Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 30 Jul 2010 13:35:48 +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/Jul/30/t1280497021uo7er8nrfl7omei.htm/, Retrieved Thu, 02 May 2024 04:53:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78200, Retrieved Thu, 02 May 2024 04:53:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact230
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Centrummaten omze...] [2010-07-30 11:59:49] [f5ecd041e4b32af12787a4e421b18aaf]
- RMP   [Classical Decomposition] [Decompositie omze...] [2010-07-30 13:06:27] [f5ecd041e4b32af12787a4e421b18aaf]
- RM        [Exponential Smoothing] [Exponential smoot...] [2010-07-30 13:35:48] [05b8da000f2ebbd12b039a4b088dd3f2] [Current]
Feedback Forum

Post a new message
Dataseries X:
56
55
54
52
72
71
56
46
47
47
48
50
44
38
33
33
52
54
39
22
31
31
38
42
41
31
36
34
51
47
31
19
30
33
36
40
32
25
28
29
55
55
40
38
44
41
49
59
61
47
43
39
66
68
63
68
67
59
68
78
82
70
62
68
94
102
100
104
103
93
110
114
120
102
95
103
122
139
135
135
137
130
148
148
145
128
131
133
146
163
151
157
152
149
172
167
160
150
160
165
171
179
171
176
170
169
194
196
188
174
186
191
197
206
197
204
201
190
213
213




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78200&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78200&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78200&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.653714754766023
beta0.0529159338485531
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.653714754766023 \tabularnewline
beta & 0.0529159338485531 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78200&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]0.653714754766023[/C][/ROW]
[ROW][C]beta[/C][C]0.0529159338485531[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78200&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78200&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
alpha0.653714754766023
beta0.0529159338485531
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134453.1428952991453-9.14289529914532
143841.0687479080939-3.06874790809392
153333.8175397197737-0.817539719773748
163332.67636593279890.323634067201063
175251.04238941405820.95761058594183
185452.52264496167441.47735503832563
193938.06043635041200.93956364958796
202228.0708335569269-6.07083355692687
213124.66342884324786.33657115675216
223128.66945519769192.33054480230812
233831.09563438460456.90436561539552
244237.6672896987644.332710301236
254131.4166430463079.5833569536930
263134.4910323904657-3.49103239046567
273628.53224486816847.46775513183162
283434.2779806135972-0.277980613597194
295153.5249638002933-2.52496380029329
304753.8428273489417-6.84282734894171
313134.4017908131469-3.40179081314695
321919.6428349077232-0.642834907723216
333024.76431058724255.23568941275745
343327.30938126657805.69061873342196
353634.2781032352321.72189676476797
364037.15427053574692.84572946425313
373232.2812411328842-0.281241132884190
382524.56975068266200.430249317337953
392825.29509562943472.70490437056531
402925.40616170530323.59383829469679
415546.7011567421888.29884325781202
425553.26895039610121.73104960389878
434041.5904110003053-1.59041100030529
443829.99967273478898.00032726521112
454444.1346471304973-0.134647130497271
464144.4685044366325-3.46850443663246
474944.90055042242674.09944957757329
485950.62745772582728.3725422741728
496149.383078694256411.6169213057436
504751.2060666636596-4.20606666365965
514351.03797926002-8.03797926002
523945.4121877876488-6.41218778764881
536662.42734130231453.57265869768548
546864.09971207637423.90028792362581
556353.2325848468589.767415153142
566853.324167232086314.6758327679137
