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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 20 Dec 2013 10:57:25 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/20/t13875550576ga7ms4axpl6u96.htm/, Retrieved Thu, 25 Apr 2024 09:16:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232459, Retrieved Thu, 25 Apr 2024 09:16:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-20 15:57:25] [9e6a405f514733ea23d87e4507d39d29] [Current]
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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 time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232459&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232459&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232459&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 time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.653714754765269
beta0.0529159338487423
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.653714754765269 \tabularnewline
beta & 0.0529159338487423 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232459&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]0.653714754765269[/C][/ROW]
[ROW][C]beta[/C][C]0.0529159338487423[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232459&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232459&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
alpha0.653714754765269
beta0.0529159338487423
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134453.1428952991453-9.14289529914529
143841.0687479081001-3.06874790810005
153333.817539719777-0.817539719776953
163332.67636593279920.32363406720075
175251.04238941405670.95761058594335
185452.52264496167191.47735503832813
193938.0604363504090.939563649590994
202228.0708335569242-6.07083355692425
213124.66342884325026.33657115674977
223128.66945519768712.33054480231291
233831.09563438460066.90436561539942
244237.66728969875774.33271030124232
254131.41664304629559.58335695370454
263134.4910323904589-3.49103239045893
273628.53224486817347.46775513182665
283434.2779806135975-0.277980613597549
295153.5249638002971-2.52496380029712
304753.8428273489477-6.84282734894771
313134.4017908131552-3.40179081315522
321919.6428349077239-0.642834907723906
333024.76431058725155.2356894127485
343327.30938126657745.69061873342261
353634.27810323523191.72189676476812
364037.15427053574582.84572946425422
373232.2812411328822-0.281241132882208
382524.56975068265420.430249317345787
392825.29509562944062.70490437055941
402925.40616170530283.59383829469715
415546.70115674218578.29884325781428
425553.2689503960941.73104960390599
434041.5904110003066-1.59041100030659
443829.99967273479318.00032726520686
454444.1346471305058-0.134647130505776
464144.4685044366422-3.46850443664219
474944.90055042243564.0994495775644
485950.62745772583028.37254227416979
496149.383078694251511.6169213057485
504751.2060666636474-4.2060666636474
514351.0379792600276-8.03797926002758
523945.4121877876618-6.41218778766178
536662.42734130232913.57265869767086
546864.09971207637273.90028792362732
556353.23258484685379.76741515314632
566853.324167232086914.6758327679131
576770.1733260239206-3.17332602392058
585968.4285043070838-9.42850430708381
596868.4411291716198-0.441129171619849
607873.37848265721444.62151734278557
618271.374709244894810.6252907551052
627067.60510938520312.39489061479694
636271.1884931498462-9.18849314984618
646866.09704567161061.90295432838937
659493.0166363768110.983363623189007
6610294.03133230510627.96866769489378
6710088.917730028488311.0822699715117
6810492.676313844766611.3236861552334
69103102.1450162347750.854983765224773
