C]22.1483639175637[/C][/ROW]
[ROW][C]60[/C][C]141[/C][C]151.332849074934[/C][C]-10.3328490749335[/C][/ROW]
[ROW][C]61[/C][C]139[/C][C]145.031341184667[/C][C]-6.03134118466684[/C][/ROW]
[ROW][C]62[/C][C]150[/C][C]141.523119180371[/C][C]8.47688081962903[/C][/ROW]
[ROW][C]63[/C][C]142[/C][C]147.792181311597[/C][C]-5.79218131159712[/C][/ROW]
[ROW][C]64[/C][C]149[/C][C]144.476571978162[/C][C]4.52342802183841[/C][/ROW]
[ROW][C]65[/C][C]166[/C][C]148.094211922245[/C][C]17.9057880777547[/C][/ROW]
[ROW][C]66[/C][C]150[/C][C]160.855010785671[/C][C]-10.8550107856706[/C][/ROW]
[ROW][C]67[/C][C]139[/C][C]154.307020784486[/C][C]-15.3070207844856[/C][/ROW]
[ROW][C]68[/C][C]140[/C][C]144.601798651166[/C][C]-4.60179865116598[/C][/ROW]
[ROW][C]69[/C][C]158[/C][C]141.976848731923[/C][C]16.0231512680775[/C][/ROW]
[ROW][C]70[/C][C]169[/C][C]153.300400909665[/C][C]15.6995990903345[/C][/ROW]
[ROW][C]71[/C][C]186[/C][C]164.602190120188[/C][C]21.3978098798116[/C][/ROW]
[ROW][C]72[/C][C]177[/C][C]179.967291311006[/C][C]-2.96729131100591[/C][/ROW]
[ROW][C]73[/C][C]175[/C][C]179.051636965889[/C][C]-4.05163696588895[/C][/ROW]
[ROW][C]74[/C][C]187[/C][C]177.363001855268[/C][C]9.63699814473156[/C][/ROW]
[ROW][C]75[/C][C]176[/C][C]184.919567858533[/C][C]-8.91956785853279[/C][/ROW]
[ROW][C]76[/C][C]185[/C][C]179.994368975079[/C][C]5.00563102492123[/C][/ROW]
[ROW][C]77[/C][C]204[/C][C]184.414872756345[/C][C]19.5851272436547[/C][/ROW]
[ROW][C]78[/C][C]188[/C][C]198.797406527676[/C][C]-10.7974065276758[/C][/ROW]
[ROW][C]79[/C][C]171[/C][C]192.790660008809[/C][C]-21.7906600088094[/C][/ROW]
[ROW][C]80[/C][C]171[/C][C]179.185568261652[/C][C]-8.1855682616521[/C][/ROW]
[ROW][C]81[/C][C]182[/C][C]174.549805460315[/C][C]7.45019453968504[/C][/ROW]
[ROW][C]82[/C][C]185[/C][C]180.430369601644[/C][C]4.56963039835631[/C][/ROW]
[ROW][C]83[/C][C]200[/C][C]184.446926883265[/C][C]15.5530731167351[/C][/ROW]
[ROW][C]84[/C][C]192[/C][C]195.978231480081[/C][C]-3.97823148008075[/C][/ROW]
[ROW][C]85[/C][C]185[/C][C]194.43896121132[/C][C]-9.43896121131974[/C][/ROW]
[ROW][C]86[/C][C]195[/C][C]189.142442203319[/C][C]5.85755779668142[/C][/ROW]
[ROW][C]87[/C][C]190[/C][C]194.116402976218[/C][C]-4.11640297621847[/C][/ROW]
[ROW][C]88[/C][C]195[/C][C]192.38991821833[/C][C]2.61008178167032[/C][/ROW]
[ROW][C]89[/C][C]213[/C][C]195.180193374192[/C][C]17.8198066258078[/C][/ROW]
[ROW][C]90[/C][C]194[/C][C]208.330860788221[/C][C]-14.3308607882209[/C][/ROW]
[ROW][C]91[/C][C]171[/C][C]199.869790366035[/C][C]-28.8697903660349[/C][/ROW]
[ROW][C]92[/C][C]171[/C][C]181.359035828613[/C][C]-10.3590358286127[/C][/ROW]
[ROW][C]93[/C][C]186[/C][C]175.061342276947[/C][C]10.9386577230526[/C][/ROW]
[ROW][C]94[/C][C]182[/C][C]183.097853661088[/C][C]-1.09785366108844[/C][/ROW]
[ROW][C]95[/C][C]193[/C][C]183.096116882899[/C][C]9.903883117101[/C][/ROW]
[ROW][C]96[/C][C]185[/C][C]190.551535724279[/C][C]-5.551535724279[/C][/ROW]
[ROW][C]97[/C][C]172[/C][C]187.634317509139[/C][C]-15.634317509139[/C][/ROW]
[ROW][C]98[/C][C]185[/C][C]177.801814728192[/C][C]7.19818527180817[/C][/ROW]
[ROW][C]99[/C][C]179[/C][C]183.280558408641[/C][C]-4.28055840864096[/C][/ROW]
[ROW][C]100[/C][C]182[/C][C]181.053596935095[/C][C]0.946403064905155[/C][/ROW]
[ROW][C]101[/C][C]193[/C][C]182.323117694313[/C][C]10.6768823056866[/C][/ROW]