576770.1733260239246-3.17332602392462
585968.4285043070775-9.42850430707755
596868.4411291716005-0.441129171600537
607873.37848265719874.62151734280127
618271.374709244887610.6252907551124
627067.60510938522062.39489061477937
636271.1884931498553-9.1884931498553
646866.09704567160281.90295432839717
659493.01663637679620.983363623203758
6610294.03133230509897.96866769490114
6710088.917730028486111.0822699715139
6810492.676313844761811.3236861552382
69103102.1450162347870.854983765213376
7093101.998622743614-8.99862274361436
71110106.5504719888253.44952801117455
72114117.06491965552-3.06491965552
73120113.1301328340696.8698671659308
74102104.940289415024-2.94028941502401
7595101.725076612879-6.72507661287882
76103102.8702640319260.129735968074158
77122129.036354549051-7.03635454905111
78139127.67405211962511.3259478803749
79135126.3961847612478.60381523875284
80135129.0952672847795.90473271522131
81137131.6860129136695.31398708633077
82130131.486272887244-1.48627288724373
83148145.9634294176102.03657058239031
84148153.953234341842-5.95323434184226
85145152.125556798794-7.12555679879358
86128131.460430191638-3.46043019163804
87131126.6474294889254.35257051107536
88133137.844007656779-4.84400765677859
89146158.541174712991-12.5411747129909
90163160.0124597293542.98754027064592
91151152.126151540346-1.12615154034631
92157146.97851409009510.0214859099047
93152151.6468372806060.35316271939422
94149145.2686607556363.73133924436351
95172163.9764005709188.02359942908225
96167172.920210430047-5.92021043004689
97160170.516252894801-10.5162528948008
98150148.5945565347511.40544346524877
99160149.52709509370810.4729049062915
100165161.6108199855283.38918001447223
101171185.380362895994-14.3803628959942
102179191.318722250232-12.3187222502323
103171171.764514435572-0.764514435571698
104176170.4885973912045.51140260879649
105170168.4796529708611.52034702913903
106169163.6937079465395.30629205346131
107194184.6312578834629.36874211653821
108196189.3862966869546.61370331304585
109188193.778398973095-5.77839897309511
110174179.440103835476-5.44010383547618
111186179.1586232179246.84137678207557
112191186.4108416161744.58915838382612
113197204.848473566369-7.8484735663692
114206216.033667724240-10.0336677242397
115197202.316256529717-5.31625652971738
116204200.4225735367973.57742646320298
117201195.8849342989695.11506570103097
118190195.001892640157-5.00189264015745
119213210.4929825240962.50701747590352
120213209.4564069829773.54359301702263

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 44 & 53.1428952991453 & -9.14289529914532 \tabularnewline
14 & 38 & 41.0687479080939 & -3.06874790809392 \tabularnewline
15 & 33 & 33.8175397197737 & -0.817539719773748 \tabularnewline
16 & 33 & 32.6763659327989 & 0.323634067201063 \tabularnewline
17 & 52 & 51.0423894140582 & 0.95761058594183 \tabularnewline
18 & 54 & 52.5226449616744 & 1.47735503832563 \tabularnewline
19 & 39 & 38.0604363504120 & 0.93956364958796 \tabularnewline
20 & 22 & 28.0708335569269 & -6.07083355692687 \tabularnewline
21 & 31 & 24.6634288432478 & 6.33657115675216 \tabularnewline
22 & 31 & 28.6694551976919 & 2.33054480230812 \tabularnewline
23 & 38 & 31.0956343846045 & 6.90436561539552 \tabularnewline
24 & 42 & 37.667289698764 & 4.332710301236 \tabularnewline
25 & 41 & 31.416643046307 & 9.5833569536930 \tabularnewline
26 & 31 & 34.4910323904657 & -3.49103239046567 \tabularnewline
27 & 36 & 28.5322448681684 & 7.46775513183162 \tabularnewline
28 & 34 & 34.2779806135972 & -0.277980613597194 \tabularnewline
29 & 51 & 53.5249638002933 & -2.52496380029329 \tabularnewline
30 & 47 & 53.8428273489417 & -6.84282734894171 \tabularnewline