7093101.998622743608-8.99862274360787
71110106.5504719888443.44952801115613
72114117.064919655539-3.0649196555395
73120113.1301328340926.86986716590788
74102104.940289415017-2.9402894150174
7595101.725076612865-6.72507661286534
76103102.8702640319330.129735968067379
77122129.036354549063-7.03635454906347
78139127.67405211964511.3259478803554
79135126.3961847612548.60381523874585
80135129.0952672847855.90473271521509
81137131.6860129136585.31398708634174
82130131.486272887223-1.48627288722335
83148145.9634294176182.03657058238207
84148153.953234341854-5.9532343418538
85145152.125556798822-7.12555679882206
86128131.460430191645-3.46043019164523
87131126.6474294889144.3525705110862
88133137.844007656775-4.84400765677486
89146158.541174712995-12.5411747129948
90163160.0124597293852.98754027061523
91151152.126151540363-1.12615154036325
92157146.97851409010710.0214859098931
93152151.6468372805960.353162719404452
94149145.2686607556143.73133924438571
95172163.9764005709118.02359942908924
96167172.920210430039-5.92021043003908
97160170.516252894814-10.5162528948141
98150148.5945565347641.40544346523563
99160149.52709509370710.4729049062932
100165161.6108199855123.38918001448789
101171185.380362895979-14.3803628959793
102179191.318722250261-12.3187222502607
103171171.7645144356-0.764514435600347
104176170.4885973912285.51140260877193
105170168.4796529708571.52034702914304
106169163.6937079465225.30629205347753
107194184.6312578834529.36874211654847
108196189.3862966869326.61370331306793
109188193.778398973083-5.77839897308286
110174179.440103835487-5.44010383548689
111186179.158623217946.84137678206042
112191186.4108416161664.58915838383413
113197204.848473566342-7.84847356634182
114206216.033667724246-10.0336677242458
115197202.316256529747-5.31625652974654
116204200.4225735368323.57742646316765
117201195.8849342989775.1150657010225
118190195.00189264015-5.00189264015023
119213210.4929825240972.50701747590279
120213209.4564069829643.54359301703553

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 44 & 53.1428952991453 & -9.14289529914529 \tabularnewline
14 & 38 & 41.0687479081001 & -3.06874790810005 \tabularnewline
15 & 33 & 33.817539719777 & -0.817539719776953 \tabularnewline
16 & 33 & 32.6763659327992 & 0.32363406720075 \tabularnewline
17 & 52 & 51.0423894140567 & 0.95761058594335 \tabularnewline
18 & 54 & 52.5226449616719 & 1.47735503832813 \tabularnewline
19 & 39 & 38.060436350409 & 0.939563649590994 \tabularnewline
20 & 22 & 28.0708335569242 & -6.07083355692425 \tabularnewline
21 & 31 & 24.6634288432502 & 6.33657115674977 \tabularnewline
22 & 31 & 28.6694551976871 & 2.33054480231291 \tabularnewline
23 & 38 & 31.0956343846006 & 6.90436561539942 \tabularnewline
24 & 42 & 37.6672896987577 & 4.33271030124232 \tabularnewline
25 & 41 & 31.4166430462955 & 9.58335695370454 \tabularnewline
26 & 31 & 34.4910323904589 & -3.49103239045893 \tabularnewline
27 & 36 & 28.5322448681734 & 7.46775513182665 \tabularnewline
28 & 34 & 34.2779806135975 & -0.277980613597549 \tabularnewline
29 & 51 & 53.5249638002971 & -2.52496380029712 \tabularnewline
30 & 47 & 53.8428273489477 & -6.84282734894771 \tabularnewline
31 & 31 & 34.4017908131552 & -3.40179081315522 \tabularnewline
32 & 19 & 19.6428349077239 & -0.642834907723906 \tabularnewline
33 & 30 & 24.7643105872515 & 5.2356894127485 \tabularnewline
34 & 33 & 27.3093812665774 & 5.69061873342261 \tabularnewline
35 & 36 & 34.2781032352319 & 1.72189676476812 \tabularnewline
36 & 40 & 37.1542705357458 & 2.84572946425422 \tabularnewline
37 & 32 & 32.2812411328822 & -0.281241132882208 \tabularnewline