[ROW][C]102[/C][C]173[/C][C]190.211802021856[/C][C]-17.2118020218562[/C][/ROW]
[ROW][C]103[/C][C]155[/C][C]179.294602416338[/C][C]-24.2946024163377[/C][/ROW]
[ROW][C]104[/C][C]164[/C][C]163.355205406161[/C][C]0.644794593838554[/C][/ROW]
[ROW][C]105[/C][C]188[/C][C]164.050752888146[/C][C]23.9492471118537[/C][/ROW]
[ROW][C]106[/C][C]186[/C][C]180.579130685925[/C][C]5.42086931407496[/C][/ROW]
[ROW][C]107[/C][C]200[/C][C]184.821693646902[/C][C]15.1783063530976[/C][/ROW]
[ROW][C]108[/C][C]185[/C][C]195.757001945171[/C][C]-10.7570019451714[/C][/ROW]
[ROW][C]109[/C][C]173[/C][C]189.268473443797[/C][C]-16.2684734437969[/C][/ROW]
[ROW][C]110[/C][C]190[/C][C]178.904497327943[/C][C]11.0955026720569[/C][/ROW]
[ROW][C]111[/C][C]190[/C][C]186.921025866953[/C][C]3.07897413304687[/C][/ROW]
[ROW][C]112[/C][C]193[/C][C]189.631009109423[/C][C]3.36899089057707[/C][/ROW]
[ROW][C]113[/C][C]195[/C][C]192.575964582482[/C][C]2.42403541751816[/C][/ROW]
[ROW][C]114[/C][C]178[/C][C]194.920868424391[/C][C]-16.9208684243911[/C][/ROW]
[ROW][C]115[/C][C]163[/C][C]184.159580773583[/C][C]-21.1595807735828[/C][/ROW]
[ROW][C]116[/C][C]165[/C][C]170.310964906069[/C][C]-5.31096490606942[/C][/ROW]
[ROW][C]117[/C][C]188[/C][C]166.962936899931[/C][C]21.0370631000692[/C][/ROW]
[ROW][C]118[/C][C]182[/C][C]181.440900523568[/C][C]0.559099476431896[/C][/ROW]
[ROW][C]119[/C][C]200[/C][C]182.273208866255[/C][C]17.7267911337449[/C][/ROW]
[ROW][C]120[/C][C]177[/C][C]194.770127666612[/C][C]-17.7701276666124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79293&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79293&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
371710
46970-1
58968.320951019104120.6790489808959
68881.35068448009646.64931551990357
77385.1090039904545-12.1090039904545
86376.2116492394221-13.2116492394221
96466.4159536513059-2.41595365130593
106463.78785172441350.212148275586472
116562.91451382552462.08548617447537
126763.3158849286793.68411507132097
136964.82856677427774.1714332257223
147166.71767387765124.28232612234882
157068.73361522141071.26638477858934
167268.75448713603873.24551286396132
178870.134928466562817.8650715334372
188381.48286022510741.51713977489263
197681.9504448776355-5.95044487763555
207077.3659160343971-7.36591603439715
217571.74670308028283.25329691971724
227173.2474597250049-2.2474597250049
237571.05312335003583.94687664996421
248173.03728038994167.96271961005844
258777.79714993223889.20285006776119
269083.49749765122796.50250234877214
278087.477866025888-7.47786602588803
288582.04520930636592.95479069363412
2910583.604458370846921.3955416291531
3010497.7223830900946.2776169099061
3198101.838810011358-3.83881001135829
329499.1632391829005-5.16323918290045
3310795.540892662509311.4591073374907
34112103.1421486261098.8578513738911
35121109.11858647077811.8814135292222
36118117.2575981361440.742401863856216
37120117.9794544077612.02054559223934
38122119.5784042672032.42159573279731
39109121.474647980217-12.4746479802173
40112113.285528188319-1.28552818831938
41132112.54026103659419.4597389634056
42127125.8661654047291.13383459527054
43116126.988282385836-10.9882823858359
44113119.892895209147-6.89289520914699
45123115.4427308475767.55726915242428
46125120.719783279664.28021672034031