31 & 31 & 34.4017908131469 & -3.40179081314695 \tabularnewline
32 & 19 & 19.6428349077232 & -0.642834907723216 \tabularnewline
33 & 30 & 24.7643105872425 & 5.23568941275745 \tabularnewline
34 & 33 & 27.3093812665780 & 5.69061873342196 \tabularnewline
35 & 36 & 34.278103235232 & 1.72189676476797 \tabularnewline
36 & 40 & 37.1542705357469 & 2.84572946425313 \tabularnewline
37 & 32 & 32.2812411328842 & -0.281241132884190 \tabularnewline
38 & 25 & 24.5697506826620 & 0.430249317337953 \tabularnewline
39 & 28 & 25.2950956294347 & 2.70490437056531 \tabularnewline
40 & 29 & 25.4061617053032 & 3.59383829469679 \tabularnewline
41 & 55 & 46.701156742188 & 8.29884325781202 \tabularnewline
42 & 55 & 53.2689503961012 & 1.73104960389878 \tabularnewline
43 & 40 & 41.5904110003053 & -1.59041100030529 \tabularnewline
44 & 38 & 29.9996727347889 & 8.00032726521112 \tabularnewline
45 & 44 & 44.1346471304973 & -0.134647130497271 \tabularnewline
46 & 41 & 44.4685044366325 & -3.46850443663246 \tabularnewline
47 & 49 & 44.9005504224267 & 4.09944957757329 \tabularnewline
48 & 59 & 50.6274577258272 & 8.3725422741728 \tabularnewline
49 & 61 & 49.3830786942564 & 11.6169213057436 \tabularnewline
50 & 47 & 51.2060666636596 & -4.20606666365965 \tabularnewline
51 & 43 & 51.03797926002 & -8.03797926002 \tabularnewline
52 & 39 & 45.4121877876488 & -6.41218778764881 \tabularnewline
53 & 66 & 62.4273413023145 & 3.57265869768548 \tabularnewline
54 & 68 & 64.0997120763742 & 3.90028792362581 \tabularnewline
55 & 63 & 53.232584846858 & 9.767415153142 \tabularnewline
56 & 68 & 53.3241672320863 & 14.6758327679137 \tabularnewline
57 & 67 & 70.1733260239246 & -3.17332602392462 \tabularnewline
58 & 59 & 68.4285043070775 & -9.42850430707755 \tabularnewline
59 & 68 & 68.4411291716005 & -0.441129171600537 \tabularnewline
60 & 78 & 73.3784826571987 & 4.62151734280127 \tabularnewline
61 & 82 & 71.3747092448876 & 10.6252907551124 \tabularnewline
62 & 70 & 67.6051093852206 & 2.39489061477937 \tabularnewline
63 & 62 & 71.1884931498553 & -9.1884931498553 \tabularnewline
64 & 68 & 66.0970456716028 & 1.90295432839717 \tabularnewline
65 & 94 & 93.0166363767962 & 0.983363623203758 \tabularnewline
66 & 102 & 94.0313323050989 & 7.96866769490114 \tabularnewline
67 & 100 & 88.9177300284861 & 11.0822699715139 \tabularnewline
68 & 104 & 92.6763138447618 & 11.3236861552382 \tabularnewline
69 & 103 & 102.145016234787 & 0.854983765213376 \tabularnewline
70 & 93 & 101.998622743614 & -8.99862274361436 \tabularnewline
71 & 110 & 106.550471988825 & 3.44952801117455 \tabularnewline
72 & 114 & 117.06491965552 & -3.06491965552 \tabularnewline
73 & 120 & 113.130132834069 & 6.8698671659308 \tabularnewline
74 & 102 & 104.940289415024 & -2.94028941502401 \tabularnewline
75 & 95 & 101.725076612879 & -6.72507661287882 \tabularnewline
76 & 103 & 102.870264031926 & 0.129735968074158 \tabularnewline
77 & 122 & 129.036354549051 & -7.03635454905111 \tabularnewline
78 & 139 & 127.674052119625 & 11.3259478803749 \tabularnewline
79 & 135 & 126.396184761247 & 8.60381523875284 \tabularnewline
80 & 135 & 129.095267284779 & 5.90473271522131 \tabularnewline
81 & 137 & 131.686012913669 & 5.31398708633077 \tabularnewline
82 & 130 & 131.486272887244 & -1.48627288724373 \tabularnewline
83 & 148 & 145.963429417610 & 2.03657058239031 \tabularnewline
84 & 148 & 153.953234341842 & -5.95323434184226 \tabularnewline
85 & 145 & 152.125556798794 & -7.12555679879358 \tabularnewline
86 & 128 & 131.460430191638 & -3.46043019163804 \tabularnewline
87 & 131 & 126.647429488925 & 4.35257051107536 \tabularnewline
88 & 133 & 137.844007656779 & -4.84400765677859 \tabularnewline
89 & 146 & 158.541174712991 & -12.5411747129909 \tabularnewline