38 & 25 & 24.5697506826542 & 0.430249317345787 \tabularnewline
39 & 28 & 25.2950956294406 & 2.70490437055941 \tabularnewline
40 & 29 & 25.4061617053028 & 3.59383829469715 \tabularnewline
41 & 55 & 46.7011567421857 & 8.29884325781428 \tabularnewline
42 & 55 & 53.268950396094 & 1.73104960390599 \tabularnewline
43 & 40 & 41.5904110003066 & -1.59041100030659 \tabularnewline
44 & 38 & 29.9996727347931 & 8.00032726520686 \tabularnewline
45 & 44 & 44.1346471305058 & -0.134647130505776 \tabularnewline
46 & 41 & 44.4685044366422 & -3.46850443664219 \tabularnewline
47 & 49 & 44.9005504224356 & 4.0994495775644 \tabularnewline
48 & 59 & 50.6274577258302 & 8.37254227416979 \tabularnewline
49 & 61 & 49.3830786942515 & 11.6169213057485 \tabularnewline
50 & 47 & 51.2060666636474 & -4.2060666636474 \tabularnewline
51 & 43 & 51.0379792600276 & -8.03797926002758 \tabularnewline
52 & 39 & 45.4121877876618 & -6.41218778766178 \tabularnewline
53 & 66 & 62.4273413023291 & 3.57265869767086 \tabularnewline
54 & 68 & 64.0997120763727 & 3.90028792362732 \tabularnewline
55 & 63 & 53.2325848468537 & 9.76741515314632 \tabularnewline
56 & 68 & 53.3241672320869 & 14.6758327679131 \tabularnewline
57 & 67 & 70.1733260239206 & -3.17332602392058 \tabularnewline
58 & 59 & 68.4285043070838 & -9.42850430708381 \tabularnewline
59 & 68 & 68.4411291716198 & -0.441129171619849 \tabularnewline
60 & 78 & 73.3784826572144 & 4.62151734278557 \tabularnewline
61 & 82 & 71.3747092448948 & 10.6252907551052 \tabularnewline
62 & 70 & 67.6051093852031 & 2.39489061479694 \tabularnewline
63 & 62 & 71.1884931498462 & -9.18849314984618 \tabularnewline
64 & 68 & 66.0970456716106 & 1.90295432838937 \tabularnewline
65 & 94 & 93.016636376811 & 0.983363623189007 \tabularnewline
66 & 102 & 94.0313323051062 & 7.96866769489378 \tabularnewline
67 & 100 & 88.9177300284883 & 11.0822699715117 \tabularnewline
68 & 104 & 92.6763138447666 & 11.3236861552334 \tabularnewline
69 & 103 & 102.145016234775 & 0.854983765224773 \tabularnewline
70 & 93 & 101.998622743608 & -8.99862274360787 \tabularnewline
71 & 110 & 106.550471988844 & 3.44952801115613 \tabularnewline
72 & 114 & 117.064919655539 & -3.0649196555395 \tabularnewline
73 & 120 & 113.130132834092 & 6.86986716590788 \tabularnewline
74 & 102 & 104.940289415017 & -2.9402894150174 \tabularnewline
75 & 95 & 101.725076612865 & -6.72507661286534 \tabularnewline
76 & 103 & 102.870264031933 & 0.129735968067379 \tabularnewline
77 & 122 & 129.036354549063 & -7.03635454906347 \tabularnewline
78 & 139 & 127.674052119645 & 11.3259478803554 \tabularnewline
79 & 135 & 126.396184761254 & 8.60381523874585 \tabularnewline
80 & 135 & 129.095267284785 & 5.90473271521509 \tabularnewline
81 & 137 & 131.686012913658 & 5.31398708634174 \tabularnewline
82 & 130 & 131.486272887223 & -1.48627288722335 \tabularnewline
83 & 148 & 145.963429417618 & 2.03657058238207 \tabularnewline
84 & 148 & 153.953234341854 & -5.9532343418538 \tabularnewline
85 & 145 & 152.125556798822 & -7.12555679882206 \tabularnewline
86 & 128 & 131.460430191645 & -3.46043019164523 \tabularnewline
87 & 131 & 126.647429488914 & 4.3525705110862 \tabularnewline
88 & 133 & 137.844007656775 & -4.84400765677486 \tabularnewline
89 & 146 & 158.541174712995 & -12.5411747129948 \tabularnewline
90 & 163 & 160.012459729385 & 2.98754027061523 \tabularnewline
91 & 151 & 152.126151540363 & -1.12615154036325 \tabularnewline
92 & 157 & 146.978514090107 & 10.0214859098931 \tabularnewline
93 & 152 & 151.646837280596 & 0.353162719404452 \tabularnewline
94 & 149 & 145.268660755614 & 3.73133924438571 \tabularnewline