47137123.86491664726913.1350833527311
48127133.075814585494-6.07581458549441
49123129.403838412512-6.40383841251247
50128125.4340593530212.56594064697863
51114127.4760886818-13.4760886817996
52120118.6564931411691.34350685883147
53143119.73364962471423.2663503752856
54135135.714087904054-0.714087904053855
55119135.698058948203-16.6980589482034
56117124.819309133994-7.81930913399405
57132119.76338293301812.2366170669823
58139128.22981577299410.7701842270062
59158135.85163608243622.1483639175637
60141151.332849074934-10.3328490749335
61139145.031341184667-6.03134118466684
62150141.5231191803718.47688081962903
63142147.792181311597-5.79218131159712
64149144.4765719781624.52342802183841
65166148.09421192224517.9057880777547
66150160.855010785671-10.8550107856706
67139154.307020784486-15.3070207844856
68140144.601798651166-4.60179865116598
69158141.97684873192316.0231512680775
70169153.30040090966515.6995990903345
71186164.60219012018821.3978098798116
72177179.967291311006-2.96729131100591
73175179.051636965889-4.05163696588895
74187177.3630018552689.63699814473156
75176184.919567858533-8.91956785853279
76185179.9943689750795.00563102492123
77204184.41487275634519.5851272436547
78188198.797406527676-10.7974065276758
79171192.790660008809-21.7906600088094
80171179.185568261652-8.1855682616521
81182174.5498054603157.45019453968504
82185180.4303696016444.56963039835631
83200184.44692688326515.5530731167351
84192195.978231480081-3.97823148008075
85185194.43896121132-9.43896121131974
86195189.1424422033195.85755779668142
87190194.116402976218-4.11640297621847
88195192.389918218332.61008178167032
89213195.18019337419217.8198066258078
90194208.330860788221-14.3308607882209
91171199.869790366035-28.8697903660349
92171181.359035828613-10.3590358286127
93186175.06134227694710.9386577230526
94182183.097853661088-1.09785366108844
95193183.0961168828999.903883117101
96185190.551535724279-5.551535724279
97172187.634317509139-15.634317509139
98185177.8018147281927.19818527180817
99179183.280558408641-4.28055840864096
100182181.0535969350950.946403064905155
101193182.32311769431310.6768823056866
102173190.211802021856-17.2118020218562
103155179.294602416338-24.2946024163377
104164163.3552054061610.644794593838554
105188164.05075288814623.9492471118537
106186180.5791306859255.42086931407496
107200184.82169364690215.1783063530976
108185195.757001945171-10.7570019451714
109173189.268473443797-16.2684734437969
110190178.90449732794311.0955026720569
111190186.9210258669533.07897413304687
112193189.6310091094233.36899089057707
113195192.5759645824822.42403541751816
114178194.920868424391-16.9208684243911
115163184.159580773583-21.1595807735828
116165170.310964906069-5.31096490606942
117188166.96293689993121.0370631000692
118182181.4409005235680.559099476431896
119200182.27320886625517.7267911337449
120177194.770127666612-17.7701276666124







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121183.381890953853161.11375555955205.650026348156
122183.840914934828156.924021136214210.757808733441
123184.299938915802153.290849553622215.309028277982
124184.758962896777150.014833025366219.503092768189
125185.217986877752146.989158269221223.446815486282
126185.677010858727144.148932351368227.205089366085
127186.136034839701141.45136390676230.820705772643