90 & 163 & 160.012459729354 & 2.98754027064592 \tabularnewline
91 & 151 & 152.126151540346 & -1.12615154034631 \tabularnewline
92 & 157 & 146.978514090095 & 10.0214859099047 \tabularnewline
93 & 152 & 151.646837280606 & 0.35316271939422 \tabularnewline
94 & 149 & 145.268660755636 & 3.73133924436351 \tabularnewline
95 & 172 & 163.976400570918 & 8.02359942908225 \tabularnewline
96 & 167 & 172.920210430047 & -5.92021043004689 \tabularnewline
97 & 160 & 170.516252894801 & -10.5162528948008 \tabularnewline
98 & 150 & 148.594556534751 & 1.40544346524877 \tabularnewline
99 & 160 & 149.527095093708 & 10.4729049062915 \tabularnewline
100 & 165 & 161.610819985528 & 3.38918001447223 \tabularnewline
101 & 171 & 185.380362895994 & -14.3803628959942 \tabularnewline
102 & 179 & 191.318722250232 & -12.3187222502323 \tabularnewline
103 & 171 & 171.764514435572 & -0.764514435571698 \tabularnewline
104 & 176 & 170.488597391204 & 5.51140260879649 \tabularnewline
105 & 170 & 168.479652970861 & 1.52034702913903 \tabularnewline
106 & 169 & 163.693707946539 & 5.30629205346131 \tabularnewline
107 & 194 & 184.631257883462 & 9.36874211653821 \tabularnewline
108 & 196 & 189.386296686954 & 6.61370331304585 \tabularnewline
109 & 188 & 193.778398973095 & -5.77839897309511 \tabularnewline
110 & 174 & 179.440103835476 & -5.44010383547618 \tabularnewline
111 & 186 & 179.158623217924 & 6.84137678207557 \tabularnewline
112 & 191 & 186.410841616174 & 4.58915838382612 \tabularnewline
113 & 197 & 204.848473566369 & -7.8484735663692 \tabularnewline
114 & 206 & 216.033667724240 & -10.0336677242397 \tabularnewline
115 & 197 & 202.316256529717 & -5.31625652971738 \tabularnewline
116 & 204 & 200.422573536797 & 3.57742646320298 \tabularnewline
117 & 201 & 195.884934298969 & 5.11506570103097 \tabularnewline
118 & 190 & 195.001892640157 & -5.00189264015745 \tabularnewline
119 & 213 & 210.492982524096 & 2.50701747590352 \tabularnewline
120 & 213 & 209.456406982977 & 3.54359301702263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78200&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]13[/C][C]44[/C][C]53.1428952991453[/C][C]-9.14289529914532[/C][/ROW]
[ROW][C]14[/C][C]38[/C][C]41.0687479080939[/C][C]-3.06874790809392[/C][/ROW]
[ROW][C]15[/C][C]33[/C][C]33.8175397197737[/C][C]-0.817539719773748[/C][/ROW]
[ROW][C]16[/C][C]33[/C][C]32.6763659327989[/C][C]0.323634067201063[/C][/ROW]
[ROW][C]17[/C][C]52[/C][C]51.0423894140582[/C][C]0.95761058594183[/C][/ROW]
[ROW][C]18[/C][C]54[/C][C]52.5226449616744[/C][C]1.47735503832563[/C][/ROW]
[ROW][C]19[/C][C]39[/C][C]38.0604363504120[/C][C]0.93956364958796[/C][/ROW]
[ROW][C]20[/C][C]22[/C][C]28.0708335569269[/C][C]-6.07083355692687[/C][/ROW]
[ROW][C]21[/C][C]31[/C][C]24.6634288432478[/C][C]6.33657115675216[/C][/ROW]
[ROW][C]22[/C][C]31[/C][C]28.6694551976919[/C][C]2.33054480230812[/C][/ROW]
[ROW][C]23[/C][C]38[/C][C]31.0956343846045[/C][C]6.90436561539552[/C][/ROW]
[ROW][C]24[/C][C]42[/C][C]37.667289698764[/C][C]4.332710301236[/C][/ROW]
[ROW][C]25[/C][C]41[/C][C]31.416643046307[/C][C]9.5833569536930[/C][/ROW]
[ROW][C]26[/C][C]31[/C][C]34.4910323904657[/C][C]-3.49103239046567[/C][/ROW]
[ROW][C]27[/C][C]36[/C][C]28.5322448681684[/C][C]7.46775513183162[/C][/ROW]
[ROW][C]28[/C][C]34[/C][C]34.2779806135972[/C][C]-0.277980613597194[/C][/ROW]
[ROW][C]29[/C][C]51[/C][C]53.5249638002933[/C][C]-2.52496380029329[/C][/ROW]
[ROW][C]30[/C][C]47[/C][C]53.8428273489417[/C][C]-6.84282734894171[/C][/ROW]
[ROW][C]31[/C][C]31[/C][C]34.4017908131469[/C][C]-3.40179081314695[/C][/ROW]
[ROW][C]32[/C][C]19[/C][C]19.6428349077232[/C][C]-0.642834907723216[/C][/ROW]
[ROW][C]33[/C][C]30[/C][C]24.7643105872425[/C][C]5.23568941275745[/C][/ROW]