95 & 172 & 163.976400570911 & 8.02359942908924 \tabularnewline
96 & 167 & 172.920210430039 & -5.92021043003908 \tabularnewline
97 & 160 & 170.516252894814 & -10.5162528948141 \tabularnewline
98 & 150 & 148.594556534764 & 1.40544346523563 \tabularnewline
99 & 160 & 149.527095093707 & 10.4729049062932 \tabularnewline
100 & 165 & 161.610819985512 & 3.38918001448789 \tabularnewline
101 & 171 & 185.380362895979 & -14.3803628959793 \tabularnewline
102 & 179 & 191.318722250261 & -12.3187222502607 \tabularnewline
103 & 171 & 171.7645144356 & -0.764514435600347 \tabularnewline
104 & 176 & 170.488597391228 & 5.51140260877193 \tabularnewline
105 & 170 & 168.479652970857 & 1.52034702914304 \tabularnewline
106 & 169 & 163.693707946522 & 5.30629205347753 \tabularnewline
107 & 194 & 184.631257883452 & 9.36874211654847 \tabularnewline
108 & 196 & 189.386296686932 & 6.61370331306793 \tabularnewline
109 & 188 & 193.778398973083 & -5.77839897308286 \tabularnewline
110 & 174 & 179.440103835487 & -5.44010383548689 \tabularnewline
111 & 186 & 179.15862321794 & 6.84137678206042 \tabularnewline
112 & 191 & 186.410841616166 & 4.58915838383413 \tabularnewline
113 & 197 & 204.848473566342 & -7.84847356634182 \tabularnewline
114 & 206 & 216.033667724246 & -10.0336677242458 \tabularnewline
115 & 197 & 202.316256529747 & -5.31625652974654 \tabularnewline
116 & 204 & 200.422573536832 & 3.57742646316765 \tabularnewline
117 & 201 & 195.884934298977 & 5.1150657010225 \tabularnewline
118 & 190 & 195.00189264015 & -5.00189264015023 \tabularnewline
119 & 213 & 210.492982524097 & 2.50701747590279 \tabularnewline
120 & 213 & 209.456406982964 & 3.54359301703553 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232459&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]-9.14289529914529[/C][/ROW]
[ROW][C]14[/C][C]38[/C][C]41.0687479081001[/C][C]-3.06874790810005[/C][/ROW]
[ROW][C]15[/C][C]33[/C][C]33.817539719777[/C][C]-0.817539719776953[/C][/ROW]
[ROW][C]16[/C][C]33[/C][C]32.6763659327992[/C][C]0.32363406720075[/C][/ROW]
[ROW][C]17[/C][C]52[/C][C]51.0423894140567[/C][C]0.95761058594335[/C][/ROW]
[ROW][C]18[/C][C]54[/C][C]52.5226449616719[/C][C]1.47735503832813[/C][/ROW]
[ROW][C]19[/C][C]39[/C][C]38.060436350409[/C][C]0.939563649590994[/C][/ROW]
[ROW][C]20[/C][C]22[/C][C]28.0708335569242[/C][C]-6.07083355692425[/C][/ROW]
[ROW][C]21[/C][C]31[/C][C]24.6634288432502[/C][C]6.33657115674977[/C][/ROW]
[ROW][C]22[/C][C]31[/C][C]28.6694551976871[/C][C]2.33054480231291[/C][/ROW]
[ROW][C]23[/C][C]38[/C][C]31.0956343846006[/C][C]6.90436561539942[/C][/ROW]
[ROW][C]24[/C][C]42[/C][C]37.6672896987577[/C][C]4.33271030124232[/C][/ROW]
[ROW][C]25[/C][C]41[/C][C]31.4166430462955[/C][C]9.58335695370454[/C][/ROW]
[ROW][C]26[/C][C]31[/C][C]34.4910323904589[/C][C]-3.49103239045893[/C][/ROW]
[ROW][C]27[/C][C]36[/C][C]28.5322448681734[/C][C]7.46775513182665[/C][/ROW]
[ROW][C]28[/C][C]34[/C][C]34.2779806135975[/C][C]-0.277980613597549[/C][/ROW]
[ROW][C]29[/C][C]51[/C][C]53.5249638002971[/C][C]-2.52496380029712[/C][/ROW]
[ROW][C]30[/C][C]47[/C][C]53.8428273489477[/C][C]-6.84282734894771[/C][/ROW]
[ROW][C]31[/C][C]31[/C][C]34.4017908131552[/C][C]-3.40179081315522[/C][/ROW]
[ROW][C]32[/C][C]19[/C][C]19.6428349077239[/C][C]-0.642834907723906[/C][/ROW]
[ROW][C]33[/C][C]30[/C][C]24.7643105872515[/C][C]5.2356894127485[/C][/ROW]
[ROW][C]34[/C][C]33[/C][C]27.3093812665774[/C][C]5.69061873342261[/C][/ROW]
[ROW][C]35[/C][C]36[/C][C]34.2781032352319[/C][C]1.72189676476812[/C][/ROW]
[ROW][C]36[/C][C]40[/C][C]37.1542705357458[/C][C]2.84572946425422[/C][/ROW]
[ROW][C]37[/C][C]32[/C][C]32.2812411328822[/C][C]-0.281241132882208[/C][/ROW]