128186.595058820676138.866553448505234.323564192847
129187.054082801651136.372686972348237.735478630953
130187.513106782625133.953307086532241.072906478719
131187.9721307636131.595660862018244.348600665182
132188.431154744575129.289647483546247.572662005604

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 183.381890953853 & 161.11375555955 & 205.650026348156 \tabularnewline
122 & 183.840914934828 & 156.924021136214 & 210.757808733441 \tabularnewline
123 & 184.299938915802 & 153.290849553622 & 215.309028277982 \tabularnewline
124 & 184.758962896777 & 150.014833025366 & 219.503092768189 \tabularnewline
125 & 185.217986877752 & 146.989158269221 & 223.446815486282 \tabularnewline
126 & 185.677010858727 & 144.148932351368 & 227.205089366085 \tabularnewline
127 & 186.136034839701 & 141.45136390676 & 230.820705772643 \tabularnewline
128 & 186.595058820676 & 138.866553448505 & 234.323564192847 \tabularnewline
129 & 187.054082801651 & 136.372686972348 & 237.735478630953 \tabularnewline
130 & 187.513106782625 & 133.953307086532 & 241.072906478719 \tabularnewline
131 & 187.9721307636 & 131.595660862018 & 244.348600665182 \tabularnewline
132 & 188.431154744575 & 129.289647483546 & 247.572662005604 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79293&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]121[/C][C]183.381890953853[/C][C]161.11375555955[/C][C]205.650026348156[/C][/ROW]
[ROW][C]122[/C][C]183.840914934828[/C][C]156.924021136214[/C][C]210.757808733441[/C][/ROW]
[ROW][C]123[/C][C]184.299938915802[/C][C]153.290849553622[/C][C]215.309028277982[/C][/ROW]
[ROW][C]124[/C][C]184.758962896777[/C][C]150.014833025366[/C][C]219.503092768189[/C][/ROW]
[ROW][C]125[/C][C]185.217986877752[/C][C]146.989158269221[/C][C]223.446815486282[/C][/ROW]
[ROW][C]126[/C][C]185.677010858727[/C][C]144.148932351368[/C][C]227.205089366085[/C][/ROW]
[ROW][C]127[/C][C]186.136034839701[/C][C]141.45136390676[/C][C]230.820705772643[/C][/ROW]
[ROW][C]128[/C][C]186.595058820676[/C][C]138.866553448505[/C][C]234.323564192847[/C][/ROW]
[ROW][C]129[/C][C]187.054082801651[/C][C]136.372686972348[/C][C]237.735478630953[/C][/ROW]
[ROW][C]130[/C][C]187.513106782625[/C][C]133.953307086532[/C][C]241.072906478719[/C][/ROW]
[ROW][C]131[/C][C]187.9721307636[/C][C]131.595660862018[/C][C]244.348600665182[/C][/ROW]
[ROW][C]132[/C][C]188.431154744575[/C][C]129.289647483546[/C][C]247.572662005604[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79293&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79293&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
121183.381890953853161.11375555955205.650026348156
122183.840914934828156.924021136214210.757808733441
123184.299938915802153.290849553622215.309028277982
124184.758962896777150.014833025366219.503092768189
125185.217986877752146.989158269221223.446815486282
126185.677010858727144.148932351368227.205089366085
127186.136034839701141.45136390676230.820705772643
128186.595058820676138.866553448505234.323564192847
129187.054082801651136.372686972348237.735478630953
130187.513106782625133.953307086532241.072906478719
131187.9721307636131.595660862018244.348600665182
132188.431154744575129.289647483546247.572662005604



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')