[ROW][C]34[/C][C]33[/C][C]27.3093812665780[/C][C]5.69061873342196[/C][/ROW]
[ROW][C]35[/C][C]36[/C][C]34.278103235232[/C][C]1.72189676476797[/C][/ROW]
[ROW][C]36[/C][C]40[/C][C]37.1542705357469[/C][C]2.84572946425313[/C][/ROW]
[ROW][C]37[/C][C]32[/C][C]32.2812411328842[/C][C]-0.281241132884190[/C][/ROW]
[ROW][C]38[/C][C]25[/C][C]24.5697506826620[/C][C]0.430249317337953[/C][/ROW]
[ROW][C]39[/C][C]28[/C][C]25.2950956294347[/C][C]2.70490437056531[/C][/ROW]
[ROW][C]40[/C][C]29[/C][C]25.4061617053032[/C][C]3.59383829469679[/C][/ROW]
[ROW][C]41[/C][C]55[/C][C]46.701156742188[/C][C]8.29884325781202[/C][/ROW]
[ROW][C]42[/C][C]55[/C][C]53.2689503961012[/C][C]1.73104960389878[/C][/ROW]
[ROW][C]43[/C][C]40[/C][C]41.5904110003053[/C][C]-1.59041100030529[/C][/ROW]
[ROW][C]44[/C][C]38[/C][C]29.9996727347889[/C][C]8.00032726521112[/C][/ROW]
[ROW][C]45[/C][C]44[/C][C]44.1346471304973[/C][C]-0.134647130497271[/C][/ROW]
[ROW][C]46[/C][C]41[/C][C]44.4685044366325[/C][C]-3.46850443663246[/C][/ROW]
[ROW][C]47[/C][C]49[/C][C]44.9005504224267[/C][C]4.09944957757329[/C][/ROW]
[ROW][C]48[/C][C]59[/C][C]50.6274577258272[/C][C]8.3725422741728[/C][/ROW]
[ROW][C]49[/C][C]61[/C][C]49.3830786942564[/C][C]11.6169213057436[/C][/ROW]
[ROW][C]50[/C][C]47[/C][C]51.2060666636596[/C][C]-4.20606666365965[/C][/ROW]
[ROW][C]51[/C][C]43[/C][C]51.03797926002[/C][C]-8.03797926002[/C][/ROW]
[ROW][C]52[/C][C]39[/C][C]45.4121877876488[/C][C]-6.41218778764881[/C][/ROW]
[ROW][C]53[/C][C]66[/C][C]62.4273413023145[/C][C]3.57265869768548[/C][/ROW]
[ROW][C]54[/C][C]68[/C][C]64.0997120763742[/C][C]3.90028792362581[/C][/ROW]
[ROW][C]55[/C][C]63[/C][C]53.232584846858[/C][C]9.767415153142[/C][/ROW]
[ROW][C]56[/C][C]68[/C][C]53.3241672320863[/C][C]14.6758327679137[/C][/ROW]
[ROW][C]57[/C][C]67[/C][C]70.1733260239246[/C][C]-3.17332602392462[/C][/ROW]
[ROW][C]58[/C][C]59[/C][C]68.4285043070775[/C][C]-9.42850430707755[/C][/ROW]
[ROW][C]59[/C][C]68[/C][C]68.4411291716005[/C][C]-0.441129171600537[/C][/ROW]
[ROW][C]60[/C][C]78[/C][C]73.3784826571987[/C][C]4.62151734280127[/C][/ROW]
[ROW][C]61[/C][C]82[/C][C]71.3747092448876[/C][C]10.6252907551124[/C][/ROW]
[ROW][C]62[/C][C]70[/C][C]67.6051093852206[/C][C]2.39489061477937[/C][/ROW]
[ROW][C]63[/C][C]62[/C][C]71.1884931498553[/C][C]-9.1884931498553[/C][/ROW]
[ROW][C]64[/C][C]68[/C][C]66.0970456716028[/C][C]1.90295432839717[/C][/ROW]
[ROW][C]65[/C][C]94[/C][C]93.0166363767962[/C][C]0.983363623203758[/C][/ROW]
[ROW][C]66[/C][C]102[/C][C]94.0313323050989[/C][C]7.96866769490114[/C][/ROW]
[ROW][C]67[/C][C]100[/C][C]88.9177300284861[/C][C]11.0822699715139[/C][/ROW]
[ROW][C]68[/C][C]104[/C][C]92.6763138447618[/C][C]11.3236861552382[/C][/ROW]
[ROW][C]69[/C][C]103[/C][C]102.145016234787[/C][C]0.854983765213376[/C][/ROW]
[ROW][C]70[/C][C]93[/C][C]101.998622743614[/C][C]-8.99862274361436[/C][/ROW]
[ROW][C]71[/C][C]110[/C][C]106.550471988825[/C][C]3.44952801117455[/C][/ROW]
[ROW][C]72[/C][C]114[/C][C]117.06491965552[/C][C]-3.06491965552[/C][/ROW]
[ROW][C]73[/C][C]120[/C][C]113.130132834069[/C][C]6.8698671659308[/C][/ROW]
[ROW][C]74[/C][C]102[/C][C]104.940289415024[/C][C]-2.94028941502401[/C][/ROW]
[ROW][C]75[/C][C]95[/C][C]101.725076612879[/C][C]-6.72507661287882[/C][/ROW]
[ROW][C]76[/C][C]103[/C][C]102.870264031926[/C][C]0.129735968074158[/C][/ROW]
[ROW][C]77[/C][C]122[/C][C]129.036354549051[/C][C]-7.03635454905111[/C][/ROW]
[ROW][C]78[/C][C]139[/C][C]127.674052119625[/C][C]11.3259478803749[/C][/ROW]
[ROW][C]79[/C][C]135[/C][C]126.396184761247[/C][C]8.60381523875284[/C][/ROW]
[ROW][C]80[/C][C]135[/C][C]129.095267284779[/C][C]5.90473271522131[/C][/ROW]
[ROW][C]81[/C][C]137[/C][C]131.686012913669[/C][C]5.31398708633077[/C][/ROW]