[ROW][C]38[/C][C]25[/C][C]24.5697506826542[/C][C]0.430249317345787[/C][/ROW]
[ROW][C]39[/C][C]28[/C][C]25.2950956294406[/C][C]2.70490437055941[/C][/ROW]
[ROW][C]40[/C][C]29[/C][C]25.4061617053028[/C][C]3.59383829469715[/C][/ROW]
[ROW][C]41[/C][C]55[/C][C]46.7011567421857[/C][C]8.29884325781428[/C][/ROW]
[ROW][C]42[/C][C]55[/C][C]53.268950396094[/C][C]1.73104960390599[/C][/ROW]
[ROW][C]43[/C][C]40[/C][C]41.5904110003066[/C][C]-1.59041100030659[/C][/ROW]
[ROW][C]44[/C][C]38[/C][C]29.9996727347931[/C][C]8.00032726520686[/C][/ROW]
[ROW][C]45[/C][C]44[/C][C]44.1346471305058[/C][C]-0.134647130505776[/C][/ROW]
[ROW][C]46[/C][C]41[/C][C]44.4685044366422[/C][C]-3.46850443664219[/C][/ROW]
[ROW][C]47[/C][C]49[/C][C]44.9005504224356[/C][C]4.0994495775644[/C][/ROW]
[ROW][C]48[/C][C]59[/C][C]50.6274577258302[/C][C]8.37254227416979[/C][/ROW]
[ROW][C]49[/C][C]61[/C][C]49.3830786942515[/C][C]11.6169213057485[/C][/ROW]
[ROW][C]50[/C][C]47[/C][C]51.2060666636474[/C][C]-4.2060666636474[/C][/ROW]
[ROW][C]51[/C][C]43[/C][C]51.0379792600276[/C][C]-8.03797926002758[/C][/ROW]
[ROW][C]52[/C][C]39[/C][C]45.4121877876618[/C][C]-6.41218778766178[/C][/ROW]
[ROW][C]53[/C][C]66[/C][C]62.4273413023291[/C][C]3.57265869767086[/C][/ROW]
[ROW][C]54[/C][C]68[/C][C]64.0997120763727[/C][C]3.90028792362732[/C][/ROW]
[ROW][C]55[/C][C]63[/C][C]53.2325848468537[/C][C]9.76741515314632[/C][/ROW]
[ROW][C]56[/C][C]68[/C][C]53.3241672320869[/C][C]14.6758327679131[/C][/ROW]
[ROW][C]57[/C][C]67[/C][C]70.1733260239206[/C][C]-3.17332602392058[/C][/ROW]
[ROW][C]58[/C][C]59[/C][C]68.4285043070838[/C][C]-9.42850430708381[/C][/ROW]
[ROW][C]59[/C][C]68[/C][C]68.4411291716198[/C][C]-0.441129171619849[/C][/ROW]
[ROW][C]60[/C][C]78[/C][C]73.3784826572144[/C][C]4.62151734278557[/C][/ROW]
[ROW][C]61[/C][C]82[/C][C]71.3747092448948[/C][C]10.6252907551052[/C][/ROW]
[ROW][C]62[/C][C]70[/C][C]67.6051093852031[/C][C]2.39489061479694[/C][/ROW]
[ROW][C]63[/C][C]62[/C][C]71.1884931498462[/C][C]-9.18849314984618[/C][/ROW]
[ROW][C]64[/C][C]68[/C][C]66.0970456716106[/C][C]1.90295432838937[/C][/ROW]
[ROW][C]65[/C][C]94[/C][C]93.016636376811[/C][C]0.983363623189007[/C][/ROW]
[ROW][C]66[/C][C]102[/C][C]94.0313323051062[/C][C]7.96866769489378[/C][/ROW]
[ROW][C]67[/C][C]100[/C][C]88.9177300284883[/C][C]11.0822699715117[/C][/ROW]
[ROW][C]68[/C][C]104[/C][C]92.6763138447666[/C][C]11.3236861552334[/C][/ROW]
[ROW][C]69[/C][C]103[/C][C]102.145016234775[/C][C]0.854983765224773[/C][/ROW]
[ROW][C]70[/C][C]93[/C][C]101.998622743608[/C][C]-8.99862274360787[/C][/ROW]
[ROW][C]71[/C][C]110[/C][C]106.550471988844[/C][C]3.44952801115613[/C][/ROW]
[ROW][C]72[/C][C]114[/C][C]117.064919655539[/C][C]-3.0649196555395[/C][/ROW]
[ROW][C]73[/C][C]120[/C][C]113.130132834092[/C][C]6.86986716590788[/C][/ROW]
[ROW][C]74[/C][C]102[/C][C]104.940289415017[/C][C]-2.9402894150174[/C][/ROW]
[ROW][C]75[/C][C]95[/C][C]101.725076612865[/C][C]-6.72507661286534[/C][/ROW]
[ROW][C]76[/C][C]103[/C][C]102.870264031933[/C][C]0.129735968067379[/C][/ROW]
[ROW][C]77[/C][C]122[/C][C]129.036354549063[/C][C]-7.03635454906347[/C][/ROW]
[ROW][C]78[/C][C]139[/C][C]127.674052119645[/C][C]11.3259478803554[/C][/ROW]
[ROW][C]79[/C][C]135[/C][C]126.396184761254[/C][C]8.60381523874585[/C][/ROW]
[ROW][C]80[/C][C]135[/C][C]129.095267284785[/C][C]5.90473271521509[/C][/ROW]
[ROW][C]81[/C][C]137[/C][C]131.686012913658[/C][C]5.31398708634174[/C][/ROW]
[ROW][C]82[/C][C]130[/C][C]131.486272887223[/C][C]-1.48627288722335[/C][/ROW]
[ROW][C]83[/C][C]148[/C][C]145.963429417618[/C][C]2.03657058238207[/C][/ROW]
[ROW][C]84[/C][C]148[/C][C]153.953234341854[/C][C]-5.9532343418538[/C][/ROW]