[ROW][C]82[/C][C]130[/C][C]131.486272887244[/C][C]-1.48627288724373[/C][/ROW]
[ROW][C]83[/C][C]148[/C][C]145.963429417610[/C][C]2.03657058239031[/C][/ROW]
[ROW][C]84[/C][C]148[/C][C]153.953234341842[/C][C]-5.95323434184226[/C][/ROW]
[ROW][C]85[/C][C]145[/C][C]152.125556798794[/C][C]-7.12555679879358[/C][/ROW]
[ROW][C]86[/C][C]128[/C][C]131.460430191638[/C][C]-3.46043019163804[/C][/ROW]
[ROW][C]87[/C][C]131[/C][C]126.647429488925[/C][C]4.35257051107536[/C][/ROW]
[ROW][C]88[/C][C]133[/C][C]137.844007656779[/C][C]-4.84400765677859[/C][/ROW]
[ROW][C]89[/C][C]146[/C][C]158.541174712991[/C][C]-12.5411747129909[/C][/ROW]
[ROW][C]90[/C][C]163[/C][C]160.012459729354[/C][C]2.98754027064592[/C][/ROW]
[ROW][C]91[/C][C]151[/C][C]152.126151540346[/C][C]-1.12615154034631[/C][/ROW]
[ROW][C]92[/C][C]157[/C][C]146.978514090095[/C][C]10.0214859099047[/C][/ROW]
[ROW][C]93[/C][C]152[/C][C]151.646837280606[/C][C]0.35316271939422[/C][/ROW]
[ROW][C]94[/C][C]149[/C][C]145.268660755636[/C][C]3.73133924436351[/C][/ROW]
[ROW][C]95[/C][C]172[/C][C]163.976400570918[/C][C]8.02359942908225[/C][/ROW]
[ROW][C]96[/C][C]167[/C][C]172.920210430047[/C][C]-5.92021043004689[/C][/ROW]
[ROW][C]97[/C][C]160[/C][C]170.516252894801[/C][C]-10.5162528948008[/C][/ROW]
[ROW][C]98[/C][C]150[/C][C]148.594556534751[/C][C]1.40544346524877[/C][/ROW]
[ROW][C]99[/C][C]160[/C][C]149.527095093708[/C][C]10.4729049062915[/C][/ROW]
[ROW][C]100[/C][C]165[/C][C]161.610819985528[/C][C]3.38918001447223[/C][/ROW]
[ROW][C]101[/C][C]171[/C][C]185.380362895994[/C][C]-14.3803628959942[/C][/ROW]
[ROW][C]102[/C][C]179[/C][C]191.318722250232[/C][C]-12.3187222502323[/C][/ROW]
[ROW][C]103[/C][C]171[/C][C]171.764514435572[/C][C]-0.764514435571698[/C][/ROW]
[ROW][C]104[/C][C]176[/C][C]170.488597391204[/C][C]5.51140260879649[/C][/ROW]
[ROW][C]105[/C][C]170[/C][C]168.479652970861[/C][C]1.52034702913903[/C][/ROW]
[ROW][C]106[/C][C]169[/C][C]163.693707946539[/C][C]5.30629205346131[/C][/ROW]
[ROW][C]107[/C][C]194[/C][C]184.631257883462[/C][C]9.36874211653821[/C][/ROW]
[ROW][C]108[/C][C]196[/C][C]189.386296686954[/C][C]6.61370331304585[/C][/ROW]
[ROW][C]109[/C][C]188[/C][C]193.778398973095[/C][C]-5.77839897309511[/C][/ROW]
[ROW][C]110[/C][C]174[/C][C]179.440103835476[/C][C]-5.44010383547618[/C][/ROW]
[ROW][C]111[/C][C]186[/C][C]179.158623217924[/C][C]6.84137678207557[/C][/ROW]
[ROW][C]112[/C][C]191[/C][C]186.410841616174[/C][C]4.58915838382612[/C][/ROW]
[ROW][C]113[/C][C]197[/C][C]204.848473566369[/C][C]-7.8484735663692[/C][/ROW]
[ROW][C]114[/C][C]206[/C][C]216.033667724240[/C][C]-10.0336677242397[/C][/ROW]
[ROW][C]115[/C][C]197[/C][C]202.316256529717[/C][C]-5.31625652971738[/C][/ROW]
[ROW][C]116[/C][C]204[/C][C]200.422573536797[/C][C]3.57742646320298[/C][/ROW]
[ROW][C]117[/C][C]201[/C][C]195.884934298969[/C][C]5.11506570103097[/C][/ROW]
[ROW][C]118[/C][C]190[/C][C]195.001892640157[/C][C]-5.00189264015745[/C][/ROW]
[ROW][C]119[/C][C]213[/C][C]210.492982524096[/C][C]2.50701747590352[/C][/ROW]
[ROW][C]120[/C][C]213[/C][C]209.456406982977[/C][C]3.54359301702263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78200&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78200&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
134453.1428952991453-9.14289529914532
143841.0687479080939-3.06874790809392
153333.8175397197737-0.817539719773748
163332.67636593279890.323634067201063
175251.04238941405820.95761058594183
185452.52264496167441.47735503832563
193938.06043635041200.93956364958796
202228.0708335569269-6.07083355692687
213124.66342884324786.33657115675216
223128.66945519769192.33054480230812
233831.09563438460456.90436561539552
244237.6672896987644.332710301236