[ROW][C]85[/C][C]145[/C][C]152.125556798822[/C][C]-7.12555679882206[/C][/ROW]
[ROW][C]86[/C][C]128[/C][C]131.460430191645[/C][C]-3.46043019164523[/C][/ROW]
[ROW][C]87[/C][C]131[/C][C]126.647429488914[/C][C]4.3525705110862[/C][/ROW]
[ROW][C]88[/C][C]133[/C][C]137.844007656775[/C][C]-4.84400765677486[/C][/ROW]
[ROW][C]89[/C][C]146[/C][C]158.541174712995[/C][C]-12.5411747129948[/C][/ROW]
[ROW][C]90[/C][C]163[/C][C]160.012459729385[/C][C]2.98754027061523[/C][/ROW]
[ROW][C]91[/C][C]151[/C][C]152.126151540363[/C][C]-1.12615154036325[/C][/ROW]
[ROW][C]92[/C][C]157[/C][C]146.978514090107[/C][C]10.0214859098931[/C][/ROW]
[ROW][C]93[/C][C]152[/C][C]151.646837280596[/C][C]0.353162719404452[/C][/ROW]
[ROW][C]94[/C][C]149[/C][C]145.268660755614[/C][C]3.73133924438571[/C][/ROW]
[ROW][C]95[/C][C]172[/C][C]163.976400570911[/C][C]8.02359942908924[/C][/ROW]
[ROW][C]96[/C][C]167[/C][C]172.920210430039[/C][C]-5.92021043003908[/C][/ROW]
[ROW][C]97[/C][C]160[/C][C]170.516252894814[/C][C]-10.5162528948141[/C][/ROW]
[ROW][C]98[/C][C]150[/C][C]148.594556534764[/C][C]1.40544346523563[/C][/ROW]
[ROW][C]99[/C][C]160[/C][C]149.527095093707[/C][C]10.4729049062932[/C][/ROW]
[ROW][C]100[/C][C]165[/C][C]161.610819985512[/C][C]3.38918001448789[/C][/ROW]
[ROW][C]101[/C][C]171[/C][C]185.380362895979[/C][C]-14.3803628959793[/C][/ROW]
[ROW][C]102[/C][C]179[/C][C]191.318722250261[/C][C]-12.3187222502607[/C][/ROW]
[ROW][C]103[/C][C]171[/C][C]171.7645144356[/C][C]-0.764514435600347[/C][/ROW]
[ROW][C]104[/C][C]176[/C][C]170.488597391228[/C][C]5.51140260877193[/C][/ROW]
[ROW][C]105[/C][C]170[/C][C]168.479652970857[/C][C]1.52034702914304[/C][/ROW]
[ROW][C]106[/C][C]169[/C][C]163.693707946522[/C][C]5.30629205347753[/C][/ROW]
[ROW][C]107[/C][C]194[/C][C]184.631257883452[/C][C]9.36874211654847[/C][/ROW]
[ROW][C]108[/C][C]196[/C][C]189.386296686932[/C][C]6.61370331306793[/C][/ROW]
[ROW][C]109[/C][C]188[/C][C]193.778398973083[/C][C]-5.77839897308286[/C][/ROW]
[ROW][C]110[/C][C]174[/C][C]179.440103835487[/C][C]-5.44010383548689[/C][/ROW]
[ROW][C]111[/C][C]186[/C][C]179.15862321794[/C][C]6.84137678206042[/C][/ROW]
[ROW][C]112[/C][C]191[/C][C]186.410841616166[/C][C]4.58915838383413[/C][/ROW]
[ROW][C]113[/C][C]197[/C][C]204.848473566342[/C][C]-7.84847356634182[/C][/ROW]
[ROW][C]114[/C][C]206[/C][C]216.033667724246[/C][C]-10.0336677242458[/C][/ROW]
[ROW][C]115[/C][C]197[/C][C]202.316256529747[/C][C]-5.31625652974654[/C][/ROW]
[ROW][C]116[/C][C]204[/C][C]200.422573536832[/C][C]3.57742646316765[/C][/ROW]
[ROW][C]117[/C][C]201[/C][C]195.884934298977[/C][C]5.1150657010225[/C][/ROW]
[ROW][C]118[/C][C]190[/C][C]195.00189264015[/C][C]-5.00189264015023[/C][/ROW]
[ROW][C]119[/C][C]213[/C][C]210.492982524097[/C][C]2.50701747590279[/C][/ROW]
[ROW][C]120[/C][C]213[/C][C]209.456406982964[/C][C]3.54359301703553[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232459&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232459&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
134453.1428952991453-9.14289529914529
143841.0687479081001-3.06874790810005
153333.817539719777-0.817539719776953
163332.67636593279920.32363406720075
175251.04238941405670.95761058594335
185452.52264496167191.47735503832813
193938.0604363504090.939563649590994
202228.0708335569242-6.07083355692425
213124.66342884325026.33657115674977
223128.66945519768712.33054480231291
233831.09563438460066.90436561539942
244237.66728969875774.33271030124232
254131.41664304629559.58335695370454
263134.4910323904589-3.49103239045893
273628.53224486817347.46775513182665
283434.2779806135975-0.277980613597549
295153.5249638002971-2.52496380029712