254131.4166430463079.5833569536930
263134.4910323904657-3.49103239046567
273628.53224486816847.46775513183162
283434.2779806135972-0.277980613597194
295153.5249638002933-2.52496380029329
304753.8428273489417-6.84282734894171
313134.4017908131469-3.40179081314695
321919.6428349077232-0.642834907723216
333024.76431058724255.23568941275745
343327.30938126657805.69061873342196
353634.2781032352321.72189676476797
364037.15427053574692.84572946425313
373232.2812411328842-0.281241132884190
382524.56975068266200.430249317337953
392825.29509562943472.70490437056531
402925.40616170530323.59383829469679
415546.7011567421888.29884325781202
425553.26895039610121.73104960389878
434041.5904110003053-1.59041100030529
443829.99967273478898.00032726521112
454444.1346471304973-0.134647130497271
464144.4685044366325-3.46850443663246
474944.90055042242674.09944957757329
485950.62745772582728.3725422741728
496149.383078694256411.6169213057436
504751.2060666636596-4.20606666365965
514351.03797926002-8.03797926002
523945.4121877876488-6.41218778764881
536662.42734130231453.57265869768548
546864.09971207637423.90028792362581
556353.2325848468589.767415153142
566853.324167232086314.6758327679137
576770.1733260239246-3.17332602392462
585968.4285043070775-9.42850430707755
596868.4411291716005-0.441129171600537
607873.37848265719874.62151734280127
618271.374709244887610.6252907551124
627067.60510938522062.39489061477937
636271.1884931498553-9.1884931498553
646866.09704567160281.90295432839717
659493.01663637679620.983363623203758
6610294.03133230509897.96866769490114
6710088.917730028486111.0822699715139
6810492.676313844761811.3236861552382
69103102.1450162347870.854983765213376
7093101.998622743614-8.99862274361436
71110106.5504719888253.44952801117455
72114117.06491965552-3.06491965552
73120113.1301328340696.8698671659308
74102104.940289415024-2.94028941502401
7595101.725076612879-6.72507661287882
76103102.8702640319260.129735968074158
77122129.036354549051-7.03635454905111
78139127.67405211962511.3259478803749
79135126.3961847612478.60381523875284
80135129.0952672847795.90473271522131
81137131.6860129136695.31398708633077
82130131.486272887244-1.48627288724373
83148145.9634294176102.03657058239031
84148153.953234341842-5.95323434184226
85145152.125556798794-7.12555679879358
86128131.460430191638-3.46043019163804
87131126.6474294889254.35257051107536
88133137.844007656779-4.84400765677859
89146158.541174712991-12.5411747129909
90163160.0124597293542.98754027064592
91151152.126151540346-1.12615154034631
92157146.97851409009510.0214859099047
93152151.6468372806060.35316271939422
94149145.2686607556363.73133924436351
95172163.9764005709188.02359942908225
96167172.920210430047-5.92021043004689
97160170.516252894801-10.5162528948008
98150148.5945565347511.40544346524877
99160149.52709509370810.4729049062915
100165161.6108199855283.38918001447223
101171185.380362895994-14.3803628959942
102179191.318722250232-12.3187222502323
103171171.764514435572-0.764514435571698
104176170.4885973912045.51140260879649
105170168.4796529708611.52034702913903
106169163.6937079465395.30629205346131
107194184.6312578834629.36874211653821
108196189.3862966869546.61370331304585
109188193.778398973095-5.77839897309511
110174179.440103835476-5.44010383547618
111186179.1586232179246.84137678207557
112191186.4108416161744.58915838382612
113197204.848473566369-7.8484735663692
114206216.033667724240-10.0336677242397
115197202.316256529717-5.31625652971738
116204200.4225735367973.57742646320298
117201195.8849342989695.11506570103097
118190195.001892640157-5.00189264015745
119213210.4929825240962.50701747590352
120213209.4564069829773.54359301702263







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121207.092155244158194.83616965225219.348140836066
122196.390141896129181.511526378341211.268757413917
123203.847727131254186.530975858222221.164478404285
124205.540964359967185.892588125736225.189340594198
125216.206117278357194.290389530211238.121845026503
126231.571257682240207.426886537931255.715628826548
127226.199640682604199.848686708472252.550594656737
128231.197991442581202.651100964909259.744881920253
129225.067414671224194.327104315254255.807725027195
130217.373502862963184.436328866192250.310676859733
131238.943930823285203.801980289545274.085881357025
132236.750011493138199.391961074474274.108061911802

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 207.092155244158 & 194.83616965225 & 219.348140836066 \tabularnewline
122 & 196.390141896129 & 181.511526378341 & 211.268757413917 \tabularnewline
123 & 203.847727131254 & 186.530975858222 & 221.164478404285 \tabularnewline
124 & 205.540964359967 & 185.892588125736 & 225.189340594198 \tabularnewline
125 & 216.206117278357 & 194.290389530211 & 238.121845026503 \tabularnewline
126 & 231.571257682240 & 207.426886537931 & 255.715628826548 \tabularnewline
127 & 226.199640682604 & 199.848686708472 & 252.550594656737 \tabularnewline
128 & 231.197991442581 & 202.651100964909 & 259.744881920253 \tabularnewline
129 & 225.067414671224 & 194.327104315254 & 255.807725027195 \tabularnewline
130 & 217.373502862963 & 184.436328866192 & 250.310676859733 \tabularnewline
131 & 238.943930823285 & 203.801980289545 & 274.085881357025 \tabularnewline
132 & 236.750011493138 & 199.391961074474 & 274.108061911802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78200&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]207.092155244158[/C][C]194.83616965225[/C][C]219.348140836066[/C][/ROW]
[ROW][C]122[/C][C]196.390141896129[/C][C]181.511526378341[/C][C]211.268757413917[/C][/ROW]
[ROW][C]123[/C][C]203.847727131254[/C][C]186.530975858222[/C][C]221.164478404285[/C][/ROW]
[ROW][C]124[/C][C]205.540964359967[/C][C]185.892588125736[/C][C]225.189340594198[/C][/ROW]
[ROW][C]125[/C][C]216.206117278357[/C][C]194.290389530211[/C][C]238.121845026503[/C][/ROW]
[ROW][C]126[/C][C]231.571257682240[/C][C]207.426886537931[/C][C]255.715628826548[/C][/ROW]
[ROW][C]127[/C][C]226.199640682604[/C][C]199.848686708472[/C][C]252.550594656737[/C][/ROW]
[ROW][C]128[/C][C]231.197991442581[/C][C]202.651100964909[/C][C]259.744881920253[/C][/ROW]
[ROW][C]129[/C][C]225.067414671224[/C][C]194.327104315254[/C][C]255.807725027195[/C][/ROW]
[ROW][C]130[/C][C]217.373502862963[/C][C]184.436328866192[/C][C]250.310676859733[/C][/ROW]
[ROW][C]131[/C][C]238.943930823285[/C][C]203.801980289545[/C][C]274.085881357025[/C][/ROW]
[ROW][C]132[/C][C]236.750011493138[/C][C]199.391961074474[/C][C]274.108061911802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78200&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78200&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
121207.092155244158194.83616965225219.348140836066
122196.390141896129181.511526378341211.268757413917
123203.847727131254186.530975858222221.164478404285
124205.540964359967185.892588125736225.189340594198
125216.206117278357194.290389530211238.121845026503
126231.571257682240207.426886537931255.715628826548
127226.199640682604199.848686708472252.550594656737
128231.197991442581202.651100964909259.744881920253
129225.067414671224194.327104315254255.807725027195
130217.373502862963184.436328866192250.310676859733
131238.943930823285203.801980289545274.085881357025
132236.750011493138199.391961074474274.108061911802



Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')