304753.8428273489477-6.84282734894771
313134.4017908131552-3.40179081315522
321919.6428349077239-0.642834907723906
333024.76431058725155.2356894127485
343327.30938126657745.69061873342261
353634.27810323523191.72189676476812
364037.15427053574582.84572946425422
373232.2812411328822-0.281241132882208
382524.56975068265420.430249317345787
392825.29509562944062.70490437055941
402925.40616170530283.59383829469715
415546.70115674218578.29884325781428
425553.2689503960941.73104960390599
434041.5904110003066-1.59041100030659
443829.99967273479318.00032726520686
454444.1346471305058-0.134647130505776
464144.4685044366422-3.46850443664219
474944.90055042243564.0994495775644
485950.62745772583028.37254227416979
496149.383078694251511.6169213057485
504751.2060666636474-4.2060666636474
514351.0379792600276-8.03797926002758
523945.4121877876618-6.41218778766178
536662.42734130232913.57265869767086
546864.09971207637273.90028792362732
556353.23258484685379.76741515314632
566853.324167232086914.6758327679131
576770.1733260239206-3.17332602392058
585968.4285043070838-9.42850430708381
596868.4411291716198-0.441129171619849
607873.37848265721444.62151734278557
618271.374709244894810.6252907551052
627067.60510938520312.39489061479694
636271.1884931498462-9.18849314984618
646866.09704567161061.90295432838937
659493.0166363768110.983363623189007
6610294.03133230510627.96866769489378
6710088.917730028488311.0822699715117
6810492.676313844766611.3236861552334
69103102.1450162347750.854983765224773
7093101.998622743608-8.99862274360787
71110106.5504719888443.44952801115613
72114117.064919655539-3.0649196555395
73120113.1301328340926.86986716590788
74102104.940289415017-2.9402894150174
7595101.725076612865-6.72507661286534
76103102.8702640319330.129735968067379
77122129.036354549063-7.03635454906347
78139127.67405211964511.3259478803554
79135126.3961847612548.60381523874585
80135129.0952672847855.90473271521509
81137131.6860129136585.31398708634174
82130131.486272887223-1.48627288722335
83148145.9634294176182.03657058238207
84148153.953234341854-5.9532343418538
85145152.125556798822-7.12555679882206
86128131.460430191645-3.46043019164523
87131126.6474294889144.3525705110862
88133137.844007656775-4.84400765677486
89146158.541174712995-12.5411747129948
90163160.0124597293852.98754027061523
91151152.126151540363-1.12615154036325
92157146.97851409010710.0214859098931
93152151.6468372805960.353162719404452
94149145.2686607556143.73133924438571
95172163.9764005709118.02359942908924
96167172.920210430039-5.92021043003908
97160170.516252894814-10.5162528948141
98150148.5945565347641.40544346523563
99160149.52709509370710.4729049062932
100165161.6108199855123.38918001448789
101171185.380362895979-14.3803628959793
102179191.318722250261-12.3187222502607
103171171.7645144356-0.764514435600347
104176170.4885973912285.51140260877193
105170168.4796529708571.52034702914304
106169163.6937079465225.30629205347753
107194184.6312578834529.36874211654847
108196189.3862966869326.61370331306793
109188193.778398973083-5.77839897308286
110174179.440103835487-5.44010383548689
111186179.158623217946.84137678206042
112191186.4108416161664.58915838383413
113197204.848473566342-7.84847356634182
114206216.033667724246-10.0336677242458
115197202.316256529747-5.31625652974654
116204200.4225735368323.57742646316765
117201195.8849342989775.1150657010225
118190195.00189264015-5.00189264015023
119213210.4929825240972.50701747590279
120213209.4564069829643.54359301703553







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121207.092155244136194.836169652227219.348140836045
122196.390141896108181.511526378323211.268757413892
123203.847727131246186.530975858221221.164478404271
124205.540964359956185.892588125734225.189340594178
125216.20611727832194.290389530184238.121845026456
126231.571257682196207.426886537898255.715628826494
127226.199640682574199.848686708453252.550594656696
128231.197991442577202.651100964915259.744881920239
129225.06741467123194.32710431527255.807725027191
130217.373502862961184.436328866199250.310676859723
131238.943930823287203.801980289554274.085881357019
132236.750011493135199.391961074477274.108061911793

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 207.092155244136 & 194.836169652227 & 219.348140836045 \tabularnewline
122 & 196.390141896108 & 181.511526378323 & 211.268757413892 \tabularnewline
123 & 203.847727131246 & 186.530975858221 & 221.164478404271 \tabularnewline
124 & 205.540964359956 & 185.892588125734 & 225.189340594178 \tabularnewline
125 & 216.20611727832 & 194.290389530184 & 238.121845026456 \tabularnewline
126 & 231.571257682196 & 207.426886537898 & 255.715628826494 \tabularnewline
127 & 226.199640682574 & 199.848686708453 & 252.550594656696 \tabularnewline
128 & 231.197991442577 & 202.651100964915 & 259.744881920239 \tabularnewline
129 & 225.06741467123 & 194.32710431527 & 255.807725027191 \tabularnewline
130 & 217.373502862961 & 184.436328866199 & 250.310676859723 \tabularnewline
131 & 238.943930823287 & 203.801980289554 & 274.085881357019 \tabularnewline
132 & 236.750011493135 & 199.391961074477 & 274.108061911793 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232459&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]207.092155244136[/C][C]194.836169652227[/C][C]219.348140836045[/C][/ROW]
[ROW][C]122[/C][C]196.390141896108[/C][C]181.511526378323[/C][C]211.268757413892[/C][/ROW]
[ROW][C]123[/C][C]203.847727131246[/C][C]186.530975858221[/C][C]221.164478404271[/C][/ROW]
[ROW][C]124[/C][C]205.540964359956[/C][C]185.892588125734[/C][C]225.189340594178[/C][/ROW]
[ROW][C]125[/C][C]216.20611727832[/C][C]194.290389530184[/C][C]238.121845026456[/C][/ROW]
[ROW][C]126[/C][C]231.571257682196[/C][C]207.426886537898[/C][C]255.715628826494[/C][/ROW]
[ROW][C]127[/C][C]226.199640682574[/C][C]199.848686708453[/C][C]252.550594656696[/C][/ROW]
[ROW][C]128[/C][C]231.197991442577[/C][C]202.651100964915[/C][C]259.744881920239[/C][/ROW]
[ROW][C]129[/C][C]225.06741467123[/C][C]194.32710431527[/C][C]255.807725027191[/C][/ROW]
[ROW][C]130[/C][C]217.373502862961[/C][C]184.436328866199[/C][C]250.310676859723[/C][/ROW]
[ROW][C]131[/C][C]238.943930823287[/C][C]203.801980289554[/C][C]274.085881357019[/C][/ROW]
[ROW][C]132[/C][C]236.750011493135[/C][C]199.391961074477[/C][C]274.108061911793[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232459&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232459&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
121207.092155244136194.836169652227219.348140836045
122196.390141896108181.511526378323211.268757413892
123203.847727131246186.530975858221221.164478404271
124205.540964359956185.892588125734225.189340594178
125216.20611727832194.290389530184238.121845026456
126231.571257682196207.426886537898255.715628826494
127226.199640682574199.848686708453252.550594656696
128231.197991442577202.651100964915259.744881920239
129225.06741467123194.32710431527255.807725027191
130217.373502862961184.436328866199250.310676859723
131238.943930823287203.801980289554274.085881357019
132236.750011493135199.391961074477274.108061911793



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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')